Development and validation of energy demand uncertainty model for electric city buses

Transportation Research Part D 63 (2018) 347–361

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

Development and validation of energy demand uncertainty model for electric city buses

T

⁎

Jari Vepsäläinen , Klaus Kivekäs, Kevin Otto, Antti Lajunen, Kari Tammi School of Engineering, Aalto University, Espoo, Finland

A R T IC LE I N F O

ABS TRA CT

Keywords: Electric vehicle Energy demand Uncertainty Modelling Simulation

The prediction of electric city bus energy demand is crucial in order to estimate operating costs and to size components such as the battery and charging systems. Unfortunately, there are unpredictable dynamic factors that can cause variation in the energy demand, particularly concerning driver choices and traffic levels. The impact of these factors on energy demand has been difficult to study since fast computing sufficiently accurate dynamic simulation models have been missing, properly quantified in terms of relevant inputs which contribute to energy demand. The objective is to develop and validate a novel electric city bus model for computing the energy demand, to study the nature and impact of various input factors. The developed equation-based model predicted real-world electric city bus energy consumption within 0.1% error. The most crucial unmeasurable input factors were the driven bus route, the number of stops, the elevation profile, the traffic level and the driving style. This understanding can be used to specify routes and stops for a given electric bus battery capacity. Worst-case scenarios are also necessary for electric bus sizing analysis. The best- and worst-case levels of the crucial factors were identified and with them synthetic best- and worst-case speed profiles were generated to demonstrate their effect to the energy demand. While the measured nominal consumption was 0.70 kWh/km, the computed range of variation was between 0.19 kWh/km and 1.34 kWh/km. For design sizing purposes, an electric city bus can have a broad range of possible energy consumption rates due to mission condition variations.

1. Introduction The electrification of public transportation brings out new challenges such as the trade-off between the battery energy capacity and the operating range (Kunith et al., 2016). The energy density of an electric vehicle battery compared to liquid fuels is 25–100 times less (Besselink et al., 2010). The resulting range limitation emphasizes the importance of optimal battery sizing. Unfortunately, though, this increased importance through less available energy also brings increased sensitivity to how the energy is consumed. In this paper, we study the impact on energy demand variation between best- and worst-case electric bus energy consumption scenarios quantified from field data. We show the energy consumption can deviate by over a factor of two from nominal due to bus operating scenarios alone. As will be discussed, there are multitude of studies concerning the energy demand prediction of both hybrid electric vehicles (HEVs) and battery electric vehicles (BEVs) with different objectives and simulation models. Fiori et al. (2016) developed and validated a computationally efficient quasi-steady power-based BEV consumption model intended for large number of tests which is also our target. However, while optimizing the battery and vehicle performances with a novel simulation model, Janiaud et al. (2010) noted ⁎

Corresponding author. E-mail address: jari.vepsalainen@aalto.fi (J. Vepsäläinen).

https://doi.org/10.1016/j.trd.2018.06.004

1361-9209/ © 2018 Elsevier Ltd. All rights reserved.

