>116 may include performing a full discharge of the battery 116 at a specified a discharge current (I_dch). In this regard, for example, the actual capacity ( [Image Omitted]

_Ø) may be determined using equation (3):

$\begin{matrix} Q_{\emptyset} = I_{dch} t_{dch}, & (3) \end{matrix}$

where I_dchis the specified discharge current and t_dchis the time it takes to fully discharge the battery 116. In some embodiments, the computing device 126 and/or the battery testing device 102 may be configured to determine a temperature dependent actual capacity ( [Image Omitted] _t) of the battery 116 using equation (4):

$\begin{matrix} Q_{t} = \frac{Q_{\emptyset}}{1 + α (t_{2} - t_{1})}, & (4) \end{matrix}$

where α is the temperature coefficient (e.g., the temperature may impact the capacity of the battery). In some embodiments, as shown by equations (1)-(4), the temperature dependent actual capacity ( [Image Omitted] _t) of the battery 116 may be influenced by a number of factors. For example, the temperature dependent actual capacity (_t) of the battery may be influenced by electrochemical equivalent of the active substances from which the electrodes (e.g., positive electrode 114 and negative electrode 112) of the battery 116 are made, the discharge current (I_dch) (e.g., the strength of the discharge current (I_dch)), temperature (e.g., ambient temperature around the battery 116), the utilization factor (β), the battery type (e.g., a lead battery type, a lithium ion battery type, etc.), electrode thickness (e.g., thickness of the positive electrode 114 and/or the negative electrode 112), electrode surface area (e.g., surface area of the positive electrode 114 and/or the negative electrode 112), phase transformation of the battery 116, and/or the like.

In some embodiments, the computing device 126 and/or the battery testing device 102 may be configured to determine the capacity of the battery 116 at a discharge rate of 1 ampere (Q_dch), which may be determined using equation (5):

$\begin{matrix} Q_{dch} = I^{k} t, & (5) \end{matrix}$

where I is the actual value of the discharge current, t is the actual time it takes to discharge the battery 116 and k is Peukert's constant. In some embodiments, based at least in part on equation (5), the computing device 126 and/or the battery testing device 102 may be configured to determine equation (6) in which the capacity of the battery 116 at a discharge rate of 1 ampere (Q_dch) is expressed in terms of the utilization factor (β) (e.g., the utilization factor being the coefficient of usability of the active mass of an electrode (e.g., the positive electrode 114 and/or the negative electrode 112)), the mass of the active mass (m) of the electrodes, and the electrochemical equivalent of the substance at discharge (k⁽⁶⁾):

$\begin{matrix} Q_{dch} = k^{(6)} β m, & (6) \end{matrix}$

In some embodiments, the computing device 126 and/or the battery testing device 102 may be configured to determine the change in volume of the active mass of the positive electrode 114 based at least in part on a discharge of at least some current from the battery 116 using equation (7):

$\begin{matrix} V_{PAM}^{I} = V_{PAM}^{'} + S_{PAM}^{'} Δ δ_{PAM}^{'}, & (7) \end{matrix}$

where V_PAM^Iis the change in volume of the active mass, V′_PAMis the volume of the active mass before discharge of at least some current from the battery 116, S′_PAMis a one-sided geometrical surface of the positive electrode 114, and Δδ′_PAMis the thickness variation of the positive electrode 114 as a result of the discharge of at least some current from the battery 116.

In some embodiments, the computing device 126 and/or the battery testing device 102 may be configured to determine the change in volume of the active mass of the negative electrode 112 based at least in part on a discharge of at least some current from the battery 116 using equation (8):

$\begin{matrix} V_{NAM}^{II} = V_{NAM}^{′′} + S_{NAM}^{′′} Δ δ_{NAM}^{′′}, & (8) \end{matrix}$

where V_NAM^IIis the change in volume of the active mass, V″_NAMis the volume of the active mass before discharge of at least some current from the battery 116, S″_NAMis a one-sided geometrical surface of the negative electrode 112, and Δδ″_NAMis the thickness variation of the negative electrode 112 as a result of the discharge of at least some current from the battery 116.

