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Design of an adaptive EMS for fuel cell vehicles
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Design of an adaptive EMS for fuel cell vehicles K. Ettihir, M. Higuita Cano, L. Boulon*, K. Agbossou Hydrogen Research Institute, Universite du Quebec Trois-Rivieres, P.O. Box 500, Trois-Rivieres, Quebec, G9A 5H7, Canada
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abstract
Article history:
This paper addresses the energy management strategy (EMS) for a fuel cell hybrid electric
Received 21 February 2016
vehicle (FC-HEV). In this work, model parameters are identified online by using the square
Received in revised form
root unscented Kalman filter (SR-UKF) method to seek a variation in the fuel cell perfor-
15 July 2016
mances. Then, an optimization algorithm is used on the updated model to find the best
Accepted 26 July 2016
efficiency and power operating points. This process is used into two strategies: (i) A hys-
Available online xxx
teresis energy management strategy (EMS) and (ii) an optimal EMS based on Pontryagin's minimum principle, for a FC-HEV. The effectiveness of the proposed EMSs is demonstrated
Keywords: Fuel cell
by conducting studies on a FC-HEV model. © 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Adaptive control Pontryagin's minimum principle Kalman filter Vehicle
Introduction An interesting solution to produce near zero local emission electricity in an embedded system (as hybrid vehicle) is the fuel cell system (FCS). The most practical FCS for fuel cell hybrid electric vehicles (FC-HEV) is the proton exchange membrane fuel cell (PEM-FC) thanks to its low operating temperature and pressure, tolerance to carbon dioxide and solid membrane [1]. Furthermore, hydrogen with high purity can be produced with renewable energies, such as electrolysis and biomass processes (e.g., photosynthetic or fermentative organisms) to produce near zero global emission electricity [2,3]. A good durability is ensured for the PEM-FC when slow load dynamics are applied in practice [4]. Consequently, an energetic buffer such as battery, supercapacitor, flywheel should be used with the PEM-FC to satisfy the fast dynamic
load for the traction power on a vehicle DC bus [5]. Additionally, hybridization of sources makes it possible to approach the performance of a conventional vehicle in terms of autonomy [6]. As the energy is distributed between two sources, energy management strategy (EMS) is required. In the literature, two classes define the EMS of the FCHEV: the rule-based and the optimization-based controls [7]. The rule-based controls are based on efficiency map such as Feroldi et al. [8] and Ettihir et al. [9]. The second approach is based on optimization of a cost function, which frequently defines the criterion regarding the fuel consumption, system efficiency, or system power [10]. For example, Bernard et al. [11] design an EMS based on Pontryagin's minimum (PMP) to reduce the hydrogen consumption and perform experimental validation. Fares et al. [12] develops an optimal power splitting strategy based on a weighted dynamic programming technique. The optimal management shows a
* Corresponding author. E-mail addresses: [email protected] (K. Ettihir), [email protected] (M. Higuita Cano), [email protected] (L. Boulon), [email protected] (K. Agbossou). http://dx.doi.org/10.1016/j.ijhydene.2016.07.211 0360-3199/© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Ettihir K, et al., Design of an adaptive EMS for fuel cell vehicles, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.07.211
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List of symbols Acronyms APMP Adaptive Pontryagin's Minimum Principle EMS Energy Management Strategy ESP Extremum Seeking Process FCHEV Fuel Cell Hybrid Electric Vehicle FCS Fuel Cell System PEMFC Proton Exchange Membrane Fuel Cell HRI Hydrogen Research Institute IM The Induction Motor LSV Low Speed Vehicle MEPT Maximal Efficiency Point Tracking ME Maximal Efficiency MPPT Maximal Power Point Tracking MP Maximal Power PMP Pontryagin's Minimum Principle SOC State of Charge of the battery SRUKF Square Root Unscented Kalman Filter Greek symbols a The fitting parameter of the fuel cell Squadrito model, e The empirical parameter of the lead acid battery arc temperature when charging, e The empirical parameter of the lead acid battery ard temperature when discharging, e The empirical parameter of the activation b1:::4 overpotential, e g The scaling parameter l The forgetting factor The process noise, e nk x The inverse of the limiting current iL, A1 s The fitting parameter of the fuel cell Squadrito model, e The direct magnetic flux of the induction motor fdr rotor, Wb fqr The quadratic magnetic flux of the induction motor rotor, Wb u The shaft speed of the induction motor rotor, rad/s Roman symbols b The Tafel slope, V The charge and discharge current rate of the lead C10 acid battery, Ah The amount of useful charge available of the lead Cn acid battery, Ah The parameter corresponds to a nonlinear dk observation on wk, e The error of the system identification, e ek The Nernst potential of the fuel cell voltage, V Enernst F The Faraday constant, C mol1 f1,2d The empirical parameter of the hydrogen molar flow The hydrogen molar flow, mol/s Fh2 G(.) The nonlinear mapping function parametrized by the vector wk, e
HHV i0 ids ifc ilim iqs J k Kk Kboc Kbod Ls M Ncell p P1:::4 c P1:::4 d Pwk R r Re Relectronic Rprotonic SOC0 Swk Tem Tfc Tr Vo Vact Vboc Vbod Vc Vcell Vconc Vd Vohmic Wi wk
The high heating value, U The exchange current, A The direct current of the induction motor rotor, A The fuel cell current, A The limiting current density of the fuel cell, A The quadratic current of the induction motor rotor, A The inertia of the induction machine, kg m2 The time step, e The Kalman gain, e The empirical parameter of the Vboc variation with the state of charge (electrolyte concentration), e The empirical parameter of the Vbod variation with the state of charge (electrolyte concentration), e The stator inductance of the induction motor rotor, H The mutual inductance of the induction motor rotor, H The cell number of the fuel cell, e The pole number of the induction motor, e The empirical parameter of the internal resistance variation of the Vc , e The empirical parameter of the internal resistance variation of the Vd , e The covariance matrix, e The gas constant, J mol1 K1 The ohmic resistance of the fuel cell, U The measurement noise covariance, e The resistance to electron flow through electrode, U The resistance to proton flow in the membrane, U The initial state of charge of the battery, % The time step, e The electromagnetic torque of the induction motor, Nm The fuel cell temperature, K The resistive torque, Nm The open circuit voltage of the fuel cell, V The activation overvoltage the fuel cell voltage, V The discharge open circuit voltage parameter of the lead acid battery, V The charge open circuit voltage of the lead acid battery, V The charging voltage of the lead acid battery, V The cell potential of the fuel cell, V The concentration overvoltage the fuel cell voltage, V The discharging voltage of the lead acid battery, V The ohmic overvoltage the fuel cell voltage, V The variable weighting parameters, e The parameters correspond to a stationary process with identity state transition matrix, e
