DESC:FIELD OF INVENTION
The present invention relates to estimation of the life of lithium-ion batteries in electric circuits/vehicles. In particular it estimates the cycles of failure versus the Depth Of Discharge (DOD) in order to control the operation of the electric circuits/vehicle in response to such an estimation to prolong the battery life as needed.
BACKGROUND AND PRIOR ART:
A typical rechargeable lithium-ion battery includes a negative electrode and a positive electrode separated by an electrolyte. Lithium ions move from the negative electrode through the electrolyte to the positive electrode during discharging and from the positive electrode through the electrolyte to the negative electrode during charging.
Cyclic charging/discharging degrades the electrodes and, in turn, can reduce the capacity of the battery. The mechanical and/or electrochemical mechanisms of degradation are not well understood and, as a result, models that have been developed for the estimation of battery health are based primarily on short-term empirical testing that is particular to a specific battery system. Although useful in some aspects, short-term empirical testing may be inaccurate and insufficient for mathematically modelling slow electrochemical processes over much longer periods.
Estimating the life of lithium ion batteries is a longstanding issue for electric vehicles as well as energy storage applications. Lithium ion battery degradation is one of the most critical considerations in battery sizing for automotive as well as energy storage applications. Battery degradation estimation is, therefore, significant in determining the economic viability of energy storage projects.
In US 9,509,021 B2, the estimation of the capacity loss is a function that includes a state-of lithiation (SOL) swing and fracture of solid-electrolyte interphase (SEI) of an electrode of the lithium-ion battery module. This may be considered as the first physics based derivation relating the capacity loss to the state-of-lithiation swing. From a battery degradation physics perspective, however, the SEI growth and the SEI-cracking-reformation, may both contribute significantly to total degradation and thereby to the life of the battery.
Although, this method captures the SEI-cracking-reformation mechanism very well, it misses out on an important part of capacity loss, namely due to the SEI growth mechanism during cycle of addition to that during calendar aging. Further, though Depth Of Discharge (DOD) is one of the major factors affecting the battery cycle life, the exact relation between the capacity loss and the Depth Of Discharge (DOD) is not taken into consideration. The present invention, however, proposes to reformulate the equation of capacity of loss in terms of Depth Of Discharge(DOD) and demonstrate the capability of this equation in estimating the ‘cycles to failure’ against Depth Of Discharge (DOD). An exact mathematical formulation to calculate the cycles to failure is defined in the present invention.
It is also desired to have a method and device, which makes predictions with just a couple of variable parameters, and is easy to use.

Prior Art and Relevant References:-
US 9,509,021 B2 ‘Deshpande’ Dated October 17th 2014
Theory of SEI Formation in Rechargeable Batteries: Capacity Fade, Accelerated Aging and Lifetime Prediction by Matthew B. Pinson and Martin Z. Bazant at MIT Cambridge, MA
US10446879 B2 ‘Povey et al.’ Dated May 5th 2015
CN109991542 ‘WU QIONG’ Dated March 27th 2019
"Lithium-ion battery life technical sheet," Saft; www.saftbatteries.com, Bagnolet - France.
J. Li, A. M. Gee, M. Zhang and W. Yuan, "Analysis of battery lifetime extension in a SMES-battery hybrid energy storage system using a novel battery lifetime model," Energy, vol. 86, no. 0360-5442, pp. 175-185, 2015.

In a prior disclosure (A) when batteries are cycled at ‘mild’ operating conditions such as ‘moderate’ temperatures (15-45 degree Centigrade) at nominal charge-discharge rates – which incidentally corresponds to the vast majority of EV and energy storage applications, the battery degrades with Mode 2 fracture where SEI cracking and re-healing is the dominant mechanism of capacity loss. Although depth of discharge (DOD) is said to be one of the major factors affecting the battery cycle life, in the said prior art the exact relation between the capacity loss and the DOD is neither well defined nor taken into consideration. Hence, there is a need for a method for determining capacity loss in terms of DOD capable of estimating the cycles to failure against DOD as also to factor in the SEI growth mechanism during cycling in addition to the calendar aging.
In another prior disclosure (B) only SEI growth is considered for the capacity loss and battery cycle life is only measured in the calendar time and not in terms of the number of cycles. Further, the method is complex and requires multiple parameters to be found before it can be applied. Hence, there is a need for a method which is simplistic and has minimum variable parameters.
In another prior disclosure (C) on board data measurement controllers are used to estimate the battery health and does not estimate battery life. Measurement is at a particular point in time and is incapable of predicting the capacity loss in future. Hence, there is a need for a method which can be used for estimating capacity loss throughout the expected life of the battery by the usage conditions alone and without the need for any onboard data for estimating the capacity degradation.
In another prior disclosure (D) ‘Deep Learning’ techniques are used which do not use a physics-based mechanism for estimation of battery life, rather it is highly based on the data fed during the training phase. The disclosure is based on a system which is trained based on a large amount of experimental data. Hence, there is a need for a method which can be industrially applied without a large amount of data and is physics based using SEI growth in addition to SEI cracking-reformation for estimating battery life.
Data from reference documents (E) and (F) mentioned above have been used to verify the validity of the method as described in the present invention.

