U.S. patent application number 17/405258 was filed with the patent office on 2022-03-17 for method and apparatus for determining the state of health and state of charge of lithium sulfur batteries.
This patent application is currently assigned to Oxis Energy Limited. The applicant listed for this patent is Oxis Energy Limited. Invention is credited to Daniel Auger, Abbas Fotouhi, Monica Marinescu, Geraint Minton, Greg Offer, Mark Wild.
Application Number | 20220082631 17/405258 |
Document ID | / |
Family ID | |
Filed Date | 2022-03-17 |
United States Patent
Application |
20220082631 |
Kind Code |
A1 |
Wild; Mark ; et al. |
March 17, 2022 |
METHOD AND APPARATUS FOR DETERMINING THE STATE OF HEALTH AND STATE
OF CHARGE OF LITHIUM SULFUR BATTERIES
Abstract
Systems and methods for accurately determining the state of
health (including state of charge and relative age) of a Lithium
Sulfur battery, module or cell. The invention uses an operational
model of a Lithium Sulfur cell or battery to predict model
parameters under a range of conditions related to state of charge
and state of health. Operational models include the memory effect
due to the unique chemistry of a Lithium Sulfur cell that precludes
the user of other methodologies for State of health determination
for Lithium Sulfur batteries. Model parameters are identified in
real life applications and parameters are compared to those of the
operational Lithium Sulfur model employing Kalman filtering. The
output includes an estimate of state of health and other key
performance indicators. Key performance indicators are compared
with measured values of for example resistance to provide feedback
to the estimate process in order to improve accuracy. The system
can be implemented as software or firmware in an application.
Inventors: |
Wild; Mark; (Abingdon,
GB) ; Offer; Greg; (Greater London, GB) ;
Marinescu; Monica; (Greater London, GB) ; Auger;
Daniel; (Bedfordshire, GB) ; Fotouhi; Abbas;
(Bedfordshire, GB) ; Minton; Geraint; (Abingdon,
GB) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Oxis Energy Limited |
Abingdon |
|
GB |
|
|
Assignee: |
Oxis Energy Limited
Abingdon
GB
|
Appl. No.: |
17/405258 |
Filed: |
August 18, 2021 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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15566661 |
Oct 13, 2017 |
11125827 |
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PCT/GB2016/051066 |
Apr 18, 2016 |
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17405258 |
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International
Class: |
G01R 31/392 20060101
G01R031/392; G01R 31/367 20060101 G01R031/367; H01M 10/48 20060101
H01M010/48; B60L 58/12 20060101 B60L058/12; G01C 21/34 20060101
G01C021/34; H01M 10/052 20060101 H01M010/052 |
Foreign Application Data
Date |
Code |
Application Number |
Apr 16, 2015 |
GB |
1506497.5 |
Claims
1-36. (canceled)
37. A method for generating a model of a secondary electrochemical
cell in which capacity can be lost due to active reactant species
becoming inactive in use, the model being operable to predict the
electrical characteristics of the cell in use based on a model
representative of the internal state of the cell that correlates a
terminal voltage of the cell to an operational condition of the
cell for all states of charge, SOC, wherein the model
representative of the internal state of the cell is an equivalent
circuit network model comprising a number of modelled electrical
elements, the equivalent circuit network model being parameterised
by the properties of the constituent electrical elements of the
equivalent circuit network model, the method comprising: generating
data representative of the behaviour of the cell in use across the
range of operational conditions of the cell for all states of
charge, SOC; identifying, based on the generated data
representative of the behaviour of the cell in use, the parameters
of the equivalent circuit model as a function of the State of
Charge that cause the equivalent circuit to have electrical
characteristics that produce a behaviour of the equivalent circuit
model that correspond to the generated data representative of the
behaviour of the cell in use.
38. A method as claimed in claim 37, wherein the electrochemical
cell has a Lithium Sulfur chemistry.
39. A method as claimed in claim 37, wherein the equivalent circuit
network model consists of a voltage source in series with an ohmic
resistance and one or more diffuse resistances represented as RC
pairs, wherein the voltage of the voltage source, and the
resistances and capacitances of the ohmic resistance and RC pairs
parameterise the equivalent circuit model.
40. A method as claimed in claim 37, wherein the operational
condition of the cell includes one or more of: a terminal voltage
of the cell; a deemed open circuit voltage of the cell; a current
load on the cell; a temperature of the cell; an internal resistance
of the cell.
41. A method as claimed in claim 37, wherein generating data
representative of the behaviour of the cell in use across the range
of operational conditions of the cell for all states of charge,
SOC, includes predicting a terminal voltage behaviour of the cell
at different states of charge of the cell for different operating
conditions using a high fidelity physical model of the cell.
42. A method as claimed in claim 37, wherein generating data
representative of the behaviour of the cell in use across the range
of operational conditions of the cell for all states of charge,
SOC, includes; controlled testing the behaviour of standard cells
of the design of the modelled cell under a range of different
working conditions including: receiving measurements of the cell's
terminal voltage at different charge/discharge rates and
temperatures and states of charge; and optionally receiving
measurements of the cell's internal resistance at different
charge/discharge rates and temperatures and states of charge.
43. A method as claimed in claim 42, wherein controlled testing the
behaviour of standard cells of the design of the modelled cell
under a range of different working conditions includes applying
current pulses to the cell at set discharge rates and leaving a
relaxation time between the said pulses sufficient to allow the
cell's terminal voltage to revert to an open circuit voltage.
44. A method as claimed in claim 43, wherein controlled testing the
behaviour of standard cells of the design of the modelled cell
further includes starting from a deemed full state of charge of the
test cell and proceeding to apply the current discharge pulses
until the cell's terminal voltage drops below a pre-determined
level used to calibrate a full state of discharge for the test
cell.
45. A method as claimed in claim 43, further comprising: taking the
cell's terminal voltage at the end of the relaxation phase between
each pulse to be the open circuit voltage of the cell at that state
of charge.
46. A method as claimed in claim 45, wherein identifying the
parameters of the equivalent circuit model as a function of the
State of Charge includes using the cell's open circuit voltage at
that state of charge to identify the parameter value for the
voltage source of the equivalent circuit network model at that
state of charge.
47. A method as claimed in claim 43, wherein identifying the
parameters of the equivalent circuit model as a function of the
State of Charge includes using the instantaneous drop in the cell's
terminal voltage at the start of a current pulse to identify the
parameter value for the ohmic resistance component of the
equivalent circuit network model at that state of charge.
48. A method as claimed in claim 43, wherein identifying the
parameters of the equivalent circuit model as a function of the
State of Charge comprises includes using the gradual drop in cell's
terminal voltage continuing from the instantaneous voltage drop to
identify parameter values of the resistances and capacitances of
the RC pairs for that state of charge contributing to the diffusion
resistance component of the equivalent circuit network model.
49. A method as claimed in claim 37, further comprising using a
prediction error minimisation technique to refine the parameter
values of the cell model representative of the internal state of
the cell in use identified based on the generated data
representative of the behaviour of the cell in use.
50. A method as claimed in claim 37, further comprising storing in
a parameter value resource the identified parameter values for the
equivalent circuit network model for modelling the behaviour of the
cell at all States of Charge across the range of operational
conditions of the cell, wherein the parameter value resource is
optionally a lookup table.
51. A method as claimed in claim 37, further comprising fitting the
identified parameter values for the cell model to functions
dependent on the state of charge.
52. A method as claimed in claim 51, wherein the parameter values
are stored in a parameter value resource as a function of state of
charge.
53. A method of generating a memory model of a secondary
electrochemical cell having a Lithium Sulfur chemistry in which
capacity can be lost due to active reactant species becoming
temporarily inactive in use, the memory model being operable to
track, in use, an amount of active reactant in the cell and/or an
amount of temporarily inactive reactant in the cell and optionally
an amount of permanently inactive reactant in the cell, the method
comprising: establishing a set of rules relating the different
manifestations of the reactant species of the Lithium Sulfur cell
chemistry, the amounts of the reactant species in those different
manifestations, the reactions in which those different
manifestations of reactant species participate during charge and
discharge, and the reaction rates thereof; parameterising the
modelled reaction rates by one or more of: the operating conditions
of the cell; the modelled amounts of the different manifestations
of reactant species; the internal state of the cell; the electrical
characteristics of the cell in use; and identifying the
parameterised values for the modelled reaction rates by:
theoretical predictions for the cell based on a high fidelity
physical model; or fitting or deriving the parameter values
empirically or semi-empirically based on tests of standard
cells.
54. A method as claimed in claim 53, wherein the memory model
representative of the variation in the amount of active reactant
species in the cell is a simplified physical model that groups the
reactant species of the cell into three groups representing high
order manifestations, medium order manifestations and low order
manifestations, and wherein the model divides the charge and
discharge curves of the cell into a high plateau and low plateau
and assumes that reactions between the high-to-medium order
manifestations dominate the high plateau and reactions between the
medium-to-low order manifestations dominate the low plateau.
55. A method as claimed in claim 54, wherein the memory model
assumes that, when the cell terminal voltage falls below a boundary
level between the high and low plateaus, the reactions between the
high-to-medium order manifestation do not occur, leading to a
remaining amount of high order manifestations of reactant becoming
deemed temporarily inactive and unable to contribute to the
remaining capacity of the cell.
56-78. (canceled)
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This is a continuation application of, and therefore claims
the benefit to, U.S. patent application Ser. No. 15/566,661, filed
Oct. 13, 2017, which is a U.S. National Stage Application of, and
claims the benefit to, PCT/GB2016/051066, filed Apr. 18, 2016,
which claims priority to United Kingdom patent application s/n GB
1506497.5, filed Apr. 16, 2015, the contents of each is
incorporated herein by reference in its entirety.
TECHNICAL FIELD
[0002] The present invention relates generally to methods and
apparatuses for determining state of charge and state of health of
a secondary cell that is susceptible to the memory effect of a
change in capacity due to dynamic cycling of the cell in normal
use. The present invention finds particular utility in cells having
a Lithium Sulfur chemistry. The present invention also relates to
applications of the methods and apparatuses in battery management
systems and energy system controllers, and in rangefinding and
routefinding apparatuses and methods for use in electric
vehicles.
BACKGROUND
[0003] The ability to reliably determine the amount of remaining
charge of a secondary cell providing a rechargeable battery for use
as a power source in, for example, portable electronic goods and
electric vehicle transport is highly valued by manufacturers and
consumers alike in order to calculate the remaining usage time or
available distance for vehicles.
[0004] In the case of gasoline vehicles the fuel level can simply
be measured, however in electric and hybrid vehicles and in
electronic devices because the battery is used as their power
source it is more difficult to measure residual energy accumulated
in the battery. Despite this difficulty various techniques have
been developed.
