# Influence of Energy Management System Control Strategies on the Battery State of Health in Hybrid Electric Vehicles

^{*}

## Abstract

**:**

## 1. Introduction

- Rule-based Energy Management Systems: these approaches manage the power demands by implementing fixed rules. Usually, the rules are based on the efficiency maps of the thermal engine and the electric installed motors in order to define the best working points in terms of efficiency. The simplest version of rule-based EMS follows a determinist approach, that is when these control systems operate only on the switching on/off of the thermal engine to convert mechanical power to electrical energy and lead the state of charge (SOC) of battery back to an acceptable level. These types of control systems are generally used when the thermal engine does not provide traction [9,10]. On the other hand, control systems are based on power demand, where the main input is the driver’s power request, and the main goal of the electric engine is to guarantee adequate support to the thermal engine. The latter would always operate at optimal working points, while an electric motor will try to fulfill driver demands [11,12]. The most efficient version of rule-based EMS is the “multimode” strategy. This is probably more complex in comparison with the others, but presents a better effectiveness with regards to the fuel consumption reduction. These management algorithms generally include a fully electric driving and a fully thermal driving mode, and other hybrid modes. In hybrid modes, the thermal engine may have the task of supporting traction, and at the same time recharging the battery, or simply a marginal role in the traction or operating at predefined working points [13,14,15,16,17].
- Optimization-based Energy Management Systems: the main goal of these approaches is to achieve the global optimum by minimizing a cost function that, in the case of HEVs, is generally based on the fuel consumption or emissions of air pollutants. These strategies, in order to work, need several input parameters, such as driving cycles and other physical constraints of ICEs, electric energy storage (ESS) and EM. These aspects make these control approaches non-random [8]. The most common strategies of this group are equivalent consumption minimization strategies (ECMS) and model predictive control-based strategies (MPC). The ECMS, in order to minimize the overall fuel consumption, takes into account the fuel used by the thermal engine and also the ideal fuel consumed by the battery. Instead, the MPC takes advantage of dynamic programming techniques to manage all energy flows to achieve the final goal in accordance with the considered driving cycle. Additionally, in this case the cost functions generally take into account the evolution of the states of charge of battery in relation to fuel consumption. Some examples in the literature of this approach are presented in [18,19,20,21,22,23].

## 2. Vehicle Modelling and Validation

#### 2.1. Battery Mathematical Model

_{b}), the filtered current (${i}_{b}^{*}$), the exponential zone amplitude (A

_{b}) and the exponential zone time constant inverse (B

_{b}).

_{ref}is equal to a full discharge, DOD(n) is the current cycle depth of discharge, and $1/\rho $ is the stress exponent related to the depth of discharge. Similarly, the impact of the C-rate of charge and discharge current is also evaluated through Equations (4) and (5), respectively:

_{Chargeref}and I

_{Dischref}represent the reference currents for battery stress evaluation in charge and discharge, while I

_{Chargeavg(n)}and I

_{Dischargeavg(n)}represent the average charge and discharge currents for the cycle n. The terms $\frac{1}{\gamma 1}$ and $\frac{1}{\gamma 2}$ are the stress exponents of the charge and discharge currents.

_{a}(n) and T

_{ref}are the operating temperatures during the cycle n and the reference temperature for battery degradation assessment, and φ is the Arrhenius constant.

_{Cref}represents the number of cycles to the end of the battery life when subjected to charge and discharge cycles, with a value of DOD = DOD

_{Ref}, I

_{Charge}= I

_{ChargeRef}, I

_{Disch}= I

_{DischRef}and T

_{a}= T

_{Ref}. The term θ(n) is the product of all stress factors, and it is evaluated by Equation (8):

_{c}) and the number of equivalent cycles (N

_{eq}) defines the degradation index. Clearly, as the number of cycles increases, the index will also evaluate the cumulative degradation up to that point. The degradation index is given by Equation (10).

