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Electrical Vehicle Modeling: A Fuzzy Logic Model for Regenerative Braking
Ricardo Maia1, Marco Silva1,2, Rui Araújo1, and Urbano Nunes1
1Institute for Systems and Robotics (ISR-UC), andDepartment of Electrical and Computer Engineering (DEEC-UC),
University of Coimbra, Pólo II, PT-3030-290 Coimbra2IPC-ISEC, Polytechnic Institute of Coimbra, Rua Pedro Nunes, Coimbra
[email protected], [email protected], [email protected], [email protected]
Abstract
This paper presents a fuzzy logic model of regenerative braking (FLmRB) for modeling EVs’ regenerative braking systems (RBS).The model has the vehicle’s acceleration and jerk, and the road inclination as input variables, and the output of the FLmRB isthe regeneration factor, i.e. the ratio of regenerative braking force to total braking force. The regeneration factor expresses thepercentage of energy recovered to the battery from braking. The purpose of the FLmRB development is to create realistic EVmodels using as least as possible manufacturers intellectual property data, and avoiding the use of EV on-board sensors. To tunethe model, real data was gathered from short and long-distance field tests with a Nissan LEAF and compared with two types ofsimulations, one using the proposed FLmRB, and the other considering that all the braking force/energy is converted to electriccurrent and returned back to charge the battery (100% regeneration). The results show that the FLmRB can successfully infer theregenerative braking factor from the measured EV acceleration and jerk, and road inclination, without any knowledge about the EVbrake control strategy.
Keywords:
Electric Vehicle, Regenerative Braking System, Fuzzy Inference System.
1. Introduction
Electric vehicles (EV) have become a commercial transporta-tion solution. According to the Electric Vehicles Initiative(http://www.iea.org), the aggregated goal for all countrieswith known deployment targets is 7.2 million in EV sales for2020. However, nowadays autonomy is still one of the majorobstacles to massive adoption of EVs, resulting in practice onEVs use being restricted to urban areas. In this context, the re-search and development of EV modeling and simulation tools,particularly aimed for road traffic analysis, plays an importantrole. For example, the implementation of algorithms for bestroute following by EVs could lead to energy savings and to theimprovement of vehicle autonomy range. A major advantageof EV systems is the possibility of energy regeneration duringbreaking. However, the amount of regenerated energy dependson how the vehicle implements the distribution of braking en-ergy among the braking sub-systems, i.e. it depends on theamount of energy that is recovered to the battery pack and onthe amount of energy released as heat in the mechanical brakesystem. Energy regeneration requires time to restore movementinto energy. Large deceleration rates imply the major use ofmechanical brakes [7], decreasing the degree of energy regen-eration.
This paper proposes a fuzzy logic approach for modelingthe braking force distribution in EV RBS. The EV model usedhere is an improvement of the model proposed in [12]. There
are three main advancements. First, motivated by the fact thatthere are no equal batteries, the real voltage and current infor-mation is used for battery modeling instead of using a generallookup table built for the battery model being used (that typi-cally would be provided by the manufacturer). Second, a betterapproximation is employed for the computation of the equiv-alent mass of the vehicle’s rotating parts, giving a more accu-rate result. Third, a generic fuzzy logic framework is proposedfor modeling existing regenerative braking systems, specificallyfor designing a FLmRB which models the distribution of to-tal braking torque between mechanical non-regenerative torque(e.g. friction-based) and regenerative torque. The results ofthe proposed FLmRB were compared with real-world data ob-tained with a Nissan LEAF in road tests. Although the FLmRBhas been designed and verified with a Nissan LEAF EV, theFLmRB framework is targeted to design suitable models forany EV by adjusting the fuzzy logic rules using human ex-pert knowledge, or by using an intelligent optimization method,such as the hierarchical genetic algorithm proposed in [13], tolearn/improve the structure and parameters of the fuzzy model.
The paper is organized as follows. Section 2 introduces re-lated work. In Section 3, the EV model is given. The FLmRBframework is designed in Section 4. In Section 5, simulations,experiments with a Nissan LEAF EV and corresponding resultsare presented. Finally, Section 6 gives concluding remarks.
1
Nomenclature
α Inclination angle of the road (upward-sloping or downward-sloping) [rad].
β Ratio of regenerative braking force to the total braking force.
ηb Battery efficiency.
ηm Motor efficiency.
ηt Transmission and gears efficiency.
µrr Coefficient of rolling resistance of the tire.
ωrad Motor angular speed [rad/s].
ωrpm Motor angular speed (revolutions per minute).
ρ Air density [Kg/m3].
τ+req Torque required from the motor on traction events [N·m].
τ−req Torque required from the motor on braking events [N·m].
τg Torque required by gearbox/transmission [N·m].
τb Braking torque [N·m].
τmax Motor maximum tractive torque [N·m].
τmechF Braking torque on front wheels [N·m].
τmechR Braking torque on rear wheels [N·m].
τmech Mechanical braking torque [N·m].
τmin Motor maximum braking torque [N·m].
τreg Regenerative braking torque [N·m].
τreq Torque required from the motor [N·m].
ϕ Jerk, the derivative of acceleration [m/s3].
A Frontal area of the vehicle [m2].
a Vehicle acceleration [m/s2].
C Battery capacity [A·H].
Cd Vehicle’s drag coefficient.
Eoc Open circuit voltage [V].
Fad Aerodynamic drag force [N].
Fhc Hill climbing force [N].
Fla Linear acceleration force [N].
Frr Rolling resistance force [N].
Fte Tractive effort [N].
G Gear ratio.
g Acceleration due to gravity [m/s2].
Ibat Battery current [A].
K0 Battery parameter.
K1 Battery parameter.
K2 Battery parameter.
K3 Battery parameter.
K4 Battery parameter.
mc Curb weight (vehicle mass with battery pack) [Kg].
mI Vehicle equivalent mass increase due to the angular moments of the rotatingcomponents [Kg].
mv Total vehicle mass, with load and occupants masses [Kg].
Pacc Power consumed by accessories [W].
Preq Required power from battery [W].
r Wheel radius [m].
R+in
Battery internal resistance [Ω].
R−in
Battery internal resistance [Ω].
S OC Battery state of the charge.
S OC0 S OC at beginning of the test.
Tα Set of linguistic terms defined for α [rad].
Tβ Set of linguistic terms defined for β.
Tϕ Set of linguistic terms defined for ϕ [m/s3].
Ta Set of linguistic terms defined for the acceleration a [m/s2].
v Vehicle speed [m/s].
Vt Battery pack terminal voltage [V].
2. Related Work
Several works have proposed approaches for implementationof braking strategies. In [2], an intelligent control strategy tocontrol the pressure of the brake actuator using artificial neuralnetworks is proposed and implemented in an microcontroller.While the aim of the method was to improve the braking pro-cess, it cannot be applied to quantify the distribution of the to-tal braking torque between mechanical non-regenerative torque,and regenerative torque in electronic braking systems in EVs.[8] presented five control strategies for energy management sys-tems in fuel cell vehicles. Although fuel cell vehicles are unableto perform energy regeneration, this drawback was reduced bycombining the fuel control system with an energy store sys-tem, such as a battery, a supercapacitor, or a combination ofboth. By placing focus on regenerative braking, [4] proposed aGA-based neural network to design an energy recovery systemfor an electric motorcycle. [21] designed a regenerative brak-ing force controller based on fuzzy logic using desired brakingforce, vehicle speed, and battery state of the charge (SOC) asthe inputs, and the ratio of the regenerative braking force asthe output. It also uses battery temperature to produce a com-pensation coefficient in order to limit the regenerated current.
