Multi-objective Electric Vehicle Charging Strategies at Energy Hubs with Justice-informed Profit Distribution among Users

Introduction

Climate change necessitates a sustainable transition to renewable energy, with electrification playing a central role. The energy transition has rapidly increased in the number of electric vehicles (EVs) and the share of energy generated through intermittent renewable sources [1]. This has placed increased stress on an electricity grid that was not designed for the irregular electricity supply from an energy mix increasingly dominated by renewable energy sources and does not coincide with daily demand profiles [2]. Charging stations supported by on-site renewable generation, a battery energy storage system (BESS) and vehicle-to-grid (V2G) charging as shown in Figure 1 can help overcome these challenges by providing additional flexibility [3].

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At the same time, the energy transition should not reinforce economic and social inequalities. Unlike conventional refuelling, EV charging sessions take significantly longer, making users’ ability to choose when and where to charge increasingly important. Moreover, as EV adoption grows, a larger share of users will lack access to home charging [4], further limiting their charging options. This makes flexibility capital, understood as users’ capacity to adapt their energy use in light of the constraints and demands of everyday life, a key dimension of social justice in the energy transition [5]. However, this capacity is not equally distributed. Disadvantaged households face greater constraints on when and where they can charge their vehicles, limiting their ability to take advantage of cheaper charging opportunities and exposing them to charging disadvantage [6].

This work combines cost- and emission-optimal control of an EV charging hub with equitable mechanisms for distributing the benefits of smart charging among users.

Related literature: This paper pertains to two research streams: cost functions for controlling energy hubs and different cost distribution methods among participants.

In a recent literature review, authors compare optimal electric vehicle charging station (EVCS) power management strategies [7]. Optimisation-based controllers for EVCS operation include model predictive control (MPC) [8, 9, 10], which has the advantage of providing optimal actions over a prediction horizon while enforcing constraint satisfaction. The objective functions of these optimisation-based methods may consider different goals. Most commonly, controllers minimise the total economic cost of charging station owners or users [11, 12]. In other cases, cost functions account for component amortisation costs [13], grid power stabilisation

Control Systems Technology section, Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands. E-mails: {t.m.stolwijk, d.fernandez-zapico, a.piazza1, m.r.salazar}@tue.nl. [14, 15] or green house gas (GHG) emissions [16], [17]. Other work explores the multi-objective optimisations using combinations of the aforementioned cost functions [9], [18], [19]. However, as far as authors are aware, no previous work compares the Pareto fronts achievable by different (smart) EV charging strategies for multi-objective optimal control of a charging energy hub.

Many works use a utilitarian cost function to minimise the total operating costs, which does not consider the social implications for individual EV users. Some papers address this through the use of heuristics, which have no optimality guarantees and, in most cases, lack social substantiation [15], [20]. Another approach is cost division based on game theory. In [21], authors use Nash bargaining to find a profit distribution between a fast charging hub and a nearby BESS. Furthermore, in [22] Nash bargaining determines the optimal operation of an energy network with multiple energy generators. Another paper [23] proposes a carbon emission allocation scheme based on the marginal contribution to emissions of energy storage in an energy market. Other work uses a dynamic pricing scheme for a charging station [24]. They aim to minimise the perceived unfairness due to price differences between different users with similar energy requests. In [25], authors present a framework for determining the applicability and comparability of different social cost functions.

In conclusion, as far as the authors are aware, there is no previous work on the Pareto front of objective functions considering price and emissions for a charging energy hub operated under multiple smart charging strategies. Additionally, the use of a socially substantiated allocation method to fairly divide the savings generated by smart charging among cooperating users does not exist yet.

Statement of contributions: The main contributions in this paper are twofold: First, we present a comparison of multiple (smart) charging strategies for an energy hub. We show that through optimal control the operating costs and GHG emissions for EV charging can be significantly reduced by leveraging dynamic charging and V2G. Secondly, we propose two game-theoretic methods to distribute these savings among users and the operator. Beyond implementing Nash bargaining, we introduce a sufficientarian extension that caps the charging price to ensure that lower-income households with limited scheduling flexibility retain sufficient access to affordable charging, whilst not significantly affecting the overall revenues.