[0005] An important metric for determining secondary cells is
therefore State of charge, SOC, which indicates the remaining
energy stored in a rechargeable battery until recharge is required.
State of discharge, conversely, indicates the energy provided by
the rechargeable battery since the last recharge.
[0006] Specifically, SOC is a percentage indicator of the amount of
capacity remaining in a cell until a recharge is needed, compared
to the total capacity provided by that cell in that charge cycle,
Q.sub.t. Supposing SOC.sub.0 to be the initial SOC percentage at
time t.sub.0, the cell's SOC percentage at time t is defined
as:
S .times. O .times. C = SOC 0 + 1 .times. 0 .times. 0 * .intg. t 0
t .times. I .function. ( t ) Q t .times. d .times. t
##EQU00001##
where I is the current, which is defined as negative for
discharging and positive for charging, and Q.sub.t is the cell's
maximum capacity in Ah.
[0007] Thus in order to track and determine SOC it is necessary to
set an initial value SOC.sub.0 of the State of Charge. In Lithium
ion and other rechargeable battery types this is usually achieved
with reference to the maximum open circuit voltage (OCV) prior to
discharging the cell or battery. However, for certain cell types as
will be explained below, notably Lithium Sulfur cells, the OCV is
affected by a very strong "memory effect" (i.e. hysteresis), also
known as a "cumulative memory effect", which means that the maximum
open circuit voltage (OCV) can be achieved at very different SOCs
depending on the cell's recent history.
[0008] In this regard, Lithium Sulfur chemistry offers unique
challenges for state of charge estimation compared to other
rechargeable batteries types. For example, as can be seen from the
illustrative plot of OCV against state of charge for an example
Lithium Sulfur cell as shown in FIG. 1, the discharge curve is not
linear, like in Lithium Ion cells. Instead, the LiS cell OCV curve
exhibits, from a 100% SOC, a short capacity high plateau 101 at a
fairly constant OCV followed by a rapid change 102 to a long
capacity "low" plateau at 103 of constant OCV around 2.15V, which
continues until the OCV drops rapidly 104 as the cell approaches 0%
SOC. The long plateau at 103 effectively precludes the direct use
of OCV for reliable SOC determination for Lithium Sulfur
rechargeable batteries.
[0009] Others attempts have been made to improve the accuracy of
the initial SOC determination, including using resistance and
temperature measurements to improve accuracy in real life
applications, but even this does not work because the internal
resistance of Lithium Sulfur cells is strongly affected by the
abovementioned "memory effect" and it is not always possible to
return the cell to a known state before the next discharge.
[0010] Another known method that does not require knowledge of the
starting capacity involves coulomb counting to determine the amount
of energy used during discharge or stored during charge. However,
Lithium Sulfur cells have parasitic reactions during charging which
means the Faradaic efficiency is significantly less than 100%. This
shuttling of polysulfides dissolved in the electrolyte during
charging avoids overcharging but precludes the use of coulomb
counting in SOC determination, so coulomb counting does not work
for LiS cells.
[0011] U.S. Pat. No. 7,688,075 B2 discloses using calibrated
Lithium Sulfur cells and linear correlation with embedded look up
tables of SOC verses resistance populated from extensive laboratory
studies on standard cells at varying temperatures and ages. This
method utilises a unique feature of Lithium Sulfur cell chemistry
in that it causes a predictable and gradual change in resistance
during discharge unlike Lithium ion cells. This method relies on
determining the resistance of the cell at 100% SOC by taper
charging, charging to a maximum voltage and then reducing current
to sustain that voltage until the current is equal to a
pre-determined constant minimum current. This provides a precise
measure of SOC under well-defined conditions.
BRIEF SUMMARY OF THE INVENTION
[0012] The present inventors have recognised that the above methods
do not take into account another unique feature of Lithium Sulfur
chemistry which is that, under dynamic use conditions, the
parameter Q.sub.t changes in a wide range due to active species
becoming temporarily inactive in use.
[0013] The mechanism for this is that the active cathode material
(Sulfur) dissolves into the electrolyte unlike in Lithium ion
batteries. The maximum capacity (Q.sub.t) at 100% SOC or state of
discharge (SOD) for any charge cycle is determined by the
conversion of active Sulfur in the cathode to Lithium sulphide plus
the conversion of intermediates remaining in the electrolyte from
previous cycles. The concentration of intermediates in the
electrolyte from previous cycles is determined by the temperature,
charge/discharge rates and depths of charge or discharge of
previous cycles (i.e. the operational conditions).
[0014] Thus, in order to obtain a state of health that is both
precise and accurate in a dynamic or real life system, the present
inventors have recognised that the history of the cell must be
taken in to account in the state of health calculation.
[0015] Here, state of health, SoH, is a figure of merit that
combines the remaining energy stored in a rechargeable battery and
the aging effects of use of the rechargeable battery related to the
remaining life of the rechargeable battery in terms of calendar
life and/or cycle life.
[0016] Specifically, SoH is a percentage indicator of the maximum
usable capacity (measured in Amp-hours Ah) in any given charge
cycle, Q.sub.usable (i.e. Q.sub.t for that cycle, compensating for
temporarily inactive and optionally also permanently inactive
species), compared to the total rated capacity of the cell,
Q.sub.T.
[0017] As, interest in Lithium Sulfur batteries has increased due
to its favourable energy density and low cost materials to lighten
the load of portable devices and extend the range of electric
vehicles. Lithium Sulfur batteries are typically manufactured in
variable pouch cell format with lightweight components that offer
superior theoretical energy density to the current state of the art
for mobile electric devices and electric vehicles. Therefore it is
desirable to provide methods and apparatuses for reliably
determining state of charge and state of health of a secondary cell
such as a Lithium Sulfur cell that is susceptible to the memory
effect of a change in capacity due to dynamic cycling of the cell
in normal use.
[0018] It is in the above context that the present invention has
been devised.
[0019] Thus, viewed from a first aspect the invention provides
apparatus for modelling a state of charge, SOC, of a secondary
electrochemical cell in which capacity can be lost due to active
reactant species becoming inactive in use, comprising: a cell model
module operable to predict the electrical characteristics of the
cell in use based on a model representative of the internal state
of the cell that correlates a terminal voltage of the cell to an
operational condition of the cell for all states of charge, SOC; a
memory effect module operable to model the usable capacity of the
cell in use based on a memory model representative of the variation
in amount of active reactant species in the cell that correlates
the proportion of the rated capacity of the cell, Q.sub.t, that is
usable capacity, Q.sub.usable, during use based on an operational
history of the cell; wherein the apparatus is configured such that
the cell model module and/or memory effect module adjusts the cell
model module in use based on an operational history of the cell to
compensate for the prediction of the usable capacity of the cell by
the memory effect module.
[0020] In accordance with this aspect of the invention, the
provision of a memory effect module that models the usable active
capacity of the cell based on its recent operational history, and
which can be used to adjust the cell model module accordingly,
results in an apparatus for modelling a state of charge of a cell
that can compensate for the change in capacity of the cell due to
active species being rendered temporarily and/or permanently
inactive in use due to dynamic cycling. Thus a reliable model of
the internal state of the cell can be produced that can account for
the cell's operational behaviour in wide operational range in real
world use cases.
[0021] The electrochemical cell may have a Lithium Sulfur
chemistry. Alternatively the modelled cell may have another
chemistry that suffers from the so-called memory effect by which
capacity can be lost due to active reactant species becoming
inactive in use.
[0022] Optionally, the operational condition of the cell includes
one or more of: a terminal voltage of the cell; a deemed open
circuit voltage of the cell; a current load on the cell; a
temperature of the cell; an internal resistance of the cell.
[0023] Optionally, the model representative of the internal state
of the cell is an equivalent circuit network model comprising a
number of modelled electrical elements, the equivalent circuit
network model being parameterised by the properties of the
constituent electrical elements of the equivalent circuit network
model. The equivalent circuit network model may consist of a
voltage source, in series with an ohmic resistance and one or more
diffuse resistances represented as RC pairs. Optionally, the
equivalent circuit network models the cell behaviour by a deemed
open circuit voltage of the cell being taken as the voltage source,
and the parameterised properties of the ohmic and diffuse
resistances being selected to drop the voltage in the circuit down
to the terminal voltage of the cell under a given current load and
temperature, at a given state of charge. An equivalent circuit
network (ECN) is a particularly effective model that is capable of
being parameterised to model the behaviour of the cell in use.
[0024] Instead of an ECN, other models may be used. Optionally, the
model representative of the internal state of the cell is a
parameterised physics-based cell model.
[0025] Optionally, the apparatus further comprises a parameter
value resource configured to be usable to provide to the cell model
module values for the parameters of the cell model for the modelled
behaviour of the cell at the given operational conditions.
Optionally, the parameter values for the cell model are dependent
on the modelled state of charge of the cell. Optionally, the
parameter values for the cell model are derived empirically or
semi-empirically based on tests of standard cells. Optionally, the
parameter values for the cell model are stored in a parameter value
resource, optionally a lookup table.
[0026] Optionally, the memory model representative of the variation
in amount of active reactant species in the cell tracks an amount
of active reactant in the cell and/or an amount of temporarily
inactive reactant in the cell and optionally an amount of
permanently inactive reactant in the cell. Optionally, the memory
model representative of the variation in the amount of active
reactant species in the cell comprises a set of rules relating the
different manifestations of the reactant species of the cell, the
amounts of the reactant species in those different manifestations,
the reactions in which those different manifestations of reactant
species participate during charge and discharge, and the reaction
rates thereof. Optionally, the modelled reaction rates are
parameterised by one or more of: the operating conditions of the
cell; the modelled amounts of the different manifestations of
reactant species; the internal state of the cell; the electrical
characteristics of the cell in use. Optionally, the parameterised
values for the modelled reaction rates are derived by theoretical
predictions for the cell, or fitted or derived empirically or
semi-empirically based on tests of standard cells.
[0027] Optionally, the memory model representative of the variation
in the amount of active reactant species in the cell is a
simplified physical model that groups the reactant species of the
cell into three groups representing high order manifestations,
medium order manifestations and low order manifestations, and
wherein the model divides the charge and discharge curves of the
cell into a high plateau and low plateau and assumes that reactions
between the high-to-medium order manifestations dominate the high
plateau and reactions between the medium-to-low order
manifestations dominate the low plateau. Optionally, the memory
model assumes that, when the cell terminal voltage falls below a
boundary level between the high and low plateaus, the reactions
between the high-to-medium order manifestation do not occur,
leading to a remaining amount of high order manifestations of
reactant becoming deemed temporarily inactive and unable to
contribute to the remaining capacity of the cell. Such a simplified
physical model may in certain circumstances adequately account for
the variation in capacity of cells during dynamic use.
