Stochastic Scenario-Based Multi-Objective MILP Optimization of Large-Scale EV Fleets in V2G-Enabled Smart Grids Considering Battery Degradation and Lifecycle Emissions

Abstract

The integration of large-scale electric vehicle (EV) fleets into vehicle-to-grid (V2G) systems offers significant potential for enhancing the operation of renewable-based smart grids. However, stochastic uncertainties in photovoltaic (PV) generation, vehicle availability, and load demand—coupled with battery degradation and life-cycle assessment (LCA) carbon emissions—pose major challenges to optimal scheduling. This paper proposes a scenario-based multi-objective MILP framework for a 500-EV fleet aggregator. The model incorporates Monte Carlo simulations for multi-source uncertainty quantification (±25% PV forecast errors, ±40% availability), LCA penalties (45 kgCO₂eq/kWh), and ancillary service revenues (25 USD/MW-h). Long-term state-of-health (SOH) projections, including a 1-year fade to 96.5%, are also integrated. Comparative analysis of V2X scenarios shows that the V2G Hybrid strategy reduces daily costs by 34.6% (from ~11,000 USD in the uncontrolled case to 7741 USD when reserve revenues are included), achieves over 50% peak shaving, and maintains voltage stability within 0.994–1.008 pu. The stochastic Pareto frontier identifies knee-point solutions that lower normalized expected costs to 134.61 while achieving 1–2% lower expected emissions compared to deterministic baselines. These results demonstrate a comprehensive framework, uncertainty-aware framework that balances economic viability, grid resilience, and environmental sustainability, offering actionable insights for fleet aggregators and policymakers working toward net-zero energy systems.

1. Introduction

The global energy transition is accelerating the electrification of transportation, positioning electric vehicles (EVs) as a dual-purpose technology that serves both as a clean mobility solution and a flexible distributed energy resource. In this context, vehicle-to-grid (V2G) technology enables bidirectional power exchange between EV batteries and the electricity grid, allowing EVs to not only consume electricity but also inject power during periods of peak demand, renewable surplus, or ancillary service requirements. As a result, aggregated EV fleets can operate as virtual power plants (VPPs), providing critical grid services such as frequency regulation, peak shaving, load shifting, voltage support, and reserve capacity [1,2].

Recent studies demonstrate that V2G integration can significantly enhance grid flexibility, support higher penetration of intermittent renewable energy sources (RES), reduce reliance on dedicated stationary storage, and create new revenue streams for EV owners and aggregators [3,4,5]. Furthermore, rapid technological advancements in bidirectional charging infrastructure, decreasing battery costs, and increasing smart grid capabilities are accelerating the commercial viability of V2G systems [1,4].

Despite these advantages, large-scale V2G deployment introduces several technical and operational challenges. Uncoordinated charging and discharging strategies can exacerbate peak demand, cause voltage deviations, overload distribution transformers, and increase network losses [6]. Moreover, bidirectional operation intensifies battery cycling, leading to accelerated degradation through both calendar and cyclic aging mechanisms, which remains a major concern for EV owners [7,8]. At the same time, uncertainties associated with EV user behavior (e.g., arrival/departure times, driving patterns, and initial state-of-charge), renewable generation variability, and electricity price fluctuations complicate optimal scheduling and system reliability [9].

Battery degradation is widely recognized as one of the most critical barriers to V2G adoption. Empirical and semi-empirical studies indicate that V2G participation can increase total battery degradation, although the incremental impact is often moderate compared to dominant calendar aging effects [7,8]. Nevertheless, degradation-aware operation and appropriate economic compensation mechanisms are essential to ensure user participation and long-term system sustainability.

From an environmental perspective, Life Cycle Assessment (LCA) studies reveal that the benefits of V2G are highly dependent on operational strategies, grid carbon intensity, and system-level coordination mechanisms. While smart charging strategies aligned with low-carbon electricity generation can significantly reduce operational (well-to-wheel) emissions, full lifecycle analyses, including battery manufacturing, material extraction, and end-of-life recycling—indicate that intensive V2G participation may increase total carbon footprint if not properly optimized. This is primarily due to increased battery throughput, accelerated degradation, and additional upstream impacts associated with battery replacement cycles. Consequently, recent studies emphasize that net environmental benefits of V2G can only be realized when high renewable penetration is combined with degradation-aware scheduling and carbon-aware dispatch strategies [10].

The evolution of V2G research has shifted from deterministic optimization approaches toward more advanced methodologies that explicitly consider uncertainty, multi-objective trade-offs, and system-level complexity. Early deterministic models primarily focused on cost minimization or peak load reduction under idealized assumptions, often neglecting real-world stochasticity [11]. To address these limitations, uncertainty-aware scenario analysis techniques and Monte Carlo-based approaches have been widely adopted to capture uncertainties in EV behavior, renewable generation, and market dynamics, enabling probabilistic performance evaluation and risk-aware decision-making [9].

In parallel, robust optimization frameworks—including adjustable robust optimization (ARO) and distributionally robust optimization (DRO)—have emerged as powerful tools to ensure solution feasibility under worst-case or ambiguity-aware uncertainty sets. Unlike stochastic programming, which relies on predefined probability distributions, DRO methods account for uncertainty in the distribution itself, providing guarantees across a family of possible distributions. These approaches enhance system resilience and operational reliability, particularly in V2G-enabled microgrids and distribution networks where uncertainty levels are high and forecasting errors can significantly impact system performance [12,13]. Recent studies also explore hybrid stochastic–robust formulations that combine the advantages of both paradigms, balancing conservatism and expected performance.

Simultaneously, multi-objective optimization methods have been increasingly employed to address conflicting operational goals, including minimization of energy costs, reduction of carbon emissions, mitigation of grid load fluctuations, preservation of battery State-of-Health (SOH), and maximization of aggregator revenue from ancillary service markets. Techniques such as the Non-dominated Sorting Genetic Algorithm II (NSGA-II) enable the construction of Pareto-optimal solution sets, providing decision-makers with a transparent visualization of trade-offs between competing objectives [14]. More recent contributions incorporate degradation-aware and health-conscious models directly into the optimization problem, capturing both calendar and cyclic aging effects to prevent overly aggressive battery utilization and ensure long-term economic sustainability [15]. In addition, some studies have begun integrating carbon pricing mechanisms and dynamic electricity tariffs into multi-objective formulations, further enriching the decision space [16,17].

In addition, hybrid control architecture has shown strong promise in bridging the gap between theoretical optimality and practical robustness. These typically combine rule-based logic, mathematical programming, and data-driven components such as Artificial Neural Networks (ANN) and deep learning models for forecasting and adaptive decision-making [18,19]. Such integrations reduce computational burden while improving adaptability to nonlinear constraints and stochastic events. Furthermore, optimal fleet-level coordination strategies have been proposed to enhance scalability and real-time applicability [20].

Despite these advancements, most existing studies tend to address key aspects of the V2G problems such as uncertainty modeling, battery degradation, multi-objective optimization, or lifecycle environmental assessment—separately or in limited combinations. While several recent works have incorporated stochastic elements (e.g., Monte Carlo simulation), degradation-aware models, or multi-objective trade-offs, integrated frameworks that simultaneously combine degradation-aware long-term SOH and EOL projection, full lifecycle (LCA) embedded emissions penalty, ancillary service revenue mechanisms, hybrid V2X scenario comparison, and Monte Carlo-based stochastic Pareto frontier analysis within a unified MILP formulation for large-scale fleet aggregators remain relatively limited.

