Modelling and simulation of onboard chargers

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Universit`

a degli Studi di Pisa

Scuola di Ingegneria

Master of Science in Electrical Engineering

Modeling and Simulation of

Onboard Chargers

Candidate

Mikalai Bazas

bazasmikalai@gmail.com

Supervisors

Prof. Massimo Ceraolo

Universit`a di Pisa

Ing. Christian Duelk

Daimler AG, Ulm

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Sperrvermerk

Die vorgelegte Arbeit mit dem Titel ”Modeling and Simulation of Onboard Chargers” beinhaltet vertrauliche Informationen und Daten der Daimler AG.

Dieser Sperrvermerk bezieht sich auf die komplette Arbeit.

Bez¨uglich der vom Sperrvermerk betroffenen Abschnitte darf die Arbeit nur vom

Erst-und Zweitgutachter sowie berechtigten Mitgliedern des Prüfungsausschusses eingesehen werden. Eine Vervielfältigung und Veröffentlichung eines solchen Abschnittes ist auch auszugsweise nicht erlaubt.

Dritten d¨urfen vom Sperrvermerk betroffene Abschnitte nur mit der ausdr¨ucklichen

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CHAPTER

1

Abstract

The target of this master thesis has been the optimization of the charging process of the entire on-board system of an electrical vehicle in terms of time. This process uses high-power DC current.

The simulations have been conducted over the Simulink based model of the charging system. The process has been analyzed in detail, all the influence variables that affect it have been studied, and their degree of influence has been reported.

As the result, a program under the form of Matlab script has been obtained. This script takes into account the given work- and ambient-conditions, the user required temperature constraints and decides autonomously which is the charging strategy to be applied. This strategy is a set of input variables that should be given to the charging system, in order to make the process as quick as possible.

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CHAPTER

2

Introduction

The aim of this thesis is the optimization of the charging time of charging process. In this Chapter all the important causes of slowing down of the charging process will be listed and discussed. In the second part of this Chapter the charging system will be described. The following chapters will list which are the input regulating variables available.

2.1 The Charging System of Electric Vehicle

The Charging system includes all the electrical components that can influence the charg-ing process, changcharg-ing the chargcharg-ing power delivered to the battery. These components are: battery(including BMS), heating and cooling components, all other electrical loads on board of the vehicle that can consume electrical energy during charging process and potentially decrease the charging power delivered to the battery. These components are represented on the fig. 2.1

The fig. 2.1 is a hybrid figure where both signals and powers are combined. The purpose of it is to highlight the names of variables used to identify the powers consumed by certain parts of circuits. It will be clarified in the following subsections which of them are the input(control) signals.

2.1.1 Battery and BMS

The Battery is the most complicated component of the charging system as a whole, and it is modeled as in fig. 2.2.

Physically, Battery is a union of piles of Li-ion cells placed in series and in parallel, together with casing, cables, tubes of cooling & heating system. For the optimization purpose it was not of a vital importance which exactly was the type of ions in the chemistry of the battery. What was really important to know is how the battery behaves in different temperature scenarios.

The subsystem Battery is a model of physical battery together with its BMS. It is a BMMS(Battery Monitor and Management System), to be more precise. This means that

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Figure 2.1: Charging system. Hybrid scheme.

the BMS does not only monitor the actual state of the battery but also has the ability to interact with the charging process. In order to prevent the damage or premature aging of the battery BMS can limit the level of charging/discharging current I. In the library that was used for simulations a BMS was an active component integrated inside the Simulink block without any possibility to separate it or turn it off.

A BMS may monitor the state of the battery as represented by various items, the most important of them are:

Voltage: total voltage, voltages of individual cells, minimum and maximum cell voltage

Temperature: average temperature, coolant intake temperature, coolant output temperature, or temperatures of individual cells

Current: current in or out of the battery Coolant flow of heating or cooling process

State of charge (SOC) or depth of discharge (DOD) State of health (SOH)

Additionally, a BMS may calculate values based on the above items, such as: Maximum charge current as a charge current limit

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Figure 2.2: Model of the Battery

Internal impedance of a cell (to determine open circuit voltage) Charge [Ah] delivered or stored

The central controller of a BMS communicates internally with its cell level hardware. A BMS may protect its battery by preventing it from operating outside its safe operating area, such as:

Over-current (may be different in charging and discharging modes) Over-voltage (during charging)

Under-voltage (during discharging) Over-temperature

2.1.2 The AC/DC Converter

The onboard AC/DC converter is designed for low levels of power, typically few kW of domestic AC power. The reason of such a low converting power is the weight of converter: every single object carried during the guide is an increase of energy consumption. This

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thesis is dealing with the simulation of quick (high power) charging processes, battery is considered to be charged always with high levels of DC currents coming directly from the DC stations. Since we are considering all the possible thermal and electric effects on the onboard charging system of the vehicle, our viewpoint is that this stationary converter is an external part of the charging system. The variable P grid is not a fixed value for the charging system, but the maximum threshold available: the charging system may not necessarily use all the power available(i.e. due to thermal limits of the BMS).

Usually, the higher the level of power the battery can accept is, the quicker it will reach its 100% of the SOC. In practice, the physical meaning of what the optimization algorithm does is: try to force the battery work in those conditions, where battery acceptance of current is on high and try to spend as less energy as possible to make it work in that zone. Later, when the thermal effects will be discussed, we shall see that this optimal value of charging current is not always coincident with the maximum value of accepted current.

2.1.3 Cooler and Chiller

The cooling circuit is composed of 2 components: NT-cooler and Chiller. The first one is a normal radiator with a cooling fan. The power that it consumes may vary slightly, proportionally to the coolant pump speed. The value of this power is very small, compared to what the other components of charging circuit consume.

Figure 2.3: Chiller-cooler, Simulink block.

The second component of the cooling circuit is a Chiller. The Chiller is a machine that removes heat from a coolant liquid via a vapor-compression or absorption refrigeration cycle. The power that it consumes is a non-linear function of its input/output delta

temperature and of the coolant speed. The Chiller is much more effective than the

Cooler in terms of the heat extracted. From the other side, the power that it consumes is several times bigger.

