Multi-objective energy management optimization and parameter sizing for proton exchange membrane hybrid fuel cell vehicles

Multi-objective energy management optimization and parameter sizing for proton exchange membrane hybrid fuel cell vehicles

Energy Conversion and Management 129 (2016) 108–121 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www...

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Energy Conversion and Management 129 (2016) 108–121

Contents lists available at ScienceDirect

Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Multi-objective energy management optimization and parameter sizing for proton exchange membrane hybrid fuel cell vehicles Zunyan Hu a,b, Jianqiu Li a,b, Liangfei Xu a,b,c, Ziyou Song a, Chuan Fang a,b, Minggao Ouyang a,⇑, Guowei Dou d, Gaihong Kou d a

State Key Lab of Automotive Safety and Energy, Tsinghua University, Beijing 100084, PR China Collaborative Innovation Center of Electric Vehicles in Beijing, PR China Institute of Energy and Climate Research, IEK-3: Electrochemical Process Engineering, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany d SAIC Motor Co., Ltd., Shanghai 201804, PR China b c

a r t i c l e

i n f o

Article history: Received 5 July 2016 Received in revised form 25 September 2016 Accepted 26 September 2016

Keywords: Fuel cell electric vehicle Energy management Parameter sizing Dynamic programing Durability Soft-run strategy

a b s t r a c t The powertrain system of a typical proton electrolyte membrane hybrid fuel cell vehicle contains a lithium battery package and a fuel cell stack. A multi-objective optimization for this powertrain system of a passenger car, taking account of fuel economy and system durability, is discussed in this paper. Based on an analysis of the optimum results obtained by dynamic programming, a soft-run strategy was proposed for real-time and multi-objective control algorithm design. The soft-run strategy was optimized by taking lithium battery size into consideration, and implemented using two real-time algorithms. When compared with the optimized dynamic programming results, the power demand-based control method proved more suitable for powertrain systems equipped with larger capacity batteries, while the state of charge based control method proved superior in other cases. On this basis, the life cycle cost was optimized by considering both lithium battery size and equivalent hydrogen consumption. The battery capacity selection proved more flexible, when powertrain systems are equipped with larger capacity batteries. Finally, the algorithm has been validated in a fuel cell city bus. It gets a good balance of fuel economy and system durability in a three months demonstration operation. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Increasing awareness of environment pollution and the growing energy crisis have spurred interest in developing new energy technologies for automobiles. The fuel cell hybrid vehicle (FCHV), with its low environment impact, long range and zero pollution, has attracted the attention of enterprise and government. Although fuel cell hybrid system has been very popular in some areas, such as photovoltaic solar panels, wind turbine and fuel cell hybrid generation systems [1], and a battery-fuel cell hybrid powertrain system [2]. It suffers from great efforts from high manufacturing costs and a short service life. The powertrain system of the FCHV is more complex than that of conventional vehicles, and usually contains at least two energy sources: a fuel cell system (FCS) and an energy storage system ⇑ Corresponding author. E-mail addresses: [email protected], [email protected] (Z. Hu), [email protected] (J. Li), [email protected] (L. Xu), ziyou. [email protected] (Z. Song), [email protected] (C. Fang), [email protected] edu.cn (M. Ouyang), [email protected] (G. Dou), [email protected] com (G. Kou). http://dx.doi.org/10.1016/j.enconman.2016.09.082 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

(ESS), for example, a lithium battery (Li-battery) system or a super capacitor (CS) [3]. Both parameter sizing of the components and energy management strategy (EMS) must be optimized. The system that links the two parts is called intercoupling. The EMS is designed to achieve an optimal power allocation between the two energy sources. Applying optimization theory, two approaches can be defined: rule-based strategies and optimization-theory-based strategies. Usually a rule-based strategy can be used for real-time control. Hemi et al. [4] used a fuzzy logic algorithm to control the powertrain system. It was effective in real-time control, but the optimization results were dependent on the design of the fuzzy rule. Optimization-theory-based strategies are more effective in optimization. Dynamic programming [5] is the most commonly used algorithm for global optimization. And Pontryagin’s minimum principle (PMP) combined with markov chain [6] or traffic preview information [7] are effective for the forward optimization process. However, global optimization algorithms can’t be used in real-time control directly, which require too much computation, it usually works as the theoretical guidance of real-time control strategy design.

