DC Charging of Heavy Commercial Plug-in Hybrid Electric Vehicles

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Institutionen för systemteknik

Department of Electrical Engineering

Examensarbete

DC Charging of Heavy Commercial Plug-in Hybrid

Electric Vehicles

Examensarbete utfört i datorteknik

vid Tekniska högskolan vid Linköpings universitet av

Oscar Hällman LITH-ISY-EX--15/4878--SE

Södertälje 2015

Department of Electrical Engineering Linköpings tekniska högskola

Linköpings universitet Linköpings universitet

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DC Charging of Heavy Commercial Plug-in Hybrid

Electric Vehicles

Examensarbete utfört i datorteknik

vid Tekniska högskolan vid Linköpings universitet

av

Oscar Hällman LITH-ISY-EX--15/4878--SE

Handledare: Robert Sjödin

Scania CV AB

Kent Palmkvist

isy_{, Linköpings universitet}

Examinator: Mattias Krysander

isy, Linköpings universitet

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Avdelning, Institution Division, Department

Computer Engineering

Department of Electrical Engineering SE-581 83 Linköping Datum Date 2015-06-22 Språk Language Svenska/Swedish Engelska/English Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport

URL för elektronisk version http://www.ep.liu.se

ISBN — ISRN

LITH-ISY-EX--15/4878--SE Serietitel och serienummer Title of series, numbering

ISSN —

Titel Title

DC-laddning av tunga kommersiella plug-in-hybridfordon DC Charging of Heavy Commercial Plug-in Hybrid Electric Vehicles

Författare Author

Oscar Hällman

Sammanfattning Abstract

En lösning för att kunna minska avgasutsläpp från tunga fordon är att helt eller delvis fram-föra fordonet helelektriskt. Detta innebär att en betydande elektrisk energikälla måste finnas ombord på fordonet. På grund av den stora energikapacitet som källan måste ha så kommer fordonet antingen behöva avvaras en stor del av dess nyttotid för att ladda upp källan alter-nativt ladda med en högre effekt till kostnad av högre förlusteffekter och livslängd på en-ergikällan. Detta arbete innehåller en förstudie på högeffektslikströmsladdning av hybrid-batterier från befintlig infrastruktur anpassad till elektriska hybridbilar. Delar av arbetet innefattar: modellering av batteripack och likspänningsomvandlare, formulering av mpc-regulator till batteripack, analysering av laddningsstrategier och batterirestriktioner genom simulering. Arbetet påvisar att en längre laddtid ökar energieffektiviteten och minskar bat-teridegraderingen. Arbetet har även visat att en laddningsstrategi med liknande egenskaper som konstant-ström/-spännings-laddning bör användas för att ladda upp ett batteri från tomt till fullt.

Nyckelord

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Abstract

A solution to reduce exhaust emissions from heavy commercial vehicles are to haul the vehicles completely or partially electric. This means that the vehicle must contain a significant electric energy source. The large capacity of the en-ergy source causes the vehicle to either sacrifice a large part of its up time to charge the source or apply a higher charge power at the cost of power losses and lifetime of the energy source. This thesis contains a pre-study of high-power dc-charge of hybrid batteries from existing infrastructure suited to electric hybrid cars. Following parts are included in the thesis: modeling of a battery pack and a dc-dc converter, formulation of a mpc controller for the battery pack, analysis of charging strategies and battery restrictions through simulations. The thesis results shows that a longer charging time increases the energy efficiency and re-duces the degradation in the battery. It also shows that a charging strategy similar to constant-current-constant-voltage charging should be used for a full charge of an empty battery.

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2.2.2 Quadratic Programming . . . 14 3 Method 15 3.1 Modeling . . . 15 3.1.1 Battery Pack . . . 15 3.1.2 DC-DC Converter . . . 16 3.2 Control Formulation . . . 17 3.2.1 Control Construction . . . 18 3.2.2 Charge References . . . 21 3.2.3 Voltage Reference . . . 22 3.3 Simulation . . . 22 3.3.1 Evaluation Environment . . . 23 3.3.2 Charge Time . . . 23 3.3.3 Voltage Control . . . 24 v

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vi Contents 3.3.4 Current Restriction . . . 24 3.4 Implementation . . . 24 3.4.1 Converter Measurements . . . 24 4 Results 27 4.1 Modeling Results . . . 27 4.1.1 Battery Pack . . . 27 4.1.2 DC-DC Converter . . . 29 4.2 Simulation Results . . . 30 4.2.1 Charge Time . . . 30 4.2.2 Voltage Control . . . 32 4.2.3 Current Restriction . . . 33 4.3 Implementation Results . . . 34 4.3.1 Measurement Results . . . 35 4.4 Discussion . . . 36 5 Closure 37 5.1 Conclusions . . . 37 5.2 Future Work . . . 38 Bibliography 41

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Notation

Symbols and abbreviated terms Abbreviation Signification

ac _{Alternating Current}

bev Battery Electric Vehicle

bjb Battery Junction Box

bms Battery Management System

cc-cv Constant Current Constant Voltage

ccs Combined Charging System

can Controller Area Network

dc _{Direct Current}

evse _{Electric Vehicle Supply Equipment}

hv _{High Voltage}

mpc _{Model Predictive Control}

ocv _{Open Circuit Voltage}

phev _{Plug-in Hybrid Electric Vehicle}

plc Power Line Communication

pwm Pulse Width Modulation

soc State Of Charge

soh State Of Health

res Rechargeable Energy storage System

v2g Vehicle to Grid

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1

Introduction

This chapter introduces the thesis with a short background, objective and the limitations for the thesis.

1.1 Background

The solution to quick charging of phevs (Plug-in Hybrid Electric Vehicles) and bevs (Battery Electric Vehicles) are high power dc-chargers (Direct Current). The reason why dc-charging is preferred instead of ac-charging (Alternating Cur-rent) is because the ac requires a rectifier in the vehicle to be able to store the charged energy and a high power input requires a heavier and more expensive rectifier. The gain in time with this way of charging has the drawbacks of effi-ciency loss and greater impact in battery life time [1]. By studying the charging process of a high power dc-charger and modeling the electric characteristics of the battery pack, an energy efficient control strategy can be implemented. The aim of the control strategy is mainly to prevent damage on the battery due to violation of its safety restrictions and reduce the efficiency loss due to the high power, but also consider the ageing effects applied to the battery cells during the charge. Charging scenarios can differ a lot depending on factors like initial soc (State Of Charge) , total battery capacity, battery characteristics and charge time available.