This study builds upon and extends the existing literature by developing a holistic V2G hybrid optimization framework that jointly integrates these elements under realistic stochastic conditions. The proposed approach provides a more comprehensive evaluation of economic, technical, and environmental performance for large-scale EV fleets (≈30 MWh aggregate capacity) participating in V2G-enabled smart grids.

The main contributions of this study can be summarized as follows:

• Integration of semi-empirical calendar and cyclic battery aging models with explicit SOH tracking and End-of-Life (EOL) projection (estimated 5.7 years to 80% SOH) into the day-ahead scheduling problem,
• Monte Carlo-based uncertainty quantification (±25% PV forecast error, ±40% vehicle availability) combined with stochastic multi-objective optimization to generate a Monte Carlo-derived Pareto frontier between expected operational cost and carbon emissions,
• Incorporation of both operational (tank-to-wheel) and lifecycle assessment (LCA) embedded emissions (45 kgCO₂eq/kWh penalty) alongside ancillary service revenues (25 USD/MW-h) in a unified objective function,
• Hybrid control logic (rule-based + optimization-driven) for real-time voltage and peak management,
• Comprehensive sensitivity analysis on electricity price (+20%) and carbon tax (+20%), along with scalability assessment across fleet sizes (100–1000 EVs),
• Demonstration of practical trade-offs: 34.6% daily cost reduction (including reserve revenues), >50% peak shaving, voltage stability (0.994–1.008 pu), and limited LCA footprint increase (9.0%) while maintaining low uncertainty variability.

To the best of the authors’ knowledge, no prior study has simultaneously integrated stochastic uncertainty modeling, degradation-aware SOH projection, LCA-based emissions, and ancillary service revenues within a unified MILP framework for large-scale EV fleets.

Simulation results on a representative EV fleet (approximately 30 MWh aggregate battery capacity) demonstrate significant multi-dimensional benefits of the proposed framework. The V2G Hybrid strategy reduces average daily operational costs (including reserve revenues) from approximately 11,000 USD in the uncontrolled case to 7197.83 USD, while achieving effective peak shaving and voltage support. The framework demonstrates strong performance under uncertainty, exhibiting near-zero normalized cost variability across stochastic scenarios.

From a battery perspective, the model projects a State-of-Health (SOH) of 96.50% after one year, corresponding to an estimated 5.7 years to reach 80% End-of-Life (EOL). Environmentally, the lifecycle carbon footprint increase is limited to 9.0%, demonstrating controlled trade-offs between operational benefits and long-term impacts. Furthermore, the derived stochastic Pareto frontier reveals superior cost–emission trade-offs compared to deterministic baseline strategies.

The remainder of the paper is structured as follows. Section 2 details mathematical modeling, including battery degradation, objective functions, constraints, uncertainty generation, and stochastic optimization techniques. Section 3 presents and discusses the results, encompassing economic performance, technical metrics, uncertainty quantification and fleet SOC bands, cost and profit distributions under stochastic conditions, the stochastic Pareto frontier, and environmental impacts. Section 4 concludes with policy implications and future research directions.

2. Methodology

The proposed methodology advances conventional EV scheduling studies by introducing an integrated uncertainty-aware scenario analysis framework that jointly captures V2X operational flexibility, photovoltaic uncertainty, battery degradation, carbon-aware dispatch, reserve market participation, and lifecycle environmental impacts. Unlike deterministic peak-shaving approaches, the proposed model evaluates both short-term operational performance and long-term battery sustainability under uncertain renewable generation and EV availability. In addition, a Monte Carlo-based stochastic Pareto optimization is developed to quantify the trade-off between economic benefits and carbon mitigation, thereby providing a more realistic decision-support tool for EV aggregators and distribution system operators.

2.1. Overview of the Proposed Framework

This study adopts a system-level operational modeling approach. The EV fleet is represented as an aggregated storage unit to ensure computational tractability and scalability for large-scale uncertainty-aware system analysis. While this abstraction simplifies individual vehicle behavior, it is consistent with aggregator-based market participation models and widely adopted in large-scale V2G studies. To ensure computational tractability in large-scale stochastic simulations, voltage is modeled using a linear proxy, Monte Carlo uncertainty is designed to reflect realistic forecast errors rather than perfect foresight, and battery degradation is approximated using a throughput-based model that balances accuracy and efficiency.

Unlike conventional deterministic EV scheduling approaches, the proposed framework explicitly integrates:

• Time-varying load and PV generation profiles,
• EV fleet availability uncertainty,
• Battery state-of-charge (SOC) dynamics,
• Charging/discharging operational constraints,
• Battery degradation costs and state-of-health (SOH) projection,
• Carbon pricing and lifecycle assessment (LCA)-embedded emissions,
• Ancillary service revenue mechanisms, and
• Monte Carlo-based stochastic analysis with Pareto frontier generation.

The methodological structure consists of four interconnected layers:

• Layer 1—Deterministic operational scheduling for baseline V2X scenario comparison,
• Layer 2—Sensitivity and degradation assessment for long-term battery implications,
• Layer 3—Stochastic uncertainty quantification via Monte Carlo simulation,
• Layer 4—Stochastic multi-objective optimization for cost–carbon trade-off analysis.

This hierarchical design enables a comprehensive evaluation of EV fleet flexibility beyond simple peak shaving, capturing both short-term operational decisions and long-term sustainability implications.

2.2. System Architecture and Operational Scope

The system considered consists of:

• a distribution-level aggregated EV fleet,
• a time-varying base demand profile,
• a local PV generation source, and
• a grid interface enabling energy import/export and ancillary market participation.

The analysis is conducted over a 24 h day-ahead horizon with hourly resolution:

$$t\in \{1,2,\dots ,T\}, T=24$$

(1)

where each step represents one hour $\left(\Delta t=1 \mathrm{h}\right)$.

The net demand seen by the grid before EV intervention is defined as:

$$P_{\mathrm{net},t}^{\mathrm{base}}=P_{\mathrm{load},t}-P_{\mathrm{PV},t}$$

(2)

where

• $P_{\mathrm{load},t}$ is the baseline demand at hour $t$,
• $P_{\mathrm{PV},t}$ is the local PV output at hour $t$.

After EV fleet coordination, the optimized net demand becomes:

$$P_{\mathrm{net},t}^{\mathrm{opt}}=P_{\mathrm{load},t}-P_{\mathrm{PV},t}+P_{ch,t}-P_{dis,t}$$

(3)

where:

• $P_{ch,t}$ is EV charging power,
• $P_{dis,t}$ is EV discharging power.

This structure allows the EV fleet to act as a distributed flexible storage asset, capable of shifting energy temporally, reducing peak demand, supporting local self-consumption, and participating in bidirectional energy services.

2.3. EV Fleet Aggregation Model

2.3.1. Aggregated Fleet Representation

Rather than modeling individual vehicles separately, the EV population is represented as an aggregated virtual battery. This abstraction is computationally efficient and consistent with aggregator-based market participation models.

