Functional Model-based Resource Management: An Application to the

Electric Vehicle Thermal Control

Baptiste Boyer

1,2 a

, Philippe Fiani

, Guillaume Sandou

, Emmanuel Godoy

and Cristina Vlad

Sherpa Engineering, R&D Department, 92000, Nanterre, France

Universit

e Paris-Saclay, CNRS, CentraleSup

elec, Laboratoire des Signaux et Syst

emes, 91190, Gif-sur-Yvette, France

Keywords:

Resource Management, Control Design, Multi-level Control, Systems Modeling, Functional Modeling,

Thermal Management, Model based System Engineering, Complex Systems, Electric Vehicle, Optimization

Problem.

Abstract:

Environmental and economical constraints lead to designing more and more complex systems. To face these

issues, Model Based System Engineering proposes an approach based on an interconnected multi point of

view system modeling. Each representation of the system has a different abstraction level that is valuable

at different stages of the system design and suits its own objectives respectively: 1) purposes and global

constraints deﬁnition, 2) architecture choices, components sizing and strategies testing, 3) accurate simulation

results on various scenarios. Interconnections between the different levels have two objectives: on one hand be

able to deﬁne the requirements of a lower level using higher level information and on the other hand send back

simulation variable values from a lower level to evaluate the higher level requirements satisfaction. Resource

management is carried out through a functional model, which is a macroscopic and low-complexity model

of the system providing fast simulation results. In this paper, this multi-level methodology is applied to the

thermal system management of an electric vehicle in order to optimize its resource management. The different

levels design and the development of their interconnections are detailed.

1 INTRODUCTION

The impact of carbon emissions, resource depletion

and over-consumption on global warming and envi-

ronmental issues is now well established. In order

to take into account these constraints in the design

stages, engineers develop systems that are more and

more complex, leading to some issues:

• A single system handles with several sources and

consumers belonging to different energetic ﬁelds

(mechanical, electrical, thermal, etc.).

• There are multiple objectives (economical, eco-

logical, sizing, etc.).

• The technological structure is complex.

Moreover, the development of these complex systems

faces two antagonist issues. On one hand, each com-

ponent of the system needs to be developed by engi-

neers specialized in the component ﬁeld. On the other

hand, the system needs to be thought and designed

https://orcid.org/0000-0002-5560-1538

as a whole including all the interconnections between

components.

The main purpose in the control design is to opti-

mize the global consumption of the system while re-

specting all the constraints. To achieve this goal, the

system needs to be modeled in a way that describes

well both sources and consumers as well as their inter-

connections. These models deal with different physi-

cal ﬁelds and can become complex and burdensome,

making them difﬁcult to handle and modify. A higher

level of model abstraction is needed to make it easier

to understand and handle.

The modeling methodology introduced in (Fiani

et al., 2016) and (M

ukc

u et al., 2016) presents

how to address the system design from three differ-

ent points of view (detailed below), each of them hav-

ing its own abstraction level, and how to easily switch

between them. This methodology is based on the

systemic approach concept introduced in (Von Berta-

lanffy, 1968). The system description is inspired

by the Bond Graph methodology, which has been

shown to be well-suited to systemic modeling and

multi-domains simulation in (Brunet et al., 2005) and

Boyer, B., Fiani, P., Sandou, G., Godoy, E. and Vlad, C.

Functional Model-based Resource Management: An Application to the Electric Vehicle Ther mal Control.

DOI: 10.5220/0009769905650575

In Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2020), pages 565-575

ISBN: 978-989-758-442-8

565

Functional Units

S1 C1

C2S2

Internal

Model

Multi-Physical Units

Internal

Model

S1 C1

C2S2

Reduction

Adaptation

Teleological Units

Global

Control

Internal

model

Figure 1: Diagram of electric vehicle cooling and heating circuits (Fiani et al., 2019).

(Borutzky, 2010). The three different modelings are

listed below from the highest abstraction level to the

lowest and will be detailed in Section 2 :

• A teleological modeling where the global mis-

sions and the main properties of the system are

deﬁned.

• A functional modeling that is composed of basic

modular blocks having a speciﬁc function. Blocks

are connected to each other with EMI (Energy,

Flow, Matter) ﬂow needs and supplies.

• A multi-physical modeling that is composed of all

physical components and equipment of the sys-

tem. At this level, the behaviour of the compo-

nents and interactions between each other are de-

ﬁned by physical laws.

This methodology is interesting because each ab-

straction level has its own speciﬁcities and is used at

different stages in the system design. As illustrated

in Figure 1, this methodology is a circular approach

in which each higher abstraction level can be seen

as a reduction from the lower one. The teleologi-

cal level does not require neither much time nor any

technical knowledge to be developed and gives a ﬁrst

global overview of the system and its main charac-

teristics. Hence, it is often the ﬁrst one to be elab-

orated. The functional model is then developed as a

reﬁnement of the teleological one, where the differ-

ent functions of the system and their interactions are

deﬁned. By construction, the functional model con-

tains both a control and an operation part that make

the model self-sufﬁcient, i.e. it can be run on its own.