Superscripts b: The sign denote the estimation of a variable
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reduction of the hydrogen consumption in comparison with state machine control algorithms. Most of the time, these EMSs depend on static models which are validated on numerous operating [13]. However, the PEM-FC is a multiphysics system [14], and its performances depend on operating condition (e.g., temperature, gas relative humidity, gas stoichiometry, pressure and aging) [15e17]. As a consequence an accurate modeling is a difficult and time consuming task. Moreover, aging phenomena modify the FCS behavior and they are not well known yet. Therefore, it is necessary to track the performance drifts of the PEM-FC with seeking methods [18,19]. There are two ways to identify the performance of a FCS, in real time. The first is the use of extremum seeking strategies, such as the maximum power point tracking (MPPT) [20e22]. The second method is to use an online parametric identification of a model coupled to an optimization algorithm [23,24]. This paper focus on this second one. Basically, maximum power is not the only interesting operating point on a FCS. For instance, the energy management system presented here deals with two simultaneously identified points: the maximum power and the maximum efficiency. In this case, MPPT technics are not well adapted. So, in our study, the two-step method is used. An identification algorithm is applied to a semi-empirical model of a PEM-FC. Then the identified model is used to optimize the performances (power and efficiency) of the PEM-FC. A semi-empirical model is used because it offers a trade-off between the physical meaning and the calculation cost [25]. Various studies propose contributions on the topic of online identification coupled with optimization of FCSs in order to find the best performance. Methekar et al. [26] has developed an adaptive control of the FCS with a Wiener model and proposed a numerical validation. Dazi et al. [27] simulated a predictive control to determine the maximum power operation of the FCS. Ramos et al. designated a MPPT control thanks to hardware in the loop [28]. Gene et al. [29] conducted an experiment to validate realtime optimization of a solid oxide FCS. Kelouwani et al. [30] presented an experiment on the pursuit of maximum efficiency of the PEM-FC. The study of Kelouwani et al. is based on a polynomial model of the efficiency of the PEM-FC and seeks the best efficiency by tuning the control variables (current, stoichiometry, temperature). In this work, the maximum efficiency and the maximum power are both tracked using online identification and sequential optimization. Moreover, a new step is done since these results are used at the vehicular level to design an adaptive power split between the battery and the PEM-FC. This paper proposes a two-step extremum seeking process (ESP) for tracking specific operation points for maximum efficiency (ME) and maximum power (MP) see Fig. 1. The ESP is based on the online identification of a semi-empirical model followed by an optimization process performed on this up-to-date model (in order to find the MP and ME operating points). The output of the ESP is the value of the ifc current corresponding to the MP and to the ME points of the PEM-FC. First the ESP is used in a simple EMS based on a hysteretic behavior [25] to avoid the chattering effect. Then the ESP is used with an optimal EMS based on the Pontryagin's minimum principle (PMP). The simulation results
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are provided with a specific emphasis on the study of the hydrogen consumption by comparing the two EMS in a SOC sustaining mode. The EMSs are applied on the model of the FC-HEV Nemo (low-speed vehicle) developed at the Hydrogen Research Institute [9]. The architecture of the hybrid system used in this paper is built around a 335 Ah battery pack, and a 2.5 kW Axane PEM-FC is used as a range extender. The powertrain is based on a 5 kW induction machine controlled by an inverter connected to the DC bus. The rest of the paper is organized as follows. Section: Fuel Cell Hybrid Electric Vehicle Model presents the FC-HEV model developed to apply the EMSs. The ESP (online identification and ME/MP seeking) (Fig. 1) are described in Section Extremum seeking process. The EMSs designed are presented in Sections EMS: hysteresis power splitting and EMS: optimal power splitting. The comparative study between the two EMSs designed is performed in Section Energy management comparison. The conclusion and perspectives are discussed in Section Conclusion.
Fuel cell hybrid electric vehicle model There are four parts in this section. (a) PEM-FC model; (b) lead acid battery model; (c) induction motor model and finally (d) the physical environment. Basically, this work deals with two different FC model. The first one, presented in this section, represents in the simulations the PEM-FC of the FC-HEV (PEMFC system block in Fig. 1). For the experimental work, this first model will be replaced by the real system. The second one will be used for the parameters identification (Step 1 in Fig. 1, see part 3.2).
The model of PEM fuel cell The expression of the single cell voltage Vcell is (1): Vcell ¼ Enernst þ Vact þ Vohmic þ Vconc
(1)
The cell potential Vcell (V) (1) involves a Nernst potential Enernst (V). Vact is an overvoltage caused by activation energy barrier at the beginning of electrochemical reaction, and a semi empirical expression of the activation overvoltage is given by (2) and b14 are empirical parametric values [31]: h i (2) Vact ¼ b1 þ b2 Tfc þ b3 Tfc ln cO2 þ b4 Tfc ln ifc
The ohmic overvoltage Vohmic depends on the current ifc (A), the electronic resistance (resistance to electron flow through electrode) and the protonic resistance (resistance to proton flow in the membrane) respectively Relectronic and Rproton is given by (3): Vohmic ¼ ifc Rproton þ Relectronic
(3)
The concentration overvoltage Vconc that arises when the PEM-FC is in high current density is defined (4): RTfc ifc ln 1 (4) Vconc ¼ 2F ilim
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Fig. 1 e Global view of the 3 step EMS.
The lead acid battery pack model
and a stator flux oriented control (8, 9) and controlled with a voltage source inverter [34].
The model of the lead acid battery is given by the model presented in Ref. [32]. Semi empirical equations of the charge and discharge voltages, Vc and Vd are given (5, 6): 3 2 ibat 4 P1c P3c þ þ P4c 5 Vc ¼ ½Vboc Kboc SOC þ C10 ð1 SOCÞ1:2 1 þ iP2c
3 M Tem ¼ p Fdr iqs Fqr ids 2 Ls
bat
ð1 arc DTÞ ibat Vd ¼ ½Vbod Kbod ð1 SOCÞ C10 2 3 P P 1d 3d þ þ P4d 5ð1 ard DTÞ 4 ð1 SOCÞ1:2 1 þ iP2d bat
(5)
J
du ¼ Tem Tr dt
(8)
(9)
Where Tem (Nm) is the electromagnetic torque and depends on IM parameters, ids (A), iqs (A), fdr (Wb), fqr (Wb) respectively direct and quadratic current and magnetic flux of the rotor and the stator.
