Description:FIELD OF THE INVENTION

The present invention relates to battery management in electric vehicles. More particularly, the present invention relates to a system and a method for tuning an Extended Kalman Filter of a State of Charge estimation unit for consistently estimating a State of Charge of each of a plurality of cells, each of a different electrochemistry.

BACKGROUND

In recent years, electric vehicles (EVs) such as two-wheeled vehicles have gained widespread popularity due to heightened environmental concerns and increased cost competitiveness vis-a-vis conventional internal combustion engine vehicles. Typically, an electric vehicle includes one or more battery packs as a power source which provides power to an electric motor of the EV for propulsion.
Battery packs in electric vehicles may include cells from different vendors, and in turn be of different electrochemistries. For instance, a first battery pack may contain cells with a Nickel Manganese Cobalt (NMC) Oxide electrochemistry and a second battery pack may contain cells with a Nickel Cobalt Aluminum (NCA) oxide electrochemistry. The decision to include a diversity of cell chemistries or cell vendors, or both, could be driven by cost, diversifying vendor portfolio and improvements to state of the art of cell technologies. A "battery pack" is the unit that is made up of a collection of "cells". Some scooters might have multiple battery packs, that is there could be two or three physically distinct battery packs. It is to be noted that the "cells" that make up a given battery pack are always of the same electrochemistry. Further, in one example, there may be one battery pack on the scooters. In another example, there may be two scooters with battery packs, each of which comprises cells from different vendors, but each pack comprises cells from the same vendor and hence of the same chemistry. Thus, the two battery packs are of different electrochemistries.
Eventually, the diversity in the electrochemistry of the cells used in each battery pack is expected to increase. Even if each of the battery packs are made of different electrochemistries, the end user experience should only depend on the energy specifications of the scooter type being used. For example, a scooter with a 3.6 kWh battery should deliver the same range, top speed and acceleration regardless of cell electrochemistry used in each of the battery pack variants used in the scooters.
EVs are equipped with estimators of State of Charge (SoC) of the battery pack which is displayed for the user to plan how long a trip, called range estimate, may be made on the EV before charging becomes necessary. One important parameter that dictates the reliability of the range estimate is the SoC. This number indicates the remaining capacity in the battery pack. Two battery packs designed to deliver the same overall energy, say 3.6 kWh, should deliver the same range when installed on the same scooter type and exposed to the same drive cycle, but an inaccurate SoC estimate can make this untrue. For instance, underestimating the SoC, that is estimating 0% as the SoC while the actual is, for example, 10%, which could mean ending the ride session prematurely, thereby delivering a lesser range than actually available. The dynamics of each cell, the accuracy with which a mathematical model of the cell in the battery has been derived and the how well the SoC estimator that uses an “Extended Kalman Filter” (EKF) has been tuned are the key reasons for differences in accuracies of SoC estimation.
One such prior art discloses an implementation of a method for cell equalization. The method uses other information such as the individual cell state-of-charge (SoC) estimates, and individual capacities and/or cell Coulombic efficiencies, possibly available from a dual extended Kalman filter. The method defines or refers to an operational SoC range between a minimum and a maximum. The minimum and maximum could be constants or could be dynamic based on functions of other variables. SoC can be measured relative to maximum charge or relative to maximum discharge for each cell. When the SoC is not consistent across the cells, a prioritizing scheme is used to determine which cells require equalization.
Another prior art discloses a method for estimating state of charge (SoC) of an energy storage device. The method includes estimating a first SoC and a second SoC by one or more processors of a battery management system (BMS). Further, the method includes determining a state of charge error as a function of the SoC1 and the SoC2. Furthermore, the method includes determining a Kalman filter gain as a function of a battery charge storage capacity variance, a current variance and a voltage variance of the battery by the one or more processors. Further, the method includes estimating the SoC of the battery at a first time by a Kalman filter as a function of the SoCerror and the Kalman filter gain and both the SOCerror and the Kalman filter gain determined at the second time.
Therefore, in view of the problems mentioned above, it is advantageous to provide a system and a method that can overcome one or more of the problems and limitations for tuning an existing Extended Kalman Filter of a State of Charge estimation unit mentioned above.

SUMMARY

This summary is provided to introduce a selection of concepts, in a simplified format, that are further described in the detailed description of the invention. This summary is neither intended to identify key or essential inventive concepts of the invention nor is it intended for determining the scope of the invention.
To overcome or at least mitigate one of the problems mentioned above in the state of the art, a method and a system for tuning an Extended Kalman Filter of a State of Charge estimation unit is needed configured for consistently estimating a State of Charge of each of a plurality of battery packs, each comprising cells of variable electrochemistry.
In an embodiment of the present invention, a method for tuning an Extended Kalman Filter of a State of Charge estimation unit is disclosed. The method is for consistently estimating a State of Charge of each of a plurality of cells, wherein one of the cells is designated as a reference cell. The method includes determining a time constant (t) map as a function of State of Charge for each cell of the plurality of cells. The method includes identifying a slowest time constant (t) map among the determined time constant (t) maps for a particular cell. The method includes determining whether a slowest time constant (t) map of the reference cell matches with the identified slowest time constant (t) map for each cell of the plurality of cells. The method includes iteratively adjusting values of one or more parameters of the Extended Kalman Filter gains for the cell with the slowest time constant (t) map not matching with the slowest time constant (t) map of the reference cell.
In another embodiment of the present invention, a system for tuning an Extended Kalman Filter of a State of Charge estimation unit is disclosed. The State of Charge estimation unit is configured for consistently estimating a State of Charge of each of a plurality of cells. The system includes the plurality of cells, each of a different electrochemistry, wherein one of the cells is designated as a reference cell. The system includes a processing module configured for tuning the Extended Kalman Filter of the State of Charge estimation unit for consistently estimating the State of Charge of each of the plurality of cells. The processing module is configured for determining a time constant (t) map as a function of State of Charge for each cell of the plurality of cells. The processing module is configured for identifying a slowest time constant (t) map among the determined time constant (t) maps of each cell. The processing module is configured for determining whether a slowest time constant (t) map of the reference cell matches with the identified slowest time constant (t) map for each cell of the plurality of cells. The processing module is configured for iteratively adjusting values of one or more parameters of the Extended Kalman Filter gains for the cell with the slowest time constant (t) map not matching with the slowest time constant (t) map of the reference cell.
To further clarify the advantages and features of the present invention, a more particular description of the invention will be rendered by reference to specific embodiments thereof, which are illustrated in the appended drawings. It is appreciated that these drawings depict only typical embodiments of the invention and are therefore not to be considered limiting of its scope. The invention will be described and explained with additional specificity and detail with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein:
Figure 1 illustrates a flowchart depicting a method for tuning an Extended Kalman Filter of a State of Charge estimation unit for consistently estimating a State of Charge (SoC) of each of a plurality of cells, each of a different electrochemistry, according to an embodiment of the present invention;
Figure 2 illustrates a flowchart depicting a method for determining a time constant (t) map as a function of State of Charge for each cell of the plurality of cells, according to an embodiment of the present invention;
Figure 3 illustrates a system for tuning an Extended Kalman Filter of the State of Charge estimation unit for consistently estimating the State of Charge (SoC) of each of a plurality of cells, each of a different electrochemistry, according to an embodiment of the present invention;
Figure 4 illustrates a flowchart depicting a method for tuning the estimators of State of Charge (SoC) of the two cells, until the identified slowest time constant (t) of each cell matches with the slowest time constant (t) of a reference cell, according to an embodiment of the present invention;
Figure 5 illustrates a graph showing the results of a simulation of SoC estimator of cells with different electrochemistry depicting inconsistent performance;
Figure 6A and 6B illustrates a graph showing a comparison of slowest time constant (t) map as a function of State of Charge for each the cell (A) and the cell (B), according to an embodiment of the present invention;
Figure 7 illustrate a graph showing a result of the simulation of SoC estimation after performing a method for tuning the Extended Kalman Filter of the State of Charge estimation unit, on each of the cell (A) and the cell (B) of the different electrochemistry; and
Further, skilled artisans will appreciate that elements in the drawings are illustrated for simplicity and may not have necessarily been drawn to scale. For example, the flow charts illustrate the method in terms of the most prominent steps involved to help to improve understanding of aspects of the present invention. Furthermore, in terms of the construction of the device, one or more components of the device may have been represented in the drawings by conventional symbols, and the drawings may show only those specific details that are pertinent to understanding the embodiments of the present invention so as not to obscure the drawings with details that will be readily apparent to those of ordinary skill in the art having the benefit of the description herein.