_{BOL}and Q

_{EOL}represent the capacity of the non-degraded battery and end-of-life battery, respectively. Similarly, R

_{BOL}and R

_{EOL}represent the non-degraded and end-of-life battery resistance. Typically, the Q

_{EOL}is equal to 0.8Q

_{BOL}, but instead R

_{EOL}is equal to 1.2 R

_{BOL}. The exponents α and β are the capacity and resistance degradation exponents of the cell. The values of α and β, as well as the values of ρ, γ1, γ2, and ϕ are calculated by performing specific laboratory tests in which the battery is degraded under controlled load conditions. The value of the constants for the cell, presented in Table 2, have been defined by Li et al. in [32] for MSM, and by Motapon et al. in [35] for an aging model.

#### 2.2. Calculation of the Driving Forces

^{TM}M refers to Equation (13):

_{a}is the air density, C

_{D}is the drag coefficient, A is the vehicle’s frontal area and v is the longitudinal velocity. To evaluate the rolling resistance force, for each wheel, AVL Cruise

^{TM}M refers to Equation (14):

_{w}is the vertical load acting on the wheel and c

_{w}is the rolling resistance factor. Li et al. [32] considered the total rolling resistance force as a constant force of 70 N, named F

_{r}*, acting on the vehicle (four wheels). To obtain the same result in CruiseM, considering that Equation (14) refers to one wheel, c

_{w}has to be calculated by Equation (15):

^{TM}M refers to Equation (16):

_{r}is the road inclination angle. The inertia force is evaluated by Equation (17):

_{tot}is the total necessary torque, considered as the sum of front axle torque (C

_{f}) and rear axle torque (C

_{r}), and R

_{w}is the wheels’ rolling radius. Table 3 shows the values of the parameters for Equations (15)–(18) with reference to the considered vehicle.

#### 2.3. Front and Rear Axle Torque, Speed, and Power

_{f}and the C

_{r}, and therefore the torque requested by the ICE and EM. C

_{f}, which depends on C

_{ICE}, can only be positive, while C

_{r}, which depends on C

_{EM}, can be positive (motor) or negative (generator). ICE torque, angular velocity and requested power are evaluated by Equations (19)–(21):

_{FFD}is the front final drive transmission ratio, τ

_{GB}is the gear box transmission ratio, η

_{GB}is the gear box efficiency and η

_{FFD}is the front final drive efficiency. P

_{ICE}is the ICE power, the product of its angular velocity (ω

_{ICE}) and torque (C

_{ICE}). The instantaneous torque and angular velocity, in accordance with Figure 2, define the instantaneous fuel consumption.

_{RFD}is the rear final drive transmission ratio, and η

_{RFD}is the real axle final drive efficiency. The sign of the efficiency exponent depends on the operating conditions of the EM. When EM operates as a motor (positive power), it has to overcome energy losses in the final reducer, so the efficiency divides the torque. Otherwise, EM operating as a generator can only absorb the power not dissipated within the final reducer, so the efficiency multiplies the torque. The product between the requested torque and EM angular velocity (ω

_{EM}) returns the electric machine power (P

_{EM}).

_{EM}is mechanical power that is converted into electrical power from the EM to the battery pack. Equation (25) estimates the electrical power required (or supplied) to the battery:

_{B}is the electrical power required (or supplied) to the battery, η

_{EM}is the EM efficiency (Figure 3), η

_{EB}is the battery efficiency (Figure 4) and η

_{PE}is the AC/DC inverter and DC line efficiency. When the electric machine is running as a motor and requires P

_{EM}, the battery provides P

_{EM}with the contribution of the power dissipated in the electronic components (the efficiencies divide P

_{EM}). When the electric machine provides P

_{EM}, a part of this power is dissipated into the electronic components, so the efficiencies multiply P

_{EM}. In Equation (21), the term −1 comes from the sign convention used for batteries (negative power for discharge, positive power for recharge). Table 4 collects the powertrain efficiencies not involved in the maps already shown. The values have been presented by Li et al. in [32].

## 3. Validation Procedure

## 4. The Energy Management System

- -
- Full Electric mode: all the traction is provided by the electric machine that drains energy from the battery.
- -
- Load Point Moving (LPM) mode: ICE delivers constant torque (Tc). If the engine power exceeds the driving cycle request, the electric machine operates as a generator and converts the excess mechanical power into electric recharging power. Otherwise, if the engine power is less than the driving cycle request, the electric machine operates as a motor and supplies the missing power.
- -
- Full Thermic: all the traction is demanded to the internal combustion engine; no electrical power is allowed to avoid overspeed of the electric machine.
- -
- Recharging mode: if the battery state of charge reaches its lower limit value, the energy management system actuates the recharging mode. The ICE torque command is the minimum among:
- Ctot plus its twenty percent value (considered at the clutch node)
- Maximum ICE available traction torque
- Maximum EM available generator torque

_{recharging}value, to avoid the battery operating in a critical and unsafe zone.

