Cell disconnection detection
By using a model-based cell capacity estimator and a Kalman filter to detect cell open circuits in the battery management system, the problem of difficult detection of cell open circuits within a cell string during vehicle operation is solved, thereby improving the stability of the battery system and the lifespan of the cells.
Patent Information
- Application Number
- CN202480073235.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2023-11-20
- Filing Date
- 2024-11-18
- Publication Date
- 2026-06-16
AI Technical Summary
Existing technologies are insufficient to effectively detect open circuits in parallel battery cell strings during vehicle operation, leading to accelerated degradation due to overcharging and discharging of the cells. Furthermore, conventional detection methods are impractical in real-time environments.
A cell capacity estimator based on two models is used for detection. The first estimator is sensitive to long-term degradation, while the second estimator is sensitive to instantaneous changes. Potential open circuits are marked by comparing the outputs of the two models. The cell series capacitance is estimated in real time and open circuits are detected by combining a Kalman filter and an interactive multi-model structure.
This enables reliable detection of cell open circuits in a real-time embedded battery management system, mitigating cell degradation and improving the stability and lifespan of the battery system.
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Figure CN122228442A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to monitoring of battery cell strings, such as in a vehicle battery management system where the battery powers the vehicle. Background Technology
[0002] Battery modules, such as those used in vehicle power and many other applications, typically comprise multiple cell strings. Each cell string consists of several cells connected in parallel to meet capacity and maximum current requirements that would be impossible to achieve using only a single cell. Multiple cell strings are often connected in series to achieve the desired module voltage and maximum power output. Such battery modules are typically designed so that the electrical connections between the cells in a cell string allow for uniform current sharing among all parallel cells. Cells in a cell string can be connected in parallel in various ways, but it is common to achieve this by soldering the cells to an electrical busbar or similar component.
[0003] Various circumstances can cause a specific cell within a parallel cell string to disconnect electrically. This results in the total load current being shared by a smaller number of cells in the string. Consequently, each cell experiences a higher-than-expected current, causing it to charge and discharge faster. This leads to a reduction in the capacitance of the cell string and any modules containing it, and accelerates cell degradation.
[0004] Without adding a separate current sensor for each cell, it is difficult to detect open circuits in such parallel cell strings. In some ways, controlled charge-discharge cycles can be used to attempt to accurately measure changes in the total capacity of the cell string or module, but while such tests can be used in controlled environments (e.g., during manufacturing and related testing), implementing such controlled cycles during normal vehicle operation or other application scenarios is generally impractical.
[0005] This invention relates to the above-mentioned problems and other problems in the related prior art. Summary of the Invention
[0006] This invention provides an apparatus and method for detecting cell open circuits within a parallel cell string, which remains reliable and undamaged even as cell capacity degrades over time, and can be easily implemented in a real-time embedded battery management system environment, such as in vehicles or other applications. Cell open circuit detection operates by comparing the outputs of two model-based estimators of the cell string capacity. The first estimator is tuned to detect long-term degradation of the cell string capacity (sometimes referred to as healthy state capacity), while the second estimator is tuned to be more sensitive to rapid or transient changes in the cell string capacity. The operation can then be based on the following two principles: Since a cell circuit break is an instantaneous event, the second estimator will respond faster than the first. Observing the difference between the capacity estimates of the first and second estimators (e.g., expressed as a fraction of the nominal 100% capacity or the total change relative to that nominal capacity) can be used to flag potential circuit breaks when the difference becomes large enough. When no circuit break is present, the capacity estimates of both estimators should change at approximately the same rate.
[0007] - The number of disconnected cells that occur at a specific time, within a specific time interval, or in total since initialization can be determined in various ways. However, since the capacity estimates of both estimators are expected to decrease over time as cell degradation occurs, the number of disconnected cells can be determined based on a comparison of the capacity of the second estimator with a baseline capacity that can remain constant but can be reset periodically, for example, when the first estimator indicates a significant decrease in capacity due to degradation.
[0008] To perform concurrent or real-time estimation of the capacitance of a battery cell string, the first and second estimators typically require at least measurements of the voltage across the battery cell string and the current flowing through it, and preferably also measurements of the temperature of the battery cell string. In the described apparatus and method, the first and second estimators are preferably also stateful: any form of recursive state estimation can be used, requiring only measurements of the physical parameters of the battery cell string at the current time step (t=k) and the state at the previous time step (t=k-1), although specific examples of the invention use Kalman filters, such as extended Kalman filters, for this purpose.
[0009] Then, each of the two estimators provides a separate estimate of the cell string's capacity, which can be expressed as a capacity loss relative to 100% nominal capacity. This estimate is then used by appropriate logic implemented in the software to flag open cells in the cell string. For example, this logic could calculate the difference between the capacity estimates from the two estimators and use this difference to determine whether and when an open cell has occurred. Subsequently, this logic also uses at least one of the capacity estimates (typically at least the estimate from the second capacity estimator) and any other relevant inputs from the estimators to estimate the possible number of disconnected cells.
[0010] Specifically, the present invention provides an apparatus for monitoring open-circuit events in a battery cell string, each open-circuit event comprising the electrical disconnection of one or more cells from the cell string, the cells in the cell string being electrically connected in parallel with each other such that the cell string has capacitance. The apparatus may include a cell string measurement result input device arranged to receive measurement results of one or more physical parameters of the cell string. Regardless of the number of such measurement results received, the apparatus subsequently includes a degradation-sensitive capacity estimator arranged to receive the measurement results and calculate a first estimate of the capacitance based on the measurement results; an open-circuit-sensitive capacity estimator arranged to receive the measurement results and calculate a second estimate of the capacitance based on the measurement results; and an open-circuit detector arranged to detect the open-circuit event by comparing the first and second capacitance estimates.
[0011] The first and second capacitance estimates of the battery cell string can be described as concurrent or real-time capacitance estimates. This means that the device operates in real time to receive the measurement results of the battery cell string and calculate and use the two capacitance estimates. Of course, the capacity estimator and circuit breaker detector do not need to operate continuously, but can be turned on periodically as needed, depending on available computing resources and other factors. This could result in capacity estimation and circuit breaker detection being performed at time intervals ranging from fractions of a second to minutes or hours.
[0012] One or more physical measurements may include the voltage across the battery cell string and the current through the battery cell string, and typically also the temperature of the battery cell string. These measurements are then used to calculate updated capacity estimates and to detect any open-circuit events indicated by these updated capacity estimates.