DETAILED DESCRIPTION OF FIGURES

For the purpose of promoting an understanding of the principles of the present invention, reference will now be made to the various embodiments and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the present invention is thereby intended, such alterations and further modifications in the illustrated system, and such further applications of the principles of the present invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the present invention relates.
It will be understood by those skilled in the art that the foregoing general description and the following detailed description are explanatory of the present invention and are not intended to be restrictive thereof.
Whether or not a certain feature or element was limited to being used only once, it may still be referred to as “one or more features” or “one or more elements” or “at least one feature” or “at least one element.” Furthermore, the use of the terms “one or more” or “at least one” feature or element do not preclude there being none of that feature or element, unless otherwise specified by limiting language including, but not limited to, “there needs to be one or more…” or “one or more elements is required.”
Reference is made herein to some “embodiments.” It should be understood that an embodiment is an example of a possible implementation of any features and/or elements of the present invention. Some embodiments have been described for the purpose of explaining one or more of the potential ways in which the specific features and/or elements of the proposed invention fulfil the requirements of uniqueness, utility, and non-obviousness.
Use of the phrases and/or terms including, but not limited to, “a first embodiment,” “a further embodiment,” “an alternative embodiment,” “one embodiment,” “an embodiment,” “multiple embodiments,” “some embodiments,” “other embodiments,” “further embodiment”, “furthermore embodiment”, “additional embodiment” or other variants thereof do not necessarily refer to the same embodiments. Unless otherwise specified, one or more particular features and/or elements described in connection with one or more embodiments may be found in one embodiment, or may be found in more than one embodiment, or may be found in all embodiments, or may be found in no embodiments. Although one or more features and/or elements may be described herein in the context of only a single embodiment, or in the context of more than one embodiment, or in the context of all embodiments, the features and/or elements may instead be provided separately or in any appropriate combination or not at all. Conversely, any features and/or elements described in the context of separate embodiments may alternatively be realized as existing together in the context of a single embodiment.
Any particular and all details set forth herein are used in the context of some embodiments and therefore should not necessarily be taken as limiting factors to the proposed invention.
The terms “comprises”, “comprising”, or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process or method that comprises a list of steps does not include only those steps but may include other steps not expressly listed or inherent to such process or method. Similarly, one or more devices or sub-systems or elements or structures or components proceeded by “comprises... a” does not, without more constraints, preclude the existence of other devices or other sub-systems or other elements or other structures or other components or additional devices or additional sub-systems or additional elements or additional structures or additional components.
Embodiments of the present invention will be described below in detail with reference to the accompanying drawings.
For the sake of clarity, the first digit of a reference numeral of each component of the present invention is indicative of the Figure number, in which the corresponding component is shown. For example, reference numerals starting with digit “1” are shown at least in Figure 1. Similarly, reference numerals starting with digit “2” are shown at least in Figure 2.
It is to be noted that the term ‘State of Charge’ may be referred to as ‘SoC’ and may reflect the same meaning and may be used interchangeably in the description and figures. It is to be noted that the term ‘State of Charge estimation unit’ may be referred to as ‘SoC estimating unit’ or ‘SoC estimator’ and may reflect the same meaning and may be used interchangeably in the description and figures. It is to be noted that the term ‘Extended Kalman Filter’ may be referred to as ‘EKF’ and may reflect the same meaning and may be used interchangeably in the description and figures.
To explain the best method of performing the invention, following is an example describing the technical need for the method (100) disclosed herein.
Considering a scenario, where an Original Equipment Manufacturer (OEM) launches a scooter model with a 3.6 kWh battery pack. Assuming that the production of all these scooters starts off with a manufacturer providing a first battery pack comprising cells with one electrochemistry. A few months after sales start, an alternative manufacturer needs to be onboarded providing a second battery pack comprising cells with a different electrochemistry. Now, there will be customers of the same scooter model, but, internally, their scooters may have battery packs from different vendors and hence with a different electrochemistry. The SoC calculation for these battery packs may be performed using the well-known “Coulomb counting” method, which basically measures the current being drawn from a battery -in the case of riding, or the current being fed to the battery - in case of charging and integrates the current over time to estimate the SoC. The equation for Coulomb counting is shown below.
SoC=SoC_0+ (? idt)/Q

where SoC0 is the initial value of SoC (SoC is unitless number between 0 and 1), i is the current in Amperes and Q is the capacity of the battery in Ampere-second (A.s) and t, in dt, is the independent variable time in seconds (s).

