WO2022096898A2

WO2022096898A2 - A system, a vehicle, a method, and a computer readable medium

Info

Publication number: WO2022096898A2
Application number: PCT/GB2021/052892
Authority: WO
Inventors: Richard Stocker; Puneet MATHUR
Original assignee: Horiba Mira Limited
Priority date: 2020-11-09
Filing date: 2021-11-09
Publication date: 2022-05-12
Also published as: WO2022096898A3

Abstract

A system, a vehicle, a method, and a computer readable medium A system including one or more devices configured to: receive battery measurements corresponding to a charging profile of a battery during a first battery charging cycle, wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determine the number of amp hours accumulated during the constant voltage phases; and determine a battery capacity state-of-health using the number of amp hours accumulated during the constant voltage phases.

Description

Title: A system, a vehicle, a method, and a computer readable medium

Description of Invention

Embodiments of the present invention relate to a system, such as a system including a battery management system and/or a remote computing device, along with associated vehicles, methods and computer-readable media.

Batteries are used in a wide variety of applications, including vehicles, which may be electric vehicles. Electric vehicles have particularly demanding battery requirements due to the large operating temperature range, emphasis on energy density and requirement for long battery lifetimes. Long-life applications pose particular design challenges due to the complex ageing processes of the batteries.

A battery is typically formed from one or more cells (i.e. electrochemical cells). As such, references herein to a battery may be a reference to one or more cells. Likewise, a reference to a cell may be a reference to a battery or a part of a battery.

Two key aspects of cells which evolve over time are their ability to store charge (capacity) and their ability to transfer charge (resistance). Both capacity and resistance have significant impacts on vehicle range, performance, efficiency, heat generation and safety. Conventional electric vehicles include a Battery Management System (BMS) to manage usage of the battery. However, the BMS typically only has access to information about how a battery (such as a lithium-ion battery) performs over its useable operational range when the battery is new. As the characteristics of the battery evolve with ageing, this information may become less representative of the true characteristics of the battery, leading to sub-optimal battery management.

Fast charging of batteries is increasingly important in a variety of applications, including in electric vehicles. A key objective of fast charging is safely maximising current input to minimise vehicle downtime. However, fast charging is particularly sensitive to battery ageing condition and comes with a significant risk of lithium plating, which occurs when the anode voltage decreases below 0V^Li/Li+. This presents a serious safety concern.

Furthermore, the root causes of changes in battery characteristics are often not directly observable, being internal changes in the mechanical, electrical and chemical structures within the cell. This means these changes must be quantified through indirect observation processes using a range of information from cell behaviour. Such processes can be very computationally demanding.

There is a need, therefore, to alleviate one or more problems associated with the prior art.

An aspect of the present disclosure provides a system including one or more devices configured to: receive battery measurements corresponding to a charging profile of a battery during a first battery charging cycle, wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determine the number of amp hours accumulated during the constant voltage phases; and determine a battery capacity state-of-health using the number of amp hours accumulated during the constant voltage phases. The system may be further configured to use the battery capacity state-of- health to control an aspect of the operation of the system during a second battery charging cycle.

The one or more devices may include a battery management system and/or a remote computing device.

The one or more devices may include the battery management system and the remote computing device, and the battery management system may be configured to send the battery measurements to the remote computing device.

The battery management system may be further configured to control the charging profile of the battery during the first battery charging cycle.

The battery capacity state-of-health may be determined according to the equation:

wherein SoH_Cap is the battery capacity state-of-health, f Ah_aged is the number of amp hours accumulated during the constant voltage phases, and f Ah_new is a baseline number of amp hours accumulated during constant voltage phases executed at the same plurality of target battery voltages.

The system may be further configured to: determine a mean resistance of the battery during the constant voltage phases; and determine battery power fade state-of health using the mean resistance of the battery during the constant voltage phases. The system may be further configured to use the battery power fade state-of- health to control an aspect of the operation of the system during the second battery charging cycle.

The battery power fade state-of-health may be determined according to the equation:

wherein SoH_Pf is the battery power fade state-of-health, R_Aged is the mean resistance of the battery during the constant voltage phases, R_New is a baseline mean resistance of the battery during constant voltage phases executed at the same plurality of target battery voltages, and SoH_Cap is the battery capacity state-of-health.

The mean resistance of the battery may be determined according to the equation:

wherein R is the mean resistance, V_oc is the open-circuit voltage of the battery, I is current, and t is time.

The number of amp hours accumulated may be determined according to the equation:

wherein V is voltage, Ah is amp hours, t is time, and I is mean current during each evaluated discrete timestep dt. At least one target battery voltage may correspond to an electrode phase change or plateau.

Each constant voltage phase may be maintained until a charging current decreases to a predetermined threshold.

The p ^rredetermined threshold may ³ be in the range — 10 C to — 100 C or — 10 C to — 50 C.

The charging profile may comprise a plurality of constant current phases.

The system may be further configured to monitor the relative ratios of the constant current and constant voltage phases of the charging profile.

Controlling the aspect of the operation of the system may include controlling at least one of a maximum charge current limit, maximum discharge current limit, maximum voltage limit, minimum voltage limit, maximum charge power limit, or maximum discharge power limit.

The system may be further configured to send the battery capacity state-of- health to a display device for presentation to a user and/or to a remote data analysis module.

The system may be further configured to send the battery power fade state-of- health to a display device for presentation to a user and/or to a remote data analysis module. Another aspect provides a method of operating a system including one or more devices, the method comprising: receiving battery measurements corresponding to a charging profile of a battery during a first battery charging cycle wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determining the number of amp hours accumulated during the constant voltage phases; and determining a battery capacity state-of-health using the number of amp hours accumulated during the constant voltage phases.

The method may further include using the battery capacity state-of-health to control an aspect of the operation of the system during a second battery charging cycle.

The method may further include: determining a mean resistance of the battery during the constant voltage phases; and determining battery power fade state-of health using the mean resistance of the battery during the constant voltage phases.

The method may further include using the battery power fade state-of-health to control an aspect of the operation of the system during the second battery charging cycle.

Another aspect provides a computer readable medium storing instructions which, when executed by a processor, cause the performance of any of the above methods.

Another aspect of the present disclosure provides a battery management system configured to: control a charging profile of a battery during a first battery charging cycle wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determine the number of amp hours accumulated during the constant voltage phases; determine a battery capacity state-of-health using the number of amp hours accumulated during the constant voltage phases; and use the battery capacity state-of-health to control an aspect of the operation of the battery management system during a second battery charging cycle.

The battery management system may be further configured to: determine a mean resistance of the battery during the constant voltage phases; determine battery power fade state-of health using the mean resistance of the battery during the constant voltage phases; and use the battery power fade state-of-health to control an aspect of the operation of the battery management system during the second battery charging cycle. The battery power fade state-of-health may be determined according to the equation:

The mean resistance of the battery may be determined according to the equation:

wherein V is voltage, Ah is amp hours, t is time, and I is mean current during each evaluated discrete timestep dt.

At least one target battery voltage may correspond to an electrode phase change or plateau. Each constant voltage phase may be maintained until a charging current decreases to a predetermined threshold.

The charging profile may comprise a plurality of constant current phases.

The battery management system may be further configured to monitor the relative ratios of the constant current and constant voltage phases of the charging profile.

The aspect of the operation of the battery management system may include controlling at least one of maximum charge current limit, maximum discharge current limit, maximum voltage limit, minimum voltage limit, maximum charge power limit, or maximum discharge power limit.

The battery management system may be further configured to send the battery capacity state-of-health to a display device for presentation to a user and/or to a remote data analysis module.

The battery management system may be further configured to send the battery power fade state-of-health to a display device for presentation to a user and/or to a remote data analysis module.

Another aspect provides a vehicle including a battery management system as above.

Another aspect provides a method of operating a battery management system, the method comprising: controlling a charging profile of a battery during a first battery charging cycle wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determining the number of amp hours accumulated during the constant voltage phases; determining a battery capacity state-of-health using the number of amp hours accumulated during the constant voltage phases; and using the battery capacity state-of-health to control an aspect of the operation of the battery management system during a second battery charging cycle.

The method may further include: determining a mean resistance of the battery during the constant voltage phases; determining battery power fade state-of health using the mean resistance of the battery during the constant voltage phases; and using the battery power fade state-of-health to control an aspect of the operation of the battery management system during the second battery charging cycle.

Another aspect provides a computer readable medium storing instructions which, when executed by a processor, cause the performance of the above method.

Another aspect provides a method of determining battery management system calibration parameters, the method including: receiving battery data at a data analysis module, the battery data including one or more parameters associated with a battery; using the data analysis module to determine one or more battery management system calibration parameters; and outputting the or each battery management system calibration parameter to a remote battery management system, the remote battery management system being remote from the data analysis module, wherein the one or more battery management system calibration parameters include at least one of: an open circuit voltage-state of charge map, a battery capacity state-of-health, or a maximum charging current limit.

The method may further include: transmitting the battery data from the remote battery management system to the data analysis module.

Transmitting the battery data from the remote battery management system to the data analysis module may include transmitting the battery data from the remote battery management system which is part of a vehicle.

The battery data may include at least one of: battery constant-current charge current and voltage data, battery open circuit voltage data, battery capacity state-of-health data, battery power fade state-of-health data, battery voltage data, battery resistance data, battery relaxation event data, battery temperature data, battery state-of-charge data, or battery current data.

The remote battery management system and the data analysis module may be communicatively coupled by a network including the internet.

Baseline battery characterisation data may be used to determine at least one battery management system calibration parameter.

The baseline battery characterisation data may include at least one of a half cell voltage curve, full cell load voltage curve, full cell open circuit voltage curve, or battery voltage limits. The battery may be a lithium-ion battery.

The data analysis module may determine at least one battery stoichiometry parameter, which is used to determine at least one battery management system calibration parameter.

A battery capacity state-of-health may be at least partially calculated using the equation:

wherein Relative Capacity Age X) is the battery capacity state-of- health at a particular battery age X, SoC_{Acc Age X} is an accessible state-of- charge range at the battery age X, SoC_{Acc Baseiine} is an initial accessible state- of-charge range, and LAMPE is a loss of cathode active material as a percentage of initial cathode capacity.

A battery open circuit voltage, used to determine at least part of the open circuit voltage-state of charge map, may be at least partially calculated using the equation:

wherein V_{fc ocv} is a full-cell open circuit voltage, V_{ca ocv} is a cathode open circuit voltage, SoC_An is an anode state-of-charge, V_{An ocv} is an anode open circuit voltage and SoC_Ca is a cathode state-of-charge.

A maximum charging current limit may be at least partially calculated using the equation:

wherein Cr_ceu is a maximum cell C-rate, SoC_an is an anode state-of- charge, Cr_{mnY nri} is a maximum anode C-rate, LAMPE is a loss of cathode active material as a percentage of initial cathode capacity and LR is a loading ratio.

The maximum anode C-rate may be at least partially calculated using the equation:

Cr_max,an f SoC_an, T) charge

wherein

is the maximum anode C-rate, SoC_nrl is an anode state-of-charge, V_{an ocv} is an anode open circuit voltage, T is temperature, Cr_an is an anode C-rate, S_stat is a static resistance scaling parameter, R_c0.an is an anode constant resistance, R_{e an} is an anode current-dependent resistance, P_{e an} is a current-dependent resistance power term, V_{d an} is an anode dynamic voltage, and S_Dynan is an anode dynamic resistance scaling parameter.

The anode state-of-charge may be used to calculate a full-cell state of charge at least partially using the equation

SoCf_C relative to anode axis

Wherein SoCf_C is a full cell state-of-charge, SoC_An is the anode state-of- charge, SoC_Ca is a cathode state-of-charge, V_fcocv is a full-cell open circuit voltage, V_Min is a predefined minimum voltage threshold, V_Max is a predefined maximum voltage threshold, Off is an electrode offset and LR is a loading ratio

Another aspect provides a method of determining battery management system calibration parameters, the method including: receiving battery data at a data analysis module, the battery data including one or more parameters associated with a battery; using the data analysis module to determine one or more battery management system calibration parameters; and outputting the or each battery management system calibration parameter to a battery management system, wherein the one or more battery management system calibration parameters include at least one of: an open circuit voltage-state of charge map, a battery capacity state-of-health, or a maximum charging current limit; and wherein the data analysis module is part of a vehicle and the battery management system is also part of the vehicle.

Aspects of the present disclosure are described, by way of example only, with reference to the accompanying drawings, in which:

Figure 1 shows an example battery charging profile according to some aspects of the described technology;

Figure 2 shows a battery management system according to some aspects of the described technology;

Figure 3 shows a vehicle according to some aspects of the described technology;

Figure 4 shows battery data according to some aspects of the described technology;

Figure 5 shows a battery characterisation process according to some aspects of the described technology; Figure 6 shows a BMS calibration parameter determination process according to some aspects of the described technology;

Figure 7 shows BMS calibration parameters according to some aspects of the described technology;

Figure 8 shows half-cell potential with state-of-charge at a variety of electric currents for graphite (8a) and NMC-111 (8b) half-cells;

Figure 9 shows half-cell model and real voltage - state of charge curves for graphite electrode charge (9a), NMC electrode charge (9b), graphite electrode discharge (9c) and NMC electrode discharge (9d);

Figure 10 shows ICA curve changes from identical initial conditions for ohmic resistance (10a), anode dynamic resistance (10b) and cathode dynamic resistance (10c);

Figure 11 shows a process used to derive ageing and cell behaviour information according to some aspects of the described technology;

Figure 12 shows examples of cell stoichiometry variations including balanced stoichiometry (12a), anode offset (12b), oversized anode (12c) and oversized cathode (12d);

Figure 13 shows illustrations of cell stoichiometry (13a), full cell voltage and ICA with SoC (13b), anode half-cell voltage and ICA with SoC (13c) and cathode half-cell voltage and ICA with SoC (13d).

