Charging Ahead with E-Buses: Benefits, Costs, and Transition Roadmap

Abstract

This paper reaches a recommendation for the 10-year e-bus transition roadmap for New York City. The lifecycle model of emission reduction demonstrates the ecological and financial impacts of a complete transition from the current diesel bus fleet to an all-electric bus fleet in New York City by 2033. This study focuses on the NOx pollution, which is the highest among all major cities by Environmental Protection Agency (EPA) and greenhouse gases (GHG) with annual emissions of over five million tons. Our model predicts that switching to an all-electric bus fleet will cut GHG emissions by over 390,000 tons and NOx emissions by over 1300 tons annually, in addition to other pollutants such as VOCs and PM 2.5. yielding an annual economic benefit of over 75.94 million USD. This aligns with the city mayor office’s initiative of achieving total carbon neutrality. We further model an optimized transition roadmap that balances ecological and long-term benefits against the costs of the transition, emphasizing feasibility and alignment with the natural replacement cycle of existing buses, ensuring a steady budgeting pattern to minimize interruptions and resistance. Finally, we advocate for collaboration between government agencies, public transportation authorities, and private sectors, including electric buses and charging facility manufacturers, which is essential for fostering innovation and reducing the costs associated with the transition to e-buses.

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Yang, A. , Wan, K. and Jin, A. (2024) Charging Ahead with E-Buses: Benefits, Costs, and Transition Roadmap. Open Journal of Applied Sciences, 14, 2717-2748. doi: 10.4236/ojapps.2024.149178.

1. Introduction

1.1. Background

The growing recognition of environmental sustainability’s significance and the pressing imperative to address climate change have spurred a worldwide shift towards eco-conscious practices and policies [1]. This trend is particularly evident in urban transportation, where there’s a marked surge in the use of battery-operated vehicles [2]. Governments worldwide are promoting green commuting options, like metro systems, to their citizens. Despite these strides, further steps are essential. A critical initiative in this direction is the replacement of diesel buses with their electric counterparts. E-buses offer the dual benefits of being both environmentally friendlier and potentially more cost-effective. Thus, formulating a thorough strategy for this transition is vital.

1.2. Problem Statement and Analysis Process

This report is to outline a comprehensive 10-year transition roadmap for the adoption of e-buses in metropolitan areas. Our approach is described in three phases, as illustrated in Figure 1. We chose New York City, the largest urban hub in the U.S., as a primary case study to demonstrate our model. Task 1 focuses on assessing the environmental benefits of transitioning to a fully electric bus fleet. Task 2 delves into the financial implications of this shift. Building on the findings of the first two tasks, Task 3 employs a constrained optimization model to formulate an optimal 10-year transition plan. The model is applied to three diverse U.S. cities—New York City, Chicago, and San Diego, to evaluate its efficacy across different geographic contexts.

Figure 1. Flow chart of analysis process.

Our research adopts a data-driven approach. To estimate the ecological and financial outcomes of transitioning to e-buses, we gather a diverse array of data sets. These include emissions statistics for greenhouse gases and other key air pollutants from both diesel buses and e-buses, urban bus ridership figures, bus procurement costs, and expenses related to charging infrastructure. To analyze this data, we utilize various mathematical models and algorithms. For instance, we employ the K-means clustering algorithm to benchmark air quality in the top 20 U.S. cities. In addition, ridge regression is used to forecast future trends of model variables.

2. Task 1: Ecological Benefits of Transitioning to E-Buses

To create a model to estimate the ecological consequences of transiting to an all-electric bus fleet, we proceed in two steps: 1) Estimate the emission reduction of air pollutants, which include greenhouse gases and five other major air pollutants; 2) Estimate the economic value of emission reduction in terms of US dollars.

2.1. A Lifecycle Model of Emission Reduction

To estimate the emission reduction from bus electrification, we develop a lifecycle model by comparing emissions from both the production and the operation phases of e-buses and diesel buses. Specifically,

(1)

The essence of this framework can be seen in Figure 2. This figure demonstrates that although e-buses have zero emission during their operation phase, their total life cycle emission is not zero. This is because emissions exist during the electricity generation and battery production phases. Because emissions from vehicle production (excluding battery production) are common to both e-buses and diesel buses, they cancel out when calculating the emission reduction. Finally, we need to include emissions from diesel bus operation and diesel production to derive the emission reduction.

Figure 2. A lifecycle model of emission reduction.

2.1.1. Model Assumptions and Variable Definition

Before we specify our model, here are the key assumptions and their justifications:

Assumption 1. Lifecycle emissions from diesel buses and e-buses include those emitted during the following three phases: 1) The production phase (vehicle production for both diesel buses and e-buses, but battery production for e-buses only); 2) The fuel or energy production phase (either diesel production for diesel buses or electricity generation for e-buses); 3) the operation phase. This is the most critical assumption of this lifecycle model of emission reduction. Emissions from both operation and non-operation phases of buses are both important contributions of the total emission. It is particularly important to consider non-operation emissions of e-buses because they typically generate zero emissions when in use. Such lifecycle emission assessment approach has been adopted in previous research on bus electrification (see [3]).

Assumption 2. Emissions from vehicle production for a diesel bus is identical to emissions from vehicle production for an e-bus.

The major steps in producing a bus involves chassis production, body production, powertrain production. They are fairly similar in the overall production process if the same size and materials are used [4], and therefore are often assumed to be identical when assessing emission reduction of e-buses (e.g., see [3]).

Assumption 3. Emissions from e-bus operation is zero.

E-buses are often referred to as zero-emission buses because they are run on batteries. The electricity used to charge e-buses may not be generated with zero emission, but they are already included in the electricity generation emissions in this model.

Assumption 4. Lifecycle emissions of buses include the following six major emissions: Green-house Gases (GHG), NOx, Volatile Organic Compounds (VOC), PM10, PM2.5, and SO2.

To evaluate the ecological impact of bus electrification, we consider these six major contributors of emissions. GHGs are gases in the earth’s atmosphere that trap heat. Scientific studies have shown that greenhouse gases are the cause of global warming and climate change. GHGs include carbon dioxide CO2, Methane CH4, Nitrous oxide N2O, and fluorinated gases (See the definition of GHG on EPA’s website: https://www.epa.gov/ghgemissions/overview-greenhouse-gases). In environmental studies, GHG emission factors are often expressed as Carbon Dioxide Equivalent, i.e., CO2eq to capture the fact that there exist multiple greenhouse gases. Note that CO2 contributes to 79% of GHG emissions from human activities in the U.S. in 2021 (EPA website).

