Driving and Energy Profiles of Urban Bus Routes Predicted for Operation with Battery Electric Buses

Abstract

Battery electric buses are used for operation on urban bus routes. The main disadvantage of battery electric buses is their limited range that depends on energy consumption. This paper presents a new approach to the estimation of energy consumption on urban bus routes based on driving and energy profiles. The energy consumption results from the travel parameters along the bus route. The travel parameters are described by driving profiles. The determination of driving profiles is based on GPS location data recorded by a receiver on a bus. Location data are recorded at consecutive track points at a constant frequency. For each track point, the distance to the preceding track point is determined using the location data, and then the speed and acceleration are calculated. The analyzed bus route is divided into sections. For each section, travel parameters consisting of travel time, speed parameters, and acceleration parameters are determined. Using travel parameters, the energy consumption is estimated for individual sections and the entire bus route. The estimated energy consumption is described by energy profiles. Experimental results have been obtained for the selected urban bus route under various traffic conditions. For the assumed model of energy consumption, the energy consumed on the entire bus route is 1.8 KWh/km at off-peak hours and 2.1 KWh/km at peak hours. The driving and energy profiles describe the urban bus routes well and allow evaluation of the suitability of the bus route for operation with battery electric buses.

1. Introduction

In urban areas, electric buses powered by traction batteries are increasingly being used in public transport. The use of electric buses reduces air pollution and traffic noise and also allows for limited operating expenditures. The main limitation in the use of electric buses powered by traction batteries is their relatively short range, which depends on the capacity of the traction batteries and the energy consumed during driving along a bus route. The energy consumption on urban bus routes is variable and depends on the topology of the bus route, traffic conditions, and driving style, and also on the ambient temperature. The range of electric buses should be taken into account during the scheduling of electric buses operated on urban routes and in planning the recharging process of the traction batteries. Driving profiles for the bus route allow for the assumed energy model of an electric bus by estimating the energy consumption and the expected range for the bus route under various traffic and temperature conditions. For a description of the operation of electric vehicles equipped with traction batteries, various approaches are applied.

The energy consumption of an electric bus can differ depending on the type of bus route. On various bus routes, the amount of energy consumed and recovered by regenerative braking is changeable. To determine the dependence of energy consumption on the type of bus route, a simulation platform is used [1]. The energy consumption of an electric bus depends on the ambient temperature. At a subzero temperature, energy consumption increases significantly. The additional energy consumption in harsh weather conditions demands appropriate infrastructure and planning [2]. The electric vehicle propelled by traction batteries can be assessed by comparison with a conventional vehicle of the same type propelled by an internal combustion engine. The comparison concerns energy consumption within and around the city under different traffic conditions and for different driving styles [3]. The energy consumption of an electric vehicle can be predicted on the basis of its kinematic parameters. The kinematic parameters for the moving vehicle are correlated with real-world data on energy consumption. The energy consumption is predicted using models with different levels of aggregation of the input parameters [4].

The energy consumption in the case of electric vehicles is directly related to the need to charge them. The use of electric buses for the operation of bus routes requires a suitable charging infrastructure. For establishing charging infrastructure, a dynamic optimization model can be used. The model assumes the types of bus stops correlated with the charging time and the location of the chargers [5]. The organization of the proper charging infrastructure, the planning of special bays [6], and the decision about the location of charging stations [7] are significant problems that must be managed by city authorities [8,9]. Various methods of distributing charging stations are proposed, including a search for optimal routes using various parameters. Among others, the cost of time [10], accessibility by foot [11], and type of trip [12] are considered.

Owing to their limited operation range, electric buses used on urban bus routes need the charging infrastructure in the city area. Electric buses can be charged at the depot and also at the charging station in the chosen locations. The assumption of the number of charging points and their location allows for creation of a scheduling model for electric buses [13]. The charging time for the traction battery is relatively long. The charging infrastructure can consist of traction battery exchange stations where discharge batteries are rapidly replaced by fully charged ones, and the scheduling model is adapted to the charging infrastructure with traction battery exchange stations [14]. The scheduling of diesel buses differs from the scheduling of battery electric buses. The scheduling of battery electric buses can take into account battery charging methods such as depot plug-in charging, plug-in or pantograph fast charging, wireless charging, and battery swapping. The introduction of electric bus technology requires investment in the charging infrastructure and its placement, investment in an electric bus fleet, the charging scheduling, and the electric bus scheduling [15].

Diesel buses are increasingly replaced by battery electric buses. For costs, the operation of bus routes with battery electric buses can be compared to operation with diesel-powered buses. The costs taken into account include bus purchasing costs, lifecycle costs, fuel and electricity costs, maintenance costs, and also future costs. The conversion of diesel-powered buses to electric buses results in additional effects, such as health benefits and a reduction in negative environmental impact [16].

The use of electric vehicles changes the way urban logistics are organized [17], because it causes a different approach to route planning for deliveries [18], or creates new opportunities for the development of new forms of transport and integration with existing ones. The use of electric vehicles is preceded by analyses and planning. The decision to use electric vehicles is influenced by the attitude of users [19]. The energy consumption of an electric vehicle depends on the driving technique. Various driving techniques for plug-in hybrid electric vehicles result in different energy consumption [20]. The use of electric vehicles causes their depreciation. The residual value depends on the type of electric vehicle [21].