Figure 14 shows ICA curve changes from identical initial conditions with LLI (14a), LAMNE (14b), LAMPE (14c) and normalised change in cell capacity for each degradation mode (14d);

Figure 15 shows ICA curves at C/3 charge for sample cells at different stages of ageing; and

Figure 16 shows a system according to some aspects of the described technology.

Figure 1 shows an example of a charging profile comprising a plurality of constant voltage phases (indicated with arrows) according to some described arrangements (see the top graph of battery voltage over time during a charge cycle). Figure 1 also illustrates the reduction of charging current during the constant voltage phases and transition to constant current charging when the charging current decreases to a predetermined threshold (see the middle graph of charging current over time). The lower graph shows the state of charge of the battery over the same time period.

Figure 2 shows a battery management system 14 according to some described arrangements (which may be provided independently of, for example, a vehicle 10 and/or battery 12).

With reference to figure 3, a battery 12 and battery management system (BMS) 14 may be used in any application where it is advantageous to provide electrical power without using a mains power supply. Examples may include emergency backup power (for use in the event of a mains power failure or other failure) or uninterruptible power supplies, electric vehicles, solar power storage, portable battery packs, or provision of electrical power in locations with no access to mains electricity.

Aspects of the technology will be described specifically with reference to a battery 12 and BMS 14 in a vehicle 10, but it will be appreciated that this is illustrative only and the same teachings apply to batteries 12 and BMSs 14 in other applications too.

Accordingly, the battery 12 and BMS 14 may be mounted to (i.e. carried by) and may be part of the vehicle 10. The vehicle 10 may be an electric vehicle 10 which may be any electrically-powered vehicle, including but not limited to cars, vans, trucks, buses, lorries, motorcycles, electrically assisted pushbikes, scooters, quad bikes, all-terrain vehicles, boats, submarines, hovercraft, drones, aeroplanes (both fixed wing and/or rotary) etc. The vehicle 10 may be any vehicle 10 which may be propelled or driven by electric power. The vehicle may therefore include a motor operably coupled to the battery 12. The vehicle 10 may be a hybrid vehicle 10 further comprising an internal combustion engine or other power source (e.g. fuel cell). In some instances, the combustion engine or other power source may provide at least some of the power for propelling the vehicle 10. In some instances, the BMS 14 and battery 12 may be provided as part of a vehicle 10 but may not be used to provide power for propelling the vehicle 10, instead the BMS 14 and battery 12 may provide power for one or more auxiliary parts of the vehicle 10 (such as a crane which is part of or attached to the vehicle 10, a refrigeration unit of the vehicle 10 or attached to the vehicle 10, or the like).

In any event, the vehicle 10 may include the battery 12 and the BMS 14. The vehicle may also include a display device 16 which may be connected to the BMS 14. The display device may display information, notifications, and/or alerts from the BMS 14 to a user. The battery 12 may be configured to power directly or indirectly a means of propulsion such as a propeller, track(s) or wheel(s), for example. The BMS 14 may be configured to manage one or more operations in relation to the battery 12, including for example battery 12 usage (discharge and charging), according to one or more characteristics of the battery 12. Such characteristics may include, for example, a state-of- health (SOH) of the battery 12. Battery management performed by the BMS 14 may include management of one or more limits including maximum charge current limit, maximum discharge current limit, maximum voltage limit, minimum voltage limit, maximum charge power limit, maximum discharge power limit, etc. A maximum charge or discharge current limit may include a maximum peak charge or discharge current limit and/or a maximum continuous charge or discharge current limit. Likewise, a maximum charge or discharge power limit may include a maximum peak charge or discharge power limit and/or a maximum continuous charge or discharge power limit.

The limits managed by the BMS 14 may be defined as a function of state-of- charge, state-of-health and/or temperature. The limits may also be a function of time, with a peak limit being set for a first time period and a continuous limit being set for a second time period. The first (peak) time period may be shorter than the second (continuous) time period and the peak limit may be less restrictive than the continuous limit.

The BMS 14 may perform functions additional to those stated above. For example, the BMS 14 may determine a battery or cell state-of-charge and/or a battery or cell state-of-health. Furthermore, the BMS 14 may control the battery 12 charging profile (e.g. by controlling charge current and/or charge voltage). The charging profile may be controlled according to predetermined voltage or current limits as set out above. The BMS 14 may be calibrated with these limits at the beginning of life of the battery 12 or cell. As described in the aspects of the technology below, the BMS 14 may be recalibrated with new limits, or BMS calibration parameters, (e.g. the BMS 14 may reduce or otherwise amend the defined limits) as a function of temperature, state-of- charge or state-of-health, ensuring battery 12 safety.

In some versions, the battery or cell state-of-charge and/or battery or cell state-of-health may be determined by a remote computing device 60 (e.g. using battery measurements received from the BMS 14) - see below.

A battery SOH may be an assessment of the state of health of the battery 12 and may include one or more parameters representative of one or more aspects of the battery’s 12 operation. The one or more parameters may include capacity data and/or resistance data for the battery 12. The SOH may comprise a battery capacity state-of-health and/or a battery power fade state- of-health.

In some aspects of the described technology, a battery SOH may be determined or estimated using local computation. In other words, a battery SOH in the vehicle 10 may be determined or estimated using the BMS 14 (which is “on-board”, i.e. mounted to and carried by (or otherwise part of) the vehicle 10).

Local computation of the battery SOH may be limited in its complexity for a number of reasons (such as the availability of local computational capacity or test equipment). For example, the BMS 14 must be sized, weighted, and/or costed to fit to the vehicle 10 and the BMS 14 must be sufficiently robust to survive the expected operating environments (and lifetime) of the vehicle 10. In some cases the BMS may be supplemented by additional data logging and processing capability, which might enhance its capability for performing calculations on-board.

It is not, therefore, practical to include expensive, large, heavy, and/or complex equipment in the BMS 14 to assess the SOH of the battery 10. Likewise, with limited computational resources available in the BMS 14 simpler calculations are favourable.

Further limitations on the ability of the BMS 14 to determine or estimate a battery SOH accurately may result from, for example, limited accuracy and/or resolution of voltage, temperature or current measurement systems (which may be part of the BMS 14 and/or battery 10). Furthermore, any estimated states which may be used in determining or estimating a battery SOH, such as an estimated state-of-charge, for example, may themselves be inaccurate, introducing further inaccuracies.

In other words, reliance on local resources (e.g. the BMS 14) for determining the battery SOH imposes limitations on how that battery SOH can be determined and means that accurate battery SOH information may be impossible (or very difficult) to obtain. A further difficulty in accurately estimating or determining a battery SOH may result from the user requirements for the operational availability of the system (such as the vehicle 10) to which the battery 12 is providing power.

In particular, there may be an expectation of a high level of availability from a user of the system (such as the vehicle 10), meaning that any process of determining or estimating the battery SOH should preferably avoid inconveniencing the user by preventing use of the system or otherwise decreasing its availability (or hindering its operation substantially). For example, processes which negatively impact available battery capacity or total charging time of the battery 12 substantially should preferably be minimised or avoided. In the case of a vehicle 10, for example, users are likely to complain to manufacturers if the battery 12 takes significantly longer to charge as a result of the BMS 14 determining the battery SOH or if the range of the vehicle 10 is decreased (even temporarily) as a result of reduced available battery capacity as a result of the BMS 14 determining the battery SOH. Furthermore, battery charging profiles which include a period of battery relaxation prior to charging may cause the user to wrongly assume that there is a malfunction in the battery charging system due to the absence of immediate battery charging.

Indeed, whilst these issues are common to many applications, user expectations in relation to vehicles are particularly high - given the consumer nature of the users in many instances and the user expectations set by longstanding familiarity with vehicles powered by internal combustion engines.

Despite these challenges, there is a need for accurate battery SOH information to be determined or estimated.

For the avoidance of doubt, herein the terms “determining” and “estimating” are generally used interchangeably and refer to determining, for example, the battery SOH. Some described aspects of the technology, therefore, seek to provide battery SOH estimates without substantially inconveniencing the user of the system (such as the vehicle 10). The battery SOH may be provided as a battery power fade SOH and/or a battery capacity SOH, or a parameter determined by a combination of the two. The battery SOH may be used to control an aspect of the operation of the BMS 14 during a battery charging cycle.

In some versions (see below) the battery SOH may be determined by the remote computing device 60. Accordingly, the analysis techniques described herein may be implemented by the BMS 14 (e.g. via local or “on-board” computation) or may be implemented by the remote computing device 60 (e.g. “off-board”). Therefore, although the following techniques/analysis are described with reference to the BMS 14, it should be understood that some or all of the following techniques/analysis may be implemented by the remote computing device 60.

Batteries are conventionally charged using “constant current-constant voltage” (CC-CV) charging wherein a constant current is maintained until a pre-defined charge target voltage is reached, at which point constant voltage charging is applied, maintaining the battery voltage at the pre-defined charge target voltage while the charging current decreases to a pre-defined charge current cut-off threshold. Conventional charging is essentially a two-step process, the first step being to charge the battery at constant current, and the second step being to charge (or maintain the charge of) the battery at constant voltage.

In some aspects of the described technology a charging profile may be used to charge a battery 12 whilst also, at the same time, enabling a SOH estimation to be made. The charging profile may be determined and/or controlled by the BMS 14. For example, the BMS 14 may include a charging circuit which is configured to provide electrical power to the battery 12 to charge the battery 12 according to the charging profile. In some examples, the BMS 14 may be coupled in electrical communication with a separate charging circuit which is not part of the BMS 14. Therefore, the BMS 14 may control the charging circuit to operate in accordance with the charging profile and that profile may be defined by the BMS 14.

A charging profile is defined herein by virtue of the electrical current and voltage applied to the battery 12 over time. For the avoidance of doubt, references to “current” herein are references to “electrical current”.

The charging circuit may be of a conventional configuration and may include one or more of a rectifier and an inverter, for example. The charging circuit may, however, be controlled by the BMS 14.

The charging profile may include a plurality of constant voltage phases (wherein “phases” refers to a period of time in the charging profile). Each of the plurality of constant voltage phases may occur at a respective plurality of target battery voltages (i.e. each constant voltage phase of the plurality of constant voltage phases may be implemented when the battery voltage reaches a respective predetermined target voltage).

The duration of each of the plurality of constant voltage phases may be determined based on a charging current during the constant voltage phase or may be for a predetermined period of time, for example (see below).

Each of the plurality of constant voltage phases may be implemented such that the target voltages are generally equally spaced throughout the range of battery voltages for the charging profile (i.e. throughout a battery depth-of- discharge window). For example, the target voltages may be spaced according to a particular fraction or percentage of the battery voltage range, such as 20% intervals (e.g. if a battery has a minimum voltage of 3.3V and a maximum voltage of 4.1V, therefore having a voltage range of 0.8V, the target voltages may be spaced in increments of 0.16V). The target voltages may also be spaced according to predetermined SoC intervals, for example 20% intervals. An OCV-SoC map may be used to determine the target voltage corresponding to a predetermined SoC or SoC interval..

For example, the predetermined target voltages which trigger implementation of a constant voltage phase may be in increments of approximately 0.1V (or a value between 0.1V and 1V). These increments may be referred to as a voltage interval (which may be a predetermined voltage interval) for the predetermined target voltages - i.e. the voltage between the predetermined target voltages.

The predetermined voltage intervals may be determined with reference to a maximum voltage of the battery 12; for example, the predetermined voltage intervals may be larger for a battery 12 having a larger maximum voltage or smaller for a battery 12 having a smaller maximum voltage.

The predetermined voltage intervals may be equal across the entire charging profile or a portion of it. However, in some versions, the predetermined voltage intervals may vary across the charging profile such that the interval increases or decreases as the battery voltage increases.

The use of a greater number of constant voltage phases during the charging profile may provide more accurate SOH estimates, at the cost of longer charging times. Conversely, a charging profile having fewer constant voltage phases may provide a quicker charging time, at the cost of less accurate SOH estimates. Therefore, the number of constant voltage phases used may need to be selected dependent on the application of the battery 12 (in some situations an increased charging time may be more acceptable than others). The charging profile may include any number of constant voltage phases. A good balance between accuracy and charging time may be achieved with a charging profile including between 2 and 10 constant voltage phases, for example, such as 2, 3, 4 or 5 constant voltage phases. A charging profile may, of course, include more than 10 constant voltage phases, particularly if there are no restrictions on total charging time.

In some versions, the BMS 14 may be configured to control the charging profile to have more or fewer constant voltage phases for different charging cycles. So, for example, the majority of charging cycles may have a charging profile with fewer constant voltage phases than a minority of charging profiles (such that charging times are minimised for the majority of charging cycles but more accurate information can be obtained during a minority of the charging cycles).

The BMS 14 and/or remote computing device 60 may be configured to determine a battery SOH, including a battery capacity SOH and/or a battery power fade SOH, as part of a particular charging profile. For example, the BMS 14 may implement a charging profile which includes a battery SOH estimation. Likewise, some charging profiles may not include a SOH estimation. The BMS 14 may send battery measurements corresponding to the charging profile to the remote computing device 60 for use in the determination of the battery SOH.

The BMS 14 may determine the charging profile to be implemented in a particular charging cycle based on predetermined vehicle 10 or battery 12 use conditions, for example a distance travelled, amp hour throughput and/or elapsed period of time since the beginning-of-life of the battery 12. The BMS 14 may for example be configured to determine a battery 12 SOH (using a charging profile having a plurality of constant voltage phases) at a predetermined interval since the last determination by the BMS 14 of the battery 12 SOH (such as a distance interval, amp hour throughput interval, and/or elapsed period of time interval). Additionally, the BMS 14 may determine the charging profile to be implemented in a particular charging cycle based on the local time in the locality of the battery 12 (for example implementing a charging profile having more constant voltage phases overnight). The BMS 14 may receive an input from a remote device (e.g. remote computing device 60) which may be used by the BMS 14 to determine the charging profile to be implemented in a particular charging cycle. For example, the BMS 14 may receive a capacity or power fade SOH for the battery 12 from the remote computing device 60. The BMS 14 may implement a particular charging profile based on a disparity between a received battery SOH and a stored battery SOH, for example. Alternatively, the BMS 14 may receive an input from a remote device (which may be the remote computing device 60) which instructs the BMS 14 to implement a particular charging profile. For example, the remote device may instruct the BMS 14 to implement a particular charging profile (which may include determination of a battery SOH) when a disparity between a remote device modelled load voltage curve and/or ICA curve and a real constant-current load voltage curve and/or ICA curve falls outside a predetermined threshold.

