1003 Equivalent fuel consumption optimal control of a ... Articles/Equivalent fuel... · Equivalent fuel consumption optimal control of a series hybrid electric vehicle J-P Gao1,2,

Equivalent fuel consumption optimal controlof a series hybrid electric vehicleJ-P Gao1,2, G-M G Zhu3*, E G Strangas3, and F-C Sun2

1Henan University of Science and Technology, Luoyang, People’s Republic of China2Beijing Institute of Technology, Beijing, People’s Republic of China3Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA

The manuscript was received on 24 November 2008 and was accepted after revision for publication on 29 April 2009.

DOI: 10.1243/09544070JAUTO1074

Abstract: Improvements in hybrid electric vehicle fuel economy with reduced emissionsstrongly depend on their supervisory control strategy. In order to develop an efficient real-timesupervisory control strategy for a series hybrid electric bus, the proposed equivalent fuelconsumption optimal control strategy is compared with two popular strategies, thermostat andpower follower, using backward simulations in ADVISOR. For given driving cycles, global optimalsolutions were also obtained using dynamic programming to provide an optimization target forcomparison purposes. Comparison simulations showed that the thermostat control strategyoptimizes the operation of the internal combustion engine and the power follower controlstrategy minimizes the battery charging and discharging operations which, hence, reducesbattery power loss and extends the battery life. The equivalent fuel consumption optimal controlstrategy proposed in this paper provides an overall system optimization between the internalcombustion engine and battery efficiencies, leading to the best fuel economy.

Keywords: automotive systems, hybrid powertrain systems, series hybrid electric vehicle,supervisory control strategy

1 INTRODUCTION

Increasing concerns about global climate change

and ever-increasing demands on fossil fuel capacity

call for reduced emissions and improved fuel eco-

nomy. Hybrid electric vehicles (HEVs) attract more

attention because of their inherent advantages of im-

proved fuel economy, reduced harmful emissions,

and better performance compared with conven-

tional vehicles. Among the three basic kinds of HEV

(series, parallel, and split), the series hybrid electric

vehicle (SHEV) predominates as an urban transpor-

tation tool owing to its outstanding transient perfor-

mance and simple architecture.

Improvements in fuel economy and emissions of

HEVs strongly depend on their supervisory control

strategy [1]. At any moment, the supervisory control

strategy needs to determine the power distribution

between the primary energy converter (an internal

combustion engine) and the renewable electrical

storage system (battery), so that the power require-

ment and other constraints are satisfied, and also the

fuel consumption and harmful emissions are mini-

mized. To achieve the above objectives, many kinds

of supervisory control strategy for an SHEV have

been proposed and developed in the past. These

control strategies can be classified into mainly two

groups. One is devoted to global optimization, such

as strategies based upon dynamic programming

(DP) [2–4] and strategies based on optimal control

theories [5, 6]. Because of heavy computation

requirements they are difficult to apply for real-time

control and are usually used for offline simulation

applications. The other group deals with instanta-

neous optimization and is targeted on real-time

control, such as thermostat (on–off) control strategy

[7], power follower strategy [8–11], and power split

*Corresponding author: Department of Mechanical Engineering,

Michigan State University, 148 ERC South, East Lansing, MI

48824, USA.

email: [email protected]

1003

JAUTO1074 F IMechE 2009 Proc. IMechE Vol. 223 Part D: J. Automobile Engineering

at MICHIGAN STATE UNIV LIBRARIES on April 2, 2015pid.sagepub.comDownloaded from

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strategy [12, 13], including equivalent fuel consump-

tion control strategy [14, 15] and minimization of

power dissipation control strategy [16].

In this paper, a series hybrid electric transit bus

has been chosen for the hybrid configuration. The

bus powertrain was developed in cooperation with

Michigan State University, Kettering University, and

TransTeq. The project was partially funded by the

Michigan Economic Development Corporation.

For the first prototype bus, thermostat control

strategy (TCS) was used. In order to develop an

efficient control strategy for this hybrid bus, TCS and

power follower control strategy (PFCS) were com-

pared and analysed. Subsequently an equivalent fuel

consumption optimal control strategy (EFCOCS) was

proposed and discussed in this paper.

The equivalent consumption minimization strat-

egy (ECMS) [14] requires many control parameters

to be determined or tuned through simulations and

experiments while, for the proposed EFCOCS, the

optimization problem has been simplified signifi-

cantly, which reduces the required control para-

meters to four. This simplifies the control-para-

meter-tuning process. The other main difference

between ECMS and the proposed EFCOCS is in the

calculation of the equivalent fuel consumption of

electric energy used. In ECMS, the equivalent fuel

consumption is proportional to the electric energy

used, regardless of the powertrain operational con-

ditions; i.e. the conversion efficiency from fuel to

electric energy used is fixed and, most often, the

average efficiency is used. While in the proposed

EFCOCS the equivalent fuel consumption of the

battery energy used is a function of the difference

between the actual battery state of charge (SOC) and

target SOC. The proposed strategy can be imple-

mented in real time by solving a one-dimensional

optimization problem. The proposed control strat-

egy was developed and validated on the basis of a

series powertrain model. Comparison simulation

results of three control strategies (thermostat, power

follower, and proposed equivalent fuel consump-

tion), together with the global optimization solution

[2–4, 12, 17, 18], show that the proposed EFCOCS

not only extends the battery life but also improves

the fuel economy of the hybrid bus.

