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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 universitet SE-581 83 Linköping, Sweden Linköpings tekniska högskola Linköpings universitet 581 83 Linköping 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 Södertälje, 22 juni 2015 Avdelning, Institution Division, Department Datum Date Computer Engineering Department of Electrical Engineering SE-581 83 Linköping 2015-06-22 Språk Language Rapporttyp Report category ISBN Svenska/Swedish Licentiatavhandling ISRN Engelska/English Examensarbete C-uppsats D-uppsats — LITH-ISY-EX--15/4878--SE Serietitel och serienummer Title of series, numbering Övrig rapport ISSN — URL för elektronisk version http://www.ep.liu.se Titel Title DC-laddning av tunga kommersiella plug-in-hybridfordon Författare Author Oscar Hällman DC Charging of Heavy Commercial Plug-in Hybrid Electric Vehicles Sammanfattning Abstract En lösning för att kunna minska avgasutsläpp från tunga fordon är att helt eller delvis framföra 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 alternativt ladda med en högre effekt till kostnad av högre förlusteffekter och livslängd på energikällan. Detta arbete innehåller en förstudie på högeffektslikströmsladdning av hybridbatterier från befintlig infrastruktur anpassad till elektriska hybridbilar. Delar av arbetet innefattar: modellering av batteripack och likspänningsomvandlare, formulering av mpcregulator till batteripack, analysering av laddningsstrategier och batterirestriktioner genom simulering. Arbetet påvisar att en längre laddtid ökar energieffektiviteten och minskar batteridegraderingen. 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 Keywords PHEV, DC-Charge, Heavy Trucks, Battery Modeling, Half Bridge Converter Modeling 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 energy 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 dccharge 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 reduces 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. iii Contents Notation 1 Introduction 1.1 Background 1.2 Objective . . 1.3 Limitations . 1.4 Outline . . . vii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 2 3 2 Theory 2.1 Charge Equipment . . . . . . . . . 2.1.1 Charging Station . . . . . . 2.1.2 DC-DC Converter . . . . . . 2.1.3 Battery Junction Box . . . . 2.1.4 Communication Module . . 2.1.5 Battery Management System 2.1.6 Battery Pack . . . . . . . . . 2.1.7 Auxiliary Sources . . . . . . 2.2 Control Theory . . . . . . . . . . . . 2.2.1 Model Predictive Control . . 2.2.2 Quadratic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 6 8 10 10 10 11 12 12 13 14 3 Method 3.1 Modeling . . . . . . . . . . . . . 3.1.1 Battery Pack . . . . . . . 3.1.2 DC-DC Converter . . . . 3.2 Control Formulation . . . . . . 3.2.1 Control Construction . . 3.2.2 Charge References . . . 3.2.3 Voltage Reference . . . . 3.3 Simulation . . . . . . . . . . . . 3.3.1 Evaluation Environment 3.3.2 Charge Time . . . . . . . 3.3.3 Voltage Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 15 15 16 17 18 21 22 22 23 23 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v . . . . . . . . . . . . . . . . . . . . . . . . . . vi Contents 3.3.4 Current Restriction . . . . . . . . . . . . . . . . . . . . . . . 3.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Converter Measurements . . . . . . . . . . . . . . . . . . . . 4 Results 4.1 Modeling Results . . . . . . 4.1.1 Battery Pack . . . . . 4.1.2 DC-DC Converter . . 4.2 Simulation Results . . . . . . 4.2.1 Charge Time . . . . . 4.2.2 Voltage Control . . . 4.2.3 Current Restriction . 4.3 Implementation Results . . 4.3.1 Measurement Results 4.4 Discussion . . . . . . . . . . 24 24 24 . . . . . . . . . . 27 27 27 29 30 30 32 33 34 35 36 5 Closure 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 37 38 Bibliography 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notation Symbols and abbreviated terms Abbreviation ac bev bjb bms cc-cv ccs can dc evse hv mpc ocv phev plc pwm soc soh res v2g Signification Alternating Current Battery Electric Vehicle Battery Junction Box Battery Management System Constant Current Constant Voltage Combined Charging System Controller Area Network Direct Current Electric Vehicle Supply Equipment High Voltage Model Predictive Control Open Circuit Voltage Plug-in Hybrid Electric Vehicle Power Line Communication Pulse Width Modulation State Of Charge State Of Health Rechargeable Energy storage System Vehicle to Grid vii 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 Current) 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 efficiency 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. 