A State-of-health-oriented Power Management Strategy for

A State-of-health-oriented Power Management Strategy forMulti-source Electric Vehicles Considering Situation-based

Optimized Solutions in Real-timeAhmed M. Ali1, Bedatri Moulik2, Nejra Beganovic3, and Dirk Soffker4

1,4 Chair of Dynamics and Control, University of Duisburg-Essen, Duisburg, 47057, Germanyp1q [email protected], p4q [email protected]

2 Department of Electrical and Electronics Engineering, Amity University, 201303 Noida, [email protected]

3 Department of Electronics Design, Mid-Sweden University, 85170 Sundsvall, [email protected]

ABSTRACT

This paper presents a novel situation-based power and batteryhealth management strategy for fuel cell vehicles. In suchhybrid powertrains, the synergy role of batteries is essentialto minimize overall power consumption and maintain higherelectric efficiency of the fuel cell. On the other side, life-time degradation of the battery is associated to the recurrentcharging/discharging cycles. The proposed power manage-ment strategy addresses the trade-off between these contra-dictive objectives. Vehicle states in each situation are definedin terms of driver-related characteristic variables (power de-mand and speed) corporately with a powertrain-related vari-able (on-board battery’s state of charge). Optimal power han-dling solution for each situation is searched offline consid-ering different optimization criteria: range extension, life-time maximization, and power consumption minimization. Aweighted fusion of these optimized solutions can be imple-mented online based on desired driving strategy, leading tosituation-based optimized solution. This contribution aimsto provide flexible power handling options meeting perfor-mance requirements (energy efficiency and driveability) with-out scarifying battery’s lifetime. Simulation tests using differ-ent driving cycles are conducted for evaluation purpose.

1. INTRODUCTION

1.1. Motivation

Combustion of fossil fuels is one of the major sources of en-vironmental degradation, not only due to related collateralthermal losses but rather due to the harmful exhaust emis-sions. Besides, the continual decay in global reserves offossil fuel sets forth the promotion of renewable energy inmodern transportation systems as an urgent necessity (Ehsaniet al., 2018). Hybrid electric vehicles implement auxiliary

power sources to mitigate the dependency on internal com-bustion engines (ICE). Intelligent hybridization paradigmsoffer flexible power assist and recuperation among on-boardpower sources to avoid inefficient operations of the ICE.Such ICE-based hybrids are considered as a short-term solu-tion towards the All-electric vehicle (AEV), achieving zero-emissions. However, preclusion of the ICE is a challengingstep, due to the high energy density of gasoline and dieselfuels. Advances in electric storage technologies, i.e. batteryand supercapacitor, enabled AEVs to achieve a competitiveperformance compared to ICE-based vehicles (Onori et al.,2016).

Electric batteries are major components in electrified drive-lines. Lithium-Ion (Li-Ion) batteries have higher energy den-sity than capacitors and can take over dynamic power de-mands better than fuel cells; hence, they are widely imple-mented in electric drive-lines (Khaligh & Li, 2010). How-ever, the lifetime of Li-Ion batteries is highly influencedby the intensity of operating conditions, i.a. the powerthroughput, depth of charge/discharge, and overheating. Non-optimal scheduling of battery’s charging/discharging cyclesleads to capacitance fade and decay in the ampere-hour(AH)-throughput. Rapid degradation of the state-of-health(SoH) leads to an earlier replacement of the battery andconsequently increases running-costs of the electric vehi-cle (Kouchachvili et al., 2018).

Power management strategies (PMSs) play an essential roleto retain optimal operating conditions in hybrid and electricpowertrains. A typical objective of PMSs is to maximizethe energy efficiency (mileage per unit energy) of the power-train by reducing the total power consumption per trip (Silvaset al., 2017). This objective is conflicting with battery’shealth as it implies the assignment of intense and transientpower demands to the battery, which shortens its lifetime and

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ANNUAL CONFERENCE OF THE PROGNOSTICS AND HEALTH MANAGEMENT SOCIETY 2019

leads to an ahead-of-time replacement of such costly com-ponent (Moura et al., 2013). Considering the retention ofbattery’s lifetime within the objectives of PMS has a signif-icant potential to achieve the balance between the contradic-tive goals: instantaneous cost (energy use) and running-cost(battery lifetime) of hybrid powertrains. Moreover, meetingthe desired performance requirement (implied by the driver)at various load conditions, without scarifying the targetedobjectives, is a challenge in such lifetime-conscious PMSs,that received further attention from researchers in the last fewyears (Silvas et al., 2017).