The paper is organized as follows. In section 2, the

SHEVsystemsare reviewed.Section3discusses theTCS

and PFCS and proposes the equivalent fuel consump-

tion control strategy. The comparison simulation res-

ults of all three control strategies are presented in

section 4. Section 5 adds some conclusions.

2 SERIES HYBRID ELECTRIC VEHICLE SYSTEM

In this section, the architecture and system para-

meters of the series hybrid electric bus are

introduced. Component models of the main power-

train power source (the engine–generator set and the

battery) are presented on the basis of the char-

acteristics of the selected components. The engine–

generator set model was constructed on the basis of

the efficiency map obtained from fuel economy

experiments on the diesel engine and the perfor-

mance experiments of the generator, while the

battery model was built on the basis of an internal

resistance model and calibrated using experimental

data from charging and discharging performance

tests. The basic cost function of the energy manage-

ment problem for the SHEV is introduced on the

basis of the architecture, parameters, and model.

This makes it possible to propose an efficient

supervisory optimal control strategy for the series

hybrid electric bus.

2.1 Basic structure and parameters

Similar to many other SHEVs, the present SHEV bus

utilizes a combination of two energy sources, fuel

and electricity, shown in Fig. 1. This bus has two

different power sources: the main power source (the

Fig. 1 Architecture of an SHEV

1004 J-P Gao, G-M G Zhu, E G Strangas, and F-C Sun

Proc. IMechE Vol. 223 Part D: J. Automobile Engineering JAUTO1074 F IMechE 2009



engine–generator set) provides main power by

converting the fuel’s chemical energy to mechanical

energy using an internal combustion engine and

then to electric energy using a generator; the

assistant power source (the battery pack) acts as an

electric power equalizer to provide the rest of the

required power (positive or negative) through its

charging and discharging processes.

When a hybrid bus is being driven, based on the

power command from the driver and SOC of the

battery, the supervisory controller needs to calculate

the overall power requirement Pr and the power

requirement of the main power source (engine–

generator set) Pg based upon the specific control

strategy used. The engine controller will adjust its

operation to produce the requested electric power Pg

for the generator, and the battery supplies the

remaining electric power Pb5Pr2Pg. The total

electric power of Pg and Pb is supplied to the electric

motor to drive or break the entire vehicle, so that the

vehicle will reach the desired speed. Note that,

during the control strategy development the SHEV,

the electric drive unit and generator power inverter

dynamics are ignored and their efficiencies are

considered as part of the corresponding electrical

machine and generator efficiencies.

Table 1 lists the main technical parameters of the

SHEV presented here.

2.2 Model of the main components of the SHEV

2.2.1 Engine–generator set model

The electric power Pg generated by the engine–

generator set can be described by the two equations

Pe~vsTs

~ge Ts,vsð ÞPf

~ge Ts,vsð Þ _mmHLHV ð1Þ

Pg~Pegg Ts,vsð Þ~UbusIg ð2Þ

where Ts and vs are the engine output torque and

speed respectively, ge(Ts, vs) and gg(Ts, vs) are the

efficiency maps of the engine and generator respec-

tively, m and HLHV are the fuel mass flowrate and the

corresponding fuel low heating value (a known

constant that is a function of the type of fuel used),

Pf5 mHLHV, Pe5vsTs, and Pg are the fuel power,

engine mechanical power, and generator output

power respectively, and finally Ubus and Ig are the

electric bus voltage and generator current respec-

tively. C(Ts, vs) is defined as the fuel economy of the

engine–generator set in grams per kilowatt hour [1],

where

C Ts,vsð Þ~ _mm

vsTs

~1

ge Ts,vsð ÞHLHV

ð3Þ

Then the total fuel flow wg of the engine can be

expressed in terms of C(Ts, vs) according to

wg~C Ts,vsð ÞPfge Ts,vsð Þ~C Ts,vsð ÞTsvs ð4Þ

where both the engine speed vs and torque Ts

belong to a set V defined by

0¡Ts¡Tmax vsð Þ ð5Þ

max ve,min,vg,min

� �¡vs¡min ve,max,vg,max

� � ð6Þ

where Tmax(vs) is the maximum engine output

torque as a function of the engine speed, ve,min

and ve,max are the minimum and maximum angular

speeds respectively of the engine, and vg,min and

vg,max are the minimum and maximum angular

speeds respectively of the generator.

