Modelling and design of a highly modular Sodium-Metal halides battery system

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University of Pisa

Information Department Electronic Engineering

Modelling and design of a highly modular Sodium-Metal

halides battery system

Candidate: Ian Biagioni

Supervisor:

Prof. Roberto Saletti

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Abstract

The following document aims to show the initials steps for the design of a battery system based on sodium metal halides chemistry.

Before starting the design of the BCS (Battery Control System), a complete com-prehension of the battery behaviour is necessary to decide on the proper sizing of the components and the best algorithms for processing.

A brief overview on the state of art of these batteries and on battery system design will be presented to give the reader a proper background on the arguments.

Than the chemical behaviour of a single cell is studied to understand the important parameters that have to be taken into consideration to realize simplier models that can be used on the BCS to estimate the state of the battery.

Two different simplified models will be presented, obtained from two different approach to the problem.

A large part of the work is dedicated to the thermal modelization and aims to provide a good estimation of the temperature distribution inside the battery.

After completing the modelling part, the initial steps for the design of an innovative BCS are presented.

The results obtained are preliminary for future works on a complete design of the system.

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List of Figures

2.1 BCS features [1] . . . 8

2.2 Example of OCV-SoC relation (Li-Po battery) [1] . . . 9

2.3 ZEBRA cells in series fail rappresentation . . . 12

3.1 Battery schematization . . . 15

4.1 Parameter meaning [25] . . . 21

4.2 General equivalent circuit model for a battery [27] . . . 22

4.3 Old generation ZEBRA cell and particular of behaviour [25] . . . 23

4.4 Basic circuit model and series resistance behaviour [25] . . . 25

4.5 Parameter identification focusing on a single current pulse [28] . . . 26

4.6 Relative error of the model vs experimental data. In green the old model, in blue the proposed one [28] . . . 27

4.7 OCV vs SoC characteristic [19] . . . 28

4.8 Circuit model with considering the iron reaction [25] . . . 29

4.9 Voltage behaviour at high current pulse and RF e contribution [25] . . . 30

4.10 RN i, RN it and RF e relation to layer radius [25] . . . 30

4.11 Complete circuital model of the ZEBRA battery [29] . . . 31

4.12 Current pulse used to determine the parameters [29] . . . 32

4.13 Parameters values [29] . . . 33

4.14 Validation in discharge condition [29] . . . 34

4.15 Validation in charge condition [29] . . . 35 5.1 Aging effects of working near operative temperature range limits [30] . 36

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5.2 48TL200 external geometry [9] . . . 38

5.3 48TL200 estimated geometry . . . 40

5.4 WDS technology physical characteristics [36] . . . 41

5.5 Cell composition expressed in percentual of weight [4] . . . 43

5.6 Temperature evolution of the 48TL200 in different situations [9] . . . . 44

5.7 Equivalent thermal circuit in stationary conditions . . . 46

5.8 Heater power consumption vs ambient temperature in floating condition [9] 46 5.9 Cell structure with nickel core . . . 48

5.10 Meshed battery . . . 50

5.11 ∆T versus ρ−1_{T h} . . . 52

5.12 Planar temperature gradient at the top of the cells . . . 52

5.13 Planar temperature gradient in the middle part of the cells . . . 53

5.14 Planar temperature gradient at the bottom of the cells . . . 53

5.15 Equivalent thermal circuit . . . 55

5.16 Temperature evolution in different internal points of the battery. The red line rappresent the experimental evolution from Fig. 5.6a . . . 60

5.17 Proposed geometry with five holes . . . 61

5.18 Particular of the gradient temperature in front of one hole . . . 63

5.19 Planar temperature gradient at the top of the cells . . . 63

5.20 Planar temperature gradient in the middle part of the cells . . . 64

5.21 Planar temperature gradient at the bottom of the cells . . . 64

5.22 Temperature of the slices from yellow (bottom slice) to red (top slice) . 65 6.1 BMS scheme on the 48TL battery [39] . . . 68

6.2 Hierarchical structure proposed for the BCS . . . 69

6.3 Proposed architecture for a highly modular BCS . . . 72

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Chapter 1 Introduction

For decades several electric implementations have been limited by the absence of a reli-able energy storage system. The evolution of the battery chemical technologies along-side the development of embedded systems capable of precise control of the battery status allowed a big expansion of the possible fields of application of electric solution. The most studied batteries technology are all based on lithium being the solid element with the lowest density at ambient temperature and due to its high electrode potential. Other than the lithium based one, there are several batteries technology that can win over the other solutions in certain applications.

One of these types of batteries is based on the Sodium Metal halides technology. Even if its electrical characteristics are a bit worse than other batteries, it is one of the best technologies in terms of reliability, safety and capability to work in harsh environment. However its diffusion has been limited by the few research that has been done on the implementation of a simple battery modelization. Only in the last years the interests for this type of battery has been rising so that several companies and groups of research have started to work on this technology.

The University of Pisa, the University of Cagliari, the KACTS center of technology and science and the Solid Power company has started a collaboration on this subject. The UNIPI group has focused its attention to the realization of an innovative battery control system for this type of battery.

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1.1 Objectives

This thesis work consists in the preliminary research on the battery technology and on the development of the models that are necessary for a proper management of the battery.

The main focus of the discussion will be concentrated on the electric and on the thermal characterization and modellization of the battery.

Taking into consideration the results obtained, an original architecture will be pro-posed for the electronic control system implementation and the battery geometrical structure.

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Chapter 2 Background

2.1 Battery control system

In recent years the rapid growth of importance of portable electronic devices, electric vehicles and smart grid application has driven the research for better batteries tech-nology. Along with the development of cells with higher power and energy density, it is equally important to develop an accurate control to provide a safe, reliable and cost efficient system. [1]

Usually referred as BMS (Battery Management System) or BCS (Battery Control Sys-tem), it performs several monitoring and control tasks at different organization level (such as cells, string cells or battery pack) that allows to check for the state of the battery and to better use the energy contained within considering its state.

To achieve this purpose, a BCS usually contains the following features (as shown in figure 2.1):

Cell monitoring (SOC estimation and battery safety and protection) Thermal management

Charge control Cell balancing SOH estimation

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Figure 2.1: BCS features [1]

Cell monitoring

To evaluate the battery state, it’s necessary for the BCS to measure the current, voltage and temperature of each electro-chemical cell that compose the battery. Monitoring these quantities having an appropriate model of the cell behaviour allows the BCS to determine the condition of the battery and to avoid critical situation (like short circuit condition or insulation loss).

One of the most important parameter is the SoC (State of Charge) defined as

SoC = Qc Qn

(2.1) where Qc is the remaining charge that can be extracted from a cell/battery and

Qn is the nominal capacity of the cell/battery. It is usually written as percentage and

indicates how much charge remains inside the cell/battery.

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indi-cates how much discharged is a cell/battery and is defined as

DoD = 1 − SoC (2.2)

Another important parameter is the Open Circuit Voltage (OCV) that indicates the voltage measured between the cell electrodes when there is no current flow and in stationary condition. It is function of the SoC and it is usually weakly influenced by temperature. It is characteristic of the composition of the cell.