[0028] Optionally, the memory effect module is configured to model
the usable capacity of the cell, Q.sub.usable, for a given set of
operating conditions, based on the amount of active reactant
species in the cell given the cell's history modelled by the memory
model.
[0029] Optionally, the apparatus is configured to adjust the cell
model module in use based on a prediction of the usable capacity of
the cell by the memory effect module by adjusting the parameter
value resource to provide parameter values to compensate for the
loss in usable capacity of the cell. Optionally, the parameter
value resource is configured to use the parameter values for the
cell model corresponding to a given low current charge or discharge
rate as a baseline parameter set, and wherein the apparatus is
configured to adjust the parameter value resource such that when
the terminal voltage drops below the boundary voltage, the
parameter value resource skips the baseline parameter values to
continue from the same ohmic resistance value corresponding to the
same terminal voltage at the low plateau, wherein the skipped
capacity represents the capacity loss due to temporarily inactive
species.
[0030] Viewed from a second aspect, the present invention provides
apparatus for estimating a state of charge, SOC, of a secondary
electrochemical cell in use in which capacity can be lost due to
active reactant species becoming inactive in use, comprising: a
cell operational condition monitor module configured to receive
measurements of the operational conditions of the cell in use; a
cell model module operable to predict the electrical
characteristics of the cell in use based on a model representative
of the internal state of the cell that correlates a terminal
voltage of the cell to an operational condition of the cell for all
states of charge, SOC; a memory effect module operable to model the
usable capacity of the cell in use based on a memory model
representative of the variation in amount of active reactant
species in the cell that correlates the proportion of the rated
capacity of the cell, Q.sub.t, that is usable capacity,
Q.sub.usable, during use based on an operational history of the
cell; wherein the apparatus is configured such that the cell model
module and/or memory effect module adjusts the cell model module in
use based on an operational history of the cell to compensate for
the prediction of the usable capacity of the cell by the memory
effect module; a state estimator module configured to operate the
cell model module and the memory effect module based on the
measurements of the operational conditions of the cell received
during use by the cell operation condition monitor module to
estimate an internal state of the cell in use; and a state of
charge estimator module configured to operate the cell model module
based on the estimated internal state of the cell to estimate a
state of charge of the cell.
[0031] In accordance with this aspect of the invention, the
apparatus for modelling the state of charge of the cell can be
applied to reliably estimate the state of charge of a cell in use,
in which the estimation of the internal state of the cell by the
cell model module is adjusted to compensate for the memory effect
of capacity variation due to dynamic cycling of the cell as a
result of the memory effect module tracking the usable capacity of
the cell based on its recent operational history.
[0032] The electrochemical cell may have a Lithium Sulfur
chemistry. Alternatively the modelled cell may have another
chemistry that suffers from the so-called memory effect by which
capacity can be lost due to active reactant species becoming
inactive in use.
[0033] Optionally, the state of charge estimator module is further
configured to provide an estimate of the state of health of the
cell as a ratio of the modelled usable capacity of the cell,
Q.sub.usable, to the rated capacity of the cell, Q.sub.t.
[0034] Optionally, the state estimator module is configured to
refine the estimated state at each time interval by operating as an
iterative feedback loop in which a prediction of the internal state
of the cell based on the cell model projecting forward the
estimated internal state of the cell at the previous time interval
to the current time interval is corrected based on the measured
operational conditions of the cell to update the estimate of the
current internal state of the cell. Optionally, the state estimator
module is configured as a kalman-type filter, optionally as a
kalman filter, an extended kalman filter, an unscented kalman
filter, a particle filter or a Luenberger state estimator.
Optionally, the state estimator module is configured to operate a
prediction error minimisation technique to identify estimates of
the parameters of the cell model representative of the internal
state of the cell in use. Optionally, the state estimator module is
configured to solve a set of fuzzy logic rules to identify
estimates of the parameters of the cell model representative of the
internal state of the cell in use. Use of Kalman-type filters may
be particularly effective at giving a smooth an accurate estimation
of the state of charge of the cell, that is improved by a
correction-estimation loop providing feedback, and which may avoid
the need for look up tables storing empirically- or
theoretically-derived parameter values entirely.
[0035] Optionally, the measurements of the operational conditions
of the cell received by the cell operational condition monitor
module in use includes: a terminal voltage of the cell; a current
load on the cell; and optionally a temperature of the cell; and
optionally an internal resistance of the cell.
[0036] Optionally, the cell model module and the memory effect
module are provided by an apparatus in accordance with any of the
above-statements in accordance with the first aspect of the
invention.
[0037] Optionally, the apparatus further comprises cell operational
condition measurement means including: a terminal voltage sensing
circuit; and a current load sensing circuit; and optionally: a cell
internal resistance sensing circuit comprising a switching circuit
including a balancing resistor; and a temperature sensor.
[0038] Optionally, the apparatus further comprises one or more
processors and computer readable medium storing instructions, which
when executed by one or more processors, cause the processor or
processors to implement the apparatus in accordance with any of the
above statements of the invention.
[0039] Optionally, the parameter values for the cell model
representing the internal state of the cell are identified in use
of the model or in empirical derivation of the parameter values
from test cell data, by prediction error minimisation technique.
Optionally, the prediction error minimisation technique defines a
scalar fitness function.
[0040] Viewed from a third aspect, the present invention provides a
battery management system comprising plural cells or energy system
controller for coupling to plural cells, comprising: apparatus in
accordance with any of the above statements of the invention
arranged to estimate the state of charge, SOC, and optionally State
of Health, SoH, of the said plural cells in use. Use of the
apparatuses for modelling or estimating the state of charge of a
cell find particular utility in battery management systems and
energy system controllers for providing an output indication of a
remaining charge or capacity in plural cells providing a battery
pack.
[0041] Viewed from a fourth aspect, the present invention provides
apparatus for estimating a range of an electric vehicle comprising
a plurality of secondary electrochemical cells arranged to power
the vehicle in which capacity can be lost due to active reactant
species becoming inactive in use, the apparatus comprising:
apparatus in accordance with any of the above statements in
accordance with the second or third aspects of the invention
configured to operate to estimate a state of charge and a remaining
capacity of the cells in use; and a range estimation module
configured to estimate a range of the electric vehicle based the
estimation of the state of charge and a remaining capacity of the
cells in use and the predicted operational conditions of the cells
in use in the vehicle. In accordance with this aspect, use of the
apparatus for estimating a state of charge of a cell allows
reliable estimation of a range of an electric vehicle.
[0042] Viewed from a fifth aspect, the present invention provides
apparatus for planning a route for an electric vehicle comprising a
plurality of secondary electrochemical cells arranged to power the
vehicle in which capacity can be lost due to active reactant
species becoming inactive in use, comprising, apparatus for
estimating a range of an electric vehicle in accordance with the
above statement of the fourth aspect of the invention; and a route
planning module configured to plan a route towards a desired
destination based at least in part on an estimated range of the
electric vehicle produced by the range estimation module based on
the predicted operational conditions of the cells following that
route. In accordance with this aspect, the use of the reliable
range estimation for electric vehicles can facilitate route
planning.
[0043] Optionally, the apparatus further comprises a route
optimisation module for selecting an optimal route towards a
destination from plural routes planned by the route planning
module.
[0044] Viewed from a sixth aspect, the present invention provides
computer readable medium comprising instructions which when
executed by one or more processors, cause the processor or
processors to implement the apparatus in accordance with any of the
above statements of the invention.
[0045] Viewed from a seventh aspect, the present invention provides
a method for generating a model of a secondary electrochemical cell
in which capacity can be lost due to active reactant species
becoming inactive in use, the model being operable to predict the
electrical characteristics of the cell in use based on a model
representative of the internal state of the cell that correlates a
terminal voltage of the cell to an operational condition of the
cell for all states of charge, SOC, wherein the model
representative of the internal state of the cell is an equivalent
circuit network model comprising a number of modelled electrical
elements, the equivalent circuit network model being parameterised
by the properties of the constituent electrical elements of the
equivalent circuit network model, the method comprising: generating
data representative of the behaviour of the cell in use across the
range of operational conditions of the cell for all states of
charge, SOC; identifying, based on the generated data
representative of the behaviour of the cell in use, the parameters
of the equivalent circuit model as a function of the State of
Charge that cause the equivalent circuit to have electrical
characteristics that produce a behaviour of the equivalent circuit
model that correspond to the generated data representative of the
behaviour of the cell in use
[0046] While the above-described aspect of the invention sets out
the method in relation to the use of an ECN model for the cell, it
is to be understood that this is not limiting, and is not an
essential feature of the invention. Alternative cell models can be
used, including physics-based cell models and high fidelity models
that can be parameterised and used to model the behaviour of the
cell in use, as with the ECN models.
[0047] The electrochemical cell may have a Lithium Sulfur
chemistry. Alternatively the modelled cell may have another
chemistry that suffers from the so-called memory effect by which
capacity can be lost due to active reactant species becoming
inactive in use.
[0048] Optionally, the equivalent circuit network model consists of
a voltage source in series with an ohmic resistance and one or more
diffuse resistances represented as RC pairs, wherein the voltage of
the voltage source, and the resistances and capacitances of the
ohmic resistance and RC pairs parameterise the equivalent circuit
model.
[0049] Optionally, the operational condition of the cell includes
one or more of: a terminal voltage of the cell; a deemed open
circuit voltage of the cell; a current load on the cell; a
temperature of the cell; an internal resistance of the cell.
[0050] Optionally, generating data representative of the behaviour
of the cell in use across the range of operational conditions of
the cell for all states of charge, SOC, includes predicting a
terminal voltage behaviour of the cell at different states of
charge of the cell for different operating conditions using a high
fidelity physical model of the cell.
[0051] Optionally, generating data representative of the behaviour
of the cell in use across the range of operational conditions of
the cell for all states of charge, SOC, includes: controlled
testing the behaviour of standard cells of the design of the
modelled cell under a range of different working conditions
including: receiving measurements of the cell's terminal voltage at
different charge/discharge rates and temperatures and states of
charge; and optionally receiving measurements of the cell's
internal resistance at different charge/discharge rates and
temperatures and states of charge. Optionally, controlled testing
the behaviour of standard cells of the design of the modelled cell
under a range of different working conditions includes: applying
current pulses to the cell at set discharge rates and leaving a
relaxation time between the said pulses sufficient to allow the
cell's terminal voltage to revert to an open circuit voltage.