For a given engine, within the operational space

defined by equations (5) and (6), the engine

efficiency map ge(Ts, vs) can be obtained from

engine fuel economy mapping tests. Figure 2 shows

Table 1 Technical parameters of the SHEV

Item Parameter Value

Vehicle Total mass 16 500 kgCurb mass 14 660 kg

Fuel converter Type DieselRated power 171 kW

Generator Type Brushless permanentmagnet

Rated power 100 kWPeak Power 150 kW

Energy storagesystem

Type Lithium battery packRated voltage 360VRated capacity 90AhVoltage range 300–420V

Motor Type Brushless permanentmagnet

Rated power 200 kWPeak power 300 kWMaximum torque 1300NmSpeed range 0–5000 r/min

Fuel consumption control of a series hybrid electric vehicle 1005




the engine efficiency map used in this paper, and

C(Ts, vs) and wg can be obtained from equations (3)

and (4).

2.2.2 Battery model

In comparison with subsystem models of other

components in a hybrid vehicle system, the

battery model is the most complicated, especially

for the SOC estimation. There are many models

available in ADVISOR, including the RC model,

the internal resistance (Rint) model, the funda-

mental lead acid model, and the neural network

model [18]. In this paper, the Rint model was

used in the SHEV model because of its simplicity

and effectiveness for the lithium batteries used in

the bus.

The electrical model in the Rint model consists of

a voltage source (open-circuit voltage VOC) and a

resistor (internal resistance Rb), shown in Fig. 3.

Both parameters are functions of the SOC, the

temperature T, and the current flow direction (e.g.

whether the battery is charging or discharging),

according to

VOC~V SOC,Tð Þ ð7Þ

Rb~Rch SOC,Tð Þ, for Ibv0

Rdis SOC,Tð Þ, for Ibw0

�ð8Þ

The SOC for the Rint model can be estimated by

performing ampere–hour counting, including the

Coulomb efficiency losses during battery charging,

as given by

SOC~A hð Þmax{ A hð Þused gCoulombð Þ

A hð Þmax

ð9Þ

where gCoulomb is the Coulomb efficiency of the

battery pack, (A h)max is the maximum capacity of

the battery pack, and (A h)used is the used capacity of

the battery pack defined as

A hð Þused~Ð t0 Ib dt, Ibw0Ð t0 IbgCoulomb dt, Ibv0

(ð10Þ

where Ib is the electric current provided by the

battery. Based on the equivalent circuit in Fig. 3, the

equations

Pb~UbusIb

~ VOC{IbRbð ÞIb~VOCIb{Ib

2Rb ð11Þ

Ib~VOC+

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV 2OC{4RbPb

q2Rb

ð12Þ

Fig. 2 Fuel economy map of the engine

Fig. 3 Equivalent circuit in the Rint model of a batterypackage





where Pb is the electric driving power provided by the

battery. Additionally, in order to protect the battery,

the SOC and charging and discharging current have to

be limited according to

SOCL¡SOC¡SOCU ð13Þ

Ib,min¡Ib¡Ib,max ð14Þ

where SOCU and SOCL are the given upper and lower

bounds respectively of the SOC for the battery, and

Ib,min and Ib,max are the given maximum charge

current and minimum discharge current respectively

for the battery.

2.3 Energy management problem for the SHEV

This section discusses the power balance under

driven and braking conditions and formulates the

corresponding optimization problem.

Figure 4 shows the architecture of the SHEV and

its energy flow. The power balance equation when

the vehicle is being driven is

Pr~PgzPb ð15Þ

and the power balance equation when the vehicle is

braking becomes

Pc~PgzPbg ð16Þ

where Pc and Pbg are the electrical power to be

charged into battery and the electrical power gen-

erated by the electrical machine during braking

respectively.

The energy management problem (or the super-

visory control problem) can be considered as an

optimal control problem that minimizes the cost

function J subject to the constraint equations (15)

and (16) with J given by

min J~ wTs,vsð Þ [V

Ts,vsð Þ ð17Þ

where w is the minimization cost function and V is

the engine operational region defined by equations

(5) and (6). Let w equal wg defined in equation (4),

and the optimization problem becomes minimizing

the engine fuel consumption over the constraint set

V. The cost function can also be used to minimize

the harmful emissions, wasted power, or the combi-

nation of fuel consumption and harmful emissions.

3 CONTROL STRATEGIES FOR THE SHEV

The key control strategy for the SHEV is the power

distribution between the engine–generator set and

the battery under specific power requirement Pr.

