Multi-objective trade-off optimal control of energy management for hybrid system

Technical Paper
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Abstract

Currently, energy management control mainly focuses on single-objective optimization (SOO). Even if multi-objective optimization (MOO) problem is studied, it is often converted into an SOO problem by using the weighted sum method. Obviously, it cannot really reflect the essential strengths of MOO. In this paper, a parallel hybrid electric vehicle is taken as the research object. The fuel economy, emissions, and drivability performance are taken as optimization objectives. The parameters of energy management and driveline system are optimized. Considering the constraint conditions of the dynamic performance and charge balance, the fast non-dominated sorting differential evolution algorithm (NSDEA) is proposed to solve the multi-objective optimization problem. Then multi-group sets of Pareto solutions with good distribution and convergence are obtained. The simulation results of NSDEA show that the fuel economy is increased by 20.26% on average. The emissions evaluation index is optimized by 11.33% on average, and the maximum carbon monoxide (CO) optimization value reaches 21.9%. The average of drivability evaluation index (jerk) is up to 20.84%, and 40.32% for maximum. Obviously, the above obtained results are discrete points. They only represent some optimal solutions. Based on the above sets, the locally weighted scatter plot smoothing method is used to fit continuous curve and surfaces. Then, the multi-objective Pareto trade-off optimal control surface is established to further obtain the optimal solutions. This study can provide more reference for the optimal control strategy and lay a foundation for multi-objective energy management of the actual vehicle.

Keywords

Hybrid system Energy management Multi-objective Trade-off Optimization 

List of symbols

Ai

Fitting coefficient of the external characteristic mathematical model

Ak

Fitting coefficient matrix of the universal characteristic mathematical model

cl_n

Engagement times of clutch

CR

Crossover probability

CRmax

Maximum value of the crossover probability

CRmin

Minimum value of the crossover probability

DN

Equation index of components’ action times

dmax–min

Maximum value among the minimum distance between individual vectors

dmini

Minimum distance between individual i and j

Di

Crowding distance

E

Rate of pollutant emissions

ECO

Emission rate of carbon monoxide (CO)

EHC

Emission rate of hydrocarbon (HC)

\(E_{{{\text{NO}}_{x} }}\)

Emission rate of nitrogen oxides (NO x )

f

m dimensional target vector

F

Variation constant

f2

Comprehensive evaluation index of emissions

fc_n

Starting times of engine

F(x)

Target vector

Fmin

Minimum value of zoom factor

Fmax

Maximum value of zoom factor

f(Uit)

Target value of test individuals

f(Xit)

Fitness value of target individuals

fmi(·)

The mth target function of individual i

fmj( · )

The mth target function of individual j

|fmi(x) − fmj(x)|

The distance between individual i and j

G

Current generation number

Gmax

Maximum generation number

gb_j

Jerk generated by gearbox

gb_n

Shifting times of transmission

ge

Specific fuel consumption

gj

j dimensional inequality constraint vectors

hk

k dimensional equality constraint vectors

i

Order of engine speed variable for engine torque fitting

j

Order of engine speed fitting

k

Fitting order

k2

Fitting coefficient matrix of emission characteristic for pollutants

k(t)

The gear ratio of transmission

l

Order of engine speed variable for universal characteristic fitting

m

The number of target vectors

n

the nmber of decision variables which constitute x decision space

ne

Engine speed (r/min)

nm

Motor speed (r/min)

nw

Wheel speed (r/min)

Np

Population number

Nobj

Target number

N

Population size

Pm

Motor power (kW)

Pe

Engine power (kW)

Pw

Vehicle power (kW)

ρm

Motor speed ratio

ρ(k(t))

Total drive ratio of the corresponding gears

QCO

Emission amount of CO pollutant (g/L)

QHC

Emission amount of HC pollutant (g/L)

\(Q_{{{\text{NO}}_{x} }}\)

Emission amount of NO x pollutant (g/L)

Qfc

Fuel consumption of the engine (L/100 km)

randij

The random number of corresponding genes

s

Model order

sgn

Symbol function

SOC

State of charge

SOCmax

Maximum value of SOC

SOCmin

Minimum value of SOC

t

Driving time (s)

T

Required torque (N m)

Tchg

Preset charging torque (N m)

Tchgs

Additional actual charging torque (N m)

Tcl

Clutch torque (N m)

Te

Engine torque (N m)

Tm

Motor torque (N m)

Tw

Total of engine and motor torque (N m)

Uit

Test individual

uijt

The jth gene of individual i of the tth generation

vijt

Mutated individual gene

vit+1

The ith variant individual generated by the tth generation

w1

Input power of clutch (kW)

w2

Output power of clutch (kW)

W

Weighting coefficient

x

Decision space

xmin

Minimum value of the optimized vector

xmax

Maximum value of the optimized vector

xr1t

The target individual 1 of the tth generation

xr2t

The target individual 2 of the tth generation

xr3t

The target individual 3 of the tth generation

xijt

Target individual gene

Xit

Target individual

Xit+1

Selected individual

y

Objective evaluation index

ηc

Charger efficiency

ηd

Final drive efficiency

ηe

Engine efficiency

ηm

Motor efficiency

ηt

Transmission efficiency

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant no. 51305473); Project Funded by China Postdoctoral Science Foundation (Grant no. 2014M552317); Postdoctoral Science Funded Project of Chongqing (Grant no. xm2014032). Finally, the authors are grateful to the anonymous reviewers for their helpful comments and constructive suggestions.

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interests, including specific financial interests and relationships relevant to the subject of this paper.

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.School of Mechatronics and Automotive EngineeringChongqing Jiaotong UniversityChongqingChina
  2. 2.Chongqing Key Laboratory of System Integration and Control for Urban Rail Transit VehicleChongqingChina
  3. 3.School of Mechanical EngineeringSichuan University of Science and EngineeringZigongChina

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