The accuracy of the output of this equation is dependent on the following factors:
Errors in current measurement (i);
The battery pack’s actual capacity (Q);
The initial SoC (SoC_0).
None of the above are ever completely error free. Some reasons for the errors are:
Errors in the sensed current.
The battery pack’s capacity can be slightly different part to part owing to manufacturing process noise.
The initial SoC can be initialized erroneously by virtue of voltage sensing errors, or cell characterization errors.
In the event that the SoC calculated as above deviates from the actual SoC, the SoC estimation method needs to correct the estimate.
If the errors in SoC estimation are not corrected, the differences in performances of the scooters are evident to customers in the form of range inconsistencies, or different rates of SoC updates on scooter’s dashboard or display. These issues are most evident when the SoC estimation has accumulated errors.
Let us take the example of two scooters belonging to the same scooter model each containing a different battery pack of a different electrochemistry.
The two scooters may have started with the same initial error in SoC estimate (say x%). This error could have accumulated due to an improper initialization in software. These two scooters then travel the same distance and then are parked for a duration of 6 hours. It is desirable that the SoC estimation units in each scooter smartly correct for the initial error, so that by the end of the parking duration, the error in SoC displayed is close to zero. However, if the SoC estimation unit for each cell is not tuned uniformly so as to deliver similar dynamic performance, the SoC displayed on these two scooters will correct themselves at different rates.
A "battery pack" or batteries (as referred to herein in the present disclosure) is the unit that is made up of a collection of "cells". Some scooters might have multiple battery packs (which means there could be two or three physically distinct battery pack boxes). It is to be noted that the "cells" that make up a battery pack are always of the same electrochemistry. Further, in one example, there may be one battery pack on the scooter. In another example, there may be two scooters with battery packs, each of which comprises cells from different vendors, but each pack comprises cells from the same vendor and hence of the same chemistry. Thus, the two battery packs are of different electrochemistries.
Typically, battery packs contain cells arranged in a series -parallel arrangement. Let's take a fictitious example of a battery pack. There may be three "columns" inside the battery pack, which may contain two cells connected in parallel. There are three such columns connected in the series. On a typical Battery Management System (BMS) hardware, measurements of voltages of each column are available. In the present fictitious example, the BMS has three voltage measurements corresponding to each column. Each cell in this battery pack is of the same electrochemistry, and therefore expected to be identical. Further, it can be assumed that the current is split equally between the two cells in parallel.
Now, in accordance with an embodiment of the present disclosure, when the SoC estimator (EKF) is tuned, it can be tuned based on one cell's data (for example, the impulse response as mentioned in at step (212) with reference to Figure 2 described further below). After tuning, a "Q" and "R" parameter values are obtained for the EKF. Since all the cells are identical, the processing module chooses to deploy only three EKF algorithms (corresponding to the three cells in parallel), each given the same "Q" and "R" as parameters, but each being fed the corresponding column's voltage. Further, the column's EKF is provided with a current value of i/2 (two cells in parallel, therefore the current gets split into two equal parts). We then use the SoC estimate provided by the EKF as the SoC of the column.
Once the system has three SoC estimates (one for each column), the disclosed method and system is configured to mix them in a manner of a particular choosing before publishing it as the entire battery pack's SoC (the number displayed on scooter dashboard). For example, the disclosed method and system may choose to publish only the max SoC, or min SoC, or an average of all the SoCs.
Thus, the method (100) and the system (300) as described below with reference to Figure 1 and 3 represents a tuning strategy for the Extended Kalman Filter of a State of Charge estimation unit, that can ensure that SoC estimation is consistent and uniform across each cell of a plurality of cells, regardless of their cell electrochemistry.
Figure 1 illustrates a flowchart depicting a method (100) for tuning an Extended Kalman Filter of a State of Charge estimation unit for consistently estimating a State of Charge of each of a plurality of cells, each of a different electrochemistry, according to an embodiment of the present invention.
The order in which the method steps are described below is not intended to be construed as a limitation, and any number of the described method steps can be combined in any appropriate order to execute the method or an alternative method. Additionally, individual steps may be deleted from the method, without departing from the spirit and scope of the subject matter described herein.
The method (100) may be performed by at least one processing module (332) as described with reference to Figure 3, without departing from the scope of the present invention. The method (100) includes steps for tuning an Extended Kalman Filter of a State of Charge estimation unit (334) as shown and described with reference to Figure 3, for consistently estimating a SoC of each of the plurality of cells, each of a different electrochemistry while maintaining uniformity in the performance of the estimators. The term SoC indicates the level of charge of an electric battery relative to its capacity. In one example, the term SoC is expressed as percentage (0 percent refers to empty charge and 100% refers to full charge).
At step (102), the method includes determining a time constant (t) map as a function of State of Charge for each cell of the plurality of cells. As known, in the state of the art, the RC time constant, also called tau (t), the time constant (in seconds) of an RC circuit, is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e.[seconds]. It is the time required to charge the capacitor, through the resistor, from an initial charge voltage of zero to approximately 63.2% of the value of an applied DC voltage, or to discharge the capacitor through the same resistor to approximately 36.8% of its initial charge voltage. The determination of the time constant (t) map as a function of State of Charge for each cell is explained in detail with reference to method of Figure 2.
It is to be noted that, the time constant (t) map as a function of State of Charge for each cell may either be calculated, or it can be obtained experimentally using cell cyclers. Further, this time constant (t) map as a function of State of Charge for each cell can also be obtained in real-time on the scooter while the scooter is running by making certain measurements or on the cloud by sending the measurement data to the cloud.
The disclosed implementation of the method at the laboratory level, using cell cyclers, is explained with an example. Take a few sample cells (A) and perform impulse response tests and obtain system identification on those cells. The obtained parameters can be averaged. Tune the EKF for this cell type and use the obtained EKF parameters in the model that may be implemented on a battery pack A (for example) that is designed for these cells. Note that this process need not be done for every cell that is going into the pack. This is a one time characterization.
When battery pack B is being designed, and it has cells (B) of a different electrochemistry, then the above steps are repeated for sample cells (B) of that electrochemistry. This is where a disclosed tuning method (100) is applied to ensure that the EKF tuned for cell B performs similar to the performance of the EKF for cell A. If we ensure this, we ensure that the SoC estimates of each column in our battery packs A and B, of the current example, and thereby the final SoC estimations perform uniformly.
Continuing with the method (100), at step (104), the method includes identifying the slowest time constant (t) map among the determined time constant (t) maps. In one example, the slowest time constant (t) map corresponds to the slowest eigenvalue of the EKF for each cell of the plurality of cells, wherein each cell is of a different electrochemistry. The determination of the time constant (t) map as a function of State of Charge for each cell of the plurality of cells is explained in detail with reference to the method of Figure 2.
An Extended Kalman Filter (EKF) is a method that is popularly used for SoC estimation. The EKF takes measurements of the current, terminal voltage of the battery while delivering or consuming that current and delivers a SoC estimate. To do this, the EKF needs a “state-space” model of the battery. The most used model is a double RC pair “Electrochemical Equivalent Model” (ECM) known in the state of the art. The dynamics of the EKF directly affect the performance of SoC estimation on the electric vehicle. Since the dynamics in turn rely on the parameters of the ECM model being used, and the way the EKF has been tuned, the results could vary greatly as the electrochemistry of the cell changes due to implementation of different batteries of different electrochemistry.
The following discrete ECM model for the battery is used to formulate an Extended Kalman Filter.
V_(1,k)= e^((-?T)/(R_1 C_1 )) V_(1,k-1)+ i_(k-1) R_(1 ) (1-e^(-?T/(R_1 C_1 )) )
V_(2,k)= e^((-?T)/(R_2 C_2 )) V_(2,k-1)+ i_(k-1) R_(2 ) (1-e^(-?T/(R_2 C_2 )) )
SoC_k=?SoC_(k-1) + i?_(k-1) ?T/Q