Organisation: The remainder of this paper is structured as follows: § 2 presents a model for the EVCS and introduces the different EV charging strategies. This is subsequently formulated into a multi-objective optimisation problem that aims at minimising combinations of economic cost and GHG emissions in Section III. In Section IV we first propose a cost allocation method based on Nash bargaining. Furthermore, we present a sufficientarian approach to reduce the inequality caused by users’ temporal inflexibilities. § 5 presents a case study for a charging energy hub on a university campus. Finally, conclusions are drawn in Section VI together with an outlook on future work.

Charging Energy Hub Model

This section presents the model of the energy hub used for the multi-objective optimisation, accounting for component degradation and amortisation costs. We consider the EVCS from Figure 1, which includes power flows from the grid connection ($P_{\mathrm{g}}$), the BESS ($P_{\mathrm{b}}$), solar panels ($P_{\mathrm{pv}}$) and the EV chargers ($P_{\mathrm{ev}}$). A central controller determines optimal component power flow to meet the charging load as

BESS

We model the BESS using the approach described in [26], [27], with the relaxed second order conic relaxation of the quadratic model for the battery losses as

where $P_{\mathrm{ib}}(t)$ is the internal battery power and $P_{\mathrm{sc}}(t)$ is the short-circuit power, which we model as a piece-wise linear function of $E_{\mathrm{b}}(t)$ following [26], [27]. Subsequently, we calculate the energy stored in the BESS using

where there are upper ($\overline{E}_{\mathrm{b}}$) and lower ($\underline{E}_{\mathrm{b}}$) limits for $E_{\mathrm{b}}(t)$ and, similarly, $P_{\mathrm{b}}(t)$ must be between an upper ($\overline{P}_{\mathrm{b}}$) and lower ($\underline{P}_{\mathrm{b}}$) bound. Lastly, we use a periodic constraint on $E_{\mathrm{b}}(t)$ for the optimisation window of length $T$ (e.g., 24 h):

We model battery degradation as a linear version of [28], [29], where the amortisation of the battery per kWh

where $C_{\mathrm{b},\mathrm{life}}$ is the lifetime cost of the battery per installed kWh, $E_{\mathrm{b}}^{\mathrm{inst}}$ is the installed battery capacity in kWh, the battery lifetime $l_{\mathrm{b}}$ is the total number of cycles and $E_{\mathrm{b}}^{\mathrm{cyc}}$ is the amount of energy charged and discharged per cycle. We calculate the BESS amortisation costs with the net internal usage of the battery as a relaxed linear constraint

where $c_{\mathrm{b}}(t)$ is the instantaneous amortisation cost rate at time $t$ for the BESS.

Power Grid

The charging station can exchange power with the grid, incurring a variable cost

where $p_{\mathrm{imp}}(t)$ and $p_{\mathrm{exp}}(t)$ are the importing and exporting prices at time $t$ respectively. We assume that $p_{\mathrm{imp}}(t) \ge p_{\mathrm{exp}}(t)$ and given that we aim to minimise the total energy cost, we can losslessly relax this equation to

where $P_{\mathrm{g}}(t)$ is bounded by the energy contract or grid infrastructure limitation as

In addition, we consider the costs of the grid infrastructure. Since these costs depend on the size of the grid connection and thus the peak amount of concurrent EV charging sessions, we calculate the amortisation costs depending on the energy charged in each charging session

where $a_{\mathrm{g}}$ is the average amortisation of the grid per kWh charged to an EV, $C_{\mathrm{g,life}}$ is the lifetime cost for the grid connection per kW of installed capacity and $E_{\mathrm{ch,lg}}$ is the expected total amount of energy charged to vehicles in the lifetime of the grid infrastructure.