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2.1.4 Heater

A Heater provides heat to the circuit by transforming the electrical energy into heat in a dissipative manner. The Heater is located in the same loop of a cooling circuit and uses the same liquid for supplying heat to the battery. Obviously, when the heater is on, cooling components must stay off and vice versa.

Figure 2.4: Heater, Simulink block.

The Chiller could also be used for heating, but it was preferred to use only Heater at those temperature conditions. The power consumed and the effect produced by the Heater is several times bigger than the power consumed and the effect produced by the Chiller.

2.2 Causes of Slowing Down of the Charging Process

2.2.1 Battery temperature

The Battery itself would have accepted much bigger values of charging current than those that can enter to it due to BMS protecting limits. The BMS is an active component of the charging circuit. We have no ability to change the BMS limits during the whole charging process. However, knowing the reasons of such behavior of the BMS can be useful in order to be able to ”overpass” BMS limits by acting directly against the causes of these limits. Basically, we can modify the charging strategy in such a way that the charging process does not fall into the ”limitation zones”.

Depending on the actual battery temperature conditions, due to the safety reasons of the BMS, time of charging can be sensitively different for different values of battery temperature.

The BMS has its own control logic, the aim of which is to prevent the premature aging of the battery. Revealing in advance, from the conducted simulations on a given battery model, we noticed that the most convenient range of temperature is between [+25 ⇐⇒ +35]. In other words, this is the range where the battery manages to accept the highest charging currents. The way how the battery temperature can influence the charging time will be discussed in Chapter Sensitivity Analysis on fig. 3.26.

Typically, the BMS acts at particularly low or particularly high temperature scenarios. The following sections will highlight the most common reasons of why the BMS limits the current. Understanding these causes permits to organize the charging process better and may suggest new logic for a quicker charging profile.

According to the study ”Temperature dependent ageing mechanisms in lithium-ion bat-teries - a post-mortem study” [14], the dominating ageing mechanism for T < 25 is

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Lithium Plating, while for T > 25the cathodes show degeneration and the anodes will be increasingly covered by SEI layers.

2.2.2 Charging at Low Temperature, Lithium Plating

Graphite is used as a negative electrode material in most Li-ion batteries [10] and also in the battery under examination. Graphite mainly determines the overall aging behavior. The most important degradation mechanisms of the graphite electrode are continuous growth of the solid electrolyte interphase (SEI) and metallic lithium deposition on the graphite electrode in preference to lithium intercalation. This phenomenon is called Li plating [9, 8, 1, 11]. Plating can be reversible or irreversible [8]. Reversible plating describes deposited lithium with durable electrical contact with the negative electrode. Reversibly plated lithium is stripped during the discharge step. This reversible part does not cause any capacity loss(fig. 2.5).

In contrast, irreversibly plated lithium exhibits only fragile electrical contact with the

negative electrode. Such lithium may become electrically isolated from the graphite

electrode during the stripping process. Irreversible plating, i.e. dead lithium, is thus mainly responsible for the capacity losses during low temperature charging with high currents.

Irreversible plating is a function of SOC and temperature.

Lithium plating is different from all other degradation processes in terms of its tempera-ture dependence [14].

Below 25, the ageing rates increase with decreasing temperature [14].

The graphite electrode exhibits poor intercalation kinetics for lithium ions at low temper-atures. This kinetic hindrance causes high polarization of the negative electrode which favors lithium plating. [8]

Several studies show that Li plating can be drastically enhanced at sub-ambient temper-atures [11, 12, 7].

Charging with high current and at a high SOC is a typical aging mechanism of Li-ion batteries at low temperatures [8, 9, 1, 5].

Decreasing temperature leads to slow reaction kinetics of the graphite electrode, the electrolyte becomes sensitively denser, the ions begin to move slower in it. This causes fast supersaturation of the lithium concentration at the SEI interfaces. Thus, decreasing the temperature plating conditions are reached earlier(at lower SOC) [8].

It is expected that high charge(typical for low SOC) currents lead to the formation of relatively thick dendrites with a limited distance from the electrode surface. Small charge currents(typical for high SOC) correspond to slow lithium deposition and therefore lead to rather fine and fragile dendrites which are prone to electrical isolation [2]. This effect is graphically illustrated on fig. 2.5.

The consequences of Li plating can be severe safety problems, because metallic Li tends to be deposited in the form of dendrites [6, 13]. In the worst case scenario, such a dendrite may pierce the separator and short-circuit the cell. On the other hand, Li plating can also lead to loss of active lithium and capacity fading. Plated lithium may react with the electrolyte (adding to SEI growth) or become disconnected from the graphite forming a reservoir of inactive metallic lithium [6].

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Figure 2.5: Simplified model of the lithium plating-stripping process at different SOC levels.

limits the maximum value of current for low temperatures. To accelerate the charging process batterys temperature needs to be increased. During the charging process a certain quantity of heat is being dissipated on the internal resistance of the battery. This is an auto-heating phenomena, where the auto-heating power is P = Rint∗ I2 . The value of the internal resistance is higher at lower temperatures, it can even be two times bigger that at high temperatures. The reason of this is the electrolyte density that restricts the ion flow speed. The lower the temperature is, the higher the electrolyte density will be. On the other side, due to the BMS limits, the current flowing through the internal resistance will be much less at low temperatures. The term of current is in a square and the reduction of it by the BMS is so significant that it makes the auto-heating power be of few watts only.

The auto-heating effect is too small if we expect a fast charging scenario. That’s why additional heating power is used.

When optimizing the heating process, several variables should be studied: Heating off temperature

Heating power

If we consider the charging as a fast uninterrupted process, the Heating on temperature is not a variable, but a parameter. If time is a priority factor, it will always be the most convenient method to start heating at lowest temperature possible. Since the temperature can only rise during the charging process(the cooling mechanisms are not active for low temperature scenarios), and the charging process is considered uninterrupted - in this way the lowest temperature will be the initial battery’s temperature. In other words, if heating is useful for a given scenario - it will be most effective way to start heating immediately from the beginning. In fast charging scenarios once the battery is in a ”high-current acceptance” range, the values of charging current are typically big enough to cover the heat losses from the battery towards the cold ambient. That makes no need to switch the heating on and off multiple times: once the Heater is off there will be no need to turn it on again.

