thermal management in plug-in hybrid electric vehicles: a ... · (nmpc), thermal management,...

1

Thermal Management in Plug-In Hybrid ElectricVehicles: a Real-Time Nonlinear Model Predictive

Control ImplementationJ. Lopez-Sanz, Carlos Ocampo-Martinez Senior Member, IEEE, Jesus Alvarez-Florez, Manuel

Moreno-Eguilaz, Rafael Ruiz-Mansilla, Julian Kalmus, Manuel Graeber, Gerhard Lux

Abstract—A real-time nonlinear model predictive con-trol (NMPC) for the thermal management (TM) of theelectrical components cooling circuit in a Plug-In Hy-brid Electric Vehicle (PHEV) is presented. The elec-trical components are highly temperature-sensitive andtherefore working out of the ranges recommended bythe manufacturer can lead to their premature aging oreven failure. Consequently, the goals for an accurateand efficient TM are two: to keep the main component,the Li-ion battery, within optimal working temperatures,and to consume the minimum possible electrical energythrough the cooling circuit actuators. This multi-objectiverequirement is formulated as a finite-horizon optimalcontrol problem (OCP) that includes a multi-objectivecost function, several constraints and a prediction modelespecially suitable for optimization. The associated NMPCis performed on real-time by the optimization packageMUSCOD-II and is validated in three different repeatabletest-drives driven with a PHEV. Starting from identicalconditions, each cycle is driven once being the cooling

J. Lopez-Sanz and G. Lux are with Innovation and AlternativeMobility Department, SEAT Technical Center, Autovia A-2, Km.585 Apdo. de Correos 91, 08760 Martorell, Spain, e-mails: [email protected], [email protected]

C. Ocampo-Martinez is with Automatic Control Department, Uni-versitat Politecnica de Catalunya, Institut de Robotica i InformaticaIndustrial (CSIC-UPC), Llorens i Artigas, 4-6, 08028 Barcelona,Spain, e-mail: [email protected]

J. Alvarez-Florez is with the Center for Engines and HeatInstallation Research (CREMIT), Technical University of Cat-alonia, Barcelona Tech., 08028 Barcelona, Spain, e-mail: [email protected]

M. Moreno-Eguilaz is with the Center Innovation Electronics,Motion Control and Industrial Applications (MCIA), Technical Uni-versity of Catalonia, Barcelona Tech., 08028 Barcelona, Spain, e-mail: manuel.moreno. [email protected]

R. Ruiz-Mansilla is with the Green Technologies ResearchGroup (GREENTECH), Technical University of Catalonia, BarcelonaTech.,08028 Barcelona, Spain, e-mail: [email protected]

J. Kalmus works at TLK-Thermo GmbH, Hans-Sommer-Str.5,38106 Braunschweig, Germany, e-mail: [email protected]

M. Graber works at TLK Energy GmbH, Steppenbergweg 30,52074 Aachen, Germany, e-mail: [email protected]

This work was supported by the catalan Government: la Gen-eralitat de Catalunya. Corresponding author: Jorge Lopez-Sanz [email protected]

Manuscript received XXX; revised XXX.

circuit controlled with NMPC and once with a conventionalapproach based on a finite-state machine. Compared to theconventional strategy, the NMPC proposed here results ina more accurate and healthier temperature performance,and at the same time, leads to reductions in the electricalconsumption up to 8%.

Index Terms—nonlinear model predictive control(NMPC), thermal management, plug-in hybrid electricvehicles (PHEV), Li-ion battery cooling.

I. INTRODUCTION

IN electrified vehicles, an accurate TM of the electrictraction components is crucial to avoid premature

costly repairs and ensure safety and performance require-ments [1]. Among them, the Li-ion battery package isthe most critical due to its cost and its direct relation tothe vehicle autonomy, which is definitely the electro-mobility market penetration bottleneck. Accurate TMsolutions for Li-ion batteries are based usually on liquidcooling systems with complex pipes configurations thatallow several options for heat dissipation. To controlthese circuits, multiple electrical actuators are needed.Since a misuse of electrical actuators contributes to afurther decrease in vehicle autonomy, optimal controlmethods become quite attractive for accurate and effi-cient TM. Compared to the classical approach of usingtuned Proportional-Integral-Derivative (PID) controllersaccording to a set of rules learned from experience,optimization-based methods such as NMPC exploit theirpotential in systems with, among others,

• multiple inputs multiple outputs (MIMO),• several goals that can be contradictory,• numerous constraints to be fulfilled.Although the many advantages, there are also some

challenges for NMPC to spread in the automotive sector.The computational burden is one of them. A proof of thisfact is the large number of existing offline applications inliterature compared to the online category. Moreover, itis common that real-time capable NMPC applications are

2

not validated directly in the real vehicle, but in a simplercontext. This is the case of [2], where NMPC for adaptivecruise control is tested in a Hardware in the Loop(HIL) configuration on a dynamic engine test bench or[3], where an NMPC application for optimal trajectorygeneration in Long Heavy Vehicles Combinations thatvalidated the controller in a motion simulator. In [4], thereal-time NMPC strategy for an hybrid electric vehicle(HEV) power management is validated in simulationsand the same is done in [5] to show the potential ofNMPC for HEV fuel and emissions minimization. Thevalidation through simulation/test bench environments inall these examples and many more is a necessary firststep for every real-time application.

