A Specification Independent Control Strategy for Fuel Cell Hybrid Vehicles

IFAC-PapersOnLine 49-11 (2016) 369–376
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2405-8963 © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Peer review under responsibility of International Federation of Automatic Control.
10.1016/j.ifacol.2016.08.055
© 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
A Specification Independent Control Strategy for Simultaneous Optimization of
Fuel Cell Hybrid Vehicles Design and Energy Management
Marco Sorrentino, Cesare Pianese, Mario Cilento

Department of Industrial Engineering, University of Salerno, Fisciano (Salerno) 84084, Italy
(Tel: +39 089 964100; e-mail: msorrentino@unisa.it).
Abstract: The present work proposes an in-deep analysis of a heuristic control strategy, developed in such a
way as to enhance model-based design of fuel cell hybrid electric vehicles (FCHEVs). Particularly, suited
normalization and denormalization techniques are proposed, so as to adapt optimized control rules to a
number of FCHEV powertrains, ranging from low to high degree of hybridization. A scenario analysis was
conducted to verify the effectiveness of proposed powertrain-adaptable control strategies, thus revealing their
high potential, both to reduce the off-line development phase, as well as to enable simultaneous preliminary
optimization of FCHEV powertrain sizing and real-time energy management.
Keywords: Fuel Cells, Fuel Cell Vehicles, Hybrid Vehicles, Energy Management, Specification
Independency, Model-based Design, Optimization.

1. INTRODUCTION
Light duties vehicles impact for about 16% (Environmental
Protection Agency, 2014) on global CO2 emissions. The
associated growing number of environmental problems has
made the sustainable transportation paradigm become an
increasingly popular solution, thanks to the favorable
characteristics of high efficiency and low (or zero) emissions
(Onat et al., 2015; Katrasnik, 2013). Particularly, the
concepts of electrification and hybridization of cars are
nowadays recognized as those to be pursued as soon as
possible. If until some months ago such a need appeared not
to be so stringent, the recent events, involving traditional cars
emission levels, together with the well-known progressive
reduction of fossil fuels reserves, caused it to suddenly
become more severe. Therefore, main OEMs are now
switching from a medium-term development outlook towards
a short term one.
When comparing all existing XEV powertrains, hydrogen-
fueled vehicles (either FCEVs or FCHEVs) have more
advantages over thermal hybrid vehicles (i.e. hybrid electric
vehicles-HEVs), such as high fuel-economy (km/kg), related
to the use of fuel with higher energy density, high efficiency
and reduced environmental impact from a tank-to-wheel
point of view. On the other hand, purely electric technology
(i.e. electric vehicles-EVs) presents inferior autonomy and
performance with respect to FCHEV cars, due to the current
technological limits of batteries, and may determine
troublesome on electrical grid infrastructure (Sorrentino et
al., 2013). Nevertheless, FCHEV technology has not yet had
significant market developments, mainly due to the currently
very expensive hydrogen production, as well as the absence
of distribution and refueling infrastructures that will ensure
the dissemination and distribution in a large scale. To tackle
the above constraints, governmental and research institutions
are now increasing the cooperation with main OEMs, as
demonstrated by the increasing awareness of EU funding
bodies towards the high potential offered by FCHEV-based
hybridization, even in a short-term prospective (The Fuel
Cells and Hydrogen Joint Undertaking, 2015).
Moreover, recent proposals of major automakers (Toyota and
Honda) show that hydrogen technology is overall ready to
start a minimal competition to alternative sustainable
mobility (Greene et al., 2013). It is therefore important to
focus on increasing the competitiveness of such vehicles in
terms of fuel economy, thus overcoming the transitional
problems related to hydrogen.
In this context the development of mathematical tools, which
can potentially integrate in one single process the
optimization of powertrain design and subsequent definition
of real-time effective and applicable control strategies, can
definitely contribute to speeding-up technological growth of
XEVs (Hu and Wu, 2013), and particularly of FCHEVs (The
Fuel Cells and Hydrogen Joint Undertaking, 2015).
Moreover, the definition of development procedures, which
are versatile enough to be deployed on FCHEV powertrains
with different degree of hybridization, are nowadays
considered as a key factor to promote market penetration of
hydrogen fueled cars (European Commission, 2015). To
achieve this scope, in the current work the physical meaning
of a rule-based control strategy (Sorrentino et al., 2011) is
deeply analyzed, with the final aim of extending its
applicability to a variety of powertrains, by means of suitable
normalization/denormalization techniques. Indeed, such
versatile and multi-purpose tools, based on extensive use of
normalized models (Sorrentino et al., 2015) and maps, can
provide substantial contributions toward a greener
transportation paradigm in many research fields (Agbli et al.,
2016).
The article is organized as follows: first the basic equations,
here utilized to assess mass impact of vehicle hybridization,
as well as related traction power demand and hydrogen
Preprints, 8th IFAC International Symposium on
Advances in Automotive Control
June 19-23, 2016. Norrköping, Sweden
Copyright © 2016 IFAC 378


