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Develop of a fuel consumption model for hybrid vehicles a

b

a,⁎

a

Yan-Tao Zhang , Christian G. Claudel , Mao-Bin Hu , Yu-Hang Yu , Cong-Ling Shi a b c

c,⁎

T

School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China Department of Civil, Architectural and Environmental Engineering, University of TEXAS at Austin, TX, USA Beijing Key Lab of MFPTS, China Academy of Safety Science and Technology, Beijing 100012, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Fuel consumption Hybrid vehicles Traﬃc Flow Eco-Driving

Despite extensive work on the fuel consumption of vehicles, the evaluation of hybrid electric vehicles (HEVs) requires a model that can predict fuel consumption second by second. In this paper, a fuel consumption model for hybrid vehicles is developed based on the operation of internal combustion engine (ICE), electric machine (EM) and battery. The fuel consumption model for engine is based on steady-state fuel mapping with a transient correction. EM and battery module (EBM) is introduced to estimate the fuel consumption for diﬀerent modes of hybrid vehicle. The Argonne National Laboratory (ANL) measurements of diﬀerent driving cycles including the steady-state cycle, the Urban Dynamometer Driving Schedule (UDDS) cycle, the Highway cycle and the United States 06 (US06) cycle are used to veriﬁed the model. With cellular automaton simulation, we study the fuel consumption in traﬃc ﬂow and show that the fuel consumption can be signiﬁcantly reduced by hybrid mode. The mean fuel saving is approximately 30% in the traﬃc ﬂow on a horizontal road. The fuel consumption of traﬃc ﬂow under uphill, downhill, tailwind and headwind conditions also showes considerable fuel saving. The model can be used to evaluate the fuel economy of HEVs, and provide eco-driving route-choice suggestions for drivers.

1. Introduction

1.2. Literature review

1.1. Motivation

The control and management of HEV power systems has been taken into consideration by various perspectives. The pioneer works mainly focus on upgrading the control strategy of HEV power systems to reduce fuel conumption. For instance, Barsali et al. proposed a control strategy to minimize fuel consumption by oﬀering electricity generator instantaneous power in advance [5]. Amjadi et al. studied the design of intelligent control strategy for coordinating power distribution among batteries, ultracapacitors, and motors in ultracapacitor- supported plugin HEVs [6]. The energy management and waste heat recovery problems have also been widely studied. Marzougui et al. studied the energy management for hybrid power system consisting of fuel cell, ultracapacitor and battery [7]. Nader et al. proposed to use the Brayton cycles to recover the engine waste heat of a serial HEV and investigated the potential fuel consumption savings [8]. Recently, more researches focus on the optimization problem of energy management. Sorrentino et al. developed a mathematical procedure for the co-optimization of design and energy management of FCHVs [9]. Li et al. proposed an online adaptive equivalent consumption minimum strategy for FCHVs and showed that the new strategy had the least hydrogen consumption and oﬀered the longest durability of fuel cell [10].

Energy and environmental issues resulting from transportation are becoming increasingly serious. By a rough estimation, transportation consumes 59% of oil and produces 22% of carbon dioxide annually world-wide [1]. With the growing desire for “lucid waters and lush mountains”, the vehicle industry is facing unprecedented pressure of developing energy eﬀecient systems, such as intelligent driving-support systems [2] and hybrid power systems [3], to help control and reduce fuel consumption. Hybrid electric vehicles (HEVs) and fuel cell hybrid vehicles (FCHVs) have appeared to be a promising technological solution because HEVs have both high fuel economy and low pollutant emission level by integrating ICEs with EMs [4]. On the one hand, HEVs perform better in running long trip. On the other hand, the management strategy of HEVs almost keeps the engine working in its highest eﬃciency area, so that the emission is controlled to a low level. However, to this end, the quantitative evaluation of fuel eﬃciency for different HEVs remains an open question. The vehicle industry requires a model to predict the fuel consumption of HEVs in various conditions.

⁎

Corresponding authors. E-mail addresses: [email protected] (M.-B. Hu), [email protected] (C.-L. Shi).

https://doi.org/10.1016/j.enconman.2020.112546 Received 12 November 2019; Received in revised form 7 January 2020; Accepted 25 January 2020 0196-8904/ © 2020 Elsevier Ltd. All rights reserved.

