Online EnerMana for HEV (IEEE Trans,Model,DP,Solution)

8/2/2019 Online EnerMana for HEV (IEEE Trans,Model,DP,Solution)

1/13

3428 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 6, NOVEMBER 2008

Online Energy Management forHybrid Electric Vehicles

John T. B. A. Kessels, Member, IEEE, Michiel W. T. Koot,Paul P. J. van den Bosch, Member, IEEE, and Daniel B. Kok

AbstractHybrid electric vehicles (HEVs) are equipped withmultiple power sources for improving the efficiency and perfor-mance of their power supply system. An energy management (EM)strategy is needed to optimize the internal power flows and satisfythe drivers power demand. To achieve maximum fuel profitsfrom EM, many solution methods have been presented. Optimalsolution methods are typically not feasible in an online applica-tion due to their computational demand and their need to havea priori knowledge about future vehicle power demand. In thispaper, an online EM strategy is presented with the ability to mimicthe optimal solution but without using a priori road information.

Rather than solving a mathematical optimization problem, themethodology concentrates on a physical explanation about whento produce, consume, and store electric power. This immediatelyreveals the vehicle characteristics that are important for EM. Itis shown that this concept applies to many existing HEVs as wellas possible future vehicle configurations. Since the method onlyfocuses on typical vehicle characteristics, the underlying algorithmrequires minor computational effort and can be executed in realtime. Clear directions for online implementation are given in thispaper. A parallel HEV with a 5-kW integrated starter/generator(ISG) is selected to demonstrate the performance of the EM strat-egy. Simulation results indicate that the proposed EM strategyexhibits similar behavior as an optimal solution obtained fromdynamic programming. Profits in fuel economy primarily arisefrom engine stop/start and energy obtained during regenerative

braking. This latter energy is preferably used for pure electricpropulsion where the internal combustion engine is switched off.

Index TermsEnergy management (EM), fuel economy, hybridelectric vehicle (HEV), incremental fuel cost.

I. INTRODUCTION

OVER the years, the automotive industry has put much

effort into developing vehicles that satisfy todays high

standards on safety and comfort and simultaneously com-

ply with strict environmental regulations. One of the leading

Manuscript received October 22, 2007; revised January 6, 2008. First

published March 5, 2008; current version published November 12, 2008. Thereview of this paper was coordinated by Mr. D. Diallo.

J. T. B. A. Kessels was with the Control Systems Group, Department ofElectrical Engineering, Technische Universiteit Eindhoven, 5600 Eindhoven,The Netherlands. He is now with TNO Science and Industry, 5700 Helmond,The Netherlands (e-mail: [email protected]).

M. W. T. Koot is with Vision Dynamics, 5652 Eindhoven, The Netherlands(e-mail: [email protected]).

P. P. J. van den Bosch is with the Control Systems Group, Department ofElectrical Engineering, Technische Universiteit Eindhoven, 5600 Eindhoven,The Netherlands (e-mail: [email protected]).

D. B. Kok is with the Micro Hybrid Systems and Energy ManagementGroup, Ford Dunton Technical Center, SS15 6EE Basildon, U.K. (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2008.919988

technologies on the road to sustainable mobility is the hy-

brid electric vehicle (HEV) [24]. By applying a secondary

power source, these vehicles offer a significant improvement in

fuel economy compared with vehicles with a traditional drive

train.

HEVs require an advanced energy management (EM) strat-

egy to control the power of the primary and secondary power

source [3]. Many solutions have already been presented in the

past, covering heuristic approaches [1], [5] as well as advanced

strategies based on optimization techniques [6], [8], [9], [12],[14], [19], [21], [22]. In particular, the optimization concept

offers a well-defined solution to the stated EM problem. How-

ever, online implementation is often not possible due to their

computational demand. Another obstacle is the need for a priori

knowledge in terms of exact predictions about the future driving

cycle, see, e.g., [20]. To circumvent this problem, Guzzella and

Sciarretta propose the Equivalent Consumption Minimization

Strategy (ECMS) [8], which is directly derived from an optimal

solution, but no prediction information is needed. Likewise,

this concept is also demonstrated by Delprat et al. [6], em-

phasizing the direct relation with optimal control. Nonetheless,

owing to the mathematical problem formulation, the important

vehicle characteristics for EM cannot easily be recognized inthe available numerical solution. As a result, difficulties appear

when predicting the impact of new vehicle technologies on the

performance of EM. In addition, the EM system itself remains

a complex optimization algorithm, and its decision process

cannot easily be decomposed into elementary decisions.

Dual to the ECMS method, this paper presents an online

EM strategy based on physical insight into the EM problem.

Although the concept still originates from optimal control,

a detailed analysis leads to a clear understanding of vehicle

characteristics, which are dominant for EM. This yields direct

information about when to produce, store, and consume electric

power, as well as which components are responsible for theseactions. Rather than solving one complex optimization prob-

lem, insight is generated into the decision process behind EM.

Adequate rules are defined to cut down the system complexity

of the EM strategy. This way, a real-time implementation is

easily satisfied because of the low computational demand; the

EM strategy only exploits typical vehicle characteristics that are

relevant for EM.

An early publication of the proposed EM strategy appeared

in [12], but then, the research focused on vehicles with a

traditional drive train. Subsequently, a proof of concept was

published in [11], showing experimental results with a demon-

strator vehicle on a roller dynamometer. This paper presents

0018-9545/$25.00 2008 IEEE


2/13

KESSELS et al.: ONLINE ENERGY MANAGEMENT FOR HYBRID ELECTRIC VEHICLES 3429

Fig. 1. Three alternative vehicle topologies (arrows indicate nominal power flow). (a) S-HEV. (b) P-HEV. (c) S/P-HEV.

a generalized concept for existing HEVs and possible future

configurations. By means of three popular HEV topologies,

i.e., a series (S), parallel (P), and series/parallel (S/P) HEV, the

validity of the proposed concept will be demonstrated. It will

be shown that the EM strategy achieves a performance close to

the optimal strategy (based on exact prediction information) but

without the need for knowledge about the future driving cycle.

In addition, a formal strategy derivation is presented to point outthat the method is physically and mathematically sound. Clear

algorithms for online implementation are given as well.

This paper is organized as follows. An adequate vehicle

model is presented in Section II. This model is used in

Section III to explain the physical background of the EM

decision process. This section also defines different operating

modes that will be used by the EM algorithm. A formal problem

definition for the EM strategy is given in Section IV, and

the mathematical derivation of the strategy can be found in

Section V. This latter section also presents an exact description

for online implementation, including a method to estimate the

driving characteristics online in the vehicle. The simulation re-sults focus on the P-HEV topology and are given in Section VI.

Finally, conclusions can be found in Section VII.

II. VEHICLE MODEL

This paper focuses on three popular HEV topologies. First,

the S-HEV does not have a mechanical connection between

the internal combustion engine (ICE) and the wheels, and its

model is shown in Fig. 1(a). Next, the P-HEV is demonstrated

in Fig. 1(b). In P-HEV, the ICE and the electric machine can

both give tractive force to the wheels, offering freedom for EM.

The third vehicle configuration is the S/P-HEV, and its model is

visualized in Fig. 1(c). The S/P-HEV has maximal freedom forEM due to its versatile power split device. In these three vehicle

topologies, one can recognize similar components. These are

discussed below.

Rather than focusing on vehicle dynamics, the correspond-

ing models concentrate on fueling characteristics and energy

efficiency. As a result, only dynamic aspects necessary for EM

are considered. A good example of EM including all dynamic

equations can be found in [15].

