**1. Introduction**

Globally, road transportation accounts for 17% of all emissions of carbon dioxide (CO2) [1]. Electric vehicles (EVs) offer a solution for the reduction of emissions in the road transport sector, particularly for passenger vehicles. Two characteristics of EVs already make a convincing case for their adoption: (1) the high efficiencies of electric propulsion and (2) lower or zero tailpipe emissions.

The net CO2 emissions per kilometer driven by Battery Electric Vehicles (BEVs), however, depend on the energy mix used for electricity generation. Based on Well-to-Wheel comparison, the use of BEVs can greatly reduce transport-related net emissions when they are powered by electricity generated from renewable sources [2]. There is thus a need both to shift road transportation toward electric propulsion as well as to simultaneously increase the renewable fraction of the electricity used to power it.

Currently, the charging of the majority of EVs is uncoordinated or unscheduled, i.e., they begin charging at the moment when they are plugged in. Unscheduled charging of electric vehicles can cause

increased demand for electricity at peak times. These peaks are expected to increase to over 50% even at 30% EV penetration in the Netherlands [3]. Higher peak loads lead to local issues such as overloading of transformers and other infrastructure in distribution networks, increased grid congestion, power imbalances and voltage dips [4,5]. At a more global level, higher peak loads can result in higher electricity costs and greater carbon emissions [6].

Scheduled or smart charging of EVs can greatly reduce the peak demand for electricity and avoid local congestion in electrical power systems [7]. This reduces the costs for the provision of ubiquitous and affordable EV charging facilities. In this manner, it lowers one of the main barriers to EV adoption: a lack of accessible charge points. In addition, by matching EV charging with the availability of locally produced renewable energy (such as that produced by solar photovoltaics), smart charging can also result in increasing the penetration of renewables in the mobility sector. EV charge scheduling strategies, which aim to reduce local peak demands and congestion, require knowledge of future electricity demands and renewable energy production. However, this uncertainty remains either neglected or seldom addressed in the literature on smart charging.

In [8], the impact of EV charging on residential distribution grids is investigated, but although the household demands are forecasted stochastically, the arrival of other EVs in the future are not considered. The power demand of a single EV is considerably larger than the loads in the household profiles considered in the study and the energy required for a daily charging session is in the range of a household daily energy demand [9]. The lack of EV load forecasting is thus a considerable oversight—particularly from a peak shaving perspective. In [10], a fleet of V2G compatible EVs is considered, whose scheduling is to be optimized for the purpose of providing spinning reserves. Although the formulation acknowledges and accounts for the unexpected departure of EVs, it assumes that the aggregator has accurate information on both the EV driving patterns as well as their States of Charge (SoCs), based on which demands are calculated.

In [11], EVs are scheduled for peak reduction and self-consumption within a microgrid. A car-sharing setup is considered, where the users reserve vehicles in advance for the trips they plan. In such a case, the deviation from the planned schedule is small, assumed to be always less than an hour. EVs that are not used in such a car-sharing scheme are not considered. Similarly, in [12], fuel cell electric vehicles are scheduled for V2G energy dispatch in a microgrid. However, although load forecasting is performed with an assumption of accuracy, mobility-related uncertainty associated with the future arrival of vehicles remains unaddressed.

Neglect or incomplete consideration of future EV demand in these models can cause smart charging strategies to perform worse than expected. When designing an optimal strategy, it is critical that uncertainty of vehicle charging demand (both in terms of timing as well as magnitude) is taken into account. This work investigates and quantifies the effect of this uncertainty. It is taken into consideration to develop strategies based on Model Predictive Control (MPC) for scheduling EV charging.

The paper is divided into sections as follows: Section 2 describes the physical system considered i.e., the solar parking lot, EVs and Electric Vehicle Supply Equipment (EVSE) and its modeling. Section 3 introduces the proposed methods of charge scheduling based on MPC methodology and their formulation. Section 4 illustrates the results obtained from running the simulations and discusses their relevance. Finally, Section 5 provides the conclusions and insights provided by the paper together with interesting directions for future research.

## **2. System Description**

The system considered in this work is a solar charging carport for the charging of electric vehicles as seen in Figure 1. It was modeled in MATLAB and was used to generate inputs for the scheduling strategy. It includes a solar photovoltaic (PV) array, stationary storage and LED lighting connected to a DC bus, coupled bidirectionally with a grid-connected AC bus, which also enables AC charging.

**Figure 1.** System configuration of a smart solar parking lot.

#### *2.1. Solar Parking Lots*

A solar array that was roof-mounted over the parking lot to generate electricity was considered. The total solar PV array generation capacity of 120 kWp was distributed over 40 parking spaces, corresponding to 3 kWp of generation per parking space. Power generation was simulated based on weather data from the Cabauw weather station located in the province of Utrecht in The Netherlands [13]. The data was used to simulate the typical power of the solar power array for one year with a time resolution of 15 min. Solar power generation was modeled using PVLib, a validated open-source tool developed by Sandia National Labs [14]. Table 1 describes the solar PV array characteristics used in the model.

**Table 1.** Description of solar photovoltaic array characteristics.

