# Optimal techno-economic and environmental design of a renewable energy based charging station including second life batteries

Evelise Antunes, Bruno Sareni, Xavier Roboam

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Evelise Antunes, Bruno Sareni, Xavier Roboam. Optimal techno-economic and environmental design of a renewable energy based charging station including second life batteries. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0042. hal-05077088

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# Optimal techno-economic and environmental design of a renewable energy based charging station including second life batteries

Evelise Antunes, Bruno Sareni, Xavier Roboam

LAPLACE, UMR CNRS, Toulouse INP, UT3, Université de Toulouse, ENSEEIHT, 2 rue Camichel, 31071 CEDEX 07

Toulouse, France

E-Mail: {antunes, sareni, roboam}@laplace.univ-tlse.fr

## ACKNOWLEDGMENT

This work has been carried out in the frame of the I-ReVE project supported by the Programme d'Investissements d'Avenir (PIA) operated by ADEME, in cooperation with RETROFLEET and SIREA.

**Index Terms**—Charging infrastructure for EV's, Microgrid, Multi-objective optimization, Degradation, Environmental impacts.

**Abstract**—Photovoltaic panels combined with second life batteries (SLBs) represent an interesting solution for avoiding the reinforcement of electricity grids when setting up electric vehicle charging stations. This paper presents an integrated design approach aiming at minimizing the Net Present Cost (NPC) and the Global Warming Potential (GWP) of such charging stations, while performing an optimal dispatch. The case study compares the co-optimization of charging stations installed at a school bus depot with first life stationary batteries (FLBs) or with SLBs. The results showed that the addition of PV panels and stationary batteries increases the income of such charging stations and reduces the load shedding, compared with grid only systems. For the case with FLBs, there is a low or null presence of batteries in the optimal design solutions, due to the high installation cost and production emissions. However, the low cost and emissions of SLBs leads to optimal configurations with a high presence of batteries, increasing even more the charging station's incomes and the satisfaction of the EVs' charging needs.

## NOMENCLATURE

**Objective functions:**

NPC Net Present Cost.

GWP Global Warming Potential.

**Decision variables related to microgrid design:**

$P_{PV,peak}$ PV peak power installed.

$E_{BT,ini}$ Initial battery capacity installed.

**Decision variables related to power flow dispatch:**

$P_{grid,in}^k$ Power supplied by the grid at time $k$.

$P_{grid,out}^k$ Power sold to the grid at time $k$.

$P_{BT,ch}^k$ Charging stationary battery power at time $k$.

$P_{BT,dch}^k$ Discharging stationary battery power at time $k$.

$P_{shed}^k$ Load shedding power at time $k$.

**Parameters:**

$\Delta t$ Simulation time step in hours.

$Y$ Project duration in years.

$y$ Year when the investment or operation were made.

$\tau$ Discount rate.

$C_{PV,install}$ Unitary installation cost of the PV.

$C_{BT,install}$ Unitary installation cost of the battery.

$EF_{PV}$ Emission factor for the production of PV panels in kgCO$_2$eq/kWp.

$EF_{BT}$ Emission factor for the production of a battery in kgCO$_2$eq/kWh.

$EF_{grid}$ Emission factor for the energy drawn from the grid with a given electric mix in kgCO$_2$eq/kWh.

$C_{grid,in}^k$ Unitary price of the grid energy at time $k$.

$C_{grid,out}$ Resale price to the grid.

$C_{BT}, E_{BT,exch}$ Unitary wear cost of the battery.

$C_{tariff,EV}$ Tariff paid by EVs users.

$P_{CS}^k$ Aggregated power demanded by the EVs connected at the charging station at time $k$.