The predetermined target voltages may be chosen to correspond to important state-of-charge regions based on battery 12 structure. In some examples, at least one predetermined target voltage may be chosen to correspond to an electrode phase change or plateau, which may be predetermined (e.g. for that type of battery or cell) by cell characterisation and/or stoichiometry analysis techniques such as Incremental Capacity Analysis (ICA).

As battery characteristics change with battery ageing, the predetermined target voltages may correspond to a different electrode state-of-charge depending on the battery 12 age. The predetermined target voltages may be recalibrated as the battery 12 ages so the recalibrated target voltages correspond to the same electrode state-of-charge regions as the predetermined target voltages. The recalibration may be based on the results of off-board computation (as described below).

In some aspects of the technology, the charging profile may be such that the battery 12 may be charged under constant current until a first target battery voltage is reached (i.e. a constant current phase).

The charging profile may be such that the battery 12 may then be charged under constant voltage until the charging current decreases to a predetermined current threshold (i.e. based on a charging current during the constant voltage phase, as mentioned above). The predetermined current threshold is less than the charging current during the constant current phase.

Choosing a low current for the predetermined current threshold may be advantageous, as resistance effects are less significant at lower currents. Furthermore, as resistance is a function of current, the application of a lower current threshold provides a larger data set from which to determine the average resistance (as described below). Despite their separate causes, resistance and capacity are difficult to separate during analysis. Constant voltage charging with a low (i.e. small) predetermined current threshold may help to alleviate this problem, as charging to a low current diminishes the influence of resistance. This means the resistance at the endpoint of each constant voltage step may have a negligible effect on open circuit voltage, therefore improving capacity estimation. The predetermined current threshold may be defined with reference to the C-Rate, and may be in the range

to — C, or — C to — C, or — C to — C (wherein “C” is the C-Rate). The charging C- Rate (or discharge C-Rate) is a measure of the rate at which a battery is charged or discharged, defined as the current through the battery divided by the theoretical charge throughput under which the battery would receive or deliver its nominal rated capacity in one hour. In some aspects of the technology, constant voltage charging may be maintained (during a constant voltage phase) until the charging current decreases to the predetermined current threshold, at which point constant current charging commences (in a constant current phase). Battery 12 open circuit voltage may be determined when the predetermined current threshold is reached. The determination of the battery 12 open circuit voltage may necessitate a small delay between the predetermined current threshold being reached and constant current charging commencing.

The charging profile may then alternate between constant current and constant voltage phases according to the number of constant voltage phases, until charging is complete or otherwise ceased.

The point at which charging is deemed to be complete may be determined by the BMS 14 and may vary in accordance with the battery SOH.

In some aspects of the technology, the number of amp hours accumulated during the constant voltage phases may be determined (e.g. by the BMS 14 and/or by the remote computing device 60 - e.g. using battery measurements received from the BMS 14) using measurements of the charging current during the constant voltage phase and its duration. This measurement may be performed by the BMS 14.

The number of amp hours accumulated may be determined (e.g. by the BMS 14 and/or remote computing device 60) according to the equation:

where V is voltage, Ah is amp hours, t is time, and T is mean current during each evaluated discrete timestep dt. The BMS 14 and/or remote computing device 60 may determine a baseline number of amp hours accumulated during constant voltage phases executed at the same plurality of target battery voltages. The baseline number of amp hours may, therefore, be associated with a charging profile which has a first number of constant voltage phases associated with a first set of predetermined target voltages and a first predetermined voltage interval (or first set of intervals).

The BMS 14 and/or remote computing device 60 may determine a battery capacity SOH using the measured number of amp hours accumulated during the constant voltage phases in a charging profile. In particular, the battery capacity SOH may be estimated by comparing the number of amp hours accumulated during the constant voltage phases of the present or most recent charge cycle, f Ah_aged, for the battery 12, with a baseline number of amp hours, f Ah_new, (wherein the present or most recent charge cycle may have had the first number of constant voltage phases associated with the first set of predetermined target voltages, and the first number (or first set) of predetermined voltage intervals). The present or most recent charge cycle may have occurred, therefore, after the charge cycle from which the baseline number of amp hours was determined.

The battery capacity SOH may be estimated (i.e. determined), by the BMS 14 and/or remote computing device 60, according to the equation:

where SoH_Cap is the battery capacity state-of-health, f Ah_aged is the measured number of amp hours accumulated during the constant voltage phases, and f Ah_new is the baseline number of amp hours. The BMS 14 and/or remote computing device 60 may estimate the battery capacity SOH by taking an average (e.g. mean) value, such as a rolling average, of the number of amp hours accumulated during the constant voltage phases in a predetermined number of the most recent charge cycles (for example, the average across the five most recent charge cycles). The number of charge cycles chosen to calculate the average (e.g. thee, seven, ten, etc.) may be chosen to strike a balance between smoothing out anomalous results and providing the most up-to-date SOH estimation. For example, an average based on a larger number of charge cycles may be less susceptible to inaccuracies due to anomalous results but may be less representative of the present characteristics of the battery 12.

The battery capacity SOH may be estimated, by the BMS 14 and/or remote computing device 60, by taking an average value, such as a rolling average, of the battery capacity SOH estimated in a predetermined number of the most recent charge cycles (for example, the average (e.g. mean) across the five most recent charge cycles). For example, if the three most recent SOH estimates were 92%, 91%, and 90%, the SOH may be averaged to 91%. The number of charge cycles chosen to calculate the average (e.g. three, seven, ten, etc.) may be chosen to strike a balance between smoothing out anomalous results and providing the most up-to-date SOH estimation. For example, an average based on a larger number of charge cycles may be less susceptible to inaccuracies due to anomalous results but may be less representative of the present characteristics of the battery 12.

In some aspects of the technology, the BMS 14 and/or remote computing device 60 determines the mean resistance of the battery 12 during the constant voltage phases. The mean resistance of the battery 12 during the constant voltage phases may be determined by the BMS 14 and/or remote computing device 60 once charging ceases or may be determined whilst the battery 12 is undergoing charging. The mean resistance of the battery 12 may be determined, by the BMS 14 and/or remote computing device 60, according to the equation:

where R is the mean resistance, V_oc is the open-circuit voltage of the battery 12, I is charging current, and t is time. In some aspects, the BMS 14 and/or remote computing device 60 may determine or otherwise have provided a baseline mean resistance of the battery 12 during constant voltage phases executed at the same target voltages or predetermined voltage interval (or set of intervals) - which may be the first interval or set. The baseline mean resistance may be determined over the same number of constant voltage phases. The baseline mean resistance may be stored in the BMS 14 and/or remote computing device 60 memory as R_New .

The open-circuit voltage of the battery 12 may be determined by the BMS 14 and/or remote computing device 60 using an open-circuit voltage map as a function of state-of-charge and temperature. The open-circuit voltage map stored in the BMS 14 and/or remote computing device 60 may be recalibrated as the battery ages using off-board computing as described below. This may improve the accuracy of the resistance calculation.

The battery power fade SOH, SoH_Pf, may be estimated, by the BMS 14 and/or remote computing device 60, using a determined mean resistance of the battery 12 during the constant voltage phases. In particular, the battery power fade SOH may be estimated by comparing the mean resistance of the battery 12 during the constant voltage phases of the present or most recent charge cycle with the baseline mean resistance of the battery 12 (the present or most recent charge cycle, used to define R_Aged, may have used the same predetermined target voltages or voltage interval or intervals as were used to determine the baseline). The battery power fade SOH may be estimated (i.e. determined) by the BMS 14 and/or remote computing device 60 according to the equation:

where SoH_Pf is the battery power fade state-of-health, R_Aged is the mean resistance of the battery 12 during the constant voltage phases, R_New is a baseline mean resistance of the battery 12 during constant voltage phases executed at the same plurality of target battery voltages, and SoH_Cap is the battery capacity state-of-health.

SoH_Pf may include SoH_Cap as indicated above to account for the faster open circuit voltage change, and consequently higher resistance estimate, at lower capacities. The capacity SoH may be temporarily reset to 100% to prevent the OCV change in the maps being influenced by the previous capacity SoH.

The battery power fade SOH may be estimated, by the BMS 14 and/or remote computing device 60, by taking an average (e.g. mean) value, such as a rolling average, of the mean resistance of the battery 12 in a predetermined number of the most recent charge cycles (for example, the average across the five most recent charge cycles). The number of charge cycles chosen to calculate the average (e.g. thee, seven, ten, etc.) may be chosen to strike a balance between smoothing out anomalous results and providing the most up-to-date SOH estimation. For example, an average based on a larger number of charge cycles may be less susceptible to inaccuracies due to anomalous results but may be less representative of the present characteristics of the battery 12.

The battery power fade SOH may be estimated, by the BMS 14 and/or remote computing device 60, by taking an average (e.g. mean) value, such as a rolling average, of the battery power fade SOH determined in a predetermined number of the most recent charge cycles (for example, the average across the five most recent charge cycles). For example, if the three most recent SOH estimates were 92%, 91%, and 90%, the SOH may be averaged to 91%. The number of charge cycles chosen to calculate the average (e.g. three, seven, ten, etc.) may be chosen to strike a balance between smoothing out anomalous results and providing the most up-to-date SOH estimation. For example, an average based on a larger number of charge cycles may be less susceptible to inaccuracies due to anomalous results but may be less representative of the present characteristics of the battery 12.

The baseline values may be obtained, by the BMS 14 and/or remote computing device 60, for any of the characteristics determined from measurements (e.g. of battery voltage and/or current) during the constant voltage phases. Baseline values may include a baseline number of amp hours accumulated during constant voltage phases executed at the same predetermined voltage interval or intervals (i.e. plurality of target battery voltages) used in a subsequent charging profile and/or a baseline mean resistance of a battery 12 during constant voltage phases executed at the same predetermined voltage interval or intervals (i.e. plurality of target battery voltages) used in a subsequent charging profile and/or a baseline relative ratio of constant current and constant voltage phases of a charging profile. The baseline values may be determined over the same number of constant voltage phases used in a subsequent charging profile.

The baseline values may be obtained, by the BMS 14 and/or remote computing device 60, from the battery 12 when the battery 12 meets certain age criteria (e.g. a “new” battery). The age criteria may include a certain number of charge cycles and/or a calendar age. For example, the baseline values may be obtained from the battery 12 when the battery 12 has undergone fewer than five charge cycles and/or has a calendar age of less than one month. In particular, the baseline values may be obtained from the battery 12 and that battery 12 may then subsequently be analysed using any of the methods described herein.

In some aspects of the technology, baseline values may be determined in situ by the BMS 14 and/or remote computing device 60. For example, the BMS 14 and/or remote computing device 60 may record a first set of results (e.g. number of amp hours accumulated and/or mean battery resistance) obtained from the battery 12 as a baseline for that battery 12. The baseline values may be an average of a predetermined number of results (for example, the average (e.g. mean) of the first three sets of results obtained from that battery 12).

In some aspects of the technology, baseline values may be predetermined for a particular type or structure of battery 12 and supplied to a BMS 14 and/or remote computing device 60 for use with any battery 12 of that type or structure. Such arrangements may be useful in second-life applications, for example, in which an aged battery 12 may be repurposed for a new application. In situ baselines obtained from an aged battery 12 may not be representative of 100% battery SOH, due to the battery 12 age and possible SOH decline.

The battery capacity SOH and/or battery power fade SOH may be sent to a display device 16 by the BMS 14 and/or remote computing device 60 for presentation to a user.

In some aspects of the technology, the relative ratios of the constant current and constant voltage phases of the charging profile may be monitored by the BMS 14 and/or remote computing device 60. A baseline relative ratio may be determined and the monitoring of the relative ratios may include the determination of the deviation of the relative ratios from the baseline ratio. A predetermined tolerance (e.g. 10%) may be set for the deviation of the ratios from the baseline ratio. A battery capacity state-of-health determined by a data analysis module and a battery capacity state-of-health determined by the battery management system 14 may be weighted based upon the relative ratios. The weight assigned to the battery capacity state-of-health determined by the BMS 14 may be reduced when the relative ratios fall outside the predetermined tolerance. The battery capacity SOH and/or battery power fade SOH may also be monitored by the BMS 14 and/or remote computing device 60.

A user may be notified - e.g. via a display device communicatively coupled to the BMS 14 and/or remote computing device 60 and configured to display information to the user regarding the operation of the BMS 14 - if the battery capacity SOH or battery power fade SOH fall below a predetermined threshold. The display device may be the on-board display device 16 or may be a remote display device communicatively coupled to the BMS 14 and/or remote computing device 60. The threshold may be defined relative to baseline measurements where the baseline measurements represent 100% SOH (e.g. if a battery SOH falls below 75%). In some cases a notification may be additionally or alternatively issued to a remote user (e.g. an engineer or other service personnel) via a remote display device (possibly via remote computing device 60).

In some aspects of the technology the methods described herein may be performed only in a predetermined battery temperature range. The BMS 14 may, therefore, include a battery temperature sensor configured to determine the battery temperature. The BMS 14 may be configured to send the battery temperature measurements to the remote computing device 60. The remote computing device 60 may, therefore, be configured to receive the battery temperature measurements. The inclusion of a temperature criterion may lead to improved SOH estimation accuracy. The temperature range may be defined as an absolute temperature range, for example 10-40 °C. The temperature range may be defined based on cell characterisation data and/or an optimum operating temperature range for the particular battery 12.

