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Real time optimal energy management strategy targeting at minimizing daily operation cost for a plug-in fuel cell city bus Liangfei Xu, Fuyuan Yang*, Jianqiu Li, Minggao Ouyang, Jianfeng Hua State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, PR China
article info
abstract
Article history:
This paper proposes an optimal real-time energy management strategy targeting at daily
Received 23 May 2012
operation optimization for a plug in proton exchange membrane fuel cell electric vehicle
Received in revised form
(PFCEV) for public transportations. A novel real-time optimal energy management strategy
15 July 2012
based on the determined dynamic programming (DDP) strategy is proposed, namely the
Accepted 17 July 2012
DBSD (charge Depleting e Blended e Sustaining e Depleting) strategy. A simulation model
Available online 15 August 2012
is set up to compare the DDP strategy, the DBSD strategy and the CDCS (Charge Depleting and Charge Sustaining) strategies. Compared to the CDCS strategy, the daily operating
Keywords:
cost can be reduced by 6.4% with the DBSD strategy, and it can be reduced by 9.5% with the
Plug in fuel cell electric vehicle
DDP strategy. On-road testing with the DBSD strategy shows that, the daily operation cost
Energy management
is 510.2 Sig. $ (100 km)1. The electric energy consumption in pure battery driven mode is
Dynamic programming
about 1.68 kWh km1, and the equivalent hydrogen consumption in hybrid driven mode is
Optimal control
about 0.14 kg km1.
Charge depleting charge sustaining
Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Blended
1.
Introduction
Electric vehicles (EVs) have been greatly concerned because of limited fossil fuel energy and strict regulations on reducing the greenhouse gas in the past years [1]. EVs can be classified into three typical types, namely battery electric vehicles (BEVs), fuel cell electric vehicles (FCEVs) and hybrid electric vehicles (HEVs). Although great progress has been made in the fields of advanced battery materials, battery system control and diagnosis technologies, BEVs are primarily suitable for short distances in urban areas in the current stage. Proton Exchange Membrane (PEM) FCEVs are favored in automotive applications for being quiet, highly efficient and environmentally friendly. Compared to a BEV with a similar vehicle configuration, the driving distance of an FCEV can be much longer because the energy density of the hydrogen gas is more considerable than that of the battery system. However, the
daily operating cost of an FCEV is very high because of the expensive high-pressed hydrogen gas. Other bottlenecks exist in the fuel cell durability, the infrastructure construction, the system integration, etc. In recent five years great progresses in FCEVs have been made. United Technologies Corporation (UTC) reported that, its 120 kW Fuel Cell System PureMotion Model 120 had been operating for 7000 h without changing any subsystems until the end of June, 2010. This working life time was much longer than the target proposed by Department of Energy (DOE) of the United States in 2009. General Motor Company (GM) developed several generations of PEM fuel cell vehicles. In March of 2010 the fifth PEM fuel cell vehicle was launched, the Chevrolet Equinox FCEV. With the same output power 94 kW, the size of the fifth PEM fuel cell engine was about half of that of former generations, and the weight was reduced by 100 kg. The cost of noble metal Pt in one engine was reduced from 80 g to 30 g. GM claimed that the
* Corresponding author. Tel.: þ86 10 62795825; fax: þ86 10 62785708. E-mail addresses:
[email protected] (L. Xu),
[email protected] (F. Yang). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2012.07.074
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 5 3 8 0 e1 5 3 9 2
consumption of Pt in one engine will decrease to 10 g in 2015. Toyota Company also invested in PEM fuel cell vehicles in recent decades. Both of the consumption of noble metal Pt and the system cost have greatly reduced. High officer of Toyota announced that, the retailing price of a PEM fuel cell vehicle can be reduced to 50,000 $ in 2015, meaning that the vehicle can be put into normal market. An HEV utilizes an Internal Combustion Engine (ICE) as a primary power source, and an energy storage system as a secondary power source. It consumes fossil oil and is not zero emission. By optimizing the operating status of the engine and recycling braking energy, the fuel consumption can be drastically reduced compared to a traditional vehicle. It has been greatly developed and is now stepping into commercialization. It is regarded as a transient product between traditional vehicles and green vehicles in the future. A plug in electric vehicle can be regarded as a hybrid vehicle with plug-in functions. Considering the present situation of the Chinese new energy industry, a plug in PEM fuel cell (PFCEV) city bus was developed. It was equipped with a PEM fuel cell stack as an auxiliary power unit, and three Li-ion battery packages of a large capacity. The drive mileage of the vehicle is longer than that of a pure battery powered city bus with similar configuration. It is zero emission and independent of fossil oil. For a PFCEV city bus it becomes a challenging problem to split power between the two power sources in an optimal way so as to minimize the daily operating cost. The strategy deal with this problem is normally called an energy management strategy. Researchers have done plenty of work on this topic. It can be classified into several types, e.g. rule-based strategies, on/off-line optimal strategies, frequency decoupling strategies [2,3]. The problem can be regarded as a global optimal problem or a real-time optimal problem, which can be solved by using dynamic programming algorithm or based on the optimal control theory. G. Paganelli proposed an instantaneous optimal strategy for an Internal Combustion Engine (ICE) hybrid system. Fuel consumption was reduced by 17% with this strategy [4]. Prof. Huei Peng of the University of Michigan researched on the Determined Dynamic Programming (DDP) for a hybrid vehicle, and deduced a real-time optimal algorithm for practical control [5]. His research group also did some work on the Stochastic Dynamic Programming (SDP), showing that the SDP algorithm can be more adaptive than DDP in practical traffic conditions [6]. J.P. Torreglosa et al. studied the equivalent consumption minimization strategy for a PEM fuel cell/battery hybrid system [7]. L.M. Fernandez et al. did research on the energy management strategies for a fuel cell hybrid tramway with two d.c. converters [8]. Ahmad Fadel et al. proposed an optimization approach with fuel mass flow rate as the cost function [9]. Zhihong Yu et al. presented an innovative optimal strategy, which makes the global optimization into a real time control strategy. With this strategy vehicle energy consumption was minimized, and the battery and the fuel cell system were kept in a healthy way [10]. Tomaz studied the energy flows in plug-in hybridelectric vehicles, showing that the energy management strategy can be designed based on an analysis of energy flows within the power-train [11]. Saeid Bashash et al. did
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some research on the optimized charge pattern of a plug-in hybrid electric vehicle, considering the total cost and the battery health degradation [12]. B. Vural et al. presented a study on different energy management strategies for vehicular applications [13]. A wavelet transform based energy management strategy was developed and tested by Prof. Mi [14]. Moreover, energy management strategies for plug in HEVs are specially paid attention to. Scott J. Moura et al. studied the tradeoff relationships between battery capacity and optimal strategy. Two energy management strategies for plug in hybrid electric vehicles, namely Blended Strategy (BS) and Charge Depleting Charge Sustaining (CDCS) strategy, were compared. As a result, the BS approach intends to minimize the entire cost, including fuel cost and electric cost. And the CDCS strategy prefers to minimize the fuel cost only [15]. Jeffrey Gonder et al. from National Renewable Energy Laboratory presented three potential energy management strategies for plug in HEVs, namely All Electric Range (AER)-focused strategy, engine-dominant blended strategy and electricdominant blended strategy. Engine-dominant blended strategy is suitable for long distance drive, since the engine benefits from the efficiency maximization approach. Electricdominant blended strategy is appropriate for a short distance, because it can deliver effective utilization of the electrical energy [16]. This paper studies an optimal real-time applicable energy management strategy targeting at minimizing the daily operating cost for a plug in PEM fuel cell city bus. The powertrain structure and system model is firstly described in Section 2. Section 3 presents the global optimal problem for a daily operating cycle on Singapore Bus Route 179, solves the problem with the DDP method, and deduces a four-step realtime applicable optimal strategy. In Section 4 several different strategies are compared in a simulation model, showing the effectiveness of the optimal strategy. Section 5 gives the onroad testing results of the city bus on Singapore Bus Route 179. In Section 6, methods to reduce the operating cost are discussed. Section 7 is the conclusions.
