A Development of Optimal Design and Operation Algorithm for Battery-Powered Electric City Tour Bus System

Abstract

After overcoming COVID-19, the tourism demand around the world is on the rise again. At the same time, the interest in eco-friendliness is growing again, and efforts are being made to build an eco-friendly tourism ecosystem. In this study, assuming that a battery-powered electric city tour bus is adopted instead of an existing internal combustion engine city tour bus, we tried to develop optimal design and operation algorithms for battery-powered electric city tour bus systems. The developed algorithm pursues the maximization of the profit, which is calculated through the ticket price paid by tourists using the city tour bus and the overall cost of the electric city tour bus system. In addition, the decision variables of the algorithm are the daily number and interval of operations of the electric city tour bus, which are related to the tourism demand, the battery capacity of the electric city tour bus, and whether a pantograph-type wireless charger is installed or not at the bus stop. The operations research method is used to develop the design algorithm, and numerical examples are derived as the result of the optimal design to verify the proposed algorithm by referring to the operating situation of the Blue Trolley Line in Oahu, Hawai’i. As a result, it is found that profit maximization can be achieved by changes in the daily number and interval of operations on designated routes.

1. Introduction

In the past few years, the world’s attention has been buried in the health field due to COVID-19. However, with the gradual response to COVID-19, the tourism demand is increasing and interest in the environment is growing again. The efforts to rebuild the tourism industry, which was nearly devastated by COVID-19, are increasing around the world, and people are seeking to build a system for environmentally conscious and sustainable tourism, even at this time [1]. In the tourism industry, there have been various efforts to promote a sustainable tourism approach that considers the environment. Hotels promote the use of multi-use items while minimizing the use of single-use items in room and amenities by disinfecting and repacking cups and tableware used in guest rooms before providing them to customers. In addition, several OTAs provide a service to enable eco-friendly tourism by displaying information about the amount of carbon generated when using a hotel or a transportation option when a customer searches for a hotel or flight reservation [2]. Moreover, city tour buses, one of the representative city tour products, are increasingly being operated as electric buses instead of conventional internal combustion engine buses in many cities visited by tourists [3].

Among the various elements of tourism, transportation is one of the most harmful things for the environment [4]. Of course, means of transportation that are used not only for tourism but also in everyday life tend to have many adverse effects on the environment. As a result, these means of transportation are continuously evolving into forms that emit less or no environmental pollutants, and currently alternatives such as electric vehicles and hydrogen-powered vehicles are commonly used in real life [5]. However, many cities famous for tourism operate city tour buses for the purpose of providing convenient access to tourist attractions and scenic views, and in most cases the services are still provided using conventional internal combustion engine buses. As shown in Figure 1, in Oahu, Hawai’i, which is famous as an eco-friendly tourist destination, the city tour bus system named the Waikiki Trolley is still operated as an internal combustion engine bus. Therefore, the city tour bus services using such internal combustion engine buses need to be improved by using eco-friendly buses such as electric buses as soon as possible.

In spite of these advantages, it is required to invest lots of money in general to replace a conventional city tour bus system with an electric bus system; therefore, lots of things need to be considered to minimize the overall investment costs [3]. In particular, since electric buses do not use fossil fuels such as diesel or gasoline and use electric energy as fuel, they should be equipped with electric batteries rather than simple fuel tanks, and a charging station to provide electric energy should be prepared separately. However, the batteries themselves are expensive enough to be half the price of an electric bus, and the charging facilities are also expensive; therefore, the overall investment costs can be minimized only via optimal system design. Regarding the battery capacity, the initial investment cost can be reduced if a battery with a small capacity is installed in the city tour bus, although the operation cost may increase due to frequent replacements caused by complete discharging of the battery. In addition, the charging facilities and related initial investment costs can be decided according to the charging method. There are slow charging methods such as plug-in charging and rapid charging methods such as ground-based wireless charging or pantograph wireless charging. In general, the slow charging methods use low-voltage electricity, so the initial installation cost or the cost of the electric energy can be reduced, but more vehicles may need to be purchased because of the idle time involved in slow charging [6]. The pantograph-type wireless charging method has some advantages over plug-in-type charging. It is possible to automate the connection between the charger and the bus, which can be charged with greater power [7].

