ISO/TR 20891:2020

TECHNICAL ISO/TR
REPORT 20891
First edition
2020-10
Space systems — Space batteries
— Guidelines for in-flight health
assessment of lithium-ion batteries
Systèmes spatiaux - Batteries spatiales - lignes directrices pour
l'évaluation en vol de la santé des batteries lithium-ion
Reference number
©
ISO 2020
© ISO 2020
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ii © ISO 2020 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and abbreviated terms . 1
3.1 Term and definitions . 1
3.2 Abbreviated terms . 1
4 Overview . 2
4.1 General . 2
4.2 Battery capacity . 4
4.3 Battery impedance . . 4
4.3.1 General. 4
4.3.2 Electrochemical impedance spectroscopy (EIS) . 5
4.4 Battery internal resistance . 8
5 Specificities of spacecraft telemetry and resulting limitations .11
5.1 General .11
5.2 Signal digitization .11
5.3 Temperature .12
5.4 Voltage .12
5.5 Current .12
5.6 Sampling frequency .13
5.7 Synchronisation .13
5.8 On-board memory .13
6 Main methods for the evaluation of battery ageing parameters .14
6.1 Global method: fitting of a numerical model to in-flight data .14
6.1.1 General.14
6.1.2 Model structure .14
6.1.3 Data fitting .16
6.2 Evaluation of battery capacity .25
6.2.1 Direct method .25
6.2.2 Indirect method .30
6.3 Measurement of battery internal resistance .32
6.3.1 Direct internal resistance measurement .32
6.3.2 Indirect measurement of battery resistance .34
6.3.3 Correlation of internal resistance to capacity .46
6.4 Measurement of battery spectral impedance .47
6.4.1 General.47
6.4.2 Time domain identification of a dynamic model .48
6.4.3 Derivation of impedance from frequency domain processing of transients .49
6.4.4 Derivation of impedance from frequency domain processing of disturbances .50
7 Recommendations for easing battery in-flight health assessment .51
7.1 General recommendations.51
7.2 Recommendations related to battery characterization prior to flight.52
7.3 Recommendations related to spacecraft telemetry performance .52
7.4 Recommendations related to spacecraft operations.52
7.5 Recommendations related to data formatting .52
7.6 Recommendations related to data processing .53
Bibliography .54
Foreword
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This document was prepared by Technical Committee ISO/TC 20, Aircraft and space vehicles,
Subcommittee SC 14, Space systems and operations.
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iv © ISO 2020 – All rights reserved

Introduction
The charge and discharge cycle of a battery is not 100 % efficient, with each cycle side reactions can
occur that eventually accumulate and cause degradation of the battery's performance. Understanding
how the battery’s performance changes throughout the mission is a subject of importance; and accurate
determination of the battery’s current SoH is essential in a large number of situations, for example:
— the routine assessment of battery performance to allow early detection of anomalies (by comparing
its actual versus predicted performance);
— the setting of alarm thresholds to ensure adequate energy;
— detection of battery anomalies that can put at risk the spacecraft passivation and/or de-orbiting
strategy;
— decisions regarding mission extension beyond initial target life;
— evaluating the remaining capability of a spacecraft upon occurrence of an anomaly;
— feedback to the battery manufacturer to improve the performance predictions.
However, it is often difficult to properly assess the in-flight status, due to various factors:
— Flight electrical load profiles differ significantly to load profiles used to characterize battery
performance models and the battery’s SoH; for example, the total available battery capacity, which is
the most important parameter, is not directly accessible during flight since its simple measurement
by full discharge of the battery goes against the spacecraft operational safety.
— The quality of the accessible data from telemetry is sometimes poor: insufficient telemetry
resolution and/or accuracy, lack of synchronization between related parameters like current and
voltage, possibly large load consumption fluctuations introducing a high level of noise, delivery of
data under a form not easy to process, etc.
