Loss Minimization Algorithm for EV Hybrid Energy Storage Optimization

Loss Minimization Algorithm Based Strategy for
EV Hybrid Energy Storage System Optimization
Alexander González Medina
Facundo Aguilera
Manuel Javier Vidal Cué
Grupo de Electrónica Aplicada
IITEMA, CONICET-UNRC, Argentina
[email protected]
Grupo de Electrónica Aplicada
IITEMA, CONICET-UNRC, Argentina
[email protected]
Grupo de Electrónica Aplicada
IITEMA, CONICET-UNRC, Argentina
[email protected]
Abstract—This work proposes an energy management strategy
that optimizes an objective function evaluating losses and energy
consumption in a hybrid energy storage system of an electric
vehicle. This strategy is based on a loss minimization algorithm
that iterates the objective function evaluated for the reference
signals. Furthermore, supercapacitor voltage and temperature
protection measures were implemented to avoid penalizing situations. The proposed strategy is validated by simulation using the
electric vehicle model provided by the IEEE 2024 VTS Motor
Vehicles Challenge (MVC). The results show that the strategy can
improve the overall power distribution performance. Moreover,
this proposal obtained the best final score among the 44 presented
in MVC.
Index Terms—energy management strategy, electric drive, loss
minimization algorithm, supercapacitor, electric vehicle.
I. I NTRODUCTION
Climate change and global warming have become great
concerns of our time. In relation, nearly 30% of carbon
emissions are due to transportation, specifically due to combustion engines. This is why, recently, electric vehicles (EVs)
have gained an incredible attraction as a secure alternative.
However, EVs lack the reliability and efficiency that its predecessor has. To address these issues, the annual Motor Vehicle
Challenge (MVC) was launched with the support of the IEEE
Vehicular Technology Society in 2016. The challenge aimed
to optimize a certain EV problem. In past editions, problems
were centered on an energy management system (EMS) with
different objectives, such as: reducing the operation cost of
a hybrid vehicle, or battery state-of-charge (SoC) of a dualmotor all-wheel drive. Notwithstanding, models used in these
editions did not consider or represent real power losses over
an entire driving cycle [1].
In the MVC 2024 edition, the problem consisted of a
simulation model that takes into consideration more accurate
modeling of the losses and efficiency of the power electronics
converters and electric machines. With this in mind, contest
teams needed to satisfy two objectives: to propose an EMS
to reduce energy consumption and to propose a suitable
powertrain losses management strategy to reduce the losses
of power electronics converters, inverters, and the e-machine.
The EMS plays a major role in EV performance since it
must provide proper control and distribution of energy to reach
larger distances more efficiently [2]. Among the broad range of
hybrid energy storage systems (HESS), one of the most widely
used is the battery-supercapacitor configuration. Batteries have
high energy density but lack power density, the opposite of
a supercapacitor (SC); which means that a complementary
architecture, if well controlled, can overcome weaknesses of
both components [3]. In this regard, plenty of research work
has been done to optimize battery-SC HESS. In general, works
are divided into three main approaches depending on what
they are based on: rules, frequency analysis, and optimization
algorithms [4]. Rule-based EMS distributes overall power as
defined by a set of rules. The low computational demand and
reliability of this method make it suitable for real applications
[5], [6]. A more intuitive approach is the Frequency-based
(FB) EMS, which consists of dividing the demand of power
according to its frequency components, considering that it
is healthier for batteries to supply mean values (or DC
component) and leave power peaks to the SCs [7], [8]. On
the other hand, a better performance can be achieved by an
Optimization-based (OB) EMS, where an objective function is
minimized through an optimization algorithm or a combination
of them. This method requires a lot of information which in
real applications is difficult to collect [9]–[11].
Another issue that must be addressed in the performance of
EVs is the minimization of losses throughout their propulsion
system. Loss minimization control (LMC) has been extensively researched to achieve higher efficiency, less energy
waste, and prevention of temperature rise [12], [13]. In general,
LMC strategies can be classified into two groups: modelbased (loss-model and simple-state control) and physicalbased (search control) [14], [15]. Model-based methods are
generally faster because they are simply the development of
mathematical expressions and can be processed in real-time.
A drawback of these techniques is that they depend closely
on system parameters and may not consider the interrelation
with no modeled coupled subsystems. In contrast, physicalbased methods do not strictly depend on system parameters
because they focus on finding the set of inputs that results in
minimum losses, making them very robust. However, this setsearch process can take a considerable amount of time, which
is not of interest in fast dynamic drives.
