Urban Bus Network Electrification

Abstract

Electric busses are spreading in cities in hope of mitigating local air pollution. Currently, battery electric busses are more expensive and require novel operational methods to optimize their use (e.g., applying daytime charging, and operating trolleybuses). Despite these, the electrification of urban busses is usually ad-hoc, preliminary planning is superficial, and does not consider the relationships among bus lines. This chapter introduces a method regarding charging infrastructure planning, electric bus type selection, and cost estimation. Based on the characteristics of the vehicle, charging infrastructure, bus service (lines, timetable, etc.), and energy consumption, a line-group optimization is introduced, which is the main novelty. The method was applied in a case study considering static terminal and dynamic catenary charging. The results help operators to boost the electrification of the urban bus network.

1. Introduction

Electric buses help reducing local air and noise pollution, especially in cities [1, 2]. As the consequence of technological developments, especially in the battery industries, electric buses with high range are available in the market. Different bus types are used from high-capacity battery electric buses to trolleybuses without autonomous running capacity. The bigger the battery capacity is, the longer the distance covered autonomously is (Figure 1).

Figure 1.

Flexibility based on the autonomous range of electric buses.

Static (in the depot, at the terminus, or bus stops) and dynamic in motion (catenary) charging solutions are applied in the urban bus network. The exclusive use of depot charging results in higher battery requirements. To reduce battery capacity, buses are charged during daytime with static chargers at common terminals (Figure 2a) or in movement with dynamic chargers along common sections of bus lines (Figure 2b).

Figure 2.

Bus network characteristics: Asterisk (a), common section (b).

In practice, the bus network is more complex, including common sections, and terminals. Furthermore, there is a strong relationship between the number of electric buses and charging units, battery capacity, and charging power. The research questions are how big battery capacity is needed and how big charging power in static chargers or how long dynamic chargers is needed.

More than 100,000 electric buses are running in the world, mostly in China. According to the expectations, the market size will grow fast, and at the end of 2027 almost 700,000 battery electric buses will be on the roads [3].

Therefore, a charging infrastructure and electric bus fleet determination methodology were developed to minimize the total cost of deployment and the procurement costs of the charging infrastructure and buses. The novelty of the method is that the optimization is performed for the network and not for only one bus line. Practically, cost minimization can be performed for lines with the same terminus or with significant common section(s).

The remainder of this chapter is structured as follows. In Section 2, the literature is reviewed. The electrification methodology is described in Section 3. The application of the method in Budapest, as a case study, is summarized in Section 4. Finally, conclusions are drawn.

2. Literature review

Several researchers deal with electric buses, developing methods for infrastructure planning or elaborating operational methods to overcome the drawbacks of electric buses such as range limitation and longer charging time.

Baumeister et al. [4] dealt with the optimal design of the catenary system for trolleybuses considering the energy demand of vehicles and mileage. The method minimizes overhead line extension and development costs. In addition, Paternost et al. [5] investigated the power supply of the catenary network using a data-driven approach, in which the current and power of each traction substation are measured. A power supply estimating method was developed to evaluate future development; the energy consumption at sections can be estimated with an error of 7%.

For e-buses with static chargers, the location and charging capacity determination are the most studied areas. Lin et al. [6] dealt with evaluating and fitting the connections between transport and energy networks. It has been established that in order to minimize maintenance costs in terms of time and space, the construction of charging infrastructure, considering the attributes of the electric network, should be optimized. Wang et al. [7] gives an example of simultaneous optimization of charging power and battery capacity, while Wang et al. [8] dealt with static fast-charging systems. It was proved that pantograph charging could be used to minimize the capacity of the battery. They found that a 13% cost reduction can be achieved with the use of a fast-charging system instead of static, slow charging.

A location planning method for the terminal charger was developed [9], considering the distribution network but not considering other charging opportunities. Clustering algorithms and swarm optimization was used. It was stated that battery electric buses should be operated mostly in an urban environment because of the range limitation. However, e-buses can also be used in intercity and long-distance transport [10]. Though, it was found that 26–60 minutes break for charging should be applied, which can extend the travel time significantly.

The state of charge of the battery and the use of the battery highly influence the availability of the vehicle. Charging scheduling [11] and timetable redesign [12, 13] are widely accepted approaches in electric bus operation. Well-scheduled terminal charging helps e-buses to achieve similar availability to diesel buses [14]. Due to the fixed route and predictable passenger traffic, there is a huge advantage in the charging schedule of public transport vehicles. Therefore, the charging demand of vehicles can be estimated more easily than in the case of passenger cars. In this regard, Wang et al. [15] developed a charging strategy considering energy consumption and electric price alteration to ensure accurate and cost-optimal charging scheduling. Knowing these issues, Leou et al. [16] bring a niche in the research with the minimization of charging costs by shifting charging to off-peak periods. To manage the high grid load caused by charging, a stationary energy storage system can be installed. Using a state of charge (SoC) control strategy for a battery with a 40 kWh stationary energy storage, the momentary power demand from the electric grid can be reduced by more than 70% [17].