2.
Power-train structure and system model
2.1.
Power-train structure
The PFCEV city bus is a cooperative product of several units, including the Tsinghua University, Beijing Sino Hytec and Higer Bus Company Limited. Nanyang Technological University of Singapore also helped to design the power-train system. The city bus was designed for a demonstrational program in Youth Olympic Games of 2010, both in the Olympic Village and on the 179 bus route. The length of the vehicle is about 12 m, and its unloaded weight is 15 tons. The maximal velocity is about 60 km h1, and the accelerating time from zero to maximal speed is about 20 s. The power-train structure is shown as in Fig. 1(a). It is driven by an electric motor with rated power of 100 kW, powered by a Li-ion battery system as a primary power source and a PEM fuel cell stack as an auxiliary power unit. The maximal output torque of the electric motor is 1121 N m, and
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the maximal speed is about 6000 r min1. Three Li-ion battery packages with rated voltage of 380 V and a rated capacity of 180 A h are connected serially, meaning that almost 68.4 kWh electric energy can be stored in the battery system. The maximal output power of the fuel cell engine is 40 kW, and its output voltage fluctuates between 360 V and 540 V. The pressure of the stored hydrogen gas in tanks can be between 20 and 30Mpa, corresponding to 16e24 kg at normal temperature. A d.c. converter is installed to link the fuel cell stack, the battery and the electric motor together. Parameters for the PFCEV city bus are shown as in Table 1.
2.2.
System model
A feed forward-backward model was developed to simulate the performance of the PEM fuel cell vehicle, containing several blocks: the driver’s model, the vehicle control strategy, the d.c. converter model, the PEM fuel cell model, the battery model, the electric motor model and the vehicle dynamic model.
2.2.1.
Driver’s model
Driver’s model simulates the behavior of the driver. Input signals are desired velocity Vtg and actual velocity Vact, and output signals are positions of accelerating/braking pedals (a/b). A PID algorithm is used to calculate the pedal positions basing on the velocity error (Dv) between desired velocity and actual velocity, described as follows. Dv ¼ vtg vact
a¼
b¼
8 > > < > > : 8 > > < > > :
(1)
Zt Dvdt þ Kp1 Dv; Dv > 0
Ki1 0
(2)
0 ; Dv 0 Zt Dvdt Kp1 Dv; Dv 0
Ki1 0
(3)
0 ; Dv > 0
where Ki1, Ki2, Kp1, Kp2 are positive coefficients.
2.2.2.
PEM fuel cell
The system structure of the PEM fuel cell stack is shown as Figure 6 in [17]. On the cathode side a compressor is utilized to supply compressed air. On the anode side, the pressure of the hydrogen gas is firstly reduced by a proportion pressure control valve. Then it is maintained at a stable level using a pressure maintaining valve. Both of the air and the hydrogen gas are humidified before getting into the stack. In order to avoid water flooding at the anode side, a pulse solenoid is installed to purge flooding water, resulting in an extra hydrogen loss. The hydrogen fuel mass flow rate (g s1) can be calculated as follows. : mH2 ¼ Nifc Mhydrogen = uf ne F
(4)
where N is the number of cells that connect serially, ifc is the fuel cell stack current, Mhydrogen is the molar mass of hydrogen gas, ne is the number of transferred electrons, uf is the fuel utilization rate and F is the Faraday’s constant. The air flow rate (g s1) is calculated as follows. :
mair ¼ l0 Lst Nifc Moxy =ð2ne FÞ
(5)
where l0 is the excess air ratio, Lst is the air coefficient, and Moxy is the molar mass of oxygen gas. The power consumption of the air compressor can be written as follows. h i. : ðk1Þ=k Pcp ¼ mair $cp;air $Tatm $ pcp 1 hcp (6) Fig. 1 e (a) Structure of the power-train of the PEM fuel cell/ Li-ion battery hybrid city bus (b) Schematic diagram of the buck d.c. converter (c) Equivalent circuit diagram of the Thevenin model for the battery.
where cp,air is the heat capacity of the air, Tatm is the temperature of the atmosphere, pcp is the pressure ratio, k is the polytropic exponent. The fuel cell net efficiency is then defined as follows.
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used, Rint model, Thevenin model [18] and RC model [19]. Based on our research, an extended Thevenin model is used to describe the dynamic performance of the battery. The equivalent circuit diagram of the Thevenin model is illustrated in Fig. 1(c). The state space equation is shown as follows.