Solar Plant

The amortisation costs associated with the installation and maintenance of the PV panels are constant over time as

where $a_{\mathrm{pv}}$ is the amortisation cost of the PV installation per time unit, $C_{\mathrm{pv,life}}$ is the lifetime cost for the PV panels per kW of installed peak generation power, $l_{\mathrm{pv}}$ is the lifetime of the PV panels and $P_{\mathrm{pv}}^{\mathrm{inst}}$ is the peak generation power of the PV installation.

EV charging strategies

We model the charging process assuming perfect knowledge for each user $n$ of the energy desired $E_{\mathrm{ch},n}$ and the arrival and departure times of the session. We introduce a new time variable $\tau_n = t - t_{\mathrm{c},n}$ which tracks time for user $n$ relative to the origin set by the connection time $t_{\mathrm{c},n}$. We model the charging process linearly as

where the charging power $P_{\mathrm{ch},n}(\tau_n)$ can modify the energy level $E_{\mathrm{ev},n}(\tau_n)$ until disconnection time $\tau_{\mathrm{d},n}$ when $E_{\mathrm{ev},n}(\tau_n = \tau_{\mathrm{d},n}) = E_{\mathrm{ch},n}$.

We consider three EV charging strategies in this work. The simplest charging strategy is nominal charging, in which EVs start charging at full power until the energy request is fulfilled. This is formulated as

where the time needed to meet the demand is $\tau_{\mathrm{ch},n} = \frac{E_{\mathrm{ch},n}}{\overline{P}_{\mathrm{ch}}}$. Then, we consider two smart strategies. First, V2G allows charging to dynamically adjust within its limits as

Second, V1G is a variant in which we prevent the EV battery from discharging as

We can obtain the total EV power demand at time $t$ as

where $N_{\mathrm{ev}}$ is the total number of users in the optimisation window and $\mathbf{1}_x$ is an indicator function set to 1 if $x$ is true and 0 otherwise.

We model EV battery degradation similarly to (5) and (6) to obtain the instantaneous amortisation cost rate $c_{\mathrm{evb},n}$ of the EV battery of user $n$. Furthermore, we model the charger amortisation cost following (9) as

where $a_{\mathrm{ch}}$ is the amortisation cost per kWh charged to an EV for the chargers, $C_{\mathrm{ch,life}}$ are the lifetime costs for a single charger, $N_{\mathrm{ch}}$ is the number of chargers at the energy hub and $E_{\mathrm{ch,lch}}$ is the expected total amount of energy charged to vehicles in the lifetime of the chargers.

Optimal Hub Operation

We operate the energy hub with the goal of minimising total operational cost. In this work, we consider a combination of two types of costs: economic costs $C^{\mathrm{eco}}$ and greenhouse gas emission costs $C^{\mathrm{GHG}}$. We can express the lifetime costs required to compute the corresponding amortisation and degradation costs from the previous section as

where $\alpha\in[0,1]$ indicates the weight of the function. Similarly, we compute importing and exporting prices in (7) based on both metrics. This approach allows us to obtain a Pareto front by solving the optimisation problem for varying weights.

The objective function $J$ in Problem 1 considers both operator and user terms. We define the cost of the operator as

which includes all the component costs covered by the energy hub operator. We can also define the cost of each user $n$ as

Additionally, to ensure charging powers are evenly distributed between EVs over time, we include a regularisation term in $J$ as

where $\alpha_{\mathrm{r}}$ is a regularisation weight. We then formulate the optimal operation of the hub as Problem 1, where the decision variables are $P_{\mathrm{ch},n}$ and $P_{\mathrm{ib}}$.

Problem 1 (Optimal Hub Operation Problem):

For comparison, we introduce a no-BESS configuration to the three charging strategies used in Problem 1, where we remove the BESS unit and employ the nominal charging strategy (12).

Profit sharing methods

The smart charging strategies used to obtain optimal hub operation produce cost savings. This opens up the discussion on how to fairly distribute cost savings among participating users and charging station operators. In this section we propose a justice-informed cost allocation method based on Nash bargaining. Furthermore, we present a sufficientarian approach to reduce the inequality caused by users’ temporal inflexibilities.