The purpose of this article is to use NMPC for theTM of the Li-ion battery (BAT) and the power elec-tronics (PE) in a PHEV prototype. The validation of thefeedback control designed by using the optimization toolMUSCOD-II [6] is done by means of a comparison toa finite-state machine control. The novelty of this paperis that the optimizer runs on an Intel R©CoreTM i5-3320MProcessor with the two cores operating at 2.6 GHz andwith 8 GB of RAM on real-time and overtakes the TMcontrol by means of an electronic control unit (ECU)bypass performed on a rapid prototyping (RP) module.This NMPC implementation corresponds to a new stepin the NMPC standardization road map suggested in Fig.1, where the final goal is to have the algorithm runningembedded in the vehicle. In this sense, [7] points FPGAor multicore microprocessors as the suitable platforms toexploit parallelization of the NMPC controller design.

Offline NMPCOnline NMPC

Simulations

Online NMPC HIL

Online NMPC RP

embedded

Online NMPC

embeddedFPGA?

SIMULATION VEHICLE

Fig. 1: NMPC roadmap in the automotive sector.

The remainder of this paper is structured as follows.Section II presents a brief description of the controlplant. Section III gives an overview of the model, moreextensively treated in [8], and defines the goals andconstraints of the control problem. Section IV dealswith the numerical solution of the NMPC problem. InSection V, the hardware implementation in the vehicle ispresented and Section VI describes the driving scenariosin which validation took place. Finally, Section VIIshows the results and the conclusions and final remarksare drawn in Section VIII.

Fig. 2: The studied cooling circuit.

II. PROBLEM STATEMENT

The cooling circuit to be controlled by NMPC canbe seen in Fig. 2. The purpose of the circuit is to keepthe BAT, PE and charger modules in the temperatureregions that assure safety, suitable operation and reduceageing caused by thermal stress. With this circuit, theheat generated in the electrical components due to theJoule Effect can be dissipated to the air or to the AirConditioning (AC) circuit. Notice that:

• Only the driving situation is treated here, not thecharging one. For this reason, the charger representsonly a passive thermal mass in the circuit.

• The coolant is a water/glycol mixture and its pos-sible paths are shown in the blue and black contin-uous lines in Fig. 2.

• The heat transfer with the air is done by means ofa coolant/air heat exchanger, the cooler in Fig. 2.

• The heat transfer to the AC-circuit is done by acoolant/refrigerant heat-exchanger parallel to theevaporator called chiller in Fig. 2.

The heat transfer can be controlled through thecoolant flow by six electrical actuators: two pumps, threesolenoid valves and one fan, all in gray in Fig. 2. Thecontrol signals for these actuators are from the right topclockwise:

• V alveCOOLER: Enables/disables the coolant flowthrough the cooler. Here, “0”: the valve allows thecooler path; “1”: stands for the bypass.

• PWMFAN : The fan increases the air mass flow ratein front of the cooler and thus the heat exchange.It is controlled by a pulse width modulated (PWM)signal.

3

• PWMPE : The electrical pump before the PE isalso governed by a PWM signal.

• V alveCHILLER: Enables/disables the coolant flowthrough the chiller. The value “1” is for chilleractive, “0” stands for chiller inactive.

• V alveCIRCUIT : Enables switching betweenbig/small circuit configurations. If V alveCIRCUIT

is set to “1”, the big circuit configuration isactive and the coolant flows through the charger,the cooler, the chiller, the BAT and the PE,consecutively. On the contrary, if V alveCIRCUIT

is set to “0”, the coolant flows through twoseparate circuits: the BAT-chiller circuit and thecharger-cooler-PE circuit. Consequently, in thismode, the heat transfer between the BAT-chillerand the PE-charger-cooler is disabled. Notice thatto propel the coolant in two different separatedcircuits, two electric pumps are required.

• PWMBAT : The electrical pump in front of thechiller is also governed by a PWM signal.

As previously said, the high number of electricalactuators offers an accurate TM but also supposes a chal-lenge in efficiency: to spend as less electrical energy aspossible. With the control strategy discussed in SectionIII, the aim is to formulate and solve this problem.

III. MODELING AND OPTIMAL CONTROL PROBLEM

FORMULATION

The development of a system model is a crucial stepfor the NMPC strategy since it provides the predictiveability. The model of the cooling circuit in Fig. 2 is asystem of ordinary differential equations (ODE) of theform x(t) = f(x(t), u(t), p), where x ∈ Rnx representsthe states of the plant, u ∈ Rnu stands for the controlinputs and p ∈ Rnp for the time-invariant parameters. Itis important to highlight that all the states x are availablefrom sensors equipped in the real vehicle.

Given the complexity and length of the mathematicalmodel of the considered system, the reader can find itsmain lines in [8], as well as the interaction of the vari-ables and constitutive elements of the resultant model.The model has been written in the software Dymola [9],which is based on the object-oriented language Modelica[10] and is a combination of physical equations andmeasurements stored in look-up tables that describe thecooling circuit behavior in multiple domains.