Energy Conversion and Management 207 (2020) 112546

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Nomenclature

a A b bopt C0 C1,C2 CD Cr dn Ebatt g G i io ig l Lie, j , Mie, j P Pe PEM Qeg Qe Qg r Te Tm Tw ua uw Va

Vc Vmax

Vehicle instantaneous acceleration (m/s2) Vehicle windward force area (m2) Instantaneous consumption rate (g/KW·h) Optimal instantaneous consumption rate (g/KW∙h) Constant road rolling resistance coeﬃcient Speed-related road rolling resistance coeﬃcients Air resistance coeﬃcient Road rolling resistance coeﬃcient Distance between two neighboring vehicles (m) Battery discharge power (KW) Gravitational acceleration (m/s2) Gravity (N) Road slope The ﬁnal ratio of vehicle Gear ratio of the AMT Length of vehicle (m) Regression coeﬃcients for the MOEe Randomization probability in NaSch model Power of engine (KW) Power of electric machine (KW) Gasoline consumption for charging the battery (cc/s) Electricity consumption rate (kw∙h) Gasoline consumption (cc/s) Wheel radius (m) Torque of engine (Nm) Torque of electric machine (Nm) Torque of wheel (Nm) Speed of vehicle (km/h) Speed of wind (km/h) Speed of vehicle (m/s)

Critical speed of vehicle (m/s) Maximum speed of vehicle (m/s)

Greek

ρ ρc ρd ρg δ βij ωm ωe ωw ηT ηEM

Road occupation rate Critical road occupation rate Air density (kg/m3) Gasoline density (kg/m3) Rotational mass coeﬃcient Corresponding coeﬃcients Rotational speed of the EM (r/min) Rotational speed of the engine (r/min) Rotational speed of the wheel (r/min) Transmission eﬃciency of machine Transmission eﬃciency of EM

Abbreviations AMT batt EM HEV ICE ITS MOEe NaSch opt SOC VT-Micro

Automatic machine transmission Battery Electric machine Hybrid electrical vehicle Internal combustion engine Intelligent transportation system Measuer of Eﬀectiveness (mL/s) Nagel-Schreckenberg model Optimal State of Charge Virginia Tech Microscopic model

vehicles [21]. Rios-Torres and Malikopoulos developed a microscopic simulation framework to study the impact of connected and automated vehicles (CAVs) on fuel consumption in a merging on-ramp system [22]. In an urban traﬃc scenario, the eﬀects of traﬃc lights on fuel consumption can be also important. In [23], Tang et al. studied the eﬀects of signal lights on fuel consumption and emissions. Zhao et al. proposed a dynamic traﬃc signal timing optimization strategy to minimize the energy consumption and traﬃc delay for vehicles passing through an intersection [24]. The work of [21] and [23] are conducted based on the car-following model in the traditional fundamental diagram framework. In the new framework of three-phase traﬃc theory, Hemmerle et al. studied the impact of synchronised ﬂow on fuel consumption of conventional and electrical vehicles [25,26]. These work mostly consider traﬃc ﬂow on a horizontal road. The eﬀects of slope and wind are not taken in to consideration. In this paper, we develop our fuel consumption model of engine based on a steady-state fuel mapping model with transient correction. The Argonne National Laboratory (ANL) measurements of diﬀerent driving cycles including the steady-state cycle, the UDDS cycle, the Highway cycle and the US06 cycle are used to veriﬁed the engine model. In particular, our model can be applied to study various traﬃc conditions, such as traﬃc ﬂow with wind or slope. The capability of this model is proved by simulation experiments based on cellular automaton traﬃc model. Here we study the fuel consumption in the traﬃc ﬂow by utilizing the Nagel-Schreckenberg (NaSch) cellular automaton (CA) model [27]. The NaSch model was developed to describe the traﬃc ﬂow phenomena with high accuracy and robustness. One advantage of CA models lies in that this kind of models can provide second-by-second state of vehicles in the traﬃc ﬂow with relatively simple updating rules [28]. Therefore, the result of NaSch model can be comparative to the car-following model, but with a relatively lower computational cost