$P_{grid,lim}$ Grid limit for input and output power.
<table><tr><td>η<sub>bat</sub></td><td>Battery efficiency.</td></tr><tr><td>SoC<sub>min</sub></td><td>Battery minimum State of Charge.</td></tr><tr><td>SoC<sub>max</sub></td><td>Battery maximum State of Charge.</td></tr><tr><td>SoC<sup>ini</sup></td><td>Battery initial State of Charge.</td></tr><tr><td>SoH<sub>ini</sub></td><td>Battery initial State of Health.</td></tr><tr><td>SoH<sub>EoL</sub></td><td>State of Health for the battery End of Life.</td></tr></table>

Intermediate variables:

<table><tr><td>C<sup>y</sup><sub>i</sub></td><td>Investment cost at year y.</td></tr><tr><td>C<sup>y</sup><sub>o</sub></td><td>Operation cost at year y.</td></tr><tr><td>C<sub>s</sub></td><td>Salvage value of the battery at the end of its lifetime at year Y.</td></tr><tr><td>P<sup>y</sup><sub>PV</sub></td><td>PV power installed at year y.</td></tr><tr><td>E<sup>y</sup><sub>BT,ini</sub></td><td>Battery capacity at 100% of state of health installed at year y.</td></tr><tr><td>σ</td><td>Salvage factor of the battery.</td></tr><tr><td>E<sup>SoH<sub>Y</sub></sup><sub>BT,exch</sub></td><td>Exchangeable energy obtained with SoH<sub>Y</sub>.</td></tr><tr><td>E<sup>SoH<sub>ini</sub></sup><sub>BT,exch</sub></td><td>Exchangeable energy up to SoH<sub>ini</sub>.</td></tr><tr><td>E<sup>SoH<sub>EoL</sub></sup><sub>BT,exch</sub></td><td>Exchangeable energy up to SoH<sub>EoL</sub>.</td></tr><tr><td>E<sub>grid,in,tot</sub></td><td>Total energy supplied by the grid during the project lifetime.</td></tr><tr><td>n<sub>BT</sub></td><td>Total number of batteries used during the project lifetime.</td></tr><tr><td>P<sup>k</sup><sub>PV</sub></td><td>PV production at time k.</td></tr><tr><td>P<sup>k</sup><sub>curt</sub></td><td>PV curtailment at time k.</td></tr><tr><td>SoC<sup>k</sup></td><td>Battery State of Charge at time k.</td></tr><tr><td>E<sup>k</sup><sub>BT,tot</sub></td><td>Total battery capacity at time k.</td></tr></table>

# I. INTRODUCTION

To address the climate crisis and reduce greenhouse gas emissions, electrification of transport is proving to be an increasingly attractive option. Proof of this is Regulation (EU) 2019/631 of the European Parliament [1], which bans the sale of new passenger cars and new light commercial vehicles emitting CO₂ starting in 2035. It is often said that electric vehicles (EVs) do not emit CO₂ because there are no direct emissions during their operation phase. However, their emissions during operation phase are related to grid electric mix used for charging them, i.e., this mix will determine the CO₂ emissions caused by the EVs use. Then, it is important to study ways to improve the electric mix of electric vehicle charging stations (EVCSs).

The association of photovoltaic (PV) panels in parking lots with electric vehicle supply equipments (EVSEs), forming a microgrid, has emerged as an alternative to improve the electric mix and to avoid the electricity grid reinforcement [2]. One example is a report by the International Energy Agency [3], which sets out the preliminary criteria and conditions for the feasibility of a microgrid of this type.

Other studies also include stationary batteries in the microgrid to circumvent the intermittence of PV production, to optimize the energy management of that microgrid and to reduce its environmental impact, specially if second life batteries (SLBs) are used [4]–[6]. The cost and environmental impact of a PV powered charging station with stationary storage are compared with the ones of a EVCS supplied only by the grid in [7]. Using recent PV technologies and a recycled infrastructure, the PV powered solution presented 32.1% less carbon impact and the use of second life batteries (SLBs) was suggested to reduce even more the CO₂ emissions. In addition to the potential of reducing CO₂ emissions, EVCSs that combine PV production and stationary batteries can bring economic and social benefits [8].

To achieve the best benefits with this kind of charging station, it is important to implement an optimal power and energy dispatch strategy and also to optimize the rated power or capacity of the energy resources (PV and battery) [9]. The optimal design of an extreme fast charging station composed of energy storage and PV panels was performed in [10]. The objective was to minimize the annualized cost of the charging station, considering a coordinated charging of the EVs. The environmental impacts and the battery degradation were not considered and the problem could be modeled as a Mixed-Integer Linear Programming (MILP) formulation. However, when the design is optimized, the operation needs to be simulated over several years. In that case, the battery degradation must also be taken into account since it affects the number of battery replacements over the EVCS life duration [11]. Failure to take this degradation into account can lead to incorrect results for the operation and the estimation of the cost, up to an underestimation of 20% [12]. In [13] the battery degradation was taken into account while performing an optimal sizing and operation of the charging station. However, the environmental aspect was not included.