1.2. Previous work

1.2.1. Optimal PMS in real-time

Battery’s lifetime-conscious PMSs have been under con-sistent development to achieve the above-mentioned goalsin real-time. Methods of PMSs can be categorized intooptimization-based and rule-based ones (Silvas et al., 2017).Optimization-based algorithms are sophisticatedly formu-lated to define optimal control policies for specific drivingcycles. Such algorithms, i.a. dynamic programming or ge-netic algorithms, are time-intensive and hence are typicallyused as benchmark solutions to define optimized trajecto-ries for battery’s state-of-charge SoCb, that achieves minimalhealth degradation for the considered driving cycle (Ettihiret al., 2016). On the other hand, rule-based algorithms aredefined as simple if-else rules and hence are suitable for real-time applications. In such algorithms, experience-based ormanufacturer-given knowledge is used to derive the controlrules, i.e. charging/discharging boundaries and power assis-tance/recuperation limits of the battery (Wang et al., 2019).

To enhance the solution optimality of power managementdecisions in real-time, two main approaches have beenpresented in literature: first, defining situative rule-basedsolutions; second, conducting a limited-horizon optimiza-tion (Zhang et al., 2015). The first approach implements of-fline situatively optimized control policies during online ap-plication. Vehicle situations, to which optimal solutions areassigned, are defined in terms of multiple characteristic vari-ables, i.a. vehicle speed or SoCb. On the other hand, limited-horizon optimization considers either a simplified powertrainmodel or an equivalent cost conversion to solve an optimalcontrol problem in real-time. The cost function to be mini-mized comprises the estimated lifetime degradation and totalenergy use over the upcoming limited horizon. Kalman filtersare widely implemented to estimate future trajectory of SoCb

based on approximate battery models, such that estimationerrors due to model inaccuracies can be consistently reducedusing feedback control (Ali & Soffker, 2018).

1.2.2. Modeling of Battery degradation

Battery degradation models in literature have been presentedin two ways: first, analytical models of the physical-chemicalreactions within battery cells have been developed to acquiremore insight into capacity fade mechanisms and the sourcesof battery aging (Lipu et al., 2018). From an electrochemicalperspective, emulating the change in solid electrolyte inter-face (SEI) film thickness is a typical example of such mod-els (Moura et al., 2013). Full knowledge of modeling param-eters is essential for such models, which is either intricate toyield or time-consuming to estimate (Bashash et al., 2010).Second, empirical and semi-empirical aging models are usedbased on generic simplified relations to be fitted to relatedexperimental results (Yue et al., 2019). These are simple, yetaccurate models and hence widely implemented in lifetime-conscious PMSs. Such models are based on emulating threemain physical phenomena: 1) capacity fade, 2) increase ofinternal resistance, and 3) decay in remaining lifetime of thebattery.

Fade of capacity refers to the battery’s inability to hold thesame amount charge after repeating cycles or usage, as usu-ally batteries are replaces when no longer capable of holding20 – 30 % of their nominal capacitance (Yue et al., 2019).Furthermore, a merge between ohmic equivalent circuits andempirical relations can be used to express the change in bat-tery’s internal resistance (Remmlinger et al., 2011). Fac-tors believed to influence the degradation process of batter-ies can be summarized as: operating temperature, allowableboundaries for SoCb, depth-of-discharge (DOD), high cur-rent throughput, recharging time(s), and storage conditions(humidity, duration, etc.) (Yue et al., 2019). Due to the lack ofcrisp analytical interrelations between such factors, empiricalmodeling of battery’s degradation became indispensable to anaccurately assess between these factors. Therefore, empiricalbattery degradation models has been increasingly consideredin lifetime-conscious PMSs due to the ease of implementationand tuning requirements of such models (Hoke et al., 2011;Fotouhi et al., 2018).