Based on the literature review, a timetable redesign is a used approach; however, it may reduce the service quality. Furthermore, usually, one type of charging infrastructure (static or dynamic) is investigated without considering the mixture of them.

In this research, our previous results will be used as a base. With the analysis of static and dynamic chargers, Csonka [18] found that either static or dynamic chargers are preferred for each line out of the equilibrium point, considering the charging infrastructure cost. However, the consumption of buses during a route and the vehicle scheduling were considered with a rough estimation. In this research, the energy consumption calculation was improved based on Szilassy and Földes’ study [19] to get more comprehensive results.

3. Methodology

As a basic principle, we considered the current bus lines and timetables. Static terminus charging and dynamic catenary charging were analyzed. Static chargers at intermediate stops were neglected as their use may require travel time alteration. To store the daily energy demand in buses, a high battery capacity is needed in each vehicle, that is expensive and heavy. Furthermore, one charging unit is needed for each bus at the depot that is not efficient in the case of a huge fleet. Therefore, static charging in the depot was only considered as supplementary charging, and buses were considered to have a smaller battery capacity to minimize the vehicle mass. Thus, the vehicles must be charged several times a day.

The same steps were identified in the application of electric buses with static chargers, and trolleybuses with dynamic catenary chargers. However, the calculation method can be different. The steps are as follows:

1. Modeling (physical and energy model)

2. Scenario building

3. Energy consumption calculation

4. Possible charging time determination

5. Charged energy estimation

6. Energy balance calculation

7. Calculating the number of vehicles needed

8. Determining the charging vehicles at the same time

9. Determining the charging devices (number of static chargers, sections of dynamic chargers)

10. Procurement cost estimation

3.1 Physical and energy model building

The energy model is presented in Figure 3, summarizing the energy losses from the energy grid to the drivetrain. The energy losses are expressed with efficiency rate in the case of energy loss during charging and during the power conversion to operate the auxiliary systems. In addition, the consumption rate expresses the loss from the battery to the drivetrain.

Figure 3.

Energy model.

Every bus stops (i,j ∊1…n, where n is the total number of stops) are considered as a node. Each section has a direction and connects two nodes. Each section is indicated by its origin and destination node, e.g., section ij. The smallest section is between two stops; the biggest section is between the two terminals. The more detailed the section division is, the more accurate the estimation is.

3.2 Scenario building

Different scenarios can be built by varying the applied vehicles and charging units. In the case of dynamic chargers, scenarios can be built by forming different catenary networks. The scenarios can be compared based on the cost.

3.3 Energy consumption calculation

The E_DEMAND,ij energy consumption is estimated between two charging points on a line; namely between terminus in the case of battery electric bus application and between two stops in the case of trolleybus application.

The energy consumption in a section can be estimated by calculating the running dynamics considering the acceleration force and speed on a route, and by calculating the auxiliary system consumptions [19]. Based on the two energy categories - E_DRIVE driving dynamic energy consumption and E_AUX auxiliary energy consumption -, the E_DEMAND total energy demand in kWh can be determined for each ij section (Eq. (1)).

$$E_{\mathit{\text{DEMAND}},\mathit{ij}}=E_{\mathit{\text{DRIVE}},\mathit{ij}}+E_{\mathit{AUX},\mathit{ij}}$$E1

The E_DRIVE driving dynamic energy consumption in a section is calculated by Eq. (2).

$$E_{\mathit{\text{DRIVE}},\mathit{ij}}=\left(\gamma +b_{\mathit{ij}}+e_{\mathit{ij}}\right)·l_{\mathit{ij}}$$E2

where γ is the consumption rate [kWh/km], which depends on the drivetrain (η_drive), and recuperation efficiency (η_recup); b is the braking loss [kWh/km]; e is the elevation loss [kWh/km], l is the length of the ij section [km]. The c consumption is a generalized correction value expressing the difference according to bus type and categories (e.g., single or articulated buses). The b breaking loss is estimated from the kinetic energy considering the number of stops in an ij section (Eq. (3)).

$$b_{\mathit{ij}}=\frac{s_{\mathit{ij}}·m_{\mathit{ij}}·v_{max,\mathrm{ij}}^2}{2·l_{\mathit{ij}}}$$E3

where s is the number of stops on the section, m is the mass of the vehicle on a section which may fluctuating due to the passenger load, and v_max is the maximum speed available on the section. The mass of the vehicle may alter in sections expressing the general passenger load. The e_ij elevation loss in a section is calculated from the potential energy (Eq. (4)).

$$e_{\mathit{ij}}=\frac{m_{\mathit{ij}}·g·∆h_{\mathit{ij}}}{l_{\mathit{ij}}}$$E4

where g is the acceleration of gravity [m/s²], ∆h is the height difference on a section [m].