70
Velocity (km.h-1)
60 50
8 > 1=C1 V1 1=ðC1 R1 Þ 0 dV1 =dt > > þ ½ibat ¼ > < dV =dt 1=C2 0 1=ðC2 R2 Þ V2 2 > V1 > > > : ½Vbat ¼ ½ 1 1 V þ ½R0 ½ibat þ ½Vocv 2
40 30 20 10 0 0
10
20
30
40
50
60
t (min)
Fig. 2 e Velocity curve of the 179 bus route of Singapore city for one route.
: hfc ¼ Pfc Pcp Paux mH2 LHV
DC converter
The output voltage of the PEM fuel cell stack changes between 360 V and 540 V. And the range of Li-ion battery system is between 280 V and 400 V. A buck d.c. converter is designed and installed to link the PEM fuel cell system, the Li-ion battery and the d.c. to a.c. inverter for the electric motor. The schematic diagram of the converter is shown as in Fig. 1(b). The d.c. converter efficiency is defined as follows. hdc ¼ ðPdc Þ= Pfc Pcp Paux
2.2.4.
(8)
Battery model
The Li-ion battery is modeled based on the equivalent circuit model. There are several typical models those are most widely
Table 1 e Parameters for the plug-in fuel cell city bus. Parameter (Unit) Unladen vehicle mass m (kg) Frontal area A (m2) Drag coefficient CD Rolling resistance coefficient Mechanical efficiency hT (%) Mass factor PEM fuel cell maximal power (kW) PEM fuel cell voltage range (V) Stored hydrogen pressure (Mpa) DC/DC maximal power (kW) Li-ion battery rated capacity (A h) Li-ion battery rated voltage (V) Electric motor peak power (kW) Electric motor peak torque (N m) Electric motor rated power (kW) Electric motor maximal rotational speed (r min1)
Value 1.5 104 7.5 0.7 1.8 102 95 1.1 40 360e540 20e30 40 180 380 180 1.121 103 100 6 103
(9)
where V1 and V2 are polarized voltages, C1 and C2 are polarized capacitors, R1 and R2 are polarized resistances, ibat is the battery current, R0 is the ohmic resistance, Vocv is the open circuit voltage and Vbat is the battery working voltage. Parameters of capacitors, resistances and open circuit voltages are functions of State of Charge (SOC). Relationships between these parameters and SOC were found by testing. Data can be found in [20]. The parameter SOC is defined as follows.
(7)
where LHV is the low heat value of hydrogen (121 MJ kg1), Paux is other auxiliary components’ power consumption, including the water pump and cooling fans.
2.2.3.
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Zt SOC ¼ SOC0
Ibat hcolm =Qbat dt
(10)
0
where SOC0 is the initial SOC, Qbat is the battery capacity, and hcolm is the column efficiency. The ohmic resistance, the open circuit voltage are functions of the battery SOC and the inner temperature. The rated voltage of the battery is 360 V, and the average discharging resistance can be regarded as 30 mU. Because of the limitation of the electro-chemical reactions of the Li-ion battery, the working voltage should not exceed upper and lower limits. In another words, the output power of the battery should not exceed the maximal and minimal value.
Pbat;max ¼ Vmin ðVocv Vmin Þ=Rdis Pbat;min ¼ Vmax ðVocv Vmin Þ=Rchg
(11)
where Vmin (280 V) and Vmax (400 V) are the allowed minimal and maximal working voltage of the battery, determined by material properties.
2.2.5.
Electric motor model
A vehicular electric motor works in diverse modes, e.g. driving mode, braking mode and sliding mode. Power balance equations of the electric motor are shown as follows. 8 < Pele ¼ Vbat Im T u ¼ Pele hdr ðTdr ; um Þ : dr m Tbr um ¼ Pele =hbr ðTbr ; um Þ
(12)
where hdr and hbr are drive and brake efficiencies respectively, and Pele are the electric power into/out of the electric motor. Parameter Vbat is the battery output voltage, and Im is the input current of the inverter. Parameters Tdr and Tbr are driving and regenerative braking torques, respectively. Parameter um is the rotational speed. The maximal efficiency is about 89.5%. More than 90% of the working points features an efficiency >80%. The power balance equation for the hybrid power-train can be described as follows. Pbat þ Pdc ¼ Pele þ Pvh
aux
(13)
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where Pvh_aux is the auxiliary power of the power-train. The electric power of the electric motor should also not exceed the upper and lower limits determined by the battery as shown in Eq. (11).
2.2.6.
Vehicle dynamic model
We use traditional vehicle dynamic model in the simulating model. The equation indicates a relationship between the vehicle velocity and the output power of the electric motor. When the vehicle drives, it can be written as follows [21].
8 < SOCL SOC SOCH subject to : Vmin Vbat Vmax : 0 Pdc Pdc;max
where Cfc and Cbat are hydrogen refueling cost for the PEM fuel cell system and battery charging cost respectively. Vbat is the battery working voltage, SOCL and SOCH are the bottom and upper limits of the battery SOC. The two costs can be formulated as follows. Cbat
mgfucosa þ 0:5CD Aru3 þ dmu
du þ mgusina ¼ Pele hT hdr dt
(14)
where m is the vehicle mass, g is the gravity, f is the rolling resistance coefficient, a is the road slop angle, r is the air density, CD is the air drag coefficient, A is the front area, d is the rotational inertial coefficient, u is the vehicle velocity, and t is the time. Parameters hT and hdr are the transmission efficiency and electric motor driving efficiency, respectively. When the vehicle brakes, it can be described as mgfucosa þ 0:5CD Aru3 þ dmu
du þ mgusina ¼ Pele hT =hbr þ Pbk dt (15)
where Pbk is the mechanical brake power delivered by the mechanical brake system, hbr is the efficiency during regenerative braking process.
2.2.7.
Vehicle control strategy
The vehicle control strategy mainly has two functions. One is to determine the output torque of the electric motor according to the driver commands, the other is to split power between the two power sources, namely the energy management strategy. The former can be described as follows, where b1 and b2 are accelerating and braking pedal positions, respectively.
Tdr ¼ f4 ðb1 ; um Þ Tbr ¼ f5 ðb2 ; um Þ
(16)
The latter is what is studied in this paper. The target of the strategy is to calculate the target power of the PEM fuel cell system. In this power-train system, it is to calculate target power of the dc converter Pdc.