A control strategy using a couple of fuzzy logic controllers isstudied in [6] for adjusting the braking force allocation. As in-put information, it is used the brake pedal displacement, and theslip ratio of the wheel, not being useful in traffic simulators.
Other similar proposals for new or improved regenerativebraking strategies can be found in [20] and [14]. The workscited above in this paper propose either new strategies to per-form regenerative braking or some improvement to some al-ready existing RBS. However, there is a lack of an RBS model-ing methodology that can be applied in a variety of existing (andspecific) EVs for building an RBS model of the distributionof total braking torque between mechanical non-regenerativetorque (e.g. friction-based) and regenerative torque. The goalof the work presented in this paper is to develop a methodologyfor building models of RBS strategies, rather than developing aRBS strategy.
3. Electric Vehicle Modeling
This section briefly presents how the EV was modelled andwhich characteristics were included in the model. The EVmodel herein formulated, shown schematically in Figure 1,is based on [11] and [7]. The modeling architecture can be
2
Preq
TrialDrive
Cycle
SOC
Figure 1: Diagram of the EV powertrain model.
adapted to be used in traffic simulators, such as the SUMO sim-ulator [10], or simulators which are based on Simulink. Thesystem has three subsystems: Wheel & Gear Subsystem, Power
Driver Subsystem, and Energy Storage Subsystem. The subsys-tems will be presented in the following subsections.
3.1. Wheel & Gear Subsystem
The Wheel & Gear Subsystem takes from the vehicle drivedata, the time-referenced speed v and (road) inclination angleα as input variables and produces five outputs: torque requiredby gearbox τg, motor angular speeds ωrpm and ωrad, accelera-tion, a, and derivative of the acceleration, the Jerk, ϕ. To ob-tain τg, the mechanical force Fte needed to produce the desiredspeed at inclination α has to be calculated. This mechanicaleffort Fte, i.e. the force transmitted by the motor to the gear-box/transmission and from this to the vehicle driving wheels,can be expressed as:
Fte = µrrmvg cos(α)︸ ︷︷ ︸
Frr
+12ρACdv2
︸ ︷︷ ︸
Fad
+mvg sin(α)︸ ︷︷ ︸
Fhc
+ (mv + mI)a︸ ︷︷ ︸
Fla
,
(1)where Frr is the rolling resistance force, Fad is the aerodynamicdrag force, Fhc is the hill climbing force, Fla is the linear ac-celeration force, and g and ρ are physical constants represent-ing the acceleration due to the gravity, and the air density, re-spectively. µrr is the tire rolling resistance coefficient, A is thefrontal area of the vehicle, Cd is the vehicle’s drag coefficient, αis the road inclination angle, v is the vehicle speed, and a is thevehicle acceleration. The vehicle mass, mv, takes into consid-eration the vehicle mass itself with battery pack (curb weight,mc), as well as the load and occupants masses.
In order to obtain a more accurate model of Fla, the rota-tional acceleration should be considered, in order to model theforce needed to accelerate the rotating parts. EVs’ electricalmotors can achieve high angular speeds (e.g. the Nissan LEAFmaximum motor speed is 10390 [rpm]). The increase of vehi-cle equivalent mass due to the angular moments of the rotat-ing components, mI , is approximated by the following modeladopted from [7]:
mI = mc(0.04 + 0.0025 G2), (2)
where G is the gear ratio.
It should be noted that Fte (and τg) will be positive if thebattery pack is supplying current to the motor, or negative ifthe current is in opposite flow, charging the battery pack. Thefirst two terms in (1), (Frr and Fad) are frictional forces, thusthey are non-negative. Therefore, only the last two terms of(1) (Fhc and Fla), together, are able to make Fte negative. Thiscan happen when the EV is going downhill (α < 0) or is de-celerating (a < 0). Fte is provided by the traction motor, whichdevelops enough motor torque τg, to supply Fte via gearbox andtransmission. Considering the losses on the gearbox and trans-mission, τg can be approximated by:
τg =
Fte r
G
1
ηt
, if Fte > 0,
Fte r
Gηt, if Fte < 0,
(3)
where ηt is the transmission and gears efficiency, and r is thewheel radius. τg will be considered a traction torque if τg > 0(Fte > 0) or a braking torque τg = τb otherwise (τg < 0,Fte < 0). Traction torque is provided by the electric mo-tor which drains current from battery and delivers mechanicalpower to the wheels. Braking torque is provided by the brakesystem, composed partially by the mechanical brake and par-tially by the electric motor acting as generator, which appliesits electrical torque to the wheels (usually the front wheels).
3.2. Power Driver Subsystem
The Power Driver Subsystem, shown in Figure 2, models theelectric motor/controller. This subsystem takes the torque re-quired by the gearbox τg, which is the torque the Power DriverSubsystem has to supply, and calculates: (i) the torque τreq re-quired from the motor, taking into account the motor torquelimits (τmax and τmin), i.e. the maximum traction and brakingtorques achieved by the motor, (ii) the amount of mechanicaltorque τmech applied by the mechanical brake system duringbraking phases, (iii) the motor efficiency ηm, and (iv) Preq, therequired power that the battery pack shall supply.
The evaluation about whether τg exceeds the tractive or re-generative capacity of the motor (torque limits) during tractionand braking, respectively, is done in the Tq Limit+ and Tq Limit-
subsystems, respectively. If τg > τmax, this means that the mo-tor cannot give such traction torque, which implies the motor
3
required
torque
(pos)
angular
speed
gearbox
torque
Tractive Torque
required
torque
(neg)
angular
speed
gearbox
torque mechanical
braking
torque
Braking Torque
Tq Limit +
Tq Limit -
required
torque
angular
speedeciency
required
torque
eciency
angular
speed
required
power
motor eciency
power requirement
Preq
Figure 2: Power driver subsystem.
torque to become limited to τg = τmax. As a consequence, from(3), Fte also becomes limited, which implies a reduction of thevehicle speed that results from (1). Otherwise, if τg < τmin, thismeans that the motor cannot give such braking torque, and partof the braking torque must be supplied by the mechanical brak-ing system, giving a mechanical torque τmech = τg − τmin. Thus,the required torque τreq, i.e. the torque required from the mo-tor after discounting from τg the part that is beyond the motorlimits, is:
τreq =
τmax, if τg > τmax,
τg, if τmin 6 τg 6 τmax,
τmin, if τg < τmin.
(4)
The Tq Limit+ subsystem works with positive values of τg (trac-tion) and adjusts target speed as appropriate, and the Tq Limit-
subsystem works with negative values of τg = τb (braking) anddistributes braking torque between the brake plates and motoras appropriate. In equation (4) it is assumed that braking is per-formed with as much as possible electrical braking torque, onlysubject to electrical motor braking torque limits. However, anEV can use some different braking strategy that should be mod-eled. Thus, (4) is reformulated as follows:
τreq =
τ+req = τmax, if τg > τmax (traction),
τ+req = τg, if 0 6 τg 6 τmax (traction),
τ−req = τreg = βτg = βτb, if τg < 0 (braking),
(5)
where τ+req, is the torque required from the motor on tractionevents, τ−req = τreg, is the torque required from the motor on
braking events, i.e. the regenerative braking torque, and the re-generative braking factor β is a function of some collection ofvariables that represent the instantaneous driving situation (e.g.acceleration, jerk, road inclination). τ+req = 0 on a braking eventand τ−req = 0 on a traction event.