1.3. Problem statement and contribution

Although the balance between battery degradation and energyefficiency is considered as an optimal solution to lifetime-conscious PMSs, inconsideration of driver’s demand may de-grade the applicability of such solutions (Yue et al., 2019).Providing optimized power management solutions that meetvariable driver requirements, i.e. extended mileage or persis-tent accelerations, with minimal mitigation of battery’s life-time is less introduced in literature (Lipu et al., 2018). Suchsituation-based PMSs have a significant potential to accom-modate unscheduled driving loads without scarifying the de-sired optimality.

This contribution proposes a situation-based PMSs that de-

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fines optimal power handling decisions for different drivingsituations. The battery degradation is represented to the costfunction as an empirical residual lifetime model. Five casesof cost function minimization are solved, considering grad-ual change of the weighting factors between the objectives:energy efficiency and lifetime degradation. The optimizedsolutions for these cases are used to generate a Pareto frontfor the optimization problem. For real-time application, theoptimized solutions can be merged to flexibly fulfill differentdriver’s demand and retain the Pareto optimality.

This contribution is organized as follows: in chapter 2, thepowertrain configuration and parameters modeling are pre-sented. The lifetime-oriented PMS is explained in chapter 3.Simulation results, analysis, and discussion are given in chap-ter 4, followed by the conclusion and future work in chapter5.

2. POWERTRAIN CONFIGURATION

The implemented powertrain in this study is an all-electrichybrid one, that comprises a fuel cell (FC), battery (B), andsupercapacitor (SC) as shown in Fig. 1. The power sourcesare set up in a series-parallel topology, whereby the fuel cellis the primary power source and both the battery and super-capacitor are auxiliary ones. Each power source is coupledwith an inline DC/DC converter to retain a unified voltageubus at the load side. This drive-line topology is investigatedto achieve optimal performance for fuel cell hybrid power-trains (Ozbek et al., 2013).

Figure 1. Driveline topology and operating principle of thefuel cell hybrid electric powertrain.

Modeling of powertrain operation is based on calculatingtraction power demand pd within the vehicle backward model(VBM) given the desired speed (from driving cycle) as

pd “ fxv

“

¨

˚

˚

˝

ma`AρCd

2pv ´ vdq

2

loooooooomoooooooon

Air drag

` mg sin θlooomooon

Grade res.

`µmg cos θ,loooomoooon

Rolling res.

˛

‹

‹

‚

v,

(1)

where fx denotes traction force, mg vehicle curb weight, alongitudinal acceleration, ρ air density,A vehicle frontal area,Cd air drag coefficient, vd wind speed, µ rolling resistancecoefficient, and θ is the road grade. Online power handlingstrategies are decided by the situation-based PMS. Besides, asupervisory control module is implicitly defined in the PMSto ensure the operation within safe limits of individual pow-ertrain components.

The supervisory control is programmed in state machine lan-guage as shown in Fig. 2. The states are grouped based onthree main modes of operation: power idle, demand, andrecuperation. The inputs pd, SoCb, and the supercapacitorstate-of-charge SoCsc are used to define the state transitionswithin each mode. The operating boundaries to be retainedare SoCmin

b , SoCmaxb , SoCmin

sc , SoCmaxsc , and pmax

fc . Op-timized power handling decisions not conforming to theseboundaries are overridden by the supervisory control and ex-cluded during offline optimization process. The demandedpower from each source pfc, pb, and psc are defined as

pfc “ ufc ifc, (2)pb “ ub ib, and (3)psc “ usc isc, (4)

such that

ufc « ub « usc « ubus, (5)

which implies that desired output current from each sourcerifc ib iscs

T represent the control signal to respective DC/DCconverter. Operation of the DC/DC converter can be simpli-fied as

iin “ ioutc

uin

1

µconv, (6)

where the suffices in and out denote input and output currentand voltage, c is a constant representing desired bus voltage,and µconv is the tabulated conversion efficiency based on ex-perimental validation of the simplified model (Ozbek et al.,2013). The output iout in each DC/DC converter becomesifc, ib, and isc for the fuel cell, battery, and supercapacitoraccordingly. Fuel cell voltage can be calculated consideringactivation-, ohmic-, and concentration-voltage losses, uact,uohm, and, uconc, as

ufc “ ncpuofc ´

`

c1 ` c2`

1´ e´ifcc3˘˘

looooooooooooomooooooooooooon

uact

...

