SE2151358A1 - Joint optimization of routes and driving parameters for cycle degradation minimization in electric vehicles - Google Patents

Abstract

A method for estimating an impact of a selected route on a state of health, SoH, of a battery in a heavy-duty vehicle (100), such as a truck or semi-trailer, the method comprises predicting a required power profile for a given route at least partly based on a road topology of the route,configuring a dynamic battery model, and feeding the predicted power profile to the dynamic battery model, thereby obtaining a predicted state of charge, SoC, profile for the given route, andconfiguring a degradation model for the battery of the heavy-duty vehicle (100), and feeding the predicted SoC profile of the route to the degradation model, thereby obtaining the impact of the selected route on the SoH of the battery.

Description

Jointly optimization of routes and driving parameters for cycle degradation minimization in electric vehicles Dias Longhitano, P* Tidriri, K. ** Bérenguer, C**** Echard, B* **** * Uníw. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, Grenoble, Francde-maíl: pedradias.l0nghitan0@110l110.com) ** Uníw. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, Grenoble, Francde-maíl: khaoula.tidriríêflïgrenoble-ínglfr *** Uníw. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, Grenoble, Francde-maíl: christophe.berenguerêflïgrenoble-inpfr) **** Volw Trucks, Francde-maíl: benjamin.echard2@110l110.c0m) Abstract: Electric vehicles are becoming more common and Will soon be the norm in terms of road transportation, Which justifies the interest of researches in topics related to health management and exploitation of such vehicles. So far, however, electric vehicle management emphasizes charging strategies and routing optimization, mainly focused on energy consumption and no investigation has been performed on the impact that routing and driving parameters, such as maximum speed and acceleration, have on the useful life of a battery and therefore on the long term exploitation cost of a fleet of electric vehicles. This paper proposes deterministic method to estimate the impact of a route in the state of health of a battery. This method is used to optimize routes While respecting operational constraints, such as delay penalties, and the impacts of such optimization on the long-term cost are estimated through simulations, mimicking real driving conditions and traffic randomness.

Keywords: Battery health management, decision making, multi-objective optimization, degradation and reliability models, electric vehicle. 1. INTRODUCTION To deal With the climate change consequences, several global actors have announced efforts to reduce emissions. For example, through the communication of the European Green Deal (EGD) REF, Europe announces, among other things, the intention to reach a zero net emission of green- house gases by 2050. This Will impact the automotive sec- tor and the number of Electric vehicles (EV°s) Will become immense, according to the EGD 77 by 2025, about 1 million public recharging and refuelling stations Will be needed for the 13 million zero - and low-emission vehicles expected on European roads". lt also highlights the importance of ensuring "a safe, circular and sustainable battery value chain for all batteries".

With different countries and global actors adopting similar stances, it is natural that research on health management for vehicles and batteries have become such important topics Within the literature. HoWever, the relationship be- tWeen routing, vehicle exploitation and degradation is not Well explored even for conventional vehicles. One can cite Robert et al. (2019) Where missions and maintenance oper- ations are scheduled for a fleet of trucks Without consider- ing routing details and Jbili et al. (2018) Where the routing * Sponsor and financial support acknowledgment goes here. Paper titles should be Written in uppercase and loWercase letters, not all uppercase. is considered. ln both of those Works, vehicle are treated as single component systems With non neglectable failure probabilities that must be, in some sense, minimized. Since failures tend to happen rarely in the lifetime of a vehicle, those methods are not applicable for most of the useful life of a vehicle Where failure probabilities are neglectable, not being adaptable for reducing the long-term exploitation cost.

For EV°s in particular, the relationship between routes, driving parameters and degradation can be impactful in terms of battery end of life, since some of the main stress factors Xu et al. (2018) such as Depth of discharge (DOD) and mean state of charge (mSoC) can be correlated to vehicle routes and exploitation. Exploring this link can lead to optimization of vehicle usage, improvement of use- ful life of batteries and even tools for better dimensioning maintenance contracts in the future. ln this paper, a method for estimating battery degradation based on routes and driving parameters is proposed. lt is then integrated in a decision making optimization problem that finds the best route, maximum speed and acceleration in terms of energy consumption, degradation and delay, and then, through simulations, optimization is validated, assessing the impact the randomness of real traffic condi- tions can have on it.