A. Fuel Tank(F)

The fuel in the tank is the primary energy source in all vehicle

configurations. In this paper, the chemical energy content of

fuel is denoted by the lower heating value hf (in joules pergram).

B. ICE

In the literature, the fuel consumption of an ICE is usually

shown by a static nonlinear map, describing the relation be-

tween the crankshaft torque m (in newton meter), the enginespeed (in radians per second), and the fuel rate f(m, )(in grams per second). Here, it is preferred to define the fuel

consumption as a function of engine power Pm (in watts) andspeed as

fuelrate = f(m, ) = f(Pm|) (in grams per second).(1)

The notation with the conditional operator | is introduced toemphasize the dependency of Pm on . The advantage of thisnotation becomes clear when explaining the control objective

of an EM strategy.

Contrary to P-HEV and S/P-HEV, the S-HEV has no me-

chanical connection between the ICE and the wheels. There-fore, ICE is allowed to run in several operating points (m, )


3/13


and still deliver equal power Pm = m. From an efficiencypoint of view, it will be beneficial to operate the engine only

in those operating points that entail minimum fuel use for a

given power request. The set of operating points that fulfill this

criterion is called the e-line (economy line), and for a given

power request Pm, the corresponding e-line operating point is

uniquely defined as

Pe-linem = arg min(m,)Q(Pm)

f(m, ) (in watts) (2)

with

Q(Pm) = {(m, ) | Pm = m} . (3)

As a result, (1) simplifies for the S-HEV into the following

description:

fuelrate = f

Pe-linem

(in grams per second). (4)

C. MG

An HEV also uses an electric machine for vehicle propulsion.

Depending on the power flow direction, this machine operates

in either motor mode or generator mode. Therefore, the electric

machine will be addressed in this paper as motor/generator

(MG) as well. It is assumed that appropriate facilities exist

in the electric power net to actively control the power of all

electrical components.

At its mechanical side, the signals of interest are the speed

MG (in radians per second), the torque MG (in newton me-ters), and the mechanical power Pem = MG MG (in watts).

The electric side only considers the electric power Pe (in watts)without notion of the voltage and current. When operating ingenerator mode, Pe and Pem take a positive value. On the otherhand, these signals become negative valued during motor mode.

For each mode, the corresponding efficiency is defined as

Motor mode:

mm(MG, MG) =PemPe

=MG MG

Pe[] (5)

Generator mode:

gm(MG, MG) =Pe

Pem=

PeMG MG

[]. (6)

It is assumed that both efficiencies can be measured and that

they remain fixed for a given sampling interval. This way, the

model of the electric machine can be expressed by one single

equation

Pem = max

mmPe,

1

gmPe

(in watts). (7)

Similar to [20], the model (7) introduces linear losses for the

MG, although it does not provide a good description of the

friction losses at zero power. In [13], it is shown how these

losses can be included as a speed-dependent offset term, but this

extension is not taken into account here. The power limitations

of the electric machine are defined at its mechanical side as

Pemmin Pem Pemmax. (8)

TABLE IPARAMETER LIST FOR DRIVE TRAIN MODEL

For the S-HEV, there is another electric machine present, but

this device only operates in generator mode. The model for this

generator G is adopted from (7) as

Pg = gmPgm (in watts). (9)

D. Drive Train (D)

The power demand Pd from the drive train is calculated witha quasi-static backward-calculating vehicle model. Depending

on the selected vehicle topology, this model encompasses dif-

ferent vehicle components. The vehicle chassis and the final

drive are present in all vehicle topologies. For a given ve-

hicle speed v(t) (in meters per second) and road slope (t)(in radians), the corresponding wheel force Fw(t) (in newtons)is equal to

Fw(t) = mv(t) +1

2CdAdv(t)

2

+ mg [sin((t)) + Cr cos((t))] . (10)

A description of all the parameters is given in Table I. Further-more, this table also provides the parameter values for a mid-

sized vehicle as used in the simulation environment.

The drive train torque d(t) (in newton meters) and therotational speed d(t) (in radians per second) in S-HEV andS/P-HEV follow by taking into account the wheel radius wr(in meters) and the final drive ratio fr[] as

S-HEV and S/P-HEV:

d(t) =

frwr

v(t)d(t) =

wrfr

Fw(t). (11)

Different from these vehicle configurations, the drive train of

the P-HEV incorporates a gearbox. To that end, the gear ratio

gr(t)[] is added to the previous equations

P-HEV:

d(t) =

frwr

gr(t)v(t)

d(t) =wrfr

1gr(t)

Fw(t). (12)

Finally, the mechanical power request Pd (in watts) from thedrive train is equal to

Pd(t) = d(t)d(t) = v(t)Fw(t). (13)

E. Power Split (PS)

P-HEV and S/P-HEV have more than one power sourceavailable for vehicle propulsion. Therefore, they make use of a


4/13


Fig. 2. Description of planetary gear train.

mechanical power split to connect the individual power sources

to the drive train. The power split is assumed to have no energy

losses and provides the following power balance:

P-HEV: Pm = Pd + Pem (in watts) (14)

S/P-HEV: Pm = Pd + Pem1 + Pem2 (in watts). (15)

In P-HEV, the power split establishes a direct connectionbetween ICE and the drive train, whereas the connection of

the MG includes an additional gear. On the other hand, the

power split of the S/P-HEV is built up with an electronically

controlled Continuously Variable Transmission (eCVT) using

a planetary gear train (see Fig. 2). Recently, various eCVT

configurations have been developed for future HEVs, all using

similar hardware technologies [17]. As a result, they can still

rely on the same concept for EM.

The configuration selected here is derived from a Toyota

Prius, where the ICE is directly coupled to the carrier gear, see,

e.g., [16]. The first MG (MG1) is linked to the sun gear, whereas

the second MG (MG2) is linked to the ring gear. In addition, the

drive train is linked to the ring gear. Therefore, the power at the

ring gear Pr (in watts) is aggregated from the drive train powerand the power through MG2 as

Pr = Pd + Pem2. (16)

The kinematics of a planetary gear train define the relation

between the rotational speeds of the ring gear r, sun gear s,and carrier gear c. Using the radii of the ring gear Rr (inmeters) and the sun gear Rs (in meters), the rotational speedsin the system are described by

s + rZ = c(Z+ 1) (17)

with the basic gear ratio Z[] defined as

Z =RrRs

. (18)

By assuming that there is no inertia present in the planetary gear

train, and when there is no energy dissipation, the law of power

conservation describes the static relation between all powers

applied to the eCVT. Given the speed and torque , as definedin Fig. 2, the following relation emerges:

Psun + Pc + Pr = 0 (19)

ss + cc + rr = 0. (20)

In addition, the torques acting on the sun, carrier, and ring gear

have to be balanced in all situations as

s + c + r = 0. (21)

The relations (17), (20), and (21) provide a complete descrip-

tion of the planetary gear train. Nevertheless, for practical

situations, it is convenient to replace (20) and (21) with analternative representation. A description with the basic gear

ratio follows from the substitution of (17) and (21) into (20).

This yields two linear equations, i.e.,

r = Zs (22)

c = (Z+ 1)s. (23)

Note that these relations are also found by considering two

special situations for (17) and (20), i.e., c = 0, and r = 0.