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2 1 Introduction

1.2 Objective

The objective of this thesis is to pre-study high power hv (High Voltage) dc-charging of heavy commercial phevs. Things to evaluate in the study are:

• How does different charging times affect the efficiency and the ageing of the charging equipment?

• Can safety restrictions such as current, voltage and soc of the battery be en-sured with an automatic control of the power drained from the evse (Elec-tric Vehicle Supply Equipment)?

The work will be studied through simulations of models designed and adapted to measurements and parameters of crucial charge equipments obtained from technical specifications.

1.3 Limitations

Limitations done in this thesis will be stated below with explanations and moti-vations.

• The battery model will not include an explicit soh (State Of Health) , only the most dependent factors will be mentioned in the theory. The motivation for this is to keep the thesis within a reasonable framework. An explicit model of soh would require years of research.

• The formulation of the control strategy will assume that the maximum charging time and final soc is given by the user (i.e. not solved in the optimisation). To solve these two inputs in the total optimisation would require even further more inputs to be able to find the optimal charging formulation.

• If the final soc cannot be reached at the given time (due to limitations in battery, charge equipment etc.), the charge strategy should charge as much as possible because it cannot exceed the physical boundaries.

• The strategy will not consider options like v2g (Vehicle to Grid) . v2g uses the storage capacity in the vehicles batteries to achieve financial gains depending on the current energy price [2].

• The temperature of components during charging is assumed to be constant T0. Due to T0, all parts will be modeled to this specific temperature. Most of the components have a non-linear temperature dependency and a com-bination with the heat transfers result in a very complex system that would exceed the framework of the thesis.

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1.4 Outline 3

• The internal battery impedances are assumed to be constant and not depen-dent of soc. As with the temperature, this parameters will change depend-ing on the soc but to get a decent explanation of this behaviour needs lots of work.

• Physical values of the battery pack has been censored in the tables and graphs of the thesis.

1.4 Outline

The thesis contains five chapters and the contents of each chapter are stated be-low.

Chapter 1: Introduces the thesis.

Chapter 2: Explains the general theories used in the thesis.

Chapter 3: Applies the theory mentioned in the previous chapter with the spe-cific methods for this thesis.

Chapter 4: Contains all results of the work done according to the previous chap-ter.

Chapter 5: Summarise the thesis with conclusions made and the remaining work to be done in the subject.

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2

Theory

This chapter presents the theory applied to the thesis. The first part contains an overview of the charge equipment followed by a deeper description of each com-ponent displayed in the overview. The second part contains the control theory and calculation method for the automatic control.

2.1 Charge Equipment

This section contains theory and information of the charging equipment. An overview of all charging parts and with which interface they are connected to each other can be seen in Figure 2.1. The different communication interfaces in the overview are: plc (Power Line Communication), can (Controller Area Net-work) and Con which is a summation of logical detections and signals. Table 2.1 contains a list of all components shown in Figure 2.1 with a short description and which section the component is further described.

Table 2.1:Components shown in the overview of Figure 2.1.

Abbreviation Description Section

evse _{Charging station} _2.1.1

Combo2 Contact 2.1.1

Com Unit Communication unit 2.1.4

bms _{Battery Management System} _2.1.5

dc_/dc _Converter _2.1.2

bjb Connection box 2.1.3

res Battery pack 2.1.6

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6 2 Theory

EVSE Combo2 DC/DC BJB RES BMS Com

Unit Auxiliary_Source

Vehicle Charging station PLC Con CAN HV

Figure 2.1:Overview of the dc-charging components and how they are con-nected to each other.

2.1.1 Charging Station

The evse that will be used is defined as a type 2 mode 4 dc-charging according to [3]. It is a dc-charging station with specifications shown in Table 2.2. The charging standard used will be ccs (Combined Charging System), which are used by car brands like: BMW, Volkswagen, GM, Porsche and Audi [4].

Table 2.2:Charging station parameters.

Output parameter Value

Voltage range 50 − 500V

Current max 125A

Power max 50kW

The contact to be used with the evse is a Combo2 contact [5]. Contact pins can be seen in Figure 2.2 and pin descriptions with mode 4 dc-charging in Table 2.3

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2.1 Charge Equipment 7 PP CP N PE L1 L2 L3 DC− DC+

Figure 2.2:Pin layout of a Combo2 contact.

Table 2.3:Pin configuration of the Combo2 contact in mode 4 dc-charging.

Pin Max U/I Description

PP 30V/2A Detects connection between evse and

bev_/phev.

CP 30V/2A Communicates between evse _and

bev/phev using plc.

PE 850V/125A Ground used in all charging modes used

through the contact.

DC+ 850V/125A Positive charging input used with

dc-charging.

DC- 850V/125A Negative charging input used with

dc-charging.

N 480V/20A Not used.

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8 2 Theory

2.1.2 DC-DC Converter

Because the evse infrastructure mostly applies to the car industry, which use lower battery voltage [4], a dc-dc converter is needed to be able to charge the truck battery with a car evse. Useful parameters of the dc-dc converter used [6], can be seen in Table 2.4 where the over voltages shows at which value (even at no operation) the converter will break down.

Table 2.4: dc-dc converter parameters.

Output parameter Value

Over voltage 800V

Max continuous power 120kW

Input parameter Value

Over voltage 445V

Current max 400A

Control parameter Value

Switching frequency 39kHz

Efficiency typical 98%

The dc-dc converter has a half bridge topology. A basic schematic of this topol-ogy can be seen in Figure 2.3. The converter converts the dc-input through switches (transistors, thyristors etc. [7]) to a high frequency ac signal. This ac signal is transformed through the transformer and rectified to the dc-output.