The analysis of travel time is utilized for travel planning. Travel time depends on many factors and is variable. The analysis of bus travel time can be performed using automatic vehicle location data and automated vehicle counter data. The terminal-to-terminal travel time consists of running time and dwelling time. The data collected affect two bus routes on different working days [22]. For the prediction of bus travel time, the similarity of historical profiles can be used. In this method, the historical and current behaviors of a vehicle are taken into account. Historical behavior is represented by historical profiles, and current behavior is described by data recorded on the vehicle for which travel time is predicted. In this method, GPS location data are used [23].

Machine learning methods are useful for the prediction of travel time. A support vector machine can be employed to predict travel time in road sections. Before predicting travel time, the set of data is used for training the support vector machine [24]. Various methods of machine learning, such as artificial neural networks, support vector machines, and Bayes networks, can be used to predict travel speed of buses. These methods are based on real-time traffic conditions data and are compared with each other. Input data are obtained from GPS devices installed in buses [25]. Dynamic bus travel time prediction based on GPS date can be provided using prediction methods based on historical average, Kalman filtering, and an artificial neural network. These three methods were evaluated and compared with each other, taking into account the accuracy and robustness of the prediction. The bus travel time prediction using the artificial neural network proved to be better than the other two methods [26].

Traffic is affected by the quality of the pavement and its changes over time. Asphalt pavement moduli can be assessed using data obtained from built-in sensors. The optimal placement of the sensors allows for monitoring the moduli of the asphalt pavement and the traffic load [27]. Traffic flow can be predicted using visual methods. Visual methods are applied to quantify traffic density and flow features. For flow prediction, suburban road images were used [28]. Improving the energy efficiency of electric buses can be obtained by applying a multispeed gearbox. For the determination of energy reduction, the two-speed gearbox and the continuously variable transmission were applied [29].

The ability to estimate the energy consumption in the operation of electric buses is of great importance. Estimation of energy consumption for electric buses is difficult and depends on many various factors. Models describing multiple factors are used to estimate the energy consumption of electric buses [30]. The energy consumption of an electric bus can be estimated by using the deep learning approach. Single trip energy consumption is established using a convolutional neural network and trip data that include state of charge, speed, and temperature [31]. The energy consumption of electric buses is related to driving behaviors and environmental properties. Battery efficiency can be evaluated by taking into account the distance traveled and changes in battery’s state of charge [32].

GPS data are useful for describing the travel time on the bus route and in its sections. For the description of travel time, the running and stopping sections are distinguished, and the travel time is described using the classification algorithm [33]. The accuracy of GPS data is due to factors such as the number of visible satellites, satellite position, signal delay, and clock errors of the satellite and the GPS receiver. Increasing the accuracy of GPS data can be obtained by using reference station networks and various software algorithms [34].

The practical accuracy of GPS data depends mainly on the measurement environment. The greatest inaccuracies are found in densely built-up areas of city centers and in wooded areas. Medium inaccuracies are obtained in areas with housing-estate-type development. The smallest inaccuracy is achieved in open areas and in sparsely built-up areas. For typical GPS receivers, the accuracy of GPS data is significantly less dependent on the type of GPS receiver than on the measurement environment [35]. In an urban area, the accuracy of GPS data is changeable and influenced by building density and the presence of electromagnetic fields interfering with the GPS signal. The accuracy of positioning and reliability, for various types of GPS receiver, can be determined in different modes such as static mode in an open area, dynamic mode at fixed minimum speed on a carriage way, static mode in a built-up area, and dynamic mode at fixed maximum speed in a built-up area [36].

The operation of electric buses is linked to numerous issues. Important issues such as energy management, battery technologies, charging infrastructures, vehicle technologies, and sustainability can be considered in many aspects [37]. The main aim of the work is to develop a method for estimating the energy consumption of electric buses operated on urban bus routes. In the proposed method for estimating energy consumption, GPS data are recorded along the bus route at a constant frequency. Based on GPS data, driving profiles are determined for the bus route divided into sections. The driving profiles describe the distribution of travel time, speed, and acceleration along the bus route. The energy profiles are determined using the driving profiles and the assumed energy consumption model. The energy consumption model corresponds to the real energy consumption of the electric bus. The energy consumption is estimated on the basis of the energy profiles for the analyzed bus route and the assumed model of the energy consumption.

The proposed method for the estimation of energy consumption differs significantly from the well-known methods such as kinematic methods (e.g., [4]) and methods using machine learning (e.g., [31]). The novelty of the proposed method lies in the assumption that only GPS data are used to determine the driving and energy properties of the bus route. This new approach also involves the application of a model of energy consumption and the correlation of driving profiles with the energy profiles described by the energy factor. The energy consumption expressed by using energy factors is transformed into kilowatt hours for the selected specific type of electric bus. The proposed method for determining driving and energy profiles can be useful for assessing the suitability of urban bus routes for operation with electric buses and allows for predicting energy consumption, which facilitates bus scheduling and charging scheduling for various types of electric buses.

2. Materials and Methods

In urban traffic, the energy consumption of electric buses powered by electric batteries can be estimated on the basis of driving parameters, which depend on many factors. Factors that affect the energy consumption of electric buses are driving parameters along the urban bus route that result from its topography and current traffic conditions. Driving parameters can be determined using GPS data obtained from a GPS receiver on a bus driven on the bus route. Location data are recorded by a GPS receiver at a constant frequency. Data from a single measurement describe one track point. All track points form a track along the bus route. Each track point has the sequential number, denoted by i, and is described by the set of location data

$$L_i=\left\{i,{\mathsf{\phi }}_1,{\mathsf{\lambda }}_i,h_i,dat{e}_i,tim{e}_i\right\}$$

(1)

where i is the sequential number of the track point; φ_i is the latitude and λ_i is the longitude, both in decimal degrees; h_i is the elevation above sea level given in meters; date_i and time_i are the measurement date and GMT time. The numbering of track points starts from the starting number. The track point with a starting number is an initial track point, and no calculations are performed for it. On the bus route, the changes in elevation are small, and therefore elevation is not taken into account.