In addition to GHG, we also consider five major criteria air pollutants associated with vehicle production and operations: NOx, Volatile Organic Compounds (VOC), PM10, PM2.5, and SO2. According to EPA’s website, air pollution emitted from transportation contributes to poor air quality, leading to negative impacts on the health and welfare of people. Major pollutants include particulate matters (PM), nitrogen oxides (NOx), and volatile organic compounds (VOC). Most notably, the transportation sector is responsible for about 45% of NOx total emissions inventory in the U.S. We also include sulfur dioxide (SO2) because it is an additional major air pollutant from coal-fired electricity generation.

The variables used in Problem 1’s model are listed in Table 1.

Table 1. Variable definition.

Notation

Description

Reduction of emission i

Diesel bus emission i

E-bus emission i

Diesel bus emission i during diesel production

Diesel bus emission i during operation

E-bus emission i during electricity generation

E-bus emission i during battery production

Economic cost of emission i

2.1.2. Model Specification

Our lifecycle model of emission reduction can be expressed as:

(2)

As shown in Figure 2, the emission reduction comes from four components: 1) Diesel production emission; 2) Diesel bus operation; 3) Electricity generation for e-bus; 4) Battery production for e-bus.

(3)

where i indicates six emissions shown in Figure 2. Next, we conduct analysis by splitting the six emissions into two groups: GHG and criteria air pollutants.

2.1.3. Greenhouse Gas (GHG) Emission Reduction

The GHG emission reduction is calculated by

(4)

The equation models the difference between the green house gas emission of diesel bus and electric bus. There are 2 main factors that will affect the emission of greenhouse gas of a diesel bus: the operation of the bus and the diesel production. On the other hand, the electrical bus produce green house gas mainly through production of batteries and the GHG emitted while generating electricity. Therefore, we can substitute the variables above to have a more detailed formula for the amount of green house gas emission.

In the following calculation, GHG emission is calculated as the number of grams of Carbon Dioxide Equivalent, i.e., CO2eq.

  • Diesel production The diesel production GHG emission takes the medium of the green-house gas emissions from three European studies, which is 15.8 grams per mega joule per bus [5]-[7]. We convert it to 385.26 grams per mile per bus by assuming that 1 mega joule produces 1 gallon of diesel, which in turn supports 6 miles of bus operating distance.

  • Diesel Operation The diesel operation GHG emission is 2680 grams per mile per bus [8].

  • Battery Production The battery that New York City currently is using for its 15 electric bus is LiNiCoMn Lithium ion batteries. These batteries produce an average of 85,000 carbon dioxide equivalent gram per Kilowatt hour (KWh). We further assume that e-buses adopted in New York City has a lifetime of 12 years with an estimated annual mileage of 36,500 miles. Over the 12 years, three batteries need to be used because a typical battery life is 4 years. After conversion, an e-bus produces about 174.66 grams per mile per bus.

  • Electricity Generation To calculate the electricity generation emission per bus in a city, we need to know the component of powers that generate electricity and their corresponding air pollutant emissions. Given the data from US Energy Information Administration, we can calculate the CO2 equivalent emission gram per kilowatt per hour.

(5)

where j = electricity generation source, j ∈ {coal, natural gas, nuclear, renewables}. These four sources contribute to over 99% of U.S. total electricity generation (see Table 2). We further assume that 1KWh runs an electric bus for 1 mile. This is a reasonable assumption as the typical range is between 0.67 miles to 2 - 3 miles. In the end, we get that the electricity generation emission is 257.59 grams per mile per bus in New York City. GHG emissions from electricity generation are also calculated for Chicago, San Diego, and US Average using their corresponding electricity power grid mix. The results are displayed in Table 2.

Table 2. GHG emission from electricity generation.

Electricity Generation Source

GHG Emission (g/mile)

US Average

New York City

Chicago

San Diego

Coal

820

16.20%

0.00%

14.20%

0.10%

Natural Gas

490

45.30%

50.40%

19.60%

27.30%

Nuclear

12

18.20%

22.60%

55.60%

9.40%

Renewables

30

19.60%

26.40%

10.20%

62.50%

Total Emission (g/mile)

--

362.87

257.59

222.21

154.47

In the end, we plug in the amount of GHG emission of the four categories into Equation (4) and the amount of GHG emission reduction is 2633.01 grams per mile per e-bus.

2.1.4. Criteria Air Pollutant Emission Reduction

Next we consider criteria air pollutant emission reduction for the aforementioned five air pollutants: NOx, VOC, PM2.5, PM10, and SO2. Following [3], pollutant emissions are mostly from diesel bus operation and electricity generation, while the emissions from vehicle production and battery production are ignorable for the five key air pollutants studied here. Therefore, the equation we will use to calculate emission reduction becomes

(6)

According to [3], the emission factors of the five major air pollutants during the phase of diesel bus operation are listed in the first column of the right panel in Table 3. The emission factors of e-buses depend on the electricity generation sources. Among the four major sources listed in Table 3, coal is the only one that leads to pollutant emission. In contrast, natural gas, nuclear, and renewables have ignorable emissions of air pollutants [3]. Therefore, we can calculate pollutant emissions by taking into account of the electricity power grid mix in a city (from Table 2) according to the following equation:

(7)

where j = electricity generation source, j ∈ {coal, natural gas, nuclear, renewables}.

Table 3. Criteria air pollutant emission from bus operations.

Electricity Generation Source

Bus Type and Location

Pollutant (g/mile)

Coal

Natural Gas

Nuclear

Renewables

Diesel Bus

E-Bus in New York City

E-Bus in Chicago

E-Bus in San Diego

NOx

0.35

0

0

0

9.14

0

0.05

0.0004

VOC

0

0

0

0

0.09

0

0

0

PM2.5

0

0

0

0

0.18

0

0

0

PM10

0

0

0

0

0.28

0

0

0

SO2

0.37

0

0

0

0.04

0

0.05

0.0004

The results are displayed in Table 3.