I in IT V in + − N 1 N2 VT + −

Figure 2.3:Schematic of a half bridge converter (without filters). The relation between the input Vinand output VT can be described with [7]

VT

Vin

= N2

N1

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2.1 Charge Equipment 9

where N1 and N2defines the coil turns and D = ton/tperiod where ton, tperiod is

the time when the switches at the input side is on respectively the time of the switching period.

The power losses of a half bridge dc-dc converter can be divided into semicon-ductor and transformer losses. The semiconsemicon-ductor losses comes from non-ideal components whom contributes with power losses Pswat switching points because

the semiconductor current must increase before the potential in the semiconduc-tor can decrease and vice versa. These losses depend on the current while the semiconductors are conducting, the semiconductor voltage while not conducting, semiconductor characteristics and the switching frequency. The semiconductors also contributes with losses Pcondwhile they are conducting due to small voltages

in the semiconductors Vsc. The conduction losses depend on the semiconductor

currents, characteristics and the conduction time. Assuming that the semicon-ductor voltages are equal in each semiconsemicon-ductor and that the efficiency is ideal gives Pcond ≈ VscIin(1 + Vin/VT)D where D is defined as in equation (2.1). An

example of these losses can be seen in Figure 2.4 where Pswis the sum of Ponand

Pof f. off on t_on u t_on 0 U 0 I 0 P loss t period P cond P_on P_off P cond P_on P_off

Figure 2.4:Example of power losses in semiconductors.

The transformer losses consists of magnetic losses in the core Pcore and resistive

losses from the coils PR. The core losses comes from hysteresis in the transformer

core and mainly depends on switching frequency, magnetic flux density, temper-ature and core geometrics. The resistive losses occur due to resistances in the lines (mostly from the transformer coils) and it mainly depends of length and resistivity of the coils.

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10 2 Theory

2.1.3 Battery Junction Box

The bjb (Battery Junction Box) connects all hv-components, i.e. master res (Rechargeable Energy storage System) unit, dc-dc converter, auxiliary energy sources and extra slave res units.

2.1.4 Communication Module

The Communication unit is the link between the bms (Battery Management Sys-tem) and the other dc-charging components. The Communication unit also con-tains plc interface, since this standard is used by ccs to communicate with the evse[8]. The Power Line Communication uses a high frequency serial communi-cation on a low frequency power signal. In the ccs standard, the power signal is a 1 kHz pwm (Pulse Width Modulation) signal with 5% duty cycle [9], an exam-ple of this can be seen in Figure 2.5 where a high frequency signal is applied to a 1kHz pwm signal. 0 1 2 3 4 5 0 1 2 3 4 5 6 7 PLC example Time [ms] Voltage [V] 0.7 0.95 0 1

Figure 2.5:An example of how a plc signal can look like.

The module also controls the connector lock in the Combo2 contact, to make sure that the connection cannot be disrupted while high power is applied on the connectors.

2.1.5 Battery Management System

The bms observe and controls the res and components that affect the res, like cooling systems and charging units. Future control strategy for dc-charging will be done here, or at least parameter estimations like soc. The communication interface used by the bms is can, as also seen in the overview in Figure 2.1.

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2.1 Charge Equipment 11

2.1.6 Battery Pack

The battery pack or res used in this thesis is Lithium-Ion cell type. In this pre-study the battery temperature is assumed to be constant at 25oC, since it has quite complex dependency of its temperature and would require loads of work to describe it with decent accuracy. General battery restrictions can be seen in Figure 2.6. The restrictions prevent the risk of hot spots in the Battery cells [10]. The decreasing charge and discharge currents at high and low soc occurs due to high electron density at the anode and cathode.

0 Power [kW] Battery restrictions 0 Current [A] 0 50 100 700 Voltage [V] State of Charge [%]

Figure 2.6:Battery restrictions at 25oC, allowed area is marked grey.

The ocv (Open Circuit Voltage) of the battery pack can be seen in Figure 2.7 and it is slightly different depending on if the battery is being charged or discharged. Both the restrictions and ocv is based on data given from the cell manufacturer. To study the soh qualitative, the battery pack ageing can be divided in calendar ageing and cycle ageing. Calendar ageing is a very slow process mostly dependent of soc and time. It can therefore be neglected in studies of charging processes. The primary factor of cycle ageing is the charging currents where higher currents degrade the battery faster [1; 11].

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12 2 Theory

0 50 100

0 700

Open Circuit Voltage

State of Charge [%]

V OCV

[V]

Charge Discharge

Figure 2.7:Open Circuit Voltage at 25oC.

2.1.7 Auxiliary Sources

As seen in Figure 2.1, there is also an ability to add auxiliary energy sources. Two examples of auxiliary sources are inductive charging from road pick-ups and pantograph charging. An example of this can be seen in Figure 2.8.

Pantograph

Inductive Pickup

Figure 2.8:Auxiliary charging equipment attached on a vehicle.

2.2 Control Theory

This section contains the theory of the automatic control applied to the simula-tions used in the thesis.

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2.2 Control Theory 13

2.2.1 Model Predictive Control

A mpc (Model Predictive Control) is a time discrete mathematical controller that predicts the model states x up to the number of total predictions N at the current time k (in other terms ˆx(k) to ˆx(k + N − 1)). From this prediction it estimates the optimal value for the upcoming control signal u(k) that minimizes a function z that is desirable to control. This operation is done on-line and is repeated at each time update [12]. Since it is using a mathematical optimisation, boundaries and restrictions can be added explicitly. A mathematical explanation of an algorithm using mpc with reference signal (r) and integral action [13] is described as

min λmin≤λ≤λmax N −1 X j=0 ||_{z(k + j) − r(k + j)||}2 Q1+ ||u(k + j) − u(k + j − 1)|| 2 Q2 (2.2)

with the a state space model formulated as

x(k + 1) = Fx(k) + Gu(k) (2.3a)

z(k) = Mx(k) (2.3b)

The λ in equation (2.2) describes the restrictions of the system with the bound-aries λminand λmax. Calibration parameters in the mpc are the weight matrices