´ ifc Rfcloomoon

uohm

...

´ ifc

ˆ

c4 ifcimax

˙c5

looooooomooooooon

uconc

q, (7)

3


Figure 2. Supervisory control as a state machine program

where nc denoted the number of cells in the stack, uofc theopen circuit voltage, c1, ..., c5 constants based on experimen-tal validation, Rfc the internal resistance of the fuel cell,and imax is the maximum delivery current (Ozbek et al.,2013).The supercapacitor is modeled as

usc “ uosc ´Rsc isc ´1

csc

ż tf

ti

isc dt, (8)

where uosc is the open circuit voltage,Rsc and Csc are equiva-lent capacitance and internal resistance of the supercapacitoraccordingly, and ti and tf are initial and final time of an in-finitesimal simulation step. Both Cb and Csc are staticallymodeled neglecting the capacitance loss due to components’aging and lifetime degradation. The state of charge of (SoC)is calculated as

SoC “ SoCi ´1

Qnom

ż tf

ti

I dt, (9)

where SoCi is the initial state of charge, Qnom the rated ca-pacity, and I is either ib or isc. The actual power delivery paat motor terminals should conform to calculated power de-mand pd considering conversion losses as

pa “ pfc ` pb ` psc

“ pfc ` pb ` psc ` losses, (10)

so that pfc, pb, and psc are determined based on the split ratio

ψ “ rβ γs as“

pfc pb psc‰T““

β γ 1´ pβ ` γq‰Tpa, (11)

subjects to the constraint

β ` γ ď 1, @ tβ, γu P r0, 1s. (12)

The motor/generator (M/G) is mechanically coupled to a pro-grammable load-motor emulating the load pl in terms of therolling resistance and air drag according to the speed inputv. Modeling of the Li-ion battery is based on the equivalentcircuit as

ub “ uob ´Rb ib ´1

Cb

ż tf

ti

ib dt, (13)

where uob is the open circuit voltage and Rb and Cb are bat-tery’s capacitance and internal resistance accordingly. Capac-itance loss of the battery Qloss is simply considered propor-tional to the number of charging/discharging cycles ncyclesas

Qloss “ c6 ncycles, (14)

where, the change in uob and Cb due to Qloss is statically de-fined within look-up tables (MATLAB, 2019). Residual life-time of the battery Lres is estimated empirically consideringthe operating temperature Tb, the depth-of-discharge DoD,and the power throughput pb according the work presented

4


in (Hoke et al., 2011) as

Lres “ fp Qloss, Tb, p1´ SoCbq, pb, c7...c10q, (15)

where the constants c6–c10 are tuned such that Lres matchesa nominal lifetime Lnom at 104 cycles before reaching toQloss “ 80%. The considered battery degradation model hasthe following limitation: First, ncycles is calculated consider-ing only complete cycles from maximum to minimum SoCb;second, the effect of ambient temperature on Tb is neglected;third, the uncertainty of linearly anticipated Lres is omitted.However, such this model has been plausibly implementedin many lifetime-conscious PMSs, where the main objectiveis to define optimal control strategy considering the trade-offbetween energy efficiency and battery degradation (Fotouhiet al., 2018).

3. BATTERY’S LIFETIME-ORIENTED PMS

3.1. Situation-based PMS

Situation-based PMSs are based on defining specific ve-hicle states, to which the control parameters can be opti-mized (Gong et al., 2008). Vehicle states can be definedheuristically or based on multiple characteristic variablesfrom driving data history. For online application, vehiclestates are recognized in real-time and the optimized solu-tions can be assigned accordingly. Situation-based PMSs areproved to have low computational requirements and being ca-pable of yielding near-optimal solutions for the power man-agement problem. An illustration of the working principle ofsituation-based PMS is given in Fig. 3. In this contribution,

