Exploring the effect of battery capacity on electric vehicle sharing programs using a simulation approach

Transportation Research Part D 77 (2019) 164–177

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Transportation Research Part D journal homepage: www.elsevier.com/locate/trd

Exploring the effect of battery capacity on electric vehicle sharing programs using a simulation approach

T

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Songhua Hua, Peng Chenb, Feifei Xinc, , Chi Xiec a b c

Department of Civil and Environmental Engineering, University of Maryland, College Park, MD, USA School of Public Affairs, University of South Florida, Tampa, FL, USA Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai, China

A R T IC LE I N F O

ABS TRA CT

Keywords: Electric cars Battery capacity Carsharing Range anxiety Discrete-event simulation

Aided by mobile computing technology, shared electric vehicles (SEVs) have become an accessible and affordable mobility option. However, limited battery capacity remains a major obstacle for large-scale adoption of SEVs, and greatly undermines their popularity. In this study, a discrete-event simulation approach was employed to estimate how battery capacity affects the performance of a carsharing program. Results show that limited battery capacity lowered user satisfaction and vehicle utilization in the program. Increased charging speed, maximum range, and vehicle-to-trip ratio help mitigate these negative effects. Specifically, increasing the maximum range or charging speed contributes to the increment of the average SEV usage time and the percentage of satisfied rental requests. A higher vehicle-to-trip ratio contributes to a greater level of user satisfaction but a lower level of vehicle utilization. Additionally, the negative effects of battery capacity are greatly diminished after charging speed is increased to a certain threshold. These findings help capture the trade-off between charging facility investment, vehicle utilization, and user satisfaction. Increasing charging speed and maximum range are necessary if operators want to maximize vehicle utilization and promote user satisfaction. However, this investment must also account for cost-effectiveness.

1. Introduction Vehicles’ electrification, sharing, and automation are considered the three main transportation revolutions over the past halfcentury (Sperling, 2018). While autonomous vehicles are still being tested, the combination of electric vehicles (EVs) and carsharing has matured into shared electric vehicles (SEVs), which have expanded quickly throughout the world. Compared with conventionally fueled vehicles (FVs), EVs reduce greenhouse gas emissions, fossil fuel dependence, and maintenance costs. Therefore, SEVs generate more environmental, energy and economic benefits for both society and carsharing operators (Egbue and Long, 2012; Fagnant and Kockelman, 2014). Additionally, EVs are compatible with many emerging technologies. Incorporating EVs into carsharing programs is considered a cornerstone in the shift towards a future ‘Mobility as a Service’(MaaS) system (Fairley, 2013). Furthermore, SEVs provide opportunities to increase the exposure of EVs to potential buyers, which may indirectly contribute to increasing the market share of EVs (Bühler et al., 2014). Despite automakers placing their bets on SEV technology, SEVs have not yet become mainstream. Many individuals are hesitant to use SEVs. The limited driving range, slow charging speed, and poor access to both SEVs and charging facilities all discourage SEVs’

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Corresponding author. E-mail address: [email protected] (F. Xin).

https://doi.org/10.1016/j.trd.2019.10.013

1361-9209/ © 2019 Elsevier Ltd. All rights reserved.

