Design and analysis of a fuel cell supercapacitor hybrid construction vehicle

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Design and analysis of a fuel cell supercapacitor hybrid construction vehicle Tianyu Li a, Huiying Liu b,c,*, Dingxuan Zhao a,d, Lili Wang a a

School of Mechanical Science and Engineering, Jilin University, 130025 Changchun, China School of Electronics and Information Engineering, Changchun University, 130022 Changchun, China c College of Communication Engineering, Jilin University, 130025 Changchun, China d Yanshan University, 066004 Qinhuangdao, China b

article info

abstract

Article history:

Fuel cell hybrid construction vehicles (FCHCVs) are an attractive long-term option for the

Received 26 October 2015

propulsion of CVs. This paper presents an approach for the design and analysis of an

Received in revised form

FCHCV with supercapacitors as the energy-storage device. The design stage includes

28 April 2016

determination of the topology of the electrical system, energy flow analysis, and a deter-

Accepted 5 May 2016

mination of the energy-storage system. Due to the markedly changing loads, super-

Available online xxx

capacitors with high specific power and high durability seem the best choice. A control strategy based on Pontryagin's minimum principle is proposed considering hydrogen

Keywords:

consumption, the state of charge of the supercapacitors, and fuel cell durability in the cost

Fuel cell

functions. With the selected design and proposed strategy, we propose a power source

Construction vehicle

sizing methodology, and its economic influence is evaluated for both present and future

Supercapacitor

FCHCVs. This study was performed with a system-level model of an FCHCV in MATLAB

Pontryagin's minimum principle

environment. Simulation results demonstrate the superiority of the proposed strategy.

Hydrogen economy

Optimal power source sizes can be chosen by specific criteria of hydrogen consumption

Loader

and powertrain cost. FCHCVs will become very attractive, assuming that the related costs are reduced in the future. © 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Construction vehicles (CVs) are important construction equipment, and include loaders, bulldozers and scrapers. Compared with passenger cars, CVs have additional operating loads, because they typically move and work at the same time. CVs have disadvantages of low energy efficiency, high fuel consumption, poor emissions, and noise. Energy saving and emission reduction with respect to CVs have always been

hotspots in the construction industry. With the increasing energy shortage and environmental pollution, these problems have become of deeper concern. In recent years, hybrid CVs have been introduced and developed, but they could not be separated from conventional engines and they are not ‘green’ power sources. With the successful application of fuel cell (FC) hybrid vehicles (FCHVs), there is enough interest to look at their application to CVs. The first application of an FC hybrid CV (FCHCV) is an underground loader. In 2000, Wagner and INCO Company carried out tests on an FC-powered electric

* Corresponding author. School of Electronics and Information Engineering, Changchun University, 130022 Changchun, China. Tel.: þ86 137 5632 3616. E-mail address: [email protected] (H. Liu). http://dx.doi.org/10.1016/j.ijhydene.2016.05.040 0360-3199/© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Li T, et al., Design and analysis of a fuel cell supercapacitor hybrid construction vehicle, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.05.040

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underground loader [1e3]. The Fuelcell Propulsion Institute and Vehicle Projects LLC jointly promoted a project for FCpowered mining vehicle. In 2004, Caterpillar participated in the project and introduced an FC underground loader based on the R1300 underground loader, with a proton exchange membrane FC (PEMFC) and a nickel metal hydride battery [4]. The current research mainly focuses on the field of FC underground loaders [5,6]. Because there are no waste gas emissions, FC underground loader reduced the entire mining cost, as compared with the battery electric loaders; thus it has a great advantage [7e9]. FC mining equipment is well suited to applications in the mining industry, which is one of the future directions of industrialization. Due to the complex working environment, the operating load on CVs can change markedly and frequently. To drive the hydraulic system in CVs, the maximum required power could account for 40e60% of the rated power of the engine [10]. A standalone FC system cannot meet the demands of the frequently changing load, especially during cold-start, peak power demand or transient events, for CVs application. In addition, the FC system cannot store the regenerative energy. Therefore, to employ FC in CVs, there must be at least an auxiliary power source to improve vehicle performance. Hybridization with high specific energy storage devices such as battery and supercapacitor (SC) has important advantages in FC system [11,12]. Hybridization can help operate FC system in better operating conditions, leading to an increase of FC system performance. The energy-storage system (ESS) is usually a battery module, a SC module, or a combination of both. A lot of work has been conducted to investigate the comparison, optimal sizing and control strategies for FC-batteries, FC-SC, and FC-batteries-SCs hybrid vehicles [11e13]. These studies have referenced significance for the design and analysis of FCHCVs. CVs are usually equipped with a fluid torque converter, and the powertrain efficiency is poor. By hybridization, FCHCVs can improve powertrain efficiency and recover the braking energy, the energy saving effect will be much attractive. In addition, FCHCVs can also address the problems of vibration and noise from diesel engines. Though a lot of efforts have been made in order to introduce FCHVs to commercial applications, however, the main limitation is the cost and durability of the FC stack (FCS) system, which is generally regarded as the main challenge to the commercialization of various FCHVs [14e17]. Technologies and policies related to the cost problem could to be further improved. With regard to the durability of the FCS, the United Technologies Corporation and other companies have continuously introduced high durability FCS products [18]. For automotive applications, the FCS usually works under complex operating conditions, including start/stop and frequently changing load condition. This is the main reason why the durability of automotive FCS is shorter than that of the stationary ones. For FCHCVs, the performance of the FCS can be improved by properly distributing the power demand between the FCS and ESS. The power distribution is linked to energy management strategy (EMS) of the hybrid system. Currently, the EMS of FCHVs can be divided into two major groups: one is based on the heuristic concept, the other is based on the optimal control theory. The former mainly indicates strategies based on control rules, such as rule-based algorithms and