Given the importance of techno-economical and environmental impacts in this type of microgrid, this article presents an integrated design approach for co-optimizing the system, i.e., coupling the sizing and operation optimization. For the design, the problem is written as a bi-objective optimization, where one objective is to minimize the Net Present Cost (NPC) and the other objective is to minimize the Global Warming Potential (GWP). The optimal dispatch is efficiently solved, i.e. low time consuming for large time horizon, modeling it as a linear problem and minimizing the operation cost, while taking account of the aging of the stationary battery.
The Section II presents the methodology used for the co-optimization coupling the system design and the dispatch of energy resources. Then, Section III presents the formulation of the optimal dispatch problem during the microgrid operation. The case study for which the methodology was applied is detailed in Section IV and the results are presented in Section V.

## II. CO-OPTIMIZATION OF THE ELECTRIC VEHICLE CHARGING STATION

The objective of this work is to compute the PV peak power ($P_{PV,peak}$) and initial battery capacity ($E_{BT,ini}$) of an EVCS, like the one presented in Fig. 1, that grant the minimum NPC and minimum GWP, while considering the technical constraints of its operation during a defined lifetime. Therefore, a bi-objective optimization problem needs to be solved, in which one objective function is the NPC, obtained as

$$NPC = \sum_{y=1}^{Y} \frac{(C_{i}^{y} + C_{o}^{y})}{(1 + \tau)^{y}} - \frac{C_{s}}{(1 + \tau)^{Y}}, \quad (1)$$

where Y is the project duration in years; τ is the discount rate; $C_o^y$ is the operation cost at year y, which is determined by the chosen dispatch strategy (section III); $C_i^y$ is the investment cost at year y, obtained with

$$C_{i}^{y} = P_{PV}^{y} \cdot C_{PV,install} + E_{BT,ini}^{y} \cdot C_{BT,install}, \quad (2)$$

where $P_{PV}^y$ is the PV power installed at year y, $C_{PV,install}$ is the unitary cost of PV installation, $E_{BT,ini}^y$ is the battery capacity at 100% of state of health installed at year y, and $C_{BT,install}$ is the unitary installation cost of the battery; and, $C_s$ is the salvage value of the battery at the end of its lifetime, obtained as

$$C_s = \sigma \cdot E_{BT,ini} \cdot C_{BT,install}, \quad (3)$$

<figure><img src="image_2.png" /><figcaption>Fig. 1: Architecture of the charging station.</figcaption></figure>

where $\sigma$ is the salvage factor defined by the interpolation of the energy exchanged as

$$\sigma = \frac{E_{BT,exch}^{\text{SoH}_Y} - E_{BT,exch}^{\text{SoH}_{\text{EoL}}}}{E_{BT,exch}^{\text{SoH}_{\text{ini}}} - E_{BT,exch}^{\text{SoH}_{\text{EoL}}}}, \quad (4)$$

where $E_{BT,exch}^{\text{SoH}_Y}$ denotes the exchangeable energy of the last battery obtained with SoH$_Y$, $E_{BT,exch}^{\text{SoH}_{\text{ini}}}$ is the exchangeable energy up to SoH$_{ini}$, and $E_{BT,exch}^{\text{SoH}_{\text{EoL}}}$ is the exchangeable energy up to SoH$_{EoL}$.

The other objective function is the GWP in kgCO$_2$eq, computed as

$$\text{GWP} = \text{EF}_{\text{grid}} \cdot E_{\text{grid,in,tot}} + \text{EF}_{\text{PV}} \cdot P_{\text{PV,peak}} + n_{\text{BT}} \cdot \text{EF}_{\text{BT}} \cdot E_{\text{BT,ini}} - \sigma \cdot \text{EF}_{\text{BT}} \cdot E_{\text{BT,ini}}, \quad (5)$$

where $EF_{PV}$ is the emission factor for the production of PV panels in kgCO$_2$eq/kWp, $EF_{BT}$ is the emission factor for the production of a battery in kgCO$_2$eq/kWh, $EF_{grid}$ is the emission factor for the energy drawn from the grid with a given electric mix in kgCO$_2$eq/kWh, $E_{grid,in,tot}$ is the total energy supplied by the grid, and $n_{BT}$ is the total number of batteries used during the project lifetime.