Assuming that the shape of the Earth is an ideal sphere, the distance between the current track points and the track point immediately preceding it, expressed in meters, is given by

$$d_i=\frac{q}{360}\sqrt{{\left({\mathsf{\phi }}_i-{\mathsf{\phi }}_{i-1}\right)}^2+{\left[\left({\mathsf{\lambda }}_i-{\mathsf{\lambda }}_{i-1}\right)\cos \mathsf{\phi }\right]}^2}$$

(2)

where q is the length of the equator, equal to 40,075.704 km. Examples of the calculated distance to the immediately preceding track point for selected track points are presented in

Table 1. Examples of the calculated distance to the immediately preceding track point.

Number of Track Point	Latitude φi (deg.)	Longitude λi (deg.)	Distance di (m)
2040	50.2117387298	18.9849107713	5.42
2041	50.2117123269	18.9848578814	4.78
2042	50.2116916236	18.9848175645	3.68
2043	50.2116812300	18.9847944304	2.01
2044	50.2116729319	18.9847856294	1.12
2045	50.2116673160	18.9847834501	0.64
2046	50.2116622031	18.9847787563	0.66
2047	50.2116551623	18.9847656805	1.22
2048	50.2116462775	18.9847475756	1.63
2049	50.2116329502	18.9847282134	2.03
2050	50.2116181981	18.9847121201	2.00
2051	50.2116021886	18.9847009722	1.95
2052	50.2115805633	18.9846981224	2.42
2053	50.2115568426	18.9847101085	2.78
2054	50.2115259971	18.9847340807	3.83
2055	50.2114917990	18.9847632498	4.34

. For the single track point, the data include the number of the track point, the latitude and longitude in decimal degrees obtained from the GPS receiver, and the calculated distance to the immediately preceding track point.

For each track point, a speed is assigned that corresponds to the average speed between the current track point and the immediately preceding track point. The speed assigned to the single track point is determined as follows:

$$v_i=\{\begin{array}{l}0\mathrm{if}\left(v_{i-1}>0\wedge d_i<d_{\mathrm{tre}}\right)\vee \left(v_{i-1}=0\wedge d_i<d_{\mathrm{tre}}+\Delta d_{\mathrm{tre}}\right)\hfill \\ d_{i}f\mathrm{otherwise}\hfill \end{array},$$

(3)

where f is the frequency with which location data are recorded, d_tre is the threshold value for the distance to the preceding track point for motionless classification, and Δd_tre is the width of hysteresis. Hysteresis is introduced to reduce the effect of location data fluctuation on the measurement results for a motionless GPS receiver. When the GPS receiver on the bus is motionless, minor changes in location data are recorded due to measurement inaccuracy. For distance values less than the threshold values, it is assumed that the bus is motionless, otherwise it moves. The measurement frequency is expressed in hertz, and thus the speed is given in meters per second.

In addition to the speed, the acceleration value is assigned to the track points. For each track point, the acceleration is calculated relative to the immediately preceding track point using the equation

$$a_i=\left(v_i-v_{i-1}\right)f,$$

(4)

where speed is given in meters per second and frequency in hertz, thus acceleration is expressed in meters per second squared.

Denoting by a_tre the threshold value for acceleration, it is assumed that for an acceleration value greater than or equal to −a_tre and less than or equal to a_tre, the speed of the bus is constant or equal to zero. Track points are classified as one of four types. The types of track points are the stop track point, the constant speed track point, the acceleration track point, and the deceleration track point. The type of track points is indicated by flags. The single flag can take an arithmetic value of 1 or 0. The stop flag of the track point, denoted by stop_i, is determined as

$$sto{p}_i=\{\begin{array}{l}1\mathrm{if}-a_{\mathrm{tre}}\le a_i\le a_{\mathrm{tre}}\wedge v_i=0\hfill \\ 0\mathrm{otherwise}\hfill \end{array},$$

(5)

and the constant speed flag of the track point, denoted by speed_i, as

$$spee{d}_i=\{\begin{array}{l}1\mathrm{if}-a_{\mathrm{tre}}\le a_i\le a_{\mathrm{tre}}\wedge v_i>0\hfill \\ 0\mathrm{otherwise}\hfill \end{array}.$$

(6)

The acceleration flag of the track point, denoted by acce_i, is determined as

$$acc{e}_i=\{\begin{array}{l}1\mathrm{if}{a}_i>a_{\mathrm{tre}}\hfill \\ 0\mathrm{otherwise}\hfill \end{array},$$

(7)

and the deceleration flag of the track point, denoted by dece_i, as

$$dec{e}_i=\{\begin{array}{l}1\mathrm{if}{a}_i<-a_{\mathrm{tre}}\hfill \\ 0\mathrm{otherwise}\hfill \end{array}.$$

(8)

For each track point, exactly one flag is equal to 1, whereas the other flags are equal to 0. The flag equal to 1 defines the type of track point.

The location data of the track points are supplemented by the speed value, acceleration value, and flags. After supplementation of location data, the single track point is represented by the extended set of data in the form

$$P_i=\left\{i,{\mathsf{\phi }}_1,{\mathsf{\lambda }}_i,h_i,dat{e}_i,tim{e}_i,v_i,a_i,sto{p}_i,spee{d}_i,acc{e}_i,dec{e}_i\right\}.$$

(9)

A bus route is divided into sections. The division into sections is in accordance with the location of the bus stops on the bus route. Each section includes the part of the bus route stretching between two neighboring bus stops and the bus stop that the bus reaches moving along the section.

