Battery Sizing for Mild P2 HEVs Considering the Battery Pack Thermal Limitations - MDPI

applied
 sciences
Article
Battery Sizing for Mild P2 HEVs Considering the Battery Pack
Thermal Limitations
Gulnora Yakhshilikova 1, * , Ethelbert Ezemobi 1 , Sanjarbek Ruzimov 1,2 and Andrea Tonoli 1

 1 Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Torino, Italy;
 ethelbert.ezemobi@polito.it (E.E.); sanjarbek.ruzimov@polito.it (S.R.); andrea.tonoli@polito.it (A.T.)
 2 Department of Mechanical and Aerospace Engineering, Turin Polytechnic University in Tashkent,
 Tashkent 100095, Uzbekistan
 * Correspondence: gulnora.yakhshilikova@polito.it

 Abstract: Small capacity and passively cooled battery packs are widely used in mild hybrid electric
 vehicles (MHEV). In this regard, continuous usage of electric traction could cause thermal runaway
 of the battery, reducing its life and increasing the risk of fire incidence. Hence, thermal limitations on
 the battery could be implemented in a supervisory controller to avoid such risks. A vast literature on
 the topic shows that the problem of battery thermal runaway is solved by applying active cooling
 or by implementing penalty factors on electric energy utilization for large capacity battery packs.
 However, they do not address the problem in the case of passive cooled, small capacity battery
 packs. In this paper, an experimentally validated electro-thermal model of the battery pack is
 integrated with the hybrid electric vehicle simulator. A supervisory controller using the equivalent
 consumption minimization strategy with, and without, consideration of thermal limitations are
 discussed. The results of a simulation of an MHEV with a 0.9 kWh battery pack showed that the
 thermal limitations of the battery pack caused a 2–3% fuel consumption increase compared to the
 case without such limitations; however, the limitations led to battery temperatures as high as 180 ◦ C.
 


 The same simulation showed that the adoption of a 1.8 kWh battery pack led to a fuel consumption
 

 reduction of 8–13% without thermal implications.
Citation: Yakhshilikova, G.; Ezemobi,
E.; Ruzimov, S.; Tonoli, A. Battery
 Keywords: mild hybrid electric vehicle; battery electro-thermal model; equivalent consumption
Sizing for Mild P2 HEVs Considering
 minimization strategy; fuel consumption; thermal limitation; battery-pack sizing
the Battery Pack Thermal Limitations.
Appl. Sci. 2022, 12, 226. https://
doi.org/10.3390/app12010226

Academic Editor: Dong-Won Kim 1. Introduction
Received: 2 December 2021 Powertrain hybridization seems to be a viable mid-term solution for the reduction of
Accepted: 22 December 2021 vehicle fuel consumption and tailpipe emissions [1–4]. Hybrid Electric Vehicles (HEVs) can
Published: 27 December 2021 be of series, parallel or combined (series-parallel, power-split) configurations [1,2]. Parallel
 configurations offer a cost-effective solution due to: easier integration of the HEV modules
Publisher’s Note: MDPI stays neutral
 in an existing powertrain; the presence of a single electric motor (EM); and a small electric
with regard to jurisdictional claims in
 battery (especially in mild HEVs) [2,3].
published maps and institutional affil-
iations.
 Among parallel HEV architectures, the so-called P2 configuration is gaining the utmost
 attention of vehicle manufacturers as well as researchers due to its scalability and an
 increased number of operating modes [2–4]. As shown in Figure 1, in a P2 configuration,
 the electric machine (EM) is installed on the input shaft of the gearbox after the main clutch
Copyright: © 2021 by the authors. C0. Opening the C0 allows for driving in pure electric as well as for an efficient regeneration
Licensee MDPI, Basel, Switzerland. of the braking energy. By adding the clutch C1, the EM can be used as a starter to crank the
This article is an open access article ICE as well as for gear shifting.
distributed under the terms and Depending on the location of the EM, the P2 configuration can be on-axis or off-axis.
conditions of the Creative Commons The off-axis P2 HEVs have a stage of parallel axis gear, chain or belt drives (Figure 1) with
Attribution (CC BY) license (https:// advantages in terms of the axial size of the powertrain and the potential to have a smaller
creativecommons.org/licenses/by/ electric machine running at higher speed than the ICE.
4.0/).

Appl. Sci. 2022, 12, 226. https://doi.org/10.3390/app12010226 https://www.mdpi.com/journal/applsci

Appl. Sci.
Appl. Sci. 2022,
 2022, 12,
 11, 226
 x FOR PEER REVIEW 22 of
 of 23
 25

 Figure 1.
 Figure 1. Schematic
 Schematic of
 of the
 the P2
 P2 HEV
 HEV powertrain.
 powertrain.

 Owing
 Depending to the onpossibility
 the location of of
 scaling
 the EM, the the
 EMP2 and the battery module,
 configuration P2 is compatible
 can be on-axis or off-axis.
 with
 The off-axis P2 HEVs have a stage of parallel axis gear, chain or belt drives (Figuresmaller
 both mild and plug-in HEV, the mild P2 being characterized by a relatively 1) with
 EM power and
 advantages batteryofcapacity
 in terms the axial[5,6].
 size An analysis
 of the of commercially
 powertrain available
 and the potential toMHEVs shows
 have a smaller
 that mostly
 electric they have
 machine running a battery
 at highercapacity
 speedinthan the range
 the ICE. of 0.5–2 kWh [6,7].
 Fuel
 Owing consumption
 to the possibilityreduction is the main
 of scaling the EM design
 and goal of Mildmodule,
 the battery HEVs, and P2 isthis requires
 compatible
 an
 with both mild and plug-in HEV, the mild P2 being characterized by a relativelytosmaller
 integrated design of the powertrain components as well as the control strategy avoid
 jeopardizing the vehicle’s dynamic performance [8,9].
 EM power and battery capacity [5,6]. An analysis of commercially available MHEVs A wide range of controllers has been
 proposed to this end in the literature. Rule-based supervisory
 shows that mostly they have a battery capacity in the range of 0.5–2 kWh [6,7]. controllers are the simplest to
 implement, however, they have limited performance when compared
 Fuel consumption reduction is the main design goal of Mild HEVs, and this requires to optimization-based
 counterparts
 an integrated[10]. design Optimization-based
 of the powertrain controllers
 components like
 as dynamic
 well as the programming
 control strategy (DP)to[9–11],
 avoid
 equivalent consumption minimization strategy (ECMS)
 jeopardizing the vehicle’s dynamic performance [8,9]. A wide range of controllers has [11–13], and model predictive
 control (MPC) [14]
 been proposed to are
 thismore
 end performant in finding
 in the literature. a globalsupervisory
 Rule-based minimum ofcontrollers
 fuel consumption.
 are the
 However, they need a higher computational effort, require prior knowledge about the
 simplest to implement, however, they have limited performance when compared to opti-
 driving cycle, and hence can mainly be used in offline control strategies [10,13]. Comparable
 mization-based counterparts [10]. Optimization-based controllers like dynamic program-
 results to the ECMS can be obtained by implementing fuzzy logic rules, which can be very
 ming (DP) [9–11], equivalent consumption minimization strategy (ECMS) [11–13], and
 complex in the case of a large number of control variables [15].
 model predictive control (MPC) [14] are more performant in finding a global minimum of
 The ECMS was first proposed by [12] as a real-time controller offering a near-optimal
 fuel consumption. However, they need a higher computational effort, require prior
 solution without prior knowledge of the drive cycle [13,16]. Furthermore, it allows for the
 knowledge about the driving cycle, and hence can mainly be used in offline control strat-
 constraint of various system variables by integrating them in a cost function by means of
 egies [10,13]. Comparable results to the ECMS can be obtained by implementing fuzzy
 penalty functions. The main principle of the ECMS is to minimize the total equivalent fuel
 logic rules, which can be very complex in the case of a large number of control variables
 consumption at each time instant, including the contribution coming from the electrical
 [15].
 energy to or from the battery. The optimization is constrained by the battery state of
 The ECMS was first proposed by [12] as a real-time controller offering a near-optimal
 charge (SOC) and the maximum/minimum torque of the EM and ICE [12,15]. Additionally,
 it is wellwithout
 solution known prior that theknowledge
 battery of is the drive cycle [13,16].
 a safety-critical system Furthermore,
 that might itcauseallows a for
 firethe
 at
 constraint of various system variables by integrating
 high temperatures. Hence, most battery management systems (BMS) monitor the batterythem in a cost function by means of
 penalty functions.
 temperature The main
 in real-time principle
 to operate atof thethan
 less ECMS 55 ◦isCto[16–18].
 minimize the totalofequivalent
 A review fire incidencefuel
 consumption at each time instant,
 associated with electric and HEVs can be found in [19]. including the contribution coming from the electrical
 energyThetocontrol
 or from the battery
 of the battery.temperature
 The optimization can be is constrained by
 accomplished by systems
 the battery state of
 of different
 charge (SOC) and the maximum/minimum torque of the
 complexity, from simple passive cooling (heat is conducted through the battery casing andEM and ICE [12,15]. Addition-
 ally, it isconvection),
 natural well knowntothat activethecooling
 battery [17,18]
 is a safety-critical
 (resorting tosystemair or that
 liquid might cause a fire
 as a coolant, or byat
 high temperatures.
 other means such asHence, using phase most battery
 change management
 materials [20]). systems (BMS) monitor the battery
 temperature
 The influencein real-time
 of battery to operate at less on
 temperature thanthe55performance
 °C [16–18]. Aand review of fire incidence
 fuel consumption of
 associated with electric and HEVs can be found in [19].
 HEV is discussed in [13], considering a 100 Ah capacity Lithium battery. Penalty factors
 The control
 for different ambientof the battery temperature
 temperature and drivecan cyclebe combinations
 accomplished are by systems
 integrated of with
 different
 the
 complexity, from simple passive cooling (heat is conducted
 cost function of the ECMS supervisor. A battery aging semi-empirical model is taken through the battery casing
 into
 and natural
 account alongconvection), to active cooling
 with its temperature [17,18]showing
 dynamics, (resorting to air
 that cold orambient
 liquid astemperature
 a coolant, or
 by other
 causes means such
 a frequent charge as using phase change
 and discharge of thematerials
 battery due [20]).
 to the battery capacity reduction

