Patent Publication Number: US-2020292622-A1

Title: An Energy Storage Device Monitoring Technique

Description:
FIELD 
     The present disclosure relates to the monitoring of the condition of cells within an electrochemical storage device, such as a battery. 
     BACKGROUND 
     As portable devices are provided with additional functionality, and as electrical power is adopted in place of alternative power sources (such as in electric vehicles), battery performance is becoming a key limiting factor on device adoption. In order to provide users with a satisfactory experience, there is a desire not only to enhance fundamental battery life but also to ensure accurate information is provided in order to manage expectations and optimise battery use. To this end, battery management systems (BMS) are provided to allow indications of battery characteristics to device users. For example, the user of an electric vehicle may be provided with information regarding the expected range of the vehicle and the user of a mobile phone may be provided with an estimated percentage of battery life remaining. 
     To estimate the range of a vehicle, for example, it is desirable to have an understanding not only of the battery&#39;s state of charge (SOC) but also state of health (SOH). An accurate estimation of these properties is not trivial and requires more than mere knowledge of cell voltage. 
     Batteries degrade through various mechanisms over time and individual cells in a pack may age differently. This unequal degradation can lead to reduced overall pack performance and lifetime which means particular cells may need to be controlled or replaced accordingly. Moreover, the performance of the pack will be determined by the weakest cell. Hence a good diagnosis method capable of accurately identifying such cells with detailed state-of-health information is required. 
     Efforts have been made to develop techniques to monitor battery state-of-health. However, many such techniques are not suitable for practical implementation, requiring complex and expensive equipment such as in-situ nuclear magnetic resonance or x-ray computational tomography. Other techniques have proposed using entropy and enthalpy measurements at specific cell potentials where each potential was related to a particular electrode. For example, DuBarry et al (Cell degradation in commercial LiFePO4 cells with high-power and high-energy designs, J. Power Sources. 258 (2014) 408-419) proposed a mechanistic model to go with an incremental capacity analysis in which the model compares the dQ/dV peaks with its fresh cell equivalent to quantify cell state-of-health in terms of degradation modes such as loss of lithium inventory, loss of active materials and ohmic resistance increase. In this approach, each dQ/dV peak represents a combined phase of both positive and negative electrodes. 
     To avoid the requirement for a separate current measurement for each cell, differential thermal voltammetry (DTV) has been proposed introduced as a complimentary tool to slow-rate cyclic voltammetry (SRCV) and incremental capacity analysis. Examples of this approach can be found in “Differential thermal voltammetry for tracking of degradation in lithium-ion batteries” (Wu et al, J. Power Sources. 273 (2015) 495-501) and “Novel application of differential thermal voltammetry as an in-depth state of health diagnosis method for lithium-ion batteries” (Merla et al, J. Power Sources. 307 (2016) 308-319). 
     DTV only requires temperature and voltage measurements (i.e. no current measurement is required) and it is carried out by measuring the change in cell surface temperature during a constant current discharge. The DTV parameter, dT/dV is calculated by taking the differential of the temperature, dT/dt divided by the differential of the potential, dV/dt. Plotted against cell potential, the result gives as much information as a SRCV but with the addition of the entropic term. 
     Existing experiments for DTV have been carried out on individual cells under natural thermal boundary conditions. In reality, the cells would be connected into a pack with a thermal management system. Furthermore, existing approaches have been developed for constant current discharge which meant that the diagnosis required a dedicated discharge cycle in application. 
     There remains, therefore, a need to provide a technique for analysis of state of health of cells within a battery under realistic conditions. In particular, there is a desire to avoid cost and complexity in this analysis and also ensure that the analysis does not intrude on the desired operation of the battery. 
     SUMMARY 
     According to a first aspect of the disclosure, there is provided a method of monitoring the condition of one or more cells within an electrochemical energy storage device, the method comprising: 
     operating the electrochemical device at a current comprising a predefined time-varying component for a first period of time; 
     sensing voltage across each of the plurality of cells during the first time period; 
     sensing a measure of heat generation within each cell during the first time period; 
     calculating an estimate of the open circuit potential of the electrochemical storage device from the predefined time varying component of the current and the sensed voltage during the first time period; 
     calculating, for each cell, a function which relates a ratio of the time derivatives of the sensed measure of heat generation and voltage to the open circuit potential; and 