Figure 2.2: Example of OCV-SoC relation (Li-Po battery) [1]

The OCV and the cell behaviour when connected to a load are used to estimate the SoC of the cell. Besides the importance of knowing how much charge is left inside the battery, the SoC estimation is critical to ensure the good health of the cells. In most of the cells technologies, overcharge and overdischarge situations lead to a rapid loss of performance or high chance of critical failure. Therefore knowing the SoC with high precision is essential to extract as much charge as possible without damaging the

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battery.

Thermal management

The temperature is another factor that has to be taken into account. Each cell tech-nology has an optimal working range of temperature outside which various parameters (such as capacity and internal resistance) degrade, lowering the efficiency of the sys-tem. Furthermore certain range of temperature can cause critical failure (e.g. battery explosion) endangering the environment in which the battery is installed.

The BCS need to be able to control the temperature in a certain degree or at least stop the battery utilization in case the temperature range conditions are not satisfied.

Charge control

From an user point of view, the charging speed for a battery has to be as high as possible but there are limitations due to the chemical or physical characteristics of the battery. If these restraints are not respected, damages can occur to the battery.

Cell balancing

Tipically a battery is composed by several cells. Depending on the application, the cells can be connected in series (to increase the output voltage) or in parallel (to increase the capacity of the battery and the maximum output current). However if there is a mismatch between the cells voltage or capacity, the entire battery can’t work efficiently. If there is a voltage difference between parallel cells, internal currents can manifest degrading the battery capacity. In case of difference in capacity, some cells can’t be completely charged or discharged.

Cell balancing techniques have been developed to handle these problems in the proper way.

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SOH estimation

Another critical aspect that has to be considered is the battery aging. Depending on the battery life history (number of charge-discharge cycles, temperature history, etc), its performance can degrade until the battery can’t work anymore respecting the specification.

The State of Health (SoH) parameter is used to estimate the remaining lifespan of a battery. The SoH can be defined in different ways depending on the application or the minimal specification needed.

The classical definition consider the loss of capacity [2]

SoH(t) = Qmax(t) Qn

(2.3) where Qmax(t) stands for the maximum capacity of the battery at a certain time

and Qn is the nominal capacity at the time of manufacture.

2.2 Molten salt batteries

The idea of using molten sodium as anode and β-alumina (β00-Al2O3) as solid electrolyte

brought to the realization of two types of batteries based on two different cathodes composition, sulphur and nickel. In both cell technologies, the β-alumina electrically insulate the cathode from the anode but allow the passage of sodium ions when the temperature is above 250°C. Considering that the sodium melts around 100°C, the β-alumina conduction condition is more strict, setting the operating temperature lower limit of these technologies at 250°C. Because of that, they are also known as high temperature batteries. [3]

NaS vs ZEBRA

Both technologies have similar characteristics. The NaS battery (the one based on a sulphur cathode) works at slightly higher temperature (300°C at minimum) than the other one but the major differences can be found when speaking about safety and

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ro-bustness to failure. The NaS cathode composition degrade the β-alumina insulation functionality during time. Moreover if the solid electrolyte breaks, the anode and the cathode components come into contact so that a violent exothermic reaction occurs resulting in a dangerous situation and critical battery failure [4]

The showed problems of the NaS battery are not present in the ZEBRA battery (the one base on nickel cathode), whose name stands for Zero Emissions Batteries Research Activity (acronym taken from the project Zeolite Battery Research Africa that origi-nally developed the technology). The β-alumina layer is not degraded by the chemical of the cell and even if it breaks, the reaction that occurs doesn’t cause dangerous situ-ations. In particular a short-circuit path is created between the terminals so that the cell can’t be used as an energy accumulator anymore.

Figure 2.3: ZEBRA cells in series fail rappresentation

However this still allows the use of these cells connected in series at the cost of losing some potential, making this technology much more resistent to critical failure. Considering the similarities between the two technologies and the advantages of the nickel cathode, the ZEBRA battery is considered as an evolution of the NaS one [4].

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2.2.1 ZEBRA battery

The ZEBRA project started in the late ’70 in South Africa with the idea of developing a cell technology based on a metal halide (nickel chloride) cathode in a liquid electrolyte (N aAlCl4). In later years the technology has been developed by Beta Reasearch &

Development Ltd from England while the main production came from AEG Zebra Marketing in Germany. [5]

Today the battery cathode is composed by a mix of nickel and iron to improve the battery characteristics. The only companies that are currently on the market with this technology are General Electrics (that acquired Beta R&D in 2007 [6]) with the Durathon battery and FZ Sonick SA (originated in 2010 from the collaboration between FIAMM and MES-DEA; this last one bought the ZEBRA patent from Daimler Benz that acquired AEG in 1999) with different battery solutions.

Characteristics

The ZEBRA battery characteristics made this technology to be a good solution in several applications such as EVs (Electric Vehicles), energy storage and UPS (Uninter-ruptible Power Supply). It presents a specific energy of 120Wh/Kg, a specific power of 150W/Kg and a volumetric density of energy of 180Wh/l [4]. Considering these characteristics, the ZEBRA technology places amongs the bests battery technologies (even if behind some technologies based on lithium).

Apart from this, the ZEBRA technology presents different advantages that made it competitive on the energy storage market:

High safety [3,7,8]

Low ambiental impact [12]

Wide range of working temperature (-20°C to 60°C limited by electronics) [9] Performances weakly affected by ambient temperature [9]

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Unitary coulombic efficiency

Long life (10-15 years of utilization and 5000+ cycles) [10,11]

Fails to short-circuit, increasing series configuration robustness to fail If not heated, can maintain its SoC indefinitely

No maintenance needed [9]

No self-discharge due to side reactions

Can provide sequential peak of high power at low internal resistance

These characteristics make the ZEBRA battery a perfect solution for all the appli-cation in which high safety standards are required such as on oil platform, in implant close to oil pipes, for submarine propulsion etc.

The major disadvantage of this technology is the fact that the battery has to work at high temperature (250°C to 350°C). During discharge, the internal temperature is sustained by the energy loss on the internal resistance of the battery so it has no effects on the discharge efficiency. While inactive, the battery has to be maintained at high temperature to be able to provide power. The energy cost to maintain the internal temperature can be seen as self-discharge. To limit this effect, ZEBRA batteries are coated with a thermal insulation material.

The fact that the battery is weakly affected by ambient temperature, doesn’t need maintenance, has a high resistance to failure and has a long life makes it a perfect solution for harsh environment and hard reachable places. In particular, energy storage and UPS applications in the desert is a niche market for this battery since it doesn’t risk to dangerously fail like other technologies and the high ambient temperature limit the self-discharge through heat loss.

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Chapter 3 Chemical model

Sodium-Metal halides cells have a complex chemical environment. In addition to the chemical species that directly intervene in the cell reaction, there are several additives whose role is to improve the chemical stability and to lower the aging rate of the cells [13–16]. Despite their importance in the battery functionality, discussion of their effects is beyond the scope of this work.

3.1 Overview

To comprehend how the battery works is practical to concentrate on each part sepa-rately.