Nash Bargaining

We formulate this profit sharing problem as a Nash bargaining problem, which is part of cooperative bargaining problems. When agents generate a surplus by cooperating, Nash bargaining provides a trade-off among all agents, maximising agent improvement with respect to a fallback position. In this work, we define the bargaining problem between EV users and the energy hub operator. The utility function of user $n$ is

where $C_{\mathrm{ev},n}^{\mathrm{Nash}}$ is the charging cost paid by user $n$ under Nash bargaining. Similarly, the utility of the hub operator is

In Nash bargaining, resource allocation maximises the product of utility improvements. We define the objective function of this maximisation problem as

where $u_{\mathrm{op}}^{\mathrm{d}}$ and $u_{\mathrm{ev},n}^{\mathrm{d}}$ are the disagreement utilities of the operator and user $n$, respectively. We assume that in case of disagreement, the operator does not meet any charging demand and therefore has utility

where $J_{\mathrm{op}}^{\mathrm{d}}$ is the optimal value of Problem 1 with no charging demand. For users, we assume charging takes place at a different station with utility

where $J_{\mathrm{ev},n}^{\mathrm{d}}$ is the battery degradation cost of user $n$ under nominal charging in (12) and the disagreement cost $C_{\mathrm{ev},n}^{\mathrm{d}}$ is

where $\beta>1$ is multiplier considering the operator profit margin and $P_{\mathrm{ch},n}^{\mathrm{nom}}$ is the nominal charging strategy in (12).

We follow [30] and use a log-transform for the nonlinear objective function in (20). Furthermore, we introduce a weight so that users get a utility improvement proportional to the energy charged. The transformed utilities of users $v_{\mathrm{ev},n}$ and the operator $v_{\mathrm{op}}$ are

which can be implemented using an exponential cone resulting in an exponential cone optimisation problem. We constrain the utility improvements by

The equivalent minimisation objective function of the problem is the negative of the transformation of (20)

The resulting Nash bargaining optimisation problem is then as follows.

Problem 2 (Nash bargaining problem):

Sufficientarian Nash Bargaining

Nash bargaining allocates savings by treating all agents as symmetric strategic actors, maximising the product of utility improvements relative to a disagreement point. This symmetry, however, does not account for the fact that users differ in how much flexibility they have to adapt their charging behaviour. EV charging sessions must be planned around a user’s schedule in a way that conventional refuelling does not, placing a disproportionate burden on users with tight schedules or no access to home charging. As shown in the literature on flexibility capital [5], lower-income households tend to have less scheduling flexibility, leaving them unable to shift charging to cheaper time windows [6]. Under plain Nash bargaining, these users tend to pay higher prices for constraints they cannot control, compounding existing inequalities [31].

To mitigate this, we introduce a sufficientarian extension of Nash bargaining [32], [33]. Sufficientarianism holds that the primary distributive objective is not to equalise outcomes, but to ensure that everyone reaches a sufficient threshold of well-being or access to essential opportunities [34], [35]. In our context, this means ensuring that all users have access to charging at an affordable price, irrespective of their capacity to shift demand. We implement this by adding an upper limit $\overline{p}_{\mathrm{ev}}$ on the per-kWh charging price, ensuring that the most constrained users are not charged beyond a threshold consistent with affordable household energy expenditure. We represent this limit by adding another constraint to Problem 2:

where $\overline{p}_{\mathrm{ev}}$ is the upper limit on the charging price. We set $\overline{p}_{\mathrm{ev}}$ at the 90th percentile of the Nash bargaining price distribution, using a quantile to locate the threshold within the price distribution [36]. The constraint operationalises the sufficientarian objective of protecting users from excessive charging costs. However, sufficientarianism does not prescribe a specific price threshold, making its calibration context-dependent. The choice should therefore be examined through sensitivity analysis of alternative thresholds, considering the trade-off between protecting financially constrained users and maintaining an efficient allocation.