Roulc- + ._ÉÉEÉ':'ÉÉE9_. para-wei ar: -19 p: :mia ...Éïlhuu l Pfsåacâon ' Fig. l. THIS--ONE---IS---T-EÅTBORAR¥--->Å»l\ïQ---W1LL---BE~ RElVl-AQE This paper is structured as follows: ln section 2 the problem statement and the main hypotheses are presented. Section 3 covers the degradation and dynamic model of the battery as well as its connections to routing. The optimization problem is discussed in section 4. Section 5 presents the results and section 6 concludes the paper. 2. PROBLEM STATEMENT The goal of this paper is to present a model to correlate vehicle usage and routing with battery degradation, and use this relation to optimize routes and vehicle parameters such as maximum allowed speed and acceleration, in order to maximize useful life while respecting deadlines and other operational constraints. ln this problem, a vehicle has a set of points in space to visit (missions), with known addresses. lt will be possible then to use a degradation estimation to quantify severity of any route, and use this information to optimize mission planing, informing the best route, in terms of degradation, delay and energy consumption, as well as what should be the maximum speed and acceleration. A decision epoch T arrives whenever a set of missions must be performed. Vehicles will start from a known location (headquarters) and will need to go back to it at the end of the mission plan.

The main hypotheses necessary are listed bellow: o All the information related to topology and nominal driving conditions is known in advance, which in- cludes maximal allowed speed, road inclination, pres- ence of crossroads, traffic lights, etc. o The operational constraints related to deliveries are also known, including the list of all the points in space where deliveries must be made and their deadlines. o Battery degradation and dynamics follow the models presented in the following sections, with all relevant parameters known in advance. o All relevant battery parameters are known in ad- vance. 3. MODELLING BATTERY SOH EVOLUTION FROM THE ROUTE PROFILE ln order to develop a comprehensive link between routes, maximum speed, maximum acceleration and battery SoH evolution, several models have to be combined. The method is composed of three main steps: First, using information available on road topology, a required power profile is predicted for a given route. Second, this power profile is used to feed the battery dynamic model, creating a predicted SoC profile for this route. Finally, in the third step, SoC profile is used by a degradation model which will provide the SoH evolution.

The scheme of such method is shown in Figure l Fig. 2. Typical force diagram of a vehicle 3.1 Quasí-static Vehícle Model and Road Topology The usual forces applied on a generic vehicle are repre- sented in figure 2.

By applying Newton°s second law and multiplying the resulting equation by the instantaneous speed v, one can obtain the instantaneous required mechanical power for a given speed v and acceleration a. pair Cu) A173 Pmec : 2 + mgv sin a + mgCTv + mao (1) where m is the total mass of the vehicle, g is the gravity acceleration, a is the instantaneous street inclination, CT is the rolling resistance coefficient, Cu, is the drag coefficient, A is the frontal area of the vehicle, p is the air density.

To convert Pmec to electrical power, it is necessary to account for the power train efficiency 17(v,a) considered to be a function of instantaneous speed and acceleration. This function was obtained through a high fidelity truck simulator developed at the Volvo group, where different simulations had been performed and the ratio between electrical and mechanical power was analyzed for different speeds and accelerations.

Pelec : TIO), fiÛpmec ln routing problems for EV°s, it is natural to translate information on the route (topology, traffic lights and so on), into expected speed and acceleration profiles. ln Basso et al. (2019), for example, authors considered that drivers would accelerate with constant acceleration until reaching road nominal speed and also accounted for traffic lights and crossroads, considering them as stop points where instantaneous speed must be zero. To achieve good results, they have considered several particular cases, such as, for example, short street stretches, where nominal speed cannot be reached.

Nowadays, it is possible to modify vehicle maximum speed and maximum acceleration remotely and, because those parameters can affect Pdec they are considered as opti- mization variables and be incorporated in the optimization problem described in following sections.

Expected speed and acceleration profiles are built con- sidering that vehicles will accelerate with their maximum acceleration until reaching either their maximum speed or road nominal speed,.Figure 3 show two vehicles following the same route with different driving parameters. Vehicle l accelerates until road nominal speed with maximum possible acceleration while vehicle 2 has its speed and acceleration limited.