Z. Hu et al. / Energy Conversion and Management 129 (2016) 108–121

In addition to reducing fuel consumption, how to improve the durability of FCS and ESS is also important. Torreglosa et al. [8] present a hierarchical control algorithm to satisfy the load power demand, to maintain the hydrogen tank level and the SoC of the battery, and to take also economic aspects into account. Guo et al. [9] proposed a complex rule-based strategy to keep the state of charge of the batteries within an optimal range and meet power demand of the locomotive at a high efficiency. Xu et al. proposed a three mode (start up, normal working and shut down) real-time control strategy [10], combined with an adaptive supervisory controller (ASC) [11], to minimize the fuel consumption, extend the battery charge, and improve the fuel cell durability of a fuel cell/ Li-battery hybrid city bus. However, the optimization strategies of system durability in prior researches are usually based on the engineering experience, and the adaptability of EMS in different configurations is not taken into consideration. The optimization of components parameter sizing is another focus of the study, because it decides the potential of powertrain system and affects the efficiency of EMS. Muhsen et al. [12] proposed a differential evolution based multi-objective (Loss of load probability, life cycle cost and the volume of excess water) optimization algorithm to optimally size a photovoltaic water pumping system (PVPS). Gan et al. [13] developed a model-based sizing tool for Hybrid wind–photovoltaic–diesel–battery system by empirical approach, life-cycle cost and performance analysis. Ravey et al. [14] proposed a novel methodology based on the statistical description of driving cycles to size the energy source of FCEV, and applied it to a collection truck working in fixed cycles. However, prior researches of parameter sizing mainly focus on the dynamic performance or system cost. The influence of parameter sizing on EMS design is ignored. Because the optimizations of the EMS and parameter sizing are linked, some authors have tried to optimize them simultaneously. Kavvadias et al. [15] proposed an electrical-equivalent load following strategy for a trigeneration plant with better economical efficiency and performance characteristics, and a parametric analysis design method to define the optimal investment size. Hung et al. [16] developed a combined optimal sizing and control approach by using the global search method to minimize the accumulated energy consumed during predefined cycle. Liu et al. [17] proposed a power source sizing model by applying the Pontryagin’s minimum principle (PMP) as an energy management strategy, to optimize the battery life and reduce battery energy loss, fuel consumption, and powertrain cost. While the FCS durability is neglected and the influence of parameter sizing on EMS design is still unclear. From the literature review, the following conclusions were reached about the boundedness of prior researches: (1) The adaptation of EMS is imperfect, and can only can be applied to a specific FCEV. In addition, the optimization results are off-line and need much computation, which is unsuitable for real-time control strategy design. (2) The optimization of parameter sizing and the EMS are usually separate issues, prior researches mainly focus on the optimal results of EMS, and the impact of parameter sizing on the EMS design is uncertain. (3) Fuel cell durability plays a minor role in the optimization of parameter sizing and the EMS design. While fuel cell stack is a very expensive and damageable component, which can’t be neglected. In consequence, the multi-objective real-time EMS design by taking Li-battery size into consideration for FCHV is a novel issue, which few literatures has discussed. To be specific, fuel economy and system durability, parameter sizing, and EMS design are three

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intercoupling problems. The fuel economy, including Li-battery durability and FCS durability, is minimized by using the DP approach. In the DP analysis, the characteristic of optimization results for a system with different size Li-batteries and auxiliary power consumption are considered and compared. Generally, the service life of Li-battery is longer than FCS’s. When FCS is scrapped, the rest service life of Li-battery is wasted. With advances in fuel cell service life, how to balance the fuel economy and manufacturing cost is also considered. At last, all the factors above need to be considered simultaneously, when designing a real-time EMS. In consequence, it’s necessary to propose an adaptive real-time energy management design strategy to solve these problems simultaneously. This paper proposes a novel multi-objective optimization EMS design using a soft-run strategy for the design of a fuel cell/Libattery hybrid system energy management algorithm. A soft-run strategy based on DP focuses on fuel economy, system durability and the adaptation of the Li-battery sizing. Section 2 describes the structure of a hybrid powertrain system and introduces a mathematic model for fuel economy, Li-battery durability, and fuel cell durability. Section 3 defines the soft-run strategy based on the optimization results of the DP algorithm. Section 4 discusses the evolution of a soft-run strategy with battery sizing change, and the validation through simulations of two strategies based on the soft-run strategy. Section 5 defines a life cycle cost function and the optimization of Li-battery sizing with different service lives of the fuel cell stack. Section 6 presents the validation of the Soft-run strategy in a fuel cell city bus. Section 7 presents the conclusions. 2. Structure of the powertrain and multi-objective quantitative model How to model the powertrain system and the optimization objectives is the basis for this problem. Especially for a multiobjective optimization problem, the weight of each part in the quantitative model can significantly affect the optimization results. 2.1. Fuel cell system The configuration of powertrain system on which this paper is based is shown as Fig. 1. The FCS is connected to the bus via DC/ DC converter and supplies energy to the motor in parallel with the Li battery. This research attempts to improve fuel economy and durability by optimizing the power distribution strategy. Based on related parameters of the FCHV in Table 1, this paper introduces a multi-objective optimization problem and defined in terms of fuel economy and system durability. 2.2. Equivalent hydrogen consumption model The energy consumption of a FCHV involves both hydrogen and electricity. When evaluating fuel economy, it is necessary to ensure

Fig. 1. Structure of FCEV.

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which takes a fixed value; and t 1 , n1 , t 2 and t 3 are idle time, startstop count, duration of heavy loading, and heavy load time, respectively. From bench testing results, the degradation coefficients of each category are k1 , k2 , k3 and k4 . If the FCS cannot work under adverse operating conditions, it also cannot work forever, and b represents the natural decay rate. The coefficient Kp is a modified coefficient for on-road systems and the difference between two FCS systems. Table 2 presents all these parameters. Since the units used for D/FCdegrad and hydrogen consumption are

Table 1 Parameters of FCHV. Cycle info

Speed-time curve

NEDC cycle

Vehicle parameters

Mass Frontal area Correction coefficient of rotating mass Coefficient of rolling friction Tire rolling radius Drag coefficient Total reduction ratio

1860/2235 kg 2.18 m2 1.05

Motor speed range Motor torque range LI-battery type

0–11,500 rmp 300 to 300 N m Lithium iron phosphate battery 16 Ah 12.5 C, 17.5 C

Powertrain parameters

Battery capacity Charge-discharge C-rate of Libattery Braking energy recovery efficiency DC/DC average efficiency Maximum power of FC stack

0.0086 316 mm 0.31 8.928

ð1Þ

where DmH2 is instantaneous hydrogen consumption associated with DC/DC converter output power (Pdc). Eq. (2) is used to calculate the equivalent hydrogen consumption of the battery system DmH2equ1 [18]. avg

dc fce avg

:

V batrate DQ bat

gdc gbatchg

avg gfce

avg LHV

DmH2 equ2 ¼

D/FCdeg rad MFC

DQ bat > 0 charging DQ bat < 0; discharging

ð2Þ

where gdc is the efficiency of the DC/DC convertor, gbatdis_avg/ gbatchg_avg are average battery discharge and charge efficiencies, LHV is the low heat value of hydrogen, V batrate is the average working voltage of Li-battery, and DQbat is the electric quantity change of the Li battery. Charge-discharge efficiency is considered in this equivalent model. Both charge energy (DQbat > 0) or discharge energy (DQbat < 0) show losses in the charge-discharge process. 2.3. Equivalent fuel cell degradation model There is no consensus on the best mathematical model for fuel cell system degradation. Since the output power is the only variable that can be manipulated in the energy management optimization process, an empirical formula or semi-rational formula of FCS degradation is acceptable. It has been suggested that fuel cell system degradation is due to the operating condition, which can be classified into four categories: load changing, startup and shutdown, idling and high power load [19]. The empirical formula for the voltage decline percentage of an FCS, is shown as Eq. (3).

D/FC deg rad ¼ D/FCaddition þ D/FC normal ¼ Kpððk1 t 1 þ k2 n1 þ k3 t 2 þ k4 t 3 Þ þ bÞ

ð4Þ

10%C H2

where C H2 is the hydrogen price, and the performance degradation of 10% is the maximum allowable value for the FCS in automotive applications. So DmH2 equ2 represents the equivalent hydrogen consumption of the performance degradation.

0.94 40 kW

DmH2 ¼ f ðP dc Þ

DmH2 equ1 ¼

sumption (DmH2 equ2 ) based on the price of FCS and hydrogen, as shown in Eq. (4).

60%

that the final SoC in a test cycle is consistent with the start. If there is deviation in the value of SoC, the electricity deviation must be converted into hydrogen consumption. The direct hydrogen consumption MAP can be derived from bench tests and calculated by Eq. (1)

8 V bat DQ bat g batdis < rate g g LHV

different, it is difficult to achieve optimum result. In order to solve this problem, D/FCdegrad is converted into equivalent hydrogen con-

ð3Þ

where D/FC degrad is the performance decline, defined as the percentage voltage drop in a fixed current; D/FC additon is the performance degradation caused by adverse operating conditions; D/FC normal is physical decay caused by the materials or manufacturing process,

2.4. Equivalent battery degradation model The Li-battery degradation rate is determined by the charge and discharge cycles, temperature, depth of discharge and other factors. The mathematical model of battery degradation can be expressed as Eq. (5) [20].





n ¼ Ae

Ea þBC R RT Bat



ðAh Þ z

ð5Þ

where n is battery capacity decline as a percentage; Ea, R, TBat, Z represent the battery activation energy, molar gas constant, Kelvin temperature of Li-battery, and a time factor; and Ah and CR are the current flux and charging rate. This model is often used to evaluate the service life of a Li battery. However, it is inaccurate for a single cycle, so the model is discretized by Eqs. (6) and (7).



1 z

Ea þBC R zRT Bat



Dn ¼ DAh zA e DAh ¼

1 3600

Z

t pþ1



z1 z

ð6Þ

n

jIBat jdt

ð7Þ

tp

In a discrete model, n is regarded as a constant in a cycle. Based on on-road test data, the battery temperature can also be regarded as a constant, since its fluctuation is very small. The degree of battery degradation is also converted into the equivalent hydrogen consumption by Eq. (8).

DmH2 equ3 ¼

DnM Bat 20%C H2

ð8Þ

where DmH2 equ3 is equivalent hydrogen consumption. A capacity loss of 20% often indicates the end-of-life of an automotive Li battery.

Table 2 Coefficients for performance degradation model. Coefficient

Values (unit)

Definitions

k1 k2 k3

0.00126 (%/h) 0.00196 (%/cycle) 0.0000593 (%/h)

k4 Kp b

0.00147 (%/h) 1.47 0.01 (%/h)

Output power less that 5% of max power One full start-stop Absolute value of load variations rate is larger than 10% of max power per second Higher than 90% of maximal power Natural decay rate

Z. Hu et al. / Energy Conversion and Management 129 (2016) 108–121

2.5. Multi-objective quantitative model In this research, the multi-objective optimization problem was broken into three parts: fuel economy, FCS degradation and Libattery degradation. All were converted into equivalent hydrogen consumption. The multi-objective optimization problem could therefore be expressed by Eq. (9).

min J ¼ min

X

DmH2 þ kB DmH2 equ3 þ   kC DmH2 equ1 þ kA DmH2 equ2

! ð9Þ

where J is the optimization objective, and kA, kB, and kC are the weighting coefficients of the three parts, which are used to accommodate different requirements in actual design. In this research, all the coefficients were set to 1. All equivalent hydrogen consumptions are associated with Pdc. The optimization target was therefore to find the control variable series {Pdc} that gave the minimum value of J in a pre-defined cycle. In the optimization process, SoC, Pdc and battery output were limited to a pre-defined range, as shown in Eq. (10).

8 SoC low < SoCðiÞ < SoC high > > > < jSoCðendÞ  SoC j < DSOC best > Pdc low < PdcðiÞ < Pdc high > > : Pbat low < PbatðiÞ < Pbat high

Solving an optimization problem with constraints is challenging, but it can be simplified by converting the constraints into equivalent hydrogen consumption using the penalty functions in Eqs. (11) and (12) [21].

