Emissions in transportation represent a critical contributor to global environmental challenges, accounting for a significant portion of greenhouse gas emissions worldwide. It accounts for about a quarter of the total emissions (Vision, 2050), necessitating urgent decarbonization efforts to align with international climate agreements. Electric vehicles (EVs) are considered a viable option to reduce emissions from the transport sector, especially if they are charged with renewable power (Hussain and Musilek, 2022a). Therefore, the penetration of EVs is increasing day by day. For example, a total of 14% of all new cars sold were electric in 2022, up from around 9% in 2021 and less than 5% in 2020. Over 2.3 million EVs were sold in the first quarter of 2023, about 25% more than in the same period last year. It is expected that about 14 million EVs will be sold by the end of 2023, representing a 35% year-on-year increase (IEA Global EV, 2023). The International Energy Agency (IEA) has also increased the expected share of EVs by 2030 to 35% from 25% in the previous year’s outlook report (IEA Global EV, 2023). In addition different issues related to power electronics and their monitoring and control are discussed in (Liu, 2021; Wang et al., 2022). Similarly, the impacts on weak grids is discussed in (Shao et al., 2023) and on low carbon energy economy in (Luo et al., 2024).

However, the transition to EVs as a viable solution for reducing greenhouse gas emissions in the transportation sector presents several challenges for the power sector (Khan et al., 2022; Zhang et al., 2022). For example, at the power system level, accommodating the increased demand necessitates additional power plants to cater to EVs’ energy needs and serve as reserves (Heuberger et al., 2020). This heightened demand strains local infrastructure, causing technical issues like voltage fluctuations, network congestion, and phase imbalances, particularly at the distribution level (Hou et al., 2017). Moreover, in residential circuits, the peak EV load coincides with the peak residential load (weekday evenings) and can easily overload the local equipment (Fachrizal et al., 2021; Zhang H. et al., 2023). This is especially challenging for apartment complexes where several EVs are parked and charged together (Hussain and Musilek, 2022b). In addition, the impact of EVs on the air quality in China is assessed in (Lyu et al., 2024) for different cities throughout the lifecycle of EVs. Different types of dispatch strategies are also discussed in the literature such as distributed dispatch (Li et al., 2022) and dynamic dispatch (Duan et al., 2023). Finally, decentralized energy control is discussed in (Shirkhani et al., 2023) and an adaptive lightweight defect detection model is proposed in (Lei et al., 2023).

To address these issues, related to equipment overloading in distribution systems, several studies are conducted in literature. These studies can be broadly divided into two categories. In the first group of studies, system-level measures are suggested to manage the load of EVs. For example (Almutairi and Alyami, 2021), proposes per-unit load estimation of EVs to model and analyze various penetration levels of EVs in different locations (Tran et al., 2019). suggests using home solar panels to charge EVs, aiming to reduce power surges and enhance grid stability (Kong et al., 2022). introduces an optimization model for managing EV charging loads in distribution networks, employing a bi-level programming approach to select charging stations and manage loads. Additionally (Mazhar et al., 2023), evaluates machine learning-based methods for managing EV load in smart cities. Several studies also proposed dynamic pricing as a method to manage EV loads. For instance (Limmer and Rodemann, 2019), proposes dynamic pricing at EV charging stations to reduce peak demand charges and increase operator profits. Similarly (Moghaddam et al., 2019), suggests dynamic pricing to shift loads during evening peaks, aiming to minimize overlaps with residential peak hours and reduce network instability risks. Furthermore (Sayarshad et al., 2021), introduces a dynamic pricing model for urban freight transport involving electric and conventional vehicles, aiming to reduce costs and delays. Different aspects of EVs models such variations in electrical parameters and underlying voltage tracking control are discussed in (Zhang et al., 2021; Zhang X. et al., 2023).