1 2 1 1.2 Introduction Objective The objective of this thesis is to pre-study high power hv (High Voltage) dccharging 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 ensured with an automatic control of the power drained from the evse (Electric 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 motivations. • 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 combination with the heat transfers result in a very complex system that would exceed the framework of the thesis. 1.4 Outline 3 • The internal battery impedances are assumed to be constant and not dependent of soc. As with the temperature, this parameters will change depending 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 below. 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 specific methods for this thesis. Chapter 4: Contains all results of the work done according to the previous chapter. Chapter 5: Summarise the thesis with conclusions made and the remaining work to be done in the subject. 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 component 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 Network) 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 Combo2 Com Unit bms dc/dc bjb res Charging station Contact Communication unit Battery Management System Converter Connection box Battery pack 2.1.1 2.1.1 2.1.4 2.1.5 2.1.2 2.1.3 2.1.6 5 6 2 PLC Con CAN HV EVSE Com Unit Combo2 Auxiliary Source DC/DC Charging station BJB Theory BMS RES Vehicle Figure 2.1: Overview of the dc-charging components and how they are connected 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 Current max Power max 50 − 500V 125A 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 2.1 7 Charge Equipment PP L1 CP PE L2 N 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 CP 30V/2A PE 850V/125A DC+ 850V/125A DC- 850V/125A N L1-L3 480V/20A 480V/20A Detects connection between evse and bev/phev. Communicates between evse and bev/phev using plc. Ground used in all charging modes used through the contact. Positive charging input used with dccharging. Negative charging input used with dccharging. Not used. Not used. 8 2.1.2 2 Theory 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 Voltage range Over voltage Max continuous power 150 − 750V 800V 120kW Input parameter Value Voltage range Over voltage Current max 50 − 430V 445V 400A Control parameter Value Voltage range Switching frequency Efficiency typical 9 − 16V 39kHz 98% The dc-dc converter has a half bridge topology. A basic schematic of this topology 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. + Vin Iin IT N1 N2 − + VT − Figure 2.3: Schematic of a half bridge converter (without filters). The relation between the input Vin and output VT can be described with [7] VT N = 2D Vin N1 (2.1) 2.1 9 Charge Equipment where N1 and N2 defines 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 semiconductor and transformer losses. The semiconductor losses comes from non-ideal components whom contributes with power losses Psw at switching points because the semiconductor current must increase before the potential in the semiconductor 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 Pcond while 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 semiconductor voltages are equal in each semiconductor and that the efficiency is ideal gives Pcond ≈ Vsc Iin (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 Psw is the sum of Pon and Pof f . on u ton U off I 0 Ploss 0 P cond 0 Pon Poff tperiod 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, temperature 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. 10 2.1.3 2 Theory 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 System) and the other dc-charging components. The Communication unit also contains plc interface, since this standard is used by ccs to communicate with the evse [8]. The Power Line Communication uses a high frequency serial communication 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 example of this can be seen in Figure 2.5 where a high frequency signal is applied to a 1kHz pwm signal. PLC example 7 1 6 0 Voltage [V] 5 0.7 0.95 4 3 2 1 0 0 1 2 3 4 5 Time [ms] 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. 