Fuel economy evaluation of fuel cell hybrid vehicles based on equivalent fuel consumption

Fuel economy evaluation of fuel cell hybrid vehicles based on equivalent fuel consumption

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Fuel economy evaluation of fuel cell hybrid vehicles based on equivalent fuel consumption C.H. Zheng a, C.E. Oh b, Y.I. Park c, S.W. Cha a,* a

School of Mechanical and Aerospace Engineering/SNU-IAMD, Seoul National University, San 56-1, Daehak-dong, Gwanak-gu, Seoul 151-742, Republic of Korea b Hyundai Heavy Industries Co., Ltd., 102-18, Mabuk-dong, Giheung-gu, Yongin-si, Gyeonggi-do 446-716, Republic of Korea c School of Mechanical Design and Automation Engineering, Seoul National University of Science and Technology, 172 Gongreung 2-dong, Nowon-gu, Seoul 139-743, Republic of Korea

article info

abstract

Article history:

Fuel cell hybrid vehicles (FCHVs) have become a major topic of interest in the automotive

Received 22 July 2011

industry owing to recent energy supply and environmental problems. Consequently, fuel

Received in revised form

economy evaluation methods of FCHVs have a popular research topic. The initial state of

28 September 2011

charge (SOC) and the final SOC of the battery have to be identical in an evaluation of the

Accepted 29 September 2011

fuel economy of an FCHV. In an actual driving situation or during a forward simulation,

Available online 8 November 2011

however, the final SOC depends on the power management strategy, which is usually different from the initial SOC. To consider the effect of the difference between the initial

Keywords:

and final SOC on fuel economy evaluation, the concept of equivalent fuel consumption,

Fuel cell hybrid vehicle (FCHV)

based on the optimal control, is introduced in this paper. A rule-based power management

Fuel economy

strategy is applied to an FCHV, and its fuel economy is evaluated in terms of the equivalent

Equivalent fuel consumption

fuel consumption and compared to the optimal control result.

Optimal control

Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

Rule-based strategy

1.

Introduction

The energy supply problem has become a major issue recently, and proton exchange membrane (PEM) fuel cell vehicles have accordingly become a subject of major interest among academia and the automotive industry. As a power source, a fuel cell system (FCS) has relatively low power rate and cannot recover the braking energy. Thus, the size and cost of the FCS will be increased if the FCS is the only power source in a vehicle. The secondary power source which has relatively high power rate and can recuperate the braking energy is needed and a battery could be one of the candidates for the secondary power source. An FCHV can provide sufficient power during its acceleration and can recuperate the kinetic

reserved.

or potential energy of the vehicle during braking by hybridization of an FCS and a battery. Fuel cell hybrid vehicles have many outstanding advantages, such as higher energy efficiency and lower emissions compared to internal combustion engine vehicles. The fuel economy of an FCHV depends on its power management strategy, which determines the power distribution between the FCS and the battery. Many researchers have studied different power management strategies for FCHVs, including optimal or near-optimal strategies based on optimal control theory and rule-based strategies. To evaluate the fuel economy of an FCHV adequately, the initial SOC and final SOC of the battery have to be the same. In previous research in this area, the value of the final SOC of the battery can be set when

* Corresponding author. Tel.: þ82 2 880 1700; fax: þ82 2 880 1696. E-mail address: [email protected] (S.W. Cha). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.09.147

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Table 2 e Powertrain information of the FCHV. Component

Value

Electric motor FCS Battery Efficiency of converters

75 kW 45 kW, 18 kW/s 1.5 kWh 95%

Fig. 1 e Powertrain arrangement of an FCHV.

a strategy is based on the dynamic program (DP) [1] or the classical optimal control theory [2]. However, the final SOC depends on a strategy of applying a rule-based algorithm [3] or a fuzzy logic [4], and it is usually different from the initial SOC. To consider the effect of the difference between the initial SOC and the final SOC on the fuel economy, this paper presents a new fuel economy evaluation method in which the concept of equivalent fuel consumption is introduced. The idea of equivalent fuel consumption stems from the idea of the optimal control based on Minimum Principle. The fuel economy of a rule-based power management strategy is evaluated using this concept and compared to the optimal control result.

2.