The major advantage of this modeling is the possibil-

ity to quickly simulate the system already in the ﬁrst

design stages; it will be especially useful for architec-

ture choices and components sizing. An adaptation of

the teleological level enables the transmission of the

global constraints from the highest level of abstrac-

tion to the functional one. As the design progresses,

a model much closer to experimental observations is

needed. The expansion of each function of the sys-

tem as a set of physical components and the deﬁni-

tion of their interactions lead to the development of

the multi-physical model. Instead of starting from

scratch for the control design of this level, an adap-

tation of the control part of the functional level can

act as the multi-physical model supervisor. Finally,

the end-missions of the system can be introduced in

the control of this lowest abstraction level by a new

adaptation of the teleological level.

The ﬁrst objective of this work is to connect the

functional model to a global supervisor (correspond-

ing to the teleological level) containing macroscopic

constraints and criteria that can be transmitted to the

functional model through the resolution of an opti-

mization problem that will ensure a better resource

management. The second objective is to build the

control of the multi-physical model using setpoint

values coming from the control part of the func-

tional representation. The coupling between func-

tional and multi-physical models was demonstrated in

ukc

u et al., 2017) on the power-train of a hybrid

electric vehicle and it will be extended here for ther-

mal issues.

In this paper, the methodology is applied to a use-

case consisting in the thermal management system of

an electric vehicle (EV). In internal combustion en-

gine vehicles, cabin heating is ensured by the thermal

energy dissipated by the engine while its cooling is

ensured by a refrigerant loop. The development of

battery electric vehicles brings some new issues:

ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics

566

• Electric machine does not dissipate enough en-

ergy to satisfy the heating needs.

• The battery has sizable heating and cooling needs

that must be taken into account.

• Battery temperature has a direct inﬂuence on its

efﬁciency, which is a key parameter for the vehi-

cle autonomy.

• The non-negligible impact of battery temperature

on its service life was demonstrated in (Gross and

Clark, 2011).

• The battery charge dissipates a huge amount of

energy that must be evacuated, especially in the

case of fast charging.

Due to these new constraints, a multitude of dif-

ferent technical solutions have been developed, lead-

ing to as many different architectures, as shown in the

large review presented in (Zhang et al., 2018). Hence,

thermal management in electric vehicle is becoming

an important research topic for car manufacturers.

Section 2 describes three models with different

abstraction levels (teleological level, functional level

and multi-physical level), the interconnection be-

tween these models as well as the advantages and

the challenges of the interconnection. In Section 3,

the EV thermal management system is detailed and

modeled at the three levels of abstraction.The issue of

energy management between the consumers is intro-

duced and an optimization problem is formulated at

teleological level of abstraction to address this prob-

lem. Section 4 provides the simulation results of the

functional model, which are confronted to simula-

tions of the multi-physical model for validation. Fi-

nally, concluding remarks and perspectives are pre-

sented in Section 5.

2 MODELING METHODOLOGY

FOR SUPERVISOR

ARCHITECTURE DESIGN

This section describes the three abstraction levels

of modeling introduced in (Fiani et al., 2016) and

ukc

u et al., 2016) and shows how they can be

interconnected between each other.

2.1 Teleological Modeling

The teleological modeling is the one with the higher

level of abstraction and it does not require any tech-

nical knowledge to be elaborated. At this level, only

the main missions and expectations of the system are

represented. Some of the requirements that can be ex-

pressed at this level are listed below:

• Financial and realization time constraints.

• Ecological international standards.

• Constraints related to the integration of the system

in its environment.

• Global performances of the system (lifetime, au-

tonomy, operation energetic cost, etc.).

• Some comfort criteria like maximal noise or vi-

bration levels.

At teleological level are also deﬁned some arbitra-

tion rules that deﬁne weighted or heuristic priorities

between the different purposes of the system. For an

electric vehicle, this arbitration level could be illus-

trated by different operation modes:

• A sportive mode that focuses on the power-train

performances.

• A comfort mode, where comfort parameters are

optimized (compressor noise, cabin temperature,

speed variations smoothness).

• A normal mode that tries to meet all criteria, as

best as possible, without favoring any of them.

• An eco mode, in which priority is given to energy

savings.

In the earliest design stages, this level gives a good

overview of the main missions and limitations of the

system while in the last stages, it can be used to in-

troduce optimization algorithms to minimize a global

cost function (ﬁnancial cost, energy amount, etc.).

2.2 Functional Modeling

The concept of functional modeling has been devel-

oped in (Fauvel et al., 2014) and (M

ukc

u et al.,

2016) and has been illustrated on a hybrid vehicle in

ukc

u et al., 2017). This representation is based

on the use of modular functional blocks assembled to-

gether and connected by EMI ﬂow exchanges. Each

block is composed of both a control part that deter-

mines the ﬂow needs to be transferred to the neigh-

bour blocks, and an operation part that incorporates

the ﬂow supplies received by the block into simple

models, in order to estimate the different variable val-

ues. This architecture of each block enables the func-

tional model to be run on its own. A few functional

elements have been introduced in (M

ukc

u et al.,

2016) and extended to thermal ﬁeld in (Fiani et al.,

2019).