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that it is vital to use dynamic models for powertrain sizing purposes. Unfortunately, the commercial dynamic simulation models are computationally heavy, as Genikomsakis and Mitrentsis (2017) stated when designing a computationally fast physics-based BEV consumption model, with the main powertrain components represented with efficiency maps. Here, we also aim for computational lightness and build on their work by adding physics-based models of the batteries and the motor. Given these works, we seek here a computationally efficient, dynamic and physics-based electric city bus model designed to study the variation in the battery energy demand caused by factors such as driving style, traffic level, route characteristics, etc. Computation speed has commonly not been of interest with previous dynamic physics-based electric city bus modeling efforts, e.g. (Halmeaho et al., 2016). Here we seek computational efficiency in addition to accurate quantification of energy demand, to then allow for iterative considerations of multiple scenarios. The objective of this paper is to develop a fast-computing electric city bus model and validate it with real-world test data. The model will act as a platform to understand possible energy demand under widely varying scenarios. 1.1. State-of-the-art Factors affecting BEV energy consumption have been studied with data based models using real-world measurements. Wu et al. (2015) constructed a mobile data collection system on a BEV automobile to study the impact of route type on the energy demand. Based on the measured data, they present a consumption estimate for the route studied. Their analysis revealed that the energy consumption is higher when driving inside a city than on highway routes. Younes et al. (2013) came to the same conclusion and further analyzed some of the key factors contributing to the energy consumption of an EV. These factors were route type, driving style and ambient temperature. However, the effect of driving style was unclear in their study due to lack of real-time measurements. Kontou and Miles (2015) have studied the effect of driving style to electric city bus energy consumption. They measured the energy consumption of 46 drivers and noted that some of the drivers were consistent (only variation of 0.2 kWh/km). However, the most inconsistent drivers’ had even 10 times as much variation in energy consumption. Driving on mountainous roads compared to level routes and a decreased ambient temperature were shown to increase the energy consumed. These effect of ambient temperature was also similarly noted in (Lai, 2015) and (Fiori et al., 2016). While these experimental measurements based results are conclusive, we seek here a physics-based model derivation of the critical inputs to allow parametric changes to different scenarios. Many energy consumption studies have been completed on mission related factors, including traffic, driving style, route, and elevation profile. These studies have been more focused on internal combustion engine (ICE) vehicles. Driving style factors such as aggressive accelerations have been found to account for 10–20% of fuel consumption increase with urban busses (Ma et al., 2015) and 30–40% with passenger vehicles (Zhou et al., 2016). Zhou et al. (2016) also noted that determined, calm and anticipatory driving style can reduce the fuel consumption by 15–25% and optimized autonomous driving could enhance fuel economy by 20%. Evans (1978) studied the effect of traffic on overall fuel consumption and estimated that a 1% increase in trip time due to traffic increases the fuel consumption by 1.1%. Furthermore, for city buses on the same route, higher average speed indicates less traffic stops which reduces the fuel consumption (de Abreu e Silva et al., 2015). Moreover, Lajunen (2013) showed that optimizing the mission speed profile can increase the energy efficiency of electric city buses up to 19%. We seek here to extend these results to BEV buses using parametric physics-based models. In addition to the factors affecting the nominal energy demand, the energy demand sensitivity has been studied by Diaz Alvarez et al. (2014), who trained a neural network to predict the energy consumption of electric vehicles based on position data acquired from BEV driver’s smartphones. They performed a sensitivity analysis where the variance in the energy consumption was studied for each variable value. The studied variables were limited to driving style characteristics. The conclusion was that positive acceleration jerks caused most of the variation in the overall consumption and the average speed had the least effect in urban city cycles. Asamer et al. (2016) used a longitudinal dynamic model (LDM) of the BEV to perform a sensitivity analysis with a broader scope of variables. They concluded that drive efficiency, rolling resistance coefficient and the utilization of auxiliary devices cause the most variation in the energy demand, and that the vehicle mass is only significant in uphill routes. Simpler models have also been preferred in other studies concerning the BEV energy demand estimation (Hayes et al., 2011). More adequate models such as in (Janiaud et al., 2010; Sehab et al., 2011; Lajunen, 2012) focus on the sizing of the electrical powertrain for specific mission profiles. Lajunen (2014) presented a detailed analysis of hybrid and electric city busses. His simulations showed that the energy consumption of an electric city bus is less sensitive to varying mission profiles than hybrids or conventional diesel busses. However, electric busses were also demonstrated to have the most variation in capital costs. In a more recent study, Lajunen and Tammi (2016) present the distribution of energy losses in an electric city bus with different powertrain configurations. Approximately 90% of the energy is consumed to power the electric motor, the auxiliary devices and to compensate for the rolling resistance loss of the tires as presented in Fig. 1. The amount of rolling resistance is proportional to the mass of the vehicle and the required auxiliary power for heating, ventilation and air conditioning (HVAC) is relative to the ambient temperature. We here seek to build on these works to assess the impact of mission related factor variations, including traffic, driving style, route, and elevation profile. We seek this in a physics-based computational formulation, to thereby allow consideration of many alternative scenarios. This will enable determination of large contributors and also of worst case scenarios for sizing analysis and potential electric bus route limitations. 1.2. Energy consumption variability Energy demand variability has many possible sources. We call these sources noise factors. Such factors contributing substantially 348

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Fig. 1. Distribution of the energy losses of an electric city bus on a city route (Lajunen and Tammi, 2016).

to the energy demand variation in the aforementioned studies can be both unknown or known and quantified in terms of contribution. Instead, here we classify inputs as known which we can quantify, and unknown which remains as residual variation. The known factors are further subdivided into tolerance and extensive variations, as depicted in Fig. 2. Our subdivision here is different than in (Johansson et al., 2006), who’s subdivision is based on manifestation environment. We consider the tolerance noise factors as those that represent manufacturing variability, aging, and wear of components. As these change, they potentially can significantly influence energy efficiency. To ensure adequate performance margin against such influences, they can affect the decision on the nominal control factor values as set by the designer in Fig. 2. Such considerations are as discussed in the robust design domain which was originally introduced by Taguchi (1986). We consider extensive noise factors as variation in operating conditions of the bus, including payload, headwind, ambient temperature, etc. Extensive noise factors are more dynamically unpredictable in time, yet the shape of their variation distribution over time can be estimated based on time series data. The variation of the tolerance noise is generally smaller than the extensive noise and can be static in time by varying unit-to-unit or bus-to-bus installation. Finally, we also consider unknown contributors to variability. Contributors from unknown factors are the difference between measured data and model predictions using the noise factors above. Considering the time series data between measurements and predictions, the difference over time forms a distribution which can be considered random, ideally with zero bias. Further, the impact of unknown factors can be studied as a part of noise factor simulations by estimating the maximum- and minimum effects on the energy demand.