2.1.5. Economic Benefit of Emission Reduction

In this section, we translate the emission reduction of GHG and air pollutants obtained earlier into economic benefit, specifically, into US Dollars (USD) according to the following equation:

(8)

where indicates six major emission components shown in Figure 2.

According to a World Bank report [9], the shadow prices of GHG (CO2eq) in the next ten years will be increasing. Both low and high estimates are displayed in Table 4.

Table 4. Shadow price of GHG from world bank 2017 guidance (USD/ton).

Year

2024

2025

2026

2027

2028

2029

2030

2031

2032

2033

Low Estimate

44

45

46

47

48

49

50

51

52

53

High Estimate

87

89

91

94

96

98

100

102

105

107

Economic damages of air pollution is estimated based on a data source from European Commission [10], which is shown in Table 5. These pollutant prices are calculated as the average of EU 28 countries with the currency converted from Euro to USD.

Table 5. Pollutant price from EU 28 countries in 2019 (USD/ton).

Pollutant

NOx

VOC

PM2.5

PM10

SO2

Average

23,856

1344

426,720

24,976

12,208

Plugging in the amount of GHG and pollutant emission reduction (in g/mile) obtained earlier, we then use Equation (8) to calculate the economic value an e-bus would generate per mile of driving. The detailed results will be illustrated in the next section.

2.2. Results and Analysis

2.2.1. Ecological Benefits of Transitioning to an All-Electric Bus Fleet

According to our earlier calculations in Section 2.1, we have the ecological implications of transitioning to e-buses in the unit of per mile per e-bus. Now further assuming that the annual mileage of buses is 365,000 miles (=10 hours per day × 10 miles/hour × 365 days), we can calculate the annual ecological implications of converting a diesel bus to an e-bus. The estimated ecological benefits per e-bus conversion are displayed in Table 6.

Table 6. Ecological benefits of NYC bus electrification (per e-bus per year).

Pollutant

NOx

VOC

PM2.5

PM10

SO2

GHG

Total

Emission Reduction (ton/year)

0.334

0.003

0.006

0.010

0.001

96.10

--

Economic Benefit (USD/year)

7959.5

4.6

2757.3

258.8

17.9

7688.4

18,686.5

According to Table 6, the annual GHG reduction per e-bus is 96.10 tons. With the GHG price increasing over the 10 years from 2024 to 2033 (see Table 4), the average annual economic benefit of GHG reduction will increase to $7688.4 per e-bus by year 2033. The annual pollutant reduction per e-bus is 0.355 ton, and the annual economic benefit of pollutant reduction is $10,998.1 per e-bus, bringing the total economic benefit of emission reduction to $18,686.5 per e-bus per year by 2033 (see Figure 3). Among the five air pollutants, NOx emission reduction contributes most to the overall emission reduction both in terms of weight and economic benefit as shown in Table 6.

Finally, we are ready to evaluate the total ecological benefits of transitioning to an all-electric bus fleet in New York City. To do so, we assume the fleet size is 4064 (according to our prediction of bus ridership in 2033, see Section 3 for details). The total emission reduction and economic benefit are shown in Figure 4.

Figure 4 shows that the total annual GHG emission reduction is 390,570 tons after transition to an all-electric bus fleet in New York City by 2033 and the associated economic benefit is over $31.25 million. Benefits from pollutant reduction are also huge, making the total economic benefit to be over $75.94 million. Among the five air pollutants, NOx reduction contributes to over $32.35 million economic benefit.

Figure 3. Estimated ecological benefits of NYC bus electrification in year 2024-2033 (USD/ bus). The error bars indicate the high and low ranges of GHG benefit estimation.

Figure 4. Ecological benefits of an all-electric bus fleet in New York City (Year 2033).

2.2.2. Impact on Air Quality: K-Means Clustering of U.S. Top-20 Metropolitan Areas

After establishing evaluations of the impact of emission reduction in New York City, a standardized model is needed to assess the impact of bus electrification on the overall air quality. We adopted the K-means clustering algorithm to compare air quality and GHG emissions across top-20 metropolitan areas in the U.S. in 2022 (see Table 7 for the data). By doing this, we will understand how New York City’s air pollution and GHG emission compare to other cities before and after e-bus transition.

K-means clustering is an iterative, data-partitioning algorithm that assigns observations X to exactly one of K clusters defined by centroids, where K is chosen before the algorithm starts. In this algorithm, the data set X includes the air quality indexes of NO2, O3, PM10, PM2.5, SO2, and GHG of top-20 cities in the U.S. K is set to be 3 so that the algorithm will cluster these 20 cities into three groups. Let µk denote the centroids of the partitions and Ck denote cluster k. Then, the sum of squares of the distances from the centroid is represented by

Table 7. Air quality in U.S. top-20 metropolitan areas (2022, data source: EPA).

Core Based Statistical Area (CBSA)

2010 Population

NO2 (ppb)

O3 (ppm)

PM10 (µg/m3)

PM2.5 (µg/m3)

SO2 (ppb)

GHG (ton)