F. Battery (B)

The battery model is constructed from two elements, i.e., an

energy storage buffer and a static efficiency map. The efficiency

map expresses the relation between the power Pb (in watts) atthe battery terminals and the net internal power Ps (in watts).For convenience, the efficiency map is modeled through an ef-

ficiency number 0 bat 1. Physically, one can make a dis-tinction between the losses that occur during charging (Ps 0)and discharging (Ps < 0). Denoting these losses through theparameters + 1 and 1, respectively, with bat=

+

results in the following parameterization:

Pb = maxPs, 1+

Ps . (24)A simple integrator is used to model the energy storage buffer

of the battery, i.e.,

Es(t) = Es(0) +

t0

Ps(t)dt (in joules). (25)

The theoretical energy capacity Ecap (in joules) is used tonormalize the stored energy in the battery, and its energy status

is defined by the state of energy (SOE) as

SOE(t) =

Es(t)

Ecap 100 [%]. (26)

G. EL

The electric load (EL) denotes the electric power demand of

all auxiliaries present in the vehicle. It is assumed that this load

is power based, and its power demand is represented by PL(in watts).

H. Electric Power Net

The power net accumulates the power flow from all electric

devices. For simplicity, it is assumed that the required powerconverters (including their energy losses) are incorporated into


5/13


Fig. 3. Fuel consumption ICE matches piecewise linear function (ICE speed

constant).

the electric machine and ELs. Furthermore, no losses are as-

sumed in the wiring system. This way, the power net reduces to

the following power balance:

S-HEV: Pe + Pg = Pb + PL (27)

P-HEV: Pe = Pb + PL (28)

S/P-HEV: Pe1 + Pe2 = Pb + PL. (29)

III. STRATEGY OUTLINE

From an EM strategy, it is expected that it supplies the total

(electric) power demand with the highest efficiency and, hence,minimum fuel usage. By controlling the power through the MG,

it decides upon efficient operating points of many vehicle com-

ponents. The storage capacity of the battery takes care of the un-

balance between the generated power and the requested power.

To obtain insight into the decision process of an EM strategy,

emphasis will be put on the fuel map of the ICE. Therefore,

the fuel function f(Pm|) in (1) from a 2.0 gasoline ICEis shown in Fig. 3. In contrast to existing literature, the fuel

map is deliberately presented as a function of engine power

Pm using separate curves for different engine speeds . Thisway, it reveals three areas where there exists an almost linear

(affine) relation between f and Pm. Typically, the slope ofthis curve remains almost constant within each area and equals

the following definition:

(Pm|) =f(P|)

P

P=Pm

(in grams per joule). (30)

Intuitively, it is clear that expresses the additional fuel massflow to produce a small amount of mechanical power given a

certain power level Pm. Hence, expresses the incremental fuelcost. With the help of this definition, each fuel curve can be

approximated as a piecewise affine function

f(Pm|) fi() +i()Pm

for i = 0, 1, . . . , N f; Pm i (31)

and with Nf + 1 line segments

i = {Pm|Pmi Pm Pmi+1}. (32)

For this particular engine, it is sufficient to take Nf = 2

f(Pm|)

0, ifP

m < Pm1f1 + 1Pm, ifPm1 Pm < Pm2f2 + 2(Pm Pm2), ifPm Pm2

(33)

where Pm1 = f1/1 < 0 denotes the fuel cutoff point, andPm2 > 0 indicates a point close to the maximum engine power.Note that all parameters fj , j , and Pmj depend on , although

the influence on j is limited (jhf = 2.4 4.0[]). Thisimmediately puts a limitation on the possible benefits of any

EM strategy, since profits in fuel economy arise in the fol-

lowing ways.

1) Producing less power with the ICE and thereby requestingenergy from the battery are favorable for large values

ofj .2) Producing extra power with the engine and storing the

surplus energy in the battery are favorable for small

values ofj .3) For a constant ICE power Pm, a reduced engine speed

decreases the fuel use f1. Moreover, if the ICE is turnedoff, the battery becomes the primary power source, and

although recharging requires additional fuel, this can still

economically be attractive since f1 has been eliminated.

Now suppose that 1, 2, and f1 of ICE are constant. In

this case, the EM strategy can only benefit from the followingmechanisms to improve the vehicles fuel economy.

Regenerative braking (R): In a traditional vehicle, the me-

chanical friction brakes become active when the

driver wants to decelerate the vehicle. From an en-

ergy point of view, this is not an economic solu-

tion, since all kinetic energy is wasted into heat.

To recover the energy that comes available during

braking periods, one can operate the electric machine

in generator mode. This way, the electric machine

absorbs power from the drive train and stores it in

the battery. In terms of fuel economy, this is the

most economical way to charge the battery, sinceit requires no additional fuel. Nevertheless, for a

correct driveability of the vehicle, it is not allowed

to recuperate all braking energy solely from the front

or rear wheels. Therefore, the potential available

energy reduces for a two-wheel drive. In addition, the

power ratings of the electric machine and the charge

acceptance of the battery limit the actual amount of

stored energy.

Engine stop/start: In a traditional vehicle, the ICE is kept

idle when the driver requests no propulsion power.

A simple method to save fuel is to stop the engine at

those moments (e.g., waiting for traffic lights). For

driver comfort, a quick vehicle response is preferredwhen the driver wants to move on, but given the


6/13


fact that a powerful electric machine is present in an

HEV, smooth engine cranking is no problem.

Motor only (MO): Except for exclusively applying engine

stop/start at moments when the vehicle stands still

(or during R), an HEV can also apply electric drive

and still keep the ICE off. This situation is referred to

as the MO mode. In particular, the selection of MOduring vehicle launch turns out to be an excellent

way to utilize the energy from R.

All the mentioned methods take place with the ICE turned

off. Furthermore, their economic profits rely on the absolute

(constant) value of 1, 2, and f1 rather than variations overtime. This is different when the ICE is turned on. In that case,

the EM strategy considers the changes in and discriminatesbetween the following modes of operation.

Baseline (BL): By definition, the BL situation implies that

the battery is not used so that Pb = 0. Physically, thismeans that the mechanical power delivered by the

ICE continuously matches the vehicle power demandPd plus PL.

Motor assist (MA): In the situation of MA, ICE produces

less mechanical power than requested by the drive

train and the auxiliary loads. The battery supplies the

remaining part so that Pb < 0. MA should be appliedat moments when is relative high. In (33), thiscorresponds to the area where 2 becomes active.Typically, these areas are characterized by the fact

that ICE operates near its maximum power limits

(see Fig. 3).

Charging mode (C): In C, ICE produces additional mechan-

ical power such that the electric machine can charge

the battery: Pb > 0. Different than in R, this mode re-quires additional fuel consumption, so C is preferred

when is small. According to (33), this will be in thearea where 1 holds.

The given strategy outline focuses on HEVs with the ICE as

the primary energy source. Future vehicle configurations possi-

bly appear with alternative power sources, e.g., a fuel cell stack

[3], [24]. Nevertheless, all new technologies currently known

still exhibit the input/output description from (31) so that a

similar reasoning for EM is still valid. If variations in i and/orfi are present in (31), the EM system is able to improve theenergy efficiency of the vehicle. The EM strategy decides which

mode should become active and what power is needed for all

components. This decision process relies on an optimization

algorithm and will be introduced in the next section.

IV. PROBLEM FORMULATION

From a control point of view, the EM strategy decides upon

two variables, i.e., the electric machine power Pem and theengine-running signal S {0, 1}. By manipulating these twovariables, the EM strategy is aiming at minimum fuel costs.