StaterecognitionEnvironmentt

Driver demandSB-optimal

solutions

Vehiclestate

VehicleSB-PMstrategy

Data-bankState

definition

SB-PMoptimization

•

•

vehicle parameters•

•

Offl

ine

Data-bankState

definition

SB-PMoptimization

Figure 3. Operating principle of situation-based powermanagement system.

a multi-dimensional space (grid-space) is defined for linearmapping of vehicle states. The axes of grid-space are the se-lected characteristic variables, to which specific discretizationlevels are assigned. An exemplification of alternative struc-tures of grid-space is shown in Fig. 6. In a previous workof the authors (Ali et al., 2019), the impact of different char-acteristic variables on total cost minimization is statisticallyanalyzed, putting forth that certain constellations (set of axisat certain discretization levels) outperforms all other constel-lations at various driving cycles. This contributions proceedswith a constellation comprising the variables: vehicle speedon V-axis, power demand on P-axis, and SoCb on B-axis.

Numerical values for discrete levels of grid-space axes are

P5

P7

P9

V4

V5

V6

D1

D2

D3

C5:

50 states

C3:

60 states

C1:

20 states

P5

V4

D3

P (1)5

P (5)5

V4(1)

V4(4)

D3(1)

D3(3)

s38

s12

C3: [s , ...,s ]1 60

Figure 4. Implementation of characteristic variables ingrid-space structure with focus on state definition in an

exemplified constellations C3.

subject to an optimization process that aims to improve therepresentation of all vehicle states in grid-space. This can beexplained, for instance, for the V-axis as

V n “ rV1, V2, ..., Vns , (16)

is the vector comprising n discrete levels for vehicle speed.The optimization task is defined as

minimize J1 “ fpNv, Vnq, (17a)

s.t.Vnpiq P rvmin vmaxs, (17b)

where Nv denotes points’ count of v in the data-bank, f afunction defining the difference in points’ count between theintervals rV n

i : V ni`1s, where i “ 1, 2, ..., n as shown in

Fig. 5. This optimization process is conducted simultane-ously for the other P- and B-axes. The acquired achievementby solving Eqn. (17a) is shown in Fig. 6, where more ho-mogeneous representation and less number of missed statedcould be achieved in the optimally discretized grid-space.

0 20 40 60 80 100 120 140

Vehicle speed [km/h]

0

2

4

6

Den

sity

(co

unts

)

Vn(3)

Vn(n)

Vn(2)

Vn(1)

x 100

Figure 5. Projection of discrete values for Vn on thehistogramic plot of vehicle speed in the data-base.

Optimal power split ratio for each vehicle state is defined as

Ψ “ rψ1 ψ2 ... ψms, (18)

where ψi denotes the split ratio associated to respective vehi-cle state si @ i P t1, 2, ...,mu, where m is the total number ofvehicle states in grid-space. The optimization task is definedas

min J “ min rα1 α2s

„

obj1pΨ, x, tqobj2pΨ, x, tq

, (19)

5


060

2

36

4

6

12 120

Power

8

Speed

-12 80-36 40

-60 0

x10

5

(a)

0

1

2

3

Power Speed

4

Vopt

4(4)

. . . .

Vopt

4(1)

x10

5

Popt

5(5)

Popt

5(1)

. . . .

(b)Figure 6. Improving vehicle states representation in

grid-space using optimally-spaced axes in (6b) compared toequally-spaced ones in (6a).

for

obj1pΨ, x, tq “

ż tf

t0

pfc dt and (20)

obj2pΨ, x, tq “

ż tf

t0

Lloss dt, (21)

s.t.

SoCminb ă SoCb ă SoCmax

b , (22a)

SoCminb ă SoCb ă SoCmax

b , (22b)

iminfc ă ifc ă imax

fc , (22c)

iminb ă ib ă imax

b , (22d)

iminsc ă isc ă imax

sc , and (22e)β ` γ ď 1, @ tβ, γu P r0, 1s, (22f)

where t0 and tf denote initial and final simulation time, α1

and α2 weighting factors, Lloss “ the lifetime degradation ofthe battery pLnom ´ Lresq, and x the state vector defined as

x “ rifc ib isc Qloss T SoCb SoCscs . (23)

The formulation of objectives obj1 and obj2 sets forwardthe conflict between minimizing the pfc and Lres simulta-neously, whereby the conventional lifetime-oriented strategyby minimizing ib, is not sufficient to achieve the balance be-tween both objectives. The optimization problem is a typicalmulti-objective one, solved as a weighted-sum minimizationto introduce interactive effect through different values for theweighting factors α1 and α2.