fuzzy logic algorithms [19,20]. These strategies are relatively simple and they could not guarantee the optimal hydrogen economy. The optimal control theory has been introduced to EMS, such as strategies based on dynamic programming (DP) and Pontryagin's minimum principle (PMP) [15,21,22]. Although DP approach can guarantee global optimality, the driving cycle must be known in advance, so it is difficult to be used for online control. PMP-based strategies can optimize the power distribution online, and they can take into consideration the FC durability and hydrogen economy at the same time. Another important challenge to FCHCVs is to choose the optimal powertrain topology and power source size, in combination with an optimal EMS. Thus, an FCHCV with high hydrogen economy, reliability, performance, and low cost can be designed. To this end, the design and analysis of an FC-based hybrid system oriented to CVs applications are studied in this paper. We hope to address the problems of cost and durability of the FCS through optimal control strategies and optimal power source sizes, with attractive performance. FCHCVs research is particularly significant, and it has good applications in construction machinery. This paper is organized as follows: In Section System structure, the topology of the electrical system for an FCHCV is discussed, including energy flows analysis of the hybrid system, and a determination of ESS. The system model of the FCHCV is established in Section System model. In Section EMS based on PMP, a PMP-based control strategy is proposed, considering hydrogen consumption, state of charge (SoC) of SC, and FC durability in cost functions. In Section Results and discussion, comparison simulations of the proposed strategy, basic PMP strategy and DP strategy are performed. Based on the selected design and the proposed strategy, a power source sizing methodology is proposed, and economic influence for power source sizing is evaluated for both present and future FCHCV. Finally, the conclusions are summarized in Section Conclusion.

System structure The electrical structure for an FCHCV essentially involves an FCS with auxiliary systems, an ESS, and driving components which are generally electrical motors. The FCS is an electrical power source, because its DC output voltage drops with the increase of the working current according to its polarization characteristic, it needs to incorporate a power converter to regulate the voltage change. The ESS can store energy produced by the FCS and deliver the energy to loads. In addition, the ESS can store energy recovered from braking though electric motor/generator. Therefore, the power converter of the ESS must be a bidirectional converter, which allows energy flows in both directions. In this section, we address the design of the electrical structure for an FCHCV, focusing on the determination of the electrical topology and the selection of the ESS, and the energy flows in FCHCV are analyzed. This paper takes a typical 5-ton wheel loader as a prototype to study the FCHCV. Loader is a typical CV, the research of the FC hybrid loader can also apply to other CVs.

Please cite this article in press as: Li T, et al., Design and analysis of a fuel cell supercapacitor hybrid construction vehicle, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.05.040

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Topology of the electrical system The determinations of adequate topologies for hybrid electric vehicles have been discussed in Refs. [23,24], where different topologies and energy flows in hybrid system are analyzed, and the advantages and disadvantages of different cases are discussed. In this paper, the topology of the FCHCV depends on the following aspects: (1) Characteristics of the loads; (2) Possibility of energy recovered from the loads; (3) Range of voltage in the FCS, ESS, and motors. In this paper, the issues above are considered before determining the topology of the electrical system, and the topology is shown in Fig. 1. In this topology, the FCS is connected to a DC bus through a boost converter, since the DC bus voltage is normally high. ESS is connected to the DC bus through a bidirectional converter which allows the energy flows from regenerative braking. For the driving components, there are two DC brushless motors: one is used for driving the vehicle powertrain system; the other is used for driving the hydraulic system, which includes the working pump, steering pump, and shift pump. The hydraulic system in CVs can achieve bucket operation, steering control, pilot control, etc. The converter that connects the ESS and DC bus is important for implementing the EMS, which is used to regulate the energy flows between the ESS and DC bus. The converter that connects the FCS and DC bus is used to regulate the energy flows from the FCS; in addition, it can cope with the polarization characteristic of the FCS. Although there are various FC technologies available for vehicular applications, according to the scientists and vehicle developers, the prime candidate is always the PEMFC [25,26]. PEMFC has a higher power density and lower operating temperature than other types of FC. This paper used PEMFC as the electrical power source for CVs application. This research will contain the analysis of cost, durability and performance of the hybrid system, and the optimal EMS for FCHCV.

Analysis of the energy flows in FCHCV There are many energy flows in the FCHCV, Fig. 2 depicts the energy flows from the hydrogen tank toward the wheels and bucket through convertors, power bus, and electric motors.