Case Study

For this case study, we consider a charging energy hub with adapted data from different sources. The EV charging demand dataset belongs to a university campus in California, US, using Level 2 AC chargers [37]. We size the components of the hub according to the total charging demand in the hub. We use hourly day-ahead electricity price and emission information from the Netherlands for 2025 [38], [39]. On top of this, we add the importing electricity tax to the economic cost for the Netherlands [40]. For the PV power, we use data from a solar farm in California, US, [41]. Based on the data available, we work in discrete time steps with a resolution $\Delta t = 15$ min and use the forward Euler method to discretise (3) and (12). We use an optimisation window of 5 days. Table 2 shows additional parameters used in this case study.

Parameter	Description	Value	Unit
Components
$E_{\mathrm{b}}^{\mathrm{inst}}$	BESS capacity	100	kWh
$\bar{E}_{\mathrm{b}}$	Max. BESS energy	90	kWh
$\underline{E}_{\mathrm{b}}$	Min. BESS energy	10	kWh
$\bar{P}_{\mathrm{b}}$	Max. BESS power	10	kW
$\underline{P}_{\mathrm{b}}$	Min. BESS power	−10	kW
$\bar{P}_{\mathrm{g}}$	Max. grid power	150	kW
$\underline{P}_{\mathrm{g}}$	Min. grid power	−150	kW
$\bar{P}_{\mathrm{ch}}^{\mathrm{V2G}}$	Max. EV charging power	11	kW
$\underline{P}_{\mathrm{ch}}^{\mathrm{V2G}}$	Min. EV charging power	−11	kW
$\bar{P}_{\mathrm{ch}}^{\mathrm{V1G}}$	Min. EV charging power	0	kW
Datasets
$P_{\mathrm{pv}}^{\mathrm{inst}}$	Installed PV capacity	21	kW$_{\mathrm{p}}$
	Avg. number of EVs	29.1	day$^{-1}$
	Avg. EV connection time	6.06	h
	Avg. EV charging demand	8.92	kWh
Optimisation
$\Delta t$	Time step resolution	0.25	h
$\alpha_{\mathrm{r}}$	Regularisation weight	$1 \cdot10^{-6}$

To compute the amortisation costs of the components, we determine their lifetime costs expressed in economic terms and as CO$_2$ equivalent emissions. We compute economic component lifetime cost as $C_{\mathrm{life}}^{\mathrm{eco}} = \mathrm{CAPEX}+\mathrm{OPEX}\cdot l$, considering the capital expenditure (CAPEX) and the operational expenditure (OPEX) of the component over its lifetime $l$. For the component lifetime cost expressed in GHG emissions $C_{\mathrm{life}}^{\mathrm{GHG}}$, we use the global warming potential value stemming from component lifetime analysis. For the EV batteries, we assume identical amortisation parameters across users. Since we do not know the battery type and capacity of the EVs, we assume that during a cycle the battery is fully charged and discharged. Table 3 shows the values used to determine all amortisation costs in this case study.