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Figure 2.6: Plating effect and dendrite growth

2.2.3 Charging at High Temperature

Above 25 ageing is accelerated with increasing temperature[14].

At high values of battery’s temperature the charging current is being limited again by the BMS. High values of current would have reduced the life cycles and caused the premature aging of the battery. Keeping the battery’s temperature lower than a certain value can permit much higher values of acceptable charging currents. This is the reason why cooling is used in fast charging for high temperature scenarios. Typically cooling with a chiller is an energy-expensive process. When the maximum available power is limited a good compromise should be found in order not to subtract too much power for cooling from charging.

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CHAPTER

3

Sensitivity Analysis

The purpose of sensitivity analysis is to understand which input variables influence the charging process, which of them have the major effect and which can be neglected. This will be useful for understanding which input variables in the optimization algorithm should have the major effect. We should make several simulations, varying only one of variables at a time. The simulations will be performed in the same conditions when studying different influence variables: the same initial battery temperature, the same ambient temperature, the same maximum grid power available. The purpose is to observe the effect on charging time at those conditions, let’s call them ”standard” conditions. In this Chapter the research was organized in the following way:

1. Description of all variables that influence the charging process, discussion of their effect on charging time and on the system in general.

2. Classification of effective variables based on their influence degree on charging time. Identification of input variables have the biggest effect on charging time and variables that are almost neglectable.

For any single variable under analysis, the configuration of the system was kept constant and all the tests were conducted varying only the variable under examination. Thus, we want to observe only the variable under examination influencing the system.

3.1 Influence Variables

In this subsection I will classify all the input variables of the charging system. Here, with ”input variables” we list all the control variables of the system. Even if some variables are not directly the input variables of charging system, but their variation may produce an effect on charging time - we call them, not properly, variables. Let’s list all of these variables:

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T cooler on T chiller on Q flow T heater on T heater off P heater

Heating power P heater is taken as constraint variable. The algorithm will take in account the maximum temperature of inlet fluid and in order to prevent the heating fluid from boiling inside the fluid tubes. If this maximum fluid temperature overpasses a certain value, a constraint will be violated and the algorithm will restart the simulation with the lower value for P heater.

For better understanding of the behavior of the charging process, the effect of the following parameter of simulation will be discussed :

Temp batt init

3.2 P converter

As mentioned in section 2.1.2 P converter is not a real input of the system. It is a max-imum value of power available for all the charging system, in this sense it is a threshold, a limit of a system. Nevertheless, the influence of this limit was studied: varying this value gives us the idea of how the charging process will change in scenarios with different charging powers available.

As expected: the bigger the available power is, the quicker the charging process will be. The charging time tends to decrease until the BMS of the battery begins to limit the values of input current.

In the testing environment, cooling and heating were forced to remain OFF. The initial temperature of the battery was such that even with the highest values of charging cur-rents, battery temperature reached its maximum during the charging process that did not lead to forcing the BMS to limit the value of charging current. These conditions were chosen intentionally to observe only the effect of charging power on charging time. As can be seen from fig. 3.1, the decrease of charging time is not proportional to the increase of charging power(the slope of a blue curve is not constant). In order to understand why it happens, let’s have a look on the power and the energy plots of fig. 3.2 and fig. 3.3. The point at 80% of SOC was taken as a reference - at this point cell voltages are only a function of battery temperature. From the power plots we notice that the bigger available P converter was, the bigger the power entering the battery was. For all the powers the limit of the BMS was still not reached - that can be seen on fig. 3.2 on the right. The red limiting value seems to be far from reaching, but in fact, it is not so unreachable: this limit value is the value for only first instances of charging process, where BMS permits high ”overcharging” values of current. After few seconds, due to thermal reasons, BMS

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10 20 30 40 50 60 Overall DC Power Available / kW

Charging Time SOC 20 − 80%

Chrg Mode DC | Ambient Temp 25°C Batt Init Temp 25°C | Cooler is Off | Chiller is Off

Heater is Off

10 20 30 40 50 6030

35 40 45

Maximum Battery Temperature During the Charging Process / °C

Charging Time Max Batt_Temp 10 20 30 40 50 60 25 30 35 40 45

Overall DC Power Available / kW

Temperature / °C

Chrg Mode DC | Ambient Temp 25°C Batt Init Temp 25°C | Cooler is Off | Chiller is Off

Heater is Off

Max Temp During Charge Process T

Batt at 80% SOC

T

Coolant Batt_in at 80% SOC

T

Coolant Batt_out at 80% SOC

Figure 3.1: Charging time and battery temperature for different values of P converter

limits roughly the current value, but in the picture, since those values of power were never reached, the limit seems high and unreachable.

The level of power consumed by LV loads remains always the same, since in all the simulations the cooler, heater or chiller were never activated. Exactly for this motivation, the energy consumed by the LV loads decreases with the power rise: the longer a constant-power load remains on, the more energy it will spend.

Let’s observe the power dissipated on the internal ”resistance” of the battery. Let’s call it for now Pdiss. Pdiss= Rbatt· I2, so it is a function of two terms. With the P converter rise, the I delivered to the battery will also rise. That will cause the rise of Pdissand thus, the rise of the battery temperature. But with the temperature rising, the Rbatt tends to be decreasing: as it has been mentioned in section 2.1.1, the Rbatt is not a real resistance. Rbatt represents mainly the effects of electrolyte to oppose the reaction on electrodes. Contrary to what happens with the real resistor, here, with the temperature rising the value of Rbatt will be decreasing. Anyway, in the expression of power, the decrease of term R is lover then the increase of term I where the last is in the second power. This leads to higher losses for higher values of P converter and exactly this fact justifies the inhomogeneity in slope of the blue curve on fig. 3.1 on the left.

Summing, P converter influences the charging time significantly. One more time: P − converter is not an input variable, but some kind of a maximum threshold. P converter is fixed by the limit of our system.