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The initial energy from hydrogen tank is degraded. The arrows of different colors in Fig. 2 correspond to the energy transferred between components, the energy loss of each component, and the regenerative energy from braking. Each component has a few energy loss, except the DC power bus which is considered ideal. Wheels and bucket employ energy to overcome various working resistances. The flow from wheels to ESS is the energy flow from regenerative braking to ESS, and it is also diminished due to the energy loss. If the energy loss of each component is taken into consideration, the regenerative energy available will be much lower.

ESS: batteries or/and SCs Characteristics of relevant examples of ESS are shown in Table 1. Batteries have higher specific energy than SCs, and they can provide power for a longer period of time. SCs provide the lowest cost per Farad, and an extremely high cycling capability up to 500,000 cycles. The charge and discharge times of SCs can vary from fractions of a second to several minutes, and SCs can serve as a cost effective alternative to batteries for vehicular applications. Different types of FCHVs require ESS with different performance characteristics. According to existing research on ESSs for FCHVs [11,12,27], the advantages and disadvantages of different types of ESSs are shown in Table 2. Before choosing the type of ESS, the operating load spectra of a 5-ton wheel loader under V-type operation on native soil are shown in Fig. 3 [28]. Fig. 3(a) shows the load torque of the transmission, Fig. 3(b) shows the load pressure of the working pump and steering pump in the hydraulic system. As can be seen, the load changes frequently and markedly. The loads at the different working stages are quite different: the load torque and load pressure under transportation conditions are low, whereas under shoveling and unloading conditions, they become high and volatile. Thus, to meet these operating requirements, FCHCV needs an ESS that can meet markedly changing power demand. In addition, the ESS must be able to be deeply charged and discharged at high current and high rates for hundreds of thousands of cycles without major changes in characteristics.

Fig. 1 e Topology of the electrical system for FCHCV. Please cite this article in press as: Li T, et al., Design and analysis of a fuel cell supercapacitor hybrid construction vehicle, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.05.040

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Fig. 2 e Energy flows in FCHCV.

Table 1 e Characteristics of relevant examples of ESS.

Lead-acid battery Ni-MH battery Lithium battery SC

Wh/kg

W/kg

Cycle lives

30e50 60e80 180e200 up to 5

300 4e500 300e1500 up to 1000

300e500 500e1000 >2000 >500,000

electrical motors. Preq can be satisfied by FCS net power PFC and SCs output power PSC, as follows: Pr eq ðtÞ ¼ Pdr ðtÞ þ PHS ðtÞ þ Paux ðtÞ

(1)

Pr eq ðtÞ ¼ PFC ðtÞ þ PSC ðtÞ

(2)

Fuel cell system To the end, we choose SCs as the ESS, because their advantages are more attractive for CVs application. FC-SCs can fully meet the power demand of FCHCV. This paper did not choose FC-Batteries and FC-Batteries-SCs for their disadvantages. However, batteries and SCs are complementary in the development of FCHVs, the combination of both should be explored in the future research.

System model Model overview To study the FCHCV, it is necessary to rely on an accurate and practical system model. In this paper, a system-level, energybased FCHCV model is introduced for energy management studies. The target FCHCV is a 5-ton wheel loader, and its specifications are listed in Table 3. The hybrid system was modeled in MATLAB environment, which can provide a flexible set of models and data. The driver model is implemented as an automatic controller to meet the operating loads at each time step. The auxiliary loads including heating and cooling, the numerous electronics, can be a negligible proportion of the overall power demand. Thus, taking these auxiliary loads into account for energy analysis is essential. The total required power, Preq, of the FCHCV consists of driving power Pdr for the powertrain system, operating power PHS for the hydraulic system, and electrical power Paux for auxiliary loads. Auxiliary loads vary with time, but a constant power demand, Paux ¼ 10 kW, was used in the simulator to represent the average power demand in this study. Pdr and Pop are converted to electrical power by

In this study, a quasi-static model is established for the FCS, which is widely accepted for system-level energy management problem formulation and fuel consumption estimation [29]. The output power of the FCS depends on temperature, air pressure and humidification of the FCS; these effects can be incorporated through characteristic curves obtained from experimental data. The characteristics of the FCS of different sizes used in the paper are shown in Fig. 4, including net power-current characteristics, relationships between the net power and hydrogen consumption rate, and an efficiency map of the FCS operating at varying power outputs. These curves were obtained by a polynomial fitting method, parts of these data are sourced from available literature and FCS manufacturers [30,31]. From the characteristic curves of the FCS as shown in Fig. 4, it can be found that the power rises with the current of the FCS, it is approximately nonlinear and direct proportional to the current.

Supercapacitor system An accurate dynamic model of the SC system is essential for determining the SoC of SC. Through experimental studies, it has been found that the current-to-voltage behavior of SC is significant in hybrid vehicle systems, and the net electrical dynamic behavior of SC can be predicted through approximation by an equivalent electrical circuit [21,22]. In this section, the SC system model was developed based on a simple RC equivalent circuit model [32]. The SC current can be calculated from the requested power, as follows:

Please cite this article in press as: Li T, et al., Design and analysis of a fuel cell supercapacitor hybrid construction vehicle, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.05.040

Relatively highest cost and need complex control methods. Batteries þ SCs

SCs

SCs have highest specific power, they can supply great quantities of instantaneous power demand with better performance, and SCs can be charged or discharged at high-current. This type has the highest fuel economy, and can extend the battery lifetime due to reduced battery stress.