V_(t,k-1)= V_ocv (?SoC?_(k-1) )+ V_(1,k-1)+ V_(2,k-1)+ i_(k-1) R_0

The error dynamics of the EKF can then be represented by the following equation:
e_k=(A-GCA) e_(k-1)

where matrix A comprises the parameters from the first equation, and G is the Kalman Gain calculated by the EKF algorithm. The eigenvalues of the matrix (A-GCA) represent the speed with which the EKF can correct the SoC estimate, thereby delivering a metric for comparing the EKF performance for different A matrices (which will be different for each cell type).
The eigenvalues can be converted into a time constant (with a unit of seconds) using linear algebra, and this number can be plotted across all SoC points. For a third order system as disclosed herein, there will be three ‘time constants’, for example, these three-time constants can be sorted into the fastest, medium, and slowest time constant. In the method outlined in this present invention, the slowest time constant is used as the parameter to perform the tuning.
The method (100) at step (104) uses the time constant (t) corresponding to the slowest eigenvalue of the close loop EKF system as a measure of its close loop performance. By tuning the EKF gain across each cell, so that this time constant is nearly the same across all SoC bands, a consistent performance of SoC estimation across each cell is ensured. The process of tuning the EKF gain across each cell is explained from step (106) to step (110).
At step (106), the method (100) includes determining whether a slowest time constant (t) map of the reference cell matches with the identified slowest time constant (t) map for each cell of the plurality of cells.
At step (108), the method includes iteratively adjusting values of one or more parameters of the Extended Kalman Filter gains for the cell with the slowest time constant (t) map not matching with the slowest time constant (t) map of the reference cell. The values of the one or more parameters refer to "Q" and "R" of the EKF gains. The one or more parameters of EKF gains are adjusted while ensuring stability of the closed loop filter. As known in the state of the art, the ‘Q’ and ‘R’ correspond to the process and measurement noise covariance matrices, respectively. The parameter, ‘Q’ is a covariance matrix associated with the noise in states, whereas ‘R’ is just the covariance matrix of the measurement noise. ‘R’ may be found by processing the measurements while the output of the system is held constant.
The manner in which the time constant (t) map as a function of State of Charge for each cell of the plurality of cells is determined is explained in detail below.
Figure 2 illustrates a flowchart depicting a method (202) for determining a time constant (t) map as a function of State of Charge (SoC) for each cell of the plurality of cells, according to an embodiment of the present disclosure. The order in which the method steps are described below is not intended to be construed as a limitation, and any number of the described method steps can be combined in any appropriate order to execute the method or an alternative method. Additionally, individual steps may be deleted from the method, without departing from the spirit and scope of the subject matter described herein.
The method (202) may be performed by at least one processing module (332) as described with reference to Figure 3, without departing from the scope of the present disclosure. The method (202) includes the steps for determining the time constant (t) map as a function of State of Charge for each cell of the plurality of cells (338B, 338C). In one example, the cell (338B) and the cell (338C) include cells of different electrochemistry.
At step (212), the method (202) includes measuring an impulse response of each cell of the plurality of cells (338B, 338C). In one example, the impulse response of each cell may be determined by applying a sufficiently narrow pulse of current to each cell and the output voltage is monitored, and the output voltage can be calculated. This output voltage is the measured impulse response of the cell in the battery.
At step (214), the method (202) includes using the measured impulse response for identification of a state space model. At step (216), the method (202) includes using the identified state space model for Extended Kalman Filter gain tuning (216) to achieve stable operation of an estimation model. The step (214) and step (216) are explained in detail above in Figure 1.
At step (218), the method (202) includes determining the close loop system’s eigenvalues using the Extended Kalman Filter gain tuned for stability. At step (220), the method includes converting the determined eigenvalues to a plurality of time constants based on a mathematical model. In one embodiment, the determined eigenvalues are converted to a plurality of time constants {ti, (wherein, the value of ‘i’ is 1 to n)} based on the mathematical model (also referred to as state space model).
In one example, the eigenvalues can be converted into a time constant (with a unit of second) using linear algebra, and this number can be plotted across all SoC points. For a third order system as disclosed herein, there will be three ‘time constants’ that may be sorted into the fastest medium and slowest time constant. In the method outlined in this present invention, the slowest time constant is used as the parameter to perform the tuning.
At step (222), the method (202) includes selecting a maximum value of the time constant of the plurality of converted time constants; wherein the maximum value time constant is the slowest time constant. The slowest time constant is a time constant corresponding to the slowest eigenvalue of the close loop Extended Kalman Filter as a measure of its close loop performance. At step (224), the method (202) includes utilizing the slowest time constant for determining the time constant (t) map as the function of State of Charge for each cell of the plurality of cells (338B, 338C).
Figure 3 illustrates a system (300) for tuning an Extended Kalman Filter of the State of Charge estimation unit for consistently estimating the State of Charge (SoC) of each of a plurality of cells, each of a different electrochemistry, according to an embodiment of the present invention.
In an embodiment, the system (300) may include, but is not limited to, a processing module (332), the Extended Kalman Filter of the State of Charge estimation unit (334), a display (336), a reference cell (338A) and the plurality of cells (338B, 338C) each of a different electrochemistry. It is to be noted that the system (300) is explained with respect to three cells (338A), (338B), and (338C) however, it should be noted that the present system can be similarly applied to multiple cells.
The system 300 may be implemented on a vehicle, in accordance with an embodiment of the present disclosure. The vehicle may be an electric vehicle.
An Electric Vehicle (EV) or a battery powered vehicle including, and not limited to two-wheelers such as scooters, mopeds, motorbikes or motorcycles; three-wheelers such as auto-rickshaws, four-wheelers such as cars and other Light Commercial Vehicles (LCVs) and Heavy Commercial Vehicles (HCVs) primarily work on the principle of driving an electric motor using the power from the batteries provided in the EV. Furthermore, the electric vehicle may have at least one wheel which is electrically powered to traverse such a vehicle. The term ‘wheel’ may be referred to any ground-engaging member which allows traversal of the electric vehicle over a path. The types of EVs include Battery Electric Vehicle (BEV), Hybrid Electric Vehicle (HEV) and Range Extended Electric Vehicle. However, the subsequent paragraphs pertain to the different elements of a Battery Electric Vehicle (BEV).
In construction, an EV typically comprises hardware components such as a battery or battery pack enclosed within a battery casing and includes a Battery Management System (BMS), an on-board charger, a Motor Controller Unit (MCU), an electric motor and an electric transmission system. In addition to the hardware components/elements, the EV may be supported with software modules comprising intelligent features including and not limited to navigation assistance, hill assistance, cloud connectivity, Over-The-Air (OTA) updates, adaptive display techniques and so on. The firmware of the EV may also comprise Artificial Intelligence (AI) & Machine Learning (ML) driven modules which enable the prediction of a plurality of parameters such as and not limited to driver/rider behavior, road condition, charging infrastructures/charging grids in the vicinity and so on. The data pertaining to the intelligent features may be displayed through a display unit present in the dashboard of the vehicle. In one embodiment, the display unit may contain an Liquid Crystal Display (LCD) screen of a predefined dimension. In another embodiment, the display unit may contain an Light-Emitting Diode (LED) screen of a predefined dimension. The display unit may be a water-resistant display supporting one or more User-Interface (UI) designs. The EV may support multiple frequency bands such as 2G, 3G, 4G, 5G and so on. Additionally, the EV may also be equipped with wireless infrastructure such as, and not limited to Bluetooth, Wi-Fi and so on to facilitate wireless communication with other EVs or the cloud.