The simulation model presented in the MVC corresponds
to a fast dynamic system, although processing time is not
a restriction in this case. Due to the aforementioned, in
this paper, a Loss Minimization Algorithm (LMA) based
Coupling and
EV chasis model
Proposed strategy
msc
isc
Energy management
Temperature
msc
protection
udc
vve
isc
LMA
usc
Jbat (ĩ∗bat )
ibat
mbat
idc
SC
minv
idc
mbat
ibat
Battery
M
Drive cycle Measurements
i∗bat
Proposed
∗
strategy id
∗
vve
Battery and
SC control
msc
Motor
control
minv
mbat
Drive id control
i∗q
Fig. 1. Studied EV configuration
ω
strategy for optimizing both energy consumption and losses is
proposed. This LMA is an iterative method that searches the
set of battery and motor current references that minimizes two
different condition-based cost functions that are partly based
on the loss model of the electric subsystems of the vehicle. In
addition, temperature protection and a flux weakening strategy
are also developed. As a reference, this strategy earned 1st
place as it obtained the best scores for this simulation model.
The paper is organized as follows. Section II describes the
challenge EV powertrain model and cost function. Section
III presents the proposed strategy. Finally, the results of the
applied strategy are shown in Section IV.
II. C HALLENGE EV MODEL AND COST FUNCTION
The configuration of the EV proposed as the platform for
the MVC is illustrated in Fig. 1. This platform is based on
a racing vehicle developed at the University of Nottingham
which includes a battery-SC HESS [1]. Each energy storage
source is connected to the DC-link through two bidirectional
DC/DC power converters. Moreover, the traction permanent
magnet synchronous machine (PMSM) is powered from the
DC link through a three-phase inverter.
The control laws for each of the three power converters
are already provided by the MVC model, including vehicle
speed, motor current, DC-link voltage, SC, and battery current
controls. With this platform, the objective of the challenge is to
design a strategy that generates the battery current reference,
i∗bat , and the motor d current reference in the d-q reference
frame, i∗d , which are left as two degrees of freedom in the
model. The performance of the proposed strategy is scored by
using the following cost function along a driving cycle:
J = k1 ∆fsoc + k2 ∆fusc + k3 σcell + k4 Ereg +
tot
k5 Ploss
+ k 6 Nd + k 7 NT ,
(1)
where k1 = k2 = k6 = 1, k3 = 10, k4 = 0.001, k5 = 0.1 and
k7 = 50 represent weighting factors.
∆fsoc = 100 − SoCf is the percentage of the battery energy
consumed throughout the driving cycle. SoCf is the final state
of charge (SOC) and is obtained from the battery cells model
included in the MVC model.
∆fusc = usc0 − uscf , where usc0 and uscf are the initial and
final SC voltages, respectively.
imax
SC ch
ĩ∗bat
LMA
Jd (ĩ∗d )
Field weakening
−
i∗
+ SC ch
+
−
+
i∗bat
+
−1
ĩ∗d
min(id1 , id2 )
i∗d
i∗dF W
Fig. 2. Proposed strategy diagram.
σcell is the standard deviation of battery cell current measured throughout the driving cycle.
Ereg is the regenerative energy of the battery and is obtained
by integrating the negative battery power produced during
deceleration intervals in the driving cycle.
tot
The fifth term accounts for the total losses Ploss
, and is
obtained as:
tot
bat
SC
inv
em
Ploss
= P̄loss
+ P̄loss
+ P̄loss
+ P̄loss
,
(2)
bat
SC
inv
em
where P̄loss
, P̄loss
, P̄loss
and P̄loss
are the mean losses of
the DC-DC battery power converter, the DC-DC SC power
converter, the inverter and the traction electric machine, respectively. Power converter losses are based on conduction
and switching loss models of the EV power modules. The
electric machine losses model includes copper, iron core, and
stray losses.
Nd is the total number of power modules. The number of
power modules in parallel for each power converter is left
as a design variable for the competition. A high number of
modules in parallel may reduce the converter power losses,
while a reduced number increases the junction temperature.
NT is the number of power modules that exceed a junction
temperature of 175° C at any time during the driving cycle.