New York-Newark-Jersey City, NY-NJ-PA

19,567,410

20

0.074

27

21

11

5,464,914

Los Angeles-Long Beach-Anaheim, CA

12,828,837

25

0.095

92

33

4

10,543,740

Chicago-Naperville-Elgin, IL-IN-WI

9,461,105

17

0.074

134

30

45

1,910,900

Dallas-Fort Worth-Arlington, TX

6,426,214

14

0.082

82

27

16

3,745,116

Philadelphia-Camden-Wilmington, PA-NJ-DE-MD

5,965,343

14

0.07

50

23

7

1,408,892

Houston-The Woodlands-Sugar Land, TX

5,920,416

18

0.084

140

27

14

192,444

Washington-Arlington-Alexandria, DC-VA-MD-WV

5,636,232

15

0.066

36

17

3

291,407

Miami-Fort Lauderdale-West Palm Beach, FL

5,564,635

13

0.068

104

22

2

4,656,432

Atlanta-Sandy Springs-Roswell, GA

5,286,728

16

0.069

48

19

4

323,653

Boston-Cambridge-Newton, MA-NH

4,552,402

12

0.07

36

17

9

524,680

San Francisco-Oakland-Hayward, CA

4,335,391

13

0.068

38

24

15

410,374

Detroit-Warren-Dearborn, MI

4,296,250

14

0.071

77

33

108

21,144,031

Riverside-San Bernardino-Ontario, CA

4,224,851

29

0.105

1547

32

3

1,349,415

Phoenix-Mesa-Scottsdale, AZ

4,192,887

26

0.081

431

33

5

15,842,569

Seattle-Tacoma-Bellevue, WA

3,439,809

16

0.075

33

69

3

1,002,377

Minneapolis-St. Paul-Bloomington, MN-WI

3,348,859

12

0.061

118

19

15

1,459,487

San Diego-Carlsbad, CA

3,095,313

15

0.079

196

17

1

3,130,578

St. Louis, MO-IL

2,787,701

10

0.076

175

24

44

771,495

Tampa-St. Petersburg-Clearwater, FL

2,783,243

9

0.067

53

16

71

6,217,739

Baltimore-Columbia-Towson, MD

2,710,489

15

0.069

20

16

3

1,002,377

US Top-20 City Average

5,821,206

16.15

0.0752

171.85

25.95

19.15

4,069,631

(9)

where J(Ck) denotes the sum of squares of the distances from the centroid. The goal of the algorithm is to solve the following optimization problem:

(10)

(11)

The solution algorithm for K-Means is defined as follows:

  • Standardize the original data. Formalize the given data with Equation (12) to make their mean as zero and variance as one:

(12)

where ,

  • Initialize k centroids. Initially, randomly choose k observations as centroids.

(13)

  • Assign given points. For a given cluster assignment C of the data points, compute each point’s distance to each centroid. Assign these points according to their least distance to the nearest centroid.

(14)

  • Update Centroid. Recalculate each cluster’s mean value and replace the centroid with this mean value until every centroid does not change.

(15)

Otherwise, repeat the Assign Step and Update Step until the convergence condition is satisfied.

The K-means clustering algorithm gives us the following three levels of air pollution in comparison within the top-20 metropolitan areas, as shown in the right panel of Figure 5. The minimum, the lower line, the upper line, and the maximum are calculated for each of the six air pollutants. The lower line and the upper line are calculated as the mean of the pollutant indicators of the centroids. Falling below the lower line, between the lower line and the upper line, and above the upper line represent low, medium, and high level of air pollution.

Figure 5. Air quality: New York City vs. US top-20 city average.

In order to visualize the air quality comparison between New York City and other cities, we plot a radar chart. Because the six air quality measures have highly different ranges, we scale all measures into a common interval of [0, 1] with the minimum being 0 and the maximum being 1. The left panel of Figure 5 indicates that New York City has low levels of O3, PM10, PM2.5, and SO2 as they fall under the lower line. This is likely due to the lack of coal-fired electric generation in the region (as indicated in Table 2). However, New York City has the highest level of NO2 pollution (above the upper line) and second highest emission of GHG (above the lower line).

According to our earlier analysis, a complete bus electrification in New York City will generate an annual reduction of 1356 tons of NOx emission, 13.8 tons of VOC emission, as well as 390,570 tons of GHG emission. Because O3, known as ozone, is a secondary air pollutant formed as a result of photochemical reactions between primary pollutants, such as nitrogen oxides (NOx) and volatile organic compounds (VOC), reduction of NOx and VOC will lead to reduced O3.

3. Task 2: Financial Implications of Transitioning to E-Buses

Task 2 requires us to construct a model to predict the financial implications of transitioning to e-buses. We model a 10-year horizon to estimate the cost increase needed to acquire and maintain an e-bus fleet compared to the current diesel bus fleet.

In order to make these calculations, we separated the considerations into two categories: Initial and operational prices. Initial prices refer to variables such as the capital cost of one electric bus, or the price of purchasing one electric charger. Operational prices refer to costs such as the annual electricity and diesel for a bus, or the maintenance of the electric chargers.

3.1. A Total Cost of Ownership (TCO) Model

3.1.1. Variable Definition

The variables that will be used in Task 2 are listed in Table 8.

Table 8. Variable definition.

Notations

Descriptions

Notations

Descriptions

Set of years 2024-2033

Fleet size in year t

Purchase price of an e-bus

Operation price of an e-bus

Purchase price of a charger

Purchase price of a diesel bus

Operation price of a diesel bus

Ridership in year t

Current amount of buses in NYC

Price of electricity annually needed

Maintenance price of electric bus

Maintenance price of chargers

Cost of materials

Cost of labor

Price of diesel annually needed

Maintenance price of diesel bus

Maximum ridership of bus in a day

Maximum traffic in a day

Maximum service years of electric buses

Maximum service years of diesel buses

3.1.2. Model Creation

We construct a Total Cost of Ownership, TCO model to analyze the increased capital needed to maintain and transition to a fully electric bus system. Various factors are considered, including the price of purchasing and maintaining chargers, the slow decrease in the popularity of public transportation, and the prices of electricity and diesel. We calculated the difference between the TCO of a fully electric bus model and the TCO of a fully diesel bus model to analyze this increased capital. This difference can be summarized as

(16)

where represents the difference in TCOs of the electric and diesel bus models, and are the electric bus model’s TCO and the diesel bus model’s TCO in year t, respectively. Furthermore,

(17)

where is the fleet number in year t, is the possible max fleet charging at the same time in year t, is the purchase price of an e-bus, is the operation price of an e-bus, and is the purchase price of the charger. Similarly,

(18)

where is the purchase price of a diesel bus and is the operation price of a diesel bus.

3.1.3. Bus Fleet Size Needed

In order to create this model, we analyzed the number of people who used the MTA bus system in years 2012 to 2019. We noticed an overall decrease in the popularity of using buses, which means in the future, it would not be necessary to purchase as many electric buses as the current fleet of buses. We were then able to predict the ridership in Table 9:

Table 9. Predicted amount of people taking buses.

Year

2023

2024

2025

2026

2027

2028

2029

2030

2031

2032

2033

Ridership (Nt)

616,639

598,368

580,098

561,827

543,556

525,286

507,015

488,745

470,474

452,203

433,933

We can express the fleet of buses needed as the amount of people decreases as

(19)

where is the ridership of year t and is the current amount of buses in NYC. As of 2021, there were 5780 buses in the MTA fleet, and due to the aftermath of Covid-19 and lack of public transportation usage we feel it is safe to assume there would be little change in the fleet size as the city finishes its recovery from the pandemic [11]. Applying the above data to this formula provides the predicted bus fleet in Table 10:

Table 10. Predicted amount of people taking buses.