Each section is defined by the range of track points. The first track point in the section is the track point recorded after the bus has started from the bus stop. The last track point in the section is the track point immediately preceding the first track point in the next section. Each track point belongs to exactly one section. Each section includes track points with numbers from the range

$$i_{k\min }\le i\le i_{k\max }$$

(10)

where k is the number of the section.

The sections of the bus route are described by the set of parameters as follows:

$$S_{(k)}=\left\{k,v_{(k)},a_{(k)},sto{p}_{(k)},spee{d}_{(k)},acc{e}_{(k)},dec{e}_{(k)}\right\}$$

(11)

where k is the number of the section; v_(k) is the average constant speed within the section calculated for the track points whose flag speed_i = 1; and a_(k) is the average acceleration within the section calculated for the track points whose flag acce_i = 1, stop_(k), speed_(k), acce_(k), dece_(k) are the sums of the stop, constant speed, acceleration, and deceleration track points in the section, respectively. Parentheses indicate that the symbol in them refers to the section of the bus route.

The sums of the stop, constant speed, acceleration, and deceleration track points are calculated as follows:

$$sto{p}_{(k)}={\displaystyle \sum _{i=i_{k\min }}^{i_{k\max }}sto{p}_i},spee{d}_{(k)}={\displaystyle \sum _{i=i_{k\min }}^{i_{k\max }}spee{d}_i},acc{e}_{(k)}={\displaystyle \sum _{i=i_{k\min }}^{i_{k\max }}acc{e}_i},dec{e}_{(k)}={\displaystyle \sum _{i=i_{k\min }}^{i_{k\max }}dec{e}_i}.$$

(12)

The average speed and acceleration within the section are given by

$$v_{(k)}=\frac{1}{spee{d}_{(k)}}{\displaystyle \sum _{i=i_{k\min }}^{i_{k\max }}{v}_{(i)}spee{d}_i},a_{(k)}=\frac{1}{acc{e}_{(k)}}{\displaystyle \sum _{i=i_{k\min }}^{i_{k\max }}{a}_{(i)}acc{e}_i}.$$

(13)

For each section, the section stop, constant speed, acceleration, and deceleration time, given in seconds, are calculated as follows:

$$t_{(k)\mathrm{stop}}=\frac{sto{p}_{(k)}}{f},t_{(k)\mathrm{speed}}=\frac{spee{d}_{(k)}}{f},t_{(k)\mathrm{acce}}=\frac{acc{e}_{(k)}}{f},t_{(k)\mathrm{dece}}=\frac{dec{e}_{(k)}}{f}.$$

(14)

The section stop, constant speed, acceleration, and deceleration time are the time parameters. The time parameter is also the section travel time. The section travel time is given by

$$t_{(k)\mathrm{trav}}=t_{(k)\mathrm{stop}}+t_{(k)\mathrm{speed}}+t_{(k)\mathrm{acce}}+t_{(k)\mathrm{dece}}.$$

(15)

The electric bus driving on the bus route consumes electric energy stored in traction batteries. Energy consumption along the bus route is variable and depends on the total travel time and changes in speed, acceleration, and deceleration. For the single section, this can be expressed by the energy factor e_(k) as

$$e_{(k)}=e_{(k)\mathrm{trav}}+e_{(k)\mathrm{speed}}+e_{(k)\mathrm{acce}}-e_{(k)\mathrm{dece}},$$

(16)

where e_(k)trav, e_(k)speed, e_(k)acce, are the energy consumption components resulting from the travel time, driving at constant speed, acceleration, respectively, and e_(k)dece is the energy recovery component resulting from deceleration while the acceleration value is negative.

In the assumed theoretical model for the energy consumption of the electric bus, the energy consumption components depend on the energy consumption coefficients and time parameters. For a single section of the bus route, the energy consumption components are estimated as follows:

$$e_{(k)\mathrm{trav}}=c_{\mathrm{trav}}{t}_{(k)\mathrm{trav}},e_{(k)\mathrm{speed}}=c_{\mathrm{speed}}{t}_{(k)\mathrm{speed}},e_{(k)\mathrm{acce}}=c_{\mathrm{acce}}{t}_{(k)\mathrm{acce}},e_{(k)\mathrm{dece}}=c_{\mathrm{dece}}{t}_{(k)\mathrm{dece}},$$

(17)

where c_trav, c_speed, c_acce are the energy consumption coefficients for the travel time, driving at constant speed, accelerating, respectively, and c_dece is the of energy recovery coefficient. Hence, the energy consumption for the single section of the bus route is estimated in the form of the energy factor given by

$$e_{(k)}=c_{\mathrm{trav}}{t}_{(k)\mathrm{trav}}+c_{\mathrm{speed}}{t}_{(k)\mathrm{speed}}+c_{\mathrm{acce}}{t}_{(k)\mathrm{acce}}-c_{\mathrm{dece}}{t}_{(k)\mathrm{dece}}.$$

(18)

Considering energy consumption, a moderate speed of the electric bus is beneficial. It is assumed that at a constant average speed of 10 m/s (36 km/h), the value of the energy consumption coefficient is defined equal to 1 (c_speed = 1). For driving at constant speed, the coefficient of energy consumption increases for higher speeds and decreases for lower speeds. The value of the energy consumption coefficient for driving at constant speed is defined as the numerical value of the average constant speed within the section, expressed in meters per second, (v_(k)) divided by 10.