III. P ROPOSED STRATEGY
The strategy developed to minimize the scoring function
(1) is presented in this section. A simplified diagram of the
strategy is shown in Fig. 2. The following subsections explain
the two fundamental blocks that comprise this solution.
A. Analysis of cost function for scoring
The selection of the battery current reference and the d
motor current references affect differently each of the terms
defined in the cost function (1). In particular, an optimal
battery current reference ĩ∗bat , in general terms, should: avoid a
reduction of the battery SOC, avoid variations on the battery
voltage at the end of the driving cycle, reduce variation in
battery current, avoid charging the battery and reduce losses
in the power converters of the SC and the battery.
With respect to the losses in the power converters, they
include switching and conduction losses and are modeled as:
x
x 2
Ploss
= mx Ron
ix + axsw |ix | ,
ibat <0
where ubat is the battery voltage. This term increases significantly due to the integration operation. In addition, during
regenerative braking intervals, the penalization obtained if the
battery is charged is much higher than the penalization of
charging the SC, i.e.
bat
SC
k4 Ereg + k5 Ploss
≫ k5 Ploss
.
, imin
and δ definition
imax
j
j
= it
imax
j
= it
imin
j
it =
imin
+ imax
j
j
2
(3)
where index x ∈ {SC, bat} refers to SC or battery, respectively, mx is the modulation index, Ron is the on-state
x
power device resistance, and axsw = γsw
fsw is a constant
which models the switching losses linearly to the current. The
x
constant fsw denotes the switching frequency and γsw
is the
ratio between switching energy and current, obtained from the
device datasheet [1].
bat
SC
Simulation model parameters shows that Ron
< Ron
and
bat
SC
asw < asw . Therefore, it can be stated that a strategy that
minimizes losses in these power converters will prioritize the
battery as an energy source.
With respect to the battery charging penalization (the fourth
term in (1)), the regenerative energy of the battery is defined
as:
Z t
,
(4)
ubat |ibat | dτ
Ereg =
0
Start
(5)
Therefore, during regenerative braking, it is preferable to
charge the SC instead of the batteries. Thus, it is necessary
to discharge the SC according to the vehicle speed to avoid
overvoltages during regenerative braking.
Given the aforementioned, the following set of rules is
proposed to define an optimal battery current reference ĩ∗bat :
1) Battery as an energy source is prioritized when idc > 0.
2) SC must store the energy if idc < 0 (ensuring Ereg = 0).
3) The SC should be discharged according to the EV kinetic
energy.
4) The final SC voltage must be the same as the initial
voltage. However, it is not necessary to enforce this
condition throughout the entire driving cycle, but only
towards the end.
On the other hand, an optimal d motor current reference
ĩ∗d should endeavor to reduce losses in the power converters
and the PMSM and to implement a flux weakening strategy
to allow high VE speeds.
The energy management and id control strategies were
designed based on this analysis, as described below.
B. Energy management
The energy management strategy consists of an LMA that
generates the optimal ĩ∗bat , together with two mechanisms
< 2δ
imax
− imin
j
j
False
True
ĩ∗j = it
Stop
False
Jj (it + δ) >
Jj (it − δ)
True
Fig. 3. Loss minimization algorithm.
that prevent hazardous situations, namely: charge/discharge
(functioning inside the LMA) and temperature protection of
the SC, as shown in Fig.2. The outputs are processed to obtain
the final i∗bat .
1) LMA: The objective of the LMA block in Fig. 2 is to
generate an optimal battery current reference ĩ∗bat based on
system measurements. To this end, a new cost function for
control is designed by selecting only the terms that depend on
the battery currents in (1), as follows:


if Fch = 1,
Pb2
Jbat (ibat ) = Pb1 + Pb2 + Pb3
if vve ≥ kv ∆usc ,


Pb1 + Pb2 + Pb3 + Pb4 otherwise.
(6)
All terms in Jbat (ibat ) are evaluated in function of ibat with
a binary search-based LMA to obtain the optimal ĩ∗bat for the
actual condition [14]. The flowchart of the LMA is shown in
Fig. 3. In this algorithm, a first definition of imin
and imax
j
j
fixes the initial search interval, where j ∈ {bat, d}, and δ
defines the step amplitude. In each iteration, the midpoint it
is calculated, and the cost function is evaluated in two points:
if J(it +δ) > (it −δ) then imax
= it , otherwise imin
= it . The
j
j
max
iteration continues until ij
− imin
< 2δ, where the output
j
optimal current is defined as ĩ∗j = it . The initial minimum
value is set as imin
bat = 0 and therefore, no battery charging
current is allowed as the output of the energy management
LMA.