1. INTRODUCTION
a short term one.
2016).


1. INTRODUCTION
a short term one.
2016).


1. INTRODUCTION
a short term one.
2016).


1. INTRODUCTION
a short term one.
2016).

370 Marco Sorrentino et al. / IFAC-PapersOnLine 49-11 (2016) 369–376
consumption, are briefly recalled. Afterwards, the heuristic
control strategy is described, followed by a detailed physical
analysis of best rules, as addressed by a model-based
optimization analysis run on several hybridization degree
values. The normalization and denormalization techniques
are then proposed and verified via suitable scenario analyses.
2. MATHEMATICAL MODELS OF THE TOOL
2.1 Mass model
A parametric model was used to assess the impact of
hybridization on vehicle mass. By referring to the vehicle
architecture shown in Fig. 1, the mass of an FCHEV
(MFCHEV) can be obtained by adding the mass of major
hybridizing devices to the vehicle body mass (Mbody). This
latter is derived from the mass of the reference conventional
vehicle (MCV) by subtracting the contributions due to the
original gear box, as follows:
)(*
, GBICECVICECVbody mmPMM  (1)
Then, vehicle mass can be determined adding the
hybridization devices and by imposing that the HFCV power
to weight ratio (i.e. PtW ) equals conventional vehicle (CV)
one, thus ensuring HFCV guarantees the same CV
acceleration performance:
HTBCBCEMEMFCFCbodyFCHEV MNMmPmPMM  **
(2)
where the last term represents hydrogen tank mass.
Fig. 1. Fuel cell powertrain schematic (Series architecture).
The number of battery cells (NBc) is determined by knowing
the rated power of the electric motor EM (PEM*) and FC
system (PFC*), as well as the power of a single battery cell
(PBc*), assumed hereinafter constantly equal to 1.25 kW
(Nelson et al. 2007):
*
**
Bc
FCEM
P
PP
Nc

 (3)
CV
*
CV,ICE
*
EM
PtW
*
EM
HFCV
M
P
PP
M 

(4)
Table 1 lists the unit mass here assumed for each powertrain
component. It is worth remarking that P* variables refer to
generic component rated power.
Table 1 Components unit mass (Thomas et al., 1998 -
Klell, 2010).
mICE = internal combustion engine (kg kW-1
) 2
mGB = gear box (kg kW-1
) 0.478
mEM = electric motor (including inverter) (kg kW-1
) 1
mFC = PEM fuel cell system (kg kW-1
) 3.7
MHT = hydrogen tank (kg kW-1
) 1.9
MBC = single cell battery mass (kg cell-1
) 4.67
2.2 Longitudinal vehicle model
Fuel economies in this paper are evaluated by means of a
backward longitudinal vehicle model, whose basic equations
are presented below. Traction power is estimated as:
  v
dt
dv
MvACCvgMP effxrHFCVtr  3
5.0)sin()cos(  (5)
where α and ρ are the road grade and air density,
respectively, while Meff equals 1.1 MHFCV to suitably account
for rotational inertia. For non-negative Ptr values, the
mechanical power to be supplied by the EM is (see Fig. 1):
tr
tr
EM
P
P