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broad adoption (Egbue and Long, 2012). In addition, many SEV users suffer from range anxiety - users fear that SEVs may not have sufficient battery to reach their destinations (Egbue and Long, 2012; Franke et al., 2012). Battery capacity also generates negative externalities for carsharing programs. To be specific, the long charging time and insufficient battery capacity lower the utilization rate of SEVs, decrease user satisfaction, and make the carsharing industry unprofitable (Illgen and Höck, 2018). Many customers may turn away from carsharing programs and in turn impair the popularity of such programs. Understanding how the battery capacity of SEVs affects carsharing programs is important for operators to promote car usage, increase user satisfaction, and maximize overall social welfare. However, research related to the effect of SEVs on carsharing programs is scarce. This study raises the following question: “How does a carsharing program that deploys EVs perform with different vehicle-to-trip ratios (SEV count divided by trip count), charging speeds, and maximum battery capacities, regarding user satisfaction and vehicle utilization?” Because scenarios with data regarding these variables are extremely limited, statistical models and machine learning algorithms cannot be used to answer this question. In such a context, simulating future scenarios is more suitable for foreseeing challenges, and validated predictions can be considered as evidence for future policy design. In this study, a discrete-event simulation approach was employed to estimate how SEV features may affect the performance of a carsharing program. This approach simulated the operation of a carsharing program step-by-step and captured the status of vehicles and stations in various settings. One month of observed carsharing program data were taken as the input to simulate and validate the estimated demand for SEVs. When designing the simulation model, vehicle utilization and user satisfaction were employed as key measurements to evaluate the carsharing program’s performance. The average daily usage time of SEVs was employed to represent vehicle utilization, and the percentage of satisfied rental requests was used to represent user satisfaction. It is worth mentioning that the profit of a carsharing program is positively related to or even proportional to vehicle utilization. Three parameters, including vehicle-to-trip ratio, charging speed, and the maximum range of SEVs, were incorporated into design the simulation scenarios. Findings of this study help operators understand how different settings of SEVs may influence the performance of a carsharing program, as well as gain insight into the trade-off between facility investment, vehicle utilization, and user satisfaction. On one hand, operators may increase the number of SEVs, charging speed, and the maximum range of SEVs to an optimal value. On the other hand, there is a risk in improving facilities because of the added cost, which may be greater than the revenue earned from any additional orders. With simulated outcomes, operators can sort out the optimal values of these parameters and build better business models to maximize vehicle utilization. This, in turn, can satisfy user demand and promote the social welfare that SEVs can bring to the public. 2. Literature review 2.1. The adoption of SEVs The first SEV dates back to 1974 (Illgen and Höck, 2018). However, because of technical limitations, EVs were phased out of the carsharing industry for almost forty years (Shaheen and Cohen, 2013). In recent years, with the help of technological advancements and public support, SEVs have experienced a resurgence (Shaheen and Chan, 2015). By late 2013, carsharing programs in approximately 14 countries had deployed EVs in their fleets (Shaheen and Chan, 2015). The fade and resurgence of SEVs have drawn researchers’ attention regarding the benefits and feasibility of deploying EVs in carsharing programs (Rabbitt and Ghosh, 2013). In terms of benefits, carsharing can significantly decrease private car ownership, reduce CO2 emissions, provide cost savings, and promote the use of alternative transportation modes (Rabbitt and Ghosh, 2013). As for feasibility, existing studies have focused on the question of who potential users of SEVs are. In general, the motivation for using SEVs is split into four types: economic, social, environmental, and symbolic (Cartenì et al., 2016; Rezvani et al., 2015). Compared to private cars, most SEV users believe that SEVs are more affordable, eco-friendlier, and will be more popular in the future. Studies also point out that motivation and attitudes are significantly affected by users’ socioeconomic characteristics, such as income, car ownership, educational attainment, and household structure (Cartenì et al., 2016; Kim et al., 2015). Beyond motivation, barriers to adopting SEVs have also been analyzed in the literature. Battery capacity is a major barrier preventing people from using EVs (Egbue and Long, 2012; Rezvani et al., 2015). Other frequently discussed factors include limited driving range, long recharge time, poor access to chargers, and range anxiety of users (Egbue and Long, 2012; Wang et al., 2016). For example, Zoepf and Keith analyzed users’ selection among different types of shared vehicles (e.g. gasoline, hybrid, or electric vehicles). Their results indicated that users preferred not to take SEVs even if the range of the SEVs was sufficient for long-distance driving (Zoepf and Keith, 2016). Franke et al. published a series of studies that discussed users’ range anxiety (Franke and Krems, 2013a; Franke et al., 2012). Their results suggested that users’ comfortable range was approximately 75–80% of their available range resources (Franke and Krems, 2013a). In other words, if a user had to drive 75–80 km, they would choose an EV with an available driving range greater than 100 km. Some other studies have focused on incorporating range anxiety into a transportation network. For example, Jiang and Xie studied how range anxiety affected drivers’ choice between EVs and FVs in a transportation network (Jiang and Xie, 2014). Xie et al. developed and applied a network equilibrium model to analyze route choices and flow patterns reshaped by the range anxiety of EV drivers (Xie et al., 2017). Zhang et al. studied the impact of charging requirements on SEV operations (Zhang et al., 2019). 2.2. Discrete-Event simulation In a carsharing program, companies expect shared cars to be operated efficiently for the maximum amount of profit. Decisions made by carsharing operators can be categorized into two types (Repoux et al., 2015; Weikl and Bogenberger, 2015). First, strategic 165

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and tactical decisions are concerned with fleet size (Barth and Todd, 1999; Cepolina and Farina, 2012; El Fassi et al., 2012; Nakayama et al., 2002), the number and location of shared-car stations (de Almeida Correia and Antunes, 2012; El Fassi et al., 2012), and the number of employees (Kek et al., 2009). Second, operational decisions are concerned with shared-car relocation policies (Barth and Todd, 1999; Kek et al., 2009; Weikl and Bogenberger, 2015). Simulation and optimization are two major approaches used in prior studies to aid decision making (Jorge et al., 2014; Nourinejad and Roorda, 2014). A discrete-event simulation approach can model each vehicle’s events over a specific period step-bystep. Events here refer to the processes that occur when using an SEV, including the charging process when idling, the running process during a trip, and the allocation process when a user chooses an SEV. A simulation approach offers a more detailed representation of carsharing programs (Jorge et al., 2014), while an optimization approach makes simplified assumptions and requires full prior knowledge of a carsharing program (Jorge et al., 2012; Jorge et al., 2014). These two approaches are mutually compatible, and many researchers combine these two approaches. For example, optimization can be used to calculate the optimal parameters of different scenarios, and simulation can validate the outcome (Boyacı et al., 2017; Jorge et al., 2012; Jorge et al., 2014; Kek et al., 2009). When modeling carsharing programs that deploy EVs, many operational characteristics of EVs have been considered as core parameters (Boyacı et al., 2017; Brendel et al., 2018; Cepolina and Farina, 2012; Illgen and Höck, 2018; Nakayama et al., 2002; Weikl and Bogenberger, 2015). A frequently examined operational characteristic is the change in an EV’s battery, also called the change in the State of Charge (SOC). State of Charge (SOC) is essentially a fuel gauge for an EV. The distance an EV can drive is used to measure battery capacity. For example, an SOC of 50 km means that an EV can drive 50 km before its battery is exhausted. Barth and Todd were the first to employ a simulation approach to analyze the performance of a carsharing program with different battery charging schemes (Barth and Todd, 1999). Their results found that the performance of a carsharing program was affected by the number of charging facilities and the average trip distance. Weikl and Bogenberger introduced a relocation model to a carsharing program (Weikl and Bogenberger, 2015). In their study, trips where SEVs were being charged or unplugged were treated as service trips. Both relocation and service trips were considered in order to approximate real-world SEV operation. Repoux et al. defined a minimum threshold for the SOC to determine if an SEV could be rented or not. SEVs could only be assigned to users when their SOCs were greater than the minimum threshold. Their findings show that demand satisfaction decreased slowly with an increase in the minimum threshold (Repoux et al., 2015). A similar minimum threshold was defined by Brendel et al. to avoid deep discharge. Their results show that increasing the charging threshold led to an increase in battery life but a decrease in the SEVs’ utilization rate (Brendel et al., 2018). Recently, a simulation study was conducted by Illgen and Höck to analyze how different types of SEVs can affect a carsharing program. Their results indicate that increasing the maximum range of SEVs contributed to an increase in user satisfaction and vehicle utilization (Illgen and Höck, 2018). Although some studies have investigated the performance of SEVs using a discrete-event simulation approach, several knowledge gaps remain. First, many EV-related factors, such as charging speed, driving range, and range anxiety, have rarely been jointly considered (Barth and Todd, 1999; Boyacı et al., 2017; Cepolina and Farina, 2012; Weikl and Bogenberger, 2015). Second, most prior studies simulated scenarios with small fleet sizes and station numbers (Brendel et al., 2016; Brendel et al., 2018; Bruglieri et al., 2014; Cepolina and Farina, 2012). This is unlike real-world scenarios, especially for big carsharing programs in large cities. In terms of methodology, this discrete-event simulation approach focuses on addressing the issue of relocation and oversimplifies the charging process. For example, most existing studies assume that SEVs are fully charged before being assigned to a user (Brandstätter et al., 2017; Brendel et al., 2018; Weikl and Bogenberger, 2015), and that a minimum threshold can be used to determine whether an EV should be recharged or not (Brendel et al., 2018; Repoux et al., 2015). These assumptions are somewhat unrealistic and may lead to seriously biased results.