Appl. Sci. 2022, 12, 226 3 of 23

 in cold ambient temperatures. The limitation of the electric traction due to high battery
 temperatures is not considered in the work [13].
 Padovani et al. has studied how battery aging is affected by high or low temperatures,
 and high SOC [21]. A penalty for using the battery at high temperatures is included in the
 cost function. Considering a 7 kWh lithium-ion battery, an ambient temperature of 15 ◦ C
 running on an Artemis drive cycle, the battery temperature does not exceed 35 ◦ C. The
 lower operating temperatures in this work can be attributed to the large battery size.
 Sarvaiya et al. [22] compared different control strategies incorporating the battery
 ageing model in the cost function. Considering the EPA driving cycle, and a pure electric
 vehicle with a relatively large 9 kWh lithium-ion battery, high temperatures are not an issue,
 with the temperature reaching 32 ◦ C from a 30 ◦ C ambient temperature.
 An accurate electro-thermal model of the battery pack is needed to study the influence
 of the battery temperature in HEV. Battery heat generation induced by the electrical current
 can be divided into irreversible and reversible components [23,24]. The former is related to
 the Joule and polarization effects due to the current flowing through the internal resistance
 and charge transfer. The latter is due to the entropy change, which is related to the
 temperature dependence of the open circuit voltage (OCV). Barcellona and Piegari in [25]
 propose a model that can predict the thermal behaviour of a pouch lithium-ion battery
 cell based on its current and ambient conditions. The model only takes the effect of
 the OCV and internal resistance into account. However, the resistive-capacitive (RC)
 parallel branches are not included in the model of the battery, as the thermal time constant
 greatly outweighs the electrical one. Madani et al. in [26] review the determination of
 thermal parameters of a single cell, such as internal resistance, specific heat capacity,
 entropic heat coefficient, and thermal conductivity. These parameters are then used for the
 design of a suitable thermal management system. A lumped-parameter thermal model
 of a cylindrical LiFePO4/graphite lithium-ion battery is developed in [27] to compute the
 internal temperature.
 Thermal management systems with active heating and cooling can be adopted for
 controlling the temperature in the battery pack [28–30]; however, the additional cost and
 complexity would not be affordable, especially in 48 V micro or mild hybrid electric vehicles.
 Conversely, 48 V micro or mild hybrids are potentially characterized by high-temperature
 fluctuations due to the large C-rate reached in boost and recuperation due to the small
 battery capacity.
 The influence of battery temperature limitations on the fuel consumption of mild HEVs
 and the study of battery capacity, above which temperature does not represent a criticality,
 seems to be still largely unattended in the vast literature on the topic. Additionally, most
 of the literature that addresses energy management problems has adopted a simplified
 analytical model to estimate battery SOC and temperature. Such models can only be
 accurate under limited scenarios and hence could impose a limitation on model accuracy
 in a wider range of applications.
 Hence, the main contribution of the present work is to address the following points:
 (a) to extend the existing control strategies to include the thermal limitations in the case
 of a 48 V P2 Mild HEV with passive cooling; (b) to validate the electro-thermal model of
 the battery by means of existing experimental data; and (c) to investigate the influence of
 the battery capacity on reaching thermal limitations and determine the minimum battery
 capacity to avoid thermal runaway.
 The paper is organized as follows: In Section 2, the backward model of the con-
 ventional vehicle and P2 HEV are developed. The model of the conventional vehicle is
 validated using the experimental results reported in [31,32]. Furthermore, the electro-
 thermal model of the battery and its experimental validation are presented in this section.
 Section 3 presents the supervisory controller based on ECMS considering the thermal
 limitations of the battery. Section 4 reports the results of the simulation. Finally, Section 5
 summarizes the main findings of the paper.

of the battery. Section 4 reports the results of the simulation. Finally, Section 5 summarizes
 the main findings of the paper.

 2. Vehicle
Appl. Sci. 2022, 12, 226 Performance Modelling 4 of 23

 The vehicle model shown in Figure 2 follows the backward approach widely adopted
 in the literature, especially for the design of the supervisory controller and the HEV com-
 2. Vehicle Performance Modelling
 ponents [11,33,34]. The detailed description of each subsystem and the underlying equa-
 The vehicle model shown in Figure 2 follows the backward approach widely adopted
 tions are given in theinfollowing
 the literature,table withfor
 especially reference
 the designto
 of the HEV datacontroller
 the supervisory summarized
 and the in
 HEVTable
 compo-
 1. nents [11,33,34]. The detailed description of each subsystem and the underlying equations are
 given in the following table with reference to the HEV data summarized in Table 1.

