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http://dx.doi.org/10.1080/00207160.2013.829567
http://hdl.handle.net/10251/51290
Taylor & Francis
Guardiola García, C.; Plá Moreno, B.; Blanco Rodriguez, D.; Reig Bernad, A. (2014).
Modelling driving behaviour and its impact on the energy management problem in hybrid
electric vehicles. International Journal of Computer Mathematics. 91(1):147-156.
doi:10.1080/00207160.2013.829567.
Modelling Driving Behaviour and its Impact
on the Energy Management Problem in Hybrid
Electric Vehicles
C. Guardiola, B. Pla, D. Blanco-Rodr´ıguez & A. Reig
a ∗ ∗
a
CMT Motores T´ermicos, Universidad Polit´ecnica de Valencia, Valencia, Spain
Abstract
Perfect knowledge of future driving conditions can be rarely assumed
on real applications when optimally splitting power demands among differ-
ent energy sources in a Hybrid Electric Vehicle (HEV). Since performance
of a control strategy in terms of fuel economy and pollutant emissions is
strongly affected by vehicle power requirements, accurate predictions of
future driving conditions are needed.
This paper proposes different methods to model driving patterns with
a stochastic approach. All the addressed methods are based on the sta-
tistical analysis of previous driving patterns to predict future driving con-
ditions, some of them employing standard vehicle sensors while others
require non conventional sensors (for instance GPS or IRS). The different
modelling techniques to estimate future driving conditions are evaluated
with real driving data and optimal control methods, trading off model
complexity with performance.
Keywords: HEV; PHEV; hybrid electric vehicle; energy management;
optimal control
1 Introduction
The Energy Management Problem in HEV, hereinafter EMP, consists in finding
the control policy which minimises the fuel consumption of the vehicle under
a set of restrictions over a defined driving cycle. The EMP has been exten-
sively addressed in the literature [12, 4], generally from the Optimal Control
perspective, applying methods such as Dynamic Programming (DP) [17, 16],
Pontryagin’s Minimum Principle (PMP) [13, 15, 14] or ad hoc methods, being
Equivalent Consumption Minimisation Strategy (ECMS) [9, 8] the most popular
among them.
∗ ∗
This research has been supported by Ministerio de Ciencia e Innovaci´on through Project
TRA2010-16205 uDiesel
1
Despite being exhaustively studied during the last decade, the EMP is still
a challenging problem. First of all, the complexity of the system to optimise
makes difficult to develop models accurate enough to capture the system be-
haviour with affordable computational cost. The backward quasi-static ap-
proach is generally employed to model the vehicle dynamics, because of its
compromise between accuracy and computational burden [11].
The EMP is also rather hard to solve because of the difficulty which involves
the charge-sustainability condition [3]. This is usually addressed by a hard
constraint, imposing the integral of the battery power to be zero over the driving
cycle [4], which may be too restrictive in some cases. To avoid the use of such
a hard constraint, some authors propose different approaches [7, 10].
Finally, another important issue defining the EMP is the driving cycle itself.
Driving style, road profile or traffic conditions have a strong impact on vehicle
fuel consumption and optimal control [18] making specific cycle optimisations
useless with other cycles. Although Optimal Control techniques require a priori
knowledge of the driving cycle very limited future information is available on-
line. The present paper is aimed to propose and describe different methods to
estimate future driving conditions in order to address the EMP from an Optimal
Control approach.
The paper is organised as follows: in section 3 the control problem is for-
mulated, followed by section 4, which provides the theoretical description of the
proposed methods to estimate the driving profile. All the techniques employed
to estimate the driving cycle will be combined with the ECMS optimisation
technique, while the DP will be used to provide a benchmark solution. Sec-
tion 5 shows the simulation results, comparing the performance of proposed
cycle estimation techniques, and analysing the effect of the driver’s behaviour
on the fuel consumption and the optimal control strategy. Finally, conclusions
are presented in section 6.
2 Case study
A series hybrid vehicle is presented as a simple case study to illustrate the
impact of the driving behaviour on the EMP. The powertrain consists of a
genset (internal combustion engine and generator both coupled together), a
Ni-MH battery and an electric motor that provides traction to wheels.