2.1 11 Charge Equipment 2.1.6 Battery Pack The battery pack or res used in this thesis is Lithium-Ion cell type. In this prestudy the battery temperature is assumed to be constant at 25o C, 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. Voltage [V] Current [A] Power [kW] Battery restrictions 0 0 700 0 50 100 State of Charge [%] Figure 2.6: Battery restrictions at 25o C, 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]. 12 2 Theory Open Circuit Voltage Charge Discharge VOCV [V] 700 0 0 50 100 State of Charge [%] Figure 2.7: Open Circuit Voltage at 25o C. 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 simulations used in the thesis. 2.2 13 Control Theory 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 x̂(k) to x̂(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 N −1 X λmin ≤λ≤λmax ||z(k + j) − r(k + j)||2Q1 + ||u(k + j) − u(k + j − 1)||2Q2 (2.2) j=0 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 boundaries λmin and 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 Q2 sets 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)T Q1 (MX − R) + (ΩU − δ)T Q2 (ΩU − δ) with the individual matrices and vectors described as r(k) x(k) u(k) r(k + 1) x(k + 1) u(k + 1) U = , R = , X = . . . . . . . . . r(k + N − 1) x(k + N − 1) u(k + N − 1) X = F x(k) + GU 0 0 · · · 0 0 I G F 0 0 · · · 0 F = . , G = . .. .. .. .. .. .. . . . . F N −1 F N −2 G · · · FG G 0 Q1 Q2 Q2 Q1 Q1 = , Q2 = .. .. . . Q2 Q1 (2.4) (2.5a) (2.5b) (2.5c) (2.5d) 14 2 M M = 2.2.2 M .. . M , I −I Ω = I .. . .. . −I I , u(k − 1) 0 δ = .. . 0 Theory (2.5e) Quadratic Programming To solve the mpc algorithm explained in the Section 2.2.1, quadratic programming [14] can be applied. Quadratic programming determines the control signal vector U that minimizes the function 1 min U T H U + Γ T U U 2 (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 = G T MT Q1 MG + ΩT Q2 Ω (2.7a) Γ = G T MT Q1 MF x(k) − G T MT Q1 R − ΩT Q2 δ (2.7b) with the matrix and vector elements as in equation (2.5). 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 , R2 and C2 that describes the dynamic voltages V1 and V2 , the parameter Vocv that models the ocv, the internal resistance Rs and the terminal voltage and current VT and IT . 15 16 3 R1 Rs − Method R2 V1 + V2 − + IT + C VOCV C 1 2 VT − Figure 3.1: Schematic of the res model. VT in Figure 3.1 is described with VT = Vocv (soc) + Rs IT + V1 + V2 (3.1) where the potentials V1 and V2 have the dynamic behaviour described with −1 V̇1 R1 C1 V̇2 = 0 ˙ soc 0 0 −1 R2 C2 0 0 V1 0 V2 + 0 soc 1 C1 1 C2 IT 1 Qtot (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 25o C. Since the model will be used to evaluate 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, Vocv was set as the mean of the two curves. The remaining parameters R1 , C1 , R2 and C2 were determined through the least square algorithm min f (IT ,meas ) = ZV X 2 V1+2,meas − V1,model (IT ,meas ) + V2,model (IT ,meas ) ZV = R1 C1 R2 C2 T V1+2,meas = VT ,meas − Rs IT ,meas − Vocv (socmeas ) (3.3a) (3.3b) (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 demands to transmit to the evse [16], a decent model of the dc-dc converter efficiency ηdc is needed. As mentioned in [17], this model can be described with 3.2 17 Control Formulation PT Pin (3.4a) PT = VT IT (3.4b) Pin = Vin Iin (3.4c) ηdc = With the voltages and currents VT , Vin , IT and Iin defined 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) Ploss = Psw + Pcond + Pcore + PR (3.6) where 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 , Vin and VT as ! VT 2 (3.7) + 1 Iin PR ∝ Iin Pcore ∝ 1 Psw ∝ Vin Iin Pcond ∝ Vin 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 2 Ploss,model = kP 1 + kP 2 Iin + kP 3 Iin + kP 4 Vin Iin + kP 5 VT Iin /Vin (3.8) where the values kP i , i = 1, . . . , 5 describes the proportional behaviour of equation (3.7). The parameters in equation (3.8) gets defined through least square approximations X 2 min f (ZP ,meas ) = Ploss,meas − Ploss,model (ZP ,meas ) (3.9a) Zk T Zk = kP 1 kP 2 . . . kP 5 T ZP ,meas = Iin,meas Vin,meas VT ,meas Ploss,meas = Vin,meas Iin,meas − VT ,meas IT ,meas (3.9b) (3.9c) (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 beginning of this section. Different charge and voltage references are found at the end of this section. 18 3.2.1 3 Method Control Construction A mpc controller was applied with the structure described with equation (2.2) in T T the theory Section 2.2.1, where z = VT soc , u = IT and x = V1 V2 soc ocv . 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 −1 1 0 0 0 C V̇ V 1 1 R1 C1 1 1 −1 V̇2 0 V2 C2 0 0 = + 1 IT R2 C 2 (3.10a) soc 0 0 0 soc Qtot ˙ 0 kocv ˙ ocv 0 0 0 0 ocv Q tot ! VT 1 = soc 0 1 0 0 1 ! V1 ! 