However, several studies report that system-level management and pricing policies alone may not be suitable for effectively managing the load of EVs (Hussain and Musilek, 2021; Geotab, 2023; Hussain and Musilek, 2021; Zhang et al., 2021; Zhang X. et al., 2023; Sayarshad et al., 2021; Moghaddam et al., 2019; Limmer and Rodemann, 2019; Mazhar et al., 2023; Kong et al., 2022; Tran et al., 2019; Almutairi and Alyami, 2021; Lei et al., 2023; Shirkhani et al., 2023; Shirkhani et al., 2023; Duan et al., 2023). This is primarily due to local equipment, especially in distribution systems, often experiencing overload from direct connections of EVs, resulting in technical issues such as voltage fluctuations and network congestion (Geotab, 2023). Moreover, implementing EV charging infrastructure might not universally suit all communities, especially in residential or commercial settings (Almutairi and Alrumayh, 2022). Consequently, a second group of studies has emerged recently, focusing on local demand management of EVs to mitigate local equipment overload, discussed below.

The growing adoption of EVs is discussed in (Tulabing et al., 2018), where localized demand control is proposed to prevent grid congestion. Simulations suggest that a 40% EV participation rate ensures grid resilience despite 100% EV adoption. Additionally (Chen and Chang, 2016), introduces a demand response-based method for EVs, employing cloud-based management to minimize costs. Meanwhile (Hussain et al., 2023), presents a welfare-focused model for realizing Vehicle-to-Vehicle (V2V) communication to manage EV charging stations with multiple EVs (Ahmadi et al., 2023). discusses various approaches for mitigating EV charging costs, including strategies such as solar power connections and V2X approaches. Furthermore, a comprehensive review conducted in (Zhang et al., 2020) focuses on energy management strategies for EVs, highlighting clustered EV demand management as a significant challenge.

From the literature review, it is evident that numerous studies have explored managing EV load both at the system and local levels. However, most of these studies have concentrated on single homes, analyzing their collective impact on the system. In shared parking stations like residential apartments and commercial centers, EVs can readily overload local equipment, such as transformers. Additionally, allocating power to EVs during system peak load hours poses a complex challenge, involving factors such as customer satisfaction levels, available equipment capacity, and the number of chargers in each locality. The existing literature has not comprehensively considered all these factors together. It is imperative to consider all these factors collectively to present various options for policymakers aimed at maximizing EV owners’ satisfaction. These options may include installing more chargers or upgrading local equipment by the utility. Furthermore, this multi-factor analysis is essential for selecting the optimal number of chargers for a given number/percentage of EVs in any shared parking location.

To address the research gaps identified in the previous paragraphs, a multi-factor EV load management framework is proposed in this study. The aim of this framework is to offer insights into determining the optimal number of chargers and capacity constraints of local equipment (transformers). These insights will assist policymakers and utilities in planning system upgrades and installations suitable for accommodating a specific level of EVs. The framework’s implementation involves several steps. The major contributions of this study are as follows:

• EV driver behavior is estimated using the National Household Travel Survey (NHTS) dataset. Subsequently, EV parameters are utilized to determine the daily energy demand of EVs.

This analysis aims to further enhance the understanding of the framework’s performance under different conditions.

The reminder of the paper is organized as follows. Introduction section is followed by modeming of EV demand (Section 2), where vehicle driving parameters and EV parameters are extracted. In section 3, an optimization problem is formulated to allocate power to EVs considering various factors such as number of chargers, number of EVs, and capacity of the distribution equipment such as transformers. The performance of the proposed method is evaluated for a residential apartment complex in Section 4. A sensitivity analysis of various factors, including the number of chargers, the penetration level of EVs, and the limits of the transformer’s capacity in conducted in Section 5. Finally, conclusions and future research direction are discussed in Section 6.