     determining a measure of the state of health of each cell based on the calculated function. 
     According to a second aspect of the disclosure, there is provided a system for monitoring the condition of one or more cells within an electrochemical energy storage device, the system comprising a device configured to: 
     operate the electrochemical device at a current comprising a predefined time-varying component for a first period of time; 
     sense voltage across each of the plurality of cells during the first time period; 
     sense a measure of heat generation within each cell during the first time period; 
     calculate an estimate of the open circuit potential of the electrochemical storage device from the predefined time varying component of the current and the sensed voltage during the first time period; 
     calculate, for each cell, a function which relates a ratio of the time derivatives of the sensed measure of heat generation and voltage to the open circuit potential; and 
     determine a measure of the state of health of each cell based on the calculated function. 
     The present disclosure provides a system and method which can accurately identify differences in state of health between cells within an electrochemical energy storage device, such as a battery. The electrochemical energy storage device may comprise a single cell or a plurality of cells. It has been shown that by estimating open circuit potential from the response to a defined time varying input current, the ratio of time derivatives of a measure of heat generation and voltage can offer insight into the condition of each cell. This is achieved without a requirement for direct current measurement within each cell, or other complex measurement systems. 
     The electrical energy storage device may be in the form of a battery. The electrical energy storage device may comprise a Faradaic, pseudo-Faradaic and/or non-Faradaic electrochemical storage device. For example the electrical energy storage device may be or comprise one more or all of a battery or batteries, capacitors, supercapacitors, hybrid battery-supercapacitors and other similar devices. 
     In some preferred embodiments, the measure of heat generation is a temperature measurement. Alternatively or additionally, the measure of heat generation is a heat flux measurement. Temperature measurement devices are widely available and can be relatively cheaply implemented. Heat flux measurement may provide a more accurate reflection of the true entropic state of the cell, particularly in temperature controlled conditions (e.g. where the battery is actively cooled) which may otherwise interfere with a pure temperature measurement. 
     In preferred embodiments, the step of operating the electrochemical device at a current comprises charging the electrochemical device. Alternatively, the step of operating the electrochemical device at a current may comprise discharging the electrochemical device. Where the operation comprises charging the device, it can be implemented into the controlled conditions already provided in many systems during charging, rather than having an impact on battery usage during often less controlled discharge. 
     In a preferred embodiment, the step of operating the electrochemical device at a current comprises applying an intermittent current profile. Alternatively, the step of operating the electrochemical device at a current comprises applying an oscillating current profile. 
     Preferably, the method further comprises, prior to calculating the ratio of time derivatives, smoothing values of the sensed measure of heat generation. In preferred embodiments, the step of smoothing comprises applying a moving average. In this manner outlying results within a set of measured values are not given undue weight in later calculations. 
     In preferred embodiments, the step of calculating an estimate of open circuit potential comprises fitting a rest profile of the sensed voltage to a power law model. Alternatively or additionally, the step of calculating an estimate of open circuit potential comprises applying a diffusion equation to the sensed voltage. These techniques have been shown to provide adequate estimates of the open circuit potential from limited data. 
     In preferred embodiments, the step of determining a measure of the state of health of each cell comprises analysing peaks within the calculated function. Peaks within the calculated function have been found to reflect the state of health of the cell. These thus represent a parameter that indicates changes in state of health which can be readily identified without burdensome complex analysis of the data distribution. 
     Preferably, the method further comprises calculating an operating range for each cell from the measure of the state of health for that cell. In this manner a parameter to ensure future operation is tailored to the current state of health so as to ensure optimum overall cell usage can be identified. The method may, for example, further comprise operating the electrochemical storage device such that each cell remains within its operating range. 