X  kC ðDmH2 equ1 þ kA DmH2 equ2 Þ  P min J ¼ min þkB DmH2 equ3 þ DmH2 þ h ( hi ðki Þ ¼

aðDki þ 1Þ2 Dk i –0 0

Dk i ¼ 0

The optimization procedure of a DP algorithm is a reverse solving process. From the last discretized step N, the optimal decision Pdc on any SoC condition is calculated as Eq. (13). m

J N;opt ðSoCÞ ¼ min J N ðSoC; Pdc;i Þ i¼1

11   J N1;opt ðSoC N Þ ¼ min JN ðSoC N ; Pdc;i Þ þ J N;opt ðSoC N1 Þ

ð14Þ

SoC N ¼ SoC N1 ðPdc;N1 Þ

ð15Þ

The optimization result, Pdc and J N1;opt ðSoCÞ, are also stored in the MAPs. By iteration, the whole optimization process follows Eq. (16). 11   J P;opt ðSoC P Þ ¼ min J P ðSoC P ; Pdc;i Þ þ J Pþ1;opt ðSoC Pþ1 Þ i¼1

ð11Þ

ð12Þ

where h is the equivalent hydrogen consumption, Dk is the limit of the allowable variation range, and a is the weighting coefficient of the different constraints. The values of the penalty functions reflect the extent to which the variable remain within a defined range, and Dk represents how far the variable exceeds the restrictions. In short, Eq. (11) is the terminal multi-objective optimization function.

ð13Þ

J N;opt ðSoCÞ represents the value of the evaluation indexes J for a certain SoC at step N, and Pdc;i is the output power of the DC/DC convert, which can be in any part of the decision space. The optimal result of the SoC state, Pdc, and JN;opt ðSoCÞ is stored in two MAPs. When step N is completed, the DP algorithm begins step N  1. However, the evaluation indexes J at step N  1 cannot make an accurate judgment, because the global impacts of this step are unknown. The SoC at step N is determined by the SoC state and Pdc at step N  1. As the optimal result of any arbitrary SoC at step N has been stored in MAPs, the optimal results can be directly obtained at step N from the SoC and Pdc at step N  1. So the evaluation indexes of step N  1 must include J at step N  1 and the related optimal result at step N. It’s shown as Eqs. (14) and (15).

i¼1

ð10Þ

111

ð16Þ

Finally, the optimization results can be presented as a matrix of Pdc, Pdcopt = g(t, SoC). Depending on the MAP, the powertrain system can make an optimal decision by SoC at any time in the predefined cycle. The New European Driving Cycle (NEDC) was used in the simulation. And the optimization MAP of the DP optimization results in NEDC cycle is shown as Fig. 2. The x-axis, y-axis, z-axis is time, SoC and Pdc, respectively. Any point with a certain time and SoC corresponds to a fixed point Pdc in the graph. In the forward simulation process, the effectiveness of the DP was verified by table lookup, for which the MAP is used in the energy management module. 3.2. Soft-run strategy design

3. Multi-objective optimization strategy: soft-run strategy According to the global optimization result, a multi-objective optimization strategy is proposed to solve the problem defined in Section 2.5. 3.1. Global optimization results A DP algorithm is an effective approach to solving a global optimization problem in a predefined cycle. It can greatly reduce the calculation time by transforming multi-stage decision processes into a single-phase decision problem. Therefore, a DP algorithm was used to solve the optimization problem defined by Eq. (11). For a predefined cycle, the energy demand at any time is a known quantity. Factoring in the calculation time and accuracy of the results, the state variable (SoC) is discretized as {0%, 1%, . . . , 99%, 100%}, decision variable (Pdc) is discretized as {0 kW, 1 kW, . . . , 39 kW, 40 kW}, and time is discretized as {1 s, 2 s, 3 s, . . .}. This separates the test cycle into single steps.

As an off-line optimization algorithms, the DP algorithm cannot meet the need for real-time control. However, it offers clues to online algorithm design, and the DP results are applied to our on-line algorithm design. For a powertrain system with zero auxiliary power consumption, the DP optimization results were shown as Fig. 3. Fig. 3(a) gives the speed-time curve and power-time curve, and Fig. 3(b) shows the power-time curves of the different power sources. Whether under acceleration or braking, the fuel cell output power was constant from 0 s to 1000 s. The output power demand increased only when power demand increased continuously. The Li battery delivered dynamic power most of time. Since the SoC endpoint value was approximately equivalent to the beginning value and the FCS worked at an almost fixed level, it was close to the average power demand point. Fig. 3(c) shows the histogram of fuel cell output. The output power of the FCS was focused at a few points after DP optimization, allowing the powertrain system to achieve better economy and durability.

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(a) NEDC cycle

(b) Optimization MAP

Fig. 2. Optimization result of DP algorithm in NEDC cycle.

(a) Time-power and timevelocity curve

(b) Output power of two power sources

(c) histogram of fuel cell output

The frequency histograms of Power demand 0.5 0.4 0.3 0.2 0.1 0 -40

-20

0

20

40

60

Pm le(kW) e

(d) power demand and fuel cell output

(e) histogram of power demand

(f) the efficiency curve of FCS

Fig. 3. Forward simulation results of DP algorithm.

Fig. 3(d) shows the relationship between power demand and fuel cell output, which is significant in the design of a powerfollowing energy management algorithm. As shown in the figure, the curves can be divided into three regions. When power demand was negative, or less than 25 kW, in region A, FCS output power was kept at 5 kW. As power demand increased in region B, the output power increased approximately linearly. When power demand was >40 kW, it has a step change in region C,. Fig. 3(e) shows the histogram of power demand. Power demand above 40 kW was less than 2% and above 20 kW was less than 10%. The FSC output power was almost sufficient in region A. Fig. 3(f) shows the efficiency curve of the FCS, on which the steady output points choice in Fig. 3(c) and (d) were based. The

maximum efficiency point was at 5 kW in the linear part of the low output power region, and 10 kW represented the next turning point of the efficiency curve. The high-efficiency working area was at output power between 10 kW and 28 kW, with 15 kW as the maximum efficiency point and 37 kW as the heaviest load point. According to the analysis in Fig. 3(d)–(f). These DP optimization results yield rules for multi-objective optimization strategy: (1) Keeping the FCS working at a few stable points is beneficial for economy and durability. The selection of working points is dependent on the characteristics of the FCS and the power demand.