 Figure
 Figure 2. The scheme of 2. The scheme
 backward of backward simulator.
 simulator.
 Table 1. Mazda CX9 2016 [31].
 Table 1. Mazda CX9 2016 [31].
 Parameter Unit Variable Value
 Parameter Unit VariableVehicle Value
 Nominal mass kg M 2041
 Frontal Area
 Vehicle m2 Af 2.4207
 Nominal mass kg
 Aerodynamic drag coefficient - Cx 2041 0.316
 Frontal Area Gear ratios m 2 - igb
 1st—3.49; 2nd—1.99; 3rd—1.45;
 2.4207
 4th—1; 5th—0.71; 6th—0.6
 Aerodynamic drag coefficient Final Drive Ratio- - ifinal 0.316 4.41
 Tire size - P255/50VR20
 1st—3.49; 2nd—1.99; 3rd—1.45;
 Gear ratios Passenger Capacity- 7
 Internal Combustion4th—1;Engine 5th—0.71; 6th—0.6
 SAE Net Torque @ rpm Nm 310 @ 2000
 Final Drive Ratio Fuel System -
 - 4.41 Direct Injection
 Gasoline
 Tire size SAE Net power @ rpm - kW P255/50VR20 169 @ 5000
 Displacement L 2.5
 Passenger Capacity Electric Motor 7
 Internal
 Maximum Combustion Engine
 power kW 27
 Maximum torque @ rpm Nm Tem.max 65 @ 4000
 SAE Net Torque @ rpm Nm (Sanyo NCR18650GA Lithium-ion310
 Battery cell)@ 2000
 Fuel System Nominal voltage - V Gasoline Direct Injection 3.6
 Nominal capacity Ah Ctot 3.0
 SAE Net power @ rpm Minimum battery kW SOC % SOClow 169 @ 500060
 Displacement Maximum battery SOC L % SOChigh 2.5 80
 Operating temperature ◦C −20~60
 Electric Motor ◦ C
 Ambient temperature θ amb 20
 Maximum power Battery Pack Configurations
 kW - 14s6p
 27 and 14s12p

 Maximum torque @ rpm Nm . 65 @ 4000
 2.1. Longitudinal Vehicle Dynamics
 Battery (Sanyo NCR18650GA Lithium-ion cell)
 In this subsystem, the required traction force to overcome the resisting forces (i.e., aerod-
 Nominal voltage
 ynamic and rolling resistance V forces) is calculated as: 3.6
 Nominal capacity Ah 1
 3.0
 Minimum battery SOC Fw = %M · dv/dt + M
 SOClow· g · f r + · ρ air · C x · A f · v2
 60 (1)
 2
 Maximum battery
 where SOCM is the vehicle mass; % v andSOC dv/dthigh
 are longitudinal speed80 and acceleration; f r is
 Operating temperature
 coefficient of rolling °C
 resistance; C x is aerodynamic drag −20~60
 coefficient; ρ air is air density; A f is
 vehicle frontal area; FW is°C
 Ambient temperature 
 the longitudinal force on the wheels. The 20resisting force due to
 road inclination is not considered in the analysis.

Appl. Sci. 2022, 12, 226 5 of 23

 The total torque required on the wheels TW , includes the drag torque in the axle
 bearings Tloss and torque due to inertia of the wheels JW , they are added to the torque of
 the traction force on wheels FW :

 dv 1
 Tw = Fw · Rw + 4 · Jw · · + Tloss . (2)
 dt Rw

 The wheel rolling radius RW of the tire is calculated as:

 Drim · 25.4
  
 AR
 Rw = ε · +W · . (3)
 2 100

 The coefficient ε takes into account the tire deflection, which for radial tires is in
 the range ε = 0.92 − 0.98 [35]. The nominal wheel radius can be obtained from the tire
 markings, i.e., the rim diameter Drim , nominal width W and aspect ratio AR.
 Moreover, the angular speed of the wheel shaft is then found from the rolling radius
 and the speed v:
 v
 ωw = . (4)
 Rw
 2.2. Gearbox and Gearshift Logic
 The gearbox model converts the wheel torque and speed to the corresponding ones at
 the input of the gearbox. A simple vehicle speed-based gearshift strategy is implemented
 in the model, accounting for the constraint of ICE maximum speed. Gearshift speeds
Appl. Sci. 2022, 11, x FOR PEER REVIEW 6 of are
 25
 defined by analyzing the gearshift experimental data from Argon National Laboratory
 (ANL) Figure 3 shows the gearshift logic. To avoid frequent gear shifting, upshifts and
 downshifts are performed with a hysteresis that varies with the engaged gear.
 Gear

 Speeddependent
 Figure3.3.Speed
 Figure dependentgearshift
 gearshiftlogic.
 logic.

 Therequired
 The torque T
 required torque gb and
 andangular
 angularspeed speedω gb at at
 thethe
 gearbox
 gearbox input can can
 input be computed
 be com-
 from the final gear ratio i and the gear ratio of the gearbox
 puted from the final gear ratio and the gear ratio of the gearbox , as:
 f i gb , as:
  T
 ⎧ = Tgb = i f ·η f ·axle i f Taxle
 i gb ·ηgb >> 0 0
 ⎪ ⋅ ⋅ T ⋅ ·η ·η (5)
  T = axle f gb i f T ≤0 (5)
 ⎨ = gb ⋅ ⋅ 
 i · i axle
 ⎪
 f gb
 ≤0
 ⎩ ⋅ 
 where the efficiencies of the final gear and the gearbox are considered as = = 0.98.
 = ⋅ ⋅ (6)
 In a conventional vehicle and are the ICE torque and speed at the gearbox.

Appl. Sci. 2022, 12, 226 6 of 23

 where the efficiencies of the final gear and the gearbox are considered as η f = ηgb = 0.98.

 ω gb = ωw · i f · i gb (6)

 In a conventional vehicle Tgb and ω gb are the ICE torque and speed at the gearbox.
 When considering a HEV, the supervisory controller splits the same torque between the
 ICE and the EM depending on the established rules.

 2.3. Internal Combustion Engine
 The fuel consumption map of Mazda CX9 2016 ICE used in the simulation is shown in
 Figure 4 as obtained from experimental data [32]. The adoption of a static map typically
 leads to an estimate of the fuel consumption that is usually lower than what is measured in
 dynamic conditions by means of a chassis dynamometer [36]. However, this difference is
 in the range of 1–4% depending on the driving cycle [36], with more aggressive driving
Appl. Sci. 2022, 11, x FOR PEER REVIEW 7 of 25
 cycles being associated with the upper bound of this range. In this paper, the extra fuel
 consumption due to transient operation is neglected.
 450 20
 7 19
 18

 12 1
 6
 17

 1
 400 10 16
 9 15
 5

 20
 350 8 1
 13 4 19
 12 18
 7 17
 11 16
 4 10
 300 6 9
 15

 5 8 13
 3 12
 250 11
 7 10
 4 6 9
 200
 2 5
 3 7
 150 6
 4
 5
 100 1 2 3
 4

 50 2 3
 1
 2
 0 1
 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
 ice
 [rpm]

 Figure 4. Fuel consumption map of Mazda CX9 2016 internal combustion engine obtained in steady
 state conditions.
 state conditions.