Despite these eﬀorts, the quantitative assessment of HEV fuel economy remains an open topic. Recently, Liu et al. studied the impacts of real-world driving and driver aggressiveness on the fuel consumption of 48 V mild hybrid vehicles [11]. It was found that aggressive driving can lead to approximately 25% increase of fuel consumption with conventional vehicle, while HEVs can partially mitigate the eﬀects of aggressive driving on fuel consumption. To better evaluate the fuel economy of HEV driving systems, models that can precisely predict fuel consumption second by second are required. The existing fuel consumption models of conventional vehicles can be classiﬁed to two categories, i.e., steady-state models and transient models. The steady-state fuel consumption models estimates fuel consumption rate based on steady-state dynamometer data including parameters of engine speed, torque, and engine load [12,13]. However, these models are appropriate only under steady-state conditions, and might show large discrepancies from tests under transient conditions [14,15]. One typical transient model is the Virginia Tech microscopic (VT-micro) model proposed by Ahn et al. with driving tests to formulate the relationship between vehicle speed, acceleration and fuel consumption [16]. Steadystate and transient conditions can show obvious diﬀerences in estimating fuel consumption [17]. Lindgren et al. reported that the fuel consumption rate under transient conditions can be 6% to 30% larger than that under steady-state conditions [18,19]. To overcome the deﬁciency of steady-state models, recently, a valuable transient correction framework is introduced to the steady-state model [20]. With transient correction, the prediction accuracy of fuel consumption models can be signiﬁcantly improved. As shown in the literature review above, most previous researches mainly focus on the fuel consumption of a single vehicle. The eﬀects of vehicle interaction in the traﬃc ﬂow are neglected. In this perspective, Tang et al. analyzed the eﬀects of on-ramp on the fuel consumption of 2

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whereηT is the transmission eﬃciency, io and ig are the gear ratio of the AMT and the diﬀerential gear ratio, respectively, Te is the engine torque, and Tw is the torque of wheel. Meanwhile, the vehicle’s longitudinal dynamics can be expressed as follows:

[29]. 1.3. Novelty of this contribution This paper presents a model for determining the fuel consumption of HEVs based on steady-state mapping with transient corrections, while at the same time, the split of power sources between EM and engine is taken into account. To the best of our knowledge, no relevant research work in the literature proposes a fuel consumption model for the HEVs. In the presented paper, the eﬀect of various traﬃc conditions can also be modeled by a set of parameters in the fuel consumption formulations. The main contributions of this paper in comparison with other research works in this area are as follows:

1 Tw = ⎡mgCr cos θ + CD ρd A·Va2 + mg sin θ + δm ·a⎤·r 2 ⎣ ⎦

where m is the vehicle mass in kilograms, g is the gravity acceleration in m/s2 , θ is the road-grade in degrees, Va is the vehicle speed in m/s , r is the radius of wheel in m , δ and a (m / s 2) is the vehicle’s rotational mass coeﬃcient and acceleration, respectively. Cr is the rolling resistance coeﬃcient, which can be written as:

V V 4 Cr = C0 + C1·⎛ a ⎞ + C2·⎛ a ⎞ ⎝ 100 ⎠ ⎝ 100 ⎠

(i) Proposing a fuel consumption model for hybrid vehicles based on the operation of engine, EM and battery, and deriving appropriate consumption curves in the ANL driving cycles. (ii) Providing a easy-to-apply method for the split of energy source between EM and engine, and subsequently, deriving acceptable fuel consumption prediction for the hybrid mode. (iii) Implementing the model to predict fuel consumption in various traﬃc conditions, including the situation of diﬀerent traﬃc densities, on a slope, or with wind. Because the suggested model is based on the moving dynamics of vehicle, it can eﬀectively predict fuel consumption in these conditions, while traditional models mainly obtain fuel consumption on horizontal roads. (iv) Presenting fuel consumption predition for HEVs in diﬀerent traﬃc conditions. The result shows considerable fuel saving, and proves the capability of this model in predicting fuel consumption of HEVs.

(3)

where C0 , C1 and C2 are diﬀerent rolling resistance coeﬃcients. According to vehicle standard, the range value of C0 , C1 and C2 can be kg deﬁned as in Table 1. CD, ρd 3 , A (m2) , represent air resistance coefm ﬁcient, air density, and windward force area of the vehicle head, respectively. Eq. (1) can be rewritten as:

( )

Te =

Tw ηT ∙io ∙ig

(4)

Meanwhile, the relationship between the rotational speed of the wheel ωw (r/min) and that of the engine ωe (r/min) is written as follows:

ωe = ωw ·io·ig

(5)

Then the power of engine is: (6)

Pe = Te·ωe

1.4. Paper organization

Using Eqs. (2)–(5) and Va =ω w r , Eq. (6) can be written as follows:

The rest of the paper is organized as follows. The model description is presented in the second section. The simulation results of fuel consumption in traﬃc ﬂow are discussed in Section 3. Finally, the related conclusions are drawn in Section 4.

Pe =

u ·G sin θ u 3· C A u ·δm 1 ⎛ ua·GCr cos θ ·a ⎞ + a + a D + a ηT ⎝ 3600 3600 76140 3600 ⎠ ⎜

⎟

(7)

Here, ua is the speed of vehicle in kilometers per hour, Pe is the power of engine in Kilowatts, and G = mg . The above equations can be applied to various vehicles and traﬃc simulation models. Using Eqs. (1)–(7), the longitudinal dynamics of vehicle can be translated into torque and speed of engine, and then the fuel consumption can be obtained by steady-state mapping.