OBJECT OF THE INVENTION:

It is an object of the present invention to provide an improved method to be used on battery management system (BMS) or energy management system (EMS) or on battery design software and device and model for estimating “cycles/years to failure” of lithium-ion batteries by combining effects of SEI growth and SEI cracking/reforming mechanisms for various Depth Of Discharges (DoDs); which is simple to use with least variables providing appropriate controls suggestion to prolong battery life as per the need of the user.
BRIEF DESCRIPTION OF DRAWINGS:

Fig 1 provides a schematic representation depicting electrode particle (1) (grey) in a lithium ion battery, said particle is encapsulated with an SEI layer (2) (black), expanded electrode particle (1a), growth in SEI thickness (2a), fractures in the SEI layer (3) and new side reaction (3a)(orange).

Fig 2 is a graphical representation of Cycles to failure versus DOD comparing the graph of the estimation as per the method in the present invention (in blue) with the data published by SAFT (in red) which is the Reference document (E) mentioned above. The figure shows a good agreement between the experimental data and the model estimation. The figure demonstrates the ability of the method and device as described in the present invention to accurately estimate the cycles to failure with availability of minimum data.

Fig 3 is a graphical representation of Cycles to failure versus DOD, comparing the graph of the estimation as per the method in the present invention (in blue) with the data published by Li et al (in red) which is the Reference document (F) mentioned above.
Fig 4 is a Process Flow Diagram: An example process flow diagram showing the method and device as described in the present invention using the model (Equation 13f).
Fig 5 is a diagram showing load (11), battery (12), battery management system (13) and system control (14).
SUMMARY OF THE INVENTION:
The present invention relates to a device for estimating the capacity of lithium-ion batteries comprising of a Battery Management System (13) connected to a load (11), a lithium-ion battery module (12) and a system control (14) wherein the Battery Management System (13) comprises of a parameter estimator, a state estimator, and a controller used to measure State of Charge (SoC), Voltage, Temperature, and RMS current; wherein the Battery Management System (13) determines the start and end of a charge cycle, the depth of discharge, and the expected degradation to the battery module (12) to calculate the cycles to failure of the battery module (12)

The present invention further relates to the Battery Management System (13) of the device for estimating the capacity of lithium-ion batteries wherein the power demand of the load (11) is limited by the system control (14) as a response to the calculated cycles to failure of the lithium-ion battery module (12)

The present invention further relates to the Battery Management System (13) of the device for estimating the capacity of lithium-ion batteries wherein the start and end of a charge cycle and the depth of discharge of the battery module (12) is controlled by the system control (14) as a response to the calculated cycles to failure of the battery module (12)

The present invention further relates to the Battery Management System of the device for estimating the capacity of lithium-ion batteries further comprising a memory module to store the cycles to failure of the battery module (12) in place of a prior stored cycles to failure of the battery module (12)

The present invention further relates to the Battery Management System of the device for estimating the capacity of lithium-ion batteries further comprising a display module to display the cycles to failure of the battery module (12), the power demand of the load (11), the start and end of a charge cycle and the depth of discharge of the battery module (12)

The present invention also relates to a method for estimating the capacity of lithium-ion batteries comprising of a Battery Management System (13) connected to a load (11), a lithium-ion battery module (12) and a system control (14) wherein the Battery Management System (13) comprises of a parameter estimator; a state estimator; and a controller used to measure State of Charge (SoC), Voltage, Temperature, and RMS current; wherein the Battery Management System (13) determines the start and end of a charge cycle, the depth of discharge, and the expected degradation to the battery module to calculate the cycles to failure of the battery module (12)

The number of cycles to failure N are determined by the Battery Management System (13) as:

?_(i=2)^N¦(i-1)(3i-5) ?(a")^3 (DOD)?^6-(N)(N-1) (a")^2 (DOD)^4+(N)a" (DOD)^2-K' t^?-(1-(Q_N ) ¯)=0
wherein, (Q_N ) ¯ represents the capacity retention criteria defining the battery failure for a given load (11), DOD represents the Depth of discharge and a"=a^' r^2 where r is a proportionality constant with DOD such that DOD = r (state of lithiation swing of the negative electrode at the end of 1st lithiation cycle)

The present invention further relates to the method for estimating the capacity of lithium-ion batteries wherein, the incremental capacity loss on a charge cycle n based on the DOD, rms current, temperature, the duration of that cycle and the previous SEI growth capacity loss is determined by the Battery Management System (13) in a differential form as:
+ d?(Q_Totalloss )¦|_(cycle n)=a^' r^2 (?DOD?_n )^2+??K'?_(@I_n ) (?(+ Q_(loss_SEIgrowth ) ¦|_(@(t-dt)) )/?K'?_(@I_n ) )^((?-1)/?) dt
Wherein, Q_Totalloss is total capacity loss, Q_(loss_SEIgrowth )is cell capacity lost due to SEI growth, dt represents the duration of n^th cycle and ?(+ Q_(loss_SEIgrowth ) ¦|_(@(t-dt)) )/?K'?_(@I_n ) is the SEI growth capacity loss from the previous cycle

