1 Optimal Thermal Management and Charging of Battery Electric Vehicles over Long Trips

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Optimal Thermal Management and Charging of

Battery Electric Vehicles over Long Trips

Ahad Hamednia, Victor Hanson, Jiaming Zhao, Nikolce Murgovski, Jimmy Forsman, Mitra Pourabdollah, Viktor

Larsson, and Jonas Fredriksson

Abstract—This paper studies optimal thermal management

and charging of a battery electric vehicle driving over long

distance trips. The focus is on the potential beneﬁts of including

a heat pump in the thermal management system for waste heat

recovery, and charging point planning, in a way to achieve

optimality in time, energy, or their trade-off. An optimal control

problem is formulated, in which the objective function includes

the energy delivered by the charger(s), and the total charging

time including the actual charging time and the detour time

to and from the charging stop. To reduce the computational

complexity, the formulated problem is then transformed into a

hybrid dynamical system, where charging dynamics are modelled

in the domain of normalized charging time. Driving dynamics

can be modelled in either of the trip time or travel distance

domains, as the vehicle speed is assumed to be known a priori,

and the vehicle is only stopping at charging locations. Within

the hybrid dynamical system, a binary variable is introduced

for each charging location, in order to decide to use or skip

a charger. This problem is solved numerically, and simulations

are performed to evaluate the performance in terms of energy

efﬁciency and time. The simulation results indicate that the time

required for charging and total energy consumption are reduced

up to 30.6 % and 19.4 %, respectively, by applying the proposed

algorithm.

Index Terms—Grid-to-meter energy efﬁciency, thermal man-

agement, charging, heat pump, charge point planning

I. INTRODUCTION

RECENTLY electric vehicles (EVs) have gained consid-

erable attention among researchers, manufacturers, and

users, due to their advanced and sustainable technologies

for counteracting drawbacks of conventional vehicles, e.g.

limited fuel resources, severe environmental impact, and high

maintenance and operating costs [1]. Accordingly, the EV

market has grown rapidly over the last few years, and several

car companies have stated that they will only produce electric

vehicles in the near future [2]. In particular, battery electric

vehicles (BEVs) are identiﬁed as a promising choice for

achieving the decarbonized light-duty vehicle ﬂeet. However,

there still exist several challenges impeding the widespread

deployment of BEVs, mostly related to energy cost, limited

driving range, charging time, and thermal management. These

issues become even more important to consider when planning

for long-distance trips, i.e. exceeding the vehicle’s range [3].

N. Murgovski and Jonas Fredriksson are with the Department of Electrical

Engineering, Chalmers University of Technology, Gothenburg 412 96, Swe-

den.

A. Hamednia, V. Hanson, J. Forsman, M Pourabdollah, and Viktor Larsson

are with the Department of Vehicle Energy and Motion Control, and J. Zhao

is with the Exterior Systems team, Volvo Car Corporation, Gothenburg 405

31, Sweden (e-mail: ahad.hamednia@volvocars.com).

Although the range can vary over a large distance win-

dow [4], still the majority of cost-effective BEV models fail

to fully meet the range requirement of long trips, highlighting

the signiﬁcance of reducing total energy consumption as well

as improving fast charging technology, for higher customer

acceptance of BEVs. Lately, a high-power fast charging tech-

nology has been introduced, aiming at recharging a battery

up to 80 % state of charge (SoC) within 15 min, in order to

provide more convenient long-trip experiences [5].

Apart from the charger’s rated power, the charging time is

also highly inﬂuenced by the fast charging properties of the

battery. This is mainly characterised by the battery’s chemistry,

SoC, temperature, and health state, which may negatively

affect the charging rate [6]. Thus, solutions associated with

the BEV’s fast charging are required to incorporate various

aspects rather than just focusing on increasing the maximum

power provided by the charger [7], [8].

One crucial factor that can signiﬁcantly improve charging

time, total energy consumption, and passenger comfort, es-

pecially in harsh climates, is to develop an adequate thermal

management (TM) [9], [10]. Lithium-ion (Li-ion) batteries,

known as a widely used alternative in the market, are highly

temperature sensitive [11]. Excessive battery temperatures

can cause corrosion and even explosion by creating bubbles,

bulges, sparks, and ﬂames [12]. Furthermore, at sub-zero

Celsius temperatures, the battery performance is severely

deteriorated due to a considerably slowed electrochemical

process within the battery cells [13], [14]. This yields a severe

reduction in the cell’s available power and energy, thereby

signiﬁcantly increasing the charging time [15]. Moreover, to

minimize the total energy consumption of the vehicle, it is

essential to incorporate the TM when optimising the grid-

to-meter energy efﬁciency of the BEV [16]–[18]. In this

context, several research works have been conducted, mainly

by formulating an optimal control problem (OCP) that can be

solved by different optimization tools.

Dynamic programming (DP) [19] is used in [20] for devel-

oping an algorithm for the TM of a vehicle that is unplugged

from the electrical grid and parked outside at a low ambient

temperature. The goal of this study is to ﬁnd an optimal trade-

off between contained energy in the battery pack, and the

cell degradation of being exposed to cold weather. However,

the main disadvantage of the DP approach is expressed as

the curse of dimensionality, which refers to the exponential

growth of computational time with the dimension of the OCP.