In some embodiments, the state of charge of the battery 116 may be determined based at least in part on the thermodynamic and/or electrochemical factors described above (e.g., based at least in part on equations (1)-(8)). In this regard, for example, the factors are the interdependent connection between the capacity of the battery 116 and the strength of the discharge current, the length of time that the discharge current is applied for, the temperature, the usability of the active masses in the battery 116, and/or the like.

In some embodiments, at least in part to determine the state of charge, the computing device 126 may be configured to cause the battery testing device 102 to apply a plurality of resistive loads 402 to the battery 116. Each of the plurality of resistive loads 402 are applied for an associated time period of a plurality of time periods. For example, a first resistive load may be applied to the battery 116 for a first time period and a second resistive load may be applied to the battery 116 for a second time period.

In some embodiments, each of the plurality of resistive loads 402 are applied to at least one of a plurality of regions 502 of one or more electrodes associated with the battery 116 (e.g., negative electrode 112 and/or the positive electrode 114). For example, each of the plurality of resistive loads 402 may be applied to a first region 502A of the plurality of regions 502, a second region 502B of the plurality of regions 502, and/or a third region 502C of the plurality of regions 502.

In some embodiments, a porosity of one or more electrodes associated with the battery 116 may vary throughout one or more electrodes associated with the battery 116. For example, 95 percent of the one or more electrodes associated with the battery 116 may be associated with a first porosity and 5 percent of the one or more electrodes associated with the battery 116 may be associated with a second porosity. In some embodiments, the variation in the porosity of one or more electrodes associated with the battery 116 may impact the state of charge determination. For example, in order to accurately determine the state of charge of the battery 116 it may be desirable to determine the state of charge of the battery based at least in part on resistive loads that have been applied to a region of one or more electrodes associated with the battery 116 most representative of the overall porosity of the one or more electrodes (e.g., the first porosity). In this regard, at least in part by applying each of the plurality of resistive loads 402 to at least one of the plurality of regions 502, the computing device 126 and/or battery testing device 102 may be configured to accurately determine the state of charge of the battery 116 (e.g., the computing device 126 and/or battery testing device 102 may be able to determine the state of charge of the battery 116 such that the porosity of a portion of one or more electrodes associated with the battery 116 does not cause an inaccurate state of charge to be determined).

In some embodiments, the plurality of resistive loads 402 may be applied to the battery 116 in stages. For example, a first portion of the plurality of resistive loads 402 may be applied to the battery 116 in a first stage and a second portion of the plurality of resistive loads 402 may be applied to the battery 116 in a second stage (e.g., if there are four resistive loads in the plurality of resistive loads 402, three resistive loads may be applied in the first stage and one resistive load may be applied in the second stage). In some embodiments, after applying the first portion of the plurality of resistive loads 402 to the battery 116 a preliminary state of charge of the battery may be determined. In some embodiments, after applying the second portion of the plurality of resistive loads 402 to the battery 116, the state of charge of the battery 116 may be determined. In some embodiments, the preliminary state of charge may be the same as the state of charge. In some embodiments the preliminary state of charge may be different than the state of charge.

In some embodiments, by applying the plurality of resistive loads 402 to the battery 116, the battery testing device 102 may be configured to generate a corresponding plurality of discharge currents associated with the battery 116 (e.g., a plurality of currents discharged by the battery 116). In some embodiments, the computing device 126 may be configured to receive, from the battery testing device 102, a plurality of measured voltages. In this regard, for example, the battery testing device 102 may be configured to determine the plurality of measured voltages. In some embodiments, each of the plurality of measured voltages may be associated with one of the plurality of time periods (e.g., the computing device 126 receives a measured voltage for each time period of the plurality of time periods).