3. Study area and methodology 3.1. Study area This study used the largest carsharing program in China, EVCARD, as an example to simulate how a carsharing program performs with varying vehicle-to-trip ratios, charging speeds, driving ranges, and users’ range anxiety. One month (April 2017) of observed data were selected for the simulation. During April 2017, there were 2,252 shared-car stations, 3,765 SEVs, and 11,267 parking spaces with charging piles in Shanghai, serving almost 77,750 users with 442,246 transactions generated. A transaction refers to the process where a user reserved, borrowed, used, and lastly returned an SEV. The number of monthly aggregate transactions at each station is shown in Fig. 1. In a carsharing program, users borrow and return SEVs using their smartphones. Users are required to plug in borrowed EVs after returning them. During this study, for EVCARD Shanghai, all charging piles were equipped with slow charging technology with a speed of 6 h/150 km. 150 km was employed as the base mileage since it was the maximum range for EVCARD’s SEVs. Since new technologies have been developed, SEVs charging speed and maximum range have both improved since this data was recorded. Therefore, in the following simulation analysis, charging speed was considered as a parameter varying from 0 h/150 km to 6 h/ 150 km with an increment of 0.5 h/150 km. To clarify, 0 h/150 km represents a scenario where EVs have been completely substituted with FVs. Meanwhile, the maximum range of SEVs was also considered as a parameter varying from 50 km to 500 km with an increment of 50 km. Maximum ranges smaller than 150 km were considered since there are many EVs with small maximum ranges (Illgen and Höck, 2018).

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Fig. 1. EVCARD’s monthly transactions (April 2017) at shared-car stations.

3.2. Methodology In this section, the discrete-event simulation and its five modules are described in detail. The initialization module set up input parameters, including the study area, the study period, the initial location of SEVs, the number of SEVs, and the number of charging piles. The trip generator module generates rental requests, including timestamps, origins, and destinations based on observed transaction data. The SOC update module renewed the status of SEVs after each round of the simulation, including the processes of SOC consumption and recharging. The vehicle selection module allocated SEVs to users based on their trip distances and range anxiety. The evaluation module evaluated the simulation outcome with key measurements. The analytical process is detailed in Fig. 2. 3.2.1. Initialization module The initialization module set input parameters for simulation scenarios using observed data. A fleet with 3765 SEVs was simulated in this study. Each simulation time step was set as 10 min, a value similar to that of many previous studies (Brendel et al., 2018; de Almeida Correia and Antunes, 2012; Jorge et al., 2012). The study period (one month) was split into 4320 simulation time segments (30 days * 24 h * 60 min / 10 min = 4320 simulation segments). To best approximate a real-world carsharing system, this study set an initial scenario based on historical transactions at each station. This was unlike some prior studies that randomly and evenly distributed initial vehicles (Bruglieri et al., 2014; Nourinejad and Roorda, 2014). If a station had more transactions historically, more SEVs were allocated to that station initially. The equation used to calculate the initial number of SEVs at each station is shown in Eq. (1): TA NVi = ⎡ I i × TNV ⎤ ⎣ ∑i = 1 TAi ⎦

(1)

where NVi is the initial number of SEVs at station i, TAi is the number of historical transactions (monthly aggregate counts) at station i, I is the number of stations (in this study I = 2,252), TNV is the number of SEVs (in this study TNV = 3,765), and [.] is the function used to round from a floating number to an integer. After determining the number of SEVs at each station initially, an SEV status matrix, as shown in Fig. 2, was built to record and update each SEV’s status during each simulation segment. For each SEV k, the following tuple, Eq. (2), was used to record its information at time t:

Vehk, t = (Vid , Dk, t , ETk, t , VoSk, t , SOCk, t )

(2) 167

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Fig. 2. A flow chart of the whole simulation.