In some aspects of the technology a minimum threshold for state-of-charge increase during battery 12 charging may be used by the BMS 14 and/or remote computing device 60, wherein the battery state-of-charge must increase by at least the threshold amount in order for a SOH estimate to be made and/or to be treated as valid. For example, the threshold state-of- charge increase may be in the range 5% to 50%. For example, the threshold may be 10% state-of-charge increase. The inclusion of such a threshold may improve SOH estimation accuracy by discounting data obtained from an insufficient sample size. An initial state-of-charge threshold may also be set such that a SOH estimate is only made and/or treated as valid if a battery 12 charging profile begins below the state-of-charge threshold. For example, the initial state-of-charge threshold may be 70%, such that battery SOH is not estimated, or the estimate is not treated as valid, if the battery state-of-charge was above 70% when charging commenced.

The BMS 14 and/or remote computing device 60 may include a processor which is configured to execute instructions in order to perform the methods described herein. The processor may be coupled for communication with a computer readable medium (which may be part of the BMS 14 and/or remote computing device 60 or provided separately) for storing those instructions for execution. The processor may be communicatively coupled to or include a charger for the battery 12 and may be configured to receive, from the charger, information such as a charging current and voltage. The processor may additionally or alternatively be configured to transmit, to the charger or onboard generator, information such as battery charge voltage and/or current demand based on the implemented charging profile. The processor may be further communicatively coupled to the charger to allow the processor to control the charger based on the methods described. The processor may be communicatively coupled to other components of the BMS 14 and/or remote computing device 60 which may include a computer memory and the like to enable the execution of the instructions.

Some aspects include the computer readable medium, storing instructions which, when executed by a processor, cause the performance of any of the methods described herein.

Derivations of the equations used in some aspects of the technology are provided below.

The equation:

may be derived from Ohm’s law as follows.

Ohm’s law:

Differentiate both sides with respect to time and rationalise to get instantaneous resistance calculation: dV dV_oc dR _ -dt --d _ dV dV_oc dt di di di dt

Re-integrate rationalised equation

Make discrete:

Constant voltage charging condition: dV = 0, therefore effective mean resistance:

There are benefits to using the method described above for calculating mean resistance. Ohm’s law is calculated based on the voltage differential due to resistance against current, but in normal operation there may be uncertainty in open circuit voltage based on possible state-of-charge error. This means voltage differential due to resistance, and therefore resistance, may not be calculated accurately. The method described herein may overcome this problem by calculating the rate of change of voltage relative to open circuit voltage with current. Although the open circuit voltage is sensitive to state-of-

charge (SoC), the ^dV°^c gradient and therefore the gradient is relatively d(SoC) dl flat in the typical useable SoC range of the CC-CV capacity and power fadeSoH estimation algorithm. This means Ohm’s law may be applied without substantial error from open circuit voltage uncertainty due to state-of-charge estimation error. The use of gradient may also reduce the error due to inaccuracy in voltage and current sensing. Averaging across a sample may reduce random error, and the ratio nature of SoH may minimise systematic error.

Figure 1 illustrates the application of the charging profile described herein to a 28Ah NMC/graphite sample cell. The techniques described herein (e.g. estimation of battery capacity SOH and battery power fade SOH) were tested on the sample cell when new and when the sample cell had been aged for 9 months using the Federal Urban Driving Schedule (FUDS) drive cycle. The sample cell was tested using a Hardware-in-the-Loop setup, starting at 10% SoC and charged using a charging profile comprising a plurality of constant voltage phases (in particular five constant voltage phases) until a SoC of 85% was reached. A second set of tests were conducted to evaluate the accuracy of the SOH estimates with partial charging starting from 40% SoC to the same endpoint. Characterisation tests were also performed with high accuracy current, voltage and temperature sensing. A capacity test was performed on the sample cell when new and when aged with C/50 constant voltage discharge and charge to provide a true capacity estimate. Hybrid Pulse Power Characterisation (HPPC) tests were also performed, with long relaxation periods every 10% SoC for resistance estimation with respect to SoC. The resistance across the SoC range was taken from the average of the relaxation pulses as shown in tables 1a and 1b. The resistances were calculated from the difference between the load and open circuit voltages using Ohm’s law.

Table 1a shows the resistance results at different SoC for the new sample cell from characterisation testing. Table 1b shows the resistance results at different SoC for the aged sample cell from identical characterisation testing. Table 2 compares the estimated capacity SOH to real test results and Table 3 compares the estimated power fade SoH to real test results for the full and partial charge test conditions. The capacity results have estimation difference (A) of <1.5% for both full and partial charge cases. The power fade SoH estimation A is 4.63% for full charge and 7.7% for partial charge as shown in Table 3.

Table 1a: Resistance from HPPC tests for new cell

Table 1b: Resistance from HPPC tests for aged cell

Table 2: Capacity SOH estimates vs real values

Table 3: Power fade SOH estimates vs real values

The results show cell resistance increased by approximately 46% with ageing, which may impact the capacity estimate by affecting the number of amp hours accumulated during the constant voltage charge phases. To assess this, the ratio of CC-CV charging was evaluated for the full and partial charging test scenarios with results shown in Table 4. It was found that while absolute amp hour throughput decreased in both regions, as expected due to capacity change, the ratio between them remained very similar. This means the capacity estimation remains accurate despite the resistance change by ensuring repeatability of capacity estimation over the same constant voltage phases, even if the charging starts at different SoC points.

Table 4: CC-CV ratios for full and partial charging of new and aged sample cell

Whilst some aspects have been described with reference to operations performed by the BMS 14 which may be part of the vehicle 10, for example, it is also possible - in some arrangements - for the analysis (or parts thereof) described herein to be performed remotely from the BMS 14 and, in some instances, from the vehicle 10.

In some such arrangements, therefore, there may be provided a remote computing device 60 (see figure 16) which is communicatively coupled (e.g. via a wired or wireless communications link) to the BMS 14. This communicative coupling may be via a network 70 which may include a local area network and/or a wide area network and/or which may include a mobile telephone network, for example. The network 70 may include the Internet. A single remote computing device 60 may be communicatively coupled to multiple BMSs 14 (as depicted in figure 16).

The remote computing device 60 may be any device which is remote from the BMS 14 and may connect to the BMS 14 via a wired or wireless communications link. For example, the remote computing device 60 may be a cloud computing device or may be a portable tool which connects to the BMS 14 via a wired communications link. As such the BMS 14 may include a communication unit which may be a network interface card and/or modem, for example.

The BMS 14 may be configured to send measurements (for example voltage or current measurements) to the remote computing device 60. The measurements may therefore be referred to as battery measurements, and may include voltage, current, and/or temperature measurements for the battery 12. In particular, the battery measurements may include measurements of battery voltage and/or charging current and/or temperature over time (see e.g. Fig. 1). The battery measurements may therefore include associated time measurements.

The BMS 14 may be configured to receive information from the remote computing device 60 and that received information may have been determined by the remote computing device 60 based at least in part on the measurements sent by the BMS 14.

The remote computing device 60 may, therefore, be configured to determine a battery SOH using some or all of the techniques described above (e.g. using the battery measurements sent by the BMS 14). For example, the remote computing device 60 may be configured to determine the battery capacity SOH and/or the battery power fade SOH. The remote computing device 60 may be configured to send the determined battery SOH (e.g. battery capacity SOH and/or battery power fade SOH) to the BMS 14. The BMS 14 may be configured to use the battery SOH (e.g. battery capacity SOH and/or battery power fade SOH) received from the remote computing device 60 to control an aspect of the operation of the BMS 14 during a battery charging cycle as described herein. In some versions, the determined battery SOH (e.g. battery capacity SOH and/or battery power fade SOH) may be used in a simulation or model, such as a vehicle simulation or model. The simulation or model may, therefore, simulate or model the impacts of the battery SOH on other components of a test system (e.g. vehicle). For example, the impacts of the battery SOH on an associated motor, regenerative braking system, or HVAC (heating, ventilation, and air conditioning) system may be simulated or modelled.

The remote computing device 60 may determine cell stoichiometry, open circuit voltage and/or an initial resistance estimate while the BMS 14 may determine battery 12 resistance at several SoC points. In some versions, as described above, the remote computing device may determine the battery 12 resistance at several SoC points using battery measurements received from the BMS 14. The remote computing device 60 may determine individual electrode resistances using this data through ICA and/or load voltage curve optimisation. The anode resistance may be used to determine a maximum charging current limit as described in more detail below.

For example, with the above described processes in mind, the remote computing device 60 may determine the battery SOH using current and voltage measurements (and timing information) sent by the BMS 14 to the remote computing device 60.

In general, the use of the remote computing device 60 resolves some of the issues of limited computational resources of the BMS 14. However, in some instances, the use of the remote computing device 60 may allow information to be collated in relation to a large number of different batteries 12 (i.e. from a plurality of different BMSs 14) and to perform calculations to provide information to one or more of the BMSs 14 based on the collated information. Moreover, the remote computing device 60 may have more data storage capacity than the BMS 14 and so may be able to analyse a greater volume of data - which may be data associated with multiple batteries 12 or from a single battery 12 over a longer period of time than possible by the BMS 14 alone. In some versions, as described in further detail below, data which may be uploaded from the BMS 14 to the remote computing device 60 may include information which identifies the battery 12 (e.g. battery identification data). The remote computing device 60 may use the battery identification data to associate battery data with a particular battery. This may be particularly useful in second-life battery applications, (e.g. when a particular battery 12 is transferred from a first device having a first BMS, to a second device having a second BMS) by enabling the remote computing device 60 to associate battery data uploaded by the second BMS with battery data uploaded by the first BMS for the same battery. The remote computing device 60 may, therefore, store a history of battery data for a particular battery 12 which is independent of the BMS 14.

The remote computing device 60 may be a server, for example. The remote computing device 60 may include a plurality of computing devices and may be provided as a cloud computing device.

Calculations and analysis which is performed remotely from the vehicle 10 (and/or the BMS 14) may be referred to herein as “off-board”.

Off-board analysis may lead to improved accuracy in parameter estimates, faster data processing, and/or the ability to determine more complex battery characteristics or parameters, for example.

Although the BMS 14 typically has limited resources, it will be understood that the off-board analysis described herein may equally be implemented by a BMS 14 or other on-board computer if the BMS 14 or on-board computer has sufficient processing power. For example, an autonomous vehicle may have sufficient processing power to perform the methods described herein in relation to off-board processing.

One example of an application in which off-board analysis may be advantageous is fast charging of batteries 12, which is particularly sensitive to battery 12 ageing. Fast charging of Li-ion batteries 12, in particular, comes with a significant risk of lithium plating, which occurs when the anode voltage decreases below 0V Li/Li+. Defining a charge current limit that maintains the anode voltage close to 0V Li/Li+ may ensure the battery 12 is charged at or approaching the fastest possible rate without compromising safety. However, the anode voltage is not directly observable during charging cycles, and its relationship with current, state-of-charge, and temperature, changes significantly with battery 12 ageing. Computationally demanding analysis techniques may be implemented using off-board analysis to determine a maximum charging current limit, for example.

In some aspects of this technology the BMS 14 configured to perform any method described above may be calibrated with a maximum charging current limit determined by any of the methods described below. However, a BMS 14 calibrated with a maximum charging current limit determined by any of the methods described below may not perform the above methods.

Additionally, electrochemical cell behaviour, including in Li-ion cells, can change in other complex ways, with the open circuit voltage-state of charge (OCV-SoC) relationship, transient voltage reaction to current, temperature dependency of capacity and resistance, and cell relaxation time to open circuit voltage (OCV) after usage all possibly changing with battery 12 ageing. A change in any of these characteristics may affect the relevance of the original calibration of BMS 14. It is desirable, therefore, to determine (i.e. monitor and quantify) any changes in characteristics which may affect the performance of the BMS 14.

The BMS 14 may be calibrated with various battery 12 data or parameters at its start of life. However, the BMS 14 may have only limited ability, or even no ability, to update or adapt these parameters as the battery 12 ages. In cases in which the BMS 14 is able to adapt these parameters, such adaptation may be typically based on local, or on-board, parameter estimates, which may have limited accuracy due to limited local processing power, sensing accuracy, and/or data acquisition and storage capability, for example. The use of remote or off-board analysis may provide improved accuracy due to an increase in computing power and/or data storage capability, for example.

An off-board analysis approach may be used in some aspects of the technology described herein to quantify battery parameters and calibrate (or recalibrate) the BMS 14. This may lead to improved battery 12 management, including for example faster and/or safer fast charging throughout a battery 12 lifetime, and prolongation of battery 12 life through adaptation of battery 12 control.

In some aspects of the technology, the determination of BMS 14 calibration parameters may be performed according to the methods described herein using local computational resources of the BMS 14. However, the use of remote computational resources of the remote computing device 60 may be advantageous, for example by enabling the use of simpler, cheaper computing hardware in the BMS 14, as complex computational analysis is handled remotely. The use of the remote computing device 60 may also allow for more complex and robust approaches, considering extra aspects such as error/un certainty estimates and use of more sophisticated approaches from multiple data aspects. For example, during charging of the battery 12 or at some other convenient time, the BMS 14 may connect to a wireless communications network (such as a Wi-Fi network at the location where the battery 12 is charged or a mobile telephone network). The wireless communications network provides a communicative coupling to the remote computing device 60 (for example, over the internet). In some versions, the BMS 14 may connect to a charging station over a wired or wireless communication link and the charging station may then connect to a network (which may include the internet 70) to provide the communicative coupling to the remote computing device 60. Data (such as measurements of, for example, voltage and current along with durations, and/or information about the charging profile and/or the local temperature, and/or capacity SOH, and/or power fade SOH, and/or resistance data which may be determined by the BMS 14 as described previously) may be uploaded from the BMS 14 to the remote computing device 60 using the communicative coupling. The data may also include information which identifies one or more of the user, the vehicle 10, the battery 12, the type of vehicle 10, the type of battery 12, and the like.