[0013] To detect open-circuit events, an open-circuit sensitive capacity estimator can be tuned to be sensitive to instantaneous changes in capacitance, and a degradation sensitive capacity estimator can be tuned to be sensitive to long-term degradation of capacitance. For example, the degradation sensitive capacity estimator and the open-circuit sensitive capacity estimator can be tuned or arranged such that, in response to a change in capacitance, such as an open-circuit event or a step change in the actual capacitance of the cell string, the second capacitance estimate has a higher rate of change than the first capacitance estimate. The capacity estimator can be tuned to optimize this difference in rate of change for event detection and open-circuit counting; however, typically, in response to the same open-circuit event or a step change in the actual capacitance, the second capacitance estimate may have a rate of change at least five times or at least ten times higher than the first capacitance estimate.
[0014] The circuit breaker detector can be more specifically arranged to detect a circuit breaker event based on the difference between first and second capacitance estimates, for example, when the difference between the first and second capacitance estimates exceeds an event detection threshold. Since the capacitance estimates may contain noise, the circuit breaker detector can be arranged to detect and flag a circuit breaker event only if both the first and second estimates indicate a circuit breaker event within a specific time interval (e.g., a period of time, a certain number of time steps, or the number of iterations of the estimator), for example, when the difference between the two capacitance estimates exceeds the event detection threshold for at least a predetermined debouncing interval.
[0015] The circuit breaker detector can also be configured to determine, at least using a second capacitance estimate, the number of cells that have been disconnected in one or more circuit breaker events. The determined number of disconnected cells may correspond to the number of cells that were disconnected during a brief, specifically detected circuit breaker event or over a longer period of time (e.g., during a time interval following such an event).
[0016] More specifically, the device can be arranged to maintain a periodically reset baseline capacity estimate, and the circuit breaker detector is then arranged to determine the number of cells disconnected in one or more circuit breaker events based on the difference between the baseline capacity estimate and a second capacity estimate. The baseline capacity estimate can be set constant to provide a stable reference point for determining the number of circuit breakers, but can then be periodically reset to correspond to a concurrent first capacity estimate, thereby ensuring that the reference point reflects changes in cell string capacity due to gradual cell degradation. Just before resetting the baseline capacity, the difference between the baseline capacity and the second capacity estimate indicates the capacity loss due to the circuit breakers, from which the number of circuit breakers since the last reset can be calculated.
[0017] Each of the degradation-sensitive capacity estimator and the open-circuit-sensitive capacity estimator may include one or more state models or open-circuit models of the cell string, each state model representing a different corresponding capacity model estimate of the cell string. Each state model is arranged to advance to a new state in response to a received measurement of one or more physical parameters of the cell string, the new state having the same capacity model estimate as before. In particular, each state model may be implemented as a Kalman filter, or more specifically, as an extended Kalman filter.
[0018] More specifically, each of the degradation-sensitive capacity estimator and the open-circuit-sensitive capacity estimator may include an interactive multi-model structure comprising multiple such state models arranged to track the current state of the cell string in response to receiving measurements of one or more physical parameters. Within each of the degradation-sensitive capacity estimator and the open-circuit-sensitive capacity estimator, each state model may represent a cell string with a different capacitance. For each capacity estimator, the estimated capacitance of the cell string may correspond to the state model that best fits the current physical parameter measurements.
[0019] For a degradation-sensitive capacity estimator, the state model can represent a range of capacities close to the current best capacity estimate. For a circuit-sensitive capacity estimator, each state model can represent a string of cells with a different number of disconnected cells, and the estimator can subsequently maintain weights indicating the probability that each state model best fits the measured results of concurrent physical parameters. In addition to using at least a second capacity estimate, the circuit detector can subsequently use these weights (e.g., in the form of a probabilistic mass function) to determine the number of cells disconnected in one or more circuit-breaking events.
[0020] The aforementioned device can be implemented in hardware, software, or a combination of both, but will typically be implemented using software configured to execute on a suitable computer system. Such a computer system will typically include one or more microprocessors, memory for storing the software and related data, and suitable input / output mechanisms, which may include one or more displays, network connectivity, electronics for receiving measured physical parameters of the cell strings and other data related to the battery module, and electronics for transmitting control signals related to the management of the battery module. Typically, the device and related software can be implemented as part of a battery management system in a vehicle, or in various other implementation environments.
[0021] To this end, the present invention also provides the above-described apparatus, but it further includes a battery and a sensor, the battery comprising a string of cells, and the sensor being arranged to obtain one or more physical measurement results and transmit the one or more physical measurement results to a string of cells measurement result input device.
[0022] The present invention also provides a vehicle including the above-described device, wherein a battery is arranged to provide power to the vehicle.
[0023] The present invention also includes methods corresponding to the above-described apparatus, such as a method for monitoring open-circuit events in a battery cell string, each open-circuit event comprising one or more cells being electrically disconnected from the battery cell string, the cells in the battery cell string being electrically connected in parallel with each other such that the battery cell string has capacitance. The method includes: receiving measurement results of one or more physical parameters of the battery cell string; calculating a first estimate of the capacitance based on the measurement results using a degradation-sensitive capacitance estimator; calculating a second estimate of the capacitance based on the measurement results using an open-circuit-sensitive capacitance estimator; and detecting the open-circuit event by comparing the first and second capacitance estimates.
[0024] In response to changes in capacitance, such as a circuit breaker event or a step change, the second capacitance estimate has a higher rate of change than the first capacitance estimate, or has a rate of change at least five times or at least ten times higher than the first capacitance estimate.
[0025] The method can continue to detect an open circuit event when the difference between the first capacitance estimate and the second capacitance estimate exceeds an event detection threshold, and optionally, when the difference exceeds the event detection threshold for at least a predetermined debouncing interval.
[0026] The method may also include: determining the number of cells that were disconnected in the circuit-breaking event using at least a second capacitance estimate.
[0027] Each of the degradation-sensitive capacity estimator and the open-circuit-sensitive capacity estimator may include one or more state models or open-circuit models of a cell string, each state model defining a corresponding capacity model estimate for the cell string, and each state model being arranged to advance to a new state in response to received measurements of one or more physical parameters of the cell string. For the open-circuit-sensitive capacity estimator, each state model may represent a cell string with a different number of disconnected cells.