The term Pb1 accounts for the battery discharge as:
Pb1 = k1 ∆soc ,
(7)
where ∆soc = 100 − SoC(ibat ). SoC(ibat ) represents the
modeling of the battery SOC expressed in function of ibat .
The term Pb2 is defined as:
Pb2 = k2 |∆usc | ,
(8)
where ∆usc = usc0 − usc (ibat ). usc (ibat ) is the SC voltage
represented in function of ibat , by considering isc = idc −ibat .
Similarly, power converter losses are considered with:
bat
Pb3 = k5 Ploss
(ibat ),
SC
Pb4 = k5 Ploss
(ibat ),
(9)
bat
SC
where Ploss
(ibat ) and Ploss
(ibat ) are the battery and SC power
converter losses defined in function of ibat , respectively.
From the provided EV model, it can be deduced that the
four terms in (6) exhibit linear or quadratic behavior with
positive coefficients. Therefore, the cost function Jbat (ibat )
is a concave function, with an absolute minimum. This allows
the use of an LMA algorithm described in Fig. 3.
The flag Fch and the coefficient kv in (6) are used to control
the SC charge/discharge, as described below.
2) SC charge/discharge: From the condition described
in (5), it can be concluded that the energy management LMA
will prefer the use of the battery as an energy source if the
four terms are used in the cost function defined in (6) (see
rule 1 in Section III-A). Therefore, the discharge of the SC
must be forced to fulfill rule 3 defined in Section III-A.
The forced discharge is accomplished with the second
condition in (6), where the coefficient kv is defined to reduce
the SC voltage in function with the vehicle speed vve . Note
that the term Pb4 is not taken into consideration in this second
condition, and thus the SC will be preferred as the energy
source when vve ≥ kv ∆usc , discharging the capacitor. This
SC discharge must be high enough to store all the vehicle
kinetic energy during braking intervals, avoiding SC overvoltage conditions.
Given that the coefficient kv cannot be perfectly defined for
all braking conditions, in general, ∆usc ̸= 0 when the vehicle
reaches null speed. Therefore, the charging flag Fch in (6) is
activated during low speeds to reduce the SC voltage variation
at the end of the cycle. In this condition, Jbat = Pb2 giving
maximum priority to the SC charging current. These forced
SC charges cause additional losses in power converters. This
is why the charging flag is only activated after a constant time
tch is reached. Consequently, the charging flag is defined as:
(
1 if vve ≤ Vch and t > tch ,
Fch =
(10)
0 otherwise,
where Vch is a small constant speed, t is the current time, and
tch is the time when low speed SC charging is activated.
3) Temperature protection: Power module junction temperature Tj in the DC-DC power converters can be estimated
based on the modulation index mx , circulating current, and
ambient temperature Ta . Therefore, given a maximum junction
temperature Tmax = 175 ◦ C, the maximum current imax
to
x
avoid over-temperature in any of the power modules (upper or
lower) can be obtained by solving the following equation:
x
|mx − 0.5| Ron
(imax
)2 + axsw |imax
|=
x
x
1
(Tmax − Ta ),
Rth
(11)
where Rth is the junction-heatsink thermal resistance.
The maximum is obtained for the SC power converter to
generate saturation limits for the SC current reference i∗sc (see
Fig. 2), as follows:
usc
imax
Nsc imax
(12)
SC ch =
SC − Im ,
udc
where usc and udc are the SC and DC-link voltages, respectively, Nsc is the number of power devices in parallel in the
SC power converter and Im is a constant security term.
The SC current limit is used to avoid the penalization
defined in the seventh term in (1). Finally, the output battery reference current from the Energy Management block is
defined with the following equations:
i∗SC ch = idc − ĩ∗bat ,

max

iSC ch
î∗SC ch = −imax
SC ch

∗
iSC ch
(13)
if î∗SC ch > imax
SC ch ,
∗
if îSC ch < −imax
SC ch ,
(14)
otherwise.
i∗bat = idc − î∗SC ch .
(15)
C. Drive id control
The drive id control includes an LMA and a flux weakening
strategy, as shown in Fig. 2. These systems generate the ĩ∗d and
i∗dF W current references, and the minimum of them is used as
the strategy i∗d reference.
