Bacterial foraging algorithm for the optimal on-line energy management of a three-

power-source hybrid powertrain

Po-Lin Shih1,a, Yi-Hsuan Hung1,b, Syuan-Yi Chen1,c, Chien-Hsun Wu 2,d

1 Dept. of Industrial Technology, National Taiwan Normal Univ., Taipei, Taiwan

2 Dept. of Vehicle Engineering, National Formosa Univ., Yunlin, Taiwan

ar22263222@gmail.com, bhungyh@ntnu.edu.tw, cchensy@ntnu.edu.tw, dchwu@nfu.edu.tw

Abstract

This research aims for developing the online energy

management optimization for a three-power-source hybrid

powertrain based on Bacterial Foraging Approach (BFA). The

hybrid vehicle dynamics was constructed first by modeling

control-oriented subsystems on the Matlab/Simulink

platform. They are: the spark-ignition engine, traction motor,

lithium battery set, integrated starter generator (ISG),

regenerative braking, transmission, energy management

strategy, and driving cycles. For the rule-based control, 5

modes were developed (system ready，EV，hybrid，range

extension, and regenerative braking) according to the vehicle

speed (or motor rotational speed). For the BFA, it was

established for search two control outputs: the power split

ratios with three given inputs: rotational speed, required

power, and battery state-of-charge (SOC). Three main

procedures for optimal solutions were: 1)chemotaxis,

2)reproduction, and 3)elimination-dispersal. Ten bacteria

were selected for the 2-dimensional optimal search according

to the cost function with physical constraints: the equivalent

fuel consumption of three power sources. To evaluate the

“degree of optimization”, the Equivalent Consumption

Minimization Strategy (ECMS) was developed for two

power-split ratios based on 5 for-loop search (SOC, engine

power, demanded power, motor power, and rotational speed).

Three control laws were integrated into the hybrid

powertrains with a test scenarios: FTP-72 cycle. The

equivalent fuel consumption for three cases (rule-based

control, BFA, ECMS) are: 2100.6g, 1604.1g and 1400.9g.

The equivalent fuel reduction percentage compared to the

rule-based control for BFA and ECMS are [19.8%, 33.3%].

The degree of optimization for BFA compared to ECMS was

87%. It proves that the BFA was suitable for on-line energy

management for hybrid powertrains. Real vehicle verification

for vehicle control unit (VCU) implementation will be

conducted in the future.

Key words: Energy Management, Optimal Control, Bacterial

Foraging Algorithm, and Hybrid Electric Vehicle

Introduction

Hybrid electric vehicles (HEVs) have been widely

produced in international automakers nowadays. The added

high-power electric devices enhances the overall vehicle

performance (max. power, max. torque, acceleration, etc.)

while decreases the pollutants and energy consumption [1-3].

To optimize the vehicle system, the powertrain designs and

control strategies are two main approaches [4], or even the

integration the system design and control [4]. For the control

strategies, recently, the biologically inspired optimization

algorithms have been studied because the highly efficient

computation for on-line control, global optimization, and

applications for various industrial fields [5]. Among them,

BFA is characterized by parallel optimization search,

insensitivity to initial values, and high global optimization

ability [6]. In this study, BFA was thus used for the energy

management of a three-power-source hybrid powertrains.

The implementation in a real vehicle will be conducted in

the future.

Hybrid System Configuration

Figure 1 illustrates the configuration of a three-power-

source HEV. For the control signals, the vehicle control unit

(VCU) receives the commands from the driver and control

units, and sends the power (torque) distribution signals to the

motor control unit (MCU), integrated starter generator control

unit (ISGCU), and engine control unit (ECU) and the battery

management system (BMS). For the electric energy path, the

high-power lithium battery is governed by a battery

management system (BMS) which evaluates the state-of-

charge (SOC). The regulated power is delivered from the

battery to the motor and ISG drivers. The DC power is thus

modified to drive the motor and the ISG. Contrarily, the

recovered power (i.e. regenerative braking power) is sent

back from the two devices as the generators to the battery for

the SOC balance. For the mechanical power flow, the engine

converts the fuel energy into the rotational mechanical power.