Year

2023

2024

2025

2026

2027

2028

2029

2030

2031

2032

2033

Bus Fleet

5780

5603

5432

5261

5090

4919

4748

4577

4406

4235

4064

3.1.4. Operational Costs E-Bus

We consider both the operational costs of diesel and e-buses in this model. In order to calculate the operational costs for a year of operation for the e-bus system, we use the following equation:

(20)

where refers to the price of electricity, refers to the price of maintaining an electric buses, and refers to the price of maintaining chargers.

  • Annual cost of electricity: In order to find the price of electricity per year, we will need to find the total mileage of a NYC bus every year. At its highest usual speed, an NYC bus travels at 10 miles per hour, and bus operators work on a 10 hour shift [11]. Therefore, we can extrapolate that annually, we can expect an NYC bus to have 10 mph × 10 hours × 365 days = 36,500 miles of mileage every year.

Electricity averages around 0.08 cents per kilowatt, and an electric bus uses approximately 2.8 kilowatts per mile. Therefore, the cost of electricity for one electric bus on average can be represented as 2.8 × 0.08 × 36,500 ≈ 8000 dollars per year [12].

  • Maintenance of Chargers: The price of maintaining one charger can be written as

(21)

where is the cost of materials, and is the cost of labor. The material per charger will cost 11,500 dollars and require 72 hours of labor, which with a fully-loaded electrician salary of 87.85 dollars per hour results that the maintenance per charger is approximately 17,825 dollars. However, each charger can supply electricity to multiple buses around the clock. We assume one charger is needed for every four electric buses. The average cost for charger maintenance is 4456 dollars per bus [12]. Therefore,

(22)

Diesel Buses

The operational costs of a diesel bus per year can be expressed as

(23)

where represents the price of diesel, and represents the price of maintaining a diesel bus.

Price of diesel: From our calculations that a bus travels an annual 36,500 miles, we can write that. given today’s rates, the total cost of diesel evaluates to about 28,000 dollars per year [12]. Therefore,

(24)

3.1.5. Purchasing Cost

E-bus The MTA lists the price of a standard E-bus as 1,033,000 dollars. Therefore, the price of purchasing the needed E-buses in year t can simply be written as

(25)

Diesel Bus The MTA lists the price of a standard diesel bus as 635,000 dollars. Therefore, the price of purchasing the needed diesel buses in year t can simply be written as

(26)

3.1.6. Maximum Fleet Size Needed

Clearly, having the chargers necessary to charge every single one of the buses in our fleet would be far too costly and illogical. We use data from the George Washington Bridge to extrapolate the total bus needs of the city. On the George Washington Bridge, the maximum amount of people on the bridge is 18,500 at 5 p.m, as seen in the following Figure 6:

Figure 6. Hourly traffic on George Washington Bridge.

As the bridge reportedly accounts for 8 percent of the traffic in the city, we can calculate the total traffic in NYC. Furthermore, a reported 12 percent of vehicles in the city are buses, so we can calculate the maximum amount of people in buses in one hour in NYC as

(27)

where represents the maximum traffic recorded and represents the maximum ridership of buses at the same time. From this, we evaluate that a maximum of 345 buses will be needed at one time since a standard NYC bus has a limit of 80 people [12].

3.1.7. Cost of Charging Facilities

An MTA report stated that it costed them 50 million dollars for their purchase of charging facilities needed for 60 electric buses [13]. Therefore, the cost of purchasing a charger per bus is approximated at 50,000,000/60 ≈ 833,000 dollars. We then conclude that given the current maximum number of buses that need to be charged at once, i.e., 345 from above estimation, purchasing chargers will cost 287,385,000 dollars.

3.1.8. Future Prediction

The general formula of polynomial fitting can be represented with this equation:

(28)

where x is the predictor variable, y is the response variable, is the coefficient, and k is the order of the polynomial.

Finding the best parameters of this polynomial function aims to minimize the residual error between the value estimated by the polynomial and the actual data . norm of this residual error is then optimized by n training samples:

(29)

To obtain the minimum of this objective function, the partial derivatives of R2 with respect to the coefficients ai is derived:

(30)

which is expressed in matrix form as:

(31)

This is a Vandermonde matrix and can be rewritten as:

(32)

which is Solving this equation yields

(33)

The regularization term is applied to avoid the over-fitting problem. Here we use the L2 norm of the coefficient as the penalty:

(34)

where λ is inferred by sensitivity analysis to control the effects of regularization.

In Figure 7, it is evident that when , decreasing λ further by factors of 10 has very little impact on the resulting regression line. Even when λ is increased by a factor of 10 several times, the mode is still relatively insensitive to this change. We found that λ is obtained to be 0.1.

Figure 7. Prediction of future volume.

The solution to the optimization is calculated by

(35)

3.2. Results and Analysis

3.2.1. Solution of the TCO Model

In our data, we found that the cost of maintaining a diesel bus and an electric bus were extremely similar. Therefore, it will not impact our calculation of the difference in TCOs. By substituting the values we found into the original TCO model, our findings are summarized in Figure 8.

Because of the decrease in popularity of buses, the difference in cost of ownership will decrease further every year. While buses may be losing popularity in New York City, we firmly believe that the introduction of completely net-zero emission buses will promote and give New Yorkers a reason to ride.

Years

TCO ($/year)

2023

2,471,930,084

2024

2,398,958,688

2025

2,325,987,291

2026

2,253,015,895

2027

2,179,193,674

2028

2,106,222,277

2029

2,033,250,881

2030

1,960,279,485

2031

1,886,475,088

2032

1,813,503,692

2033

1,740,532,296

Figure 8. TCO difference and components.

3.2.2. Net Benefits in the Long Run

By joining the ecological benefits and economical costs together, our findings support the conclusion that, after the initial investment of charging facility construction is made, switching to electric bus fleet is more beneficial in the long run. For New York City, the post-transition yearly-average net gain per bus is estimated to be

(36)

where is the estimated ecological benefits per e-bus in year 2033 (Table 6).