 if 0trP (6)
PEM can also be expressed as a function of fuel cell system
and battery power, as follows:
)( BFCEMEM PPP  if 0trP (7)
where the η variables correspond to efficiency terms. On the
other hand, when Ptr < 0, the regenerative braking mode is
active, resulting in the following expression for the electrical
energy delivered by the EM:
trEMtrEM PP   if 0trP (8)
During regenerative braking, battery can be charged by the
fuel cell system, thus the following equation holds for
negative Ptr values:
FCEMB PPP  if 0trP (9)
It is worth remarking here that electric motor efficiency is
computed by means of normalized maps derived from the
model library proposed in (Rousseau et al., 2004). Instead,
fuel cell system efficiency is computed by means of the
following relationship, obtained by curve fitting experimental
data acquired on a dedicated fuel test-bench available at the
energy and Propulsion laboratory at University of Salerno
(Sorrentino et al., 2013).
3FC2
2
FC1
2FC1
FC
qPqPq
pPp


 (10)
3. HEURISTIC CONTROL STRATEGY
3.1 Best rules definition via optimization analysis
This section discusses in detail the two heuristic rules
proposed in (Sorrentino et al., 2011) and then extended to
fuel cell vehicles in (Sorrentino et al., 2013). The optimal
values of electric power supplied by FC (i.e. PFCsupply) and
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Marco Sorrentino et al. / IFAC-PapersOnLine 49-11 (2016) 369–376 371
dSOC (maximum allowable oscillation around targeted
battery state of charge - SOC) are estimated online as a
function of the average power demand:
)P(fP trplysup,FC  (11)
)( trPgdSOC  (12)
By solving the following minimization problem (over an
extended range of average traction power demand), it is
possible to find the optimal f and g functions:
dt)t,P(mmin OFFFCSplysupFCHtP 2OFFFC,plysupFC 
  (13)
Subject to the constraint:
fSOCendSOC )(
(14)
Solving the above minimization problem corresponds to
identifying the best engine intermittency (i.e. tFCS-OFF, which
is the time during which FCS is kept off) and power level at
which the fuel cell system should be operated for a given
average traction power demand trP . This latter variable is
estimated over a time horizon (th) with either an a-priori or a-
posteriori method (see Sorrentino et al. 2011), here set to
th=10 min (see Fig. 2).
Fig. 2. dSOC indirect determination from the optimal SOC
trajectory, as addressed by the solved minimization problem
(see Eq. (12)) for an assigned trP value.
The solutions can be studied by analyzing the resulting two
maps associated to Eqs. (11) and (12). Particularly, in this
study several maps couple were obtained through above
described optimization, each corresponding to a different
degree of hybridization (DH), the latter variable
corresponding to the ratio between rated battery and electric
motor power. Table 2 lists main specifications of the
FCHEVs here considered, obtained by deploying the mass
model described in section 1 for varying nominal fuel cell
system power, while keeping constant the power to weight
ratio. Each optimized map was normalized, in such a way as
to become potentially extendable to different degrees of
hybridization, as discussed later on. Normalization of the
map relating to PFCsupply is straithforward, as it can be simply
obtained as the ratio of Eq. (11) data divided by rated fuel
cell system power (see Eq. 15). On the other hand, Eq. (16) is
here proposed to account for the impact of larger/smaller
battery size when extending a map optimized on one of the
FCHEVs listed in Table 2 (e.g. PFC*=30 kW) to another one
(e.g. PFC*=50 kW):
*
FC
plysupFC
norm,plysupFC
P
P
P  (15)
CapdSOC=dSOC BATTrefnorm  (16)
It is worth noting that in Eq. (16) CapBATTref represents the
battery capacity [kWh] of the powertrain, on which the
optimization was performed (see Table 2). Thus, Eq. (16)
allows introducing specification independency in optimal
thermostatic management of FCHEV, provided that rule
extension is accomplished by appropriately rescaling the
dSOCnorm with respect to new powertrain specifications. The
latter aspect, which actually corresponds to the
denormalization phase, is described in detail in the following
(see section 3.2).
Table 2 FCHEV specifications assumed to derive the
optimized rules maps. PEM* refers to the rated power of
the electric motor installed on board.
PFC*
(kW)
Battery
mass
(kg)
Battery
Capacity
(kWh)
FCHEV
mass
(kg)
PEM*
(kW)
20 271 46 1594.08 92.13
30 234 39 1593.70 92.10
40 196 33 1593.31 92.08
50 159 27 1592.92 92.06
60 121 20 1592.54 92.04
Fig. 3 and Fig. 4 show all the normalized maps obtained.
Below is an explanation on the physical behavior, as
addressed by the optimization analysis conducted over the 5
vehicles listed in Table 2.
For all vehicles, normalized fuel cell power exhibits a
monotonic increase. This behavior could in principle appear
unexpected, as commonly fuel cell systems work at best
efficiency at relatively low power. Nevertheless, the fact that
fuel cell system efficiency falls quite close to its optimal
value, in a wide range (Arsie et al., 2006), justifies the above-
noticed general load following behavior for fuel cell supply