— The battery is operating in flight in a way that is generally very different from the test conditions
at qualification or acceptance. As a consequence, if no in-flight assessment has been made at the
beginning of life, the direct comparison between current in-flight status and available ground
testing data can be difficult and in any case more difficult than a comparison with the initial in-
flight behaviour.
— The battery is operated under time variant conditions in a large bandwidth of different time
scales, e.g. switching heater circuits vs. variations of the charge profile and eclipse length for a LEO
satellite with drifting orbit. Low frequency variations introduced by drifting orbits or seasons are
considered for the computation of trends and averaging over several orbits.
— The processing of data to derive the health status is not straightforward and is usually performed
by identifying the ageing parameters of a model. Therefore, the representativeness of this model is
a key issue. In addition, even with a good model, the results are not always satisfactory.
Therefore, it has been found of interest to provide detailed information about the means currently
used or envisioned to perform in-flight battery health assessment and to make recommendations to
spacecraft builders, operation managers and batteries manufacturers that would make it easier. This is
the subject of this document.
It is important to highlight that, according to the definition given in 3.1.1, assessing the health status
allows to verify that the battery behaves as well as or possibly better than anticipated. It is not aimed at
providing an evaluation of any sort of “absolute ageing” nor to predict further evolution, even if this can
be the case with some methods and their on-board implementation.
TECHNICAL REPORT ISO/TR 20891:2020(E)
Space systems — Space batteries — Guidelines for in-flight
health assessment of lithium-ion batteries
IMPORTANT — The electronic file of this document contains colours which are considered to be
useful for the correct understanding of the document. Users should therefore consider printing
this document using a colour printer.
1 Scope
This document provides detailed information on the various methods of assessing the health status
of lithium-ion space batteries in flight and makes recommendations to battery suppliers, spacecraft
manufacturers and operators to ease this assessment.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 17546, Space systems — Lithium ion battery for space vehicles — Design and verification requirements
3 Terms, definitions and abbreviated terms
3.1 Term and definitions
For the purposes of this document, the terms and definitions given in ISO 17546 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1.1
battery health
state of the battery, which is healthy if both the amount and the rate of degradation of its performance
are lower than or equal to the predicted ones at the same time into the mission
3.2 Abbreviated terms
ADC analogue to digital converter
BoL beginning of life
CC constant current
CV constant voltage
DoD depth of discharge
EIS electrochemical impedance spectroscopy
EMF electro-motive force (a.k.a. open circuit voltage)
EoC end of charge
EoCV end of charge voltage
EoD end of discharge
EoDV end of discharge voltage
EoL end of life
ESA European Space Agency
GEO geostationary earth orbit
LEO low earth orbit
NCA nickel cobalt aluminium (lithium-ion cathode composition)
NIBHM non-Intrusive battery health monitoring
SoC state of charge
SoH state of health
RTL round trip loss
4 Overview
4.1 General
The SoH of a battery reflects its capability to fulfil the needs of a mission, i.e. whether the performance
is at or above the expected level. Typically, the performance itself covers requirements such as;
a) the capability to deliver and absorb a certain amount of energy, under a certain load profile and
with a defined voltage range;
b) the capability to deliver a certain power for a given duration, while maintaining a certain voltage.
Theoretically, assessing this SoH can be conceived as the simply monitoring the battery behaviour (e.g.
the battery voltage) in the orbit and comparing it against previously set baselines but, in reality, it is far
less straightforward.
Figure 1 — Schematic of energy usage in satellite battery
2 © ISO 2020 – All rights reserved

As Figure 1 shows, the deliverable energy a) of a battery is dependent on the mission phase and
operational strategy. In many cases this not only shows characterizing the mission energy profile but
also includes understanding the proportion of contingency energy, i.e. the energy needed to reach a safe
mode, as part of the recovery of a major on-board failure. There is also some usable energy that will
not be used at the extremes of SoC (to mitigate the accelerated lifetime degradation that occurs with
repeated use of energy in these segment of the SoC window). As energy is not expected to be drawn
from the contingency or protective margins of the battery in nominal operating conditions, observing
energy in these segments is simply not possible during mission.