The present invention further relates to the method for estimating the capacity of lithium-ion batteries wherein, the total capacity loss after n charge cycles is determined by the Battery Management System (13) as:
+ ?(Q_Totalloss )¦|_(cycle n)=+ ?(Q_Totalloss )¦|_(cycle n-1)+a^'' (?DOD?_n )^2+??K'?_(@I_n ) (?(+ Q_(loss_SEIgrowth ) ¦|_(@(t-dt)) )/?K'?_(@I_n ) )^((?-1)/?) dt
Wherein, the total capacity loss after n charge cycles is the total capacity loss on the previous cycle n-1 and the incremental capacity loss on the cycle n

The present invention further relates to the Battery Management System of a method for estimating the capacity of lithium-ion batteries wherein the Battery Management System (13) calculates the capacity retention for an expected usage profile for energy storage in battery module (12) and the power demand of the load (11)

DETAILED DESCRIPTION OF THE INVENTION:

The terms and words used in the following description and claims are not limited to the bibliographical meanings, but, are merely used by the inventor to enable a clear and consistent understanding of the invention. The description given herein is only representative of the illustrative embodiments and examples. Only for the sake of convenience, the description has focused on a limited number of representative examples of the drawings. However, the drawings and/or illustrations and/or the appended claims in no way limit the scope of the invention. It is understood that modifications and/or alterations of the drawings/illustrations of this invention other than those specifically set forth herein may be achieved by those skilled in the art and that such modifications and alterations are to be considered as falling within the overall scope of this invention.
Terms used herein are used only in order to describe an exemplary embodiment rather than limiting the present invention. In this case, singular forms include plural forms unless interpreted otherwise in context.
List of symbols and definitions:
? Q?_(loss_SEIcrack) cell capacity loss due to SEI cracking (Ah)
(? ?Q?_(loss_SEIcrack) )_i cell capacity loss due to SEI cracking (Ah) on cycle i
SOL state-of-lithiation of the host material
?SOL state-of-lithiation swing of the negative electrode
? ?SOL?_n state-of-lithiation swing of the negative electrode at the end of nth lithiation cycle
a proportionality constant co-relating ?SOL with capacity loss due to SEI cracking (Ah)
k proportionality constant co-relating the state of lithiation swing ?SOL of the negative electrode with the cell capacity? Q?_n
Q_(loss_SEIgrowth ) cell capacity lost due to SEI growth (Ah)
K power law constant co-relating capacity loss due to SEI growth with time (Ah ?hr?^(-?) )
? power law constant for the capacity loss due to SEI growth
t duration of operation (hour)
K_stg power law constant co-relating the fractional capacity loss due to SEI growth with time during storage (?hr?^(-?) )
K_cyc power law constant co-relating the fractional capacity loss due to SEI growth with time during cycling (?hr?^(-?) )
? Q?_n cell capacity retained after n cycles (Ah)
? Q?_0 initial cell capacity (Ah)
? Q?_(loss_total) total capacity loss (Ah)
?(Q_n ) cell capacity on nth cycle normalized with the initial cell capacity
a",a^',r
proportionality constants
DOD depth of discharge (fraction)
SOC State of charge

The method as described in the present invention is the first physics-based equation to predict ‘cycles to failure’ at various DODs. With only two variable parameters the method is easy to use and is particularly pragmatic, given the inherently limited nature of battery degradation data available; especially given the rate of development of new commercial cells. In the present disclosure also validates the method and demonstrates the ease of use, using various datasets from the energy storage literature.
Commonly used organic solvents in lithium ion batteries such as Ethylene Carbonate (EC), Dimethyl Carbonate (DMC), etc., are unstable and undergo decomposition at the electrode-electrolyte interface under the operating conditions. As shown in figure 1 this results in the formation of a Solid-Electrolyte Interface (SEI) layer (2) and consequent capacity loss. Moreover, the SEI formed does not passivate completely and more side-reactions during battery usage leads to SEI thickening over time (2a). The growth of SEI is a current dependent, time dependent phenomenon. During the charge/discharge processes, the electrode material expands and contracts, leading to mechanical degradation of electrode particles as well as the SEI layer (2). As the electrode particle (1) expands, the SEI layer around the expanded electrode particle (1a) fractures (3). As the thickened SEI layer (2a) fractures, electrode surface gets exposed to the electrolyte forming a new side reaction (3a) causing further capacity loss. The larger the electrode expansion, the higher is the possibility of electrode fracture (3); and in turn, capacity loss will be more pronounced.
Prior art document (A) demonstrates that capacity loss due to SEI fracture (?Q_(loss_SEIcrack)) during i^th cycle is proportional to the square of the state of lithiation swing (?SOL) of the negative electrode during that cycle
(? ?Q?_(loss_SEIcrack) )_i?[(?SOL)^2 ]_i (Eq. 1)
? (? ?Q?_(loss_SEIcrack) )_i=a[(?SOL)^2 ]_i (Eq. 2)
where a is a proportionality constant.
For n consecutive cycles
? Q?_(loss_SEIcrack)=a{?_(i=1)^n (?? SOL?_i )^2 } (Eq. 3)
Here ?? SOL?_i is the state of lithiation swing on cycle i.
The capacity loss due to SEI thickness growth is typically modeled as a Power Law with respect to time t.
Q_(loss_SEIgrowth )=K t^? (Eq. 4)
Here K and ? are the Power Law Constants.
In a differential form, the equation 4 can be written as:
?dQ?_(loss_SEIgrowth )=?K t^(?-1) dt (Eq. 4a)
?dQ?_(loss_SEIgrowth )=?K (+ Q_(loss_SEIgrowth ) ¦|_(@(t-dt))/K)^((?-1)/?) dt (Eq. 4b)