- -
- Braking: during the braking phases it is assumed that the total braking force is demanded by the rear axle, which is connected to the electric machine and can operate regenerative braking. The rear axle braking torque is saturated at the generator torque boundaries.

_{sw}, SPD

_{FT}, SOC

_{L}, SOC

_{RECH}and TC. The parameters’ values can substantially change the operation of the vehicle and the ability to achieve the different operating modes. The study investigates the effect of torque delivered by the engine in the LPM mode in terms of fuel economy and battery degradation. The value of TC is subject to definition, while the value of the other calibration constants is defined by the authors’ experience, but subject to optimization in future work.

_{n}is the nominal battery voltage, C is the battery capacity, SOC

_{i}is the battery state of charge at the beginning of the trip and SOC

_{f}is the final state of charge. E

_{Electric}represents the electrical energy consumed (when ∆SOC is positive), or absorbed (when ∆SOC is negative), by the electric machine. Assuming that the power is provided only by the ICE, Equation (27) is as follows:

_{ICE}is the power provided by the ICE for recharging the battery pack, η

_{GB}is the gearbox efficiency, η

_{FDiff}is the front differential unit efficiency, η

_{RDiff}is the rear differential unit efficiency, η

_{PE}is the DC line efficiency and η

_{Batt}is the battery and inverter efficiency (Figure 4).

_{ICE}is the internal combustion engine efficiency. By replacing Equation (28) with Equation (27), Equation (29) can be obtained:

_{tot}collects all the efficiencies already presented, as in Equation (30):

_{ELfuel}, by obtaining Equation (31):

_{Realfuel}value is closely related to the optimization of the working points of the ICE and EM. This paper intends to identify the TC value which minimizes m

_{Realfuel}value for urban routes driven in the city of Messina and correlate it with the battery degradation. The values of the other parameters presented in Table 6 (SPD

_{sw}, SPD

_{FT}, SOC

_{L}, SOC

_{RECH}) are assumed to be optimal in terms of fuel economy in this work, but they will be subject to optimization processes in future work.

## 5. Experimental Driving Cycles

## 6. Results

_{i}) for the two proposed driving cycles. For each driving cycle, different scenarios were evaluated in terms of fuel consumption, considering the following parameters:

- -
- the TC torque from 50 Nm to 120 Nm with steps of 10 Nm;
- -
- the initial state of charge assuming the values of 100%, 65%, and 30%.

^{2}/s

^{3}) and considering that the cycle took place mainly on primary roads, it can be concluded that the exclusive use of the battery (full electric mode) affects its end of life more than hybrid mode. Low SOCi and low TC values mean that, in hybrid mode, the torque delivered by the ICE is used almost entirely for traction, which means that the electric motor demands or delivers small amounts of current to the battery. As TC charging torque increases, the battery is more stressed, and this thesis is supported by the fact that at TC = 70 Nm the trend between the hybrid and the electric mode is reversed. Before 70 Nm, the SOCi is the parameter with more influence on the battery aging (and so the distance travelled in full electric mode), but from a TC equal to 70 Nm torque itself becomes the most damaging parameter for the battery.

^{2}/s

^{2}). This results in two conclusions:

- (1)
- The average speed of cycle 2 causes the control system to command the hybrid mode more often than in driving cycle 1.
- (2)
- The value of v*a suggests that, on average, more traction power is required from the car in cycle 2 than in cycle 1.