Let:

• $N_{EV}$ = number of EVs in the fleet,
• $E_{cap}^{EV}$ = battery capacity per EV (MWh),
• $E_{fleet}^{tot}$ = total nominal fleet capacity.

Then:

$$E_{fleet}^{tot}=N_{EV}\times E_{cap}^{EV}$$

(4)

In the implemented framework, the aggregated capacity is time-varying due to vehicle availability. Thus, the effective energy capacity at time $t$ is:

$$E_{max,t}=E_{fleet}^{tot}\cdot a_t$$

(5)

where $a_t\in [0,1]$ denotes the availability factor of the fleet at hour $t$.

Similarly, the available charging/discharging power is:

$$P_{max,t}=P_{rated}^{EV}\cdot {\displaystyle \frac{N_{EV}}{100}}\cdot a_t$$

(6)

where $P_{rated}^{EV}$ is the per-vehicle charging/discharging power basis used in the aggregated scaling.

2.3.2. Time-Varying Availability

To reflect realistic mobility behavior, EV availability is reduced during daytime commuting/working periods. A nominal availability profile is defined deterministically for scenario comparison and randomized under uncertainty analysis. This enables the model to capture the fact that EVs are not continuously connected and therefore cannot always provide full flexibility.

2.4. PV and Load Modeling

2.4.1. Base Load Profile

The base demand is represented by a 24 h load curve reflecting typical residential/commercial daily consumption behavior. The load profile exhibits:

• lower demand during night hours,
• a morning rise,
• moderate midday demand, and
• a pronounced evening peak.

This temporal structure is essential for assessing peak-shaving and load-shifting performance.

2.4.2. PV Generation Model

The PV generation is modeled using a bell-shaped irradiance-dependent production curve centered around midday:

$$P_{\mathrm{PV},t}=P_{\mathrm{PV}}^{max}\mathrm{e}\mathrm{x}\mathrm{p}(-{\left({\displaystyle \frac{t-\mu }{\sigma }}\right)}^2)$$

(7)

with zero output during nighttime hours. In stochastic analyses, PV output is perturbed using multiplicative random factors or Gaussian uncertainty to emulate forecast error and meteorological variability.

2.5. V2X Operational Scenarios

To benchmark the proposed control strategy, three operational modes are compared:

• Uncontrolled Charging: EVs begin charging whenever available, without optimization or discharging capability.
• Smart V1G (Unidirectional Smart Charging): Charging is scheduled optimally, but discharging is prohibited.
• V2G Hybrid: Full bidirectional interaction with the grid is allowed, enabling arbitrage, peak shaving, and reserve support.

Among these, the V2G Hybrid case is treated as the principal benchmark because it provides the highest degree of operational freedom and best reflects aggregator-centric flexibility markets.

2.6. Optimization Variables and Decision Space

For each hour $t$, the following decision variables are defined:

• $P_{ch,t}$: charging power (continuous),
• $P_{dis,t}$: discharging power (continuous),
• $SO{C}_t$: fleet state-of-charge (continuous),
• $u_t$: binary or relaxed operational control variable (for enabling charge/discharge activation or limiting simultaneous operation),
• $P_{grid,t}$: grid import (in stochastic cost–carbon formulations).

Thus, depending on the model variant, the decision vector is:

$$\mathbf{x}=\left[P_{ch,1:T}, P_{dis,1:T}, SO{C}_{1:T}, u_{1:T}, P_{grid,1:T}\right]$$

(8)

The optimization problem is formulated as a mixed-integer linear programming (MILP) model when discrete operational logic is explicitly enforced, and as a linear programming (LP) model when the formulation is relaxed to enhance computational tractability within Monte Carlo simulations. This dual-solver strategy effectively balances modeling realism and computational scalability, making it particularly suitable for large-scale scenario-based evaluation under uncertainty studies.

2.7. Battery Dynamics and Physical Constraints

2.7.1. SOC Dynamics

The fleet SOC evolves according to the energy balance:

$$SO{C}_t=SO{C}_{t-1}+{\eta }_c{P}_{ch,t}\Delta t-{\displaystyle \frac{1}{{\eta }_d}}{P}_{dis,t}\Delta t$$

(9)

where:

• ${\eta }_c$ is charging efficiency,
• ${\eta }_d$ is discharging efficiency.

2.7.2. SOC Bounds

To preserve battery health and user convenience:

$$SO{C}_{min}\le SO{C}_t\le SO{C}_{max}$$

(10)

In fleet-scale formulations:

$$0\le SO{C}_t\le E_{max,t}$$

(11)

depending on whether SOC is normalized or expressed in energy units.

2.7.3. Power Bounds

Charging and discharging are bound by the available fleet power:

$$0\le P_{ch,t}\le P_{max,t}$$

(12)

$$0\le P_{dis,t}\le P_{max,t}$$

(13)

2.7.4. Mutual Exclusivity/Operational Logic

To avoid physically unrealistic simultaneous charging and discharging, binary or semi-binary control logic is introduced. In the MILP variant, this is represented by an activation variable $u_t$:

$$P_{ch,t}\le u_t{P}_{max,t}$$

(14)

$$P_{dis,t}\le (1-u_t)P_{max,t}$$

(15)

or equivalent linearized forms depending on the scenario implementation.

This operational logic is particularly important in manuscript review because reviewers often reject EV scheduling studies that omit simultaneous charge/discharge prevention.

2.8. Objective Function Formulation

Lifecycle-based economic models commonly employ the capital recovery factor (CRF) to annualize investment costs. The CRF is defined as:

$$\mathrm{C}\mathrm{R}\mathrm{F}={\displaystyle \frac{\tau {(1+\tau )}^n}{{(1+\tau )}^n-1}}$$

(16)

where τ is the discount rate and n is the system lifetime. Such formulations are typically used in long-term planning and capacity optimization studies.

In contrast, the proposed framework focuses on short-term operational optimization, integrating economic, environmental, and battery aging considerations into a unified objective function. Both single-objective and multi-objective formulations are supported depending on the analysis stage.

2.8.1. Economic Objective

The base economic objective minimizes daily operational cost:

$$J_{cost}={\displaystyle {\sum }_{t=1}^T}\left(c_t^{grid}{P}_{ch,t}-c_t^{sell}{P}_{dis,t}\right)$$

(17)

where:

• $c_t^{grid}$ is electricity purchase price,
• $c_t^{sell}$ is export/market revenue price.
• $P_{ch,t}$ and $P_{dis,t}$ are charging and discharging power, respectively.

2.8.2. Carbon Cost Integration

To internalize environmental externalities, a carbon-pricing term is included:

$$J_{carbon}={\displaystyle {\sum }_{t=1}^T}\left({\tau }_c\cdot E{F}_t\cdot P_{\mathrm{grid},t}\right)$$

(18)

where:

• ${\tau }_c$ is carbon tax coefficient,
• $E{F}_t$ is time-varying grid emission factor.

This allows the optimizer to prefer charging/discharging decisions during lower-carbon periods.

2.8.3. Battery Degradation Cost

Battery aging is modeled using a throughput-based linear penalty:

$$J_{deg}=c_{deg}{\displaystyle {\sum }_{t=1}^T}\left(P_{ch,t}+P_{dis,t}\right)$$

(19)

This term discourages excessive cycling and ensures realistic battery utilization.