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The anode reaction is

2N a *) 2N a++ 2e− (3.1)

In this section only sodium in liquid state is present. A layer of β-alumina separates the anode from the other parts of the battery working as a solid electrolyte. The crystalline structure of this material allows the flow of sodium ions while acting as a good electric insulator. The high ionic conductivity manifests only at temperatures higher than 250°C. Due to this and the absence of secondary reaction in normal working conditions, self-discharge is not present in these types of batteries and they preserve their charge status at low temperature. To assure a good ionic conduction, a metal wick system is used so that the sodium is sticked to the β-alumina surface through capillarity. [17]

The main difference with the Sodium-Sulphur battery is found in the cathode. Metal Halides batteries cathode is mainly constituted by nickel and a secondary electrolyte in liquid state. To ensure a stable path for the battery current, an excess of nickel is present so that it works both as a reactant and as a conductor. The secondary electrolyte is sodium-tetrachloroaluminate (N aAlCl4, called Melt for simplicity). Its

main purpose is to transport the sodium ions between the β-alumina and the N iCl2.

Moreover if the β-alumina breaks, the sodium reacts with the Melt causing the following reaction

3N a + N aAlCl4 ↔ Al + 4N aCl (3.2)

Having only solid or ionic products and the reaction quickly stops, it doesn’t in-crease the internal pressure so that the battery doesn’t risk to explode. The aluminum generated from this reaction also forms a path of low resistance between the cathode and the anode. This implies that in fault condition, a broken cell is seen like a short circuit so that a circuit made of several cell in series can continue to operate at lower

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voltage. The cathode reaction is

N iCl2 + 2e− *) N i + 2Cl− (3.3)

So that the overall reaction is

2N a + N iCl2 *) N i + 2N aCl (3.4)

Giving an open circuit voltage (OCV) of 2.58V.

To obtain better performances from Metal halides batteries, a secondary reagent can be added so that another reaction is present inside the battery.

2N a + F eCl2 *) F e + 2N aCl (3.5)

Although the reaction is similar to the one involving Nickel, its OCV is 2.35V. During discharge, while consuming N iCl2 population, the internal resistance of the

battery increases. When N iCl2presence is too low, the potential between the electrodes

fall under 2.35V and the F eCl2 reaction starts to intervene. In commercial batteries

this happens around 30% of State of Charge (SoC). The result is to lower the internal resistance of the battery at low level of SoC so that higher values of current can be provided.

Another critical aspect to consider is the battery behavior when working outside of the 0-100% range of SoC. When all nickel and iron are dechlorinated in the cathode, the battery enters the overdischarge phase and the same reaction that intervene when β-alumina breaks (3.2) takes place.

3N a + N aAlCl4 *) Al + 4N aCl (3.6)

This reaction is reversible in the cell environment if not prolonged for too much time. The aluminium and sodium chloride accumulate in the cathode increasing the internal pressure and causing maldistribution of current with the possibility of high

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concentration of flux in the electrolyte. Both cases can cause beta-alumina fractures. It is important to note that in overdischarge situation there is a poor amount of sodium in the anode so that the classic ”fail reaction” can’t take place. If the battery breaks in this situation there is no formation of the short-circuit between the terminals [5]. During charge operation, the battery enters the overcharge phase if all the NaCl is depleted. In this case the potential at the electrodes rises above 3.05 V and the following reaction takes place

2N aAlCl4+ N i *) 2N a + 2AlCl3+ N iCl2 (3.7)

If all the nickel is consumed or at high charge rate, another overcharge reaction can take place

2N aAlCl4+ N i *) 2N a + 2AlCl3+ Cl2 (3.8)

The second reaction is very unlikely to happen in commercial batteries because there is a large excess of nickel in form of current collector. In both cases Na is formed so that, if the overcharge phase continue for too much time, the beta-alumina can break due to excess of sodium in the anode. In this case, the classic ”fail reaction” can take place.

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Chapter 4 Simplified models

Among all the BCS tasks, the SoC estimation is one of the most important and resource consuming one. There are different approaches for handling this problem such as: [2]

Coulomb counter: it consists in integrating the current flow of the battery. It needs a very precise electronic setup and is affected by offset errors in the electron-ics. Moreover it needs to know the initial SoC of the battery and can’t estimate the loss of charge not associated to the current flow.

Neural network: it consists in training a neural network with a large amount of data on a precise type of battery. It is very precise (if properly trained) but needs a lot of computational resources and a big preliminary data collection process. OCV : it estimates the SoC using its relation with the OCV of the battery. It

works fine if the relation is a one-to-one correspondence but is affected by a huge error if the relation is flat in certain ranges.

Model based: it estimates the SoC comparing the battery behaviour with the corresponding model behaviour that is implementd in the system. More complex models are more precise.

The neural network and OCV solutions are not practical to use in a BCS for ZEBRA batteries due to lack of experimental data and considering the flatness of the OCV-SoC relation. The BCS always monitor the current flow of a battery so that implementing

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the Coulomb counter solution is almost costless if high precision is not needed. In particular it can be used alongside a model based solution to facilitate the estimation.

Model based approach

A proper model of the cell behaviour is necessary to lower the error of the estimation as much as possible without being too complex. When designing a BCS it is very important to consider the resources available and the cost of the system in relation to the project specification. A complex model needs more resources causing the cost of the system to increase. A simpler model, even if less precise, can be a better choice as long as it meets the specifications. [18]

There are different types of models depending on their purpose and on the available resources:

Mathematical model: it uses empirical equations obtained through experiments. It generates very abstract model poorly connected to the real physical behaviour of the battery. [2]

Full experimental model: it’s a special case of the mathematical model. It is based on look-up tables builded via experimental data collection [19,20]. It needs a LUT value for each condition in which the battery can operate.

Electrochemical model: it models the microscopic behaviour of the battery (chem-ical reactions and phys(chem-ical behaviour) to explicit their connection to the macro-scopic effects (voltage and current) [21]. It is the most complex but precise model. In certain cases it can be simplified making assumptions that have to be verified via experiments. [18, 22–24]

Equivalent circuit model: the behaviour of a battery is comparable to that of a circuit. It is necessary to understand the dynamics of the chemistry inside the battery to be able to chose an appropriate circuit topology. The parameter values of the circuit need to be estimated via experimental data [25] or determined via electrochemical model [18].

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4.1 Equivalent circuit model

To obtain an equivalent circuit model of a battery, two steps are needed A circuit topology

An experimental characterization of the components of the chosen circuit

The initial efforts have to be concentrated on the choice of the topology. If the circuit chosen doesn’t have the right capability to replicate the battery behaviour, it will be impossible to obtain a good result via components characterization.

In general a battery is defined by the following aspects. OCV

Capacity

Internal resistance

Transient behaviours (e.g. relaxation)

The internal resistance models the initial step in the voltage value when a step is applied on the current. All the other effects that doesn’t immediately follows the current behaviour are transient effects.

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To model these behaviours it is practical to use the Thevenin theoreme to obtain a basic topology where to start. [27]

Figure 4.2: General equivalent circuit model for a battery [27]

The left part of the circuit models the electrical potential of the battery. The ca-pacitor models the capacity of the battery and intervenes on the right circuit through the generator controlled by the SoC. The current flow of the battery intervenes on the charge stored through the current generator controlled by the load current iL.

