Submitted:
30 April 2026
Posted:
01 May 2026
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Abstract
Keywords:
1. Introduction
2. Methodology
- Arrival and departure timestamps for each EV
- Number of connected EVs at each time step
- Requested energy per EV.
2.1. Optimization Model
2.1.1. Objective Function
2.1.2. Constraints
3. Case Study
3.1. Public Charger Data
3.2. Electricity Cost
3.3. Assumptions
- 1.
- The optimization is conducted over an aggregated dataset of all public chargers, effectively modeling them as a single virtual power plant. As a result, the physical location of individual chargers is abstracted and not explicitly considered.
- 2.
- It is assumed that the departure time and energy demand of each EV are known at the time of connection to the charger.
- 3.
- The overall state of energy in the parking lot is determined by the aggregated state of energy of the connected EVs, taking into account their minimum and maximum allowable state of energy. For modeling consistency, each EV is assumed to have a battery capacity of 65 kWh, with operational limits set between 20% and 100% state of charge.
- 4.
- As the model aggregates all chargers into a unified system, inter-EV energy exchange is assumed to be feasible without incurring any energy losses.
- 5.
- The size of an EV was assumed to be 65 kWh and the minimum and maximum state of charge was assumed to be 0.2 and 1 respectively.
- 6.
- The EVs were assumed to arrive at a SOC of 0.4 and will depart with their requested energy if it is within the SOC limits, otherwise it will depart with SOC of 1.
- 7.
- Although the charge stations are connected to the grid at different connection points, it is considered that the peak tariff will be based on the aggregated peak demand of all EVs.
- 8.
- The conversion rate of Swedish Kronas (SEK) to Euro (€) is assumed to be fixed throughout the horizon at 11.1 SEK/€.
- 9.
- The VAT associated with the energy consumption has been omitted in this study.
3.4. Scenarios
- 1.
- Avg: For each charging session, the energy demand is averaged over its connection time. These session-level profiles are then aggregated across all chargers.
- 2.
- DC11 (Direct Charging 11 kW): Charging begins immediately upon connection, drawing power at a constant rate of up to 11 kW until the requested energy is delivered.
- 3.
- DC22 (Direct Charging 22 kW): Similar to DC11, but the charging power is limited to 22 kW.
- 4.
- DC50 (Direct Charging 50 kW): Similar to DC11, but the charging power is limited to 50 kW.
- 5.
- SC11 (Smart Charging 11 kW): Charging is optimized over the connection duration to minimize electricity costs, with a maximum power of 11 kW. The requested energy is guaranteed to be delivered before departure.
- 6.
- SC22 (Smart Charging 22 kW): Same as SC11, but with a maximum charging power of 22 kW.
- 7.
- SC50 (Smart Charging 50 kW): Same as SC11, but with a maximum charging power of 50 kW.
- 8.
- V2G1 (Vehicle-to-Grid 1): Charging is optimized over the connection period with bidirectional energy flow. The charger can both charge and discharge at a maximum of 50 kW. Peak power is calculated as the difference between charging and discharging power as seen in Eqn. 5.
- 9.
- V2G2 (Vehicle-to-Grid 2): Similar to V2G1, but peak power cost is calculated based on both charging and discharging power as seen in Eqn. 5.
4. Results and Discussion
4.1. Key Takeaways
4.2. Limitations and Suggestions for Future Work
5. Conclusion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
| V2G | Vehicle to Grid |
| EV | Electric Vehicles |
| SDDP | Stochastic Dual Dynamic Programming |
| G2V | Grid to Vehicle |
| MILP | Mixed Integer Linear Programming |
| EMS | Energy Management System |
| SEK | Swedish Kronas |
| VAT | Value Added Tax |
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| Rated Power (kW) |
Occurrence |
|---|---|
| 22 | 881 |
| 11 | 18 |
| 8.3 | 26 |
| 3.6 | 373 |
| Total | 1298 |
| Parameter | Costs |
|---|---|
| Energy tax | 0.03955 €/kWh |
| Energy certificate cost | 0.00045 €/kWh |
| Transmission cost | 0.01 €/kWh |
| Peak cost (monthly) | 5.54 €/kW |
| Performance Metric |
Avg1 | DC11 | DC22 | DC50 | SC11 | SC22 | SC50 | V2G1 | V2G2 |
|---|---|---|---|---|---|---|---|---|---|
| Cost Overall (k€) |
327.15 | 351.20 | 361.07 | 371.98 | 98.53 | 97.88 | 97.86 | 96.29 | 97.06 |
| Cost Peak (k€) |
12.14 | 20.54 | 25.11 | 32.07 | 15.26 | 14.79 | 14.79 | 14.79 | 14.79 |
| Maximum peak power (kW) |
674 | 916 | 1064 | 1286 | 680 | 680 | 680 | 680 | 680 |
| Total energy charged (MWh) |
579 | 579 | 579 | 579 | 589 | 589 | 589 | 633 | 618 |
| Total energy discharged (MWh) |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 44 | 29 |
| Total charge- discharge (MWh) |
579 | 579 | 579 | 579 | 589 | 589 | 589 | 589 | 589 |
| Delta w.r.t DC50 (%) |
-12.1 | -5.6 | -2.9 | 0.0 | -73.5 | -73.7 | -73.7 | -74.1 | -73.9 |
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