The HEV has been modelled with a backwards model. The battery model
consists of a resistance and a global efficiency (both variable with SoC) [14],
while genset and electric motor are modelled with quasi-static maps. Vehicle
dynamics are computed via a resistance equation assessing aerodynamic drag
(drag coefficient of 0.32), rolling resistance and vehicle inertia (vehicle mass of
1262 kg).
Figure 1 depicts the cited HEV series architecture studied in the present
paper as well as the actual power flow that occurs along the powertrain. As
shown, power required by the vehicle (P
req
) is only satisfied by the mechanical
power produced by the motor MG1 (P
m,1
). This motor is fed by either the
2
Battery
74 kW
6.9 Ah
Engine
75 kW
MG2
60 kW
MG1
49 kW
Fuel
P
f
P
ice
P
m,2
P
el
P
m,1
+
+
Figure 1: Approached HEV series architecture, machines specifications and
power flow. Arrows show the positive direction for power flows
generator MG2 or the batteries (P
m,2
and P
el
respectively). The generator MG2
is driven by the engine mechanical power (P
ice
) at the expense of consuming
fuel (P
f
), meanwhile batteries release or absorb energy modifying their internal
stored energy (E
b
). Note that the variation of the energy stored in the battery
(−P
b
) and the electrical power provided by it (P
el
) may be positive (driving the
vehicle) or negative (absorbing energy), while the electrical power provided by
the generator MG2 (P
m,2
) is always positive.
Given the vehicle speed profile the power required by the vehicle becomes an
input whereby the powertrain has a single degree of freedom, namely the power
split between the battery and the generator. Accordingly, in the present paper,
the relative power provided by the generator (P
m,2
/P
max
m,2
) has been chosen as
control variable (u).
The described HEV model was run with urban and highway real driving
cycles where two non-professional drivers did the same route.
3 Problem statement
In general, the EMP consists on finding the control law u (t) to be applied over
a defined driving run with duration t
f
− t
0
in order to minimise the following
cost function:
J =
Z
t
f
t
0
P
f
(u (t)) dt (1)
The only dynamic equation in the problem is that governing the evolution
of the energy stored in the battery:
−
˙
E
b
= P
b
(2)
The problem is constrained as the powertrain must produce the mechanical
power demanded by the vehicle to follow the driving cycle. The formulation of
this constraint depends on the powertrain layout. In the case at hand a series
3
HEV architecture is considered, where the vehicle wheels are exclusively driven
by the electric motor:
P
req
(t) = P
m,1
(t) (3)
Additional constraints should also be included in order to take into account
the limitations in the power ranges of the powertrain elements:
P
min
ξ,i
≤ P
ξ,i
(u (t)) ≤ P
max
ξ,i
(4)
where subscript ξ refers to the internal combustion engine, battery or electric
motor.
Finally, the battery is subject to limitations on the energy which is able to
store, but also, the net battery charge variation in a long enough cycle should
be roughly zero to ensure the battery charge sustainability. Then, the following
constraints should be also considered:
Z
t
f
t
0
P
b
(u (t) , E
b
(t)) dt = 0 (5)
For the sake of reasonableness, the last constraint will be relaxed so that the
energy stored in the battery should reach the reference level within a certain
time horizon. This approach is consistent with the limitations in the information
about future driving conditions. Both the methods employed to estimate the
driving conditions within a reduced time horizon and the corresponding charge
sustainability constraints will be described in the following section.
4 Methods to estimate driving behaviour
The formulation of the methods proposed in this paper is oriented so that they
may be combined with the ECMS to solve the EMP. The ECMS was presented
in [9] and its main contribution is that under certain conditions, the integral
problem presented in (1) can be replaced by a set of problems to be solved at
each instant. To cope with this objective, the energy level of the battery should
be included in the cost function in order to take into account the potential of
discharging the batteries in the current moment and recharging them in the
future or vice versa. Accordingly, the cost may be re-defined as:
f (u (t) , E
b
(t) , t) = P
f
(u (t) , t) + sP
b
(u (t) , E
b
(t) , t) (6)
where the parameter s is an equivalence factor to transform electrical into an
equivalent fuel power. According to [13] the ECMS is a simplification of the
Pontryagin’s Minimum Principle approach in which the Lagrangian parameter
s = s (t) is considered constant over the driving cycle. Of course, the solution
provided by the ECMS depends on the value of the corresponding s parameter.
For a given cycle, the optimal s value may be obtained by means of shooting
methods [14] or by analysing the optimal solution previously calculated [3]. Note
4