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(2) Having the FCS work in idle condition, when power demand is zero or negative, should be avoided, as this reduces system economy and durability. It is preferable to set a minimum FCS output power to charge Li battery. The precise working point is dependent on the efficiency curve of the FCS. (3) A step change strategy should be used to meet dynamic power demand. We can limit the FCS work at three points: a minimum point, a highest efficiency point, and a high power point. The FCS switches between these points under specific situations and the rate of power change in step change process should be limited, in order to avoid damaging the FCS. These rules were named, aimed at keeping the fuel cell system stable and reducing output power volatility, as ‘‘soft-run strategy,” because they provide soft working conditions for the fuel cell system. A soft-run strategy can use a range of real-time control algorithms, like fuzzy logic and rule base.

(a) 8 Ah, 0 kW

(d) 16 Ah, 0 kW

(g) 24 Ah, 0 kW

4. Evolution of multi-objective optimization results with battery capacity change The soft-run strategy needs more details to adapt to different powertrain systems and drive cycles. In this research, the FCS size was fixed and it mainly focused on battery capacity selection to analyze the evolution process of the multi-objective optimization results. The average power demand can also significantly influence the power point distribution of the optimization results. Considering the consumption of video or air-conditioning, the auxiliary power was divided into three levels: 0 kW, 2 kW, and 4 kW.

4.1. Adaptation optimization of the soft-run strategy As auxiliary power increased, the average power demand became higher and the histogram of fuel cell output appeared totally different. 8 Ah, 16 Ah, and 24 Ah batteries were chosen as

(b) 8 Ah, 2 kW

(c) 8 Ah, 4 kW

(e) 16 Ah, 2 kW

(f) 16 Ah, 4 kW

(h) 24 Ah, 2 kW

(i) 24 Ah, 4 kW

Fig. 4. Histograms of DP optimization in different battery capacities and auxiliary power demand.

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examples, and the histograms of the DP optimization results at the three auxiliary power levels are shown in Fig. 4. As shown in Fig. 4(a)–(c), the output power histogram was irregular under auxiliary power variation, when the battery capacity was 8 Ah. As the capacity of the battery increased, the auxiliary power variation only changed the percentage of certain fixed output power points; hence, the multi-objective optimization results were similar at different auxiliary power demand levels. Fig. 4(g)–(i) shows the optimization results of the powertrain system with a large-capacity Li battery. The output power of the FCS was distributed in several narrow regions. When applying a soft-run strategy to the design of a real-time control algorithm, that is favorable for the adaptability of the multi-objective optimization control algorithm. A powertrain system with a smallcapacity battery requires more regulation through the algorithm design. Although the percentage of each power point was established, the temporal spatial distribution characteristic of the FCS output

(a) 0 kW, 8 Ah

(d) 2 kW, 8 Ah

(g) 4 kW, 8 Ah

demand remained unknown. To handle powertrain systems with different capacity Li batteries and power demands, the soft-run strategy requires adaptive rules in the real-time algorithm design. The most commonly used state variables for real-time control algorithm design are SoC and power demand, which can be used as switchover conditions. The evolution of switchover conditions at different Li-battery capacities is shown below. Fig. 5 shows the relationship between power demand and FCS output. Based on the analysis in Section 3.2, the figure can be divided into three regions. Region A represents the low-power output working condition, and remains at a constant value most of the time. However, the upper limit value of region A is raised with auxiliary power demand increasing. Region B represents the dynamic middle power output working condition. When using an 8 Ah Li battery, region B is complex, composing a linearly increasing part and a constant part. At higher auxiliary power demand, the percentage of the two parts is uncou-

(b) 0 kW, 16 Ah

(c) 0 kW, 24 Ah

(e) 2 kW, 16 Ah

(f) 2 kW, 24 Ah

(h) 4 kW, 16 Ah

(i) 4 kW, 24 Ah

Fig. 5. Relationship between power demand and fuel cell output in different battery capacities and auxiliary power demand.

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ple. With a larger capacity battery, region B tends to maintain a constant value, regardless of whether auxiliary power demand increases or not. This is because the larger capacity battery can bear a larger charge current and store more energy. This allows FCS to output a larger current, whose efficiency is higher. A larger capacity battery therefore contributes to the adaptation of the algorithm design. Region C represents the high output-power working condition. The output power in region C is also constant. As the battery capacity increases, the lower limit value of region C gradually decreases. The design of a real-time control algorithm for a powertrain system at 24 Ah or 16 Ah is comparatively simple, in that it consists of three specific power points and switches between these points is based on the power demand. For a powertrain equipped with an 8 Ah Li battery, modeling region B is complex under a power demand-based method, which may significantly complicate the soft-run strategy. To help simplify the algorithm for a powertrain system with small-capacity battery, we analyzed the relationship between SoC and the output power of the FCS.

As shown in Fig. 6(a), (d), and (g), the scatter diagrams can be divided into several parts, based on their approximately linear relationship to SoC. When SoC was below a certain lower limit, the FCS worked at a high-level output point. When SoC was above the upper limit, the FCS worked at a low-level output point. When SoC was kept in the middle range, the FCS worked at either a lowlevel or middle-level point. These characteristics can be applied to the real-time control algorithm design. While not all powertrain systems have these characteristics, the scatter diagrams show that they are more distinct in system with a small-capacity Li battery. Therefore, in a powertrain system equipped with a small-capacity Li battery, the SoC-based method can benefit from a soft-run strategy. From the above analysis, it can be concluded that: when the powertrain system is equipped with a large-capacity Li battery, the power demand-based method is recommended for soft-run strategy design. With smaller capacity batteries, the SoC-based method is the better choice for real-time strategy design. Combining the working point selection strategies produced the detailed design flow diagram shown in Fig. 7.