Batteries cannot be charged or discharged at high-current, which will reduce lifetime of batteries. Batteries have fewer cycle lives than SCs. Lower specific energy. Batteries

Higher specific energy.

Advantages

Table 2 e Advantages and disadvantages of different types of ESSs.

Disadvantages

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ISC ¼

VSC 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V2SC  4RSC $PSC 2RSC

5

(3)

where ISC is the operating current, VSC is the open circuit voltage and RSC is the internal resistance of the SC. Both VSC and RSC depend on the SC SoC. The SoC is the ratio of the amount of charge left in a cell and the total charge cell capacity. Through Coulomb counting method, the SoC at each time can be calculated as: Z SOCðtÞ ¼ SOCðt0 Þ 

t

ISC ðtÞdt

to

Qmax

(4)

where Qmax denotes the maximum battery capacity.

Vehicle model The outlet pressure of hydraulic pumps is used to describe the operating load of the hydraulic system, which can be converted to the driving torque MHS of the hydraulic system, as follows: X

MHS ¼

pi qi 2phPi iHSi

(5)

where pi, qi and hpi are the outlet pressure, displacement, and efficiency of each hydraulic pump, respectively. iHSi is the gear ratio between each hydraulic pump and the motor. The power demand of the hydraulic system can be expressed as: PHS ¼

MHS $nHS 9550

(6)

where nHS represents the speed of motor for driving the hydraulic system. The two motors in the FCHCV convert the electrical power into rotational mechanical power. This conversion involves an efficiency loss. Static models were established for the motors and the efficiency maps of the motors are considered in the calculations. The required powers of the two motors are calculated as follows: PHS hMHS

(7)

nMD ¼

vi0 ig 60 2pRW

(8)

TMD ¼

Fd RW i0 ig hD

(9)

PMD ¼

2pnMD TMD 60,100hMD

PMHS ¼

(10)

where PMHS and hMHS are the required power and the efficiency of the motor driving hydraulic system, respectively. nMD, TMD, PMD and hMHS represent the speed, torque, required power, and efficiency of the motor that drives the drivetrain, v is the velocity of the vehicle, i0 represents the final drive ratio, ig represents the transmission gear ratio, RW is the radius of the

Please cite this article in press as: Li T, et al., Design and analysis of a fuel cell supercapacitor hybrid construction vehicle, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.05.040

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Fig. 3 e Load torque of the transmission (a), load pressure of the working pump and steering pump (b) in a 5-ton wheel loader.

Table 3 e Vehicle Specifications in FCHCV model. Specifications Vehicle mass Rated load Maximum speed Working pump Steering pump Front area Radius of wheel Front gear ratio Back gear ratio Main drive ratio Wheel reducer ratio Drivetrain efficiency Air drag coefficient Rolling resistance coefficient

Value 16,800 kg 5000 kg 37 km/h 140mL/r 63mL/r 10 m2 0.75 m 4.287, 2.263, 1.230, 0.650 4.690, 2.201, 1.197, 0.651 6.35 3.701 0.90 0.37 0.03

wheel, hD is the efficiency of the drivetrain, and Fd is the total driving force of the vehicle. The total driving force of the vehicle is related to various resistances, including rolling resistance Ff, gradient resistance Fw, air resistance Fs, and acceleration resistance Fa. The dynamic balance formulas of FCHCV are as follows.

Fd ¼ Ff þ Fw þ Fa þ Fs

(11)

8 Ff ¼ mgf cos q > > > > > > > < Fw ¼ mg sin q 2

Fs ¼ KA Sðv  vw Þ > > > > > > dv > : Fa ¼ dm dt

(12)

where m is the mass of the vehicle, g is the gravitational acceleration, f represents the rolling resistance coefficient, q is the slope angle of road, KA is air resistance factor, S is the front area of the vehicle, vw is wind speed, d is the conversion factor of rotating mass. dv/dt is the change in vehicle speed over a time step, and t is the time step duration.

EMS based on PMP FCHCV needs EMS to reasonably distribute the power demand and distinct power sources. The EMS must satisfy the constraints of powertrain components, while trying to achieve

Fig. 4 e Characteristics of the FCS of different sizes: characteristics of net power and current (a), characteristics of net power and hydrogen consumption rate (b), and efficiency map of the FCS (c). Please cite this article in press as: Li T, et al., Design and analysis of a fuel cell supercapacitor hybrid construction vehicle, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.05.040