The ECU of the EV is responsible for managing all the operations of the EV, wherein the key elements of the ECU (10) typically includes (i) a microcontroller core (or processor unit) (12); (ii) a memory unit (14); (iii) a plurality of input (16) and output modules (18) and (iv) communication protocols including, but not limited to CAN protocol, Serial Communication Interface (SCI) protocol and so on. The sequence of programmed instructions and data associated therewith can be stored in a non-transitory computer-readable medium such as memory unit or storage device which may be any suitable memory apparatus such as, but not limited to read-only memory (ROM), programmable read-only memory (PROM), electrically erasable programmable read-only memory (EEPROM), random-access memory (RAM), flash memory, disk drive and the like. In one or more embodiments of the disclosed subject matter, non-transitory computer-readable storage media can be embodied with a sequence of programmed instructions for monitoring and controlling the operation of different components of the EV.
The processor may include any computing system which includes, but is not limited to, Central Processing Unit (CPU), an Application Processor (AP), a Graphics Processing Unit (GPU), a Visual Processing Unit (VPU), and/or an AI-dedicated processor such as a Neural Processing Unit (NPU). In an embodiment, the processor can be a single processing unit or several units, all of which could include multiple computing units. The processor may be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the processor is configured to fetch and execute computer-readable instructions and data stored in the memory. The instructions can be compiled from source code instructions provided in accordance with a programming language such as Java, C++, C#.net or the like. The instructions can also comprise code and data objects provided in accordance with, for example, the Visual Basic™ language, LabVIEW, or another structured or object-oriented programming language. The one or a plurality of processors control the processing of the input data in accordance with a predefined operating rule or artificial intelligence (AI) model stored in the non-volatile memory and the volatile memory. The predefined operating rule or artificial intelligence model is provided through training or learning algorithms which include, but are not limited to, supervised learning, unsupervised learning, semi-supervised learning, or reinforcement learning.
Furthermore, the modules, processes, systems, and devices can be implemented as a single processor or as a distributed processor. Also, the processes, modules, and sub-modules described in the various figures of and for embodiments herein may be distributed across multiple computers or systems or may be co-located in a single processor or system. Further, the modules can be implemented in hardware, instructions executed by a processing unit, or by a combination thereof. The processing unit can comprise a computer, a processor, such as the processor, a state machine, a logic array, or any other suitable devices capable of processing instructions. The processing unit can be a general-purpose processor which executes instructions to cause the general-purpose processor to perform the required tasks or, the processing unit can be dedicated to performing the required functions. In another embodiment of the present disclosure, the modules may be machine-readable instructions (software) which, when executed by a processor/processing unit, perform any of the described functionalities. In an embodiment, the modules may include a receiving module, a generating module, a comparing module, a pairing module, and a transmitting module. The receiving module, the generating module, the comparing module, the pairing module, and the transmitting module may be in communication with each other. The data serves, amongst other things, as a repository for storing data processed, received, and generated by one or more of the modules. Exemplary structural embodiment alternatives suitable for implementing the modules, sections, systems, means, or processes described herein are provided below.
Referring now to Figure 3 again, the system (300) is configured for tuning an Extended Kalman Filter of a State of Charge estimation unit (334) for consistently estimating a State of Charge of each of the plurality of cells (338B, 338C). The system (300) includes the reference cell (338A) and the plurality of cells (338B, 338C) each of a different electrochemistry and the processing module (332).
The State of Charge estimation unit (334) is configured for consistently estimating the State of Charge of each of a plurality of cells (338B, 338C).
The system (300) includes a processing module (332) configured for tuning the Extended Kalman Filter of the State of Charge estimation unit (334) for consistently estimating the State of Charge of each of the plurality of cells (338B, 338C). The processing module (332) is configured for determining a time constant (t) map as a function of State of Charge for each cell of the plurality of cells (338B, 338C). The processing module (332) is configured for identifying a slowest time constant (t) map among the determined time constant (t) maps.
The processing module (332) is configured for determining whether a slowest time constant (t) map of the reference cell (338A) matches with the identified slowest time constant (t) map for each cell of the plurality of cells (338B, 338C).
In one embodiment, the processing module (332) is configured for determining the time constant (t) map as the function of State of Charge for each cell of the plurality of cells (338B, 338C) based on at least one of an online mode or an offline mode or experimentally using cell cyclers. In one embodiment, the online mode comprises determining the time constant (t) map as the function of State of Charge using a processing module (332) on a vehicle or on a cloud.
The implementation of the disclosed method (100), by the processing module (332) at laboratory level using cell cyclers is explained with an example. In one exemplary embodiment, a few sample cells (A) are taken. Further, a step of performing impulse response and system identification is carried on those cells to obtain one or more parameters (Q and R). The obtained parameters can be averaged. Tune the EKF for this cell type and use the obtained EKF parameters in the model, that shall run on battery pack A (for example) that is designed for these cells. It is to be noted that this process need not be done for every cell that is going into the battery pack. This is a one-time characterization.
When battery pack B is being designed, and it will have cells (B) of a different electrochemistry, then the above steps are repeated for sample cells (B) of that electrochemistry. This is where the method (100) is applied for tuning to ensure that the EKF tuned for cell B performs similar to the EKF for cell A. If this is ensured then the SoC estimates of each column in the battery packs A and B (reference to the above context discussion), and thereby the final SoC would perform uniformly.
The implementation of the disclosed method (100), by the processing module (332) on the scooter in real-time is explained with an example. In one example, the implementation includes the below steps:
Ask the scooter to enter a "diagnostic mode". Using the charger, apply an impulse on the battery pack and record the impulse response from each column (three columns in our fictitious case described hitherto). Obtain the parameters of the models using each column’s impulse response. The obtained parameters can be averaged. Perform the step of EKF tuning, tau map calculation, and iterations to match the tau map to a reference. This process can be done on the scooter's ECU. Lastly, update the EKF gains to be used for the EKF.
The implementation of the disclosed method (100), by the processing module (332) on the cloud is explained with an example. Ask the scooter to enter into a "diagnostic mode". Using the charger, apply an impulse on the battery pack and record the impulse response from each column (three columns in our fictitious case). Obtain the parameters (Q and R) of the models using each column’s impulse response. The obtained parameters may be averaged. Perform the EKF tuning, tau map calculation, and iterations to match the tau map to a reference. This process can be done by sending the impulse response data to the cloud and the computations are carried on the cloud. Update the EKF gains to be used for the EKF on the scooter.
The processing module (332) is configured for iteratively adjusting values of one or more parameters of the Extended Kalman Filter gains for the cell with the slowest time constant (t) map not matching with the slowest time constant (t) map of the reference cell (338A). The processing module (332) is configured for iteratively adjusting the values of one or more parameters of the Extended Kalman Filter gains of the cell with the slowest time constant (t) map using at least one of a manual method, or a semi-automatic method utilizing a constrained grid search or optimization techniques, or an automatic method utilizing one or more machine learning methods.
It is to be noted that, the processing module (332) is configured for choosing values of one or more parameters of the Extended Kalman Filter gains determined for a battery of the electrochemistry of the given battery while estimating the State of Charge of the given battery.