0, ETk, t ≤ t VoSk, t = ⎧ 1, ETk, t > t ⎨ ⎩

(3)

where Vehk, t is the information of SEV k at time t, Vid is the vehicle’s ID, Dk, t is the destination of vehicle k ’s latest trip with a starting 168

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time before time t, ETk, t is the ending time of vehicle k ’s latest trip with a starting time before time t, and SOCk, t is the SOC of vehicle k at time t. To simplify, the trip distance is used as the measurement for energy. For example, an SOC of 100 km means that an SEV has enough battery to drive 100 km. VoSk, t is the status of vehicle k at time t. If the vehicle k is occupied at time t, then VoSk, t = 1, else VoSk, t = 0 . The calculation of VoSk, t is based on the relationship between ETk, t and t, as shown in Eq. (3). The vehicle status matrix was updated after time t. The update procedure of SOCk, t is introduced in Section 3.2.3. The update procedures of Dk, t , ETk, t and VoSk, t are detailed in Section 3.2.4, and these three parameters are related to the next trip that a vehicle is assigned to. 3.2.2. Trip generator module The trip generator module generated rental requests in a simulation scenario. Observed transactions could not be directly used as input for the demand for two reasons (Brendel et al., 2016). First, carsharing programs cannot serve all rental requests due to the inadequate supply of vehicles or spatial mismatches between users and cars. These unsuccessful rental requests were not recorded in the observed transactions. Hence, observed transactions only reflect partial demand. Second, there were some relocation and service trips. In other words, the trip status shown in the transaction data was the joint outcome of both users and operators. Directly using observed transactions as input for simulation may therefore incur biases. As some unique spatiotemporal features exist in the observed transactions, randomly generated rental requests without detailed consideration of real-world situations at each station may also be inaccurate. Based on the observed transactions, Fig. 3 includes a series of graphs presenting details of the monthly data. Fig. 3 (a) and (b) show histograms of trip distance and trip duration. Fig. 3 (c) shows the hourly transactions counted during a week. Fig. 3 (d) presents the spatial distribution of aggregate monthly transactions. In this study, the average trip distance was 19.21 km, and the mean trip duration was 53.87 min. As shown, observed trips were not randomly distributed spatially or temporally. Trips between some stations were more frequent. This imbalanced distribution of transactions in time and space needed to be accounted for when creating the new sample.

• Trip distance distribution (Fig. 3 (a)) and trip duration distribution (Fig. 3 (b)). • Hourly transactions counted during a week (Fig. 3 (c)). • The spatial distribution of monthly aggregate transactions (Fig. 3 (d)). The process for generating the sample from the observed data is as follows. First, the origin, the destination, the starting time, and the ending time of each trip were extracted from the transactions and regrouped into a trip pool. Then, newly generated trips were randomly resampled from the pool with replacement. Third, the energy demand and vehicle IDs of each regenerated trip were recalculated. To simplify this process, the distance was employed as the measurement of energy demand. In other words, the unit for energy demand analysis was set as kilometers (km). Distances between different stations were estimated using the ‘OSMNX’ package in Python (Boeing, 2017). Three levels of trip demand were analyzed, including 100,000 trips, 450,000 trips, and 900,000 trips, corresponding to low-demand, medium-demand, and high-demand carsharing programs. Finally, the regenerated trips, DEj , are denoted in Eq. (4) (Brendel et al., 2018):

DEj = (Vidj , Oj , Dj , STj, ETj, EDj )

(4) th

where Vidj is the vehicle ID distributed to the j trip. The determination of Vidj is introduced in Section 3.2.4. Oj , Dj , STj, ETj represent the origin, the destination, the starting time, and the ending time of the jth trip, respectively. EDj is the energy demand for the jth trip. 3.2.3. SOC update module The SOC update module updated the energy status of each SEV after every round of simulation. The SOC of an SEV increased if it was idle at a station and decreased if it was occupied. The amount the SOC decreased by was determined by the energy demand of the trip, while the amount the SOC increased by was determined by three values: the capacity of remaining energy at the station, the maximum energy demand of the SEV, and the maximum energy a charging pile could provide during one simulation time step. To simplify this analysis, charging speed was assumed to be constant. If there were more than one vehicle charging at a station, vehicles with less SOC were charged first. The update algorithm is described by Eqs. (5) ~ (8):

SOCk, t − EDj , VoSk, t = 1, VoSk, t + 1 = 0 SOCk, t + 1 = ⎧ SOC ⎨ k , t + ESi, k , t , VoSk , t = 0, VoSk , t + 1 = 0 ⎩

(5)

ESi, k, t = min (MRk − SOCk, t , SES, AESi, t , k )

(6)

k−1

AESi, t , k = SES × NCPi − ∑m = 1 ESm, t

SES =

MRk SP × 60

(7)

× SS

(8)

where SOCk, t + 1 is the SOC of vehicle k at time t + 1, EDj is the energy demand of the last trip for vehicle k, ESi, k, t is the available energy for vehicle k at time t at station I, and VoSk, t is the status of vehicle k at time t. If the vehicle k was occupied at time t, then VoSk, t = 1, else VoSk, t = 0 . AESi, t , k is the remaining energy at station i during the period from time t to time t + 1 when charging the vehicle k, SES is the maximum energy that can be offered to an SEV during the period from time t to time t + 1, MRk is the maximum 169