While the adoption of EVs is increasing worldwide, their penetration levels remain relatively low compared to conventional vehicles. Consequently, most shared parking lots are primarily designated for conventional vehicles, with only a limited number of slots equipped with chargers for EVs. This study considers this prevalent scenario where conventional vehicles dominate the parking spaces. Figure 1 illustrates the system configuration, comprising a residential apartment complex with a shared parking lot. The designated EV spots within the parking lot are equipped with chargers. Both the building and the charging stations are connected to the utility grid via the same transformer. Hence, effective management of the EV load in the charging station becomes crucial since the peak load of residential buildings often coincides with the peak load of EVs. This synchronization occurs because many EV owners tend to park their vehicles and commence charging upon arriving home in the evenings.

Estimating the load of EVs involves several sequential steps. Initially, data pertaining to drivers’ travel behavior is required, followed by data related to EVs (Yang et al., 2024). Due to the limited availability of large datasets specifically for EV drivers, conventional vehicle data is commonly utilized, as seen in other studies (NHTS, 2023). The NHTS data is considered reliable and has been utilized by numerous researchers for similar analyses. Therefore, in this study, NHTS data is employed to estimate driver behavior. An overview of the various steps involved is presented in Figure 2. The data is first pre-processed to rectify any erroneous reporting, such as missing fields or unrealistic speeds. Subsequently, vehicle trips are recorded, and daily mileages are computed for each vehicle.

In this study, stochastic simulation models for PEV deployment are implemented using a data-driven approach that integrates key components such as driver behavior, PEV characteristics, charging infrastructure, grid integration, and policy and market factors. The models utilize historical data and statistical methods to simulate driver behaviors, including trip lengths, frequencies, and charging preferences, based on datasets like the NHTS. The models also consider the need for charging infrastructure and assess the grid impact of PEV charging, taking into account factors like charger placement and capacity. Policy and regulatory analysis are incorporated to evaluate the impact of government policies on EV adoption.

The objective function is designed to minimize the energy difference between the required energy demand ( E i d e m ) and the allocated energy ( E i a l l ) for EV i. In this study, to emulate the real-life behavior of EV consumers, a first-come-first-served approach is implemented. Therefore, the energy gap is penalized based on the difference between the maximum number of intervals (T) and the arrival time of EV i ( T a i ). This penalization ensures that the EVs arriving first will occupy the available chargers. It should be noted that E i a l l is the decision variable in the objective function while all other factors are parameters. min ∑ i ∈ I E i d e m − E i a l l ⋅ T − T a i (1)

Several constraints are necessary to ensure the equitable allocation of available energy among EVs while adhering to physical constraints such as the availability of chargers and the capacity of the transformer. For instance, Eq. 2 ensures that the total allocated power to any EV ( E i a l l ) should not exceed the required power ( E i d e m ) for that EV. It is important to note that an EV may not be fully charged within a single time interval ‘t’. Thus, the total allocated power to any EV becomes the accumulation of power allocated to it across all intervals before its departure, mathematically represented as Eq. 3 where E i , t a is the energy allocated to EV i at time t. Moreover, within each interval ‘t', the maximum chargeable power for any EV is constrained by the charger’s rating, as depicted in Eq. 4. Here, R c h denotes the charger’s rating in kW, and B i , t c h is a binary variable introduced to monitor the active chargers. For instance, if a charger is in use during any time interval t for any EV i, the value of B i , t c h will be 1; otherwise, it will be zero. It should be noted that E i a l l , E i , t a , and B i , t c h are variables in these constraints while all other factors are parameters.

Additional constraints are necessary to ensure that the capacity limits of the transformer are not breached. Eq. 5 stipulates that the total power drawn by all EVs during any time interval ‘t’ should be less than or equal to the capacity of the transformer ( C t t x ). It is important to note that C t t x represents the remaining capacity of the transformer after catering to the building’s load. Eq. 6 signifies that the sum of chargers utilized by all EVs during any time interval ‘t’ should be less than or equal to the number of available chargers ( N c h ). Furthermore, EVs are only allowed to charge when they are available at the parking station. To enforce this constraint, (7) is introduced. This equation implies that outside of parking intervals, such as before the arrival time ( T a i ) and after the departure time ( T d i ), the amount of power allocated to EV i should be forced to zero. E i a l l ≤ E i d e m (2) E i a l l = ∑ t ∈ T E i , t a (3) E i , t a ≤ R c h ⋅ B i , t c h (4) ∑ i ∈ I E i , t a ≤ C t t x (5) ∑ i ∈ I B i , t c h ≤ N c h (6) E i , t a = 0   i f t ≥ T d i ‖ t < T a i (7)