An important goal of this paper is to propose the FLmRBframework for determining a model of β, in order to charac-terize the braking strategy of an EV. Regardless of the brakingstrategy (e.g. (4), or (5)), the total braking torque τb is definedfor τg < 0 and is given by:
τb = τg = τmech + τreg, (6)
where τmech is the mechanical braking portion of the total brak-ing torque and τreg is the regenerative braking portion. TheTq Limit- subsystem in Figure 2 is implemented by (6), and bythe proposed FLmRB described in Section 4.2.
Finally, taking into account the motor efficiency ηm, and thepower required by the accessories energy consumption, Pacc,the power requirement of the vehicle, Preq, is calculated by:
Preq =
τ+req ωrad
1
ηm
+ Pacc, if τreq > 0,
τ−req ωrad ηm + Pacc, if τreq < 0.
(7)
3.3. Energy Storage Subsystem
The Energy Storage Subsystem (Figure 1) input is Preq, whicheither represents the power required from the vehicle batterysystem both to develop the tractive effort and for accessories en-ergy consumption, Pacc, or represents the power supplied back
4
+
-
+
-
Figure 3: Battery equivalent circuit.
to the battery during regenerative braking. From Preq (7), ateach time interval, the following variables are calculated as de-scribed in this subsection: the required battery current Ibat, thenew battery terminal voltage Vt, and the new battery state ofcharge S OC.
EV drive range depends on several variables external to thevehicle, such as road pavement quality and status, and weatherconditions like rain, air temperature, and wind speed. Temper-ature is a variable that has a major influence over S OC. Es-timating S OC is not a mathematical process performed in anuniversal way [18].
In this work, the goal is to develop a method to model theEV energy and range, specially taking into consideration re-generative braking, with minimal dependence on informationobtained from EV monitoring and control systems, but usingpreferably variables that can be measured from independent in-struments like inertial measurement units, GPS, and hall effectcurrent probes. In the conducted experiments to model the re-generative braking behavior, the temperature effect has not beenconsidered in the S OC estimation algorithm, due to the lack ofcell temperature related data. The experimental tests for modelbuilding were conducted with air temperature close to 25Cand no energy consumption from the EV climate control sys-tem (switched off). The use of the Nissan LEAF has motivatedthe users to know more technical details of the vehicle, what ledthem to create discussion forums, such as the online forum forthe Nissan LEAF car1, where the LEAF EV CAN bus and itsmessage contents are described.
For modeling the EV battery pack, two approaches were con-sidered. The first approach is based on the voltage/discharge ca-pacity plots of the cells inside the 24 [kWh] battery installed inthe LEAF which are available at the Automotive Energy SupplyCorporation web page [1] (plots 90A, 60A, 1C, and 1/3C). Theapproach is based on two lookup tables built from these plots,and representing the open circuit battery voltage, Eoc, versusS OC and R+
in. The second approach, which performed better,
is based on the work of Plett [16] to model Eoc and follows thecurrent integration method also known as coulomb counting. Itconsists of using real voltage and current data obtained from ex-perimental trials to create the battery model. The battery modelused herein is represented in Figure 3. It consists of an internalvoltage source Eoc, two ideal diodes, and two inner resistancesR+
inand R−
inwhich represent the battery internal discharging and
charging resistances. The voltage at the terminals of the battery
1http://www.mynissanleaf.com/, acessed on August, 08, 2014.
is given by:
Vt = Eoc − R Ibat =
Eoc − R+in
Ibat, if discharging,
Eoc − R−in
Ibat, if charging,(8)
where R = R+in
in a discharging situation and R = R−in
in a charg-ing situation. R+
inand R−
inare piecewise constants estimated in
10% SOC intervals and stored in a lookup table. Assuming thatEoc follows the Combined Model as described in [16], and using(8), yields:
Vt = K0−R Ibat−K1
S OC−K2 S OC+K3 ln(S OC)+K4 ln(1−S OC).
(9)Parameters K0, . . . ,K4 are constant. K0, . . . ,K4 and R+
inand R−
in
are obtained using a least squares approximation based on cur-rent, voltage, and SOC readings obtained from the EV CANbus. The data collected from trials at a specific sampling ratewith the EV dashboard fuel bars going from full to empty wasregistered in a time ordered data set containing three variables(Vtk , Ibatk , S OCk), k = 1, . . . ,N, where k is the number of thesample, and N is the trial length (i.e. the total number of sam-ples). In order to obtain the parameters in (9), a column vector
Y = [Vt1 ,Vt2 , . . . ,VtN]T
is built with the battery voltage measurements, and a matrix
H = [h1,h2, . . . ,hN]T
is constructed with the rows formed by data vectors
hTj =
[
1,−I+bat j,−I−bat j
,− 1S OC j
,−S OC j, ln(S OC j), ln(1 − S OC j)
]
where the index corresponds to the time instant j. Y and H
are assembled for the formulation of the Y = Hθ least squaresproblem that is then used to jointly estimate the parameters ofequation (9). If Ibat > 0, a discharge current occurs and I+
bat j=
Ibat, I−bat j= 0; Else if Ibat < 0, then I+
bat j= 0, and I−
bat j= Ibat;
Else (Ibat = 0) both I+bat j= 0, and I−
bat j= 0. Therefore:
I+bat j= (Ibat + |Ibat |)/2,
I−bat j= (Ibat − |Ibat |)/2.
Under these conditions, assuming that H has full rank, and thatthe number of data patterns is greater than or equal to the num-ber of parameters in vector θ (i.e. N > 7),
θ = [K0,R+in,R
−in,K1, . . . ,K4]T ,
then a solution for the vector of parameters can be computedusing the pseudo-inverse least squares method, as follows [3]:
θ = (HT H)−1HT Y.
Then, Eoc can be calculated from (8), and (9) (see also Figure3) by:
Eoc = K0 −K1
S OC− K2 S OC + K3 ln(S OC) + K4 ln(1 − S OC).
(10)
5
After this procedure, a closer fit for R+in
and R−in
is calculatedusing least squares estimation again to obtain R+
inand R−
infrom
(9) and (10) using the collected Vtk , Ibatk , S OCk values. Thisis achieved using (10) to build Eoc with the collected S OCk
values, i.e. Eock= Eoc for S OC = S OCk (k = 1, . . . ,N). Then,
a matrix H =[
h1, h2, . . . , hN
]Tis defined to have rows h
T
j =
[I+bat j, I−
bat j], Y = [Eoc1 − Vt1 , Eoc2 − Vt2 , . . . , EocN
− VtN]T , and
Y = Hθ, where θ = [R+in,R−
in]T . The solution for θ using Y and
H is: θ = (HT
H)−1HT
Y.The total power provided by the battery, EocIbat, is modeled
as the sum of Preq and the power dissipated in the battery in-ternal resistance: EocIbat = RinI2
bat+ Preq, where Rin = R+
in(if
charging) or Rin = R−in
(if discharging). Depending on the cur-rent flow, the outputs of the Energy Storage Subsystem (Figure1), Ibat, and S OC, are finally calculated as follows:
Ibat =
Eoc −√
E2oc − 4 R−
inPreq
2 R−in
, if discharging,
Eoc −√
E2oc − 4 R+
inPreq
2 R+in
, if charging,
(11)
S OC =
S OC0 −1
C
∫
Ibat(t) dt, if discharging,
S OC0 −ηb
C
∫
Ibat(t) dt, if charging,
(12)
where ηb is the recharging efficiency of the battery, and the out-put Vt is obtained from (8).