It must be mentioned once again that P converter is not a real variable of the system, but some kind of a constraint. Nevertheless, in some scenarios under certain circumstances it can be more convenient to charge with lower powers and obtain the lower charging times. The reasons can be multiple, the main of them being the following one: with lower charging power less heat inside the battery is produced and the battery may remain in a

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10 15 20 25 30 35 40 45 50 55 60 Overall DC Power Available / kW

Power at 80% SOC

Chrg Mode DC | Ambient Temp 25°C | Batt Init Temp 25°C Cooler is Off | Chiller is Off | Heater is Off

Entering into the Battery Requested by Chiller Requested by Heater

Requested by Cool Pump & LV Loads Power−Losses on R_int of the Battery

10 15 20 25 30 35 40 45 50 55 60

Power at 80% SOC

Requested by Chiller Requested by Heater

10 20 30 40 50 60

Charging Power at 80% SOC

Effective Power

Maximum Power Permited by BMS

10 20 30 40 50 60

0

Power at 80% SOC

EKMV Coolant Pump Heater

Figure 3.2: Power requested by different components at SOC of 80% for different values of P converter

better temperature-acceptance region with no need of additional cooling.

The conclusion of sensitivity analysis of P converter is that even if it is a parameter of the charging system, we can impose the charging system to work with lower values of P converter than the maximum available. That makes the parameter P converter to become a variable of the charging system.

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Energy

Accumulated in Battery Consumed by Chiller Consumed by Heater

Consumed by Cool Pump & LV Loads Losses on R_int of the Battery

Energy

Consumed by Chiller Consumed by Heater

Figure 3.3: Energy consumed by differ-ent compondiffer-ents during all the charging process for different values of P converter

3.3 T cooler on

Let’s observe now the influence of a real input of the charging system: the triggering turn-on temperature of the cooling circuit T cooler on. T cooler on is the value of bat-tery temperature at which the cooler activates. In the examined case cooling only by the radiator does not produce a huge effect neither on charging time nor on the battery temperature. The quantification of the effect on charging time can be seen on fig. 3.4. In this figure we can see the derivative of charging time in respect to cooler on temper-ature, calculated as a quotient _{∆CoolerOnT emp.}∆ChargingT ime. On the right scale of the right graph of fig. 3.4 we can read how the values of time derivative are small. The derivative becomes null for values of T cooler on > 35 , because at those charging conditions the battery temperature does not even reach 34, that’s why after 35 the cooler will never turn on.

The reasons why the effect of T cooler on on charging time is small are multiple. Among the main ones we can refer to the following: the level of charging power assumed was not extremely high and the level of ambient temperature is in a good range.

If we take a look on graphs of temperatures on fig. 3.5 on the left, we can observe that the later the cooler is turned on, the bigger maximum battery temperature will be. Again, in terms of the internal resistance of the battery: its values are decreasing with the temperature rising(see fig. 3.5 on the right). The explanation of it is written in section 2.1.1.

The purpose of the sensitivity analysis is to understand, how big the effects of any single input variable are. As a default case was chosen the one with ”normal” conditions. Certainly, in extreme conditions the effect of cooling will look better(more decidedly). Talking about powers, the main factor effecting the current acceptance of the battery is its temperature. The temperature did not change significantly, and anyway it did not

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20 25 30 35 40 45 50

Cooler On Temperature / °C

Charging Time

Chrg Mode DC | Chrg Power 30.0 kW | Ambient Temp 20°C Batt Init Temp 20°C | Chiller is Off | Heater is Off

Charging Time SOC 20 − 80% Max Batt_Temp

20 25 30 35 40 45 5028

30 32 34

20 25 30 35 40 45 50

Charging

Time

Charging Time SOC 20 − 80% First Order Derivative

20 25 30 35 40 45 50−0.015 −0.01 −0.005 0

First Order Derivative of Time to Cooler On Temperature / (min/°C)

Figure 3.4: Charging time and battery temperature for different values of T cooler on

overpass the BMS limits, so there should not be an effect in terms of acceptable powers(see fig. 3.6 on the right). The maximum accepted by BMS power was never overpassed. The only explanation of why the charging time changes is because the part of power was spent on cooling, instead of being delivered to the battery. NT-cooler consumes relatively few energy(can be seen on the lower part of the right graph on fig. 3.6).

Optimization of charging process is also a research of an optimal charging profile, where we can charge as much as we can, possibly spending almost nothing on cooling. It is a re-search of a compromise for the battery temperature that should not overpass a dangerous value(not necessarily the value of BMS limit) and for power delivered to the cooling. The cooler’s off temperature is taken as T Cooler of f = T Cooler on − 1. As it has been mentioned, the cooler’s effect on the battery is usually not so big, that’s why in fast charging processes the heat produced during the charging process on the internal resistance of the battery is much bigger than the heat extracted with the help of NT-cooler. That’s why, usually, when the cooler is turned on it does not get switched off until the end of the simulation process, so there is no need to observe T Cooler of f as an another input variable.

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20 25 30 35 40 45 50 20 22 24 26 28 30 32 34 Cooler On Temperature / °C Temperature / °C

Max Temp During Charge Process T_Batt at 80% SOC

T_{Coolant Batt_in} at 80% SOC

T

First Order Derivative

20 25 30 35 40 45 500 0.1 0.2 0.3 0.4 0.5 0.6 0.7

First Order Derivative of Battery´s Max Temp to Cooler On Temp / (°C/°C) 20 25 _{Cooler On Temperature / °C}30 35 40 45 50

R_int of the Battery

R_0 R_SOC80 R_max

Figure 3.5: Temperatures of the battery and cooling fluid in different instants, varying the T cooler on (left); Values of the internal resistance of the battery at different instants, varying the T cooler on (right)

20 25 30 35 40 45 50

Power at 80% SOC

Entering into the Battery Requested by Chiller Requested by Heater Constant LV Loads Requested by Coolant Pump Power−Losses on R_int of the Battery

20 25 30 35 40 45 50 Cooler On Temperature / °C Power at 80% SOC Requested by Chiller Requested by Heater Constant LV Loads Requested by Coolant Pump Power−Losses on R_int of the Battery

20 25 30 35 40 45 50

Actually Entering in Battery Maximum Power Permited by BMS

20 25 30 35 40 45 50 Cooler On Temperature / °C Power at 80% SOC EKMV Coolant Pump Heater

Figure 3.6: Power requested by different components at SOC of 80% for different values of T cooler on

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20 25 30 35 40 45 50

Energy

Accumulated in Battery Consumed by Chiller Consumed by Heater Consumed by Constant LV Loads Consumed by Coolant Pump Losses on R_int of the Battery

20 25 30 35 40 45 50

Energy

Consumed by Chiller Consumed by Heater Consumed by Constant LV Loads Consumed by Coolant Pump Losses on R_int of the Battery

Figure 3.7: Energy consumed by different components during all the charging process for different values of T cooler on

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3.4 T chiller on

A Chiller is another component of the cooling circuit. It requires much more power than the NT-cooler, but its cooling effect is also stronger. In this Section we shall observe and discuss the influence of turning on the chiller on charging time. Specifying: the triggering variable T chiller on is the value of the battery cell temperature at which the chiller is turned on.