As an alternative approach, Pontryagin’s Maximum Principle

(PMP) [21] is applied in [22], for maximising the expected

arXiv:2210.03393v1 [eess.SY] 7 Oct 2022

𝑵𝐜𝐡𝐠

Fig. 1. A BEV starts its trip from point A, and drives in hilly terrain. The indices 1,2,. . . represent the charging stations, and Nchg denotes the total number

of charging locations.

battery life with minimum energy consumed. PMP suggests

a way to reduce the computational complexity of the high-

dimensional optimisation problems, by adjoining system dy-

namics to the objective function and neglecting constraints on

state variables. Furthermore, several TM strategies have been

proposed using Model Predictive Control (MPC) scheme for

increasing energy efﬁciency via optimal cooling/heating [23]–

[25]. Moreover, the TM is studied for vehicles with a given

drive cycle [26], or with future speed prediction, to be incor-

porated into the energy efﬁciency analysis [16]. In the context

of the TM of electriﬁed vehicles, several research efforts

have been carried out with a focus on waste heat recovery

(WHR) [27], referred to as an energy recovery process by

transferring heat from one part to another part within the ve-

hicle and, thus, improve the energy efﬁciency. In [28], a multi-

level WHR system with an improved heat transfer capacity is

developed, where the battery temperature is maintained within

an appropriate range. Also, a novel HP system is designed

for electric buses in [29], where the heating performance of

the TM system is enhanced in cold environments. Despite the

contributions provided by developing numerous TM strategies

for vehicles, the technical literature lacks investigation on joint

optimal charging and TM over long trips, with a WHR ability

and charge point planning.

As an extension to our earlier work [30], this paper ad-

dresses a BEV driving on a road with hilly terrain. The

vehicle’s travelled distance is greater than its range; there is

thus a need for at least one charging stop along the route. In

this paper, the following goals are addressed:

•Develop an algorithm to achieve optimal charging and

TM of a BEV on long trips, capturing both driving and

charging modes of the vehicle.

•Quantify the trade-off between charging time and energy

efﬁciency.

•Investigate the beneﬁts of including a heat pump (HP) in

the TM system for WHR.

•Plan the charging locations, in favour of obtaining opti-

mality in time, energy, or their trade-off.

To achieve the above-mentioned goals, an OCP is for-

mulated for charging and TM of a BEV. The objective of

the OCP is to ﬁnd the optimal compromise between the

energy delivered by the charger(s), and the total charging

time referred to as the actual charging time and the detour

time to and from the charging locations. The TM system

includes an HP, a high-voltage coolant heater (HVCH), and

heating, ventilation, and air conditioning (HVAC). HP is used

for the WHR purposes, and HVCH and HVAC are employed,

respectively for heating and cooling of the battery and cabin.

The driving dynamics can be described in either of the space or

trip time domains. However, charging dynamics is modelled in

terms of normalized charging time. Thus, the OCP transforms

into a hybrid dynamical system (HDS). Note that the actual

charging time is treated as a scalar variable, which is optimized

simultaneously with the optimal state and control trajectories

that belong to the driving and charging modes. Also, for each

charging location, a binary variable is deﬁned to optimally plan

the charging stops, in favour of further optimising the energy

efﬁciency and/or trip time. Such formulation procedure turns

the HDS into a mixed-integer optimisation problem.

The rest of the paper is outlined as follows. In Section II,

electrical and thermal modelling of the electric powertrain are

addressed. Section III illustrates the constraints on the battery

and grid power values. In Section IV, the HDS is formulated,

covering the vehicle’s operation during both driving and

charging modes. In Section V simulation results are presented.

Section VI discusses the obtained results. Finally, Section VII

includes the conclusion of the paper and suggestions regarding

possible future research directions.

II. MODELLING

This section addresses the vehicle driving mission and a

multi-domain conﬁguration of an electric powertrain, describ-

ing the connection of the powertrain components via electrical,

thermal, and mechanical paths.

A. Vehicle driving mission

Consider a BEV that starts its trip from point A, and drives

in hilly terrain, as depicted in Fig. 1. As the vehicle moves

forward, the battery is depleted. The battery temperature may

be adjusted by different heating/cooling sources within the

powertrain. Along the driving route, multiple charging pos-

sibilities are considered, as the vehicle’s trip length is greater

than its range. In realistic driving situations, it is preferable

to plan the charging stops, to achieve optimal trip time and/or

charging cost.

In this paper, we assume the vehicle speed to be known a

priori, in which the vehicle stops only during charging (and

not during driving). This allows us to identically formulate

the driving dynamics, in either space or trip time domains,

without adding any complexity to the algorithm developed

later in Section IV. Here, we freely choose the spatial domain

to associate the system trajectories with space-deﬁned events,

such as speed limits and charging locations. Thus, the vehicle’s

driving time, t, is calculated by integrating the vehicle speed,

t(s) = Zs

v(x),(1)

where sand vdenote travelled distance and the vehicle

speed, respectively. The formulation of charging dynamics is

postponed to Section IV.