As can be observed in (5), the GWP only includes the equivalent CO$_2$ emissions due to the production phase of PV panels and batteries, integrating the replacements during the project lifetime, and the energy drawn from the grid during operation phase. The environmental impact related to the end of life process should be included in a future work.

The only constraints considered in the optimal design are the bounds of $P_{PV,peak}$ and $E_{BT,ini}$. The others depend on power flow dispatch strategy.

Since the microgrid co-optimization results in a bi-objective optimization problem, we investigate Pareto-optimal solutions, i.e. a solution is qualified as optimal if it is not dominated by any other solution of the search space. There are some algorithms in the literature well suited for multi-objective optimization, e.g. NSGA-II. However, as we only have two decision variables, i.e. $P_{PV,peak}$ and $E_{BT,ini}$, related to the microgrid sizing in our problem, a screening of the search space is feasible in an appropriate computation time.

This screening is an exhaustive search, where the simulation of the EVCS is performed for many values of $P_{PV,peak}$ and $E_{BT,ini}$. Therefore, both objective functions are computed for each one of these points and then, the non-dominated points and the Pareto front are obtained. A diagram of this process is illustrated in Fig. 2.

## III. OPTIMAL DISPATCH

The optimal dispatch of the energy resources of the charging station shown in Fig. 1 is carried out by
<figure><img src="image_3.png" /><figcaption>Fig. 2: Framework of the co-optimization.</figcaption></figure>

modeling it as a power flow optimization problem in which the objective is to reduce the total operation cost. In this section, all powers are modeled as positive variables, with the generator/consumer convention. This section presents the objective function, the constraints and the approach used to include the battery degradation model.

### A. Objective function

We solve the optimization problem that minimizes the cost of operating the charging station over the time interval $K$, that goes from the first simulation step to the end of the project duration. The objective function is composed of the costs and incomes from the exchanges with the grid, the profit of the station made with the EV charging, and the wear cost due to the battery use and its aging. The resulting optimal dispatch problem can be written as

$$ \min \Delta t \cdot \sum_{k \in K} \left( C_{\text{grid,in}}^k \cdot P_{\text{grid,in}}^k - C_{\text{grid,out}} \cdot P_{\text{grid,out}}^k \right. \\ \left. \qquad + C_{\text{BT},E_{\text{BT,exch}}} \cdot (P_{\text{BT,ch}}^k + P_{\text{BT,dch}}^k) \right. \\ \left. \qquad - C_{\text{tariff,EV}} \cdot (P_{\text{CS}}^k - P_{\text{shed}}^k) \right), \quad (6) $$

where the decision variables are the power supplied by the grid $P_{\text{grid,in}}^k$, the power sold to the grid $P_{\text{grid,out}}^k$, the charging and discharging stationary battery power, $P_{\text{BT,ch}}^k$ and $P_{\text{BT,dch}}^k$, respectively, and the shedding power $P_{\text{shed}}^k$ (that could also be seen as a slack variable). Moreover, $\Delta t$ is the time step, $C_{\text{grid,in}}^k$ is the unitary price of the grid energy, $C_{\text{grid,out}}$ the resale price to the grid, $C_{\text{BT},E_{\text{BT,exch}}}^k$ is the unitary wear cost, $C_{\text{tariff,EV}}$ is the tariff paid by EVs users, and $P_{\text{CS}}$ is the aggregated power demanded by the EVs connected at the charging station.