Pulsed power profiles in b) may occur for a duration too short to be captured by the telemetry. It is
thus necessary to infer the health status from only the observable data, by estimating the value of the
parameters driving the battery performance.
At a simplistic level, the capabilities of the battery can be expressed using the following fundamental
formulae:
EQ= V (1)
N
where
E is the battery energy (Wh);
Q is the battery capacity (Ah);
V is the nominal voltage at which the charge is delivered (V).
N
VV=±IR (2)
TOCV
where
V is the terminal voltage (V);
T
V is the open circuit voltage of the battery (V);
OCV
I is the current in (or out) of the battery (A);
R is the resistance (or internal impedance) of the battery (Ω).
PI=±VI R (3)
OCV
Where P is the power developed by the battery (W).
RR=+RR+ (4)
Ω CT dif
where
R is the ohmic (electronic) resistance (Ω);
Ω
R is the charge transfer resistance (Ω);
CT
R is the diffusion resistance (Ω).
dif
From the formulae, it can be seen that the battery capacity and voltage (driving factor of a) above) and
internal impedance (driving factor of b)) are the main contributors to the battery performance and
that the evolution of these factors through ageing leads to a reduction of both the operating voltage at a
[7]
given discharged energy and the discharge rate .
Other parameters, like self-discharge or diffusion time constant, are also quite sensitive to ageing but
have, at most, a second order influence on the performance. This does not mean, though, that they
cannot be useful indicators of the battery SoH.
It is worth noting that many parameters (such as resistance and SoC) have a temperature dependency,
which should be considered when choosing a test temperature or interpreting telemetry data.
4.2 Battery capacity
The simplest and most direct way of measuring a battery capacity is to perform a full discharge at a
known rate (the lower the current the less resistive effects that will be observed). Unfortunately, this is
usually not compatible with safe operation of the spacecraft. Therefore, the difficulty of estimating the
capacity depends on the way the battery is used on board.
On a GEO, the total number of eclipses over the lifetime is small and consequently the battery can be
used at a relatively large DoD, in the range of 70 % to 80 %. In such operating conditions, most of the
discharge curve is accessible directly via the telemetry and, given the large fraction of the orbit period
that is devoted to charging, the battery has time to reach a stable state, usually taper under almost zero
current.
Conversely, in a LEO, the very large number of eclipses forces to limit the operating DoD to values around
20 % and the quick succession of eclipse and sunlight regimes does not allow the battery to reach any
steady state (here the diffusion plays a significant role). Furthermore, due to seasonal variations of
the sun illumination and even more pronounced variations in the case of a drifting orbit, the repetitive
profile of the battery state from orbit to orbit is not even converging towards a stationary profile. It is
therefore much more difficult to observe directly a stable battery behaviour.
4.3 Battery impedance
4.3.1 General
A rechargeable intercalation battery functions by internal ion flow motivating external electron flow
(discharge) or external electron flow motivating internal ionic movement (charge). When subjecting a
cell to a flow of current, a chemical change occurs within it. This chemical change causes the build-up or
dissipation of obstacles to the current. These obstacles are known as polarizations:
a) Ohmic polarization is caused by ohmic internal resistance of the cell against the flow of the current.
This ohmic resistance (R ) consists of an electronic resistance and an ionic one.
Ω
— The electronic resistance can be seen in positive current collectors (foil and electrode terminal),
positive active materials, positive conductive materials, negative current collectors (foil and
electrode terminal) and negative active materials. Contact resistance between positive current
collector and positive active materials is also an electronic resistance because the oxide thin
layer is formed on the surface of the aluminium current collector foil. Since the positive active
material shows a characteristic in electronic conductivity similar to a semiconductor, mixed
conductive material like carbon keep electronic network in positive electrode layer. On the
other hand, negative current collectors made of copper and negative active materials made of
carbon have lower electronic resistance than positive ones.