15 20 25 30 35 40

Chiller On Temperature / °C

Charging Time

Chrg Mode DC | Chrg Power 30.0 kW | Ambient Temp 15°C Batt Init Temp 15°C | Cooler is Off | Heater is Off

15 20 25 30 35 4022

24 26 28 30

Charging Time SOC 20 − 80% Max Batt_Temp

15 20 25 30 35 40

Charging

Time

15 20 25 30 35 40−0.2

−0.15 −0.1 −0.05 0

First Order Derivative of Time to Chiller On Temperature / (min/°C)

Charging Time SOC 20 − 80% First Order Derivative

Figure 3.8: Charging time and battery temperature for different values of T chiller on As in case of T cooler on, the simulations will be made in normal warm temperature conditions As can be noticed from both graphs on fig. 3.8 - after a certain temperature for this particular scenario it is pointless turn on the chiller. From the left graph we can see that in all the scenarios T batt does not reach temperatures higher than circa 30. That is the value of T chiller on after which the derivate on the right graph _{∆ChillerOnT emp.}∆ChargingT ime becomes zero, that confirms what has been stated before.

It is useful to observe the progression of the derivate on the right graph of fig. 3.8. The module of it was decreasing at the beginning, but then at a certain point there was the inversion of the derivate slope, followed by its cancelling.

The reasons of such behavior are multiple. A Chiller is a complex physical system, the power that it consumes is a complex function depending on the delta temperatures of a coolant circuit at its input/output terminals(fig. 3.9). For better understanding, we can have a look at what exactly happens with the power distributed between the components

of the charging system. On fig. 3.10 and on fig. 3.11 we can notice how non-linear

the behavior of chiller is in terms of power that it consumes. From the left graph on fig. 3.9 we can notice, that the outlet temperatures of cooling fluid are also non-linear with the change of T chiller on. That means, that the inlet temperature of the battery will vary significantly in scenarios with different T chiller on and all the other conditions remaining the same. Different values of battery inlet cooling fluid will give different T batt conditions, that, in its turn, will effect the current acceptance.

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15 20 25 30 35 40 10 20 30 Chiller On Temperature / °C Temperature / °C

15 20 25 30 35 400

0.5 1

First Order Derivative of Battery´s Max Temp to Chiller On Temp / (°C/°C)

T

15 20 25 30 35 40

R_0 R_SOC80 R_max

Figure 3.9: Temperatures of the battery and cooling fluid in different instants, varying the T chiller on (left); Values of the internal resistance of the battery at different instants, varying the T chiller on (right)

From the other point of view, the power spent on cooling with the chiller, if it was not effecting the current acceptance of the battery, could be used for increasing directly the charging power. Again, it is a soft equilibrium between balancing the charging and the cooling powers. These ”balance” will be performed by our optimization algorithm.

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10 15 20 25 30 35 40 45

Power at 80% SOC

Entering into the Battery Requested by Chiller Requested by Heater Constant LV Loads Requested by Coolant Pump Power−Losses on R_int of the Battery

10 15 20 25 30 35 40 45 Chiller On Temperature / °C Power at 80% SOC Requested by Chiller Requested by Heater Constant LV Loads Requested by Coolant Pump Power−Losses on R_int of the Battery

15 20 25 30 35 40

Actually Entering in Battery Maximum Power Permited by BMS

15 20 25 30 35 40 Chiller On Temperature / °C Power at 80% SOC EKMV Coolant Pump Heater

Figure 3.10: Power requested by different components at SOC of 80% for different values of T chiller on

Figure 3.11: 3D plot of power consumed by chiller for different values of T chiller on during the charging process

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3.5 Q flow

In this Section the effect of variation of the volumetric flow will be discussed. The coolant pump permits the variation of volumetric flow in the range of [1 - 12] liters/minute. We shall vary the volumetric flow within all this range when the NT-cooler is on. Undoubt-edly, there shall be also an effect of variation of q flow when the chiller is on, but that is a more complex situation, because it influences also the power consumed by the chiller, involving thus another variable in the sensitivity analysis. So, for this Section only NT-cooler will be on during the simulation, meanwhile chiller will remain always off.

0 2 4 6 8 10 12

Volumetric Flow / l/min

Chrg Power 30.0 kW | Ambient Temp 25°C | Batt Init Temp 25°C Cooler On Temp 25°C | Chiller is Off | Heater is Off

0 2 4 6 8 10 1232

34 36

Charging Time Max Batt_Temp 0 2 4 6 8 10 12 24 26 28 30 32 34 36

Temperature / °C

T_{Coolant Batt_in} at 80% SOC T_{Coolant Batt_out} at 80% SOC

Figure 3.12: Charging time and battery temperature for different values of Q flow As can be noticed from the values on scale of the left graph on fig. 3.12, the influence of variable Q f low on charging time is very small. It is almost equal to the influence of the variable T cooler on in absolute terms (see fig. 3.4 for comparison). Again, the non-linearity in the curve of charging time is due to the fact that a part of power instead of being delivered to the battery directly for charging, is spent on cooling. It is assumed that the power consumed by the coolant pump is directly and linearly proportional to the volumetric flow(see fig. 3.13 (right)). From the fig. 3.13 we can also notice that at those charging conditions the temperature did not limit the charging process in terms of BMS limits.