Speed Profile Comparison 'Hf- fi-s. jk w ss ë 'Ü 5 *D cv CJ.. UH " »»»»»» »« vehmel w i ------- -- vehicle 2 LI'- 113-'3 2YIJD '5éí1 INTO SVT0 E-ÖÛ 'fime (s) Fig. 3. Short street stretch With stop point at beginning and end Kinetic Battery :Model (Éirxftxilïantscd Eiurxery' Model CZJC) (Vi) ß i v Ro l ' _ 229% rim; im , § V00 (500) \',5,,,,,_§ - zh Y Fig. 4. Battery Dynamic model: kiBam + second order ECM With those assumptions, the knowledge on the inclination of each route stretch and Equation (l), it is possible to predict a poWer profile given a particular route and driving parameter. To connect routes to battery degradation, it is necessary to connect poWer profile to SoC profile, Which characterises a driving cycle. To do so, a model to represent battery dynamics is used. 3.2 Battery Dynamic Model The chosen model for battery dynamics is taken from Oliva et al. (2013) Which combines the Kinetic Battery Model model (kiBam) ManWell and McGoWan (1993) With an second order equivalent circuit model This model is represented in Figure 4. This model can capture recovery and requires loW computational effort, making it suitable for this application. kiBam is an abstraction Where the battery is seen as tWo Wells,representing available charge and the bound charge. The model tWo parameters: capacity charge c and battery rate constant k . lt yields to tWo difference equations. ECM leads to tWo difference equations that can be used to infer battery voltage over time. The systern of equations that describe the dynamic behaviour of the battery is: wrmi : Giwrk + a2w2,k + Öiík Hfmn : Gswrk t (Mwzk t 52% fi _í . 3 vsyfil : e HSCS Usyç Jr ~R5e RSCS Jr RS) tk ( l At __ _m , men : G Rlcl Um + (_1916 Rlcl + Rz)1k Where wLk is the bound charge at instant k, wgyç is the available charge, ik is the current at instant k,y5,k is the voltage difference on resistor s - With resistance RS - and capacitor s - With capacitance CS - at instant k, UM is the voltage difference on resistor l - With resistance R; and capacitor l With capacitance C¿. ln this model, SoC at instant k can be directly obtained through: wrk Sock : ccnßßoo (4) Where Cm is the battery nominal capacity.

Since the input of dynamic systern 3 is the current, SoC profile can be estimated based on electrical poWer profile thanks to the relation: Pelec VBattk ik (5) Vgank, the voltage of the battery at instant k is, in this model: Vbank (SCC) : VOC(SOC) + Retk + Dyk + Usyç Where V00 is the open circuit voltage defined by a SOC level and RO is the resistance of resistor RO, from the ECM model . 3.3 Battery Degradatton Model Battery degradation is usually defined in terms of the capacity of the battery. lt is a very standard approach to consider the state of health (SoH) of a battery as: CT SOH(T) : CT (7) Where CT is the maximum capacity of the battery at the decision epoch T, and Cm is its nominal capacity. When SoH falls under a given threshold - Which changes according to battery application - the battery must be replaced.

Because degradation in batteries is a very complex phe- nomenon, different techniques have been employed to esti- mate end of life and model degradation. Considering that machine learning algorithms Were implemented, as Well as stochastic approaches and physics based models, one can conclude that scientific community has not yet converged to a model capable of capturing the full reality of the degradation process, nonetheless, battery stress factors are Well-known, and most authors agree that depth of discharge(DoD), mSoC and temperature are among the main drivers of cycle degradation.

Without loss of generality - since the proposed approach for optimization of routes Will affect the stress factors themselves and can be employed With different modeling approaches that can account for other stress factors related to SoC profile - the chosen model for degradation is an empirical one, based on the version presented by Xu et al. (2018), Where those aforementioned stress factors are considered. The SoH is consider to vary according to: SoH : effd (s) Where fd is a function of the stress factors chosen. ln this Work, only cycling degradation is considered, Which yields to: N fdov) : :I WSÃSÜST (9) i:1 Where N is the number of cycles, i is an index that indicates each cycle, w,- is 1 for a full cycle or 0.5 for a partial cycle. S5, S0- and ST are stress factors related to DoD, SoC and temperature respectively. They are usually empirically determined, and the chosen function, taken from Xu et al. (2018) are: Sa : ek,,(o'-o,ef) ST : ekflT-Tfejnlgf S5 :aö4+böß+cög+dö+e (10) Both o, ö can be computed through the usage of the RainfloW-Counting algorithm l\/latsuichi and Endo (1968) on SoC profile. T can be computed as simply the average temperature of each cycle. Throughout this Work temper- ature Will be considered as a normally distributed random Variable centered around the average temperature that should be guaranteed by the battery management system of trucks.