The physical equations of the model come mainlyfrom energy balances. In the thermal domain, for in-stance, at each electric component the first thermody-namic law, (1), is applied to describe how the heat flowinduced by the Joule effect Qinduced is dissipated in

10 0 10 20 30 40 50 600

50

100

150

200

250

300

Costc T

DangerousBadNormal

GoodOptimal

200 400 600 800 1000 1200 1400LV Power in W

0.0

0.5

1.0

1.5

2.0

2.5

Costc P

BAT Temperature in degC

Fig. 3: Cost terms included in the objective function toevaluate accuracy and efficiency of the TM.

the coolant Qcoolant, the ambient air Qambient and thecomponent itself, that is,

dU(t)

dt= Qinduced(t)− Qambient(t)− Qcoolant(t).

The model consists of around 500 equations and 1300variables that arise from the equations explicitly de-scribed inside the different submodels and the automaticgenerated connection equations. With the help of themodel-export methodology described in [11], it is quitestraightforward and error-free to pass the high numberof equations to the MUSCOD-II. To get an overview ofthe system states contained in the dynamic model, (1)corresponds with a condensed form of the model, wherethe relation between variables used here and controlinputs are found in [8].

Furthermore, to measure the performance of the sys-tem, a so called objective or cost function was devel-oped. This cost function is an indirect measurement ofthe system performance. To this end, the performanceindices of Fig. 3 are used to evaluate the TM in termsof accuracy and efficiency. The cost term cT (on the leftof Fig. 3) describes, with the following polynomial, theeffect of the working temperature on the battery, so thatthe further from the optimal range, the more promotedthe aging mechanisms, i.e.,

cT (T ) = a4 T4 − a3 T

3 + a2 T2 − a1 T + a0,

where a0, a1...a4 are the corresponding parameters re-sultant from the curve fitting. The penalty term cP (onthe right of Fig. 3) is the linear function cP (P ) = P−b0

b1,

which depends on the electrical power P of the actua-tors and where again b0, b1 are calibration parameters.Besides, cP indicates that the more electrical power isused for the TM, the less attractive it is. Table I showsthe electrical actuators used according to their requestedamount of electric power.

4

x(t)

dTinPE−PUMP

dtdTinBAT−PUMP

dtdToutJUNCTION

dtdToutCHILLER

dtdToutCHARGER

dtdToutPE

dtdEBAT

dtdToutBAT

dtdToutCOOLER

dtdvdtdMdtdndt

dTambient

dt

=

f(x(t),u(t),p)

mMIDDLE TMIDDLE+mBIG TBIG+minPE−PUMPTinPE−PUMP

mV ALV EmLOOP TLOOP +mSMALL TSMALL+minBAT−PUMP

TinBAT−PUMP

mV ALV EmoutCOOLER

ToutCOOLER+mBY PASS TBY PASS+moutJUNCTION

ToutJUNCTION

mV ALV E

Qthm

mCHILLER cpCHILLER

Qthm

mCHARGER cpCHARGER

Qthm

mPE cpPE

PHV + PlossBAT

Qthm

mBAT cpBAT

Qthm

mCOOLER cpCOOLER

0000

(1)

The total cost associated to the TM is given by c,which is the sum of the two penalty terms in Fig. 3, i.e.,c = cT + cP . Besides the model and objective function,the physical constraints definition is an important step inthe control problem formulation. Hence, the saturationlimits of the control signals, middle column in TableI, were defined as minimal and maximal constraints.Nevertheless, for PWM input signals of the pumps, morerestrictive minimal constraints were used, i.e.,

umin[1630

]≤

u[PWMBAT

PWMPE

]. (2)

With these restrictive constraints it is assured that aminimal coolant amount flows through the componentsto protect them from a sudden change in temperature.Similarly to the control signals, the constraints for thesystem states are defined as follows:

xmin

−10 ◦C−10 ◦C−10 ◦C−10 ◦C−10 ◦C−10 ◦C1 kWh−10 ◦C−10 ◦C−10 km/h−500 Nm−104 rpms−10 ◦C

≤

x

TinPE−PUMP

TinBAT−PUMP

ToutJUNCTION

ToutCHILLER

ToutCHARGER

ToutPE

EBAT

ToutBAT

ToutCOOLER

vMn

Tambient

≤

xmax

65 ◦C65 ◦C65 ◦C65 ◦C65 ◦C65 ◦C8 kWh65 ◦C65 ◦C

200 km/h500 Nm104 rpms

65 ◦C

, (3)

TABLE I: Actuators electrical power

Actuator Control Signal Electricalpower

Cooler valve V alveCOOLER ∈ {0, 1} lowFan PWMFAN ∈ [10, 90] highBAT pump PWMBAT ∈ [0, 100] mediumChiller valve V alveCHILLER ∈ {0, 1} lowCompressor V alveCHILLER ∈ {0, 1} highCircuit valve V alveCIRCUIT ∈ {0, 1} lowPE pump PWMPE ∈ [0, 100] medium

where it must be highlighted that the maximal workingtemperature for the coolant in this circuit is 65◦C. Hence,the open-loop optimal control problem (OCP) associatedto the cooling circuit is formulated as follows:

minx∗(·),u∗(·)

∫ t0+Hp

t0

(cT + cP )dt (4a)

subject to

x(t) = f(x(t), u(t), p) ∀t ∈ τ (4b)

xmin ≤ x ≤ xmax ∀t ∈ τ (4c)

umin ≤ u ≤ umax ∀t ∈ τ (4d)

0 = x(t0)− x0. (4e)

Given an initial value of the states, x0, at time t0, thegoal of the strategy is to find the optimal sequence ofcontrol inputs and states, u∗(·), x∗(·), that minimizes theobjective function in (4a), and satisfy the constraints in(9b-9e), for a given prediction horizon of length Hp.