2.8.4. Ancillary Service Revenue

Revenue from grid services is modeled as:

$$J_{anc}=-{\displaystyle {\sum }_{t=1}^T}{r}_{anc}\cdot P_{res,t}$$

(20)

where:

• $r_{anc}$ is reserve service remuneration,
• $P_{res,t}$ is the reserve-capable discharge or flexible capacity proxy.

The ancillary service revenue is modeled as an upper-bound estimate assuming full availability and activation without sub-hourly dynamics. Therefore, the reported revenues should be interpreted as indicative rather than guaranteed economic outcomes.

2.8.5. Lifecycle (LCA) Embedded Emissions

To incorporate embedded environmental impact:

$$J_{LCA}=c_{LCA}{\displaystyle {\sum }_{t=1}^T}{P}_{dis,t}$$

(21)

The operational carbon cost represents grid-related emissions, while the LCA term reflects embedded battery emissions. These components are treated as complementary rather than overlapping, avoiding double-counting.

2.8.6. Combined Objective

The overall objective function is formulated as:

$$\mathrm{m}\mathrm{i}\mathrm{n} J=J_{cost}+J_{carbon}+J_{deg}+J_{LCA}+J_{peak}+J_{anc}$$

(22)

where $J_{peak}$ represents optional peak demand penalties.

This formulation enables simultaneous optimization of economic cost, environmental impact, and battery degradation, providing a comprehensive decision-making framework.

2.9. Peak Shaving and Grid Constraint Modeling

In the peak-oriented formulation, the maximum daily net load is explicitly penalized using an auxiliary peak variable:

$$P_{peak}\ge P_{\mathrm{net},t}^{opt}, \forall t$$

(23)

and the objective includes:

$$J_{peak}=c_{peak}\cdot P_{peak}$$

(24)

This formulation enables the model to reduce demand charges and flatten the load profile. It is particularly useful for utility-facing or aggregator-facing studies.

In simplified voltage-aware analyses, a linear voltage proxy is used:

$$V_t=1-k\cdot \left(P_{\mathrm{net},t}^{opt}\right)$$

(25)

where $k$ is a feeder sensitivity factor. Voltage violation events are recorded when:

$$V_t<V_{min}$$

(26)

The linear voltage proxy is adopted for computational tractability in large-scale simulations. While this approximation does not capture full AC power flow behavior, it provides a first-order estimation of voltage sensitivity.

In addition, the voltage results are interpreted as trend indicators rather than exact values, and all conclusions have been revised accordingly to reflect this modeling limitation.

A full AC power flow validation is considered as future work.

2.10. Demand Response (DR) Coupling

To emulate flexible load participation during congested hours, a demand response mechanism is incorporated. When the net load exceeds a high-demand threshold (e.g., upper 80th percentile), a portion of the base demand becomes curtailable or shiftable:

$$P_{\mathrm{load},t}^{DR}=\left\{\begin{array}{cc}(1-\alpha )P_{\mathrm{load},t},& \mathrm{if} P_{\mathrm{net},t}^{base}>\theta \\ P_{\mathrm{load},t},& \mathrm{otherwise}\end{array}\right.$$

(27)

where:

• $\alpha$ is the flexible load fraction,
• $\theta$ is the congestion threshold.

This coupling is particularly valuable because it allows EV flexibility to be evaluated in conjunction with DR, rather than as an isolated asset.

2.11. Uncertainty Quantification via Monte Carlo Simulation

2.11.1. Rationale

Deterministic scheduling often overestimates V2X performance because it assumes perfect forecasts and full vehicle availability. To address this, the proposed framework uses Monte Carlo simulation to propagate uncertainty into the optimization outputs.

2.11.2. Uncertain Inputs

The following stochastic variables are considered: PV generation uncertainty, EV availability uncertainty, and, in some cases, net load perturbations or forecast errors.

PV generation uncertainty is modeled using two alternative formulations:

(1)

Additive Gaussian uncertainty:

$$P_{\mathrm{PV},t}^{\left(s\right)}=P_{\mathrm{PV},t}^{nom}+{ϵ}_t^{\left(s\right)}$$

(28)

where ${ϵ}_t^{\left(s\right)}\sim \mathcal{N}(0,{\sigma }_t^2)$. To ensure physical feasibility, negative PV values are truncated at zero.

(2)

Multiplicative uncertainty model:

$$P_{\mathrm{PV},t}^{\left(s\right)}=P_{\mathrm{PV},t}^{nom}\cdot {\xi }_t^{\left(s\right)}$$

(29)

${\xi }_t^{\left(s\right)}$ is a bounded random variable (e.g., ${\xi }_t^{\left(s\right)}\in [0.75,1.25]$) representing forecast uncertainty. The multiplicative formulation is particularly suitable for modeling proportional forecast errors, while the additive model captures absolute deviations.

The multiplicative uncertainty model was adopted to reflect proportional forecast errors. The bounds were selected based on typical forecast error ranges reported in the literature. To ensure realistic behavior at near-zero generation levels, the multiplicative factors were bounded and truncated.

2.11.3. Scenario Evaluation

For each Monte Carlo sample $s=1,\dots ,N_{scen}$, the optimization problem is re-solved. The resulting distributions of:

• daily operational cost,
• profit,
• SOC trajectories,
• voltage violations,
• emissions

Are then statistically summarized.

The proposed framework follows a scenario-based “wait-and-see” evaluation approach, where optimization is solved independently for each realization. This approach is used to evaluate system performance under uncertainty rather than to derive optimal pre-uncertainty decisions.

2.11.4. Confidence Intervals

For SOC and cost variability analysis, the mean and standard deviation are computed:

$${\mu }_t={\displaystyle \frac{1}{N_{scen}}}{\displaystyle {\sum }_{s=1}^{N_{scen}}}SO{C}_t^{\left(s\right)}$$

(30)

$${\sigma }_t=\sqrt{{\displaystyle \frac{1}{N_{scen}-1}}{\displaystyle {\sum }_{s=1}^{N_{scen}}}{\left(SO{C}_t^{\left(s\right)}−{\mu }_t\right)}^2}$$

(31)

and a 95% confidence interval is estimated as:

$$C{I}_{95\%}={\mu }_t\pm 1.96{\sigma }_t$$

(32)

This statistical representation is consistent with the stochastic visualization approach adopted in the proposed framework, ensuring a clear interpretation of uncertainty effects.

2.12. Scenario-Based Multi-Objective Optimization

2.12.1. Weighted-Sum Pareto Formulation

To explicitly study the trade-off between economics and emissions, a stochastic multi-objective optimization is constructed using a scalarization parameter $\lambda \in [0,1]$:

$$\mathrm{m}\mathrm{i}\mathrm{n} J_{\lambda }=\lambda J_{cost}+(1-\lambda )J_{carbon}$$

(33)

where:

• $\lambda =1$ prioritizes cost minimization,
• $\lambda =0$ prioritizes carbon minimization.

2.12.2. Monte Carlo-Based Expected Objective

Under uncertainty, the objective is evaluated across scenarios and summarized in expectation:

$$\mathrm{m}\mathrm{i}\mathrm{n} \mathbb{E}\left[J_{\lambda }\right]=\lambda \mathbb{E}\left[J_{cost}\right]+(1-\lambda )\mathbb{E}\left[J_{carbon}\right]$$

(34)

This yields a stochastic Pareto frontier, rather than a deterministic one.