power map. Moreover, Fig. 4 indicates that fuel cell power
supply does not differ significantly at low traction power,
whereas the discrepancy between one map and another
becomes larger as trP increases. This is mostly due to the
normalization effect (see Eq. 15).
More interesting, from the physical point of view, is the
dSOCnorm map behavior, illustrated in Fig. 3. Particularly, at
low traction power the optimization algorithm proposes,
independently from degree of hybridization, monotonically
increasing behavior. This happens thanks to the sudden
increase in fuel cell power supply in these conditions (see
Fig. 4, which particularly guarantees easily achieving charge
sustaining behavior). Then, varying DH impact starts
increasing beyond trP =3 kW, because of a balance between
the involved energetic flows: vehicles with a low degree of
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hybridization can afford working with higher dSOCnorm
excursions, thanks to the higher power that can be supplied
by the FC system. The latter behavior continues up to
significantly high trP values: only after trP =15 kW the
increasing trend reduces, thus leading dSOCnorm to set on a
plateau region above this value. On the other hand, vehicles
with higher degree of hybridization can afford an increasing
dSOCnorm trend within a smaller trP range, as well as with
reduced slope (e.g. PFC*=40 kW). After reaching a maximum,
for such powertrains it is necessary to reduce dSOCnorm
excursions to meet charge-sustaining constraint (see Eq. 14).
The values of dSOCnorm for PFC*=20 kW, however, are very
close to zero when trP values are high (e.g. over 10 kW): this
indicates the increasing difficulty in guaranteeing charge-
sustaining battery operation, with the fuel cell system turned
on for most of the time. In fact, for trP values above 15 kW,
the case corresponding to PFC*=20kW loses physical sense,
since the power given by the fuel cell system becomes lower
than that required.
Fortunately, urban/suburban driving are mostly characterized
by trP lower than 10 kW on average. Thus, the results
yielded on output by the optimization analysis can be
considered safe for all analyzed powertrains.
0 5 10 15 20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Ptr
[kW]
dSOCnorm[kWh]
PFC
*=20 kW
PFC
*=30 kW
PFC
*=40 kW
PFC
*=50 kW
PFC
*=60 kW
DH
Fig. 3. Maps of normalized dSOC.
After having analyzed the physical coherence of proposed
rule-based energy management strategies, it is worth
remarking how such rules were already proven effective for
series hybrid architectures, via suitable comparison with both
dynamic programming and genetic algorithm optimization
results, as discussed in a previous contribution (Sorrentino et
al., 2011). Therefore, it is justified the main proposal of this
paper, namely to verify if subsequent denormalization of
normalized optimal maps can provide useful contributions,
both in terms of reducing the time required for offline
development of energy management strategies, as well as
enhancing the joint optimization of powertrain sizing and
energy management.
0 5 10 15 20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ptr
[kW]
PFCsupplynorm[/]
PFC
*=20 kW
PFC
*=30 kW
PFC
*=40 kW
PFC
*=50 kW
PFC
*=60 kW
DH
Fig. 4. Maps of normalized PFCsupply.
3.2 Maps normalization and denormalization
Once vehicle specifications are determined, extension of one
of the optimal rules maps presented and discussed in the
previous section firstly entails normalizing the x-axis, which
represents traction power demand. Such an additional
normalization is required to account for the fact that maps
developed for lower degrees of hybridization are expected to
retain higher extendability features as compared to high DH
powertrains, as discussed in the previous section.
A first denormalization technique is given by Eq. (17), by
dividing average traction power demand by rated power of
the reference solution (i.e. PFCref*):
*
FCref
tr
norm,tr
P
P
P  (17)
Then, denormalization can be obtained by simply multiplying
the right hand side of Eq. (1) by the PFC* of the vehicle,
which the map is extended to:
*
FC*
FCref
tr
denorm,tr P
P
P
P  (18)
Regarding the first technique, it is worth noting how the
closer norm,trP to 1, the less extendable the associated
normalized map will be, as it would cause rated fuel cell
power be potentially insufficient both to provide useful
traction power, as well as to compensate for trasmission
losses (see Eqs. 6 and 7). With this respect it is however
worth recalling once again that all optimized maps ensure
safe operation for regular passenger cars driven on typical
driving paths.
The second technique consists in scaling trP with respect to
the nominal electric motor power, as follows:
*
EMref
tr
norm,tr
P
P
P  (19)
Denormalization for this second technique is thus given by
the following expression:
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*
EM*
EMref
tr
denorm,tr P
P
P
P  (20)
As for maps ordinates (see Fig. 3 and Fig. 4), such values are
denormalized by referring to the normalization definitions
given above (see Eqs. 15 and 16):
PP=P *
FCnormFCsupply,FCsupply  (21)
Cap
CapdSOC
=dSOC
BATT
BATTref%
denorm