Cfc ¼ Mh2 be Pfc Dt sgnðPbat Þ ¼ Mele Pbat hdis avg hchg avg Dt
3.1.
(19)
Mh2 and Mele are prices for hydrogen gas and electric energy, 0.0445 Sig. $ g1 and 0.25 Sig. $ kWh1, respectively. The d.c. converter output power Pdc is the control variable, and the battery SOC is the state variable. The parameter be is the hydrogen consumption rate in g w1, Pfc is the fuel cell stack power, Dt is the control cycle of the vehicle controller. Pbat is the battery output power, Pbat > 0 while discharging, and Pbat < 0 while charging. Parameters hdis_avg and hchg_avg are average discharging and charging efficiencies of the battery, respectively. Constraints for the problem are shown as in Eq. (18).
3.2. Mathematical solution based on dynamic programming The global optimal problem described in Section 3.1 can be solved using a numerical iteration method, the DDP [22]. We define a new variable Jp as follows. Jp ¼ min
N1 X Cfc;k þ Cbat;k
(20)
k¼p
The DDP problem can be solved step by step from the end to the start of the entire cycle as follows. Step 1: to solve the static minimizing problem.
JN1 ¼ min Cfc;N1 þ Cbat;N1
(21)
We can get the functions of minimal cost and the optimal output power of d.c. converter v.s. SOC.
JN1 ¼ fN1 ðSOCÞ Pdc;N1 ¼ Pdc;N1 ðSOCÞ
(22)
Step 2: i ¼ 2wN, to solve the iteration minimizing problem
JNi ¼ min JNiþ1 þ Cfc;Ni þ Cbat;Ni
3. Global optimization problem, DDP strategy and its simplification
(18)
(23)
Incorporating the battery state space Eqs. (10,11), we can get
Problem description
JNiþ1 ðSOCÞ ¼ fNi ðSOCÞ JNi ¼ min fNi ðSOCÞ þ Cfc;Ni ðSOCÞ þ Cbat;Ni ðSOCÞ
(24)
Solving the one variable function problem, we can get The optimal strategy targets at minimizing the operation cost in the whole cycle. In order to simplify the problem, we firstly calculate the required power of the vehicular power-train {Prq ¼ Pele þ Pvh_aux}, and treat it as the input of the optimal problem. The target of the strategy is to get the minimized operating cost J. J ¼ min
N1 X k¼0
Cfc;k þ Cbat;k
(17)
JNi ¼ JNi ðSOCÞ Pdc;Ni ¼ Pdc;Ni ðSOCÞ
(25)
Step 3: to get the optimal matrix Pdc,opt (k, SOC) as follows. Pdc;opt ðk; SOCÞ ¼ Pdc;k ðSOCÞ;
k ¼ 0wN 1
(26)
where Pdc,opt(k,SOC) is the optimal output power of the PEM fuel cell system through the d.c. converter. A GUI program in Matlab was developed as shown in Fig. 3 of [23]. The DDP
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strategy is influenced by several parameters, e.g. the upper and lower limits of SOC (SOCL, SOCH), as being studied in [23].
3.3.
Driving cycles of Singapore 179 bus route
Energy management strategies for plug-in fuel cell vehicles are influenced by driving cycles and driving distance per charge greatly. If the driving distance per charge can be covered by the AER, it is obviously that the fuel cell should be turned off during operation. Otherwise, part of the energy in the fuel cell system should be consumed in an optimal way so as to minimize the operating cost. The studied city bus was designed for a demonstrational program in the first Youth Olympic Games. The demonstrational program was carried out on two routes. One was the Olympic Village route in the Nanyang Technological University, and the other was the Bus Route 179 which connects the University and the Boonlay Station. Because the driving distance per cycle of the first route is much shorter than that of the second one, we take the Bus Route 179 into consideration to design the optimal energy management strategy. Singapore Bus Route 179 connects the Nanyang Technological University and the Boonlay Station. The starting and the ending bus stations are the same one, Boonlay. The first bus starts at 6:00 in the morning, and the last bus ends at 00:20 of the next morning. One bus takes about 14e28 cycles per day, depending on traffic conditions. Fig. 2 illustrates the velocity curve of the Bus Route 179. The maximal speed is about 60 km h1, the cycle time is about 58 min, and the driving distance per cycle is about 9.8 km. The idle status occupies 60% of the cycle time. The average velocity is about 25.4 km h1 with the exception of idle status. As an average level, we consider a PFCEV city bus runs 18 cycles per day, meaning that 176 km and 17.7 h per day.
3.4.
DDP and DBSD strategies
If we want to apply the DDP strategy into practice, we need to store the matrix Pdc,opt(k,SOC) into the microcontroller, measure the operating time and battery SOC perfectly. However, nowadays the microcontroller for vehicle control
90 80
Charge Depleting
Charge Depleting
70
Charge Sustaining
Blended strategy
SOC (%)
60 50
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targets can’t offer such a high performance. This is the reason why the DDP can only be used in simulation model. It is therefore the DDP strategy must be simplified to make it realtime available. The result of the DDP strategy is influenced by several parameters, e.g. SOCL, SOCH, Vmin, Vmax and initial SOC. For a PFCEV city bus the battery is charged at night, its initial SOC is kept between 90% and 100% at the beginning of a daily operation. Fig. 3 presents the optimal SOC trajectory with SOCL ¼ 0.2, SOCH ¼ 0.8 and initial SOC ¼ 0.9. This curve gives some hints on how to control the power split between the two power sources in an optimal way. According to the battery discharging process, the entire operation can be divided into four parts, charge depleting, blended, charge sustaining and charge depleting. At the first stage, the fuel cell is turned off, and the driving energy is only provided by the battery. At the second state, both of the fuel cell system and the battery deliver the driven energy, and the battery SOC decreases gradually. At the third stage, the battery SOC is kept sustaining. At the fourth stage, the fuel cell is turned off again, and the vehicle is driven by the battery system. According to this process, we construct a DBSD (charge Depleting, Blended, charge Sustaining and charge Depleting) strategy as follows, which is a simplified form of the DDP strategy. 8 > <
Pdc
0; t < t1 k1 ðSOC SOC1 Þ þ k3 Prq;avg ; t˛½t1 ; t2 ¼ > : k2 ðSOC SOC2 Þ þ Prq;avg ; t˛ðt2 ; t3 0; t˛ðt3 ; t4
(27)
where t4 ¼ 17.7 h is the ending time of the whole process. The eight parameters (t1wt3, k1wk3, SOC1, SOC2) can be optimized using the genetic algorithm to minimize the error between the DBSD and DDP strategy. The optimized intervals for the eight variables are as follows.