Q1, Q2 and prediction length N . The matrix Q1 sets the weight of difference between the signal z and reference value r and the matrix Q2sets the weight of differences in the control signal u. The sum notation in equation (2.2) can be formulated in matrix form as

(MX − R)TQ₁_{(MX − R) + (ΩU − δ)}TQ₂_{(ΩU − δ)} _(2.4) with the individual matrices and vectors described as

U =               u(k) u(k + 1) .. . u(k + N − 1)               , X =               x(k) x(k + 1) .. . x(k + N − 1)               , R =               r(k) r(k + 1) .. . r(k + N − 1)               (2.5a) X = F x(k) + GU (2.5b) F ₌                I F .. . FN −1                , G₌                0 0 0 · · · ₀ G 0 0 · · · ₀ .. . . .. ... ... ... FN −2G · · · _FG _G ₀                (2.5c) Q₁₌               Q1 Q1 . .. Q1               , Q₂₌               Q2 Q2 . .. Q2               (2.5d)

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14 2 Theory M₌               M M . .. M               , Ω=               I −_I _I . .. ... −_I _I               , δ =               u(k − 1) 0 .. . 0               (2.5e)

2.2.2 Quadratic Programming

To solve the mpc algorithm explained in the Section 2.2.1, quadratic program-ming [14] can be applied. Quadratic programprogram-ming determines the control signal vector U that minimizes the function

min

U

1 2U

T_{H U + Γ}T_U _(2.6)

The mpc formulation in equation (2.4) can be converted to the quadratic form in equation (2.6), this gives the values of Γ and H as

H = GTMTQ₁MG_{+ Ω}TQ₂Ω (2.7a)

Γ = GTMTQ₁MF_{x(k) − G}TMTQ₁_{R − Ω}TQ₂_δ _(2.7b)

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3

Method

In this chapter, methods used in the thesis are presented. The first part describes the methods used for modeling the charge equipment. It is followed by methods for constructing the control system and simulation environment. The last part in this chapter contains the implementations done for the converter measurements.

3.1 Modeling

This section contains the modeling methods for the charge equipment. The first part contains the modeling of the res while the last part describes the converter.

3.1.1 Battery Pack

In [15], a model of ideal analogue circuit elements were applied to an automotive battery pack with successful results. This model is usually used for modeling battery cells. A similar model was applied to the battery pack used in this thesis and the circuit elements with the current and voltages of the model can be seen in Figure 3.1. The model is based on: the filter parameters R1, C1, R2and C2that describes the dynamic voltages V1 and V2, the parameter Vocvthat models the ocv_{, the internal resistance R}_s_{and the terminal voltage and current V}_T _{and I}_T_.

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16 3 Method V_T + − R s R 1 R2 V_OCV C1 C2 I T V₁ + − − V₂ +

Figure 3.1:Schematic of the res model.

VT in Figure 3.1 is described with

VT = Vocv(soc) + R_sI_T + V₁+ V₂ (3.1)

where the potentials V1and V2have the dynamic behaviour described with         ˙ V1 ˙ V2 ˙ soc         =           −₁ R1C1 0 0 0 _R−1 2C2 0 0 0 0                   V1 V2 soc         +           1 C1 1 C2 1 Qtot           IT (3.2)

Equation (3.2) also contains the dynamic behaviour of the soc where Qtot is the

total capacity of the battery pack. The internal resistance Rs was defined from

manufacturer data at the temperature 25oC. Since the model will be used to eval-uate charging, it might be a good choice to use the charge curve in Figure 2.7 for the Vocv. But because the remaining parameters were estimated towards both charging and discharging currents and the small deviation between the curves in Figure 2.7, Vocvwas set as the mean of the two curves. The remaining parameters R1, C1, R2and C2were determined through the least square algorithm

min ZV f (IT ,meas) = X V1+2,meas−

V1,model(IT ,meas) + V2,model(IT ,meas)

2 (3.3a) ZV = R1 C1 R2 C2 T (3.3b) V1+2,meas = VT ,meas−RsIT ,meas−Vocv(soc_meas) (3.3c) with measured data of the res. The measurements were done at different soc: 0, 0.25, 0.5, 0.75 and 1, where soc is defined as the battery pack window used. The mean value of ZV from equation (3.3) with these measurements became the

final values for the model. Results of this model can be seen in the results Section 4.1.1.

3.1.2 DC-DC Converter

To make sure how much power that is required and what voltage/current de-mands to transmit to the evse [16], a decent model of the dc-dc converter ef-ficiency ηdc is needed. As mentioned in [17], this model can be described with

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3.2 Control Formulation 17 ηdc= PT Pin (3.4a) PT = VTIT (3.4b) Pin= VinIin (3.4c)

With the voltages and currents VT, Vin, IT and Iindefined as in Figure 2.3.

To parametrise this model, the behaviour of efficiency ηdc needs to be captured. To get a model of the converter efficiency, the power losses were studied. The total power losses can be summarized as

PT = Pin−Ploss (3.5)

where

Ploss= Psw+ Pcond+ Pcore+ PR (3.6)

and contains the losses described in Section 2.1.2. From Figure 2.4 and the theory mentioned in Section 2.1.2, it can be seen that each power loss is proportional to Iin, Vinand VT as Pcore∝1 Psw∝VinIin Pcond∝ VT Vin + 1 ! Iin PR∝Iin2 (3.7)

since the switching frequency, temperature and component characteristics can be approximated as constant or negligible. With equations (3.6) and (3.7), a model of the power losses can be defined as

Ploss,model = kP 1+ kP 2Iin+ kP 3Iin2 + kP 4VinIin+ kP 5VTIin/Vin (3.8)

where the values kP i, i = 1, . . . , 5 describes the proportional behaviour of

equa-tion (3.7). The parameters in equaequa-tion (3.8) gets defined through least square approximations

min

Zk

f (ZP ,meas) =

X

Ploss,meas−Ploss,model(ZP ,meas)

2 (3.9a) Zk = kP 1 kP 2 . . . kP 5 T (3.9b) ZP ,meas=

Iin,meas Vin,meas VT ,meas

T

(3.9c) Ploss,meas= Vin,measIin,meas−VT ,measIT ,meas (3.9d)

applied to the converter measurement described in Section 3.4.1.