According to the previous study [19], the E_AUX auxiliary energy consumption can be calculated based on the power and their usage time by Eq. (5). The power demand for cooling/heating the passenger compartment and tempering the vehicle battery is influenced by the temperature as well. For instance, the following consumers can be considered: HVAC (Heating, Ventilation and Air Conditioning) system, BTMS (Battery Thermal Management System), electric power steering, air compressor, doors, parking brake, and wiper system.

$$E_{\mathit{AUX}}=\frac{P_{\mathit{AUX}}}{{\eta }_{\mathit{pc}}·t_{\mathit{ij}}}$$E5

where t_ij is the travel time in a section; η_pc is the power converter efficience rate; P_AUX is the power demand of the auxiliary systems calculated by summing the power demand of the auxiliary systems.

3.4 Possible charging time determination

For electric buses with static charger: The t_ch periods spent a bus at a terminal are determined. Periods spent at the terminals are considered if the arrival or departure times are within the analyzed time interval, or the driver starts or ends the resting time within the time interval. Note that technology time for charging should be considered (e.g., approaching the charging station, connection time) thus, the possible charging time is shorter than the actual time spent at a terminal. Moreover, no need to analyze the whole day; rush hours may provide a good estimation as the charging demand is expected to be the highest. The longer the considered time interval is, the higher the reliability of the method is. Figure 4 depicts the running and possible charging intervals of different buses running on different lines. Terminal A is a common terminal; all the buses may charge there. Bus 1 must be charged at terminal A, bus 2 can be charged at terminal B and bus k can be charged at terminal 3.

Figure 4.

Possible charging intervals of buses.

For trolleybuses with dynamic catenary chargers: The t_ch exact time interval spent at in a section according to the timetable is determined.

3.5 Charged energy estimation

The charged energy by bus k at a charging facility (static charging station or dynamic catenary charging) is calculated by Eq. (6), considering the charging loss.

$$E_{\mathit{\text{CHARGED}}}=t_{\mathit{ch}}·P·{\eta }_{\mathit{ch}}$$E6

where t_ch is the charging time of a bus at terminal i or section ij, P is the nominal charging power at station i (static a charging) or on section ij (dynamic catenary charging), and η_ch is the charging efficiency rate, which expresses all the losses of battery charging. This consists of transformer losses, cable losses, battery monitoring system (BMS) losses, battery component resistance, and voltage drop on various electric components.

The battery capacity and the current SoC influences the chargeable energy. Namely, batteries cannot be overcharged (Eq. (7)).

$$\frac{E_{\mathit{\text{CHARGED}}}}{B}\le 1-\mathit{SoC}$$E7

where SoC is the state of charge of the battery; B is the battery capacity.

3.6 Energy balance calculation

The energy balance (ε_ij) of a bus in a section is the rate of energy demand and charged energy.

For electric buses with static chargers: The energy balance is calculated by Eq. (8).

$${\epsilon }_{\mathit{ij}}=\frac{E_{\mathit{\text{DEMAND}},\mathit{ij}}}{E_{\mathit{\text{CHARGED}}}}$$E8

ε_ij should be equal or higher than 1 in order to charge enough energy to cover the energy demand of the section. Additional time is needed; as the timetable is fixed, a so-called n_ts turn shift is applied for the bus.

If the n_ts turn shift is 1, bus k skips one departure. If the additional time is not enough to reach ε_ij ≤ 1, another turn shift is needed. Every turn shift requires an additional bus in the fleet. To analyze whether the energy balance is ε_ij ≤ 1, the calculation of charged energy (Eq. (6)) should be modified; the headway time is added to the charging time as many times as many turn shifts are needed (Eq. (9)).

$$E_{\mathit{\text{CHARGED}}}=\left(n_{\mathit{ts}}·t_{\mathit{hw}}+t_{\mathit{ch}}\right)·P_i·{\eta }_{\mathit{ch}}$$E9

where t_hw is the headway between k and k + 1 bus.

Figure 5 depicts a case when the turn shift is 1; each departure is shifted by one. Serving all of the original departures results in the need for an additional bus.

Figure 5.

The alteration of departures resulting from turn shift.

For trolleybuses with dynamic catenary chargers: Besides the battery charging, the running energy should be provided. The energy balance is calculated by Eq. (10).

$${\epsilon }_{\mathit{ij}}=\frac{E_{\mathit{\text{DEMAND}},\mathit{ij}}+B\left(1-\mathit{SO}{C}_i\right)}{E_{\mathit{\text{CHARGED}},\mathit{ij}}}$$E10

where SoC is the state of charge at the beginning of the section. If ε_ij ≤ 1 the battery can be fully charged at the end of the section.

Both in the case of static and dynamic charging, if the B is higher than the E_DEMAND, the bus can be applied. The current SoC of a bus usually is not lower than a minimum level (e.g. SoC = 20%). This condition is formulated by Eq. (11).

$$B·{\eta }_{\mathit{\text{batt}}}\ge E_{\mathit{\text{DEMAND}},\mathit{ij}}$$E11

where η_batt is the capacity utilization of a battery (if the required minimum SoC is 20%, η_batt is 0.8).