• Source: receives an EMI ﬂow need (power in the

case of an energetic system) from another element

Functional Model-based Resource Management: An Application to the Electric Vehicle Thermal Control

567

and delivers a ﬂow supply depending on the need

and internal limitations of the source.

• Consumer / Effector: requests an EMI ﬂow to an-

other block that can provide it. The ﬂow is used

to achieve the effector’s objective thanks to a con-

troller or to satisfy the consumer’s ﬂow need.

• Storage: stores EMI according to its maximal ca-

pacity. It can behave as a source (deliver EMI

ﬂow), consumer (receive EMI ﬂow) or both, de-

pending on the system and the scenario.

• Distributor: functional block that collects ﬂow

needs from all the consumers connected to it and

distributes the sum of the ﬂow needs to all the

sources connected to it. The distributor collects

also the ﬂow supplies from the sources and dis-

tributes them to the consumers according to their

request. The distribution to the sources or to the

consumers is made accordingly to their own avail-

ability/acceptance. Distributors can have either a

heuristic strategy or a more complex optimization

algorithm depending on the system.

• Transformer: converts a primary ﬂow in another

one (electrical to mechanical power for example).

An optional efﬁciency coefﬁcient and ﬂow lim-

itations are available. The process is reversible,

eventually with a different efﬁciency coefﬁcient.

A transformer can convert two or more ﬂows in

another one and conversely (chemical reaction for

example).

• Actuator: element transforming electrical power

into an action. It receives an action request

(ﬂow, temperature) and asks for electrical power

to achieve the setpoint.

• Exchanger: interface exchanging EMI ﬂow be-

tween two circuits. It receives a ﬂow request from

both neighbours and sends an action request to

two actuators to satisfy the needs. It gets back an

action from the actuators and calculates the ﬂow

transferred and its limitations to each neighbor, to

achieve an equilibrium state. The exchanger block

is fully symmetrical, its both neighbours are con-

sidered as consumer blocks.

These seven elements presented above constitute

the building blocks of the functional modeling. A

multitude of models in a large variety of ﬁelds can

be created by assembling these blocks together. Each

block has some editable parameters that can be ad-

justed to ﬁt the considered system.

Figure 2 shows the functional model of a complex

system using the seven elements introduced above.

Each geometrical shape corresponds to a speciﬁc el-

ement related by arrows that indicate only the need

E2M

Tranformer

Vehicle

Motion

Electrical

Auxiliaries

Battery

Cooling

Thermal

Exchanger

Exterior

Air

Pump

Fan

Electrical

Storage

Electrical

Grid

Electrical

Distributor

Electrical

Mechanical

Thermal

Energetic field:

Figure 2: Simpliﬁed functional model of an electric vehicle.

direction (the supply is implicitly in the opposite di-

rection). Green, red and blue arrows represent power

needs (in their respective energetic ﬁelds) while green

arrows correspond to ﬂow needs. The system rep-

resented is an electric vehicle composed of elements

from three different ﬁelds:

• A mechanical part with the vehicle motion effec-

tor.

• A thermal part composed by a source, a thermal

exchanger and an effector (battery cooling).

• The electrical part, which is the main one, com-

posed by a source, a storage, a distributor that

manages the electrical power needs from two

actuators, a transformer and a consumer (radio,

headlights, etc.).

In the very early stages of the system design, this

model can already be run and provides quick simula-

tion results. The architecture can be easily changed

and the sizing of the components can be adjusted.

Moreover, the energy distribution strategy can be im-

plemented and tested in this functional model, which

is time saving.

2.3 Multi-physical Modeling

According to (Fiani et al., 2016), multi-physical mod-

eling is well suited to represent a technological ele-

ments architecture. A 0D-1D multi-domains model-

ing is necessary and sufﬁcient to accurately represent

a complex system. Each component of the model

is ruled by analytical laws based on the real physi-

cal behaviour of the component in its respective ﬁeld

(electrical, mechanical, etc.). Components are con-

nected between each other with physical links con-

taining both a ﬂow and an effort variables. Table 1

lists the different ﬂow and effort variables correspond-

ing to each physical domain.

The main advantage of multi-physical modeling

is, as long as the model is well calibrated, to provide

very accurate simulation results compared to what can

be experimentally observed. However, the price to

ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics

568

Table 1: Multi-physical ports and connectors (Fiani et al.,

2016).

Energetic ﬁeld Effort Flow

Mechanical rotation Torque (N.m) Speed rot (rad/s)

Mechanical translation Effort (N) Speed (m/s)

Hydraulic Pressure (Pa) Flow (kg/s)

Thermal Temperature (K) Therm ﬂow (J/s)

Thermo-ﬂuid

Pressure (Pa) Flow (kg/s)

Temperature (K) Enthalpie ﬂow (J/s)

Electric Voltage (V) Current (A)

pay for this accuracy is the simulation time, which

can be very long as soon as the model gets complex.

This is the reason why this kind of modeling is very

useful for the model validation but it should not be

used for designing architecture or control strategies.