Intervals for t1 < t2 < t3: [0.1, 17.7] h, calculating step: 0.1 h; Intervals for k1 w k2: [1, 10] kW%1, calculating step: 1 kW%1; Intervals for k3: [0.1, 0.9], calculating step: 0.1; Intervals for SOC1 > SOC2: [0.1, 0.9], calculating step: 0.1;
The eight parameters are regarded as the genes. They comprises a chromosome which is described using an eight dimensional vector w ¼ [t1, t2, t3, k1, k2, k3, SOC1, SOC2]T. An encoding strategy with a 16-bit binary code is designed. Genetic operations such as population initialization, fitness function, selection, crossover, mutation are programmed. Results of the genetic algorithm are shown as in Table 2. Prq,avg is the average power requirement of the power-train, including the electric motor and the auxiliary components. Compared to the DDP strategy, the DBSD strategy avoids storing huge data in the microcontroller.
40
4. Comparison of different strategies in simulation model
30 20 10 0
4.1. 2
4
6
8
10
12
14
16
t (h)
Fig. 3 e Optimal SOC trajectory of a DDP strategy.
CDCS strategies
18
The CDCS strategy is widely known and utilized in plug in vehicles. With this strategy, the electric vehicle works in pure
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Table 2 e Parameters for the DSBD strategy. Values
t1 t2 t3 t4 k1 k2 k3 SOC1 SOC2
0.3 h 12.9 h 17.3 h 17.7 h 8 kW%1 2 kW%1 0.2 0.7 0.6
a
90 80
CDCS5
70 60 SOC (%) SO
Parameters
CDCS4
DBS BSD
50 CDCS3
40 DDP DD 30 20
battery electric mode at the first stage. After the battery SOC decreases to a certain level, it switches to hybrid mode where the battery SOC is kept constant. It can be formulized as follows. Pdc ¼
CDCS2
10 CDCS1 0 0
2
4
6
8
10
12
14
16
18
t (h)
0; SOC> SOCb Prq;avg kðSOC SOCb Þ; SOC SOCb
(28)
b
Costt per 100 km (Sig.$.(10 100km)-1)
640
where SOCb is the battery SOC threshold value, and k > 0 is a positive coefficient. Parameters of SOCb and k can be adjusted to achieve a good system performance.
620 600
CDCS 5 CD
CDCS 4 CD
580
4.2.
CDCS 3 CD
Comparison in the simulation model
The DDP strategy (SOC0 ¼ 90%, SOCL ¼ 0.2 and SOCH ¼ 0.8), the DBSD strategy and several CDCS strategies (SOCb ¼ 10%, 30%, 50%, 70%, 90%) are compared in a simulation model. Results are shown as in Fig. 4(a)e(c). Fig. 4(a) illustrates the SOC trajectories with different strategies. With a CDCS strategy, the PFCEV city bus operates as a pure battery electric vehicle at the first stage. The battery SOC decreases until it reaches the threshold value. The battery is kept charge sustaining afterward, and the SOC fluctuates below the threshold value. The threshold values for five CDCS strategies are 10%, 30%, 50%, 70% and 90%, respectively. The SOC trajectories for DBSD and DDP strategies are also drawn in Fig. 4(a). The two differ in the blended process. With the DBSD strategy, the battery SOC decreases almost linearly, while with the DDP strategy it decreases exponentially. Fig. 4(b) indicates the relationship between the daily operating cost and the maximal velocity difference, which is defined as the maximal absolute difference in the simulation model between target and actual velocities, DVh;max ¼ maxð Vtg Vact Þ. It is affected by two factors, the driver’s behavior and the power that can be delivered by the two power sources. Because of the time delay in the feedback controller of the driver’s model, the maximal velocity difference can never be eliminated. When the battery SOC is kept in a low level, the two power sources can’t supply enough power during accelerating processes, leading to a large maximal velocity difference. The daily operating cost is composed of two parts, the hydrogen refueling cost and the battery recharging cost. During the demonstrational project in Singapore of 2010, the price for the hydrogen gas that is utilized to refueling the hydrogen station is 44.48 Sig. $ kg1, which is equivalent to 1.32 Sig $. kWh1 considering the low heat value of the
560
CDC DCS 2
540 CDCS 1 CD
520 500
DBS BSD 480
DDP
460 440 2
3
4
5
6
7
8
-1 Δ Vh,max (km.h )
c
Hydrog ogen consumption (kg) 26 25
CDCS 5 CD
24 CDCS 4 23 CDCS 3 CD 22
CDCS 2
21 CDCS 1 20 DBSD
19 DDP DD 18 17 2
3
4
5
6
7
-1 Δ Vh,max (km.h )
Fig. 4 e Comparison of different strategies (the DDP strategy, the CDCS strategies and the DBSD strategy) (a) SOC trajectories (b) Trade-off relationship between daily operating cost and maximal velocity difference [ max(jVtgLVactj) (c) Trade-off relationship between hydrogen consumption and maximal velocity difference [ max(jVtgLVactj).
8
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hydrogen gas. The price for the electric energy from the grid is 0.25 Sig. $ kWh1, which is less than 1/5 of the price of the hydrogen gas. Considering the fact that the energy concerting efficiency of the PEM fuel cell system from the hydrogen chemical energy in the high-pressed tank to the electric energy out of the d.c. converter is around 50%, and the battery charging/discharging efficiencies are as high as 90e95%, the price for the electric energy from the battery is around 1/10 of that of the hydrogen gas. As shown in Fig. 4(b), the operating cost decreases with the increment of maximal velocity difference. For the five CDCS strategies, the operation cost for every 100 km driving distance increases from 496 to 638.5 Sig. $ with the increment of battery sustaining SOC level from 10% to 90%. And the maximal velocity difference decreases from 7.75 to 2.15 km h1. The operation cost for every 100 km driving distance for the DDP and DBSD strategies are lower than the CDCS strategies, 448.8 and 464.1 Sig. $, respectively. Compared to the lowest level of CDCS strategies, the operating cost of DDP and DBSD strategies are reduced by 9.5% and 6.4%, respectively. Fig. 4(c) presents the relationship between hydrogen consumption and maximal velocity difference. For the five CDCS strategies, the hydrogen consumption for the entire driving distance increases from 19.3 to 25.3 kg with the increment of battery sustaining SOC level from 10% to 90%. And the maximal velocity difference decreases from 7.75 to 2.15 km h1. The hydrogen consumption for the DDP and DBSD strategies are lower than the CDCS strategies, 17.4 and 18.0 kg, respectively. Compared to the lowest level of CDCS strategies, the operating cost of DDP and DBSD strategies are reduced by 9.8% and 6.7%, respectively.