3.7 Calculating the number of vehicles needed

For electric buses with static chargers: The n_ebus number of e-buses needed is the sum of currently needed conventional buses and the number of turn shifts (Eq. (12)).

$$n_{\mathit{\text{ebus}}}=n_{\mathit{bus}}+n_{\mathit{ts}}$$E12

where n_bus is the number of currently needed buses.

For trolleybuses with dynamic catenary chargers: The n_tbus number of trolleybuses needed is not changed. The sections with a catenary system should be optimized in order to serve the line with the same number of vehicles.

3.8 Determining the charging vehicles at the same time

For electric buses with static chargers: The n_ch(t) number of charging buses at a terminal in period t (e.g., minute) can be calculated based on the number of buses staying at the terminal (Eq. (13))

$$n_{\mathit{ch}}\left(t\right)=\sum p\left(t\right)$$E13

Where p is the probability of charging, each bus at the terminal has a probability of charging. The probability value is determined according to the energy balance. A possible representation of the values is presented in Table 1. The possibility of a free charging unit can be increased by increasing the difference between p and max(ε) in each category because more chargers will be deployed. However, it reduces the utilization rate.

ε	0–0.29	0.3–0.39	0.4–0,54	0.55–0.74	0.75–0.79	0.8–1
p	0.3	0.4	0.7	0.8	0.9	1

Table 1.

Probability of charging.

For trolleybuses with dynamic catenary chargers: The n_ch(t) number of connected and charging trolleybuses at section period t is counted (Eq. 14)). A p probability is also introduced to express the probability that a vehicle is being charged in period t.

$$n_{\mathit{ch}}\left(t\right)=n_{\mathit{\text{tbus}},\mathit{ij}}\left(t\right)·p$$E14

where n_tbus(t) is the number of trolleybuses in the section at a given period. The considered t period should be small (maximum 1 minute) as the needed charging power is influenced by the vehicle trajectory. The peak power is given if all the vehicle in the section accelerates.

3.9 Determining the charging devices

In this step, we determine the number of charging devices at terminals and sections where a catenary system is needed.

For electric buses with static chargers: The n_d number of charging devices at a terminal should be able to serve the maximum demand for charging. It can be calculated based on the maximum number of charging buses in a period (Eq. (15)).

$$n_d=⌈max\left(\sum n_{\mathit{ch}}\left(t\right)\right)⌉+1$$E15

For trolleybuses with dynamic catenary chargers: A greedy-like deployment strategy is applied. The section should be selected for catenary deployment where the rate of vehicles can be served, and length is the highest.

If the charged energy on the whole line is more than the energy demand, there is no need to designate a new catenary section (Eq. (16)).

$$\sum E_{\mathit{\text{CHARGED}},\mathit{ij}}\ge \sum E_{\mathit{\text{DEMAND}},\mathit{ij}}+\sum B\left(1-\mathit{SO}{C}_i\right)$$E16

If the charged energy is not enough to cover the rest of the section(s) additionally catenary section(s) should be designated.

• Either the catenary system should be extended to select a neighboring section; in this way, the deployment cost can be minimalized,

• Or an individual section (without a neighboring section with catenary) should be selected (e.g., where the number of charged vehicles in the same t interval is high); in this way, the deployment cost may be higher as electricity grid investments may occur.

For procurement cost optimization, bidirectional catenary network deployment is suggested. With the summarization of the l_ij section lengths where the catenary system should be installed, the l_ch total length of dynamic chargers is given.

3.10 Procurement cost estimation

The estimated procurement cost is counted by Eq. (17) for electric bus purchase and static chargers’ deployment (P_ebus) and by Eq. (18) for trolleybus purchase and catenary network deployment (P_tbus).

$$C_{\mathit{\text{ebus}}}=n_{\mathit{\text{ebus}}}·c_{\mathit{\text{ebus}}}+n_{\mathit{ch}}·c_{\mathit{ch}}$$E17

$$C_{\mathit{\text{tbus}}}=n_{\mathit{\text{tbus}}}·c_{\mathit{\text{tbus}}}+l_{\mathit{ch}}·c_{\mathit{cat}}$$E18

where c_ch is the nominal cost of the static charger, c_cat is the nominal cost of a catenary, c_ebus is the cost of an electric bus, c_tbus is the cost of a trolleybus.

The C_grid grid development cost (Eq. (19)) is estimated based on the summarized peak power at a i terminus or in a ij section.

$$C_{\mathit{\text{grid}}}=P_{\mathit{\text{peak}}}·c_{\mathit{\text{grid}}}$$E19

where c_grid is the nominal cost of grid development, including power plant capacity extension and the development of the transmission and distribution network. P_peak is the peak power calculated according to Eq. (20).

$$P_{\mathit{\text{peak}}}=n_{\mathit{ch}}\left(t\right)·P$$E20

The more detailed cost data are available, the less approximated results are given. Note: additional infrastructure elements, such as charging devices in depot, maintaining, and repairing devices, were out of the scope of this study.