2. Simulation model The proposed dynamic electric city bus model was developed using MATLAB’s Simulink modelling environment. The purpose of the model is to represent the electric motive power system and auxiliary equipment in terms of dynamic energy consumption at the sub-second time scale, to adequately represent real-time power consumption. Further, the intent is to represent the system at the level of components, such as the battery, motor, motor controller, internal bus heating and air conditioning, etc. This also requires the subsecond representation of the power system inputs, including for example the speed command of the virtual driver, and the time series ambient temperature changes over the course of a day. The model block diagram is as shown in Fig. 3. Typically, dynamic simulation models such as sought here for an electric bus power system require great computational effort (Orfila et al., 2017). Therefore, some

Fig. 2. The control and noise factors that shape the output response of energy demand. The noise factors are divided into unknown, tolerance and extensive types according to their variation behavior. 349

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Fig. 3. The energy and information topology model of the electric city bus. The torque of the electric drive is driven by the speed command given by the virtual driver. The power supplied by the battery is controlled with the cascaded controlling system.

simplifications were made to reduce the computation time. The calculation flow starts with the driver speed command. The speed demand is compared to the simulated real-time speed in the speed controller. The speed and current controllers form a cascaded control system where the former governs the slow mechanical system and the latter the fast-paced electrical phenomena. The current controller sets the voltage of the inverter which excites the motor with the power supplied from the battery. The motor torque is then conveyed with a single-speed gearbox to the rear wheels that thrust the vehicle forward. In Fig. 4, the forces acting on the vehicle body are governed by

m v ·dvx / dt = ΣFx −Fres−m v g sinθ

(1)

Fres = Fr + Fd

(2)

Fr = fr m v g Fd = 0.5Cd ρa Av (vx + vhw

(3)

)2

(4)

ρa = (pa / Ra Ta)

(5)

where vx is the vehicle speed, vhw is the headwind, g is the gravitational acceleration, Fx is the tractive force and m v is the mass of vehicle. The resistive forces Fres considered are the rolling resistance Fr and the aerodynamic drag Fd . The rolling resistance coefficient is denoted with fr , the drag coefficient with Cd and the cross sectional area of the vehicle as Av . The density of air ρa is depended on the ambient temperature Ta , air pressure pa and the spesific gas constant for air Ra . The effect of air humidity on air resistance can be neglected and the air pressure can be assumed to be constant, because environmental humidity or pressure changes do not significantly affect air density compared to temperature changes. Steering, vibrations and tire dynamics are neglected. The electric city bus model considers only forward movement and longitudinal dynamics. The lithium-ion battery nominal voltage, specific energy and capacity, discharge properties and safety characteristic depend on the cathode and anode materials (Hentunen, 2012). Lithium-Iron-Phosphate (LiFePO4) batteries offer a long cycle life and adequate safety properties, even though at the price of mediocre energy density. These characteristics fulfil the requirements of an electric city bus and thus European Batteries EB 45 Ah LiFePO4 cells were selected. For the battery model, the precise battery state-of-charge (SOC) estimation and the dynamic voltage drop description were needed. Therefore, the Thevenin circuit model in Fig. 5a was applied (He et al., 2011). The model is governed by (6)

ub = uoc−Rint ib n

uoc =

∑ (ck × (1−SOC )k)

(7)

k=0

Fig. 4. The free-body diagram of the electric city bus with the effective forces. 350

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Fig. 5. (a) The Thevenin circuit model that considers the transient voltage behavior. (b) The internal resistance of the battery that grows as the temperature decreases. t

SOC = 1−(1/Q r)·

∫ (ib) dt

(8)

0

(9)

Rint = Rss + R τ

where the battery terminal voltage ub is the open-circuit voltage uoc subtracted by the resistive losses caused by the internal resistance Rint . The open-circuit voltage uoc is a nonlinear approximation of the voltage as a function of SOC , which is the LiFePO4 cell behavior fitted with to a k th polynominal ck and Qr is the coulombic capacity of the battery (Gao et al., 2002). The internal resistance consists of the steady-state Rss and the transient portion R τ which in parallel with the capacitance Cτ causes a transient response in the battery voltage according to (10)

dub/ dt = (1/ Cτ )·(ib−ub/ R τ )

The internal resistance transforms the electrical energy into heat proportional to the current supply. The thermodynamical temperature rise is not considered yet the resistance is estimated to depend on the constant battery temperature as shown in Fig. 5b. In addition, as the battery slowly decomposes the internal resistance starts to irreversible increase due to the growth of the solid electrolyte interphase (SEI) (Zhang, 2006). The SEI growth-rate and breaking point of the battery are challenging to estimate (Barré et al., 2013). These state-of-health (SOH) factors depend on the cathode mix, cycle life, storage SOC and the operating temperature (Groot, 2012; Ecker et al., 2014). Other relevant issues are voltage imbalance between the cells, malfunctioning cells and safety concerns due to the highly reactive lithium (Lu et al., 2013). The cycle-based aging in the battery model is described with