5

Coolingcircuit x0 u⇤

objectives &constraints

Model Optimizer

PlantOCP

Fig. 4: Optimal control problem outline

NMPC Controller:

OCP1

Control plant:

Coolingcircuit

u

x

OCP2

OCPM

Algorithm

Fig. 5: Control scheme of NMPC

IV. NUMERICAL SOLUTION OF THE NMPC PROBLEM

To attend model-plant mismatches and overcome pos-sible disturbances, the open-loop scheme in Fig. 4 mustbe closed resulting in the NMPC scheme in Fig. 5.The main idea behind NMPC is to formulate and solverepetitively a new OCP at each time instant accordingto the receding horizon strategy. At a certain instant k,the measurement of the plant x is used to initialize theODE with x(t0) = x used in the constraint (4e) and theOCP is solved to find the optimal control sequence u∗ forthe given prediction horizon. From the solution sequenceu∗, only the first element is applied to the systemand the whole procedure is repeated for the next timeinstant k + 1 with new sensors measurements comingas the closed-loop system feedback, thus receding theprediction horizon.

There exist several numerical methods for solving anOCP, as reported in [12]. The optimization tool used inthis research, MUSCOD-II, relies on efficient and robustDMS algorithm [13] that reformulates the OCP as a non-linear programming (NLP) problem that is then solvedby an iterative solution procedure, a specially tailoredSequential Quadratic Programming (SQP) algorithm [6].Notice that the discretization of the continuous optimalcontrol problem is done inside MUSCOD-II.

Finally, it must be added that MUSCOD-II relieson the so called Real-Time Iteration (RTI) scheme forachieving robust online performance. The main ideaof this algorithm is to exploit the similarity betweensubsequent OCP for performing the SQP steps in adifferent order as accustomed, prioritizing this way a

PC

RapidPrototyping

module

CANlog

ECU1

CoolingCircuit

ECU2

A/CCircuit

CAN buses

Interface

NMPC Vehicle

(USB)

(Ethernet)

u', x

(CAN)

chiller control(CAN)

original chiller control

chiller control(CAN)

x(CAN)

(CAN)

x(CAN)

u'(CAN)

(physical)

(physical)

u': pumps, valves and fan control signals

CAN card

Fig. 6: Hardware implementation for the cooling circuitcontrol manipulation.

fast response time to disturbances. For more informationabout the RTI scheme, the reader is referred to [14].It must be added that the state of the plant, availablefrom several CAN buses, was sampled every 10 ms.Nevertheless, the communication between the vehicleand MUSCOD-II was asynchronous, being states andcontrols exchanged as soon as MUSCOD-II performeda new step with the RTI scheme. Using a predictionhorizon of 200 seconds and two shooting points, themaximal measured response time of MUSCOD-II was2.5 s, which is quite acceptable amount in this case.

V. HARDWARE IMPLEMENTATION

The PHEV used in this research is a prototype ofa Golf GTE equipped with extra sensors placed in thecooling circuit to read all relevant information. In total,17 thermocouples of type K with accuracy of ±1◦Cwere used to measure 15 coolant temperatures, the airtemperature in front of the cooler and the air temperatureon the roof of the vehicle. In addition, three turbine flowmeters with a linearity of 0.1% were used to measurethe coolant volume flow rate. With the aim of beingable to compare the standard control with the NMPCin successive driving tests, the design in Fig. 6 wasimplemented. With this implementation, it can be switchbetween two operation modes as explained next.

A. NMPC Mode

MUSCOD-II runs in the Laptop held by the co-pilot,being connected to a rapid prototyping (RP) modulethrough an Ethernet connection. The control signals aresent by means of the Universal Serial Bus (USB) con-nected Controller Area Network (CAN) card to the RPmodule. The electronic control unit (ECU1) is equippedwith an emulator test probe (ETK) that allows that thecontrol signals arriving to the ECU1 via the RP ETK

6

connection, are taken instead of the original code in theECU1 software. This way the original physical electricconnections to the actuators in the cooling circuit canbe kept. Furthermore, the states of the controlled plant,output signals of the temperature sensors installed in thecooling circuit and other signals running in the CANbuses of the vehicle are sent to MUSCOD-II throughthe RP module.

Since the chiller valve is physically stimulated fromanother ECU (ECU2) that is not equipped with ETK, aCAN logger is needed (top right corner of Fig. 6). TheCAN logger performs a gateway that splits the CAN buscontaining the original command for this valve. This waythe V alveCHILLER calculated in MUSCOD-II can beused instead of the original vehicle demand.