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1 2 3 4 5 6 7 8 9 10 11 12

Power at 80% SOC

1 2 3 4 5 6 7 8 9 10 11 12

Power at 80% SOC

0 2 4 6 8 10 12

Effective Power

0 2 4 6 8 10 12

Power at 80% SOC

Figure 3.13: Power requested by different components at SOC of 80% for different values of Q flow

1 2 3 4 5 6 7 8 9 10 11 12

Energy

1 2 3 4 5 6 7 8 9 10 11 12

Energy

Consumed by Cool Pump & LV Loads

Losses on R_int of the Battery Figure 3.14: Energy consumed

by different components during all the charging process for dif-ferent values of Q flow

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3.6 T heater on

T heater on is the temperature of the battery at which the heater is turned on. For this analysis we needed to run the simulations at significantly lower temperatures, on the other hand, heating makes sense only at such low temperatures, where the current acceptance of the battery is compromised by the BMS.

For all the simulations the power of the heater was assumed to be constantly equal to 2 kW, when the heater was on. The heater’s power could also be a variable, and

in fact it will be used as an input variable for the optimization algorithm. For the

sensitivity analysis only the triggering temperatures will be observed: T heater on and T heater of f .

For this the sensitivity analysis, the heater was turned on always at different

tempera-tures: T heater on and was kept on until the battery was reaching +15 or until the

charging process was not finished.

−25 −20 −15 −10 −5 0 5 10

Heater On Temperature / °C

−25 −20 −15 −10 −5 0 5 10−20 −10 0 10 20 30

Maximum Battery Temperature During the Charging Process /

°C Charging Time Max Batt_Temp −25 −20 −15 −10 −5 0 5 10 −30 −20 −10 0 10 20 30 40 Heater On Temperature / °C Temperature / °C

Batt at 80% SOC

T_{Coolant Batt_out} at 80% SOC

Figure 3.15: Charging time and battery temperature for different values of T heater on It is immediately observed from the fig. 3.15 how important the heating is. Charging times are almost 5 times bigger in the areas where the charging process was conducted

without heating. For turning on temperatures from and above -15 the heater did not

turn on, because the auto-heating process of the battery was not even able to bring the battery up to those temperatures. This auto-heating process is the heat dissipated on Rint of the battery. As is shown on fig. 3.16 left, the values of Rintat those temperatures are very high, but from the other side as can be seen from fig. 3.16 right, that the values of the current flowing into the battery are very low, and since the value of heating power is R = Rint· I2, the term of I is in the second grade and it prevails over the Rint.

Having a look at what happens with powers, we can notice how heating can increase the maximum acceptable current and thus also the maximum accepted power of the battery: on the bar plot of fig. 3.17 we can see, that in a certain instant the entering power with

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−25 −20 −15 −10 −5 0 5 10 Heater On Temperature / °C

R_0 R_SOC80 R_max

−25 −20 −15 −10 −5 0 5 10

Battery Current at 80% SOC

−25 −20 −15 −10 −5 0 5 10

Battery Terminal Voltage at 80% SOC

I Batt BMS I Limit_Charge V_Batt BMS V Max

Figure 3.16: Values of the internal resistance of the battery (left); values of battery OCV and entering current at SOC of 80% and BMS limits (right) for different values of T heater on

heating is several times bigger than without heating. Undoubtedly, the heater is a very ”expensive” component in terms of energy - in our case it is working with 2 kW of power over the grid with 30 kW. In some other cases, the grid can be a less powerful one while the heater can be even bigger than 2 kW. From these plots can be noticed, that in low temperature conditions, heating is very important in terms of charging time(but not always in terms of energy efficiency), because despite having a powerful grid not all the power can be used. The algorithm shall search the optimum values of heating power and of the heater on/off temperatures for the quickest charging.

If we take a look at how many energy is spent on different components(fig. 3.18) it is curious to observe, that despite such a big power that heater consumes, it was able to reduce the energy consumed by other components: all the constant-power loads that were on during the charging process, were basically less time on with the heating. Thus LV loads consumed less. Another matter for the energy dissipated on the Rint of the battery: without heating its value was so low, that despite a long time of charge(with low currents) the energy dissipated on it was comparable to the energy dissipated on Rint in case of high-current charging at higher temperatures after heating.

From the charging time graph on fig. 3.15 we can conclude, that heating is very important at lower temperatures and it is convenient to heat up as soon as possible in order to bring the battery in a good current-acceptance zone, otherwise more time will be spent on charging. T heater on is not really a variable for the optimization algorithm: if we are not in a bad current-acceptance zone due to the temperature reasons, it will be convenient to begin to heat up as soon as possible and with the maximum heater’s power available - the real question is when it is convenient to stop the heating. That’s why the next Section is so important.

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−25 −20 −15 −10 −5 0 5 10

Heater On Temp / °C

Power at 80% SOC

−25 −20 −15 −10 −5 0 5 10

Power at 80% SOC

−25 −20 −15 −10 −5 0 5 10

Effective Power

−25 −20 −15 −10 −5 0 5 10 Heater On Temperature / °C Power at 80% SOC EKMV Coolant Pump Heater Power at 80% SOC

Figure 3.17: Power requested by different components at SOC of 80% for different values of T heater on

−25 −20 −15 −10 −5 0 5 10

Energy

−25 −20 −15 −10 −5 0 5 10

Energy

Figure 3.18: Energy spent on different components at SOC of 80% for different values of T heater on

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Figure 3.19: 3D plot of heater’s power during all simulation for different values of T heater on

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3.7 T heater off

As it has been mentioned in the previous Section - heating is very important for improving the charging time. In this Section we shall observe the effects of T heater off on charging process and particularly on charging time.

0 5 10 15 20 25

Heater Off Temperature / °C

−25 −25 −20−20 −15−15 −10−10 −5−5 0 5 10 15 20 25−20 −10 0 10 20 30

Charging Time Max Batt_Temp −30 −20 −10 0 10 20 30 −30 −20 −10 0 10 20 30 40 50

Temperature / °C

Figure 3.20: Charging time and battery temperature for different values of T heater off In the fig. 3.20 we can see that T heater off has also a pretty big effect on charging time, more or less like T heater on. From the charging time curve we can notice three interesting things: the slope of the curve is not constant, there is a saturation and the most important one is that there is a local minima, after which charging time is increasing with the rise of T heater off - fig. 3.21 left.