Therefore, this study aims to develop an algorithm for the optimal system design of a city tour bus that minimizes the overall costs by assuming a situation in which the existing city tour bus is replaced with an electric bus capable of pantograph-type wireless charging, which is a rapid charging method. For this purpose, a mathematical-model-based optimization technique is applied in this study, and the decision variables are the daily number and intervals of operations of the electric city tour bus, the capacity of the batteries to be equipped in the electric buses, and the stops where wireless charging facilities can be installed. The daily number and intervals of operations of the electric city tour bus system can affect the customer demand for the city tour bus service. In general, if the daily number of operations increases, more tourists can be recruited, while the tighter the interval, the more tourists tend to prefer it. Moreover, the battery capacity to be equipped in the electric bus and the stop where the wireless charging facility is installed may vary according to the daily number and intervals of operations of the city tour bus. As a result, this study intends to develop an algorithm for the optimal system design of an electric city tour bus that can minimize the overall cost by considering such sensitive decision variables comprehensively.

This paper consists of six sections, and the details of each section are as follows. Section 1 is an introduction. The general flow of the research motivation is introduced, including the background, necessity, and topic of the research. Section 2 is a literature review. The theoretical background of the battery-powered electric bus is confirmed through previous studies. Section 3 is the model development section, where the problem and the mathematical model are presented. Section 4 outlines the solution procedure and describes how the algorithm is developed. Section 5 is a numerical experiment. The results of the algorithm are derived and analyzed through numerical examples. Section 6 presents the conclusions. The implications identified based on the experiment results, the limitations of the study, and the future research directions are presented.

2. Literature Review

The pantograph-type wireless charging method has the advantage of being able to perform charging not only in bus garages but also at bus stops, whereas the existing plug-in charging methods can only perform charging at bus garages. For this reason, research on the technical aspects of electric buses using the pantograph-type wireless charging method is being actively performed. Ortenzi et al. [8] designed ultra-fast charging infrastructure based on supercapacitors used to charge an energy storage system mounted on electric bus. The proposed ultra-fast charging infrastructure can provide up to 180 kW of power within 30 s. They divided the charging process into three steps to limit the maximum charge current and showed that the charging system is effective from both technical and economical points of view. In addition, Ortenzi et al. [8] presented the ABB fast charging system. The Hess-ABB TOSA is a bus using an ABB that consists of a 40 kWh energy storage unit and an automatic energy transfer system at the bus station. This electric bus requires 2 charges on the 18 km route. The first charging point uses a 400 kW power supply and takes 15 s to charge, while the second charging point uses a 200 kW power supply and takes 3~4 min to charge. It was stated that these systems require expensive components. Zagrajek et al. [9] studied the impact on the power system when a new charging point is installed with the introduction of an electric bus. They planned to introduce electric buses on 12 bus lines and place pantograph quick charging points at 17 terminals. As a result, there was no problem with the power quality and the effect of introducing electric buses on the power system of Warsaw is negligible. Vehviläinen et al. [10] determined the effects of temperature and weather conditions on the efficiency of electric buses through the collection and analysis of weather conditions and electric city bus data. They conducted the research in Tampere, Finland, and the results showed that the average energy consumption in winter is 40 to 45% higher than in summer. Moreover, they found that sufficient safety infrastructure is required due to faults and additional energy consumption under severe weather conditions and proper training is needed to prevent excessive energy consumption according to driving styles. Mathes et al. [11] presented the impacts of electric buses using the pantograph charging method on passenger safety and noise. They figured out that electromagnetic emissions from quick chargers can pose a health risk, but the magnetic and electrical emissions are well below the safety standard limits. Although noise is generated during the operation and charging process of the pantograph system, it was found to be lower than the basic noise generated by a diesel bus. Al-Saadi et al. [12] studied the impact of an ultra-fast charging solution of an electric bus on the power grid. As a result of their study, the voltage fluctuation due to fast charging was found to be much lower than ±10%, which is the value limit of the power quality standard (EN50160), confirming that there is no problem in terms of power quality. In addition, the average value of the total harmonic current distortion (THDv) is only 3%, indicating that harmonic current contamination is not a problem.