With the degradation model established, using the pre- dicted SoC profile, it is possible to estimate cycle degra- dation for a given route and driving parameters, according to Figure 1. 4. OPTllVllZATlON PROBLEM FORMULATION ln order to find the best exploitation strategy for a vehicle, minimizing degradation is not enough, since there are other costs related to missions. ln this Work, delay and energy costs are considered, leading to a cost C that can be expressed as: C : Cclelay "f Cenergy "f Cdeg Delay cost is considered to be proportional to delays themselves and can be expressed as: P adam, : o, :I maxfi, _ 1,-, o] (12) i:1 Where Cd is a constant that is related to the cost of penalties, P is the total number of points to be visited, t,- is the arrival time at point i and l,- is the deadline of point i.

Similarly, energy cost is considered directly proportional to the consumed energy: M Cenergy : Cs Z ei 1:1 Where CG is the price of the kWh, e,- is the energy spent by vehicle i and M represents the full fleet of vehicles.

Finally, to account for battery degradation, We consider Cdeg, that can be Written as: M ock, - GW :j ASOH, i:1 (14) Where Cba, is the price of a neW battery and ASOH, is the variation of SoH for vehicle i.

Speed Profile Comparison 100 - ; " _ (__. ' ' -š 2 - z. :». E* É , 15 _ \~.~.\~\\\«._}\«\\_.~\<\\¿ \\~.\\\\\¿3\.,_\\qxw;.w.~\vx>w\§;-\wsyx-§ ä . \ t \ . . \ \ ,,f;/ff :w "wa (snuva: i i . G ZDÛÛ 4000 ÖGOšB BOQO Lïistcmcrï- (m) SQC Profile Comparison """"""" .__ ' ke; . ._ ~~<\ 50 C / "Cšåäßu ,_ \.\:¿~." G 2005 410130 ëOC-'ü 80:39 fiistanc-z- (m) Fig. 5. Comparison betWeen simulations in free floW and With other vehicles Notice that all those terms can be computed With the models and hypotheses presented before, Which makes the the optimization problem come doWn to finding the route r, maximum speed om" and acceleration om" that minimizes (11): fwmffffåm,, C (15) Optimization Was carried out by genetic programming.

. RESULTS AND DISCUSSION To estimate performance of the optimization method and the degradation prediction based on routes, SUlVlO (Lopez et al. (2018)) Was used. SUlVlO is an open source, micro- scopic, multi-modal traffic simulator, Which can be used to reproduce different traffic scenarios. With it, it is possible to knoW hoW the randomness of a more realistic environ- ment can affect degradation estimation based on routes as Well as the impact of route optimization in the long term. .1 Tmfiïc conditions impact on degradation estimqtion FolloWing the method shoWn in Figure 1, it is possible to, given a route, a maximum vehicle speed and a maximum vehicle acceleration, estimate the degradation caused by a displacement. This prediction hoWever is subjected to incertitude that arises from traffic conditions. Vehicles interact With each other, Which causes unpredicted stops and deceleration, impacting the quality of the SoC profile estimation.

Figure 5 shoWs the comparison betWeen speed and SoC profile both in a simulation in free floW and in a simulation With other vehicles, randomly moving through space. ln the free floW simulation, the vehicle can freely accelerate until reaching road nominal speed, at Which it remains having to break only once due to a curve. The simulation With more vehicles starts similarly but While in road nominal speed, the vehicle reaches a point of the route Where it interacts With other vehicles, having to brake and keeping a speed inferior to the nominal one, until it reaches a point Where it can accelerate once again. lt can also be seen that the presence of other vehicles affected SoC trajectory. ln free floW, due to the bigger average speed, charge Was consumed faster in steady speed. HoWever, because charge is intensively consumed While accelerating - Which happened more often in the scenario With more vehicles - at the end of both simulations SoC level remained similar.

To quantify hoW traffic randomness affects cycle degrada- tion estimation, l\/lonte Carlo simulations Were carried out. ln all simulations a random number of vehicles make ran- dom displacements and a chosen vehicle performs the same route With imposed maximum speed and acceleration. This information is used to estimate fd(]\7) - and therefore SoH degradation - according to the method presented in 1. The normalized error betWeen expected fd and simulated fd can be seen in Table 1.

Table 1. Effect of random traffic on fd(N) estimation Number of Vehicles Fd(N) Error(%) 0 .062 10 .062 50 .064 100 .087 200 .093 400 .128 As can be seen, the error for free floW scenarios is around 6%, this value remains constant for scenarios With feW vehicles. With more than 100 random vehicles, their in- teractions start reducing the accuracy of fd estimation. .2 Long-term Route Impact Since SoH evolves slowly, the effect of an individual cycle is neglectable, hoWever, the choice of route and driving parameters can have an impact in the long term.