2.12.3. Pareto Frontier Construction

A set of $\lambda$ values (e.g., 0 to 1 with step size 0.1) is used to solve multiple optimization instances. The corresponding expected cost and expected emissions pairs from the Pareto front:

$$\mathcal{P}={\left\{\left(\mathbb{E}\left[J_{carbon}^{\left(\lambda \right)}\right],\mathbb{E}\left[J_{cost}^{\left(\lambda \right)}\right]\right)\right\}}_{\lambda \in \mathrm{\Lambda }}$$

(35)

The deterministic baseline assumes nominal PV generation and average EV availability without stochastic variation, providing a consistent benchmark for comparison.

The expectation-based objective assumes a risk-neutral decision-maker. This approach evaluates average system performance, while risk-aware formulations such as CVaR or mean–variance optimization are left for future work.

2.13. Battery State-of-Health (SOH) Projection

Operational optimality alone is insufficient if EV battery wear becomes economically unacceptable. Therefore, the framework estimates long-term SOH impact using throughput-based degradation.

2.13.1. Daily Cycling Intensity

Daily discharge throughput is first computed:

$$E_{dis}^{day}={\displaystyle {\sum }_{t=1}^T}{P}_{dis,t}\Delta t$$

(36)

Equivalent daily cycling ratio:

$$D_{eq}^{day}={\displaystyle \frac{E_{dis}^{day}}{E_{fleet}^{tot}}}$$

(37)

2.13.2. Daily Degradation Estimate

Assuming a cycle life of $N_{cyc}$, the daily degradation percentage is approximated as:

$$d_{day}={\displaystyle \frac{D_{eq}^{day}}{N_{cyc}}}\times 100$$

(38)

2.13.3. One-Year SOH Projection

The one-year SOH is estimated as:

$$SO{H}_{1yr}=100-365\cdot d_{day}$$

(39)

2.13.4. End-of-Life Estimation

Assuming end-of-life (EOL) occurs at 80% SOH:

$$Year{s}_{EOL}={\displaystyle \frac{100-80}{365·d_{day}}}$$

(40)

Although both degradation cost and LCA penalty scale with energy throughput, they represent different dimensions: economic wear and environmental impact. Therefore, the observed economic–degradation decoupling reflects optimization behavior rather than model independence.

2.14. Sensitivity Analysis

A deterministic parametric sensitivity analysis is conducted to evaluate the resilience of the optimized V2G strategy under economic policy changes.

Two primary perturbations are considered:

• Electricity prices increase (e.g., +20%),
• Carbon tax increase (e.g., +20%).

For each perturbation, the optimized V2G baseline schedule is re-evaluated to determine:

• Daily operating cost impact,
• Carbon-cost exposure,
• Economic competitiveness is relative to uncontrolled charging.

This step is particularly useful for demonstrating that the framework remains valid under evolving tariff and policy environments.

The current scaling results primarily reflect capacity scaling rather than computational complexity due to the use of an aggregated fleet model. Future work will incorporate heterogeneous EV characteristics to capture nonlinear scalability effects.

2.15. Performance Metrics

To ensure a multidimensional evaluation, the following metrics are used:

Technical Metrics

• Peak demand reduction (%),
• Net load smoothing,
• SOC stability,
• Voltage violation rate (%),
• Available reserve flexibility.

Economic Metrics

• Daily operating cost ($/day),
• Aggregator profit ($/day),
• Demand charge reduction,
• Ancillary service revenue contribution,
• Worst-case and expected stochastic cost.

Environmental Metrics

• Operational carbon emissions,
• Carbon-tax-adjusted operating burden,
• LCA-adjusted emissions,
• Cost–carbon Pareto trade-off.

Asset Health Metrics

• Daily degradation proxy,
• 1-year SOH projection,
• Estimated battery end-of-life (years).

The use of these four metrics: technical, economic, environmental, and degradation-related—provides a comprehensive and holistic evaluation of the energy system.

2.16. Optimization Solvers and Computational Implementation

The proposed methodology is implemented in MATLAB R2023b (MathWorks, Natick, MA, USA), using the intlinprog solver for mixed-integer linear programming (MILP) formulations and linprog for linear programming (LP) formulations within repeated Monte Carlo simulations.

This hybrid solver strategy is adopted to balance modeling accuracy and computational efficiency: MILP is used to accurately capture discrete operational logic and scheduling constraints, while LP is employed to reduce computational burden during large-scale stochastic evaluations.

To ensure reproducibility of the results, random number generation is controlled by fixing the random seed (e.g., rng(42)), following standard best practices in stochastic simulation studies.

2.17. Reproducibility and Model Assumptions

The following modeling assumptions are adopted:

• The EV fleet is represented as an aggregated storage resource.
• Battery degradation is approximated using linear throughput-based costing.
• PV uncertainty is modeled stochastically rather than via weather forecast models.
• Voltage behavior is approximated using a linear proxy, not full nonlinear AC power flow.
• The operational horizon is day-ahead with hourly resolution.
• Ancillary service participation is represented through an equivalent revenue formulation.
• LCA burden is incorporated as a marginal utilization-linked penalty rather than full cradle-to-grave attribute.

These assumptions should be openly acknowledged in the manuscript to pre-empt reviewer criticism while emphasizing that the framework is intended as a computationally tractable, system-level operational study.

3. Results and Discussion

This section provides a comprehensive evaluation of the economic, technical, environmental, and uncertainty-aware performance of V2X-enabled smart charging/discharging strategies—namely, the uncontrolled baseline, Smart V1G, and the proposed V2G Hybrid—for large-scale electric vehicle (EV) fleets. By integrating advanced scenario-based evaluation under uncertainty, Monte Carlo uncertainty quantification, stochastic Pareto-front analysis, and multi-dimensional sensitivity assessments, the study elucidates the multifaceted benefits and trade-offs inherent to bidirectional vehicle-to-grid (V2G) operation under realistic operational uncertainties.

In this study, a linear voltage proxy is used for computational tractability. While this simplifies AC power flow behavior, similar approximations are widely adopted in large-scale scenario-based uncertainty studies. Uncertainty levels (±25% PV, ±40% availability) are selected based on typical forecast errors reported in the literature. Although a simplified aggregated model is used, the results are consistent with reported V2G performance ranges in the recent literature (20–40% cost reduction, limited battery degradation), validating the practical relevance of the proposed framework. Based on values reported in the recent literature, a representative emission factor of approximately 45 kgCO₂eq/kWh is adopted as a throughput-linked penalty. This term is used to internalize the upstream environmental impacts associated with battery manufacturing and material extraction, which are allocated to the additional energy cycled due to V2G participation [21].

3.1. Economic Superiority and Comparative Performance of V2X Strategies

The economic performance of the proposed V2X-enabled strategies is evaluated through a comparative analysis of the uncontrolled charging baseline, Smart V1G, and the V2G Hybrid configurations under both deterministic and stochastic conditions.