(6)
Where C10 (Ah) and DT (K) represent the rated capacity and the temperature deviation. Vboc, Vbod, Kboc, Kbod, P1dc, P2dc, P1c, P2c, P3c, P4c, P1dc, P2d, P3d, P4d, arc, ard are empirical parameters that take into account the water level, resistive losses and temperature. Expression of SOC is [33]: Z Ibat dt (7) SOC ¼ SOC0 þ Cn Where Cn (Ah), SOC0 (%) is the amount of useful charge available and the initial SOC respectively.
The induction machine modeling The induction Motor (IM) is controlled with the field oriented control method. The IM is modeled with the Park transform
Extremum seeking process In this section the ESP is described and is a key step of the adaptive EMSs. The performance criteria needed for the global EMS are the ME and the MP. The calculus of these criteria is performed with the PEM-FC voltage Vfc, the PEM-FC current ifc and the PEM-FC hydrogen molar flow Fh2. The PEM-FC current is the control variable but an estimation of the voltage and of the molar flow is needed to deduce the MP and the ME. Then the first step is the online identification of the PEM-FC voltage and the hydrogen molar flow using the square root unscented Kalman filter (SR-UKF) algorithm. The SR-UKF algorithm is used to identify the PEM-FC models (voltage and hydrogen molar flow) and it is based on the successive update of the model parameters. When the online estimation is performed the estimated model are used to calculate the performance
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criteria (MP and ME) by using sequential optimization algorithm. The aim is to determine the optimal current ifc which corresponds to the maximum of the efficiency and the power of the PEM-FC.
b b k ¼ w w k þ Kk dk d k
(22)
U ¼ Kk Sdk
(23)
The SR-UKF algorithm
n o Swk ¼ cholupdate S wk ; U; 1
(24)
The SR-UKF is used for PEM-FC parameters estimation [35,36]. The state space representation of the system identification is defined as (10, 11): wkþ1 ¼ wk þ nk
(10)
dk ¼ Gðxk ; wk Þ þ ek
(11)
Where wk, nk and k2f1; …; ∞g are the system parameter, the process noise vectors and the step, respectively. The nonlinear system is represented by G(xk,wk), dk define a nonlinear observation on wk and ek the error of the system identification. The recursive equations for implementing the SR-UKF are defined in (12)e(24). Van der Merwe et al. [37] provide the implementation of this algorithm: Initialization: io n h b 0 Þðw w b 0 ÞT b 0 ¼ E½w; Sw0 ¼ chol E ðw w w
(12)
b 0 is the initial estimation of the vector of parameters Where w and is calculated using covariance. Sw0 is defined as matrix square root of the matrix covariance and is calculated with Cholesky factorization. The iterative process begins with the time update and sigma point calculation (13)e(17): b b w k ¼ w k1
(13)
1=2 Swk1 Sw k ¼ l
(14)
Swk, l are the Cholesky factor and the forgetting factor. i h b b b Wkjk1 ¼ w k w k þ gSwk w k gSwk
(15)
Dkjk1 ¼ G xk ; Wkjk1
(16)
bk ¼ d
2L X
ðmÞ
Wi Di;kjk1
(17)
i¼0
Where Wi and g are variable weighting parameters, for more precision see Ref. [35,36]. Then the measurement updates Equations (18e24):
qffiffiffiffiffiffiffiffiffiffi h ipffiffiffiffiffi ðcÞ bk Re W1 D1:2L;k d Sdk ¼ qr
(18)
o n bk ; WðcÞ Sdk ¼ cholupdate Sdk ; D0;k d 0
(19)
Pwk dk ¼
2L X
ðcÞ
Wi
h ih iT bk b Wi;kjk1 w Di;kjk1 d k
(20)
i¼0
Pwk dk Kk ¼ SdTk Sdk
(21)
Where choleupdate is the Cholesky factor of rank 1.
The estimation of the PEM-FC characteristic curves The aim of this part is to obtain the parameters to estimate the power and the efficiency curves for the next step (sequential optimization algorithm). Two equations are necessary to deduce the PEM-FC power and the efficiency. The first one is the hydrogen molar flow and the second one is the PEM-FC voltage. The hydrogen consumption is directly dependant of the FC current [31]. A linear expression is used to link the hydrogen molar flow Fh2 with the PEM-FC current ifc. Equation (25) is used in the SR-UKF algorithm to estimate the linear parameters f1 and f2. Fh2;k ¼ f1k ifck þ f2k
(25)
In a previous study, it was demonstrated that the model Squadrito et al. [38] is well suited for on-line identification [25]. The FCS is a very multiphysics system and all the phenomena (including aging) cannot be taken into account in an EMS design dedicated model. So, in this paper, it is chosen to work with a simple polarization curve model but to update its parameters during the fuel operation in order to remain close of the real behavior. A semi empirical model is chosen to meaningful numerical values of the parameters. The concentration losses have to be taken into account in order to highlight the MP operating point. Squadrito et al. defines a static semi-empirical model of the PEM-FC on the basis of references [39,40] (26): (26) Vfck ¼ Vok bk log ifck rk ifck þ ak isfck ln 1 xifck (25) and (26) give the important parameters necessary to estimate the PEM-FC power and efficiency. These parameters are adapted online to take into account the multi-physics fluctuations of the PEM-FC performances. To deduce the SRUKF algorithm the vectors of parameters is defined as (27): (27) wk ¼ Vok bk rk ak f1k f2k Also Equations (25) and (26) give the information on the variables necessary to build dk the nonlinear observation on wk given by (28): i h dk ¼ Vfck Fh2;k (28) The nonlinear system is represented by G(xk,wk) and in our case the state xk is the PEM-FC current ifc. The SR-UKF is applied on the system and Figs. 2 and 3 show that the semi-empirical model coupled with the SR-UKF algorithm is able to deduce the performance of the PEM-FC. The PEM-FC power and efficiency are determined by using the following equations: b fc ifc bfc ¼ V P
(29)
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b h fc ¼
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bfc Paux P bh P
(30)
2
Where Paux (W) is the auxiliary power (assumed as constant) bh HHV is the estimation of the consumed hydrogen bh ¼ F and P 2 2 power during the electricity production.