(a) 0 kw, 8 Ah

(b) 0 kw, 16 Ah

(c) 0 kw, 24 Ah

(d) 2 kw, 8 Ah

(e) 2 kw, 16 Ah

(f) 2 kw, 24 Ah

(g) 4 kw, 8 Ah

(h) 4 kw, 16 Ah

(i) 4 kw, 24 Ah

Fig. 6. Relationship between SoC and fuel cell output under different battery capacities and auxiliary power demand.

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So-run strategy design

Baery Capacity Judgment

Pdc;i

Global opmizaon

<16Ah? Yes

NO

SoC based method

Power demand based method

Opmized working points

Working poins selecon

Highest efficiency point Minimum power point High power point

Real-me SoC based control method

Real-me power demand based control method

Fig. 7. Algorithm design framework for a soft-run strategy.

4.2. Simulation verification In this research, soft-run strategy was verified using simple real-time control algorithms. The SoC-based and power demandbased control methods were chosen as examples, though in the future, other advanced algorithms may be used to realize the soft-run strategy. The output of the FCS is discrete under a soft-run strategy, though oscillations may be generated in the critical region. The hysteretic characteristics of the FCS output were therefore added to the algorithms to maintain stability. Based on the efficiency curve of the FCS, 4 kW, 12 kW and 30 kW were chosen as the working points of the FCS net output power in the algorithm design. For the SoC-based control method, 65% and 55% were chosen as the upper and lower limit values of the switchover condition, respectively. The control logic is shown as Eq. (17).

8 Phigh SOC < SOC 1 > > > > > SOC > SOC 3 & Pdc;i1 ¼ Phigh > < Peff ¼ Peff SOC 1 6 SOC 6 SOC 2 & Pdc;i1 ¼ Peff > > > Peff SOC < SOC 4 & Pdc;i1 ¼ Plow > > > : Plow SOC > SOC 2 8 30 kw SOC < 0:55 > > > > > > < 12 kw SOC > 0:6 & P dc;i1 ¼ 30 kw ¼ 12 kw 0:55 6 SOC 6 0:65 & Pdc;i1 ¼ 12 kw > > > 12 kw SOC < 0:6 & P dc;i1 ¼ 4 kw > > > : 4 kw SOC > 0:65

ð17Þ

Base on Fig. 6, 8 kW and 22 kW were chosen as the lower and upper limit values of the switchover conditions for the power demand-based control method, respectively. The working points of the FCS were the same in the SoC-based method. The control logic is shown as Eq. (18).

Pdc;i

8 Phigh Pdem < Pdem1 > > > > > Pdem > SOC 3 & Pdc;i1 ¼ P high > < Peff ¼ Peff Pdem1 6 Pdem 6 Pdem2 & Pdc;i1 ¼ P eff > > > Pdem < Pdem4 & Pdc;i1 ¼ P low > Peff > > : Plow Pdem > Pdem2 8 30 kw Pdem > 22 kw > > > > > > < 12 kw Pdem < 20 kw & Pdc;i1 ¼ 30 kw ¼ 12 kw 8 kw 6 Pdem 6 22 kw & Pdc;i1 ¼ 12 kw > > > 12 kw Pdem > 10 kw & Pdc;i1 ¼ 4 kw > > > : 4 kw Pdem < 8 kw

ð18Þ

DP, SoC-based and power demand-based control methods were compared by simulating a powertrain system equipped with different-capacity Li batteries. This is shown in Fig. 8. Equivalent hydrogen consumption was defined as the combination of direct hydrogen consumption, battery energy change, and equivalent degradation consumption, as defined in Eqs. (2), (4), and (8). When the battery capacity was >8 Ah, the two real-time algorithms performed as well as the DP algorithm. This demonstrated that the algorithms designed using a soft-run strategy successfully realized multi-objective optimization. However, the equivalent hydrogen consumption of the SoCbased control method at 8 Ah was little better than that of DP. This is because the final SoC value is constrained in the DP algorithm, but not in the other two algorithms. The SoC change after an NEDC cycle is compared, in Fig. 9.

Fig. 8. Equivalent hydrogen consumption comparison with DP, SoC-based method, and power demand-based method at different battery capacities.

Z. Hu et al. / Energy Conversion and Management 129 (2016) 108–121

117

Fig. 9. SoC change comparison for DP, SoC-based method, and power demand-based method at different battery capacities.

(a) Per kilometer performance degeneration percentage of fuel cell and Li-battery at different battery capacities

(b) Equivalent hydrogen consumption of DP optimization at different battery capacities

Fig. 10. Optimal results of DP at different battery capacity.

When the battery capacity was very small, the two real-time control algorithms performed unstably causing notable performance degradation. The design of a multi-objective strategy for a powertrain system can be very complex and sensitive to power demand change. The best solution would be to avoid this battery size selection in the system design phase. This is discussed in the next section. 5. Multi-objective optimization in parameters sizing

Fig. 11. Optimal average life cycle cost at different battery capacities.

The stability of the DP algorithm was significantly better than those of other methods. In the SoC-based control method, the fluctuation of SoC was limited by the control logic. The power demandbased control method performed poorly in maintaining SoC. Therefore, SoC closed-loop feedback may be added to the power demand-based control method in some situations.