2. Fuel consumption model The method of developing fuel consumption model for HEVs is divided into four parts: (i) vehicle model, describing the vehicle’s longitudinal dynamics; (ii) fuel consumption model for the ICE; (iii) fuel consumption model for the EM and battery, including the method for splitting the energy source of EM and engine; (iv) model veriﬁcation. The details of the model are described as follows.

2.2. Fuel consumption for the engine Here we consider the fuel as gasoline. The equation of gasoline consumption rate per unit time (Q g ) can be written as:

2.1. Vehicle model In general, HEVs can be categorized into parallel HEVs and series HEVs by the powertrain conﬁguration [30]. Parallel HEVs can be simultaneously powered by ICE and EM. In a series HEV, the drive system is solely powered by the EM that draws its power from the on-board battery unit, which is charged by the vehicle engine. The powertrain architecture of the studied vehicle with a singleshaft parallel hybrid conﬁguration is shown in Fig. 1, which is widely used in many hybrid models. The automatic machine transmission (AMT) is a key component to adjust the operating conditions of ICE and EM to work in their own high-eﬃciency areas. The EM could work as a generator while charging the battery. The clutch might be used to change the operating modes of the powertrain, such as EV mode, engine-drive mode, hybrid drive mode and regenerative-brake mode. The relationship between the torque of wheel and the output torque of engine during the running of the vehicle can be written as follows:

Tw = ηT ·io·ig ·Te

(2)

Fig. 1. Conﬁguration of the hybrid powertrain.

(1) 3

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operation of AMT and clutch. Obviously, the vehicle is in full enginedrive mode if Vc = 0, and in full EV mode if Vc = Vmax (here Vmax is the maximal possible velocity of the vehicle). For simplicity, the regenerative-brake mode is not considered in this study. When the EM is engaged, the power of EM can be written as follows:

Table 1 The value of rolling resistance coeﬃcient. Rolling resistance coeﬃcient

Value

C0 C1 C2

0.0072–0.120 0.00025–0.00280 0.00065–0.002

PEM =

Pe ·b Qg = 367.1ρg g

3

3

∑i =0 ∑ j=0

βij v ia j

(10)

where Tm is the torque of EM, ωm is the rotational speed of EM (r/min) , and ηEM represents the EM eﬃciency, which is a function of torque and rotational speed of EM. For simplicity, here we set ηEM = 0.8 for all driving conditions. Then the electricity consumption rate per unit time can be written as:

(8)

where ρg is the density of gasoline, ρg g is usually set as 7N/Liter , b (g/ KW∙h) is the instantaneous consumption rate corresponding to the current engine torque and rotational speed. The value of b can be obtained through engine test. The fuel consumption map of a Mazda engine considered in this paper is shown in Fig. 2. Note that the fuel consumption model described above is based on the steady-state fuel maps. To account for the eﬀect of transient state, a transient fuel consumption model is needed. Currently, there are two kinds of methods for developing transient fuel consumption model, i.e., transient-correction-based models and direct-variables-based models. Here we developed our model with transient-correction-based method. We adopted the transient correction for fuel consumption rate as follows [20]:

Qc =

Tm·ωm ηEM

Qe =

PEM 3.6 × 106

(11)

We assumed that the battery operates well, and neglect the thermal temperature eﬀects and transients. Moreover, the battery state of charge (SOC) can be quickly charged, because of the characteristics of the Lithium Titanate battery. Initially, the battery is in the state of full capacity. When the SOC of the battery is lower than a preset value, the battery will be charged to full capacity with an electric quantity of Ebatt by the EM, where the EM is utilized as a generator powered by the engine. In this process of charging the battery, the engine is adjusted to operate in its optimal eﬃciency area (or with its lowest fuel consumption rate). Similar as Eq.(8), the gasoline consumption for charging the battery can be written as:

(9)

where βij are corresponding coeﬃcients for speed power “i ” and acceleration power “ j ” respectively. 2.3. Fuel consumption for the EM and battery

Qeg = For the convenience of analysis, here we proposed a simpliﬁed model for EM and battery. For the hybrid driving mode, it is important to determine the split strategy of power source between EM and engine. Here the split of power source between EM and engine is deﬁned as follows. When a vehicle is operated in the hybrid driving mode, we assume that EM and battery will be engaged to provide driving force to the vehicle when its speed is lower than a critical value of Vc . On the other hand, if the vehicle’s speed is higher than Vc , ICE will begin to work and the vehicle will be solely driven by the engine. Vc is the operational parameter of the HEV powertrain, which is determined by the

Ebatt ·bopt 367.1ρg g

(12)

where bopt is the optimal fuel consumption rate of the engine. For the Mazda engine, bopt =240 g/kW∙h (See Fig. 2). Thus the electricity consumption of EM is ﬁnally converted to fuel consumption. Combine with Eqs. (1)–(7), the above equations (Eqs. (10)–(12)) can be used to predict the fuel consumption of HEVs in the hybrid driving mode. These equations are suitable for instantaneous fuel predictions of both continuous time driving process (such as ANL tests) and discretized time data (such as CA simulations).