In electric buses, electric energy is used not only to propel an electric traction motor but also to supply heating, air conditioning, and other electric devices. The energy consumption of electric devices depends on the travel time. For the travel time, the energy consumption coefficient is defined equal to 0.25 (c_trip = 0.25) and is the same for all sections of the bus route.

The highest energy consumption occurs when the electric bus accelerates. For acceleration, the energy consumption coefficient is defined as the numerical value of the average acceleration within the section, expressed in meters per second squared, (a_(k)) enlarged by 1.

During deceleration of the bus, energy is recovered. The assumption is made that the amount of energy recovered depends only on the time of deceleration and the average deceleration value within the section of the bus route does not affect it. The energy recovery coefficient for electric bus deceleration is defined equal to 1 (c_dece = 1) and is the same for all sections of the bus route.

Using location data, the length of the bus route can be determined. The length of the single section determined on the basis of the location data, expressed in meters, is calculated as follows:

$$l_{(k)}=\frac{1}{f}{\displaystyle \sum _{i=i_{k\min }}^{i_{k\max }}{v}_i},$$

(19)

where the frequency is expressed in hertz and the speed is expressed in meters per second. The length of the entire bus route is equal to the sum of the lengths of all sections. Using the length of the sections, the normalized energy factor can be calculated for each section of the bus route as the quotient of the energy factor determined for the section and the length of the section.

The energy consumption coefficients are defined according to the selected electric bus model. For the selected electric bus model, the energy consumption is estimated using the energy factors that can be converted to physical energy units on the basis of the real parameters for the electric bus considered.

3. Results

Measurements were carried out on the number 297 bus route in the city of Katowice. Katowice city lies in the southern part of Poland within the conurbation and has around 300,000 inhabitants. The starting bus stop for the number 297 bus route is located at the bus station in the city center. The bus route leads in a south direction and reaches the housing estate. The bus route then circles the housing estate and heads toward the city center in the opposite direction along the same streets. The bus route ends at the same bus stop where it begins, at the bus station in the city center. The length of the entire bus route is approximately 16 km. The terrain of the bus route is flat. The elevation along the bus route varies slightly, within the range 250–350 m above sea level.

The 297 bus route consists of 26 sections and includes sections of intensive traffic in the city center and the vicinity of the city center, and sections of low traffic in the housing estate. Sections are denoted by numbers 1 through 26. Section number 1 begins with the starting bus stop. Sections numbered 1 through 11 lead to the housing estate, sections numbered 12 through 15 circle the housing estate, and sections numbered 16 to 26 head back to the city center. Sections numbered 1 through 11 and numbered 16 through 26 are located along the same streets but in opposite directions.

The electric bus, equipped with a GPS receiver, is driven along the bus route. The location data obtained from the GPS receiver are recorded and stored in the GPX format file. The location data are recorded at a frequency of 1 hertz (f = 1 Hz). Because the location data are recorded with an interval of 1 s, the number of track points is equal to the number of seconds. The location data were obtained during two trips. The trip during off-peak hours is denoted as Trip 1, and the trip at afternoon peak hours as Trip 2. The recorded tracks do not include small parts of the location data for Section 1 and Section 26 under the roof of the bus station, where the highly distorted GPS signal prevented correct measurements. The location data were collected on working days at different times of the day and under similar good weather conditions.

3.1. Driving Profiles

The track points are assigned to the appropriate sections of the bus route. The threshold value for the distance between two consecutive track points, classified as the motionless GPS receiver, is set to 1 m (d_tre = 1 m). The threshold value for acceleration is set to 0.3 m per second squared (a_tre = 0.3 m/s²). For individual track points, speed and acceleration are calculated and then stop, constant speed, acceleration, and deceleration flags are determined. Example parameters for the selected track points are provided in

Table 2. Parameters for the selected track points.

Number of Track Point	vi (m/s)	ai (m/s2)	stopi (s)	speedi (s)	accei (s)	decei (s)
2040	5.42	−0.59	0	0	0	1
2041	4.78	−0.64	0	0	0	1
2042	3.68	−1.10	0	0	0	1
2043	2.01	−1.67	0	0	0	1
2044	1.12	−0.89	0	0	0	1
2045	0.00	−1.12	0	0	0	1
2046	0.00	0.00	1	0	0	0
2047	1.22	1.22	0	0	1	0
2048	1.63	0.41	0	0	1	0
2049	2.03	0.40	0	0	1	0
2050	2.00	−0.03	0	1	0	0
2051	1.95	−0.05	0	1	0	0
2052	2.42	0.47	0	0	1	0
2053	2.78	0.36	0	0	1	0
2054	3.83	1.05	0	0	1	0
2055	4.34	0.51	0	0	1	0

.

For each section of the bus route, aggregated parameters are determined for Trip 1 at off-peak hours and Trip 2 at peak hours. The aggregated parameters include the sums of stop track points (stop_(k)), constant speed track points (speed_(k)), acceleration track points (acce_(k)), and deceleration track points (dece_(k)) within the sections. Due to the fact that the location data were recorded at a frequency of 1 Hz, the sums of stop, constant speed, acceleration, and deceleration track points are numerically equal to the stop, constant speed, acceleration, and deceleration time expressed in seconds, respectively. The section parameters also include the average constant speed, the average acceleration, and the travel time within the sections.