To evaluate the effectiveness of the proposed allocation scheme and to offer insights to policymakers, this study introduces an index. This index gauges the satisfaction level of EV owners by assessing the allocated power to each EV and comparing it with the required energy. It can be mathematically modeled as S I i = 100 ⋅ 1 − E i d e m − E i a l l E i d e m (8)

Where E i d e m represents the energy demand, and E i a l l signifies the allocated energy to EV i. This index is designed to reach a value of 100 when the entire energy demand is met before the departure time. Conversely, it will assume a value of zero when no energy demand is fulfilled, and the departure time has arrived. Operating as a continuous index, it spans values from zero to 100 inclusively, contingent upon the amount of energy received by each EV.

To facilitate visualization, this section focuses on 10 selected EVs, constituting roughly 3% of the total vehicle fleet. Table 1 displays the parameters associated with these selected EVs. The original load demand for each EV is randomly generated within the range of (Liu, 2021; EV Database, 2023) kWh, aligning with the survey data discussed in the previous section. Furthermore, the arrival times of these EVs correspond to the survey data, reflecting the trend of vehicles arriving home mostly during the afternoon and evening hours. Similarly, the departure time of most vehicles is early morning the following day. Therefore, the arrival and departure times for each EV are randomly generated (separately) following a normal distribution. The mean and standard deviation of EV arrival and departure times are based on the NHTS survey data, discussed in the previous section. EVs with both short and long parking durations are selected for this analysis to consider different types of drivers. The parking duration is determined based on the arrival and departure times. In this section, two chargers are considered. Additionally, the transformer’s capacity (remaining capacity after serving the building load) is set at 35 kW. The profile of the residential apartment complex on a selected day is shown in Figure 6.

This section conducts an analysis of the proposed method’s performance using a fleet of 10 EVs based on the parameters outlined in the input data section. The evaluation assesses the performance concerning energy allocation, charger utilization, and driver satisfaction (utilizing the proposed satisfaction index). The performance of the proposed method is compared with conventional method (named as continuous), where once EVs occupies the charger it remains connected until it is fully charged.

In this section, the variation of the number of chargers from 2 to 6 is simulated across five different cases. A fleet of 20 EVs is considered, with a transformer limit set at 35 kW. For each case, computations include the total power consumed by the chargers, the utilization count of chargers in each interval, and the overall satisfaction of the community. The respective results are displayed in Figures 10–12, specifically showcasing intervals with non-zero values of charging power.

Figure 10 demonstrates an anticipated increase in power consumption with the rising number of chargers. Notably, the total power consumption is constrained to 35 kW for specific intervals in the C-5 and C-6 cases, aligning with the transformer’s available capacity. Figure 11 illustrates that the maximum count of chargers is employed during the evening hours due to the arrival of a higher number of EVs at home. However, it is essential to note that, across each case, the maximum available chargers are utilized.

Examining the satisfaction index in Figure 12 reveals a significant increase in satisfaction levels for the initial three cases, reaching a saturation point in the last two cases. Notably, the satisfaction level for the last two cases remains consistent. This outcome suggests that, considering the fixed transformer capacity and driving behaviors of EV owners, increasing the number of chargers beyond 5 does not notably affect satisfaction. Such results hold vital importance for policymakers to determine the minimum necessary number of chargers for a given EV count.

In this section, the share of the EV fleet incrementally increased up to 50% across five simulation cases. Starting from around 3% of the total fleet (320 vehicles), the penetration rate is doubled in each case until it reaches 50% (160 EVs). For consistency, the number of chargers remains fixed at five, and the transformer capacity is set at 35 kW throughout these simulations.