When the vehicle is being driven, the propulsion

power distribution is between the engine–generator

set and the battery, shown in equation (15); while the

vehicle is under braking, the power distribution

is between the electrical power charged to battery

and generated through braking regeneration, shown

in equation (16). In order to develop an efficient

supervisory control strategy for the series hybrid

bus, two common control strategies are to be

discussed and analysed, and a new optimal control

strategy is proposed in this section.

3.1 Thermostat control strategy

TCS is also called on–off control strategy. Under this

strategy, the engine operates with a fixed power at its

highest efficiency point, and it turns on and off

based upon the SOC of the battery. Let Sg(t) be the

on–off state of the engine–generator set. The

equation Sg(t)5 1 implies that the engine is on,

and Sg(t)5 0 means that the engine is off. The TCS

Fig. 4 Energy flow in the SHEV





control logic can be expressed as

Sg tð Þ~0

if SOC t{ð ÞoSOCU or

SOC t{ð ÞwSOCL and Sg t{ð Þ~0

�

1if SOC t{ð Þ¡SOCL or

SOC t{ð ÞvSOCU and Sg t{ð Þ~1

�8>>><>>>:

ð18Þ

The corresponding TCS power distribution is de-

scribed as

Pg tð Þ~ 0, Sg tð Þ~0

Pe Ts,g,vs,g

� �gg Ts,g,vs,g

� �, Sg tð Þ~1

(

ð19Þ

Pb tð Þ~0, SOC tð ÞvSOCL

Pr tð Þ{Pg tð Þ, SOCL¡SOC tð Þ¡SOCU

Pr kð Þ, SOC tð ÞwSOCU

8><>:

ð20Þwhere the pair (Ts,g, vs,g) are the given engine–

generator set operational condition that provides the

best fuel economy.

3.2 Power follower control strategy

The basic idea of the PFCS can be described as follows.

Let the engine–generator set be the main power

source and the supervisory control adjusts the output

power of the engine–generator set to follow the

vehicle’s driving power requirement Pr. The engine–

generator set is active under almost all driving

conditions, except for those conditions when low

driving power is required and the SOC is greater than

SOCU. The state control logic of the engine–generator

set is based upon the thresholds map shown in Fig. 5

and the corresponding power output is determined by

Pg tð Þ~

0, if Sg tð Þ~0

Pg,min,

if Sg tð Þ~1 and

SOC tð ÞwSOCU

ProPg,min

� �8><>:

Pgm tð Þ, if Sg tð Þ~1 and

SOCL¡SOC tð Þ¡SOCU

�

Pg,max,if Sg tð Þ~1 and

SOC tð ÞvSOCL

�

8>>>>>>>>>>>>><>>>>>>>>>>>>>:

ð21Þ

where

Pgm tð Þ~PrzPchSOCUzSOCL

2{SOC tð Þ

� �ð22Þ

where Pch is the selected charge power magnitude,

Pg,min and Pg,max are minimal and maximum electric

power outputs respectively of the engine–generator

set, and Pb,max in Fig. 5 is the given maximum

requested power allowed when the engine–generator

is off.

From equation (21), there are four operation

modes for the engine–generator set. The following

is a detailed discussion associated with the four

operational modes.

Case 1: In this case, Pg(t)5 0 (or Sg(t2)5 0), and the

requested power is less than either Pg,min or Pb,max.

The series hybrid powertrain is operated within the

dark-grey region (see Fig. 5) and the operational

range can be extended to the connected gridded

region due to hysteresis.

Case 2: In this case, the requested power Pr is greater

than either Pg,min or Pb,max. The powertrain is

operated in the grey area where SOC> SOCU and it

can be horizontally extended left to the gridded

region.

Case 3: In this case, the powertrain is operated

within the middle of the grey area between SOCL

and SOCU lines for any requested power Pr.

Case 4: In this case, the powertrain is operated

within the lower grey area (below the SOCL line)

for any requested power Pr.

Note that the gridded area of Fig. 5 is the

hysteresis used to prevent high-frequency on and

off operations of the internal combustion engine,

where Pb,max is the requested power hysteresis limit.

One important factor that needs to be considered is

the dynamics of engine–generator set; i.e. the rate of

engine–generator power output is limited between

Pmin and Pmax according to

_PPmin¡ _PPg tð Þ¡ _PPmax ð23Þ

Fig. 5 PFCS





In order to avoid frequently turning on and off the

engine–generator set, a minimal off-time tmin is

required for the engine–generator set to being

turned on again; i.e. the off-time tg,off should be

greater than the minimal off-time according to

tg,offotmin ð24Þ

In the PFCS, the battery pack works as a power

equalizer through charging or discharging itself. Its

control logic is described as

Pb tð Þ~ Pr tð Þ{Pg tð Þ, Sg~1

Pr tð Þ, Sg~0

�ð25Þ

3.3 Equivalent fuel consumption optimal controlstrategy

The two control strategies discussed above are

derived from basic rules. Their main advantage

is that an exact hybrid powertrain model is not

required for supervisory control and, therefore, they

are simple and robust. On the other hand, they are

not optimized for the best fuel economy.