Capacity loss represented by a power-law term above encapsulates both SEI growth during storage (i.e., chemical reactions while no current is being applied) as well as during operation (side reactions under an applied current load). The value of the power law constant K would be dependent on the operating current.

During cycling, K= K_cyc and K_cyc=f(Current,SOC,Temperature) (Eq. 4c)
During storage K= K_stg (SOC,Temperature) (Eq. 4d)
As the applied current approaches zero, value of K_cyc gets closer to K_stg at a given temperature and an average state of charge (SOC).
K_cyc =K_stg (Eq. 5)
The total capacity loss during cycle aging is the addition of the capacity loss due to SEI cracking-reformation and the capacity loss due to SEI growth. The total capacity loss can be calculated as:
? Q?_(loss_total)=? Q?_(loss_SEIcrack)+Q_(loss_SEIgrowth ) (Eq. 6)
Q_(loss_total)=a{?_(i=1)^n (?? SOL?_i )^2 }+K t^? (Eq. 7)

When a cell is cycled continuously with constant depth of discharge (DOD) window at a constant charge-discharge current, based on the derivation in Prior Art Document (A) referred to above, the equation (6) can be rewritten as:
?(Q_n )=1-(n)ak(?? SOL?_1 )+(n)(n-1) (ak)^2 (?? SOL?_1 )^2-?_(i=2)^n (i-1)(3i-5) ?(ak)^3 (?? SOL?_1 )?^3-K' t^?
(Eq. 8)
As the equation indicated, the capacity loss during for a constant DOD cycling can be calculated based on the state of lithiation swing of the first cycle ?? SOL?_1.
Here the fractional capacity retention on nth cycle is ?(Q_n ) ; and ?(Q_n )=Q_n/Q_0 .
Q_n- Capacity retention on cycle n
Q_0- Initial capacity
As per the definition of ?? SOL?_n
?? SOL?_n=kQ_(n-1) , i.e., k=?? SOL?_n/Q_(n-1)
Equation (8) can be reformulated as
?(Q_n )=1-(n)a'(?? SOL?_1 )^2+(n)(n-1) (a^' )^2 (?? SOL?_1 )^4-?_(i=2)^n (i-1)(3i-5) ?(a^' )^3 (?? SOL?_1 )?^6-K' t^?
(Eq. 9)
Here a^'=a/Q_0 and K^'=K/Q_0 .
For continuous cycling at a rms current I, the value of K would be the average value ?K_cyc (SOC)|?_(@I) over the usage state of charge (SOC) window.
K=1/(?SOC?_max-?SOC?_min ) ?_(?SOC?_max)^(?SOC?_min) ?K_cyc (SOC)|?_(@I) dSOC=1/DOD ?_(?SOC?_max)^(?SOC?_min) ?K_cyc (SOC)|?_(@I) dSOC
(Eq. 9b)
The quantity state of lithiation swing, is not a measurable quantity and that renders the equation 8 unusable for most of the applications.
The prior art mentions degradation and building mathematical models for estimating battery degradation, however translating this knowledge to pragmatic models for practical applications is difficult. A simplified model for cycle life estimation is however missing in the prior art. This is because, the inherent complexity of degradation during cycling wherein various factors such as charge rate, discharge rate, depth of discharge, mean state of charge (SOC) etc. may contribute simultaneously towards capacity loss. Mechanisms such as SEI growth, SEI cracking, particle cracking , particle isolation , electrode delamination, lithium plating, copper dissolution etc. are known to play a role in lithium ion battery degradation during cycling and it is challenging to de-convolute these effects unless the data has specific features implying the presence of one or the other. A physics-based model that includes all these effects becomes highly complex with a large number of possible fitting parameters and therefore needs extensive experimental datasets to optimize.

Although it’s widely recognized in the prior art literature that DOD is one of the major factors affecting the battery cycle life, yet the exact relation between the capacity loss and the DOD is mostly empirically calculated. Empirical relations such as analogues of the Wöhler curve are used to estimate the ‘cycles to failure’ for battery cycling with various ‘Depth of discharges (DODs)’ along with the rain-flow cycle counting techniques to estimate battery life for varying DOD usage profiles.