depending on the fault diagnosis and tolerant control strategy. The entire program is executed once every 10 ms. Meanwhile, a modified coefficient l regarding the PEM fuel cell cooling water temperature etc. are defined to modify the optimal output power as follows. 8 > <
Pdc
tg
0; t < t1 k1 ðSOC SOC1 Þ þ k3 Prq;avg l; t˛½t1 ; t2
¼ > : k2 ðSOC SOC2 Þ þ Prq;avg l; t˛ðt2 ; t3 0; t˛ðt3 ; t4
(29)
where l is the product of several coefficients l ¼ l1 Tfc l2 ðTbat Þl3 Vmin fc l4 Vmin
bat
l5 Vmax
bat
(30)
where l1 to l5 are the modification coefficients for the PEM fuel cell cooling water temperature, the battery inner temperature, the minimal cell voltage of the PEM fuel cell stack, the minimal and the maximal cell voltages of the battery package, respectively. Piecewise linear functions are designed for the five parameters. Take the parameter l1 for an example. The operating range of the PEM fuel cell cooling water temperature is divided into three parts, Tfc < Tfc0, Tfc0 < Tfc < Tfc1, Tfc > Tfc1. l1 ¼ 1 when Tfc < Tfc0, l1 ¼ 0 when Tfc > Tfc1, l1 decreases linearly from 1 to zero when Tfc0 < Tfc < Tfc1. By using such a function, the PEM fuel cell cooling water temperature can be kept below Tfc1. Similar functions are designed for parameters l2 to l5. The PFCEV city bus was tested on the 179 bus route of Singapore city. Because of the limited objective conditions, the on-road testing was carried out in the middle of the day on two days, and data for several cycles were collected. In Section 5.2, the power-train performance for one cycle is analyzed. In Section 5.3, the statistic results for power-train performance for one day operation (18 cycles) are deduced based on these data for several cycles.
5. On-road testing results of Singapore bus route 179
5.2. On-road performance in one cycle of Singapore 179 bus route
5.1. Real-time strategy with a finite state machine based on DBSD
Fig. 5(a)e(f) illustrate the on-road performance of the PEM fuel cell city bus on the Singapore 179 bus route for one cycle. Fig. 5(a) shows the performance of the PEM fuel cell stack. The output current ranges between 0 and 95 A, and the output voltage ranges between 370 and 520 V. The equivalent resistance can be deduced from the data, 0.48 U. The fuel cell net efficiency hfc and the fuel cell power distribution are illustrated in the third subplot. The net efficiency is obtained by experiments. The efficiency when the fuel cell net power is 5 kW is a bit low. Normally at this point, the net efficiency is relatively high. This is because the electric motor controller for the air compressor of the fuel cell stack works not very well. The output power focuses between 33 and 35 kW for most of the time, corresponding to a net efficiency of 56%. During the testing, the cooling water temperature is kept around 47 and 60 C. Fig. 5(b) illustrates the performance of the Li-ion battery. The output current ranges between 80 and 370 A, and the output voltage ranges between 360 and 376 V. The equivalent resistance is about 30 mU according to the voltage and current data. Fig. 5(c) shows the performance of the electric motor. The two red lines are external characteristic curves during driving and regenerative braking processes. The red numbers on the
In order to apply the DBSD strategy into the real PEM fuel cell city bus, some parameters need to be considered for safety reasons, e.g. the PEM fuel cell cooling water temperature, the battery system temperature, the lowest cell voltage of PEM fuel cells, and the lowest and highest cell voltages of Li-ion battery. A real-time applicable strategy with a finite state machine based on the DBSD strategy is developed. According to this strategy, the PEM fuel cell system operates in five states, namely “shutdown”, “starting”, “shutting down”, “normal” and “abnormal” states. The program starts from the “shutdown” state. When it receives a “start” command from the driver, it goes into the “starting” state, where the output power of the dc converter increases gradually so as to heat the stack itself. After the cooling water temperature reaches the normal level, e.g. 65 C, the program jumps into the “normal” state. If some exceptions of the fuel cell stack occur, e.g. detecting extremely low cell voltages, the program goes into the “abnormal” state, where the output power of the dc converter decreases gradually. It can go back to the normal state or change into the “shutdown” state,
Fig. 5 e On-road testing for one 179 bus route cycle during the charge sustaining process (a) PEM fuel cell system (b) Li-ion battery system (c) distribution of the electric motor working points (d) Power split between fuel cell and the battery (e) trajectories of hydrogen pressure, temperature and battery SOC (f) Energy flow of the power-train.