An exemplary BMS 14 calibration parameter determination process 40 is illustrated in figure 6. The process 40 may be implemented using a data analysis module. The data analysis module may be implemented using, for example, a set of machine readable instructions which are executable by a processor and that processor may be part of the BMS 14 or the remote computing device 60. In some versions, parts of the data analysis module are implemented by the BMS 14 and parts by the remote computing device 60. In other words, the data analysis module may be on-board (for example incorporated into the BMS 14) or off-board (i.e. remotely implemented) or may be split between on-board and off-board (i.e. split between the BMS 14 and remote computing device 60). The data analysis module may be used to determine BMS calibration parameters (e.g. 501 , 502, 503).

In some aspects of the technology, battery data 20 may be obtained for the battery 12 (e.g. from the BMS 14) and provided to the data analysis module (see figure 4) and this may be over the aforementioned communicative coupling, for example.

The battery data 20 may include one or more of: battery constant-current charge current and voltage data 201 , battery open circuit voltage data 202, battery capacity state-of-health data 203, battery resistance data 204, battery relaxation event data 205 (a relaxation event 205 may include a relaxation of current to zero or near-zero), battery temperature data 206, battery state-of- charge data 207, or battery current data 208. All of the battery data 20 may be provided to the data analysis module or a subset of the battery data 20 may be provided to the data analysis module. In general, more accurate results may be obtained by providing more of battery data 20 to the data analysis module. The battery data 20 may also in some versions include battery power fade state-of-health data and/or battery voltage data. The battery power fade SOH data may be determined by the BMS 14 as described above.

The battery constant-current charge current and voltage data 201 may be determined by the BMS 14 during a charging profile which does not include a battery SOH estimate or a plurality of constant voltage phases - i.e. the battery constant-current charge current and voltage data 201 may be obtained during a charging profile including a single constant voltage phase (e.g. a conventional CC-CV charging profile). The battery capacity state-of-health data 203 and the battery resistance data 204 may be obtained using the CC- CV charging profile and analysis described above, for example by the BMS 14. Battery voltage, temperature or current data may be measured (i.e. obtained) by the BMS 14 (and, in particular, by an on-board electronic control unit (ECU) which may be part of the BMS 14). In some versions, the ECU is not part of the BMS 14 but is separately provided and is configured to communicate with the BMS 14 over a wired or wireless link provided, for example, on the vehicle 10 (if the battery 12 is in a vehicle 10 in such examples) or other system of which the battery 12 is a part.

The battery data 20 may be transmitted from the BMS 14 (and/or the ECU) to the data analysis module. Accordingly, the BMS 14 (and/or the ECU) and the data analysis module may be communicatively coupled by a wired or wireless communications link - see the above description in relation to the communicative coupling, for example.

In some aspects of the technology, new battery 12 (or cell) characterisation data, which may be known as baseline battery characterisation data, may be provided to the data analysis module. This baseline battery characterisation data may be provided by the BMS 14 (and/or the ECU) and/or may be provided from experimental results for that battery 12 or type of battery 12, for example (and may be provided by a further computing device communicatively coupled to the remote computing device 60 and/or the BMS 14 (in the same manner as the communicative coupling described above) and which may be associated with a test facility and/or battery manufacturer).

Baseline battery characterisation data may be used to determine at least one BMS 14 calibration parameter. Baseline battery characterisation data may include at least one of: half-cell voltage curves (for the positive and negative electrodes), initial cell stoichiometry data, battery voltage limits, battery current limits, full cell load voltage curve, full cell open circuit voltage curve, or a useable electrode state-of-charge range. The half-cell voltage curves may be voltage curves with lithiation, current and/or temperature. The characterisation data may also include static and/or dynamic resistance scaling parameters for each electrode half-cell voltage curve. The initial cell stoichiometry data may include an initial offset and/or loading ratio as defined herein. The half-cell voltage curves may be a set of half-cell voltage curves.

An example new battery characterisation process 30 is illustrated in figure 5.

The characterisation process 30 may include determination of: individual electrode characterisation 30a, half-cell voltage curves with lithiation, current and/or temperature 301 , cell voltage limits 304, estimated initial electrode usage in full cell cycling from simulated OCV (a useable electrode state-of- charge range) 303, full cell characterisation (using time and/or frequency domain methods such as hybrid pulse power characterisation or electrochemical impedance spectroscopy) 30c, characterised baseline incremental capacity analysis (ICA) data 30d (e.g. from constant-current cycling, optionally at different currents and temperatures), initial cell stoichiometry data 302, and/or open circuit voltage - state-of-charge maps with temperature 30e.

The initial cell stoichiometry data 302 may include an initial offset, an initial loading ratio and/or initial half-cell resistance scaling parameters. The initial cell stoichiometry data 302 may be determined using stoichiometry modelling by curve fitting the stoichiometry model to characterised baseline ICA data 30d. The stoichiometry model may be populated with data obtained from the half-cell voltage curves 301. The initial cell stoichiometry data 302 may be determined at a plurality of temperatures.

The determination of BMS 14 calibration parameters, by the data analysis module, may comprise a number of steps as illustrated in figure 6.

Battery constant-current charge current and voltage data 201 may be used to create a real ICA curve or curves 40a. In a step 40b, half-cell voltage curves with lithiation, current and/or temperature 301 , initial cell stoichiometry data

302, battery temperature data 206 and/or battery resistance data 204 may be used with ICA curve 40a to fit a cell stoichiometry model comparing real and simulated ICA curves to determine ageing mode data, cell stoichiometry data and resistance scaling parameters^ Stoichiometry ageing mode data 401 and/or electrode resistance change data 402 may be determined and quantified using the results of step 40b. The stoichiometry ageing mode data 401 may include LLI (loss of lithium), LAMPE (loss of cathode active material) and/or LAMNE (loss of anode active material) parameters. The electrode resistance change data 402 may include a state-of-charge independent resistance scaling parameter and/or a state-of-charge dependent anode resistance scaling parameter and/or a state-of-charge dependent cathode resistance scaling parameter.

A battery stoichiometry parameter may include a LLI, LAMPE, and/or LAMNE parameter, for example.

In a step 40c, relaxation event data 205, temperature data 206 and/or stoichiometry ageing mode data 401 may be used to generate a full cell OCV- SoC curve. This may be used to output an OCV-SoC BMS calibration parameter 501 , which may be an OCV-SoC map.

In particular, an OCV-SOC map may be determined by fitting a modelled ICA curve to a real ICA curve using electrode half-cell data and initial cell stoichiometry data. In this process, offset and loading ratio may be determined and used to determine the OCV-SOC map.

In a step 40d, cell voltage limits 304, estimated initial electrode usage in full cell cycling from simulated OCV (a useable electrode state-of-charge range)

303, stoichiometry ageing mode data 401 and battery capacity state-of-health data 203 may be used to estimate a relative battery capacity which may be output as a battery 12 capacity state-of-health BMS 14 calibration parameter 502.

In a step 40e, half -cell voltage curves with lithiation, current and/or temperature 301 may be used with electrode resistance change data 402 to create an anode load voltage map with state-of-charge, current, and/or temperature. In particular, the resistance change data 402 may include the state-of-charge independent resistance scaling parameter, and/or the state-of- charge dependent anode resistance scaling parameter.

In a step 40f, the maximum charge current limit for the anode may be determined. In a step 40g, the anode current limit may be used with the stoichiometry ageing mode data 401 and initial cell stoichiometry data 302 to convert the anode current limit to a full-cell current limit. This may be used to output a maximum charging current limit BMS 14 calibration parameter 503.

In some aspects of the technology, the maximum charging current limit may be set to ensure the anode voltage does not drop below 0 V vs Li/Li⁺. In some examples, a cell other than a Li-ion cell may be used, for example a lithiumsulfur cell or lithium battery cells with a solid state electrolyte, so any reference to lithium may be replaced as necessary to reflect the structure of the alternative cell type.

Figure 7 illustrates BMS 14 calibration parameters 50 which may be determined by the data analysis module. The BMS 14 calibration parameters may include one or more of an open circuit voltage - state of charge (OCV- SoC) map 501, a battery capacity state-of-health 502, and a maximum charging current limit 503. The maximum charging current limit 503 may be a maximum charging current limit map as a function of state-of-charge and/or temperature. The parameters described above may be derived using a combination of halfcell and full-cell modelling. A data analysis module may determine at least one battery stoichiometry parameter, which may be used to determine at least one BMS calibration parameter. The battery stoichiometry parameter may be determined by half-cell and/or full-cell modelling.

In half-cell modelling, the creation of physically representative simulated load voltage curves may be underpinned by accurate characteristic representations of each electrode. A first step in the creation of such curves may be to identify the electrode chemistries and obtain representative raw data. In some aspects of the technology, the electrodes may be cycled (e.g. using half-cell cycling with a lithium counter-electrode) in such a manner as to obtain their constant load characteristics under a range of currents and temperatures, as shown for example in Figure 8. To obtain better accuracy and expand the resistance modelling capability of individual electrodes, a more complex electrode cycling programme using dynamic testing methods such as EIS or current interrupt may be used.

Simulated load voltage curves may be constructed from a combination of electrode OCV and impedance data. The impedance contribution may be split into its constituent component parts, which may include diffusion, ohmic, and charge transfer contributions for example. The impedance contribution could alternatively be split based on parameter dependence such as state-of-charge or temperature dependence. The model may be employed through dismantling and cycling of a target battery 12 or cell’s specific electrode materials, or at the risk of an accuracy penalty, a generic library of electrode data for different designs and chemistries may be built and used to provide reference information for a chosen target battery 12 or cell.

A half-cell voltage may be estimated based on an OCV map and three distinct resistance terms as shown in equation B2, which describes half-cell voltage based on half-cell OCV and static and dynamic resistance terms. The OCV- SoC relationship for each electrode may be derived from the average of the lowest current charge and discharge curves from electrode cycling (see figure 8) as shown in equation B1. The resistance terms may include a constant resistance R_c0, a resistance and current power scaling term for estimating current-dependent but SoC-independent resistance R_e and a voltage map V_d representing the influence of SoC and current dependent resistance. To account for varying behaviour with current direction, resistance terms may be calculated separately for charge and discharge.

V_{ocv e} represents electrode open circuit voltage, SoC represents electrode state-of-charge, V_{Lowest c}, charge represents the lowest current charge voltage curve, V_{Lowest c}, Discharge represents the lowest current discharge voltage curve, V_e represents electrode voltage, Cr_ceu represents the cell C-rate, P_e represents a current dependent resistance power term, T represents temperature and Cr represents C-rate.

Coefficients in equation B2 may be determined using parameter optimisation on individual electrode characterisation data (e.g. electrode load voltage data) and may include global and/or local optimisation methods such as particle swarm optimisation, for example. The error between model data and real data may be minimised using optimisation goals such as minimisation of root-mean- square-error (RMSE) or mean absolute error (MAE). An example model fitting is shown in figure 9, which depicts half-cell model fittings (i.e. simulated load voltage curves) against real voltage curves for graphite electrode charging (9a), NMC electrode charging (9b), graphite electrode discharge (9c) and NMC electrode discharge (9d). “C” indicates the C-rate and “S” indicates the simulated curves.

Full-cell modelling may incorporate results obtained from half-cell modelling as described above. Full-cell modelling may include the creation of full-cell load voltage and/or ICA curves. .

In some aspects of the technology, the stoichiometric relationship between electrodes in a battery or cell may be defined using a loading ratio (LR) (equation B3) and offset (equation B4). Cell stoichiometry data may be used to determine the lithiation, and resultant behaviour, of each electrode relative to the defined full-cell state-of-charge, thereby enabling modelling of full-cell behaviour. The LR gives the relative capacity of the electrodes, which defines the relative change in lithiation for each based on full-cell current application. The offset gives the misalignment of the electrodes, indicating the lithiation state of the anode when the cathode is fully lithiated i.e. cathode SoC at 0% anode SoC. Taking one electrode as a reference, for example the cathode, the relative SoC of the anode based on the cathode reference scale can be calculated based on the loading ratio and offset as shown by equation B5.

(B4) Offset(Ofn = SoC_Ca SoC_An = 0)

(B5) SoC_An = (SoC_Ca * LR) + Of f where LR is the loading ratio, C_an is the anode capacity, C_ca is the cathode capacity, SoC_Ca is the state-of-charge of the cathode, and SoC_An is the state-of- charge of the anode. In some aspects of the technology the relative C-Rate each electrode is subjected to may also be quantified, and may be used in the generation of half-cell simulated load voltage curves. In some aspects of the technology where the cathode is the reference electrode, the modelled C-Rate matches the full cell as shown in equation B6 with the anode C-Rate being scaled by the LR as shown in equation B7 to account for the relative electrode sizes and therefore expected current densities. In alternative aspects of the technology the anode may be used as the reference electrode.

The resistive behaviour of each electrode may not match the corresponding characterised electrode curves, and may change over time. To account for this, in some aspects of the technology resistance scaling parameters may be introduced based on SoC-independent (static) and SoC-dependent (dynamic) resistances. The static resistance scaling may be applied using a single parameter S_stat which applies to both electrodes. Figure 10 illustrates ICA curve changes from identical initial conditions with ohmic resistance change (10a), change in anode dynamic behaviour (10b) and change in cathode dynamic behaviour (10c). A dynamic resistance change may affect the full-cell curve differently for each electrode, as shown in Figure 10, so a separate scaling parameter may be implemented for the anode, S_Dynan, and cathode, S_{Dyn ca}. This may lead to the anode voltage equation B9 and cathode voltage equation B8 after incorporating the scaling parameters to the generic half-cell voltage equation B2. In this case, the S_stat parameter serves to scale the magnitude of the static resistances, while the S_Dynan and S_{Dyn ca} parameters scale the C-Rate used for the dynamic voltage maps, to simulate different magnitude behaviour based on the electrodes’ changing sensitivity to applied current.