In the uncontrolled charging scenario, the daily operating cost reaches approximately 11,000 USD, primarily due to peak-coincident charging behavior and the absence of coordinated scheduling. By contrast, the Smart V1G strategy reduces the daily cost to approximately 7600 USD by optimally shifting charging demand away from high-price periods, corresponding to a cost reduction of 30.9%. The baseline V2G Hybrid configuration achieves a comparable daily operating cost of 7741 USD. While this value is slightly higher than that of Smart V1G under purely energy-based operation, the V2G Hybrid framework enables additional revenue streams through bidirectional energy exchange and ancillary service participation. When reserve market revenues are incorporated, the effective daily cost is reduced to 7197 USD, representing an overall cost reduction of 34.6% compared to the uncontrolled scenario. This result confirms that the economic advantage of V2G Hybrid operation is primarily driven by its ability to monetize flexibility services beyond conventional load shifting. Figure 1 illustrates the comparative economic performance of the evaluated V2X strategies.

To evaluate robustness under market and policy uncertainty, a sensitivity analysis is conducted considering a +20% increase in electricity prices and a +20% increase in carbon tax. Under increased electricity prices, the V2G Hybrid cost rises proportionally to 9290 USD, reflecting expected market exposure while still remaining significantly below the uncontrolled baseline. In contrast, the impact of carbon tax variation is negligible, with costs increasing marginally to 7745 USD (approximately +0.05%). This behavior can be attributed to the carbon-aware optimization framework, which inherently schedules charging and discharging actions during lower-emission periods, thereby reducing sensitivity to carbon pricing. The detailed numerical results under different operating conditions are summarized in

Table 1. Daily operating costs of different V2X strategies under various conditions (USD).

Strategy	Normal Conditions	+20% Electricity Price	+20% Carbon Tax
Uncontrolled Charging	11,000	N/A	N/A
Smart V1G	7600	N/A	7650
V2G Hybrid (baseline)	7741	9290	7745
V2G Hybrid (with reserve)	7197	N/A	N/A

.

In Table 1, “N/A” denotes cases where sensitivity analysis was not performed. This analysis is primarily conducted for the V2G Hybrid configuration, as it represents the most advanced and practically relevant operational strategy.

Overall, the results highlight three key advantages of the V2G Hybrid strategy. First, it achieves cost performance comparable to state-of-the-art Smart V1G under baseline conditions while unlocking additional economic benefits through ancillary service participation. Second, it exhibits strong resilience to market and policy variations, particularly with respect to carbon pricing. Third, the integration of probabilistic performance evaluation significantly reduces operational uncertainty, enabling more reliable decision-making for EV aggregators in real-world conditions.

3.2. Peak Shaving, Load Optimization, and Grid Technical Performance

The technical performance of the proposed V2G Hybrid strategy is evaluated in terms of peak shaving capability, load profile optimization, coordinated charging/discharging behavior, state-of-charge (SOC) dynamics, and voltage stability.

The impact of the V2G Hybrid strategy on load profile reshaping is illustrated in Figure 2. As shown in Figure 2a, the optimized load curve exhibits a substantial reduction in peak demand compared to the uncontrolled case. During the critical peak period (hours 10–15), peak demand is reduced by approximately 50–60%, effectively flattening the load profile and mitigating stress on the distribution network.

The corresponding SOC dynamics are presented in Figure 2b, where the aggregated SOC fleet increases during low-demand periods through coordinated charging and reaches a plateau before the peak demand interval. This is followed by a controlled discharge phase, during which stored energy is utilized to support the grid. The SOC trajectory remains within predefined operational limits, ensuring adequate energy reserves while avoiding excessive battery utilization.

The coordinated charging and discharging behavior are illustrated in Figure 2c, where positive values represent charging periods and negative values indicate discharging events. Charging is concentrated during off-peak periods, while discharging occurs during peak demand intervals. This coordinated behavior enables efficient temporal energy shifting without introducing secondary peaks and ensures physically consistent operation.

Further system-level performance is evaluated through the PCC power and voltage profiles, as shown in Figure 3. The V2G Hybrid strategy significantly smooths the load profile compared to the uncontrolled case (Figure 3a), while maintaining voltage levels within a narrow range of 0.994–1.008 pu (Figure 3b). These results indicate that the proposed approach not only reduces peak demand but also contributes to stable voltage regulation under varying operating conditions. Minor deviations remain within acceptable operational limits and do not indicate system instability.

The technical performance of the proposed V2G Hybrid strategy is further evaluated through system-level indicators, including voltage sensitivity, power flow behavior, and cost–loss trade-offs, as shown in Figure 4. Figure 4a shows the effect of the DSO penalty weight on minimum voltage levels. As the penalty increases, voltage regulation improves, ensuring that the system operates above critical limits. Figure 4b presents the EV charging and discharging power profiles, where short-duration, high-magnitude discharging occurs during peak demand periods, while charging is distributed over off-peak intervals. This reflects an optimized strategy that stores energy gradually and deploys it during critical periods. Figure 4c illustrates the impact of system losses on voltage stability. As losses increase, the minimum voltage decreases gradually but remains within acceptable operational limits, indicating sufficient system robustness. Figure 4d shows the trade-off between operating cost and total system losses. The results reveal a smooth relationship, indicating that improved technical performance can be achieved with a modest increase in cost. Overall, the results confirm that the proposed framework maintains stable and efficient operation while balancing economic and technical objectives.

The technical performance of the proposed framework is assessed in terms of peak load reduction, load profile smoothing, and voltage stability. The optimized load profile shows a significant reduction in peak demand compared to the uncontrolled scenario. Charging is shifted to low-demand periods, while controlled discharging supports the grid during peak hours. This coordinated behavior results in a smoother load profile without introducing secondary peaks, demonstrating the effectiveness of the optimization strategy in managing temporal energy distribution. Voltage levels remain within a stable operating range throughout the simulation period. Given the use of a linear voltage approximation, these results are interpreted as trend indicators rather than exact values. Overall, the results confirm that the proposed framework improves both grid stability and operational efficiency.

3.3. Uncertainty Quantification and Monte Carlo Results

To evaluate the robustness of the proposed V2G Hybrid strategy under realistic operating conditions, a comprehensive Monte Carlo simulation framework is employed, incorporating uncertainties in photovoltaic (PV) generation, EV availability, electricity prices, carbon taxes, and initial state-of-charge (SOC) levels. The results provide a probabilistic assessment of system performance across a large number of stochastic scenarios.

The uncertainty in SOC behavior is illustrated in Figure 5a, which presents the mean SOC trajectory along with the corresponding 95% confidence interval. The results show that the SOC follows a controlled and predictable pattern, with a gradual increase during charging periods and a regulated decrease during discharging intervals. Importantly, the confidence band remains relatively narrow throughout the day, particularly during critical peak periods, indicating that the proposed control strategy effectively limits stochastic variability while preserving sufficient operational flexibility.

The economic performance under uncertainty is further evaluated through the probability distribution of daily operating costs, as shown in Figure 5b. The distribution is tightly concentrated around the mean value of approximately 7200 USD, with most realizations falling within a narrow range. The 95% confidence interval is approximately ±277 USD, corresponding to less than 4% variation. This compact distribution indicates a high level of cost predictability and low operational risk, which is a critical requirement for practical deployment and market participation.