4. Regenerative Braking Framework
This section introduces basic principles of RBS and detailsthe proposed FLmRB.
4.1. Regenerative Braking
Braking systems of EVs are designed to recover back to bat-tery as much energy as possible from the amount of energy thatwould be normally dissipated by a mechanical brake system,converting kinetic and potential energies into electric current,that is used to recharge the EVs’ battery pack. The recharg-ing efficiency ηb is less than 1 due to battery internal resistance,and cable and cable contacts resistance. With a suitable con-trol strategy, it is possible to make the electric traction motoroperate as a generator, producing negative torque on the wheelsand recovering electric energy. This possibility achieves greaterimportance if the vehicle is driving in a stop-and-go patternin urban areas. Regenerative braking may act strongly in ur-ban scenarios, enabling the increase in the vehicle operatingrange. If the electric motor can produce sufficient torque tosupply the total required braking torque on wheels, τb, all thecorresponding energy, excluding losses, is converted into elec-tric current by the power controller and fed back into the bat-tery pack. Otherwise, i.e. if the electrical brake is not sufficientto attain the required total braking torque, then the controller
calculates how the total braking torque will be split betweenwheels brake plates (mechanical brake) and the electric motor(electrical brake, commanded by the controller). This distribu-tion of braking torque must achieve the requirement of quicklyreducing the vehicle speed by using the total braking torque,and maintaining the vehicle direction controllable by the steer-ing wheel. The global goal is to ensure both the EV’s brakingperformance and its ability to recover as much braking energyas possible [7]. The mechanical braking torque, τmech, is dis-tributed between front and rear wheels, while the electrical one,τreg, is applied only to the driven axle (the front axle for passen-ger cars, normally). Therefore, equation (6) can be expressedby:
τb = τmechF + τmechR︸ ︷︷ ︸
τmech
+τreg, (13)
where τmechF is the mechanical braking torque on the frontwheels, and τmechR is the mechanical braking torque on rearwheels. In terms of front and rear axles, τmechF + τreg is of-ten produced over the front axle and τmechR over the rear one.This distribution is based on the traditional theory of brakingforce distribution and the Economic Commission for Europe(ECE) regulation [5]. The brake control strategy defines thebraking force strength to properly reduce the vehicle speed, andthe distribution of braking effort between front and rear wheelsto guarantee vehicle stability, and defines the strategy to recoveras much braking energy as possible. Basically, there are threedifferent brake control strategies defined by [7]: (1) series brak-ing with optimal braking feel, (2) series braking with optimalenergy recovery, and (3) parallel braking.
Commonly, traffic simulators are applicable in traffic man-agement tasks, such as traffic lights evaluation, route choice,re-routing, evaluation of traffic surveillance methods, vehicularcommunications, traffic forecasting [10]. In these contexts, itis not important for traffic simulators to take into considerationyaw stability. Thus, in this work the slip of the tire and the brak-ing force distribution between the front and the rear wheels wasnot taken into consideration. Instead, τmech was considered asa whole. In this work, the goal is to model β, the portion of τb
which is regenerated, i.e.:
β =τreg
τb
. (14)
4.2. Fuzzy Logic Model for Regenerative Braking
Fuzzy inference systems (FISs) are widely used to implementnew brake control strategies used in RBSs as discussed in Sec-tion 2. In this work, to model existing RBSs control strategies,a Mamdani FIS is proposed in order to map between a selectedset of input variables and the regenerative ratio β. Brake pedaldisplacement information is usually used in regenerative brak-ing controllers, but the way this information is processed andmapped to real vehicle braking is dependant on EV maker’sbraking mapping strategy. One of the goals for the FLmRB isto be integrated in microsimulation software, which is usuallyused to analyze traffic flow, vehicle consumption and emission,traffic jam, car following models, and so on. In this context, the
6
important issue is the target vehicle speed, not its individual in-ternal variables which determine the observed vehicle brakingperformance. A RBS model which has the pedal displacementinformation as one of its inputs is not generic. Thus, it wasdecided not to include this information in the FLmRB model.The proposed FLmRB objective is to use only data obtainedexternally to vehicle’s control and communication architecture.In order to identify among the measurable variables, those thatmost influence the regenerative braking, and are the most wellsuited to be used as inputs to the FLmRB, short-distance ur-ban tests were made with a Nissan LEAF EV, and the resultsof the tests were compared with simulations, considering 100%regeneration in the simulations. The test site and pathways fol-lowed by the EV are shown in Figure 4. In Figure 5, it is showna set of results of tests which are relevant for the discussion,and where the simulated values of Ibat were obtained consider-ing a regeneration factor β = 1. In the encircled area in Figure5a, it can be observed, by the small value of the measured cur-rent when compared to the simulated current, that just a smallamount of braking energy was regenerated. The difference isactually wasted by the mechanical brake. Large decelerationrates require more braking force than the motor can supply orthe battery can receive safely. In Figure 5b, with high jerk, mostof the energy was also consumed by the mechanical brake. Theexplanation is that in a heavy braking event the vehicle mustslow down quickly and the motor is unable to produce the re-quired braking torque [7]. Figure 5c shows the joint influence ofacceleration, jerk, and inclination over the regeneration factor.The vehicle acceleration and road inclination of a moving vehi-cle are variables which are clearly correlated to the mechanicalenergy of the vehicle. Consequently, it is plausible that thesevariables are also correlated to the value of energy recoveredby regenerative breaking. Motivated by the above observations,three input variables were chosen for the FLmRB: (1) vehicleacceleration, a, (2) vehicle jerk, ϕ, and (3) road inclination, α.
The output of the FLmRB is the regenerative braking factor,β, which enables the computation of the required braking torqueto be applied by the motor, from the total braking torque (14).β is used in the Tq Limit- subsystem, described in Section 3.2,to calculate the amount of regenerative braking torque. TheFLmRB is designed as a FIS composed by the following op-erators: singleton fuzzifier, minimum t-norm, Mamdani mini-mum implication, maximum aggregation, and centroid defuzzi-fier. For more details about FIS design and operators reference[19] is suggested. The overall structure of the FLmRB is shownin Figure 6.
4.2.1. FLmRB Input Variables
The selected input variables are:
• Acceleration (a): when the vehicle is decelerating (a < 0),the regeneration factor grows with the increase of de-celeration. The acceleration of an automobile during anabrupt braking is about −0.7 [g] [15]. The set of linguisticterms defined for the acceleration linguistic variable, a, isTa = A1, A2, A3, A4, A5, A6, A7, A8, A9, A10 with universeof discourse of [−0.7, 0.05] [g]. The fuzzy membership
functions associated to A1, . . . , A10 are shown in Figure 7a,and are defined by triangular and trapezoidal shapes;
• Jerk (ϕ): the regeneration factor is decreased whenthe jerk increases. The set of linguistic terms de-fined for the jerk linguistic variable, ϕ, is Tϕ =
J1, J2, J3, J4, J5, J6, J7, J8, J9, J10, J11 with universe ofdiscourse of [−3.5, 3.5] [m/s3]. The membership functionsassociated to J1, . . . , J11, are shown in Figure 7b, and aredefined by triangular and trapezoidal shapes;
• Inclination (α): in order to provide flexibility and gener-ality for most of the occurring road inclinations, it was as-sumed a [−20%,+20%] grade operating range. The set oflinguistic terms defined for the inclination linguistic vari-able, α, is Tα = I1, I2, I3, I4, I5, I6, I7 with universe of dis-course of [−20, 20] [%]. The membership functions asso-ciated to I1, . . . , I7 are shown in Figure 7c, and are definedby triangular and trapezoidal shapes.