In order to optimize the power split between the

engine–generator set and battery to achieve the

best fuel economy possible, an EFCOCS is pro-

posed in this paper on the basis of the SHEV

model.

The electric energy discharged from the battery

needs to be recharged back to the battery in the

future. This is equivalent to a certain fuel consump-

tion of the engine–generator set (e.g. positive fuel

consumption). On the other hand, the energy

charged to the battery at any moment will also be

discharged from the battery to drive the vehicle in

the future. This is equivalent to a certain fuel saving

for the engine–generator set (e.g. negative fuel

consumption).

Since the operation conditions of a series hybrid

powertrain in the future are unknown, the equiva-

lent fuel consumption is proposed to be used for

battery charge and discharge operations according

to

wb~CdisPb~CdisVOCIb, Ibw0

CchPb~CchUbusIb, Ib¡0

�ð26Þ

where Cdis and Cch are equivalent fuel economy

coefficients for battery discharging and charging

operations defined by

Cdis~a1 1zb1 SOC{SOCUzSOCL

2

� �� ð27Þ

Cch~a2 1{b2 SOC{SOCUzSOCL

2

� �� ð28Þ

where b1> 0 and b2> 0 respectively and a1, b1, a2,

and b2 are weighting coefficients to be selected

on the basis of the characteristics of the hybrid

powertrain system and its operational conditions.

Assuming that both b1 and b2 are zeros, constant

charge and discharge coefficients will be obtained,

where Cdis5 a1 and Cch5 a2. Ideally, a1 is the

equivalent fuel consumption to draw one unit of

electric power from the battery, and, similarly, a2is the equivalent fuel consumption to charge one

unit of electric power back to the battery. In order

to account for the battery power charged by

braking regeneration, a1 can be selected to be

smaller than its definition to make it cheap to

discharge from the battery. For this simulation the

optimized a1 is around 60 per cent of a2 (see

Table 2).

Terms associated with b1 and b2 are used to

optimize the battery operations. Considering equa-

tion (27), when the SOC is equal to the average of

SOCU and SOCL, the second term of equation (27)

is zero. When the SOC is greater than the average

of SOCU and SOCL, the second term is positive,

which encourages battery usage due to high

discharge efficiency, and vice versa. Similarly for

battery charge operation, from equation (28) it can

be seen that, when the SOC is greater than the

average of SOCU and SOCL, the second term is

negative, which discourages battery charging due

to low charge efficiency since the second term is

negative.

Now the total fuel consumption at a given

moment can be expressed as the sum of actual fuel

consumption of the engine–generator set and the

equivalent fuel consumption of the battery pack.

This provides a unified representation of the energy

used from both the fuel and the battery. The

proposed EFCOCS control strategy is the solution

of the minimization problem

Table 2 Charge and discharge coefficients

a1 b1 a2 b2

Initial 0.000 010 1.00 0.000 010 1.00Optimal 0.000 038 1.74 0.000 050 1.00





minTs,vsð Þ [V

J~ minTs,vsð Þ [V

w Ts,vsð Þ

~ minTs,vsð Þ [V

twg Ts,vsð Þzwb Ts,vsð Þs ð29Þ

where

where equation (4) (wg(Ts, vs)) and equation (12)

(wb(Ts, vs)) are used to obtain equation (30). The

desired electric power of the engine–generator set is

given by

Pg tð Þ~

0if Sg t{ð Þ~0 and

SOC t{ð ÞwSOCU

�

Pg,min

if Sg t{ð Þ~1 and

SOC t{ð ÞwSOCU

�

Ts optvs opt

if Sg t{ð Þ~1 and

SOCL¡SOC t{ð Þ¡SOCU

�

Pg,max

if Sg t{ð Þ~1 and

SOC t{ð ÞvSOCL

�

8>>>>>>>>>>>>><>>>>>>>>>>>>>:

ð31Þ

where Ts_opt and vs_opt are the optimal solutions of

equations (29) and (30).

Note that the constraint set V is defined by

equations (5) and (6), and gg is the generator efficiency

map as a function of both Ts and vs (see equation (2)).

The basic control strategy of EFCOCS, when the

vehicle is driven, is very close to that of PFCS. The

only difference is that, under the conditions that Sg51

and SOCL(SOC(t)(SOCU, the power required to be

provided by the engine–generator set is based upon

the optimization result of equations (29) and (30).

Similar to the PFCS case, the power output rate and

the off-time of the engine–generator set should also be

limited (see equations (23) and (24)), and the battery

supplies the rest of the power to meet the total power

requirement (see equation (25)).