4. RESULTS ANALYSIS AND DISCUSSION

4.1. Offline optimization results

Five different cases are assigned to solve Eqn. (19), based onthe values of α1 and α2 shown in Table 1. The optimizationcases vary from highest priority for battery’s health in case-1 up to highest priority for minimizing fuel cell energy incase-5. The cost minimization problem in each case is solvedusing non-dominant sorting genetic algorithms (NSGA-II),

based on the work presented in (Deb et al., 2002; Lin, 2011).This contribution considers 100 generations, each of 50 pop-ulations to acquire the optimal solution using NSGA-II. Themutation and crossover rates are adaptively set based on thesize of explored space. The driving cycle used for offline op-timization is based on standard regulations for abuse testingof Li-ion batteries as shown in Fig. 7 (Ruiz et al., 2018).

Table 1. Values of the weighting factors for eachoptimization case.

Case-1 Case-2 Case-3 Case-4 Case-5α1 1 3 5 7 9α2 9 7 5 3 1

Figure 7. Speed profile during offline optimization showingrepeating acceleration, coasting, and deceleration rounds for

5.56 hours.

Optimization results for the cost function, including all in-dividual solutions from the first generation and the evolvedbest solution from each generation up to the end are shown inFig. 8. The significance of random exploration of the solutionspace can be perceived from the figure, leading to rapid con-verge to the global. Moreover, given a normalized measurefor both objectives during the optimization, it can be noticedthat penalizing inefficient usage of the battery leads to bettervalues of total cost in cases 1–3. Contrarily, reducing thesepenalties in cases 4 and 5 results in relative increase of thetotal cost. This point is discussed quantitatively in the sequel.Objectives-wise, the direction of solution’s evolution towardsoptimality can be contextually explained, given the weight-ing factors for each case (see Table 1). In case-1, a verticalevolution can be notices (minimizing obj2), towards a gradu-ally horizontal advance in case-5 (minimizing obj1), meetingthe optimality criterion in each case. The best ten solutionsin each case are shown in Fig. 9. While the ordinate of allsolutions almost cover the whole span of obj2, their abscissafalls « 50 % of the achievable span for obj1, which pointsout the minimal requirements on the fuel cell as a primarypower source. Besides, a patent vicinity can be identifiedbetween the solutions in cases 1 and 2, where α2 still out-weighs α1, which promotes battery health concerns in obj2.A pseudo Pareto front is established for this control problemusing curve fitting tools based on available results.

4.2. Online application and comparative evaluation

For the online testing and evaluation of developed situation-based health-conscious power management system (SB-HC),

6


Figure 8. Evolution of the cost function minimization through generations and iterations using NSGA-II.

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75

obj1

1

1.5

2

obj 2

Case-1 Case-2 Case-3 Case-4 Case-5 Fitted Pareto front

Figure 9. Fitted curve for the optimality Pareto front of thecost minimization problem based on best results in each

case.

nine repeated US06 driving cycles have been considered. Foreach of these driving cycles, one of the optimized solutions ora merge between two solutions have been applied as shown inFig. 10. This scheme aims to emulate different driver’s atti-tudes, to which optimized solutions can be flexibly assignedto retain battery’s lifetime without scarifying the driveabil-ity. The developed method is comparatively evaluated againsta single-case optimized rule-based one, which implementsno weighting factors into the rules optimization. The rec-

0 600 1200 1800 2400 3000 3600 4200 4800 5400

Time [s]

0

50

100

150

Spee

d [

km

/h]

0

1

2

3

4

5

6

Appli

ed c

ase

solu

tion

Figure 10. Applying different control strategies over ninerepeated us06 driving cycles; dashed lines for merged

solutions between two consequent cases.