(B6) Cr_ca = Cr_cell

(B7) Cr_an = ^

where T represents temperature, Cr_ca represents cathode C-rate, Cr_ceu represents cell C-rate, Cr_an represents anode C-rate, LR represents loading ratio, V_ca represents cathode voltage, SoC_Ca represents cathode state-of- charge, V_caocv represents cathode open circuit voltage, S_stat represents a static resistance scaling parameter, R_c0,ca represents cathode constant resistance, R_{e ca} represents cathode current-dependent resistance, P_e, ca represents a cathode current-dependent resistance power term, V_{d ca} represents cathode dynamic voltage, S_Dynca represents a cathode scaling parameter, V_An represents anode voltage, SoC_An represents anode state-of- charge, V_{an ocv} represents anode open circuit voltage, R_c0.an represents anode constant resistance, R_{e an} represents anode current-dependent resistance, P_e, an represents an anode current-dependent resistance power term, V_{d an} represents anode dynamic voltage, and S_Dynan represents an anode scaling parameter.

The resistance scaling parameters may initially be calculated through ICA optimisation to characterised baseline ICA data 30d. Subsequently, they can be updated through ICA optimisation to ICA data obtained from current and voltage data from the BMS 14 during battery 12 charge (said current and voltage data 201 first being converted to ICA data).

In some aspects of the technology, LLI, LAMPE and LAMNE parameters and their effects on cell offset and LR may be modelled. The LR may be adjusted by the relative degradation of each electrode through equation B10. For the offset, it may be assumed in some aspects of the technology that LLI happens entirely due to solid electrolyte interphase (SEI) layer formation during charging of the battery 12. When this occurs, the SoC of the cathode increases through delithiation, but the lithium does not cause the anode SoC to increase, with the lithium instead becoming part of the SEI composition. This causes the anode to shift to a higher SoC relative to the cathode, as the cathode SoC is higher relative to that of the anode. With LAMPE, it is assumed the shift is in the opposite direction. This is because as LAMPE reduces cathode capacity, the cathode remains the reference electrode and so the relative anode size along the rescaled cathode state-of-charge axis expands due to a shift in the LR. To retain the original alignment with absolute lithium balance, the offset may be adjusted to shift the anode to a lower relative cathode SoC to compensate. A correction for offset with degradation according to some aspects of the technology is shown in equation B11.

The adjustment of the LR and offset does not address the case in which the overall cell capacity is reduced without affecting cell stoichiometry parameters. In this case, for the same applied cell level current, the electrodes will see a higher current density, affecting load potentials. This may be accounted for as shown in equation B12 and equation B13. With the cathode being the reference, scaling the C-Rate modelling by LAMPE adjusts the cathode C-rate, and the anode C-rate may be adjusted by a combination of LAMPE and LR.

equation B10 Loading Ratio adjustment with ageing

(B11) Off_AgeX = Off_Baseline + LLI - LAMPE equation B11 Offset adjustment with ageing

equation B12 Cathode C-rate adjustment with ageing

equation B13 Anode C-rate adjustment with ageing

LR_AgeX represents loading ratio at the evaluated ageing interval, which may correspond to a particular month in some aspects of the technology; LR_Baseiine represents an initial or baseline loading ratio, LAMNE represents loss of anode active material, LAMPE represents loss of cathode active material, Off_AgeX represents offset at the evaluated ageing interval, which may correspond to a particular month in some aspects of the technology; Off_Baseiine represents an initial or baseline offset, LLI represents loss of lithium, and Cr_{ca AgeX} represents cathode C-rate at the evaluated ageing interval, which may be a particular month in some aspects of the technology. In the above, LAMNE, LAMPE and LLI are expressed in the form of percentage degradation. It will be understood that they could alternatively be converted into fractions rather than percentages.

In some aspects of the technology, a flow process as illustrated in figure 11 may be used to derive key ageing and cell behaviour information using ICA. The process may include a characterisation stage 60 comprising determination of real half-cell electrode curves (anode and cathode) 601. The half-cell electrode curves (anode and cathode) 601 may therefore comprise the individual electrode characterisation 30a. At a step 602, these curves may be used to determine key parameters, including for example SoC-independent resistance, SoC-resistance maps, and/or electrode SoC-OCV maps. A parameter determined in the step 602 may be the anode load voltage map with state-of-charge, current and/or temperature used in step 40e. The process may also include lifetime input data 61. Lifetime input data 61 may be derived from on-board measurements (e.g of voltage and/or current) and/or characterisation data, for example by the BMS 14. The lifetime input data 61 may include initial constant current tests producing full-cell constantcurrent charge curve data 611 which may lead to initial ICA curves 615. Lifetime constant current tests producing full cell constant-current charge curve data 612 may lead to lifetime ICA curves 616. The constant-current charge curve data 611 may, therefore, comprise the battery constant-current charge current and voltage data 201 or full cell characterisation data 30c. The constant-current charge curve data 612 may, therefore, comprise the battery constant-current charge current and voltage data 201. The initial ICA curves 615 may, therefore, comprise the characterised baseline ICA 30d. The lifetime ICA curves 616 may comprise the real ICA curve 40a.

The lifetime input data 61 may further include relative battery 12 capacity 613 (e.g. battery capacity SOH), which may be obtained by the BMS 14 using the charging profiles described above. The relative battery capacity 613 may therefore comprise the battery capacity state-of-health data 203. The lifetime input data 61 may further comprise localised mean resistance measurements 614 which may be obtained by the BMS using the charging profiles described above. The localised mean resistance measurements 614 may therefore comprise the battery resistance data 204.

The intervals at which lifetime input data 61 is obtained may be based on time intervals and/or charge throughput intervals. The intervals may not be linearly spaced, instead being determined by the reaching of one or more thresholds for battery capacity SOH and/or battery power fade SOH as determined by the BMS 14 using the charging profiles described above. The intervals may also include a time or charge throughput tolerance based on opportunity to ascertain the on-board data. A simulation and optimisation process 62 may comprise a plurality of steps 621-624. At a step 621 an ICA model may be populated with half-cell data which may include any of the key parameters determined in step 602. At a step 622 initial cell stoichiometry data (e.g. offset, loading ratio) and initial resistance scaling parameters may be determined by optimising a model fit to the initial ICA curves 615 . . The step 622 may therefore determine the initial cell stoichiometry data 302. At a step 623, ageing mode parameters (e.g. LLI, LAMNE, LAMPE parameters) and resistance scaling parameters may be determined by optimising a model fit to lifetime ICA curves 616. The step 623 may therefore correspond to the step 40b. At a step 624, the ageing mode parameters and resistance scaling parameters may be cross-correlated with the relative battery capacity 613 and localised mean resistance measurements 614 respectively to verify accuracy.

Outputs may be generated at a step 63. The outputs may include capacity state-of-health 631 , OCV-SoC map 632, ageing mode parameters (such as LLI, LAMPE and/or LAMNE parameters) 633 and resistance scaling parameters 634. The capacity SOH 631 may comprise the battery capacity SOH BMS calibration parameter 502. The OCV-SoC map 632 may comprise the OCV-SoC BMS calibration parameter 501. The ageing mode parameters 633 may comprise the stoichiometry ageing mode data 401 and may be used in the step 40g to determine the maximum charging current limit BMS 14 calibration parameter 503. The resistance scaling parameters 634 may comprise the electrode resistance change data 402.

To facilitate the process in Figure 11 the stoichiometry model may generate an estimate of load voltage and subsequently ICA, cell OCV with full-cell SoC, and/or an estimate of cell capacity relative to when the cell was new. The generated electrode half-cell voltage curves from equation B8 and equation B9 may be aligned based on reference cathode SoC to determine load voltage and OCV from equation B14 and equation B15. In both cases, the anode may be related to the cathode by the SoC relation in equation B5, using the regions of the anode accessible to the cathode and vice-versa. The voltage and OCV curves may then be scaled to the full cell SoC definition relative to the cathode full cell definition through equation B20 to allow comparison with the real data. The load voltage curve may then be treated as a real voltage curve for ICA comparison.

The full-cell model OCV curve may be used for validation against real OCV points, and also as the basis for capacity SOH estimation. The capacity of the full cell may be calculated based on the OCV model result to eliminate the influence of resistance, making it the highest theoretical capacity of the cell. The useable SoC range of the full cell curve, referenced to the cathode SoC axis, may be found by defining the points at which the OCV curve intersects the minimum and maximum cell voltage limits through equation B16. This may then be compared to initial or baseline results for a given cell which normalises the results to show the relative capacity to new through equation B17, using LAMPE to account for the reduced capacity in the reference cathode SoC axis.

(B14) V_fc = V_ca - interp(SoC_An, V_An,SoC_Ca) equation B14 Full cell voltage from half cell voltages

(B15) V_fCiOCV V_{ca ocv} i-ⁿi^erP(.SoC_An, V_{An ocv}, SoC_Ca) equation B15 Full cell OCV from half cell OCVs

equation B16 Accessible SoC based on FC OCV SoC range within the cell voltage limits

equation B17 Relative capacity based on accessible SoC range and rescaling of cathode axis due to LAMPE

V_fc represents full cell voltage, V_ca represents cathode voltage, SoC_An represents anode state-of-charge, V_An represents anode voltage, SoC_Ca represents cathode state-of-charge, V_{fc ocv} represents full cell open circuit voltage, V_{ca ocv} represents cathode open circuit voltage, V_Anocv represents anode open circuit voltage, SoC_Acc represents an accessible state-of-charge range, V_Max represents a maximum voltage limit, V_Min represents a minimum voltage limit, AgeX represents an ageing interval which may correspond to a particular battery age in some aspects of the technology, and Baseline represents an initial result which may be obtained before cell cycling.

The half-cell and full-cell modelling approaches described above may be used to derive cell stoichiometry parameters from cell voltage, current and temperature data. Cell voltage, current and temperature data may be measured by an ECU which may be a part of the BMS 14. The outputs of halfcell and full-cell models may be used to calibrate (or recalibrate) a BMS. However, cell stoichiometry parameters typically cannot be directly input to a BMS, with the BMS instead requiring parameters in the form of estimated cell capacity or capacity SoH, OCV-SOC maps, or maximum charging current limits for example.

Cell capacity SoH and cell OCV-SOC maps may be determined from cell stoichiometry parameters via equations B17 and the combination of equations B15 and B16 respectively. Uncertainties may be introduced due to sensor resolution and noise, data transmitting, internal cell temperature deviations and possible modelling mis-fits. The accuracy/reliability of the cell capacity SoH and cell OCV may be improved by cross-validating these outputs with equivalent local or on-board results. For example, the capacity SoH may be cross-referenced or compared to the estimated capacity SoH determined through the CC-CV charging profile described above (by a BMS, for example). Alternatively, the estimated capacity SoH may be used as a reference input for relative capacity in a dual-criteria optimisation in which ageing modes are fitted to both ICA curves and relative capacity.

OCV estimation may be validated by cross-referencing relaxation events (e.g. when current relaxes to zero) and a corresponding OCV value. Uncertainty in OCV may be quantified by comparing relaxation-based OCV values to expected OCV values based on cell stoichiometry at a given SoC and temperature.

In some aspects of the technology, maximum charging current limits may be determined. Such limits may be defined in the case of a Li-ion battery such that the anode voltage does not drop below 0 V vs Li/Li⁺, which is known to cause lithium plating. An anode voltage at a particular SoC, current and/or temperature may be calculated using parameters obtained directly or indirectly from cell stoichiometry information or data, such as anode resistance scaling and anode OCV relative to full cell SoC, for example. In particular, an anode model may be used to derive a maximum charging current limit as a function of anode SoC by rearranging equation B9 to equation B18. The limits of equation B18 are defined to ensure the anode voltage stays above 0V Li/Li+. This may provide an anode C-rate limit with anode SoC. The conversion of anode current limit to cell current limit may be performed through the rearrangement of equation B7 to equation B19. The anode SoC is relative to the cathode SoC axis when the cathode is used as the reference electrode, which in turn is in a different scale to the full cell SoC axis. The full cell SoC may be rescaled based on the accessible cathode SoC, expressed via equation B20. The cathode SoC relationship to the anode may be determined by rearranging equation B5 into equation B21. By substituting equation B21 into equation B20, the relationship between full cell and anode SoC may be determined in equation B22, which allows scaling of equation B19 to give the current limits relative to cell level magnitude and SoC.

equation B18 Anode current limit calculation based on anode voltage limit before lithium plating occurs.

equation B19 Cell current limit with anode SoC based on anode current limit and relevant cell stoichiometry factors

equation B20 Full cell SoC relative to cathode SoC

equation B22 Full Cell SoC relative to anode SoC

Cr_max,an represents maximum anode C-rate, SoC_an represents anode state-of- charge, V_{an ocv} represents anode open circuit voltage, Cr_an represents anode C-rate, S_stat represents a static resistance scaling parameter, R_c0.an represents anode constant resistance, R_{e an} represents anode current-dependent resistance, P_{e an} represents a current-dependent resistance power term, V_{d an} represents anode dynamic voltage, S_Dynan represents an anode dynamic resistance scaling parameter, Cr_ceu represents cell C-rate, LAMPE represents loss of cathode active material, SoCf_C represents full cell state-of-charge, SoC_Ca represents cathode state-of-charge, V_{fc ocv} represents full cell open circuit voltage, V_Min represents minimum voltage limit, V_Max represents maximum voltage limit, Off represents offset, and LR represents loading ratio.

In some versions, in order to determine the anode potential above Ov vs Li/Li+ the data analysis module (which may be implemented using remote computing device 60) may adjust the individual electrode resistance scaling parameters, degradation/ageing modes and/or full cell degradation/ageing mode parameters (e.g. LLI, LAMNE and/or LAMPE parameters) using parameter optimisation to realign baseline/initial parameters (e.g. initial stoichiometry and/or resistance scaling parameters) through adapting the modelled ICA curve relative to real ICA derived from on-board current and voltage measurements, which then allows emulation of the change in cell stoichiometry over lifetime and therefore updating of the charge current limits.