This estimation is based on the current purchase price of e-buses and charger maintenance costs. In the long term, we expect these costs will drop significantly with the technological advances and economy of scale following the broader adoption of electric buses. Therefore, we expect the positive gains of future e-bus fleet can only be larger.

4. Task 3: Optimizing the 10-Year E-Bus Transition Roadmap

Given the ecological benefits and financial feasibility of switching from traditional diesel vehicles to electric buses, we build a mathematical model that can aid to craft transition roadmaps for different cities. The plan aims to transition into a fully e-bus fleet by the end of year 2033. It aligns closely with the natural replenishment process of the existing bus fleet. As illustrated in Figure 9, the model optimizes the transitional process to balance the dual objectives of increasing ecological benefits and lowering the associated financial costs. It also takes the practicality of government budgeting into consideration by spreading the purchases of new buses into more years and mitigating large budget variation from year to year.

Figure 9. Optimization model aligns with the replenishment process of the existing bus fleet and harvests the benefits at controlled cost. The e-bus icon is downloaded from Adobe.

4.1. Assumptions

Assumption 1. The city has an active diesel bus fleet serving the current public transportation needs. The operational capacity of the bus program and its future growth are exogenous to our transition plan. The in-transition fleet and the eventual fully electric one run the same pre-determined bus program in terms of bus number and capacity, except in a more eco-friendly way.

Justification: Our model targets to build a transition roadmap for an established metropolitan area with a population over half million people. Public bus programs are usually determined by people’s transportation needs and city’s budget constraints. This report does not have the scope of completely redesigning the capacity and routes of the metropolitan’s bus program.

Assumption 2. Each bus has a limit of maximum service year, after which it must be retired and does not have further redemption value. The existing bus fleet has distributed ages that warrants a natural replenishment procedure.

Justification: The decommissioning and replenishing is mandatory for safety and liability reasons.

Assumption 3. The transition plan can early-retire some diesel buses before they reach maximum service year.

Justification: Early retirement on selected buses is necessary to achieve the targeted full transition by the end of 10 years. Early-retired diesel buses are replenished with e-buses. Within the existing fleet, the model can early-retire those worst polluting buses.

Assumption 4. The full electric bus fleet has salvage value at the end of 10-year transition period. The salvage value of each bus, after an initial 10% discount, is assumed to be linearly proportional to its remaining service life and purchase cost.

Justification: Even though this planning model focuses on the 10-year transition period, it needs to incorporate the salvage value into consideration as part of the long-term planning. The linear depreciation model is one common method in financial accounting.

Assumption 5. The purchase of new electric buses are spread into years. The purchase in any year cannot be 20% more than the yearly average of the eventual target.

Justification: A practical roadmap needs to smooth the purchase and update into multiple years. The gradual transition helps to mitigate any potential resistance from stakeholders, and gives all teams more time to overcome the learning curves in operation and management.

4.2. Optimization Model

Optimization Objective and Constraints

The model runs constrained optimization with the aid of MATLAB [14] [15]. The concept of constrained optimization is demonstrated in Figure 10. The variables of the optimization model are summarized in Table 11. This model optimizes the decision variables , which are the numbers of new e-buses purchased in the coming 10 years.

The optimization objective is to minimize the net present value of the financial and environmental costs in next 10 years, net of the salvage value of the full e-bus fleet at the end of the period.

The optimization is subject to following constraints:

1) Mandatory target of full e-bus fleet at the end of 10 years.

2) Purchase in any year cannot be 20% more than the yearly average of the eventual target.

Figure 10. Constrained optimization model has objectives to maximize benefits and minimizes costs.

Table 11. Variable definitions.

Notation

Description

Notation

Description

t

1 to 10, representing year 2024-2033

Ne0

Initial number of electric buses

Nd0

Initial number of diesel buses

Nt

Total number of vehicles, including both diesel and electric buses

Le

Maximum service years of electric buses

Ld

Maximum service years of diesel buses

NDt

Number of buses at maximum service year

Pet

Forecasted purchase price of one e-bus

Pdt

Forecasted purchase price of one diesel bus

Cet

Yearly operation and maintenance cost of each electric bus, including electricity cost

Cdt

Yearly operation and maintenance cost of each diesel bus, including fuel cost

Ft

Average cost of building new charging facilities for each newly purchased electric bus.

Eet

Yearly ecological cost of one e-bus.

Edt

Yearly ecological cost of one diesel bus.

Gt

Government subsidies, modeled as the percentage of (Pet + Ft).

r

Annual discount rate, 5%

Nrt

Number of buses retired each year

Net, Ndt

Number of active electric, diesel buses

(37)

(38)

where operation, maintenance and ecological costs of active fleet

(39)

acquisition costs of new buses, including the construction costs of new charging facilities

(40)

and salvage value at the end of year 2033

(41)

4.3. Transition Roadmap for New York City

With the aid of this optimization model, we craft a roadmap to transition the mostly combustion engine bus fleet to a fully electric one in 10 years.

In this gradual transition plan, diesel buses retire, which are replenished by electric buses over years. The mix of buses in the fleet is illustrated in Figure 11 and Table 12. The downward trend of total fleet size is extrapolated from the shrinking trend of NYC bus ridership in years 2012 to 2019.

Figure 11. E-bus transition roadmap (left axis) and e-bus purchase schedule (right axis).

Table 12. 10-year roadmap: transition from a mostly diesel bus fleet to a fully e-bus fleet.

Year

2024

2025

2026

2027

2028

2029

2030

2031

2032

2033

Diesel Buses

5285

4804

4324

3843

3293

2635

1976

1317

659

0

Electric Buses

318

628

937

1247

1626

2113

2601

3089

3576

4064

4.3.1. Transition Schedule

Purchase of new electric buses (Figure 11) started at a relatively lower rate of around 309 vehicles per year in the first four years. They are allocated to partially replenish the retired vehicles as the total fleet size is shrinking.

In these first several years, no buses are retired before their maximum service age. This is due to the expensive purchase price of e-buses available to US cities as well as the high construction cost of charging facilities, which we will analyze in more details in later chapter.

The purchase will accelerate in year 2028 and stabilize at 488 e-buses per year in the last five years. This acceleration is necessary to achieve our target of full transition by year 2033, and it is bounded by our constraint to smooth the purchase budgeting over years.