To introduce electric buses using the pantograph charging method, research on the technical aspects is important, although when operating electric buses on the actual route, operational research is also needed to determine the optimal way to minimize costs. For this purpose, studies on the operational aspects of pantograph-charging-type electric buses are also being actively conducted. Wang et al. [6] developed an optimization model for charger deployment and fleet scheduling for electric buses using the pantograph charging method. They presented a real case study in Oslo, Norway, to examine the applicability of the proposed model and showed that the opportunity charging method, whereby buses can be charged at the stops, has a cost-effective advantage of saving up to 13.38% of the total annual cost compared to the end station charging method. Zeng et al. [13] suggested an optimal electric bus charging schedule that solves grid and battery problems when charging is possible at stops and terminals. They introduced the peak-to-average-power ratio, hourly electricity price, and battery wear formula while guaranteeing the original bus schedule. The proposed model was formulated as a mixed integer program and solved using existing solvers, even for large-scale problems. The cost of the battery wear has been shown to have a bigger impact on operations than the cost of charging. Dirks et al. [14] presented a way to integrate battery-powered electric buses into city bus networks while minimizing the total cost of ownership and analyzed the potential to reduce nitrogen oxide emissions. A case study was conducted in Aachen, Germany, assuming a situation in which nighttime charging at the bus garage and pantograph charging at the starting and ending points of the route are possible. They showed that the comprehensive integration of battery-powered electric buses is practicable and economic. Verbrugge et al. [15] developed a real-time scheduling and optimization (RTSO) algorithm for charging multiple electric buses in one depot. They assumed that the operator is already operating a fleet of battery-powered electric buses and tested this in several charging scenarios. The results of the tests found that up to 10% charging cost savings can be achieved. López et al. [7] researched an in-depth review of urban public transport using electric buses with different charging strategies (depot charging, opportunity charging) and charger types (wire charging, inductive charging, traditional pantograph, inverted pantograph) through a SWOT analysis. Case studies of five cities and a real case study with real data from Madrid were performed. They showed that the best charging technology depends on the operational needs, and each bus company should choose the solution that best suits their needs.

As an eco-friendly means of transportation, the electric charging method is receiving a lot of attention, and various studies are being conducted. In the field of tourism, as the interest in sustainable tourism increases, research on electric means of transportation is being performed. Ko and Song [3] developed two mathematical models for operating city tour buses from a sustainable perspective, the first of which has two objective functions that minimize the total investment cost and CO₂ emissions. They decided the number of electric buses and the battery capacity using Pareto solutions in model I. The second model examined the optimal unit service price through the results of model I and the economic incentive from the social energy saving program. The proposed model through the scientific methodology makes it possible to build and manage a sustainable tourism system. Kwag et al. [16] dealt with personal electric mobility systems with wireless electric charging methods such as electric scooters. They derived the optimal location and length of the wireless charging infrastructure considering the types and travel characteristics of tourists while minimizing the total investment cost. They found that urban tourism can not only provide opportunities to attract tourists through electric personal mobility options, which can promote outdoor activities, but can also solve transportation problems from a sustainable perspective. Łapko [17] compared conventional motors and electric motors for sustainable marine tourism and analyzed the advantages and disadvantages of each solution. It was showed that electric motors are a great alternative to internal combustion engines for low-power motors, but in the case of high-power engines, the weight and cost of the system increase because they require multiple batteries. Puchongkawarin and Ransikarbum [18] developed a 2-stage decision support system for the purpose of improving the quality of tourism logistics and public transportation services. In the first stage, the influencing factors and satisfaction of the tourism logistics and public transport were evaluated using a mixed research method. The second stage used the data from the first stage to develop new routes to potential destinations and service locations. Nikiforiadis et al. [19] conducted a survey on the island of Rhodes, Greece, to find out the willingness of tourists to use shared electric vehicles for travel. As a result of the survey analysis, it was anticipated that electric car-sharing will create greater demand than other means of electric mobility, such as electric moto-sharing and electric bike-sharing, and electric-car sharing is a good way to attract market share in the car rental business.

In this study, the changes in tourist demands using city tour bus services according to the daily number and interval of operations are significantly considered. Unlike the demand for general public transportation, the tourist demand using city tour bus services such as the ‘Waikiki Trolley’ is expected to rise as the daily number of operations increases and the interval of operations decreases. The profits according to the changes in the daily number and interval of operations at the corresponding route are verified, and they are derived in terms of profit maximization, reflecting the characteristics of the tourist demand. In addition, suitable stops for installing a pantograph-type wireless charger and the battery capacity of the city tour bus are determined simultaneously by analyzing the energy consumed when moving between stops; that is, the contribution of this study is the consideration of the characteristics of city tour bus services together, rather than simply minimizing the overall cost when introducing a pantograph-type wireless charging electric bus system into the city tour bus service. In addition, the operation cost of the electric city tour bus system is considered when calculating the overall cost. The overall cost consists of the initial investment costs (costs of the bus purchase, battery purchase, and charger installation) and operation costs (cost of battery replacement and charging). Previous studies generally aimed to minimize the initial investment cost. However, this study considers not only the initial investment cost, but also the operation cost reflected in the battery performance deterioration within the legal end of life of the electric city tour bus.

3. Model Development

In this section, the definitions of the problem, the notation used in developing the mathematical model, and the objective function and constraints of the developed mathematical model are described to present the mathematical model developed in this study.