The ISG downstream the engine is directed connected to the

engine. The traction motor on the other side is linked to the

transmission as well. Therefore, the power flows (torques) of

the three power sources are directly combined to drive the

final transmission, and then to accelerate the 1st-ordered

vehicle dynamics [7-8]. The related dynamic equations have

been studied in [9]

Bacterial Foraging Algorithm on HEV

Figure 2 illustrates the process of the BFA for the energy

management optimization among three power sources. Two

variables: and are defined as the power split

ratios, which represents the ratios of engine power

and motor power divided by the demanded power,

respectively.

dmde PP /P;/P (1)

The process of the BFA is separated into three main parts.

1)Chemotactic loop: in this step, the bacterium conducts

tumble or swim actions. The new position after a tumble

action can be expressed as:

)()(),,(),,1( rrClkjlkj rr (2)

where )(r is the random direction of a tumble action,

which is defined as

)()(

)()(

rr

rr

T

(3)

The fitness (cost) function is define as follows: 𝑭𝑰𝑻 = 𝟏/[�̇�𝒇𝒖𝒆𝒍 + ƒ(𝑺𝑶𝑪)�̇�𝒈 + ƒ(𝑺𝑶𝑪)�̇�𝒎] + 𝜷𝒑 = 𝟏/[�̇�𝒇𝒖𝒆𝒍 +

ƒ(𝑺𝑶𝑪)𝑩𝑺𝑭𝑪𝒂𝒗𝒈

𝟑𝟔𝟎𝟎× 𝑷𝒊𝒔𝒈 + ƒ(𝑺𝑶𝑪)

𝑩𝑺𝑭𝑪𝒂𝒗𝒈

𝟑𝟔𝟎𝟎× 𝑷𝒎] + 𝜷𝒑 (4)

The physical meaning of Eq. (4) is the inverse of the

summation of the engine fuel and the equivalent “battery

fuel” [10].

2)Reproduction loop: after the bacteria search for the fitness

function, those who have fitness values in the lower half will

be cancelled, while the remaining bacteria split into two

bacteria that are placed in the same location.

3) Elimination-dispersal loop: in the step, the bacteria will be

cancelled and dispersed to a new location in the search space

if a random probability is higher than a predefined threshold.

It is to prevent the local optimization occur.

Fig. 1 Configuration of a Three-Energy-Source EV

Fig. 2 Mechatronics of the Three-Energy-Source EV

Simulation Results and Discussion

The vehicle that we chose is a 1700kg vehicle. The

maximal power of the engine, motor, and ISG are 70kW,

65kW, and 40 kW, separately. The electric capacity of the

350 V battery moduleis 7 kW. For the BFA setting, the

bacteria number is 10. The elimination-dispersal loop number

is 30, while the chemotactic loop number is 1. The simulation

program was coded on the Matlab/Simulink platform. For the

comparison of control strategies, the equivalent consumption

minimization strategy (ECMS) was organized by 5 for-loops.

For the rule-based control, 5 modes (IG mode, EV mode,

hybrid mode, Range-Extended mode, Reg mode) were

designed [11-16]. The driving cycle that we chose is FTP

cycle, where the total operation time is xx seconds. The max.

speed is 90.72 km/hr.

Fig. 3 Demanded speed of FTP driving cycle

After the BFA process, the simulation results are shown

below. Fig. 4 illustrates the two power split ratios for BFA.

Fig.4 Two power split ratios by BFA

Helpful Hints

Fig. 5 Comparison of engine output power of three control strategies

Fig. 6 Comparison of motor output power of three control strategies

Fig. 7 Comparison of ISG output power of three control strategies

Fig. 8 Comparison of battery SOC of three control strategies

Fig. xx Comparison of energy and equivalent fuel

TABLE I

COMPARISON OF THE FUEL CONSUMPTION OF THE THREE

CASES

Rule-based BFA ECMS

FC (ml) 1306.11 1188.11 981.3

Equivalent

FC (g) 1887.66 1512.83 1273.21

Equivalent

FC

Improvement

(%)

-- 19.8 33.3

Conclusion This study

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