4.2.2. FLmRB Output Variable
The output of the proposed FLmRB is the regeneration fac-tor, β, the ratio between the regenerative braking torque appliedby the traction motor and the total braking torque. The setof linguistic terms defined for the regeneration factor linguis-tic variable is Tβ = R1,R2,R3,R4,R5,R6,R7,R8,R9,R10 withuniverse of discourse of [0, 1], where 0 means only mechanicalbraking and 1 means only regenerative braking. The member-ship functions associated to R1, . . . ,R10 are shown in Figure 7d,and are defined by triangular and trapezoidal shapes.
4.2.3. FLmRB Rules
Using the input and output linguistic variables defined in theprevious subsections, a FIS is designed to infer the regenerationfactor. The designed FIS contains a set of multiple-inputs singleoutput (MISO) IF-THEN rules with three inputs and one output,of the following form:
IF premise1 AND premise2 AND premise3 THEN conclusion.
The set of fuzzy rules Frules is composed by one fuzzy rulefor each combination of linguistic terms of the antecedent lin-guistic variables (defined in Ta, Tϕ, Tα). Thus the number ofrules is |Frules| = |Ta| × |Tϕ| × |Tα| = 10 × 11 × 7 = 770. All theFLmRB design and tuning, including for example the choice ofthe t-norm, implication and aggregation operators, the defuzzi-fication methods, and the design of the number of membershipfunctions, and the consequent linguistic terms of the rules, areobtained from human knowledge, in pilot studies, and by trialand error. The tuning of the consequent terms is guided by thegoal of matching as well as possible the simulated and real val-ues of the battery current. The FLmRB design was started witha few number of linguistic terms and increasing the number ofterms during the analysis to make them more flexible. Since themodel was obtained through human know-how and from shortdistance tests, the options taken for FLmRB modeling where
7
Figure 4: Short-distance urban tests with 530 [m] (upper left), 500 [m] (lower left), and 900 [m] (right) in length.
Table 1: Fuzzy Rules of the FLmRB. Antecedent variables: acceleration (a),jerk (ϕ), and road inclination (α). Consequent variable: regenerative brakingfactor (β).
Rule 1: If a is A1 and ϕ is J1 and α is I1 Then β is R3
Rule 2: If a is A1 and ϕ is J1 and α is I2 Then β is R3
.
.
.
.
.
.
Rule 386: If a is A6 and ϕ is J1 and α is I1 Then β is R4
.
.
.
.
.
.
Rule 539: If a is A7 and ϕ is J11 and α is I7 Then β is R10
Rule 540: If a is A8 and ϕ is J1 and α is I1 Then β is R1
Rule 541: If a is A8 and ϕ is J1 and α is I2 Then β is R5
.
.
.
.
.
.
Rule 770: If a is A10 and ϕ is J11 and α is I7 Then β is R10
chosen in order to enable to have a proper human insight of therules. The rules have the following structure:
IF a is Ai and ϕ is J j and α is Ik THEN β is Rx,
where Ai ∈ Ta for i = 1, . . . , 10, J j ∈ Tϕ for j = 1, . . . , 11,Ik ∈ Tα for k = 1, . . . , 7, and Rx ∈ Tβ for x = 1, . . . , 10. Part ofthe set of fuzzy rules is shown in Table 12.
5. Experiments and Results
This section presents the Nissan Leaf model parameters, thedata acquisition system, and the simulation results of the pro-posed FLmRB.
2The complete set will be available
5.1. Vehicle Specifications
The model presented in Section 3 is suitable to be ap-plied/instantiated to any EV. A Nissan LEAF, 2011 version,was used in the experiments presented in this paper. The ve-hicle parameters used in this work are shown in Table 2a. Ta-ble 2b shows the lookup tables for the values of R+
inand R−
in,
which have been calculated by the method presented in Section3.3. The motor efficiency ηm (see Figure 2) was obtained from[17]. It also takes into consideration the efficiencies of the in-verter and AC cables. ηm is modeled as a function that takesvalues in the range [85%, 95%], as the motor torque τreq variesin the range [0, 280] [Nm], and the motor speed ωrpm varies inthe range [0, 10390] [rpm].
5.2. Data Acquisition System
The data acquisition system used in the experimental testsincluded an Xsens MTi-G, 6-DOF Attitude and Heading Ref-erence System3 (AHRS), which was used for the measurementof the instantaneous position, inclination, and speed. The cur-rent and voltage of the battery pack were acquired via the EVCAN bus to an onboard computer and stored at a frequency of10 [Hz]. To validate the EV readings, a current probe was alsoused to measure the inverter current. A diagram of the dataacquisition system is shown in Figure 8. The data sets result-ing from the tests and used in the experiments are available athttp://home.isr.uc.pt/˜rui/publications/.
3http://www.xsens.com/products/mti-g/, accessed August, 08,2014
8
Table 2: (a) Nissan Leaf model parameters; (b) Internal resistance as function of S OC.
(a)
motorτmax Maximum tractive torque 280 [Nm]τmin Maximum braking torque −127 [Nm]
battery
K0 Eoc parameter 367.7789K1 Eoc parameter 3.2085K2 Eoc parameter 14.3522K3 Eoc parameter 1.138K4 Eoc parameter 6.0957ηb Battery efficiency 97 [%]C Battery capacity 65 [AH]
vehicle
G Gear ratio 7.937µrr Rolling resistance coefficient 0.007mv Vehicle mass 1, 761 [Kg]mc Curb weight 1, 521 [Kg]A Frontal area 2.29 [m]
Cd Drag coefficient 0.28r Wheel radius 0.309 [m]
Pacc Accessories power 269 [W]ηt Transmission efficiency 83 [%]
othersρ Air density 1.25g Gravity acceleration 9.8 [ms−1]
(b)
S OC 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0R+
in[Ω] 0.0830 0.0830 0.0892 0.0997 0.1051 0.0894 0.0919 0.1135 0.1026 0.0997
R−in
[Ω] 0.0620 0.0620 0.0587 0.0691 0.0593 0.0928 0.0906 0.0664 0.0892 0.0250
5.3. Methodology Applied in FLmRB Modeling
In the first step, short-distance tests were made in a urbanarea and data were collected to establish the relationship be-tween input and output variables, aiming at adjusting mem-bership functions and fuzzy rules of the FIS.The membershipfunctions parameters were adjusted by trial and error throughthe know-how obtained in analyzing these short-distance testsdata. The Matlab Fuzzy Logic Toolbox and its Fuzzy Logiccontroller block were used, allowing the tuning of the member-ship functions parameters and design the fuzzy rules. Selectedtests used in this step are illustrated in Figure 5. During thetests, a variety of situations, such as harsh braking, harsh accel-eration, and freewheel, among other strategies were explored.Tests were executed in flat streets, and in streets with positiveand negative slopes.
The focus was to determine the influence of the vehicle ac-celeration and jerk, and street inclination over the regenerationfactor. After having adjusted the FLmRB, a number of long-distance tests were made in the city of Coimbra, in urban andsub-urban areas, for verification purposes and fine-tuning.