 2.4. Electric Motor
 2.4. Electric Motor
 For
 For aa given
 givenangular
 angularspeed
 speedωem andand
 a mechanical
 a mechanical torque request
 torque request EM
 Tem , the , thesubsystem
 EM sub-
 evaluates the electric power absorbed from the battery in
 system evaluates the electric power absorbed from the battery in dischargedischarge phases P phases
 bat.dchg or
 released
 . to it during the charging phases
 or released to it during the chargingP . This electric
 bat.chgphases . power is computed by means
 . This electric power is com-
 of the static
 puted efficiency
 by means of themap
 staticofefficiency
 the EM (Figure
 map of5):the EM (Figure 5):
 -- in discharging
 in discharging mode:
 mode:

 Pem
 . ==
 Pbat.dchg (7)
 
 ηem

 -- in charging
 in charging mode:
 mode:

 . ==Pem
 Pbat.chg · η⋅ gen
 (8)
 (8)
 where the mechanical power is calculated as
 = ⋅ (9)

80

 0.
 0 .7
 EFF

 81
 5
 60 EM
 4 GEN
 0. 8 00.7
 .728
Appl. Sci. 2022,40
 12, 226 00.8 0.7
 .814 5 7 of 23
 00.72

 1

 7
 0.8

 0.8
 .78

 0 .8
 0.97 0.75
 0.81
 0.84
 20

 4
 0. 8
 where0the
Appl. Sci. 2022, 11, x FOR PEER REVIEW
 0.84
 .9 0.9
 mechanical 0.87
 power Pem is calculated
 0.87 as 0.8
 4
 8 of 25
 0.87
 0
 0.84 0.87 Pem = Tem · ωem (9)
 0.9 0.87 0.8
 0.9 0.87 4
 80
 0.8

 -20 0.84
 0.81
 0.97

 0.
 4

 0 .7
 0.75 EFF

 81
 0.8 .7 8
 00.72
 0.8

 5
 0.8

 60 EM
 08.814.75
 7
 1

 -40 .8 4 0. 0 00.7
 GEN
 0 .728
 0.8 40 .728
 4 00.7 00.8 0.7
 .814 5
 00.72

 1

 7
 -60 0.8
 0.8 .78

 0 .8
 0.97 0.75
 0.81
 0.84
 20 4
 0. 8
 5

 0.9 0.87 4
 0.8
 81
 0.7

 0.9 0.87
 0.84 0.87
 0.

 -80 0
 0 2000 4000 6000 0.84 8000 10,000
 0.87 12,000 14,000 16,000 18,000
 0.9 0.87 0
 0.9 0.87 .84
 [rpm]
 0.8

 -20 em 0.84
 0.81
 0.97
 4

 0.75
 0.8 .7 8
 00.72
 0.8
 0.8

 .814
 7

 00.8 0.75
 1

 Figure 5. Static efficiency -40
 map of the electric motor and
 78
 maximum torque characteristic lines.
 0. 8 . 2
 4 00.7
 -60
 2.5. Battery Performance and Electro-Thermal Model
 5
 81
 0.7
 0.

 -80
 The essence of incorporating a battery
 0 2000 4000 6000 electro-thermal
 8000 10,000 12,000 model in the18,000
 14,000 16,000 vehicle model
 (Figure 2) is to provide information to the ECMSemcontroller [rpm] for efficient fuel consumption
 minimization whileFigurepreventing thermal runaway. At each time instant , the adopted
 Figure 5.5.Static
 Staticefficiency
 efficiencymap mapof ofthe
 theelectric
 electricmotor
 motorand
 andmaximum
 maximumtorque torquecharacteristic
 characteristiclines.
 lines.
 ECMS controller requires information of the state of charge ( ), the temperature ,
 and the rate of the2.5.
 2.5. Battery
 Batteryof
 change Performance
 Performance and
 the temperatureandElectro-Thermal . This
 Electro-Thermal Model
 Model
 information is the output of the
 The essence of incorporating a battery electro-thermal
 battery pack electro-thermalThe essence model of incorporating
 that takes athe battery request model
 electro-thermal
 power 
 model in
 in the
 as the vehicle
 vehicle
 input model
 model
 (from
 (Figure 2) is to provide information to the ECMS controller for
 (Figure 2) is to provide information to the ECMS controller for efficient fuel consumption efficient fuel consumption
 Equations (8) and (9). Considering the
 minimization 14s6pthermal
 battery configuration, timethe batteryk, the consists of
 minimizationwhile whilepreventing
 preventing thermal runaway.
 runaway.At each
 At each instant
 time instant adopted ECMS
 , the adopted
 a series module pack (SMP)
 controller
 ECMS composed
 requires
 controller information
 requires of a series
 of the state
 information of fourteen
 of charge SOC (14)(k)modules.
 , the temperature
 . of the state of charge ( ), the temperature ,
 Each θ,ofand thethe
 modules consists ofratesixof(6)
 and thetheparallel
 change
 rate of the cells,
 of change otherwise
 the temperature θ.known
 of the temperature as
 This informationparallel
 . This is thecell
 output
 information modules
 isofthe (PCM).
 theoutput
 battery pack
 of the
 electro-thermal
 The pack modelbattery model
 pack electro-thermal
 is developed that takes
 from the model the power request
 that takes the
 electro-thermal P as input
 batpowerof
 model (from
 request
 a singleEquations
 cell (8)
 as input and
 accord- (9).
 (from
 Considering
 Equations (8)the 14s6p battery configuration, the battery consists of the a series module pack
 ing to the work of [37].
 (SMP) First, anand (9). Considering
 enhanced the 14s6p battery
 self-correcting (ESC)configuration,
 single-cell modelbattery
 is consists
 devel- of
 a series module pack (SMP) composed of a series of fourteen (14) modules. Each of six
 composed of a series of fourteen (14) modules. Each of the modules consists of the
 oped to form the building
 (6) block
 parallel
 modules cells,for
 consists ofthe
 otherwise PCM
 six (6) known thatas
 parallel isparallel
 cells, scaled tomodules
 cell
 otherwise obtain
 known as the
 (PCM). SMP.cell
 parallel The resulting
 modules (PCM).
 model is validated withThe an pack model
 experimental is developed
 datasetfrom the
 at electro-thermal
 an ambient model of
 environmental
 The pack model is developed from the electro-thermal model of a single cell accord- a single cell according
 tempera- to
 the work of [37]. First, an enhanced self-correcting (ESC) single-cell
 ing to the work of [37]. First, an enhanced self-correcting (ESC) single-cell model is devel- model is developed to
 ture of 20 °C.
 form
 opedthe building block for blockthe PCM thatPCM is scaled
 that to obtain totheobtain
 SMP. theTheSMP.
 resulting model is
 takestointo
 The cell modelvalidated form
 with
 the building
 consideration
 an experimental
 for the
 both
 dataset the
 at anstatic
 ambient
 is scaled
 and the dynamic
 environmental voltage
 temperature
 The resulting
 ofchar-
 20 ◦ C.
 model is validated with an experimental dataset at an ambient environmental tempera-
 acteristics as shownturein The
 Figure
 of 20cell 6. A detailed
 °C. model takes intodescription
 considerationof each
 both the subsystem
 static and theofdynamic the batteryvoltage
 characteristics
 pack model is given below. as shown in Figure 6. A detailed description of each subsystem of the battery
 The cell model takes into consideration both the static and the dynamic voltage char-
 pack model is given below.
 acteristics as shown in Figure 6. A detailed description of each subsystem of the battery
 pack model is given below.

 Figure 6. Schematic component of the battery pack electro-thermal model. The variables in dotted
 Figure 6. Schematic component
 Figureare
 blocks theof the component
 6. Schematic
 inputs battery
 and pack
 outputsof
 totheelectro-thermal
 thebattery
 batterypack model. The
 electro-thermal
 model. variables
 model. in dotted
 The variables in dotted
 blocks are the inputs and outputs
 blocks are the inputs and outputs to the battery model. to the battery model.
 The static voltage computed from the OCV block is integrated with the dynamic
 The
 voltage static
 from thevoltage
 dynamiccomputed
 process from the OCV
 to obtain block
 an ESC cellismodel.
 integrated with the dynamic volt-
 The static voltage
 age computed fromprocess
 from the dynamic the OCV block
 to obtain anis integrated
 ESC cell model.with the dynamic volt-
 age from the dynamic process to obtain an ESC cell model.