(22)
4. SIMULATION RESULTS
4.1 Scenario analysis
In this section, the above-developed maps, along with related
normalization and denormalization techniques, are verified
through an extended model-based scenario analysis. The
following aims are pursued: assessing the physical adherence
of optimized maps; verifying maps extendability to different
powertrains, via comparison between fuel economies yielded
by optimized and normalized maps; comparing and
evaluating the two x-axis normalization techniques.
The powertrains examined in this analysis are 15 overall: 5
corresponding to the FCHEVs of Table 2 and further 10,
obtained by increasing and decreasing power to weight ratio
( PtW ) by 20 % with respect to Table 2 data, as shown in
Table 3. Fuel economies are estimated by deploying the
FCHEV model of section 2.2 on the new european driving
cycle.
Table 3 Cases investigated in the scenario analysis
x-axis normalization
technique
Technique 1
(i.e. Eq. 16)
Technique 2
(i.e. Eq. 18)
Table 2 specs,
corresponding to
058.0PtW 
A1 A2
070.0PtW  B1 B2
046.0PtW  C1 C2
The results obtained in cases A1 and A2 are shown in Fig. 5
and Fig. 6. For each powertrain, the color of a series indicates
the reference (i.e optimized) map used. The red color
indicates the use of an optimized map (PFC*=PFCref*). On the
x-axis of the bar graphs there is the value of the rated FC
system power, whereas the y-axis provides the simulated
fuel-economy (FE) values, here expressed as driven
kilometers per kilogram of consumed hydrogen.
Fig. 5 and Fig. 6 show that the optimized maps lead to higher
FE in most cases. The slight deviations, occurring when
adopting normalized maps, are in this case low enough to
justify the effectiveness of both normalization techniques
proposed for the x-axis of Fig. 3 Fig. 4.
It is worth remarking here that by “optimized map” it is only
intented to refer to the heuristic maps yielded on output by
the specific procedure described in section 3.1. Of course, in
some cases such maps can be outperformed by normalized
ones, as a consequence of their subsequent implementation
on the fluctuating power demand trajectory characterizing
every driving cycle. This is due to having developed the maps
minimizing the consumption for an assigned average traction
power and not introducing an instantaneous power demand.
This error is partially absorbed as the heuristic strategy is
updated every th time horizon, when implemented for on-
board energy management. Moreover, the intrinsic features of
series configuration ensure the reliability of energy (i.e.
average power)-dependent strategies, as compared to
instantaneous optimization algorithms, such as ECMS, which
on the other hand require extensive calibration efforts
(Sciarretta and Guzzella, 2007; Musardo et al., 2005). This is
the reason why the current study mainly focuses on verifying
the potentiality of the proposed rule-based control strategy as
a specification independent energy management algorithm.
In any case, the FE values estimated in the other cases (i.e.
B1, B2, C1 and C2, whose detailed bar-plots are omitted here
for sake of brevity) confirm that, overall, optimized maps
guarantee achieving best performance for most of the 30
simulations associated to Table 3 cases. Moreover,
discrepancies between optimized and normalized maps are
always bounded within +/-2 %, thus confirming the reliability
of the proposed normalization/denormalization techniques.
From a physical point of view, the first x-axis normalization
technique (expressed by Eq. 17) has to be considered as the
most relevant. Indeed, normalizing with respect to the FC
system power is more coherent with the intrinsic features of
the intelligent thermostatic management enabled by the
proposed heuristic control strategy, which decouples the main
source of traction energy (i.e. the FC system) from the
wheels.
Fig. 7 resumes the overall scenario analysis outputs, by
illustrating the trajectories of best fuel economy obtained for
each powertrain. Such a figure underlines how the lower the
power to weight ratio, the more suitable the range-extender
like solution (i.e. high degree of hybridization). Within the
analyzed range of rated fuel cell system power, the range-
extender solution remains the best, although higher power to
weight ratio seems justifying the selection of a lower degree