Although an HEV is a complex dynamical system, it is as-

sumed that there exists a static relation between the manipulated

variables and the momentary fuel consumption. Therefore, itis possible to formulate the fuel costs by means of algebraic

relations. The optimal EM strategy follows from the solution of

a standard optimization problem

minx

J(x) subject to G(x) 0 (34)

where J(x) is the objective function, and G(x) expresses theconstraints on the decision variable x. The function J repre-sents the cumulative fuel use of ICE over an arbitrary driving

cycle with time length te as

S-HEV: J(Pem, S) =

te0

f

Pe-linem (t)

S(t)dt (35)

P-HEV: J(Pem, S) =

te0

f(Pm(t)|(t)) S(t)dt (36)

S/P-HEV: J(Pem1, Pem2, S) =

te0

f(Pm(t)|(t)) S(t)dt. (37)

Note that the decision variable x covers two different signaltypes, i.e., the power of the electric machine Pem(t) and theengine-running signal S(t). Whereas Pem can take positive andnegative values, the signal S switches between two discretevalues {0, 1}.

Evaluation of the cost functions (35)(37) is done in the

following way. By selecting a predefined driving cycle, the

required drive train power Pd is calculated from (13). Fur-thermore, it is assumed that the EL power PL is also given.Depending on the selected HEV topology, the vehicle model in

Section II describes the exact relation between Pd and PL andthe corresponding fuel cost f, provided that the decision vari-ables Pem and Sare known. How to calculate these variables isexplained in Section V.

Except for concentrating on the overall fuel consumption

of the vehicle, the EM system also has the responsibility of

satisfying several constrains. For example, the operating range

of the engine, electric machine, and battery are limited in power.

Therefore, inequality constraints are introduced to limit the

minimum and maximum power flow through these compo-

nents, e.g.,

Pmmin(t) Pm(t) Pmmax(t) t [0, te] (38)

Pemmin(t) Pem(t) Pemmax(t) t [0, te] (39)

Pbmin(t) Pb(t) Pbmax(t) t [0, te]. (40)

According to the standard optimization problem (34), these

constraints have to be rewritten in terms of G(x) 0. Again,the relations from the vehicle model in Section II are used.

In addition to the constraints mentioned above, the EM

system also has the responsibility of guaranteeing a charge-

sustaining vehicle. A charge-sustaining strategy claims that the

battery satisfies a minimum SOElevel at the end of the drivingcycle. This is achieved by including an end-point constraint on

the energy level of the battery, e.g.,

Es(te) Es ref Es(0) +

te0

Ps(t)dt Es ref (41)


7/13


where Es ref is an arbitrarily selected reference value thatshould be satisfied at t = te, e.g., Es ref = Es(0).

V. ONLINE STRATEGY

Many methods are known for calculating the optimal solution

of (34) subject to (38)(41). Probably the most celebratedmethod is dynamic programming (DP) [2]. This optimization

technique provides an optimal solution to the described EM

problem, with its limited resolution enforced by the selected

grid accuracy.

Typically, EM strategies using DP provide a benchmark

regarding the maximum potential fuel savings. A real-time

EM strategy using DP is hampered by two restrictions. First,

a priori knowledge is needed about the vehicle power demand

(i.e., Pd(t) and PL(t) need to be known in advance alongthe entire driving cycle). Second, calculations from DP over

a lengthy driving cycle are computationally demanding. To

overcome both problems, this paper proposes a novel online

implementation for EM, which originates from physical insight

into the EM problem. The underlying strategy is strongly

related to the ECMS method from [8], although the mathe-

matical backgrounds originate from [23]. The method is able

to mimic the optimal solution from DP without the need for

having prediction information about the future driving cycle.

Moreover, it does not suffer from complex calculations and is

generally applicable to present and future HEV configurations.

The next section describes the EM strategy for S-HEV

and P-HEV. Details regarding the S/P-HEV are given in

Section V-B.

A. EM for S-HEV and P-HEV

To make the EM strategy generally applicable, the opti-

mization problem (34) is rewritten with an alternative decision

variable such that x covers the net battery power Ps, togetherwith the engine-running signal S. This is possible since thebattery efficiency model (24) and the description of the electric

power net (27)(29) provide a unique relation between Ps andthe controlled variable Pem. For S-HEV and P-HEV, this meansthat (35) and (36) translate into

J(Ps, S) =

te

0(Ps, S|Pd, PL, )dt (42)

where

S-HEV: (Ps, S|Pd, PL, )

= f

Pe-linem

S (in grams per second) (43)

P-HEV: (Ps, S|Pd, PL, )

= f(Pm|)S (in grams per second). (44)

According to this description, two subproblems are defined

since the engine-running signal S takes only two values {0, 1}.Furthermore, the end-point constraint (41) is reformulated

such that the integral constraint is avoided in the optimizationproblem.

First, consider the situation with S = 1. This allows the HEVto operate in modes BL, MA, and C. Without the inequality

constraints G(x) 0, the optimization problem from (34) re-duces to

minPs

te

0

(Ps|Pd, PL, )dt. (45)

Next, the end-point constraint (41) will be added. In the case

where the energy level of the battery at t = te has to be equalto the initial starting value Es(0), the inequality constraintchanges into an equality constraint

Es(0) +

te0

Ps(t)dt = Es(0)

te0

Ps(t)dt = 0. (46)

A new problem definition is formulated from (45) together

with the equality constraint (46). For convenience, it is written

in discrete time, although the sampling interval T has beenomitted, i.e.,

minPs

Npk=1

(Ps(k)|Pd(k), PL(k), (k))

subject to

Npk=1

Ps(k) = 0. (47)

Finding a solution for this optimization problem can be done

by incorporating the equality constraint into the Lagrangian

function using a Lagrange multiplier . A similar approach has

been followed in [8]. The following Lagrangian L is defined:

L (Ps(1), . . . , P s(Np), )

=

Npk=1

(Ps(k)|Pd(k), PL(k), (k))

Npk=1

Ps(k). (48)

Physically, this new objective function makes sense, because it

adds the energy exchange with the battery to the fuel consump-

tion of the ICE. The quantity represents the correspondingfuel cost when energy is stored or taken from the battery. It is

clear that there exists a strong relation between this quantity

and the definition of , as given in (30). The minimum value

for L(Ps(1), . . . , P s(Np), ) can be calculated by solving thefollowing set of equations:

L (Ps(1), . . . , P s(Np), )

Ps(k)

= (Ps(k)|Pd(k), PL(k), (k))

Ps(k) = 0 (49)

for 1 k Np, and

L (Ps(1), . . . , P s(Np), )

=

Npk=1

Ps(k) = 0. (50)

To guarantee a global optimal solution,(Ps(k)|Pd(k), PL(k), (k)) has to be a convex function at


8/13


each time instant k. This observation is justified by the shapeof the fuel curves (31) in combination with the model for the

MG (7) and the battery model (24). This convexity implies that

there exists one unique solution (Ps (1), . . . , P s (Np),

) tothe set ofNp + 1 equations in (49) and (50).