[0028] The present invention also provides one or more computer programs arranged to implement the above-described apparatus or perform the above-described method steps when executed on a suitable computer system; and also provides one or more computer-readable media carrying such computer program code. Attached Figure Description
[0029] Embodiments of the present invention will now be described with reference to the accompanying drawings, in which: Figure 1 An embodiment of the invention is described, in which a monitor is implemented to monitor the cell strings in a battery module; Figure 2 It shows the use of Figure 1 The monitor determines the performance of the first capacity estimate (solid line) and the second capacity estimate (dashed line) of the cell string, together with the baseline capacity estimate (short dash) and the detection of open circuit events; Figure 3 It schematically illustrates how this can be achieved. Figure 1 The logic of the circuit breaker detector; Figure 4 It is shown Figure 1 The flowchart of the monitor performing tasks; Figure 5 This illustrates how the circuit breaker logic can be used. Figure 1 The flowchart uses two estimators to provide capacity estimates for detecting circuit breaker events; and Figure 6 This demonstrates how an interactive multi-model architecture can be used to achieve this. Figure 1 Each estimator. Detailed Implementation
[0030] Now for reference Figure 1 The document illustrates a battery module 10 and a monitor 100 for monitoring the battery module 10. The battery module 10 can be mounted, for example, on the road or in another vehicle, and the monitor 100 can form part of a battery management system installed in such a vehicle for managing and monitoring the battery module. A complete battery typically includes many such battery modules 10. It is certainly possible for the monitor 100 to be located away from the battery module setup, particularly not in the vehicle carrying the battery module or other devices including the battery module, but connected to the vehicle or other devices via a network connection such as a cellular data connection. However, the monitor 100 and the associated battery monitoring techniques described herein are particularly useful in that they are suitable for operation within a battery management system located in the same vehicle or device as the battery module, with reduced computational power consumption.
[0031] Battery module 10 includes one or more strings 20 of cells 30. Typically, such battery module 10 will include multiple such strings of cells electrically connected in series to provide a higher voltage output at battery module terminals 40 than a single string of cells could provide. Each string of cells will also include multiple cells electrically connected in parallel to increase the capacity of each string, i.e., the ability of the string to deliver power to a load, typically measured in kWh, or sometimes Ah. For example, in a typical road vehicle battery, each string of cells may include approximately 5 to 20 individual cells connected in parallel and have a capacity of approximately 50 to 500 Wh. Suitable cell types may be 21700 cylindrical cells (21 mm in diameter, 70 mm in length), such as the Mollicel P45B cell, but larger or smaller cells, as well as cells of different shapes and forms, such as pouch cells or prismatic cells, may also be used. Battery module 10 may contain approximately 10 to 20 such cell strings connected in series, providing a total voltage of approximately 20 to 100V between the battery module terminals. To form a complete battery, multiple such battery modules may typically be connected in parallel or in series, for example, approximately 5 to 20 such modules for a typical automobile.
[0032] The individual cells 30 in the cell string 20 can be connected in parallel in various ways, such as using... Figure 1 The bus 50 shown is connected to the same polarity terminal of all cells in the cell string. These electrical connections can be manufactured by soldering or other methods. Various conditions—such as design defects, assembly or soldering errors, rough handling of the battery module, thermal shock, or dynamic load impact—can cause individual cells to disconnect electrically from the cell string 20. Of course, a failure in the electrical connection of only one terminal of a particular cell is sufficient to cause this. Sometimes only one cell may disconnect from the cell string at any given time, but sometimes multiple cells may disconnect substantially simultaneously, for example, due to a single dynamic load impact. Generally, we refer to the electrical disconnection of only one cell from the cell string, or the electrical disconnection of multiple cells at substantially the same time, or within a suitable finite period of time (which may depend on the implementation of the monitor), as an open-circuit event.
[0033] An open circuit event causes the total load current through battery module 10 to be shared by the reduced number of cells in the cell string affected by the event. This forces the remaining connected cells in the cell string to charge and discharge faster than before the event. Not only does the capacity of the cell string and the entire module decrease, but the cells in the affected cell string also degrade more rapidly, potentially operating close to or exceeding safe current limits in extreme cases.
[0034] In existing technologies, such open-circuit events within individual cell strings can be difficult to detect because most existing battery modules only contain sensors for measuring the total current flowing through the module. Attempting to provide separate sensors to detect the current flowing through each individual cell would make the battery management system more complex.
[0035] therefore, Figure 1 The device includes a monitor 100 for monitoring each of one or more battery cell strings 20. Figure 1 The instructions specify how the monitor can be connected to monitor only one of these cell strings, but the monitor's functionality can certainly be replicated for each cell string to be monitored, or operated, for example, using a time-division multiplexing mode, thus effectively acting independently for each of the multiple cell strings 20. Similarly, the monitor can act independently for each of the cell strings 20 in each of the multiple battery modules. In practice, the monitor 100 will typically be implemented primarily or entirely in software on a suitable computer system, and is usually implemented as part of a larger software component that forms part of the battery management system 110.
[0036] The monitor 100 receives one or more physical measurement results from the cell string 20 at the cell string measurement result input device 120. M These physical measurements are then used to detect open circuit events. M Typically, this will include at least the current flowing through the cell string. I and the voltage at both ends of the cell string or at the cell string. V And typically includes at least one temperature measurement result of the cell string. T Temperature measurements can be taken at a single point or multiple points within or near a specific cell string, or the temperature of an associated heatsink or similar structural element associated with that cell string, or a single temperature measurement can be used for all cell strings within the battery module. Current I It allows for convenient measurement at a single point for multiple series-connected cell strings 20, rather than for each individual cell string 20. Figure 1 In the middle, these physical measurement results M The measurements are obtained by one or more sensors 60 positioned at appropriate locations relative to the cell string. Physical measurement results can be transmitted to the monitor 100 in various ways, but are typically transmitted as electrical data signals and received by the monitor 100 at a cell string measurement result input device 120, which may include various combinations of electronics and computer hardware and software, but in any case, makes these measurements available to other parts of the monitor 100, as described below.
[0037] The monitor 100 includes two elements 130 and 140, each element being used to measure physical results.M Individual estimates of the parallel power generation capacity of the cell string 20 are provided. These elements can be implemented using a stateful model that represents the cell string and can advance its state at discrete time intervals based on updates of available physical measurements. For example, such a stateful model can be implemented using a Kalman filter, or more specifically, using an interactive multi-model arrangement, each arrangement using multiple such Kalman filters, as discussed in more detail below.