Fig. 2. Fuel consumption contour map of engine (unit of speciﬁc gasoline consumption: g/kWh, 2014 Mazda 2.0L SKYACTIV Engine) [31]. 4

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2.4. Model veriﬁcation

Table 2 Simulation parameters of the vehicle.

To verify the fuel consumption model, we utilized the public available data of Argonne’s National Laboratory (ANL) [32] and compared the result with the VT-Micro model. The ANL data are collected under four experimental cycles: the steady-state cycle, the UDDS cycle, the US06 cycle, and the Highway cycle (See Fig. 3). For comparison, we show the results of our model and the classical VT-Micro model. Ahn et al. ﬁrst proposed the VT-Micro model in 2002 [16]. They utilized vehicle’s instantaneous speed and acceleration proﬁles as inputs to predict individual vehicle’s fuel consumption. In the VT-Micro model, the fuel consumption is formulated as follows: 3

ln(MOEe ) =

Parameters

Values

Vehicle mass Vehicle front area VehicleCr VehicleCD Wheel radius Air density Gasoline density ηT Gear shift

1550 kg 2 m2 0.0135 0.31 0.33m 1.239 g/L 0.7143 g/ml 0.9 6

3

e ⎧ ∑i = 0 ∑ j = 0 (Li, j v ia j ) a ≥ 0

⎨∑3 ∑3 (Mie, j v ia j ) a < 0 ⎩ i=0 j=0

hybrid vehicles by using our new model for the four driving cycles of ANL. Fig. 6 shows the fuel consumption of conventional vehicle, and hybrid vehicle with critical speed Vc = 50 Km/h for the UDDS driving cycle. Obviously, hybrid vehicle shows a better fuel economy as compared with conventional vehicle. Especially when the speed is low, the hybrid vehicle shows almost zero fuel consumption. Table 3 shows the fuel saving percentage with diﬀerent critical speed of Vc for the four ANL driving cycles. In general, the fuel saving increases with Vc . In particular, fuel saving can be up to 17.52% in a UDDS driving cycle when Vc = 50 Km/h . The fuel saving in the highway cycle is relatively lower, mainly because the engine is already running in the high eﬃciency area for this cycle.

(13)

where MOEe (Measure of Effectiveness, mL/s) is vehicle’s instantaneous fuel consumption rate, v and a are the instantaneous speed and acceleration, Lie, j and Mie, j are the regression coeﬃcients for the MOEe at speed power “i ” and acceleration power “ j ” respectively. Using our model and the VT-micro model, the relevant fuel consumption rate of UDDS cycle is predicted. The parameters of the fuel consumption model are listed in Table 2. The fuel consumption prediction results of our model and the VT-micro model are shown in Fig. 4. A comparison of the model results under the UDDS cycle between the measured and predicted fuel consumption values is shown in Fig. 5. Compared with the VT-Micro model, our model shows a better prediction especially in the cases of rapid acceleration and deceleration (Fig. 4(a)). The result of VT-Micro model is relatively lower (Fig. 5(b)), while our model shows a better ﬁtting (Fig. 5(a)). The maximal error of our model may occur when the vehicle speed is close to zero. This is because our model is based on steady-state fuel mapping with a transient correction. In general, the steady-state fuel mapping does not contain the result near zero speed (See Fig. 2). Therefore, the predictions near zero speed will be based on transient correction. However, the result is acceptable, because the estimation error seldom exceeds 0.2 cc/s. Hybrid electric vehicles show signiﬁcant superiority in fuel economy. Here, we further study the consumption performance of

3. Fuel consumption in the traﬃc ﬂow In this section, we adopted the NaSch CA model to simulate traﬃc ﬂow of diﬀerent vehicle densities, and then estimate the fuel consumption based on our model. We showed the model’s capability by considering three diﬀerent factors that may aﬀect the fuel consumption: (i) traﬃc condition, (ii) road slope, and (iii) wind resistance. We consider ﬁve scenario of traﬃc conditions: (1) Traﬃc ﬂow on a horizontal road, without wind; (2) Traﬃc ﬂow on an uphill slope, without wind; (3) Traﬃc ﬂow on a downhill slope, without wind;

Fig. 3. Four diving cycles of Argonne’s National Laboratory. 5

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Fig. 4. Fuel consumption rate prediction results by our model and the VT-Micro method for the UDDS driving cycle. (a) Our model results; (b) VT-Micro model results; (c) Comparison of model error of our model and VT-Micro model.