## 7. Conclusions

^{TM}M and simulations were implemented on real driving cycles based on two different paths located in Messina (Italy). The control system efficiency was tested by varying two main parameters, such as TC and SOC

_{i}. The main results are as follows:

- The ICE efficiency is generally proportional to the TC, but the degradation of the battery is affected mostly by the recharging power;
- If analyzing the trend of the instantaneous fuel consumption, the variation of TC provides the main contribution and its trend does not considerably change from one cycle to the other;
- If analyzing the trend of battery degradation, the variation of TC gives different results and the specific paths with its typical kinematic parameters affect the battery aging itself much more.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Minh, V.T.; Moezzi, R.; Cyrus, J.; Hlava, J. Optimal Fuel Consumption Modelling, Simulation, and Analysis for Hybrid Electric Vehicles. Appl. Syst. Innov.
**2022**, 5, 36. [Google Scholar] [CrossRef] - Dingel, O.; Ross, J.; Trivic, I.; Cavina, N.; Rioli, M. Model-Based Assessment of Hybrid Powertrain Solutions. In Proceedings of the SAE Technical Papers; SAE International: Warrendale, PA, USA, 2011. [Google Scholar]
- Previti, U.; Brusca, S.; Galvagno, A. Passenger Car Energy Demand Assessment: A New Approach Based on Road Traffic Data. In E3S Web of Conferences; EDP Sciences: Les Ulis, France, 2020; Volume 197. [Google Scholar]
- Cucinotta, F.; Raffaele, M.; Salmeri, F. A Well-to-Wheel Comparative Life Cycle Assessment between Full Electric and Traditional Petrol Engines in the European Context; Springer: Berlin/Heidelberg, Germany, 2021; ISBN 9783030705657. [Google Scholar]
- Chan, C.C. The State of the Art of Electric, Hybrid, and Fuel Cell Vehicles. Proc. IEEE
**2007**, 95, 704–718. [Google Scholar] [CrossRef] - Un-Noor, F.; Padmanaban, S.; Mihet-Popa, L.; Mollah, M.N.; Hossain, E. A Comprehensive Study of Key Electric Vehicle (EV) Components, Technologies, Challenges, Impacts, and Future Direction of Development. Energies
**2017**, 10, 1217. [Google Scholar] [CrossRef] - Lee, Y.; Kim, C.; Shin, J. A Hybrid Electric Vehicle Market Penetration Model to Identify the Best Policy Mix: A Consumer Ownership Cycle Approach. Appl. Energy
**2016**, 184, 438–449. [Google Scholar] [CrossRef] - Ehsani, M.; Singh, K.V.; Bansal, H.O.; Mehrjardi, R.T. State of the Art and Trends in Electric and Hybrid Elec-tric Vehicles. Proc. IEEE
**2021**, 109, 967–984. [Google Scholar] [CrossRef] - Zhang, P.; Yan, F.; Du, C. A Comprehensive Analysis of Energy Management Strategies for Hybrid Electric Vehicles Based on Bibliometrics. Renew. Sustain. Energy Rev.
**2015**, 48, 88–104. [Google Scholar] [CrossRef] - Kim, M.; Jung, D.; Min, K. Hybrid Thermostat Strategy for Enhancing Fuel Economy of Series Hybrid Intrac-ity Bus. IEEE Trans. Veh. Technol.
**2014**, 63, 3569–3579. [Google Scholar] [CrossRef] - Wang, E.; Ouyang, M.; Zhang, F.; Zhao, C. Performance Evaluation and Control Strategy Comparison of Su-percapacitors for a Hybrid Electric Vehicle. In Science, Technology and Advanced Application of Supercapacitors; IntechOpen: London, UK, 2019. [Google Scholar]
- Zhao, Z.; Yu, Z.; Yin, M.; Zhu, Y. Torque Distribution Strategy for Single Driveshaft Parallel Hybrid Electric Vehicle. In Proceedings of the 2009 IEEE Intelligent Vehicles Symposium, Xi’an, China, 3–5 June 2009; pp. 1350–1353. [Google Scholar]