### B. Constraints

To determine the optimal dispatch, the system constraints must also be considered. In this study, the power balance is given by

$$ P_{\text{grid,in}}^k + P_{\text{PV}}^k + P_{\text{BT,dch}}^k + P_{\text{shed}}^k = P_{\text{CS}}^k + P_{\text{BT,ch}}^k + P_{\text{grid,out}}^k + P_{\text{curt}}^k \quad (7) $$

where $P_{\text{PV}}^k$ is the PV production and $P_{\text{curt}}^k$ is the PV curtailment (slack variable to store the PV surplus that cannot be used by the system nor be sold to the grid). The grid limit is also taken into account, for the power purchased and sold as

$$ P_{\text{grid,in}}^k \le P_{\text{grid,lim}} \quad (8a) $$

$$ P_{\text{grid,out}}^k \le P_{\text{grid,lim}} \quad (8b) $$

The battery operation is limited by its State of Charge (SoC), which update and limit verification is done by

$$ \text{SoC}^{k+1} = \text{SoC}^k - \left( \frac{P_{\text{BT,dch}}^k}{\eta_{\text{bat}}} - P_{\text{BT,ch}}^k \cdot \eta_{\text{bat}} \right) \cdot \frac{\Delta t}{E_{\text{BT,tot}}^k} \quad (9a) $$

$$ \text{SoC}_{\min} \le \text{SoC}^k \le \text{SoC}_{\max} \quad (9b) $$

$$ \text{SoC}^0 = \text{SoC}^{\text{ini}} \quad (9c) $$

$$ \text{SoC}^{\text{end}} \ge \text{SoC}^{\text{ini}} \quad (9d) $$

where $\eta_{\text{bat}}$ is the battery efficiency, $E_{\text{BT,tot}}^k$ is the total battery capacity, that depends on the battery state of health (SoH), $\text{SoC}_{\min}$ and $\text{SoC}_{\max}$ are the minimum and maximum SoC, respectively, and $\text{SoC}^{\text{ini}}$ is the initial SoC.

### C. Integration of stationary battery degradation model

As mentioned before, the total battery capacity is function of its SoH. There are several ways to model the degradation that occurs as result of battery operation [11]. A family of models widely used in the literature is based on the concept of cumulative exchanged energy, that can be obtained from the time integral of $P_{\text{BT,ch}}$ and $P_{\text{BT,dch}}$. If we compute $E_{\text{BT,tot}}^k = E_{\text{BT,in}} \cdot \text{SoH}$, with SoH = $f(P_{\text{BT,ch}}, P_{\text{BT,dch}})$, the optimization problem is no longer described only with linear equations. However, non-linear optimization problems can have longer computation times and loss of global optimum.

To overcome the non-linearity, we consider that $E_{\text{BT,tot}}$ remains constant during the optimal dispatch horizon. In order to reduce errors, we divide the project horizon in shorter periods, solving the optimization for each one of these periods. At the end of each reduced horizon, we compute the cumulative exchanged energy
<figure><img src="image_4.png" /><figcaption>Fig. 3: Charging station optimal dispatch procedure with update of the State of Health (SoH) of the stationary battery at the end of each week.</figcaption></figure>

to obtain the new SoH and then the updated $E_{BT,tot}$. This procedure is illustrated in Fig. 3. For the case study presented in this article, the global project horizon is at the scale of years and we chose a weekly horizon to perform the optimal dispatch.

The reduced horizon was defined with some heuristic tests, which showed that one week is necessary to take account of the usage difference between weekdays and weekends, and the conclusion in [12] which says that one week is enough to reduced errors.

## IV. CASE STUDY

To apply the proposed methodology, we consider an EVCS installed in a school bus depot with a project duration of 24 years. This EVCS has two AC EVSEs of 22 kW and one DC EVSE of 50 kW, and a grid subscription with peak fee of 0.2144 €/kWh and and off-peak fee of 0.1357 €/kWh (between 10pm and 6am). The surplus of PV's production resale price is 0.078 €/kWh, and the charging tariff $C_{tariff, EV}$ is 0.374 €/kWh.

The main objective of the EVCS is to load school buses in such a way as to meet their energy demand and circulation timetable (Table I). To increase the economic return, the employees can charge their personal EVs. However, these do not have priority over the buses, i.e., if there is not enough power to charge both EVs and buses, the buses demand is satisfied and the rest of the power is used to charge the EVs, leading to load shedding of the EVs.