The right part of the circuit models the dynamic behaviour of the battery. R0 models

the internal resistance (in fact all the capacitor are short-circuits in the instants fol-lowing a current pulse) and all the RC parallel networks model the transient effects. The number of RC needed is application dependent and has to be chosen as a trade-off between the precision needed and the computational costs (both rises with the number of RC). [27]

Several groups of research has worked on the development of a proper circuit model for the ZEBRA battery. In particular the group from UNICA (University of Cagliari), led by professor Alfonso Damiano, started working on a model in 2015 [26] reaching the conclusion that an innovative solution was needed in order to achieve a good accuracy in all the SoC range. At the beginning of 2018 the research group in UNIPI and the one in UNICA started their collaboration in order to reach a better solution.

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4.1.1 Old generation ZEBRA

For simplicity it is practical to start the modelling from the old generation of ZEBRA battery. [26–28] In these batteries only nickel is present as metal in the cathode so that the only reaction that has to be taken into account is the one presented in Eq. 3.4 and below.

2N a + N iCl2 *) N i + 2N aCl (4.1)

whose OCV is 2.58V. To decide the topology needed for the circuit is usefull to refer to the cell physical behaviour schematized in Fig. 4.3.

Figure 4.3: Old generation ZEBRA cell and particular of behaviour [25]

In the cathode of a ZEBRA cell, a reaction front is present both in charge and in discharge operations. This is caused by the fact that the reaction is biased due to the high electric conductivity of the nickel current collector (distributed along all the cathode) in comparison to the ionic conductivity of the Melt. When a cycle of charge or discharge of the battery is performed, at the begining of the operation the

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reaction front always starts next to the β-alumina evolving to the center of the cell. If consecutive cycles of charge and discharge are performed, different charged-discharged layer can stock inside the cathode [25] making the modelization much more complex. Even if theorized, this effect is not treated in literature and it’s still needed to be checked through specific experiment. For these reasons, it will not be considered in the presented models.

Considering the chemical reaction and the cell physical behaviour, the model in Fig. 4.4 can be realized where:

RN i models the electric resistance of the cathode and the ionic resistance of the

beta-alumina

RN it models the ionic resistance in the Melt and it depends on the position of

the reaction front (referred as layer radius in Fig. 4.4)

CN it models the ionic diffusion delay in the Melt of the N a+ ions and it is layer

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Figure 4.4: Basic circuit model and series resistance behaviour [25]

Considerations from UNICA group [26, 28] suggested that another RC parallel cir-cuit is necessary to modelize the fast transient response caused by the reaction kinetics and surface effects from double-layer formation. Moreover the reaction front position will not direcly considerated as a variable of the model. The internal resistance is related to the SoC with two different relations, one in charge and one in discharge operations [28]. This approach is equivalent in considering the position of the reaction front not taking into account the possibility of stacking charged-discharged layer. The identification of the parameters values is performed using their definition (Fig. 4.5). The battery is stimulated using current pulses alternated to relaxation periods at zero current. The variations of voltage in the instants immediatly after the current variations are used to determine the value of the RN i (R0 in the figure). While the

current is constant, the dynamic behaviour is evaluated. The relaxation duration have to be long enough to reach a stationary condition in order to evaluate the OCV value.

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Special care has to be taken when chosing the current pulse value. The batteries used in these tests are constituted by iron doped cells so that high level of current can trigger additional reactions. It’s important to chose a value of current low enough to not make this happen.

Figure 4.5: Parameter identification focusing on a single current pulse [28]

The parameters found have been used as starting point for an optimization tool for fitting the response of the circuit on the experimental data. Refer to the UNICA paper [28] for the parameter estimated values.

Experimental results has proved the effectiveness of using two RC networks (Fig. 4.6). It is important to remember that experimental data are taken on commercial ZEBRA batteries so that iron is present. Since its effects are visible only at low SoC, only the error confrontation at high SoC is acceptable for the validation of the model. The increasing of the error value with the time flow is expected for the same reason.

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Figure 4.6: Relative error of the model vs experimental data. In green the old model, in blue the proposed one [28]

4.1.2 Iron doped ZEBRA

The actual cell technology for ZEBRA batteries consists in adding a certain quantity of iron to the cathode so that another reaction occurs in certain conditions of SoC and current.

2N a + F eCl2 *) F e + 2N aCl (4.2)

whose OCV is around 2.35V. With the addition of iron, the cell can provide high sequential current pulse at lower SoC thanks to the additional reaction that intervenes in parallel to the nickel reaction to sustain the current flux. This happens when the voltage drop is enough to make the potential between the cell terminals falls under 2.35V [25, 29]. This advantage is gained at cost of a high increase of complexity in the modelization and at cost of a loss in specific energy. This happens because a certain quantity of capacity is discharge at lower voltage. In commercial cells the iron capacity is around 20% of the total capacity determining the OCV-SoC relation in Fig. 4.7.

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Figure 4.7: OCV vs SoC characteristic [19]

Since the iron reaction intervenes only in certain conditions, the results for the old generation cell are still valid. The equivalent circuit obtained for the nickel reaction is a good basis to develop the new topology for the complete cell behaviour modelling. In particular, for high level of SoC the circuit has to behave like the one obtained when only the nickel reaction is considered.

The effect of iron doping is essentially to substain the current flux in certain conditions. This behaviour is equivalent to adding a branch for the iron reaction in parallel to the nickel one. This branch has to be active only when the conditions are right. Starting from these considerations and resuming the results for the old generation battery, two different approaches can be considered.

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Reaction front dependent model

Referring to Fig. 4.4 and the paper where this solution has been discussed [25], the following circuit can be obtained.

Figure 4.8: Circuit model with considering the iron reaction [25]

The nickel branch parameters have been discussed in previous section. RF e value

is in function of the reaction front and the discharge condition of the capacity contri-bution of the iron. The relation between RF eand the iron SoC is essential to take into

account that after high pulse of current at high SoC of the battery there is an internal circulation of current that recharge the iron capacity.

The parameters identification for this model starts from the results obtained consider-ing only the nickel reaction. Considerconsider-ing that the nickel parameters are correct, high current pulses are applied on the battery and the experimental results are compared to the simulated ones where only the nickel branch is considered. The differences found are attributed to the RF e effects (Fig. 4.9).

This approach gives good results at high level of SoC (when the reaction front is near the β-alumina) because the nickel parameter estimation is affected by low error. At high level of DoD the iron contribution affects the nickel parameter identification even at low current pulse, mixing their effects. This can be seen looking at the resistances values relations with the layer radius (Fig. 4.10). The dashed lines are the experimen-tal results obtained while the continuous lines are the expected trends. Qualitatively

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the resistance related to nickel has to increase its value with the advance of the reaction front but a drop in its value can be seen at the end of discharge (low values of Sr).