The solution is calculated with information from the entire

driving cycle, i.e., Pd(k), PL(k), and (k) are assumed to beknown at each time instant k = 1, . . . , N p. However, if

is

known, all Np equations from (49) are entirely decoupled. Thismeans that calculating Ps (k) can be done by solving (49) withPd(k), PL(k), and (k) only known at time k. For a rigorousproof, see [23]. As a result, the optimal solution Ps (k) from(47) is also found by minimizing the given criterion at each

time instant k, i.e.,

Ps = arg minPs

{(Ps|Pd, PL, ) Ps} . (51)

The solution presented so far only considers the cost criterion

in combination with one equality constraint. Returning to the

original problem, one has to guarantee that the inequality

constraints from (38)(40) are not violated. The vehicle model

can be used to rewrite all constrains in terms of Ps. Next, theseconstraints are combined into one new constraint on Ps with theupper and lower bound Psmax and Psmin, respectively. Finally,a feasible solution for the original problem is obtained through

saturation ofPs with these new boundaries, i.e.,

PS1s = sat [Ps ]PsmaxPsmin

=min(max(Ps , Psmin) , Psmax) . (52)

The corresponding fuel cost for the power setpoint PS1s is

fS1

=

PS1

s |Pd, PL,

PS1

s . (53)

It is important to notice that these extra constraints can be added

without violating the optimality of the calculated solution. After

all, the function (Ps|Pd, PL, ) was assumed to be a convexfunction. By applying saturation on Ps, this function still pre-serves convexity, and hence, the optimal solution is uniquely

defined. It is clear that an optimal value for Ps will sometimesappear at its boundary. Therefore, the value for might bedifferent for the situation where saturation is included. How to

find a suitable value for will be discussed in Section V-C.Now consider the situation with S = 0. Therefore, engine

is turned off, and MO becomes active. A necessary condition

for MO is that the electric motor is able to handle the powerrequest Pd and that the battery can supply the power from theelectric motor and PL. Both requirements are satisfied when thefollowing inequalities hold:

Pd Pemmin Pdmm

PL Pbmin. (54)

During braking phases, an engine stop is also preferred,

whereas the MG stores energy from R in the battery. All vehicle

configurations considered in this paper are front-wheel driven,

but for a correct driveability of the vehicle, recuperation of

free kinetic energy requires interaction between the front and

rear wheels. Although the distribution of the front and rearwheel braking forces is beyond the scope of this paper, it is

important to realize that the EM system cannot recover all avail-

able kinetic energy solely at the front wheels. The parameters

that determine the ideal braking force distribution are, among

others, the desired vehicle deceleration and the cargo weight.

A good introduction to the braking force distribution in HEVs

is given in [7]. Without loss of generality, it is assumed here

that the braking force at the front wheels is fixed at 60%, i.e.,rb = 0.60[], whereas the rear wheels take care of the remain-ing part. Now the power from the electric machine during MO

is equal to

PMOe = min

1

mmPMOem , gmP

MOem

(55)

with PMOem = Pd during vehicle propulsion (Pd 0), andPMOem = rb Pd is available during R (Pd < 0)

PMOem = sat [max(rb, Pd, Pd)]PemmaxPemmin

. (56)

Although the ICE is turned off, it should be noted that P-HEV

suffers from additional losses at the power split due to the

engine drag torque. In this paper, these losses are neglected.

Similar to the electric machine, the battery is also limited

in power. In particular, during R, the charge acceptance of the

battery is important, and incorporating these limitations yields

the following net battery power:

PMOs = min

1

PMOb ,

+PMOb

(57)

with PMOb = sat PMOe PLPbmaxPbmin . (58)ICE is not running during MO, and therefore, the momen-

tary fuel consumption is zero. The additional fuel costs for

recharging the battery afterward are estimated using the optimal

Lagrange multiplier as

fS0 = PMOs . (59)

Finally, to select MO instead of the other modes, the following

condition must be satisfied [calculated from (53) and (59)]:

fS0 < fS1. (60)

The final control law for Ps comprises the combination of allpossible situations. This means that MO becomes active when

both (54) and (60) are satisfied. Discrimination between the

other modes is done in (51) and (52). This can be numerically

done by taking a grid for Ps and evaluating the criterion in (51)for all the grid points. Altogether, this yields the following EM

strategy law for Ps:

PEMs (Pd, PL, , ) =

PMOs , if(54) (60)PS1s , elsewhere.

(61)

The actual power setpoint for the MG is calculated from theS-HEV or P-HEV model equations in Section II.


9/13


TABLE IICALCULATIONS FOR S/P-HEV TO DETERMINE (c, c)

B. EM for S/P-HEV

The S/P-HEV topology incorporates two electric machines

(i.e., MG1 and MG2), which both require a suitable control law

for EM. Together with the engine stop/start feature, the EM

strategy decides upon three variables, i.e., Pem1, Pem2, andS. Similar to the configurations from the previous section, Sonly takes two discrete values {0, 1}; therefore, the objective

function in (37) can be rewritten into

J(Pem1, Pem2, S) =

te0

(Pem1, Pem2, S|d, d, PL)dt (62)

where

(Pem1, Pem2, S|d, d, PL) = f(c, c)S [g/s]. (63)

Contrary to the other HEV configurations, it is preferred to cal-

culate the fuel use of S/P-HEV in (63) with separate speed and

torque signals (c, c) rather than power Pd. This is enforced bythe mechanical power split, which uses a planetary gear train for

connecting MG1, MG2, and ICE to the drive train. According

to the model description in Section II, ICE is connected to the

ring gear, and its operating point (c, c) is uniquely defined bythe three decision variables together with the power request of

the driving cycle. The necessary steps to calculate c and c aresummarized in Table II. Note that the calculations in Table II

are only valid when d = 0. However, this restriction has nofurther consequences because it is not economically attractive

to switch on the ICE and charge the battery when the vehicle

stands still. This observation is justified by the fact that ICE has

a relatively large fuel offset when it runs idle, and there exist

enough other driving moments where charging of the battery

can be done more efficiently. Hence, d = 0 implies S = 0.In addition, different from S-HEV and P-HEV, S/P-HEV

requires individual constraints to limit the speed and torque

range of ICE. A single constraint for the power from ICE

would be too conservative. Given the minimum and maximum

torque line of the engine, it follows that this constraint is time

dependent. A similar reasoning also holds for the engine speed,

leading to the following constraints:

min(t) c(t) max(t) (64)

mmin(t) c(t) mmax(t) t [0, te]. (65)

Altogether, S/P-HEV offers significantly more freedom for

EM, but it is still possible to apply a similar optimization ap-proach as described in Section V-A. This means that the discrete

variable S will be eliminated by creating two subproblems.First, the situation with S = 1 is considered so that ICE ispermanently on. For a given drive train request (d, d), theoptimal power setpoints for MG1 and MG2 are calculated by

PS1em1, P

S1em2

= arg min(Pem1,Pem2)Q(d,d)

{(Pem1, Pem2|d, d, PL)

Ps} (66)

where the set Q only covers the feasible setpoints for MG1 andMG2 to satisfy the constraints (38)(40), (64), and (65) as

Q(d, d) =

(Pem1, Pem2)|Pem1min Pem1 Pem1max Pem2min Pem2 Pem2max Pbmin Pe1 + Pe2 PL Pbmax mmin c mmax min c max

. (67)

The signals c and c are calculated according to the steps listed

in Table II. The model from MG1 and MG2 in (7) is usedto calculate the electric power Pe1 and Pe2, respectively. Thenet battery power Ps is calculated from the battery model (24).Eventually, the result from (66) is used to estimate the minimum

expected fuel cost when the engine is turned on, i.e.,

fS1 =

PS1em1, PS1em2|d, d, PL

PS1s . (68)

Now consider the situation with S = 0 so that the engine isturned off. In S/P-HEV, MG2 takes care of the drive train power,

whereas the battery must be able to handle the corresponding

power request and PL. Apparently, this situation turns out tobe similar to S-HEV and P-HEV so that (54)(60) also apply

here, taking into account that the electric machine correspondsto MG2; therefore, Pem = Pem2.

Altogether, the EM system defines the control law for Pem1and Pem2. The combination of the individual modes for S = 0and S = 1 leads to the following strategy description:

PEMem1 (Pd, PL, , ) =

0, if(54) (60)PS1em1, elsewhere

(69)

PEMem2 (Pd, PL, , ) =

PMOem2, if(54) (60)PS1em2, elsewhere.