5.4. Simulation Results
The proposed FLmRB was evaluated by comparing simu-lated (FLmRB) and real-world data in two long-distance testsinurban and suburban areas, named as Test#1 and Test#2, with103 [km], and 112 [km] in length, respectively. Figure 9 showsthe speed profiles for Tests #1 and #2, which have aver-age speeds of 72.2 [km·h−1], and 45.1 [km·h−1], respectively.Test#1 was made in a suburban area, and Test#2 was mademainly on urban areas. Figure 10 presents, as an illustrativeexample, the time evolution results of the FLmRB output, the βparameter, in a segment of Test#2. However, although β is theoutput of the model, a figure showing this parameter may not be
Table 3: Battery current Mean Squared Error (MSE), considering all the currentmeasurements (all), and considering only the negative measurements of current(neg), when using FLmRB and not using FLmRB (100% regeneration).
with FLmRB without FLmRB(100% regeneration)
Test#1 (all) 481.56 496.27Test#1 (neg) 155.40 165.54Test#2 (all) 329.56 374.35Test#2 (neg) 101.99 143.15
the most informative because β is not accessible to be measuredand compared in an EV. Thus, the effectiveness of the FLmRBis better verified through the charge balance of the EV’s bat-tery in comparison with the simulation, via the battery stateof the charge (SOC), battery current, and battery voltage vari-ables. Table 3 summarizes the results of simulations, both usingFLmRB and not using FLmRB (100% regeneration). The sec-ond column of the table shows the mean squared error (MSE)between the battery current estimated with the FLmRB, and themeasured battery current. The third column shows the MSEbetween the battery current estimated without the FLmRB, andthe measured current. There are two computations of MSE foreach test, first, considering all values of battery current “(all)”,and second, considering only the negative values of battery cur-rent “(neg)”. The “(neg)” values take into consideration onlythe regenerated current. A lower error is observed when usingthe FLmRB to estimate the battery current; and this improve-ment is larger in Test #2, which was mainly performed in urbanareas, and has a higher number of regeneration episodes.
Figure 11 illustrates parts of the two tests showing the batterycurrent estimated with the FLmRB, as well as the measuredbattery current. It shows the effectiveness of the FLmRB.
Figure 12 shows the S OC along the runs. At end of the run,
9
0 100 200 300 400 500 600 700−6
−4
−2
0
2
4
6
a[m
/s2]
0 100 200 300 400 500 600 700−300
−200
−100
0
100
200
300
I bat[A
]
Distance travelled [m]
a
Ibat (simulated)
Ibat (measured)
(a) Influence of acceleration (a).
120 140 160 180 200 220 240 260−4
−3
−2
−1
0
1
2
3
ϕ[m
/s3]
120 140 160 180 200 220 240 260−80
−60
−40
−20
0
20
40
60
I bat[A
]
Distance travelled [m]
ϕ
Ibat (simulated)
Ibat (measured)
(b) Influence of jerk (ϕ).
320 330 340 350 360 370 380 390 400 410 420−10
−8
−6
−4
−2
0
2
4
6
8
10
320 330 340 350 360 370 380 390 400 410 420−10
−8
−6
−4
−2
0
2
4
6
8
10
Distance travelled [m]
a · 2 [ms−2]
ϕ · 2 [ms−3]
α [%]
Ibat/10 (simulated) [A]
Ibat/10 (measured) [A]
(c) Influence of acceleration (a), jerk (ϕ), and inclination (α).
Figure 5: Influence of several variables on regeneration, illustrated by resultsof tests with the vehicle: (a) Influence of acceleration; (b) influence of jerk; and(c) influence of acceleration, jerk, and inclination.
regenerationfactorjerk
F I S
FLmRB
acceleration
inclination
Figure 6: Overall structure of the fuzzy logic model of regenerative braking.
the measured S OC of Test#1 was 19, 3 [%] and the S OC simu-lated with the FLmRB was 19.25 [%], while, without FLmRB,the estimated S OC was 21.35 [%]. At the end of Test#2, themeasured S OC was 13.6 [%], and the S OC simulated with theFLmRB was 14.22 [%], while, without FLmRB, the estimatedS OC was 19.29 [%]. In Table 4, the MSE of the battery S OC ispresented. Better results are achieved in the case of the FLmRBtests.
Figures 13 and 14 show the amount of electrical and mechan-ical braking torques applied, obtained in the test runs with the
−0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
0
0.2
0.4
0.6
0.8
1
a [g]
Degreeofmem
bership
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
(a) Acceleration.
−3 −2 −1 0 1 2 3
0
0.2
0.4
0.6
0.8
1
ϕ [m/s3]
Degreeofmem
bership
J1
J2
J3
J4
J5
J6
J7
J8
J9
J10
J11
(b) Jerk.
−20 −15 −10 −5 0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
α [%]
Degreeof
mem
bership
I1
I2
I3
I4
I5
I6
I7
(c) Inclination.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
β
Degreeof
mem
bership
R1
R2
R3
R4
R5
R6
R7
R8
R9
R10
(d) Regenerative braking factor.
Figure 7: Fuzzy membership functions of the linguistic terms of the 4 variablesassociated to the FLmRB FIS: (a) acceleration a, (b) jerk ϕ, and (c) inclinationα input variables; and (d) regenerative braking factor output variable β.
Table 4: Battery S OC MSE.
with FLmRB without FLmRB(100% regeneration)
Test#1 2.49×10−5 1.82×10−4
Test#2 9.57×10−5 1.09×10−3
10
GPS sensor
CAN adapter
Database
Current probe
Figure 8: Data Acquisition System.
0 10 20 30 40 50 60 70 80 90 1000
20
40
60
80
100
120
Speed[km/h
]
Distance travelled [km]
(a)
0 20 40 60 80 1000
20
40
60
80
100
120
Speed[km/h
]
Distance travelled [km]
(b)
Figure 9: Speed profiles of (a) Test#1, performed in suburban areas, and (b)Test#2, performed mainly in urban areas.
105.5 105.6 105.7 105.8 105.9 106 106.1 106.2 106.3 106.4 106.5−3
−2
−1
0
1
2
105.5 105.6 105.7 105.8 105.9 106 106.1 106.2 106.3 106.4 106.5−3
−2
−1
0
1
2
Distance travelled [km]
β
a [ms−2]
ϕ [ms−3]
α/20 [%]
Figure 10: Example of the time evolution of the FLmRB output, the β parame-ter, obtained in a part of Test#2.
FLmRB. Figure 15 shows the traction energy, ETraction, the me-chanical braking energy, EMechanicalbrake
, and the electric brakingenergy, ERegenerative, applied to the wheels. These energies are
62 63 64 65 66 67 68 69 70 71 72−150
−100
−50
0
50
100
150
Distance travelled [km]
I bat[A
]
measuredwith FLmRB
(a)
50 50.5 51 51.5 52 52.5 53 53.5 54 54.5 55−150
−100
−50
0
50
100
150
200
Distance travelled [km]
I bat[A
]
measuredwith FLmRB
(b)
Figure 11: Battery current of (a): Test#1; (b): Test#2.