In vast majority of Battery Energy Storage Systems (BESS) and EV applications, the battery is expected to be used for several years with up-to few equivalent cycles per day. While battery cycling operation may result in SEI growth and SEI cracking/reformation, the non-operational period of the battery would continue to add to the SEI growth loss. From a battery degradation modeling perspective, it means the SEI growth and the SEI-cracking-reformation, may both contribute significantly to total degradation. Interestingly, although Deshpande et al [Prior disclosure (A)] captures the SEI-cracking-reformation mechanism very well, it missed out on an important part of capacity loss, namely that due to the SEI growth mechanism during cycling in addition to that during calendar aging. Moreover, the disclosures made therein co-relates the SEI cracking to state-of lithiation-swing but falls short of finding the relation with Depth of Discharge which is a more commonly used terms in this field.

According to the present invention, however, the cell capacity retained after n cycles is calculated as under by the use of depth of discharge (DOD)
?(Q_n )=1-(n)a" (DOD)^2+(n)(n-1) (a")^2 (DOD)^4-?_(i=2)^n (i-1)(3i-5) ?(a")^3 (DOD)?^6-K' t^?
(Eq. 10)
Here a"=a^' r^2 where r is a proportionality constant with DOD=r ?? SOL?_1
Equation (10), as described in the present invention is a method which gives the relation between the ‘cycles to failure’ for a given DOD cycling and the expected degradation. The equation has only 2 constants a" and K'.
If SEI growth is assumed to be a diffusion limited process (solvent diffusion through SEI to the electrode surface), the equation becomes:
?(Q_n )=1-(n)a" (DOD)^2+(n)(n-1) (a")^2 (DOD)^4-?_(i=2)^n (i-1)(3i-5) ?(a")^3 (DOD)?^6-K' t^0.5
(Eq 11)
The value of ? is observed to be typically following a square root of time (?=0.5) proportionality, indicating the above mentioned diffusion limited process.
Cycles to failure calculations:
Again rearranging the above equation 10 to estimate the number of cycles to failure, according to the present invention the equation 10 becomes:
?_(i=2)^N¦(i-1)(3i-5) ?(a")^3 (DOD)?^6-(N)(N-1) (a")^2 (DOD)^4+(N)a" (DOD)^2-K' t^?-(1-(Q_N ) ¯)=0
(Eq 12)
Here N represents the cycles to failure and ?(Q_N ) represents the capacity retention criteria defining the battery failure for a given application.
For cases, where varying DOD is used for the operation, with carrying current, the capacity loss can be calculated numerically modifying the equation 7 in a differential form, and appropriate substitution for the depth of discharge
+ (d?(Q_Totalloss ))/dt¦|_(cycle n)=(d?(Q_(loss_SEIcracking ) ))/dn dn/dt+(d?(Q_(loss_SEIgrowth ) ))/dn dn/dt (Eq 13a)
+ (d?(Q_Totalloss ))/dt¦|_(cycle n)=a^' [(?SOL)^2 ]_n dn/dt+d/dt (?K'?_(@I_n ) t^? ) (Eq 13b)
Here dt represents the duration of n^th cycle
Again substituting, the state of lithiation swing with the depth of discharge of that cycle,
+ (d?(Q_Totalloss ))/dt¦|_(cycle n)=a^' r^2 (?DOD?_n )^2 dn/dt+??K'?_(@I_n ) t^(?-1) (Eq 13c)
Substituting, the time variable t with the SEI growth capacity loss from the previous cycle, following equation can be obtained
+ d?(Q_Totalloss )¦|_(cycle n)=a^' r^2 (?DOD?_n )^2+??K'?_(@I_n ) (?(+ Q_(loss_SEIgrowth ) ¦|_(@(t-dt)) )/?K'?_(@I_n ) )^((?-1)/?) dt (Eq 13d)
Equation 13d can be used for calculating incremental capacity loss on a given cycle based on the DOD, rms current, temperature, the duration of that cycle and the previous SEI growth capacity loss.
+ ?(Q_Totalloss )¦|_(cycle n)=+ ?(Q_Totalloss )¦|_(cycle n-1)+a^' r^2 (?DOD?_n )^2+??K'?_(@I_n ) (?(+ Q_(loss_SEIgrowth ) ¦|_(@(t-dt)) )/?K'?_(@I_n ) )^((?-1)/?) dt
(Eq 13e)
Using a^''=a^' r^2 for simplification
+ ?(Q_Totalloss )¦|_(cycle n)=+ ?(Q_Totalloss )¦|_(cycle n-1)+a^'' (?DOD?_n )^2+??K'?_(@I_n ) (?(+ Q_(loss_SEIgrowth ) ¦|_(@(t-dt)) )/?K'?_(@I_n ) )^((?-1)/?) dt
(Eq 13f)
The total capacity loss after n cycles, can be calculated based on the total capacity loss on the previous cycle n-1 and the incremental capacity loss on the cycle n as shown by equation 13e.
The equation 13d, 13e and 13f are a very powerful equations that allow calculation of capacity loss for various current and varying depth of discharge (DOD) for an application where the DOD and current of application is continuously varying.
Equation 13f can be easily implemented in devises such as battery management system and system sizing soft-wares such as HOMER to calculate the capacity retention for an expected usage profile for energy storage and electric vehicle applications as mentioned in the simplified Process Flow at Figure 4
Figure 4 is an example process flow diagram showing the use of the model (Equation 13f) to calculate on board state of health after a certain usage and the expected battery degradation over the expected usage profile of the battery in that particular application. The method as described in the present invention is performed by the battery management system (13) as shown in Figure 5 in the preferred embodiment of the present invention however the same may also be used by system sizing softwares.
The battery usage conditions such as current of operation, the depth of discharge in a particular cycle, temperature of operation could affect the rate of capacity fade. With the presented model, the values of the parameters a^'',?K'?_(@I_n ), - predetermined during the model calibration phase, are used to determine the capacity loss due to the SEI growth and SEI cracking mechanisms using equation 13f.
As shown in Figure 4, when the battery is being used, the parameters such as RMS current, voltage temperature and state of charge (SOC) are monitored continuously. These parameters are used to determine the start and end of a cycle. Typically, significant change in charge/discharge rate would mark end of a usage cycle. Once a cycle is marked to be complete, the depth of discharge is determined. With the data of RMS current, depth of discharge, the duration of usage and existing capacity loss, new capacity retention is determined using the model presented (equation 13f). Appropriate constants associated with SEI cracking and SEI growth loss are used to execute calculation in the model. Such a methodology is used for state of health SOH determination. Once the new value of SOH is estimated it is used for determination of DOD in the next usage cycle. For the remaining useful life (RUL) calculations and/or estimated degradation for an expected degradation model, expected usage pattern is processed using the model. The SOH estimation and RUL estimation algorithms are combined in one process as shown in the diagram or they could be separated and used independently.
Figure 5 is a diagram showing an embodiment of the present invention where Load (11) could be an electric vehicle or an electric grid or any other system which is demanding/supplying power to the battery (12). The battery management system (BMS) (13) understands the current state of the battery and decides how much the battery can support in-terms of power delivery or power storage. The System control (14) communicates with the system external to the battery and determines the expected power demand/supply from/to battery. It communicates with the BMS (13) and aims to limit the power demand/supply to/from the battery according the battery capability based on the conditions such as state of charge (SOC), state of health (SOH), temperature etc.
The battery management system (BMS) (13), is responsible for the efficiency, safety, and longevity of Lithium-ion batteries. The advanced battery management systems carefully controls the battery charge discharge current, the operating voltages, the temperature response of the battery etc based on the user provided data for the battery and or onboard learning of battery state. Battery state includes parameters such as battery state of power, battery of health etc. The advanced BMS (13) may use various mathematical models, along with numerical techniques such as but not limited to kalman filtering, machine learning algorithms, neural network methods etc in conjunction with the on-board measurement of the voltage, current, temperature data to estimate battery states.
The present invention comprises of a device and method which performs the algorithm embedded on the advance BMS/EMS, takes the voltage, current, temperature inputs from the battery pack as the battery is used in the field and processes the data to determine the state of health of the battery on board. By processing the existing usage data such as depth of discharge (DOD), the resting SOC, the average SOC window, weighted average temperature etc., the algorithm, further estimates the expected battery usage in terms of charge discharge rates, DODs, average SOCs during resting, temperature distribution etc for the rest of the life. This data is processed through the algorithm to project the Remaining Useful Life (RUL) before the battery reaching the battery End of Life (EOL). The BMS should be connected to current sensors, voltage sensors, temperature sensors providing battery data at various locations with the battery pack/rack/container as it’s being used. The BMS should have a microprocessor with sufficient memory for running the algorithms provided.