(70)

The number of MG pairs influences the overall complexity

of the EM system. Nevertheless, the calculations for S/P-HEVhave a similar complexity as for S-HEV and P-HEV. As a

result, the numerical calculations are not ready to explode

for more advanced vehicle configurations. In addition, future

vehicle configurations, possibly equipped with even more MG

pairs, will be able to keep the numerical complexity of the EM

strategy limited. For example, an HEV constructed with in-

wheel motors for its power train gives rise to an EM system with

multiple MG pairs. Without considering additional driveability

issues for safe and stable vehicle operation, the presented EM

algorithm can still be applied.

All these strategies have in common that they only rely on

the present state of the vehicle including . This means that

knowledge about the future driving cycle is not needed. Thecalculation of will be explained below.


10/13


Fig. 4. Feedback diagram for estimating .

C. Adaptive EM Strategy

Every driving cycle requires a different to achieve apreferred energy level in the battery at the end of the driving

cycle. This corresponds to the situation where the energyneed for Pd and PL is balanced with the energy for batterycharging. It is important to notice that power-requesting modes

such as MO and MA take less energy from the battery for

higher values of . Conversely, mode C stores more energyin the battery when increases. As a result, there exists aunique solution for where the energy from R and C equalsthe energy for MO and MA (including the battery losses for

temporarily storing energy). Then, it follows that the SOEreturns to its initial value at the end of the driving cycle. Thisobservation is also recognized by Delprat et al. [6]. By means

of simulations, Section VI shows that the EM strategy with

mimics the optimal solution from DP, provided that there are

no restrictions in the buffer size from the battery. It follows

that exactly knowing the future driving cycle is not a strict

requirement for excellent performance (see also [18]).

To calculate , accurate information about the vehicle powerdemand is required along the entire known driving cycle. This

is inconvenient for online implementation because it requires,

among others, an exact prediction of the vehicle speed, includ-

ing external disturbances such as wind or road inclination. In-

stead of focusing on how to obtain this prediction information,one can also rely on the driving behavior from the past. Assum-

ing that the speed profile from the past provides a good repre-

sentation of the future driving cycle, there are several methods

to estimate an appropriate value (see [4], [12], and [19]).The method that has been selected here results in an adaptive

strategy, as presented in [12]. The basic idea is that the SOEof the battery indicates whether is estimated correctly or not.In the case has been selected too small, the battery becomesdepleted in the end. Conversely, when is selected too high, thebattery becomes fully charged. From a control point of view,

this corresponds to a leveling control problem where SOE

should be kept near a nominal value SOEref. A proportionalintegral (PI) controller with a rather small bandwidth fulfills

this requirement. The block diagram is shown in Fig. 4, with equal to

(t) = 0 + KPe(t) + KI

t0

e()d (71)

with 0 as an initial guess. Selecting the parameters KP and KIfor a small closed-loop bandwidth allows for a tracking error

between the actual SOE and SOEref. This freedom is neededby the EM system to temporarily store/retrieve energy into/from

the battery. On the other hand, a charge-sustaining strategy mustkeep the SOE sufficiently close to SOEref to prevent battery

depletion or overcharging. Therefore, the bandwidth of the PI

controller should not be too small.

A suitable bandwidth should be selected according to the

power spectrum of upcoming driving cycles. Only the fre-

quency components outside the bandwidth of the PI controller

contribute to the fuel profits from the EM system. Frequencies

inside the bandwidth are counteracted by the PI controllerto establish a charge-sustaining strategy. Consequently, these

frequency components will not provide any profits in fuel

economy. Appropriately tuning of the parameters KP and KIis described and analyzed in [10] and [13].

VI. SIMULATION RESULTS

Although the EM strategy applies to all three HEV configu-

rations, the results shown in this section focus on the situation

with P-HEV. Compared with a vehicle with a traditional drive

train, only minor changes are necessary to create a P-HEV.

As will be shown in this section, a P-HEV with a small

hybridization factor offers significant benefits in fuel economy.

Examples with S-HEV or S/P-HEV can be found in [10].

The P-HEV configuration represents a mild HEV equipped

with a 2.0 SI engine and an ISG. Simulations are done for theNew European Driving Cycle (NEDC) with the corresponding

drive train power Pd calculated from the backward-facing vehi-cle model in Section II. The clutch is located between the power

split and the drive train.

The battery and the ISG can both handle electric power up to

5 kW. During motor mode and generator mode, the efficiency

of the ISG is equal to mm = gm = 0.8[]. Therefore, itsmechanical power Pem ranges between 4000 and 6250 W.

The effective battery capacity is assumed to be Ecap = 2.0 MJ,and its efficiency is equal to bat = 0.85[]. These batteryparameters represent a 36-V battery with a rated capacity of

Cbat = 30 Ah. Only 50% of its capacity is effectively availablein terms of energy, i.e.,

Ecap 0.5 3600 Cbat Unombat

= 0.5 3600 30 36 = 2.0 MJ. (72)

For this vehicle configuration, seven alternative EM strate-

gies are evaluated. All strategies start at SOE = 75%. Thefirst simulation (Sim1) only applies mode BL with the engine

always running and the battery power permanently zero, so thatS = 1, and Pb = 0. The second simulation (Sim2) evaluates acontrol strategy obtained from DP. The DP strategy provides an

optimal strategy within the selected grid accuracy and serves

as a benchmark. The third simulation (Sim3) uses the EMstrategy from (61) with taken constant. A careful selectionof guarantees that the SOE at the end of the driving cycleequals 75%. It is important to recognize that Sim3 is equal tothe situation with no feedback (i.e., zero bandwidth) for the

PI controller. Consequently, Sim3 achieves maximum profitsin fuel economy, whereas restrictions for a charge-sustaining

strategy are lacking.

Sim4 applies the same strategy as Sim3, but now, is

estimated with the PI controller from Section V-C. Finally,the last three simulations (Sim5, Sim6, and Sim7) are added


11/13


TABLE IIIFUEL CONSUMPTION OF P-HEV ON NEDC

to give insight into the performance of the EM strategy and

how it depends on the individual operating modes. All three

strategies are derived from Sim3, but by excluding specificmodes, the effects of MA, MO, R, and C are investigated. Sim5demonstrates the added value of MA in combination with C by

excluding R and MO. Sim6 shows the large impact of R onfuel economy by using its recovered energy solely for MO. In

this simulation, MA and C are excluded from the EM strategy.

In addition to R, battery charging with C is also an effective

method to gather energy for MO. In Sim7, the benefits fromMO in combination with C are elucidated.