Qr = 3600Q Ah f1 (N )

(11)

f1 (N ) = 1−0.2(N / Nnom)

(12)

Where f1 is the estimated linear capacity fade, Q Ah is the ampere-hour capacity of the battery and N is the number of used cycles (Chen and Rincón-Mora, 2006; Hentunen et al., 2011). One cycle considers the full charge and discharge of the battery. The cycle threshold Nnom depends on the battery chemistry and represents the state when 80 % of the original capacity is remaining. This point is argued to be the indicator of the breaking point or the end-of-life (EOL) of the battery, after which it should no longer be used to power a BEV (Spotnitz, 2003; Groot, 2012). The modelled LiFePO4 battery provides the electrical power for the electrical motor model, which is a permanent magnet synchronous machine (PMSM). The PMSM is excited with the inverter’s 3-phase voltage, which generates phase currents proportional to the produced electromagnetic torque. The dynamic efficiency of the inverter is dependent on the torque and speed of the motor, as shown in Fig. 6. The sinusoidal phase voltages and currents are fixed to rotor coordinates with the direct-quadrature (dq) transformation. The resistive losses of the winding are considered, while magnetic saturation, hysteresis losses and eddy currents are neglected. The motor model is described by

u s = R s i s + dψ s / dt + jωs ψ s

(13)

ψ s = Ls i s + ψf

(14)

TM = (3/2) p ·Im { i s ψ s∗}

(15)

dωr / dt = (1/ Jt )·(TM −TL)

(16) 351

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Fig. 6. The efficiency of the inverter as a function of motor torque and speed.

ωs = pωr

(17)

where u s is the rotor voltage vector, R s is the resistance of the windings and i s is the rotor current vector which consists only of id in steady state and iq is used only in the field weakening region. In the field weakening region the magnetic flux is weakened to reach higher speeds at the cost of reduced available torque. The permanent flux induced by magnets is noted as ψf and the motor inductance with Ls . Furthermore, ωs is the electrical speed of the motor, ωr is the physical speed of the motor and p is the number of the pole pairs. Motor mechanical and load torques are TM and TL , respectively. The total moment of inertia reduced to the motor is Jt , which considers the rotor, tire and driveline inertias. In addition to the propulsion, the motor is also used for energy regeneration when decelerating. However, utilizing only the motor for braking can lead to battery overload (Sanguinetti et al., 2017) and motor control instability. If the battery is charged when full or with excessively high currents, the battery lifetime will shorten substantially. Therefore, different braking modes are applied to combine the use of mechanical brakes and regenerative motor braking, as shown in Table 1; assisted regeneration and non-regenerative. The mode selection depends on the battery SOC, vehicle speed and deceleration. The assisted regeneration mode is activated only if all the corresponding conditions are satisfied. In the assisted regenerative braking mode, the motor regenerates energy within its operation capabilities while rest of the braking power demand is provided with the mechanical brakes if needed. The non-regenerative braking mode is entered if even one of the conditions is violated, in which case only the mechanical brakes are applied. 3. Model validation For model validation purposes, experimental test runs were completed in Finland on the Espoo city bus line 11 from Tapiola station to Friisilä station using a prototype electric city bus (Laurikko et al., 2015). The measured prototype electric city bus was converted from a diesel bus. The time spent on the route was just under 26 min, the length of the route was 10.4 km and the rest of the route descriptive parameters are listed in Table 2. The route consisted of suburb areas with the speed limit of 40 km/h and a short 60 km/h speed limit zone. The measured and simulated vehicle speed profiles on the route are shown in Fig. 7. The Root-mean-square error (RMSE) between the simulated and measured speed profile was 0.095 km/h. When compared to the average speed, the RMSE was 0.39%. The elevation profile of the route was also measured and added to the model. The nominal parameters for the simulated test-drive were adapted from the prototype and are presented in Table 3. The propulsion energy for the vehicle was supplied by the battery model. The measured and simulated battery currents, voltages and SOCs are presented in Fig. 8. Although, the measured and simulated voltages and currents are not identical, the integrated energy consumption on the route was measured at 0.7009 kWh/km and the simulated consumption was 0.7002 kWh/km, corresponding to a 0.1% difference. In comparison, Halmeaho et al. (2016) reported a 1.5% error in energy consumption with their electric bus simulations and Fiori et al. (2016) reported 5.86% with passenger EVs. However, the validation was only made using one real-world cycle, unlike in the study carried out by Fiori et al. (2016), where they validated the model for multiple cycles on multiple routes. Certainly, the fidelity of our model prediction will also be lower when more cycles are considered. The measured energy consumption Table 1 The braking modes and respected conditions of the model. Braking mode