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some performance objectives such as maximizing fuel economy, maintaining SoC scope, and improving the durability of power sources. The EMS of the FCHCV must satisfy the following requirements: First, the FCS must be capable of supporting time-sustained driving conditions, which include markedly changing operating loads and driving loads. Second, with the assistance of ESS, the hybrid system must fulfill a response time with certain acceleration and markedly changing loads. Third, the hydraulic pumps need to be working all the time to satisfy requirements at any moment. To meet these operating requirements, the optimal method is to adopt a constant speed control on the motor for the hydraulic system. Thus, constraints were set as nMHS ¼ 1600 and iHSi ¼ 1 in this study, to satisfy the hydraulic system requirements. PMP is an optimal control theory. PMP-based EMS can instantaneously provide the necessary conditions for optimal control problems to find optimal control laws, they have been used in FCHVs [30,31,33]. In the earlier research, the performance measure of the control problem to be minimized was hydrogen consumption. Some researchers have extended this basic form by adding cost functions or state variables in order to achieve some specific goals, such as FC durability, battery durability, and economic influence [31]. This section proposes a PMP-based EMS for the FCHCV, the objective of the optimal control problem is to find the optimal power split trajectory, which can minimize the hydrogen consumption while taking into account the FCS durability. This problem can be solved by searching for the optimal trajectory of the FCS, which is the control variable. The SoC of SCs is the state variable, and the state equation of SCs is as follows: _ SOCðtÞ ¼ f ðSOCðtÞ; PFC ðtÞ; tÞ

(13)

_ where the state variable SOCðtÞ is a function of SOC(t), PFC(t), and time t. The load dynamics directly influence the current-changing rate of FCS, which has a negative effect on the FCS durability. Researchers have pointed that restricting the load dynamics has a positive effect on prolonging the FCS durability, a limitation on the current-changing rate of the FCS must be considered in the EMS [34e36]. High current density also has a negative effect on the FCS performance. When the FCS current increases, it should draw less power from the FCS and use more power from the SCs pack. In this research, we have found that the changes in the CV's load can be extreme so, in FCHCV, more attention needs to be paid to the FCS durability. The limitation on the power-changing rate of the FCS should be set in order to prolong the FCS durability [15,37]. In addition, the power-changing rate is limited in reality, this must be considered as one of the constraints of the FCS. One of the objectives of the optimal control problem is to minimize hydrogen consumption while considering the FCS durability. Thus, limitations should be set on the current-changing rate, current, and power-changing rate of the FCS to prolong the FCS durability. In this research, a new cost function, L, was introduced to avoid frequent and violent changes of the dynamic load, as below:

LðPFC ðtÞÞ ¼ L1 ðPFC ðtÞÞ þ L2 ðPFC ðtÞÞ þ L3 ðPFC ðtÞÞ 8 L ðP ðtÞÞ ¼  g1 ,ðPFC ðtÞ  PFC ðt  DtÞÞ2 > > < 1 FC g2 ,PFC ðtÞ; if IFC ðtÞ  IFCLarge L2 ðPFC ðtÞÞ ¼ 0; Otherwise > > : L3 ðPFC ðtÞÞ ¼ g3 ,ðIFC ðtÞ  IFC ðt  DtÞÞ2

7

(14)

where g1, g2 and g3 are constant tuning parameters, L1, L2 and L3 are parts of the cost function, t represents a time step, Dt is the duration of one time step, IFC represents the current of the FCS, and IFCLarge is a constant current parameter. The cost function L consists of three parts: L1 can make the optimal trajectory of the FCS net power smooth, L2 can limit the FC working current to a certain range, and L3 can limit the current-changing rate of the FCS. This cost function can allow the FCS to be operated under better conditions. SoC should work within a reasonable range. Current studies usually take boundary constraints of SoC as part of the control problem. For CVs, it can be seen from Fig. 3 that the required power changes markedly during the working cycle. Therefore, the SoC of SCs in FCHCVs will fluctuate within a wider range than normal FCHVs, and the SoC will readily cross the boundary. In this research, a cost function, S, was defined and introduced, considering range constraints and boundary constraints on SoC, as follows: 8 < a,PFC ðtÞ; 0; SðPFC ðtÞÞ ¼ : b,PFC ðtÞ;

SOCðtÞ  SOCL SOCL < SOCðtÞ < SOCH SOCðtÞ  SOCH

(15)

where a and b are constant tuning parameters, and SOCL and SOCH are the upper and lower limits of the optimum range of SoC. Considering hydrogen consumption and the FCS durability, the Hamiltonian function H of PMP-based optimal control problem can be defined as:   , _ _ þ SðPFC ðtÞÞ H SOCðtÞ; PFC ðtÞ; t ¼ mH2 ðPFC ðtÞÞ þ lðtÞSOCðtÞ þ LðPFC ðtÞÞ

(16)

The Hamiltonian is used to solve the optimal control , problem. mH2 ðPFC ðtÞÞ is the hydrogen consumption rate, which has a relationship with the FC net power PFC. l(t) is a co-state variable. PMP provides a set of necessary conditions that must be satisfied by optimal control trajectory, and the conditions are as follows: SOC*ðtÞ ¼

vH ðSOC*ðtÞ; PFC *ðtÞ; l*ðtÞÞ vl

(17)

vH ðSOC*ðtÞ; PFC *ðtÞ; l*ðtÞÞ l*ðtÞ ¼  vSOC

(18)

8   SOCðt0 Þ ¼ SOC tf ¼ SOCref > > < 0  PFC ðtÞ  PFCmax > 0  jPFC ðtÞ  PFC ðDtÞj  PFC Rate > : 0  IFC ðtÞ  IFCmax

(19)

where * denotes the optimal variable values, SOCref is a constant SoC parameter, IFCmax and PFCmax represent the maximum current and power of the FCS, and PFCRate is the maximum power-changing rate of the FCS.