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Distance travelled [km]
SOC
[%]
measuredwith FLmRBwithout FLmRB
(a)
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Distance travelled [km]
SOC
[%]
measuredwith FLmRBwithout FLmRB
(b)
Figure 12: S OC of the Battery pack. (a): Test#1; (b): Test#2.
obtained from:
ETraction =G
r· ηt
∫ T
0v · τ+req dt, (15)
EMechanicalbrake=
G
r· 1ηt
∫ T
0v · |τmech| dt, (16)
11
0 10 20 30 40 50 60 70 80 90−200
−150
−100
−50
0
50
100
150
200
250
300
Distance travelled [km]
Torque[N
.m]
Traction torque, τ+req
Braking torque (mechanical), τmech
Braking torque (electrical), τ−
req
(a)
20.8 21 21.2 21.4 21.6 21.8 22−200
−150
−100
−50
0
50
100
Distance travelled [km]
Torque[N
.m]
Traction torque, τ+req
Braking torque (mechanical), τmech
Braking torque (electrical), τ−
req
(b)
Figure 13: Simulated torque of Test#1. (a): entire test; (b): zoomed detail.
0 20 40 60 80 100−300
−200
−100
0
100
200
300
Distance travelled [km]
Torque[N
.m]
Traction torque, τ+req
Braking torque (mechanical), τmech
Braking torque (electrical), τ−
req
(a)
47.2 47.4 47.6 47.8 48 48.2 48.4 48.6−200
−150
−100
−50
0
50
100
Distance travelled [km]
Torque[N
.m]
Traction torque, τ+req
Braking torque (mechanical), τmech
Braking torque (electrical), τ−
req
(b)
Figure 14: Simulated torque of Test#2. (a): entire test; (b): zoomed detail.
ERegenerative =G
r· 1ηt
∫ T
0v · |τ−req| dt, (17)
using numerical integration by the rectangle method with asampling interval of ∆t = 0.1 [seg], where T is the durationof the run. Table 5 shows their total cumulative amounts at theend of the runs, as well as their amounts per km. In Test#1 ap-
0 10 20 30 40 50 60 70 80 90 1000
5
10
15
20
25
Distance travelled [km]
Energy[kW
h]
ET raction
ERegenerativeEMechanicalbrake
(a)
0 20 40 60 80 1000
5
10
15
20
25
Distance travelled [km]
Energy[kW
h]
ET raction
ERegenerativeEMechanicalbrake
(b)
Figure 15: Traction and braking energy dissipation in (a): Test#1; (b): Test#2.ETraction, EMechanicalbrake
, ERegenerative were obtained using (15), (16), and (17),and converted to [KWh].
Table 5: Traction energy, and energy used in braking.
Test#1 Test#2Traction energy [kWh]• total 17.29 20.92• per km 0.173052 0.185731
Braking energy [kWh]• total 3.96 6.90• per km 0.039595 0.061233
Percentage of braking energyto traction energy 22.88 32.97
Energy recovered byregenerative braking [KWh] 3.18 5.05
proximately 3.18 [kWh] were recovered with regenerative brak-ing, and in Test#2 approximately 5.05 [kWh] were recovered.These values are in accordance with the literature [7]. Figure15b (Test#2) depicts the higher benefit/applicability obtainedfrom regenerative braking in inner urban areas where brakes areactuated more often (compare with Test#1, Figure 15a) leadingto a greater amount of energy that is regenerated. Figure 9b(Test#2) shows the higher occurrence of speed variations whencompared to Figure 9a (Test#1), thus confirming the existenceof more opportunities for energy regeneration. Specifically,from Figures 15a and 15b, it is seen that, for/after the samedistance travelled, in Test#2 the energy recovered is higher thanin Test#1. On the other hand, the energy supplied from, andrecovered to, the battery pack, calculated by
ES upplied =
∫ T
0Vt ·max(0, Ibat) dt, (18)
12
0 10 20 30 40 50 60 70 80 90 1000
5
10
15
20
25
Distance travelled [km]
Energy[kW
h]
Ebattery (simulated)
Ebattery (measured)
ESupplied (simulated)
ESupplied (measured)
ERegenerative (simulated)
ERegenerative (measured)
Figure 16: Battery energies obtained by the integration of voltage and current:supplied energy, ES upplied (18), recovered/regenerated energy, ERegenerative
(19), and total energy, EBattery (20).
0 20 40 60 80 1000
5
10
15
20
25
Distance travelled [km]
Energy[kW
h]
Ebattery (simulated)
Ebattery (measured)
ESupplied (simulated)
ESupplied (measured)
ERegenerative (simulated)
ERegenerative (measured)
Figure 17: Battery energies obtained by the integration of voltage and current:supplied energy, ES upplied (18), recovered/regenerated energy, ERegenerative
(19), and total energy, EBattery (20).
ERegenerative =
∫ T
0Vt · |min(0, Ibat)| dt, (19)
EBattery =
∫ T
0Vt · Ibat dt, (20)
are shown in Figures 16 and 17, and their total cumulativeamounts at the end of the runs are shown in Table 6. By compar-ing Tables 5 and 6, it is observed that the differences betweenthe supplied energy and the traction energy are 1.73 [kWh] and2.46 [kWh] in Test#1 and Test#2, respectively. Actually, thesedifferences correspond to the mechanical and electrical lossesin the set comprised by the motor, the inverter, and the AC ca-bles connecting them.
The attained overall efficiency of the set comprised by themotor, the inverter, and the AC cables connecting them, in trac-tion, η+
overall, was 92.08% in Test#1 and 90.99% in Test#2. The
overall efficiency in braking, η−overall
, was 90.62% in Test#1 and90.19% in Test#2. These values were calculated by
η+overall =
∫ T
0τ+req · v dt
∫ T
0τ+req · v ·
1ηm
dt
, η−overall =
∫ T
0τ−req · v · ηm dt
∫ T
0τ−req · v dt
,
and they are in accordance with the information provided in[17]. η+
overallis the ratio between the total energy that the mo-
tor delivers to the gearbox and the total energy delivered to themotor. η−
overallis the ratio between the total energy delivered
Torque,
τ req[N
.m]
Vehicle speed, v [km/h]
20 40 60 80 100 120 140 160−200
−150
−100
−50
0
50
100
150
200
250
300
0.85
0.86
0.87
0.88
0.89
0.9
0.91
0.92
0.93
0.94
0.95
(a)
Torque,
τ req[N
.m]
Vehicle speed, v [km/h]
20 40 60 80 100 120 140 160−200
−150
−100
−50
0
50
100
150
200
250
300
0.85
0.86
0.87
0.88
0.89
0.9
0.91
0.92
0.93
0.94
0.95
(b)
Figure 18: Motor operating points. (a): Test#1; (b): Test#2.
to the motor and the total energy that the motor delivers to thegearbox. The motor operating points of the two tests are shownin Figure 18. Each operating point is a (torque, speed) pair ofthe run. It can be observed that during the runs, the entire rangeof motor speed (with the vehicle speed within the legal limitsof the roads), and the entire range of motor torque were ex-plored. The speed distributions of the operating points shownin Figure 18 are in accordance with the higher or lower averagespeeds of both tests. Figure 18, makes visible the motor op-eration zones for two distinct types of routes: Test#1, is madeat higher speeds around 90 [km/h], and Test#2, has a biggerconcentration of lower sampled speeds around 50 [km/h]. Al-though the EV motor/controller achieves high energy efficien-cies of as high as 95%, it is clear that the operation points arelocated more frequently in the range of [85, 92] [%]. Regret-tably, this is not the zone of best efficiency. These efficiencyvalues do not take into account the transmission and tire lossesthat are also higher at low motor torques.