     It can also be appreciated that aspects of the disclosure can be implemented using computer program code. Indeed, according to a further aspect of the present disclosure, there is therefore provided a computer program product comprising computer executable instructions for carrying out the method of the first aspect. The computer program product may be a physical/tangible storage medium. For example, the storage medium may be a Read Only Memory (ROM) or other memory chip. Alternatively, it may be a disk such as a Digital Versatile Disk (DVD-ROM) or other data carrier. It could also be a signal such as an electronic signal over wires, an optical signal or a radio signal such as to a satellite or the like. The disclosure also extends to a processor running the software or code, e.g. a computer configured to carry out the method described above. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       A preferred embodiment of the disclosure will now be described with reference to the accompanying drawings, in which 
         FIG. 1  shows a system for monitoring cells within a battery pack; 
         FIG. 2  shows the battery pack in more detail; 
         FIG. 3  illustrates a process for monitoring the condition of cells within the battery pack; 
         FIGS. 4A and 4B  illustrate estimated and actual OCV curves; 
         FIG. 5  shows an OCV corrected DTV curve; 
         FIG. 6  shows pack experimental results for 2 C (40 A) discharge; 
         FIG. 7 .shows peak fitting of differential thermal and heat flux voltammetry results for 2 C constant current discharge; 
         FIG. 8  shows a schematic of combined phase transitions in graphitic carbon negative electrode and NMC positive electrode; 
         FIG. 9  shows pack experimental results for 2 C (40 A) charge; and 
         FIG. 10  shows peak fitting of differential thermal and heat flux voltammetry results for 2 C constant current charge. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 , a system is shown comprising a battery management system  10 , a battery pack  20  and a load  30  coupled to one another. An internal or external power source  40  may also be provided. The system may be integrated into a portable device or an electric vehicle, or any other context in which power is required. In alternative embodiments, the battery pack may be replaced by a single cell. 
     The battery pack  20  is shown in more detail in  FIG. 2 . In this embodiment, the battery pack is made from four commercial 5 Ah lithium-polymer pouch cells  22  connected in parallel. The cells are manufactured by Dow Kokam (model number SLPB11543140H5) and each cell consists of a carbon graphite negative electrode and a nickel-manganese-cobalt (Ni1/3Mn1/3 Co1/3) positive electrode. Heat flux sensors with type K thermocouples (OMEGA HFS-4) were placed on the surface at the centre of the cell. The pack is prepared in a way to minimise differences in external resistance such as equal cable lengths, fastening torque (8 kN) and cleaned contact surfaces. 
     The system can be used to monitor the condition of the cells by following the method outlined in  FIG. 3 , in which an estimated open circuit potential or open circuit voltage (OCP/OCV) is calculated and compared to either dT/dV (where V is voltage across the cell and T is temperature for the cell) or dHF/dV (where HF is measured heat flux across the cell). These quantities are calculated by calculating the ratios of dT/dt or dHV/dt to dT/dt (where “t” is time). In the following description, dT/dV is the parameter used for differential thermal voltammetry (DTV) while dHV/dV is the parameter used for differential heat flux voltammetry (DHFV). 
     A mode of operation is applied to the battery pack  20  with current profile which is at least partially known. As shown in  FIG. 3 , at step s 1  raw data showing the voltage and temperature response of the battery during the time period in which the current is applied is input to the battery management system  10 . At step s 2 , this data is separated and filtered into appropriate variables/matrices for further analysis, 
     In the preferred embodiment illustrated in  FIG. 3 , the current profile comprises intermittent rest phases. That is, a charge current is which has intermittent rest periods of no applied current. The voltage response during each of these rest phases can be fitted to estimate the OCV using a designated equation at steps s 3  to s 6 . This is now described in greater detail. 
     Under charge/discharge, the measured cell potential is a combination of the OCV and its overpotential which is dependent on current and internal resistance. In a pack application such as in electric vehicles and grid level storage, current distribution between each cell will vary depending on pack architecture, interconnection resistance and state of health (SOH). In order to determine the SOH independent of cell current and resistance, it is required to analyse the DTV data with respect to its OCV. 
     The intermittent constant current charge technique consists of a constant current charging phase and a short rest phase both of which can easily be carried out by existing systems such as consumer electronics and electric vehicles etc. The rest phase is set to occur every few minutes (depending on charging current) where the rest phase itself lasts a few seconds. For example 5 s of rest every 100 s of 1 C charging. The cell potential will approach its OCV following lithium ion diffusion however this process can take hours to reach saturation. According to the preferred embodiment, the first few seconds of potential profile at rest are taken. These are fit to a designated equation (such as a power equation or diffusion equation) at step s 3  to extract the parameters of that equation at step s 4 . This can then be extrapolated to find OCV at given states of charge. The final OCV of the cell can then be estimated by extrapolating between the calculated points at step s 6 . This way the OCV can be estimated during “normal” charging and DTV/DHFV analysis can be carried out at the same time. The computation is simple enough to be handled without excessive burden on the battery management system  10 . 