[0038] The frequency at which the two components 130 and 140 update the estimated capacitance values may depend on factors such as the computing resources of the monitor 100, and factors such as whether the capacitance is expected to change rapidly due to, for example, rapid charging and discharging of the battery, and whether the specific application requires faster estimation. Typically, the estimates can be updated at intervals of seconds to hours using concurrently available measurements.
[0039] More notably, the two elements are arranged to respond to actual changes in cell series capacitance at different response rates, allowing them to be used together to provide better open-circuit event detection, as described below.
[0040] Therefore, the two components are configured as a degradation-sensitive capacity estimator 130 and an open-circuit-sensitive capacity estimator 140. The open-circuit-sensitive capacity estimator is tuned to be sensitive to instantaneous or rapid changes in capacitance (e.g., open-circuit events), which typically occur within a time interval of at most a few seconds, such as when an electrical connection fails. The degradation-sensitive capacity estimator is tuned to be sensitive to long-term degradation of the cell series capacitance, such as long-term degradation due to chemical degradation and similar effects, which typically occurs over multiple charge and discharge cycles, and therefore over time periods such as hours to days or longer.
[0041] Using the measurement result M received from the measurement result input device, the degradation-sensitive capacity estimator 130 calculates and outputs a first estimate of the cell string capacity change. EC1 The circuit-sensitive capacity estimator calculates and outputs a second estimate of the change in cell series capacity. EC2While the sensitivity of the two estimators to degradation and open circuits in the cell string 20 can be tuned in various ways, they can be arranged such that, in response to a change in capacitance, such as an open circuit event, the second capacitance estimate has a higher rate of change than the first capacitance estimate, for example, at least five or at least ten times higher. This can be measured in several ways, one being by measuring the rate of change of the corresponding capacitance estimate in a short time immediately following an actual capacitance step change or open circuit event, or by determining the length of time required for the corresponding estimate to decrease by half the amount of capacitance change from the correct actual capacitance estimate immediately preceding the step change or open circuit event, or some other suitable measurement. In other arrangements, the capacity-sensitive estimator is used to model open circuits more closely—for example, considering how the cell behaves differently when more current is applied (e.g., when an open circuit occurs), rather than viewing it as a capacity loss purely due to anticipated degradation.
[0042] First and second estimates of capacitance change are passed to a circuit breaker detector 150 of the monitor, which is configured to use these estimates to detect an open circuit event in which one or more cells in a cell string break, thus no longer being able to carry a portion of the current through the cell string. Specifically, the circuit breaker detector 150 uses a comparison between the first and second estimates to detect such an open circuit event. This comparison can take various forms, such as requiring one or more conditions to be met using these estimates. In one form, these conditions can be met when the difference between the first and second capacitance estimates exceeds a predefined event detection threshold. However, since the first and second capacitance estimates may contain noise, another condition could be that this exceedance of the threshold persists within a predefined debouncing interval, such as within a specific time period or within a specific number of recalculations of the first and second estimates, thus achieving a "debouncing" condition. Another such condition could be that once this debouncing condition is met, the open circuit event is maintained thereafter, regardless of any contrary indications in the first and second estimates.
[0043] The attributes of the detected open circuit event can be obtained from the open circuit detector 150 as event attributes. P The output, the attributes, may include, for example, determining the number of cells in a cell string that have been disconnected during one or more events, and optionally include other data, such as timestamps, deterministic metrics of the data, etc. These event attributes can then be used by the broader battery management system 110 (e.g., battery controller 160) to better manage the charging and discharging of specific cell strings, battery modules, or the entire battery, and / or to provide maintenance warnings to users of vehicles or other systems where battery module 10 is installed, or to other parties responsible for the maintenance of vehicles or other systems.
[0044] Figure 2 The diagram schematically illustrates how a circuit breaker detector 150 can be arranged to determine the number of cells that have been disconnected in one or more circuit breaker events, specifically using at least a second capacity estimate. The vertical axis of the graph represents the capacity of the cell string relative to its nominal or initial 100% capacity, while the horizontal axis represents time, such as a period of several hours. The solid curve 210 represents the first capacity estimate output by the degradation-sensitive capacity estimator 130. EC1 The dashed curve 220 represents the second capacity estimate output by the circuit-sensitive capacity estimator 140. EC2 It can be seen that during normal operation, the first capacity estimate decreases slowly as the cells in the cell string gradually degrade. Estimating capacity based on concurrently available measured parameters at any given time can be difficult to be accurate, therefore both the first and second estimates may contain considerable noise. However, during normal operation, in the absence of any open-circuit events or other rapid changes in the actual cell string capacity, the second capacity estimate is expected to be roughly consistent with the first estimate.
[0045] Then, at the time of the circuit breaker event 230, it can be seen that the second estimate... EC2 Compared to the first estimate EC1 The drop is faster, so the difference between the two quickly exceeds the event detection threshold 240 and persists for a longer time than the predetermined debouncing interval 250. Therefore, the circuit breaker event is recorded by the circuit breaker detector 150 and subsequently used as an event attribute. P Part of the output, such as Figure 1 As shown.
[0046] The circuit breaker detector 150 is arranged to determine the number of cells that have been disconnected in one or more circuit breaker events. The number of disconnected cells will typically be equivalent to a corresponding percentage loss of the original nominal 100% capacity, for example, such as... Figure 2 As shown, the disconnection of one cell in a 50-cell string results in approximately 2% capacity loss. Therefore, the number of disconnected cells in a given circuit breaker event can be determined at least using a second capacity estimate 220, and optionally other available data discussed in more detail below. For example, the number of disconnected cells in a given circuit breaker event can be determined by comparing the magnitude of change of the second capacity estimate over a suitable time range, or by comparing the change of the second estimate relative to the first capacity estimate over a suitable time range.
[0047] However, since the first capacity estimate 210 may have considerable noise and typically decreases gradually over time due to cell degradation, and considering that the number of disconnected cells in circuit breaker event 230 may not be immediately determined by the circuit breaker detector 150 immediately following the specific circuit breaker event, the inventors have found that it may be advantageous not to use the difference between the first and second estimates before and after the event, or not to use the absolute change of the second estimate before and after the event to determine the capacity loss during the event and thereby determine the number of disconnected cells during the event. (See below for further details.) Figure 6 In the described multi-model IMM method, since each model of the circuit-sensitive IMM corresponds to a battery cell string with a different number of disconnected cells, the most probable model or best-fit model of the IMM can be used to determine the number of circuit breaks.