The effects of cell stoichiometry in a Li-ion cell are illustrated in figure 12, wherein the upper curve represents a cathode potential curve and the lower curve represents an anode potential curve in all cases. In figure 12a, a balanced cell with anode and cathode of equal capacity and perfect alignment is illustrated, with the cell potential, i.e. the cathode potential minus the anode potential, being represented by the double-headed arrow. However, in reality, electrochemical cells are often not perfectly balanced. One potential imbalance in cell stoichiometry, anode offset, is illustrated in figure 12b. In this case, the relative lithiation of each electrode may be misaligned. This may affect the full cell OCV as the shift of the curves alters their respective lithiation with full cell SoC. It may also influence capacity by limiting useable active materials of each electrode. The other aspect in which electrodes may vary is in their relative capacity, i.e. one electrode may be oversized relative to the other as shown in figure 12c (oversized anode) and 12d (oversized cathode). In this case, the relative lithiation change of each electrode during charge /discharge differs, with the larger electrode being less cycled, affecting the SoC-OCV relationship and amount of electrode materials utilised. In commercial cells it is likely both imperfect alignment and sizing will be present.

Cell stoichiometry is affected by cell ageing. Ageing can reduce the capacity of both electrodes and change their offset. Furthermore, behavioural changes such as OCV profiles with SoC, available capacity, accessible electrode lithiation range, and resistance relationship with SoC may depend on changes in cell stoichiometry. In some aspects of the technology, therefore, a method for quantifying the cell stoichiometry and stoichiometry changes with ageing is applied. Cell stoichiometry may be quantified using electrode models and ICA.

ICA is a technique which enables the determination of cell stoichiometry information from voltage and capacity data during constant-current charge. An ICA curve may be constructed via the differentiation of SoC with respect to voltage as shown in equation B24, where SoC represents cell state-of-charge, and V represents cell voltage.

A characteristic profile for a particular target cell may be obtained by evaluating a constant current ICA and/or cell voltage curve over a full SoC range as shown in figure 13b. A benefit of ICA is its ability to emphasise characteristic anode and/or cathode voltage plateaus, as shown in Figure 13 c) and d) for the anode and cathode respectively (see arrows). Full cell behaviour may be influenced by features of the anode, cathode and cell stoichiometry, including for example the relative lithiation alignment of the electrodes and their relative capacities, as shown in figure 13a, where the upper curve represents the cathode and the lower curve represents the anode. The offset (middle double headed arrow) and loading ratio (upper and lower double headed arrows) are schematically depicted in figure 13a. The properties of the individual electrodes and their interaction through cell stoichiometry combine to form a unique ICA curve. With knowledge of electrode properties (e.g. obtained through half-cell characterisation or modelling), it is therefore possible to use ICA to ascertain cell stoichiometry properties.

Three modes of ageing which may be found in Li-ion cells are LLI, LAMNE and LAMPE. LLI arises mainly from layer formation in the cell and may cause a change in electrode offset by delithiating one electrode without lithiating the other. LAMNE and LAMPE reduce the capacity of each electrode to store lithium, therefore affecting the electrode loading ratio in opposing ways, as well as affecting electrode offset. As shown in Figure 14, each of these ageing mode parameters (LLI, LAMPE or LAMNE parameters) affects the ICA curve in distinct ways. The effects of LLI are illustrated in figure 14a, with the effects of LAMNE being shown in figure 14b and the effects of LAMPE being shown in figure 14c. Also shown in Figure 14d is the capacity evolution of each degradation mechanism. It can be seen from this that multiple degradation paths may lead to the same relative capacity SOH however each path changes the ICA curve uniquely. By determining cell stoichiometry changes through ageing mode parameters, the resultant changes in OCV-SoC relationship can be more accurately determined.

In some aspects of the technology, an automated process may be used to identify initial cell conditions (such as initial cell stoichiometry data) and determine ageing mode parameters (such as LLI, LAMNE and/or LAMPE parameters) by evaluation of ICA curves at one or more ageing intervals relative to the initial conditions. This process is depicted in figure 11.

In some aspects of the technology, ICA curves may be created from constant current data obtained via characterisation testing or by the BMS 14. These curves may be used as a target profile which a simulation model must fit. The constant current data may include constant current charge or discharge profiles. Constant current charge tests may be particularly suitable for automotive applications. A lower current condition may be advantageous in reducing resistance effects.

Example ICA curves are shown in figure 15 for nine sample cells under initial conditions (MO) and after ageing for one month (M1), four months (M4), six months (M6) and nine months (M9).

The optimisation aspect of the overall ICA-based stoichiometry evaluation strategy shown in figure 11 may be thought of as being split into two sections: initial stoichiometry parameter definition and ageing evaluation. Each stage may alter different parameters, as shown in table 1 .

Table 1: Parameter Variation with Ageing Analysis

Data obtained from cell characterisation testing or baseline on-board constant current load voltage profiles prior to cell ageing (baseline data) may be used to define the initial offset and LR through fitting of the cell stoichiometry model simulated ICA curve to the baseline ICA curve. After these parameters have been defined, a second optimisation may use the relative capacity and aged ICA curves defined above as part of a dual-criteria optimisation in which the ageing modes are varied to fit to both the aged ICA curves and the relative capacities. In some aspects of the technology, during both stages of the optimisation, the static and dynamic resistance scaling parameters may vary as they are likely to account first for the changes between the electrodes within the cell and the reference data, and then for the changes in the resistance behaviour with ageing. Optimisation may be performed using global optimisation such as particle swarm optimisation. An objective of the optimisation may be to minimise the disparity, for example using RMSE, between the real and simulated ICA curve voltages, and/or to minimise the disparity between the real and simulated relative capacities. RMSE or MAE may be used in the optimisation.

In some aspects of the technology, the half-cell curves and cell stoichiometry parameters may be modelled and used to fit to the constant current load curves directly. This may include ICA curve fitting using half-cell and cell stoichiometry models as described previously, with one or more of the fixed and variable parameters shown in table 1. However, in such aspects of the technology, instead of converting the real and simulated voltage curves into ICA for optimisation, the real and simulated voltage curves may be matched directly based on cell stoichiometry, resistance and degradation changes.

The accuracy of the resistance scaling parameters determined by the ICA optimisation approach can be improved by fitting to real ICA curves at different current magnitudes. This can be implemented by having different charging current setpoints performed during characterisation and during lifetime onboard the vehicle. In an illustrative example, maximum charging current limits may be determined by a data analysis module and provided to the BMS 14. The data analysis module may use incremental capacity analysis (ICA) to determine the maximum charging current limits.

Half-cell electrode curves obtained at a variety of currents may be used to fit a half-cell model to provide accurate representations of electrode data with current and SoC. This can be combined with cell offset, loading ratio and resistance scaling parameters to create a full-cell model. Baseline measurements may be taken to create a baseline full-cell model. The baseline model may be adjusted to account for battery ageing by the inclusion of LLI, LAMNE and/or LAMPE parameters and/or by redefining the resistance scaling parameters. Anode load curves with current may be constructed from the models to determine maximum anode charging current limits. The loading ratio and offset may then be used to redefine the anode charging current limits in terms of full-cell charging current limits. The maximum charging current limits may be determined as a function of temperature and/or SoC. The maximum charging current limits may be provided to the BMS 14, therefore enabling safe fast charging of the battery 12.

Representative features are set out in the following aspects, which stand alone or may be combined, in any combination, with one or more features disclosed in the text and/or drawings of the specification.

A1 . A battery management system configured to: control a charging profile of a battery during a first battery charging cycle wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determine the number of amp hours accumulated during the constant voltage phases; determine a battery capacity state-of-health using the number of amp hours accumulated during the constant voltage phases; and use the battery capacity state-of-health to control an aspect of the operation of the battery management system during a second battery charging cycle.

A2. A battery management system according to aspect A1 , wherein the battery capacity state-of-health is determined according to the equation:

A3. A battery management system according to aspect A1 or A2, further configured to: determine a mean resistance of the battery during the constant voltage phases; determine battery power fade state-of health using the mean resistance of the battery during the constant voltage phases; and use the battery power fade state-of-health to control an aspect of the operation of the battery management system during the second battery charging cycle.

A4. A battery management system according to aspect A3, wherein the battery power fade state-of-health is determined according to the equation:

A5. A battery management system according to any of aspects A3 to A4, wherein the mean resistance of the battery is determined according to the equation:

A6. A battery management system according to any preceding aspect wherein the number of amp hours accumulated is determined according to the equation:

A7. A battery management system according to any preceding aspect, wherein there are at least three constant voltage phases, at least four constant voltage phases, or at least five constant voltage phases.

A8. A battery management system according to any preceding aspect, wherein at least one target battery voltage corresponds to an electrode phase change or plateau. A9. A battery management system according to any preceding aspect, wherein each constant voltage phase is maintained until a charging current decreases to a predetermined threshold.

A10. A battery management system according to aspect A9, wherein the p ^rredetermined threshold is in the range — 10 C to — 100 C or — 10 C to — 50 C.

A11. A battery management system according to any preceding aspect, wherein the charging profile comprises a plurality of constant current phases.

A12. A battery management system according to aspect A11 , further configured to monitor the relative ratios of the constant current and constant voltage phases of the charging profile.

A13. A battery management system according to aspect A12, further configured to issue a notification to a user if the relative ratios fall outside a predetermined range.

A14. A battery management system according to any preceding aspect, wherein the aspect of the operation of the battery management system includes controlling at least one of maximum charge current limit, maximum discharge current limit, maximum voltage limit, minimum voltage limit, maximum charge power limit, or maximum discharge power limit.

A15. A battery management system according to aspect A14 wherein the maximum charge current limit, maximum discharge current limit, maximum voltage limit, minimum voltage limit, maximum charge power limit, or maximum discharge power limit is defined as a function of state-of-charge and/or temperature. A16. A battery management system according to any preceding aspect, further configured to send the battery capacity state-of-health to a display device for presentation to a user and/or to a remote data analysis module.

A17. A battery management system according to aspect A3, further configured to send the battery power fade state-of-health to a display device for presentation to a user and/or to a remote data analysis module.

A18. A vehicle including a battery management system according to any preceding aspect.

A19. A method of operating a battery management system, the method comprising: controlling a charging profile of a battery during a first battery charging cycle wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determining the number of amp hours accumulated during the constant voltage phases; determining a battery capacity state-of-health using the number of amp hours accumulated during the constant voltage phases; and using the battery capacity state-of-health to control an aspect of the operation of the battery management system during a second battery charging cycle.

A20. A method according to aspect A19, further including: determining a mean resistance of the battery during the constant voltage phases; determining battery power fade state-of health using the mean resistance of the battery during the constant voltage phases; and using the battery power fade state-of-health to control an aspect of the operation of the battery management system during the second battery charging cycle.

A21 . A computer readable medium storing instructions which, when executed by a processor, cause the performance of the method of aspect A20.

B1. A method of determining battery management system calibration parameters, the method including: receiving battery data at a data analysis module, the battery data including one or more parameters associated with a battery; using the data analysis module to determine one or more battery management system calibration parameters; and outputting the or each battery management system calibration parameter to a remote battery management system, the remote battery management system being remote from the data analysis module, wherein the one or more battery management system calibration parameters include at least one of: an open circuit voltage-state of charge map, a battery capacity state-of-health, or a maximum charging current limit.

B2. A method according to aspect B1 , further including: transmitting the battery data from the remote battery management system to the data analysis module.

B3. A method according to aspect B2, wherein transmitting the battery data from the remote battery management system to the data analysis module, includes transmitting the battery data from the remote battery management system which is part of a vehicle.

B4. A method according to any of aspects B1 to B3, wherein the battery data includes at least one of: battery constant-current charge current and voltage data, battery open circuit voltage data, battery capacity state-of-health data, battery power fade state-of-health data, battery voltage data, battery resistance data, battery relaxation event data, battery temperature data, battery state-of-charge data, or battery current data.

B5. A method according to any of aspects B1 to B4, wherein the remote battery management system and the data analysis module are communicatively coupled by a network including the internet.

B6. A method according to any of aspects B1 to B5, wherein baseline battery characterisation data is used to determine at least one battery management system calibration parameter.

B7. A method according to aspect B6, wherein the baseline battery characterisation data includes at least one of a half cell voltage curve, full cell load voltage curve, full cell open circuit voltage curve, or battery voltage limits.

B8. A method according to any of aspects B1 to B7, wherein the battery is a lithium-ion battery.

B9. A method according to any of aspects B1 to B8, wherein the data analysis module determines at least one battery stoichiometry parameter, which is used to determine at least one battery management system calibration parameter.

B10. A method according to any of aspects B1 to B9, wherein a battery capacity state-of-health is at least partially calculated using the equation: 100 — LAMPE\ - I

100 / wherein Relative Capacity Age X) is the battery capacity state-of- health at a particular battery age X, SoC_{AccAge X} is an accessible state-of- charge range at the battery age X, SoC_{Acc Baseiine} is an initial accessible state- of-charge range, and LAMPE is a loss of cathode active material as a percentage of initial cathode capacity.

B11. A method according to any of aspects B1 to B10, wherein a battery open circuit voltage, used to determine at least part of the open circuit voltage-state of charge map, is at least partially calculated using the equation:

wherein V_fcocv is a full-cell open circuit voltage, V_caocv is a cathode open circuit voltage, SoC_An is an anode state-of-charge, V_Anocv is an anode open circuit voltage and SoC_Ca is a cathode state-of-charge.

B12. A method according to any of aspects B1 to B11 , wherein a maximum charging current limit is at least partially calculated using the equation:

B13. A method according to aspect B12, wherein the maximum anode C-rate is at least partially calculated using the equation: Cr_max,an f SoC_an, T) charge

wherein Cr„,„_r„„ is the maximum anode C-rate, SoC_n„ is an anode state-of-charge, V_{an ocv} is an anode open circuit voltage, T is temperature, Cr_an is an anode C-rate, S_stat is a static resistance scaling parameter, R_c0.an is an anode constant resistance, R_{e an} is an anode current-dependent resistance, P_{e an} is a current-dependent resistance power term, V_{d an} is an anode dynamic voltage, and S_Dynan is an anode dynamic resistance scaling parameter.