When designing a hybrid powertrain system, not only the operating cost but also the manufacturing costs were important. So far, the operating cost has been taken into consideration in analyzing the adaptive soft-run strategy. The manufacturing cost of the Li battery is now taken into the optimized objective function to estimate the life cycle cost. Good Li-battery size selection can prolong the service life of the FCS, as the optimized objective function combines fuel economy and system durability. The DP optimization results of the powertrains were compared with 6–80 Ah Li battery size, as shown in Fig. 10. Fig. 10(a) shows the performance degeneration percentage per kilometer, D/FC additon and n, in the NEDC cycle. When the battery capacity was less than 10 Ah, the fuel cell and battery degradation rate increased rapidly.

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A notable result was that the performance degradation caused by the EMS was far less than that of the battery. This is because the performance degradation comprised two parts. In terms of physical decay, the service life of a fuel cell is shorter than that of a battery. The actual degradation rate is larger than the ideal one due to environmental factors and system coordination problems. However, the evolution of degradation rate as battery capacity change is the same.

Fig. 10(b) shows the equivalent hydrogen consumption per 100 km, where HC is the direct hydrogen consumption per 100 km; ECH1 is equivalent hydrogen consumption per 100 km, based on electricity consumption from Eq. (2); and ECH2 is equivalent hydrogen consumption per 100 km, taking into account both electricity consumption and durability. When Li-battery capacity was very small, the difference between ECH1 and ECH2 became very large. As the Li-battery capacity increased, the HC value

multi-objective energy management and parameter size optimization

Baery sizing opmizaon

So-run strategy design

Global opmizaon

Baery Capacity Judgment

Working poins selecon

<16Ah?

NO

Yes

NO

SoC based method

Power demand based method

Opmized working points

Highest efficiency point Minimum power point High power point

Real-me SoC based control method

Real-me power demand based control method

mul-objecve opmizaon result is OK? Yes

end Fig. 12. Multi-objective energy management and parameter size optimization design framework.

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of the fuel cell became longer, the battery capacity selection became more flexible. With the present FCS, the best battery selection for a 5000 h service life FCS was 10 Ah, which performed 1.4% better than the 16 Ah battery in the test car. In the soft-run strategy, the SoC of the Li battery fluctuated in a narrow range, which benefited its service life. When an FCS is scrapped, much of the life time of the Li-battery is wastes, which costs more than the hydrogen consumption reduction. The life cycle cost therefore becomes higher as capacity increases. However, advance in fuel cell manufacturing technology can significantly decrease the average life cycle cost and balance the service life difference. A complete multi-objective energy management and parameter size optimization is shown as Fig. 12.

increased distinctly and EHC1 decreased in an approximately linear manner. In terms of system design, battery size selection becomes a trade-off problem. A powertrain system equipped with a largecapacity battery has a high manufacturing cost, but a low operating cost. In order to solve the trade-off problem, the life cycle cost was defined by combining manufacturing costs and operating cost. The Li-battery mass change was ignored. The service life of a fuel cell vehicle was defined as that of FCS, defined in Eq. (19).

EHC3 ¼ EHC2 þ

cos tprice  100 km Llife

ð19Þ

EHC3 is the equivalent hydrogen consumption per 100 km, which includes EHC2 and the manufacturing costs. The manufacturing cost of a Li battery assumed in this research was 600RMB per Ah, the ideal service life of the FCS was about 5000 h, and an average speed of 20 km/h was assumed for the FCV across the whole service life, for an expected total mileage of 100,000 km. As the service life may be extended in the future, the evolution of the average life cycle cost EHC3 was analyzed with different FCS service lifetimes. The results are shown as Fig. 11. At any assumed service life of the fuel cell, the desirable range of battery capacity was from 8 Ah to 24 Ah. When the service life of the FCS was changed from 2500 h to 20,000 h, the best Li-battery selections were 10 Ah, 10 Ah, 12 Ah and 16 Ah. As the service life

6. Experiment validation It’s a great pity that validation of the passenger car is still ongoing. However, some similar work has been finished in a fuel cell hybrid city bus. The configuration of the powertrain system in both vehicles is the same. Some parameters of the city bus are shown in Table 3. Considering the capacity of the power battery is not very large, the SoC-based method is adopted to design real-time strategy design. The effect of the soft-run control strategy is shown in Fig. 13(a). The fuel cell city bus has just finished a 3 months demonstration operation. The output current and voltage are shown in Fig. 13(b). Based on the demonstration data, some useful indexes are get, as shown in Fig. 14. As shown in Fig. 14(a) and (b), after a three mouth demonstration operation, Electrochemical Surface Area (ECA) is about 85% percent of the initial value, and resistance has increased about 0.02 X cm2. Based on Eq. (20) [22], the voltage decline resulted by ECA decrease and resistance increase can be measured.

Table 3 Parameters of the city bus. Column

Value

Bus

Bus length Bus weight

12 m 18 t

Electric motor

Max power Rated power Max speed

150 kW 75 kW 2600 r min1

Fuel cell stack

Max power Rated power Cell number Monolithic active area

30 ⁄ 2 kW 25 ⁄ 2 kW 135 ⁄ 2 276 cm2

Capacity Rated voltage

60 Ah/34 kW h 607 V

Power battery

VðiÞ ¼ V reversible  i  r 

  i þ iH 2 RT  m  eni ln naF 10  ðLca APt:el Þ  i0 ð20Þ

The voltage decrease resulted by ECA decrease is about 0.005– 0.01 V, which is insignificant for system usage. Ohmic polarization

100

U/V

200

160

80

120

60

80

40

100

100

200

300

0 400

time/h Fuel Cell B 200

200

100

100

20

50

100

150

200

250

0 300

time/min 0 0

(a) Relationship between battery SoC and FCS output current.