Once a specified incremental degradation happens on the battery capacity, newer projections of RUL are performed in the algorithm with multiple sets of following control variables
The maximum state of charge (SOC)
The depth of discharge
The time of charging and discharging
The battery cooling onset temperatures
The maximum charge power and discharge power
An appropriate set of control variables are suggested to improve the battery life with the use concent. These control variables would be communicated to control systems.
The present invention determines the expected battery life for a second life application once the specified end of life conditions is met during the first life of the battery
The RUL calculations would be processed to determine the values of energy storage system once the battery reaches the end-of-life conditions for the specified application.
Another embodiment of the present invention invention can be used for Model based design mode or Model in Loop Mode independently or in combination with the softwares such as HOMER, PVSyst to accurately determines the battery life for the expected battery usage. The battery designing aspects such as battery size, the thermal controls, the electrical controls etc. can be tuned to meet the specified battery life. In other cases, the simulations would be useful to select the battery cells, defining experimental test methods or verification procedures.
As shown in Figure 2 to verify the validity of the method and device as described in the present invention, the equation 12 above was applied to data published in the ‘lithium ion battery life technical sheet by SAFT’ [Reference document (E) above]. As per this publication, the cells are considered to reach end of life when capacity retention reaches 70% of the initial capacity, i.e., ?(Q_N )=0.7 . The cycles to failure for the DOD = 100% and DOD = 60%, 6720 and 9610 cycles respectively, were considered as the known points and the values of constants a" and K' were established by solving equation 12 for both the cases. In absence of availability of calendar life data to estimate the value of ?, we assumed that the SEI growth is a diffusion limited process and therefore, ?=0.5. We note that, only positive and real values of a" and K' would make sense to consider. In this example, the values found were a"=3.5572×?10?^(-5) and K'=0.0009 ( ?hr?^(-0.5) ). With these two values, the cycles to failure for various DODs were calculated and compared against the experimental data provided by the publication. The estimations based on the method as described in the present invention match closely to the values provided by the publication.
As shown in Figure 3 to validate further, we use the DOD vs Cycles to Failure data presented in Li et al. [Reference document (F) above]. This publication defines 20% capacity loss as the end of life for their batteries. Among the presented data points, the cycle numbers corresponding to DOD = 100% and DOD = 70% were considered as the known points (points circled yellow in figure 3). Again, assuming diffusion limited SEI growth, the values of constants a" and K' were established as a"=8.4783×?10?^(-6) and K'=0.0024 ( ?hr?^(-0.5) ). Using equation 12, the method as described in the present invention the cycles to failure values for various DODs are estimated and we find that the estimations by the method as described in the present invention (equation 12) match very closely with the experimental values with exception of very low SOCs.