In some embodiments, each of the plurality of measured voltages may be associated with one of the plurality of regions 502 (e.g., the computing device 126 receives a measured voltage for each of the plurality of regions 502). In this regard, for example, if the plurality of regions 502 includes three regions and the plurality of time periods includes three time periods, the plurality of measured voltages may include nine measured voltages (e.g., three associated with each of the plurality of regions 502 and/or three associated with each of the plurality of time periods). For example, a matrix may be formed that includes the plurality of measured voltages (e.g., the matrix including the measured voltages for each time period and region). In some embodiments, based at least in part on the plurality of measured voltages, the computing device 126 and/or the battery testing device 102 may be configured to determine the state of charge of the battery. In this regard, for example, by generating the corresponding plurality of discharge currents associated with the battery 116 that are each associated with a particular strength and particular time period while a voltage associated with the battery 116 is measured (e.g., the plurality of measured voltages), the electrochemical reaction of the battery 116 may be assessed (e.g., to determine the state of charge of the battery 116). Said differently, because the electrochemical reaction of the battery 116 is dependent on the strength of the plurality of discharge currents (e.g., as generated by applying the plurality of resistive loads 402) the state of charge of the battery 116 may be determined by determining the plurality of voltages.

In some embodiments, it may be necessary to select the plurality of resistive loads 402 such that the resistive loads can provide the necessary discharge current strengths as well as select the plurality of time periods such that each of the plurality of resistive loads 402 are applied for a necessary time period. In some embodiments, the battery testing device 102 may be able to determine the plurality of measured voltages which are dependent on the capacity of the battery 116 (e.g., such that the state of charge of the battery 116 may be determined). In some embodiments, at least one of the plurality of resistive loads 402 may be selected such that at least one of the plurality of measured voltages is an open circuit voltage (e.g., the restive load is large).

In some embodiments, each of the plurality of measured voltages are dependent on a potential (e.g., a voltage) of the positive electrode 114 and/or a potential of the negative electrode 112. In this regard, since a voltage associated with the battery 116 (e.g., a measured voltage) is the sum of the potential of the positive electrode 114 and the potential of the negative electrode 112, which depend on the strength of the discharge current (e.g., the number of amperes of the discharge current), it means that the voltage associated with the battery 116 also depends on the value of the discharge current. In some embodiments, the value of the discharge current, represents the speed of the occurring electrochemical process of releasing electrical energy from the battery 116 to the plurality of resistive loads 402, which is represented by equation (9):

$\begin{matrix} i = {nFk}^{'} C_{ox} \exp (- \frac{α n F ε}{RT}) i = {nFk}^{'} C_{red} \exp [- \frac{(1 - α) n F ε}{RT}], & (9) \end{matrix}$

where (ε) is the potential of the electrode, (n) is the number of electrons involved in the current generating process, (F) is Faraday's constant, (R) is the universal gas constant, (T) is temperature (e.g., temperature in Kelvin), (k′) is the rate constant, (α) is the electrochemical active substance involved in the reaction, (C_ox) is the concentration of the oxidized form of the active substance involved in the reaction, and (C_red) is the concentration of the reduced form of the active substance involved in the reaction.

In some embodiments, based on equation (9) showing the dependency of the speed of the electrochemical processes in the battery 116 on the potential of the positive electrode 114 and/or the potential of the negative electrode 112, it follows that as the values of the potential of the positive electrode 114 and/or the potential of the negative electrode 112 is lowered, the voltage associated with the battery 116 correspondingly lowers, meaning that the available charge in the active masses of the battery 116 is diminishing. In this regard, by keeping a constant speed of the electrochemical discharge process of the battery 116, the voltage associated with the battery 116 may be determined from which the state of charge of the battery 116 may be determined. For example, one or more mathematical algorithms may be used to determine the state of charge from the plurality of measured voltages.

In some embodiments, based on the above, the computing device 126 and/or the battery testing device 102 may be configured to run one or more testing routines for determining the state of charge of the battery 116. In some embodiments, the one or more testing routines may each be customized for a particular battery type, battery size, and/or the like. For example, Table 1 below illustrates an example first testing routine for when the battery 116 is a lead battery that has four resistive loads applied to determine the state of charge of the battery 116.