The sequential optimization The extremum-seeking control is the step in which the optimum PEM-FC power and efficiency are tracked at the same time. So, two optimization problems are formulated each with an objective function (power and efficiency). The sequential quadratic programming (SQP) algorithm is one of the most popular methods for solving optimization problems (especially the convex problems). The SQP algorithm is a local optimization algorithm (in opposition to the global optimization) that is very useful for solving convex optimization problems. The local optimization is sufficient because the two objective functions are unimodal and smooth and contain one maximum. To obtain the current ifc that yields the optimal power or efficiency, the problem is set (31,32): Maximize: J ifc ¼ Pfc ifc (31) 4 : /ifc;min ifc ifc;max and Maximize: J ifc ¼ hfc ifc 4 : /ifc;min ifc ifc;max
(32)
Where ifc,min and ifc,max are the lower and upper bounds of ifc the PEM-FC currents. The estimated power curve in Fig. 2 provides a maximum power near 50 A and shows that it is near the maximum power of the PEM-FC characteristic. Additionally, Fig. 3 shows that the estimated efficiency curve of the PEM-FC provides a maximum efficiency near 13 A. These results confirm that the ESP algorithm is able to find the optimal set point of the PEM-FC.
Fig. 3 e Efficiency curve of the PEM-FC compared with the estimated efficiency curve.
EMS: hysteresis power splitting The state of charge management The aim is to highlight that Hysteresis EMS helps to maintain the SOC level around the reference SOCref ¼ 80% while meeting the power demand. The hysteresis EMS is based on a hysteresis algorithm (Fig. 4). In this strategy thresholds of SOC are determined. The thresholds SOCLh, SOCLi intends to active and disable high power mode to track or not the maximum power (MP). The levels SOCHh, SOCHi switch on and off the low power mode to track the maximum efficiency (ME) point.
Simulation results Simulation gives the power distribution in the FC-HEV. The EMS described before are applied and the results (Fig. 5) shows that the SOC is sustained during the test. The PEM-FC power switch between ME mode to MP mode to sustain the SOC and help the battery pack to give power to the load. During the ME mode the ESP seeks the maximum efficiency and as defined in Fig. 3 the ME is near 900 W. The same for the MP the maximum power is as expected near 2500 W. In this EMS it is clear that ESP perform the ME and MP tracking online when the hysteresis algorithm switch between ME and MP mode.
EMS: optimal power splitting Problem formulation
Fig. 2 e Power curve of the PEM-FC compared with the estimated power curve.
This step allows an online power distribution between the battery pack and the PEM-FC. Moreover, it takes into account the real-time variations of the power and efficiency curves of the FCS. The optimization of hybrid system aims to determine an optimal trajectory of the control variable (ifc) in order to minimize a criterion under constraints. Note that in the formulation of the optimization problem, the power of the
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and then the inequality constraints of the system are defined as: Pfc;min Pfc ðtÞ Pfc;max
(34)
where Pfc,min and Pfc,max are the lower and upper bounds of Pfc the PEM-FC power. SOCmin SOCðtÞ SOCmax
(35)
where SOCmin and SOCmax are the lower and upper bounds of the SOC.
Simulation results On a standard Artemis cycle online APMP EMS is simulated. It is found that under these conditions, the objectives are achieved since the SOC level is sustained around SOCref ¼ 80%. In addition, the power of the PEM-FC is maintained between the maximum efficiency and power (Pmax ¼ 2500 W and Pmin ¼ 900 W) during the cycle as shown in Fig. 6. It seems that PEM-FC power is varying highly. But the PEM-FC dynamic is respected since it is under 50 A s1 which is under the manufacturer dynamic limitation. Therefore the constraints on the PEM-FC power are also satisfied.
Fig. 4 e Chart of the hysteresis EMS.
battery pack is considered as the control variable. However, as shown in the architecture of the system, the actual control variable is the current of the PEM-FC. First consider the optimization criterion defined by the consumption of hydrogen given by (30). Then to obtain the optimal Pbat, the performance criteria can be defined as [19]:
Energy management comparison
Where Q is a function that link the battery power Pbat and the hydrogen flow Fh2 [19]. This system is subject to constraints
A comprehensive comparison is performed between the Hysteresis and the APMP EMSs for the Artemis cycle. The hydrogen energy used is evaluated as a function of the battery energy for the Artemis cycle. The data simulations are collected for different initial SOC between 76% and 83% (eight simulations) for each EMS. As the proposed management is a real time strategy, each test presents a different SOC at the end of the simulation. So, a direct energy consumption comparison is not possible. The results are plotted on Fig. 7: consumed hydrogen energy vs the SOC variation between the end and the begin of the test.
Fig. 5 e Trajectory of the power splitting obtained by the hysteresis EMS.
Fig. 6 e Trajectory of the power splitting obtained by the online A-PMP EMS.
2 6 min JðPbat Þ ¼ min4J ¼
Ztf
3 7 QðPbat ðtÞ; tÞdt5
(33)
t0
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Acknowledgments et This work has been supported by the “Bureau de l'efficacite nerge tique”, the “Ministe re des Ressources de l'innovation e bec”, the Natural Sciences and naturelles et de la Faune du Que bec, Engineering Research Council of Canada, LTE Hydro-Que be cois Nature et Technologie” the “Fonds de Recherche Que (FQRNT).
references
Fig. 7 e Hydrogen energy used versus the battery energy available for the two EMSs.
It is noted that for the different EMSs the curves are substantially linear, see Fig. 7. This representation also reflects the fact that Hysteresis EMS uses more hydrogen energy to sustain the battery pack SOC than the APMP EMS. Indeed, for a battery energy threshold given (200 kJ), we see that the hydrogen energy consumed with the APMP EMS is 4800 kJ, whereas Hysteresis EMS consumes 8.6% more energy for the given battery energy. This mean that APMP EMS gives a better power splitting for the FC-HEV since the hydrogen consumption is reduced in comparison with the Hysteresis EMS.
Conclusion This paper give a study of two EMSs coupled with an adaptive layer to identify online the maximum efficiency and the maximum power. A Hysteresis EMS is design to highlight the capability of seeking the PEM-FC maximums. Then a constrained optimization problem based on Pontriaguin's principle is formulated in order to allocate the power optimally. The online identification layer is added to the PMP EMS in order to take into account the operating point drift in real time. It has been shown that the developed adaptive management A-PMP could meet the power demand, sustain the SOC. Furthermore, the APMP EMS gives better result than Hysteresis EMS (8.6% more energy than APMP EMS) since the hydrogen consumption is reduced with the first one. This work opens perspectives for future work and should now converge to a multi-perspective. Indeed, the work of the paper deal with a single parameter: the current of the fuel cell. A next step will be multiparametric optimization. In the case of semi-empirical models including physical phenomena such as temperature, pressure and humidity, for example, need to be explored.