Item

Value

Anode pressure (atm) Cathode pressure (atm) Stack temperature ( C) Cell number Active area (cm2/cell) Membrane thickness (cm)

2 1.97 80 242 280 0.01275

parameters are used to calculate the stack-provided power and auxiliary power of the FCS model. In this model, the fuel cell voltage is calculated using a physical and empirical relationship as follows [6]: vfc ¼ E  vact  vohm  vconc

FCHV and its powertrain

Fig. 1 shows the powertrain arrangement of an FCHV. The architecture of an FCHV is similar to that of a series hybrid electric vehicle, as the electric motor is the only powertrain component that is directly connected to the wheels. The FCS and the battery are connected to the wheels through the motor and they provide electrical power to the motor. The battery can recover the braking energy through the motor. The vehicle parameters used in this research are shown in Table 1. We consulted the literature [5] for these data. The powertrain information is summarized in Table 2. A 45 kW FCS with the power rate of 18 kW/s and a 1.5 kWh battery are selected as the power sources of the FCHV. There are two DCeDC converters and one DCeAC inverter as shown in Fig. 1. In the present study, these converters are considered as ideal power converters with a constant efficiency of 95%.

2.1.

Table 3 e Parameters used in the FCS model.

(1)

Here, E is the open circuit voltage. vact, vohm, and vconc represent activation loss, ohmic loss, and concentration loss, which are caused by various physical or chemical factors. Fig. 2 illustrates the relationship between the fuel cell stack current and the FCS net power for this FCS. The relationship between the FCS net power Pfcs and the stack-provided power Pstack is as follows: Pfcs ¼ Pstack  Paux

(2)

Here, Paux represents the power consumption of the auxiliary components. In the present study, Paux represents the power consumption of the compressor, as the compressor power is up to 93.5% [7] of the total auxiliary power consumption and the power consumption of other auxiliary components is not significant. The power consumption of the compressor is as follows [6]:

FCS 50

A steady-state model [6] is used for the 45 kW FCS and the parameters utilized in this model are listed in Table 3. These

Item Vehicle total mass (kg) Final drive gear efficiency (%) Tire radius (m) Aerodynamic drag coefficient Vehicle frontal area (m2) Air density (kg/m3) Rolling resistance coefficient

Value 1500 95 0.29 0.37 2.59 1.21 0.014

Net power (kW)

Table 1 e Parameters of the vehicle.

40 30 20 10 0 0

50

100

150 200 250 Stack current (A)

300

350

400

Fig. 2 e Relationship between the fuel cell stack current and FCS net power. This graph is for the 45 kW FCS.

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2.2.

Hydrogen consumption rate (g/s)

1.4 1.2

The battery model used in this research is shown in Fig. 4(a). In this model, both the internal resistance R and the open circuit voltage (OCV) V are functions of the battery SOC. The parameters of the battery are related according to the following equation [8]:

1.0 0.8 0.6 0.4

$

SOC ¼ Q

0.2 0 0

5

10

15 20 25 30 Net power (kW)

35

40



45

Fig. 3 e Relationship between the FCS net power and fuel consumption rate. This graph is for the 45 kW FCS.

Paux ¼

Cp $Tatm $Wcp hcp



psm patm

ðg1Þ=g

 1

(3)

Here, g is the ratio of the specific heats of air (¼ 1.4), Cp is the constant-pressure specific heat capacity of air (¼ 1004 J/kg K), hcp is the compressor efficiency (¼ 80%), psm is the pressure inside the supply manifold (¼ 2 atm), patm is the atmospheric pressure (¼ 1 atm), and Tatm is the atmospheric temperature (¼ 298 K). The fuel consumption rate is related to the stack current as follows: _ h2 ¼ m

Battery

Ncell $Mh2 $Istack $l n$F

(4)

In Eq. (4) [2], Ncell represents the cell number (¼ 242), Mh2 represents the molar mass of hydrogen (¼ 2 g/mol), n represents the number of electrons acting in the reaction (¼ 2), F represents the faraday constant (¼ 96,487 C/mol), Istack represents the stack current, and l represents the hydrogen excess ratio (¼ 1.2). From Fig. 2 and the Eq. (4), it can be derived that the FCS net power and the fuel consumption rate are related to each other, as illustrated in Fig. 3. This relationship is used with the optimal control described in Section 3.

I qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi VðSOCÞ2 4RðSOCÞPbat

bat

VðSOCÞ 

2RðSOCÞ

(5)

Here, Qbat is the battery capacity, Pbat is the battery power, and I is the battery current. Fig. 4(b) shows the characteristics of the battery used in this research.