Parameter	Value	Unit	Source
BESS
$C_{\mathrm{b,life}}^{\mathrm{eco}}$	250	€/kWh	[43, 44]
$C_{\mathrm{b,life}}^{\mathrm{GHG}}$	130	kg CO$_2$e/kWh	[45]
$l_{\mathrm{b}}$	10000	cycles	[43]
$a_{\mathrm{b}}^{\mathrm{eco}}$	1.56	ct/kWh	[5]
$a_{\mathrm{b}}^{\mathrm{GHG}}$	8.1	g CO$_2$e/kWh	[5]
EV batteries
$C_{\mathrm{evb,life}}^{\mathrm{eco}}$	120	€/kWh	[46, 47]
$C_{\mathrm{evb,life}}^{\mathrm{GHG}}$	80	kg CO$_2$e/kWh	[48, 49]
$l_{\mathrm{evb}}$	5000	cycles	[46]
$a_{\mathrm{evb}}^{\mathrm{eco}}$	1.2	ct/kWh	[5]
$a_{\mathrm{evb}}^{\mathrm{GHG}}$	8	g CO$_2$e/kWh	[5]
Grid
$\mathrm{CAPEX}_{\mathrm{g}}$	70	€/kW	[50]
$\mathrm{OPEX}_{\mathrm{g}}$	27	€/kW/year	[50]
$l_{\mathrm{g}}$	40	years	[50, 51, 52]
$a_{\mathrm{g}}^{\mathrm{eco}}$	4.6	ct/kWh	[9]
$a_{\mathrm{g}}^{\mathrm{GHG}}$	1.84	kg CO$_2$e/kWh	[51, 52]
Energy tax	5.548	ct/kWh	[40]
PV
$\mathrm{CAPEX}_{\mathrm{pv}}$	800	€/kW$_{\mathrm{p}}$	[53, 54, 55]
$\mathrm{OPEX}_{\mathrm{pv}}$	9	€/kW$_{\mathrm{p}}$/year	[53, 54, 55]
$C_{\mathrm{pv,life}}^{\mathrm{GHG}}$	593	kg CO$_2$e/kW$_{\mathrm{p}}$	[56]
$l_{\mathrm{pv}}$	25	years	[54, 56]
$a_{\mathrm{pv}}^{\mathrm{eco}}$	41	€/kW$_{\mathrm{p}}$/year	[10]
$a_{\mathrm{pv}}^{\mathrm{GHG}}$	23.7	kg CO$_2$e/kW$_{\mathrm{p}}$/year	[10]
Chargers
$\mathrm{CAPEX}_{\mathrm{ch}}$	3000	€/charger	[50, 57]
$\mathrm{OPEX}_{\mathrm{ch}}$	100	€/charger/year	[50, 57]
$C_{\mathrm{ch,life}}^{\mathrm{GHG}}$	622	kg CO$_2$e/charger	[58]
$l_{\mathrm{ch}}$	15	years	[57]
$N_{\mathrm{ch}}$	40	chargers
$a_{\mathrm{ch}}^{\mathrm{eco}}$	12.7	ct/kWh	[16]
$a_{\mathrm{ch}}^{\mathrm{GHG}}$	17.5	g CO$_2$e/kWh	[16]

Pareto Front in Optimal Hub Operation

In this section, we report the results of optimal hub operation for different objective functions, based on a combination of economic and emission costs. We vary the weight $\alpha$ in (18) and solve Problem 1 for 24 days in the dataset selected to cover all months of the year. We obtain the Pareto front for all three charging strategies in Figure 2, where each point is the average operation and component-amortisation cost, relative to the total EV energy demand in the optimisation window. Additionally, we include the result for the hub configuration without a BESS unit and using nominal charging.

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Given that renewable energy generation is cheaper than fuel-based energy generation [42], we expect economic-optimal operation also produces emission-optimal operation. However, for varying values of $\alpha$ in Figure 2 there is a trade-off between minimising economic and emission costs. On top of this, we see that increasing flexibility allows to obtain lower average economic and emission costs for all values of $\alpha$. The nominal strategy without BESS has the lowest flexibility and, consequently, the highest average economic and emission cost. By adding the BESS, energy hub operation improves. Significant cost and emission savings are possible when enabling smart charging. When selecting the V1G charging strategy, EV charging can be shifted to more convenient times. Furthermore, V2G charging yields a marginal improvement with respect to V1G, thanks to the additional flexibility provided by a small number of users. A larger V2G improvement would require users to stay connected for longer periods of time, allowing the controller to charge and discharge EVs during horizons with larger price variations and, consequently, to offset the increase in EV battery degradation costs.

Fair Cost Distribution

In this section, we compare the cost distribution under the Nash bargaining solution in Problem 2 with that of its sufficientarian alternative. The latter introduces a sufficientarian concern for protecting users from excessively burdensome charging costs, particularly those with limited financial resources and scheduling flexibility. We set $\overline{p}_{\mathrm{ev}}$ at the 90th percentile of the Nash bargaining price distribution, yielding €0.369/kWh in this case study. This imposes an upper limit on charging prices, constraining the highest prices in the distribution while retaining scope for price differentiation among users.