- Yang, C.; Zha, M.; Wang, W.; Liu, K.; Xiang, C. Efficient Energy Management Strategy for Hybrid Electric Vehicles/Plug-in Hybrid Electric Vehicles: Review and Recent Advances under Intelligent Transportation System. IET Intell. Transp. Syst.
**2020**, 14, 702–711. [Google Scholar] [CrossRef] - Song, K.; Li, F.; Hu, X.; He, L.; Niu, W.; Lu, S.; Zhang, T. Multi-Mode Energy Management Strategy for Fuel Cell Electric Vehicles Based on Driving Pattern Identification Using Learning Vector Quantization Neural Network Algorithm. J. Power Sources
**2018**, 389, 230–239. [Google Scholar] [CrossRef] - Rajput, D.; Herreros, J.M.; Innocente, M.S.; Schaub, J.; Dizqah, A.M. Electrified Powertrain with Multiple Planetary Gears and Corresponding Energy Management Strategy. Vehicles
**2021**, 3, 341–356. [Google Scholar] [CrossRef] - Liu, H.; Wang, C.; Zhao, X.; Guo, C. An Adaptive-Equivalent Consumption Minimum Strategy for an Extended-Range Electric Bus Based on Target Driving Cycle Generation. Energies
**2018**, 11, 1805. [Google Scholar] [CrossRef] - Galvagno, A.; Previti, U.; Famoso, F.; Brusca, S. An Innovative Methodology to Take into Account Traffic Information on WLTP Cycle for Hybrid Vehicles. Energies
**2021**, 14, 1548. [Google Scholar] [CrossRef] - Vu, T.M.; Moezzi, R.; Cyrus, J.; Hlava, J.; Petru, M. Parallel Hybrid Electric Vehicle Modelling and Model Pre-dictive Control. Appl. Sci.
**2021**, 11, 10668. [Google Scholar] [CrossRef] - Qiang, P.; Wu, P.; Pan, T.; Zang, H. Real-Time Approximate Equivalent Consumption Minimization Strategy Based on the Single-Shaft Parallel Hybrid Powertrain. Energies
**2021**, 14, 7919. [Google Scholar] [CrossRef] - Pérez, W.; Tulpule, P.; Midlam-Mohler, S.; Rizzoni, G. Data-Driven Adaptive Equivalent Consumption Minimization Strategy for Hybrid Electric and Connected Vehicles. Appl. Sci.
**2022**, 12, 2705. [Google Scholar] [CrossRef] - Pei, D.; Leamy, M.J. Dynamic Programming-Informed Equivalent Cost Minimization Control Strategies for Hybrid-Electric Vehicles. J. Dyn. Syst. Meas. Control. Trans. ASME
**2013**, 135, 051013. [Google Scholar] [CrossRef] - Vidal-Naquet, F.; Zito, G. Adapted Optimal Energy Management Strategy for Drivability. In Proceedings of the 2012 IEEE Vehicle Power and Propulsion Conference, VPPC 2012, Seoul, Korea, 9–12 October 2012; pp. 358–363. [Google Scholar]
- Inuzuka, S.; Zhang, B.; Shen, T. Real-Time Hev Energy Management Strategy Considering Road Congestion Based on Deep Reinforcement Learning. Energies
**2021**, 14, 5270. [Google Scholar] [CrossRef] - Meng, J.; Luo, G.; Ricco, M.; Swierczynski, M.; Stroe, D.I.; Teodorescu, R. Overview of Lithium-Ion Battery Modeling Methods for State-of-Charge Estimation in Electrical Vehicles. Appl. Sci.