For all the strategies, the corresponding fuel consumption

is shown in Table III. It should be noted that Sim4 endsthe driving cycle with a slightly different SOE level, and itsfuel consumption has been corrected for this with the average

value of , see, e.g., [21] for a similar approach. An importantobservation is that Sim3 and Sim4 achieve almost similarimprovements in fuel consumption, although Sim4 does notrely on knowledge about the future driving cycle. The reason

why Sim3 performs slightly better than Sim2 is because DP isrestricted to the accuracy of the grid, whereas Sim3 does not

suffer from this limitation.Comparing Sim5 with Sim3, it follows that MA only gains

1.4% fuel reduction. This relative small benefit is explained in

two ways. First, the engine map only contains limited variations

for (see Fig. 3). In particular, in the area where it deliverslow power, the fuel curves are straight and in parallel. As a

result, C will not be profitable to generate energy for MA

due to the losses in the battery. Second, the NEDC driving

cycle has a moderate power request so that large engine powers

(where the engine map exhibits more variations for ) arebarely observed. Since MA is only profitable if variations for

exist, its contribution will be small for this particular driving

cycle.The majority of the fuel savings for EM arise by applying

MO. By switching off ICE, MO eliminates the fuel offset f1 atmoments when no (or possibly a small amount of) propulsion

power is needed. During MO, the requested energy is supplied

by the battery, and to recharge the battery, two mechanisms are

possible, i.e., R and C. According to these two methods, the

corresponding fuel savings are illustrated with two simulations

Sim6 and Sim7, respectively. Sim6 only receives energy fromR to compensate for the energy taken from the battery during

MO. This yields a fuel reduction of 15.8%. Furthermore, C is

also a viable method to charge the battery and extend the poten-

tial benefits for MO. Without R, Sim7 achieves a fuel reduction

of 17.5%, which is more than Sim6. The reason why Sim7gains more profits than Sim6 is because the energy recovered

by R is limited through the braking periods prescribed by the

driving cycle. The energy from C is only limited by power

constraints from components, and significantly more energy is

available to apply MO.

The strategies Sim5, Sim6, and Sim7 are all a subset fromSim3. Nevertheless, it can be seen that the contribution of each

individual strategy adds up to a higher fuel reduction than theperformance shown by Sim3. This is because the individualmodes of the EM strategy do not independently operate off of

each other. For example, MO receives energy from R and C.

The energy from R is produced without extra fuel cost, but the

total available energy is limited. Therefore, the EM strategy

decides upon the extra energy from C, but the additional fuel

benefits will be less.

From a computational point of view, only limited calcula-

tions are required for Sim4. This way, an online implementa-tion in the vehicle is always guaranteed. A proof of concept

is already given in [11], which presents roller dynamometer

experiments with a similar EM strategy for vehicles with a

traditional drive train. With a series-production vehicle, a fuel

reduction of more than 2.5% is achieved without major changes

to the vehicle hardware.

Considering the small difference in fuel economy between

Sim4 and Sim2, it can be concluded that the proposed onlinestrategy is very promising. In addition, the costs for the selected

vehicle hardware yield a good tradeoff between investment and

reward. Hybridization with a 5-kW ISG yields approximately

25% fuel reduction.

Nevertheless, the simulations do not include a penalty for

switching the engine on and off. Furthermore, the free energy

from R during vehicle deceleration reduces due to friction

losses in the combustion engine, and these losses are not wellcovered in the simulation model. These drawbacks come with

all the strategies, and therefore, it is reasonable to believe that

the relative difference between all simulations remains equal.

The control sequences for Sim2, Sim3, and Sim4 are shownin Fig. 5. From the SOE trajectory, it is clear that Sim2 andSim3 exhibit similar behavior. Because these strategies utilizea priori knowledge from the driving cycle, they allow larger

deviations for SOE and still return to 75% at the end of thecycle. This is different for Sim4. By construction, this strategykeeps SOE near its reference value, but the main controlactions from Sim2 and Sim3 are still visible. Another point of

attention is the control setpoint Pem. Due to the piecewise linearbehavior of the engine map, the desired control actions areoften found in extremes, sometimes giving rise to nonsmooth

switching behavior.

For this particular driving cycle, the periods where ICE is

switched off are interrupted by short periods with multiple

stop/start events (see Fig. 5). To include a penalty for switching

ICE on and off, an extra inequality constraint can be added

to (54), which becomes true only if ICE has been on for a

sufficiently long time. For example, a counter can be used

to measure the time elapsed since the last cranking event.

This way, a tradeoff emerges between extra fuel savings for

switching the ICE off versus frequent cranking of the ICE. The

engine emissions during cranking, as well as the driveabilityaspects, have to be investigated to optimize this tradeoff.


12/13


Fig. 5. Simulation results for Sim2, Sim3, and Sim4 on NEDC driving cycle.

More generally, the results presented so far have paid little

attention to the driveability aspects. However, from an EM

system, it is expected that it certainly does not harm safety

aspects or driver comfort. To satisfy all these functionalities,

the proposed EM system should become part of a supervisory

control algorithm, whereas dedicated controllers will be needed

to take care of local control actions. For example, smoothtransitions are desired when changing the power demand be-

tween ICE and EM. In addition, during braking periods, a local

controller has to take care of the power distribution between the

front and real wheels. In addition to mechanical requirements,

the electric power net also requires local power converters to

take care of the electric power flow in an efficient way. In

addition, intelligent strategies for charging and discharging the

battery are foreseen such that excessive battery wear can be

prevented. Finally, the EM system should focus on more aspects

than fuel economy alone (e.g., exhaust gas emissions during a

cold and warm engine start). Ultimately, an integrated power

train control is foreseen, where the EM system operates at a

supervisory level.

VII. CONCLUSION

This paper has presented an online concept for EM in

various HEV configurations. This concept provides not only

a mathematical solution to the EM problem but the physical

explanation behind an EM strategy as well. This way, two

important vehicle characteristics, which directly determine the

potential fuel benefits of any EM strategy, are recognized,

i.e., the slope of the fuel map with respect to engine power

and the speed-dependent fuel use when the engine runs idle.

Not only existing HEVs but also future vehicle configurationssatisfy the proposed EM concept if their primary power source

incorporates sufficient variations for both of the aforementioned

characteristics.

A practical solution has been presented on how to implement

this strategy concept in each vehicle configuration. Owing to its

low computational demand, an online vehicle implementation

is guaranteed. The charge-sustaining requirement is satisfied by

means of a feedback mechanism, comparing the actual energyin the battery with a preferred reference value. There is no need

for prediction information or complex estimators of the vehicle

status.

Simulations with a mild P-HEV have demonstrated cor-

rect control actions for the EM strategy. It turns out that

the results in fuel economy come very close to the optimal

strategy calculated with DP. This result has led to the obser-

vation that adding prediction information to the EM strategy

yields limited extra profits in fuel economy. Furthermore, it

is concluded that most fuel benefits originate from engine

stop/start during MO mode in combination with free energy

from R. Battery charging is preferably done with energy from

R, but regular battery charging during driving further extendsthe fuel profits from MO mode. It is concluded that the

low hybridization factor has an excellent return-on-investment,

with benefits in fuel economy of up to 25%. The fuel prof-

its from MA are only a few percent for the studied vehicle

configuration.

REFERENCES

[1] B. M. Baumann, G. Washington, B. C. Glenn, and G. Rizzoni, Mecha-tronic design and control of hybrid electric vehicles, IEEE/ASME Trans.

Mechatron., vol. 5, no. 1, pp. 5872, Mar. 2000.[2] D. P. Bertsekas, Dynamic Programming and Optimal Control, 2nd ed.

Belmont, MA: Athena Scientific, 2000.[3] C. C. Chan, The state of the art of electric, hybrid, and fuel cell vehicles,Proc. IEEE, vol. 95, no. 4, pp. 704718, Apr. 2007.


13/13


[4] J.-S. Chen and M. Salman, Learning energy management strategy forhybrid electric vehicles, in Proc. IEEE VPPC, Chicago, IL, Sep. 2005,pp. 6873.

[5] S. R. Cikanek and K. E. Bailey, Regenerative braking system for ahybrid electric vehicle, in Proc. Amer. Control Conf., Anchorage, AK,May 2002, vol. 4, pp. 31293134.