3. Optimal control based on minimum principle The motor power is from both the FCS power and the battery power as illustrated in Fig. 1. The objective of the optimal control problem is to find an optimal power split which minimizes the total fuel consumption during driving. The fuel consumption can be minimized if the optimal trajectory of the FCS power is obtained considering that the power required for the vehicle is given when selecting the driving cycle. We solve this problem as described below using the optimal control based on Minimum Principle. Here, the FCS power Pfcs is the control variable and the battery SOC is the state variable. The state equation of the system is given in Eq. (5). The internal resistance and OCV of the battery are functions of the battery SOC. Hence it can be simplified as follows: $

SOC ðtÞ ¼ f ðSOCðtÞ; Pbat ðtÞÞ

(6)

The power required for the motor Preq, the FCS net power Pfcs, and the battery power Pbat have the following relationship: Pfcs ðtÞ ¼ Preq ðtÞ  Pbat ðtÞ

(7)

Fig. 4 e (a) Battery model. (b) Internal resistance and OCV of battery as a function of the battery SOC. This graph is for the battery actually used in this research. We assumed that the internal resistance while charging is identical to that while discharging.

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As the power required for the motor can be derived when selecting a driving cycle, we can transform the state Eq. (6) into (8)

based on Eq. (7). The performance measure to be minimized is the total fuel consumption when the FCHV drives over a specified driving cycle from time t0 to time tf. As the FCS power and fuel consumption rate are related as shown in Fig. 3, the performance measure is expressed as follows: J¼

_ h2 m



 Pfcs ðtÞ dt

(9)

t0

We also need to consider the constraint on the system. It can be observed from Eqs. (8) and (9) that the problem is to find the trajectory of Pfcs that minimizes the total fuel consumption given the constraint as expressed in Eq. (8) and a Pfcs value that ranges from 0 to 45 kW. Thus, the performance measure is to be Ztf J¼

$ 

 _ h2 Pfcs ðtÞ þ p$ðF  SOC Þ dt m

(10)

t0

As mentioned before, the objective of the optimal control problem is to minimize the total fuel consumption. Thus, the necessary condition of the optimal control is given when the variation of the performance measure, dJ, is zero. If we introduce a Hamiltonian H, which is defined as     _ h2 Pfcs ðtÞ þ p$F SOCðtÞ; Pfcs ðtÞ (11) H¼m then the necessary conditions that derive the optimal trajectories are as follows:

Hamiltonian (g/s)

SOC change rate (1/s) Fuel consumption rate (g/s)

$ vH ¼ SOC vp $ vH ¼ p vSOC vH ¼0 vPfcs

100

50

0 0.3

0.4

0.5 0.6 Battery final SOC

0.7

0.8

Fig. 6 e Relationship between the final battery SOC and the fuel consumption (FTP75 urban driving cycle). The costate ranges from L93 to L87 here.

In the definition of the Hamiltonian (Eq. (11)), the first part is about the fuel usage and the second part is about the electric usage. p is defined as the costate, which is an equivalent parameter between fuel usage and electric usage [9]. The first necessary condition is the state Eq. (8), which is a constraint in this problem. The second necessary condition is a costate equation that determines the optimal trajectory of the costate p when the initial value of the costate is given. The third necessary condition determines the optimal trajectory of the control variable Pfcs that minimizes the Hamiltonian H. _ h2 , the battery Fig. 5 illustrates the fuel consumption rate m $ SOC change rate SOC , and the Hamiltonian H for the whole range of the FCS power when the power required for the motor Preq is 20 kW and the battery SOC is 0.7 and the costate p is set to 90. This figure shows that the optimal Pfcs, which minimizes the Hamiltonian can be obtained for this case.

(12)

4. Equivalent fuel consumption based on the minimum principle-based optimal control To consider the effect of the difference between the initial SOC and the final SOC on the fuel economy, the concept of equivalent fuel consumption is presented in this section based on

1.5 1 0.5

150

0 0

5

10

15

20

25

30

35

40

45

-3

5

x 10

0

-5 0

5

10

15

20

25

30

35

40

45

1

Fuel consumption (g)

Ztf

Fuel consumption (g)

$   SOC ðtÞ ¼ F SOCðtÞ; Pfcs ðtÞ

150

100

50

0.5

0 0 0

5

10

15

20 25 FCS power (kW)

30

35

40

45

Fig. 5 e An example of solving the optimal FCS power from the Hamiltonian.