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Design of an adaptive EMS for fuel cell vehicles K. Ettihir, M. Higuita Cano, L. Boulon*, K. Agbossou Hydrogen Research Institute, Universite du Quebec Trois-Rivieres, P.O. Box 500, Trois-Rivieres, Quebec, G9A 5H7, Canada
article info
abstract
Article history:
This paper addresses the energy management strategy (EMS) for a fuel cell hybrid electric
Received 21 February 2016
vehicle (FC-HEV). In this work, model parameters are identified online by using the square
Received in revised form
root unscented Kalman filter (SR-UKF) method to seek a variation in the fuel cell perfor-
15 July 2016
mances. Then, an optimization algorithm is used on the updated model to find the best
Accepted 26 July 2016
efficiency and power operating points. This process is used into two strategies: (i) A hys-
Available online xxx
teresis energy management strategy (EMS) and (ii) an optimal EMS based on Pontryagin's minimum principle, for a FC-HEV. The effectiveness of the proposed EMSs is demonstrated
Keywords: Fuel cell
by conducting studies on a FC-HEV model. © 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Adaptive control Pontryagin's minimum principle Kalman filter Vehicle
Introduction An interesting solution to produce near zero local emission electricity in an embedded system (as hybrid vehicle) is the fuel cell system (FCS). The most practical FCS for fuel cell hybrid electric vehicles (FC-HEV) is the proton exchange membrane fuel cell (PEM-FC) thanks to its low operating temperature and pressure, tolerance to carbon dioxide and solid membrane [1]. Furthermore, hydrogen with high purity can be produced with renewable energies, such as electrolysis and biomass processes (e.g., photosynthetic or fermentative organisms) to produce near zero global emission electricity [2,3]. A good durability is ensured for the PEM-FC when slow load dynamics are applied in practice [4]. Consequently, an energetic buffer such as battery, supercapacitor, flywheel should be used with the PEM-FC to satisfy the fast dynamic
load for the traction power on a vehicle DC bus [5]. Additionally, hybridization of sources makes it possible to approach the performance of a conventional vehicle in terms of autonomy [6]. As the energy is distributed between two sources, energy management strategy (EMS) is required. In the literature, two classes define the EMS of the FCHEV: the rule-based and the optimization-based controls [7]. The rule-based controls are based on efficiency map such as Feroldi et al. [8] and Ettihir et al. [9]. The second approach is based on optimization of a cost function, which frequently defines the criterion regarding the fuel consumption, system efficiency, or system power [10]. For example, Bernard et al. [11] design an EMS based on Pontryagin's minimum (PMP) to reduce the hydrogen consumption and perform experimental validation. Fares et al. [12] develops an optimal power splitting strategy based on a weighted dynamic programming technique. The optimal management shows a
* Corresponding author. E-mail addresses: [email protected] (K. Ettihir), [email protected] (M. Higuita Cano), [email protected] (L. Boulon), [email protected] (K. Agbossou). http://dx.doi.org/10.1016/j.ijhydene.2016.07.211 0360-3199/© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Ettihir K, et al., Design of an adaptive EMS for fuel cell vehicles, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.07.211
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List of symbols Acronyms APMP Adaptive Pontryagin's Minimum Principle EMS Energy Management Strategy ESP Extremum Seeking Process FCHEV Fuel Cell Hybrid Electric Vehicle FCS Fuel Cell System PEMFC Proton Exchange Membrane Fuel Cell HRI Hydrogen Research Institute IM The Induction Motor LSV Low Speed Vehicle MEPT Maximal Efficiency Point Tracking ME Maximal Efficiency MPPT Maximal Power Point Tracking MP Maximal Power PMP Pontryagin's Minimum Principle SOC State of Charge of the battery SRUKF Square Root Unscented Kalman Filter Greek symbols a The fitting parameter of the fuel cell Squadrito model, e The empirical parameter of the lead acid battery arc temperature when charging, e The empirical parameter of the lead acid battery ard temperature when discharging, e The empirical parameter of the activation b1:::4 overpotential, e g The scaling parameter l The forgetting factor The process noise, e nk x The inverse of the limiting current iL, A1 s The fitting parameter of the fuel cell Squadrito model, e The direct magnetic flux of the induction motor fdr rotor, Wb fqr The quadratic magnetic flux of the induction motor rotor, Wb u The shaft speed of the induction motor rotor, rad/s Roman symbols b The Tafel slope, V The charge and discharge current rate of the lead C10 acid battery, Ah The amount of useful charge available of the lead Cn acid battery, Ah The parameter corresponds to a nonlinear dk observation on wk, e The error of the system identification, e ek The Nernst potential of the fuel cell voltage, V Enernst F The Faraday constant, C mol1 f1,2d The empirical parameter of the hydrogen molar flow The hydrogen molar flow, mol/s Fh2 G(.) The nonlinear mapping function parametrized by the vector wk, e
HHV i0 ids ifc ilim iqs J k Kk Kboc Kbod Ls M Ncell p P1:::4 c P1:::4 d Pwk R r Re Relectronic Rprotonic SOC0 Swk Tem Tfc Tr Vo Vact Vboc Vbod Vc Vcell Vconc Vd Vohmic Wi wk
The high heating value, U The exchange current, A The direct current of the induction motor rotor, A The fuel cell current, A The limiting current density of the fuel cell, A The quadratic current of the induction motor rotor, A The inertia of the induction machine, kg m2 The time step, e The Kalman gain, e The empirical parameter of the Vboc variation with the state of charge (electrolyte concentration), e The empirical parameter of the Vbod variation with the state of charge (electrolyte concentration), e The stator inductance of the induction motor rotor, H The mutual inductance of the induction motor rotor, H The cell number of the fuel cell, e The pole number of the induction motor, e The empirical parameter of the internal resistance variation of the Vc , e The empirical parameter of the internal resistance variation of the Vd , e The covariance matrix, e The gas constant, J mol1 K1 The ohmic resistance of the fuel cell, U The measurement noise covariance, e The resistance to electron flow through electrode, U The resistance to proton flow in the membrane, U The initial state of charge of the battery, % The time step, e The electromagnetic torque of the induction motor, Nm The fuel cell temperature, K The resistive torque, Nm The open circuit voltage of the fuel cell, V The activation overvoltage the fuel cell voltage, V The discharge open circuit voltage parameter of the lead acid battery, V The charge open circuit voltage of the lead acid battery, V The charging voltage of the lead acid battery, V The cell potential of the fuel cell, V The concentration overvoltage the fuel cell voltage, V The discharging voltage of the lead acid battery, V The ohmic overvoltage the fuel cell voltage, V The variable weighting parameters, e The parameters correspond to a stationary process with identity state transition matrix, e