### A. Demand

In the preliminary study presented in this paper, we have simplified the complex issue of EVSEs management by considering that the buses and EVs charging needs are “a priori” set and known. Uncertainties on charging needs continue to exist in major cases but their inclusion in the optimization remains in the prospects of our current research. As the school transport must be operational under all circumstances of PV production

and battery state of charge, the maximum loading power of the buses must not exceed the grid limit of 36 kW. Hence, we can guarantee the charging of 5 buses per day (2 during the day in the 22 kW EVSEs and 3 during the night), even in absence of PV production and battery available capacity during certain days. In addition, we add the charging of 8 EVs when the EVSEs are available, distributed as follows:

* 3 EVs charging 10 kWh between 7am and 9am;

* 2 EVs charging 40 kWh each between 9am and 3pm at EVSE 3;

* 3 EVs charging 20 kWh between 3pm and 6pm.

Fig. 4 presents the aggregated demand of all EVSEs, that is repeated for each workday of the EVCS. We consider that the demand is zero during the weekends.

### B. Photovoltaic production

For the PV production, we used the PVGIS database [14] considering monocrystalline technology, the locality of the school bus depot at the French region of Auvergne-Rhône-Alpes, a peak power of 1 kWp (to easily obtain the production for each PV power tested). The actual PV array involves a slope of 6° with an azimuth angle of -18°, inverter efficiency of 97,7%, with 30 years of lifetime. We used the PV production of the year 2019 (Fig. 5) as a typical year which is repeated for each year of the project duration.

### C. Battery modeling

The technology chosen for the batteries is the lithium iron phosphate (LFP). The degradation model for a specific cell was developed with data provided by the manufacturer leading to a polynomial approximation,

<table><caption>TABLE I: School buses circulation timetable.</caption><thead><tr><td>Circulation time</td><td>Distance</td><td>Energy demand</td></tr></thead><tbody><tr><td>7am-9am</td><td>50 km</td><td>50 kWh</td></tr><tr><td>3:30pm-6pm</td><td>50 km</td><td>50 kWh</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Fig. 4: Charging station load demand during weekdays.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 5: Photovoltaic production profile.</figcaption></figure>

which is presented in Fig. 6. It is important to note that the data are measured up to 80% of SoH and the degradation after this point contain uncertainties, which will not be discussed in this study. However, the model behavior is similar to the ones presented in [15], [16]. The battery can operate between 10% and 90% of SoC, with a maximum $C_{\text{rate}}$ of 0.625C and an efficiency $\eta_{\text{bat}}$ of 95%. We consider that the battery is no longer suitable to operate when it reaches 40% of SoH and it needs to be replaced with a new one.

## D. Reference scenarios and search space

To compare the optimal design solutions, we established the following reference scenarios:

1) only grid, without PV and battery ($E_{\text{BT,ini}} = 0$ kWh and $P_{\text{PV,peak}} = 0$ kWp)

2) project demonstrator ($E_{\text{BT,ini}} = 64$ kWh and $P_{\text{PV,peak}} = 36$ kWp)

a) First Life Battery (FLB) → $\text{SoH}_{\text{ini}} = 100\%$, $C_{\text{BT,install}} = 350$ €/kWh and $\text{FE}_{\text{BT}} = 130$ kgCO$_2$eq/kWh

b) Second Life Battery (SLB) → $\text{SoH}_{\text{ini}} = 90\%$, $C_{\text{BT,install}} = 105$ €/kWh and $\text{FE}_{\text{BT}} = 39$ kgCO$_2$eq/kWh

Furthermore, in order to perform the co-optimization, we chose to sweep the variables space from 0 to 180 kWp for the PV installed power, which varies up to 5 times the demonstrator PV power, and from 0 to 640 kWh for the initial battery capacity, equivalent to 10 times the demonstrator battery capacity. Finally, we took as a hypothesis that the analysis comparing FLB and SLB will be made for the same initial capacity at 100% of SoH, e.g., for the reference scenario of the project demonstrator both FLB and SLB have 64 kWh at 100% of SoH, however the SLB will have an initial available capacity $E_{\text{BT,tot}}$ of 57.6 kWh (90% of 64 kWh). Then we will measure and compare some energy indicators for the FLB and SLB.