B. Standard Mode

The RP deactivates the bypass of ECU1 and the CANlogger sends the signal arriving from the original CANbus to the ECU2. In this mode, the original controlsignals of the vehicles for the cooling circuit and ACcircuit are taken. These control signals are set to constantvalues output by a finite-state machine with four possiblestates: heating, temperature maintaining, mild coolingand maximal cooling. The conditions for changing fromone state to another depend on the current BAT temper-ature and some sensors describing the availability of theheat exchangers to dissipate the heat.

VI. DRIVING SCENARIOS

A requirement for testing the TM of electric compo-nents is to choose a driving cycle in which significantthermal load is generated. This can be achieved witha heavy load cycle driven in the pure electric modesince the heat generated in the components is causedby the Joule Effect. To design a driving cycle with aheavy mechanical demand, three different scenarios werechosen to be performed on an open-accessible street withlow traffic density:

• Long cycle mild: A long trip of 39 km in a roadwith considerable slope in mild climate conditions.

• Long cycle hot: The same cycle in hot climateconditions.

• Constant cycle: A trip at 100 km/h constant speedin a 21 km road also with considerable slope.

A key aspect of these cycles is the effort put in thedesign to make them as repeatable as possible. Quitehelpful for this task is the adaptive cruise control (ACC)that is available in the car. Other cars are obstaclesin the road that prevent the vehicle from following

the repeatable cycle forcing the driver to accelerate orbreak abruptly and therefore they can be considered asexternal disturbances. Due to the usage of the ACC,these disturbances are held to a minimum since the ACCaccelerates and decelerates smoothly, in contrast to thedriver natural reaction, thus generates minimal extra loadto the battery. Additionally to achieve always a similarelectrical power demand to the BAT, all the tests weredriven with the car being under the same conditions.Auxiliary consumers like heating, air conditioning andventilation (HVAC) were turned off, as well as lights,radio and other electrical gadgets. Windows were openedto the same level and the weight of the car was held thesame.

To assure similar initial conditions, it is specially cru-cial to monitor the BAT temperature before driving, sinceas it takes direct influence on the objective function,small discrepancies in it will lead to non comparableconditions for the two cycles. Thus, the car is alwaysfully charged the day before in order to assure that alltemperatures in the car were close to the ambient tem-perature and not disturbed by any heat source and thatthe BAT draws always from with the same energy level.This way, once enough similar conditions are observed,ambient, battery temperatures and traffic congestion, acomparable driving cycle can be assured and the testcan start. As it will be seen in the Section VII, this testprocedure enabled enough repeatable driving cycles tocompare the results of performing a different control inthe cooling circuit.

VII. RESULTS

Experimental results from the three different cycleswill be discussed in the following subsections. They arealso summarized in Table II, where the consumption, E,cost terms, cT and cP and total cost, c, are compared forthe two operation modes, NMPC and standard, describedin Section V. Notice that in Table II a negative valuerepresents a decrease of the cost comparing NMPC tothe standard strategy.

A. Long cycle mild

As it can be seen in the top plot in Fig. 7, where theleft y-axis shows the vehicle speed and the right one thealtitude of the road, the long cycle consists of a highwayroad section, in blue, followed by a mountain that isascended to the top, in red, discharging the battery andthen descended to the bottom, in white, charging thebattery again.

The aim of this driving cycle is to keep the BATworking and thus generating heat as much time as

7

TABLE II: NMPC vs standard results in TM for three different driving cycles.

Cycle ∆E* in kWh ∆EE0

** in % ∆cTcT0

in % ∆cPcP0

in % ∆cc0

in %

Long cycle mild -0.015 -6.25 -8.1 -20.71 -9.95Long cycle hot -0.027 -8.14 -54.26 -17.12 -50.04Constant cycle 0.003 3.49 -8.2 5.09 -7.78

* ∆x stands for the measured difference in the value “x”: xNMPC − xStandard.** x0 stands for the measured value “x” in the Standard cycle: xStandard.

020406080

v i

n k

m/h

0

200

400

h i

n m

20

25

30

35

T i

n

C

DangerousBadNormalGoodOptimal

0 10 20 30distance in km

0.0

0.1

0.2

0.3

E i

n k

Wh

NMPC Standard

Highway

up down

A B C D E FG

4 km faster heating

slower slope

≈ 6% consumption reduction

Fig. 7: NMPC vs standard TM results in terms oftemperature accuracy and electrical consumption of the

actu in the long cycle mild.

possible under heavy conditions. To achieve this, in theslope road section several strategic turning points werepredefined. This way, the vehicle faces the slope forthe first time at A and drives till the highest point Bis reached, where the vehicle turns over and starts thedescent to the initial kilometric point A, now named Cin Fig. 7. Again, the vehicle turns over and drives tothe next turning point, D, lower than B and so on till,after the last turn over in G, the BAT is fully dischargedand the pure electric mode is no longer available. Thesmall variations in the speed profile during NMPC (bluesolid line) and standard control (black solid line) allow toassume that the results discussed draw from comparableconditions.

In the middle and bottom plots in Fig. 7, the TMresulting from the NMPC and standard strategies ina mild thermal scenario, ambient temperatures around14◦C and initial BAT temperature 22◦C, can be com-pared. Concerning the goal of keeping the battery withinoptimal temperatures, it can be seen in the middle plotthat NMPC reaches the optimal range about 4 km fasterthan the standard control strategy. Once inside this range,the slope decreases to maintain the BAT at this level.Moreover, the second goal, the electric consumptionshown in the plot on the bottom, is reduced by 6%. The

01234

cT

0.00.10.20.30.4

cP0 10 20 30

distance in km

01234

c

NMPC Standard

1 2 3

Fig. 8: NMPC vs standard objective function costs.