The values of the one or more parameters refer to "Q" and "R" of the EKF gains. The one or more parameters of EKF gains are adjusted to achieve stability. As known in the state of the art, the ‘Q’ and ‘R’ correspond to the process and measurement noise covariance matrices, respectively. The parameter, ‘Q’ is a covariance matrix associated with the noise in states, whereas ‘R’ is just the covariance matrix of the measurement noise. ‘R’ can be found by processing the measurements while the output of the system is held constant.
The practical implementation of the current invention will be described hereinafter with reference to Figure 3. The system (300) comprises the processing module (332), the EKF of the SoC estimator (334) and the display unit (336). The system (300) may be a part of an electric scooter or another EV. The EKF (334) is tuned to estimate the SoC of the reference cell (338A) correctly by setting the Q and R values as required. Thus, the interconnection between the reference cell (338A) and the system (300) is shown in dotted lines. As described hitherto, assume that a battery with cells (338B) with a new electrochemistry is onboarded. Now, before the battery is mounted on the scooter and sold to a customer it must be ensured that the EKF (334) is tuned to estimate the SoC of the newly onboarded battery (338B). At this stage, the inventive method (100) and (200) as described with reference to Figure 1 and Figure 2 are employed and the new Q and R values suitable for estimating the SoC of the newly onboarded battery with cells (338B) are determined and stored in a memory associated with the processing module (332) (not shown in figures for the sake of simplicity).
When a new scooter manufactured with a battery of the type of the newly onboarded battery with cells (338B) is mounted on the scooter, the processing module (332) is commanded to load the EKF (334) of that scooter with the Q and R values previously calculated for that cells type. Thus, the newly manufactured scooter with the cells of type (338B) will estimate the SoC consistently and the customer of the scooter will get the correct estimate of the SoC.
This process as described hitherto will be repeated every time a new battery type with a different electrochemistry is onboarded, for example battery with cells (338C). As a person skilled in the art will know, the process as described hitherto may be applied every time a new battery with a different electrochemistry is onboarded.
Further, it is also possible that the determination of the Q and R values for newly onboarded batteries with cells, (338B, 338C, . . .) are determined in real-time once the scooter or EV is manufactured and the customer starts using the scooter or vehicle. In this case, as described hitherto, the values of Q and R for the EKF (334) of the new scooter or vehicle may be determined by the scooter communicating the necessary measurements, for example the current being drawn by the vehicle and corresponding battery terminal voltage, to a cloud server of the manufacturer of the scooter. The part of the processing module (332) configured for determining the values of Q and R resides in the cloud server. It determines the values of Q and R for the cells of the battery based on the received measurement values and communicates the Q and R values to the scooter which then loads the newly determined Q and R values onto the EKF (334) of the new scooter. Thereby, the new scooter also starts estimating the SoC of its battery consistently as required and displaying it on the display unit (336).
Figure 4 illustrates a flowchart (400) depicting a method for tuning the estimators of State of Charge (SoC) of the two cells (for example cell (338B, 338C), until the identified slowest time constant (t) of each cell matches with the slowest time constant (t) of a reference cell (338A), according to an embodiment of the present invention.
The order in which the method steps are described below is not intended to be construed as a limitation, and any number of the described method steps can be combined in any appropriate order to execute the method or an alternative method. Additionally, individual steps may be deleted from the method, without departing from the spirit and scope of the subject matter described herein.
The method (400) may be performed by at least one processing module (332) as described with reference to Figure 3, without departing from the scope of the present disclosure. The method (400) includes steps for tuning an Extended Kalman Filter of a State of Charge estimation unit (334) for consistently estimating a State of Charge (SoC) of each of cells (338B, 338C).
In one example, the method (400) may be performed by the processing module (332) for tuning the EKF of the SoC unit (334), of the cell (338B) and (338C) of the system (300) as shown in Figure 3.
At step (444), the method (400) includes tuning the SoC EKF for achieving stability for the cell (338B). At step (446), the method (400) includes tuning SoC EKF for achieving stability for the cell (338C).
At step (448), the method (400) includes determining a time constant (t) map as a function of SoC for the cell (338B). At step (450), the method (400) includes determining a time constant (t) map as a function of SoC for battery (338C).
At step (454), the method (400) includes determining whether a slowest time constant (t) map of the reference cell (338A) matches with the identified slowest time constant (t) map for cell (338B) and (338C). Based on the output of the step (454), the processing module (332) either executes the step (452) for adjusting EKF gains by iteratively adjusting values of one or more parameters of the Extended Kalman Filter gains for the cell with the slowest time constant (t) map not matching with the slowest time constant (t) map of the reference cell, or else no further action is taken. It is to be noted that, the iterations are performed until the tau maps match a predefined threshold range, wherein the measure of the predefined threshold range" is subjective and is defined based on system requirements by the system designer. The values of the one or more parameters refer to "Q" and "R" of the EKF gains. The one or more parameters of EKF gains are adjusted while reserving stability. As known in the state of the art, the ‘Q’ and ‘R’ correspond to the process and measurement noise covariance matrices, respectively. The parameter, ‘Q’ is a covariance matrix associated with the noise in states, whereas ‘R’ is just the covariance matrix of the measurement noise. ‘R’ can be found by processing the measurements while the output of the system is held constant. The process as shown in method (400) of Figure 4 can range from being manual search to more autonomous machine learning or optimization techniques, for example gradient descent search, grid search, constrained nonlinear optimization methods, that are known in the art.
Figure 5 illustrates a graph (500) showing a simulation of SoC estimation showing inconsistent performance of cells with different electrochemistry. The graph (500) depicts the importance of method (100) as disclosed in Figure 1 for tuning the SoC estimation unit configured for different cells with different electrochemistry to deliver consistent dynamic performance.
For example, referring to Figure 5, it is observed that SoC estimation shows significantly inconsistent performance (as shown by reference numeral 564A and 564B) of cells with different electrochemistry. The process outlined in the method (400) of Figure 4 is then used to tune the two SoC estimation units of two cells with different electrochemistry until the slowest time constant matches reasonably across all SoC values.
Figure 6A and 6B illustrates a graph 600 showing a comparison of slowest time constant (t) map as a function of State of Charge for each cell (338B) and battery (338C).
Referring to Figure 6A, the graph (668A) shows the time constant (t) map where, the slowest time constant (t) map of the reference cell (338A) does not match with the identified slowest time constant (t) map for cell (338B) of the plurality of cells. The graph (668A) shows the time constant (t) map of the cell (338A) before using the tuning method (100) to match the slowest time constants.
Referring to Figure 6B, the graph (668B) shows the time constant (t) map where the slowest time constant (t) map of the reference cell (338A) matches with the identified slowest time constant (t) map for cell (338B) of the plurality of cells. The graph (668B) shows the time constant (t) map of the battery (338A) after using the tuning method (100) to match the slowest time constants.
Figure 7 illustrates a graph (700) showing the results of the simulation of SoC estimation after performing a method (100) by at least one processing module (332) for tuning the Extended Kalman Filter of the State of Charge estimation unit, on each of cell (338B) and cell (338C) of the different electrochemistry. It is observed that, after applying the method (100), the Extended Kalman Filter of the State of Charge estimation unit, for each of cell (338B) and the cell (338C), each one with a different electrochemistry, is tuned to provide consistent and uniform estimation of a State of Charge.
When the SoC estimation method (100) for tuning the EKF works perfectly, the battery pack’s actual SoC is tuned respectively. The most basic case when this is true is when the SoC follows a coulomb counting law perfectly.
?SoC?_(coulomb,final)= ?SoC?_(coulomb,initial )+ ?_(t_0)^(t_f) idt/Q

