A Comparative Analysis of Energy Management Strategies for Hybrid Electric Vehicles

TLDR: In this article, the authors present a formalization of the energy management problem in hybrid electric vehicles and a comparison of three known methods for solving the resulting optimization problem: dynamic programming, Pontryagin's minimum principle (PMP), and equivalent consumption minimization strategy (ECMS).

Abstract: This paper presents a formalization of the energy management problem in hybrid electric vehicles and a comparison of three known methods for solving the resulting optimization problem. Dynamic programming (DP), Pontryagin’s minimum principle (PMP), and equivalent consumption minimization strategy (ECMS) are described and analyzed, showing formally their substantial equivalence. Simulation results are also provided to demonstrate the application of the strategies. The theoretical background for each strategy is described in detail using the same formal framework. Of the three strategies, ECMS is the only implementable in real time; the equivalence with PMP and DP justifies its use as an optimal strategy and allows to tune it more effectively. DOI: 10.1115/1.4003267

Figures

Figure 2.10: Torque converter map

Figure 4.33: Flow chart of iterative solution for Pontryagin’s minimum principle

Figure 4.56: Comparison of the SOE profile obtained with the three strategies for the EcoCAR case, cycle UDDS.

Figure 3.4: Example of application of dynamic programming to a hybrid electric vehicle

Figure 2.17: Hydraulic pump model

Figure 4.29: Dynamic programming solution for EcoCAR, cycle UDDS

Full text

A COMPARATIVE ANALYSIS OF ENERGY
MANAGEMENT STRATEGIES FOR HYBRID
ELECTRIC VEHICLES
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the
Graduate School of The Ohio State University
By
Lorenzo Serrao, M.S.
* * * * *
The Ohio State University
2009
Dissertation Committee:
Giorgio Rizzoni, Adviser
Yann G. Guezennec
Steve Yurkovich
Junmin Wang

© Copyright by
Lorenzo Serrao
2009

Abstract
The dissertation offers an overview of the energy management problem in hy-
brid electric vehicles. Several control strategies described in literature are pre-
sented and formalized in a coherent framework. A detailed vehicle model used for
energy flow analysis and vehicle performance simulation is presented. Three of the
strategies (dynamic programming, Pontryagin’s minimum principle, and equiva-
lent consumption minimization strategy, also known as ECMS) are analyzed in
detail and compared from a theoretical point of view, showing the underlying sim-
ilarities. Simulation results are also provided to demonstrate the application of the
strategies.
ii

To the people who care about me, and look after me.
To the people who admire me, and look up to me.
To the people who loved me, and now look at me from the sky.
To my family.
iii

ACKNOWLEDGMENTS
I am deeply grateful to my advisor, prof. Giorgio Rizzoni, for the guidance and
support during the past four years, and for being of example in both academic and
personal life. I feel incredibly fortunate for the opportunity to work with him. I
also feel fortunate for having met during my school years many people that had
a profound impact on my life: my elementary school teacher, Francesca Messi-
neo, who gave an injection of confidence to a shy kid; my math teacher in middle
school, Gino Strano, who was the first to make me appreciate the beauty of math-
ematics and science; my Italian and Latin teacher in high school, Elio D’Agostino,
who made me a rational person and transmitted me his love for knowledge; and
my master’s thesis advisor, prof. Mauro Velardocchia of Politecnico di Torino, who
has always believed in me, and without whom I would not even be here.
I wish to thank my committee members for the suggestions and ideas they
provided, as well as Prof. Vadim Utkin, whose help in the initial phase of this
dissertation was extremely important to let me understand Pontryagin’s minimum
principle. I am honored for working with him.
I am greatly indebted to two people from whom I learned a lot: Chris Hubert,
who taught me most of what I know about modeling, and has always been there
to answer my questions; and CG Cantemir, who is always happy to share his all-
around engineering knowledge.
I am also grateful to the many bright students and researchers I met at CAR, for
the interesting discussions about hybrids, batteries, or just cars... and I would like
to say thanks to all my friends for their presence in my life, especially important
when one lives far away from home. From the moment they came to pick me
up at the airport the first time I came to Columbus (remember, Marcello?), and
iv

Frequently asked questions

Q1. What have the authors contributed in "A comparative analysis of energy management strategies for hybrid electric vehicles" ?

A detailed vehicle model used for energy flow analysis and vehicle performance simulation is presented. 

Q2. What are the forces that are used to propel a vehicle along a given route?

The force needed to propel a vehicle along a given route is the sum of rolling resistance, aerodynamic resistance, grade (road slope) and inertia force (acceleration):Ftrac = Froll + Faero + Fgrade + Finertia (1.1)While the first two terms are dissipative (always tend to slow down the vehicle), the grade and inertia represent conservative forces, whose effect is to modify respectively the potential and kinetic energy of the vehicle. 

Q3. What is the potential for energy recovery using regenerative braking?

In particular, the potential for energy recovery using regenerative braking is equal to the amount of kinetic and potential energy that needs to be dissipated, minus the quantity that is dissipated because of rolling and aerodynamic resistance. 

Q4. What is the purpose of the validation of the model of longitudinal vehicle dynamics and road load?

In order to validate the model of longitudinal vehicle dynamics and road load, the torque measured at the traction motors is assumed to be delivered to the driveline, and the corresponding vehicle speed is calculated and compared to the actual measurement. 

Q5. What is the torque generated by the brakes when the vehicle is stopped?

when the vehicle is stopped, the torque generated by the brakes must only equilibrating the powertrain torque and the grade force on the vehicle. 

Q6. What is the common method for solving the optimal control problem backwards?

The method most widely used for obtaining the optimal solution in case of perfect and complete information is dynamic programming [28, 29, 26, 9], which is a numerical technique for solving the optimal control problem backwards 

Q7. What is the simplest model possible for a gearing?

The simplest model possible for a gearing only accounts for the speed and torque ratios, without considering the losses due to friction. 

Q8. What is the disadvantage of object-based modeling tools?

One disadvantage of all object-based modeling tools is the false sense of security that they give to users: the fact that there is a block representing a physical component may obscure the level of detail and accuracy of the model implemented, and may lead inexperienced users to overestimate the power of these3637tools. 

Q9. What is the simplest model possible for a gearbox?

The model implemented for the gearbox is the simplest possible, and consists in a lossy gear (see previous section) with variable gear ratio and variable efficiency (which depends on gear ratio, speed, and input torque). 

Q10. What is the visible characteristic of what is sometimes called a-causal modeling?

This is the most visible characteristic of what is sometimes called a-causal modeling: the term refers to the fact that, while usually one writes equations in explicit form and has to decide which variable is an input and which is an output, in this case there is no need to define explicitly the inputs and outputs of the model, i.e. its causality. 

Q11. what is the advantage of a-causal modeling tools?

Independently from the underlying technology and the implementation templates, the advantage of all these a-causal modeling tools is the ability to compose complex systems simply by connecting their components. 

Q12. What is the relationship between the coefficients of aerodynamic resistance and the speed of the vehicle?

In these conditions, the deceleration is due only to the rolling and aerodynamic resistance: thus, measuring the speed and deceleration and using (2.68), it is possible to derive experimentally a relation between the sum of the resistances to the vehicle speed. 

Q13. What is the difference in load between axles?

In other words, if the longitudinal distance between axles in the same set is small with respect to the distance between axle sets, the difference in load on each axle of the set due to moment balancing is negligible.