Assisted regeneration

Non-regenerative

Conditions

SOC < 90% and Speed > 5 km/h and Deceleration < 4 m/s2

SOC > 90% or Speed < 5 km/h or Deceleration > 4 m/s2

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Table 2 Description of the measured driving cycle. Factor

Value

Time (s) Distance (km) Average speed (km/h) Max. speed (km/h) Number of stops Stops per km Max. acceleration (m/s2) Max. deceleration (m/s2) Roundabouts Right turns per km Left turns per km

1548 10.4 24.2 59.0 18 1.7 1.67 −2.57 3 0.58 0.38

Fig. 7. The measured and simulated vehicle speed on the tested bus route as a function of time. The measured elevation profile of the route was used as an input in the simulation model.

included the auxiliary power, as shown in Fig. 9, which was directly implemented to the model. In Fig. 10, the measured and simulated power in the period 100–300 s is displayed. The behavior of the simulated power follows the noisy measured power yet the match at each instant in time is not ideal. The RMSE in this period was 9.72 kW which is 39.4% difference to the absolute mean value. There are three distinguishable types of deviations between the measured power and simulated one. Firstly, from 115 s to 130 s the power fluctuation in the measured power is much higher than in the simulated one. This is because the real electric motor responds faster and more aggressively to regenerative braking control changes. However, the average power is quite similar in this braking event. In the period 140–160 s the power is also quite the same on average, however in this case radical changes happen in the simulated power. There is a rapid inconsistency before a deceleration, probably due to traffic, which the simulation model recognizes as a possibility to regenerate. Since this happens before the actual deceleration, the model needs to power up to keep with the demanded deceleration. The last example deviation can be seen in the period 160–170 s, where the measured power is slightly higher than the simulated and so the average power is not the same. This small difference is due to the fact that known noise factors, such as headwind and rolling resistance are not constant in reality as assumed in this simulation, since the related data was not available. Hence, the uncertainty in the prediction of energy consumed is only due to these incremental changes of minor uncertainties and the consumption prediction is thus accurate. Moreover, the transient nature of the measurements is typical in model validation, which the model does not mimic, yet the model is still capable of predicting the energy consumption accurately (Guzella and Sciarretta, 2013). In addition to the model validation, the speed of the simulation was investigated, since total computing time becomes important for studying alternative scenarios using simulations. The solver applied was the Fourth-Order Runge-Kutta with a fixed time step of 0.001 s. The simulation was repeated 60 times using the Tapiola-Friisilä route and the average computing time was 74.9 s or 20.7 times faster than real-time. The computations were run in MATLAB on an Intel(R) Xeon(R) CPU @ 3.30 processor desktop computer with 8 GB of RAM. Genikomsakis and Mitrentsis (2017) introduced this speed benchmark method and they achieved speeds of 50 000 times faster than real-time.

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Table 3 The nominal parameters for the model adapted from the real-world electric city bus. Factor

Description

Value

Unit

mv Av Cd i rt Jt fr ρa Ta Tb ηg

Total mass of the vehicle Vehicle frontal area Coefficient of drag Differential gear ratio Dynamic radius of the tires Total inertia (rotor, tire and driveline) Rolling resistance coefficient

12,400 6.2 0.6 6.5 0.43 0.82 0.01

kg m3 – – m2 kg m2 –

Density of air (when Ta = 5 °C) Ambient temperature Battery temperature Differential gear efficiency

1.27 5 20 97

kg/m3 °C °C %

Battery cell

uc Qah x1 x2 SOC Rint Cτ

Nominal voltage of the battery cell Capacity of the battery cell in ampere-hours Number of cells in series Number of cells in parallel Battery state-of-charge in the beginning Internal resistance Internal capacitance

3.2 45 192 2 89 2.5 5

V Ah – – % mΩ F

Motor

p ψf

Number of pole pairs Flux induced by the permanent magnets

6 0.4

– Vs

Ld Rs

Stator armature inductance Stator resistance

1 55

mH mΩ

General

Fig. 8. The measured and simulated battery voltage, current and SOC as a function of time.

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Fig. 9. The auxiliary power of the electric city on the validation route as a function of time.

Fig. 10. The period 100–300 s of the measured and simulated power on the Tapiola-Friisilä route.