of hybridization (i.e. high fuel cell nominal power). It is also
worth pointing out how the sudden decrease in fuel economy,
in correspondence of higher degree of hybridization, can also
be due to the intirinsically “more energetic” energy
management enabled by the proposed rule-based strategy.
Fuel economies obtained in the reference case, i.e.
corresponding to 058.0PtW  in Table 3, are in good
agreement with values declared by the manufacturer of an
FCHEV having similar PtW values (Honda FCX, 2015),
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thus confirming the physical adherence of the proposed
heuristic control strategy.
20 30 40 50 60
110
115
120
125
130
FE [km/kg]
PFC
* [kW]
Reference map 20 kW
Reference map 30 kW
Reference map 40 kW
Reference map 50 kW
Reference map 60 kW
Fig. 5 Case A1 Results.
20 30 40 50 60
110
115
120
125
130
FE [km/kg]
PFC
* [kW]
Reference map 20 kW
Reference map 30 kW
Reference map 40 kW
Reference map 50 kW
Reference map 60 kW
Fig. 6 Case A2 Results.
20 30 40 50 60
105
110
115
120
125
130
PFC
* [kW]
FE [km/kg]
A1
A2
B1
B2
C1
C2
Fig. 7 Best-case analysis outcomes.
4.2 Comparison with the case Toyota Mirai
To confer reliability to the results, this section analyzes the
FE reached by an early FCHEV to be mass-produced. The car
"Toyota Mirai" reports, among the specifications declared by
the supplier (Toyota Mirai, 2015), an FE of 100 km/kg
(hydrogen compressed to 700 bar). By relying on the
characteristic of specification independency discussed above,
the maps shown in Fig. 3 and Fig. 4 are extended, via the first
normalization/denormalization technique (see section 3.2), to
an FCHEV dimensioned according to Mirai specifications
(listed in Table 4).
Table 4 Technical specifications of "Toyota Mirai"
FCHEV
PEM* [kW] 113
PFC* [kW] 114
Battery capacity [kWh] 1.6
Autonomy [km] 500
Fuel-economy [km/kg] 100
Dimensions [mm] 4890x1815x1535
Mass [kg] 1850
Power/weight [kW/kg] 0.061
More in detail, a parametric analysis was carried out by
varying not only the degree of hybridization, but also the time
horizon th. The latter variable was selected according to the
outcomes of previous analyses (Sorrentino et al., 2011),
which highlighted its relevance when deploying the proposed
heuristic strategy (see section 3) in real-world applications.
Fig. 8 illustrates main outcomes of the proposed analysis,
which contributes to further verifying the physical coherence
of the proposed specification independent control strategy.
Particularly, the very low degree of hybridization of this
vehicle (see Table 4) requires very short time horizon to
achieve fuel economies that are comparable to those declared
by the manufacturer. This was expected since, as discussed
above, the heuristic strategy here adopted is mainly traction-
energy driven, whereas lower DH vehicles would require a
more power driven approach, such as ECMS. Nonetheless, in
some cases (e.g. PFC*=60 kW), the heuristic control strategy
achieves appreciable fuel economies, whose discrepancy
(around 15 %) with respect to declared values can be easily
justified: in particular, some key uncertainties remain when
trying to simulate a Mirai equivalent FCHEV, such as the
expected differences between real vehicle and the model of
section 2, mainly related to components unit mass and key
performance metrics (e.g. fuel cell system efficiency).
20 30 40 50 60
70
75
80
85
90
95
PFCref
* [kW]
FE [km/kg]
th1
= 1 s
th2
= 300 s
th3
= 600 s
Fig. 8 Analysis of Toyota Mirai fuel economy estimates.
4.3 SOC analysis
As a further proof of validation of the proposed specification
independent methodology, in this section the advantages of
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heuristic strategy with respect to a simple thermostatic
control (TC) are investigated. Particularly, the difference
(ΔSOC) between state of charge values at the beginning and
end of the driving cycle is estimated, so as to enable accurate
evaluation of charge sustaining capability of both strategies.
The parameter to be assessed and compared is the residual
battery energy that was extra-discharged or extra-charged,
depending on ΔSOC sign:
BATTBATT CapSOCE  (23)
In Table 5 it is compared the EBATT obtained in scenario A1
with that achieved using the following maps constants (i.e.
TC strategy):