Optionally, controlled testing the behaviour of standard cells of
the design of the modelled cell further includes: starting from a
deemed full state of charge of the test cell and proceeding to
apply the current discharge pulses until the cell's terminal
voltage drops below a pre-determined level used to calibrate a full
state of discharge for the test cell. Optionally, generating data
representative of the behaviour of the cell in use further
includes: taking the cell's terminal voltage at the end of the
relaxation phase between each pulse to be the open circuit voltage
of the cell at that state of charge. Optionally, identifying the
parameters of the equivalent circuit model as a function of the
State of Charge comprises: using the cell's open circuit voltage at
that state of charge to identify the parameter value for the
voltage source of the equivalent circuit network model at that
state of charge. Optionally, identifying the parameters of the
equivalent circuit model as a function of the State of Charge
comprises: using the instantaneous drop in the cell's terminal
voltage at the start of a current pulse to identify the parameter
value for the ohmic resistance component of the equivalent circuit
network model at that state of charge. Optionally, identifying the
parameters of the equivalent circuit model as a function of the
State of Charge comprises: using the gradual drop in cell's
terminal voltage continuing from the instantaneous voltage drop to
identify parameter values of the resistances and capacitances of
the RC pairs for that state of charge contributing to the diffusion
resistance component of the equivalent circuit network model.
[0052] Optionally, the method further comprises using a prediction
error minimisation technique to refine the parameter values of the
cell model representative of the internal state of the cell in use
identified based on the generated data representative of the
behaviour of the cell in use.
[0053] Optionally, the method further comprises storing in a
parameter value resource the identified parameter values for the
equivalent circuit network model for modelling the behaviour of the
cell at all States of Charge across the range of operational
conditions of the cell, wherein the parameter value resource is
optionally a lookup table.
[0054] Optionally, the method further comprises fitting the
identified parameter values for the cell model to functions
dependent on the state of charge. Optionally, the parameter values
are stored in a parameter value resource as a function of state of
charge.
[0055] Viewed from an eighth aspect, the present invention provides
a method of generating a memory model of a secondary
electrochemical cell in which capacity can be lost due to active
reactant species becoming inactive in use, the model being operable
to predict, the memory model being operable to track, in use, an
amount of active reactant in the cell and/or an amount of
temporarily inactive reactant in the cell and optionally an amount
of permanently inactive reactant in the cell, the method
comprising: establishing a set of rules relating the different
manifestations of the reactant species of the cell, the amounts of
the reactant species in those different manifestations, the
reactions in which those different manifestations of reactant
species participate during charge and discharge, and the reaction
rates thereof; parameterising the modelled reaction rates by one or
more of: the operating conditions of the cell; the modelled amounts
of the different manifestations of reactant species; the internal
state of the cell; the electrical characteristics of the cell in
use; and identifying the parameterised values for the modelled
reaction rates by: theoretical predictions for the cell based on a
high fidelity physical model; or fitting or deriving the parameter
values empirically or semi-empirically based on tests of standard
cells.
[0056] Optionally, the memory model representative of the variation
in the amount of active reactant species in the cell is a
simplified physical model that groups the reactant species of the
cell into three groups representing high order manifestations,
medium order manifestations and low order manifestations, and
wherein the model divides the charge and discharge curves of the
cell into a high plateau and low plateau and assumes that reactions
between the high-to-medium order manifestations dominate the high
plateau and reactions between the medium-to-low order
manifestations dominate the low plateau. Optionally, the memory
model assumes that, when the cell terminal voltage falls below a
boundary level between the high and low plateaus, the reactions
between the high-to-medium order manifestation do not occur,
leading to a remaining amount of high order manifestations of
reactant becoming deemed temporarily inactive and unable to
contribute to the remaining capacity of the cell.
[0057] Viewed from a ninth aspect, the present invention provides a
method for estimating a state of charge, SOC, of a secondary cell
in use in which capacity can be lost due to active reactant species
becoming inactive in use, comprising: receiving measurements of the
operational conditions of the cell in use; estimating an internal
state of the cell in use, by: modelling the cell using a cell model
module that estimates the electrical characteristics of the cell in
use based on a model representative of the internal state of the
cell that correlates a terminal voltage of the cell to an
operational condition of the cell for all states of charge, SOC;
predicting the usable capacity of the cell in use based on a memory
model representative of the variation in amount of active reactant
species in the cell that correlates the proportion of the rated
capacity of the cell, Q.sub.t, that is usable capacity,
Q.sub.usable, during use based on an operational history of the
cell; adjusting the cell model module in use based on an
operational history of the cell to compensate for the prediction of
the usable capacity of the cell by the memory effect module; and
estimating the internal state configuration of the cell model that
fits the received measurements of the operational conditions of the
cell; and estimating, based on the modelled internal state
configuration of the cell, the State of Charge, SOC, of the
cell.
[0058] Optionally, the method further comprises: estimating the
state of health of the cell as a ratio of the modelled usable
capacity of the cell, Q.sub.usable, to the rated capacity of the
cell, Q.sub.t.
[0059] Optionally, the method further comprises: refining the
estimated internal state of the cell at each time interval by
operating as an iterative feedback loop in which a prediction of
the internal state of the cell based on the cell model projecting
forward the estimated internal state of the cell at the previous
time interval to the current time interval is corrected based on
the measured operational conditions of the cell to update the
estimate of the current internal state of the cell.
[0060] Optionally, the method further comprises: using a
kalman-type filter, optionally a kalman filter, an extended kalman
filter, an unscented kalman filter, a particle filter or a
Luenberger state estimator to estimate the internal state of the
cell at each time interval.
[0061] Optionally, the method further comprises: using a prediction
error minimisation technique to identify estimates of the
parameters of the cell model representative of the internal state
of the cell in use.
[0062] Optionally, the method further comprises: solving a set of
fuzzy logic rules to identify estimates of the parameters of the
cell model representative of the internal state of the cell in
use.
[0063] Optionally, the measurements of the operational conditions
of the cell received by the cell operational condition monitor
module in use include: a terminal voltage of the cell; a current
load on the cell; and optionally a temperature of the cell; and
optionally an internal resistance of the cell.
[0064] Optionally, the method is operating in a battery management
system comprising plural cells or energy system controller for
coupling to plural cells.
[0065] Viewed from a tenth aspect the present invention provides a
method for estimating a range of an electric vehicle comprising a
plurality of secondary electrochemical cells arranged to power the
vehicle in which capacity can be lost due to active reactant
species becoming inactive in use, the method comprising: performing
a method in accordance with the above statement of the ninth aspect
of the invention of estimate a state of charge and a remaining
capacity of the cells in use; estimating a range of the electric
vehicle based the estimation of the state of charge and a remaining
capacity of the cells in use and the predicted operational
conditions of the cells in use in the vehicle.
[0066] Viewed from an eleventh aspect the present invention
provides a method for planning a route for an electric vehicle
comprising a plurality of secondary electrochemical cells arranged
to power the vehicle in which capacity can be lost due to active
reactant species becoming inactive in use, comprising, performing a
method in accordance with the above statement of the tenth aspect
of the invention to estimate a range of an electric vehicle; and
planning a route towards a desired destination based at least in
part on an estimated range of the electric vehicle produced by the
range estimation module based on the predicted operational
conditions of the cells following that route. Optionally, the
method further comprises selecting an optimal route towards a
destination from plural routes planned by the route planning
module.
BRIEF DESCRIPTION OF THE DRAWINGS
[0067] Certain preferred embodiments of aspects of the invention
will now be described, by way of example only, and with reference
to the accompanying drawings, in which:
[0068] FIG. 1 is an illustrative discharge curve for an example
Lithium Sulfur cell plotting OCV against state of charge;
[0069] FIG. 2 is a graph illustrating the gradual change the ohmic
resistance of an example Lithium Sulfur cell against degree of
discharge (i.e. 1-SOC) as a function of discharge rate and
temperature;
[0070] FIG. 3 is a schematic Illustration of an apparatus for
estimating an SOC and SOH according to an exemplary embodiment of
the present invention;
[0071] FIG. 4 is a simplified circuit diagram illustrating the cell
operational condition measurement means and the operation of the
internal resistance sensing circuit;
[0072] FIG. 5 is a schematic illustration of an apparatus for
estimating an SOC and SOH according to an exemplary embodiment of
the invention, in which the controller and memory are shown in more
detail;
[0073] FIG. 6A is a voltage vs time plot and FIG. 6B is a current
load vs time plot showing example experimental test results from an
ECN model parameterisation experiment using a test LiS cell;
[0074] FIG. 7A shows a first example simple equivalent circuit
network models for the behaviour of LiS cells;
[0075] FIG. 7B shows a second example simple equivalent circuit
network model for the behaviour of LiS cells;
[0076] FIG. 8A shows a detail of the current load against time, for
a current pulse shown in FIG. 6;
[0077] FIG. 8B shows a detail of the terminal voltage of the test
LiS cell against time, for a current pulse shown in FIG. 6;
[0078] FIGS. 9A and 9B show, respectively, the parameterised values
of R.sub.1 and R2 as a function of SOC at 10.degree. C. and a
current discharge rate of 0.1 C;
[0079] FIG. 10 shows the ECN-predicted and experimental discharge
curves for a 0.1 C constant current discharge rate, and standard
experimental data for a discharge curve for a 0.2 C constant
current discharge rate;
[0080] FIG. 11A illustrates the capacity variation of a same cell
undergoing dynamic cycling, as shown in FIG. 11B which shows the
cell voltage against time for the pre-pulsing, pulsing, and
post-pulsing cycles;
[0081] FIG. 12A shows reading the look-up table for R.sub.O as
dictated by a simple memory model for a 0.1 C and a 0.5 C discharge
rate;
[0082] FIG. 12B plots the modelled discharge curves for the ECN
adjusted by the simple memory model;
[0083] FIG. 13 shows discharge curves predicted by the ECN cell
model adjusted by the simplified memory model to predict the
variation of Q.sub.t with different current discharge rates;
[0084] FIG. 14, which shows the comparative R.sub.O plots from
adjusting the reading of the R.sub.O values for 0.1 C for different
discharge rates;
[0085] FIG. 15 shows an illustration of the general form of the
equivalent circuit model for Lithium Sulfur batteries;
[0086] FIGS. 16A-D show evaluated RMSE values for the cell's
voltage at different charge levels in a prediction error
minimisation method, together with the identified parameter
values;
[0087] FIG. 17 which illustrates an example method of state of
charge/state of health estimation in accordance with an embodiment
of the invention;
[0088] FIG. 18 shows a schematic illustration of a real time
SOC/SOH estimation using an operational equivalent circuit model
and Kalman filtering;
[0089] FIG. 19 shows an example system architecture for Parameter
Estimation and Interpretation using a simple Kalman filter as a
state estimator;
[0090] FIG. 20 shows an example system architecture for Parameter
Estimation and Interpretation using a non-linear Kalman filter as a
state estimator;
[0091] FIG. 21 shows an example system architecture for Parameter
Estimation and Interpretation using Multiple Hypothesis filters as
a state estimator;
[0092] FIG. 22 shows an example system architecture for Parameter
Estimation and Interpretation using Fuzzy Logic as a state
estimator;
[0093] FIG. 23 shows the prediction results for various prediction
horizons from 0.5 to 2% SOC increments using a simplified
equivalent circuit; and
[0094] FIG. 24 is a flow diagram illustrating a method for
estimating a range and planning a route of an electric vehicle in
accordance with an embodiment of aspects of the invention.