3.1. Problem Description

In this study, we try to develop an algorithm for optimal system design for a battery-powered electric city tour bus system that can maximize profits by considering both the revenue from the ticket price paid by tourists using the city tour bus and the overall cost. It is assumed that a pantograph-type wireless charging electric bus system is applied to a city tour bus service operated using an internal combustion engine bus. It is further assumed that a pantograph-type electric city tour bus system is introduced for the Blue Line of the ‘Waikiki Trolley’, a city tour bus service operating in Oahu, Hawai’i, for easy understanding of the problem. Figure 2 shows the entire operation route of the Blue Line of the ‘Waikiki Trolley’. The total distance per trip is about 52 km and consists of 11 stops starting from Waikiki, passing through Kahala Mall, going around the East Coast, and returning from Sea Life Park. The Blue Line of the ‘Waikiki Trolley’ takes 120 min per trip, stays for about 2 min at each stop, and passes non-stop at stop 7, Halona Blow Hole.

There are four decision variables for the mathematical model being developed in this study, namely the daily number and interval of operations of the electric city tour bus, the battery capacity of the batteries to be equipped in the electric buses, and the stops where wireless charging facilities are installed. All decision variables have a significant impact on the overall cost of the electric city tour bus system, but among them the daily number and interval of operations of the electric city tour bus also affect the tourist demand to use the city tour bus service. In general, when the daily number of operations increases and the interval decreases, the demand from tourists who want to use the city tour bus service also tends to increase, as shown in Figure 3. Since the total operation time is assumed to be changed, the operation interval and the daily number of operations can be adjusted independently.

In this study, it is assumed that a pantograph-type wireless charging electric bus is introduced, then it is known that 80% to 20% of the total battery capacity can be used in general because it corresponds to a rapid charging method [16]. When the battery’s SOC exceeds 80%, the charging time increases rapidly [20]. To prepare for emergencies such as broken chargers, situations where the battery’s SOC is less than 20% are avoided. Therefore, it is assumed that the battery capacity of the city tour bus is charged to 80% at stop 1, where the city tour bus departs, and the pantograph-type wireless charger is installed by default. A battery-powered electric city tour bus departing from stop 1 should have at least 20% of its total battery capacity remaining by the time it reaches each subsequent stop, and it should have at most 80% of its total battery capacity at the time of departure at each stop, no matter how long it has been charged using the pantograph-type wireless charger. In addition, when an electric city tour bus arrives at a stop installed with a pantograph-type wireless charger, it can be charged within the predetermined stop time. When designing the electric city tour bus system in this study, the battery capacity to be equipped in the electric city tour bus and the stop where the pantograph-type wireless charger is installed need to be determined so that the above operation conditions could be satisfied.

Finally, the overall cost of the electric city tour bus system includes five kinds of costs, such as the initial battery-powered electric bus purchase cost (excluding batteries), the battery purchase cost to be equipped in the battery-powered electric bus, the battery replacement cost, the installation cost of the pantograph-type wireless charger, and the electric charging cost, while the overall planning horizon is nine years from the purchase of the initial battery-powered electric buses to their legal end of life.

3.2. Notations

The following notation is defined to model the mathematical formulation for developing the algorithm for the optimal system design of the electric city tour bus system.

3.3. Mathematical Model

The mathematical model developed in this study reflects the defined problem and consists of objective and constraint formulations, as follows. The objective function of the mathematical model is to maximize the profit obtained by subtracting the overall cost of the electric city tour bus system from the total revenue generated by tourists using the city tour bus, as expressed in Equation (1). The period for calculating the objective function value is during the legal operation period of the battery-powered electric bus:

Maximize

$$\begin{gathered} p·d·ntd·lc-ceb·neb-cbp·nbp·neb-ccs·ncs \\ -e·nt·ntd·lc·cec-cbp·nbp·neb·nbr \end{gathered}$$

(1)

Subject to

$$d=\alpha ·n{t}^{\gamma }+\beta ·it$$

(2)

$$neb\ge \lceil \frac{dt}{it}\rceil$$

(3)

Equation (2) represents the daily tourist demand of the city tour bus service, which is determined by the daily number and interval of operations. When the daily number of operations increases, the tourist demand does not rise proportionately due to the law of diminishing marginal utility [21,22]. As the marginal utility diminishes, the increase in tourist demand narrows. Equation (3) presents the calculation of the minimum required number of electric city tour buses, considering the time taken to operate the designated route and the operation interval. For example, if it takes 120 min to travel a designated route once and the operation interval is 20 min, the minimum number of buses required for operation is 6:

$$nbp=\frac{cb}{cp}$$

(4)

$$ncs\ge \lceil \frac{e}{rp·ct}\rceil$$

(5)

$$e=e{c}_b·\left(1-\frac{wb-\frac{cb}{\rho }}{web}·\delta \right)·td$$

(6)