3.2 Control Formulation

The construction and calibration of the battery controller is shown in the begin-ning of this section. Different charge and voltage references are found at the end of this section.

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18 3 Method

3.2.1 Control Construction

A mpc controller was applied with the structure described with equation (2.2) in the theory Section 2.2.1, where z =VT soc

T

, u =IT

and x =V1 V2 soc ocv T

. The state space system for the mpc was defined as an extension of the VT model

and state space model in equations (3.1) and (3.2), but here the ocv is added too through the constant kocv. The mpc model was applied as

            ˙ V1 ˙ V2 ˙ soc ˙ ocv             =               −1 R1C1 0 0 0 0 _R−1 2C2 0 0 0 0 0 0 0 0 0 0                           V1 V2 soc ocv             +                 1 C1 1 C2 1 Qtot kocv Qtot                 IT (3.10a) VT soc ! = 1 1 0 1 0 0 1 0 !             V1 V2 soc ocv             + Rs 0 ! IT (3.10b)

which was discretised with zero order hold. The kocvis taken as the mean of ∂ocv_∂soc at 0 ≤ soc ≤ 1, which can be found in Figure 3.2. The small deviation in Figure 3.2 occur because of the non-linear behaviour as seen in Figure 2.7. To ensure that the safety limitations of the battery pack seen in Figure 2.6 were held and the soc were kept in its defined range, the restrictions to the mpc system were set as

soc≤1 (3.11a)

VT ≤VT ,max (3.11b)

IT ≤

(

IT ,max soc< socb

IT ,max+ kI,max(socb− soc) soc≥ socb (3.11c)

where kI,max > 0 defines the first linear decrease of current that occurs at the

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3.2 Control Formulation 19

0 0.25 0.5 0.75 1

−50% k +50%

Partial derivative of OCV

SOC

∂

OCV/

∂

SOC

Figure 3.2: ∂ocv_∂soc as a function of soc.

With a sample time tsampleof 1 second, the number of prediction steps N were set

to approximately one minute to make sure that upcoming restrictions could be managed smoothly. The Q1 weight matrix of difference between the output val-ues of z and reference signal r were set significantly low for the battery voltage VT, because it does not follow a special reference in a charging scenario. Rest of

the weights: Q2input u difference and the weight between output and reference for soc were set equal. All calibration parameters can be seen in Table 3.1.

Table 3.1: mpccalibration parameters.

Parameter Value N 50 Q1 10−₁₀ 0 0 100 ! Q2 100

The step response of the system from socminto socmaxcan be seen in Figure 3.3

and the lowest charging time defined as t0,min. The limits of the charge time de-pends of the voltage and current restrictions, which can be seen in Figure 3.4. As seen in Figure 3.3, the response time t0can be divided into a linear region where the restrictions are constant and a settling part tsettle where the restrictions are

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20 3 Method 0 1 Step response time SOC t 0,min t settle Linear region

Figure 3.3:Response of a step from socminto socmax.

Max Restrictions V T 0 b 1 Max SOC I T actual value restriction

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3.2 Control Formulation 21

Since the prediction horizon is significantly lower than the rise time of the sys-tem (N tsample t0,min), any time dependent restrictions cannot be applied in the mpc algorithm. This occur because the mpc must be able to predict the final time and value to apply it in the optimisation and thereby ensure that the time dependent restriction is held. The solution to apply different charging times is solved with N tsample > t0. This criterion can be fulfilled with increasing either the number of predictions N or the sampling time tsample. Drawbacks due to a

larger N is the computational time in each iteration and a larger tsampleincreases

the risk that restrictions are violated between the samples. Therefore none of this solutions were applied to this thesis and N tsampleremained smaller than the

charging time t0.

3.2.2 Charge References

Modifying the reference signal depending on charging time t0, charging inter-vals socinit to soc0 and the step response behaviour, results in a charging that minimizes power consumptions. The modified reference r(t) is described as

r(t) = socinit+

soc₀− soc_init

t0

t (3.12a)

r(t) = socinit+ (soc0− socinit)(1 − e

−_t/τ₀

+ e−α) (3.12b)

r(t) = (

soc_init+socb−socinit

t0β t t ≤ t0β

soc_b+ (soc₀− soc_b)(1 − e−(t−t0β)/τ0(1−β)_{+ e}−α₎ _{t > t}₀_β (3.12c) which contains three different reference solutions: equation (3.12a) for linear, equation (3.12b) exponential and equation (3.12c) as a compound of both. The definition of τ0is τ0= t0/α where α > 0 and the term e−αis added to equations (3.12b) and (3.12c) to make sure that the reference reaches soc0. This makes the reference to not start at socinit but for higher values of α, this phenomena can

be neglected. The β is defined as 0 < β < 1 and sets how much of the charging time t0that will apply the linear reference in the compound strategy in equation (3.12c).

The relationsoc˙ = I_T/Q_totgives that

IT(soc) = Qtot˙r(t) (3.13)

which gives the control signals assumed that no restrictions are active as IT(soc) =

Qtot

t0

(soc0− socinit) (3.14a)

IT(soc) = Qtot

τ0

soc_init− soc_{+ (soc}₀− soc_init_{)(1 + e}−α₎ _(3.14b)

IT(soc) =        Qtot t0β(socb

− soc_init₎ soc≤ soc_b

Qtot

τ0(1−β)

soc_b− soc_{+ (soc}₀− soc_b_{)(1 + e}−α₎ soc_{> soc}_b (3.14c)

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22 3 Method

with equation (3.14a) for the linear, equation (3.14b) for the exponential and equation (3.14c) for the compound reference. To get continuity of IT(soc) in

equation (3.14c), α must be defined as

α(1 + e−α) = 1 − β

β

soc_b− soc_init

soc₀− soc_b (3.15)

which can be solved easily with the approximation e−α ≈_{0. A visual example of} the references in equation (3.12) with control currents in equation (3.14) can be seen in Figure 3.5, where the tuning parameter β of the compound is 0.4.