1 V2 R + s IT 0 0 soc ocv (3.10b) which was discretised with zero order hold. The kocv is 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) (3.11b) VT ≤ VT ,max ( IT ≤ IT ,max IT ,max + kI,max (socb − soc) soc < socb soc ≥ socb (3.11c) where kI,max > 0 defines the first linear decrease of current that occurs at the higher soc, socb as seen in Figure 2.6. 3.2 19 Control Formulation Partial derivative of OCV ∂OCV/∂SOC +50% k −50% 0 0.25 0.5 0.75 1 SOC Figure 3.2: ∂ocv ∂soc as a function of soc. With a sample time tsample of 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 values 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: Q2 input 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: mpc calibration parameters. Parameter Value N 50 10−10 0 100 Q1 Q2 0 100 ! The step response of the system from socmin to socmax can be seen in Figure 3.3 and the lowest charging time defined as t0,min . The limits of the charge time depends of the voltage and current restrictions, which can be seen in Figure 3.4. As seen in Figure 3.3, the response time t0 can be divided into a linear region where the restrictions are constant and a settling part tsettle where the restrictions are harder, which can be seen in Figure 3.4. 20 3 Step response 1 SOC tsettle Linear region t 0,min 0 time Figure 3.3: Response of a step from socmin to socmax . Restrictions VT Max IT Max actual value restriction 0 b 1 SOC Figure 3.4: Restrictions of a step from socmin to socmax . Method 3.2 21 Control Formulation Since the prediction horizon is significantly lower than the rise time of the system (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 tsample increases the risk that restrictions are violated between the samples. Therefore none of this solutions were applied to this thesis and N tsample remained smaller than the charging time t0 . 3.2.2 Charge References Modifying the reference signal depending on charging time t0 , charging intervals 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 − socinit t t0 (3.12a) r(t) = socinit + (soc0 − socinit )(1 − e−t/τ0 + e−α ) ( r(t) = socb −socinit t t0 β socinit + socb + (soc0 − socb )(1 − e−(t−t0 β)/τ0 (1−β) + e−α ) (3.12b) t ≤ t0 β t > t0 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 τ0 is τ0 = t0 /α where α > 0 and the term e−α is 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 t0 that will apply the linear reference in the compound strategy in equation (3.12c). ˙ = IT /Qtot gives that The relation soc IT (soc) = Qtot ṙ(t) (3.13) which gives the control signals assumed that no restrictions are active as IT (soc) = IT (soc) = IT (soc) = Qtot (soc0 − socinit ) t0 (3.14a) Qtot socinit − soc + (soc0 − socinit )(1 + e−α ) τ0 Qtot − socinit ) t0 β (soc b Qtot socb − soc + (soc0 τ0 (1−β) (3.14b) soc ≤ socb − socb )(1 + e−α ) soc > socb (3.14c) 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 socb − socinit β soc0 − socb (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. Reference examples 1 SOC(t) b rlin rexp r com 0 0 Beta 1 IT(SOC) t/t0 0 b 1 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 Q1 in 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. 3.3 23 Simulation 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 Figure 3.6 and the simulation outputs in Figure 3.7. An implementation of this control system would require observers for the dynamic voltages V1 , V2 , the charge soc and an interpolation to achieve an estimation of Vocv . These values has to be estimated since they are not measurable on a physical battery pack. V_T SOC V_1 V_2 OCV I_T x' = Ax+Bu y = Cx+Du RES_model OCV(SOC) 1-D T(u) WorkspaceOutput u x MPC Controller Figure 3.6: Simulation model used for evaluation of reference signals in equation (3.12). Clock Display 1 V_T 2 SOC 3 V_1 4 I^2 V2I V1I 5 Scope VI V_2 Rs -K- |u| simout Abs To Workspace 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 η̄P = 1 − P¯loss P¯in (3.16) where P¯loss is defined as the mean value of the approximated power losses in the model of Figure 3.1 Ploss = (Rs IT + V1 + V2 )IT (3.17) 24 3 Method and P¯in defined as the average input power Pin = VT IT (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 t0 with 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 ,restriction represents 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 Q1 in equation (2.2) were set to ! 100 0 (3.20) Q1 = 0 10−10 for these simulations. 