— The ionic resistance is another component of ohmic polarization. The resistance makes obstacle
against the transfer of Li-ion and counter anion in liquid electrolyte impregnated in consecutive
micro-pores inside the positive electrode layer, negative electrode layer and porous separator.
This polarization usually has a very fast response time, i.e. in the order of milliseconds.
b) Activation polarization is the potential difference needed to generate currents depending on the
activation energy of electrode reaction. The activation energy has electrons transferred from
4 © ISO 2020 – All rights reserved

electrodes into electrolyte or from electrolyte into electrodes. In the case of charge reaction of
positive electrode, for example, Li de-intercalated from solid active material inside is activated on
the surface of particle, and thereafter is oxidized to Li-ion. The response can be in the order of 10
milliseconds to seconds.
c) Concentration polarization denotes the voltage loss resulting from changes in the electrolyte
concentration due to a flow of electrode reaction current through the electrode/electrolyte
interface. The concentration polarization is equivalent to a difference of the thermodynamic
potential, which is a function of concentration of electrode reaction species.
d) Diffusion polarization is a kind of concentration polarization. The diffusion polarization occurs
when electrode reaction species become insufficient at the electrode surface because of slow
supply rate driven by concentration gradient. This polarization occurs at the positive and negative
electrode surface, for example, when Li transfer from active material to electrode surface through
solid phase by diffusion process, and the intercalation to active material is also accompanied by
diffusion polarization. This response can be in the order of minutes to hours.
Therefore, it is preferable to speak about internal impedance than resistance and to consider the
impedance spectrum (i.e. impedance module and phase versus frequency) as an appropriate way to get
an insight onto these various polarizations. Its evolution with ageing can be a very effective qualitative
[5][6]
health indicator . It may even, under certain conditions, allow prediction of the battery behaviour,
[9]
at least in the short to medium term . The drawback is that the classical way of measuring it, by the
sweeping in frequency of a sine excitation current, is not straightforward to implement on-board. The
internal resistance, which can be seen as a reduced image of the impedance, is easier to access and is
therefore also a parameter of interest.
4.3.2 Electrochemical impedance spectroscopy (EIS)
In a Li-ion battery, the charge and discharge mechanism relies on several electronic and ionic processes
for successful operation. These processes occur across a range of timescales from picoseconds to
minutes and hours. By analysing the response of a battery to voltage or current with respect to time
(or frequency of excitation), the behaviour of some of these processes can be separated and understood
individually. In EIS, this is done by studying the output impedance signal from an applied sinusoidal
current or voltage. The phase shift and magnitude of the output signal can then be used to determine
the impedance.
Different internal mechanisms inside the battery can be linked to specific time domains and hence
respond to specific excitation frequencies. By altering the frequency of the input current or voltage
and investigating how the resulting phase shift (and impedance) changes with input frequency, the
relationship between individual mechanisms and their individual impedances can be isolated and
understood.
As a battery ages the performance characteristics alter. The process governing these performance
characteristics can be traced back to changes in the internal electrochemical mechanisms. These
changes (and the mechanisms responsible for them) can be observed via the changing impedance vs.
frequency relationship with lifetime.
Typically, these results are displayed in a Nyquist plot where the impedance is separated into the real
and imaginary components and the two components plotted on the X and Y axis respectively, as shown
in Figure 2.
Key
X real (Z), mΩ
Y imaginary (Z), mΩ
1 equivalent circuit
2 ohmic resistance (R ) 0 phase shift (i.e. DC)
s
3 charge transfer (R ) and double layer (C ) region, Hz
ct dl
4 Warburg impedance (Z ) solid state diffusion region, mHz
w
Figure 2 — Schematic of a Nyquist impedance plot
The key attributes of the battery can then be observed, and an equivalent circuit can be used to map the
attributes to the physical behaviour inside the battery. Figure 3 illustrates schematically.