Figure 4.9: Voltage behaviour at high current pulse and RF e contribution [25]

Figure 4.10: RN i, RN it and RF e relation to layer radius [25]

SoC based model

Taking inspiration from the previous work, the UNICA model has been further devel-oped. Note that this model has been obtained from a commercial ZEBRA battery that presents 240 cells in series. Due to this the OCV for the nickel reaction is

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and the OCV for the iron reaction is

OCVF e× 240 = 564V (4.4)

Figure 4.11: Complete circuital model of the ZEBRA battery [29]

In the nickel branch the resistances and capacitors are dependent only on the SoC. The OCV generator is dependent on SoC and it is expected to follow the classic OCV-SoC relation for ZEBRA batteries.

The iron branch is present only to take into account the iron side reaction in different situations without considering the effective SoC of the iron. To achieve this result the branch has been splitted in two and there is coulomb counters that integrates the current flux that flows in both branches. To explain its behaviour it is practical to consider different situations.

Normally the Sw switch is open and the Sel selector is connected to the lower branch. When Vbatt falls below 564V for some reasons (low SoC or high current pulse) the diode in the iron branch starts conducting and the iron contributes to the current flux. The coulomb counter integrates the current that flows in the diode branch.

When Vbatt returns above 564V and the coulomb counter is not zero, Sw switch is closed and the Sel selector is connected to the upper branch. This allows an internal

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current flux from the OCV generator to the iron branch. Since the current flows in the opposite direction compared to the other configuration, the coulomb counter integrates this current and subtract it to the previous measure. When the counter reaches zero , Sw opens the the Sel selector connects back to the lower branch.

To determine the parameters a more sophisticated approach has been used com-pared to the simple current pulse used in previous characterizations [29]. The current pulse shape is shown in Fig. 4.12.

Figure 4.12: Current pulse used to determine the parameters [29]

The parameters values has been determined each 10% of SoC applying a 5A current for a 9% of SoC loss and a 10A current for the remaining 1%. The first step is used to determine the RN i value while the second step permits to obtain a value for RF e

assuming the nickel resistance value to remain constant during these steps. These tests have been conducted both in charge and in discharged conditions. The values obtained are shown in Figures 4.15a and 4.15b.

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(a) Charge parameters

(b) Discharge parameters

Figure 4.13: Parameters values [29]

Looking at the evolution parameters values versus the SoC, the resistances values tend to increase with the SoC in charge condition and with the DoD in discharge condi-tion as expected. However the capacitance values trends are not completely explainable referring to the physical and chemical behaviour of the cell. This is probably caused by ignoring some relations between the parameters value and some conditions such as the reaction front position, current value and SoC of the iron capacity.

Validation of the model has been perfomed with arbitrary current evolutions both in charge and in discharge operations. The relative error on the voltage evolution has always remained below 2%.

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(a) Voltage evolution of the old model (in blue) and the proposed model (in green); in red the experimental measure and in purple the current evolution.

(b) Relative error of the old model (in blue) and the proposed model (in green); in red the SoC evolution.

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(a) Voltage evolution of the proposed model in green; in red the experimental measure and in purple the current evolution.

(b) Relative error of the proposed model in green; in red the SoC evolution.

Figure 4.15: Validation in charge condition [29]

Even if the model is not perfect, the results obtained are more than satisfactory considering that the presented solution is the best one that can be found in literature.

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Chapter 5 Thermal model

The thermal management is a crucial factor for ZEBRA batteries. The temperature operating range is set from 260°C to 350°C [30]. The lower limit is imposed by the necessity of having a high ionic conductivity in the β-alumina and in the Melt. Besides the worse performance, imposing the flow of sodium ions through the β-alumina at lower temperature dramatically increase the chance of breaking of the solid electrolyte. The upper limit is set because the N iCl2 and F eCl2 solubilities increase with the

temperature, triggering migratory effect of Ni and Fe that cause cathode degradation. Moreover even if the battery temperature remain inside the operative range, working near the chosen bounds increase the aging rate of the battery. [30]

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Although there have been attempts to decrease the operative temperature for ZE-BRA batteries [31, 32], the proposed solutions require to change the cathode and the solid electrolyte compositions.

Another critical aspect is that the temperature working conditions have be to re-spected for all the cells inside a battery. For this reason thermocouple are presents. Due to the necessity to limit the size of the battery (both to increase the volumetric energy density and to limit the volume that is maintained at high temperature), it is not possible to mount too many thermocouples. Moreover, referring to the 48TL series of ZEBRA battery produced by FZSoNick SA, all the cables come out from the battery from a single hole to limit the heat dispersion. It is necessary to limit the number of cables that need to be taken out to not increasing the routing process too much. For example, in the 48TL200 battery [9] there are only three thermocouples. To ensure the operative conditions, the minimal operative temperature is set to 265°C. [9]

Having a good thermal model is essential for being able to estimate the temperature gradient inside the battery with precision. Having a good understanding of the thermal behaviour can provide an usefull tool to expand the operating range or to make the battery work at more performant temperature.

In literature the only reasearch on the thermal behaviour has been done by General Eletrics on their Durathon [33]. However the GE battery is provided with an internal cooling system unlikely the batteries built by FZSoNick SA. Referring to the 48TL200 battery model, an innovative thermal model will be proposed.

Methods

To implement the thermal model, COMSOL Multiphysics 5.2 has been used. Apart the high performance and flexibility in the physical modelization, the choice has been made due to the possibility of realizing a CAD rappresentation of the battery directly inside the program. The only physical behaviour simulated have been the thermal one through the Heat transfer module.

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5.1 Battery structure

First of all a proper model of the battery structure is necessary. Starting from the outer dimensions, some hypothesis will be made on the internal geometry. Than an estimation on the battery composition is obtained by weight analisys.

5.1.1 Geometry definition

The only available informations on the geometry of the 48TL200 can be found in the battery technical manual provided by FZSoNick SA [9].

Figure 5.2: 48TL200 external geometry [9]

Front (F) 496mm

Depth (D) 558mm

Height (H) 320mm

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Since this battery is composed by 100 cells and has an almost square base, it is safe to assume that the cells disposition inside the battery is a 10x10 grid. Considering the thermal insulation to have a constant thickness, the BMS depth is

558mm − 496mm = 62mm (5.1)

To obtain more informations on the battery structure, the ST523 battery by the same producer has been taken into consideration. [34]

Width 624mm

Depth 1023mm

Height 406mm

Table 5.2: ST523 dimensions

Since the ST523 is composed by 240 cells [34] and that its width is greater than the 48TL one, the internal disposition of the cells is considered to be 12x20. Considering the BMS to have the same size as the 48TL one, the following calculations can be done making the hypothesis that the thermal insulation thickness x is constant in all directions and the cell have a square base with the side length y.

       624 − 2x = 12y 1023 − 62 − 2x = 20y ⇒        y = 42.125mm x ≈ 60mm (5.2)

Considering the same values for the 48TL,

4.125 × 10 + 60 × 2 = 541.25mm (5.3)

that is greater than the real dimensions. Even if these are not the right values, they make a good starting point to estimate the real dimensions of the internal parts. In addition to the cells, the internal volume need to have some free space for the wires routing and has to contain a heater to maintain the temperature. Looking at the cables

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dimensions and considering the cells interconnection, The free space is estimated to be 1cm thick positioned above the cells.