TABLE 1

First phase

Measuring the voltage values of the battery in open circuit

Value
Higher or equal to 11.8 V
Lower than 11.8 V

Decision
Battery testing continues
Battery for scrap

Second phase

Formation of a primary matrix of 3 regions, where defined voltage values are set for the

battery. These values in the three regions of the matrix, will be matched by a computational

mathematical algorithm with the values measured at the end of the third step of the second

phase

1^stregion
2^ndregion
3^rdregion

11.30-11.59 V
11.60-11.99 V
12.00-12.29 V

First step
Applying a resistive load to the battery for 3 seconds to

generate a discharge current of 2.5 A-2 A for 3 seconds.

Second step
Applying a resistive load to the battery for 4 seconds to

generate a discharge current of 0.8 A-1 A.

Third step
Applying a resistive load to the battery for 4 seconds to

generate a discharge current of 0.5 A-0.65 A.

Reading the measured voltages of the battery at the

end of the third step of the second phase

of the testing routine

Fourth step
Measuring voltage of the battery at the 60^thsecond after

completion of applying the resistive loads to the battery in

the second phase of the testing routine

Preliminary formation of secondary matrix with

three regions, where three battery voltage

values ranges are set

1^stregion
2^ndregion
3^rdregion

12.30-12.59 V
12.60-12.99 V
13.00-13.30 V

The testing routine includes using a mathematical algorithm to perform a comparison of the

measured values within the region of the 60^thto 100^thsecond from the beginning of the fourth

step of the second phase of the testing routine, with the values in the three regions of the

secondary matrix. After performing the comparison, the device displays the state of charge of

the battery, such as by presenting the values visually in different colours.

Red
Yellow
Green

Discharged
Half charged
Charged

In some embodiments, the computing device 126 and/or the battery testing device 102 may be configured to perform the first testing routine by first performing a first phase of the first testing routine. In some embodiments, the first phase may include measuring the battery 116 in an open circuit configuration. In some embodiments, the first testing routine only proceeds to the second phase if the voltage of the battery 116 is above a voltage threshold (e.g., 10.8 volts).

In some embodiments, the second phase of the testing routine for determining the state of charge of the battery 116 (e.g., when the battery 116 is a lead battery) may include determining at least three measured voltages (e.g., of the plurality of measured voltages) of the battery 116 at the end of three test steps. In this regard, each of the three test steps include applying a different resistive load to the battery 116 for a different time period to obtain one or more different discharge currents. Additionally, or alternatively, each of the three test steps include applying a different resistive load to a different region of the plurality of regions 502 of the battery 116 to obtain one or more different discharge currents. In some embodiments, the particular resistive loads and time periods may be determined at least in part based on equations (1), (3), (4), and (6). In this regard, the resistive loads and/or the time periods may be determined such that the resulting discharge currents would be theoretically possible for the battery 116 to produce and/or such that the battery was not damaged by performing the first testing routine. In some embodiments, at the end of the three test steps, a preliminary state of charge of the battery 116 may be determined.

In some embodiments, the second phase of the testing routine for determining the state of charge of the battery 116 (e.g., when the battery 116 is a lead battery) may include a fourth step, after the first three steps, in which a voltage of the battery 116 is measured for a particular time period (e.g., 30 to 120 seconds) when the battery 116 is in an open circuit configuration. In some embodiments, the measured voltage of the battery 116 at the end of the fourth step gives information on the recovery progress of the battery 116 after being subjected to the three resistive loads in the first three steps of the second phase. In some embodiments, the state of charge of the battery 116 may be determined from the measured voltage of the battery 116 at the end of the fourth step. In some embodiments, the indicator light 106 of the battery testing device 102 may be configured to display the state of charge of the battery 116. Additionally, or alternatively, the display panel 118 may be configured to display the state of charge of the battery 116.

