WO2013016188A1

WO2013016188A1 - Method, system, and apparatus for battery equivalent circuit model parameter estimation

Info

Publication number: WO2013016188A1
Application number: PCT/US2012/047601
Authority: WO
Inventors: Minkyu Lee
Original assignee: Navitas Solutions, Inc.
Priority date: 2011-07-22
Filing date: 2012-07-20
Publication date: 2013-01-31

Abstract

A method, system, and apparatus for optimizing a set of equivalent circuit model parameters of a battery is disclosed. The method includes measuring and/or receiving a terminal voltage, a current, and a temperature from the battery. The measured and/or received terminal voltage, measured current, measured temperature and a current time stamp is stored in a memory. An equivalent circuit and a set of equivalent circuit model parameters is determined for the battery. A set of estimated state variables based on at least one of the equivalent circuit model parameters is calculated. The set of equivalent circuit model parameters is optimized based on at least one of the estimated state variables. The system and apparatus include components configured to implement the method.

Description

[0001] TITLE: METHOD, SYSTEM, AND APPARATUS FOR BATTERY EQUIVALENT CIRCUIT MODEL PARAMETER ESTIMATION

[0002] INVENTOR: MINKYU LEE

[0003] CROSS REFERENCE TO RELATED APPLICATIONS

[0004] This application is an international application filed under the Patent Cooperation Treaty and claims priority to U.S. Provisional Application Serial No. 61/510,525 filed July 22, 2011 by Minkyu Lee and titled "Method for Battery Equivalent Circuit Model Parameter Estimation", which is incorporated by reference as if fully disclosed herein.

[0005] FIELD OF THE INVENTION

[0006] The present invention is in the technical field of estimating battery equivalent circuit model parameters of a rechargeable battery.

[0007] BACKGROUND OF THE INVENTION

[0008] In the context of rechargeable battery applications, it is desirable to be able to estimate quantities that are descriptive of the present condition of a battery. Notable quantities are open circuit voltage (OCV) of a battery or battery pack as well as other parameters associated with the equivalent circuit model of a battery.

[0009] In most real applications, however, it is not feasible to directly measure the OCV due to various restrictions. For example, in order to measure OCV, the circuit needs to be disconnected from the charger or discharger. In an electric vehicle, for example, OCV has to be measured continuously while the battery is in operation. Such application does not allow measuring OCV while in operation. Therefore, OCV also has to be indirectly estimated. The most popular method for OCV estimation is to use the equivalent circuit model. The model parameters include the battery capacity, internal resistances, and others.

[0010] An accurate estimation of the equivalent circuit model parameters is important for accurate OCV estimation and accurate estimation of other quantities such as state-of-charge (SOC). In addition, the equivalent circuit model parameters change slowly over time due to various factors such as operating temperature, SOC, C-rate, and battery aging. Any errors in this estimation of the equivalent circuit model parameters would affect regulation of the charge/discharge current and thus lead to a reduced battery capacity and battery life. Conversely, an increased accuracy in estimating the equivalent circuit model parameters increases the efficiency of the battery and lifespan.

[0011] Conventional approaches, such as those disclosed in U.S. Patent Nos. 7,521,895 and 7,593,821, simultaneously estimate the model parameters and state variables, such as equivalent circuit voltages. However, because the parameters vary more slowly compared to the state variables, this is an unnecessary waste of computing resources. Other Reference Patents include U.S. Patent No. 6,794,876, U.S. Patent No. 7,315,789, and U.S. Patent No. 7,884,613.

[0012] SUMMARY OF THE INVENTION

[0013] A method, system, and apparatus for optimizing a set of equivalent circuit model parameters of a battery are disclosed. The method includes measuring and/or receiving a terminal voltage, a current, and a temperature from the battery. The measured and/or received terminal voltage, measured current, measured temperature and a current time stamp is stored in a memory. An equivalent circuit and a set of equivalent circuit model parameters are determined for the battery. A set of estimated state variables based on at least one of the equivalent circuit model parameters is calculated. The set of equivalent circuit model parameters is optimized based on at least one of the estimated state variables.

[0014] An electronic device and/or apparatus is disclosed that includes a battery, a plurality of sensors, a processor, and a computer-readable storage medium configured to store program instructions. The stored program instructions are capable of instructing the processor to receive a measured terminal voltage, a measured current, and a measured temperature from at least one of the plurality of sensors; store the measured terminal voltage, measured current, measured temperature, and a current time stamp; determine a set of equivalent circuit model parameters; calculate a set of estimated state variables based on at least one of the equivalent circuit model parameters; and optimize the set of equivalent circuit model parameters based on at least one of the estimated state variables.

[0015] A system for optimizing equivalent circuit model parameters for a battery includes a battery and a battery management device. The battery includes at least one battery cell and a plurality of sensors in communication with each other and in electrical contact with the at least one battery cell. At least one of the plurality of sensors includes a communication interface. The battery management device includes a processor, a communication interface, and a computer readable memory configured to store program instructions capable of instructing the processor to perform a method for optimizing a set of equivalent circuit model parameters.