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Fig. 3. Spatiotemporal details of observed transaction data.

range of vehicle k, SP is the period required to fully charge an SEV with a maximum range of MRk at a charging pile, in hours, SS is the size of the time step, in minutes (in this study SS = 10 min), and NCPi is the number of charging piles installed at station i. A simple example is provided below to illuminate the SOC update process. For a station with three charging piles (NCPi = 3) and four SEVs, the SOC of the four SEVs at simulation time t are 140 km, 145 km, 147 km, and 148 km respectively. The maximum range 170

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Table 1 An example of the SOC update module over 10 min (one time step). Vid

SOCk, t

Charging Sequence

SES

MRk − SOCk, t

AESi, t , k

ESi, k, t

SOCk, t + 1

V1 V2 V3 V4

140 km 145 km 147 km 148 km

1 2 3 4

4.17 km 4.17 km 4.17 km 4.17 km

10 km 5 km 3 km 2 km

12.51 km 8.34 km (=12.51 km – 4.17 km) 4.17 km (=12.51 km – 4.17 km) 1.17 km (=4.17 km – 3 km)

4.17 km 4.17 km 3.00 km 1.17 km

144.17 km 149.17 km 150.00 km 149.17 km

of an SEV is 150 km (MRk = 150km ). The charging speed is 6 h/150 km (SP = 6h ). Each time step is 10 min (SS = 10minutes ). The steps are: 1) CalculatingMRk − SOCk, t : the maximum energy demands of the four SEVs (MRk − SOCk, t ) are 10 km, 5 km, 3 km, 3 km, respectively. 2) Calculating SES : the maximum energy that can be offered to an SEV by a charging pile during a time step is (150 * 10) / (6 * 60) = 4.17 km (SES = 4.17 km ), while the maximum energy that can be offered by three charging piles is 4.17 * 3 = 12.51 km. 3) Calculating AESi, t , k and ESi, k, t : vehicles with less SOC have a higher charging priority, so the SEV with 140 km SOC is charged first, followed by the SEV with 145 km SOC, then the SEV with 147 km SOC, and lastly the SEV with 148 km SOC. The SOCs of each SEV following the charging priority rule are shown in Table 1: To test the reasonability of this SOC update algorithm, an SEV was randomly tracked with different charging speeds. Other parameters were set as default values, as shown in Table 2. The changing pattern of an SEV’s SOC over the simulation time is plotted in Fig. 4. As indicated, the patterns of consumption and recharge can be observed. Compared with charging speeds of 3 h/150 km and 6 h/150 km, a charging speed of 1 h/150 km was able to keep the SEV’s SOC at a higher stage. In other words, the constraint of low SOCs can be mitigated by a higher charging speed. 3.2.4. Vehicle selection module The vehicle selection module allocated available SEVs to users based on their trip distances and their degrees of range anxiety. Before allocation, the supply (available SEVs) and the demand (rental requests) of station i from time t to time t + 1 were calculated following Eqs. (9) and (10):

SUPt , i = set (Vehk, t ), ETk, t < t , Dk, t = i

(9)

DEMt , i = set (DEj ), t ≤ STj < t + 1, Oj = i

(10)

where SUPt , i is the set of idle SEVs at station i from time t to time t + 1, set(.) denotes a function, Vehk, t is the kth vehicle’s information at time t, and ETk, t and Dk, t are similar terms to those denoted in Eq. (2). DEMt , i is the set of rental requests between time t and time t + 1, DEj is the jth rental request, STj is the starting time of the jth rental request, and Oj is the origin of the jth rental request. An SEV was available only when its SOC at time t was greater than the user’s energy demand. Considering the existence of range anxiety, when the number of SEVs at a station was greater than 1, the SEV with a higher SOC was allocated to users first (Hu et al., 2018). A user’s energy demand was determined by two factors, the user’s range anxiety DRA and the energy demand of the trip ED. The degree of range anxiety DRA is a magnification index that was multiplied with each user’s real energy demand because users tend to choose SEVs with higher SOCs to reduce their range anxiety (Franke and Krems, 2013b). Therefore, in this study, an SEV was available only when its SOC met the prerequisite denoted as Eq. (11):

SOCk, t ≥ DRA ∗ ED

(11)

DRA is set as 1.25 in this study, corresponding to the comfortable range in Franke’s study (Franke and Krems, 2013a). If the energy demand for the jth trip was satisfied, or if there was an available SEV k that met the jth rental request, the status of the SEV k was updated using Eq. (12). Otherwise, the SEV’s status remained unchanged and the jth trip was tagged as an unsatisfied rental request. All unsatisfied rental requests were stored in a matrix, as an element to evaluate the performance of the carsharing program in the last step. Table 2 Values of the three key simulation parameters. Variable name

Description

Low boundary

High boundary

Step size

Default value

NTrips SP

The number of rental requests (input) The period for an SEV to be fully charged with a maximum range of 150 km, in hours The maximum range of SEVs, in km

100,000 0

900,000 6

– 0.5

450,000 6

50

500

50

150

MR

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Fig. 4. AN SEV’s estimated SOC with different charging speeds.