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PMP states that the optimal solution should minimize the Hamiltonian as follow: HðSOC*ðtÞ; PFC *ðtÞ; l*ðtÞÞ  HðSOC*ðtÞ; PFC ðtÞ; l*ðtÞÞ

(20)

The Hamiltonian can be solved at each instant. As be seen from the above formulas, the cost function L can affect the optimal FC net power at each calculation step, and it will make the optimal trajectory smooth. The cost function S can affect and constraint the working range of SoC. The cost function L and S can help to obtain better performance of the optimal control problem.

Results and discussion Simulation results DP is a numerical method for solving multistage decisionmaking problems, which is well accepted as the benchmarking tool that mathematically guarantees the delivery of global optimum solution [21,38]. To evaluate the performance of the proposed strategy, DP optimization was implemented in the simulation. The detailed description of the DP algorithm comes from literature [39], and the performance measure to be minimized was hydrogen consumption. In this section, the FCHCV model was tested on three EMS: DP strategy, basic PMP strategy, and the proposed strategy. The FCHCV is equipped with a SC pack of 250 units and a 100 kW FCS. The parameters of SCs and FC used in the simulations are listed in Table 4. The loads of a 5-ton wheel loader as shown in Fig. 3 were used for the simulation. The power demand of the hydraulic system and total required power for the FCHCV during the simulation are shown in Fig. 5. As shown, the loads at the different working stages are quite different, it had large fluctuations: the maximum total required power can be up to 160 kW and the minimum can be close to 0 kW, and the demand power of the hydraulic system varies markedly over the whole test cycle. However, the loads has significant characteristics of cyclic variation. The maximum SoC bound was set to 100%, the minimum SoC bound was 60%, the upper and lower control boundaries of the SoC cost function were 90% and 70%, and the initial SoC was set to 80%. Then, a comparative analysis of the three EMS was performed. The simulation results are shown in Figs. 6e8. Table 5 lists the simulation results for hydrogen consumption with the three strategies. As shown in Figs. 6e8, the trends of the FCS net power, the FCS net power-changing rate, and the SoC of SCs, under the

Table 4 e Parameters in the FCHCV model. Parameters SC voltages SC capacity SC cycle life SC cost FC type FC cost FC stack lifetime

Value 2.85 V 3400 F 500,000 60 $/cell PEMFC 800 $/kW 2500 h

three different control strategies, are similar in general. Since the proposed PMP is an improvement of the basic PMP, their control effects are basically the same, except the variation range. DP strategy can obtain the global optimal trajectory of the FCS, however, DP doesn't limit the power-changing rate, so the FCS net power has dramatic fluctuations over the entire cycle from Fig. 6. The variation range of the net power is about from 39.14 to 91.16 kW, without full load or no load. In contrast, the trajectories of the FCS net power under basic PMP and proposed PMP are quite smooth. That is because the power split is directly influenced by control strategies, the PMP-based strategies can obtain smooth trajectories of the FCS net power. The variation range of the net power under basic PMP is about from 45.2 to 100 kW. However, the net power under the proposed strategy has the widest variation range, from 10 kW to 99.2 kW. This is because there are SoC constraints in the proposed strategy, in order to ensure SoC within a limited range, the net power has to change in a wide range. For example, the SoC is very high at about from 157 to 165 s in Fig. 8, the FCS net power should be decreased according to the proposed strategy, so it rapidly declines to minimum 10 kW. Loads of the FCS under PMP-based strategies have small fluctuations, theoretically, it has positive effect on improving the durability and performances of the FCS. As shown in Fig. 7(a), the FCS net power-changing rate under DP has dramatic fluctuations, its range is between 10 kW/s and 10 kW/s, since the FCS net power fluctuates violently. Dramatic fluctuations of loads will significantly reduce the durability and performance of the FCS. Under PMPbased strategies, the fluctuations of FCS net power-changing rate are effetely suppressed from Fig. 7(b). The range of power-changing rate under basic PMP is about between 2.8 and 3.2 kW/s, which is much smaller than that of DP. The FCS power-changing rate of basic PMP and the proposed PMP are substantially coincide, but corresponding to some intervals for extreme value of SoC, the power-changing rate under the proposed PMP becomes large. The proposed PMP introduces constraints of the FCS net power and SoC, when the SoC deviates the set range, the FCS net power will change rapidly to ensure SoC's working range. Experiments in literature [36,37] have shown that restrictions on the power-changing rate and current-changing rate can both improve the durability and performance of the FCS. Simulation results in this paper show the similar control effect, in theory, the proposed strategy can improve the durability and performance of the FCS. As can be seen in Fig. 8, SoC under the three EMS changes with the demand load experienced during the working cycle, and it has a cyclical and marked variation. DP strategy has limited the range of SoC to 60e100%. The range of SoC under basic PMP is about from 36.9 to 100%, while the range under the proposed PMP is about from 57.5 to 96.8%, which is much concentrated. With the SoC constraint introduced by the proposed strategy, the FCS provides relatively more power, leading to a smaller variation in SoC. Thus, the working scope of SoC is effectively regulated under the proposed strategy. Table 5 shows the hydrogen consumption under DP strategy, basic PMP strategy, and the proposed strategy is 1988.1 g, 2016.4 g, and 2038.5 g respectively. The

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Fig. 5 e Demand power of hydraulic system (a), and total required power of the FCHCV (b).