0 Beta 1 0 b 1 Reference examples t/t 0 SOC(t) r_lin r_exp r_com 0 b 1 I T (SOC) SOC

Figure 3.5: Reference examples as described with equations (3.12) and (3.14).

3.2.3 Voltage Reference

For some applications, a manageable battery voltage can be desired. Examples of this can be connection of hv equipment to the battery pack or connections of slave res’s to the master res for a parallel charge of the battery packs. To control the voltage of a battery pack, the penalty matrix Q1in equation (2.2) needs to be modified.

3.3 Simulation

This section describes the configurations of the simulations done in this thesis. It begins with a description of the simulation environment followed by the three methods used in simulation evaluation.

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3.3 Simulation 23

3.3.1 Evaluation Environment

The res model from Section 3.1.1 and control formulation in Section 3.2 were evaluated through simulations. The simulation environment can be seen in Fig-ure 3.6 and the simulation outputs in FigFig-ure 3.7. An implementation of this con-trol system would require observers for the dynamic voltages V1, V2, the charge soc_{and an interpolation to achieve an estimation of V}_ocv_{. These values has to} be estimated since they are not measurable on a physical battery pack.

x' = Ax+Bu y = Cx+Du RES_model x u MPC Controller 1-D T(u) OCV(SOC) Clock _Display V_T SOC V_1 V_2 OCV I_T WorkspaceOutput

Figure 3.6: Simulation model used for evaluation of reference signals in equation (3.12). Scope simout To Workspace VI -K-Rs V1I V2I I^2 |u| Abs 1 V_T 2 SOC 3 V_1 4 V_2 5 OCV 6 I_T

Figure 3.7:WorkspaceOutput block of Figure 3.6.

3.3.2 Charge Time

To evaluate how the charging time affects the total charging efficiency, the mean value of the battery efficiency was defined as

¯ ηP = 1 − ¯ Ploss ¯ Pin (3.16) where ¯Ploss is defined as the mean value of the approximated power losses in the

model of Figure 3.1

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24 3 Method

and ¯Pindefined as the average input power

Pin= VTIT (3.18)

The power losses in the resistances R1 and R2 were approximated through the voltages V1 and V2 in equation (3.17) since these are near to constant for the charging scenarios. Simulations were done at different charging times t0with the reference signals as equation (3.12).

A study in how each reference signal affects the degradation due to high current IT was done by defining the current usage ability 0 ≤ ζ ≤ 1 according to

ζ = IT ,restriction−IT IT ,restriction

(3.19) where IT ,restrictionrepresents the restriction of equation (3.11). A higher ζ-value

represents a better soh due to slower cycling ageing from terminal currents IT.

3.3.3 Voltage Control

The possibility to use the mpc controller with a voltage reference was evaluated through simulations. The parameters of the penalty matrix Q1in equation (2.2) were set to Q1= 10 0 ₀ 0 10−10 ! (3.20) for these simulations.

3.3.4 Current Restriction

A theoretical sensitivity analysis of how charging times could decrease with re-laxed restrictions of current IT were done through simulated steps from socmin

to socmaxwith different restriction IT ,max.

3.4 Implementation

Implementations done in the thesis are described in this section. This section contains the method for implementation to achieve the converter measurements.

3.4.1 Converter Measurements

To parametrise the dc-dc converter model (see Section 3.1.2) measurements were needed. The converter temperature was kept constant to keep consistency during the measurements, which was solved by connecting it with radiator hoses to cool-ing equipment. Other parts connected to the converter can be seen in Figure 3.8. With the converter connected to laboratory power equipment, measurements of Vin, Iin, VT and IT were made with the rig parameters as shown in Table 3.2.

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3.4 Implementation 25

Table 3.2: dc-dc converter rig parameters.

Parameter Value Vin 300 − 430V Iin 0 − 125A VT 600 − 690V DC/DC Power Equipment Control Unit Cooling V in + − V T + − I T I in CAN HV Hose

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4

Results

This chapter contains the results according to the methods described in Chapter 3: The modeling, simulations and implementations. The chapter ends with a discussion of the results achieved in the thesis.

4.1 Modeling Results

This section shows the validation results of the battery and converter model made in this thesis.

4.1.1 Battery Pack

The results of the battery model mentioned in Section 3.1.1 can be seen in Figure 4.1, with the model parameters as in Table 4.1. Table 4.1 also shows the estimated parameter values for each specific measurement and here it is seen that these impedances differs a bit based on the current soc, but a decent representation of the parameters can be the mean values. The modeled VT in Figure 4.1 (dark grey)

follows the dynamics of the measured VT (light grey) at soc = 0.5 well but there

is a small bias between these, probably because of uncertainty in the estimated soc_{or the confidence of ocv in Figure 2.7. The relative bias error is low and it} should be allowed to neglect its effects on the overall system.

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28 4 Results

Table 4.1: resmodel parameters.

Parameter Value

Set [soc] mean 0 0.25 0.5 0.75 1

R1[mΩ] 140 149 135 113 158 144 R2[Ω] 35.5 43.7 30.0 29.0 47.0 26.9 C1[F] 235 189 239 286 251 211 C2[kF] 1.34 1.08 1.54 1.54 0.81 1.72 650 Model Voltage V T [V] −3 0 3 E V,T [%] 0 500 1000 0 I T [A] Time [s]

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4.1 Modeling Results 29

4.1.2 DC-DC Converter

In Table 4.2, the estimated model parameters for equation (3.8) can be seen. The converter efficiency model in Section 3.1.2 was derived with equation (3.4a) where the power loss model of equation (3.8) was applied to equation (3.5). A comparison between the model values with measurement inputs and the mean values of measurements done according to Section 3.4.1 can be seen in Figure 4.2. Figure 4.3 contains a map of the modeled efficiency. Here it is observed that the efficiency decreases hugely at lower input currents because the losses mentioned in the theory Section 2.1.2 gets relatively higher compared to the total power in to the converter due to losses in the transformer.