       FIGS. 4A and 4B  demonstrate the efficacy of this process to calculate OCV using a power equation for fresh and aged cells respectively. For the purpose of these figures, cells were charged with 2 h rest every 100 s charge at various C-rates. Assuming 2 hours is enough to reach saturation (i.e. OCV), the estimated OCV was extrapolated from initial few seconds of rest data and compared to the actual value after 2 hours. 
       FIG. 4A  relies on a power equation to reach the estimated OCV. In particular, a 2nd order power equation is a simplification of the exact representation of the diffusion process to minimise computation time and requirement. The equation was used to fit the rest profile.  FIG. 4A  shows the estimated OCV (full line), the actual OCV (dotted line) and recorded cell potential (dashed line). 
       FIG. 4B  again shows OCV calculated using a power equation, this time for an aged cell.  FIG. 4B  shows the estimated OCV (full line), the actual OCV (dotted line) and recorded cell potential (dashed line). 
     Using a diffusion equation may provide a closer-to-reality representation of the diffusion process. While making few assumptions to simplify the computation, the result is accurate enough for the purpose. The two main equations are Fick&#39;s second law of diffusion for spherical coordinates and the Nernst equation. The equations are combined to relate the cell potential with respect to time with several constants including the diffusion coefficient. 
     With the OCV estimated, the next stage is develop and understanding of DTV of DHFV. At steps s 7  to s 9 , the raw temperature or heat flux data is smoothed. At step s 7 , smoothing parameters are defined. These are used to smooth data using a moving average method at step s 8 . A final check to ensure the smoothed profile and the raw data lie within pre-set limits is carried out at step s 9 . In particular, in preferred embodiments, the median of absolute deviation (MAD) is kept below a pre-set margin. For example, this may be 0.1% for temperature and 7.5% for heat flux. The skilled person will recognise that the appropriate technique and parameters can be highly dependent on the noisiness of the raw data i.e. quality of measurement equipment, data acquisition accuracy/precision etc. 
     The data is then used to calculate for dT/dV and/or dHF/dV at step s 10 . These will give a relationship between these values and the OCV.  FIG. 5  illustrates such a relationship for an individual cell with a full line (the dotted line shows an example where no adjustment had been made to adjust for OCV). 
     Current battery applications use agnostic derating where the cells are limited to operate between a preselected fixed state-of-charge (SOC) range to minimise degradation accelerated at high and/or low voltage. This is clearly not effectively utilising the available power/energy in a cell. For example batteries in a Chevrolet Volt are limited between 30% and 80% SOC and Nissan LEAF model 2013 is limited up to 80%. For electric vehicle applications especially in sports where the vehicle needs to push to its extremes, a more intelligent derating system is critical. 
     Once the OCV profile is obtained the DTV parameter can be plotted against its OCV for peak analysis. This process is illustrated at steps s 11  to s 15 . Firstly, at step s 11 , peak fitting parameters may be defined, and peaks may then be fitted to the DTV or DHFV profile with respect to OCV (step s 12 ). A check may be made to ensure that the fitting error lies within preset limits at step s 13  and peak parameters extracted at step s 14 . A comparison can then be made with historic peak parameters of that cell or others similar to it (step s 15 ). 
     The evolution in peak parameters upon ageing will give quantitative information on the cell&#39;s SOH including temperature correction. At this stage, the OCV profile can also be decoupled into positive and negative electrode to give analysis on individual electrodes using existing OCV models. 
     The stoichiometric shift determined this way can be used to generate a revised optimum operating conditions for the cell, e.g. upper potential limit (step s 16 ). This intelligent de-rating technique can maximise available power and energy while minimising accelerated degradation through cathode overcharge. 
     The ability of the disclosure to distinguish the condition of cells has been demonstrated in a series of experiments, as will be described further below. In these experiments, one deliberately aged cell and three fresh cells were placed together in the pack to determine whether the diagnosis methods could correctly determine the pack state-of-health. The aged cell was previously stored at 55 deg C. at 4.2V for approximately 15 days. The pack was prepared in a way to minimise differences in external resistance such as equal cable lengths, fastening torque (8 kN) and cleaned contact surfaces. Shunt resistors (RS 810-3273) were placed in series with each cell to measure the current distribution of the pack. 
     During the experiments, the pack was placed inside an incubator (Binder KB-23) with fan forced air convection flowing over the pack surface while keeping the incubator door open to emulate a surface cooling system to recreate conditions often found in real applications such as electric vehicles. Maccor Batter Tester series 4000 was used for measurements and loading during pack experiments whereas Bio-Logic BCS-815 was used for individual cell experiments. Pico TC-08 was used for heat flux sensor measurements and Yokogawa MX100 for shunt resistor measurements. 