Appl. Sci. 2022, 11, x FOR PEER REVIEW 9 of 25

Appl. Sci. 2022, 12, 226 8 of 23

 2.5.1. Static Component
 2.5.1.The
 Static Component
 static component of the model represents the open-circuit voltage, which is the
 measured cell voltage
 The static componentwhen of thethe
 cellmodel
 is subject to a zero-load
 represents condition.voltage,
 the open-circuit The OCV is ap-is
 which
 proximated as a function of only SOC for the temperature operating condition
 the measured cell voltage when the cell is subject to a zero-load condition. The OCV is considered
 in this work. For
 approximated asthe cell under
 a function consideration,
 of only SOC for thethe OCV is obtained
 temperature from
 operating the cell considered
 condition datasheet
 of
 inSanyo NCRFor
 this work. 18650-618 lithium-ion
 the cell under cell [38] that
 consideration, has a is
 the OCV rated capacity
 obtained fromofthe
 3200 mAh.
 cell Figure
 datasheet of
 7Sanyo
 showsNCR the voltage variation
 18650-618 acrosscell
 lithium-ion SOC[38]under open
 that has and closed-circuit
 a rated conditions.
 capacity of 3200 mAh. Figure 7
 shows the voltage variation across SOC under open and closed-circuit conditions.

 OCVand
 Figure7.7.OCV
 Figure andclosed-circuit
 closed-circuitvoltage
 voltage(CCV)
 (CCV)across
 acrossSOC
 SOCin
 incharge
 chargeand
 and discharge
 discharge phases.
 phases. The
 The
 OCV
 OCVfrom
 fromthe
 thedatasheet
 datasheetisisbetween
 betweenthe
 themeasured
 measuredterminal
 terminalvoltage
 voltagein
 incharge
 chargeand
 anddischarge
 dischargephases.
 phases.

 Themiddle
 The middlebluebluecurve
 curveshows
 showsthe theOCV
 OCVas asaafunction
 functionof ofSOC,
 SOC,as asacquired
 acquiredfromfromthe the
 datasheet. The red curve is the closed-circuit voltage at a constant charge
 datasheet. The red curve is the closed-circuit voltage at a constant charge load of 1.675 A.load of 1.675 A.
 Theyellow
 The yellowcurve
 curveisisthe
 theclosed-circuit
 closed-circuitvoltage
 voltageatataaconstant
 constantdischarge
 dischargeloadloadofof0.66
 0.66A.A.ItItcan
 can
 beseen
 be seenthat
 thatthe
 theOCVOCVtaken
 takenfrom
 fromthethedatasheet
 datasheetapproximates
 approximatesthe thetrue
 trueOCV
 OCVatatthe
 themean
 meanof of
 the closed-circuit voltages of the charge and discharge phases. The larger
 the closed-circuit voltages of the charge and discharge phases. The larger deviation of the deviation of the
 chargephase
 charge phaseresults
 resultsfrom
 fromthe
 therelative
 relative higher
 higher load
 load with
 with respect
 respect toto the
 the discharge
 discharge phase.
 phase.
 The SOC is computed through coulomb counting and it is analogous
 The SOC is computed through coulomb counting and it is analogous to a fuel gauge to a fuel gauge
 that expresses the amount of charge contained in a cell. The expression
 that expresses the amount of charge contained in a cell. The expression of SOC is shown of SOC is shown in
 Equation (10) for a given time step
 in Equation (10) for a given time step . k.

 η i ( ) 
 (k)k
 ( 
 SOC (k ++11)
 ) ==SOC
 ( ) −
 (k) − (10)
 (10)
 C tot

 where i ( k) is
 where is current
 current input
 input to
 to the
 the model—positive
 model—positiveat discharge, Ctot (Ah
 atdischarge, Ah)isisthe
 thetotal
 totalre-
 re-
 leasable capacity in a complete cycle and is the battery coulombic efficiency.
 leasable capacity in a complete cycle and η is the battery coulombic efficiency. SOC (k) is ( ) is
 the
 theSOC
 SOCatatkthkthtime
 timestep.
 step.Only
 Onlyaapercentage
 percentageofofcurrent
 currentthat
 thatisisapplied
 appliedtotothe
 thecell
 cellcontributes
 contributes
 to increasing the SOC in the charging phase. Hence, SOC is penalized with η[30]
 to increasing the SOC in the charging phase. Hence, SOC is penalized with [30]in
 inthe
 the
 charge
 chargephase.
 phase.

 2.5.2.Dynamic
 2.5.2. DynamicComponent
 Component
 Thedynamic
 The dynamiccomponent
 componentof ofthe
 thecell
 cellmodel
 modelaccounts
 accountsforforthe
 thevoltage
 voltagelosses,
 losses,including
 including
 jouleloss,
 joule loss, diffusion
 diffusion loss
 loss due
 duetotomass
 masstransfer,
 transfer,activation
 activationloss due
 loss to charge
 due to chargetransfer andand
 transfer loss
 duedue
 loss to hysteresis. The output
 to hysteresis. of theofdynamic
 The output modelmodel
 the dynamic is the predicted closed-circuit
 is the predicted voltage
 closed-circuit
 that accounts
 voltage for thesefor
 that accounts losses.
 theseThe model
 losses. Theismodel
 developed from an RC
 is developed fromcircuit
 an RC with a single
 circuit withRCa
 branch in series with a resistive branch [37] as shown in Figure
 single RC branch in series with a resistive branch [37] as shown in Figure 8. 8.

Appl.
Appl.Sci. 2022,12,
 Sci.2022, 11,226
 x FOR PEER REVIEW 9 of
 10 of23
 25

 Figure 8.8. Equivalent
 Figure Equivalent circuit
 circuit that
 that describes
 describes the
 the dynamic
 dynamic model
 model designed
 designed for
 for terminal
 terminal voltage
 voltage and
 and
 voltage loss prediction [37].
 voltage loss prediction [37].

 Thehyst
 The hystcomponent
 componentin in
 thethe circuit
 circuit accounts
 accounts forhysteretic
 for the the hysteretic contribution
 contribution of the
 of the losses.
 losses.
 The The estimated
 estimated dynamicdynamic
 voltage voltage is computed
 v̌ is computed as. as.

 v̌(k ) = =
 OCV (SOC (k ))) ++vloss
 ( (k) (11)
 (11)
 k ==Mh
 ℎk ++M s k −− R i k − R
 − 
 vloss ( ) ( ) 0 ( ) ∑ j j Rj ( ) 0 i(k) (12)
 (12)

 wherevloss
 where is isthethe voltage
 voltage loss, M0 is the
 loss, is the instantaneous
 instantaneous hysteresis
 hysteresis voltage;
 voltage; isdynamic
 M is the the dy-
 hysteresis magnitude;
 namic hysteresis R0 is the instantaneous
 magnitude; series iresistor;
 series resistor;
 is the instantaneous resistor
 Rj ( k ) is the is the diffusion
 resistor
 diffusionRcurrent;
 current; is the
 j is the parallel branch
 parallel resistance; h(k ) is theℎhysteresis
 branch resistance; is the hysteresis k ) is sign of
 voltage; s(voltage; 
 current
 is sign ofinput. It is input.
 current 1 for positive
 It is 1 forcurrent
 positiveinput, −1 for
 current negative
 input, −1 forinput and zero
 negative otherwise.
 input and zero
 The first two components at the right-hand side of Equation (12) model the instanta-
 otherwise.
 neousThe andfirst
 thetwo
 dynamic hysteresis
 components at thevoltage.
 right-hand The third
 side of component
 Equation (12) models
 modelthethe
 RCinstanta-
 branch
 of the circuit. The subscript j represents the number of branches.
 neous and the dynamic hysteresis voltage. The third component models the RC branch of The RC branch models
 the
 thelosses
 circuit.dueThetosubscript
 mass transport and charge
 j represents transfer.
 the number of The diffusion-resistor
 branches. The RC branch current i Rj that
 models the
 passes
 losses through
 due to mass the RC branchand
 transport is computed from the
 charge transfer. time
 The constant of the RC
 diffusion-resistor branch.
 current The that
 fourth
 passescomponent
 through theisRC thebranch
 series resistive
 is computed loss that
 frommodels
 the time theconstant
 joule losses.
 of the RC branch. The
 The parameters of the model appear linearly
 fourth component is the series resistive loss that models the joule according Equation (13). vloss is
 to losses.
 computed for the N data
 The parameters ofpoints of the appear
 the model experimentallinearly data and the parameters,
 according to Equation M,(13).
 M0 , R j , Ris
 0
 are computed by least square approximation.
 computed for the data points of the experimental data and the parameters,
 , , , are computed by least square approximation.
 