(4) Traﬃc ﬂow on a horizontal road with a headwind; (5) Traﬃc ﬂow on a horizontal road with a tailwind. To reproduce the possible emergence of traﬃc congestion and the stop-and-go phenomenon, the Nagel-Schreckenberg (NaSch) cellular automaton model is utilized to simulate various traﬃc situations. The NaSch model is deﬁned on a one dimensional array of cells, whose value could be 0 or 1 to indicate the status of empty or occupied by a vehicle. In this paper, the length of a cell is set to one meter, and the length of a vehicle is set to 5 cells. The NaSch model contains four consecutive steps running in parallel for all vehicles: a. Acceleration: b. Deceleration: c. Randomization: d. Position update:

Fig. 6. Fuel consumption of conventional vehicle and HEV with Vc = 50 Km/h in UDDS driving cycle.

vehicle. The randomization probability can imply the driving aggressiveness of drivers. A smaller randomization probability corresponds to a lower driving aggressiveness. Periodic boundary condition is used in the simulation, i.e., the road is a closed loop. The length of road is L = 6km . In each realization of simulation, initially, the vehicles are randomly distributed on the road with random speeds. The ﬁrst 9 × 105 seconds are abandoned as transient. Then the fuel consumption of each vehicle is obtained by averaging the result of its next 105 seconds trip. For each density, the fuel consumption result is averaged over 100 independent simulations. For comparison, we also provide the simulation results of VT-Micro.

vn→min(vn + l, vmax ) ; vn→min(vn, dn) vn→max((vn − l, 0) with probability P; xn → xn + vn

where vn and x n represent the velocity and location of nth vehicle respectively, vmax is the maximum speed of vehicles (here we set vmax = 18, which is equivalent to about 65 km/hour in reality), dn is the distance between nth and (n − 1) th vehicle, l = 5 is the length of

Fig. 5. Comparison between the measured and predicted fuel consumption. (a) Our model; (b) VT-Micro model. Here, R2 is the coeﬃcient of determination for the linear ﬁts.

6

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while it will be 2.0 Liter/hour for a hybrid vehicle with Vc = 6 m/s. The fuel saving is evident, because the battery charging is controlled by keeping the engine running in the most eﬃcient area. On the contrary, a conventional vehicle will suﬀer from the stop-and-go traﬃc that makes the engine run in the ineﬃcient area. When the traﬃc ﬂow is totally congested (ρ = 1.0), a conventional vehicle will still consume 1.35 Liters of gasoline per hour, while a hybrid vehicle does not consume any fuel at all.

Table 3 Fuel saving of HEVs in diﬀerent driving cycles. Steady-state cycle

UDDS cycle

Vc (Km/h)

Fuel Saving

Vc (Km/h)

Fuel Saving

25 50 75 100 125

2.14% 5.08% 6% 6.99% 6.64%

10 20 30 40 50

7.33% 8.01% 9.45% 12.86% 17.52%

US06 cycle

3.2. Fuel consumption on roads with slope

Highway cycle

Vc (Km/h)

Fuel Saving

Vc (Km/h)