     The pack experiment was carried out at 2 C constant current charge and discharge where the pack was rested for at least 1 hour prior to each loading to ensure equilibrium state. For discharge, the pack was initially charged to 4.2V at 1 C then held at 4.2V until current was less than 0.25 A. For charge, the preparation was the same except it was to 2.7V. Then the cells were individually characterised through constant current discharges at 1/3 C, 1 C, 2 C and 3 C. The cells were initially charged at 1 C to 4.2V then held until current was less than 0.1 A. 
       FIG. 6  shows pack experimental results for 2 C (40 A) discharge. In particular  FIG. 6  shows analysis under 2 C constant current discharge; specifically  FIG. 6( a )  shows cell current;  FIG. 6( b )  shows an incremental capacity method;  FIG. 6( c )  shows differential thermal voltammetry; and  FIG. 6( d )  shows differential heat flux voltammetry. 
     In an ideal battery pack, each cell is expected to carry 10 A. However,  FIG. 6( a )  confirms that the current path between the four cells are heterogeneous. The three fresh cells have relatively similar current profile whereas the aged cell performs very differently. This is also reflected in the dQ/dV plot of  FIG. 6( b )  as the different current profile results in different dQ term. This is due to the changes in thermodynamic overpotential and electrode stoichimetries for the aged cell. Thermodynamic overpotential is defined as the drop in potential due to internal resistances such as ohmic, ionic and charge transport. It is observed that the three fresh cells initially discharge at slightly higher than 10 A to compensate for the low power performance of the aged cell. However, towards the end of its loading, the aged cell experiences higher current for the given pack voltage where it peaks at 2.86 C (14.3 A). Operating at higher current may promote degradation mechanisms such as lithium plating on charge and electrolyte decomposition by higher heat generation. This shows that having an unhealthy cell in a battery pack decreases its performance and accelerates pack aging reducing its operational lifetime. Hence it is crucial for a battery management system to be able to correctly identify unhealthy cells to be replaced at an early stage. 
       FIG. 6( a )  also shows internal current during relaxation. Cells were at different state-of-charges and therefore after removal of load and the imposed overpotentials, the current distributes amongst the cells. This further loads the cells and over time can get worse and lead to accelerated degradation. 
       FIGS. 6( c ) and 6( d )  show DTV and DHFV results respectively. The notable differences can be immediately observed between the one aged cell and the fresh cells. 
       FIG. 7  shows peak fitting of differential thermal and heat flux voltammetry results for 2 C constant current discharge. Example peak fittings for cell  1  ( FIG. 7( a ) ) and cell  4  ( FIG. 7( b ) ).  FIG. 7( c )  shows peak position (c) while  FIG. 7( d )  shows peak width (d). 
     Each peak in these curves represents the combined phase of the positive and the negative electrode. Peak fitting analysis on the results were carried out using peakfit.m (https://terpconnect.umd.edu/˜toh/spectrum/peakfit.m) script in MATLAB where the differences in the peak parameters such as the peak position and width can give information on the cell&#39;s state-of-health.  FIGS. 7( a ) and 7( b )  demonstrate example peak fittings of DTV curves where each peak has been labelled accordingly for a combination of nickel-manganese-cobalt electrode lattice parameter evolution stage ({circle around (1)}-{circle around (2)}) and a graphitic carbon intercalation stage ( ).  FIG. 8  illustrates this concept of combined electrode phases. 
     It can be identified from the peak {circle around (1)}*  parameters as shown in  FIGS. 7( c ) and 7( d )  that the aged cell has an evident lower peak position and a wider peak width than the fresh cells for both DTV and DHFV. Peak width is taken as the width of the peak at its half height. Degradation mechanisms such as electrolyte decomposition and metal dissolution will promote an increase in thermodynamic overpotential hence resulting in lower peak position at a given current. The increase of peak width can be explained from the initial lower current of the aged cell hence a slower discharge rate. Using this method, it is now possible to quantitatively diagnose the cell state-of-health and conclude that cell  1  has significantly aged compared to the remaining cells. 
     It can also be confirmed from this diagnosis that it is sufficient to analyse only peak {circle around (1)}*  which is the first peak during discharge at approximately 3.9V. In  FIGS. 7( a ) and 7( b ) , it is observed that there is minimal overlap of the peaks above 3.8V. This suggests that DTV does not need to be carried out through the entire potential range of the cell which will further reduce the time of diagnosis i.e. it is sufficient to discharge from 4.2V to 3.8V to identify the aged cell. 