Over time these attributes may change. This may be due to several factors such as;
— the introduction of surface layers, slowing down to electrolyte /electrode transfer, increasing
resistance;
— poorer electrical connection between the electrode particles, increasing the electrical resistance;
— loss of surface area through pore clogging reducing etc.
Theoretically changes in the battery can be traced through changing impedance spectrum. The
behaviour of the EIS spectrum is translated to changes in the individual elements in an equivalent
circuit and characterized at each stage throughout the life of the battery.
6 © ISO 2020 – All rights reserved

Key
1 current collector 6 electron
2 electrode 7 electrode particle
3 electrolyte 8 electron movement
+
4 electrolyte molecule 9 Li charge transfer
+ +
5 Li ion 10 Li diffusion
Figure 3 — Cell reaction processes and their corresponding equivalent circuit element
In reality there is still some debate about some of the features observed in battery impedance spectra
and their physical meaning (e.g. magnitude of specific contributions from surface layer mechanisms
at the solid electrolyte interface). It can also be challenging to directly link an equivalent circuit based
on impedance spectrum alone to observable charge and discharge behaviour at spacecraft level in
Figure 4. For this reason, EIS is primarily used as a powerful tool to qualitatively assess changes in
battery but seldom used for quantitative modelling of battery behaviour over life.
Key
X real (Z), mΩ
Y imaginary (Z), mΩ
1 increasing ohmic resistance
2 introduction surface layer process
3 changing charge transfer resistance
4 ageing
Figure 4 — Schematic of charge state of Nyquist plot with time
4.4 Battery internal resistance
The battery internal resistance is commonly defined by the classic Kirchhoff relationship, with the
resistance equal to the ratio of change in battery voltage to change in current that produced it. As
mentioned in 4.3, the battery not being a pure resistor, the resistance measure is dependent on the
timeframe of measurement; an instantaneous sampling of the change of voltage yields the resistance
associated with the fastest mechanisms of resistances (electronic) while sampling over the course of
seconds shows the additional contributions from charge transfer and diffusion mechanisms. Extending
the resistance sampling time also sees the voltage change as a function of SoC (as per Formulae (2) and
(4)). Thus, the measured value obviously depends on the delay between the current change and the
voltage sampling. This is illustrated by Figure 5, which shows how large the difference between the
values of a cell internal resistance measured by two different methods during the same cycle can be.
R via the ESTBC method is resistance determined by voltage drop with constant low load.
int
R via supplier method is determined by the voltage drop at the end of a higher magnitude current pulse.
int
8 © ISO 2020 – All rights reserved

Key
X time (s)
Y1 cell current (A)
Y2 cell internal resistance (Ω)
1 cell current
2 R , ESBTC method
int
3 R , supplier method
int
Figure 5 — Cell internal resistance, cell current at various state of charge, according to two
different methods
The various contributors to the impedance having different time constants, one is consistent in the
choice of the sampling delay in order to ensure that the measured value is representative of the actual
ageing. Figure 6 shows the evolution with time of the same cell internal resistance measured with these
two methods: not only their values but also their evolution with ageing are markedly different (due to
the specific resistance mechanisms that the two different techniques capture and how these change
over time).
Key
X cycle number
Y resistance (Ω)
1 pulse discharge method
2 constant load method
Figure 6 — Comparative evolution of internal resistance with ageing according to the two
different measurement methods of Figure 5 (arbitrary units)
Despite its limitations, the battery internal resistance (measured consistently) can sometimes be the
best indicator of the health status of a battery. Indeed, it can occur, with some technologies and under
certain operating conditions, that the capacity does not change much during mission life (e.g. to excess
capacity of the electrode the most prone to degradation) while in the meantime the internal resistance
shows a significant evolution.
Figure 7 illustrates this situation for a real time GEO test where the capacity loss is negligible while the
internal resistance increases by almost 40 %. In such a case, the internal resistance appears as the key
parameter that would allow detecting an abnormal drift well before any impact on the capacity can be
evidenced.