2.4 Interconnections between the Three

Levels of Modeling

2.4.1 Teleological and Functional Models

The teleological level gives an overview of the sys-

tem and its global requirements (standards, criteria,

constraints, etc.) of the system. The purpose of inter-

connection is to transmit these global parameters to

the functional level. However, the inputs of the func-

tional model are only setpoints, limitations (minimum

and maximum values) of variables and activation or

not of each element. An interface has to be built to

translate the parameters from the teleological level

into information understandable by the functional el-

ements. For each global parameter, a list of all the

variables estimated by the functional model and re-

quired for the determination of the parameter has to

be established, as well as the functional elements im-

pacted by this parameter. The second step is to evalu-

ate the global requirements achievement and develop

the corresponding equations to relate it to the identi-

ﬁed functional elements.

As an example, an electric vehicle is considered to

illustrate the interconnection between the teleological

and the functional model. One of the requirements of

the teleological model is the maximum comfort noise

level, which is speed dependent (equal to wind noise

at high speeds). In the system, the loudest element is

the compressor. A relationship between compressor

power and noise level has to be established to deter-

mine the maximal power that should be provided to

the compressor.

This interconnection is illustrated in Figure 3

with:

• D

Comp

the compressor availability, i.e. the maxi-

mal power the compressor can provide.

• NoiseLvl the maximal noise level requirement.

S1 C1

C2S2





  

Teleological

requirements

(NoiseLvl, …)

Functional

requirements

comp

, …)

Estimated

variables

(VehSpd, …)

Figure 3: Relationship between teleological requirements

and functional model control.

• VehSpd the vehicle speed estimated by the func-

tional model.

2.4.2 Functional and Multi-physical Models

Both functional and multi-physical models are very

useful at different stages of the system design. On

one hand, the ﬁrst one is very helpful in the early

stages of a system design due to its quick develop-

ment, its modularity and the fast simulations results it

provides. On the other hand, the second one is used in

downstream stages to provide a model, although more

complex and time-consuming, that is much more ac-

curate than the functional one. The functional model

contains both a control and an operation part. The

idea of connecting both models is to reuse the control

part of the functional model to build the supervisor of

the multi-physical level.

However, the ﬂow exchanges are not the same be-

tween the two models. While they are energy-based in

the functional model, the multi-physical model uses

both ﬂow and effort links. Interconnecting both mod-

els is not an immediate result and requires a process

to translate data from one model to another and in-

versely. A solution, consisting in building an interface

between the two models, was developed in (M

ukc

et al., 2017). It requires, at ﬁrst, to determine, for each

multi-physical block, an equivalent in the functional

one (sometimes by combining or splitting elements).

The second step consists in building the equations be-

tween functional and multi-physical domains for each

element. Hence, the interface transforms functional

information into physical signals that are used for the

control of multi-physical components. Moreover, the

variables estimated by the multi-physical model are

sent into functional elements and replace their opera-

tion part.

Functional Model-based Resource Management: An Application to the Electric Vehicle Thermal Control

569

3 APPLICATION TO ELECTRIC

VEHICLE THERMAL

MANAGEMENT

3.1 Motivations

In an electric vehicle, the thermal system is different

from the one in a combustion vehicle as explained in

Section 1. It is mainly composed by the cabin, the

battery and the electric machine (EM). All these com-

ponents have thermal needs and different structures

have been developed by automotive constructors to

satisfy them. The main objectives are to ensure con-

venient temperature both for passengers’ comfort and

for battery, and to maintain the EM integrity. Prior to

trying to optimize the efﬁciency of the system, the ar-

chitecture that best meets the speciﬁcations has to be

elaborated and validated. The functional model is the

ﬁrst one to be designed because it offers a large ﬂexi-

bility, enables easy architecture changes and provides

quick simulation results.

3.2 System Description

The system chosen for this study is a system for which

the multi-physical model had already been developed

and validated with experimental data. The consumers

of this system are the electric machine, the battery and

the cabin. The main energy provider is a refrigerant

loop functioning as a reversible heat pump supply-

ing cold both to the battery and to the cabin as well

as heat to the cabin. The working ﬂuid used in this

system in R134a. The switch between cooling mode

and heating mode of the heat pump is ensured by a

set of regular valves that modify the course of the re-

frigerant in the pipes, and electronic expansion valves

(EXV) that increase or decrease its mass ﬂow. The

evapo-condenser, used in both operating modes, acts

as an evaporator in heating mode while it acts as a

condenser in cooling mode. A diagram of the full

thermal system is available in Figure 4a. Figure 4b

and Figure 4c show how the system behaves in cool-

ing and heating operating mode respectively.

This design is close to the one described in (Zhang

et al., 2019) with two main differences. First, an inter-

mediate water loop was added in this design between

the refrigerant and the heater core to prevent refriger-

ant, which is under high pressure, from leaking into

the air blown into the cabin. The second difference

is that in (Zhang et al., 2019), the design is adapted

to electric vehicles in cold regions. Indeed, according

to (Ding et al., 2020), the optimum operating tem-

perature range for lithium power batteries is from 10

Battery

Electrical

Machine

Air from

Ext

PTC

Compressor

Heater

Chiller

Evaporator

Water

Condenser

Heater

Core

Radiator

Evapo

Condenser

EXV

Accumu

-lator

Cabin

Air to

Ext

(a) Diagram of electric vehicle cooling and heating circuits.