100

200

300

0 400

time/h

Voltage

Current

(b) Output current and voltage of FCS

Fig. 13. demonstration results.

I/A

0 0

100

0 0

U/V

40

BATSOC (%)

FCI (A)

Output current of FCS Battery SOC

200

I/A

Fuel Cell A 200

120

Z. Hu et al. / Energy Conversion and Management 129 (2016) 108–121 1.1

0.2

Fuel Cell A Fuel Cell B

1.05

Fuel Cell A Fuel Cell B

0.18 0.16

Resistance/ (ohm·cm2)

ECA percentage

1 0.95 0.9 0.85 0.8 0.75 0.7

0.14 0.12 0.1 0.08 0.06 0.04 0.02

0

10

20

30

40

50

0

60

0

10

20

30

40

50

60

Day

Day

Hydrogen consumption per 100km (kg/100km)

(a) Remaining percentage of Electrochemical surface area

(b) Fitting resistance

12 11 10 9 8 7 6 5 4

0

10

20

30

40

50

Day

(c) Hydrogen consumption per 100 km Fig. 14. the indexes change of FCS.

is decided by output current. Because the initial average voltage of the fuel cell system under 120 A is about 0.7 V, 120 A is defined as the reference current [23]. Voltage decline resulted by ohmic polarization under reference current is about 0.0087 X, about 12.4% of maximum usage life time. As shown in Fig. 14(c), hydrogen consumption per 100 km is about 6–9 kg/100 km. Fluctuation of the hydrogen consumption is resulted by anode purge and efficiency drop. Average hydrogen consumption during previous demonstration operation is about 6–10 kg/100 km. In general, soft-run strategy for a fuel cell hybrid city bus gets a good balance of fuel economy and system durability. Especially for system durability, soft-run strategy performs better than previous algorithm.

7. Conclusions This paper first examined the multi-objective optimization problem and proposed a multi-objective optimization strategy called soft-run, which was used to help design a real-time control algorithm. The output of the FCS generally maintains a stable state, and a step change method was used to meet dynamic power demand in the soft-run strategy. The FCS was limited to several specific points, and charged the battery under idling and braking conditions.

Second, the evolution process of multi-objective optimization was discussed as the Li-battery size was changed, to optimize the adaptability of the soft-run strategy. For a powertrain system equipped with a large-capacity Li battery, the power demandbased control method proved more suitable for a soft-run strategy, while with smaller capacity Li batteries, the SoC-based control method prove superior. If SoC fluctuation is restricted in the design, either the SoC-based control method or adding a SoC closed loop to the power demand-based control method can be used. Third, a life cycle cost function was defined, and the impact of Li-battery capacity sizing on life cycle costs was discussed. With advances in fuel cell service life, the life cycle cost can be significantly improved and the capacity choice can be made more flexible. When using large or small capacity Li batteries, the life cycle cost was very high. At the optimal Li-battery choice of 10 Ah, our system performed 1.4% better than the existing one. Finally, the validation of soft-run strategy is present in a fuel cell hybrid city bus. After a three month demonstration operation, ECA is about 85% percent of the initial value, and resistance has increased about 0.02 X cm2. It gets a good balance of fuel economy and system durability. In future research, the decline mechanism of the FCS should be studied. Eq. (3) is still a purely empirical equation, and a more detailed mathematical understanding of the physical decay is needed to combine it with D/FC additon . This is the basis of the multi-objective optimization problem. Additionally, the soft-run

Z. Hu et al. / Energy Conversion and Management 129 (2016) 108–121

strategy cannot yet be directly used for real-time control, which requires an algorithm carrier. More algorithms need to be tested to optimize the application of the soft-run strategy. Above all, algorithms should be validated in the passenger car. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 51576113 and U1564209), by SAIC Key Technology of Fuel Cell Electric Vehicle (Grant No. CGB-PC-2013150), by Ministry of Science and Technology of China (Grant No. 2015BAG06B01) and Tsinghua University (independent research plan Z02-1 Grant No. 20151080411). References [1] Devrim Y, Bilir L. Performance investigation of a wind turbine–solar _ region–Ankara, photovoltaic panels–fuel cell hybrid system installed at Incek Turkey. Energy Convers Manage 2016;126():759–66. [2] Samsun RC, Krupp C, Baltzer S, Gnörich B, Peters R, Stolten D. A battery-fuel cell hybrid auxiliary power unit for trucks: analysis of direct and indirect hybrid configurations. Energy Convers Manage 2016;127:312–23. [3] Pany P, Singh RK, Tripathi RK. Active load current sharing in fuel cell and battery fed dc motor drive for electric vehicle application. Energy Convers Manage 2016;122:195–206. [4] Hemi H, Ghouili J, Cheriti A. A real time fuzzy logic power management strategy for a fuel cell vehicle. Energy Convers Manage 2014;80(4):63–70. [5] Song Z, Hofmann H, Li J, Han X, Ouyang M. Optimization for a hybrid energy storage system in electric vehicles using dynamic programing approach. Appl Energy 2015;139:151–62. [6] Hemi H, Ghouili J, Cheriti A. Combination of markov chain and optimal control solved by pontryagin’s minimum principle for a fuel cell/supercapacitor vehicle. Energy Convers Manage 2015;91:387–93. [7] Zheng C, Xu G, Xu K, Pan Z, Liang Q. An energy management approach of hybrid vehicles using traffic preview information for energy saving. Energy Convers Manage 2015;105:462–70. [8] Torreglosa JP, García P, Fernández LM, Jurado F. Hierarchical energy management system for stand-alone hybrid system based on generation costs and cascade control. Energy Convers Manage 2014;77:514–26.

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