Superscripts b: The sign denote the estimation of a variable
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reduction of the hydrogen consumption in comparison with state machine control algorithms. Most of the time, these EMSs depend on static models which are validated on numerous operating [13]. However, the PEM-FC is a multiphysics system [14], and its performances depend on operating condition (e.g., temperature, gas relative humidity, gas stoichiometry, pressure and aging) [15e17]. As a consequence an accurate modeling is a difficult and time consuming task. Moreover, aging phenomena modify the FCS behavior and they are not well known yet. Therefore, it is necessary to track the performance drifts of the PEM-FC with seeking methods [18,19]. There are two ways to identify the performance of a FCS, in real time. The first is the use of extremum seeking strategies, such as the maximum power point tracking (MPPT) [20e22]. The second method is to use an online parametric identification of a model coupled to an optimization algorithm [23,24]. This paper focus on this second one. Basically, maximum power is not the only interesting operating point on a FCS. For instance, the energy management system presented here deals with two simultaneously identified points: the maximum power and the maximum efficiency. In this case, MPPT technics are not well adapted. So, in our study, the two-step method is used. An identification algorithm is applied to a semi-empirical model of a PEM-FC. Then the identified model is used to optimize the performances (power and efficiency) of the PEM-FC. A semi-empirical model is used because it offers a trade-off between the physical meaning and the calculation cost [25]. Various studies propose contributions on the topic of online identification coupled with optimization of FCSs in order to find the best performance. Methekar et al. [26] has developed an adaptive control of the FCS with a Wiener model and proposed a numerical validation. Dazi et al. [27] simulated a predictive control to determine the maximum power operation of the FCS. Ramos et al. designated a MPPT control thanks to hardware in the loop [28]. Gene et al. [29] conducted an experiment to validate realtime optimization of a solid oxide FCS. Kelouwani et al. [30] presented an experiment on the pursuit of maximum efficiency of the PEM-FC. The study of Kelouwani et al. is based on a polynomial model of the efficiency of the PEM-FC and seeks the best efficiency by tuning the control variables (current, stoichiometry, temperature). In this work, the maximum efficiency and the maximum power are both tracked using online identification and sequential optimization. Moreover, a new step is done since these results are used at the vehicular level to design an adaptive power split between the battery and the PEM-FC. This paper proposes a two-step extremum seeking process (ESP) for tracking specific operation points for maximum efficiency (ME) and maximum power (MP) see Fig. 1. The ESP is based on the online identification of a semi-empirical model followed by an optimization process performed on this up-to-date model (in order to find the MP and ME operating points). The output of the ESP is the value of the ifc current corresponding to the MP and to the ME points of the PEM-FC. First the ESP is used in a simple EMS based on a hysteretic behavior [25] to avoid the chattering effect. Then the ESP is used with an optimal EMS based on the Pontryagin's minimum principle (PMP). The simulation results
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are provided with a specific emphasis on the study of the hydrogen consumption by comparing the two EMS in a SOC sustaining mode. The EMSs are applied on the model of the FC-HEV Nemo (low-speed vehicle) developed at the Hydrogen Research Institute [9]. The architecture of the hybrid system used in this paper is built around a 335 Ah battery pack, and a 2.5 kW Axane PEM-FC is used as a range extender. The powertrain is based on a 5 kW induction machine controlled by an inverter connected to the DC bus. The rest of the paper is organized as follows. Section: Fuel Cell Hybrid Electric Vehicle Model presents the FC-HEV model developed to apply the EMSs. The ESP (online identification and ME/MP seeking) (Fig. 1) are described in Section Extremum seeking process. The EMSs designed are presented in Sections EMS: hysteresis power splitting and EMS: optimal power splitting. The comparative study between the two EMSs designed is performed in Section Energy management comparison. The conclusion and perspectives are discussed in Section Conclusion.
Fuel cell hybrid electric vehicle model There are four parts in this section. (a) PEM-FC model; (b) lead acid battery model; (c) induction motor model and finally (d) the physical environment. Basically, this work deals with two different FC model. The first one, presented in this section, represents in the simulations the PEM-FC of the FC-HEV (PEMFC system block in Fig. 1). For the experimental work, this first model will be replaced by the real system. The second one will be used for the parameters identification (Step 1 in Fig. 1, see part 3.2).
The model of PEM fuel cell The expression of the single cell voltage Vcell is (1): Vcell ¼ Enernst þ Vact þ Vohmic þ Vconc
(1)
The cell potential Vcell (V) (1) involves a Nernst potential Enernst (V). Vact is an overvoltage caused by activation energy barrier at the beginning of electrochemical reaction, and a semi empirical expression of the activation overvoltage is given by (2) and b14 are empirical parametric values [31]: h i (2) Vact ¼ b1 þ b2 Tfc þ b3 Tfc ln cO2 þ b4 Tfc ln ifc
The ohmic overvoltage Vohmic depends on the current ifc (A), the electronic resistance (resistance to electron flow through electrode) and the protonic resistance (resistance to proton flow in the membrane) respectively Relectronic and Rproton is given by (3): Vohmic ¼ ifc Rproton þ Relectronic
(3)
The concentration overvoltage Vconc that arises when the PEM-FC is in high current density is defined (4): RTfc ifc ln 1 (4) Vconc ¼ 2F ilim
Please cite this article in press as: Ettihir K, et al., Design of an adaptive EMS for fuel cell vehicles, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.07.211
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Fig. 1 e Global view of the 3 step EMS.
The lead acid battery pack model
and a stator flux oriented control (8, 9) and controlled with a voltage source inverter [34].
The model of the lead acid battery is given by the model presented in Ref. [32]. Semi empirical equations of the charge and discharge voltages, Vc and Vd are given (5, 6): 3 2 ibat 4 P1c P3c þ þ P4c 5 Vc ¼ ½Vboc Kboc SOC þ C10 ð1 SOCÞ1:2 1 þ iP2c
3 M Tem ¼ p Fdr iqs Fqr ids 2 Ls
bat
ð1 arc DTÞ ibat Vd ¼ ½Vbod Kbod ð1 SOCÞ C10 2 3 P P 1d 3d þ þ P4d 5ð1 ard DTÞ 4 ð1 SOCÞ1:2 1 þ iP2d bat
(5)
J
du ¼ Tem Tr dt
(8)
(9)
Where Tem (Nm) is the electromagnetic torque and depends on IM parameters, ids (A), iqs (A), fdr (Wb), fqr (Wb) respectively direct and quadratic current and magnetic flux of the rotor and the stator.