Dk, t + 1 = Dj , ETk, t + 1 = ETj, VoSk, t + 1 = 1

(12)

where Dk, t + 1, ETk, t + 1, andVoSk, t + 1 are similar terms to those denoted in Eqs. (2) and (4). 3.2.5. Evaluation module In summary, three variables, the number of rental requests (NTrips), the charging speed (SP), and the maximum range of SEVs (MR), were set as core parameters in this simulation. Their values are shown in Table 2. When compared with previous studies, the number of trips was converted to a daily vehicle-to-trip ratio (VtT ratio) using Eq. (13):

VtTratio =

30 × TNV NTrips

(13)

where NTrips is the number of rental requests (input) and TNV is the number of vehicles (in this study, TNV = 3,765). Therefore, scenarios with 100,000 trips, 450,000 trips, and 900,000 trips had VtT ratios of 1.13, 0.25, and 0.13 respectively. Rental requests were generated randomly and each combination of parameters was simulated for 10 times. Then, the measurements were aggregated with the mean function to avoid biases from random selection. The simulation was implemented in Python. Two measurements, including the percentage of satisfied rental requests (SRatio) and the average usage time of each SEV per day (ADur, in minutes), were used to evaluate the performance of the carsharing program. The equations used to calculate the two parameters are denoted as Eqs. (14) and (15):

SRatio =

ADur =

NTrips − NUns NTrips

(14)

− NUns (ETj − STj ) ∑NTrips j=1

(15)

TNV × 30 th

where NUns is the number of unsatisfied rental requests, ETj is the ending time of the j satisfied rental request, and STj is the starting time of the jth satisfied rental request. 4. Results 4.1. Simulation validation To test whether the simulation could accurately match real-world data, validation was conducted. The validation approach was adopted from prior studies (Illgen and Höck, 2018). In this study, the input number of trips was set as 442,246, which is the number of observed trips during April 2017. Simulated and observed borrow and return trips at each station every 10 min (the simulation time step) were set for comparison. The r2 of the linear regression was employed to measure the quality of the simulation and was calculated with Eq. (16):

r2 = 1 −

yi, t )2 ∑iI= 1 ∑T t = 1 (yi, t −  2 ∑iI= 1 ∑T t = 1 (yi, t − yi¯, t )

(16)

yi, t is the simulation value corresponding to yi, t (i.e. where yi, t is the observed borrow/return trips at station i from time t to time t + 1,  the total number of rental requests minus the number of unsatisfied rental requests), y¯i, t is the mean of observed borrow/return trips, T is the number of stations and I is the number of simulation time segments. In this study, T = 4,320 and I = 2,252. The simulation was replicated ten times to calculate the metric of means. All linear regressions had the P-values smaller than 172

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Fig. 5. Scatter between observed borrow/return trips and simulated borrow/return trips.

0.000. For borrow trips, the average r2 value was 0.813. For return trips, the average r2 value was 0.806. The scatter plots of simulated and observed borrow/return trips are shown in Fig. 5. The obvious linear relationships indicate that the simulation was capable of capturing the operational features of real-world carsharing programs. These validation results are similar to those found in Illgen and Höck’s study, where a similar discrete-event simulation was conducted and obtained an r2 value of 0.873 (Illgen and Höck, 2018). In addition, station-level validation was conducted to examine the simulation results in more detail. For each station i, the r2 value of station i, ri2 , was calculated by Eq. (17):

ri2 = 1 −

yi, t )2 ∑T t = 1 (yi, t −  2 ∑T t = 1 (yi, t − yi¯, t )

(17)

Results of the station-level ri2 are summarized in Table 3. As shown, different simulation accuracies were observed among the 2,252 stations, since the duration of their operational time and variability in the observed transactions at each station may be different. The averaged station-level r2 was 0.731 for borrow trips and 0.755 for return trips, indicating that the simulation was able to represent the carsharing system at a station-level. 4.2. Simulation results with regards to charging speeds In this section, charging speed (SP) was set as a variable changing from 0 h/150 km to 6 h/150 km. Changing patterns of SRatio and ADur over these different charging speeds are shown in Fig. 6 and Table 4. In addition, to analyze the interactive effect of SP and VtT ratio, three different VtT ratios, 1.13 (100,000 trips), 0.25 (450,000 trips), and 0.13 (900,000 trips), corresponding to lowdemand, medium-demand, and high-demand carsharing programs, were simulated jointly with different charging speeds. Scenarios with SP = 0 h/150 km are equal to carsharing programs that deploy FVs. Compared with carsharing programs that deploy EVs, the ADur and the SRatio of shared FVs are greater than those of shared EVs because EVs need longer times to replenish energy. To mitigate the negative effects resulting from battery capacity, improved charging speeds is highly desirable. Meanwhile, when holding SP constant, with a decrease in VtT ratio, ADur increased and SRatio decreased. This is plausible because providing more SEVs in one market can improve the likelihood of successfully renting an SEV. However, the idle time of each SEV increased because the rental requests per SEV decreased. Two conclusions can be drawn from the simulation results of changing charging speed. First, a threshold of charging speed, i.e. 1.5 h/150 km, can be observed from these curves. When a charging speed is slower than 1.5 h/150 km, SRatio and ADur decrease rapidly with the decrement of charging speeds. When a charging speed reaches the threshold, SRatio and ADur stay constant. Table 3 Summary of the station-level r2 values of 2252 stations.

2

r of borrow trips r2 of return trips

Mean

St.D.

Min.

Max.