Now consider the optimization problem described

in equations (29) and (30). Note that

C Ts,vsð ÞTsvs~Tsvs

ge Ts,vsð ÞHLHVð32Þ

Define

gp Peð Þ~ minTsvs~Pe, Ts,vs [V

1


where Pe is the engine power for the given engine

torque output Ts and speed vs. Then, the optimiza-

tion problem, defined in equations (29) and (30), can

be rewritten as

where Cg is the generation coefficient that is

assumed to be a constant over the optimized region

for simplification. In the case when this is not true, a

map gg(Pe) similar to equation (30) can be generated

for gg to replace Cg.

Equation (34) indicates that the proposed two-

parameter optimization problem can be con-

verted into a two-step optimization process; i.e.

the single variable optimization problem defined

in equation (34) can be solved for Pe_opt and

then Ts_opt and vs_opt found along the constant

power line Pe_opt5 Ts_optvs_opt such that the cost

function

1


is minimized. Therefore, the optimization problem

can be solved using a one-dimensional search

program. Note that the optimal solution of equa-

tion (33) can be solved offline for a given engine,

and only one one-dimensional optimization pro-

blem needs to be solved in real time, which makes

it feasible for real-time implementation. This pro-

cedure complies with these hybrid vehicles with

serial arrangement.

J~ C Ts,vsð ÞTsvszCdis

V 2OC{VOC

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV 2OC{4Rb Pr{vsTsgg

r2Rb

, if Ibw0

C Ts,vsð ÞTsvszCch Pr{vsTsgg

, if Ib¡0

8>>>><>>>>:

min0¡Pe¡C

Pegp Peð ÞzCdis

V 2OC{VOC

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV 2OC{4Rb Pr{PeCg

� �q2Rb

, if Ibw0

Pegp Peð ÞzCch Pr{PeCg

� �, if Ib¡0

8>><>>:

ð30Þ

ð34Þ





4 SIMULATION RESULTS

Based upon the architecture and design parameters

of the hybrid bus, a backward SHEV simulation

model was built in ADVISOR [19] as shown in Fig. 6.

To evaluate the performance under actual driving

conditions, six driving cycles were selected from a

number of standard cycles in ADVISOR, shown in

Fig. 7, where FTP and IM240 driving cycles have

a high percentage of suburban or highway driving,

1015 and ECE_EUDC_LOW cycles are mainly urban

driving, and NewYorkBus and MANHATTAN driving

cycles represent congested urban driving conditions.

In order to study the fuel economy of various control

strategies under a wide range of driving conditions, a

composite driving cycle is generated, which com-

bines FTP, 1015, and NewYorkBus driving cycles.

The four control parameters (shown in Table 2) for

Fig. 6 Backward simulation model of series hybrid electric bus

Fig. 7 Relevant driving cycles used in this paper





the proposed EFCOCS control strategy were opti-

mized using the optimization software called the

hierarchical evolutionary engineering design system

(HEEDS) [20], for the global fuel economy mini-

mization during the composite driving cycle, based

upon the ADVISOR model shown in Fig. 6. HEEDS is

a powerful software package developed by Michigan

State University based on genetic algorithms to auto-

mate and expedite the design optimization process.

Initial values in the first row of Table 2 were selected

fromavailable literature.After theHEEDSoptimization,

using the ADVISORmodel, optimal control parameters

wereobtained (see the second rowofTable 2). EFCOCS

strategy simulations were completed using the optimal

coefficients obtained through HEEDS optimization; in

order to have a fair comparison, the other three driv-

ing cycles were used for control strategy evaluation

simulations. They are IM240, ECE_EUDC_LOW, and

MANHATTAN driving cycles.

4.1 Power split between the engine and thebattery

Figure 8 shows the power distribution between the

engine–generator set and the battery for the three

supervisory control strategies evaluated under the

ECE_EUDC_LOW driving cycle.

For the TCS, the output power of the engine–

generator set is either zero or a fixed value

irrespective of the overall power requirement. This

causes the battery’s output power to fluctuate over a

large range (see Fig. 8(a)).

The PFCS adjusts the engine–generator set output

power to follow the power requirement. Therefore,

the battery provides the least output power (see

Fig. 8(b)).

In the case of the proposed EFCOCS, the overall

power requirement will be split into the engine–

generator set and the battery based upon the

Fig. 8 Power distribution comparison: (a) TCS; (b) PFCS; (c) EFCOCS





proposed solution of the optimization problem, and

so the engine–generator set operated at a much

smaller but more efficient region (see Fig. 8(c)).

The averaged charge and discharge powers of

three strategies are listed in Table 3, which indi-

cates that the TCS strategy is the highest and the

PFCS strategy is the lowest, while the EFCOCS

strategy is between the TCS and PFCS strategies.

4.2 Output performance of the engine

Fuel economy and emission performance of an

internal combustion engine mainly depend on their

operation points. This directly affects the fuel

economy and harmful emissions of the hybrid bus.