6. Conclusion
From the results of the learned FLmRB, it can be con-cluded that a RBS model of a particular EV can be successfullylearned by using the proposed fuzzy expert system methodol-ogy. Namely, using the vehicle’s acceleration and jerk, and roadinclination, and using a suitable fuzzy reasoning model, it hasbeen shown that it is possible to infer the regeneration factor(β), the ratio of regenerative braking force to total braking force,during braking, while disregarding the brake pedal information.To validate and demonstrate the performance and effectivenessof the proposed framework, tests were made with real data ob-
13
Table 6: Energy supplied by, and energy recovered to, the battery.
Test#1 Test#2Energy MSE Energy MSE[kWh] [(kWh)2] [kWh] [(kWh)2]
Energy Supplied (ES upplied)• measured 18.81
0.01922.08
0.732• simulated 19.02 23.38Energy Recovered (ERegenerative)• measured 3.24
0.0544.84
0.570• simulated 3.56 6.10Total Energy (EBattery)• measured 15.57
0.02317.24
0.071• simulated 15.46 17.27
tained from a Nissan LEAF EV in long-distance road runs. Theresults of the tests were used to compare the real-world datawith the results of two types of simulations (also using real-world input data), one using FLmRB and the other considering100% regeneration. Results show that β can be calculated byFLmRB, and that by using FLmRB, the estimated battery cur-rent is closer to the real values when compared to the case ofsimulation with 100% regeneration. It was also shown that theproposed FLmRB also enables adequate estimation of the S OC.To infer β for other real EVs, it should be performed the tuningof the learned fuzzy logic system/model (FLmRB), including inparticular the consequent membership functions parameters, soas to infer an adequate and representative mapping between ap-propriate gathered EV data in one hand, and the EV energy flowin terms of regenerative braking on the other hand. In addition,the proposed approach provides the basis to achieve higher ac-curacy in EV simulations, making possible more rigorous EVenergy scientific studies in the future. For example, using thisexpert system in a traffic simulator like SUMO, it is possible tosimulate several vehicles differently tuned.
In the current stage, the EV’s RBS model is tuned by manualadjustment of the FLmRB parameters, after pilot studies analy-sis and also by trial and error. Also, a current limitation of theFLmRB is its complexity, i.e. it is used one FIS rule for eachpossible combination of the input variables (e.g. 770 rules forthe presented model).
As a future work, the authors would like to propose the ap-plication of methods to reduce the learned model complexity byapplying one of the existing methods in the literature for fuzzysystem simplification [e.g., 9]. Moreover, it is also proposed asa future work the development of an automatic learning methodfor tuning the FLmRB rules to any other EV using real-worlddata, and test the methods with other EVs.
7. Acknowledgments
This work has been supported by QREN-MAIS Centrounder project CENTRO-07-ST24-FEDER-002028. RicardoMaia and Marco Silva have been supported by the PortugueseFoundation for Science and Technology (FCT), under grantsSFRH/BD/44644/2008, and SFRH/BD/38998/2007, respec-tively. The authors acknowledge the help of Ricardo Faria inthe tests for gathering the data sets with Nissan LEAF vehicle.
References
[1] AESC (2014). Cell, module, and pack for ev applications. (website):http://www.eco-aesc-lb.com/en/product/liion_ev/. (Ac-cessed August, 08, 2014).
[2] Aleksendric, D., Živana Jakovljevic, & Cirovic, V. (2012). Intelligentcontrol of braking process. Expert Systems with Applications, 39, 11758–11765.
[3] Ben-Israel, A., & Greville, T. N. E. (2003). Generalized Inverses: Theory
and Applications. (2nd ed.). New York, USA: Springer-Verlag.[4] Cheng, C.-H., & Ye, J.-X. (2011). Ga-based neural network for energy
recovery system of the electric motorcycle. Expert Systems with Applica-
tions, 38, 3034–3039.[5] Chu, L., Yao, L., Chen, J., Chao, L., Guo, J., Zhang, Y., & Liu, M. (2011).
Integrative braking control system for electric vehicles. In 2011 IEEE
Vehicle Power and Propulsion Conference (VPPC) (pp. 1–5).[6] Chu, L., Yao, L., kun Yin, J., bo Chao, L., & Wei, W. (2011). Study on
the braking force allocation dynamic control strategy based on the fuzzycontrol logic. In 2011 IEEE 18Th International Conference on Indus-
trial Engineering and Engineering Management (IE EM) (pp. 635–639).volume Part 1.
[7] Ehsani, M., Gao, Y., & Emadi, A. (2010). Modern Electric, Hybrid Elec-
tric, and Fuel Cell Vehicles: Fundamentals, Theory, and Design. PowerElectronics and Applications Series (2nd ed.). CRC press.
[8] García, P., Torreglosa, J. P., Fernández, L. M., & Jurado, F. (2013). Con-trol strategies for high-power electric vehicles powered by hydrogen fuelcell, battery and supercapacitor. Expert Systems with Applications, 40,4791–4804.
[9] Gegov, A. (2007). Complexity Management in Fuzzy Systems A Rule Base
Compression Approach. Berlin/Heidelberg, Germany: Springer-Verlag.[10] Krajzewicz, D., Erdmann, J., Behrisch, M., & Bieker, L. (2012). Recent
development and applications of SUMO - Simulation Of Urban MObil-ity. International Journal On Advances in Systems and Measurements, 5,128–138.
[11] Larminie, J., & Lowry, J. (2003). Electric Vehicle Technology Explained.John Wiley & Sons.
[12] Maia, R., Silva, M., Araújo, R., & Nunes, U. (2011). Electric vehiclesimulator for energy consumption studies in electric mobility systems. In2011 IEEE Forum on Integrated and Sustainable Transportation System
(FISTS) (pp. 227–232).[13] Mendes, J., Araújo, R., & Souza, F. (2013). Adaptive fuzzy identifica-
tion and predictive control for industrial processes. Expert Systems with
Applications, 40, 6964–6975.[14] Nian, X., Peng, F., & Zhang, H. (2014). Regenerative braking system
of electric vehicle driven by brushless dc motor. IEEE Transactions on
Industrial Electronics, PP, 1–1.[15] Norton, R. (1961). Kinematics&Dynamics Of Machinery(Sie). McGraw-
Hill Companies.[16] Plett, G. L. (2004). Extended kalman filtering for battery management
systems of lipb-based hev battery packs: Part 2. modeling and identifica-tion. Journal of power sources, 134, 262–276.
14
[17] Sato, Y., Ishikawa, S., Okubo, T., Abe, M., & Tamai, K. (2011). De-velopment of high response motor and inverter system for the nissan leafelectric vehicle. Energy, 2013, 10–22.
[18] Schellenberg, S., Berndt, R., Eckhoff, D., & German, R. (2014). A com-putationally inexpensive battery model for the microscopic simulation ofelectric vehicles. In 80th IEEE Vehicular Technology Conference Fall
(VTC 2014-Fall). Vancouver, BC, Canada: IEEE.[19] Wang, L.-X. (1997). A Course in Fuzzy Systems and Control. Upper
Saddle River, NJ, USA: Prentice-Hall, Inc.[20] Xu, G., Li, W., Xu, K., & Song, Z. (2011). An intelligent regenerative
braking strategy for electric vehicles. Energies, 4, 1461–1477.[21] Zhang, Z., Xu, G., Li, W., & Zheng, L. (2010). Regenerative brak-
ing for electric vehicle based on fuzzy logic control strategy. In 2010
2nd International Conference on Mechanical and Electronics Engineer-
ing (ICMEE) (pp. V1–319–V1–323). volume 1.
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