Fuel Saving

20 40 60 80 100

5.81% 7.01% 8.00% 8.79% 12.43%

50 60 70 80 90

1.65% 2.66% 3.84% 7.55% 9.20%

Here, we investigated the eﬀect of road slope on the fuel consumption of vehicles. In the calculation, we assumed i ≈ sinθ ≈ tanθ and used it as the parameter for characterizing the road slope. Fig. 9 shows the fuel consumption rate for an uphill road and a downhill road, respectively. One can see that road slope has great inﬂuence on fuel consumption. On an uphill road (see Fig. 9(a)), the fuel consumption rate increases as the slope increases. When the slope is i = 0.08, the fuel consumption rate reaches 16Liter/hour, which is about three times of the fuel consumption rate on a horizontal road. In Fig. 9(a), we also show the results of VT-Micro model. Because VTMicro model does not consider the eﬀect of slope, it shows the same result for diﬀrent slopes. Compared with our model result of i = 0, VTMicro shows a lower consumption for low densities, while it shows a higher consumption for high densities. Fig. 9(b) shows the fuel consumption rate for a downhill road. Obviously, the fuel consumption rate will decrease as compared with the horizontal road. As the slope increases, the fuel consumption rate will be lower. Interestingly, in the case of free ﬂow, the fuel consumption rate for i = 0.02 is slightly lower than i = 0.04. This phenomenon can be explained as follows. The operational fuel consumption rate with the same speed is in diﬀerent area when the slope is i = 0.02 and 0.04, respectively (see Fig. 10). Although the slope i = 0.04 is with a relatively smaller torque, the engine does not operate in the most eﬃcient area. As a result, the fuel consumption of slope i = 0.04 is slightly higher than i = 0.02. Fig. 11 shows the fuel consumption rate of hybrid vehicles on an uphill road and a downhill road, respectively. It can be seen that the hybrid mode can greatly inﬂuence the fuel consumption. In the free ﬂow state, hybrid vehicles can not save much fuel, because they are running at the maximal velocity and the engines are operated in their most eﬃcient area. However, at higher densities, the fuel consumption rate will decrease with bigger Vc . For example, on an uphill road at the density of ρ = 0.45 (see Fig. 11(a)), hybrid vehicles can save about 1.2 Liter/hour with Vc = 12 m/s. On an downhill road at the density of ρ = 0.45 (see Fig. 11(b)), hybrid vehicles can save about 0.7 Liter/hour with Vc = 12 m/s.

3.1. Fuel consumption on a horizontal road without wind We ﬁrst showed some important indicators for the traﬃc ﬂow on a single-lane road. Fig. 7(a) shows the fundamental diagram (or the ﬂowdensity relation) with diﬀerent randomization probabilities. It can be seen that the traﬃc ﬂow increases linearly with density, and then decreases after the density is greater than a critical value of ρc . The increasing part is generally called the free ﬂow state, while the decreasing part is called congested state. The critical density ρc decreases with randomization probability. Fig. 7(b) shows the speed-density relation. In the free ﬂow state, vehicles are running approximately at the maximal speed (vmax ). Then the speed gradually declines to zero after ρc . Fig. 7(c)-(f) show the variation of the running states for the vehicles, i.e., ratio of acceleration, ratio of deceleration, ratio of stopping, and the ratio of following (in terms of the previous car) during the 105 seconds trip. With a larger randomization probability, the vehicles show a higher ratio of both acceleration and deceleration in the free ﬂow state, while they will show a lower ratio of acceleration and deceleration at high densities. Moreover, the vehicles show a larger ratio of stopping and a lower ratio of following at most densities with a larger randomization probability. Now we show the result of fuel consumption for both conventional and hybrid vehicles. Fig. 8(a) shows the fuel consumption of conventional vehicles with diﬀerent randomization probabilities. The fuel consumption is roughly constant in the free ﬂow state, because the vehicles are running freely at maximal velocity. With a larger randomization probability, the fuel consumption will be higher. This is because the fuel consumption is determined by both speed and acceleration. In the free ﬂow state, the speed is similar, while the ratio of acceleration is higher with a larger randomization probability (see Fig. 7(c)). That is, the vehicles need to accelerate more frequently and consume more fuel. In the congested state, the fuel consumption decreases with density. This is mainly because the vehicle speed decreases with the density (see Fig. 7(b)). At high densities, both the speed and the ratio of acceleration are lower with a larger randomization probability (see Fig. 7(b,c)). Therefore, the fuel consumption will be lower with a larger randomization probability. Fig. 8(b) shows the fuel consumption for hybrid vehicles with a ﬁxed randomization probability P = 0.1 and diﬀerent critical speeds for the hybrid mode. In the free ﬂow state region, the fuel consumption rate is similar with diﬀerent critical velocities of Vc . The hybrid mode can not save much fuel, since the vehicles are running at the maximal speed and the engines are working in their most eﬃcient area. However, at higher densities, the fuel consumption rate will decrease dramatically for hybrid vehicles. For instance, at the density of ρ = 0.5, the fuel consumption rate is 3.0 Liter/hour for a conventional vehicle,

3.3. Fuel consumption with winds According to Eq. (7), wind resistance is also an important factor in determining the fuel consumption. Note that the consumption of wind resistance is with a third-order speed dependency as shown by ua3 . In the previous sections, we mainly studied the impacts of the speed ua and the acceleration a on fuel consumption. It’s necessary to study how ua3 aﬀects the fuel consumption rate. The wind resistance power can be rewritten as:

Pw =

(ua + u w )3·CD A 76140

(14)

where u w is the speed of wind. ua is the speed of the vehicle, CD is the wind resistance coeﬃcient, A is the windward area of the vehicle. Fig. 12 shows the eﬀect of wind on the fuel consumption rate. With a tailwind, the fuel is saved as the wind speed increases (see Fig. 12(a)). In the free ﬂow, vehicles can save around 13% of fuel when the wind speed is 20 km/h. With a headwind, the fuel consumption rate increases 7

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Fig. 7. Characteristics of traﬃc ﬂow of vehicles on a single lane road. (a) Fundamental diagram (ﬂow-density relation); (b) Speed-density relation; (c) Ratio of acceleration; (d) Ratio of deceleration; (e) Ratio of stopping; (f) Ratio of following.