This section compares the simulation results under

the ECE_EUDC_LOW driving cycle.

In the TCS, shown in Fig. 9(a), the engine

operates at its highest efficiency condition when-

ever it is turned on except for during transient

conditions. This provides the highest engine effi-

ciency possible but may not provide the best

overall system fuel economy and emission perfor-

mance.

In the PFCS, shown in Fig. 9(b), the engine’s

output power follows the desired power possible

to minimize the battery charging and discharging

operation at high currents; i.e. the battery power

efficiency is optimized. Therefore, the engine oper-

ates in a relative large region over the engine

efficiency map.

In contrast, in the EFCOCS, shown in Fig. 9(c), the

efficiency of the overall system (the engine and the

battery) is considered, leading the engine to operate

in a smaller region over its efficiency map than the

PFCS does.

4.3 Output performance of the battery pack

Under the assumption that the power requirement

can be satisfied, a good control strategy should

enable the battery pack to have the following

characteristics.

1. The SOC should be restored to its target quickly.

This not only leads to a highly efficient battery

charge and discharge but also ensures that the

battery always has enough electric energy to meet

the powertrain power requirement in the future.

2. The output voltage of the battery (equal to the bus

voltage) should be close to the rated bus voltage

with as small a fluctuation as possible. This helps

to extend the battery life as well as that of other

electric components.

3. Charging and discharging the battery with a high

current should be avoided owing to the low

charge and discharge efficiency and reduced

battery life.

Under the ECE_EUDC_LOW driving cycle, it is

easy to see that in the first strategy (TCS), the

fluctuations in the battery output voltage and

current are the highest of the three control strategies

Table 3 Averaged charge and discharge powers

Controlstrategy

Averaged chargepower (kW)

Averaged dischargepower (kW)

TCS 67.63 69.18PFCS 55.17 59.42EFCOCS 63.07 65.82

Fig. 9 Comparison of the engine’s operation pointsunder the ECE_EUDC_LOW driving cycle: (a)TCS; (b) PFCS; (c) EFCOCS





(Figs 10 and 11). For the PFCS case, the fluctuations

are the smallest since the engine–generator set

output power follows the desired power very well.

The fluctuations in the last case (EFCOCS) are

between the other two strategies and are very close

to the second strategy (PFCS).

Fig. 11 Comparison of the bus currents under the ECE_EUDC_LOW driving cycle: (a) TCS; (b)PFCS; (c) EFCOCS

Fig. 10 Comparison of the bus voltages under the ECE_EUDC_LOW driving cycle: (a) TCS; (b)PFCS; (c) EFCOCS





4.4 Fuel economy performance evaluation

The fuel economy performance can be expressed in

terms of the fuel economy and electrical energy

consumption; the fuel economy can be expressed by

the net fuel consumption of the internal combustion

engine, while the electrical energy consumption can be

expressed by DSOC. Figure 12 shows the fuel economy

of this bus with different control strategies evaluated

by this method; the simulation data are obtained by

applying different control strategies under the three

different driving cycles. Global optimized fuel econ-

omy results using DP were also obtained.

From Fig. 12, it can be observed that, under the

IM240 driving cycle, the best fuel economy is the

global optimization strategy followed by EFCOCS,

TCS, and PFCS; under the MANHATTAN driving

cycle, the order changed a little and it becomes

global optimal, EFCOCS, PFCS, and TCS, while,

under the ECE_EUDC_LOW driving cycle, the order

is a function of DSOC. When DSOC is between 20.05

and 0.75, the order is global optimal, EFCOCS, PFCS,

and TCS, and, when DSOC is greater than 0.075, the

order becomes global optimal, EFCOCS, TCS, and

PFCS. Overall, the EFCOCS provide the best fuel

economy of the three control strategies (TCS, PFCS,

and EFCOCS) under three driving cycles.

DSOC sweep simulation allows the fuel economy

performance to be studied for a given control

strategy over a wide range of DSOC values under a

given driving cycle. The so-called classical ‘SOC

correction routine’ reduces the dual performance

criteria to a single criterion; i.e. all real-time control

strategies provide a fixed electric energy consump-

tion DSOC5 SOCend2 SOCstart, where SOCstart and

SOCend are the SOCs at the start and end respectively

of the simulation cycle. DSOC was selected to be zero

to compare the fuel economy performance; i.e. the

total electrical energy consumption over the simu-

lated electrical energy consumption is zero. In this

case, only the fuel consumption needs to be

compared for all simulations. Fuel economy simula-

tion results for all three control strategies (TCS,

PFCS, and EFCOCS) are listed in Table 4, together

with the global optimization results obtained using

DP. From Table 4, it can be seen that TCS provides

good fuel economy performance under the IM240

cycle (with a high percentage of highway driving),

compared with PFCS, while the PFCS performs

well under the ECE_EUDC_LOW and MANHATTAN

cycles (with a high percentage of urban driving),

compared with the TCS, but the EFCOCS provides

the best fuel economy for all driving cycles com-

pared with the TCS and PFCS; i.e. the EFCOCS has

the best fuel economy compared with the TCS and

PFCS for both highway and urban driving con-

ditions. Although the global optimization control

strategy is very difficult to implement for real-time

control, it is useful to compare its simulation results

with those of real-time control strategies to find the

distance between real-time solutions and the global

optimal solution. Comparing the fuel consumptions

of the global optimization control strategy in Table 4

with three real-time control strategies, it is clear that

Fig. 12 Fuel economy versus DSOC for the TCS, PFCS, EFCOCS, and global optimal strategies