The present invention includes a device containing Lithium ion batteries wherein the said device can measure and estimate the remaining useful life corresponding to the depth of discharge (DOD) and usage duration of the said Lithium ion batteries by collecting the required data from the said batteries and applying the method as described in equation 10 of the present invention to the data collected and stored on the device.

The said device included in the present invention further comprises of a controller, sensors, memory and output module for processing the data with various controls conditions to estimate the RUL of the said Lithium ion batteries for the expected usage and thereafter performing a set of predefined commands in response to the information recorded and/or displayed.

The said device included in the present invention further comprises of a updates the RUL upon specified incremental capacity fade and reprocess the data to update the expected usage conditions and provide a newer set of control conditions for Lithium ion batteries by performing a set of predefined commands in response to the information recorded and/or displayed.

The said device suggests the optimal control limits to prolong the battery life or to meet the target useful life based on information processed through the algorithms where its control limits could change the depth of discharge (DOD), the maximum state of charge, the minimum state of charge, the time of charging/ discharging, the cooling/heating temperature setpoints, charge power limits, discharge power limits. Some of these control limits would be implemented by the said device itself whereas some of the limits would be communicated to other control systems.

The present invention further includes a device that takes new target useful life requirement from the user during the operation and uses those conditions to redefine the control limits which could change the DOD, the maximum state of charge, the minimum state of charge, the time of charging/ discharging, the cooling/heating temperature setpoints, charge power limits, discharge power limits. Some of these controls limits would be implemented by the said device itself whereas some of the limits would be communicated to other control systems.

The present invention includes a device that can be used for Hardware in Loop (HIL), Model in Loop (MIL) simulations for the battery designing purpose. This includes battery sizing, battery thermal system design, battery electrical distribution system design etc.

The present invention includes a device which processes the battery usage data to estimate the battery remaining life for a battery second life application. The proposed devise may further process the RUL for various applications to calculate the remaining values of the battery pack/rack after a certain aging of the battery.

The present invention further includes a device that takes data from various current sensors, voltage sensors, temperature sensors, filters errors in the measurements and process the measurements appropriately to calculate signals such as State of charge (SOC), depth of discharge (DOD), charge throughput, discharge throughput etc. to be used for the RUL calculations.

The present invention further includes a device and a power grid for storage of electrical energy, containing Lithium ion batteries wherein the said device and power grid can measure and estimate the cycle numbers corresponding to the DOD of the said Lithium ion batteries by collecting the required data from the said batteries and applying the method as described in equation 10 of the present invention to the data collected and stored on the device.

The present invention further includes a device and a power grid further comprises of a controller, memory and output module for recording and displaying the cycles numbers and DOD of the said Lithium ion batteries and thereafter performing a set of predefined commands in response to the information recorded and/or displayed.

The present invention further includes a vehicle for storage of electrical energy, containing Lithium ion batteries wherein the said vehicle can measure and estimate the cycle numbers corresponding to the DOD of the said Lithium ion batteries by collecting the required data from the said batteries and applying the method described in equation 10 of the present invention to the data collected and stored on the device.

The present invention further includes a vehicle further comprising of a controller, memory and output module for recording and displaying the cycles numbers and DOD of the said Lithium ion batteries and thereafter performing a set of predefined commands in response to the information recorded and/or displayed.
Advantages of the present invention

An advantage of the present invention is that this method determines capacity loss in terms of DOD and is capable of estimating the ‘cycles to failure’ against DOD by factoring in the SEI growth mechanism during cycling in addition to the calendar aging.