Battery

Electrical

Machine

Air from

Ext

Compressor

Chiller

Evaporator

Radiator

Evapo

Condenser

EXV

Accumu

-lator

Cabin

Air to

Ext

PTC

Heater

Water

Condenser

Heater

Core

EXV

(b) The cabin and battery mixed cooling mode.

Battery

Electrical

Machine

Cabin

Air from

Ext

Air to

Ext

PTC

Compressor

Heater

Water

Condenser

Heater

Core

Radiator

Evapo

Condenser

EXV

Accumu

-lator

Chiller

Evaporator

EXV

Figure 4.

◦

C to 35

◦

C. In cold areas, the battery often needs

to be heated up, hence providing the battery’s heat-

ing needs with the heat pump is an attractive solution,

though it makes the design much more complex. In

the design shown below, the heat pump only provides

heat for the cabin while the battery’s heating needs are

provided by a heater. There is an additional positive

temperature coefﬁcient (PTC) in the cabin air loop to

supplement heating supplies to the cabin. The EM

cooling is provided by a water loop exchanging di-

rectly with external air through the radiator. In each

coolant loop, an electrical actuator and eventually a

three-way valve control the ﬂows.

A functional representation of this diagram is

shown in Figure 5. Orange and green links represent

ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics

570

Cabin

Comfort

Bat Thermal

Conditioning

EM Thermal

Conditioning

Cabin Air

Loop

Bat

Water

Loop

Water

Loop

Heater

Core

Water

Loop

Water

Condenser

Evapo

Chiller

Refri

Loop

Evapo

Condenser

Ext Air

Loop

Radiator

Figure 5: Electric vehicle thermal management diagram.

Energy

Distributor

PTC

Blower

Flow

Distributor

From

Cabin

To Elec

Source

To Heater

Core

Evapo

From

Heater Core

From

Evapo

Figure 6: Cabin air loop.

power needs and action needs (mass ﬂow, tempera-

ture, etc.) respectively. Blue blocks are effectors re-

ceiving a setpoint temperature and sending a thermal

power need to achieve it. Red blocks are exchang-

ers that receive thermal power needs from both neigh-

bours and send action needs to actuators to satisfy the

power needs. Lastly, green blocks are coolant loops,

like the cabin air loop expended in Figure 6. They are

composed of a power distributor that splits or gathers

the needs it gets, and at least one electrical actuator

(compressor, fan, blower, pump, PTC, etc.) that tries

to satisfy the action needs it receives. At functional

level, the switch between cooling mode and heating

mode is handled in the ’Refri Loop’ block.

The multi-physical model is represented in Figure

7. The blocks composing the multi-physical model

look similar to those of the functional model. How-

ever, it is important to keep in mind a major differ-

ence between the two models: while functional ele-

ments are connected to each other by means of ener-

getic links independent from their ﬁeld, the connec-

tions between physical components are composed of

both ﬂow and effort variables that are domain depen-

dent. In order to use the functional model to build

the supervisor of the multi-physical one, the intercon-

nection between analog elements in both models has

to be ensured by an interface, as described in Section

2.4.2.

3.3 Teleological Modeling for Energy

Management

The teleological level enables to introduce global con-

straints and criteria in the system control, like min-

imizing the ﬁnancial or energetic operation cost. In

this system, in most cases, electric energetic optimiza-

tion can be done only with heuristic strategies directly

implemented in the functional model (for example,

prioritize speeding the blower rather than speeding

the compressor). It means the functional model does

not really need a manager to minimize the global

energetic cost of the system, at least when there is

enough energy to satisfy all the needs. However,

when energy needs are higher than global availabil-

ity of the system, some arbitrations have to be made.

In this system, when the cabin and the battery both

need to be cooled down and the system is saturated

(i.e., needs are higher than global availability), the

cabin or the battery temperature (or both) have to be

degraded in regard to their setpoints. In this case, a

method is required to manage how each temperature

is degraded.

The ﬁrst option is to implement directly in the

distribution block (of the functional model) priorities

between the consumers when needs are higher than

availability. This method is quick to set up and priori-

ties are not necessarily exclusive but can be weighted

with coefﬁcients. The main inconvenient is that this

prioritization is based on energy and not on temper-

ature setpoints achievement. The link between en-

ergy provided and temperature is dependent on the

scenario, which reduces the modularity of this option.

The second option consists in introducing in the

teleological model a new criterion corresponding to

the system non-saturation (when needs are lower or

equal than global availability). This requirement can

be met by degrading the temperature setpoints up-

stream, resulting in lowering cabin and battery needs.

A simpliﬁed functional model is needed to estimate

the pairs of cabin and battery temperature setpoint

values that prevent the system from saturating and

lead to the closest temperature achievements to the

ideal temperatures (deﬁned by the passengers or the

constructor). The connection between the teleological

model and the functional requirements is established

by solving the following optimization problem:

min

cab

bat

δ(T

cab

, T

bat

) (1)

s.t.