Table 4 Comparison between simulation resultsunder different driving cycles

Controlstrategy

Fuel consumption (l/100 km)

IM240 ECE_EUDC_LOW MANHATTAN

TCS 34.7 47.8 63.8PFCS 36.5 45.7 56.5EFCOCS 32.9 42.3 54.7Globaloptimization

30.2 38.5 49.3





the proposed EFCOCS provides the closest results to

those provided by global optimization. This also

shows that the proposed EFCOCS is capable of

providing good fuel economy under different driving

cycles.

5 CONCLUSIONS

TCS, PFCs, and power split control strategies are the

most popular real-time supervisory control strate-

gies for SHEVs. The EFCOCS, one kind of power split

control strategy, is proposed in this paper. Evalua-

tion simulations of a backward series hybrid bus

model using ADVISOR were conducted for all three

control strategies. Results show that the TCS pro-

vides the best efficiency for the engine–generator set,

leading to good fuel economy performance under

highway driving conditions. The PFCS provides

sustainable SOC regulation with a stable bus voltage.

This improves the battery durability and that of

other electrical components with good fuel economy

performance during urban driving. The proposed

EFCOCS provides a reasonable power distribution

between the engine–generator set and battery pack,

leading to the best overall fuel economy under both

urban and highway driving conditions; it also

provides fuel economy results close to the global

optimization data. Future research will emphasize

the real-time implementation of the EFCOCS to the

HEV.

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APPENDIX

Notation

(A h)max maximum battery capacity

(A h)used used battery capacity

C(Ts, vs) fuel economy map of the engine–

generator set

Cch equivalent fuel economy

consumption coefficient for the

charging battery

Cdis equivalent fuel economy

consumption coefficient for the

discharging battery

Cg constant generation coefficient over

the optimized region for

simplification

HLHV low heating value of fuel

Ib electric current of the battery pack

Ib,max maximum battery charge current

allowed

Ib,min minimum battery discharge current

allowed

Ig generator output current

m fuel mass flowrate

Pb power required from the battery

Pbg electrical power generated during

braking regeneration

Pb,max maximum requested power allowed

when the engine–generator is off

Pc electrical power charged into battery

during braking regeneration

Pch selected charge power magnitude

Pe engine output power

Pf fuel power

Pg power generated by engine–

generator set

Pg,max maximum electric power output of

the engine–generator set

Pg,min minimum electric power output of

the engine–generator set

Pr overall power requirement

Pmax upper limit on output power rate of

change of the engine–generator

Pmin lower limit on the output power rate

of change of the engine–generator

Rb internal battery resistance

SOC state of charge

SOCend state of charge at the end of a

simulation cycle

SOCL minimum state of charge allowed for

the battery pack

SOCstart state of charge at the beginning of a

simulation cycle

SOCU maximum state of charge allowed for

the battery pack

Sg(t) on–off state of the engine–generator

set

tg,off accumulated engine–generator set

off-time since it is turned off

tmin minimal off-time allowed for the

engine–generator set

T temperature

Tmax(vs) maximum engine output torque as a

function of its speed

Ts engine output torque

(Ts_opt, vs_opt) optimal solutions for the

engine–generator set

(Ts,g, vs,g) engine–generator set operational

conditions with the best fuel

economy

Ubus electric bus voltage

VOC open-circuit voltage

a1 weighting coefficient of equivalent

fuel consumption for drawing one

unit of electric power from the

battery

a2 weighting coefficient of equivalent

fuel consumption for charging one

unit of electric power back to the

battery

b1 weighting coefficient used for

maintaining the state of charge

during the discharging operation

b2 weighting coefficient used for

maintaining the state of charge

during the charging operation

DSOC state-of-charge offset from the initial

state of charge during a simulation

cycle

gCoulomb coulomb efficiency of the battery

pack

ge(Ts, vs) engine efficiency map

gg(Ts, vs) generator efficiency map





wg total fuel flow of the internal

combustion engine

ve,max maximum engine speed allowed

ve,min minimum engine speed allowed

vg,max maximum generator speed allowed

vg,min minimum generator speed allowed

vs engine speed

V engine operational region





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