10 © ISO 2020 – All rights reserved

Key
X number of eclipse seasons
Y relative change from BoL (%)
1 C /C
meas measo
2 R/R
Figure 7 — Relative capacity (red) and internal resistance (green) variations versus eclipse
season number in real time GEO cycling
In summary, one or the other of the parameters reflecting the ageing of a battery may be preferred
in order to estimate its health status. They are carefully selected and can be accessed individually or
globally by direct or indirect methods, which are detailed in Clause 6.
5 Specificities of spacecraft telemetry and resulting limitations
5.1 General
The telemetry implemented on board a spacecraft is primarily aimed at supporting the nominal and
contingency operations, not at providing high accuracy/frequency acquisitions nor accurate timing
in view of more “technological” needs. Therefore, it is important to be aware of its specificities and
limitations.
5.2 Signal digitization
In the most usual implementation, analogue parameters are fed to an ADC that associates a digital
value coded on a defined number of bits to an input voltage in a range between zero and full scale. For
instance, a 0 V to 5,10 V input range can be coded on 8 bits (i.e. from 0 to 255), providing a quantization
step of 20 mV. This quantization is the first source of uncertainty for the measured parameter. For the
example ADC, it amounts to approximately 0,4 % of full scale.
In order to make a given parameter compatible with the ADC input voltage range, this one has usually
to be conditioned. For a voltage outside of the ADC range this can be done very simply by a resistive
divider: in the present example, a divider ratio of 1:8 would offer a range of 0 V to 41 V, adequate for the
measurement of a battery voltage operating on a typical satellite power bus (i.e. below 40 V).
For currents, an active circuit is needed to amplify the (usually small) voltage drop present at the
terminals of a measurement shunt. Here, for a voltage drop of e.g. 100 mV full scale, an amplification
factor of 51 would be necessary. A peculiarity of the battery current is its bi-directionality, while most
often the ADC is single supplied. As a consequence, the charge and discharge currents are usually
measured through the same shunt but conditioned via two different chains of opposite gain signs, which
transfer functions that cannot be perfectly matched. This can be an issue when trying to access e.g. the
round trip efficiency of the battery, which plays on small differences between the measurements of
charged and discharged energy.
5.3 Temperature
Temperature can be acquired via thermistors or platinum sensors. The latter is polarized by a current
and the voltage at its terminals to be shifted and amplified to fit with the ADC input range. For a
thermistor the conditioning is usually performed by making a resistive divider of the thermistor and of
a fixed series resistor whose value is equal to that of the sensor in the centre of the temperature range.
Supplied at a voltage equal to the top of the ADC range, their common point is directly fed to the ADC.
This is usually the case for batteries.
Whatever the parameter and the conditioning applied, the end to end transfer function from the
physical value (in volts, amps or degrees) to its digital representation throughout the useful range
needs to be established. This takes the form of a “calibration curve” and can be given as a series of
points in between which a linear interpolation can be performed or by a polynomial of a certain degree
obtained by a best fit to measured data, etc. In all cases this introduces a certain level of uncertainty, of
different impact depending on the nature and range of the parameter.
5.4 Voltage
For the battery voltage, the relative variation between EoC and EoD is rather small; the useful range is
only a limited fraction of the full scale and therefore the quantization effect is more visible. In turn, the
calibration can be optimized for this relatively small voltage extend.
5.5 Current
The current can spread the whole range from zero to full scale, both in charge and discharge.
Considering again the example of the round trip efficiency, the amount of charged energy during the
final phase of taper is very sensitive to any offset of the telemetry chain in the vicinity of zero current.
Figure 8 shows a taper charge phase observed in flight. The offset, around 60 mA, is not insignificant
and it is worth observing that, after a quite long duration of taper, where the current is almost flat, i.e.
in reality equal to zero, the telemetry drops down to zero only at the beginning of discharge, when the
ADC saturates low.