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contours are the efficiencies. The working points focus on two areas, one is the low speed [0, 500 r min1] low torque [0, 200 N m] area (average efficiency 35%), and the other is the high speed [3000 r min1, 4500 r min1] low torque [100 N m, 250 N m] area (average efficiency 85%). The recycled energy is slight. A slight parallel regenerative braking function is used in the bus, which means the braking energy is primary absorbed by the mechanical braking system. Fig. 5(d) illustrates the power split situation between different components. The PEM fuel cell system delivers power between 0 and 35 kW. The d.c. converter outputs power between 0 and 31 kW. The output power of the battery fluctuates drastically between 30 kW and 135 kW. The electric power of the electric motor follows the vehicle dynamic performance. It changes between 20 kW and 145 kW. Fig. 5(e) indicates the trajectories of the hydrogen pressure, temperature and the battery SOC. The hydrogen pressure decreases slowly from 17.5 Mpa to 16 Mpa. The hydrogen temperature changes slowly between. Battery SOC almost keeps constant around 30%. Fig. 5(f) shows the energy flow diagram of the power-train system in one cycle. Totally 1.06 kg hydrogen gas is consumed in 59 min and 9.23 km. The energy delivered by the hydrogen according to LHV is 128.3 MJ. The net efficiency of the fuel cell system (defined as net output energy/hydrogen LHV energy) is 53.2%. The fuel cell system offers a net energy of 68.3 MJ, average power 19.3 kW. The d.c. converter operates with an average efficiency of 85.7%. The output energy of the converter is 58.5 MJ, and the average power is 16.5 kW. The battery outputs a net energy of 14.3 MJ. The energy loss due to battery resistance is 0.423 MJ, with an average efficiency of 97%. The vehicle auxiliary components, e.g. the air condition, the electric steering system, consume an energy of 33.2 MJ, with an average power of 9.4 kW. The electric motor operates in driving and regenerative braking modes. The average efficiencies in two modes are 85.7% and 95% for driving and braking modes, respectively. The electric energy for driving the vehicle is 40.5 MJ, and the average power is 11.5 kW. The electric energy recycled by the electric motor is 0.978 MJ, and the average power is 0.29 kW. The regenerative braking function is very slight. Only 3% of the driving energy is recycled. The energy efficiency (mechanical driving energy/energy consumption both from hydrogen gas and the battery) is about 24%. The fuel economy is 11.5 kg(100 km)1.
5.3. Statistic results of vehicle performance on Singapore 179 bus route Vehicle performance for 18-cycle operation is deduced based on data for several cycles, as illustrated in Table 3. There are two operation modes of the power-train system during operation, battery electric vehicle (BEV) mode (also the charge depleting mode), and hybrid electric vehicle (HEV) mode (also the blended and charge sustaining mode). The entire operation time was 17.7 h. The HEV-move mode occupied 36.8%, the HEV-idle mode occupied 53.9%, the BEV-move mode occupied 4.2% and the BEV-idle mode occupied 6.1%. The drive distance was 176 km, including 90% of HEV mode and 10% of BEV mode.
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The entire hydrogen energy consumed in the testing was 668.9 kWh, corresponding to hydrogen mass of 19.9 kg. The entire electric energy was 59.2 kWh, corresponding to DSOC ¼ 0:8. From a viewpoint of energy consumption, the proportion of the HEV-move hydrogen energy in the entire energy consumption was 55.1%. The proportion of HEV-idle energy was 36.7%. The battery was charged in the HEV modes, and discharged in BEV modes. For simplification, we consider the electric energy as a whole part. The proportion of electric energy from the battery occupied 8.1%. The entire operation cost was 900 Sig. $. Hydrogen cost in HEV-move mode occupied 59%, and in HEV-idle mode occupied 39.3% of the entire cost. The proportion of electric cost was 1.6%. The entire recycled energy from the electric motor was 48.4 kWh. The recycled energy in BEV modes occupied 13%, and the left 87% was recycled in HEV modes. The battery and the PEM fuel cell needed to deliver more energy without brake regenerative strategy. The entire reduced energy was 71.7 kWh for the two power sources. The proportion in BEV-move mode was about 7%. The proportion of hydrogen energy in HEV-move mode was about 85%, and the proportion of electric energy in HEV-move mode was about 8%. Similarly, the operation fee would be higher than current if there was no regenerative strategy. Entire reduced cost was 52.1 Sig. $. The proportion in BEV-move mode was about 2%. The proportion of hydrogen cost in HEV-move mode was about 97%, and the proportion of electric cost in HEV-move mode was about 1%. The brake regenerative strategy reduced energy consumption and operation cost. The reduction ratio differs in different modes. The energy reduction ratio was 9% for the entire process. It was 8.7% in HEV modes including idle mode and move mode. The ratio increased to 13.7% in HEV-move mode. The energy reduction ratio in BEV modes was 14.5%. It increased to 22.0% when the BEV-idle mode is excluded. The cost reduction ratio was 5.5% for the entire process. It was 5.4% in HEV modes. It increased to 8.7% in HEV-move mode. The cost reduction ratio in BEV modes was 12.3%. It increased to 19.0% when the BEV-idle mode is excluded. Equivalent hydrogen consumption per 100 km is also influenced by the operation modes. The equivalent hydrogen consumption is combined of actual hydrogen consumption and equivalent consumption of battery electric energy. It was 7.8 kg(100 km)1 in HEV-move mode, and 14.1 kg(100 km)1 in HEV modes (move þ idle). The electrical consumption per 100 km in BEV mode was 100.7 kWh (100 km)1 in BEV-move mode without idle, and 167.8 kWh (100 km)1 in BEV mode with idle, respectively.
6.
Discussion
The simulation and on-road testing results of CDCS-1, DBSD and DDP strategies are summarized as in Table 4. Compared to the strategy of CDCS-1 (496 Sig. $ (100 km)1, 19.3 kg), the maximal theoretical reduction ratios in operation cost and hydrogen consumption can be 9.5% (448.8 Sig. $ (100 km)1) and 9.8% (17.4 kg), by using DDP strategy. However, the DDP strategy can’t be applied directly in real-time control. The
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Table 3 e Statistic result of on-road testing. Percentage of each part (%) Whole driving time 17.7 h
Whole driving distance 176 km Whole energy consumption 728 kWh (19.9 kg hydrogen, 59.2 kWh electric energy from the battery)
Whole operation cost 900 Sig. $
Whole recycled energy from electric motor 48.4 kWh Whole equivalent reduced energy from the two power sources 71.7 kWh
Whole reduced cost 52.1 Sig. $
Energy reduction ratio (%)
Cost reduction ratio (%)
Equivalent hydrogen consumption per 100 km (kg) Electric energy consumption per 100 km (kWh)
DBSD strategy is proposed on the basis of DDP strategy. The operating cost can be reduced by 6.4% (464.1 Sig. $ (100 km)1), hydrogen consumption by 6.7% (18.0 kg), as well as guaranteeing vehicle dynamic performance. In the on-road testing with the DBSD strategy, the operation cost increased by 2.9% (510.2 Sig. $ (100 km)1), and the hydrogen consumption increased by 3% (19.9 kg). Hydrogen gas refueling cost in the idle state occupies about 39.3% of the entire operating cost. This is because the PEM fuel cell is required to output power for the air condition in the idle state. As shown in Fig. 5(f), the average power of the air condition and other auxiliary components is about 9.4 kW, which is near the average electric power for driving the
BEV-move BEV-idle HEV-move HEV-idle HEV-move BEV-move Electric energy from the battery
4.2 6.1 36.8 53.9 90.1 9.9 8.1
Hydrogen energy in HEV move Hydrogen energy in HEV idle Hydrogen cost in HEV move Hydrogen cost in HEV idle Cost for electric energy from the battery BEV move HEV move BEV move Electric energy in HEV move Hydrogen energy in HEV move BEV move Electric energy in HEV move Hydrogen energy in HEV move Whole process HEV HEV move BEV BEV-move Whole process HEV HEV move BEV BEV-move HEV-move HEV BEV-move BEV
55.1 36.7 59 39.3 1.6 13 87 7 8 85 2 1 97 9 8.7 13.7 14.5 22.0 5.5 5.4 8.7 12.3 19.0 7.8 14.1 100.7 167.8
vehicle (11.5 kW). If the average power of the air condition can be reduced to half of its current level (4.7 kW), the entire hydrogen gas consumption can be reduced by 4.7/0.456/ 36.3 ¼ 28.4%, meaning that the daily operating cost can decrease by 28.4%*98.4% ¼ 27.9%. The braking energy regenerative strategy is another effective way to reduce hydrogen consumption. However, for the vehicle under discussion, only 3% of the drive energy is recycled. The average recycled electric power is 0.29 kW. If the percentage of the recycled energy increases to 10%, the hydrogen gas consumption can be reduced by 7/3*0.29/0.456/ 36.3 ¼ 4.1%, meaning that the daily operating cost will decrease by 4.1%*98.4% ¼ 4%.