Equation (4) indicates that the battery capacity is decided by the capacity of the battery pack and the number of applied battery packs, and Equation (5) shows the minimum number of pantograph-type wireless electric chargers to be installed at stops to provide the energy that is used when the electric city tour bus operates once on a designated route. Chargers should be installed to replace all of the energy used to operate a designated route. In addition, Equation (6) represents the amount of energy used when the electric city tour bus operates the designated route once. The lighter the weight of the bus and battery, the less energy is consumed to operate the same distance. Since the battery capacity determines the weight of the battery, it also affects the energy consumption. The energy used to operate a designated route once ranges from 60.196 kW to 66.868 kW when the battery capacities range from 50 kWh to 500 kWh. The difference in battery weight is about 3462 kg, and the effect of the weight on the energy consumption is not significant. Therefore, this study does not consider the weight of the tourists on the bus.

$$te=cb·cy·\epsilon$$

(7)

$$nbr\ge \lceil \frac{e·nt·ntd·lc}{neb}·\frac{1}{te}\rceil$$

(8)

Equation (7) represents an amount of energy that can be used while charging and discharging a battery until it is replaced. Repeated rapid charging causes the deterioration of the battery capacity [20]. The battery is replaced when its SOH (state of health) decreases to a certain level, and ε is affected by this [23]. Equation (8) describes the calculation of the number of battery replacements considering the total amount of energy used by an electric city tour bus before its legal end of life. The daily number of operations and the battery capacity affect the number of battery replacements:

$$ki=cb·so{c}_{max}$$

(9)

$$ki-k_{1,2}=k{d}_2$$

(10)

$$k{c}_s-k_{s,s^{\prime }}=k{d}_{s^{\prime }}, s^{\prime }\in S-\left\{1\right\},s^{\prime }=s+1$$

(11)

Equation (9) states that the amount of energy charged in the battery should be the upper limit of the battery’s available SOC when the electric city tour bus departs from the first stop, and Equation (10) is used for the amount of remaining energy in the battery when it arrives at the second stop, which is calculated by subtracting the energy consumed during the operation from the first stop to second stop. In the same way, the amount of energy remaining in the battery when the electric city tour bus arrives at stop s’ can be expressed by Equation (11):

$$k{d}_s+m_s·min\left\{\left(rp·ct\right),\left(cb·so{c}_{max}-k{d}_s\right)\right\}=k{c}_s \forall s\in S$$

(12)

$$k{d}_s\ge cb·so{c}_{min} \forall s\in S$$

(13)

$$ncs={\displaystyle \sum }_{s=1}^S{m}_s$$

(14)

Equation (12) indicates that when the electric city tour bus departs from stop s, the remaining amount of energy in the battery must be less than the upper limit of the battery’s available SOC, even if it is sufficiently charged with a pantograph-type wireless electric charger, and Equation (13) shows that the remaining amount of energy in the battery should always be above the lower limit of the battery’s available SOC while the electric city tour bus is in operation. Finally, Equation (14) is an equation that calculates the total number of pantograph-type wireless electric chargers installed at the stops.

4. Solution Procedure

The mathematical model developed in this study has four kinds of decision variables, such as the daily number and interval of operations of the electric city tour bus, the battery capacity to be equipped in the electric buses, and the stops where wireless charging facilities are installed, meaning the complexity of the formulation is relatively high, and the objective function is derived as a non-linear form because it consists of elements related to revenues and costs. Therefore, a genetic algorithm known as one of the meta-heuristics methodologies with excellent performance is applied to derive the optimal or near-optimal solution for the developed mathematical model [24]. The overall process of the genetic algorithm is described in Figure 4.

4.1. Initial Population Generation

When solving decision-making problems using the genetic algorithm, the first task is to define the chromosomes, which are the individual entities in a population that represent a generation. At this time, the chromosomes generally comprise decision variables in decision-making problems. In this study, the decision variables of the proposed mathematical model are the daily number and interval of operations of the electric city tour bus, the battery capacity to be equipped in the electric buses, and the stops where the wireless charging facilities are installed, so the chromosomes are designed as shown in Figure 5. The first to third genes of the chromosome represent the decision variables for the daily number and interval of operations of the electric city tour bus, and the battery capacity to be equipped in the electric buses gives different upper and lower limit values for each. In addition, the fourth to last genes represent the decision variables for the stops where wireless charging facilities are installed, which equal the number of stops, and if each gene has a value of 1, then this means that a pantograph-type wireless charger is installed, otherwise it has a value of 0.