0 5 10 15 20 25

−10

Charging Time Max Batt_Temp −25 −20 −15 −10 −5 0 5 10 15 20 25 −30 −20 −10 0 10 20 30 40 50 Heater On Temperature / °C Temperature / °C

−25 −20 −15 −10 −5 0 5 10 15 20 250.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

First Order Derivative of Battery´s Max Temp to Heater On Temp / (°C/°C)

Batt at 80% SOC

T

Coolant Batt_in at 80% SOC

T

Figure 3.21: Flex in curve of charging time(left) and derivative of battery max tempera-ture(right) for different values of T heater off

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On fig. 3.22 we can see how temperature influences the BMS limits. From this figure, for this particular scenario, it can be seen, that if the grid power available had been bigger, the battery would have been able to accept even more power from T heater off

switching off temperature of 0 and above. Having a bigger power also means having

more charging power available when heating.

0 5 10 15 20 25

−25

−25 −20−20 −15−15 −10−10 −5−5 0 5 10 15 20 25

I Batt BMS I_{Limit_Charge} V Batt BMS V_Max −30 −20 −10 0 10 20 30

Effective Power

−30 −20 −10 0 10 20 30

0

Power at 80% SOC

Figure 3.22: battery BMS V and I limits(left) and power limits(right) at 80% SOC for different values of T heater off

This explains how the final optimization algorithm should work: it should correctly decide when it is the most convenient instant to switch off the heater, to avoid overheating and thus the extra charging time. Overheating has also extra cost that can be avoided. On fig. 3.23 we can see values of power at 80% of SOC and energy spent by different components during all the charging process. The value of 80% for SOC is chosen because at that point the battery current limits are still high, but soon will be limited. That means, that the battery will most likely have almost its highest temperature around that point: it was charged with maximum currents before and soon the value of current will be limited and so the internal losses will decrease after 80% of SOC.

From the left graph of fig. 3.22 we see that for T heater off values from 5 and above the values of charging current at 80% of SOC were always the same, but the highest losses on the internal resistance correspond to the temperature of 5. fig. 3.24 explains that: as mentioned in section 2.1.1 - the internal resistance is a circuital equivalent of what happens on TV(terminal voltage) of the battery when the current is flowing through it. It basically models the effects of internal chemical reactions and represents how the reaction on electrodes opposes to the current flow. Since the electrolyte density is higher at 5 than at 10, the value of Rint is also higher, despite the behavior of a standard resistor. The figure 3.25 clearly shows the effect of ”stopping” the heating process on charging time.

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−25 −20 −15 −10 −5 0 5 10 15 20 25

Heater Off Temp / °C

Power at 80% SOC

−25 −20 −15 −10 −5 0 5 10 15 20 25

0

Power at 80% SOC

−25 −20 −15 −10 −5 0 5 10 15 20 25

Energy

−25 −20 −15 −10 −5 0 5 10 15 20 25

Energy

Figure 3.23: battery component power consumption at 80% SOC(left) and overall energy consumption during the whole charging process(right) for different values of T heater off

−30 −20 −10 0 10 20 30

Heater off Temp / °C

R_0 R_SOC80 R_max

Figure 3.24: Values of the

in-ternal resistance of the battery in different instants for different values of T heater off

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Figure 3.25: 3D plot of heater’s power during all simulation for different values of T heater off

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3.8 Temp batt init

The last parameter discussed in this chapter will be Temp batt init. As said, it is a param-eter and not an influence variable. This section, with different values of Temp batt init, can highlight better the behavior of the charging system.

−200 −10 0 10 20 30 40 50

Initial Temperature of the Battery / °C

Chrg Mode DC | Chrg Power 30.0 kW | Ambient Temp 25°C Cooler is Off | Chiller is Off | Heater is Off

−20 −10 0 10 20 30 40 50−20

0 20 40 60

Charging Time Max Batt_Temp −20 −10 0 10 20 30 40 50 −10 0 10 20 30 40 50 60

Temperature / °C

Figure 3.26: Charging time and maximum temperature of the battery for different values of Batt init temp

If we zoom the charging time curve in the part where its values tend to the constant value (fig. 3.27), we shall see that differently to what was happening for T heater off simulation (see fig. 3.21) - there is no local minima. Let me explain this difference: in both simulations T heater off and Batt init temp there is always a heat produced on the internal resistance of the battery. That is inevitable. In case of T heater off, keeping the heater on for too long was forcing the charging system to deliver a significant part

10 15 20 25 30 35 40 45 50

Charging Time Max Batt_Temp

Figure 3.27: Zoome of a charg-ing time curve of Batt init temp in its ”saturation” part.

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of energy to the heater instead of delivering it to the battery, when it was not more necessary, because the battery was already in a ”good current acceptance” temperature region.

−20 −10 0 10 20 30 40 50

I Batt BMS I Limit_Charge V Batt BMS V Max −200 −10 0 10 20 30 40 50

Effective Power

−20 −10 0 10 20 30 40 50

0

Power at 80% SOC

Figure 3.28: Battery BMS V and I limits(left) and power limits(right) at 80% SOC for different values of Batt init temp

The fig. 3.26 together with fig. 3.28 show how the battery temperature limits the current acceptance of the battery. We can notice that the BMS limits are acting at extremely low or high temperatures. The auto-heating effect of charging process at those temperatures is not so big, comparable to the heater of some decimal of kW (see the values of Power-losses on fig. 3.29).

Let’s observe the effect of extremely high temperatures. In our case the ”hottest”

simu-lation was made with Batt init temp of 50 and seemingly the charging time was not

influenced, the temperature plot on fig. 3.26 shows that the maximum battery

temper-ature reached was of 55 circa, and that began to introduce another BMS limit on

current, shown on fig. 3.28.

Basically Batt init temp is the main influence factor on charging time - it triggers the limits on BMS. What we can do to accelerate the charging process is to try to keep the temperature of the battery within a good region. Where ”good” region means the region where the BMS does not limit the values of charging current. Regression analysis helps to understand how the typical value of the dependent variable (or ’criterion variable’) changes when any one of the independent variables is varied, while the other independent variables are held fixed. A specifical linear regression approach will be adopted. We shall create a linear model for each independent variable using ordinary least squares method. Then as a comparison sample, a linear coefficient of each line model can be used.