An internal heater is present to reach and mantain the operating temperature. The heating process should happen from top to bottom because the sodium volume increase when melted. If it starts to melt from the bottom, the sodium above would act against this volume expansion and the transversal pression would increase risking the rupture of the β-alumina. For this reason the heater position is considered to be just above the free space. Wanting an uniform heat distribution inside the battery, the heater is considered to have a rectangular shape of the same dimensions of the cells pack. Searching for commercial products that can be used in this situations, it has been found that 1mm is probably a good estimation for its thickness [35]

Another aspect to be taken into consideration is the presence of the hole to take out the various cable for power and sensing. Its thermal conductivity is certainly higher than the thermal insulation one and it introduces asymmetry in the temperature gradient inside the battery. Even if it’s difficult to have a good measure of the dimensions of the hole (since the BMS is positioned in front of it), a rough estimate is obtained looking at the physical battery. It has a circular shape with a diameter close to 5cm.

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Given the simmetry of the system, only half of the battery has been drawn so that the internal geometry can be appreciated. The internal dimensions will be estimated more accurately in the next sections.

5.1.2 Materials definition

In order to obtain an appropriate thermal model, the material composition of each part of the battery has be to understood.

Thermal insulation

A research on a proper thermal insulation material has been conducted. A good solu-tion has been found in the WDS technology from Porextherm D¨ammstoffe GmbH. [36] It provides a very low thermal conductivity for a wide range of temperature allowing to reduce the volume occupied by the insulation.

Figure 5.4: WDS technology physical characteristics [36] .

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The important characteristics used in the thermal model have been taken from the WDS High datasheet [37] and are summarized in Table 5.3.

Thermal conductivity 0.025[W/m · K]

Thermal capacity 963[J/Kg · K]

Density 300[Kg/m3_]

Table 5.3: WDS physical characteristics [37]

Hole/wires

Due to the high temperature inside of the battery, copper wires tends to deteriorate very fast. Moreover the usual coating for electric cables would melt losing its electric insulation properties. Since the battery life time is in the order of ten years, another material is needed for the internal wires. A typical solution is to use nickel cables coated with glassfiber. This solution is confirmed after a visual confrontation with the BMS on the physical battery.

To simplify the hole characterization, the whole hole will be considered made of nickel.

Heater

ZI Heating Elements Technologies products [35] produces different types of heating elements. A possible solution for the ZEBRA battery is the planar heater made of mica found among their products. Mica is a generic name for a whole family of minerals so that precise thermal parameters are not defined. Since its quantity is negligible comparing to the rest of the battery, the choice of the parameters value has been found to not be a determining factor for the model behaviour. Due to this, the values are not researched and are arbitrary chosen. The parameters values used in the model are presented in Table 5.4.

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Thermal conductivity 0.5[W/m · K]

Thermal capacity 800[J/Kg · K]

Density 2900[Kg/m3_]

Table 5.4: Physical characteristics of mica

Cells

Besides the chemical species that directly intervene in the internal reaction and the structural parts (the steel case and the β-alumina), there are several other components that constitute the cell [4]. Fig. 5.5 shows a generic cell composition.

Figure 5.5: Cell composition expressed in percentual of weight [4] .

Considering all the species is not necessary and there are no clues that the 48TL cell would reflect the presented composition.

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To decide which species have to be taken into consideration it is usefull to refer to Fig. 5.6a and 5.6b.

(a) Warm-up

(b) Cooldown

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During the time where the temperature is constant, a phase change is occurring. In particular the sodium melts around 100°C while the tetrachloroaluminate melts around 157°C [5] explaining the graphs trend. The absence of the sodium plateau in the warm-up graph is probably because the characterization has been done during the first life cycle of the battery while sodium is not present [9].

It has been decided to focus on just three species to not increase too much the complexity of the model:

Nickel Sodium

Remaining components

The tetrachloroaluminate will be considered among the other components because its physical characteristic are not obtainable anywhere since it is only used in this type of battery. The thermal parameter and the quantity of this group of components will be estimated below.

The nickel is considered separately since the cathode is composed by it. In this way it can be considered as the core of the cell, forming a fixed structure usefull for the mod-eling. The quantity of nickel present is estimated by the data from the safety datasheet provided by FZSoNick SA [38]. Referring to the entire battery weight (105Kg), 14.5% is pure nickel while 8.1% is N iCl2. Considering that nickel atomic weight is 58,69u

while chlorine one is 35.45u, the total nickel weight can be obtained.

0.081 × 105 × 58.69

58.69 + 35.45 × 2 + 0.145 × 105 = 19.0768 ≈ 20Kg (5.4) That means 0.2Kg of nickel per cell.

The sodium quantity is the 4.5% of the battery weight [9] so that it is approximately 5Kg for the entire battery or 0.05Kg per cell.

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5.2 Stationary model

To determine some of the missing parameters the study of the stationary behaviour is a practical choice since several simplifications can be done.

The thermal equivalent circuit for the battery in stationary condictions is presented in Fig. 5.7.

T

amb

Q

heater

R

_{T h}

+

−

T

batt

Figure 5.7: Equivalent thermal circuit in stationary conditions

5.2.1 Geometry dimensions refining

From the 48TL200 datasheet [9] it is possible to obtain all the needed parameters except for RT h when the battery is not charging or connected to a load. It is important to

remember that the internal temperature kept by the BMS in these conditions is 265°C.

Figure 5.8: Heater power consumption vs ambient temperature in floating condition [9] .

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Considering an ambient temperature of 25°C, the power consumption associated to the heater would be 115W. It is possible to obtain a value for RT h through simple

calculations. Tbatt Qheater = RT h ⇒ 240 115 = 2.087[K/W ] (5.5)

In doing this the temperature has been considered to be constant in all the internal points of the battery. In this way Rth is determined only by the thermal insulation

and the hole contributions. Ignoring the hole and the behaviour at the corner and considering the heat flux to the ambient always perpendicular to the sides of the battery, the thickness of the insulation can be calculated with more precision. The values are referred to Table 5.2 and 5.3.

T hicknessinsulation= RT h × CT h× Abatt = 0.595[m] ≈ 60[cm] (5.6)

Where CT h is the thermal conductivity of the WDS and Abatt is the external surface

area of the battery without the BMS.

With the insulation thickness obtained, the side lenght of a cell happens to be 38[mm]. Considering that the insulation is present both in the top and bottom sides of the battery, the height of the cell can be obtained by difference and the CAD model dimensions can be corrected.

hcell = hbatt− hheater − hempty− 2 × hinsulation= 178[mm] (5.7)

5.2.2 Cell structure

To determine the cell structure it is necessary to know how much each cell weigh. Than the cell volume can be divided among the three species that compose it. For the modeling purpose, the sodium will be considered among the remaining speacies. The reason will be explained in later sections. From the CAD model it is possible to obtain the mass of the components integrating their density on the volume. The total weight

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without the cells results to be 7.31 × 2 = 14, 62 ≈ 15[Kg]. Considering the total mass of the battery to be 105Kg, the mass per cell obtained is 0.9Kg.