0.0

0.5

1.0

Co

ole

r valv

e


0.0

0.5

1.0

Cir

cuit

valv

e


0.0

0.5

1.0

Ch

ille

r valv

e0 10 20 30

distance in km

0

50

100

PW

M f

an

%


0

50

100

PW

M P

E i

n %

NMPC Standard


0

50

100

PW

M B

AT i

n %

Fig. 9: NMPC vs standard control strategies in the longcycle mild.

NMPC success in multiple objective achievements canbe seen in detail in Fig. 8.

Focusing on the temperature and consumption relatedcosts of NMPC, blue line in the top and middle plot inFig. 8, respectively, three differentiated strategic phasesfor the control can be derived: 1) Battery heating phase(blue area in Fig. 8) in which the main goal is to bringthe battery temperature to the optimum as it is shown inthe top plot with the faster decrease of the temperaturecost in NMPC inside the blue area. The prize to pay is aslightly higher electrical consumption as represented inthe middle plot, 2) Energy saving phase (yellow area inFig. 8) where the priority is to minimize the actuators

8

0 5 10 15 20 25 30 35distance in km

10

15

20

25

30

35T i

n

C

PE Temperature NMPCBAT Temperature NMPC

Ambient Temperature NMPCPE Temperature Standard

BAT Temperature StandardAmbient Temperature Standard

Optimal Temperature

Fig. 10: NMPC vs standard components and ambienttemperatures in the long cycle mild.

electrical consumption as it can be seen clearly in theyellow area of the middle plot and 3) Battery coolingphase (red area in Fig. 8) in which the temperaturecosts, this time associated to higher temperatures thanthe optimal, are again high enough to invest resources.Inside the different described phases, the control inputsfrom the NMPC strategy show a tendency as it can beseen in Fig. 9. For heating the BAT, the cooler valveis bypassed and the circuit valve enables the big circuitmode that couples the BAT and the PE. As Fig. 10 shows,this is a clever way to heat the BAT since compared toit, the PE has a higher temperature and the air flowingthrough the cooler a lower one.

Once the optimal temperature is achieved, as shownin Fig. 10, the cooler is activated as well as the twocircuit mode. The BAT is decoupled from the PE atthis moment, because the PE is warmer and the BATis already at its optimal temperature. The reason for thecooler activation is to dissipate to the air the heat thatis being generated in the PE module due to the roadslope. This way, the constraint of not exceeding 65◦C inthis module is achieved. It must also be said that, in thisphase (yellow area), the battery pump is brought down toits minimum in order to save energy. As soon as the BATtemperature starts deviating from the optimal one, about3◦C, the circuit valve enables and disables the couplingto the PE circuit intermittently.

B. Long cycle hot

The same cycle was driven under hotter conditionshaving been the vehicle parked outdoors, exposed to di-rect sunlight: average ambient temperature around 20◦Cand initial BAT temperature 31-31.5◦C. Again, despitesome punctual speed discrepancies due to different trafficsituations, the cycles in Fig. 11 are enough similar to becompared.

020406080

v in

km

/h

0

200

400

h i

n m

30323436

T in

C



0.00.10.20.30.4

E in

kW

h

NMPC Standard

≈ 8% consumption reduction

Fig. 11: NMPC vs standard TM results in terms oftemperature accuracy and electrical consumption.

02468

cT0.0

0.5

1.0

1.5

cP


02468

c

NMPC Standard

Fig. 12: NMPC vs standard objective function costs inthe long cycle hot.

As it can be seen in Table II, in this cycle thereis even more potential than in the mild climate case.The consumption is reduced this time by 8% while thetemperature trajectory is more accurate, temperaturescloser to the optimal range, than with the standardcontrol. The combination of these two goals leads to anumerical improvement of 50% in the objective function.In general, it can be said that the more cooling requiringthe situation is, the more potential NMPC has. Thisis due to the fact that the studied cooling circuit hasseveral heat sinks for actively cooling the componentsbut no heat sources for heating the battery. That meansthat under cold conditions, the only possibility is to takeadvantage from the different inertias of the componentsin the system while under hot conditions, the manycooling alternatives lead to completely different results.

The blue and black areas in Fig. 12 show the inter-vals in which most cooling resources are invested forNMPC and standard control strategies, respectively. Asit can be seen, NMPC starts investing in keeping theBAT temperature closer to the optimal sooner than thestandard control strategy. Fig. 13 illustrates the different

9


0.0

0.5

1.0

Co

ole

r valv

e


0.0

0.5

1.0

Cir

cuit

valv

e


0.0

0.5

1.0

Ch

ille

r valv

e


0

50

100

PW

M f

an

%


0

50

100

PW

M P

E i

n %

NMPC Standard


0

50

100

PW

M B

AT i

n %

Fig. 13: NMPC vs standard control strategies in thelong cycle hot.

use of the cooling resources of both strategies.

0 5 10 15 20 25 30 35distance in km

10

15

20

25

30

35

40

T i

n

C




Fig. 14: NMPC vs standard components and ambienttemperatures in the long cycle hot.