The section travel time determined for individual sections during Trip 1 at off-peak hours and Trip 2 at peak hours is presented in Figure 1. Section 7 is very susceptible to congestion. Sections 8, 25, and 26 are also susceptible to congestion, but to a lesser extent. The total travel time is equal to 3766 s (around 1 h 3 min) for Trip 1 at off-peak hours and 4369 s (around 1 h 13 min) for Trip 2 at peak hours. For Trip 2 at peak hours, the total travel time increased compared to Trip 1 at off-peak hours by around 16%.

For all sections of the bus route, stop, constant speed, acceleration, and deceleration times are calculated relative to the section travel time. The related values, multiplied by 100%, give the percent share of stop, constant speed, acceleration, and deceleration time in the section travel time. In Figure 2, Figure 3, Figure 4 and Figure 5, respectively, the related values for stop, constant speed, acceleration, and deceleration time determined for individual sections are presented.

The total travel time for Trip 1 at off-peak hours consists of the stop time equal to 1313 s (around 22 min), the constant speed time equal to 979 s (around 16 min), the acceleration time equal to 725 s (around 12 min), and the deceleration time equal to 749 s (around 12 min). The share of individual time components during entire Trip 1 at off-peak hours is 34% of the stop time, 26% of the constant speed time, 20% of the acceleration time, and 20% of the deceleration time.

The total travel time for Trip 2 at peak hours includes the stop time equal to 1633 s (around 27 min), the constant speed time equal to 1108 s (around 18 min), the acceleration time equal to 812 s (around 14 min), and the deceleration time equal to 816 s (around 14 min). At peak hours, the shares of the time components slightly changed and the stop time increased to 37%, the constant speed time decreased to 25%, and both acceleration and deceleration times decreased to 19%.

For Trip 1 at off-peak hours and Trip 2 at peak hours, the average constant speed was determined for all sections of the bus route. The average constant speed was determined using only constant speed track points. The profiles for the average constant speed at off-peak hours and peak hours are shown in Figure 6. For Trip 1 at off-peak hours, the average constant speed is in the range 3.5 m/s (12.7 km/h) in Section 26 through 13.3 m/s (47.7 km/s) in Section 3. Similarly, for Trip 2 at peak hours, the average constant speed covers the range 2.7 m/s (10.4 km/h) in Section 7 through 12.1 m/s (43.7 km/h) in Section 3.

The average acceleration and the average deceleration were determined within all sections of the bus route for both trips, Trip 1 at off-peak hours and Trip 2 at peak hours. For determining the average acceleration and the average deceleration, only the acceleration and deceleration track points were taken into account, respectively. The profiles for the average accelerations are shown in Figure 7 and the profiles for the average decelerations are presented in Figure 8.

For Trip 1 at off-peak hours and Trip 2 at peak hours, the average acceleration and the average deceleration are in the range 0.6 m/s² through 1.0 m/s² for almost all sections of the bus route, except the average acceleration within Section 26. Section 26 is located in the city center with high traffic volume, where the bus often stops, and then starts and accelerates. In addition, the road belonging to Section 26 slopes downward.

3.2. Energy Profiles

The energy factor represents the energy consumption while the electric bus is driven along the bus route. Energy consumption results from travel time and changes in the speed, acceleration, and deceleration of the electric bus on the bus route. Energy factors are determined for the sections of the bus route and for the entire bus route. The section energy factor affects one section of the bus route, whereas the energy factor for the bus route affects the entire bus route for one trip and is equal to the sum of the section energy factors.

For the single section, the energy factor is equal to the sum of the energy consumption components representing the energy consumption resulting from the travel time, the energy consumption during driving at constant speed and acceleration, minus the energy consumption component representing the energy recovery during deceleration. The values of the energy consumption components depend on the number of track points of individual types within the section and the values of the energy consumption coefficients.

The energy consumption component representing the energy consumption resulting from the travel time is the product of the number of all track points within the section and the energy consumption coefficient, which is constant and equal to 0.25 for all sections.

The energy consumption component representing the energy consumption during driving at constant speed is calculated as the product of the number of constant speed track points and the energy consumption coefficient for driving at constant speed. The energy consumption coefficient for driving at constant speed is equal to the numerical value of the average constant speed within the section, expressed in meters per second, divided by 10.

The energy consumption component representing the energy consumption during acceleration is the product of the number of acceleration track points within the section and the energy consumption coefficient equal to the numerical value of the average acceleration within the section, expressed in meters per second squared, enlarged by 1.

The energy consumption component representing the energy recovery is the product of the number of deceleration track points within the section and the energy recovery coefficient for deceleration equal to 1 for all sections.

The distributions of the energy factors for individual trips represent the energy consumption along the bus route and form the energy consumption profiles for the bus route considered. The energy consumption profiles for Trip 1 at off-peak hours and Trip 2 at peak hours are presented in Figure 9.

The values of the corresponding section energy factors for Trip 1 at off-peak hours and Trip 2 at peak hours are similar, except for Section 7, for which the value of the section energy factor increased significantly at peak hours. The energy factor for the bus route is calculated as the sum of all section energy factors and is equal to 2232 for Trip 1 at off-peak hours and 2497 for Trip 2 at peak hours. At peak hours, the energy factor for the bus route increased by 265 compared to the energy factor for the bus route at off-peak hours, which means an increase in energy consumption of around 12% at peak hours.

The distances between two consecutive bus stops are different. To normalize energy consumption profiles along the entire bus route, normalized energy factors were determined. The normalized section energy factor is the section energy factor related to the length of the appropriate section. The length of a single section in meters is calculated as the sum of the speed at all track points within the section, expressed in meters per second, divided by the frequency in hertz at which the track points were recorded. Because the recording frequency was 1 Hz, the numerical value of the sum of the speed in meters per second at all track points within the section is equal to the length of the section expressed in meters. The lengths of the sections calculated on the basis of the recorded location data for Trip 1 at off-peak hours and Trip 2 at peak hours are presented in Figure 10.