01.0dSOC
P525.0P *
FCTC,plysupFC
(24)
where the value assumed for supplied FC system power
corresponds to maximum efficiency (Sorrentino et al., 2013).
The numbers in bold refer to EBATT achieved with optimized
maps.
Table 5 EBATT analysis outcomes [kWh]
PFC* (kW)
20 30 40 50 60
PFCref*(kW)
20 0.006 -0.007 0.053 0.152 0.168
30 -0.055 0.020 0.069 0.080 0.297
40 -0.347 -0.271 -0.066 0.029 0.327
50 -0.456 -0.401 -0.261 0.126 0.055
60 -0.474 -0.499 -0.320 -0.185 0.231
TC -0.461 -0.315 0.353 0.078 0.297
As expected, in none of the simulations it is accomplished an
EBATT equal to zero. It is worth noting that such extra
consumption is accounted for as an equivalent hydrogen
consumption (Sorrentino et al., 2013). When the degree of
hybridization is high, the maps optimized and normalized
achieve close results, with EBATT values having a much lower
order of magnitude as compared to TC solution.
For PFC*=50 kW and PFC*=60 kW, minimum EBATT values
are still obtained with heuristic strategy, this time adopting
normalized maps (i.e. PFCref*=40 kW and PFCref*=50 kW,
respectively).
In terms of FE, the results obtained with the TC strategy are
reasonably close to those obtained with either normalized or
optimized maps. Nevertheless, the much higher EBATT
discrepancy makes equivalent hydrogen consumption
adaptation less reliable, a drawback which adds uncertainity
when applying TC strategy to the next driving cycle.
5. CONCLUSIONS
By optimizing heuristics rules on powertrains dimensioned
via model-based approach, control strategies are obtained for
on-board energy management of FCHEVs. Such strategies,
by adopting suitable normalization/denormalization
techniques, were proven to be highly specification
independent, thus being extendable to different vehicle
configurations.
Extensive model-based analyses were presented and
discussed, aiming at demonstrating the physical adherence of
heuristic rules and related fuel economy outcomes, on one
hand, and, on the other hand, the reliability and effectiveness
of proposed normalization/denormalization techniques.
Particularly, when adopting either optimized or normalized
map, it was shown as fuel economies are generally in favor of
a range-extender like design, whereas the analysis of charge
sustaining capabilities evidences the benefits of adopting
optimized heuristic rules rather than over-simple, non-
optimized thermostatic strategy. The comparison with the
case of Toyota Mirai shows the practical utility of the
proposed methodology, in particular for the preliminary
design of the electrical components of a hybrid fuel cell
powertrain, in addition to confirming the ability to exploit the
features of specification independency for the subsequent
extension to other vehicle configurations.
As for further areas of potential application of the proposed
methodology, it is worth mentioning its usefulness for
reducing the time for off-line development of control
strategies. Indeed, it could be possible to develop a
specification-independent control strategy on one powertrain
and, afterward, extend its applicability to other degrees of
hybridization via the proposed normalization/denormalization
techniques. Moreover, the extension can include, beyond
increasing or decreasing the degree of hybridization, also the
use of more advanced technologies, such as lighter or more
efficient fuel cell systems, and/or even some design
modifications (e.g. switching from high-power to high-
energy batteries and viceversa).
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