While NMPC invests in the chiller and moderatelyin the pumps in an intermittent way to cool down theBAT temperature, the standard control strategy showstwo clearly differentiated working points: previous to theblack region, it only uses the PE pump and the coolervalve to cool down the PE and inside the black region, assoon as the BAT temperature is too far from the optimumit uses the pumps at full and the fan at medium power.

In Fig. 14 the BAT, PE and ambient temperaturesfor both cycles are compared. Although the ambienttemperature at the end of the cycle, last 25 km, is lowerin the standard cycle, the NMPC strategy achieves amore accurate regulation of the BAT temperature. Noticealso that both PE curves are far away from the criticaltemperature of 65◦C for the component, imposed in theNMPC case by means of a constraint.

C. Constant cycle

The constant driving cycle consists of the entrance tothe highway, first 4 km in Fig. 15, and then the drive on

t

0

50

100

v i

n k

m/h

0200400600800

h i

n m

10

20

30

40

T i

n

C


0 5 10 15 20distance in km

0.000.020.040.060.08

E i

n k

Wh

NMPC Standard

Other vehicle disturbance

≈ 3.5% consumption increase

Fig. 15: NMPC vs standard TM results in terms oftemperature accuracy and electrical consumption of the

actuators in the constant cycle.

the highway at constant speed of 100 km/h. The highwayroad has a considerable slope that, together with the highspeed, leads to the full discharge of the BAT in the 17minutes duration of the whole cycle. Again, the TM withthe NMPC presents a decrease in the global cost functionc of Table II compared to the standard control. Although,the electrical consumption of the actuators is increasedby 3.5%, as it can be seen in Fig. 15, the faster heatingof the BAT to the optimal temperature compensates thisloss.

One of the main reasons for these results being lessattractive than in the other driving cycles is that this onestarts at colder temperatures, the initial BAT temperatureis 14◦C, and thus the potential of the system is reduced.The cooling circuit has several options for cooling theBAT, the cooler and chiller, but for generating heat it canonly wait to use the heat generated in the PE, which hasa lower thermal mass.

As shown in Fig. 16 and in contrast to the costs withinthe long cycle in Fig. 8, here NMPC follows nearly allthe cycle long the same strategy, to reduce the penaltyterm cT . Only at the end, after 20 km, it starts to playwith the chiller valve as shows the red arrow in Fig. 16.

It must be added that the fact that this cycle is drivenat constant speed, places the standard strategy in anadvantageous situation, since finite-state machines areusually defined with several static points at which controlexperience is available. Therefore, the less transient andthe more common the driving conditions are, the moreaccurate is this method. In this case, the standard finite-state machine shows two fixed operation points as it canbe seen with the black solid lines in Fig. 17.

Moreover, it must be added that the last 5 km of thiscycle are not as comparable as desired, since as it isshown in Fig. 18 the ambient temperature in the NMPCcase is around 3◦C above the standard control case.

10

0

5

10cT

0.0

0.5

1.0

cP


051015

c

NMPC Standard

chiller active

Fig. 16: NMPC vs standard objective function costs inthe constant cycle.


0.0

0.5

1.0

Co

ole

r valv

e


0.0

0.5

1.0

Cir

cuit

valv

e


0.0

0.5

1.0

Ch

ille

r valv

e


0

50

100

PW

M f

an

%


0

50

100

PW

M P

E i

n %

NMPC Standard


0

50

100

PW

M B

AT i

n %

chiller active

Fig. 17: NMPC vs standard control strategies in theconstant cycle.

This fact could be an extra disadvantage for the NMPCsince this happened when the BAT was already close tothe optimal temperature and hence the cooling potentialthrough the air is less. Furthermore, the presence of sometraffic before ending the cycle, as it can be seen in Fig.15, leads to a more abrupt deceleration and thus to ahigher heat generation in NMPC, being this a furtherdisadvantage at temperatures close to the optimal, as itis the case.

All in all, it can be said that even in an scenariowhere the standard control strategy can show its majorperformance, the NMPC still achieves a more accurateTM. It must be also said that the fact that one goal, theelectrical consumption, becomes worse in favor of theother goal, temperature regulation, is a mere strategicmatter. One of the advantages of the proposed NMPCstrategy is that terms in the objective function, cT andcP , can be changed or modified to achieve other results.Compared to a PID tuning method, this calibration issimpler since the parameters adjusted have a physicalmeaning whose effect on the goals can be reproducedand observed with a limited number of experiments or


10

15

20

25

30

35

T i

n

C




Difference in ambient temperature ≈ 3 C

Fig. 18: NMPC vs standard components and ambienttemperatures in the constant cycle.

simulations.

VIII. CONCLUSIONS

In this paper, a real-time NMPC for the Li-ion batteryand power electronics cooling circuit in a PHEV proto-type has been validated with three different repeatabledriving cycles performed on the road. In all studiedcases, NMPC has shown a significant decrease, from 7%up to 50%, in the total costs associated to an accurateand efficient TM when compared to a standard controlstrategy based on a finite-state machine.