ognized vehicle states during online application are shownin Fig. 11. The implemented structure of grid-space offers324 discrete states based on the characteristic variables: ve-

hicle speed, power demand, and SoCb. As the former twovariables are not control-dependent, i.e. are identical in bothcontrol methods, the difference in recognized states shouldbe only a function of SoCb. Having the same initial condi-tions, both methods achieved the same states almost up to theend of first cycle (second 500). Afterwards, different statesare achieved for each method, to which totally different so-lutions have been optimized offline. Approaching the eighthcycle (second 4000), vehicle states started to match again.Applied control cases in the last two cycles are less protec-tive regarding battery’s lifetime aspects, which retains SoCb

into similar working regions as per the RB method. The tran-

Figure 11. Vehicle states, from grid-space, for both controlmethods: SB-HC and RB.

sitions of vehicle states are explained in detail showing theSoCb and SoCsc profiles for both control methods in Fig. 12.It can be seen in Fig. 12 that RB method performs a mod-erate charge-sustaining strategy in almost three consequentus06 cycles before reaching the lower limit for SoCb. Onthe other side, the SB-HC algorithm conducts a conserva-tive strategy at the beginning, preserving the on-board chargelonger and avoiding higher DoD values. The impact of eachcontrol strategy on the synergy role of the supercapacitor canbe explained from the results shown in Fig. 12. The rapiddepletion of SoCb using Rb method put more synergy taskson the supercap., i.e. several cycles and accordingly unsched-

7


uled loading of the fuel cell. The power output profile of the

20

40

60

80

SoC

b

SB-HC RB

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Times [s]

20

40

60

80

SoC

sc

Figure 12. State of charge profiles for the battery andsupercapacitor.

battery as shown in Fig. 13 reveals more information abouteach control strategy, where the faster charge depletion us-ing RB method urged repeating recharging phases to retainSoCb above the lower boundaries. It can be seen that rela-tively more recharging power has been assigned to the batteryusing RB method more than SB-HC. This implicitly requiresunscheduled power from the fuel cell and urges the super-visory control to override the offline optimized solution, i.e.temporarily violate the optimal trajectory.

0 1000 2000 3000 4000 5000

Time [s]

-20

-10

0

10

20

30

Pow

er

[kW

]

SB-HC RB

Figure 13. Power throughput of the battery using both PMSs.

To get more insight into the operation of the fuel cell and theestimated battery degradation, accumulated pfc and ∆Lb areshown in Fig. 14. The accumulated ∆Lb in the figures is pro-portionally related to the above shown results for T . pb, andSoCb. It is presumable, that prioritizing battery’s health willinduce an increase in fuel cell energy consumption, whichreached for the overall test to 11.15 %. However, the reduc-tion in lifetime degradation is substantial « 64.63 %. Due

0

20

40

SB-HC RB

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Times [s]

0

1

2x 10

-3

Figure 14. Total consumed energy and accumulated drop inresidual lifetime using SB-HC and RB methods.

to the fact that multiple cases within the developed SB-HC

method are applied during the same test, it is more relevantto analyze the previous energy and battery degradation re-sults for cycle-based segments as shown in Fig. 15. Fromthe results, it can be concluded that using SB-HC method ledto an increasing consumption of fuel cell energy per cyclesin the first five cycles, i.e. where the battery’s lifetime hasbeen prioritized. However, in three out of the last four cy-cles, SB-HC method assigned less synergy role to the fuelcell. Regarding the battery’s lifetime degradation per cycle,the SB-HC method achieved steadily lower ∆Lb per cyclefor the whole test procedures. The last four cycles show thatSB-HC method can achieve total energy saving and yet pre-serve battery’s lifetime. This puts forth the impact of re-taining battery’s health and flexibly responding to variabledriver’s demands, which is the core of this contribution. In

2

3

4

5

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Time [s]

0

2

4x 10

-4

Figure 15. Change per one driving cycle in total consumedenergy and accumulated drop in residual lifetime for both

control methods.

Table 2, a descriptive summary of the energy efficiency andbattery’s lifetime results is presented. Energy efficiency (ηen)is a well-known measure for evaluating vehicular propulsionefficiency, based on consumed energy per 100 km. In thetable, ηen is calculated per cycle to evaluate the energy con-sumption and the total value as well. Summarized results ofbattery’s lifetime ∆Lb reveal the significant reduction in bat-tery degradation over individual cycles, i.e. various driver’sbehavior for the whole trip.