4. Case study

The method developed was applied as a case study in Budapest. Budapest is the capital of Hungary, with an extended public transport network. Besides underground and tram lines, there are approx. Two hundred fifty bus lines covering almost 3000 km and there are 15 trolleybus lines covering almost 100 km. In a general weekday, 2.5 million trips are made in which almost 50% done by buses or trolleybuses.

Eight bus terminals and seven bus line groups were analyzed. In the case of bus line groups, we investigated whether trolleybuses with dynamic catenary systems or electric buses with static terminal chargers are the most beneficial. Altogether 85 bus lines were analyzed.

4.1 Values of the variables and limitations

Timetable and vehicle scheduling at morning peak hours between 6 and 9 were investigated.

The γ consumption rate was estimated based on the general consumption given in [20]. In the case of a single vehicle, the consumption rate is γ = 0.9 kWh/km, in the case of an articulated vehicle it is γ = 1.3 kWh/km.

The v_max maximal speed was assessed based on the average speed achievable on an ij section.

• if $\overline{v}\le \mathsf{25}\mathsf{km}/\mathsf{h}$, then ${\mathsf{v}}_{\mathsf{max}}=\mathsf{30}\mathsf{km}/\mathsf{h}$,

• if $\mathsf{25}\mathsf{km}/\mathsf{h}<\overline{v}\le \mathsf{30}\mathsf{km}/\mathsf{h}$, then v_max = 40 km/h,

• if $\overline{v}>\mathsf{30}\mathsf{km}/\mathsf{h}$, then v_max = 50 km/h.

We considered the auxiliary systems given in Szilassy at Földes’ article [19]: HVAC, BMTS, air compressor, power steering, parking brake, wipers, doors, light, vending machine, and passenger information displays. For simplification, the same values were applied for single and articulated e-buses and trolleybuses. The temperature dependence of HVAC and BMTS systems is significant [20, 21]. To determine which temperature should be used during the calculation we analyzed the frequency of daily minimum temperature in winter and maximum temperature in summer between 2008 and 2019. In winter days, the chance is 16% that the daily temperature is lower than −5°C. The lowest degree was −16°C. In summer days, there is 4.2% chance that the daily temperature will be higher than 35°C. The highest degree was 39°C.

Our aim was to plan the network in the worst-case scenario. Thus, we investigated when the energy consumption is higher at lower or higher temperature. We applied step 3 in bus line 44 (articulated) and 144 (single). The estimated energy consumption is given at different temperatures in Table 2.

Line	Temperature [°C]
	−15	−10	−5	0	5	10	15	20	25	30	35
44	26.69	25.59	22.15	19.35	17.19	15.69	14.83	14.61	15.04	16.12	17.85
144	20.23	17.25	14.74	12.71	11.14	10.04	9.42	9.26	9.58	10.36	11.62

Table 2.

Estimated energy consumption at different temperature (example).

The energy consumption is higher in cold weather. We considered the energy consumption at −5°C. Accordingly, the chance that the energy consumption is higher than expected is 4% in a year. Approximately there are 15 days in a year, only in winter, when the e-buses should save some energy during a run (e.g., lower heating temperature in the passenger cabin).

The P nominal charging power of the catenary network was 100 kW. In the case of static chargers, three different nominal power was considered during the scenario building, P_i = [100, 300, 450] kWh. For a limitation, one type of charging power is applied at a terminus. The η_ch charging loss was 0.85 for e-bus at a static charger and 0.7 for trolleybuses at a dynamic charger.

Two-two vehicles with different battery capacity (B) were considered. We assumed that the useful battery capacity is half of the nominal one. The considered battery capacity and the procurement price of one vehicle are summarized in Table 3. For simplification, a static vehicle mass was used without considering the passenger load alteration; m vehicle mass is 17 tons for single vehicles and 29 tons for articulated vehicles.

		Battery capacity [kWh]		Procurement cost [EUR]
		nominal	useful
e-bus	single small	200	100	562,500
	single large	250	125	600,000
	articulated small	300	150	750,000
	articulated large	400	200	850,000
trolleybus	single small	50	25	500,000
	single large	100	50	537,500
	articulated small	50	25	587,500
	articulated large	100	50	625,000

Table 3.

Considered battery capacity and procurement cost of the vehicle.

We estimated the considered procurement cost of charging infrastructure based on empirical data and data resulting from a market analysis. The c_cat nominal cost of a catenary was 750,000 EUR/km. However, we distinguished how many lines are served an ij section. Thus, the traffic-dependent electricity grid load is considered in a simplified way; the catenary cost is 750,000 EUR/km if 1–2 lines are served, 1,000,000 EUR/km if 3–5 lines are served, and 1,500,000 EUR/km if more than 5 lines are served. Moreover, in the case of a hilly ij section, due to the more complicated terrain conditions, a higher category was considered. The c_ch is the cost of a static charger according to the 100, 300, and 450 kWh nominal capacity is 50,000, 200,000, and 450,000 EUR, respectively. c_grid nominal cost of grid development was considered 600,000 EUR/MW.