4. Uncertainty factors The results above show that the simulation model is sufficiently accurate for purposes of studying variation in energy demand. Next, we seek to identify ranges of variation in the inputs, to look for the best and worst-case scenarios. All noise variables therefore must be characterized for range limits. This presents two problems, the known (measurable) noise factors and the unknown (unmeasurable) noise factors. 4.1. Known noise The variation distribution of known noise factors can be identified and quantified, as diagrammed in Fig. 2. Here, the developed electric city bus model included 5 tolerance and 10 extensive noise factors, as shown in Table 4. The tolerance noise factors could all Table 4 The known noise factors are divided into tolerance and external noise. Noise type

Factor

Tolerance

Motor resistance, Rs

Motor inductance, Ld

Motor permanent-magnet flux, ψf

Battery capacitance, Cτ

Battery capacity, Qah

Extensive

Payload, mv

Headwind, vhw

Ambient temperature, Ta

Battery temperature, Tb

Cells in parallel, x2

Battery SOC, SOC

Rolling resistance, fr Battery Resistance, Rint

Battery Age, f1

Auxiliary power, Paux

355

Model discontinuities

Unpredictable

356

Battery SOH estimations

Magnetic saturation, hysteresis losses and eddy currents Steering

Contradiction

Complexity

Vibrations and heat transfers

Battery cell balance

Incomplete knowledge

Driver Age

Traffic and stops

Elevation profile

Driving style

Route

Simulation model reliability

Control tuning performance errors

Factor

Nature

Discontinuities are a probable cause of simulation errors and their influence is difficult to estimate accurately (Guzella and Sciarretta, 2013) The speed and current controllers are tuned intuitively and differentiate from the real-world tuning. In addition, control can never reach ideality Simulation model can never describe the real system perfectly. However, validating the model with realworld tests increases the reliability of the results The route can be suburban, city, highway or a combination of them. Lajunen and Tammi (2016) presented that the average energy consumption of a suburban route can be as low as 0.9 kWh/km while in busy city route the consumption can be as high as 1.4 kWh/km The driving style can be steady, normal or aggressive. The driving style can be very consistent and efficient or completely unpredictable as Kontou and Miles (2015) reported in their study. In the worst case, the driving style can more than double the energy consumption The route elevation profile can be uphill, downhill, fluctuating or level. An optimal road-grade design between two end points at the same elevation could reduce up to 30% compared to a flat road (Liu et al., 2017) Traffic and stops cause extra accelerations and decelerations. Traffic is one reason behind inconsistent driving style. In addition, increased idle time leads to significantly higher auxiliary power demand per kilometer, since power is consumed even at complete stand-still. The auxiliary power is a significant part of total energy consumption even at normal traffic conditions (see Fig. 1) (Lajunen and Tammi, 2016) Older drivers tend to have higher energy consumption (Knowles et al., 2012). This might be because older drivers are more accustomed to their driving habits and thus improve less after training sessions (de Abreu e Silva et al., 2015) An estimation model for cell imbalance was not found in the literature. The equalization of voltage among the cells is not necessarily random but can be product quality driven. Kontou and Miles (2015) noted that the SOC between battery modules differs, yet not significantly. In their research, the total SOC had a minor impact on energy consumption and thus the battery cell balance has some effect A general SOH estimation model has not been established yet for lithium-ion batteries. Internal resistance growth behavior and estimations of the breaking point of the battery are currently researched (Barré et al., 2013; Ecker et al., 2012, 2014) These factors can be modelled but would slow the simulation significantly. To avoid unnecessary complexity, they are commonly left out of simulation models (Fiori et al., 2016; Halmeaho et al., 2016) Depends on tire dynamics and damping which are complex models. In addition to tire losses, turning is assisted with electro-hydraulic power steering, which can consume up to 4 kW in hybrid electric heavy truck operation (Spargo et al., 2014) Model for all the bodies and their interactions would need its own independent study

Description

Table 5 The nature of unknown uncertainty factors of the electric city bus model and their estimated effect to the total variation on a scale from 1 to 10.

2

No

No

2

Yes

1

No

No

1

1

No

Yes

6

1

Yes

8

Yes

Yes

5

7

No

No

No

Included in the model?

2

1

1

Estimated effect

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be tested with a ± 10% normally distributed variation which is not unrealistic for electric components over the life of such components. The extensive factors each have their own unique distributions from the time series measurements.