Environmental performance is assessed in Figure 5c, where operational emissions and lifecycle (LCA-based) emissions are compared. The results show that while lifecycle emissions are slightly higher due to increased battery utilization, the overall increase remains limited (approximately 9%), while operational emissions are marginally reduced. This demonstrates that the proposed strategy maintains a balanced trade-off between economic benefits and environmental impact.

The overall stochastic performance is further summarized through normalized cost and profit distributions, as illustrated in Figure 6. The results indicate near-zero variance in normalized cost and consistently positive profit values across all Monte Carlo realizations, confirming that the proposed framework delivers highly stable and predictable economic outcomes even under significant uncertainty.

In particular, the narrow spread of the cost distribution suggests that the optimization framework is largely insensitive to fluctuations in key uncertain parameters, such as PV generation variability and EV availability. This level of robustness is essential for real-world deployment, where forecasting errors and operational uncertainties are unavoidable. Furthermore, the consistently positive profit distribution highlights the ability of the V2G Hybrid strategy to generate reliable economic returns, primarily driven by effective peak shaving and participation in ancillary service markets. This indicates that the EV fleet can operate not only as a flexible load but also as a dependable revenue-generating asset under stochastic conditions.

The robustness of the proposed framework is evaluated using Monte Carlo simulations that capture uncertainty in PV generation and EV availability. The state-of-charge (SOC) trajectories exhibit limited variability across scenarios, indicating stable battery operation under uncertainty. Similarly, the distribution of daily operating cost remains tightly concentrated around its mean value. This low variability indicates that the proposed framework effectively mitigates uncertainty impacts and ensures stable and predictable system performance, which is critical for real-world deployment. Environmental analysis shows that increased V2G participation slightly raises lifecycle-related emissions due to additional battery usage, while operational emissions are reduced through optimized scheduling. This result highlights a balanced trade-off between economic performance and environmental impact, supporting the overall sustainability of the proposed approach.

3.4. Probabilistic Uncertainty Analysis and Pareto-Front Analysis

To systematically explore the inherent trade-offs between economic performance and environmental impact under uncertainty, a Monte Carlo-based stochastic multi-objective optimization framework was developed. This approach generates a set of non-dominated solutions that remain consistent across a wide range of stochastic scenarios, rather than relying solely on deterministic point estimates. The resulting stochastic Pareto frontier and associated trade-off analyses are illustrated in Figure 7 and Figure 8.

Figure 7 presents the Monte Carlo-based stochastic Pareto frontier, plotting normalized expected operational cost against expected carbon emissions. The stochastic solutions (blue circles connected by lines) form a well-defined and smooth Pareto front, spanning a range of normalized expected costs from approximately 133.2 to 137. The deterministic baseline solution (red marker), located at 135.75 and 552.02 kg CO₂eq, lies above the stochastic Pareto frontier, indicating inferior performance in terms of both cost and emissions. This demonstrates that uncertainty-aware optimization consistently identifies superior operating strategies capable of achieving lower expected costs for a given emission level, or lower emissions for a given cost, compared to the traditional deterministic approach. A representative near-optimal stochastic solution achieves a normalized expected operational cost of approximately 134.6 while maintaining competitive carbon performance, reflecting a favorable balance between economic and environmental objectives. This point corresponds to a balanced operating regime where neither cost minimization nor emission reduction is overly prioritized, resulting in an efficient compromise between economic and environmental objectives.

Further insight into the multi-objective nature of the problem is provided by economic gain versus battery state-of-health (SOH) degradation analysis (Figure 8). The surface shows that substantial economic benefits (up to −300 $ daily net gain) can be realized while keeping SOH degradation extremely low, below 2.5 × 10⁻³% per day. This result is particularly significant because it addresses one of the major concerns in V2G implementation: accelerated battery aging due to frequent cycling. The proposed V2G Hybrid strategy successfully decouples economic performance from battery degradation, enabling profitable bidirectional operation without sacrificing long-term asset value.

Collectively, the stochastic Pareto-front analyses confirm that the V2G Hybrid framework delivers high-quality and consistent solutions across conflicting objectives. By explicitly accounting for uncertainty through Monte Carlo sampling, optimization avoids overly optimistic deterministic solutions and instead produces a set of stochastic alternatives that maintain strong performance across a wide range of scenarios. This represents a clear methodological advancement over conventional single-objective or deterministic V2G studies, most of which fail to quantify uncertainty or explore the full Pareto surface under realistic stochastic conditions.

The superior positioning of the stochastic solutions relative to the deterministic baseline, combined with favorable trade-offs in loss minimization and battery health preservation, underscores the practical value of the proposed approach. These findings provide fleet aggregators and distribution network operators with a rich set of Pareto-optimal operating strategies from which they can select according to their specific priorities—whether cost minimization, emission reduction, technical efficiency, or battery longevity—while maintaining guaranteed performance under uncertainty.

3.5. Multi-Dimensional Sensitivity Analysis and SOH Projection

A comprehensive multi-dimensional sensitivity analysis was conducted to evaluate the scalability, performance under uncertainty, and long-term sustainability of the V2G Hybrid strategy across varying fleet sizes and key operational parameters. The results, visualized in Figure 9 and supported by quantitative projections, provide critical insights into how the proposed approach performs under different EV penetration levels and reveal important trade-offs among economic, environmental, computational, and grid-support metrics.

As shown in Figure 9a, the operational cost decreases consistently as the number of EVs increases, indicating that larger fleet sizes provide enhanced flexibility for load shifting and energy arbitrage. This behavior confirms that higher EV penetration improves the economic efficiency of the system by enabling more effective utilization of distributed storage resources. In contrast, the emission trend remains relatively stable across different fleet sizes, suggesting that increased EV participation does not lead to a proportional increase in environmental impact when coordinated optimization is applied. This indicates that the proposed framework maintains a controlled balance between economic gains and environmental performance.

Figure 9b presents the computational performance of the optimization framework. The results show a slight increase in solution time as the number of EVs grows; however, the variation remains limited (approximately 0.065–0.075 s), demonstrating that the proposed MILP/LP hybrid approach is computationally efficient and scalable for large-scale applications.

The peak shaving performance, illustrated in Figure 9c, remains stable across all fleet sizes, indicating that the system consistently maintains its load-flattening capability. While the absolute improvement does not increase significantly with fleet size, this stability confirms that the control strategy is robust and does not degrade under higher penetration levels. The combined relationship between operational cost and peak shaving is further illustrated in Figure 9d, where different fleet sizes are mapped onto the cost–performance space. The results show that increasing fleet size leads to lower operational cost while maintaining consistent peak shaving performance, highlighting the ability of the system to improve economic outcomes without compromising technical effectiveness.

In parallel with the sensitivity analysis, a long-term battery degradation projection was performed using a detailed cycle-counting and depth-of-discharge model. The results, summarized in

Table 2. Summary of SOH projection and Monte Carlo.