 T (1)
 
 vloss (1)
  h (1) s (1) − i R − i (1)  
 j M
  vloss (2)  1
  ℎ 1 1 − 1
 h⎡(2) s(2) −i R j (2) −−i ( 2)1 ⎤ 
 T 
 M 
 0 
 = ⎢ ℎ 2 2 − 2 ⎥ (13)
    
 ..  2 = . − 2   Rj 
 .
    
 . ⎢ . ⎥ (13)
 ⋮
 
 ⎢ T⋮ ( N ) ⎥ R0
  
 vloss ( N ) h ( N ) s ( N ) − i
 ⎣ℎ − 
 Rj −−i ( N ) ⎦ 

 By
 By least
 least square approximation,X == A \\ Y.
 squareapproximation, .
 Table
 Table2 2reports thethe
 reports corresponding values
 corresponding of theof
 values electric and theand
 the electric thermal model parameters.
 the thermal model pa-
 rameters.
 Table 2. List of electrical and thermal model parameters with the estimated values.
 Table 2. List of electrical and thermal model parameters with the estimated values.
 Variable Units Value
 Dynamic hysteresis Variable
 magnitude, M - Units Value
 0.017
 Instantaneous
 Dynamic hysteresis
 hysteresisheight, M0
 magnitude, M - - negligible
 0.017
 Electric Model
 Instantaneous series resistor, R0
 Instantaneous hysteresis height, Ohms - 0.024
 negligible
 Electric Model Parallel branch resistance, R j Ohm 0.018
 Instantaneous series resistor, Ohms 0.024
 Specific heat capacity, c p J/kg. K 1200
 Parallel branch resistance, Ohm 0.018
 Thermal Model Thermal resistance, Rconv K/W 14.6
 Specific heat capacity,
 Cell mass, mcell kg / . 48.5 ×1200
 10−3
 Thermal Model Thermal resistance, / 14.6
 Cell mass, kg 48.5 × 10−3

Appl. Sci. 2022, 11, x FOR PEER REVIEW 11 of 25
Appl. Sci. 2022, 12, 226 10 of 23

 The dynamic current profile used for data collection during the experiment is applied
 The dynamic current profile used for data collection during the experiment is applied
 as input to the model to compute according to Equation (12). This profile consists of
 as input to the model to compute vloss according to Equation (12). This profile consists of
 a sequence of random charge and discharge current values applied in the range of −4.5 A
 a sequence of random charge and discharge current values applied in the range of −4.5 A
 and +4.5 A. The current profile and are shown in Figure 9.
 and +4.5 A. The current profile and vloss are shown in Figure 9.

 (a)

 (b)

 Figure
 Figure9.9. Voltage loses v loss obtained
 obtainedfor
 for an
 an applied dynamic current
 applied dynamic currentprofile.
 profile.(a)
 (a)dynamic
 dynamic current
 current
 profile.(b)
 profile. (b)voltage
 voltage losses.
 losses.

 2.5.3.
 2.5.3. The
 The Battery
 Battery Thermal
 Thermal Model
 Model
 The
 The thermal model is developed
 thermal model is developed fromfrom contributions
 contributions ofof the
 the voltage
 voltagelosses
 lossesthat
 thatare
 are
 computed from the dynamic voltage model of Equation (12). Based on
 computed from the dynamic voltage model of Equation (12). Based on lumped parameter lumped parameter
 assumption
 assumption [39],
 [39], the
 the thermal
 thermal model
 model isis designed
 designed based
 basedon onheat
 heattransfer
 transferbybyconvection
 convectionandand
 by neglecting the conduction heat transfer component according to
 by neglecting the conduction heat transfer component according to Equation (14). TheEquation (14). The
 discrete-time
 discrete-time battery
 batterysurface
 surfacetemperature
 temperature θsur f is computed considering
 is computed the power
 considering losses,
 the power
 Plosses,
 loss that is derived from the voltage losses, as the heat source.
 that is derived from the voltage losses, as the heat source.
 Ts θsur f (k( )) − θ amb
  
 θsur f (k + ( 
 1) +
 = 1) (k) +( ) + ⋅ Ploss (k) −
 =f 
 θsur ( ) (14)
 (14)
 c p · mcell Rconv
 is the battery specific heat capacity; is the cell mass; is the power is
 c p is the battery specific heat capacity; mcell is the cell mass; Ploss is the power is
 computed based on the voltage losses; is the ambient temperature; is the sam-
 computed based on the voltage losses; θ amb is the ambient temperature; Ts is the sampling
 pling time; is the thermal resistance by convection. The thermal parameters are re-
 time; Rconv is the thermal resistance by convection. The thermal parameters are reported
 ported in Table 2.
 in Table 2.

 3.3. Development
 Development of of Supervisory
 Supervisory Control
 Control Strategy
 Strategy
 Thesupervisory
 The supervisorycontrol
 controlstrategy
 strategybased
 basedononthe
 theEquivalent
 EquivalentConsumption
 Consumption Minimiza-
 Minimization
 tion Strategy
 Strategy optimallyoptimally splits
 splits the the required
 required traction
 traction torque Tgbtorque
 between thebetween the traction
 traction sources while
 sources while minimizing the objective function. In this section, three types
 minimizing the objective function. In this section, three types of ECMS are demonstrated. of ECMS are
 demonstrated. The first type is the ECMS without considering the battery
 The first type is the ECMS without considering the battery thermal limitations. The thermal limita-
 tions. The
 second typesecond type iswith
 is an ECMS an ECMS withswitching
 an on/off an on/off switching of the
 of the electric electric
 traction traction
 when when
 the battery
 the battery temperature threshold is reached. Finally, in the third type,
 temperature threshold is reached. Finally, in the third type, the thermal limitations the thermal limi-
 are
 tations are integrated into the penalty functions on the temperature and
 integrated into the penalty functions on the temperature and the temperature dynamics arethe temperature
 dynamics
 set are set infunction.
 in the objective the objective function.