4.2. Unknown noise In general, the nature of the unknown noise is commonly divided into three categories (Brugnach et al., 2008): unpredictable, incomplete knowledge and contradicted factors. The unpredictable factors cannot be modelled, the incomplete knowledge factors lack a descriptive model and the contradicted factors have more than one plausible interpretation of their behavior. Furthermore, we suggest a fourth category: complexity factors, which can be included, but are reduced out since they require excessive computing time and have only an insignificant effect on the energy consumption variation. Unknown uncertainty factors in the electric city bus simulation are categorized according to their nature in Table 5. It is not possible for any list of factors to account for all unknown uncertainty, but the list in Table 5 represents obstacles to an ideal electric city bus energy consumption model. We focus here on the unpredictable unknown factors which are identified and included in the model, but whose nominal value and variation is unmeasured and so unknown directly. While unquantified, the effect of each factor to the total energy demand variation was nonetheless estimated using a scale from 1 to 10, based on previous studies in the literature review (Evans, 1978; Younes et al., 2013; Alvarez et al., 2014; de Abreu e Silva et al., 2015; Ma et al., 2015; Wu et al., 2015; Lajunen and Tammi, 2016; Zhou et al., 2016). Of all the considered unknown noise factors, traffic, route, the number of stops, the elevation profile and the driving style were deemed to have the biggest impact on the energy demand variation as shown in Table 5. The best- and worst-case values of these significant unknown factors are complicated to determine because the factors each have their individual constrains, yet they can’t all be set at their worst-value at the same time. Otherwise the driving mission becomes impossible. Therefore, from the literature and our measurements we identified an example worst-case scenario. There exists other factor value combinations that would also result in a worst-case, which is in the limit of the bus performance, and our selection of factors values is just one of these combinations. The bestcase was determined by reversing the effect of the worst-case, i.e. changing the same grade uphill into a downhill, or by analyzing the validation cycle we have measured. Then, best- and worst-case speed and elevation time-series profiles were generated to estimate the impact on energy demand variation of these unknown noise factors. In order to designate the extreme estimated values for route, traffic and stops the validation cycle was used as a reference point. The number of stops in the reference cycle (Espoo 11) is 1.7 stops per kilometer. In the best- and worst-case scenarios, the reference stops per kilometer was halved and doubled, resulting in 0.85 and 3.4 stops per km. Thus, the average number of stops per kilometer is realistic. The number of stops are a part of route definition in addition to traffic. The effect of traffic was also simulated with limited speed at every other acceleration to 20 km/h, which is half of the nominal speed limit. Similar behavior was observed in the reference

Fig. 11. Synthetic best- and worst-case speed and elevation profiles of electric city bus energy demand. 357

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Fig. 12. The measured and simulated consumptions on the Tapiola-Friisilä route and the corresponding synthetic best- and worst-case consumptions.

speed profile (Fig. 7) and the only explanation to such behavior is traffic. The worst-case elevation profile and driving style are limited by the maximum performance of the modelled electric city bus. As shown in Fig. 11, the maximal acceleration is limited to 1 m/s2 because that is the maximum performance the bus can achieve while climbing a road with 15 % grade (Lajunen, 2012). In addition, the acceleration should not exceed 1 m/s2 to ensure that passengers can walk and move safely without falling (Karekla and Tyler, 2018). In the best-case, the driving style is steady with constant accelerations and decelerations of 0.5 m/s2. A lower average acceleration would be considered as slow and thus would intervene with normal traffic flow. In both best- and worst case scenarios, the travelled distance was 10.4 km, the same as in the measured nominal cycle. Given these variation ranges on unknown noise, the best and worst combinations were applied to the simulation model. The range limits for the known noise factors need a separate study in order to examine them further. In Fig. 12, the synthetic best- and worstcase consumptions are shown in reference to the nominal measured and simulated consumption on the Tapiola-Friisilä route. It can be seen in Fig. 12, that while the nominal route operation is well represented by the model, when considering the range of variation on inputs, the resulting consumptions were 1.34 kWh/km and 0.19 kWh/km for the best- and worst-cases, respectively. This represents a 2X range on energy consumption relative to nominal, a remarkable range that therefore clearly must be considered when designing an electric city bus and sizing components. In addition to overall energy consumption, peak power consumption is a second design consideration. The best- and worst-case powers in the period 100–300 s are shown in Fig. 13 to show a close-up behavior of power consumption. Overall we find the best-case the required propulsion peak power is only half of the worst-case peak power. The input factors of the best- and worst-cases are shown in Table 6. The reduction in stops on route increase the average speed undoubtedly. However, this correlation is reduced by the faster accelerations and decelerations in the worst-case, which have a positive effect to average speed. The extreme road-grades had a considerable difference, which probably impacted the most to the

Fig. 13. The power of the period 100–300 s in the synthetic best- and worst-case cycles. 358

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Table 6 Input values for the best-case and worst-cases. Factor

Best-case

Worst-case

Stops per kilometer (1/km) Average speed (km/h) Extreme road-grade Accelerations and decelerations

0.85 31.2 −15% 0.5 m/s2

3.4 18.7 +15% 1 m/s2

energy consumption. Nonetheless, buses typically operate in round-trips. Hence, if one way is downhill then the other is uphill, which would even each other out if the bus is charged only at one terminus.