[0048] On the contrary, such as Figure 1 and Figure 2 The circuit breaker detector shown utilizes another baseline capacity estimate maintained by monitor 100, which in Figure 1 The middle is shown as B ,exist Figure 2 This is depicted as curve 260. When the battery monitor 100 and the associated cell string are initialized to have a nominal capacity of 100%, this baseline capacity estimate 260 is also set to 100%. Subsequently, this baseline capacity estimate is maintained at a constant or substantially constant value and changes periodically only at a reset point 270, at which point it is reset to the concurrent first capacity estimate. EC1 The corresponding new value, such as a specific current value, or the average of recent values used to reduce noise effects. Reset point 270 may occur at fixed time intervals, but it may be advantageous to replace it with a value in response to the first capacitance estimate. EC1 It occurs when a certain amount decreases, for example, whenever... EC1 The capacity decreases by a specific percentage (e.g., 1%) of the nominal 100% capacity, or whenever the decrease represents a percentage (e.g., 0.6 or 1.0) of the nominal capacity of a specific number of cells (optionally a portion) in a cell string. The time interval from the reset point to the next reset point is then referred to herein as the reset interval.
[0049] Upon detecting an open circuit event 230, the open circuit detector 150 is then configured to determine the number of cells disconnected since the previous reset point 270 using the difference between the baseline capacity estimate 260 and the second capacity estimate 220. As described above, this difference can be converted into the number of disconnected cells by determining the proportion of nominal capacity represented by the difference and the number of cells represented by that proportion. This proportion does not substantially correspond to an exact number of cells, but various calculation rules can be provided to the open circuit detector to obtain the best estimate of the number of disconnected cells, such as considering the sum of the previously calculated number of disconnected cells and the current proportion of the nominal 100% capacity represented by the current second capacity estimate, or by other means.
[0050] The number of cells disconnected during circuit breaker event 230, and any other circuit breaker events that occur before the next reset point 270, can be used as... Figure 1 The parameters shown are output. P A portion of this is output by the circuit breaker detector 150. When the next reset point 270 is reached, this causes the baseline capacity 260 to decrease. The number of disconnected cells since the previous reset point 270 is no longer inherently recorded in the difference between the baseline capacity and the second capacity estimate; therefore, at least up to this point, a separate record and / or output of the number of disconnected cells since the previous reset point 270 is required. Thus, in effect, a record of the total number of disconnected cells since initialization can be continuously maintained by the circuit breaker detector and can effectively serve as an event attribute. P Output without waiting for each reset point 270 to appear.
[0051] Figure 3 The logic for detecting this circuit breaker event 230 and counting the disconnected cells is shown within the circuit breaker estimator 150. For example... Figure 1 As shown, the circuit breaker detector 150 receives first and second capacity estimates from the degradation-sensitive capacity estimator and the circuit breaker-sensitive capacity estimator. EC1 , EC2 As input, and to maintain the current baseline capacity. B The value. The circuit breaker detector 150 includes circuit breaker marker logic 310 ( Figure 5 (Its operation is shown in more detail in the diagram), and the circuit breaker marker is maintained. F If at baseline capacity B If an open circuit event is detected within the current reset interval between resets, the open circuit flag is true. As described above, the open circuit flag logic uses... EC1 and EC2 The comparison is used to detect open circuit events. The reset logic 320 periodically resets the baseline capacity estimate. B Each reset is achieved, for example, by... EC1This can be triggered by reducing the nominal 100% capacity by a specific percentage or in some other way. When a periodic reset occurs, the circuit breaker flag is also reset to false.
[0052] The circuit breaker detector 150 also includes circuit breaker counting logic 330, which immediately uses at least one circuit breaker counting operation after the circuit breaker flag 315 is set to true at a specific reset interval. EC2 Determine the number of cells that have been disconnected during the reset interval, and as follows: Figure 3 As shown, baseline capacity estimates are also used. B To determine. The circuit breaker counting logic 330 then maintains at least the first circuit breaker count. C The first circuit breaker count represents the number of cells that have been disconnected within the current reset interval, and preferably also maintains a second circuit breaker count. C’ The second circuit breaker count represents the number of cells that have been disconnected since the initialization of monitor 100 (when the nominal capacity of the cell string is set to 100%). First circuit breaker count. C The second circuit breaker count is reset to zero at each reset point. C’ It remains unchanged at each reset point.
[0053] The circuit breaker 150 outputs a second circuit breaker count, and optionally also outputs a first circuit breaker count and / or a circuit breaker flag F, depending on what other parts of the battery management system (e.g., the battery controller 160) need to use. These parameters can be continuously output during calculation and updating, or they can be output periodically, for example, at each reset point.
[0054] Figure 4 The flowchart illustrates how the monitor 100 can be operated to detect and flag open-circuit events, calculate and maintain a record of the number of disconnected cells to date, and periodically reset the baseline capacity. B In step 400, the degradation-sensitive capacity estimator and the disconnection-sensitive capacity estimator are initialized, so that the output... EC1 and EC2 The initial values are all nominal 100% capacity. Monitor 100 then repeats the loop, in which it receives the input of the measured cell string parameters, performs capacity estimation, performs event detection and open circuit counting, and can implement baseline capacity reset.
[0055] Within this loop, in step 410, from Figure 1 The cell string measurement result input device 120 reads the physical parameters. M In some embodiments, parameters can be used. MWhether the new updated value is available to trigger the repetition of the loop is unclear, but in other embodiments, this repetition may be performed at fixed time intervals, or based on the computing resources available to the monitor within the broader battery management system, or otherwise. In the second step 420 of the loop, degradation-sensitive capacity estimator 130 and open-circuit-sensitive capacity estimator 140 are subsequently activated to determine the estimated value. EC1 and EC2 The updated value.
[0056] In the third step 430 of this loop, the circuit breaker detector 150 executes circuit breaker marking logic, which is used to maintain the circuit breaker marking between consecutive resets of the baseline capacity estimate. F If an open circuit event is detected within this interval, the open circuit flag is true, as described above. Figure 3 As discussed. In the fourth step 440 of this loop, the circuit breaker 150 executes the circuit breaker counting logic, which is used to maintain the first and second circuit breaker counts. C , C’ As described above. In step 450, the circuit breaker detector outputs at least a second circuit breaker count. C’ Optionally, it also outputs a first circuit breaker count and / or a circuit breaker flag. F Finally, in step 460 of the loop, if the conditions for doing so are met, the baseline capacity is reset, also as described above.