4.3.2. Net Cost and Ecological Benefits

In this transition period, the metropolitan needs to make additional investment due to the relatively higher prices of e-buses and the extra cost of building charging facilities (Figure 12). This cost increases in year 2028 and 2029 when the purchases accelerate. On the other hand, the lower operation and maintenance cost of e-bus contributes to the downward trend of net cost in the other years when the new purchases are stable.

Figure 12. Net cost of the transition and the increasing ecological benefits.

More importantly, with the expansion of e-buses, the fleet will realize more ecological benefits year over year which is illustrated in the same Figure 12.

4.3.3. Smart Scheduling: Prioritized Decommission of the Worst Polluting Diesel Buses

The transition plan takes the working condition of buses and polluting situation of the city into consideration. It manages smart retirement-scheduling among buses of various polluting situations and city boroughs of different polluting levels (Figure 13). Starting from year 2028, it expedites the decommissioning of the heaviest pollution generating group. After its completion in year 2031, the second group is expedited. And then in year 2032, the third group is expedited.

Figure 13. Smart scheduling: worst pollution-generators are decommissioned earlier.

4.3.4. Government Funding as a Crucial Factor to the Transition

Government subsidies, such as the allocation to e-bus projects from the 2023 US Bipartisan Infrastructure Law will be crucial for the successful transition to an e-bus future. In the 10-year roadmap for New York City, we expected 50% of the transition cost will be shouldered by various government funding. This kind of government support is common among the cities that have been successful in achieving the transition to electric bus fleet, such as Shenzhen, China.

Without the needed government support, the transition cost can become prohibitively high for the transportation enterprise. Figure 14 shows the net cost could be as high as $567M in the peak year of 2029 if there was no extra government support.

Figure 14. Without extra government support, the net cost for transition can be prohibitively high.

4.3.5. Lower Cost Could Help to Realize Ecological Benefits Earlier

Compared with Shenzhen, China, the transition to the e-bus future is financially more challenging for US cities. The main concern will be the significantly higher e-bus purchase price and construction cost of charging facilities.

We encourage transportation officials and private enterprises to be more innovative and competitive in lowering these costs. For instance, cities can import lower-priced e-buses, such as BYD, to reduce the cost and encourage domestic manufacturers to be more competitive. US government can provide more synchronized support to cities and bus manufacturers so that it is easier to achieve economy of scale and lowered costs for all stakeholders.

With the optimistic expectation of this success, by assuming the e-bus prices can be lowered by 30% and the charging facility cost can be cut to $150K per new bus, we use the same optimization model to construct an alternative 10-year roadmap, which significantly expedites the transition in the first several years (Figure 15). The purchase of e-bus is not only unequal over years, it is not monotonic. Instead, it started by purchasing 488 new e-buses in the first two years and then slows down to 200+ per year for another three years. Afterwards, it accelerates again to 488 buses per year in the last five years.

Figure 15. U-shaped purchase schedule: if the adoption cost can be reduced, the transition process can be expedited.

The accelerated purchase in the first two years is justified by the fact that the ecological benefits and operation savings can be harvested perennially after the one-time investment is made. As long as the cost is justified, it is beneficial to invest earlier. Meanwhile there is financial incentive to preserve the cash and utilize the existing bus fleet till the end of their service life. These two competing drivers lead to the U-shaped purchasing schedule in this alternative roadmap. The expedited replacement in the early years helps to decommission the worst polluting maker earlier (Figure 16).

Cities have different needs in their bus programs. Each city also has its unique mix of power sources, which contribute to varying ecological benefits from the transition to the e-bus future. Nevertheless, the same analytical methodology can be applied to other metropolitan areas, such as San Diego, CA and Chicago, IL. The roadmap of e-bus transition of each city is driven by its own unique situation of multiple factors (Figure 17 and Table 13)

Figure 16. With lower adoption cost and expedited transition, the worst pollution makers are decommissioned even earlier. Transition roadmaps for San Diego, CA and Chicago, IL.

Figure 17. E-bus purchase schedule for San Diego, Chicago, and New York City. Each city has its own transition roadmap, which is determined by the varying factors.

Table 13. 10-year roadmap of transition for San Diego, CA and Chicago, IL

Year

2024

2025

2026

2027

2028

2029

2030

2031

2032

2033

San Diego Diesel Buses

688

625

563

499

435

348

260

174

87

0

San Diego Electric Buses

48

94

141

189

237

308

380

451

522

593

Chicago Diesel Buses

1937

1761

1585

1403

1169

935

701

468

234

0

Chicago Electric Buses

77

153

229

312

446

580

714

848

982

1116

5. Model Evaluation and Discussion

5.1. Sensitivity Analysis

5.1.1. Roadmap Sensitivity to Future Ridership Trend

The baseline plan for New York City was built on a decreasing bus ridership trend, which was extrapolated from the surveyed data in years 2012 to 2019. On the other hand, one major benefit of transition to e-bus would be the reduction of air pollution. It is possible that cleaner and more eco-friendly electric buses might attract more bus riders, and reduce the need of private transportation and further reduce greenhouse gas emission and other air pollution. Shenzhen’s data shows, after transition to a full e-bus fleet, the bus ridership increased by 2% [3].

If the trend of bus ridership deviates from the historical trend, the implementation plan needs to have certain level of flexibility to adapt to the new reality. We analyze the NYC’s transition plan by modelling two different future scenarios of constant ridership and another one with 1% increase per year. The results (Table 14; Figure 18 for constant ridership & Figure 19 for increasing ridership) show that the transition roadmap can be easily adjusted and adapt to potential evolution of bus ridership.

Figure 18. Alternative roadmap for the scenario of constant ridership.

Figure 19. Alternative roadmap for the scenario of increasing ridership.

Table 14. Alternative roadmaps for the scenarios of constant and increasing ridership.