0 < P

ratio

act

(H)

max

act

< 1 (2)

Functional Model-based Resource Management: An Application to the Electric Vehicle Thermal Control

571

Figure 7: Electric vehicle thermal management multi-physical model.

with δ(T

cab

, T

bat

) = (T

cab

(H) −T

cab

)

+α·(T

bat

(H) −

bat

)

and:

• α a weighting parameter used to prioritize the

degradation of one temperature in regard to the

other.

• H the time horizon used to simulate the simpliﬁed

functional model at teleological level.

• T

cab

and T

bat

the temperatures of the cabin and the

battery respectively, estimated over the time hori-

zon by the reduced functional model.

• T

cab

and T

bat

the temperature setpoints of the

cabin and the battery respectively, which are the

decision variables.

• T

cab

and T

bat

the ideal temperature setpoints of the

cabin and the battery respectively (values ﬁxed by

the user for the cabin and by the constructor for

the battery).

• P

ratio

the load level of the system taking values

between 0 and 1; these values correspond to a

paused system or a saturated system respectively.

• P

act

and P

max

act

the power provided by the limiting

actuator and the maximum power it can provide

respectively.

The cabin and battery optimal temperature set-

point values, solutions of the optimization problem

(1) will be noted T

sp,∗

cab

and T

sp,∗

bat

respectively. The

strong non linearity of the problem does not enable

the implementation of a classic predictive functional

control. The description of the method is detailed be-

low:

1. Develop a simpliﬁed functional model that can

be run faster than the full functional one. It re-

ceives some variables estimated by the full func-

tional model (battery and cabin temperatures, sys-

tem saturation, etc.).

2. Run this model over a time horizon H for T

cab

c,1

c,2

,...,T

c,n

} and T

cab

in {T

b,1

b,2

,...,T

b,n

and n

being the number of setpoint values

tested for the cabin temperature and the battery

temperature respectively.

3. Get two matrices of size n

x n

: the ﬁrst having

as elements the criterion values obtained for all

the admissible pairs (T

c,i

b, j

), with i = 1 : n

and

j = 1 : n

, and the second one being composed of

elements of 1 if the constraint (2) is satisﬁed or 0

in the opposite case.

4. Choose the (T

c,i

b, j

) pair that satisﬁes the con-

straint (2) and minimizes the criterion, such that

sp,∗

cab

, T

sp,∗

bat

) = (T

c,i

, T

b, j

5. Send the new setpoints, T

sp,∗

cab

and T

sp,∗

bat

, to the

functional model for the next time step T

. To

avoid brutal setpoint changes in entry of the func-

tional model, a ﬁrst-order ﬁlter is applied on the

setpoints.

The main advantage of this method, though it is

more complex to elaborate, is to be independent from

the scenario and based only on the setpoints. Another

beneﬁt of this approach is the possibility of includ-

ing other parameters than temperature setpoints in the

criterion as well as other constraints than system sat-

uration.

ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics

572

4 SIMULATION RESULTS

The characteristics of the EV thermal system are sum-

marized in Table 2. A strong assumption is that the

electric power is not limited, i.e. the electric battery

can provide all the electric needs.

Table 2: Thermal system characteristics.

System characteristics Value Unit

Battery mass 500 kg

Battery max thermal exchange 3000 W

Battery charge thermal exchange 5000 W

Compressor max speed 6500 rpm

Compressor displacement 34 cm

/rev

Parking fan air velocity max 1.5 m/s

130 km/h fan air velocity max 3.9 m/s

Subsection 4.1 and Subsection 4.2 present the

simulation results of two use-cases run under the same

conditions (same vehicle speed, environment, etc.).

The only difference between the two use-cases comes

from the cabin and the battery temperature setpoints

sent to the model. In the ﬁrst case, setpoints corre-

spond to ideal constant values while in the second

one, the setpoints are determined by the supervisor

described in Subsection 3.3. Table 3 lists the condi-

tions used for both use-cases. The chosen scenario

consists in a ﬁfty minutes car drive under extreme

climatic condition. The scenario also includes a 10

minutes battery charge (time interval [1200, 1800] s),

during which the passengers stay in the car.

Table 3: Cool-down scenario parameters.

Time (min) 0-20 20-30 30-50

Vehicle speed (km/h) 70 0 70

Road slope (%) 0

Exterior temperature

(

◦

Battery charge Off On Off

Sun power (W) 1000

People in the car Yes

Ideal max cabin tem-

perature T

cab

(

◦

Ideal max battery tem-

perature T

bat

(

◦

4.1 Functional Model Simulation

First, the functional model is run under the condi-

tions detailed in Table 3. The cabin and the battery

temperature setpoints are constant and equal to T

cab

and T

bat

respectively throughout the whole simula-

tion. The controller of the distributor in the refrig-

erant loop uses weighted priorities. It means that both

consumers (battery and cabin) are assured to get at

least, if needed, a predeﬁned percentage of the to-

tal available power. Here the weights are set up to

(0.5;0.5), meaning that each consumer can have half

of total available power. If one of them needs less, it

can be reported on the other one. The initial tempera-

ture of the cabin and the battery are 55

◦

C and 34

◦

respectively and the temperature setpoints are set to

their ideal max temperature (see Table 3). Simulation

results are given in Figure 8.