[0057] Figure 5 This is another flowchart, this time showing in more detail how the circuit breaker flag logic 310 can be implemented within a specific reset interval. In this flowchart, the circuit breaker flag... F More simply, it is represented as "flag". When this circuit breaker flag logic is executed for the first time after the reset point, the circuit breaker flag is set in step 510. F Set the count to false, and also set the previous value of the flag to false. This count is used to implement the debouncing interval as described above. The second value of the flag, denoted as "previous_flag", is also set to false. In step 520, for the first execution of this logic within the reset interval and all subsequent executions, then receive... EC1 and EC2 The values are compared, for example, by subtracting them to obtain the difference. Δ If the difference Δ Exceeding the event detection threshold T1 If the count is zero, the counter increments; otherwise, the count remains zero or is reset to zero. In this way, the count continues to increase, while the difference... Δ Continue to indicate possible circuit breaker events.
[0058] However, only when Δ exceeding the threshold continuouslyT1 A circuit breaker event is marked as true only after a sufficient number of occurrences. This is achieved using step 540, where the event is only marked as true if the count exceeds the debouncing threshold. T2 The flag is only set to true when the debouncing threshold is exceeded. Once the debouncing threshold is exceeded, step 550 uses the values of flag and previous_flag.
[0059] Step 540 ensures that once the flag is set to true, it will remain true until the next reset point. This ensures that even the first capacity estimate... EC1 It continues to decline due to degradation, and EC1 and EC2 The difference between them decreased to the event detection threshold. T1 The flag remains true, indicating that a circuit breaker event has occurred during the reset period.
[0060] The degradation-sensitive capacity estimator 130 and the open-circuit-sensitive capacity estimator 140 can be implemented in various ways to provide first and second capacity estimates for the desired cell string. However, they can each be implemented using one or more state models, each defining a corresponding concurrent capacity estimate for the cell string, each state model being arranged to advance to a new state in response to received measurements of one or more physical parameters of the cell string. By implementing the capacity estimators in this manner, the computational effort required to advance the capacity estimators upon receiving new measurements of the physical parameters can be reduced to an acceptable level that can be implemented on an embedded battery management system.
[0061] In particular, any or both of the capacity estimators 130 and 140 may include one or more Kalman filters. The inventors have found that extended Kalman filters may be particularly advantageous for these purposes.
[0062] Either or both of the capacity estimators can be used individually, such as Figure 6 The interactive multi-model (IMM) structure 600 shown is used for implementation. Figure 6 As shown, each IMM structure 600 includes multiple state models 610, each state model being implemented, for example, as an extended Kalman filter or other type of Kalman filter. Each state model 610 is arranged in response to measurements of one or more physical parameters received from the cell string. MThe current state of the cell string is tracked. Each state model 610 represents the cell string with a different capacitance, such that the selection function 630 of the IMM structure 600 determines which state model 610 currently best fits the measured results of the concurrent physical parameters, and can then output a capacitance estimate EC1 or EC2 corresponding to the capacitance represented by that model. Therefore, typically at any given time, there will be a best-fitting IMM model that best fits the current measurement results, and can thus be used to limit the estimated capacitance currently output by the capacity estimator running that IMM.
[0063] However, in addition to knowing the current best-fit model, selection function 630 can also maintain the weights of all state models currently being maintained by the IMM, for example as a probability mass function (PMF), which indicates the probability of each model currently best fitting the physical parameter measurement results. Then, when determining the number of cells that have been disconnected in one or more circuit breaker events, the weights or PMF of the model used in the circuit breaker sensitive capacity estimator 130 can be used by the circuit breaker counting logic 330 as additional information besides the second capacity estimate.
[0064] Each IMM's state model 610 can be controlled and defined by IMM logic 620. This IMM logic maintains the state model most relevant to the current capacity estimate and adds new state models while discarding old ones, ensuring that the IMM's state model continues to represent the entire capacity range to which the current capacity is expected to decrease, even in the event of multiple cell failures. Figure 6 In this diagram, state model 610 is shown as a range of capacities defined as X-2%, X-1%, X, X+1%, and X+2%, where X is the capacity of the current model. If the model with capacity X-1% is currently the best-fitting state model for the concurrent physical parameter measurements, then selection function 630 outputs the current capacity as X-1%. If the state of the cell string changes, making the model with capacity X-2% more consistently the best-fitting state model for the concurrent physical parameter measurements, then selection function 630 changes the current model to the X-2% model and outputs the current capacity as X-2%. If this continues, IMM logic 620 can subsequently discard the X+2% and X+1% models and add new state models with capacities X-1% and X-2%. Selection function 630 determines which model is the current model using a state transition probability matrix in conjunction with the IMM logic, which will be discussed in more detail below. However, in other arrangements, the current capacity can alternatively be determined as a weighted sum of the discrete capacities represented by the models of the IMM.
[0065] The number of state models maintained by the IMM at any given time, and the spacing between these state models 610 in terms of capacitance, can be selected to provide sufficient resolution and range for rapid capacitance changes while keeping computational resource requirements at an acceptable level. Although Figure 6 Five independent state models are shown, but each of the degradation-sensitive capacity estimator and the disconnection-sensitive capacity estimator may have more or fewer state models operating within the IMM at any given time.
[0066] For the circuit-sensitive capacity estimator, each state model can represent a cell string with a different number of disconnected cells. In other words, the spacing between any two adjacent state models of the IMM can roughly correspond to the capacity loss corresponding to the disconnection of a single cell from the cell string.
[0067] Further details on how interactive multiple models can be used for state-of-age estimation of batteries (or, in this case, cell strings) can be found in Adam Smiley's doctoral dissertation (University of Colorado Springs, 2019), entitled "Animproved approach to state-of-age estimation for lithium-ion battery cells using interacting multiple model Kalman filters." Implementations of interactive multiple models can be more generally described in E. Mazer et al.'s discussion in IEE Transactions on Aerospace and Electronic Systems, Vol. 34, No. 1, 1998. The Kalman filters used to implement these IMM models in the described embodiments can utilize various underlying physical and chemical models of battery cells, such as those described by A. Fotouhi in Renewable and Sustainable Energy Reviews 56 (2016), pp. 1008–1021, and those described by Manh-Kien Tran et al. in Battery 2021, 7, 51. In fact, the extended Kalman filter described above can be easily implemented using EKF tracking filter objects provided in MATLAB (RTM) and other commercially available toolkits.