This long-term simulation Were conducted to compare tWo vehicles that Will perform the same mission in every Work- ing session With different routes and driving parameters. The simulation set-up is as folloWs: o All simulations Were performed in a 7x7 l\/lanhattan grid containing streets With different nominal speeds. o At each simulation, representing a Working session, vehicles Will start at the same location and make a delivery at the same point in space. o Vehicle 1 Will folloW the route found by minimizing (11), With the respective driving parameters, While Vehicle 2 Will folloW the fastest route, With no limita- tions in terms of acceleration and speed, emulating a real driver. o At the each simulation, SoH, delay cost (12) and energy cost (13) are registered. o Each simulation Will happen With random traffic conditions (a random number of vehicles Will perform random displacements).

The constants of the optimization problem Were Chat : 5000, cd : low/mm) and ce : old/kWh).

Figure 6 shoWs the comparison of SoH evolution. Vehicle 1, folloWs the optimal route according to (15), and it can be seen that it has impacted SoH evolution positively.

Confiparlson of SoH 10000 - \-. \\\ "Nx masa - \¿\ _ \"f -_ \Ü'.\. \\ .x 0,99% - I F» o \.f f? \., '\..

\,\~~.\ T 'x 09930 ~ \.. "\ ._ \ m, \_ "~ \.. \ Û l l l l l I I 0 s io is 20 :s ao Working Sex-lor- Fig. 6. Long term comparison betWeen the tWo vehicles in terms of SoH Comparison of Eriergy Costs Enefrgy Cost lC 15 2D 25 3G Mvorkilxç 'Sesslon Fig. 7. Long term comparison betWeen the tWo vehicles in terms of SoH Because simulations Were limited to 200 Working sessions, both vehicles remained far from end of life. On the other hand, since SoH evolves sloWly, one can conclude that a small improvement on each driving cycle can have a huge impact on the number of Working sessions until failure. ln this example linearly extrapolating SoH trajectory for both vehicles, for a end of life threshold of 80%, vehicle 1 Would approximately 300 extra Working sessions until battery replacement.

Figure 7 shoWs the comparison betWeen energy costs. Be- cause vehicle 1 had limitations on maximum acceleration and speed, it consumed less energy, impacting its energy consumption cost.

Finally figure 8 shoWs delays costs. ln this case, vehicle 2 outperformed vehicle 1, due to limitations on speed and acceleration. The optimal schedule found presented a null expected delay but, due that traffic randomness, in some Work sessions penalties Were paid. A real time probabilistic optimization algorithm that takes into account current traffic conditions could improve this aspect.

Overall, the reduction in terms of energy consumption compensates the delay costs and the optimization algo- Comparison of Belay Costa Delivery Cost I> i i i i . i i G 5 15 20 2 5 30 Vioršung åessrc-rf Fig. 8. Long term comparison between the tWo vehicles in terms of SoH rithm has reduced the total eXploitation cost and post- poned battery replacement, Which can have a huge impact on real life applications, specially if applied to a fleet of vehicles With several deliveries to be performed everyday. 6. CONCLUSION This article presented a method for estimating cycle degra- dation on a battery for a given route, maximum vehicle speed and acceleration. This method Was used to solve a routing problem considering battery degradation, delays and energy consumption.

The performance of optimization Was validated through simulations With random traffic conditions. ln terms of the impact of routes on battery degradation, it Was shoWn that, optimizing routes on the eXploitation cost and useful life duration of the battery.

There are a lot of improvements to be made. From the modeling point of vieW, in future Works, battery dynamics and degradation Will be represented by more realistic and robust models, and the prediction of degradation based on a given route Will be validated With real vehicle data. The optimization problem can involve more realistic con- straints, such as charging necessity, delivery time, vehicle storage capacity, and more importantly, this optimization problem must be extended to the fleet, so that decisions on Which vehicle to use depending on its SoH can be made. lt is also important to highlight that traffic conditions can impact delays and therefore, it is important to incorporate real time traffic information in future Works, providing real time routing.