Referring to the materials section 5.1.2, the only known quantity for the cell composi-tion is 0.2Kg of nickel. The remaining part of the cell will be considered as a unique material since the characteristics for the Melt are not known.

To obtain a volume of nickel that respect the proportion in weight, the density of nickel is necessary. Than a cilindric core of nickel will be considered in the central part of each cell.        ρN i= 8908[Kg/m3] π × r2 core× hcell× ρN i = mN i ⇒ rcore = 0.0063[m] = 6.3[mm] (5.8)

The density of the rest of the cell can be calculated from the ratio between the remaining mass and the remaining volume.

ρother =

(mtot− mN i)

(l2

cell− π × r2core) × hcell

= 2984[Kg/m3] (5.9)

Figure 5.9: Cell structure with nickel core .

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5.2.3 Physics and bound conditions determination

To simulate the thermal behaviour of the model the Heat transfer module has been used. For each component of the battery is necessary to determine the right equations that describes the temperature evolution. Moreover the bound conditions has to be determined for the external faces of the model.

Heat transfer in solid: this is the default behaviour for all the components. It will be overridden by other equations if needed.

Initial values: sets the initial temperature value. Tamb for all the battery.

Thermal insulation: the default is that all the external faces are thermaly insu-lated. This is overridden for all the faces.

Heat source: this sets a volumetric heat generation in the heater. Due to sym-metry the heat generated is half the total value (57.5W).

Heat transmission in fluids: this sets the equations for the empty space above the cells. It is considered to be filled with air.

Heat transfer with phase change: this sets the external part of the cell behaviour to solid until a certain temperature and to fluid after a certain temperature. It is possible to select the change phase temperature and latent heat. In the stationary evaluation this is not a necessary set of equation but it will be used for the transient evaluation.

Thermal flux 1 : this sets a convective heat exchange with air for all the external faces of the battery except for the hole.

Thermal flux 2 : this sets a thermal flux on the external face of the hole consid-ering that it is connected to a nickel cable.

Symmetry: this sets symmetry condition on the symmetry plane of the battery. The symmetry condition is null flux.

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5.2.4 Meshing

To determine the mesh of the system it has been decided to follow five step:

Structured surface mesh for the faces without other elements inside them. This has been done for the heater, the core bases and the external faces of the battery except the front one.

Unstructured surface triangular mesh for the external cell bases. Extruded regular mesh for the heater volume and the cells volumes.

Transformation of the quadrilater faces of the mesh to triangular. This has been done by connecting two arbitrary opposed corners of the faces.

Tetrahedral unstructured mesh for the remaining volumes.

Figure 5.10: Meshed battery .

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5.2.5 Simulation results

A stationary solution of the system has been calculated by COMSOL. Several thermal conductivity values have been tried for the external part of the cells. For high values of conductivity, the initial hypothesis are respected and the internal temperature is equal to 265°C. For lower values of thermal conductivity the internal temperature range increases. The presence of the hole greatly affects the temperature gradient for the cells nearby. Even if it is true, the effects in the simulation are too great. The minumum cells temperature is evaluated both considering and not considering the cells next to the hole. In any case the internal temperature range remains around the target temperature of 265°C.

The results can be found in Table 5.5 where ρ−1_{T h} is the thermal conductivity of the external cell and Thole is the minimum temperature considering the cells in front of the

hole. In Figs. 5.11 the ∆T trend versus ρ−1_{T h} can be found.

ρ−1_{T h}[W/m · K] Tmax[◦C] Tmin[◦C] ∆T [◦C] Thole[◦C]

2.5 286.93 257.23 29.70 139.33 5 279.37 262.24 17.13 162.91 7.5 275.9 263.55 12.34 179 10 273.76 264.03 9.73 190.67 15 271.19 264.28 6.91 206.44 20 269.66 264.28 5.38 216.6 25 268.65 264.23 4.42 223.66 30 267.92 264.16 3.75 228.88 35 267.37 264.1 3.27 232.9 40 266.94 264.05 2.89 236.06 45 266.6 264 2.56 238.64 50 266.31 263.96 2.36 240.77 60 265.88 263.89 1.99 244.09

Table 5.5: Internal temperature extreme point evaluation versus the thermal conduc-tivity of the external part of the cells

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Figure 5.11: ∆T versus ρ−1_{T h} .

To qualitatively observe the internal gradient, the temperature distribution on dif-ferent horizontal slices of the cell pack for ρ−1_{T h} = 10[W/m · K] can be found in Fig. 5.12, 5.13 and 5.14.

Figure 5.12: Planar temperature gradient at the top of the cells .

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Figure 5.13: Planar temperature gradient in the middle part of the cells .

Figure 5.14: Planar temperature gradient at the bottom of the cells .

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5.3 Time dependent model

To characterize the thermal parameters of the cell, the stationary model proposed is not sufficient.

Firstly the internal temperature distribution is not experimentally known so that a meaningfull comparation with the simulated results is not possible. The only exper-imental data in stationary condition is the temperature at the three thermocouples whose position inside the battery is unknown.

Secondly, in stationary condition only the thermal conductivity effects are visibles. During charge or discharge the thermal capacity of the cells is a determining factor to evaluate the internal temperature evolution.

Referring to Figs. 5.6a and 5.6b, the temperature evolution during warm-up or cooldown of the battery is known. In both situations the parameters that determine the curve shape are the same. The only difference is found on the missing sodium plateau at around 100°C in the warm-up curve. As stated above, the best guess is that this curve has been evalueted during the first battery life cycle when there is no pure sodium in the anode.

Being able to ignore the sodium behaviour permits to have a less complex thermal model. For this reason only the warm-up model will be taken into consideration and the sodium part of the cell won’t be considered.

5.3.1 Equivalent circuit

As for the stationary model, it is possible to obtain an equivalent circuit for the thermal model to understand the temperature evolution over time.

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T

_amb

Q

heater

R

_iso

+

−

T

batt

C

_{T h}

Figure 5.15: Equivalent thermal circuit

To obtain the circuit in Fig. 5.15 several hypothesis has been made: The hypothesis on Rth are the same made in section 5.2.

The internal thermal resistance of the battery is completely trascurated.

All the internal parts of the battery are considered to contribute to the model only as thermal capacity.

The temperature is considered to be constant inside the battery. In this way all the thermal capacities considered above are connected in parallel.

CT h is the total thermal capacity of the battery. Its valus is equal to the sum of

all the internal components capacities.

The purpose of the equivalent circuit model is to provide a rough estimation of the external cell thermal capacitance to be used as starting point for further simulation needed to refine the model.

The circuit in Fig. 5.15 has the following analytic solution

Tbatt = Qheater× RT h × [1 − exp

−t τ

] (5.10)

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From Eq. 5.10, expliciting the τ expression and considering t1 as the time to go

from ambient temperature to the start of the phase change,

CT h = −t1 RT h× ln 1 − Tbatt Qheater×RT h ⇒ CT h = 60223J/K (5.11)

The value found corresponds to the total capacity of the internal part of the battery. Using COMSOL it is possible to obtain the mass and the specific thermal capacity for all the battery parts from the CAD (Table 5.6) and calculate the capacity of the Melt CM elt.