0.3

0.4

0.5 0.6 Battery final SOC

0.7

0.8

Fig. 7 e Relationship between the final battery SOC and the fuel consumption (NEDC 2000 driving cycle). The costate ranges from L94 to L90 here.

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60 50 Net efficiency (%)

Fuel consumption (g)

150

100

50

40

FCS mode Hybrid mode or charging mode

30

Battery mode

20 10

0

0.3

0.4

0.5 0.6 Battery final SOC

0.7

0 0

0.8

Fig. 8 e Relationship between the final battery SOC and the fuel consumption (Japan 1015 driving cycle). The costate ranges from L80 to L94 here.

the optimal control introduced in the previous Section 3. The relationship between a variable costate and a constant costate is discussed first. In the battery Eq. (5), the change rate of the battery SOC will not depend on the battery SOC if the OCV and internal resistance of the battery are nearly constant in the SOC operating range. Thus, the state Eq. (8) and the Hamiltonian (Eq. (11)) will be expressed as follows: $   SOC ðtÞ ¼ F Pfcs ðtÞ

(13)

    _ h2 Pfcs ðtÞ þ p$F Pfcs ðtÞ H¼m

(14)

Then, the relationship (Eq. (15)) can be derived in terms of the Hamiltonian (Eq. (14)) and the second necessary condition in Eq. (12). It can be observed that the costate p will be a constant parameter because the Hamiltonian H is not related to the battery SOC anymore. $ vH ¼ p ¼ 0 vSOC

(15)

In fact, for vehicle usage, most batteries operate in a certain SOC range and the OCV and internal resistance of the batteries are nearly constant in the SOC range as shown in Fig. 4(b). This characteristic of the battery makes it possible to replace a variable costate derived from the necessary condition (Eq. (12)) with a constant costate. Thus, constant costates are used in this research. In the optimal control described in Section 3, the final battery SOC depends on the value of costate p. Each costate causes a different final battery SOC and different fuel consumption. Here, we use the relationship between the final

10

20 30 Net power (kW)

40

50

Fig. 9 e Rule-based power management strategy. The efficiency graph is for the 45 kW FCS.

battery SOC and the fuel consumption to build the concept of equivalent fuel consumption. To determine how the final battery SOC and fuel consumption are related, we assessed the simulation results of the final battery SOC and fuel consumption while changing the costate p on three different driving cycles. The driving cycles are the FTP75 urban driving cycle, the NEDC 2000 driving cycle, and the Japan 1015 driving cycle. The initial SOC is set to 0.7 for the three driving cycles and the costate range is different for each driving cycle. Figs. 6, 7 and 8 illustrate the simulation results of the three driving cycles. These figures show that the final battery SOC and fuel consumption are approximately proportional to each other. We connected the first point and the last point with a straight line in each figure. These lines represent the relationship between the final battery SOC and the fuel consumption for the three driving cycles. Any other simulation result points derived from other power management strategies will always locate above these lines, as these lines are obtained from the optimal control. In these three lines, the greater costate causes lower battery final SOC and lower fuel consumption. At this point, we can evaluate the adequate fuel economy of the FCHV by the equivalent fuel consumption based on these lines. We need to determine the fuel consumption from these lines, which corresponds to the final battery SOC of 0.7, given that the initial battery SOC was set to 0.7. The second column in Table 4 shows the results of the equivalent fuel consumption on the three driving cycles. In fact, if we connect every point in each figure, there will be only a small amount of curvature [10] in each line in Figs. 6, 7 and 8. Thus, the results listed in the second column in Table 4 contain minor errors.

Table 4 e Comparison of equivalent fuel consumption for the three driving cycles. Driving cycle

FTP75 urban (11.9894 km) NEDC 2000 (11.0132 km) Japan 1015 (4.1636 km)

Equivalent fuel consumption (kg/100 km) Optimal control

Rule-based strategy

1.08 1.24 1.05

1.13 1.28 1.09

Discrepancy (%)

4.63 3.23 3.81

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150

Fuel consumption (g)

Fuel consumpt ion (g)

150

100

50

0

0.3

0.4

0.5 0.6 Battery final SOC

0.7

100

50

0 0.3

0.8

0.4

0.5 0.6 Battery final SOC

0.7

0.8

Fig. 10 e Simulation results of the rule-based power management strategy (FTP75 urban driving cycle).