B14. A method according to any of aspects B12 to B13, wherein the anode state-of-charge is used to calculate a full-cell state of charge at least partially using the equation

SoCf_C relative to anode axis

B15. A method according to any of aspects B1 to B14, the method including receiving and collating a plurality of battery data at the data analysis module from a plurality of battery management systems, and using the collated battery data to determine at least one battery management system calibration parameter. B16. A method according to any of aspects B1 to B15, the method including receiving a battery capacity state-of-health determined by the remote battery management system according to any of aspects A1 to A17 at the data analysis module, wherein the battery capacity state-of-health calibration parameter is determined by calculating the mean of a battery capacity state-of- health determined by the data analysis module and the battery capacity state- of-health determined by the battery management system, .

B17. A method according to aspect B16 wherein the battery capacity state- of-health determined by the data analysis module and the battery capacity state-of-health determined by the battery management system are weighted based upon the relative ratios of the constant current and constant voltage phases of the charging profile.

B18. A method according to aspect B17 wherein the weight assigned to the battery capacity state-of-health determined by the BMS is reduced when the relative ratios fall outside a predetermined tolerance.

B19. A method according to aspect B4 when dependent on aspect B2 wherein the battery capacity state-of-health data is a battery capacity state-of- health obtained by the battery management system by: controlling a charging profile of the battery during a first battery charging cycle wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determining the number of amp hours accumulated during the constant voltage phases; and determining a battery capacity state-of-health using the number of amp hours accumulated during the constant voltage phases. B20. A method according to aspect B4 when dependent on aspect B2 wherein the battery resistance data is a mean battery resistance obtained by the remote battery management system by: controlling a charging profile of the battery during a first battery charging cycle wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determining the number of amp hours accumulated during the constant voltage phases; and determining a mean resistance of the battery during the constant voltage phases.

B21. A method according to any preceding aspect wherein the open circuit voltage - state of charge map battery management system calibration parameter is determined at least partially using battery relaxation event data, battery temperature data, and stoichiometry ageing mode data.

B22. A method according to any preceding aspect wherein the battery capacity state-of-health battery management system calibration parameter is determined at least partially using cell voltage limits, a useable electrode state- of-charge range, stoichiometry ageing mode data and battery capacity state- of-health data.

B23. A method according to any preceding aspect wherein the maximum charging current limit battery management system calibration parameter is determined at least partially using stoichiometry ageing mode data, half-cell voltage curves with lithiation, current and/or temperature, and electrode resistance change data.

B24. A method according to aspect B23 wherein the electrode resistance change data includes at least one of a state-of-charge independent resistance scaling parameter, and/or a state-of-charge dependent anode resistance scaling parameter and/or a state-of-charge dependent cathode resistance scaling parameter..

B25. A data analysis module configured to: receive battery data, the battery data including one or more parameters associated with a battery; determine one or more battery management system calibration parameters; and output the or each battery management system calibration parameter to a remote battery management system, the remote battery management system being remote from the data analysis module, wherein the one or more battery management system calibration parameters include at least one of: an open circuit voltage-state of charge map, a battery capacity state-of-health, or a maximum charging current limit.

B26. A method of calibrating a battery management system, the method including: sending battery data to a remote data analysis module, the battery data including one or more parameters associated with a battery and the remote data analysis module being remote from the battery management system; using the data analysis module to determine one or more battery management system calibration parameters; receiving the or each battery management system calibration parameter at the battery management system; and calibrating the battery management system with the or each battery management system calibration parameter, wherein the one or more battery management system calibration parameters include at least one of: an open circuit voltage-state of charge map, a battery capacity state-of-health, or a maximum charging current limit. B27. A method of determining a maximum charging current limit for fast charging a battery, the method including: receiving battery data including parameters associated with the battery at a data analysis module, the parameters including stoichiometry ageing mode data, half-cell voltage curves with lithiation, current and/or temperature, and electrode resistance change data; using the data analysis module to determine a maximum charging current limit battery management system calibration parameter; and outputting the maximum charging current limit battery management system calibration parameter to a remote battery management system, the remote battery management system being remote from the data analysis module.

B28. A method according to aspect B27 wherein the electrode resistance change data includes at least one of a state-of-charge independent resistance scaling parameter, and/or a state-of-charge dependent anode resistance scaling parameter and/or a state-of-charge dependent cathode resistance scaling parameter.

B29. A method according to aspect B27 or B28 wherein the stoichiometry ageing mode data includes at least one of a loss of lithium (LLI) parameter, a loss of cathode active material (LAMPE) parameter or a loss of anode active material (LAMNE) parameter.

B30. A method according to any of aspects B27 to B29 wherein the maximum charging current limit is at least partially calculated using the equation:

wherein Cr_cen is a maximum cell C-rate, SoC_An is an anode state-of- charge, '

is a maximum anode C-rate, > LAMPE is a loss of cathode active material as a percentage of original cathode capacity and LR is a loading ratio.

B31. A method according to aspect B30, wherein the maximum anode C-rate is at least partially calculated using the equation:

Cr_max,an f SoC_an, T) charge

wherein Cr„,„_r„„ is the maximum anode C-rate, SoC_nrl is an anode state-of-charge, V_{an ocv} is an anode open circuit voltage, T is temperature, Cr_an is an anode C-rate, S_stat is a static resistance scaling parameter, R_c0.an is an anode constant resistance, R_{e an} is an anode current-dependent resistance, P_e, an is a current-dependent resistance power term, V_{d an} is an anode dynamic voltage, and S_Dynan is an anode dynamic resistance scaling parameter.

B32. A method of determining battery management system calibration parameters, the method including: receiving battery data at a data analysis module, the battery data including one or more parameters associated with a battery; using the data analysis module to determine one or more battery management system calibration parameters; and outputting the or each battery management system calibration parameter to a battery management system, wherein the one or more battery management system calibration parameters include at least one of: an open circuit voltage-state of charge map, a battery capacity state-of-health, or a maximum charging current limit; and wherein the data analysis module is part of a vehicle and the battery management system is also part of the vehicle.

When used in this specification and claims, the terms "comprises" and "comprising" and variations thereof mean that the specified features, steps or integers are included. The terms are not to be interpreted to exclude the presence of other features, steps or components.

The features disclosed in the foregoing description, or the following claims, or the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for attaining the disclosed result, as appropriate, may, separately, or in any combination of such features, be utilised for realising the invention in diverse forms thereof. Although certain example embodiments of the invention have been described, the scope of the appended claims is not intended to be limited solely to these embodiments. The claims are to be construed literally, purposively, and/or to encompass equivalents.

Claims

86 Claims

1. A system including one or more devices configured to: receive battery measurements corresponding to a charging profile of a battery during a first battery charging cycle, wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determine the number of amp hours accumulated during the constant voltage phases; and determine a battery capacity state-of-health using the number of amp hours accumulated during the constant voltage phases.

2. A system according to claim 1 , further configured to use the battery capacity state-of-health to control an aspect of the operation of the system during a second battery charging cycle.

3. A system according to any preceding claim, wherein the one or more devices include a battery management system and/or a remote computing device.

4. A system according to claim 3, wherein the one or more devices include the battery management system and the remote computing device, and the battery management system is configured to send the battery measurements to the remote computing device.

4. A system according to any of claims 3-4 including the battery management system, wherein the battery management system is further configured to control the charging profile of the battery during the first battery charging cycle. 87

5. A system according to any preceding claim, wherein the battery capacity state-of-health is determined according to the equation:

6. A system according to any preceding claim, further configured to: determine a mean resistance of the battery during the constant voltage phases; and determine battery power fade state-of health using the mean resistance of the battery during the constant voltage phases.

7. A system according to claim 6 when dependent on claim 2, further configured to use the battery power fade state-of-health to control an aspect of the operation of the system during the second battery charging cycle.

8. A system according to claim 6 or 7, wherein the battery power fade state-of-health is determined according to the equation:

wherein SoH_Pf is the battery power fade state-of-health, R_Aged is the mean resistance of the battery during the constant voltage phases, R_New is a baseline mean resistance of the battery during constant voltage phases executed at the same plurality of target battery voltages, and SoH_Cap is the battery capacity state-of-health. 88

9. A system according to any of claims 6 to 8, wherein the mean resistance of the battery is determined according to the equation:

10. A system according to any preceding claim wherein the number of amp hours accumulated is determined according to the equation:

11. A system according to any preceding claim, wherein at least one target battery voltage corresponds to an electrode phase change or plateau.

12. A system according to any preceding claim, wherein each constant voltage phase is maintained until a charging current decreases to a predetermined threshold.

13. A system according to claim 12, wherein the predetermined threshold is in the rang ³e — 10 C to — 100 C or — 10 C to — 50 C.

14. A system according to any preceding claim, wherein the charging profile comprises a plurality of constant current phases. 89

15. A system according to claim 14, further configured to monitor the relative ratios of the constant current and constant voltage phases of the charging profile.

16. A system according to claim 2 or any of claims 3-15 when dependent on claim 2, wherein controlling the aspect of the operation of the system includes controlling at least one of a maximum charge current limit, maximum discharge current limit, maximum voltage limit, minimum voltage limit, maximum charge power limit, or maximum discharge power limit.

17. A system according to any preceding claim, further configured to send the battery capacity state-of-health to a display device for presentation to a user and/or to a remote data analysis module.

18. A system according to claim 6 or any of claims 7-17 when dependent on claim 6, further configured to send the battery power fade state-of-health to a display device for presentation to a user and/or to a remote data analysis module.

19. A method of operating a system including one or more devices, the method comprising: receiving battery measurements corresponding to a charging profile of a battery during a first battery charging cycle wherein the charging profile comprises a plurality of constant voltage phases executed at a plurality of target battery voltages; determining the number of amp hours accumulated during the constant voltage phases; and determining a battery capacity state-of-health using the number of amp hours accumulated during the constant voltage phases. 90

20. A method according to claim 19, further including using the battery capacity state-of-health to control an aspect of the operation of the system during a second battery charging cycle.

21. A method according to claim 19 or 20, further including: determining a mean resistance of the battery during the constant voltage phases; and determining battery power fade state-of health using the mean resistance of the battery during the constant voltage phases.

22. A method according to claim 21 when dependent on claim 20, further including using the battery power fade state-of-health to control an aspect of the operation of the system during the second battery charging cycle.

23. A computer readable medium storing instructions which, when executed by a processor, cause the performance of the method of any of claims 19-22.

24. A method of determining battery management system calibration parameters, the method including: receiving battery data at a data analysis module, the battery data including one or more parameters associated with a battery; using the data analysis module to determine one or more battery management system calibration parameters; and outputting the or each battery management system calibration parameter to a remote battery management system, the remote battery management system being remote from the data analysis module, wherein the one or more battery management system calibration parameters include at least one of: an open circuit voltage-state of charge map, a battery capacity state-of-health, or a maximum charging current limit. 91

25. A method according to claim 24, further including: transmitting the battery data from the remote battery management system to the data analysis module.

26. A method according to claim 25, wherein transmitting the battery data from the remote battery management system to the data analysis module, includes transmitting the battery data from the remote battery management system which is part of a vehicle.

27. A method according to any of claims 24 to 26, wherein the battery data includes at least one of: battery constant-current charge current and voltage data, battery open circuit voltage data, battery capacity state-of-health data, battery power fade state-of-health data, battery voltage data, battery resistance data, battery relaxation event data, battery temperature data, battery state-of-charge data, or battery current data.

28. A method according to any of claims 24 to 27, wherein the remote battery management system and the data analysis module are communicatively coupled by a network including the internet.

29. A method according to any of claims 24 to 28, wherein baseline battery characterisation data is used to determine at least one battery management system calibration parameter.

30. A method according to claim 29, wherein the baseline battery characterisation data includes at least one of a half cell voltage curve , full cell load voltage curve, full cell open circuit voltage curve, or battery voltage limits.

31. A method according to any of claims 24 to 30, wherein the battery is a lithium-ion battery. 92

32. A method according to any of claims 24 to 31 , wherein the data analysis module determines at least one battery stoichiometry parameter, which is used to determine at least one battery management system calibration parameter.

33. A method according to any of claims 24 to 32, wherein a battery capacity state-of-health is at least partially calculated using the equation:

wherein Relative Capacity Age X) is the battery capacity state-of- health at a particular battery age X, SoC_{AccAge X} is an accessible state-of- charge range at the battery age X, SoC_{Acc Baseiine} is an initial accessible state- of-charge range, and LAMPE is a loss of cathode active material as a percentage of initial cathode capacity.

34. A method according to any of claims 24 to 33, wherein a battery open circuit voltage, used to determine at least part of the open circuit voltage-state of charge map, is at least partially calculated using the equation:

35. A method according to any of claims 24 to 34, wherein a maximum charging current limit is at least partially calculated using the equation: 100 - LAMPE\

100 / 93 wherein Cr_ceu is a maximum cell C-rate, SoC_An is an anode state-of- charge, Cr_{mnx nr}, is a maximum anode C-rate, LAMPE is a loss of cathode active material as a percentage of initial cathode capacity and LR is a loading ratio.

36. A method according to claim 31 , wherein the maximum anode C-rate is at least partially calculated using the equation:

Cr_max,an f(SoC_an, T) charge

wherein

is the maximum anode C-rate, SoC_n„ is an anode state-of-charge, V_{an ocv} is an anode open circuit voltage, T is temperature, Cr_an is an anode C-rate, S_stat is a static resistance scaling parameter, R_c0.an is an anode constant resistance, R_{e an} is an anode current-dependent resistance, P_{e an} is a current-dependent resistance power term, V_{d an} is an anode dynamic voltage, and S_Dynan is an anode dynamic resistance scaling parameter.

37. A method according to any of claims 35 to 36, wherein the anode state-of- charge is used to calculate a full-cell state of charge at least partially using the equation

SoCf_C relative to anode axis

38. A method of determining battery management system calibration parameters, the method including: receiving battery data at a data analysis module, the battery data including one or more parameters associated with a battery; using the data analysis module to determine one or more battery management system calibration parameters; and outputting the or each battery management system calibration parameter to a battery management system, wherein the one or more battery management system calibration parameters include at least one of: an open circuit voltage-state of charge map, a battery capacity state-of-health, or a maximum charging current limit; and wherein the data analysis module is part of a vehicle and the battery management system is also part of the vehicle.