Fig. 6 e FCS net power under DP, basic PMP, and proposed PMP.

Fig. 7 e FCS net power-changing rate under DP (a), basic PMP and proposed PMP (b).

Fig. 8 e SoC of SCs under DP, basic PMP, and proposed PMP.

Effective power source sizing Table 5 e Hydrogen consumption under DP, basic PMP, and proposed PMP. DP Hydrogen 1988.1 consumption (g)

Basic strategy Proposed strategy 2016.4

2038.5

consumption of the proposed strategy is just 2.54% higher than the optimal consumption. Thus, a positive economic influence of the proposed strategy was demonstrated. Overall, with the constraint of SoC and FCS durability in the proposed strategy, the SCs and the FCS will work under reasonable conditions, the durability and performance of the FCS can be improved. Thus, the proposed strategy is advisable for the FCHCVs.

For the power source sizing analysis of FCHCV, different power source sizes will be chosen to for testing, which will affect the FCS output power, FCS efficiency, hydrogen consumption and SoC. In this section, the power source sizing is analyzed for minimum hydrogen consumption and powertrain cost. The proposed strategy will calculate the optimal power split between the FCS and SC. A power source map is shown in Fig. 9, the unshaded region represents the range of effective power source sizes, which can meet some necessary CVs performance constraints. The boundary is decided by the constraints including maximum speed of 37 km/h, maximum tractive force of 160,000 Nm, and maximum climb gradient of 30 . The upper boundaries of SCs and FCS are set as 350 units and 120 kW respectively, to avoid a dramatic increase in powertrain cost. The effective sizes in Fig. 9 are tested in the simulation under the same driving conditions.

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consideration if the cost of the FCS decreases to a more reasonable in the future. By limiting specific criteria for hydrogen consumption and powertrain cost, the effective power sizes can be limited to a more optimal region. The region where the optimal regions of the two plots overlap can be defined as the optimal power source sizes. In this section, hydrogen consumption and powertrain cost are both considered, a comprehensive performance is preferred. Finally, the optimal power source size is defined at (100,250), where the hydrogen consumption is 2038.5 g and powertrain cost is $95,000. Fig. 9 e Range of effective power source sizes. From Fig. 10, it can be found that the hydrogen consumption and powertrain cost with different power source sizes change in the plots, which are caused by the variations of power source sizes and the FCS efficiency. As can be seen in Fig. 10(a), an obvious characteristic of the plot is that the hydrogen consumption decreases with the increase of FCS net power. When 250 units SCs are used, the FCHCV consumes 2275.7 g hydrogen with an 80 kW FCS; then, the FCHCV just consumes 1959.2 g hydrogen with a 120 kW FCS, the hydrogen consumption is reduced by nearly 13.9%. This is because high power FCS can contribute more to the power output, which can directly meet the system loads avoiding efficiency loss of the SCs. As a larger SCs size can also contribute more to the power output, hydrogen consumption basically decreases with the increasing size of the SCs. When a 100 kW FCS is used, the hydrogen consumption is 2154.9 g with 150 units SCs, it is 2017 g with 350 units SCs, which is reduced by 6.4%. Thus, the minimum hydrogen consumption is 1918.5 g at (120,350), the maximum hydrogen consumption is 2254.8 g at (80,200). This indicates that the influence of the FCS size on the hydrogen consumption is deeper than the SCs size, which is a direction for finding the optimal power source size. Fig. 10(b) illustrates the powertrain cost for different power source sizes. Because the powertrain cost rises with increasing of SC and FC sizes, obviously, the most expensive powertrain is $117,000 at (120,350) and the least is $76,000 at (80,200). As can be seen, values under the same FCS size show smaller difference. The influence of the FCS cost on total cost is much higher than the SCs. This should be taken into

Economic evaluation for power source sizing In this section, the economic influence on power source sizing is discussed for the FCHCV based on the present and future FCS cost, hydrogen cost, SCs cost, and FCS lifetime. It is assumed that high-volume production of FC for automotive applications will be realized in the future, and the production cost will be much lower. US DOE's cost target of FCS is 40 $/kW for 2020 [14,30]. In this paper, it is assumed that the FCS cost is approximately 800 $/kW at present and decreases to 40 $/kW in the future; the hydrogen production technology will be improved in the future, and the cost of the production and distribution will be reduced from 8.5 $/kg at present to 6 $/kg in the future; the cost of SC cell is 60 $/unit at present and will be reduced by half in the future. The DOE has set 5000 h of operational lifetime for the FCS for automotive applications, well the FC lifetime is normally defined as 2500 h in the current research [14,30]. The cost of the FCS, hydrogen and SC, and FC durability for both present and future cases are listed in Table 6. Cost is an important criterion when studying the power source sizing for an FCHCV. Excluding the cost of the loader itself, we are interested in the specific use-cost of the FCHCV during its entire lifecycle, which consists of FCS cost, SCs cost, cost of auxiliary equipment for FCS operation, and cost of hydrogen consumption. It is assumed that the FCHCV repeatedly works on the driving cycle above, during its entire lifetime, and the proposed strategy is applied. A new cost coefficient Ccost is introduced and defined as follows:

Fig. 10 e Hydrogen consumption (a) and powertrain cost (b) with different power source sizes. Please cite this article in press as: Li T, et al., Design and analysis of a fuel cell supercapacitor hybrid construction vehicle, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.05.040

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Table 6 e Parameters for current and future.