<figure><img src="image_7.png" /><figcaption>Fig. 6: Degradation model for a lithium iron phosphate (LFP) battery developed with measurement data provided by the manufacturer.</figcaption></figure>

## E. Other parameters

For the co-optimization, we also need the emission factors (EFs) to compute the GWP and the installation costs. The PV panels EF is equal to 534 kgCO$_2$eq/kWp, for a FLB the EF is equal to 130 kgCO$_2$eq/(kWh installed capacity), and the EF for the energy drawn from the grid is related to the French electric mix (0.055 kgCO$_2$eq/kWh drawn) [17]. The PV panels purchase and installation cost (CAPEX) $C_{\text{PV,install}}$, with the solar canopy shading park, is equal to 1500 €/kWp and the purchase cost for a FLB $C_{\text{BT,install}}$ is equal to 350 €/kWh. For the SLBs, we consider that the cost and the EF is equivalent to 30% of these FLBs' parameters.<fnref n="1" /> Finally, the NPC is computed with a discount rate $\tau$ of 4.5% [11].

## V. RESULTS AND ANALYSIS

In this section we first present the results for the optimal dispatch of the demonstrator with FLB and SLB, i.e. with a fixed EVCS sizing equivalent to the project demonstrator, in order to demonstrate some insights of the system operation. Then, the results of the co-optimization, with the Pareto fronts for the first and second life batteries, are compared.

### A. Optimal dispatch for the demonstrator sizing

The optimal dispatch of energy resources for a typical summer week in the first year of the simulation, with the project demonstrator with FLB, is presented in Fig. 7, in which it can be observed a high PV production and the battery is almost new (SoH equal to 96%). These summer conditions resulted in a week without load shedding. Moreover, there is a production surplus especially during the weekend, where almost all of the PV production is

<footnote n="1">¹The parameters without reference were provided by the industry partners.</footnote>
<figure><img src="image_8.png" /><figcaption>Fig. 7: Optimal dispatch for a summer week (week 26) of the project's first year.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8: Dispatch of the January 5th for the first year of simulation.</figcaption></figure>

sold back to the grid, boosting the EVCS income. In addition, PV production at the start of the day is greater than the demand (15 kW between 7am and 9am), which allows the stationary battery to be charged. The battery is also charged by the grid during off-peak hours so that it can be used during peak hours, thereby reducing the cost of operating the charging station.

For certain days with low PV production, typically during winter, the demonstrator battery is not sufficient to provide all the service required. One typical example is January 5th (Fig. 8), when even with the battery fully charged, part of the demand was shed. Over the 24 years of the project, the load shedding represents 0.17% and 0.27%, for FLB and SLB, respectively. This percentage is not very high and can be reduced by the co-optimization of EVCS components. It is also important to note that the maximum power demand at the 50 kW DC terminal was 13.3 kW. So there is potential to charge more EVs if the system is better sized.

Regarding the battery degradation, Fig. 9 presents the comparison between its evolution for FLB and SLB. We can see that the stationary battery has been changed twice for both cases. The FLB is changed once at around 11 years of use and again at around 22 years of use. The SLB has a slightest lower lifetime, with the first replacement around 10 years and the second at 20 years.

Finally, the 24-year simulation took about 50 s, in a laptop computer that has an Intel(R) Core(TM) i7-1165G7 @ 2.80GHz processor. This is an acceptable time to use this dispatch in an inner loop of the co-optimization problem.

## B. Screening for the co-optimization

First of all, we can compare the NPC and GWP of the reference scenarios presented in Section IV-D. The values for the objective functions and load shedding are presented in Table II.

For the demonstrator, there was no PV curtailment, i.e. all PV production was used by the microgrid or sold to the grid. We can see that even if the demonstrator was not optimized, it already present better results than the utility grid. The addition of PV panels and battery decreases the load shedding from 10% (grid only scenario) to at least 0.27%, hence increasing the EVCS income from 0.44 M€ to 0.54 M€. The GWP is very similar for the scenario with only the grid and the demonstrator with SLB. The scenario with FLB has a higher GWP, but it is equivalent to the scenario with only grid in the sense of Pareto optimality.