Year

2024

2025

2026

2027

2028

2029

2030

2031

2032

2033

Constant Ridership Diesel Buses

5278

4804

4324

3843

3363

2774

2081

1387

694

0

Constant Ridership Electric Buses

502

976

1456

1937

2417

3006

3699

4393

5086

5780

Increasing Ridership Diesel Buses

5285

4804

4324

3843

3363

2821

2115

1410

705

0

Increasing Ridership Electric Buses

553

1092

1630

2168

2706

3306

4069

4832

5595

6358

5.1.2. Sensitivity to Other Model Assumptions

The optimization model assumes one budget smoothing constraint that new purchase in any year cannot be 20% more than the average of the eventual target. This constraint turns out to be binding in the planning. Without this constraint, the model would tend to concentrate more of the purchase to the last year for most US cities. This is mainly driven by the high purchase price of e-bus, the expensive charging-facility construction cost, the preference to utilize existing buses to their maximum service year, as well as the time value of money. On the other hand, we believe this constraint is practically reasonable because significant variations in project budgeting might cause more resistance from stakeholders and even interruption in future execution. We test the sensitivity and robustness of this constraint by varying its tightness to 10% and 30%, which do lead to different roadmaps from the model (Figure 20). For a tightened constraint of 10% on budget variation, the e-bus purchases are spread to more and earlier years. For a relaxed constraint of 30%, the purchase schedule is concentrated more to the later years. These differences are expected and consistent with the intention of the constraint itself.

Figure 20. E-bus purchase schedule at different budget constraints.

The model assumes 5% yearly discount rate, which is based on the current interest rate in the US. The mandatory discount rate for public transportation projects may vary according to local laws and drift over time. Our testing of the model with discount rate from 3% to 12% barely yields any difference in the transition roadmap. The tested range covers most reasonable scenarios in foreseeable future.

5.2. Model Strengths

Our models are built with live logic and data from industry reports and research papers. They are highly relevant to the topic. It helps transportation officials, government planning entities, and general public to gain in-depth understanding of the topic and get guidance on the transition process.

The transition model is highly practical. It optimizes the balance between ecological benefits and net financial costs. The roadmap generally aligns with the natural replenishment process of existing bus fleet. For the purpose of long-term planning, it takes the salvage value into modelling formula. It also mitigates the variation in budgeting over 10 years.

The transition model is robust under various scenarios of analysis and sensitivity tests. This is rooted in the practical approach of the modelling that aligns with the natural replenishment process and constrains on fleet size and budget variation.

5.3. Model Weaknesses

We built our models with current data from environmental research and transportation industry reports, and conducted near-term forecasting. On the other hand, we recognize that the design and manufacturing of electric vehicles and charging facilities are at the frontier of technology innovation. The progress in this field can be fast and potentially interrupting. More in-depth and comprehensive investigations into the technological perspective of this subject could further strengthen the report.

6. Conclusion

The model includes a detailed transition roadmap for New York City, analyzing ecological benefits and financial costs, and outlines a step-by-step procedure for decommissioning old buses. It highlights the importance of government incentives in successful transitions for U.S. metropolitan areas. The model also addresses the challenges of acquisition costs and charging facility construction, calling for collaboration and innovation to reduce these costs and enhance financial feasibility. Similarly, we have developed practical and optimized roadmaps tailored to the unique public transportation needs and electricity sources of San Diego, CA, and Chicago, IL. The model’s robustness was also validated through sensitivity analyses across various scenarios involving bus ridership trends, budget constraints, and financial discount rates, with consistent results.

Appendix. A Report on Use of AI

OpenAI ChatGPT (Nov 5, 2023 version, ChatGPT-4)

Query1: Where can I find data on air pollutants for big cities in the U.S.?

Output: There are several sources where you can find data on air pollutants for big cities in the U.S.: The United States Environmental Protection Agency (EPA): The EPA’s Air Quality System (AQS) database contains data on ambient air quality monitoring from thousands of monitoring stations around the country. It includes data on criteria pollutants, such as particulate matter (PM2.5 and PM10), ozone (O3), sulfur dioxide (SO2), nitrogen dioxide (NO2), and carbon monoxide (CO). AIRNow is another EPA website that provides real-time air quality information. The American Lung Association: Publishes an annual “State of the Air” report which provides information about air quality in the U.S., including data on various pollutants for cities across the country. Local Environmental Agencies: State or city environmental protection agencies often have their own monitoring systems and publish data on local air quality. For example, the California Air Resources Board (CARB) provides detailed reports on air quality for California cities. International Organizations: The World Health Organization (WHO) collects and provides data on air quality, including measures from cities around the world. Scientific Data Repositories: There are various scientific data repositories such as the National Oceanic and Atmospheric Administration (NOAA) and NASA that provide atmospheric data which can be used to study air quality. Remember to check the date of the last data update to ensure the information is current. When using data for research or analysis, it’s also important to verify the data’s accuracy, completeness, and methodology to ensure it meets your needs.

OpenAI ChatGPT (Nov 5, 2023 version, ChatGPT-4)

Query2: What’s the relationship between ozone and VOC?

Output: Ozone (O3) at ground level, also known as tropospheric ozone, is not emitted directly into the air but is created by chemical reactions between oxides of nitrogen (NOx) and volatile organic compounds (VOC) in the presence of sunlight. Non-Methane Volatile Organic Compounds (NMVOCs) are a subset of VOCs that, as the name suggests, exclude methane (which is relatively less reactive) and are significant precursors to the formation of tropospheric ozone.

OpenAI ChatGPT (Nov 5, 2023 version, ChatGPT-4)

Query3: How many miles does a bus in NYC run on average in a year?

Output: The average annual mileage for a bus can vary based on the specific transit agency, the routes it services, and whether the bus is used for local or express routes. In the case of New York City’s Metropolitan Transportation Authority (MTA), which operates one of the largest bus fleets in the United States, a typical transit bus might average anywhere from 25,000 to 50,000 miles per year. Local buses that make frequent stops might be on the lower end of that range, while express buses that travel longer distances with fewer stops might be on the higher end. The MTA also operates 24 hours a day, which means some buses are in near-continuous use, contributing to higher annual mileage. For the most accurate and updated figures, one would need to refer to MTA’s operational statistics or contact them directly. These figures can change over time due to policy changes, changes in service levels, or fleet management practices.

OpenAI ChatGPT (Nov 5, 2023 version, ChatGPT-4)

Query4: How many buses are there in the New York City?

Output: The number of buses operating in New York City can vary based on the latest updates from the Metropolitan Transportation Authority (MTA), which runs the city’s public bus system. As of my last update, the MTA operated a fleet of around 5800 buses on more than 300 local and express routes. However, this number may have changed due to updates in the fleet, service changes, or policy decisions. For the most current figures, it’s best to refer directly to the MTA latest reports or their official website.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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