4.2. Evaluation by Fitness Function

Each chromosome constituting the population can be evaluated by calculating a fitness function value through a fitness function. The fitness function is generally composed of the sum of the objective function value and the penalty value. Using the decision variable value for each chromosome, the objective function value corresponding to the objective function is calculated, and when the constraint equations are violated, the penalty value is added to obtain the final fitness function value. In this study, the goal is to maximize the overall profit from the electric city tour bus system, so the chromosome is better evaluated when the fitness function value is higher, while the penalty is set to a real negative value.

4.3. Termination Condition Check

A general termination condition of a genetic algorithm occurs when the values of the chromosomes constituting the population become equal to a certain ratio or more. In addition, the genetic algorithm can be terminated when the population number updates; that is, the number of generations exceeds a certain number of iterations. In this study, the latter termination condition is applied, and the genetic algorithm is programmed to terminate after producing up to 10,000 generations.

4.4. Selection, Crossover, and Mutation

Each chromosome constituting the population may be selected to form the next generation of the population through selection. At this time, the value of the chromosome may change through crossover and mutation according to random probability. Not all chromosomes selected through selection should undergo both crossover and mutation, and they may pass to the next generation without passing through only crossover or both according to a random probability. In this study, roulette wheel selection, two-point crossover, and one-point mutation policies are adopted, and since these are general policies, detailed explanations are omitted due to space constraints.

5. Numerical Experiment

5.1. Preparation of Experiment

The experimental model deals with the operating situation of the Blue Line of the Waikiki Trolley in Oahu, Hawai’i. A numerical experiment is performed to verify the proposed algorithm for the optimal system design for a battery-powered electric city tour bus using a pantograph-type wireless charger. The total distance of the Blue Line is 51.821 km with 11 stops, and it takes 120 min for one operation. It is assumed that the distances between the 11 stops are different, and that the energy consumption varies according to the distance. In this study, to maximize profit, the daily number of operations, operation interval, battery capacity, and stops where wireless charging facilities are installed are determined. It is assumed that the daily number of operations can be changed in units of one time and the operation interval can be changed in units of 5 min. Since the capacity of one battery pack is assumed to be 50 kWh, the battery capacity can be selected in units of 50 kWh. The charging occurs with 400 kW of power, remaining for two minutes at stops where the charger is installed.

The purpose of this study is to achieve profit maximization during the trolley operation. As the daily number of operations increases, the tourist demand rises. For the same reason, a shorter operation interval increases the tourist demand. In addition, a battery with a small capacity is less expensive to purchase, but the replacement costs may increase. Moreover, the stops to install wireless charging facilities should be determined to maintain the battery’s SOC. In this situation, a set of system parameters are prepared, as shown in

Table 1. System parameters.

Parameter	Value	Reference	Parameter	Value	Reference
$p$	25	[25]	$rp$	400	[26]
$ntd$	365	[25]	$ct$	0.033	[26]
$lc$	9	[26]	$e{c}_b$	1.240	[27]
$ceb$	350,000	[26]	$wb$	2492	[27]
$cbp$	25,000	[26]	$web$	15,000	[27]
$ccs$	250,000	[26]	$\rho$	0.130	[27]
$cec$	0.420	[28]	$\delta$	0.450	[29]
$\alpha$	200	created	$td$	51.821	[25]
$\beta$	−3	created	$\epsilon$	0.900	[27]
$\gamma$	0.100	created	$so{c}_{max}$	0.800	[3]
$dt$	120	[25]	$so{c}_{min}$	0.200	[3]
$cp$	50	created

, to perform numerical experiments. The parameters for the pantograph-type wireless charging electric bus system are borrowed from previous studies, while some parameters are obtained from the ‘Waikiki Trolley’ homepage [3,22,23,24,25,26]. In addition, the remaining parameters relating to tourist demand are created in this study.

5.2. Result

In this study, it is assumed that the battery-powered electric city tour bus is charged only at the stop using a pantograph-type wireless charger. Therefore, all of the energy consumed by operation should be replaced at the stops. Since the total distance of the designated route is 51.821 km, around 60.196 kW to 66.868 kW of energy is required per operation, depending on the battery capacity (weight). It is assumed that the battery-powered electric city tour bus stops for 2 min at each stop and can be charged by 13.333 kW per stop when the pantograph-type wireless charger is installed with 400 kW of power. As a result, at least five chargers are required to replace the energy consumed for one operation. If we suppose that the battery capacity is over 500 kWh, then six chargers should be installed. It is necessary to decide where to install the charger so that the battery’s SOC range is maintained between 20% and 80% during operation.