<table><caption>TABLE II: Objective functions values for the reference scenarios.</caption><thead><tr><td>Scenario</td><td>NPC</td><td>GWP</td></tr></thead><tbody><tr><td>1) Only grid</td><td>-0.44 M€</td><td>208 tCO<sub>2</sub>eq</td></tr><tr><td>2.a) Demonstrator with FLB</td><td>-0.54 M€</td><td>219 tCO<sub>2</sub>eq</td></tr><tr><td>2.b) Demonstrator with SLB</td><td>-0.55 M€</td><td>207 tCO<sub>2</sub>eq</td></tr></tbody></table>

<figure><img src="image_10.png" /><figcaption>Fig. 9: Comparison of the degradation of first life battery (FLB) and second life battery (SLB).</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>(a) Design variable space for FLB case.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(c) Design variable space for SLB case.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>(b) Objective space for FLB case.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>(d) Objective space for SLB case.</figcaption></figure>

<caption>Fig. 10: Co-optimization results for the cases with First Life Battery (FLB) and Second Life Battery (SLB).</caption>

<table><caption>TABLE III: Mean photovoltaic curtailment and load shedding of Pareto optimal points in the case of FLB.</caption><thead><tr><td>Power PV (kWp)</td><td>PV curtailment (%)</td><td>Load shedding (%)</td></tr></thead><tbody><tr><td>72</td><td>3.91</td><td>0.88</td></tr><tr><td>90</td><td>6.79</td><td>0.67</td></tr><tr><td>108</td><td>8.92</td><td>0.21</td></tr></tbody></table>

Fig. 10 presents the decision variable space and the Pareto front for the co-optimization with FLB and SLB. In Fig. 10a it can be observed that half of the optimal solutions do not include batteries in the EVCS and the other half includes batteries with low capacity (up to 48 kWh). However, the PV presence is more relevant, with installed power from 72 to 108 kWp. In Fig. 10b, the Pareto front is presented, and it also shows the objective values for the reference scenarios *only grid* and *demonstrator with FLB*. The PV curtailment and load shedding are presented in Table III for each PV power in the Pareto front. As expected, the PV curtailment increases with the PV power, because sometimes there is more production than the sum of load and grid limit, and there is no storage to relocate the energy. The PV curtailment can be considered as a potential to recharge more EVs that may increase even more the EVCS income. Also, there is some load shedding, but always

<table><caption>TABLE IV: Mean photovoltaic curtailment and load shedding of Pareto optimal points in the case of SLB.</caption><thead><tr><td>PV power (kWp)</td><td>PV curtailment (%)</td><td>Load shedding (%)</td></tr></thead><tbody><tr><td>108</td><td>1.27</td><td>0</td></tr><tr><td>126</td><td>3.65</td><td>0</td></tr></tbody></table>

lower than 1%.

Differently from the case with FLB, the co-optimization with SLB presents optimal solutions where the battery addition improves the system performance, due to their low cost and GWP with respect to FLBs. All optimal solutions presents lower NPC, i.e. higher incomes, than with FLB, and the GWP tends to be lower. We can see in Fig. 10c that the optimal solutions form a cluster with high PV power (between 108 and 126 kWp) and high battery capacity (between 336 and 640 kWh). Table IV presents the mean values of PV curtailment and load shedding for the co-optimization with SLB. For all optimal points, there is never load shedding and the PV curtailment is lower than with FLB, because the optimal solutions include batteries that allow energy shifting.

## VI. CONCLUSION

This work has presented a methodology to obtain the optimal PV peak power and battery initial capacity
for an electric vehicle charging station, which minimizes the NPC and the GWP. Moreover, the optimal dispatch of these resources was included, resulting in a co-optimization procedure. For the case with SLB, the co-optimization results have shown an increase of charging station's income and a reduction of the CO2 emissions, compared with a EVCS powered only by the grid, due to the addition of large PV system with high storage capacity. However, when there is a large surface available to install a lot of PV panels with high peak power, it is not interesting to include first life battery with high capacities, due to its high cost and environmental impact, that degrades the values of the objective functions. Regardless this, the use of batteries (FLB or SLB) with PV panels can improve the energy performance of the EVCS, e.g. reducing the load shedding.

Future works will focus on the robust optimization of the EVCS, taking into account several uncertainties and in particular:

* the SoH behavior of LFP batteries between 80% and 40%, which has not been experimentally characterized at this stage;

* stochastic production profiles for photovoltaic panels and stochastic load demands for EVs as a function of user occurrences.

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