CM elt = CT h− Cair− Cheater− CN i= 48925J/K ⇒

CM elt mM elt ≈ 700J/Kg · K (5.12) Cair 1.96[J/K] Cheater 736[J/K] CN i 10560[J/K]

Table 5.6: Capacitances values

This estimation permits to narrow the range of the external part of the cells specific capacity both for solid and molten state.

5.3.2 Phase change parameters estimation

Apart the thermal conductivity and the thermal capacity of the external part of the cells, an important factor that has to be taken into consideration is the latent heat. Two species change phase in the operative range of internal temperature, the sodium and the Melt (N aAlCl4). The first one changes phase around 100°C and its

character-istics are known. The tetrachloroaluminate changes phase at 157°C but the thermal characteristics are not known.

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During the warm-up:

The temperature rises to 160°C in 6 hours starting from 15°C.

The temperature remains constant for 1 hour at 160°C while the NaAlCl4 melts.

The temperature rises to 265°C in 7 hours starting from 160°C. During the cooldown:

The temperature falls down to 150°C in 24 hours starting from 265°C. The temperature remains constant for 1.4

3.6 × 24 = 9.3 hours at 160°C while the

N aAlCl4 melts.

The temperature falls down to 100°C in 3.6−0.9

3.6 × 24 = 18 hours from 160°C.

The temperature remains constant for 0.7

3.6 × 24 = 4.6 hours at 160°C while the

N aAlCl4 melts.

The temperature falls down to 30°C in 168 − 18 − 4.6 − 9.3 − 24 = 112 hours from 160°C.

During the cooldown process the heater is turned off while during the warm-up the heater consumes 440W [9]. Referring to the phase change of the Melt during the warm-up and assuming that all the heat is accumulated in the cells or lost through the thermal insulation. it is possible to explicit the latent heat ∆EM elt.

∆EM elt = (Qheater − Qlost) × 1h (5.13)

Since the temperature is constant during the phase change, the battery can be considered in stationary condition. Since in this case Qlostdepends only on temperature

and that the Melt quantity is the same in warm-up and cooldown, it is possible to explicit Qlost considering there is no heat source during cooldown.

∆EM elt Qlost = 1.4 3.6 × 24h ⇒ Qlost= ∆EM elt× 3 28h (5.14)

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Replacing this result in Eq. 5.13

∆EM elt = (Qheater−

∆EM elt× 3

28h ) × 1h ⇒ ∆EM elt =

28 × 440W × 3600s

31 = 1.4307M J

(5.15) Since the external part of the cells is considered to be made of the same specie, all the external part is considered to melt so that the specific latent heat used in the model is equal to ∆EM elt mext = 1.4307 × 10 6 70Kg = 20.44KJ/Kg (5.16)

Sodium quantity verification

With the cooldown temperature evolution is also possible to verify the sodium quantity inside the battery.

Since the temperature is constant during all the phase change, the stationary model is considered to be valid. In stationary condition the power of the heater is equal to the heat dispersed to the ambient. A parametric sweep on the heater power value has been performed in order to understand how much heat is dispersed at 100°C. To narrow down the range of heat flux dispersed, the internal conductivity is set to be very high so that the internal temperature range would be narrow too. The results can be found in Table 5.7.

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P[W] Tmax[◦C] Tmin[◦C] 30 83.86 83.29 31 85.90 85.31 32 87.94 87.33 33 89.99 89.36 34 92.04 91.39 35 94.09 93.43 36 96.15 95.47 37 98.21 97.51 38 100.28 99.55 39 102.35 101.60 40 104.42 103.65

Table 5.7: Heat flow from external surfaces and correspondent internal temperature range

At 100°C the heat dispersed rseults equal to 38W. Referring to the cooldown graph in Fig. 5.6b, the latent energy is equal to

0.7

3.6 × 24h × 38W = 638.4KJ (5.17)

The latent heat for sodium is 2598J/mol and it’s atomic mass is 23g/mol so that

638, 4 × 23

2598 = 5.65Kg (5.18)

The previous sodium quntity estimation was 5Kg. This results allows to validate the quality of the model and of the hypothesis considered.

5.3.3 Results

Starting from the value obtained by the equivalent circuit and through try and error method, the values for the specific thermal capacity of the external part of the cell

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both for solid and molten phase has been estimated. In Table 5.8 the external part of the cell characteristics have been resumed.

Specific thermal capacity in solid state 450[J/Kg · K] Specific thermal capacity in molten state 300[J/Kg · K]

Specific latent heat 20.44[KJ/Kg]

Table 5.8: Thermal characteristics for the external part of the cell

The results have been convalidated confronting the simulations with the data from Fig. 5.6a.

Figure 5.16: Temperature evolution in different internal points of the battery. The red line rappresent the experimental evolution from Fig. 5.6a

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5.4 Structure variations for a modular BCS

The simplifications in the previous model demonstrated both their advantages and disadvantages. One weak point is the hole schematization. The temperature of the cells directly in contact with the hole presented a minimum temperature much lower than the rest of the cells pack. In particular the temperature goes below the operating range of the ZEBRA cell (Table 5.5 for reference). Even if the temperature of these cells obtained by the model can’t be taken as valid, it is obvious that a single hole in the center of the battery is not the best solution to decrease the internal gradient. With the ojective of making a modular BCS for a Sodium-Metal halides battery (which will be better treated in the Chapter 6) the idea of having five holes, one for each string, has been evalueted. Apart from increasing the modularity capability of the system, five holes will make the temperature gradient smoother in the cells in the front part of the battery.

5.4.1 Modular structure

The proposed structure is identical to the one presented for the 48TL200 except for the presence of five holes instead of one.

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To mantain the same heat flux from holes, their dimensions have been decided so that the sum of their external surface area would be the same than the single hole one. For practicity the holes have a square vertical section.

π × r_hole2 = 5 × l2_hole ⇒ lhole = 1.66cm (5.19)

All the previous consideration remains valid.

5.4.2 Results

For simplicity, the stationary model has been chosen to confront the two structures. The results are presented in Table 5.9. In the last column the minimum temperature from the cells in front of the hole in the previous model has shown for confrontation.

ρ−1_{T h}[W/m · K] Tmax[◦C] Tmin[◦C] ∆T [◦C] Tmin48TL200[◦C]

2.50 289.84 204.99 84.85 139.32 5 279.89 227.10 52.78 162.91 7.50 275.78 237.15 38.63 179.00 10 273.48 242.89 30.59 190.66 15 270.96 249.23 21.73 206.43 20 269.59 252.66 16.92 216.59 25 268.72 254.82 13.90 223.66 30 268.12 256.30 11.81 228.88 35 267.68 257.39 10.28 232.89 40 267.35 258.23 9.11 236.06 45 267.08 258.87 8.20 238.63 50 266.86 259.41 7.45 240.76 60 266.53 260.23 6.30 244.08

Table 5.9: Internal temperature extreme point evaluation versus the thermal conduc-tivity of the external part of the cells. The previous minimum temperature at the hole is presented in the last column

Modelling and design of a highly modular Sodium-Metal halides battery system

University of Pisa