4.2 Result and discussion

The line group running through the city center, connecting the southwest and northeast sides of the city, is described in detail. The considered lines according to the state of the network in June 2022: 5, 7, 7E, 8E, 108E, 110, 110E, 112, 133E (lines served by single buses are underlined). “E” signs mean express lines; not all the stops are served.

Step 1. Modeling: The lines have significant common sections, and some of them also have individual sections. There are lines that have the same terminal(s). Considering the common terminals and sections, three terminals and 16 sections were distinguished. Directions are distinguished on each line. There is only a short 400 m subsection in section XII where a one-directional catenary is located; we neglected it. Section borders were selected at the beginning and end of common sections. The physical model is depicted in Figure 6.

Figure 6.

Physical model.

The section length is measured on online map; the travel time on a section is given by the schedule for each line. The number of vehicles in a section at the same time considering all the lines is determined based on the timetable. The following sections are hilly sections with relevant slopes: I, II, III, IV, V, VI, X, XI.

Step 2. Scenario building: E-bus scenarios (E-bus A..F) were formed by the different charging capacities, respectively (100 kW – 450 kW, increment is 50 kW).

Two trolleybus scenarios were investigated by indicating bidirectional catenary network for different sections:

• Trolley A: XII, XIII, XIV

• Trolley B: XI, XII, XIII

Step 3. Energy consumption calculation: The consumed energy is presented for each section according to the lines. The number of stops in each section influences the consumed energy because of the breaking loss. In hilly section, elevation loss can be negative in downhill direction where the battery may be recharged. In addition, the consumed energy at the same section may differ whether single or articulated bus serves the line. Table 4 presents an excerpt of consumed energy.

Consumption	Direction	…	VI. (8E)	VII. (108E)	…	X. (110, 112)	XI. 110, 112	XI. (8E, 108E	…
bij [kWh/km]	A	…	0.51	0.36	…	0.49	0.3	0.51	…
	B	…	0.47	0.6	…	0.58	0.3	0.51	…
eij [kWh/km]	A	…	−0.67	0.02	…	−1.48	−0.22	−0.37	…
	B	…	0.84	−0.02	…	1.85	0.27	0.47	…
EDEMAND,ij [kWh]	A	…	8.74	10.94	…	−0.09	2.15	3.16	…
	B	…	20.13	12.21	…	3.34	3.24	5.01	…
EAUX,ij [kWh]	A	…	6.16	3.08	…	1.54	2.7	2.7	…
	B	…	5	3.08	…	0.77	3.46	3.46	…
EDEMAND,ij [kWh]	A	…	14.9	14.02	…	1.45	4.85	5.85	…
	B	…	25.13	15.29	…	4.11	6.7	8.47	…

Table 4.

Consumed energy values at a section (excerpt).

With the summarization of consumed energy in each section according to a line, the total energy consumed can be determined in each section. As only one terminus per each line was considered as a potential charging location, both directions should be covered with one charging. The total consumed energy is summarized in Table 5 for each line.

Direction	5	7	7E	8E	108E	110	110E	112	133E
A	61.17	59.47	25.41	67.58	57.03	26.61	22.76	25.97	75.87
B	66.02	56.09	23.75	68.04	67.87	42.21	25.73	42.21	69.74
Total	127.2	113.6	49.2	135.6	124.6	68.6	48.5	68.2	145.6

Table 5.

Consumed energy on a line.

Accordingly, e-buses with smaller battery capacity are enough for bus lines 110, 110E, 112 (single, 200 kWh nominal power) and 7, 7E (articulated 300 kWh nominal power).

Step 4. Possible charging time determination: Vehicle scheduling was used to determine the time a conventional bus spends at a terminus in the case of e-buses. In the case study area, buses and drivers are connected; there are at least a few minutes of rest for the driver at the terminus and longer during the day. During these breaks, the buses park at the terminus; charging may be possible. In the case of trolleybuses, the possible charging time is indicated by the static timetable between stations i and j. Figure 6 depicts the travel times.

Step 5. Charged energy estimation: The chargeable energy at the sections is influenced mainly by the time spent at the charging. As an example, the charged energy at static chargers per minute is 5.1, 10.2, 15.3, 17.85, 20.4, and 22.95 kWh considering the charging power 100, 200, 300, 350, 400, and 450 kW, respectively. For instance, in the case of trolleybuses, at section XI the chargeable energy in Direction A (downhill) is 21 kWh (travel time is 5 minutes) or 29.4 kWh (travel time is 7 minutes), and in Direction B (uphill) is 33.6 kWh (travel time is 7 minutes) or 37.8 kWh (travel time is 9 minutes).

Steps 6 and 7. Energy balance calculation and calculating the number of vehicles needed: Based on the energy balance, there are buses that cannot be fully charged at the terminal. Thus, turn shifts, namely additional buses, are needed. The power demand number of needed buses by terminals and lines is given in Table 6. Lines 110, 110E, and 112 are served by the same buses. The additional bus requirements are over 150% if the charging power is 100 kW and 111% if the charging power is 450 kW. In all lines except 7E and 108E, at least one additional bus is needed after the electrification. The same number of e-buses is enough to serve line 7E with 350 kW charging power, and thus Line 108E with 200 kW charging power.