(6)
Where C10 (Ah) and DT (K) represent the rated capacity and the temperature deviation. Vboc, Vbod, Kboc, Kbod, P1dc, P2dc, P1c, P2c, P3c, P4c, P1dc, P2d, P3d, P4d, arc, ard are empirical parameters that take into account the water level, resistive losses and temperature. Expression of SOC is [33]: Z Ibat dt (7) SOC ¼ SOC0 þ Cn Where Cn (Ah), SOC0 (%) is the amount of useful charge available and the initial SOC respectively.
The induction machine modeling The induction Motor (IM) is controlled with the field oriented control method. The IM is modeled with the Park transform
Extremum seeking process In this section the ESP is described and is a key step of the adaptive EMSs. The performance criteria needed for the global EMS are the ME and the MP. The calculus of these criteria is performed with the PEM-FC voltage Vfc, the PEM-FC current ifc and the PEM-FC hydrogen molar flow Fh2. The PEM-FC current is the control variable but an estimation of the voltage and of the molar flow is needed to deduce the MP and the ME. Then the first step is the online identification of the PEM-FC voltage and the hydrogen molar flow using the square root unscented Kalman filter (SR-UKF) algorithm. The SR-UKF algorithm is used to identify the PEM-FC models (voltage and hydrogen molar flow) and it is based on the successive update of the model parameters. When the online estimation is performed the estimated model are used to calculate the performance
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criteria (MP and ME) by using sequential optimization algorithm. The aim is to determine the optimal current ifc which corresponds to the maximum of the efficiency and the power of the PEM-FC.
b b k ¼ w w k þ Kk dk d k
(22)
U ¼ Kk Sdk
(23)
The SR-UKF algorithm
n o Swk ¼ cholupdate S wk ; U; 1
(24)
The SR-UKF is used for PEM-FC parameters estimation [35,36]. The state space representation of the system identification is defined as (10, 11): wkþ1 ¼ wk þ nk
(10)
dk ¼ Gðxk ; wk Þ þ ek
(11)
Where wk, nk and k2f1; …; ∞g are the system parameter, the process noise vectors and the step, respectively. The nonlinear system is represented by G(xk,wk), dk define a nonlinear observation on wk and ek the error of the system identification. The recursive equations for implementing the SR-UKF are defined in (12)e(24). Van der Merwe et al. [37] provide the implementation of this algorithm: Initialization: io n h b 0 Þðw w b 0 ÞT b 0 ¼ E½w; Sw0 ¼ chol E ðw w w
(12)
b 0 is the initial estimation of the vector of parameters Where w and is calculated using covariance. Sw0 is defined as matrix square root of the matrix covariance and is calculated with Cholesky factorization. The iterative process begins with the time update and sigma point calculation (13)e(17): b b w k ¼ w k1
(13)
1=2 Swk1 Sw k ¼ l
(14)
Swk, l are the Cholesky factor and the forgetting factor. i h b b b Wkjk1 ¼ w k w k þ gSwk w k gSwk
(15)
Dkjk1 ¼ G xk ; Wkjk1
(16)
bk ¼ d
2L X
ðmÞ
Wi Di;kjk1
(17)
i¼0
Where Wi and g are variable weighting parameters, for more precision see Ref. [35,36]. Then the measurement updates Equations (18e24):
qffiffiffiffiffiffiffiffiffiffi h ipffiffiffiffiffi ðcÞ bk Re W1 D1:2L;k d Sdk ¼ qr
(18)
o n bk ; WðcÞ Sdk ¼ cholupdate Sdk ; D0;k d 0
(19)
Pwk dk ¼
2L X
ðcÞ
Wi
h ih iT bk b Wi;kjk1 w Di;kjk1 d k
(20)
i¼0
Pwk dk Kk ¼ SdTk Sdk
(21)
Where choleupdate is the Cholesky factor of rank 1.
The estimation of the PEM-FC characteristic curves The aim of this part is to obtain the parameters to estimate the power and the efficiency curves for the next step (sequential optimization algorithm). Two equations are necessary to deduce the PEM-FC power and the efficiency. The first one is the hydrogen molar flow and the second one is the PEM-FC voltage. The hydrogen consumption is directly dependant of the FC current [31]. A linear expression is used to link the hydrogen molar flow Fh2 with the PEM-FC current ifc. Equation (25) is used in the SR-UKF algorithm to estimate the linear parameters f1 and f2. Fh2;k ¼ f1k ifck þ f2k
(25)
In a previous study, it was demonstrated that the model Squadrito et al. [38] is well suited for on-line identification [25]. The FCS is a very multiphysics system and all the phenomena (including aging) cannot be taken into account in an EMS design dedicated model. So, in this paper, it is chosen to work with a simple polarization curve model but to update its parameters during the fuel operation in order to remain close of the real behavior. A semi empirical model is chosen to meaningful numerical values of the parameters. The concentration losses have to be taken into account in order to highlight the MP operating point. Squadrito et al. defines a static semi-empirical model of the PEM-FC on the basis of references [39,40] (26): (26) Vfck ¼ Vok bk log ifck rk ifck þ ak isfck ln 1 xifck (25) and (26) give the important parameters necessary to estimate the PEM-FC power and efficiency. These parameters are adapted online to take into account the multi-physics fluctuations of the PEM-FC performances. To deduce the SRUKF algorithm the vectors of parameters is defined as (27): (27) wk ¼ Vok bk rk ak f1k f2k Also Equations (25) and (26) give the information on the variables necessary to build dk the nonlinear observation on wk given by (28): i h dk ¼ Vfck Fh2;k (28) The nonlinear system is represented by G(xk,wk) and in our case the state xk is the PEM-FC current ifc. The SR-UKF is applied on the system and Figs. 2 and 3 show that the semi-empirical model coupled with the SR-UKF algorithm is able to deduce the performance of the PEM-FC. The PEM-FC power and efficiency are determined by using the following equations: b fc ifc bfc ¼ V P
(29)
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b h fc ¼
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 6 ) 1 e9
bfc Paux P bh P
(30)
2
Where Paux (W) is the auxiliary power (assumed as constant) bh HHV is the estimation of the consumed hydrogen bh ¼ F and P 2 2 power during the electricity production.