5. Discussion and limitations Unknown noise factors were identified here according to their nature during the model development process. Yet, remaining unknown factors can always influence models from many sources, whether due to the mistakes made or the negligence of the modeler, in addition to approximations of the laws of physics used for the model. For example, the electric city bus model was constrained to forward motion only for control stability in near zero speeds. This simplification results in a discontinuity which might cause error compared to tests. Moreover, the model has rate limiters and saturation limits to avoid unrealistic behavior because exceeding these limits in real-world operation would cause component damage or even system failure. These limitations might not match the real-world limits. The surrounding environment also accounts for unpredictable uncertainty in the form of traffic and bus stops. The traffic level and other drivers’ behavior affect the driving style of the electric city bus driver. The driving style has been shown to have significant impact on the energy consumption in previous studies (Alvarez et al., 2014; Kontou and Miles, 2015; Ma et al., 2015; Wu et al., 2015; Lajunen and Tammi, 2016; Zhou et al., 2016). Furthermore, the range of possible mission profiles should be determined during the concept phase of designing a city bus. Such decisions can be thought as representing noise, since the designed bus might be used even in routes that it was not originally meant for. However, the literature also shows that speed variability has less effect on the energy consumption when the average speed is higher than 20 km/h, indicating that consumption difference between urban and highway routes is more dependent on the traffic or road elevation differences than the route type. Younes et al. (2013) state that the consumption is higher in cities because of increased stop and start driving. Beyond traffic and operation effects, unknown variability also exists in components. Furthermore, the variation between individual cell voltages in the battery pack was not considered in the depletion model given the lack of descriptive models in the literature. Battery depletion is dependent on the lowest cell voltage, therefore the battery management system (BMS) balances actively the cell voltages (Lu et al., 2013). However, the battery pack consists of hundreds of cells which makes it difficult to equalize the potential constantly. While battery SOH estimation models exist, there are differentiating views on battery degradation (Ecker et al., 2012, 2014; Barré et al., 2013). The representation of how internal resistance grows and capacity fades based on the age, used cycles and operating conditions of the battery have been studied with various synthetic aging methods with different lithium-ion chemistries, cell types and manufacturers. The high number of governing factors makes the degradation of the battery a continued area of research for lithium-ion batteries. In addition to the battery model uncertainty, detailed models of vibrations, heat transfers, steering, magnetic saturation, hysteresis losses and eddy current effects were deemed to require longer computation than was worth any increased accuracy. In summary, all crucial unknown noise factors were related to the mission operation of the bus, from designing the operation (route, elevation profile, number of stops) to the disturbances of operation (traffic, driving style). These were represented with simplified synthetic cycles which portrayed large energy demand variation reflecting the impact of typical wide range of driving behavior, landscape elevation and traffic variation. Overall, the simulation model validated well against measurements, both at sub-model level and overall energy demand. The model output speed followed the measured speed demand with a small RMSE. The overall energy demand error of the model (0.1%) was adequate compared to other works in the literature such as Halmeaho et al. (2016) (1.5%) and Fiori et al. (2016) (5.86%), though Fiori et al., 2016 used many different vehicles and routes. There was large RMSE in the momentary power estimation (39.4%), which did not impact the energy consumption prediction accuracy. Most of the RMSE is caused by the difference between the transient behavior of the model and the reality, such as during the period 115–130 s in Fig. 10. The measured data of transient power has larger amplitude, yet the amplitude difference has very small effect on the average power and thus very little impact on the average energy consumption. Hence, the unknown uncertainties, such as the model inaccuracy and model tuning difference between the model and reality, have a minor effect to the variation in energy consumption. This is the reason behind the estimated minor effect displayed in Table 5. In addition, the known uncertainties which were not measured in the validation cycle, such as the headwind and rolling resistance, also play a minor role in the momentary power estimation. The speed of the computation proved sufficient compared to alternative developed versions. While high performance computing systems could be used, the more efficient the model computation the more scenarios can be considered. Comparisons of computation speed with the literature is difficult, since this is rarely a priority and not reported in studies except with simplified models, as in 359

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(Genikomsakis and Mitrentsis, 2017). The speed of the computation is informed as a benchmark for future studies to use as a reference point. 6. Conclusion Previous studies show that significant contributors to energy consumption of an EV include variations in driving style, route, traffic, ambient temperature, rolling resistance, drive efficiency, auxiliary power consumption and vehicle mass. In our analysis, we recognized that the same factors affect the energy consumption of electric city buses, yet the effects are of different proportions. As such, electric city buses differ from EVs in that stops to pick up passengers are obligatory and that the mission profile is fixed, leaving no room for re-routing to avoid traffic. Thus, these uncertain factors needed investigation for electric city buses. To study these factors, an electrical energy consumption model was developed that corresponded the measured consumption within 0.1% error. The difference between simulated and measured data can be accounted for by the uncertainty in operating conditions, component quality and driver behavior. The measurable known noise factors need to be further investigated to establish the full range of energy demand variation. The most significant identified unmeasured factors were driving style, elevation profile, number of stops, route type and traffic related. The synthesized best- and worst-case levels of these factors resulted in an energy demand variation of 0.19 kWh/km to 1.34 kWh/km, a 2X range of variation over nominal. Such off-nominal factors therefore need be considered when sizing components and planning range limits with electric city buses. Acknowledgements We thank the VTT Technical Research Centre of Finland for their measurement data from the eBus project within the EVE program with the Finnish Funding Agency for Innovation, Tekes, as the main funding party. 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