0.731 0.755

0.114 0.108

0.149 0.174

1.000 1.000

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Fig. 6. SRatio (a) and ADur (b) changing over different SP and VtT ratios. Table 4 SRatio and ADur changing over different SP and VtT ratios. 100,000 trips (VtT ratio = 1.13)

450,000 trips (VtT ratio = 0.25)

900,000 trips (VtT ratio = 0.13)

SP (h/150 km)

ADur (minutes)

SRatio

ADur (minutes)

SRatio

ADur (minutes)

SRatio

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

54.09 54.08 54.06 53.99 53.79 53.36 53.05 52.58 52.15 51.67 51.14 50.78 50.28

97.42% 97.41% 97.40% 97.32% 97.01% 96.52% 95.88% 95.24% 94.35% 93.67% 92.93% 92.18% 91.30%

223.14 223.05 222.92 222.35 219.89 215.50 209.90 203.37 197.19 191.46 186.53 182.22 178.38

89.20% 89.19% 89.17% 88.93% 88.08% 86.60% 84.76% 82.51% 80.17% 77.92% 75.99% 74.19% 72.66%

417.96 417.79 417.22 413.15 401.38 383.95 366.61 350.97 339.66 330.22 324.01 317.73 312.43

83.02% 83.01% 82.94% 82.24% 80.21% 77.25% 74.07% 71.23% 68.95% 67.07% 65.56% 64.29% 63.22%

Alternatively, a charging speed of 1.5 h/150 km is adequate for a carsharing program, and continually increasing the charging speed is not cost-effective. Second, the effect of changing charging speeds on SEVs varies based on the VtT ratio. The smaller the VtT ratio of a carsharing program, the more severe the effect of decreased charging speed. To be specific, for three different VtT ratios (1.13, 0.25, and 0.13), with the charging speed decreasing from 0 h/150 km to 6 h/150 km, the ADur decreased by 3.81 min, 44.76 min, and 105.53 min respectively, and the SRatio decreased by 6.12%, 16.54%, and 19.80% respectively. This is sensible because increasing the VtT ratio means that more SEVs are assigned to satisfy rental requests. To some extent, the effect of providing more SEVs is substitutional to that of improving SEVs’ charging speeds. More SEVs in the system creates more energy surplus available for rental requests, and thus charging speed can be slower to reach a balance between energy consumption and replenishment. 4.3. Simulation results with regards to maximum range Similar to improving charging speeds, enlarging SEVs’ maximum range is an alternative way to mitigate the negative effects resulting from limited battery capacity. Enlarging SEVs’ maximum range is more cost-effective for carsharing operators because increasing maximum range is easier than updating charging piles in constrained, dense cities. In order to quantify the effect of different maximum ranges (MR) on the performance of a carsharing program, SEVs’ maximum range values from 50 km to 500 km with a steady increment of 50 km were simulated. Like in Section 4.2, three different VtT ratios, 1.13 (100,000 trips), 0.25 (450,000 trips), and 0.13 (900,000 trips), were simulated with different maximum ranges. Simulation results are shown in Fig. 7 and Table 5. ADur and SRatio both increased with an increase in MR. For three different VtT ratios (1.13, 0.25, and 0.13), with MR increasing from 50 km to 500 km, ADur increased by 8.37 min, 29.32 min, and 31.39 min, and SRatio increased by 8.32%, 10.04%, and 10.69% respectively. With decreased VtT ratios, the effect of decreasing MR became more severe, which is like the conclusion drawn from Section 4.2. This makes sense because when an adequate number of SEVs can be assigned, the energy demand from rental requests can be satisfied, thus making enhancing maximum range less effective. 174

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Fig. 7. Values of SRatio (a) and ADur (b) changing over different MR and VtT ratios.

Table 5 SRatio and ADur changing over different MR and VtT ratios. 100,000 trips (VtT ratio = 1.13)

450,000 trips (VtT ratio = 0.25)

900,000 trips (VtT ratio = 0.13)

MR (km)

ADur (minutes)

SRatio

ADur (minutes)

SRatio

ADur (minutes)