However, there are several reasons for the SoC to deviate from this equation. Some of these are:
The “Q” for the cells in the battery pack are different from that used in the above equation.
The current “i” that the BMS hardware senses has errors that will also get translated into the SoC using the equation above.
There are wiring or harness failures on the battery pack such as weld breaks, and loose sense wire connection.
In all such cases, the EKF is a robust method that can use the terminal voltage readings of the cells in the battery pack to correct the SoC estimate. How quickly it can correct itself is what we mean by the “aggression” of the EKF.
An aggressive EKF is beneficial for maintaining SoC accuracy, but at the cost of the SoC estimate shown on the scooter dashboard changing quickly (think of customers complaining about SoC dropping faster at low range). A sluggish EKF harms the SoC estimation accuracy but has the benefit of showing a more mellow progression of SoC on the scooter dashboard.
While there is no right or wrong way to tune the aggression of the EKF, it is obvious that the same scooter variants having battery packs of different cells, must have the same aggression.
The advantage and practical method of use of the disclosed method (100) and the system (300) as disclosed is for tuning the SoC estimation unit on each of the battery packs that are intended to go on the same electric vehicle but contain cells with different electrochemistry from different manufacturers. Despite the different electrochemistries in the battery installed in the vehicle, the batteries on the vehicle are configured to deliver the same: (i) Range consistency, (ii) SoC estimation performance, and (iii) SoC correction rate in case SoC estimation goes wrong for various reasons.
It will be appreciated that the modules, processes, systems, and devices described above can be implemented in hardware, hardware programmed by software, software instruction stored on a non-transitory computer readable medium or a combination of the above. Embodiments of the methods, processes, modules, devices, and systems (or their sub-components or modules), may be implemented on a general-purpose computer, a special-purpose computer, a programmed microprocessor or microcontroller and peripheral integrated circuit element, an ASIC or other integrated circuit, a digital signal processor, a hardwired electronic or logic circuit such as a discrete element circuit, a programmed logic circuit such as a programmable logic device (PLD), programmable logic array (PLA), field-programmable gate array (FPGA), programmable array logic (PAL) device, or the like. In general, any process capable of implementing the functions or steps described herein can be used to implement embodiments of the methods, systems, or computer program products (software program stored on a non-transitory computer readable medium).
Furthermore, embodiments of the disclosed methods, processes, modules, devices, systems, and computer program products may be readily implemented, fully or partially, in software using, for example, object or object-oriented software development environments that provide portable source code that can be used on a variety of computer platforms. Alternatively, embodiments of the disclosed methods, processes, modules, devices, systems, and computer program products can be implemented partially or fully in hardware using, for example, standard logic circuits or a very-large-scale integration (VLSI) design. Other hardware or software can be used to implement embodiments depending on the speed and/or efficiency requirements of the systems, the particular function, and/or particular software or hardware system, microprocessor, or microcomputer being utilized.
In this application, unless specifically stated otherwise, the use of the singular includes the plural and the use of “or” means “and/or.” Furthermore, use of the terms “including” or “having” is not limiting. Any range described herein will be understood to include the endpoints and all values between the endpoints. Features of the disclosed embodiments may be combined, rearranged, omitted, etc., within the scope of the invention to produce additional embodiments. Furthermore, certain features may sometimes be used to advantage without a corresponding use of other features.
List of reference numerals:
Components Reference numerals
300 System
332 Processing module
334 Extended Kalman Filter of a State of Charge estimation unit
336 Display
338A Reference cell
338B and 338C Cells with different electrochemistries
, Claims:1. A method (100) for tuning an Extended Kalman Filter of a State of Charge estimation unit (334) for consistently estimating a State of Charge of each of a plurality of cells (338B, 338C), each of a different electro-chemistry, wherein one of the cells is designated as a reference cell (338A), the method (100) comprising:
determining (102) a time constant (t) map as a function of State of Charge for each cell of the plurality of cells (338B, 338C);
identifying (104) a slowest time constant (t) map among the determined time constant (t) maps;
determining (106) whether a slowest time constant (t) map of the reference cell (338A) matches with the identified slowest time constant (t) map for each cell of the plurality of cells (338B, 338C); and
iteratively (108) adjusting values of one or more parameters of the Extended Kalman Filter gains for the cell with the slowest time constant (t) map not matching with the slowest time constant (t) map of the reference cell (338A).