DESCRIPTION OF THE EMBODIMENTS
[0095] While the following description sets out the embodiments of
the invention specifically in relation to Lithium Sulfur cells, it
is to be understood that the invention also finds utility with
other cell chemistries, particularly those in which the usable
capacity of the cell can vary in use due to active species being
rendered temporarily inactive through to dynamic loads and cycling
(i.e. variable current during a cycle, varying temperature, and
varying depths of charge and discharge). As Lithium Sulfur cells
exhibit this memory effect, the present invention is particularly
useful for reliably modelling and estimating the state of charge
and state of health of Lithium Sulfur cells in normal use
conditions.
[0096] In contrast to other common battery systems the active
material in a Lithium Sulfur cell dissolves from the cathode into
the electrolyte during discharge where it undergoes complex
inter-conversion to multiple intermediate species of varying
electrochemical activity and stability, the process is reversed on
charge. As shown in FIG. 2, the change in electrolyte composition
causes a gradual change in resistance which can be used to indicate
SOC in a steady state and calibrated system as described in the
published U.S. Pat. No. 7,688,075 B2. However, the reversible
dissolution of intermediate species is not 100% efficient and the
concentration of intermediate species remaining in the electrolyte
at the end of charge or discharge varies with charge/discharge
rate, temperature and depth of discharge or charge (before the next
charging/discharging cycle is begun). It is these species that give
rise to the variable internal resistance, and therefore internal
resistance alone is not necessarily a reliable predictor of SOC for
Lithium Sulfur cells.
[0097] For any charge or discharge the maximum usable capacity
Q.sub.t for that cycle (i.e. Q.sub.usable) is composed of the
conversion of Sulfur available in the cathode to Lithium sulphide
plus the change in concentration of intermediate species in the
electrolyte taking part in electrochemical reactions. The change in
concentration of intermediate species in the electrolyte can be
both positive and negative and is affected by other factors such as
cell materials, diffusion rates and active material degradation
rates, thus the relative state of charge depends upon the
cumulative history of previous cycles. Lithium Sulfur cells
experience a memory effect under dynamic loads. In a real life
dynamic system which can experience rapidly varying temperature,
discharge rate and charge rate as well as variable depths of charge
and discharge, pre-calibration of the SOC estimator alone cannot
give a good estimate of Q.sub.t at the `100% SOC/SOD` condition
relative to the cell resistance because the `100% SOC/SOD` state
depends on the actual environmental and operational conditions the
cell has experienced during use, which in turn dictates the level
of intermediate species dissolved in the electrolyte.
[0098] In order to achieve this the present invention provides
apparatus for modelling and estimating the SOC and SOH of the cell
that is "memory effect aware". The model uses the unique
environmental history of a cell or battery in order to identify the
current state of that cell or battery based on model
predictions.
[0099] Overlaid over the cycle to cycle SOC memory effect are time
and cycle number derived degradation processes that irreversibly
reduce the amount of active sulfur species available for reaction
and or degrade the cell materials to reduce the utilisation of
active sulfur available. SOH is accounted for by reducing the
available active materials as a function of time and cycle number
derived from experiment.
[0100] In order to determine the state of charge and state of
health of a Lithium Sulfur battery an apparatus and method for
estimating a Lithium Sulfur cell's terminal voltage under different
conditions utilising a model and cumulative history data collected
for a Lithium Sulfur cell operating under dynamic load is used.
[0101] Referring to FIG. 3, the apparatus 300 for estimating the
state of health of a cell includes a memory 301 to store the
cumulative operating conditions that a cell in use has been exposed
to, made available to the controller 302. The apparatus 300 is
coupled to Lithium Sulfur cell (not shown) in use and is configured
to estimate the SOC and SOH thereof. In this embodiment, the
apparatus further comprises the cell operational condition
measurement means including: a terminal voltage sensing circuit
303; and a current load sensing circuit 304; a cell internal
resistance sensing circuit 305 comprising a switching circuit
including a balancing resistor; and a temperature sensor 306. These
are arranged to measure or calculate and input to the controller
302 the current load on the cell, the terminal voltage on the cell,
a measure of the internal resistance of the cell and the
temperature of the cell and/or the ambient temperature. Referring
to FIG. 4, the cell operational condition measurement means 400 is
shown in more detail. Here, the cell's internal resistance is
periodically measured in real time in use by calculation from a
current pulse imposed by switching (using switch 401) a balancing
resistor 402 in order to provide the apparatus with direct feedback
of the measured internal resistance of the cell 403 in use. In
embodiments, the controller 302 may provide an estimate of the
internal resistance of the cell in use, based on the estimate of
the internal state of the cell. By comparing this with the
measurement of the internal resistance obtained using the cell
internal resistance sensing circuit 305, the controller's model of
the internal state of the cell can be adjusted using positive
feedback.
[0102] In accordance with aspects of the invention, as shown in
FIG. 5, the controller 302 implements an apparatus (i.e. the SOC
model 531 in this embodiment) for modelling the state of charge and
state of health of a cell (e.g. an LiS cell). Specifically, the
Controller 302 comprises processor 521 (which may be provided by
one or more processors) for carrying out computer readable
instructions, and RAM 522.
[0103] The memory 301 stores program logic 511 which when executed
by the controller 302 (specifically the processor 521) causes the
controller 302 to implement the apparatus for modelling and
estimating the SOC/SOH of the cell in accordance with aspects of
the invention.
[0104] Specifically, the processor 521 instantiates in RAM 522 an
SOC model 531 for modelling the state of charge and state of health
of the cell 403, by modelling the operational behaviour thereof in
its operational range.
[0105] This is achieved by the SOC model 531 including a cell model
module 532 operable to predict the electrical characteristics of
the cell in use based on a model (such as an equivalent circuit
network (ECN) or a physics-based cell model) representative of the
internal state of the cell that correlates a terminal voltage of
the cell to an operational condition of the cell for all states of
charge, SOC. The cell model is parameterised, in the example of an
ECN model, by the properties of the constituent electrical elements
of the equivalent circuit network model. The parameter values for
the ECN are provided to the cell model module 532 from a parameter
value resource 512 stored in memory 301 configured to be usable to
provide to the cell model module values for the parameters of the
ECN cell model for the modelled behaviour of the cell at given
operational conditions. Thus, for a set of given operational
conditions, and an SOC, the parameter values for the ECN can be
obtained. To generate the parameter values to create the cell model
for the cell 403, the parameter values for the cell model are
derived empirically or semi-empirically based on tests of standard
cells. The parameter values for the cell model are dependent on the
modelled state of charge of the cell. The parameter value resource
512 is optionally a lookup table.
[0106] The SOC model 531 also includes a memory effect module
operable to model the usable capacity of the cell in use based on a
memory model representative of the variation in amount of active
reactant species in the cell that correlates the proportion of the
rated capacity of the cell, Q.sub.t, that is usable capacity,
Q.sub.usable, during use based on an operational history 513 of the
cell stored in memory 301. The memory model tracks an amount of
active reactant in the cell and/or an amount of temporarily
inactive reactant in the cell (representative of the temporary
variation of capacity due to dynamic use and loading of the cell)
and optionally an amount of permanently inactive reactant in the
cell (representative of the permanent loss of capacity of the
cell). The memory model comprises a set of rules relating the
different manifestations of the reactant species of the cell, the
amounts of the reactant species in those different manifestations,
the reactions in which those different manifestations of reactant
species participate during charge and discharge, and the reaction
rates thereof. The modelled reaction rates are parameterised by one
or more of: the operating conditions of the cell; the modelled
amounts of the different manifestations of reactant species; the
internal state of the cell; the electrical characteristics of the
cell in use. The parameterised values for the modelled reaction
rates are derived by theoretical predictions for the cell, or
fitted or derived empirically or semi-empirically based on tests of
standard cells.
[0107] To account for the memory effect on the variation in
capacity of the cell in use, the SOC model 531 is configured to
adjust the cell model module 532 in use based on an operational
history of the cell to compensate for the prediction of the usable
capacity of the cell by the memory effect module. This adjusting
may be performed by the cell model module 532 and/or memory effect
module 533.
[0108] As such, the SOC model 531, once created, can be used to
model the internal state and operational behaviour of the cell in
its operational range, even taking into account the memory
effect.
[0109] However, in use, the SOC model 531 can be used to estimate
the SOC of the cell in the following way.
[0110] The program logic 511 also causes the processor 521 to
instantiate in RAM 522 a cell state estimator 534 configured to
operate the cell model module 532 and the memory effect module 533
based on the measurements of the operational conditions of the cell
received during use by the cell operation condition monitor module
400 to estimate an internal state of the cell in use. Once the cell
state estimator 534 has estimated an internal state of the cell 403
using SOC model 531, an SOC Estimator module 535, which may or may
not be a subcomponent of the cell state estimator module 534, is
configured to operate the cell model module 532 based on the
estimated internal state of the cell to estimate a state of charge
of the cell. This is achieved by using the estimated parameters for
the ECN model to determine the SOC, by reference to the parameter
value resource 512.
[0111] While the example above indicates a software-driven
implementation of components of the invention by a more
general-purpose processor 521 such as a CPU core based on program
logic stored in a memory 301, in alternative embodiments, certain
components of the invention may be partly embedded as
pre-configured electronic systems or embedded controllers and
circuits embodied as programmable logic devices, using, for
example, application-specific integrated circuits (ASICs) or
Field-programmable gate arrays (FPGAs), which may be partly
configured by embedded software or firmware.
[0112] Specific implementations of the apparatus 300 for creating
the SOC model 531 and the cell state estimator 534 for modelling
and estimating the SOC of a cell will be explained in more detail
below. In its various implementations, the present invention
provides apparatuses and methods for the precise and accurate
determination of the state of charge and state of health of Lithium
Sulfur batteries, modules or cells. The apparatus 300 is, in
embodiments, provided as part of battery management system
comprising plural cells or energy system controller for coupling to
plural cells.
Generating the Cell Model Module--Equivalent Circuit example
[0113] An equivalent circuit model is first generated for the cell
which correlates the terminal voltage, V as a function of current
and temperature for each SOC of the cell (i.e. 100% to 0%). This is
achieved using either standard battery test equipment to generate
test data from standard cells of the same type that is subsequently
analysed, or predicted using a high fidelity physical model of the
LiS cell. The output is used to parameterise the equivalent circuit
model, the parameter values being dependent on the SOC. The
parameter values and model are embedded into a battery management
system or energy system controller comprising plural cells.