**2018**, 8, 659. [Google Scholar] [CrossRef] - Campagna, N.; Castiglia, V.; Miceli, R.; Mastromauro, R.A.; Spataro, C.; Trapanese, M.; Viola, F. Battery Models for Battery Powered Applications: A Comparative Study. Energies
**2020**, 13, 4085. [Google Scholar] [CrossRef] - Cignini, F.; Genovese, A.; Ortenzi, F.; Alessandrini, A.; Berzi, L.; Pugi, L.; Barbieri, R. Experimental Data Comparison of an Electric Minibus Equipped with Different Energy Storage Systems. Batteries
**2020**, 6, 26. [Google Scholar] [CrossRef] - Padovani, T.M.; Debert, M.; Colin, G.; Chamaillard, Y. Optimal Energy Management Strategy Including Battery Health through Thermal Management for Hybrid Vehicles. In IFAC Proceedings Volumes (IFAC-PapersOnline); IFAC Secretariat: Laxenburg, Austria, 2013; Volume 7, pp. 384–389. [Google Scholar]
- Tang, L.; Rizzoni, G. Energy Management Strategy Including Battery Life Optimization for a HEV with a CVT. In Proceedings of the 2016 IEEE Transportation Electrification Conference and Expo, Asia-Pacific, ITEC Asia-Pacific 2016, Busan, Korea, 1–4 June 2016; Institute of Electrical and Electronics Engineers Inc.: Piscataway, NJ, USA, 2016; pp. 549–554. [Google Scholar]
- Atalay, S.; Sheikh, M.; Mariani, A.; Merla, Y.; Bower, E.; Widanage, W.D. Theory of Battery Ageing in a Lith-ium-Ion Battery: Capacity Fade, Nonlinear Ageing and Lifetime Prediction. J. Power Sources
**2020**, 478, 229026. [Google Scholar] [CrossRef] - Dos Reis, G.; Strange, C.; Yadav, M.; Li, S. Lithium-Ion Battery Data and Where to Find It. Energy AI
**2021**, 5, 100081. [Google Scholar] [CrossRef] - Tang, X.; Liu, K.; Li, K.; Widanage, W.D.; Kendrick, E.; Gao, F. Recovering Large-Scale Battery Aging Dataset with Machine Learning. Patterns
**2021**, 2, 100302. [Google Scholar] [CrossRef] - Li, X.; Evangelou, S.A. Torque-Leveling Threshold-Changing Rule-Based Control for Parallel Hybrid Electric Vehicles. IEEE Trans. Veh. Technol.
**2019**, 68, 6509–6523. [Google Scholar] [CrossRef] - WebPlotDigitizer. Available online: https://automeris.io/WebPlotDigitizer/ (accessed on 10 January 2022).
- Motapon, S.N.; Lupien-Bedard, A.; Dessaint, L.A.; Fortin-Blanchette, H.; Al-Haddad, K. A Generic Electro-thermal Li-Ion Battery Model for Rapid Evaluation of Cell Temperature Temporal Evolution. IEEE Trans. Ind. Electron.
**2017**, 64, 998–1008. [Google Scholar] [CrossRef] - Motapon, S.N.; Lachance, E.; Dessaint, L.A.; Al-Haddad, K. A Generic Cycle Life Model for Lithium-Ion Bat-teries Based on Fatigue Theory and Equivalent Cycle Counting. IEEE Open J. Ind. Electron. Soc.
**2020**, 1, 207–217. [Google Scholar] [CrossRef] - Smith, K.; Earleywine, M.; Wood, E.; Neubauer, J.; Pesaran, A. Comparison of Plug-in Hybrid Electric Vehicle Battery Life across Geographies and Drive Cycles. In Proceedings of the SAE Technical Papers; SAE International: Warrendale, PA, USA, 2012. [Google Scholar]
- Laresgoiti, I.; Käbitz, S.; Ecker, M.; Sauer, D.U. Modeling Mechanical Degradation in Lithium Ion Batteries during Cycling: Solid Electrolyte Interphase Fracture. J. Power Sources
**2015**, 300, 112–122. [Google Scholar] [CrossRef] - Jeoung, H.; Lee, K.; Kim, N. Methodology for Finding Maximum Performance and Improvement Possibility of Rule-Based Control for Parallel Type-2 Hybrid Electric Vehicles. Energies
**2019**, 12, 1924. [Google Scholar] [CrossRef] - Zhou, H.; Xu, Z.; Liu, L.; Liu, D.; Zhang, L. A Rule-Based Energy Management Strategy Based on Dynamic Programming for Hydraulic Hybrid Vehicles. Math. Probl. Eng.
**2018**, 2018, 9492026. [Google Scholar] [CrossRef] [Green Version] - Openstreetmap. Available online: https://www.openstreetmap.org/ (accessed on 10 March 2022).