SRatio

50 100 150 200 250 300 350 400 450 500

45.22 48.51 50.28 51.41 52.20 52.75 53.03 53.22 53.51 53.59

88.20% 90.00% 91.30% 93.12% 94.31% 95.27% 95.79% 96.11% 96.40% 96.52%

171.10 174.89 178.38 181.43 184.57 188.56 191.58 195.19 197.65 200.42

70.50% 71.65% 72.66% 73.90% 75.02% 76.49% 77.63% 78.78% 79.80% 80.54%

305.41 308.13 312.43 315.51 318.91 322.18 325.85 329.08 334.05 336.80

60.13% 61.64% 63.22% 64.58% 65.55% 66.81% 67.64% 68.67% 69.96% 70.82%

5. Discussion Using discrete-event simulation, this study answered the questions: “How does the battery capacity of SEVs affect the performance of a carsharing program? How and to what extent can the negative effects of battery capacity be mitigated?” Results show that the limited battery capacity of SEVs lowers user satisfaction and vehicle utilization in carsharing programs. However, by increasing vehicle-to-trip ratio, charging speed, and maximum range, the negative effects resulting from battery capacity can be mitigated. More importantly, prioritizing the environmental benefits of SEVs may support the development of new technologies. This study also presents solid evidence supporting the deployment of EVs into carsharing programs. Battery capacity is not an everlasting problem and will likely be solved soon aided by faster charging speeds and larger maximum ranges. This discrete-event simulation approach demonstrated high accuracy in simulating a carsharing program. Although discrete-event simulation is not a brand new method in simulating carsharing programs (Barth and Todd, 1999), a more detailed charging procedure was considered and implemented in this study to approximate the real-world charging process. Many previous studies have set many charging rules to simplify the SEVs’ charging process. For example, SEVs must be fully charged before becoming available (Boyacı et al., 2015; Brendel et al., 2018), an SEV is charging when its SOC is smaller than a minimum threshold (Brendel et al., 2018; Repoux et al., 2015), and SEVs recharge at nighttime (Illgen and Höck, 2018). In this study, charging rules were defined to be more like realworld operations by jointly considering available charging piles, charging speeds, other SEVs’ SOCs, and the maximum range of SEVs. In addition, range anxiety was considered when users chose SEVs. Users always choose SEVs with SOCs larger than their real trip distances (Franke and Krems, 2013a; Hu et al., 2018). Other studies rarely incorporated range anxiety into simulations, or simplified assumptions by limiting trip distance (Brendel et al., 2018). SRatio and ADur were used as core measurements to evaluate the performance of the carsharing system in this study. Results show that when SRatio was 97.42%, ADur was only 54.09 min (3.75% in a day). This is similar to the results found by de Almeida Correia and Antunes (de Almeida Correia and Antunes, 2012). Their results suggest that the time that vehicles are in use only accounts for 5% of a day when all rental requests are satisfied (SRatio = 100%). As stated, both cases suggest low system efficiency and severe financial loss if carsharing programs try to satisfy all rental requests, since under this rule most SEVs are idle at stations during their operational periods. This study also showed that 97.42% of rental requests were satisfied when the VtT ratio was 1.13, which is larger 175

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than theresults (0.18 to 0.24) found by Barth and Todd (Barth and Todd, 1999). The difference may be that rental requests generated in Barth and Todd’s study were stochastic, and only six SEV stations were considered, while rental requests in this study were generated based on real data, and severe spatial and temporal imbalances in the demand of SEVs existed. Therefore, more SEVs were needed if operators wanted to reach a high SRatio in a largely expanded and highly imbalanced carsharing system. In terms of charging speed and maximum range, results show that increasing charging speeds and maximum range led to an increase in both SRatio and ADur. When VtT ratio was set as 0.25, and when the maximum range increased from 50 km to 500 km, ADur increased by 29.32 min and SRatio increased by 10.04%. When charging speed increased from 6 h/150 km to 0 h/150 km, ADur increased by 44.76 min and SRatio increased by 16.54%. A charging speed of 1.5 h/150 km helps eliminate most of the negative effects resulting from limited battery capacity. Such an effect greatly varied for different VtT ratios. To specific, this effect became more obvious when the VtT ratio decreased, which is consistent with previous studies (Barth and Todd, 1999). Compared with varied charging speeds, varied maximum ranges suggest a smaller impact on a carsharing system. The reason may be that increased maximum ranges mainly help promote the success rate of rental requests for long-distance travel, but in this study, the average trip distance was 19.21 km. Further studies can increase the trip distance to estimate the effect of increased maximum range on carsharing programs with different trip distances (Barth and Todd, 1999). Compared to previous studies’ results related to battery capacity, it is interesting to note that some early studies state that the effect of battery capacity on carsharing programs is limited (Barth and Todd, 1999), while others describe more severe effects (Illgen and Höck, 2018). For example, Barth and Todd stated that the average SOC of all SEVs never dropped below 70% for the highest number of rental requests (Barth and Todd, 1999). Therefore, only when trip distance increased by three times or when the number of charging piles dropped by 50% was the carsharing program drastically affected. In this study, the simulation outcomes suggest that the effects resulting from battery capacity are more severe compared with Barth and Todd’s studies. This can be attributed to long trip distances in the real world, which this study considered in detail. The average trip distance in Barth and Todd’s study was less than 8 km, while in this study, the average trip distance was 19.21 km (based on observed data). On the other hand, some other studies have presented even more severe effects of battery capacity. For example, a noted study indicated that when the maximum range of SEVs increased from 50 km to 200 km, the SRatio increased by 17% (Illgen and Höck, 2018). The difference may lie in different recharging rules. Their study assumed SEVs mostly charged at nighttime, while this rule cannot be valid in a large and dense metropolitan setting. 6. Conclusions and future research A discrete-event simulation approach was employed in this study to simulate how different constraints impact the performance of a carsharing program. Results show that the battery capacity of SEVs lowers user satisfaction and vehicle utilization in carsharing programs. However, these negative effects can be mitigated by increasing the charging speed and enlarging the maximum range of SEVs. Vehicle-to-trip ratios also greatly impact the effects of battery capacity. The effects of battery capacity are large when the vehicle-to-trip ratio is small. It is worth mentioning that the simulation results are dependent on specific trip information. For example, trip distances, station numbers, and the temporal and spatial distribution of rental requests all contributed to greatly varied results. However, the simulation framework proposed in this study is versatile and can be easily transplanted to other carsharing programs. Results help carsharing programs’ operators better understand the features of SEVs, and the tradeoffs of investing in different elements of SEVs for a carsharing program. Although increasing charging speed and maximum range help eliminate the negative effects of EVs, operators are not recommended to endlessly pursue the fastest charging speeds and the longest driving ranges. It is a trade-off between the costs of updating facilities and the profits of increasing user satisfaction and vehicle utilization (Boyacı et al., 2015; Brendel et al., 2018; Seign and Bogenberger, 2013). Distinctly, there is an optimal solution where the total retained profit reaches a maximum. Future studies may focus on building an optimization model to approach this maximum if related data become accessible, such as the cost of employees, relocation strategies, and maintenance and depreciation costs (Boyacı et al., 2017; Bruglieri et al., 2014). Acknowledgment The authors appreciate data support from the EVCARD Shanghai carsharing program. Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.trd.2019.10.013. 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