Another advantage of the present invention is that this method is simplistic such that the equation has only two constants.

Another advantage of the present invention is that this method can be used for estimating capacity loss throughout the expected life of the batteries by the usage conditions alone and does not need any onboard data for estimating the capacity degradation.

Another advantage of the present invention is that this method can be industrially applied without the need of a large amount of data used by deep learning models.

Another advantage of the present invention is that this method is physics based using SEI growth in addition to SEI cracking-reformation for estimating battery.
,CLAIMS:We Claim
A device for estimating the capacity of lithium-ion batteries comprising of
A Battery Management System (13) connected to a load (11), a lithium-ion battery module (12) and a system control (14)
wherein the Battery Management System (13) comprises of
a parameter estimator, a state estimator, and a controller used to measure State of Charge (SoC), Voltage, Temperature, and RMS current;
wherein the Battery Management System (13) determines the start and end of a charge cycle, the depth of discharge, and the expected degradation to the battery module (12) to calculate the cycles to failure of the battery module (12)

The Battery Management System (13) of the device for estimating the capacity of lithium-ion batteries as claimed in Claim 1 wherein the power demand of the load (11) is limited by the system control (14) as a response to the calculated cycles to failure of the lithium-ion battery module (12)

The Battery Management System (13) of the device for estimating the capacity of lithium-ion batteries as claimed in Claim 1 wherein the start and end of a charge cycle and the depth of discharge of the battery module (12) is controlled by the system control (14) as a response to the calculated cycles to failure of the battery module (12)

The Battery Management System of the device for estimating the capacity of lithium-ion batteries as claimed in Claim 1 further comprising a memory module to store the cycles to failure of the battery module (12) in place of a prior stored cycles to failure of the battery module (12)

The Battery Management System of the device for estimating the capacity of lithium-ion batteries as claimed in Claim 1 further comprising a display module to display the cycles to failure of the battery module (12), the power demand of the load (11), the start and end of a charge cycle and the depth of discharge of the battery module (12)

A method for estimating the capacity of lithium-ion batteries comprising of
A Battery Management System (13) connected to a load (11), a lithium-ion battery module (12) and a system control (14)
wherein the Battery Management System (13) comprises of
a parameter estimator; a state estimator; and a controller used to measure State of Charge (SoC), Voltage, Temperature, and RMS current;

wherein the Battery Management System (13) determines the start and end of a charge cycle, the depth of discharge, and the expected degradation to the battery module to calculate the cycles to failure of the battery module (12)

The number of cycles to failure N being determined by the Battery Management System (13) as:
?_(i=2)^N¦(i-1)(3i-5) ?(a")^3 (DOD)?^6-(N)(N-1) (a")^2 (DOD)^4+(N)a" (DOD)^2-K' t^?-(1-(Q_N ) ¯)=0
wherein,
(Q_N ) ¯ represents the capacity retention criteria defining the battery failure for a given load (11)
DOD represents the Depth of discharge
a"=a^' r^2 where r is a proportionality constant with DOD such that DOD = r (state of lithiation swing of the negative electrode at the end of 1st lithiation cycle)

The method for estimating the capacity of lithium-ion batteries as claimed in Claim 6 wherein, the incremental capacity loss on a charge cycle n based on the DOD, rms current, temperature, the duration of that cycle and the previous SEI growth capacity loss is determined by the Battery Management System (13) in a differential form as:
+ d?(Q_Totalloss )¦|_(cycle n)=a^' r^2 (?DOD?_n )^2+??K'?_(@I_n ) (?(+ Q_(loss_SEIgrowth ) ¦|_(@(t-dt)) )/?K'?_(@I_n ) )^((?-1)/?) dt
Wherein,
Q_Totalloss is total capacity loss
Q_(loss_SEIgrowth )is cell capacity lost due to SEI growth
dt represents the duration of n^th cycle
?(+ Q_(loss_SEIgrowth ) ¦|_(@(t-dt)) )/?K'?_(@I_n ) is the SEI growth capacity loss from the previous cycle

The method for estimating the capacity of lithium-ion batteries as claimed in Claim 7 wherein, the total capacity loss after n charge cycles is determined by the Battery Management System (13) as:
+ ?(Q_Totalloss )¦|_(cycle n)=+ ?(Q_Totalloss )¦|_(cycle n-1)+a^'' (?DOD?_n )^2+??K'?_(@I_n ) (?(+ Q_(loss_SEIgrowth ) ¦|_(@(t-dt)) )/?K'?_(@I_n ) )^((?-1)/?) dt
Wherein,

The total capacity loss after n charge cycles is the total capacity loss on the previous cycle n-1 and the incremental capacity loss on the cycle n

The Battery Management System of a method for estimating the capacity of lithium-ion batteries as claimed in Claim 6 wherein the Battery Management System (13) calculates the capacity retention for an expected usage profile for energy storage in battery module (12) and the power demand of the load (11)