The analysis primarily focuses on the total power consumption of the chargers for each case. Additionally, a charger utilization index is devised to estimate the chargers’ utilization under varying penetration rates. The community’s satisfaction is also evaluated, and the outcomes are visualized in Figures 13–15. Figure 12 illustrates a proportional increase in charger power consumption with the growing number of EVs, which is an expected outcome. However, the power consumption becomes constrained by the remaining capacity of the transformer (35 kW), notably evident in the last three cases. Consequently, it can be inferred that the current configuration of five chargers and a 35-kW transformer capacity cannot sustain more than a 6% penetration of EVs.

Figure 14 shows the utilization level of chargers during the scheduling horizon (24 h). The utilization is computed using C U = ∑ t ∈ T ∑ i ∈ I B i , t c h T ⋅ N c h (9)

Where B i , t c h is the inary varibale indiciating the usage status of the charger, T is the total number of intervals in the scheduling horizon (24 in this case), and N c h is the number of chargers (5 in this case). Figure 14 illustrates that as the EV penetration increases, there’s a corresponding rise in charger utilization throughout the scheduling horizon. However, it is evident that there’s still some potential to further increase charger utilization in all cases. Nonetheless, this potential expansion is curtailed by the transformer’s capacity limitation, as depicted by the power consumption trends in Figure 13.

Examining Figure 15 reveals a decrease in the satisfaction level of the EV community with the escalating EV penetration rates. This decline is directly linked to the transformer’s capacity limitations. As the number of EVs increases, more capacity becomes necessary. Consequently, these results suggest that an increasing number of EVs are unable to fulfill their energy demands before their departure times.

This analysis underscores that relying solely on charger utilization as a measure is not sufficient to determine the optimal number of chargers or the EV penetration level. It is imperative to consider both charger utilization and customer satisfaction collectively to determine the most suitable number of chargers for any EV community.

In this section, five simulations are conducted by varying the capacity of the transformer. The analysis includes power consumption, charger utilization, and EV user satisfaction, displayed in Figures 16–18. For these simulations, the number of chargers remains fixed at 5, with 20 EVs considered.

Figure 16 illustrates that the charging power is restricted by the transformer’s capacity limits in the initial three cases. However, in the last two cases, the power remains below the capacity limit for most intervals. Additionally, Figure 17 demonstrates that due to these capacity constraints, all chargers are not fully utilized in the first three cases. Conversely, in the last two cases, all five chargers are utilized to maximize consumer satisfaction.

The community satisfaction index in Figure 18 shows an increase during the first three cases and remains stable in the last two cases. This implies that, for this community comprising 20 EVs and 5 chargers, a transformer capacity exceeding 30 kW proves sufficient. Moreover, increasing the transformer capacity beyond this threshold does not significantly impact consumer satisfaction levels. Such insights are crucial for utilities in planning transformer upgrades considering a certain level of EVs and chargers.

Based on the findings of this study, following policy implications can be inferred. Firstly, the study demonstrates the effectiveness of the proposed framework in efficiently allocating energy and utilizing chargers. The results show that with proper scheduling, EV energy demands can be met while ensuring charger availability and avoiding overloading the transformer. This suggests that policymakers should consider implementing similar optimization strategies in residential areas to manage EV charging effectively.

Secondly, the study highlights the importance of infrastructure planning. The analysis shows that increasing the number of chargers beyond a certain point does not significantly improve user satisfaction. This suggests that policymakers should focus on installing an optimal number of chargers based on factors such as transformer capacity and EV penetration rate. Additionally, the study suggests that increasing transformer capacity can improve user satisfaction up to a certain point, indicating that utilities should consider upgrading transformers in areas with high EV penetration.

Lastly, the study emphasizes the need for incentives to encourage EV owners to adjust their charging behavior. The satisfaction index shows that some EVs are not able to fulfill their energy demands due to charger unavailability. Incentives such as time-of-use pricing or rewards for off-peak charging could help distribute charging load more evenly and improve overall system performance.