Analyzing the results according to the two objectivesseparately, it can be said that the temperature cost wasreduced in the three studied cases while the electricalconsumption was reduced, between 6 and 8 %, onlyin the long cycle tests. In the constant cycle it wasincreased by 3.5%. Although the overall cost for thiscycle is already satisfactory, if additionally both goalsshould be improved at the same time, it would be quitestraightforward to achieve adjusting the cost functions.This is a further advantage in comparison with a PIDtuning process where the effect of the P, I and D gainson the several goals are not so intuitively and directlyattributable to them.

This may seem paradoxical, but there are two reasonsfor the constant cycle presenting the most moderate im-provement of the three cycles. On the one hand, the coldtemperatures in this cycle reduce considerably the poten-tial of the control strategy because the studied coolingcircuit cannot generate any other heat than the inducedby the Joule Effect. On the contrary, in a hot scenarioas in the long cycles studied, the heat dissipation can bedone to the ambient air or to the A/C circuit through theseveral actuators, thus leading to many control optionsfor cooling the components. Therefore, it can be saidthat under complex situations with many control options

11

NMPC methods show the highest potential. On the otherhand, the untapped potential of the standard strategy isreduced in a quite steady cycle such as the constant cycle,because finite-state machine are usually designed usingmeasured data at several stationary points. Nevertheless,it was shown that even in this situation, the NMPC is ableto grasp part of the untapped potential of the standardstrategy.

Finally, it must be concluded that the OCP formulated,by means of a simple and accurate model, and the DMSand RTI algorithm implemented in MUSCOD-II, haveled to an NMPC control strategy that has shown a stableand real-time capable performance. Future works will befocused on the improvement through the use of a drivingcycle prediction and the mixed-integer optimal controlproblem (MIOCP) formulation and solution.

REFERENCES

[1] A. A. Pesaran, “Battery Thermal Management in EVs andHEVs : Issues and Solutions,” in Advanced Automotive BatteryConference, Las Vegas, Nevada, 2001.

[2] R. Schmied, H. Waschl, R. Quirynen, and M. Diehl, “NonlinearMPC for Emission Efficient Cooperative Adaptive Cruise Con-trol,” in 5th IFAC Conference on Nonlinear Model PredictiveControl, 2015.

[3] N. V. Duijkeren, T. Keviczky, and P. Nilsson, “Real-TimeNMPC for Semi-Automated Highway Driving of Long HeavyVehicle Combinations,” in 5th IFAC Conference on NonlinearModel Predictive Control, 2015.

[4] Z. Jiangyan, S. Tielong, S. Takanobu, and K. Masaaki, “Non-linear MPC-Based Power Management Strategy for Plug-inParallel Hybrid Electrical Vehicles,” in Proceedings of the 33rdChinese Control Conference, 2014.

[5] J. Zhao and J. Wang, “Integrated model predictive control ofhybrid electric vehicles coupled with after treatment systems,”IEEE Transactions on Vehicular Technology, vol. 65, no. 3, pp.1199–1211, 2016.

[6] C. Hoffmann, L. Wirsching, M. Diehl, D. B. Leineweber,A. A. S. Sch, H. G. Bock, and J. P. Schl, “MUSCOD-II usermanual,” Heidelberg, 2010.

[7] H. Chen, S. Yu, X. Lu, F. Xu, T. Qu, and F. Wang, “ApplyingModel Predictive Control in Automotive,” in Proceedings of the10th World Congress on Intelligent Control and Automation,2012.

[8] J. L. Sanz, C. Ocampo-Martinez, J. Alvarez-Florez, M. M.Eguilaz, R. Ruiz-Mansilla, J. Kalmus, M. Graber, and G. Lux,“Nonlinear Model Predictive Control for Thermal Managementin Plug-in Hybrid Electric Vehicles,” IEEE Transactions onVehicular Technology, vol. PP, no. 99, p. 1, 2016.

[9] D. AB, “Dymola Users Manual Version 5.3a,” Lund, Sweden,2004. [Online]. Available: http://www.dynasim.com

[10] M. Association, “Modelica - A Unified Object-OrientedLanguage for Physical Systems Modeling LanguageSpecification,” Modelica Association, Tech. Rep., 2010.[Online]. Available: http://www.modelica.org

[11] M. Graber, C. Kirches, D. Scharff, and W. Tegethoff, “UsingFunctional Mock-up Units for Nonlinear Model PredictiveControl,” in Proceedings of the 9th International ModelicaConference, Munich, 2012.

[12] M. Diehl, H. J. Ferreau, and N. Haverbeke, “Efficient NumericalMethods for Nonlinear MPC and Moving Horizon Estimation,”in Nonlinear Model Predictive Control, L. et al Magni, Ed.Springer, 2009, pp. 391–417.

[13] H. G. Bock and K. J. Plitt, “A multiple shooting algorithm fordirect solution of optimal control problems,” in Proceedings 9thIFAC World Congress Budapest, vol. XLII, 1984, pp. 243–247.

[14] M. Diehl, H. G. Bock, J. P. Schlo, R. Findeisen, Z. Nagy,and F. Allgo, “Real-time optimization and nonlinear model pre-dictive control of processes governed by differential-algebraicequations,” Journal of Process Control, vol. 12, pp. 577–585,2002.

thermal management in plug-in hybrid electric vehicles: a ... · (nmpc), thermal management,...

Documents