As another example, Table 2 below illustrates an example second testing routine for when the battery 116 is a lithium-ion battery that has four resistive loads applied to determine the state of charge of the battery 116.

TABLE 2

First phase

Measuring the voltage values of the battery in open circuit

Value
Higher or equal to 11.2 V
Lower than 11.2 V

Decision
Battery testing continues
Battery for scrap

Second phase

Formation of a primary matrix of 3 regions, where defined voltage values are set for the

battery. These values in the three regions of the matrix, will be matched by a computational

mathematical algorithm with the values measured at the end of the third step of the second

phase

1^stregion
2^ndregion
3rd region

11.50-12.09 V
12.10-13.29 V
13.30-14.20 V

First step
Applying a resistive load to the battery for 3 seconds to

generate a discharge current of 2 A.

Second step
Applying a resistive load to the battery for 4 seconds to

generate a discharge current of 5.66 A

Third step
Applying a resistive load to the battery for 4 seconds to

generate a discharge current of 8 A

Reading the measured voltages of the battery at the

end of the third step of the second phase

of the testing routine.

Fourth step
Measuring voltage of the battery at the 60^thsecond after

completion of applying the resistive loads to the battery in

the second phase of the testing routine

Preliminary formation of secondary matrix with

three regions, where three battery voltage

values ranges are set

1^stregion
2^ndregion
3rd region

13.50-14.19 V
14.20-14.69 V
14.70-15.00 V

The testing routine includes using a mathematical algorithm to perform a comparison of the

measured values within the region of the 10^thto 30^thsecond from the beginning of the fourth

step of the second phase of the testing routine, with the values in the three regions of the

secondary matrix. After performing the comparison, the device displays the state of charge of

the battery, such as by presenting a percentage.

State of charge of the battery: %

In some embodiments, the computing device 126 and/or the battery testing device 102 may be configured to perform the second routing by first performing a first phase of the second testing routine. In some embodiments, the first phase may include measuring the battery 116 in an open circuit configuration. In some embodiments, the testing routine only proceeds to the second phase if the voltage of the battery 116 is above a voltage threshold (e.g., 11.2 volts).

In some embodiments, the second phase of the testing routine for determining the state of charge of the battery 116 (e.g., when the battery 116 is a lithium-ion battery) may include determining at least three measured voltages (e.g., of the plurality of measured voltages) of the battery 116 at the end of three test steps. In this regard, each of the three test steps include applying a different resistive load to the battery 116 for a different time period to obtain one or more different discharge currents. Additionally, or alternatively, each of the three test steps include applying a different resistive load to a different region of the plurality of regions 502 of the battery 116 to obtain one or more different discharge currents. In some embodiments, the particular resistive loads and time periods may be determined at least in part based on equations (1), (3), (4), and (6). In this regard, the resistive loads and/or the time periods may be determined such that the resulting discharge currents would be theoretically possible for the battery 116 to produce and/or such that the battery was not damaged by performing the first testing routine. In some embodiments, at the end of the three test steps, a preliminary state of charge of the battery 116 may be determined.

In some embodiments, the second phase of the testing routine for determining the state of charge of the battery 116 (e.g., when the battery 116 is a lithium ion battery) may include a fourth step, after the first three steps, in which a voltage of the battery 116 is measured for a particular time period (e.g., 10 to 30 seconds) when the battery 116 is in an open circuit configuration. In some embodiments, the measured voltage of the battery 116 at the end of the fourth step gives information on the recovery progress of the battery 116 after being subjected to the three resistive loads in the first three steps of the second phase. In some embodiments, the state of charge of the battery 116 may be determined from the measured voltage of the battery 116 at the end of the fourth step. In some embodiments, the indicator light 106 of the battery testing device 102 may be configured to display the state of charge of the battery 116. Additionally, or alternatively, the display panel 118 may be configured to display the state of charge of the battery 116.