1) LMA: The procedure described in Section III-B1 was
used to generate the optimal reference signal ĩ∗d intended to
reduce PMSM and inverter power losses. It should be noted
that, for a given PMSM iq current and speed, a non-zero id
reference can be used to reduce the motor losses. However,
higher motor currents increase power converter losses. Consequently, in this case, the developed cost function involves the
terms of expression (1) which depends on id , and is described
as:
Jd (id ) = Pd1 + Pd2 ,
(16)
where Pd1 is defined as:
bat
SC
inv
Pd1 = Ploss
(id ) + Ploss
(id ) + Ploss
(id ).
(17)
bat
SC
inv
Terms Ploss
(id ), Ploss
(id ) and Ploss
(id ) represent losses of
the battery, SC and inverter power converters, respectively,
expressed in function of id by considering fixed DC-link
voltage, ibat and iq .
The term Pd2 accounts for PMSM losses and is defined as:
Pd2 = Pcu (id ) + Pf e (id ) + Pstr (id ),
(18)
where Pcu (id ) represents losses in copper, Pf e (id ) represents
core losses, and Pstr represents stray losses.
The ĩ∗d reference is obtained with the LMA described in
Fig. 3, using the cost function (16).
2) Flux weakening: When the vehicle is operating at high
speeds, the back emf of the PMSM may become too large,
causing the inability of the inverter to follow current commands [16]. To avoid this situation, the following voltage
conditions must be met:
TABLE I
S CORING OBTAINED FOR DIFFERENT DRIVING CYCLES .
2q
vq2 + vd2 ,
(19)
3
where udc is the DC-Link voltage, vq and vd are the d-q
voltages applied to the PMSM.
From the PMSM and control models in [1], if current
transients in d-q are neglected, the following approximation
can be obtained:
udc ≥
vq∗ ≈ Rs i∗q + ωr Ld i∗dF W + λm ωr ,
vd∗ ≈ Rs i∗dF W − ωr Lq i∗q ,
IV. R ESULTS
The proposed strategy, illustrated in Fig. 2, was implemented in the MVC2024 EV simulation model [1]. The
strategy parameters were defined as follows:
imax
bat = 250 A,
m
δ = 0.1 mA,
kv = 1.9 ,
sV
∆fsoc (%)
f
∆usc (mV)
σcell (A)
Total losses (W)
Nd
Ereg (W.s)
NT
Final score:
MVC2024
(Submitted)
54.95
30.14
1.7906
578.62
13
4975
0
148.719
MVC2024
(Modified)
54.94
30.3
1.7899
576.64
14
784.7
0
145.318
ARTEMIS
UDDS
21.86
2.635
1.281
431.24
13
11.36
0
90.711
10.58
0.002
1.034
223.18
13
6.779
0
56.251
(20)
where vq∗ and vd∗ are the voltage reference control signals, i∗q
is the q-current reference generated by the speed control, ωr ,
Rs , Lq and Ld are the motor rotor speed, winding resistance,
and d-q inductances, respectively. i∗dF W denotes the d-current
reference generated by the flux weakening algorithm, see
Fig. 2.
Based on this analysis, the d-current reference is set as
i∗dF W = 0 when the obtained reference voltage from (20)
does not violate the voltage condition (19). Otherwise, i∗dF W
is solved to obtain the minimum d-current reference absolute
value which meets the voltage condition. It is worth mentioning that DC-Link voltage is considered constant in the flux
weakening algorithm.
imin
bat = 0 A,
Description
imin
= −10 A,
d
imax
= 1 A,
d
tch = 1800 s,
Im = 2 A.
With these parameters, the energy management LMA converges in a maximum of 21 iterations, while a maximum of
17 iterations was obtained for the id control LMA. The system
was simulated for different driving cycles to define the number
of power devices that minimize the cost function. The power
devices configuration submitted to the MVC2024 was: 2 power
modules for the battery power converter, 2 power modules for
the SC power converter, and 9 power modules for the inverter.
In addition, a modified configuration was selected after the
MVC2024 score cycle was revealed to avoid the activation of
the over-temperature protection, by using 3 power modules for
the SC.