[0114] Where experimental tests are performed, this is in order to
observe the cell's behaviour under different working conditions
such as charge or discharge rate (i.e. the ratio of the
discharge/charge current compared to the discharge/charge current
that would deliver the rated capacity (in a given timeframe) and
temperature. Each test data includes time, imposed current, battery
terminal voltage and temperature. As shown in FIG. 6B, which shows
the current load applied to the cell against time, in a typical
test method, consecutive discharge current pulses with constant
amplitude are imposed to the cell and the cell's terminal voltage
is measured. As can be seen, in the example test, 86 consecutive
current discharge pulses having a discharge rate of 1 C were
applied, each followed by 600 seconds rest.
[0115] As can be seen from FIG. 6A, which shows the terminal
voltage of the LiS cell against time, the test cell starts at full
charge 2.8-2.1V and continues until the cell's terminal voltage
drops below a pre-defined cut off voltage between 0.5 to 2.1V. The
sampling rate can vary between 0.1 seconds and 12 hours.
[0116] In the gathering of experimental test data, each current
pulse is followed by enough relaxation time (1 second to 100 hours)
for the battery terminal voltage to return to open circuit voltage
V.sub.OC and/or a steady state.
[0117] For an equivalent circuit network a model structure is then
chosen that provides suitable flexibility to fit the experimental
data balancing goodness of fit with computational complexity. An
example simple model for the behaviour of an LiS cell is shown in
FIG. 7A, in which the terminal voltage V.sub.t is produced by the
cell providing its open circuit voltage V.sub.OCV, in series with
an ohmic resistance, R.sub.0, and a diffuse resistance provided by
one or more RC pair(s) having a resistance, R.sub.p and a
capacitance, C.sub.p. The equivalent of this shown in FIG. 7B takes
the open circuit voltage as a voltage source, in series with the
ohmic resistance, R.sub.0, and a diffuse resistances provided by RC
pairs, R.sub.n, C.sub.n.
[0118] The equivalent circuit network model of the LiS cell is then
parameterised by the properties of the constituent electrical
elements of the equivalent circuit network model--i.e. the open
circuit voltage and the ohmic and diffuse resistances. The
parameterisation is performed using, e.g. the observed behaviour in
the test data.
[0119] One example method of model parameterisation takes the open
circuit voltage, V.sub.OCV as a potential source whose value is
defined by the SOC, which is determined by the current, the defined
model input. The number of RC pairs in the model structure can be
increased to improve the agreement between the model and the
experimental data. The intent of the model is to predict the total
voltage drop across the circuit as a function of time, given a
particular input current at a specified temperature. This can be
calculated provided with open circuit voltage, R.sub.n and C.sub.n.
As open circuit voltage in a lithium sulfur cell is not a true OCV,
which is equal to 2.15V +/-0.1V, for the purposes of the model the
cell potential at the end of each relaxation phase, E.sub.m, is
taken as the OCV.
[0120] Reference will now be made to FIGS. 8A and 8B, which show a
detail, respectively, of the current load against time, and the
terminal voltage of the test LiS cell against time, for a current
pulse shown in FIG. 6. As shown in FIG. 8B, the series ohmic
resistance R.sub.0 can be calculated or parameterised directly from
the experimental data by measuring the immediate voltage drop on
application of, or the immediate voltage rise on release of, a
current pulse. The immediate change in voltage is assumed to be as
a result of the ohmic resistance component of the equivalent
circuit model, and is used to calculate the same.
[0121] The remaining R.sub.n and C.sub.n values of the diffuse
resistance components that are assumed to cause the delayed
resistance leading to the curved change of the cell voltage shown
in FIG. 8B are unknown. The following parameterisation process,
using the data in the relaxation phase curve after a current pulse
has finished, is used to fit the equivalent circuit network model
to the output experimental data in order to determine them.
[0122] Mathematically, the potential difference across the
equivalent circuit network is equal to the open circuit voltage
minus the potential drops across IR.sub.0 omhic resistance and the
RC pair diffuse resistances (V.sub.1 and V.sub.2 in the case of 2
RC pairs), according to the following relation:
V=E.sub.m-IR.sub.0-V.sub.1-V.sub.2
The potential drop across each of the RC pairs is governed by the
relationship:
I = d d .times. t .times. ( C n .times. V n ) + V n R n ; n = 1 , 2
##EQU00002##
So during pulsing the cell voltage is given by:
V = E m - IR 0 - n .times. { IR n .function. [ 1 - exp .function. (
- t R n .times. C n ) ] + V n .function. ( 0 ) .times. exp
.function. ( - t R n .times. C n ) } ##EQU00003##
Where V.sub.n(0) is the initial voltage across the RC pair, assumed
to be zero at the start of each pulse. During relaxation the
voltage is given by:
V = E m - n .times. V n .function. ( 0 ) .times. exp .function. ( -
t R n .times. C n ) ##EQU00004##
Where V.sub.n(0)=IR.sub.n is the potential at the end of the
preceding pulse, which can be calculated assuming that the
capacitors are fully charged.
[0123] The fitting procedure for the unknown R.sub.n, C.sub.n
parameters uses a non-linear least squares technique or suitable
alternative, minimising the sum over all data points of the square
of the error between the model and experiment:
S = i .times. ( V i , expt - V i , mod .times. e .times. l ) 2
##EQU00005##
[0124] Where i ranges over all data points in the discharge curve.
The value is minimised using the trust--region reflective algorithm
or suitable alternative. Following estimation of all the parameters
for the ECN model using the experimental test data, look up tables
are created for each SOC for the RC branch resistances and
capacitances, the data is smoothed using best fit curve fitting, as
shown in FIGS. 9A and 9B, which show, respectively, the
parameterised values of R.sub.1 and R.sub.2 as a function of SOC at
10.degree. C. and a current discharge rate of 0.1 C. The crosses
denote the parameter estimation results and the line is the best
fit curve.
[0125] The look up tables can be stored as parameter value resource
512 in a working SOC/SOH estimator in accordance with the
invention, which are used to create a model of the standard test
LiS cell's behaviour, not taking into account any memory loss
effect.
[0126] Fitted parameters and equations for the curves are
generated, for example, in accordance with the following fitted
polynomials:
R 1 = i = 0 k .times. a i .times. SOC i ##EQU00006## R 2 = i = 0 m
.times. a i .times. SOC i ##EQU00006.2## C 1 = i = 0 l .times. a i
.times. SOC i ##EQU00006.3## C 2 = i = 0 p .times. a i .times. SOC
i ##EQU00006.4##
[0127] Depending on the form of the curve that is being fitted, two
or more polynomials may be used to fit different parts of the
curve. This is useful in the event that it is not practical to fit
the curves with just a single polynomial, and so a combination of
two or more polynomials can be used.
[0128] Where look up tables retain the parameters of the equations
against SOC. After parameterisation, the experimental and predicted
constant current discharge curves can be plotted, as shown in FIG.
10 (which shows the ECN-predicted and experimental discharge curves
for a 0.1 C discharge rate, and standard experimental data for a
discharge curve for a 0.2 C discharge rate), to validate the
model.
[0129] For solving model equations, coulomb counting is used to
determine the parameter values at a particular solution time step,
interpolation is used to determine any necessary intermediate
values in lookup tables. The equations are solved to determine the
total potential drop at that time.
Generating the Memory Effect Model
[0130] The look up tables generated by the equivalent circuit
network model are then modified by a model of the Lithium Sulfur
memory effect in order to adjust Q.sub.t based on the prior history
of the cell and the likely environmental conditions during a
specific cycle. Previous charge/discharge events and their
conditions (temperature and current magnitude) affect the
concentration of species dissolved in the electrolyte, and can thus
lead to marked variations in the instantaneous series resistance of
the cell, as can be observed in FIG. 11 where variation of Q.sub.t
can be observed, the cell capacity pre-pulsing experiment is Ca 2.5
Ah and on the first cycle post pulsing experiment the capacity
reduces to Ca. 2 Ah but on the subsequent cycle the capacity
recovers to Ca. 2.8 Ah. In detail, FIG. 11A illustrates the
capacity variation of a same cell undergoing dynamic cycling, as
shown in FIG. 11B which shows the cell voltage against time for the
pre-pulsing, pulsing, and post-pulsing cycles. The same cell
cycling at the same temperature and current gives a capacity of 2.5
Ah. It is then subjected to a simulated dynamic discharge and
charge. The next two subsequent cycles show first lower capacity of
2 Ah followed by a greater capacity of 2.8 Ah demonstrating
reversible capacity variation under dynamic load and that there is
a complex response to current variation.
[0131] This variation in Q.sub.t following dynamic cycling is a
manifestation of the memory effect.
[0132] In order to capture this memory effect and its impact on
state of charge estimation, a model additional to the equivalent
circuit model providing the cell model, but in connection to it is
used, this is the memory model which is implemented in the memory
effect module 533.
[0133] The memory model keeps track of the amount of sulfur
material present in different manifestations in the cell: currently
active reactants and products, and temporarily inactive species,
allowing the temporary variation in the usable capacity of the cell
due to the memory effect to be monitored and compensated for when
predicting SOC.
[0134] The model can also be expanded to include degradation due to
loss of active material by including a further manifestation--that
of polysulfide material rendered permanently inactive to account
for SOH, allowing the permanent reduction in the usable capacity of
the cell due to the irretrievable loss of reactant to be monitored
and compensated for when predicting SOC.
[0135] Thus, the memory model allows the SOC estimation apparatus
and method in accordance with the present invention to provide the
SOC based on how much active species (Q.sub.usable) is present and
that can still usefully contribute to Q.sub.t. State of health is
determined by Q.sub.usable/Q.sub.t=0 where Q.sub.t=0 is the
starting capacity of the cell.
[0136] The memory model effectively tracks the state of charge of
the battery by monitoring the quantity of sulfur in these different
manifestations throughout the cell lifetime for any given current
load. It is synergistic with an equivalent circuit model, or any
type of model that captures the dynamics of
precipitation/dissolution, redox reactions and diffusion through
electrolyte.
[0137] In order to generate and operate the LiS model for a given
cell, to begin with, the case of low enough current applied to the
LiS cell can be taken as a reference charge/discharge performance,
even if unrepresentative for the cell's usage. In this case, the
memory model indicates the way in which this reference information
is used in predicting/monitoring the state of charge of the cell
under any realistic current load.
[0138] A set of sulfur species together with the reactions in which
they participate is cast into a set of rules (equations) for charge
and/or discharge. The reactions can be both electrochemical and
chemical. The voltage of the cell is calculated as the equilibrium
voltage of all electrochemical reactions taking place
concomitantly, as example via Nernst equations for each allowed
reaction. The rates at which sulfur material is converted from one
manifestation to others is given by the rate of the different
reactions, but also by the amount of current passed through, the
temperature, and amount of reactant versus amount of product.