Other actions than routing and limiting speed or acceler- ation can be applied. For instance, it Would be interesting to consider optimal charging strategies in future decision making problems. Another crucial decision to be made is When to replace batteries of a vehicle, Which is affected by vehicle eXploitation. Different maintenance strategies must be also considered in future Works. When all those actions are considered together, decisions Will happen in different time scales (maintenance and replacements happen rarely throughout the life of a vehicle, While routing and charg- ing happen in a daily basis), therefore it is necessary to make them in a closed loop fashion, taking into account randomness and the the effect of previous actions in the system.

REFERENCES Basso, R., Kulcsar, B., Egardt, B., Lindroth, P., and Sanchez-Diaz, l. (2019). Energy consumption estima- tion integrated into the electric vehicle routing prob- lem. Transportation Research Part D: Transport and Enyironment, 69, 141~167.

Jbili, S., Chelbi, A., Radhoui, l\/l., and Kessentini, l\/l. (2018). Integrated strategy of vehicle routing and main- tenance. 170, 202~214. doi:10.1016/j.ress.2017.09.030.

Lopez, RA., Behrisch, l\/l., Bieker-Walz, L., Erdmann, J., Flötteröd, YP., Hilbrich, R., Liicken, L., Rummel, J., Wagner, P., and Wießner, E. (2018). l\/licroscopic traffic simulation using sumo. IEEE Intelligent Transportation Systems Conference (ITSC). lVlanWell, JF. and lVlcGoWan, J.G. (1993). Lead acid battery storage model for hybrid energy sys- tems. 50(5), 399~405. doi:https://doi.org/10.1016/0038- 092X(93)90060-2. l\/latsuichi, l\/l. and Endo, T. (1968). subjected to varying stress.

Oliva, J.A., Weihrauch, C., and Bertram, T. (2013). l\/lodel-based remaining driving range prediction in electric vehicles by using particle filtering and markov chains. ln 2015" World Electric Vehicle Symposium and Exhibition (EVS27), 1~10. doi: 10.1109/EVS.2013.6914989.

Robert, E., Bouvard, K., Lesobre, R., and Bérenguer, C. (2019). Joint assignment of missions and maintenance operations for a fleet of deteriorating vehicles. ln Proc. of 11th International Conference on Mathematical Methods in Reliability - MMR2Û19, City Uniyersity Hong-Kong, Jun 2019, Hong-Kong, China.

Xu, B., Oudalov, A., Ulbig, A., Andersson, G., and Kirschen, DS. (2018). l\/lodeling of lithium-ion bat- tery degradation for cell life assessment. IEEE Transactions on Smart Grid, 9(2), 1131~1140. doi: 10.1109/TSG.2016.2578950.

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Claims (10)

1. A method for estimating an impact of a selected route on a state of health, SoH, of a battery in a heavy-duty vehicle (100), such as a truck or semi-trailer, the method comprises predicting a required power profile for a given route at least partly based on a road topology of the route, configuring a dynamic battery model, and feeding the predicted power profile to the dynamic battery model, thereby obtaining a predicted state of charge, SoC, profile for the given route, and configuring a degradation model for the battery of the heavy-duty vehicle (100), and feeding the predicted SoC profile of the route to the degradation model, thereby obtaining the impact of the selected route on the SoH of the battery.

2. The method according to claim 1, wherein the selected route comprises a set of points in space to visit, with known addresses.

3. The method according to claim 1 or 2, where the selected route is associated with information related to vehicle speed and/or vehicle acceleration.

4. The method according to any previous claim, where the required power profile is based on a required mechanical power of the selected route and on an efficiency of a power train of the heavy-duty vehicle (100).

5. The method according to any previous claim, where the required power profile is based on an efficiency of a power train of the heavy-duty vehicle (100).

6. The method according to any previous claim, wherein the dynamic battery model combines a Kinetic Battery Model, kiBam, with a second order equivalent circuit model, ECM.

7. The method according to any previous claim, where battery degradation is defined in terms of a capacity degradation of the battery.

8. A method for selecting a route for a heavy-duty vehicle (100), comprising identifying a set of candidate routes, configuring a cost function comprising a state of health, SoH, evolution (Cdeg) of a battery on the heavy-duty vehicle (100), evaluating each route in the set of routes according to the configured cost function, and selecting the route based on the evaluation.

9. The method according to claim 8, wherein the cost function comprises an energy consumption cost (Cenefgy) and/or a cost associated with route delay (Cdeiay).

10. A method for estimating battery degradation in a heavy-duty vehicle (100) such as a truck or semi-trailer, based on route candidates and driving parameters, comprising integrating a decision making optimization problem that finds the best route, maximum speed and acceleration in terms of energy consumption, degradation and delay.