Temperature (°C)

Cabine Temperature

Tair Cabin

Tair Cabin SetPoint

Temperature (°C)

Battery Temperature

Twater Battery

Twater Bat SetPoint

0.2

0.4

0.6

Mass Flow (kg/s))

Coolants Mass Flow

Q Blower

Q Bat Pump

Q FAN

Power (kW)

Components Power

Pcomp

Pcond

Pevapo

Pchill

0 500 1000 1500 2000 2500 3000

0.6

0.8

Time [s]

System Saturation (−)

System Satruration

cost

Figure 8: Functional model simulation with constant tem-

perature setpoints.

A ﬁrst phase can be observed between 0 s and

1000 s: only the cabin is cooled down while the bat-

tery has not reached the critical temperature yet. Dur-

ing the second phase, the battery is on charge and

needs to evacuate a large thermal power, the system

becomes saturated, the setpoints can not be reached

anymore. Only the battery temperature is degraded

while the cabin temperature remains at the setpoint. It

is because the cabin needs less than 50% of the avail-

able power and gets it as explained above.

4.2 Functional Model Driven by the

Teleological Requirements

The functional model is run once again under the

same conditions introduced in Table 3, exept in this

use-case the temperature setpoints are determined by

the supervisor described in Subsection 3.3 instead of

being constant. Parameters of the supervisor are listed

in Table 4.

The coefﬁcient α determines the degradation of

the battery ideal temperature achievement in regard to

the cabin one. In this simulation, α is set to 1, which

means that both temperatures should be degraded at

the same rate.

The results are presented in Figure 9. As long as

Functional Model-based Resource Management: An Application to the Electric Vehicle Thermal Control

573

Table 4: Supervisor parameters.

Supervisor characteristics Value Unit

Time horizon H 60 s

Time step T

10 s

Weighting parameter α 1 -

Temperature (°C)

Cabine Temperature

Tair Cabin

Tair Cabin SetPoint

Ideal Tair cabin

Temperature (°C)

Battery Temperature

Twater Battery

Twater Bat SetPoint

Ideal Twater Bat

0.2

0.4

0.6

Mass Flow (kg/s))

Coolants Mass Flow

Q Blower

Q Bat Pump

Q FAN

Power (kW)

Components Power

Pcomp

Pcond

Pevapo

Pchill

0 500 1000 1500 2000 2500 3000

0.6

0.8

Time [s]

System Saturation (−)

System Satruration

cost

Figure 9: Functional model simulation with global supervi-

sor control.

the system is not saturated, it has the same behaviour

than previously without global supervisor. During the

saturation phase, between 1200 s and 2400 s, it can

be observed that both cabin and battery temperatures

are degraded at a similar rate. Taking α greater than

1 would lead to a degradation of the battery temper-

ature faster than the cabin temperature, while taking

α smaller than 1 would have the opposite effect. At

1800 s, which is the most critical moment, battery and

cabin temperatures are 2.6

◦

C and 3.2

◦

C above the

setpoint respectively. Moreover, the system saturation

is close to 1 when setpoints are degraded. This means

that the management of the temperatures degradation

rates does not affect the performance of the system,

which still uses 100% of its capacities when needed.

The control strategy can be tested and modiﬁed at this

stage to better meet the constructor requirements.

4.3 Validation on the Multi-physical

Model

The functional model is then adapted and used as a su-

pervisor for the multi-physical model. The functional

model is itself connected to a supervisor computing

the setpoints values as described in Subsection 4.2.

The simulation is run under the same conditions pre-

sented in Table 3 and the results are shown in Figure

10.

The overall behaviour of the system corresponds

to the expectations and the temperature setpoints are

Temperature (°C)

Cabine Temperature

Tair Cabin

Tair Cabin SetPoint

Ideal Tair cabin

Temperature (°C)

Battery Temperature

Twater Battery

Twater Bat SetPoint

Ideal Twater Bat

0.2

0.4

0.6

Mass Flow (kg/s))

Coolants Mass Flow

Q Blower

Q Bat Pump

Q FAN

Power (kW)

Components Power

Pcomp

Pcond

Pevapo

Pchill

0 500 1000 1500 2000 2500 3000

0.6

0.8

Time [s]

System Saturation (−)

System Satruration

cost

Figure 10: Multi-physical model simulation controlled by

adapted functional model, itself monitored by a global su-

pervisor.

achieved when it is possible (i.e. available power is

greater than total power needs). Some observations

can be made about the simulation:

• The system needs about 1000 s to achieve the

cabin temperature setpoint, which corresponds to

experimental observations for similar systems.

• The setpoint overshoots are 0.6

◦

C and 0.7

◦

for the cabin and the battery temperature respec-

tively, which is completely reasonable in this kind

of thermal system.