Gear | Ratio | Gear Upshifting (km/h) | Gear Downshifting (km/h) |
---|---|---|---|

First | 3.54:1 | 12 | - |

Second | 1.92:1 | 35 | 5 |

Third | 1.28:1 | 55 | 20 |

Fourth | 0.91:1 | 80 | 30 |

Fifth | 0.67:1 | 100 | 70 |

Sixth | 0.53:1 | - | 90 |

Differential | 4.53:1 | - | - |

Parameter | Symbol | Value |
---|---|---|

Battery capacity | Q_{max} (Q_{BOL}) | 5.65 Ah |

Battery nominal voltage | E_{0} | 230 V |

Internal resistance | R_{b} (R_{BOL}) | 0.2056 ohm |

Polarization constant | K_{1} | 0.116 V/Ah |

Polarization resistance | K_{2} | 0.116 ohm |

Exponential zone amplitude | A_{b} | 25.1477 V |

Exponential zone time constant inverse | B_{b} | 4.2404 (ah)^{−1} |

Resistance at end of life | R_{EOL} | 0.24672 ohm |

Battery capacity at end of life | Q_{EOL} | 4.52 Ah |

DOD stress exponent | ρ | 0.8 |

Charge stress exponent | γ1 | 2.34 |

Discharge stress exponent | γ2 | 0.8 |

Temperature stress exponent | ϕ | 3.7 × 10^{3} |

Capacity degradation exponent | α | 0.9708 |

Resistance degradation exponent | β | 0.9708 |

**Table 3.**Resistance force parameters [32].

Parameter | Symbol | Value |
---|---|---|

Air density | ρ | 1.19 kg/m^{3} |

Drag coefficient | C_{D} | 0.44 |

Frontal area | A | 1.77 m^{2} |

Rolling radius coefficient | c_{w} | 0.0040 |

Vehicle mass | m_{v} | 1770 kg |

Vertical wheels load | Fw | 17,363.7 N |

Wheels rolling radius | Rw | 0.305 m |

Parameter | Symbol | Value |
---|---|---|

Rear final drive ratio | τ_{RFD} | 12.4845 |

Gear box efficiency | η_{GB} | 0.96 |

Front final drive efficiency | η_{FFD} | 0.96 |

Rear final drive efficiency | η_{RFD} | 0.96 |

Power electronic efficiency | η_{PE} | 0.96 |

Parameter | Value |
---|---|

Average | 0.11% |

Standard Deviation | 0.54% |

Maximum | 0.98% |

Minimum | −0.99% |

Parameter | Meaning | Value |
---|---|---|

SPD_{sw} | Speed below which the heat engine is always switched off, except for imposed charging | 20 km/h |

SPD_{FT} | Speed above which the EM is always switched off | 65 km/h |

SOC_{L} | Critical battery state of charge under which charging is imposed | 20% |

SOC_{RECH} | Charging status beyond which, if active, the imposed charging is terminated | 35% |

TC | Constant torque generated by ICE in LPM | To be defined |

Kinetic Parameters | |||||
---|---|---|---|---|---|

Route | Ave. Speed [m/s] | Ave. Acc. [m/s^{s}] | v*a when a > 0 [m^{2}/s^{3}] | Idle Time [%] | Acc. Time [%] |

path 1 | 4.72 | 0.30 | 1.63 | 13.77 | 43.36 |

path 2 | 6.57 | 0.39 | 2.42 | 14.77 | 42.17 |

Roads Parameters | |||||

Route | Distance[km] | Primary rds [%] | Secondary rds [%] | Tertiary rds [%] | |

path 1 | 17.19 | 84.80 | 4.83 | 3.12 | |

path 2 | 5.84 | 0.00 | 53.85 | 1.19 |

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**MDPI and ACS Style**

Previti, U.; Brusca, S.; Galvagno, A.; Famoso, F.
Influence of Energy Management System Control Strategies on the Battery State of Health in Hybrid Electric Vehicles. *Sustainability* **2022**, *14*, 12411.
https://doi.org/10.3390/su141912411

**AMA Style**

Previti U, Brusca S, Galvagno A, Famoso F.
Influence of Energy Management System Control Strategies on the Battery State of Health in Hybrid Electric Vehicles. *Sustainability*. 2022; 14(19):12411.
https://doi.org/10.3390/su141912411

**Chicago/Turabian Style**

Previti, Umberto, Sebastian Brusca, Antonio Galvagno, and Fabio Famoso.
2022. "Influence of Energy Management System Control Strategies on the Battery State of Health in Hybrid Electric Vehicles" *Sustainability* 14, no. 19: 12411.
https://doi.org/10.3390/su141912411