 3.1. ECMS
 3.1. ECMS Control
 Control Strategy without Thermal Limitations
 Limitations
 To achieve
 To achieve anan effective
 effective reduction
 reduction in fuel usage,
 usage, the
 the contribution
 contributionof ofelectric
 electricmotor
 motor
 power should
 power should be
 be defined
 defined in such a way that
 that the
 the engine
 engine operates
 operatesininits
 itshigher
 higherefficiency
 efficiency
 zone. For
 zone. For this
 this reason, the ECMS was applied
 applied toto the
 theMHEV
 MHEVbackward
 backwardmodel
 modeltotodetermine
 determine
 thepower
 the power split
 split ratio
 ratio between the engine and
 and the
 theEM.EM.From
 Fromthe
 theconfiguration
 configurationofofthe
 theMHEV
 MHEV

system, the rotational speeds of the power sources are set by vehicle velocity. Hence, the
 ECMS controller splits only the torque between the engine and EM.
Appl. Sci. 2022, 12, 226 Objective function: 11 of 23

 The objective function for the ECMS is overall equivalent fuel consumption ( )
 which is evaluated as a sum of engine fuel consumption and equivalent fuel con-
 system, theof
 sumption rotational speeds
 the electric of theusage
 power power sources
 forare setpower
 the by vehicle
 drawnvelocity.
 fromHence, the
 the battery 
 ECMS controller splits only the torque between the engine and EM.
 [10,12]:
 Objective function:
 The objective function for the ECMS ( ) equivalent
 = is overall + .
 ( fuel
 ) consumption (Jecms ) (15)
 which is evaluated as a sum of engine fuel consumption mice and equivalent fuel consump-
 the( 
 tion of ) equivalent
 electric
 .
 power usagefuel
 meqvconsumption of EMfrom
 for the power drawn can the
 be battery
 computed as the fuel con-
 Pbat [10,12]:
 sumption of the ICE to provide the. same mechanical
 . power generated by electric motor
 [12]: Jecms = mice ( Pice ) + meqv ( Pbat ) (15)
 .
 meqv ( Pbat ) equivalent ( consumption
 fuel ) = ( of, ) ⋅ be computed
 EM can = ⋅ as the
 ⋅ fuel consump- (16)
 tion of the ICE to provide the same mechanical power generated by electric motor [12]:
 is the battery equivalent fuel consumption factor, depending on battery dis-
 .
 charging ( > 0)mor ( ( Tem 0)
 ing (Pbat > 0) or charging (Pbat 0) ( = 0) (17)
  LHV
 
 
 seqv = ⎪0 1
 ⋅ ⋅( Pbat = ⋅ 0) ( < 0) (17)
  ⎩ ⋅· η · η · η
 
 1
 ( P < 0)
 
 LHV ·ηice em inv bat bat
 where is the lower heating value of the fuel, is the average efficiency of the ICE,
 where is LHV is the lower heating value of the fuel, ηice is the average efficiency of the ICE,
 the average efficiency of the EM and is the average efficiency of the inverter.
 ηem is the average efficiency of the EM and ηinv is the average efficiency of the inverter.
 The mathematical model for ICE fuel consumption . rate at a given operation
 The mathematical model for ICE fuel consumption rate mice at a given operation point
 point ( , ) was obtained by steady state curve
 ( Tice , ωice ) was obtained by steady state curve fitting of the engine map fitting of the dataengine map10).
 (see Figure data (see
 Figure 10). Thecoefficients
 The regression regressionofcoefficients
 the polynomialof the polynomial
 function function
 (see Equation (see
 (18)) Equation
 were (18)) were
 estimated
 estimated accurately since the goodness of this fitting
 accurately since the goodness of this fitting indicated R-square = 0.9961. indicated R-square = 0.9961.
 .
 ( , ) = + ⋅ + ⋅ + ⋅ + ⋯
 mice ( Tice , + 2
 )=
 ωice ⋅ p00 +
 ⋅ p10 ·+ωice
 +⋅p 01 · T+ice + p⋅20 · ω⋅ice + .+. . ⋯
 2 + p · ω2 · T + . . . (18)
 + p11 · ωice · Tice + p02 · Tice (18)
 + ⋅ 2 ⋅ 21+ 3 e ⋅ ice 
 + p12 · ωe · Tice + p03 · Tice

 10.Points
 Figure 10.
 Figure Pointsofof
 thethe
 fuelfuel
 raterate
 as a as
 function of engine
 a function torque and
 of engine speed.
 torque andThe surface
 speed. represents
 The surfacethe
 represents
 curve fitting with a polynomial equation.
 the curve fitting with a polynomial equation.

Appl. Sci. 2022, 12, 226 12 of 23

 Once the objective function is expressed as a function of EM torque and engine torque
 (independent variables), then constraints were constituted based on operation limits and
 satisfying the required torque demand of the vehicle.
 Constraints:
 As shown in Equation (19), a necessary condition is to provide the required torque and
 request that the sum of torque contributions of two sources at the output of the gearbox
 be equal to torque demand at the same level. Moreover, the ICE and EM torques must be
 within the corresponding operating envelope:
 
  Tgb = ( Tem · U pulley + Tice )/i gb
 
 0 ≤ Tice ≤ Tice.max (19)
 
 − Tem.max ≤ Tem ≤ Tem.max
 

 where, U pulley —gear ratio on the pulley that connects EM to the input shaft of the gearbox
 and i gb —gear ratio of engaged gears in the gearbox.
 By minimizing the objective function (Equation (15)) over the range described in the
 constraints (Equation (18)), the optimum value of ( Tice , Tem ) can be estimated instantly,
 without considering the SOC level. When SOC is too low, the controller must restrict usage
 of the EM. On the other hand, when the SOC is near its upper threshold limit, the controller
 tends to use the EM power. Moreover, to accurately compare the fuel consumption of HEV,
 results should be indicated for the charge sustaining mode where SOC has the same level
 at the beginning and at the end of the driving cycle.
 Charge sustaining mode:
 Therefore, to maintain the battery SOC within the lower SOClow and upper SOChigh
 limits, an s-shaped correction function PFsoc was introduced to penalize the equivalent
 fuel consumption of the battery [10]. If the SOC decreases below the threshold (0.6 in this
 case), the vehicle tends to restrict the usage of electric energy, hence the PFsoc starts to rise.
 Otherwise, the correction factor is equal to 1, meaning that no limitation to utilize the electric
 power is applied. In terms of an equation, the above condition can be represented as:
 3 4
 (
 1 − 0.15 SOC + 0.05 SOC , SOC < 0.6
 PFsoc = (20)
 1, SOC ≥ 0.6

 where SOC is a normalized state of charge that can be computed as [10]:

 2 · SOC − (SOChigh + SOClow )
 SOC = (21)
 SOChigh − SOClow

 where, SOChigh = 0.80 and SOChigh = 0.60 values are used as upper and lower threshold
 limits for SOC of the battery.
 The coefficients in Equation (20) are chosen based on multiple trials to obtain the best
 fuel consumption.
 The plot in Figure 11 shows the variation of PFsoc as a function of SOC.
 Then the objective function in Equation (15) is modified with the penalization for low
 SOC values, as:
 . .
 Jecms = mice ( Pice ) + PFsoc · meqv ( Pbat ) (22)
 By minimizing this objective function, the torque split is performed to minimize the
 fuel consumption without considering the thermal limitations of the battery. However,
 as was mentioned, the optimal operating temperature range for lithium-ion batteries is
 between 15–55 ◦ C, otherwise, their safety, power and life are impacted [17,18,20]. Therefore,
 temperature limitation will be implemented in the ECMS controller in the next step.

Appl. Sci. 2022, 12,
Appl. 11, 226
 x FOR PEER REVIEW 14 of 23
 13 25

 Figure 11. Penalty function on SOC.