Scoring results are presented in Table I for different driving
cycles: the MVC2024 Score Cycle (with the submitted and
with the modified power devices configuration), ARTEMIS
and UDDS (both with the submitted configuration). Results
show that no over-temperature penalty was obtained in any of
the tests and that the final SC voltage variation is less than
31 mV. Regarding percentage, ∆fsoc was about 55% for the
Score Cycle. To provide a comparison, it can be mentioned
that the score obtained with the strategy presented as an example by the MVC for the Score Drive was 443.32. Therefore,
the submitted strategy achieved a 66% improvement in the
cost function.
The results of the transient response for the Score Cycle
with the submitted configuration are shown in Fig. 4. The
obtained EV speed is shown in Fig. 4(a). Also, results show
that the obtained ibat reference is almost always positive,
see Fig. 4(b), while id reference is always negative, see
Fig. 4(c). Moreover, because sufficiently high speeds are not
reached during the entire cycle, the flux weakening strategy
was unnecessary in this test. This is why the id reference
remained around 0, as shown in Fig. 4(c).
Fig. 4(d) shows that the SC is discharged according to the
vehicle speed, and charged during regenerative braking intervals. In addition, near the end of the cycle (at approximately
t = 1900 s), a positive battery current reference is obtained
(see Fig. 4(b)), ensuring a reduced voltage variation ∆fsoc .
The driving cycle presents abrupt braking intervals with
high regenerative energy in 100 s < t < 350 s, see Fig. 4(a).
As a consequence, as shown in Fig. 4(e), there are intervals
where the SC current (black) reaches saturation limits (blue)
near times t = 119.3 s, t = 215.8 s, and t = 314.9 s.
Fig. 4(f) shows that due to the current saturation limits, none
of the SC power modules reaches an over-temperature condition, reaching a maximum temperature of 153.95◦ C. In these
intervals, unavoidable regenerative battery charging penalties
(i.e. Ereg ) were applied resulting in the final 4975 Ws, see
the negative ibat reference intervals in Fig. 4(b). However,
note that a much greater penalty would have been incurred if
an over-temperature had occurred.
Fig. 5 shows the results obtained using 3 power modules
for the SC. The current limits to avoid over-temperature are
increased with the additional power module, see Fig. 5(a).
For this reason, there are no intervals with negative current
references in this test, see Fig. 5(b). Therefore, a better final
score is obtained with this configuration due to the reduced
regenerative battery charging penalties.
V. C ONCLUSIONS
An energy management system and a powertrain losses
management strategy for a battery-supercapacitor hybrid electric vehicle were proposed in this paper. Both strategies are
based on a loss minimization algorithm (LMA) that sets
battery and motor direct current references for each sample
time to obtain an optimal power distribution that minimizes
ibat ref. (A) Speed (km/h)
id ref. (A)
usc (V)
isc;lim (A)
by comparing it with 43 other strategies during the 2024 VTS
MVC, obtaining the best performance for the driving cycle
used for scoring.
100
50
(a)
0
ACKNOWLEDGEMENT
200
This work was supported by Agencia Nacional de Promoción Cientı́fica y Tecnológica, Consejo Nacional de Investigaciones Cientı́ficas y Técnicas (CONICET), and Universidad
Nacional de Rı́o Cuarto (UNRC), Argentina.
100
(b)
0
0
R EFERENCES
-0.2
-0.4
(c)
-0.6
160
(d)
140
120
100
(e)
0
-100
Tsc (/ C)
150
Peak temp.: 153.95°C
100
(f)
50
0
0
200
400
600
800
1000
1200
1400
1600
1800
Time (s)
100
(a)
0
-100
ibat ref. (A)
isc;lim (A)
Fig. 4. Results of submitted configuration. (a) Vehicle speed, (b) ibat
reference, (c) id reference, (d) SC voltage, (e) SC current (black) and SC
current saturation limits (blue), and (f) temperature of module 1 (black) and
module 2 (blue) of the SC power converter.
200
(b)
100
0
0
50
100
150
200
250
300
350
400
Time (s)
Fig. 5. Results of modified configuration. (a) SC current (black) and SC
current saturation limits (blue), and (b) ibat reference
designed cost functions. Also, some protection measures
were required: over-temperature protection and supercapacitor
charge/discharge. The results show that, although both strategies can handle the optimal power distribution, the protection
measures were necessary to avoid large penalties. Moreover,
a flux weakening was not required during the simulated
driving cycles. Finally, the proposed strategy was validated
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