Parameter	Value	Notes
1-Year SOH	96.50%	After optimized operation
Estimated time to 80% EOL	5.7 years	Based on daily throughput model
Mean normalized daily cost	−0.16	Monte Carlo (near-zero variability)
Mean aggregator profit	0.18	From reserve market participation
LCA carbon footprint increase	9.0%	Relative to operational emissions

, project a 1-year State-of-Health (SOH) of 96.50% for the fleet batteries. Extrapolating under realistic operating conditions, the time to reach the end-of-life threshold (80% SOH) is estimated at 5.7 years. This projected lifetime represents a significant improvement—approximately 15–20% longer—compared with typical battery longevity reported for conventional unidirectional V1G strategies in the literature. The ability to achieve such extended battery life while simultaneously delivering economic benefits and grid services highlights one of the core strengths of the V2G Hybrid approach: intelligent bidirectional control that minimizes unnecessary cycling and maintains optimal SOC windows.

The multi-dimensional sensitivity results demonstrate that the V2G Hybrid strategy scales gracefully with increasing EV fleet size. Economic benefits improve substantially, environmental impacts remain well-controlled, computational requirements stay within real-time limits, and grid support performance remains consistently strong. Crucially, these operational advantages are achieved without accelerating battery degradation, as evidenced by the favorable SOH projection. This balanced performance across economic, technical, environmental, and longevity dimensions addresses key barriers to widespread V2G adoption and provides strong evidence that bidirectional strategies can deliver sustainable value to all stakeholders—fleet owners, aggregators, distribution system operators, and society at large.

3.6. Comparison with Lifecycle Economic Models and Long-Term Assessment

To position the proposed framework within the existing literature, a comparison is made with lifecycle economic evaluation approaches, such as the capital recovery factor (CRF)-based method presented in [22].

In such approaches, investment cost, maintenance cost, and operational revenue are annualized using the CRF and modeled separately. This formulation is particularly suitable for long-term planning and capacity configuration, where asset lifetime and capital expenditure dominate decision-making.

In contrast, the proposed framework focuses on short-term operational optimization through a daily cost minimization formulation. It explicitly captures the dynamic interactions between EV fleet behavior, time-varying electricity prices, and uncertainties in renewable generation and vehicle availability.

Therefore, while lifecycle-based methods provide valuable insights into long-term economic feasibility, the present approach offers a complementary perspective by addressing real-time operational decision-making under uncertainty. This distinction highlights the applicability of the proposed framework for day-ahead scheduling and operational optimization in V2G-enabled smart grid systems.

The results further indicate that incorporating uncertainty into operational decision-making improves both economic and technical performance compared to deterministic approaches, enabling more balanced trade-offs between cost and emissions.

3.7. Comprehensive Discussion

This study provides a comprehensive evaluation of V2G-enabled EV fleet operation by integrating uncertainty-aware system evaluation, battery degradation modeling, and lifecycle environmental assessment within a unified framework. The results demonstrate that incorporating uncertainty into operational decision-making significantly enhances both economic and technical performance compared to conventional deterministic approaches. In particular, the stochastic Pareto analysis reveals that uncertainty-aware solutions consistently dominate deterministic benchmarks, achieving more balanced trade-offs between cost and emissions.

When compared with recent V2G studies (2023–2025), the proposed framework shows competitive or superior performance in several aspects. The cost savings achieved are consistent with values reported by Alamgir et al. [5], while the additional benefit from reserve market participation highlights the importance of monetizing ancillary services. Battery degradation remains well-controlled, with a projected 96.5% SOH after one year and 5.7 years to 80% EOL, aligning with Sagaria et al. [7] who reported only 0.31–0.5% additional annual aging under optimized V2G operation. Environmentally, the modest 9.0% increase in LCA-inclusive carbon footprint alongside 1–2% lower operational emissions is in line with Wohlschlager et al. [10], confirming that net benefits require carbon-aware and degradation-conscious strategies. Methodologically, the Monte Carlo-based stochastic Pareto frontier provides more robust solutions than many deterministic or heuristic multi-objective approaches commonly found in the literature.

Despite these promising outcomes, certain limitations warrant acknowledgment. The simulations assume perfect forecasts in baseline Monte Carlo inputs and a representative IEEE-like distribution network; real-world driver behavior, weather variability, and communication delays may widen uncertainty bands. Additionally, the analysis focuses on a single daily horizon; multi-day or seasonal evaluations could provide deeper insights.

Overall, the proposed V2G Hybrid framework delivers strong techno-economic and environmental performance through the unified integration of battery degradation awareness, LCA penalties, ancillary revenues, integrating probabilistic system assessment, and hybrid control for large-scale EV fleets. These results strengthen the case for practical V2G deployment in emerging markets and contribute to the development of more flexible and sustainable smart grids.

4. Conclusions

This study presented a comprehensive framework for the optimal operation of large-scale EV fleets in V2G-enabled smart grids, integrating an uncertainty-aware operational framework, battery degradation modeling, and lifecycle environmental assessment within a unified structure. Unlike conventional approaches that address these aspects separately, the proposed framework enables a coordinated and system-level evaluation of V2G operation under realistic conditions.

The results demonstrate that explicitly incorporating uncertainty into the decision-making process leads to more reliable and well-balanced solutions compared to conventional deterministic approaches. In particular, the proposed stochastic framework improves decision robustness by reducing sensitivity to variability in renewable generation, EV availability, and market signals, thereby ensuring consistent performance in terms of cost efficiency, grid support, and environmental impact.

By jointly addressing economic, technical, environmental, and degradation-related aspects, the proposed framework provides a holistic and realistic evaluation of V2G operation, overcoming key limitations of existing studies that typically focus on individual objectives in isolation. This integrated perspective allows for the identification of operating strategies that not only minimize cost but also maintain grid stability, limit emissions, and preserve battery health over time.

From a practical standpoint, the findings highlight the potential of EV aggregators operating as flexible, reliable, and economically viable distributed energy resources within modern power systems. The demonstrated ability to deliver stable performance under uncertainty, while maintaining controlled battery degradation, suggests that large-scale EV fleets can actively support grid operation without compromising long-term asset sustainability. Moreover, the inclusion of ancillary service participation further reinforces the role of EV fleets as value-generating assets in future energy markets, rather than passive loads.

Future research directions should prioritize several advancements. First, hardware-in-the-loop (HIL) validation and field demonstrations using real smart meter data and actual EV fleets would strengthen the practical applicability of the proposed framework. Second, integration of user behavior models, dynamic incentive mechanisms, and battery health-aware pricing strategies could further optimize the trade-off between grid services and owner satisfaction. Third, extending the model to multi-energy systems—including co-optimized PV, stationary BESS, and hydrogen pathways—would unlock additional synergies. To further improve robustness, future work will include multi-day and seasonal simulations to evaluate long-term operational consistency under varying conditions. Finally, comprehensive policy analyses incorporating carbon pricing, subsidies, and regulatory frameworks are essential to accelerate V2G commercialization.

In conclusion, the developed V2G Hybrid optimization framework establishes a reliable, economically viable, and technically sound solution for sustainable EV-grid integration. By delivering substantial cost savings, effective grid support, manageable battery degradation, and low uncertainty, this work contributes actionable evidence toward realizing the full potential of V2X technologies. As global EV adoption accelerates and power systems transition toward higher renewable shares, coordinated bidirectional strategies such as the one proposed here will play a pivotal role in building resilient, low-carbon, and flexible energy ecosystems. The findings provide strong justification for policymakers, utilities, and industry stakeholders to invest in V2G infrastructure and associated market mechanisms, paving the way for a smarter and more sustainable energy future.