2. The method (100) as claimed in claim 1, wherein determining (202) the time constant (t) map as the function of State of Charge for each cell of the plurality of cells (338B, 338C) comprise the steps of:
(i) measuring (212) an impulse response of each cell of the plurality of cells (338B, 338C);
(ii) using the measured impulse response for identification (214) of a state space model;
(iii) using the identified state space model for Extended Kalman Filter gain tuning (216) to achieve stable operation of an estimation model;
(iv) determining (218) the close loop system’s eigenvalues using the Extended Kalman Filter gain tuned for stability;
(v) converting (220) the determined eigenvalues to a plurality of time constants based on a mathematical model; and
(vi) selecting (222) a maximum value time constant of the plurality of translated time constants; wherein the maximum value time constant is the slowest time constant, and the slowest time constant is a time constant corresponding to a slowest eigenvalue of the close loop Extended Kalman Filter as a measure of its close loop performance; and
(vii) utilizing the slowest time constant (224) for determining the time constant (t) map as the function of State of Charge for each cell of the plurality of cells (338B, 338C).

3. The method (100) as claimed in claim 2, converting the determined eigenvalues to a plurality of time constants {t i, (wherein, the value of ‘i’ is between 1 to n)} based on a mathematical model.

4. The method (100) as claimed in claim 1, wherein while estimating the State of Charge of a given battery, choosing values of one or more parameters of the Extended Kalman Filter gains determined for a battery of the electrochemistry of the given battery.

5. The method (100) as claimed in claim 1, iteratively adjusting the values of one or more parameters of the Extended Kalman Filter gains of the cell with the slowest time constant (t) map using at least one of:
a manual method, or
a semi-automatic method utilizing a constrained grid search or optimization techniques, or
an automatic method utilizing one or more machine learning methods.

6. The method (100) as claimed in claim 2, wherein determining the time constant (t) map as the function of State of Charge for each cell of the plurality of cells (338B, 338C) based on at least one of an online mode or an offline mode or experimentally using cell cyclers.

7. The method (100) as claimed in claim 6, wherein the online mode comprises determining the time constant (t) map as the function of State of Charge using a processing module (332) on a vehicle or on a cloud.

8. A system (300) for tuning an Extended Kalman Filter of a State of Charge estimation unit (334) for consistently estimating a State of Charge of each of a plurality of cells (338B, 338C), the system (300) comprising:
the plurality of cells (338B, 338C); each of a different electro-chemistry, wherein one of the cells is designated as a reference cell (338A),
a processing module (332) configured for tuning the Extended Kalman Filter of the State of Charge estimation unit (334) for consistently estimating the State of Charge of each of the plurality of cells (338B, 338C), the processing module (332) is configured for:
determining a time constant (t) map as a function of State of Charge for each cell of the plurality of cells (338B, 338C);
identifying a slowest time constant (t) map among the determined time constant (t) maps;
determining whether a slowest time constant (t) map of the reference cell (338A) matches with the identified slowest time constant (t) map for each cell of the plurality of cells (338B, 338C); and
iteratively adjusting values of one or more parameters of the Extended Kalman Filter gains for the cell with the slowest time constant (t) map not matching with the slowest time constant (t) map of the reference cell (338A).

9. The system (300) as claimed in claim 8, wherein determining the time constant (t) map as the function of State of Charge for each cell of the plurality of cells (338B, 338C) comprise the steps of:
(i) measuring an impulse response of each cell of the plurality of cells (338B, 338C);
(ii) using the measured impulse response for identification of a state space model;
(iii) using the identified state space model for Extended Kalman Filter gain tuning to achieve stable operation of an estimation model;
(iv) determining the close loop system’s eigenvalues using the Extended Kalman Filter gain tuned for stability;
(v) converting the determined eigenvalues to a plurality of time constants based on a mathematical model; and
(vi) selecting a maximum value time constant of the plurality of translated time constants; wherein the maximum value time constant is the slowest time constant, and the slowest time constant is a time constant corresponding to a slowest eigenvalue of the close loop Extended Kalman Filter as a measure of its close loop performance; and
(vii) utilizing the slowest time constant for determining the time constant (t) map as the function of State of Charge for each cell of the plurality of cells (338B, 338C).

10. The system (300) as claimed in claim 8, wherein while estimating the State of Charge of a given battery, choosing values of one or more parameters of the Extended Kalman Filter gains determined for a battery of the electrochemistry of the given battery.

11. The system (300) as claimed in claim 8, iteratively adjusting the values of one or more parameters of the Extended Kalman Filter gains of the cell with the slowest time constant (t) map using at least one of:
a manual method, or
a semi-automatic method utilizing a constrained grid search or optimization techniques, or
an automatic method utilizing one or more machine learning methods.