• At 1200 s, the battery gets charged, a large amount

of thermal energy coming from Joule effect needs

to be dissipated, leading to a singular point on the

battery temperature curve.

• At 1800 s, the battery is disconnected and the

driver starts driving. The mass ﬂow available at

the fan is much bigger and the energy availability

for the consumers as well. The system saturation

gets down to 90 % for about one minute around

1800 s because the refrigerant loop needs to ac-

commodate to the new situation.

5 CONCLUSION

In this work, a methodology for the modeling and

design of a complex system and the development

of its control has been introduced. This methodol-

ogy uses three levels of abstraction that are based

on purposes deﬁnition, energy links and physical

laws respectively. The three levels are interconnected

and exchange information and control parameters be-

tween each other. The teleological level gives a good

overview of the system main missions. It introduces

ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics

574

global criteria and arbitration rules that can be sat-

isﬁed by means of heuristic models or by solving

optimization problems. The functional level enables

to run fast simulations and get approximated results

in the early stages of system design, which provides

a good way to test and validate control strategies.

Also, architecture changes are easy and not much

time-consuming at this level. Lastly, a multi-physical

model well calibrated can provide results close to ex-

perimental data and enables to evaluate a large vari-

ety of scenarios with good accuracy. This method-

ology was applied to a thermal management system

use-case and has provided positive results. A non-

saturation criterion has been introduced in the teleo-

logical level in order to improve the resource manage-

ment with critical conditions.

A ﬁrst perspective of this work is to use this three-

level abstraction modeling to optimize the global en-

ergy consumption of a system. An interesting use-

case could be a whole electric vehicle composed by

the thermal management and the power-train subsys-

tems.

Another objective is the extension of the func-

tional modeling to systems in which energy and mat-

ter ﬂows are coupled. A use-case could be a water

recycling system, in which consumers have both mat-

ter (water) and energy (heat) needs that must be dis-

tributed between matter or energy (or both) sources.

Future work intends to develop and implement op-

timization algorithms directly in the functional model.

Lastly, the teleological level could integrate some

levels of arbitration between several missions of the

system, which would have several operating modes

optimizing different objectives.

REFERENCES

Borutzky, W. (2010). Bond Graph Methodology: Develop-

ment and Analysis of Multidisciplinary Dynamic Sys-

tem Models. Springer-Verlag London.

Brunet, J., Flambard, L., and Yazman, A. (2005). A hard-

ware in the loop (hil) model development and imple-

mentation methodology and support tools for testing

and validating car engine electronic control unit. In

International Conference on Simulation Based Engi-

neering and Studies, TCN CAE, Lecce, Italy.

Ding, P., Wang, Z., Wang, Y., and Li, K. (2020). A dis-

tributed multiple-heat source staged heating method

in an electric vehicle. Renewable Energy, 150:1010–

1018.

Fauvel, C., Claveau, F., and Chevrel, P. (2014). Energy

management in multi-consumers multi-sources sys-

tem : a practical framework. In IFAC World Congress.,

pages 2260–2266, Cape Town, South Africa.

Fiani, P., Boyer, B., Brunet, C., and Bruniquel, G. (2019).

Utilisation de la mod

elisation

energ

etique fonction-

nelle pour la synth

ese thermique des v

ehicules hy-

brides et

electriques. In SIA Simulation num

erique :

La simulation num

erique au sein de l’innovation au-

tomobile., Saint-Quentin en Yvelines, France.

Fiani, P., Chavanne, S., Taleb, L. A., and M

ukc

M. (2016). Mod

elisation pour la conception et

l’

evaluation de syst

emes complexes. Revue Ing

enieurs

de l’automobile, 841.

Gross, O. and Clark, S. (2011). Optimizing electric vehicle

battery life through battery thermal management. SAE

International Journal of Engines.

ukc

u, M., Fiani, P., Chavanne, S., Taleb, L. A., Vlad,

C., and Godoy, E. (2017). Control architecture mod-

eling using functional energetic method: Demonstra-

tion on a hybrid electric vehicle. In 14th Interna-

tional Conference on Informatics in Control, Automa-

tion and Robotics (ICINCO), Madrid, Spain.

ukc

u, M., Fiani, P., Chavanne, S., Taleb, L. A., Vlad,

C., Godoy, E., and Fauvel, C. (2016). A new concept

of functional energetic modelling and simulation. In

The 9th Eurosim Congress on Modelling and Simula-

tion., Oulu, Finland.

Von Bertalanffy, L. (1968). General System Theory. George

Braziller, Inc.

Zhang, K., Li, M., Yang, C., Shao, Z., and Wang, L. (2019).

Exergy analysis of electric vehicle heat pump air con-

ditioning system with battery thermal management

system. Journal of Thermal Science, 29(2):408–422.

Zhang, Z., Wang, J., Feng, X., Chang, L., Chen, Y., and

Wang, X. (2018). The solutions to electric vehicle air

conditioning systems: A review. Renewable and Sus-

tainable Energy Reviews, 91:443–463.

Functional Model-based Resource Management: An Application to the Electric Vehicle Thermal Control

575