We shall use ordinary least squares or (linear least squares) method for estimating the unknown parameters in a linear regression model.

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−20−15−10−5 0 5 10 15 20 25 30 35 45 50 0

Power at 80% SOC

−20−15−10−5 0 5 10 15 20 25 30 35 45 50

0

Power at 80% SOC

−20−15−10−5 0 5 10 15 20 25 30 35 45 50

Energy

−20−15−10−5 0 5 10 15 20 25 30 35 45 50

Energy

Figure 3.29: Component power consumption at 80% SOC(left) and overall energy con-sumption during the whole charging process(right) for different values of Batt init temp

3.9 Regression analysis

In the previous Sections alle the influence variables have been mentioned and their effect on charging system has been discussed. The focus was on the relationship between each dependent variable and charging time. In this Section we shall estimate the grade of this relationship. In order to understand which of the variables has a major influence on charging time and which has the less one, we need to be able to find some kind of a comparison factor, some kind of ”grade of influence” on charging time. Regression analysis approach will be used to do that.

R.A. is a process for estimating the relationships among variables. R.A. helps to un-derstand how the typical value of the dependent variable changes when any of the in-dependent variables is varied, while the other inin-dependent variables are held fixed. The estimation target is a function of the independent variables called the regression function. We shall develop a linear regression model for each independent variable for the whole possible range of variation of independent variable. The linear coefficient of the model will be an index of influence degree.

Ordinary least squares (OLS) or linear least squares will be a method for the unknown parameters estimation in a linear regression model, with the goal of minimizing the sum of the squares of the differences between the observed responses in the given dataset and those predicted by a linear function of a set of explanatory variables. Once the parameters are estimated and the linear model is drawn, we can make a good priority analysis among the variables by comparing their linear coefficient in the obtained linear models. This linear coefficient will be an index of how quick the charging time is changing with the change of exactly this input variable. Let’s see how these linear regression models look

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like - see fig. 3.30.

−20 −10 0 10 20

y = − 4.5*x + 1.4e+02

Charging Time Linear Fitting

−20 −10 0 10 20 30 40 50

y = − 1.5*x + 84

Figure 3.30: Fitting of charging time curves for T heater off and Temp batt init

Table 3.1: Influence variables and their linear fitting equations of charging time

Input variable Linear equation

P converter y = −1.6 · x + 99

T cooler on y = −0.0045 · x + 39

T chiller on y = −0.062 · x + 41

Q flow y = −0.015 · x + 39

T heater off y = −4.5 · x + 1400

Temp batt init y = −1.5 · x + 84

3.10 Conclusions on Input Variables and Parameters

To conclude it should be stressed that that the influence of variables P converter and T heater of f is several times bigger than the influence of other input variables. This fact will be taken in account by the optimization algorithm, which will be described in the next Chapter.

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10 20 30 40 50 60

Chrg Mode DC | Ambient Temp 25°C

Batt Init Temp 25°C | Cooler is Off | Chiller is Off | Heater is Off

y = − 1.6*x + 99 Charging Time Linear Fitting 20 25 30 35 40 45 50 Cooler On Temperature / °C Charging Time

y = − 0.0045*x + 39

Charging Time SOC 20 − 80% Linear Fitting

15 20 25 30 35 40

Charging

Time

y = − 0.062*x + 41

Charging Time SOC 20 − 80% Linear Fitting

0 2 4 6 8 10 12

y = 0.015*x + 39

Figure 3.31: Fitting of charging time curves for P converter, T cooler on, T chiller on and Q flow

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CHAPTER

4

Optimization algorithm

As the result of this thesis a working program in a form of a Matlab script was developed. This script is able to find for any specific charging scenario the best set of input vari-ables that gives the minimum charging time. Thus, the algorithm indicates the optimal charging profile for the given temperature, grid and ambient characteristics.

The process of analysis and classification of all the variables on the ground of their grades of influence on charging time preceeded the program development. The present Chapter deals with algorithmic and mathematical logic description.

4.1 Script Logic Description

The developed program is a recursive whole of loops. The Matlab script calls for the execution of four functions, each of which is a stand-alone program. The developed Matlab script tries to simulate the charging process, varying initial input parameters in order to find the optimum set of input variables that will minimize the overall charging time. The logic due to which the variables are being varied is described in section 4.3. The main structure of the program is reported on fig. 4.1. This is a description of the overall Matlab script, where each step is a call of underlying function, numbered with a digit from 1 to 4. The output of each step is a set of variables, which will be used as input variables for the following step. This set corresponds to the minimal charging time found in the current step.

Once the 4th_{step of 4.1 is terminated, the value of it optimum charging time is memorized}

and compared with the optimum charging time value of the 2nd _{step(also memorized}

before). If the improvement in terms of charging time is less than 0.1 minutes, the while loop that involves steps 3 and 4 is activated. This time, at the end of each while loop, charging time of steps 3 and 4 is compared in the same manner. With each run of the loop the charging time has improved. If the improvement is less than 0.1 minutes, the entire process stops because the optimum of charging time has been found.

Modelling and simulation of onboard chargers

Universit`

a degli Studi di Pisa

Scuola di Ingegneria

Master of Science in Electrical Engineering

Modeling and Simulation of

Onboard Chargers

Candidate

Mikalai Bazas

Supervisors

Prof. Massimo Ceraolo

Ing. Christian Duelk

Contents

CHAPTER

1

Abstract

CHAPTER

2

Introduction

2.1

The Charging System of Electric Vehicle

2.1.1

Battery and BMS

2.1.2

The AC/DC Converter

2.1.3

Cooler and Chiller

2.1.4

Heater

2.2

Causes of Slowing Down of the Charging Process

2.2.1

Battery temperature

2.2.2

Charging at Low Temperature, Lithium Plating

2.2.3

Charging at High Temperature

CHAPTER

3

Sensitivity Analysis

3.1

Influence Variables

3.2

P converter

3.3

T cooler on

3.4

T chiller on

3.5

Q flow

3.6

T heater on

3.7

T heater off

3.8

Temp batt init

3.9

Regression analysis

3.10

Conclusions on Input Variables and Parameters

CHAPTER

4

Optimization algorithm

4.1

Script Logic Description