Fig. 8. Fuel consumption results: (a) conventional vehicles with diﬀerent randomization probability; and (b) hybrid vehicles with ﬁxed P = 0.1 and diﬀerent Vc . 8

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Fig. 9. Fuel consumption under uphill and downhill (P = 0.1): (a) Uphill road, (b) Downhill road.

Fig. 10. Illustration of the engine’s operational fuel consumption rate when the slope ratio are i = 0.02 and 0.04, respectively.

Fig. 11. Fuel consumption of hybrid vehicle with diﬀerent Vc under uphill and downhill conditions: (a) Uphill road, (b) Downhill road. Here P = 0.1 and i = 0.08.

tailwind and headwind, respectively. In the free ﬂow state, hybrid vehicles do not save much fuel, because they are running at the maximal speed and the engines operate in their most eﬃcient area. However, at higher densities, the fuel consumption rate will decrease much more with a larger Vc . For example, with tailwind and ρ = 0.45 (see Fig. 13(a)), hybrid vehicles can save about 0.65 Liter/hour with Vc = 12 m/s, while with headwind and ρ = 0.45 (see Fig. 13(b)), hybrid vehicles can save about 0.75 Liter/hour with Vc = 12 m/s.

as the wind speed increases (see Fig. 12(b)). Vehicles consume more fuel (about 13%) when the wind speed is u w = −20 km/h . In Fig. 12(a), the result of VT-Micro model is shown for comparison. Because VTMicro does not consider the eﬀect of wind, it shows the same result for diﬀerent wind speeds. Compared with our model, VT-Micro predicts a lower consumption for low densities, while it shows a higher consumption for high densities. Fig. 13 shows the fuel consumption rate of hybrid vehicle with 9

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Fig. 12. Fuel consumption of conventional vehicles with diﬀerent wind conditions: (a) Tailwind, (b) Headwind. Here P = 0.1.

Fig. 13. Fuel consumption of hybrid vehicles with diﬀerent Vc under tailwind and headwind conditions (u w = 20 km/h , P = 0.1): (a) Tailwind, (b) Headwind.

4. Conclusion and discussion

model accuracy. Based on this model, the eco-driving guidance for drivers can be possible by the predictions of fuel consumption in different routes. Combined with traﬃc and geographic information systems (GIS), the model can be used to provide route-choice suggestions for drivers.

In summary, a fuel consumption model for hybrid electric vehicles is developed based on the operations of engine, electric motor and battery. The model is veriﬁed using measured fuel consumption data from Argonne National Laboratory driving cycles. Compared with the classic VT-Micro model, the new model shows more precise results and can be applied to wider traﬃc ﬂow scenarios. The fuel consumption of the vehicles is aﬀected by the actual road conditions, traﬃc conditions and driving behaviors. We study the fuel consumption of vehicles in various traﬃc ﬂow scenario with cellular automaton simulation. The results show that: (i) hybrid mode can greatly save fuel, especially when traﬃc density is high; (ii) fuel eﬃciency on slope and with wind can be predicted by the new model; (iii) the saving of fuel will not be signiﬁcant when the traﬃc is in free ﬂow, mainly because the engine is already working in the most eﬃcient area. The proposed model decouples battery SOC and control problems, thus having a potential of application to diﬀerent types of hybrid conﬁgurations (e.g. HEVs, FCHVs, Plug-in HEVs), even in cases of different battery or fuel cell technologies. The model can be expected to contribute to the resolution of other fuel economy related issues for hybrid vehicles. For example, an economic analysis could be carried out, thus allowing the develop of speed proﬁle optimization for minimum-energy applications. Furthermore, in recent years, extreme weather events have become one of the most challenging issues [33]. Considering high-impact low-probability events into the model might bring beneﬁts for some related problems, such as evacuation planning and energy saving in bad weathers. In order to make sure that the new model can be applied to complex and varied driving conditions, the future work in this subject includes, but is not limited to, exploring real tests of HEVs to further verify the

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