3.3.4 Current Restriction A theoretical sensitivity analysis of how charging times could decrease with relaxed restrictions of current IT were done through simulated steps from socmin to socmax with 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 cooling 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. 3.4 25 Implementation Table 3.2: dc-dc converter rig parameters. Parameter Value Vin Iin VT 300 − 430V 0 − 125A 600 − 690V Power Equipment Iin CAN HV Hose V + in − Cooling IT + DC/DC − V T Control Unit Figure 3.8: Rig configuration for dc-dc converter. 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. 27 28 4 Table 4.1: res model parameters. Parameter Value Set [soc] mean 0 0.25 0.5 0.75 1 R1 [mΩ] R2 [Ω] C1 [F] C2 [kF] 140 35.5 235 1.34 135 30.0 239 1.54 113 29.0 286 1.54 158 47.0 251 0.81 144 26.9 211 1.72 149 43.7 189 1.08 VT [V] Model Voltage 650 EV,T [%] 3 0 IT [A] −3 0 0 500 1000 Time [s] Figure 4.1: A comparison between the measured and modelled VT . Results 4.1 29 Modeling Results 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 kP 2 kP 3 kP 4 kP 5 639W −106V 9.50mΩ 15.9 × 10−3 29.2V−1 Converter Efficiency ηDC [−] 1 0.75 0.5 VT: 600V 5 45 85 125 ηDC [−] 1 0.75 0.5 VT: 630V 5 25 50 70 ηDC [−] 1 0.75 0.5 V : 660V T 5 30 55 ηDC [−] 1 0.75 0.5 VT: 690V 5 15 25 35 Iin [A] Figure 4.2: A comparison between the measured (dark) and modeled (light) ηdc . 30 4 Results Efficiency Map 1 ηDC [−] 0.75 0.5 0.25 0 690 660 630 VT [V] 600 0 25 50 75 100 125 Iin [A] 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 , η̄P as defined in equation (3.16) and the maximal terminal voltage, VT depends 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 signal 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 t0 and 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 exponential references. 31 Simulation Results SOC(t0) 4.2 rlin 1 rexp rcom ηP,mean 0.98 0.97 0.96 0.95 VT,max 1 0.99 1 2 3 4 t0/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. Distance to restriction ζmean 0.9 0.65 lin exp com 0.4 1 2 3 4 t0/t0,min Figure 4.5: Simulation results of ζ̄(t0 ) for the three reference signals. 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 ≤ socb and the same reference contributes with the worst values if soc is near 1 since the currents is near IT ,max here. The ζ-value of the exponential reference 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 . Distance to restriction 1 ζlin 0.75 0.5 0.25 0 1 ζexp 0.75 0.5 0.25 0 ζcom 1 0.75 0.5 0.25 0 0 b 1 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 converges 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 soc in the matrix Q1 makes it float and eventually end up in a value that fulfils VT ,ref = Vocv (soc). 4.2 33 Simulation Results VT control VT,max 1 actual value reference SOC 1 0 IT,max 1 0 0 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 t0 can be seen in Figure 4.8. The figure shows the results of five different current restrictions from 1 × IT ,max to 5 × IT ,max . Here it is seen that the time to fully charge the res is quite similar and near t0,min due to the restrictions of VT , as can be observed in Figure 4.9. Step response SOC 1 5×IT,max 4×I T,max 3×IT,max 2×I T,max 1×IT,max 0 0 0.5 1 t/t0,min Figure 4.8: Response of a step from socmin to socmax with relaxed IT ,max . 34 4 Results Restrictions VT,max 1 actual value restriction 5 IT,max 4 3 2 1 0 0 b 1 SOC Figure 4.9: Restrictions of a step from socmin to socmax with 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 Figure 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 ×It,max ηP [%] t0.5soc [%] t 1 95.0 26.8 2 93.2 13.4 3 92.0 8.9 4 91.1 6.9 5 90.6 6.2 [%] 50.9 27.9 22.5 20.5 19.9 0,min t0.9soc t0,min 4.3 Value Implementation Results This section contains a summary of the physical implementation of the converter to achieve measurements for the converter model parameterisation. 4.3 35 Implementation Results 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 Pin in 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. I [A] V [V] Converter Measurements 725 600 475 350 225 100 50 0 P [kW] 55 35 20 0 T [oC] 26 25 in T 24 23 0 100 200 300 400 500 600 700 Time [s] Figure 4.10: Measurement results of the dc-dc pre-implementation. 