Table 4 e Comparison of diverse energy management strategies for 18 cycles of Singapore 179 bus route.
CDCS-1 (model) DBSD (model) DDP (model) DBSD (Testing)
Cost per 100 km (Sig. $ (100 km)1)
Hydrogen consumption (kg)
Electric energy consumption (kWh)
DSOCð%Þ
DVh;max ðkm h1
496 (100%) 464.1 (Y6.4%) 448.8 (Y9.5%) 510.2([2.9%)
19.3 (100%) 18.0 (Y6.7%) 17.4 (Y9.8%) 19.9 ([3%)
62.5 61.2 61.2 59.2
80.0 76.1 77.5 79.1
7.75 7.7 7.69 e
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7.
Conclusions
An optimal real-time energy management strategy with a four-step discharging process (DBSD) for a plug in proton exchange membrane fuel cell electric vehicle (PFCEV) on a determined bus route is proposed based on the dynamic programming algorithm. The traditional CDCS strategies, the DBSD strategy and the DDP strategy are compared with each other in simulation model, and an on-road testing for the DBSD strategy is carried out. Conclusions are as follows. 1) There is a trade-off relationship between the fuel economy (operating cost, hydrogen consumption) and the vehicle dynamic performance (maximal velocity difference). The optimal energy management strategy minimizes the operating cost and guarantees the vehicle dynamic performance during accelerating. 2) The DDP strategy is effective to minimize the daily operating cost. However, it can’t be applied in a microcontroller. A DBSD strategy can be used as a replacement of the DDP strategy in a real-time controller. With this strategy, the power-train operates in four modes, charge depleting, charge sustaining, blended and charge depleting. 3) Compared to the optimal CDCS strategy (496 Sig. $ (100 km)1), the daily operating cost can be reduced by 6.4% with the DBSD strategy (464.1 Sig. $ (100 km)1), and it can be reduced by 9.5% with the DDP strategy (448.8 Sig. $ (100 km)1). The operating cost of on-road testing of DBSD strategy is 510.2 Sig. $ (100 km)1. It is 9.9% higher than the result in the simulation model. 4) Compared to the optimal CDCS strategy (19.3 kg), the hydrogen consumption can be reduced by 6.7% with the DBSD strategy (18.0 kg), and it can be reduced by 9.8% with the DDP strategy (17.4 kg). The hydrogen consumption of on-road testing of DBSD strategy is 19.9 kg. It is 10.5% higher than the result in the simulation model. 5) With the DBSD strategy, the average efficiencies of the fuel cell system, the d.c. converter, the battery are 53.2%, 85.7% and 97%, respectively. The average efficiencies of the electric motor in the drive mode and in the brake regenerative mode are 85.7% and 95%, respectively. The air condition consumes about 25.9% of the hydrogen energy. The energy efficiency of the power-train (mechanical driving energy/energy consumption both from hydrogen gas and the battery) is about 24%. 6) Generally speaking, the operation process can be divided into two modes, pure battery electric driven mode, and hybrid driven mode. In the BEV mode, the electric energy consumption every 100 km distance is 167.8 kWh, including energy consumption both in move and idle statuses. If we only consider the BEV move mode, this value will be reduced to 100.7 kWh. 7) In the HEV mode, the equivalent hydrogen consumption every 100 km driving distance is 14.1 kg, including hydrogen consumption both in move and idle statuses. If we only consider the HEV move mode, this value will be reduced to 7.8 kg.
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8) The hydrogen refueling cost is responsible for the daily operating cost. The price of the hydrogen gas is five times that of the electric energy for the same energy. It occupies 98.4% of the entire operating cost. 9) Hydrogen gas cost in the idle state occupies about 39.3% of the entire operating cost, because the PEM fuel cell is required to output power for the air condition. If the power consumption of the air condition decreases to half of the current level, the daily operating cost will be reduced by 27.9%. 10) About 3% of the drive energy is recycled. If the percentage of the recycled energy increases to 10%, the daily operating cost will decrease by 4%. The fuel economy and daily operating cost are greatly influenced by the driving cycle. Further study should be focused on the influences of driving cycles on the vehicle performance. Moreover, it is necessary to take the performance degradation characteristics of the PEM fuel cell system and the Li-ion battery into consideration, so as to obtain a lifecycle optimal energy management strategy.
Acknowledgments This work is funded by the NSFC (National Natural Science Foundation) of China under the contract of No. 61004075, the MOST (Ministry of Science and Technology) of China under the contract of No. 2010DFA72760 and No. 2011AA11A269, and the Tsinghua University Initiative Scientific Research Program (Grant No. 2010THZ08). Thanks are also due to Nanyang Technological University of Singapore on the demonstrational program in the first Youth Olympic Games (YOG).
references
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