 3.2. ECMS Control
 Then the Strategy
 objective with Thermal
 function Limitations
 in Equation Using Temperature
 (15) is modified with the Threshold
 penalization for low
 SOC Tovalues,
 avoidas:the thermal runaway of the battery, limitations can be applied by setting
 the battery temperature θbat threshold to 55 ◦ C. Over this temperature, the usage of elec-
 (192
 tric power is limited. Hence, the ( )power
 = required ( )mainly by the ICE. This
 + is⋅ provided
 )
 is implemented by setting the penalty factor PFSO to a huge number when the battery
 temperature is over the
 By minimizing thisgiven threshold
 objective as shown
 function, in Equation
 the torque (23). As can
 split is performed tobe seen, if the
 minimize
 battery temperature ◦
 > 55 C thethe
 is θbat considering penalty factor is set to of
 a very high number i.e., as
 to
 fuel consumption without thermal limitations the battery. However,
 1000, regardless of
 was mentioned, thethe batteryoperating
 optimal SOC. temperature range for lithium-ion batteries is be-
 tween 15 − 55 °C, otherwise, their safety, power and life are impacted [17,18,20]. There-
 3 4 ◦ C and SOC < 0.6
 fore, temperature
  − 0.15 SOCwill
  1 limitation +be0.05 SOC , i f θin
 implemented ≤ 55
 bat the ECMS controller in the next step.
 i f θbat ≤ 55 ◦ C and SOC ≥ 0.6
 θ
 PFsoc = 1, (23)
 
 3.2. ECMS Control Strategy with Thermal
  1000, Limitations Using
 θbat ◦
 > 55Temperature
 C Threshold
 To avoid the thermal runaway of the battery, limitations can be applied by setting
 Then, the penalty factor PFsoc in Equation (22) is replaced with the penalty factor
 theθ battery temperature threshold to 55 °C. Over this temperature, the usage of elec-
 PFsoc which considers the thermal condition of the battery as well. By implementing such
 tric power is limited. Hence, the required power is provided mainly by the ICE. This is
 a limitation, the penalty factor works as an on/off switch triggered by the temperature
 implemented by setting the penalty factor to a huge number when the battery tem-
 threshold and battery operation outside of the designed operating temperature range can
 perature is over the given threshold as shown in Equation (23). As can be seen, if the bat-
 be avoided. However, this limitation does not include the rate of temperature change,
 tery temperature is > 55 °C the penalty factor is set to a very high number i.e., to
 which might result in a temperature overshoot due to a previous power drain from the
 1000, regardless of the battery SOC.
 battery. In the next step, the temperature change rate is also limited.
 1 − 0.15 + 0.05 , ≤ 55 °C < 0.6
 3.3. ECMS Control
 = Strategy with Thermal 1, Limitations Using Penalty
 ≤ 55 °CFunction on Temperature
 ≥ 0.6 (23)
 and Temperature Change Rate
 1000, > 55 °C
 To avoid thermal shocks in the battery, the penalty factor is represented as a cumulative
 Then,
 product the penalty
 of penalty on the 
 factorsfactor in Equation
 temperature PFθ , on(22)theistemperature
 replaced with the rate
 change penalty fac-
 PFθ. and
 tor which considers the thermal condition of the battery. as well. By implementing
 on the SOC PFsoc are applied to equivalent fuel consumption (meqv ) of the electric motor:
 such a limitation, the penalty factor works as an on/off switch triggered by the tempera-
 . .
 ture threshold and battery
 Jecms =operation
 mice ( Piceoutside
 ) + PFθ of the. ·designed
 · PF operating
 PFsoc · meqv ( Pbat ) temperature range(24)
 θ
 can be avoided. However, this limitation does not include the rate of temperature change,
 which might
 The result
 penalty in a temperature
 function on temperature overshoot
 PFθ is due
 defined to aas:
 previous power drain from the
 battery. In the next step, the temperature change rate is also limited.
 3
 PFθ = 1 + 1.75 · θ (25)
 3.3. ECMS Control Strategy with Thermal Limitations Using Penalty Function on Temperature
 and Temperature Change Rate
 To avoid thermal shocks in the battery, the penalty factor is represented as a cumu-
 lative product of penalty factors on the temperature , on the temperature change rate

tric motor:
 = ( ) + ⋅ ⋅ ⋅ ( ) (24)
 The penalty function on temperature is defined as:
Appl. Sci. 2022, 12, 226 = 1 + 1.75 ⋅ ̅ 14 of 23
 (25)
 where ̅ is normalized temperature calculated as a function of upper and lower
 temperature limit as [10]:
 where θ is normalized temperature calculated as a function of upper θhigh and lower θlow
 temperature limit as [10]: 2⋅ − + 
 ̅ = 2 · θ − (θ (26)
 θ= 
 bat − + θlow )
 high
 (26)
 θhigh − θlow
 where: = 10 °C and = 60 °C.
 = 10 ◦ 60 ◦ C. 12a, it has a value of about 1 when the battery
 = Figure
 where:
 Function
 θlow of Cisand
 plotted
 θhigh in
 Function
 temperature of PFthan
 is lower θ is plotted
 40 °C. Asin Figure 12a, ittemperature
 the battery has a value increases
 of about 1beyond
 when the battery
 40 °C, a
 temperature is lower than 40 ◦ C. As the battery temperature increases beyond 40 ◦ C,
 correction factor gets higher value, so usage of EM power will be limited.
 a correction factor PFθ gets higher value, so usage of EM power will be limited.

 (a) (b)
 Figure 12.12.
 Figure Penalty functions
 Penalty on on
 functions temperature (a) (a)
 temperature andand
 on on
 temperature change
 temperature rate
 change (b).(b).
 rate

 TheThe penalty
 penalty on on
 thethe temperature
 temperature change
 change PFisθ. used
 raterate is used
 to to avoid
 avoid a high-temperature
 a high-temperature
 change
 change rate
 rate which
 which could
 could induce
 induce thethe thermal
 thermal shock
 shock onon
 thethe battery
 battery is: is:

 = 1 + 1 ⋅ ̅ . 3 (27)
 PFθ. = 1 + 1 · θ (27)
 where ̅ is normalized temperature change rate, a function of upper and lower
 . . .
 where
 temperature change temperature
 θ is normalized limits [10]: change rate, a function of upper θ and lower θ low
 high
 temperature change limits [10]: 2⋅ − + 
 ̅ = (28)
 
 . .− .
 . 2 · θ − (θ high + θ low )
 θ =rate of .temperature
 where for upper and lower limits for . change are: (28)
 θ high − θ low
 = 0 °C/s = 6 °C/s
 where for upper and lower limits for rate of temperature change are:
 The graphical representation of is given in Figure 12b.
 . .
 θ low = 0 ◦ C/s and θ high = 6 ◦ C/s
 4. Results and Experimental Validation of the Developed Model
 AnThe graphical representation
 intermediate PFθ. is given
 step of the HEVofmodelling wasinto
 Figure 12b.the conventional vehicle
 validate
 model by comparing it to experimental data. To validate the model, experimental data
 4. Results
 from ANL [31]and
 forExperimental Validation
 a conventional of compared
 vehicle was the Developed Model
 with the results of the developed
 model simulation. Furthermore,
 An intermediate theHEV
 step of the battery electro-thermal
 modelling model was
 was to validate validated experi-
 the conventional vehicle
 model by
 mentally comparing
 using it to experimental
 a developed test bench data. To validate
 that was the model,
 developed experimental
 in-house. data from
 The simulation
 ANLof[31]
 model thefor a conventional
 mild vehicle was
 P2 HEV is discussed compared
 afterwards inwith the results of the developed model
 this section.
 simulation. Furthermore, the battery electro-thermal model was validated experimentally
 using a developed test bench that was developed in-house. The simulation model of the
 mild P2 HEV is discussed afterwards in this section.

 4.1. Experimental Validation of Conventional Vehicle Model
 The conventional vehicle model was obtained by disabling the ECMS controller,
 Electric Machine, and Battery Electro-Thermal model subsystems. This vehicle model was
 designed based on a backward model was developed in Matlab/Simulink environment
 using all characteristics and parameters of the selected vehicle. The model estimates the fuel