Figure 3 presents the charging price $\frac{C_{\mathrm{ev},n}^{\mathrm{Nash}}}{E_{\mathrm{ch},n}}$, after distributing costs through the Nash bargaining method, at a sample day with a 120 h optimisation horizon. For all V1G users, these prices come from the same price reduction relative to the disagreement price $\frac{C_{\mathrm{ev},n}^{\mathrm{d}}}{E_{\mathrm{ch},n}}$. V2G users enjoy a greater price reduction, which compensates for their increased battery degradation. We also include the sufficientarian Nash bargaining price and the upper limit price in Figure 3. This approach successfully prevents disadvantaged users from paying over the limit, while only slightly affecting the prices of others. We can also see that even with a sufficientarian cost distribution, we can see mid-day arriving users pay significantly less than the rest, highlighting the influence of the disagreement price in our approach.

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Allocation Method	Charging price [€/kWh]	EVCS profit [€/day]
Disagreement Outcome	0.348	6.94
Nash Bargaining	0.309	17.09
Sufficientarian Nash	0.306	16.28

We extend the comparison of the two methods over a longer time horizon by solving the cost distribution problem for 24 days across the year, selecting two days per month and considering a 120 h horizon window. Table I reports the average charging price and daily station profit across the year. Both distribution methods substantially improve upon the disagreement outcome. Table I shows that average charging prices under Nash bargaining and the sufficientarian alternative differ by only 1%, while their average station profits differ by 5%. Despite these relatively small differences in aggregate outcomes, Figure 4 reveals substantial differences in how charging costs are distributed among users under the two methods. The sufficientarian Nash bargaining approach respects the upper price limit by shifting the price distribution towards this threshold, thereby improving affordability for users with low flexibility capital. As a result, although the two methods yield comparable aggregate outcomes, their distributional effects differ considerably at the individual level. The choice of profit-sharing method can therefore have markedly different implications for individual users, depending on their flexibility capital: Still promoting flexibility when it is possible, whilst not punishing when it is not.

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Conclusions

In this paper, we introduced multi-objective optimal charging strategies and profit sharing methods for an electric vehicle (EV) charging energy hub equipped with a battery storage system, solar panels and a grid connection. Our case study results showed how a stationary battery and dynamic vehicle charging operations, including V2G, can significantly reduce total costs and emissions. However, these savings are only possible if there is cooperation between the operator and users. The second part of this paper examined how the savings generated through such a cooperation can be distributed between EV users and the charging station operator. We compared Nash bargaining with a sufficientarian extension that limits maximum charging prices to protect users with low flexibility capital. This constraint improves the fairness of the cost distribution while having little impact on V2G incentives, average charging prices and station profits. Ultimately, it shows that accounting for inequalities in flexibility capital can make EV charging more equitable without substantially compromising its economic benefits.

This work opens the field for the following possible extensions. Currently, the cost allocation methods solely take the economic cost into account. Future work should also consider the emissions as they also impact social welfare [9], [23]. Furthermore, we plan to implement the methods and charging strategies in real time. Finally, future research should investigate how the sufficientarian price threshold can be normatively grounded and systematically calibrated, taking into account differences in household income, charging needs, and scheduling flexibility.

Acknowledgment

This work was supported by RVO within the Charging Energy Hubs project with number NGFS23020 and was partially funded by the Dutch National Growth Fund.

References

Appendix I: Case Study Parameters

This appendix lists the parameters used in the case study of § 5. Table II reports the main technical parameters of the hub components, the main statistics of the charging data [37] and the optimisation settings. Table III reports the economic and emission parameters used to compute the amortisation costs in § 2, together with their sources. For each component, the economic lifetime cost is $C_{\mathrm{life}}^{\mathrm{eco}} = \mathrm{CAPEX} + \mathrm{OPEX} \cdot l$, and the emission lifetime cost $C_{\mathrm{life}}^{\mathrm{GHG}}$ is its global warming potential obtained from life-cycle assessments.