12 © ISO 2020 – All rights reserved

Key
X time (arb units)
Y current (A)
1 beginning of discharge, ADC saturates low
Figure 8 — Current profile observed via spacecraft telemetry chain showing offset
5.6 Sampling frequency
The acquisition rate can also be a potential concern when having to, for example, detect the trespassing
of a given threshold or to integrate current. For the former an interpolation is necessary while the
latter may experiment an uncertainty attached to the ratio of the sampling interval to the duration of
the integration. As an example, a 20 seconds sampling period on a 30 minute eclipse would introduce, in
the worst case, up to 2 % error. Again, in the round trip efficiency case, this is far from negligible w.r.t.
an energy loss of less than 10 %.
Fortunately, many spacecraft have a so-called dwell mode, allowing a faster sampling of selected
parameters for a period of time. It is common to achieve a rate of one to a few tens of hertz.
5.7 Synchronisation
Another critical aspect is the timing of the acquisitions of several parameters. Depending on the
telemetry chain design, it can be that the sampling of two parameters is separated by a duration that is
significant in regard of the sampling period. When observing e.g. the battery current/voltage behaviour
during a transient, such a lack of synchronization is an obvious issue.
5.8 On-board memory
Last, many spacecraft in LEO do not store on board the complete set of telemetry data acquired in
between to communication sessions with their ground control station. The data set can be limited to,
e.g. a sub-sampling of the parameters plus the minimum and maximum recorded during the period.
Obviously, this makes any sort of fine processing very challenging.
7.3 provides a number of recommendations aimed at increasing the usability of the data acquired via
the spacecraft telemetry chain.
6 Main methods for the evaluation of battery ageing parameters
6.1 Global method: fitting of a numerical model to in-flight data
6.1.1 General
To characterize the changing SoH of a battery a classic approach is to fit an existing numerical model of
the system to in-flight data. In principle this approach gives access to all the battery parameters (e.g.
capacity, internal resistance, diffusion), within the model representativeness and accuracy.
6.1.2 Model structure
Most often a numerical model of a flown battery or, indeed, of the cells making it, is available, from
either the battery supplier or the spacecraft manufacturer, chiefly for design purposes. Such models
can be based on various structures.
A number of very classical topology are shown in Figure 9. They are made of a number of discrete
electrical components (voltage sources, resistors, capacitors, etc.) which together represent the
observable behaviour of the cell from the electrical point of view. They are often referred to as the “black
box” model, since they do not intend to reflect the internal electrochemical and physical behaviour of
the cell.
The values of the components depend on the ageing and on the instantaneous operating conditions
(temperature, SoC, current, voltage, etc.). The mathematical functions describing their dependence
onto the operating conditions can be more or less complex, according to the needed degree of
representativeness, accuracy and timescale.
Another class of models aims at representing, down to a variable level of details, the internal electrical
and electrochemical behaviour of the cell. As an example, the model shown in Figure 10 is commonly
used at ESA for design verification and in-flight health status assessment, e.g. in view of mission
extensions. Being close to the actual cell construction, it is able to reproduce its behaviour down to
relatively small time scales.
Other models do not attempt at reproducing the internal or external cell behaviour by discrete or (semi)
continuous electrical elements but come under the form of pure mathematical descriptions. These
can be the transcription, in a form that can be processed by a computer, of the theoretical formulae of
electricity, electrochemistry, chemical kinetics and more. The variety of these models is large.
A last type of models is made of the purely empirical ones. There, the operating point of a cell under
given conditions is interpolated inside a data base built from tests performed in a variety of settings.
The main drawback of this approach is the need for a large data base, meaning a lot of testing and
resulting into high cost and long duration. It is seldom used, since building a model of the previous type
requests far less effort.
The cell behaviour being highly temperature dependent, most of the cell numerical models also provide
the thermal dissipation as an output, which is fed to the cell or battery thermal model to derive its
operating temperature. This aspect is of minor interest here, since the temperature can be read direc
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