Reaction rates are predicted, fitted or experimentally derived.
Mathematically, this effect can be described by solving the
Butler-Volmer equation or similar to extract the contribution of
each species to the total ionic current inside the cell. As a
result, the instantaneous quantity of material in each
manifestation is dependent on the history of the cell, and causes
the cell voltage and the series resistance to be dependent upon
it.
[0139] In one simplified version of the memory model, the active
material appears in three possible manifestations: high order,
medium order and low order polysulfides. The high-to-medium order
reaction dominates the higher operating voltages, giving rise to
the high order plateau, while the medium-to-low order reaction
determines the low order plateau. During discharge, if high order
polysulfides are still present when the cell is at a low plateau
voltage, they do not (or are assumed not to) react, thus becoming
temporarily inactive.
[0140] The series resistance for a low current pulsed discharge is
considered to be proportional to the amount of middle order
polysulfide dissolved in electrolyte. In the case of this simple
memory model, there are only three sulfur manifestations. As a
result, in the low plateau the proportion of active material that
is a middle order polysulfide dictates the remaining capacity of
the cell, whereas in the high plateau it would be both the high and
middle order polysulfides.
[0141] In view of this simplified memory model, a possible
mechanism will now be described for adjusting the operation of the
cell model in retrieving parameter values from the parameter value
resource 512 (i.e. the lookup tables) to compensate the cell model
for the rendering of active species temporarily inactive modelled
by the memory model.
[0142] As above, the voltage of the cell is obtained in the ECN
model as the voltage source (Em, open circuit voltage) minus the
voltage drop across the RC components in the circuit.
[0143] For example:
V c .times. e .times. l .times. l = E m - IR 0 - 1 n .times. Q C ,
n C n , where .times. .times. d .times. Q C , n dt = I .function. (
t ) - Q C , n R n .times. C n ##EQU00007##
[0144] As a result of this approach, under a current load the cell
voltage V.sub.cell reaches values corresponding to the low plateau
region despite E.sub.m corresponding to a high plateau voltage. The
difference between V.sub.cell and E.sub.m increases with current
load. As soon as V.sub.cell reaches a pre-defined boundary, V.sub.b
(the boundary voltage between the high and low plateaus), the
unreacted high order polysulfide is stored as inactive or dormant,
and the middle order polysulfide starts reacting towards low order
polysulfide, according to the dominating reaction in the low
plateau.
[0145] Compensating for this is achieved by the way in which the
look up table from the equivalent circuit model for R.sub.O is read
in use. If, in use, the cell voltage becomes less than the boundary
voltage between the high and low plateaus, i.e.
V.sub.cell.ltoreq.V.sub.b, then the position on the R.sub.O plot is
found that corresponds to the same R.sub.O value (same amount of
middle order polysulfide dissolved) in the low order plateau, as
indicated by the dotted arrow in FIG. 12A. The effect of this
adjustment in the modelled capacity when compensating based on the
memory model is shown in FIG. 12B, which plots the modelled
discharge curves for the ECN adjusted by the memory model. In
detail, FIG. 12A shows reading the look-up table for R.sub.O as
dictated by a simple memory model for a 0.1 C and a 0.5 C discharge
rate. For the 0.1 C discharge curve, the reference look-up table is
used (as this corresponds to the low enough current). However, it
can be seen that at 0.5 C, where the cell voltage drops below the
boundary voltage between the high and low plateaus, the mechanism
of using the look up table to take into account the effect of
discharge at a higher current as indicated by the dotted arrow, is
required (i.e. the reading of the R.sub.O value from the plot skips
to the corresponding R.sub.O value on the downward slope of the
R.sub.O plot). As can be seen in FIG. 12B, as a result, at 0.5 C
there is approximately 1.3 Ah temporary capacity loss compared to
discharging at 0.1 C.
[0146] The value of the jump on the capacity axis indicated by the
dotted arrow is taken as the temporarily lost capacity through
inactivation of high order polysulfides.
[0147] As shown in FIG. 14, which shows the comparative R.sub.O
plots from adjusting the reading of the R.sub.O values from the ECN
cell model for 0.1 C for different discharge rates (0.5 C and 1 C),
the higher the current, the more capacity is temporarily lost.
[0148] The simplified memory model is parametrised by fitting Vb,
the boundary between the high and the low plateaus, which can be
estimated from a low current, constant current discharge. As shown
in FIG. 13, this simplified memory model can be used to adjust the
cell model to predict the variation of Q.sub.t with current.
[0149] In another more complex variation of the memory model,
reactions as shown in Table 1 taking place independently of the
presence of electronic current are added to the model, together
with a necessary and sufficient set of additional states that
represent active and inactive material at different stages of
reduction in the polysulfide series. The number of species included
in the model is chosen to be the minimum
TABLE-US-00001 TABLE 1 Representative LiS reaction mechanisms added
to the memory model High Plateau (Ca. 4 e.sup.-) Low Plateau (12 -
n e.sup.-) Inaccessible Capacity (n e.sup.-) First Cycle,
dissolution and 2 Chemical Equilibrium Equilibrium conc. of
unreacted step reduction Li.sub.2S.sub.6 2LiS.sub.3.cndot.(radical)
intermediates S.sub.8 .sub.(S) + 2e.sup.- + 2Li.sup.+ .fwdarw.
Li.sub.2S.sub.8(Soln.) Dominating low plateau Li.sub.2S.sub.n
.sub.(Soln.) + Li.sub.2S.sub.(S) Reductive Dissociation
electrochemical reaction Irreversible Capacity Loss Li.sub.2S.sub.8
+ 2e.sup.- + 2Li.sup.+ .fwdarw. Li.sub.2S.sub.6 + Li.sub.2S.sub.2
LiS.sub.3.cndot.+ e.sup.- + Li.sup.+ .fwdarw. Li.sub.2S.sub.3
Polysulfide oxidation (or) Association and precipitation Lithium
solvent/salt reactions Li.sub.2S.sub.8 + 2e.sup.- + 2Li.sup.+
.fwdarw. 2Li.sub.2S.sub.4 Li.sub.2S.sub.3 + Li.sub.2S.sub.4
.fwdarw. Li.sub.2S.sub.6 + Li.sub.2S.sub.(S) SEI formation and
re-formation And many other reactions Loss of active surface area
Electrically isolated precipitation And many other reactions
[0150] number to adequately describe the performance of a
Lithium-Sulfur cell but generally includes redox reactions,
chemical inter-conversions such as association and dissociation of
molecules, ions and radicals and any combination thereof in
equilibrium.
[0151] A set of equations is constructed according to the procedure
above. Parametrisation of this model requires electrochemical
parameters for the reactions and species considered, such as those
available in Assary et al, J Phys. Chem C 118 (2014) otherwise
parameters can be predicted or fitted to experimental data.
Parameterisation by Prediction Error Minimisation (PEM)
[0152] An alternative method of cell and memory model generation
and parameterisation that is computationally less expensive than
the methods described above and that can therefore be used, e.g.,
to identify model parameters in real time within applications (as
well as to identify parameters in experimental test data for cell
model generation) is Prediction-Error Minimisation.
[0153] To identify the parameter values for a cell model, the
parameters of the cell model (for the parameter value resource 512)
are identified from inputs supplied from the application (i.e. cell
operational condition measurement means 400) for example by
prediction-error minimisation (PEM) (or a suitable
alternative).
[0154] The identification procedure by PEM contains three main
parts: 1) Model structure selection; 2) Fitting parameters to the
model; and 3) Identification error minimisation. These parts will
now be described in turn.
[0155] 1) Model Structure Selection
[0156] First, an equivalent circuit is selected using a combination
of capacitors and resistors in series and or in parallel. FIG. 15
shows an illustration of the general form of the equivalent circuit
model for Lithium Sulfur batteries. Here it can be seen that the
general model includes a suitable open circuit voltage 1501 as a
voltage source supplied from experimental test data or simulated
from a high fidelity physical model of the Li--S cell that takes
into account aging effects as described above, and shuttle effects.
The open circuit voltage can be further modified by additional
equivalent circuits of resistors and capacitors in series and or in
parallel to include memory effects 1502 and self-discharge 1503
specific to Li--S batteries. A series RC circuit then adjusts the
voltage source for the general trend of charge and discharge as a
function of current load, I, and temperature, T. The model
structure should be selected to balance accuracy and calculation
complexity. The model then outputs a prediction of the SOC, SOH,
internal resistance, R, of the cell, and terminal voltage, V.sub.t.
FIG. 7 represents the most basic example.
[0157] 2) Fitting Parameters to the Model
[0158] Fitness criteria are chosen to fit the parameters of the
model (i.e. the voltage source, ohmic resistance and diffuse
resistance component values). One example approach is the
identification procedure. The cell model parameters are determined
so that the least difference between measured terminal voltage
(from experimental or application data) and cell model output is
achieved. The model parameter vector (.theta.) is determined so
that the prediction error (.di-elect cons.), defined as follows, is
minimized.
.di-elect cons.(t.sub.k, .theta.)=y(t.sub.k)-y(t.sub.k|t.sub.k-1;
.theta.)
where y(t.sub.k) is the cell's output at time k and
y(t.sub.k|t.sub.k-1; .theta.) is the predicted value of the output
at time k using the parameters .theta.. The prediction error
depends on the parameter vector so an iterative minimization
procedure has to be applied. Consequently a scalar fitness function
is minimized as follows:
E N .function. ( .theta. ) = det .function. ( 1 N .times. k = 1 N
.times. .function. ( t k , .theta. ) .times. T .function. ( t k ,
.theta. ) ) ##EQU00008##
[0159] 3) Identification Error Minimisation
[0160] An identification error minimisation algorithm is selected,
one example approach is where the average error of a cell's
terminal voltage estimation is calculated using root mean square
error (RMSE) criterion defined below.
R .times. M .times. S .times. E = ( i = 1 N .times. ( V t , i - V ^
t , i ) 2 N ) 1 2 ##EQU00009##
where V.sub.t is the measured cell terminal voltage, {circumflex
over (V)}.sub.t is cell model output and N is the length of V.sub.t
in seconds. FIG. 16D shows RMSE values at different charge levels,
together with the identified ECN model parameter values of R.sub.O,
R.sub.P and C.sub.P in FIGS. 16A, 16B and 16C, respectively.