[6] S. Delprat, J. Lauber, T. M. Guerra, and J. Rimaux, Control of a parallelhybrid powertrain: Optimal control, IEEE Trans. Veh. Technol., vol. 53,

no. 3, pp. 872881, May 2004.[7] Y. Gao and M. Ehsani, Electronic braking system of EV and HEVIntegration of regenerative braking, automatic braking force control andABS, presented at the SAE Future Transportation Technol. Conf.,Costa Mesa, CA, Aug. 2001, SAE Paper 2001-01-2478.

[8] L. Guzzella and A. Sciarretta, Vehicle Propulsion SystemsIntroductionto Modeling and Optimization. Berlin, Germany: Springer-Verlag, 2005.

[9] T. Hofman, M. Steinbuch, R. Van Druten, and A. Serrarens, Rule-basedenergy management strategies for hybrid vehicles, Int. J. Elect. HybridVeh., vol. 1, no. 1, pp. 7194, Jul. 2007.

[10] J. T. B. A. Kessels, Energy management for automotive powernets, Ph.D. dissertation, Dept. Elect. Eng., Technische Univ. Eindhoven,Eindhoven, The Netherlands, 2007.

[11] J. T. B. A. Kessels, M. Koot, B. de Jager, P. P. J. van den Bosch,N. P. I. Aneke, and D. B. Kok, Energy management for the electricpowernet in vehicles with a conventional drivetrain, IEEE Trans. ControlSyst. Technol., vol. 15, no. 3, pp. 494505, May 2007.

[12] M. Koot, J. T. B. A. Kessels, B. de Jager, W. P. M. H. Heemels,P. P. J. van den Bosch, and M. Steinbuch, Energy management strategiesfor vehicular electric power systems, IEEE Trans. Veh. Technol., vol. 54,no. 3, pp. 771782, May 2005.

[13] M. W. T. Koot, Energy management for vehicular electric power sys-tems, Ph.D. dissertation, Dept. Mech. Eng., Technische Univ. Eindhoven,Eindhoven, The Netherlands, 2006.

[14] C.-C. Lin, H. Peng, J. W. Grizzle, and J.-M. Kang, Power managementstrategy for a parallel hybrid electric truck, IEEE Trans. Control Syst.Technol., vol. 11, no. 6, pp. 839849, Nov. 2003.

[15] J. Liu and H. Peng, Control optimization for a power-split hybridvehicle, in Proc. Amer. Control Conf., Minneapolis, MN, Jun. 2006,pp. 466471.

[16] J. Liu, H. Peng, and Z. Filipi, Modeling and analysis of the Toyota hybridsystem, in Proc. Int. Conf. Advanced Intell. Mechatron., Monterey, CA,Jul. 2005, pp. 134139.

[17] J. M. Miller, Hybrid electric vehicle propulsion system architectures ofthe e-CVT type, IEEE Trans. Power Electron., vol. 21, no. 3, pp. 756767, May 2006.

[18] C. Musardo, S. Benedetto, S. Bittanti, Y. Guezennec, L. Guzzella, andG. Rizzoni, An adaptive algorithm for hybrid electric vehicles en-ergy management, in Proc. FISITA World Automotive Conf., Barcelona,Spain, May 2004.

[19] C. Musardo, G. Rizzoni, andB. Staccia, A-ECMS: An adaptive algorithmfor hybrid electric vehicle energy management, in Proc. Joint 44th IEEEConf. Decision Control, Eur. Control Conf., Seville, Spain, Dec. 2005,pp. 18161823.

[20] P. Pisu andG. Rizzoni, A comparative study of supervisorycontrol strate-gies for hybrid electric vehicles, IEEE Trans. Control Syst. Technol.,vol. 15, no. 3, pp. 506518, May 2007.

[21] A. Sciarretta, M. Back, and L. Guzzella, Optimal control of parallelhybrid electric vehicles, IEEE Trans. Control Syst. Technol., vol. 12,no. 3, pp. 352362, May 2004.

[22] G. Steinmaurer and L. del Re, Optimal energy management for mildhybrid operation of vehicles with an integrated starter generator, pre-sented at the SAE World Congr., Detroit, MI, Apr. 2005, SAE Paper 2005-01-0280.

[23] P. P. J. van denBosch andF. A. Lootsma, Scheduling of power generationvia large-scale nonlinear optimization, J. Optim. Theory Appl., vol. 55,no. 2, pp. 313326, Nov. 1987.

[24] J. van Mierlo, G. Maggetto, and P. Lataire, Which energy source forroad transport in the future? A comparison of battery, hybrid and fuelcell vehicles, Energy Convers. Manag., vol. 47, no. 17, pp. 27482760,Oct. 2006.

John T. B. A. Kessels (S04M08) received theB.S. degree in electrical engineering from FontysHogescholen, Eindhoven, The Netherlands, in 2000and the M.S. and Ph.D. degrees in electrical engi-neering from Technische Universiteit Eindhoven in2003 and 2007, respectively.

After working as a Postdoctoral Researcher withTechnische Universiteit Eindhoven, in 2007, he

joined the Automotive Group of TNO Science andIndustry, Helmond, The Netherlands. His researchinterests include energy and emission management

for light-duty and heavy-duty vehicles, with emphasis on integrated powertraincontrol.

Michiel W. T. Koot was born in Sittard,The Netherlands, in 1977. He received the M.S.and Ph.D. degrees in mechanical engineering fromTechnische Universiteit Eindhoven, Eindhoven,The Netherlands, in 2001 and 2006, respectively.

He is currently with Vision Dynamics, Eindhoven.His research interests include dynamics, control, andoptimization applied to mechanical systems and au-tomotive vehicles.

Paul P. J. van den Bosch (M84) received the M.S.degree (cum laude) in electrical engineering andthe Ph.D. degree in optimization of electric energysystems from Delft University of Technology, Delft,The Netherlands.

After graduating, he was with the Control SystemsGroup, Delft University of Technology, where hewas appointed Full Professor in control engineeringin 1988. In 1993, he was appointed Full Profes-sor with the Control Systems Group, Departmentof Electrical Engineering, Technische Universiteit

Eindhoven, Eindhoven, The Netherlands. In 2004, he was a part-time Pro-

fessor with the Department of Biomedical Engineering. He is currently withTechnische Universiteit Eindhoven. His research interests concern modeling,optimization, and control of dynamicalsystems. In his career, he has cooperatedon many research projects with industry, including automotive applications,large-scale electric systems, advanced electromechanical actuators, and, re-cently, embedded systems and biomedical modeling. In addition to his scientificactivities, he has received several prizes for his educational activities and severalpatents. He has served on the editorial boards of journals (Journal A) andconference committees.

Daniel B. Kok received the B.S. degree from HogereTechnische School of Automotive Engineering,Apeldoorn, The Netherlands, in 1991 and the M.S.and Ph.D. degrees in mechanical engineering fromTechnische Universiteit Eindhoven, Eindhoven, The

Netherlands, in 1994 and 1999, respectively. HisPh.D. dissertation was entitled Design Optimisationof a Flywheel Hybrid Vehicle.

In 1994, he was a Research Associate withTechnische Universiteit Eindhoven. From 1999 to2000, he was a Project Leader on hybrid electric

vehicles with TNO Automotive, Delft, The Netherlands. In 2000, he was withthe Ford Research Center, Aachen, Germany. Since July 2005, he has been aTechnology Manager with the Micro Hybrid Systems and Energy ManagementGroup, Ford Dunton Technical Center, Basildon, U.K., where he is also aTechnical Leader.

Online EnerMana for HEV (IEEE Trans,Model,DP,Solution)

Documents

Transcript of Online EnerMana for HEV (IEEE Trans,Model,DP,Solution)