Table 4.2: dc-dc converter model parameters.

Parameter Value kP 1 639W kP 2 −106V kP 3 9.50mΩ kP 4 15.9 × 10 −₃ kP 5 29.2V−1 5 45 85 125 0.5 0.75 1 V T: 600V Converter Efficiency η DC [−] V T: 600V 5 25 50 70 0.5 0.75 1 V T: 630V η DC [−] V T: 630V 5 30 55 0.5 0.75 1 V_T: 660V η DC [−] V_T: 660V 5 15 25 35 0.5 0.75 1 V_T: 690V I in [A] η DC [−] V_T: 690V

Figure 4.2:A comparison between the measured (dark) and modeled (light)

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30 4 Results 0 25 50 75 100 125 600 630 660 690 0 0.25 0.5 0.75 1 I in [A] Efficiency Map V T [V] η DC [−]

Figure 4.3:The modeled efficiency map of ηdc.

4.2 Simulation Results

Results from the three simulation evaluations in Section 3.3 are presented in this section.

4.2.1 Charge Time

Results from Section 3.3.2 can be seen below. Figure 4.4 shows how the final soc at t0, ¯ηP as defined in equation (3.16) and the maximal terminal voltage, VT

de-pends on the charge time t0. The three different results in Figure 4.4 evaluates the three different reference signals described with equation (3.12) in Section 3.2.2. Here it is seen that the efficiency is slightly higher with the linear reference sig-nal although it requires that t0 ≥ 2.7t0,min to reach the final soc with the same signal. The exponential reference signal has the lowest efficiency but reaches the final soc at lower t0and ends up in a lower maximum terminal voltage VT than

the other reference signals. It can reach a lower voltage since VT ,max > Vocv at soc_{= 1. The balance between the linear and exponential reference signal is the} compound signal, that has its characteristics in between the linear and exponen-tial references.

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4.2 Simulation Results 31 0.98 1 SOC(t 0 ) r lin r exp r com 0.95 0.96 0.97 η P,mean 1 2 3 4 0.99 1 V T,max t 0/t0,min

Figure 4.4:Simulation results of different reference signals at different t₀.

The mean value of unused current capacity ζ behaviour of charge time t0 can be seen in Figure 4.5 for the three different charge references. From Figure 4.5 it can be seen that the references are equal in a point of soh and that a longer charging time is better for the battery pack. They are equal since the gain in the linear case at lower charge times comes from the lack of charge as seen Figure 4.4.

1 2 3 4 0.4 0.65 0.9 Distance to restriction ζ mean t 0/t0,min lin exp com

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32 4 Results

Figure 4.6 shows how ζ in equation (3.19), depends of soc for the three different reference signals in equation (3.12). The different lines in the graphs of Figure 4.6 represents different charge times where the brighter lines shows the results for lower charging times. Here it is seen that higher charging times contributes to better ζ-values and the best values are received with linear reference signal while soc ≤ soc_b _{and the same reference contributes with the worst values if soc is} near 1 since the currents is near IT ,maxhere. The ζ-value of the exponential

refer-ence signal has the opposite characteristics compared to the linear case and the compound shows an overall balance of the other references. The overshoot in the beginning of the graphs in Figure 4.6 comes from the initial input values in the simulations which were set to IT ,max.

0 0.25 0.5 0.75 1 Distance to restriction ζ lin 0 0.25 0.5 0.75 1 ζ exp 0 b 1 0 0.25 0.5 0.75 1 ζ com SOC

Figure 4.6:Simulation results of ζ(soc), darker lines represents higher t0.

4.2.2 Voltage Control

In Figure 4.7, the reference tracking of VT with Q1 as described in Section 3.3.3 can be seen. Here it is seen that the voltage has a small overshoot from the dynamics of V1 and V2 but converges to the right value. The current also con-verges to zero here, which is desirable because zero current and equal potentials is the ideal condition at connections of electrical equipment. The low weight on socin the matrix Q₁makes it float and eventually end up in a value that fulfils VT ,ref = Vocv(soc).

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4.2 Simulation Results 33

1

V

T control

V T,max actual value reference 0 1 SOC 0 0 1 I T,max time

Figure 4.7:Simulation with reference on VT.

4.2.3 Current Restriction

Simulation results of how relaxations of the current restrictions in Section 3.3.4 could decrease the charging time t0can be seen in Figure 4.8. The figure shows the results of five different current restrictions from 1 × IT ,maxto 5 × IT ,max. Here

it is seen that the time to fully charge the res is quite similar and near t0,mindue to the restrictions of VT, as can be observed in Figure 4.9.

0 0.5 1 0 1 Step response t/t 0,min SOC 5×I_T,max 4×I_T,max 3×I T,max 2×I T,max 1×I_T,max

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34 4 Results 1 Restrictions V T,max 0 b 1 0 1 2 3 4 5 SOC I T,max actual value restriction

Figure 4.9:Restrictions of a step from socminto socmaxwith relaxed IT ,max.

Some interesting parameters from the simulations above can be seen in Table 4.3 and here it is shown that the efficiency decreases, similar to the results in Fig-ure 4.4. Here t0.5soc and t0.9soc is defined as the time it takes to reach 0.5/0.9 soc. The gain of lower charge times appears to be higher in the beginning of a relaxation (2 × IT ,max) than in the end (5 × IT ,max). This occurs mainly because of

the increasing significance of the voltage restrictions VT ,max.

Table 4.3:Simulation results of current relaxation.

Parameter Value ×_I_t,max ₁ ₂ ₃ ₄ ₅ ηP [%] 95.0 93.2 92.0 91.1 90.6 t_0.5soc t0,min [%] 26.8 13.4 8.9 6.9 6.2 t0.9soc t0,min [%] 50.9 27.9 22.5 20.5 19.9

4.3 Implementation Results

This section contains a summary of the physical implementation of the converter to achieve measurements for the converter model parameterisation.