Example Method

Referring now to FIG. 6, a flowchart providing an example method 600 is illustrated. In this regard, FIG. 6 illustrates operations that may be performed by the computing device 126 and/or the battery testing device 102.

As shown in block 602, the method may include causing, by a computing device, a battery testing device to apply a plurality of resistive loads to a battery. As described above, in some embodiments, determining the state of charge of the battery may include determining a nominal capacity (Q) of the battery. In this regard, for example, the nominal capacity (Q) of the battery may be determined using equation (1):

$\begin{matrix} Q = \int_{0}^{τ_{p}} I_{dch} d τ, & (1) \end{matrix}$

where (I_dch) is a discharge current associated with the battery, (T_p) represents an amount of time that it takes for a battery of a certain capacity and at a certain discharge current strength to discharge to reach a predetermined value of a final discharge voltage, and (dτ) represents an actual time variation from the predicted amount of time it takes for a battery to reach a predetermined value of a final discharge voltage and an actual amount of time it takes for a battery to reach a predetermined value of a final discharge voltage.

In some embodiments, the nominal capacity (Q) of the battery may be proportional to the electrochemical equivalent of the active substances from which the electrodes (e.g., positive electrode and negative electrode) of battery are made. In some embodiments, the electrochemical equivalent of the active substances from which the electrodes of battery are made represents the amount of electrical energy that can be provided by a unit amount of the active substances. In some embodiments, the battery may be associated with a utilization factor (β). In this regard, for example, it may not be technically feasible to utilize all of the nominal capacity (Q) of the battery and, as such, the utilization factor (β) may be indicative the amount of the nominal capacity (Q) of the battery that can actually be utilized. The utilization factor (β) may be calculated for the battery using equation (2):

$\begin{matrix} β = \frac{Q K^{(2)}}{m}, & (2) \end{matrix}$

where (K⁽²⁾) is the theoretically necessary transformation of the active mass of the electrodes of the battery, and (m) is the mass of the active mass (m) of the electrodes.

In some embodiments, the actual capacity ( [Image Omitted] _Ø) of the battery may be determined (e.g., the actual capacity (_Ø) being different than the nominal capacity (Q) because it may not be technically feasible to utilize all of the nominal capacity (Q) of the battery). In some embodiments, determining the actual capacity (_Ø) of the battery may include performing a full discharge of the battery at a specified a discharge current (I_dch). In this regard, for example, the actual capacity ( [Image Omitted] _Ø) may be determined using equation (3):

$\begin{matrix} Q_{\emptyset} = I_{dch} t_{dch}, & (3) \end{matrix}$

where I_dchis the specified discharge current and t_dchis the time it takes to fully discharge the battery. In some embodiments, a temperature dependent actual capacity ( [Image Omitted] _t) of the battery may be determined using equation (4):

$\begin{matrix} Q_{t} = \frac{Q_{\emptyset}}{1 + α (t_{2} - t_{1})}, & (4) \end{matrix}$

where α is the temperature coefficient (e.g., the temperature may impact the capacity of the battery). In some embodiments, as shown by equations (1)-(4), the temperature dependent actual capacity ( [Image Omitted] _t) of the battery may be influenced by a number of factors. For example, the temperature dependent actual capacity (_t) of the battery may be influenced by electrochemical equivalent of the active substances from which the electrodes (e.g., positive electrode and negative electrode) of the battery are made, the discharge current (I_dch) (e.g., the strength of the discharge current (I_dch)), temperature (e.g., ambient temperature around the battery), the utilization factor (β), the battery type (e.g., a lead battery type, a lithium ion battery type, etc.), electrode thickness (e.g., thickness of the positive electrode and/or the negative electrode), electrode surface area (e.g., surface area of the positive electrode and/or the negative electrode), phase transformation of the battery, and/or the like.

