**5. Conclusions**

The goal of this work was to quantify the peak load increase when uncertainty is involved in charge scheduling of electric vehicles at a solar parking lot. It further aimed to develop strategies for scheduling charging in a manner that minimized the peak electricity load at the point of common coupling of the parking lot while taking this uncertainty into account. Since short duration high peaks have the maximum impact on transformer aging, these were the peaks that were focused on.

The set up considered included a solar parking lot with 40 spaces located at a workplace. It included a 120 kWp solar array, 40 EV charge points and a 50 kWh stationary battery. The arrival and departure of EVs, which were parked and plugged in at the parking lot, were simulated over a year. Model Predictive Control (MPC) was the method used to optimally schedule the charging of EVs in the parking lot over the year. The operation of the system was simulated over a year in terms of the energy exchanged by the parking lot with the grid.

The system was considered in three scenarios:


with a and a schedule that was robust across multiple possible EV demand forecasts. The scheduling for each scenario was formulated as an optimization problem. The operation of the solar carport was simulated in each scenario for a year based on the solution of the optimization problem. The scenarios were compared with two reference cases—unscheduled charging, which is the current norm, and charging with perfect forecasting of EV demand, which represents the limits of the effectiveness of the system at peak reduction.

The results show that for parking locations with charging, which are currently close to peak load capacity, scheduling of EVs can be used to reduce both the magnitude as well as the frequencies of peak loading on distribution level assets. The magnitude of the peak reduction is however considerably less than the peak reduction possible with perfect forecasting of future EV demand, which is often considered in the literature. Table 3 displays the results of annual peak reduction in the scenarios considered:


**Table 3.** Annual peak power across scenarios.

Without EV demand forecasting, the maximum annual peak load of the solar carport was reduced by 16% in our case relative to unscheduled charging. This was, however, considerably less effective than in the reference case with perfect forecasting, where the magnitude of the annual peak was reduced by 54%. The inclusion of a single 24 h horizon EV forecast reduced the peak in the solar parking lot by 36%, increasing the effectiveness of the scheduled charging by an additional 20%. Consideration of multiple forecasts of possible EV demand and robust adjustment of the schedule for the performance of the worst possible forecast marginally improved the effectiveness of the scheduling, reducing the peak by 39%.

In addition to reducing the magnitude of peak loads, scheduling of EV charging also has the effect of reducing the number of peaks that distribution level assets were subject to. The use of EV demand forecasting was found to have the effect of considerably reducing this number. However, in this case, the consideration of multiple forecasts provides no clear advantage over a single forecast.

An economic analysis of the system was considered out of the scope of this work. As such, the cost-benefit analysis of scheduling EV charging versus upgrade of the grid connection was not performed. However, preliminary investigation indicates that there is considerable value for the parking lot owner through the implementation of the system described in this work. In the USA, capacity charges for the grid connection at EV charging sites can be higher than \$2000/month, causing the electricity utility bills of some businesses to increase by a factor of four [22]. Similarly, in the Netherlands, the grid capacity cost is AC 190/year per charge point or 37% of the annual operational costs for the charge point excluding energy costs and about 20% of the costs including energy [23]. Although case-specific, peak reduction does have considerable economic value for system operators. This is expected to be addressed in future work.

Additionally, future research work also involves the investigation of the dependence of the scheduling on the location of the parking lot i.e., on whether the parking patterns have an influence on the choice of the objective of the charging schedule. The use of scheduling for off-grid or constrained grid capacity design of longterm parking lots for EVs may be considered. Improved methods for EV scheduling for other objectives will also be addressed in future works.

**Author Contributions:** R.G. wrote the final draft, performed some of the analysis and managed the project. Y.S. conceptualized the methodology, performed the investigation and wrote the first draft. S.F. provided guidance with the formulation of the optimization problems and their solution. Z.L. provided supervision and edited the final draft. A.v.W. provided supervision, edited the final draft and acquired funding for this work. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the European Funds for Regional Development through the Kansen voor West program gran<sup>t</sup> 00113 for the project, Powerparking, as well as the Netherlands Organization for Scientific Research as part of the Uncertainty Reduction in Smart Energy Systems (URSES+) gran<sup>t</sup> for the project 'Car as Power Plant-LIFE'.

**Acknowledgments:** The authors would like to thank Tomás Pippia for helpful discussions that contributed to this work.

**Conflicts of Interest:** The authors declare no conflict of interest.

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