5. CONCLUSION AND FUTURE STEPS

In this contribution, a novel method addressing battery degra-dation issues in power management of hybrid electric vehi-cles is presented. The method implements a situation-basedprinciple to assign optimized power handling solutions in dif-ferent vehicle states in real-time. Vehicle states are defined interms of multiple characteristic variables, i.e. vehicle speed,power demand, and SoCb. The power management problemfor the fuel cell hybrid vehicle is defined in terms of minimiz-ing two objectives: consumed energy from the fuel cell, andbattery’s degradation. The optimization problem is solved of-fline as a weighted-sum using NSGA-II.

For the offline optimization, five cases are assigned to theweighting factors, to define the optimized solutions at dif-

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Table 2. Summary of online test results for energy efficiency and battery’s lifetime.

Per cycle nr. Total

1 2 3 4 5 6 7 8 9 –

ηen [kwh/100 km]SB-HC 26.8 27.0 25.6 31.8 30.1 24.9 24.6 27.3 23.5 29.7

RB 18.6 20.3 21.3 27.0 26.2 25.8 26.3 25.8 26.2 26.7

∆Lb [x10´5 year]SB-HC 4.36 6.78 10.0 9.44 8.32 10.8 15.1 18.7 21.4 104.9

RB 7.14 13.8 20.2 21.7 22.0 22.0 22.0 21.9 22.0 172.1

ferent priority levels of each objective. These solutions canbe decisively selected by the driver or adaptively set accord-ing to the battery’s status. Results from the online applicationreveals the ability of presented method to accommodate dif-ferent driver’s priorities during the whole trip, and yet achievea significant improvement in preserving battery lifetime. Anincrease of 11 % in the fuel cell’s energy is yielded usingSB-HC; however, an improvement up to 60 % in battery’sresidual lifetime could be achieved.

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BIOGRAPHIES

Ahmed M. Ali received the B.Sc. degreeand the M.Sc. degree, both in Mechani-cal Engineering from the Military TechnicalCollege, Cairo, Egypt, in 2008 and 2015 re-spectively. He is now with the Chairof Dynamics and Control, University ofDuisburg-Essen, where he works towards

the Ph.D. degree in the field of optimal design and controlof hybrid vehicles.

Bedatri Moulik received her Bachelors de-gree in Electrical Engineering and Mas-ters degree in Control and InstrumentationEngineering from West Bengal Universityof Technology, Kolkata, India. She re-ceived her Dr.-Ing. degree from the Chairof Dynamics and Control, University of

Duisburg-Essen, Germany. She is now an Assistant Profes-sor at Amity University, Noida, India in the Department ofElectrical and Electronics Engineering.

Nejra Beganovic received the B.Sc. andM.Sc. in Electrical Engineering fromthe University of Sarajevo, Chair of Au-tomatic Control and Electronics, Bosnia-Herzegovina, in 2009 and 2011 respectively.In 2016, she has received the Dr.-Ing. de-gree from the University of Duisburg-Essen,

Chair of Dynamics and Control, Germany. From October2017 to February 2019, she was an Assistant Professor atthe International Burch University, Sarajevo. Since February2019, she is a postdoctoral researcher at Mid-Sweden Uni-versity, Department of Electronics Design, Sweden. Her re-search interests include structural health monitoring, lifetimeprognostics, and advanced signal processing methods withspecial emphasis on real-time implementation of classifica-tion and prognostic algorithms.

Dirk Soffker received the Dr.-Ing. degreein mechanical engineering and the Habil-itation degree in automatic control/safetyengineering from University of Wuppertal,Wuppertal, Germany, in 1995 and 2001, re-spectively. Since 2001, he leads the Chair ofDynamics and Control with the Engineering

Faculty, University of Duisburg-Essen, Germany. His currentresearch interests include elastic mechanical structures, mod-ern methods of control theory, human interaction with safetysystems, safety and reliability control engineering of techni-cal systems, and cognitive technical systems.

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