In some embodiments, the capacity of the battery at a discharge rate of 1 ampere (Q_dch), may be determined using equation (5):

$\begin{matrix} Q_{dch} = I^{k} t, & (5) \end{matrix}$

where I is the actual value of the discharge current, t is the actual time it takes to discharge the battery and k is Peukert's constant. In some embodiments, based at least in part on equation (5), equation (6) may be determined in which the capacity of the battery at a discharge rate of 1 ampere (Q_dch) is expressed in terms of the utilization factor (β), (e.g., the utilization factor being the coefficient of usability of the active mass of an electrode (e.g., the positive electrode and/or the negative electrode)), the mass of the active mass (m) of the electrodes, and the electrochemical equivalent of the substance at discharge (k⁽⁶⁾):

$\begin{matrix} Q_{dch} = k^{(6)} β m, & (6) \end{matrix}$

In some embodiments, the change in volume of the active mass of the positive electrode may be determined based at least in part on a discharge of at least some current from the battery using equation (7):

$\begin{matrix} V_{PAM}^{I} = V_{PAM}^{'} + S_{PAM}^{'} Δ δ_{PAM}^{'}, & (7) \end{matrix}$

where V_PAM^Iis the change in volume of the active mass, V′_PAMis the volume of the active mass before discharge of at least some current from the battery, S′_PAMis a one-sided geometrical surface of the positive electrode, and Δδ′_PAMis the thickness variation of the positive electrode as a result of the discharge of at least some current from the battery.

In some embodiments, the change in volume of the active mass of the negative electrode may be determined based at least in part on a discharge of at least some current from the battery using equation (8):

$\begin{matrix} V_{NAM}^{II} = V_{NAM}^{′′} + S_{NAM}^{′′} Δ δ_{NAM}^{′′}, & (8) \end{matrix}$

where V_NAM^IIis the change in volume of the active mass, V″_NAMis the volume of the active mass before discharge of at least some current from the battery, S″_NAMis a one-sided geometrical surface of the negative electrode, and Δδ″_NAMis the thickness variation of the negative electrode as a result of the discharge of at least some current from the battery.

In some embodiments, the state of charge of the battery may be determined based at least in part on the thermodynamic and/or electrochemical factors described above (e.g., based at least in part on equations (1)-(8)). In this regard, for example, the factors are the interdependent connection between the capacity of the battery and the strength of the discharge current, the length of time that the discharge current is applied for, the temperature, the usability of the active masses in the battery, and/or the like.

As shown in block 604, the method may include receiving, from the battery testing device, a plurality of measured voltages. As described above, in some embodiments, each of the plurality of resistive loads are applied for an associated time period of a plurality of time periods. For example, a first resistive load may be applied to the battery for a first time period and a second resistive load may be applied to the battery for a second time period.

In some embodiments, each of the plurality of resistive loads are applied to at least one of a plurality of regions of one or more electrodes associated with the battery (e.g., negative electrode and/or the positive electrode). For example, each of the plurality of resistive loads may be applied to a first region of the plurality of regions, a second region of the plurality of regions, and/or a third region of the plurality of regions.

In some embodiments, a porosity of one or more electrodes associated with the battery may vary throughout one or more electrodes associated with the battery. For example, 95 percent of the one or more electrodes associated with the battery may be associated with a first porosity and 5 percent of the one or more electrodes associated with the battery may be associated with a second porosity. In some embodiments, the variation in the porosity of one or more electrodes associated with the battery may impact the state of charge determination. For example, in order to accurately determine the state of charge of the battery it may be desirable to determine the state of charge of the battery based at least in part on resistive loads that have been applied to a region of one or more electrodes associated with the battery most representative of the overall porosity of the one or more electrodes (e.g., the first porosity). In this regard, at least in part by applying each of the plurality of resistive loads to at least one of the plurality of regions, the state of charge of the battery may be accurately determined (e.g., the state of charge of the battery may be determined such that the porosity of a portion of one or more electrodes associated with the battery does not cause an inaccurate state of charge to be determined).