Real-Time State of Charge Estimation Methods, Using Kalman-Type
Filters
[0161] Referring to FIG. 17, this illustrates an example method
1700 of state of charge estimation in accordance with an embodiment
of the invention
[0162] First, in step 1701, current, voltage and temperature are
measured in use using cell operational condition measurement means
400 during dynamic load and in step 1702 these are stored in
memory, where they are used to update a state vector that reflects
the operational history of the cell in memory 513. The measured
operational conditions in step 1701 are then input to the embedded
equivalent circuit model in step 1703 along with the cumulative
history of previous cycling conditions (for example,
charge-discharge rate and temperature) stored in tables or as a
state vector in operational history 513. The model parameters are
then predicted in step 1703 (using the cell model module 532), for
example by a PEM method. Then based on experimentally derived or
predicted look up tables from an operational model of a Lithium
Sulfur cell in step 1704 the state of health is estimated (using
the memory effect module 533) along with measurable parameters of
the system such as voltage, temperature and resistance which are
output in step 1705. In step 1706, these estimated outputs can be
used in a feedback loop by comparison of estimated data with actual
measured data to increase the accuracy in step 1707 of parameter
estimation in real time.
[0163] Unlike similar systems for common battery types for Lithium
Sulfur the equivalent circuit model additionally takes into account
the unique memory effect in Lithium Sulfur cells which varies the
maximum capacity, Q.sub.t on charge or discharge depending on
temperature and cumulative effects of charge and discharge
rates.
[0164] The memory aware model is deployed in the software or
firmware of an application such that state of charge and state of
health estimation does not rely on extensive calibration of
standard cells or extensive high volumes of test data.
[0165] Indeed, in accordance with another embodiment of this
invention, a model specific to the unique characteristics of
Lithium Sulfur chemistry including the memory effects under dynamic
load is generated from experimental data. An equivalent circuit
model (or any alternative model such as any physics based cell
model, semi or fully empirical) is implemented as part of a
real-time embedded system within the application either as software
or firmware. The current equivalent-circuit network model
parameters are continuously identified in real time using the same
approach for parameter identification and Kalman type filtering
such as extended Kalman filter, the unscented kalman filter, the
particle filter, Luenberger state estimator (observer) or any other
state observer or state estimator variant to provide the cell state
estimator 534. The algorithm update rates and numerical precision
are traded off against processor cost as application needs
dictate.
[0166] An example of such an implementation using a Kalman-type
filter as a state estimator is illustrated in FIG. 18 which shows a
schematic of a real time SOC/SOH estimation using an operational
equivalent circuit model and Kalman filtering. Here, in 1801,
measured values of current load, I, temperature, T, and terminal
voltage V, are received from the cell operational condition
measurement means 400 during dynamic load. As before, in 1802,
these are passed to memory where they are used to update, e.g., a
state vector representative of the historical operational
conditions of the cell, and then on, in 1803, to the ECN state
estimator module 534. In the prediction step of the Kalman filter,
this state estimator 534 is used to predict the internal cell state
at a given timestep in the future based on the current state, the
SOC model 531, and the current operational conditions. The
measurements at that future timestep received from the cell
operational condition measurement means 400 are then used in the
correction step of the Kalman filter. Firstly, the expected
measured value is produced in 1804 by an ECN Observation model
adjusting the ECN state predicted in 1803. This is then compared
with the actual measured operational conditions in 1805 in a
statistical adaptation model for the ECN that, using a Kalman gain,
determines a statistical adaption value that is used in
post-processing in 1806 to correct the predictions of the current
cell state from the ECN model based on the observed cell behaviour,
and which in 1807 is subsequently fed back to the memory to adjust
and improve the ECN model in an iterative fashion. The algorithm
architecture can be implemented in a number of ways. Example
deployment architectures are shown in FIGS. 19-22.
[0167] The simplest, shown in FIG. 19 uses a Kalman type filter to
estimate or identify the current parameters of an
equivalent-circuit network model, parameter estimates are
interpreted against parameter look up tables generated from Lithium
Sulfur cell models to estimate the current states of health (SoH)
and charge (SOC).
[0168] In a more complex form shown in FIG. 20, a non-linear Kalman
filter can be used for non-linear state estimation of the
equivalent circuit model and its associated memory effects. Other
simplifications include multiple hypothesis filters which use
relatively simple state estimators and then choose the most likely
SOC or SoH based on prediction errors, as shown in the architecture
in FIG. 21. An architecture using Fuzzy logic, as shown in FIG. 22,
can also be employed for state estimation and trained by the Li--S
model which incorporates an understanding of the memory effect.
[0169] In this case no database is required and the model's
parameters are tuned continuously. Given real time inputs of for
example voltage, current and temperature from the cell operational
condition measurement means 400 the cell model can be used to
predict the cell's terminal voltage.
[0170] The accuracy of the predictive model is balanced against
computational effort for on-line model identification. For on-line
prediction the model should be updated at regular intervals for a
desired prediction horizon. The lower the prediction horizon the
greater the accuracy. If there is no update delay then the RMSE
would be equal to the identification model above. FIG. 23 shows the
prediction results for various prediction horizons from 0.5 to 2%
SOC increments using a simplified equivalent circuit. In the
example increasing the prediction horizon from 1% to 2% SOC reduces
computational effort by 50% whilst the average RMSE increases from
13 to 24 mV. The prediction horizon is selected based on SOC such
that the update rate is proportional to the rate of power demand in
a vehicle.
[0171] In accordance with one embodiment of this invention Lithium
Sulfur specific lookup tables or algorithms are stored in the
battery management system or energy system controller either
integral to the battery system or within the application system as
software or firmware. The lookup tables are populated using a
software model specific to the unique characteristics of Lithium
Sulfur chemistry including memory effects under dynamic load,
parameterised from experimental data. The use of a model refers to
an equivalent circuit model (or any alternative model such as any
physics based cell model, semi or fully empirical). These lookup
tables correlate cell resistance and voltage at various
temperatures and currents relative to Q.sub.t (100% SOC or 100%
SOD) which is determined when the terminal voltage reaches a
predetermined cut off voltage. Q.sub.t at the `100% SOC/SOD` state
is determined from the predicted available active material present
in the cell derived from a stored cumulative history of the cells,
modules or battery's prior charge/discharge rates, depths of
charge/discharge and temperature profile in order to accurately
predict the maximum charge or discharge capacity for the current
charge or discharge cycle. Feedback is provided by measurement of
current, voltage and calculated resistance using the cell balancing
resistors. Cell impedance is measured through the switching of a
balancing resistor. Consecutive current pulses are imposed to the
cell by switching in and out a cell balancing resistor and the
cell's terminal voltage is measured. The test can be performed at
any state of charge when the application is idle. The sampling rate
can vary between 0.1 seconds and 60 minutes. Each current pulse is
followed by enough relaxation time (1 second to 60 seconds) for the
battery terminal voltage to return to open circuit voltage V.sub.OC
and/or a steady state. In this way state estimation does not
require extensive calibration and can be updated in real time based
on data captured during application under dynamic loads.
[0172] In accordance with another embodiment of this invention this
model is deployed in a real time battery management system or
energy system controller. Atypical form of this model could be a
look up table which returns model parameters based on a number of
inputs including SOC, current amplitude, temperature and requiring
high volumes of test data for all conditions.
[0173] This approach to terminal voltage prediction for SOH
estimation that is generally applicable to multiple cell types
given similar trend in discharge/charge characteristics. This
approach can be used for any cell chemistry and design. It is also
a method of coupling high fidelity predictions from physical models
that include all complex features of a lithium sulfur cell to
simpler embedded models whose parameters can be identified in real
time within the battery management system or energy system
controller of an application due to the reduced computational
effort required. High fidelity predictive models can be developed
from the first principles of fundamental physical theory to
describe the performance of a lithium sulfur cell exposed to
external stimuli. These models that predict the effects of
chemistry, materials, cell build, cell design and operating
conditions. The output from the high fidelity physical models of a
lithium sulfur cell take into account features such as shuttle and
degradation mechanisms, to improve SOH estimation. In this way high
fidelity models can be used to parameterise simpler embedded models
for a range of experimental conditions alongside applied current
and temperature in order to predict state of health, resistance,
voltage and resulting temperature. The embedded model is used to
predict internal states that cannot be measured directly or virtual
states (such as SOH and SOC) given the operating history of the
cell (for example current and temperature profile) either in real
time or ex-situ.
[0174] As can be seen from the foregoing, according to the present
invention by including the memory effect brought about by the
dissolution of intermediate species in the electrolyte in a device
embedded equivalent circuit model (or other model types such as
physics based or semi-empirical physics inspired models including
fully empirical cell models) along with the effects of
self-discharge, shuttle and other aging mechanisms specific to
Lithium Sulfur batteries and detecting current, temperature,
internal resistance to provide feedback, the SOH of the system can
be detected in real time and under dynamic cycling conditions. This
software/firmware solution can be implemented without adding
additional standalone devices to battery management systems for
state estimation.
[0175] As will be appreciated from the below, the provision of the
above apparatus and method for reliably estimating the state of
charge and state of health of cells, such as LiS cells, that suffer
from the memory effect, into a battery management system or energy
system controller of an electric vehicle (EV) powered at least in
part by said cells allows improved range estimation and route
planning to be performed in relation to the use of the electric
vehicle. This is illustrated with reference to FIG. 23, reference
to which will now be made.
[0176] In an exemplary embodiment, a method 2300 for estimating a
range and planning a route of an electric vehicle therefore
includes, in step 2301, performing a method as described above to
estimate a state of charge and a remaining capacity of the cells in
use.
[0177] Then, in step 2302, the method further includes estimating a
range of the electric vehicle based the estimation of the state of
charge and the remaining capacity of the cells in use.
[0178] Then, in step 2303, the method further comprises planning a
route towards a desired destination based at least in part on an
estimated range of the electric vehicle produced by the range
estimation module based on the predicted operational conditions of
the cells following that route. This may be performed using route
planning algorithms adapted to in 2304 optimise a route towards a
destination from plural routes planned by the route planning module
based on the estimated range of the vehicle along those routes, and
optionally other information such as recharge or battery-swapping
points along those routes. In addition, as the estimation of the
remaining capacity may be based on the predicted operational
conditions of the cells in use in the vehicle, for example, over a
given predicted route, for a given driving style of the driver on
that route, for given environmental conditions on that route, etc,
the range estimation and route planning algorithm can solve, e.g.
iteratively, over these factors to recommend the optimal route for
the driver to follow to reach a given destination. Typically the
route selection will be optimised based on conserving capacity
needed for completing a given journey, although alternatively
greater weight can be given to optimising for the speed of
completing a journey, or other criteria.
[0179] While this invention has been described in connection with
what is considered to be the most practical and preferred
embodiments, it is to be understood that this invention is not
limited to the disclosed embodiment and the drawings, but on the
contrary, it is intended to cover various modifications and
variations within the spirit and scope of the appended claims.
Various types of circuitry and devices can be used to implement the
measurement system as described according to this invention. It
will be understood that this is illustrative and that various
modifications can be made by those skilled in the art without
departing from the scope and spirit of this invention. This
invention is only limited by the claims that follow.
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