	Line	Current	Charging power [kW]
			100	200	300	350	400	450
Buses nr.	5	20	30	25	23	23	23	22
	7	16	24	20	18	18	18	17
	7E	18	24	20	19	18	18	18
	8E	19	29	24	22	22	21	21
	108E	3	4	3	3	3	3	3
	110/110E/112	27	36	32	30	30	30	30
	133E	19	30	24	22	22	21	21

Table 6.

Number of e-buses needed according to charging power.

Bus lines that can be electrified are summarized in Table 7 indicating the nominal battery capacity of trolley buses needed. In scenario Trolley A, the catenary network cannot provide enough energy to fulfill the autonomous sections in the case of lines 5, 8E, and 108E. In scenario Trolley B, only line 5 and 133E cannot be served by trolleybuses. In scenario Trolley B′, the catenary system is extended at Section IX to Budafoki út/Dombóvári út (additional 4.8 km) and at Section XVI to Erzsébet királyné útja (additional 1 km) to electrify bus lines 133E and 5 as well. The number of trolleybuses is the same as the current number of conventional buses.

Lines	Trolley A	Trolley B	Trolley B′
5	not served	not served	100 kWh
7	100 kWh	100 kWh	100 kWh
7E	50 kWh	50 kWh	50 kWh
8E	not served	100 kWh	100 kWh
108E	not served	100 kWh	100 kWh
110	50 kWh	50 kWh	50 kWh
110E	50 kWh	50 kWh	50 kWh
112	50 kWh	50 kWh	50 kWh
133E	not served	not served	100 kWh

Table 7.

Nominal capacity of trolleybuses needed.

Step 8 and 9. Determining the charging vehicles at the same time and the charging devices: The needed charging units at a terminal is the same as the number of buses staying at the terminal at the same time. Table 8 summarizes the number of charging devices according to charging power. The length of dynamic chargers is the same as the section length: Trolley A: 7.4 km, Trolley B: 8.1 km, Trolley B′: 13.9 km (Figure 7).

Terminal	Served lines	Charging power
		100	200	300	350	400	450
Kossuth utca	5	11	6	4	4	3	3
Bosnyák tér	110/110E/112	10	6	4	4	3	3
Nyírpalota út	7, 7E, 8E, 108E, 133E	39	20	14	12	14	12

Table 8.

Number of static chargers at terminals.

Figure 7.

Trolleybus scenarios.

Step 10. Procurement cost estimation: The procurement cost of three e-bus scenarios according to the terminals is summarized in Table 9. The table contains the peak power values. Scenario 3 is the most cost effective and has the highest charging power.

Terminal	Kossuth utca			Bosnyák tér			Nyírpalota út
Scenario	1	2	3	1	2	3	1	2	3
Charging power [kW]	100	300	450	100	300	450	100	300	450
Charging devices nr.	11	4	3	10	4	3	39	14	12
Peak power [kW]	1100	1200	1350	1000	1200	1350	3900	4200	5400
Charging devices cost [Mill. EUR]	0.55	0.8	0.9	0.5	0.8	0.9	0.195	0.28	0.36
Grid cost [Mill. EUR]	0.66	0.72	0.81	0.6	0.72	0.81	2.34	2.52	3.24
E-buses nr.	30	23	22	36	30	30	107	81	77
E-buses cost [Mill. EUR]	22.5	17.3	16.5	86.2	65.2	62.0	89.6	67.7	64.5
Total cost [Mill. EUR]	23.7	18.8	18.2	87.3	66.7	63.7	90.8	73.0	71.3

Table 9.

Procurement cost of e-bus scenarios according to terminals.

Though there are lines that can be served by lower power without increasing the number of e-buses needed, our aim was to unify the charging power at each terminal; in this way, the buses do not have to be assigned to a charger. It is noted that the additional buses increase the total cost significantly. In the case of the electrification only with e-buses, all together 18 static terminal chargers with 450 kW power and 129 e-buses are needed.

The procurement cost of trolleybus versions is detailed in Table 10. We assumed that the final aim is to replace all buses; accordingly, if a line cannot be replaced by trolleybuses, we considered the replacement of e-buses. In scenario Trolley A, 61 additional e-buses, 3 static chargers at Kossuth utca for lines 5, and 6 static chargers at Nyírpalota út for lines 8E, 108E, and 133E are needed. In scenario, Trolley B 43 additional e-buses are needed and 3–3 static chargers at Kossuth utca and Nyírpalota út for lines 5 and 133E are needed. Trolleybus scenarios and scenario E-bus are summarized in Table 10. Scenario E-bus is the best e-bus scenario and showed for comparison purposes.