The lengths of the corresponding sections determined at off-peak and peak hours are similar, demonstrating the robustness of the measurements. The total length of the bus route determined during Trip 1 at off-peak hours is equal to 16,175 m, and during Trip 2 at peak hours it is equal to 16,068 m.

The values of the normalized section energy factors for Trip 1 at off-peak hours and Trip 2 at peak hours are presented in Figure 11. The high value of the normalized section energy factor occurs for Section 26 both at off-peak and peak hours. At peak hours, the value of the normalized section energy factor increased noticeably for Sections 7, 8, and 25.

Using the length of the sections and the normalized section energy factors, the distribution of the normalized energy factor along the bus route can be determined for individual trips. The distributions of the normalized energy factor along the bus route for Trip 1 at off-peak hours and Trip 2 at peak hours are shown in Figure 12. At peak hours, a significant increase in the normalized energy factor is observed between 4 and 6 km and at the end of the bus route. Total energy consumption during the single trip corresponds to the area under the curve for the distribution of the normalized energy factor along the bus route.

The total energy consumption for the entire bus route during one trip can be described in the specification of energy consumption. The specification of energy consumption includes the energy consumption of the electric devices in the electric bus according to the travel time, the energy consumption during driving at constant speed and acceleration, the total energy consumption, the energy recovery during deceleration, and the energy required. The energy required for one trip is obtained by subtracting the energy recovered from the total energy consumption. The specification of energy consumption represented by the energy factors for Trip 1 at off-peak hours and Trip 2 at peak hours is presented in

Table 3. Specification of energy consumption represented by energy factors.

Energy Factor	Trip 1 At Off-Peak Hours	Trip 2 At Peak Hours
Consumption of electric devices	941	1092
Consumption at constant speed	745	762
Consumption at acceleration	1295	1459
Total energy consumption	2981	3313
Recovery at deceleration	749	816
Energy required	2232	2497

.

For Trip 1 at off-peak hours, the energy factor for total energy consumption is 2981 and the energy factor for energy recovery is 749. Thus, the energy factor for the energy required is 2232. At off-peak hours, the normalized energy factor for total energy consumption is 184 per kilometer, while the normalized energy factor for energy required is 138 per kilometer. For Trip 2 at peak hours, the energy factor for total energy consumption is 3313, the energy factor for energy recovery is 816, and the energy factor for energy required is 2497. At peak hours, the normalized energy factor is equal to 206 per kilometer for total energy consumption and equal to 155 per kilometer for the energy required.

The value of the energy factor corresponds to the energy expressed in kilowatt hours (KWh). In the energy consumption model assumed for an electric bus, the energy factor equal to 100 is the equivalent of the energy of 1 KWh. The distribution of energy consumption after transformation into KWh along the bus route considered for Ride 1 at off-peak hours and Ride 2 at peak hours is shown in Figure 13.

In the energy consumption model, the correlation between the energy factor and the energy expressed in KWh is linear, and therefore the shapes of the energy distribution curves along the bus route describing the energy consumption using the energy factor and expressing the energy consumption in KWh are identical. For Trip 1 at off-peak hours, the energy consumption along almost the entire bus route is approximately between 1 and 2 KWh/km, except at the end of the bus route where the energy consumption increases above 3 KWh/km. For Trip 2 at peak hours, the energy distribution curve is similar to the energy distribution curve at off-peak hours, except that a significant increase in energy consumption above 3.5 KWh/km occurs along the bus route between 4.5 and 5.5 km.

Similar to the distribution of the energy factor along the bus route, the specification of energy consumption represented by energy factors can be transformed into KWh. The specification of energy consumption expressed in KWh, at both off-peak and peak hours, is shown in

Table 4. Specification of energy consumption expressed in KWh.

Energy	Trip 1 At Off-Peak Hours (KWh)	Trip 2 At Peak Hours (KWh)
Consumption of electric devices	9.4	10.9
Consumption at constant speed	7.4	7.6
Consumption at acceleration	13.0	14.6
Total energy consumption	29.8	33.1
Recovery at deceleration	7.5	8.1
Energy required	22.3	25.0

.

For Trip 1 at off-peak hours, the total energy consumption is 29.8 KWh in which 7.5 KWh are recovered, and therefore the energy required is 22.3 KWh. At off-peak hours, the total energy consumption is 1.8 KWh/km and the energy required is 1.4 KWh/km. For Trip 2 at peak hours, the total energy consumption is 33.1 KWh, the energy recovery is 8.1 KWh, and the energy required is 25.0 KWh. At peak hours, the total energy consumption for the entire bus route is equal to 2.1 KWh/km and the energy required is 1.6 KWh/km.

4. Discussion

GPS data are suitable for determining driving profiles for urban bus routes. Using the assumed energy consumption model, the energy consumed by an electric bus can be estimated in individual sections and on the entire bus route. The results obtained for the corresponding sections during different trips show the correctness of the measurements and calculations performed. For the single track point, the displacement of the bus is calculated relative to the immediately preceding track point, reducing the typical errors for determining the position based on GPS location data in an urban area. For an unmoved bus, the displacements determined from the location data do not exceed 1 m, and the very few exceptions that occur should be treated as fatal errors, which can mostly be filtered out during data preprocessing.