FC cost ($/kW) Hydrogen ($/kg) FC stack lifetime (h) SCs cost ($/unit) SCs cycle life FCHCV lifetime (h)

Current

Future

800 8.5 2500 60 500,000 5000

40 6 5000 30 1,000,000 5000

Z

Z

Tlifetime

Ccost ¼

CFC TFCtime

$Tlifetime þ CSCs þ

Tlifetime

CH2 dt þ 0

Cop dt

(21)

0

where CFC is the FCS cost, CSCs is the SCs cost, Cop is the cost of auxiliary equipment for FCS operation, and CH2 is the cost of consumed hydrogen. TFCtime is FCS lifetime and Tlifetime is the effective lifetime of the FCHCV. The effective lifetime of the FCHCV is about 5000 h, and the lifetime of the SC is far beyond that of CVs. The FCS cost is in direct proportion to the rated power of the FCS, and the SCs cost is positively proportional to the number of SCs cells. The costs of the auxiliary equipment consist of three parts: the cost of the humidification water, the cost of the cooling water, and the electric power consumption of the air compressor, humidifier and various electronic devices. To simplify the economic evaluation, the costs of humidification water and cooling water are in proportion to the hydrogen consumption, and the electric power consumption is in proportion to efficiency and power consumption. These relationships can be expressed as follows: 8 < CFC ¼ k1 $PFCSR CSCs ¼ k2 $nSCcell : Cop ¼ Chum þ Ccold þ Celse ¼ k3 $QH2 þ k4 $QH2 þ k5 $QH2

(22)

where k1-k5 are positive proportion coefficients, PFCSR is the FCS rated power, nSCcell is the SCs cell number, QH2 is the consumed hydrogen, and h is the proportion of the power consumed by auxiliary system in the total power provided by the FCS during operation.

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The cost coefficient analysis with different power source sizes for both current and future needs was studied. The results are shown in Fig. 11. Fig. 11 illustrates the cost of the FCHCV with different power source sizes using the proposed strategy, it is assumed that the FCHCV works on the driving cycle shown in Fig. 5 for the entire lifetime. Fig. 11(a) corresponds to the case at present, and Fig. 11(b) corresponds to the case under the assumption. From Fig. 11(a), the influence of powertrain cost on total cost is obvious, the more the powertrain costs, the higher the total cost. Thus, the FCS cost is the primary factor for the total cost at present. As can be seen from Fig. 11(b), the cost in the future will be much lower than that at present, which is reduced by even more than half. Fig. 11(b) indicates that the FCS cost ceases to be the main factor for the total cost in the future. Compared with Fig. 10(a), the two plots have the same variation tendency. It can be found that the primary influence factor on the total cost in the future shifts to the hydrogen consumption during working. Thus, the FCHCV will become much more attractive in the future.

Conclusions In summary, the design and analysis of an FCHCV oriented to CVs application have been discussed in this research. The main contributions are given as follows: First, the structure of an FCHCV was analyzed and designed. The topology of the electrical system for an FCHCV is addressed, and the energy flows in the FCHCV were analyzed. Due to the markedly changing load of CVs, an FCHCV needs an ESS with high specific power and high durability; SCs seemed to be the best choice. Then, a system model was established in the MATLAB environment. Second, a PMP-based control strategy was proposed for FCHCVs in which new cost functions were introduced, considering hydrogen consumption, the SoC of SCs, and the FCS durability. The proposed strategy takes into account the characteristics of CVs, to obtain better performance of the optimal control problem. The superiority of the proposed strategy was demonstrated by comparing it with the basic PMP strategy and DP strategy in the simulation.

Fig. 11 e Cost analysis at the current (a) and in the future (b). Please cite this article in press as: Li T, et al., Design and analysis of a fuel cell supercapacitor hybrid construction vehicle, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.05.040

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Third, this paper proposed a PMP-based power source sizing methodology for the development of FCHCVs. The effective power source sizes were evaluated in the PMP-based simulation model. Simulation results for hydrogen consumption, powertrain cost were compared, and optimal power source sizes can be chosen by specific criteria. In addition, with the proposed strategy, the economic influence on power source sizing is evaluated based on the current and future FCS cost, hydrogen cost, SCs cost and FCS lifetime. FCHCVs will become much more attractive, assuming that the related technologies are improved and production costs are reduced in the future. This research provides guidance for FCHCV design, modeling, EMS, and optimal power source sizing problems.

Acknowledgment This work was supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (SRFDP) (Grant No. 20120061110023).

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