B. Multi-domain Powertrain Conﬁguration

A schematic diagram of the studied electric powertrain

is demonstrated in Fig. 2. The powertrain includes propul-

sion components, i.e. a battery for energy supply/storage,

an electric machine (EM), and a transmission system. In

addition to the propulsion components, the powertrain is

equipped with an onboard charger (OBC), as a device to

regulate the electricity ﬂow from the electrical grid to the

battery, monitor the charge rate, and protect the battery from

over-current charging. Furthermore, the electric powertrain

includes a thermal management system, comprising HVAC,

HVCH, and HP. The HVAC and HVCH are mainly used,

respectively for cooling and heating of the battery pack and

cabin compartment. Also, an HP is generally employed for

transferring heat from the heat source at low temperature, i.e.

the battery, to heat sink at higher temperature, for e.g. the

cabin compartment and/or ambient air. To achieve this, work

is required, as heat cannot spontaneously ﬂow from a colder

place to a warmer location, according to the second law of

thermodynamics [31]. As depicted in Fig. 2, the operating

principle of HPs can be summarized into a refrigeration

cycle, which consists of ﬁve major components: an evaporator,

compressor, condenser, expansion valve, and refrigerant. Thus,

the evaporator absorbs heat from the battery pack and turns

the refrigerant from liquid mode into a low-pressure gas that is

delivered to the compressor. Then the compressor pressurises

the gas and dispatches it to the condenser. Later, the condenser

cools down the hot gas, turns it into a liquid, and expels the

extracted heat from the refrigerant to the cabin compartment

and/or ambient air. Finally, the high-pressure liquid refrigerant

departed from the condenser becomes a low-pressure liquid

by passing through the expansion valve; and the cycle starts

over again. The merit of an HP is speciﬁed by a parameter

called the coefﬁcient of performance (CoP), deﬁned as a ratio

of useful heating provided (for the cabin compartment) to the

net work required, as

cop(Tb(s), Php(s)) = Qb

hp(Tb(s)) + Php(s)

Php(s),(2)

where Tbis the battery pack’s temperature, Php is the rate

of the net work put into the cycle, and Qb

hp is rate of the

heat removed from the battery pack and electric drivetrain

(ED). Hereafter, Php is called HP power. The three domains of

the powertrain conﬁguration are elaborated in Sections II-B1-

II-B3.

Transmission

Battery

Pack

HVCH

Coolant circuits

Bidirectional mechanical path

HVCH: high voltage coolant heater

ED circuit

ED: electric drivetrain

EM: electric machine

OBC

OBC: on board charger

Chiller

HVAC: heating ventilation air conditioning

HVAC

HP: heat pump

COND: condenser

COMP: compressor

Bidirectional electrical path

COMP

Valve

COND

EVAP

EVAP: evaporator

Refrigeration cycle:

Fig. 2. Schematic diagram of the studied electric powertrain, which consists

of propulsion components, i.e. a battery, an EM, and a transmission system, an

onboard charger, and a thermal management system. The thermal management

system consists of HVCH, HVAC, and a heat pump, which are used for

actively adjusting the battery pack and cabin compartment temperatures.

1) Electrical Domain: Depending on the EM’s operating

mode, i.e. generating or motoring, the electric power ﬂow

through the electrical path is bidirectional, as shown in Fig. 2.

Accordingly, electrical energy is charged to the battery during

the generating mode, or supplied to the EM during the

motoring mode. The battery is modelled using an equivalent

circuit, which includes a voltage source Uoc, known as open-

circuit voltage, and an internal resistance Rb. The open-circuit

voltage is usually proportional to the battery SoC. Also, as

the battery temperature is raised, the ions inside the battery

cells get more energized, which results in reduced resistance

against the ions’ displacement. Thus, the internal resistance

is commonly a nonlinear monotonically decreasing function

of the battery temperature [23]. Note that the slight mismatch

between the internal resistance while charging and discharging

is overlooked in this paper. The battery SoC dynamics is

calculated by

soc0(s) = −Pb(s)

CbUoc(soc(s))v(s),(3)

where Pbis battery power, including internal resistive losses,

and Cbis maximum capacity of the battery pack. Pbis negative

while charging, and is positive when discharging. Note that

throughout this paper, x0represents the space derivative of an

arbitrary variable x, i.e. x0=dx/ds.

2) Thermal Domain: According to the fundamental ther-

modynamic principle [31], the changing rate of the battery

pack’s temperature Tbis modelled using a lumped-parameter

thermal model, as

b(s) = 1

cpmbv(s)Qpass(·) + Qact(·) + Qexh(·),(4)

where cpand mbare the battery pack’s speciﬁc heat capacity

and total mass, respectively, Qpass is the rate of induced heat

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1OptimalThermalManagementandChargingofBatteryElectricVehiclesoverLongTripsAhadHamednia,VictorHanson,JiamingZhao,NikolceMurgovski,JimmyForsman,MitraPourabdollah,ViktorLarsson,andJonasFredrikssonAbstractThispaperstudiesoptimalthermalmanagementandchargingofabatteryelectricvehicledrivingoverlongdistanc...

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