The values of all displacements and speeds determined on the basis of GPS data are positive, while calculated accelerations at individual track points can be positive or negative. It was assumed that the bus does not accelerate or decelerate when its acceleration is within the assumed range of acceleration, and then the bus is either not moving or is driving at constant speed. The sum of accelerations for the value within the assumed acceleration range was calculated for such track points, and the sums of accelerations obtained are close to zero for both trips, which shows that measurement errors do not accumulate.

The measurements were performed under good weather conditions and various traffic conditions using a GPS receiver equipped with the quad helix antenna. The GPS locations of the consecutive track points were recorded at a frequency of 1 Hz. The observed inaccuracy related to the immediately preceding track point practically does not exceed 1 m. The accuracy of the measurements is evidenced by the length of the bus route calculated on the basis of GPS data obtained during both trips. The calculated length of the bus route is equal to 16,175 m for the trip at off-peak hours and 16,068 m for the trip at peak hours, thus the difference is only 107 m. The accuracy of location determined on the basis of GPS data is lower in the densely built-up city center than outside the city center where there are undeveloped areas.

The assumed theoretical model of energy consumption takes into account the travel time, the driving time at constant speed, the acceleration time, and the deceleration time for individual sections of the bus route, along with the average values of constant speed and acceleration in each section. Energy consumption has been expressed using numerical energy factors. This makes the model universal and allows it to be used for various bus models. The theoretical model of energy consumption can be adapted to specific electric buses considering their own energy consumption characteristics. The numerical values of the energy factors can be connected to physical units of energy (kilowatt hours), which, after taking battery capacity into account, allows for estimating the range for electric buses of different types. In the assumed model of an electric bus, the energy factor equal to 100 corresponds to energy equal to 1 KWh.

The transformation of the energy factors into physical units of energy (kilowatt hours) allows for determining the distribution of energy consumption along the analyzed bus routes at both off-peak hours and peak hours. For off-peak hours, the energy consumption along almost the entire bus route is approximately within the range 1 to 2 KWh, reaching 3 KWh only at the end of the bus route. At peak hours, the distribution of energy consumption along the analyzed bus routes is similar and is within the range 1–2 KWh, but between 4.5 and 5.5 km along the bus route and also at the end of the bus route the consumption exceeds 3.5 KWh.

The driving profiles are determined for the bus route and depend on its topology and existing traffic conditions. Many energy profiles can be prepared for a single bus route for various models of electric buses under different traffic conditions. Changing traffic conditions may require several passes to determine the representative set of energy profiles. The energy profiles are derived from driving profiles and depend on the parameters for the assumed energy consumption model. Using the energy profiles, the energy consumption of electric buses on the bus route can be determined. Taking into account the energy consumption models corresponding to the specific types of electric buses, the range for buses of various types can be estimated and the charging schedules can be determined.

The proposed method for the estimation of energy consumption using energy profiles is compared with kinematic methods and methods using machine learning. In kinematic methods, the kinematic model that involves the kinematic parameters for an electric vehicle is built, and on the basis of this model the energy consumption is estimated. In the methods that use machine learning, artificial neural networks are usually applied for the estimation of energy consumption. The artificial neural network requires large training datasets. The methods for the estimation of energy consumption can be compared taking into account various properties.

Table 5. Properties of the selected methods for the estimation of energy consumption.

Method	Complexity	Efficiency	Adaptability
Kinematic	medium	medium	medium
Machine learning	high	high	low
Energy profiles	medium	high	high

presents an assessment of the complexity, efficiency, and adaptability of selected methods for the estimation of energy consumption, including kinematic methods, machine learning methods, and the proposed method using energy profiles.

The kinematic methods require a kinematic model, whose construction can be complicated. Efficiency in the use of the kinematic model is limited and depends on the accuracy of the model. The adaptability of kinematic methods is moderate because adaptation to new conditions can require modifications in the kinematic model. The methods using machine learning are often based on artificial neural networks whose construction is complicated and the neural network requires training. After training the neural network, its efficiency is high. The adaptability of neural networks is low because their adaptation to new conditions often requires new time-consuming training.

The complexity of the method using energy profiles is medium and requires statistical calculations of large GPS datasets. The efficiency of the method using energy profiles is high and practically depends only on the quality of the applied energy consumption model and the accuracy of the GPS data used. The adaptability of the method using energy profiles is high, and adaptation to the new conditions may require the new set of GPS data or an uncomplicated modification in the energy consumption model.

5. Conclusions

The transformation in transport systems toward electromobility requires methods and procedures to support the decision-making processes implemented by local authorities. The presented method for determining the driving and energy profiles for urban bus routes allows assessing their suitability for operation with electric buses. The driving profiles and the resulting energy profiles can be the basis for estimating energy consumption on the analyzed bus route under various traffic conditions. Various bus routes can be compared in terms of the energy consumption of the electric buses that operate them. The use of GPS data allows for the proper determination of the driving and energy profiles, which are useful for the prediction of the energy consumed by the electric bus in individual sections of the bus route and on the entire bus route.

The proposed method for determining the driving and energy profiles allows for comparing varying bus routes with each other and evaluating their suitability for operation with electric buses. The method can also be used to choose the right electric bus model for existing bus routes. Estimation of energy consumption on bus routes allows proper planning location of charging stations and can be helpful in scheduling by taking into account the range of the various types of electric buses and traffic conditions.

Restrictions may apply to places with dense and high buildings and bad weather conditions. In both cases, location using GPS may have lower accuracy. As part of further research, measurements are planned to be performed in various building patterns and weather conditions to determine the degree of influence from these factors on the proposed method.