Fig. 12 e Simulation results of the rule-based power management strategy (Japan 1015 driving cycle).

5. Fuel economy evaluation based on the equivalent fuel consumption

5.2. Fuel economy evaluation of the rule-based power management strategy based on the equivalent fuel consumption

In this section, a rule-based power management strategy is introduced and its fuel economy is evaluated based on the equivalent fuel consumption.

5.1.

Rule-based power management strategy

The FCS efficiency is defined as hfcs ¼

Pfcs _ h2 $LHV m

(16)

In Eq. (16) [11], LHV ¼ 120,000 kJ/kg is the lower heating value of hydrogen. The rule-based power management strategy presented in this section is based on the efficiency characteristics of the FCS. Fig. 9 illustrates the strategy. It is clear that the FCS efficiency is very low when the FCS net power is less than 5 kW; hence, the battery mode is used in this region. On the other hand, the FCS efficiency is high when the FCS net power is greater than 5 kW and less than 20 kW; therefore, the FCS mode is used in this region. When the FCS net power is greater than 20 kW, the hybrid mode or battery charging mode is used. The FCS provides constant power in this region.

The process of a fuel economy evaluation based on the equivalent fuel consumption is as follows: (1) Obtain the simulation results of the final battery SOC and fuel consumption when the rule-based power management strategy illustrated in Fig. 9 is applied to the FCHV and the initial battery SOC is set to 0.7 for the three different driving cycles. (2) Plot the point which corresponds to the simulation results of the FTP75 urban driving cycle, the NEDC 2000 driving cycle, and the Japan 1015 driving cycle in Figs. 6, 7 and 8, respectively. (3) Add a straight line parallel to the previous line that intersects the point in each figure. (4) Check the fuel consumption value which corresponds to the final battery SOC of 0.7 on the line from step (3) in each figure. Figs. 10, 11 and 12 show the points from step (2) and the lines from step (3) for the three driving cycles. The equivalent fuel consumption of the rule-based power management strategy for each driving cycle is listed in the third column in Table 4.

6. Simulation results of the equivalent fuel consumption for two power management strategies

Fuel consumption (g)

150

Table 4 compares the equivalent fuel consumption derived from the rule-based power management strategy and from the optimal control. The table shows that the equivalent fuel consumption obtained from the rule-based strategy is about 4.63%, 3.23%, and 3.81% higher than that obtained from the optimal control for the FTP75 urban driving cycle, the NEDC 2000 driving cycle, and the Japan 1015 driving cycle, respectively.

100

50

0 0.3

7. 0.4

0.5 0.6 Battery final SOC

0.7

Conclusions

0.8

Fig. 11 e Simulation results of the rule-based power management strategy (NEDC 2000 driving cycle).

In an effort to evaluate the fuel economy of FCHVs correctly, the initial SOC and final SOC of the battery have to be the same. However, during actual driving scenarios or in

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a forward simulation, the final SOC of the battery depends on the power management strategy, and it is usually different from the initial SOC of the battery. To consider the effect of the difference between the initial and final SOC on an evaluation of the fuel economy, the concept of equivalent fuel consumption based on the optimal control is introduced in this research. This concept could be also used to general internal combustion engine hybrid vehicles. A rule-based power management strategy is applied to an FCHV and its fuel economy is evaluated according to the equivalent fuel consumption. The following points are drawn from this research. (1) The optimal control based on Minimum Principle optimizes the power split between the FCS and the battery and minimizes the fuel consumption by providing the necessary optimality conditions. Based on the optimal control strategy, the final battery SOC and the fuel consumption are approximately proportional to each other. Thus, their relationship can be expressed by a straight line and the equivalent fuel consumption can be derived from this line. Any other simulation result points derived from other power management strategies will always locate above this line, as it is obtained from the optimal control strategy. (2) The equivalent fuel consumption derived from the two power management strategies were compared to each other. It can be concluded that the equivalent fuel consumption obtained from the rule-based power management strategy is approximately 4.63%, 3.23%, and 3.81% higher than that obtained from the optimal control strategy for the FTP75 urban driving cycle, the NEDC 2000 driving cycle, and the Japan 1015 driving cycle, respectively.

Acknowledgment This work was supported by the Industrial Strategic Technology Development Program (10033110) under the Ministry of

Knowledge Economy, Republic of Korea and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No.2011-0001276).

references

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