Currently, in Oahu, Hawai’i, the Blue Line operates 9 times a day at 40 min intervals. The values of the daily number and interval of operations will affect the tourist demand and the profit. With the demand function assumed in the model, the profit can be maximized by increasing the daily number of operations to 14 times and reducing the operation interval to 15 min, as shown in

Table 2. The results of the optimal system design.

Daily Number of Operations	Operation Interval	Battery Capacity	Number of Tourists per Day	Revenue	Profit
14 times	15 min	150 kWh	215 people	$17,689,815	$11,248,447
Cost of bus purchase	Cost of charger installation	Cost of battery purchase	Cost of battery charging	Cost of battery replacement
$2,800,000	$1,250,000	$600,000	$1,191,368	$600,000

. The results of the study show that the profits can be maximized by predicting the actual demand and adjusting the daily number and interval of operations.

The battery capacity is determined at 150 kWh. The battery capacity affects the purchase and replacement costs of the battery. In general, batteries with the minimum available capacity required to reduce costs are adopted. However, if the battery capacity is set to 50 kWh or 100 kWh while a pantograph-type wireless charger is adopted with rapid charging at 400 kWh, the charge/discharge cycle life is remarkably reduced [30]. As the cycle life decreases, the total energy that can be used by one battery decreases, which eventually increases the cost of the battery replacement.

The stops where the pantograph-type wireless chargers to be installed are shown in

Table 3. Distance, energy consumption, amount of charging, and battery charging level for each stop.

Bus Stop	Distance (km)	Energy Consumption (kWh)	Amount of Charging (kWh)	Battery Charging Level after Arrival (kWh)	Battery Charging Level before Departure (kWh)
Starting point (1)					120.000
1 → 2	0.805	0.958		119.042	119.042
2 → 3	0.483	0.575		118.467	118.467
3 → 4	1.127	1.341		117.126	117.126
4 → 5	4.345	5.171		111.954	111.954
5 → 6	2.253	2.682	13.333	109.273	120.000
6 → 7(Non-stop) → 8	17.864	21.262	13.333	98.738	112.071
8 → 9	8.690	10.343	13.333	101.728	115.062
9 → 10	9.817	11.684	13.333	103.377	116.711
10 → 11	2.253	2.682		114.029	114.029
11 → Ending point (1)	4.184	4.980	13.333	109.049	120.000
Total	51.821	61.678

. Table 3 shows the distance, energy consumption, amount of charging, and battery charging level for each stop. A wireless charger should be installed at stop 1, which is the starting and ending point as a default. In the first half of the route, the distance between stops is relatively short, so the energy consumption is low and chargers are not installed. In the second half of the route, since the distance between stops is long, wireless chargers are installed at stops 6, 8, and 9, except for stop 7, which is not a stop. In addition, the distance between stops 10 and 11 is relatively short, so the charger is installed at only one of the two stops. By installing the charger in this way, it is possible to replace all of the energy consumed for the operation, maintaining 20–80% of the battery’s SOC.

5.3. Sensitivity Analysis

As mentioned earlier, the profit can be maximized when the daily number of operations is 14 times and the operation interval is 15 min. In this section, a sensitivity analysis is performed to identify how the profit changes according to the daily number of operations and the operation interval. The results of the sensitivity analysis are as shown in

Table 4. The results according to the changes in the daily number of operations.

Daily Number of Operations	Revenue	Cost of Bus Purchase	Cost of Charger Installation	Cost of Battery Purchase	Cost of Battery Charging	Cost of Battery Replacement	Profit
11 times	$17,180,248	$2,800,000	$1,250,000	$600,000	$936,075	$600,000	$10,994,173
12 times	$17,362,684	$2,800,000	$1,250,000	$600,000	$1,021,173	$600,000	$11,091,511
13 times	$17,531,917	$2,800,000	$1,250,000	$600,000	$1,106,270	$600,000	$11,175,647
14 times	$17,689,815	$2,800,000	$1,250,000	$600,000	$1,191,368	$600,000	$11,248,447
15 times	$17,837,869	$2,800,000	$1,250,000	$600,000	$1,276,466	$1,200,000	$10,711,403
16 times	$17,977,292	$2,800,000	$1,250,000	$600,000	$1,361,564	$1,200,000	$10,765,728
17 times	$18,109,083	$2,800,000	$1,250,000	$600,000	$1,446,661	$1,200,000	$10,812,422

and

Table 5. The results according to the changes in the operation interval.