	Trolley A	Trolley B	Trolley B′	E-bus
Catenary length [km]	7.4	9.6	13.9	—
Peak power [kW]	74,075	154,310	239,400	—
Static charger nr. (450 kW)	9	6	—	18
Trolleybuses nr.	61	83	122
E-buses nr.	67	43	—	129
Catenary cost (with grid cost) [1000 EUR]	7400	14,400	20,850	—
Static charger cost	2700	1800	—	5400
Grid cost at terminals [1000 EUR]	2430	1620	—	4860
Trolleybuses cost [1000 EUR]	34,075	47,825	72,200	—
E-buses cost [1000 EUR]	50,625	30,225	—	142,950
Total cost [1000 EUR]	97,230	95,870	93,050	153,210

Table 10.

Procurement cost of trolleybus scenarios.

The cheapest scenario is Trolley B′ in which the catenary system is the longest but there is no need for e-buses and static terminal chargers. Comparing trolleybus scenario with e-bus scenario, the total cost of scenario B′ is only 2/3 of the total cost of scenario E-bus. The main reason is the higher procurement of e-buses which is originated from the large battery capacity which cost is high. Accordingly, the best option to electrify this line group is the application of trolleybuses with autonomous running capacity and dynamic catenary system through the central common sections.

4.2.1 Summary

Considering all the eight terminals analyzed, the number of needed static chargers is 53 (32 chargers with 300 kW nominal power and 21 chargers with 450 kW nominal power); the chargers’ cost is 12,780,000 EUR, the cost of grid development is 11,430,000 EUR. The peak demand is 19,050 kW. All lines can be served by e-buses with smaller battery capacity. The estimated cost of the 253 e-buses needed is 142,877,000 EUR; the basic parameters of the vehicles are:

• 172 single buses with 200 kW nominal capacity

• 81 articulated with 300 kW nominal capacity

Currently there are 243 conventional buses serving these lines. The increment is only 4.1% (10 buses).

In most of the line groups, electrification with trolleybuses and dynamic charging is more affordable. However, there are some lines that cannot be electrified by trolleybuses (67, 122, 169E) as the individual sections are very long. In total 40 km of new bidirectional catenary network should be built, which cost 59,750,000 EUR. The estimated cost of the 310 trolleybuses needed is 170,086,000 EUR; the basic parameters of the vehicles:

• 66 single buses with 50 kW nominal capacity

• 52 single buses with 100 kW nominal capacity

• 50 articulated buses with 50 kW nominal capacity

• 142 articulated buses with 100 kW nominal capacity

Serving the lines with e-buses requires 28 e-buses (16,763,000 EUR) and static charging station development at two terminals (4,600,000 EUR). Each line needs 1 additional e-buses.

Thus, the estimated total electrification cost is 341,424,000 EUR. Note, additional infrastructure development costs at the depot is required.

5. Conclusion

In this chapter, a planning method was introduced to electrify the urban bus network. The method developed provides a line-group optimization considering the characteristics of the vehicle, charging infrastructure, and bus service (lines, timetable, etc.). Battery electric buses and trolleybuses with autonomous running capacity; moreover, static terminal chargers and dynamic catenary chargers were involved in the optimization.

The method was applied as a case study in Budapest, Hungary. Eight bus terminals and seven bus line groups (85 lines) were analyzed to be served by electric buses or trolleybuses. The main finding regarding the case study is that 4% more battery electric buses are needed without changing the service characteristics. If e-buses serve all the lines, 253 vehicles and 53 terminal chargers are needed. However, we found that electrification with trolleybuses and dynamic charging is more affordable except for 3 lines. In total 40 km of the new bidirectional catenary network should be built to serve 310 trolleybuses.

The method can be further optimized by dissolving the limitations and refining the estimated variables, such as grid costs, and available grid capacity. Another further aim is to create a charging scheduling method, as it can further optimize the number of charging devices and vehicles.

Acknowledgments

The authors express their gratitude for BKK Budapest Centre for Transport to provide bus line-related data.

Conflict of interest

The authors declare no conflict of interest.

Nomenclature

B

battery capacity

b

braking loss per kilometer

c_cat

nominal cost of a catenary

c_ch

nominal cost of static charger

c_grid

nominal cost of grid development

E_AUX

auxiliary energy consumption

E_DEMAND

total energy demand

E_DRIVE

driving dynamic energy consumption

e

elevation loss per kilometer

i

serial number of bus stop

l_ch

total length of dynamic charger

l

section length

n_bus

number of currently needed buses.

n_ebus

number of e-buses needed

n_ch

number of static chargers needed

n_tbus

number of trolleybuses needed

n_ts

turn shift

n_ch(t)

number of charging vehicles in period t

n_tbus,ij(t)

number of trolleybuses in the section at a given period

p

probability of charging

P_AUX

power demand of the auxiliary systems

P_peak

peak power of the electric grid

SoC

state of charge of the battery

t

time period in general

t_ch

charging time

t_hw

headway between buses

t_ij

travel time in ij section

γ

consumption rate per kilometer

ε_ij

energy balance

η_batt

capacity utilization of a battery

η_ch

charging efficiency

η_PC

efficiency of the power converter