The sequential optimization The extremum-seeking control is the step in which the optimum PEM-FC power and efficiency are tracked at the same time. So, two optimization problems are formulated each with an objective function (power and efficiency). The sequential quadratic programming (SQP) algorithm is one of the most popular methods for solving optimization problems (especially the convex problems). The SQP algorithm is a local optimization algorithm (in opposition to the global optimization) that is very useful for solving convex optimization problems. The local optimization is sufficient because the two objective functions are unimodal and smooth and contain one maximum. To obtain the current ifc that yields the optimal power or efficiency, the problem is set (31,32): Maximize: J ifc ¼ Pfc ifc (31) 4 : /ifc;min ifc ifc;max and Maximize: J ifc ¼ hfc ifc 4 : /ifc;min ifc ifc;max
(32)
Where ifc,min and ifc,max are the lower and upper bounds of ifc the PEM-FC currents. The estimated power curve in Fig. 2 provides a maximum power near 50 A and shows that it is near the maximum power of the PEM-FC characteristic. Additionally, Fig. 3 shows that the estimated efficiency curve of the PEM-FC provides a maximum efficiency near 13 A. These results confirm that the ESP algorithm is able to find the optimal set point of the PEM-FC.
Fig. 3 e Efficiency curve of the PEM-FC compared with the estimated efficiency curve.
EMS: hysteresis power splitting The state of charge management The aim is to highlight that Hysteresis EMS helps to maintain the SOC level around the reference SOCref ¼ 80% while meeting the power demand. The hysteresis EMS is based on a hysteresis algorithm (Fig. 4). In this strategy thresholds of SOC are determined. The thresholds SOCLh, SOCLi intends to active and disable high power mode to track or not the maximum power (MP). The levels SOCHh, SOCHi switch on and off the low power mode to track the maximum efficiency (ME) point.
Simulation results Simulation gives the power distribution in the FC-HEV. The EMS described before are applied and the results (Fig. 5) shows that the SOC is sustained during the test. The PEM-FC power switch between ME mode to MP mode to sustain the SOC and help the battery pack to give power to the load. During the ME mode the ESP seeks the maximum efficiency and as defined in Fig. 3 the ME is near 900 W. The same for the MP the maximum power is as expected near 2500 W. In this EMS it is clear that ESP perform the ME and MP tracking online when the hysteresis algorithm switch between ME and MP mode.
EMS: optimal power splitting Problem formulation
Fig. 2 e Power curve of the PEM-FC compared with the estimated power curve.
This step allows an online power distribution between the battery pack and the PEM-FC. Moreover, it takes into account the real-time variations of the power and efficiency curves of the FCS. The optimization of hybrid system aims to determine an optimal trajectory of the control variable (ifc) in order to minimize a criterion under constraints. Note that in the formulation of the optimization problem, the power of the
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 6 ) 1 e9
and then the inequality constraints of the system are defined as: Pfc;min Pfc ðtÞ Pfc;max
(34)
where Pfc,min and Pfc,max are the lower and upper bounds of Pfc the PEM-FC power. SOCmin SOCðtÞ SOCmax
(35)
where SOCmin and SOCmax are the lower and upper bounds of the SOC.
Simulation results On a standard Artemis cycle online APMP EMS is simulated. It is found that under these conditions, the objectives are achieved since the SOC level is sustained around SOCref ¼ 80%. In addition, the power of the PEM-FC is maintained between the maximum efficiency and power (Pmax ¼ 2500 W and Pmin ¼ 900 W) during the cycle as shown in Fig. 6. It seems that PEM-FC power is varying highly. But the PEM-FC dynamic is respected since it is under 50 A s1 which is under the manufacturer dynamic limitation. Therefore the constraints on the PEM-FC power are also satisfied.
Fig. 4 e Chart of the hysteresis EMS.
battery pack is considered as the control variable. However, as shown in the architecture of the system, the actual control variable is the current of the PEM-FC. First consider the optimization criterion defined by the consumption of hydrogen given by (30). Then to obtain the optimal Pbat, the performance criteria can be defined as [19]:
Energy management comparison
Where Q is a function that link the battery power Pbat and the hydrogen flow Fh2 [19]. This system is subject to constraints
A comprehensive comparison is performed between the Hysteresis and the APMP EMSs for the Artemis cycle. The hydrogen energy used is evaluated as a function of the battery energy for the Artemis cycle. The data simulations are collected for different initial SOC between 76% and 83% (eight simulations) for each EMS. As the proposed management is a real time strategy, each test presents a different SOC at the end of the simulation. So, a direct energy consumption comparison is not possible. The results are plotted on Fig. 7: consumed hydrogen energy vs the SOC variation between the end and the begin of the test.
Fig. 5 e Trajectory of the power splitting obtained by the hysteresis EMS.
Fig. 6 e Trajectory of the power splitting obtained by the online A-PMP EMS.
2 6 min JðPbat Þ ¼ min4J ¼
Ztf
3 7 QðPbat ðtÞ; tÞdt5
(33)
t0
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 6 ) 1 e9
Acknowledgments et This work has been supported by the “Bureau de l'efficacite nerge tique”, the “Ministe re des Ressources de l'innovation e bec”, the Natural Sciences and naturelles et de la Faune du Que bec, Engineering Research Council of Canada, LTE Hydro-Que be cois Nature et Technologie” the “Fonds de Recherche Que (FQRNT).
references
Fig. 7 e Hydrogen energy used versus the battery energy available for the two EMSs.
It is noted that for the different EMSs the curves are substantially linear, see Fig. 7. This representation also reflects the fact that Hysteresis EMS uses more hydrogen energy to sustain the battery pack SOC than the APMP EMS. Indeed, for a battery energy threshold given (200 kJ), we see that the hydrogen energy consumed with the APMP EMS is 4800 kJ, whereas Hysteresis EMS consumes 8.6% more energy for the given battery energy. This mean that APMP EMS gives a better power splitting for the FC-HEV since the hydrogen consumption is reduced in comparison with the Hysteresis EMS.
Conclusion This paper give a study of two EMSs coupled with an adaptive layer to identify online the maximum efficiency and the maximum power. A Hysteresis EMS is design to highlight the capability of seeking the PEM-FC maximums. Then a constrained optimization problem based on Pontriaguin's principle is formulated in order to allocate the power optimally. The online identification layer is added to the PMP EMS in order to take into account the operating point drift in real time. It has been shown that the developed adaptive management A-PMP could meet the power demand, sustain the SOC. Furthermore, the APMP EMS gives better result than Hysteresis EMS (8.6% more energy than APMP EMS) since the hydrogen consumption is reduced with the first one. This work opens perspectives for future work and should now converge to a multi-perspective. Indeed, the work of the paper deal with a single parameter: the current of the fuel cell. A next step will be multiparametric optimization. In the case of semi-empirical models including physical phenomena such as temperature, pressure and humidity, for example, need to be explored.
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Please cite this article in press as: Ettihir K, et al., Design of an adaptive EMS for fuel cell vehicles, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.07.211