Operation Interval	Revenue	Cost of Bus Purchase	Cost of Charger Installation	Cost of Battery Purchase	Cost of Battery Charging	Cost of Battery Replacement	Profit
5 min	$20,153,565	$8,400,000	$1,250,000	$1,800,000	$1,191,368	-	$7,512,197
10 min	$18,921,690	$4,200,000	$1,250,000	$900,000	$1,191,368	$900,000	$10,480,322
15 min	$17,689,815	$2,800,000	$1,250,000	$600,000	$1,191,368	$600,000	$11,248,447
20 min	$16,457,940	$2,100,000	$1,250,000	$450,000	$1,191,368	$900,000	$10,566,572
25 min	$15,226,065	$1,750,000	$1,250,000	$375,000	$1,191,368	$1,125,000	$9,534,697
30 min	$13,994,190	$1,400,000	$1,250,000	$300,000	$1,191,368	$900,000	$8,952,822
35 min	$12,762,315	$1,400,000	$1,250,000	$300,000	$1,191,368	$900,000	$7,720,947

. When the daily number of operations increases from 14 times, the profit decreases. This is because the revenue increases but the costs of battery charging and replacement increase more than that. In addition, the profit also decreases when the number of operations is reduced from 14, as the decrease in revenue is greater than the decrease in the cost of battery charging. Regarding the operation interval, when the interval is shorter than 15 min, the profit is reduced. Even the revenue tends to increase, but the number of required electric buses and the cost of the battery purchase increases more significantly. Conversely, when the operation interval exceeds 15 min, then the profit is reduced. The reason is that the reduction in revenue is greater than the decrease in the costs of the bus and battery purchases.

6. Conclusions

This study dealt with the application of an electric city tour bus system to the existing city tour bus service operated using internal combustion engine buses, reflecting the tourism trend of sustainable tourism, especially in terms of the environment. Unlike previous studies on electric vehicle system design, the daily number and interval of operations, which greatly affect the tourist demand using city tour bus services, were determined as decision variables by considering the situation in which electric bus systems are applied to conventional city tour bus services. In addition, since this study considered the pantograph-type wireless charging electric bus system, the battery capacity to be equipped in the electric city tour bus and the stop where the pantograph-type wireless charger is installed were also treated as decision variables. In general, the research on the design of electric bus systems tends to aim to minimize the initial investment cost, but this study tried to maximize the profit, which is the difference between revenues according to the tourist demand and overall cost. In addition, even regarding the overall cost, this study considered not only the simple initial investment cost but also the operation cost of the electric city tour bus system. In this study, a mathematical model was proposed to develop an algorithm for the optimal system design of an electric city tour bus service, and a genetic algorithm was devised to derive an optimal or near-optimal solution. The numerical experiments were conducted using the developed mathematical model and genetic algorithm, and the insights derived from the numerical experiments are as follows.

The results showed that profit maximization can be achieved via changes in the daily number and interval of operations along the designated route. The daily number and interval of operations should be appropriately determined by reflecting the characteristics of the tourist demand. As many pantograph-type wireless chargers are installed as possible as they can replace the energy consumed for one operation. They are installed at multiple suitable stops and can maintain the upper and lower limits of battery’s SOC.

In addition, the sensitivity analysis was performed to verify the hypothesis that the system design of the entire electric city tour service could change depending on the tourist demand from those who want to use the city tour bus service, and the insights derived are as follows. As the daily number of operations increases, both the revenue due to tourist demand and the costs of battery charging and replacement increase. A similar result was for the changes in the operation interval. When the operation interval is shortened, then both the revenue and costs of the bus purchase and battery purchase are reduced. Therefore, it is necessary to determine the optimal daily number of operations and the operation interval using quantitative and mathematical methods because the values of the daily number and interval of operations are significantly influenced by the revenue and various kinds of cost. Since the revenue and costs conflict, it is necessary to determine the appropriate daily number of operations and the operation interval.

Through this research, an algorithm for the optimal system design of an electric city tour bus using pantograph-type wireless charging, which is a rapid wireless charging method, was successfully developed. In the future, a study on the design of an electric vehicle system suitable for this context will be conducted by considering a plug-in type low-speed wired charging method or a ground-based fast wireless charging method together. In addition, the environmental costs were not considered in this study because the environmental impacts differ depending on the electricity production method, and it is difficult to measure the environmental impacts of batteries. In the future, a study on the environmental costs of electric city tour buses will also be conducted.

For sustainable tourism initiatives considering the environment, it is necessary to introduce an electric city tour bus system. However, since high initial investment costs are required, government subsidies can accelerate the introduction. In addition, when the government supports research on electric buses, it will be possible to develop and quickly apply an efficient operating system.