     In practice if the peak position of a particular cell is significantly shifted to a lower potential and/or the peak width is wider than the rest of the cells in a pack, it can be assumed that the cell is promoting unequal current distribution lowering the overall performance and the lifetime of the pack and should be replaced as soon as possible. Here the use of DTV and DHFV has been validated for identifying aged cells in a battery pack under a thermal management system. DHFV can be used when dT/dt is too small to measure due to strong cooling by the thermal management system. 
     In real application such as in electric vehicles, it may be more practical to be able to conduct the diagnosis under constant current charge. This would suggest that the diagnosis can be carried out whenever the electric vehicle is left to charge and no separate charging or discharging method is required. 
       FIG. 9  shows pack experiment results for 2 C (40 A) charge. In particular,  FIG. 9( a )  shows cell current,  FIG. 9( b )  shows results obtained using the incremental capacity method,  FIG. 9( c )  shows results obtained using differential thermal voltammetry and  FIG. 9( d )  shows results obtained using differential heat flux voltammetry. The aged cell can be identified for both DTV and DHFV. The negative peak here in  FIGS. 9( c ) and 9( d )  appears from the negative dT/dt where the forced air cooling is stronger than the heat generated by the cell or potentially from the entropy terms. 
       FIG. 10  shows peak analysis of differential thermal and heat flux voltammetry results for 2 C constant current charge. In particular,  FIG. 10( a )  shows a zoomed in differential thermal voltammetry result,  FIG. 10( b )  shows the potential at the x-axis intercept (i.e. dT/dV=0) just before the negative peak,  FIG. 10( c )  shows the potential for the negative peak and  FIG. 10( d )  shows the potential at the x-axis intercept just after the negative peak. 
       FIG. 10( a )  shows the DTV result during 2 C charge with a zoomed in figure on the negative peak. The negative peak here represents peak {circle around (1)}*  due to the negative dT/dt term.  FIG. 10( b ) , takes the potential at the initial x-axis intersect i.e. dT/dV=0 and dHF/dV=0.  FIG. 10( c )  is the potential at the lowest point of the peak and  FIG. 9( d )  shows the x-axis intersect after. It can be seen from all three parameters that the aged cell has a notably higher potential than the fresh cells for both DTV and DHFV which can be described by the stoichiometric drift of the electrodes. This method requires less computation as peak fitting is unnecessary. In practice, it may be recommend to use the potential at the initial x-axis intersect as the change is larger hence requires less resolution to measure the parameter on-board. Here the use of DTV and DHFV has been demonstrated for an on-board identification of aged cells in a battery pack under thermal management system during charge. 
     In order to validate the results above, the pack was then dismantled and characterisation tests were carried out on individual cells to validate the pack diagnosis results. The experimental setup was exactly the same but the cells were loaded individually. Constant current discharges at 1/3 C, 1 C, 2 C and 3 C were performed. Capacity results are described in Table 1. The difference in the results between the fresh and the aged cells indicate higher internal resistance and the stoichiometric shift of the aged cell which is translated into the DTV and DHFV pack analysis. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 Discharge capacity (Ah) 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 ⅓ C 
                 1 C 
                 2 C 
                 3 C 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Cell 1 
                 4.65 
                 4.53 
                 4.39 
                 4.38 
               
               
                   
                 Cell 2 
                 5.05 
                 4.97 
                 4.83 
                 4.84 
               
               
                   
                 Cell 3 
                 5.06 
                 4.97 
                 4.83 
                 4.84 
               
               
                   
                 Cell 4 
                 5.05 
                 4.97 
                 4.82 
                 4.82 
               
               
                   
                 Total 
                 19.81 
                 19.44 
                 18.87 
                 18.88 
               
               
                   
                   
               
            
           
         
       
     
     Variations and modifications will be apparent to the skilled person. Such variations and modifications may involve equivalent and other features which are already known and which may be used instead of, or in addition to, features described herein. Features that are described in the context of separate embodiments may be provided in combination in a single embodiment. Conversely, features which are described in the context of a single embodiment may also be provided separately or in any suitable sub-combination. 
     It should be noted that the term “comprising” does not exclude other elements or steps, the term “a” or “an” does not exclude a plurality, a single feature may fulfil the functions of several features recited in the claims and reference signs in the claims shall not be construed as limiting the scope of the claims. It should also be noted that the Figures are not necessarily to scale; emphasis instead generally being placed upon illustrating the principles of the present invention. Where ranges are disclosed, they should be considered to include their endpoints.