In some embodiments, the plurality of resistive loads may be applied to the battery in stages. For example, a first portion of the plurality of resistive loads may be applied to the battery in a first stage and a second portion of the plurality of resistive loads may be applied to the battery in a second stage (e.g., if there are four resistive loads in the plurality of resistive loads, three resistive loads may be applied in the first stage and one resistive load may be applied in the second stage). In some embodiments, after applying the first portion of the plurality of resistive loads to the battery a preliminary state of charge of the battery may be determined. In some embodiments, after applying the second portion of the plurality of resistive loads to the battery, the state of charge of the battery may be determined. In some embodiments, the preliminary state of charge may be the same as the state of charge. In some embodiments the preliminary state of charge may be different than the state of charge.

In some embodiments, by applying the plurality of resistive loads to the battery, a corresponding plurality of discharge currents associated with the battery may be generated (e.g., a plurality of currents discharged by the battery). In some embodiments, a plurality of measured voltages may be received. In some embodiments, each of the plurality of measured voltages may be associated with one of the plurality of time periods.

In some embodiments, each of the plurality of measured voltages may be associated with one of the plurality of regions. In this regard, for example, if the plurality of regions includes three regions and the plurality of time periods includes three time periods, the plurality of measured voltages may include nine measured voltages (e.g., three associated with each of the plurality of regions and/or three associated with each of the plurality of time periods). For example, a matrix may be formed that includes the plurality of measured voltages (e.g., the matrix including the measured voltages for each time period and region).

As shown in block 606, the method may include determining, by the computing device, based at least in part on the plurality of measured voltages, a state of charge of the battery. As described above, by generating the corresponding plurality of discharge currents associated with the battery that are each associated with a particular strength and particular time period while a voltage associated with the battery is measured (e.g., the plurality of measured voltages), the electrochemical reaction of the battery may be assessed (e.g., to determine the state of charge of the battery). Said differently, because the electrochemical reaction of the battery is dependent on the strength of the plurality of discharge currents (e.g., as generated by applying the plurality of resistive loads) the state of charge of the battery may be determined by determining the plurality of voltages.

In some embodiments, it may be necessary to select the plurality of resistive loads such that the resistive loads can provide the necessary discharge current strengths as well as select the plurality of time periods such that each of the plurality of resistive loads are applied for a necessary time period. In some embodiments, the plurality of measured voltages may be dependent on the capacity of the battery (e.g., such that the state of charge of the battery may be determined). In some embodiments, at least one of the plurality of resistive loads may be selected such that at least one of the plurality of measured voltages is an open circuit voltage (e.g., the restive load is large).

In some embodiments, each of the plurality of measured voltages are dependent on a potential (e.g., a voltage) of the positive electrode and/or a potential of the negative electrode. In this regard, since a voltage associated with the battery (e.g., a measured voltage) is the sum of the potential of the positive electrode and the potential of the negative electrode, which depend on the strength of the discharge current (e.g., the number of amperes of the discharge current), it means that the voltage associated with the battery also depends on the value of the discharge current. In some embodiments, the value of the discharge current, represents the speed of the occurring electrochemical process of releasing electrical energy from the battery to the plurality of resistive loads, which is represented by equation (9):

$\begin{matrix} i = {nFk}^{'} C_{ox} \exp (- \frac{α n F ε}{RT}) i = {nFk}^{'} C_{red} \exp [- \frac{(1 - α) n F ε}{RT}], & (9) \end{matrix}$

In some embodiments, based on equation (9) showing the dependency of the speed of the electrochemical processes in the battery on the potential of the positive electrode and/or the potential of the negative electrode, it follows that as the values of the potential of the positive electrode and/or the potential of the negative electrode is lowered, the voltage associated with the battery correspondingly lowers, meaning that the available charge in the active masses of the battery is diminishing. In this regard, by keeping a constant speed of the electrochemical discharge process of the battery, the voltage associated with the battery may be determined from which the state of charge of the battery may be determined. For example, one or more mathematical algorithms may be used to determine the state of charge from the plurality of measured voltages.