36 4.4 4 Results Discussion The parameter kocv in Section 3.2.1 is far from constant as assumed in the model equation (3.10). The variance of kocv can be seen in Figure 3.2. Since kocv only 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 kocv might 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 manufacturer 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 phenomena 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 complex circuitry than the one described with Figure 2.3 in theory Section 2.1.2. As seen in Figure 4.10, the input voltage Vin raises 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 results at different charging rates in [11]. This similarity might attest the model characterization. 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 restriction if it is later than the prediction 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,min to 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,min must be lower and therefore the restrictions like IT ,max needs to get relaxed which also would accelerate the ageing of the battery. 37 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 temperature 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 powers, 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 deriving 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. 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 actual 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 batteries and contribute with a healthier environment. 40 5 Closure Bibliography [1] Jens Groot. State-of-Health Estimation of Li-ion Batteries: Ageing Models. PhD thesis, Chalmers University Of Technology, 2014. [2] Alexander Schuller, et al. Charging Strategies for Battery Electric Vehicles: Economic Benchmark and V2G Potential. IEEE Transactions on Power Systems, 29(5), 2014. [3] Electric vehicle conductive charging system-Part 1: General requirements. IEC, 2011. IEC 61851-1. [4] Electric Vehicle Charging Infrastructure Terra multi-standard DC charging station 53. ABB, 2014. Product leaflet. [5] Combined ACDC Vehicle Inlet Type 2 - 3ACDC. Phoenix Contact, 2014. Datasheet. [6] BDC546 - Bidirectional 750V DC/DC-Converter. BRUSA Elektronik AG, 2014. Datasheet. [7] Ned Mohan, Tore M. Undeland, and William P. Robbins. Power Electronics: Converters, Applications, and Design. WILEY, third edition, 2003. [8] Electric vehicle conductive charging system-Part 24: Digital communication between a d.c. EV charging station and an electric vehicle for control of d.c. charging. IEC, 2014. IEC 61851-24. [9] Road vehicles - Vehicle-to-Grid Communication Interface-Part 1: General information and use case definition, 2013. ISO 15118-1. [10] Nader Javani, et al. Heat transfer and thermal management with PCMs in a Li-ion battery cell for electric vehicles. International Journal of Heat and Mass Transfer, 72:690–703, 2014. [11] Lian-xing Li, et al. CC-CV charge protocol based on spherical diffusion model. Journal of Central South University of Technology, 18:319–322, 2011. 41 42 Bibliography [12] Torkel Glad and Lennart Ljung. Reglerteori - Flervariabla och olinjära metoder. Studentlitteratur AB, second edition, 2003. [13] Martin Enqvist, et al. Industriell reglerteknik - Kurskompendium. Liutryck, 2014. [14] Jan Lundgren, Peter Värbrand, and Mikael Rönnqvist. Optimeringslära. Studentlitteratur AB, third edition, 2008. [15] Jianwei Li and Michael S. Mazzola. Accurate battery pack modeling for automotive applications. Journal of Power Sources, 237:215–228, 2013. [16] Road vehicles - Vehicle-to-Grid Communication Interface-Part 2: Network and application protocol requirements, 2014. ISO 15118-2. [17] Virgilio Valdivia, et al. Black-Box Behavioral Modeling and Identification of DC–DC Converters With Input Current Control for Fuel Cell Power Conditioning. IEEE Transactions on Industrial Electronics, 61(5), 2014. [18] Yusof Yushaizad, et al. Li-ion Battery Pack Charging Process and Monitoring in Electric Vehicle. Applied Mechanics and Materials, 663:504–509, 2014. [19] Hossein Maleki, et al. Li-Ion polymer cells thermal property changes as a function of cycle-life. Journal of Power Sources, 263:223–230, 2014. [20] Peter H.L. Notten, J.H.G. Op het Veld, and J.R.G. van Beek. Boostcharging Liion batteries: A challenging new charging concept. Journal of Power Sources, 145:89–94, 2005. [21] Zhu Shu-guang, et al. Recovery of Co and Li from spent lithium-ion batteries by combination method of acid leaching and chemical precipitation. Transactions of Nonferrous Metals Society of China, 22:2274–2281, 2012. Upphovsrätt Detta dokument hålls tillgängligt på Internet — eller dess framtida ersättare — under 25 år från publiceringsdatum under förutsättning att inga extraordinära omständigheter uppstår. 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