[0068] In a specific demonstration of the invention by the inventors, the two capacity estimators are implemented using two corresponding sets of interactive multi-models. Both include several extended Kalman filters (EKFs) for tracking the state of charge and overpotentials of the cell string, and each interactive multi-model uses multiple state models with different capacitance values.
[0069] The degradation-sensitive capacity estimator is implemented as a variable-structure interactive multi-model, which uses five state models at any given time, where the modeled cell string capacity range is distributed in the model with a resolution of ±1%, centered on the current model with capacity X. For example, this might result in the following state model being the current model at some point in time: Model 1: X + 2% Model 2: X+1% Model 3: X+0% Model 4: X-1% Model 5: X-2% The variable structure is prevented from operating a state model above X+4%, and instead focuses on the trend of capacitance decreasing over time.
[0070] The weights and capacitance of the IMM models are initialized around the current model with the estimated capacitance at initialization. The variable structure of the IMM automatically discards models that are no longer needed and adds new models with the required capacitance when the tracked capacity moves outside the range of the current capacity represented by the model. For example, after a period of operation, and as cells in a parallel cell string lose capacity over time, these models will tend to represent the following distribution range around the current pattern with the estimated capacitance X, because capacitance is generally expected to decrease over time: Model 1: X+0% Model 2: X-1% Model 3: X-2% Model 4: X-3% Model 5: X-4% This scheme allows for tracking of capacitance from +104% to 0% relative to the initial nominal 100% capacity, while each parallel cell string does not use more than 5 state models.
[0071] In these specific demonstrations, the out-of-charge sensitive capacity estimator used a fixed-structure IMM with six state models, each representing 0 to 5 cell disconnections relative to the nominal current capacity of the cell string. This range of 0 to 5 disconnections is the most common out-of-charge range selected empirically. More than 6 disconnections are considered as severe as 5. Of course, the implementation can vary based on the application or the observed number of out-of-charges, or a variable-structure IMM can also be used.
[0072] In these specific demonstrations, the aspects distinguished between the degradation-sensitive capacity estimator and the circuit-sensitive capacity estimator include the rate at which interactions occur between state models within the IMM, and the details of the state transition probability matrix used to transfer the current model among multiple existing models. This makes each estimator sensitive to its specified behavior (typically using capacity decay and circuit-breaking events).
[0073] Regarding the rate at which interactions occur between state models within an IMM, model interactions within the capacity estimator can be allowed to occur only under certain conditions to accumulate prediction errors, making corrections meaningful for the interactions, as well as the IMM state and output. If the circuit-sensitive capacity estimator (IMM) is allowed to correct more frequently than the degradation-sensitive capacity estimator (VSIMM), the capacity estimate output by the degradation-sensitive capacity estimator also changes faster. This ensures that instantaneous or rapid capacity losses cause the output of the circuit-sensitive capacity estimator to decrease faster than the output of the degradation-sensitive capacity estimator.
[0074] The state transition probability matrix (represented as p in Mazer et al.'s 1998 paper) (i,j) In this context, the matrix determines the transitions between existing state models and the degree of state adjustments necessary to change the model's likelihood. These transitions can be tuned to reflect either degenerate or open-circuit behavior. For example: For degradation-sensitive capacity estimators: The current model is more likely to remain unchanged because capacitance degradation occurs slowly in this scenario. This also results in lower sensitivity and slower response to sudden changes in capacitance.
[0075] - Only the current model is allowed to transition to an adjacent model. This means that if the capacity difference between adjacent models is approximately 1% of the nominal original capacity of the cell string, and the current model is currently X-1%, then the current model can only jump to X or X-2%. This is because capacity degradation occurs gradually and is unlikely to jump a discrete and high percentage due to typical use.
[0076] For circuit-sensitive capacity estimators: The current model is less likely to remain unchanged because the outage capacity loss is inherently instantaneous and discrete. This also allows for greater sensitivity to sudden capacity losses.
[0077] - Allows the current model to be changed to any other existing model, because multiple cells may disconnect at a given time, resulting in an instantaneous loss of capacity rather than a gradual loss.
[0078] However, there are certain conditions that are preferably applied equally to both estimators during IMM operation to ensure the stability and reliability of the output. Any condition that would prevent the IMM from operating fully (e.g., the cell string is unreliable, inconsistent, or unstable in certain parts of the charge state curve modeling the cell string) should be applied equally to both IMMs. This prevents the capacity estimate from one estimator from varying significantly relative to the other without any real large underlying capacity change, which could lead to erroneous open-circuit detection. An example of this is preventing the IMM from operating within a certain range of charge state values where the known model error is large.
[0079] Similarly, any conditions that prevent IMMs from interacting (allowing only prediction) and are unrelated to the behavioral differences between cell disconnection capacity loss and typical degradation capacity loss should also be balanced between the degradation-sensitive capacity estimator and the disconnection-sensitive capacity estimator. This prevents any behavioral influences unrelated to disconnection detection from affecting the relative IMM interaction rate (mentioned above). For example, these conditions could be: - Due to hardware computing limitations, the number of times the capacity estimator is activated can be reduced within a specific time period; - The capacity estimator is only allowed to activate when the estimated cell overvoltage is excessive, to prevent dynamic and less predictable voltage behavior from affecting the accuracy of capacity estimation and model interaction; and / or - Capacity estimation is only permitted if the cell model used can be effectively represented.
[0080] The last condition mentioned above is essentially to avoid capacity estimation under operating conditions where the known cell model cannot well represent the dynamic characteristics. This is because the IMM capacity, compared to the conventional Kalman filter, is more biased towards open-loop operation.
[0081] As mentioned above, the monitor 100 for detecting open-circuit events is typically implemented as part of a broader battery management system, such as in a vehicle or in some other installation scenario. The functions described above—from receiving measurements of the physical parameters of the cell strings to determining open-circuit events, detecting the number of disconnected cells, and providing such information to the broader battery management system—can be implemented in hardware, software, or a combination of both, but will typically be implemented using software configured to execute on a suitable computer system, and usually on the computer system used by the battery management system. Such a computer system will typically include one or more microprocessors, memory for storing the software and related data, and suitable input / output mechanisms, which may include one or more displays, a network connection, electronics for receiving the measured physical parameters of the cell strings and other data related to the battery module, and electronics for transmitting control signals related to the management of the battery module. This computer software may be hosted on one or more computer-readable media, transmitted as signals via a network connection, and stored in suitable non-volatile memory within the battery management system.