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4.3 Implementation Results 35

4.3.1 Measurement Results

The Figure 4.10 shows the results of the converter measurements described in Section 3.4.1. The measurements seems plausible since the current IT is lower

than Iin and that the power Pinin equation (3.4c) is higher than PT in equation

(3.4b) at all samples. The distortion in outputs VT and IT comes from the internal

switching of the dc-dc converter and depends mainly on the voltage ratio VT/Vin.

The temperature differs slightly from the reference value of 25o_{C but it can be}

approximated as constant because the small deviation can be neglected.

225 350 475 600 725 V [V] Converter Measurements 0 50 100 I [A] 0 20 35 55 P [kW] 0 100 200 300 400 500 600 700 23 24 25 26 T [ o C] Time [s] in T

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36 4 Results

4.4 Discussion

The parameter kocvin Section 3.2.1 is far from constant as assumed in the model equation (3.10). The variance of kocvcan be seen in Figure 3.2. Since kocvonly appears in the mpc model, its only used in the predictions of the mpc algorithm. As long as the prediction horizon is relatively low, the error occurred with the constant kocvmight be negligible. This assumption with its dependence should be kept in mind for future calibrations and modifications of the model.

The results shown in Figure 3.3 and 3.4 shows a cc-cv [11] behaviour which is commonly used in charging applications of Li-ion cells [18]. This might have occurred because cc-cv is close to the ideal charging strategy or that the manu-facturer have set the restrictions according to this charging strategy.

The measured mean efficiency in Figure 4.2 deviates from the model at some operating points, mainly at Iin = 30 − 50A. Several factors can cause this

phe-nomena such as: measurement distortion as seen in Figure 4.10, synchronisation deviation at the sampling of input/output values Vin, Iin, Pin, VT, IT and PT since

these were collected in different computers or that the converter has a more com-plex circuitry than the one described with Figure 2.3 in theory Section 2.1.2. As seen in Figure 4.10, the input voltage Vinraises to a higher voltage at higher

current inputs Iin. It is desirable to keep this voltage constant to get consequent

evaluation but since this is controlled with the internal logic and the supply equipment was set for delivering constant current, it was not manageable at the time.

The behavioural in the results of Figure 4.8 and 4.9 correspond well to the re-sults at different charging rates in [11]. This similarity might attest the model characterization.

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5

Closure

This chapter summarizes the report with conclusions from the results in Chapter 4 and future work in the subject.

5.1 Conclusions

A well-tuned mpc controller combined with a useful model can ensure that linear restriction is kept. But the mpc controller cannot manage different time restric-tion if it is later than the predicrestric-tion horizon of the controller. For easier charging scenarios, a simple cc-cv logic could be applied and solve the same problem. To reduce the charging time of the battery pack, lowering the final soc has a great impact! As observed in Figure 3.3, it takes about 0.5t0,minto receive the last 1/8 of soc.

Conclusions that can be made from Section 4.2.1 is that the main reason to aim for a higher charging time would be to increase life time of the battery pack rather than reduce energy losses since the slow increase of ηP with higher charging time

seen in Figure 4.4 can be neglected.

It can be noticed from the efficiency behaviour seen in Figure 4.4 and Table 4.3 that the efficiency ηP would be significantly lower for lower charging times t0. To accomplish this, t0,minmust be lower and therefore the restrictions like IT ,max

needs to get relaxed which also would accelerate the ageing of the battery.

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38 5 Closure

For optimisation of the efficiency for the whole charging chain (dc-dc and res), it is seen in Figure 4.3 that higher efficiency is received at higher currents for the converter and in Figure 4.4 that higher efficiency is received at lower currents for the battery pack. Therefore the final current will be weighted to the optimal value, max (ηP ×ηdc).

Figure 4.6 in Section 4.2.1 shows that in a point of soh, a compound reference signal is the best choice if it is intended to fully charge an empty battery pack since it has low currents at high soc and high currents has higher impact in the ageing at a high soc than a low soc [1].

Another way to both shorten the charging time and increase the life time of the battery packs is to add more battery packs to the vehicle, this would increase the possible total input power and lower the terminal currents for each pack but also add weight to the vehicle and increase investment costs.

5.2 Future Work

The res model designed in Section 3.1.1 of this thesis does not depend on temper-ature variations. The model parameters behaviour can be studied and adapted to get a model that depends on temperature.

The res restrictions in equation (3.11) has the main purpose to prevent rapid temperature increases in the cells of the battery pack [19]. A study of how the cell temperature increases as a function of current could relax the res restrictions and instead depend on a reliable temperature estimation.

Battery restrictions used in this thesis are based on continuous scenarios and by adding time dependent restrictions the charging scenario could be boosted for a short while [20].

The efficiency model shown in Figure 4.3 is quite decent for the measurements done, but since the converter can handle higher powers as seen in Table 2.4 it can be applied in other applications too. To apply the converter model to higher pow-ers, new measurements and parameters done in Sections 3.4.1 and 3.1.2 should be redone at the new operating points.

The converter topology might be more complex than the topology used for de-riving the model in Section 2.1.2. It can for example contain multiple converters connected in parallel and only uses one or a few of them at low converter loads. To model behaviours like this requires more measurements at different operating points for estimations of when converters are added or removed.

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5.2 Future Work 39

Expansion of the simulation environment with extra slave res models and a model for the bjb can through simulations evaluate and increase the knowledge of high power dc-charging of multiple batteries.

The knowledge about how much power losses that is generated while charging can be used in a real time feedforward to the cooling system.

A more explicit description of the battery degradation could be added to easier weight each factor of the problem formulation.

Larger vehicle fleets off duty could also be charged/discharged based on the ac-tual energy price (v2g). To make sure that this tactics will ensure profitable, the explicit soh estimation mentioned above must be confident since the "buy and sell" of energy will increase the battery degradation.

The restrictions of the electric infrastructure must also be taken into account if the vehicle fleet is significantly large and a fleet network is needed to make sure that all vehicles gets charged in time.

Since fast charging of hybrid battery packs degrade the soh significantly, a useful method to recycle Li-Ion battery cells [21] could decrease the cost of new batter-ies and contribute with a healthier environment.

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