[0082] Although specific embodiments of the invention have been described, those skilled in the art will understand that various alternatives and variations can be implemented without departing from the scope of the claims.
Claims
1. An apparatus for monitoring open circuit events in a battery cell string, each open circuit event comprising one or more of the battery cells being electrically disconnected from the battery cell string, the battery cells in the battery cell string being electrically connected in parallel with each other such that the battery cell string has capacitance, the apparatus comprising: A cell string measurement result input device is arranged to receive measurement results of one or more physical parameters of the cell string; A degradation-sensitive capacity estimator is configured to receive the measurement results and calculate a concurrent first estimate of the capacitance based on the measurement results; A circuit-sensitive capacity estimator is configured to receive the measurement results and calculate a concurrent second estimate of the capacitance based on the measurement results; and A circuit breaker detector is configured to detect a circuit breaker event by comparing a first capacitance estimate with a second capacitance estimate.
2. The apparatus of claim 1, wherein the one or more physical measurements include the voltage across the battery cell string and the current through the battery cell string, and optionally also include the temperature of the battery cell string.
3. The apparatus of claim 1 or 2, wherein the circuit-sensitive capacity estimator is tuned to be sensitive to instantaneous changes in the capacitance, and the degradation-sensitive capacity estimator is tuned to be sensitive to long-term degradation of the capacitance.
4. The apparatus according to any one of the preceding claims, wherein the degradation-sensitive capacity estimator and the circuit-sensitive capacity estimator are arranged such that, in response to a change in the capacity, such as a circuit-breaking event, the second capacity estimate has a higher rate of change than the first capacity estimate, or has a rate of change at least five times higher than the first capacity estimate.
5. The apparatus according to any one of the preceding claims, wherein the circuit breaker detector is arranged to detect a circuit breaker event when the difference between the first capacitance estimate and the second capacitance estimate exceeds an event detection threshold, and optionally, when the difference exceeds the event detection threshold for at least a predetermined debouncing interval.
6. The apparatus according to any one of the preceding claims, wherein the circuit breaker detector is arranged to determine, at least using the second capacitance estimate, the number of cells that have been disconnected in one or more circuit breaker events.
7. The apparatus of claim 6, wherein the apparatus is arranged to maintain a baseline capacity estimate, the baseline capacity estimate being periodically reset to correspond to the concurrent first capacity estimate, and the circuit breaker detector is arranged to use the difference between the baseline capacity estimate and the second capacity estimate prior to the next reset of the baseline capacity estimate to determine the number of cells that have been disconnected in one or more circuit breaker events since the previous reset of the baseline capacity estimate.
8. The apparatus according to any one of the preceding claims, wherein each of the degradation-sensitive capacity estimator and the circuit-sensitive capacity estimator includes one or more state models of the cell string, each state model representing a different corresponding capacity model estimate of the cell string, each state model being arranged to advance to a new state in response to a received measurement of one or more physical parameters of the cell string.
9. The apparatus of claim 8, wherein each state model is implemented as a Kalman filter, or more specifically as an extended Kalman filter.
10. The apparatus of claim 8 or 9, wherein each of the degradation-sensitive capacity estimator and the circuit-sensitive capacity estimator includes an interactive multi-model structure, the interactive multi-model structure including a plurality of state models arranged to track the current state of the cell string in response to receiving the measurement results of the one or more physical parameters.
11. The apparatus according to claim 10, wherein, For each of the degradation-sensitive capacity estimator and the circuit-sensitive capacity estimator, each state model represents the cell string with a different capacitance, and wherein, for each capacity estimator, the estimated capacitance of the cell string corresponds to the state model that best fits the concurrent physical parameter measurement results.
12. The apparatus according to claim 11, wherein, For the circuit-sensitive capacity estimator, each state model represents a cell string with a different number of disconnected cells.
13. The apparatus according to claim 11 or 12, which is dependent on claim 6, wherein the circuit-sensitive capacity estimator maintains weights indicating the probability that each state model best fits the concurrent physical parameter measurement results, and the circuit-breaking detector is arranged to also use the weights to determine the number of cells that have been disconnected in one or more circuit-breaking events.
14. The apparatus according to any one of the preceding claims further includes a battery and a sensor, the battery comprising the cell string, the sensor being arranged to obtain the one or more physical measurement results and transmit the one or more physical measurement results to the cell string measurement result input device.
15. A vehicle comprising the means of claim 14, wherein the battery is arranged to power the vehicle.
16. A method for monitoring a cell string open circuit event, each of the open circuit events comprising one or more of the cells being electrically disconnected from the cell string, the cells in the cell string being electrically connected in parallel with each other such that the cell string has capacitance, the method comprising: Receive measurement results of one or more physical parameters of the battery cell string; Using a degradation-sensitive capacity estimator, a concurrent first estimate of the capacitance is calculated based on the measurement results; Using a circuit-sensitive capacity estimator, a concurrent second estimate of the capacitance is calculated based on the measurement results; as well as The first capacitance estimate and the second capacitance estimate are used to detect open circuit events.
17. The method according to claim 16, wherein, In response to a change in the capacitance, such as a circuit breaker event, the second capacitance estimate has a higher rate of change than the first capacitance estimate, or a rate of change at least five times higher than the first capacitance estimate.
18. The method of claim 16 or 17, wherein an open circuit event is detected when the difference between the first capacitance estimate and the second capacitance estimate exceeds an event detection threshold, and optionally, when the difference exceeds the event detection threshold for at least a predetermined debouncing interval.
19. The method according to any one of claims 16 to 18, further comprising: Optionally, at least the second capacitance estimate can be used to determine the number of cells that were disconnected during the circuit breaker event.
20. The method of any one of claims 16 to 19, wherein each of the degradation-sensitive capacity estimator and the circuit-sensitive capacity estimator includes one or more state models of the cell string, each state model defining a corresponding capacity model estimate of the cell string, each state model being arranged to advance to a new state in response to a received measurement of one or more physical parameters of the cell string.
21. The method according to claim 20, wherein, For the circuit-sensitive capacity estimator, each state model represents a cell string with a different number of disconnected cells.
22. One or more computer-readable media carrying computer program code that, when executed on a suitable computer system, performs the method according to any one of claims 16 to 21.