[0016] BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a block diagram of an exemplary battery management system that is useful for understanding the present invention.

[0018] Figure 2 is an example of a equivalent circuit model of a battery that is useful for understanding the present invention.

[0019] Figure 3 is a flow chart depicting a method of model parameter estimation and optimization that is useful for understanding the present invention. [0020] Figure 4 shows an example of an optimization algorithm that is useful for understanding the present invention.

[0021] DETAILED DESCRIPTION OF THE INVENTION

[0022] This disclosure is not limited to the particular systems, devices and methods described, as these may vary. The terminology used in the description is for the purpose of describing the particular versions or embodiments only, and is not intended to limit the scope.

[0023] As used in this document, the singular forms "a," "an," and "the" include plural references unless the context clearly dictates otherwise. Unless defined otherwise, all technical and scientific terms used herein have the same meanings as commonly understood by one of ordinary skill in the art. Nothing in this disclosure is to be construed as an admission that the embodiments described in this disclosure are not entitled to antedate such disclosure by virtue of prior invention. As used in this document, the term "comprising" means "including, but not limited to."

[0024] As used in this document, a statement that a device or system is "in electronic communication with" another device or system means that devices or systems are configured to send data, commands and/or queries to each other via a communications network. The network may be a wired or wireless network such as a local area network, a wide area network, an intranet, the Internet or another network.

[0025] A "computing device" refers to a computer, a processor and/or any other component, device or system that performs one or more operations according to one or more programming instructions. The term "data" may refer to physical signals that indicate or include information. A "data bit" may refer to a single unit of data.

[0026] An "electronic device" refers to a device that includes a communication interface, a processor and tangible, computer-readable memory. The memory may contain programming instructions in the form of a software application that, when executed by the processor, causes the device to perform one or more barcode scanning operations according to the programming instructions.

[0027] A "battery" refers to any device capable of storing electrical energy. A battery may be composed of a single storage cell or of many such cells. A battery may also refer to a bank of batteries which operate as a single electrical storage device. Examples of batteries include electrolytic batteries, primary batterys, secondary batteries, electric double-layer capaciters, supercapacitors, and the like.

[0028] Disclosed herein are methods, systems and apparatus for the parameter estimation of a battery equivalent circuit model. The method described herein iteratively calculates a set of equivalent circuit model parameters until an optimized set of parameters is produced. The parameters can be calculated at a regular period or when an error associated with the set of parameters falls below a pre-defined threshold. This is advantageous because the model parameters tend to vary more slowly compared to the state variables. When the model parameters are estimated only when it is needed, e.g. when the model produces larger error than the pre-determined threshold, the computing power required for the model parameter update can be further reduced and more computing power can be dedicated to other tasks such as SOC calculation.

[0029] Referring to FIG. 1, an embodiment of a battery state estimation system 100 is illustrated. System 100 includes a battery management system (BMS) 102 and a battery 120. The BMS 102 includes a CPU 104, a computer readable memory 106, a clock 108, and an input/output (I/O) interface 110. Computer readable memory 106 may include, for example, an external or internal DVD or CD ROM drive, a hard drive, flash memory, a USB drive or the like. These various drives and controllers are optional devices. Additionally, the computer readable memory 106 may be configured to include individual files for storing any software modules or instructions, auxiliary data, common files for storing groups of results or auxiliary, or one or more databases for storing the result information, auxiliary data, and related information as discussed above.

[0030] Program instructions, software or interactive modules for performing any of the methods and systems as discussed herein may be stored in the computer readable memory which may include a read-only memory (ROM) and/or a random access memory (RAM). Optionally, the program instructions may be stored on a tangible computer readable medium such as a compact disk, a digital disk, flash memory, a memory card, a USB drive, an optical disc storage medium, such as a Blu-ray™ disc, and/or other recording medium.

[0031] The CPU 104 collects voltage, current, and temperature data from a set of sensors 130, 132, 134, 136, 138, 140 at regular intervals. In the embodiment illustrated in FIG. 1, the CPU 104 recieves the data through data connection 114. In embodiments, data connection 114 is comprised of wireless signals received and demodulated through the radio frequency (R/F) interface 112. The wireless signals are transmitted by the sensors in the battery 120. One of ordinary skill in the art will recognize that data connection 114 can be any connection suitable for transmitting sensor data, including any wireless or wired communication medium known to one of ordinary skill. In alternative embodiments, for example, data connection 114 may be a wired data connection using an Ethernet interface, a USB interface, a IEEE 1394 interface, and the like. Alternatively, data connection 114 may be a wireless data connection using an 802.11 Wifi interface, a Bluetooth interface, a near field communication interface, and the like. Further, one of ordinary skill will note that the sensors may be inside or outside of the battery.

[0032] In embodiments, the battery 120 includes one or more battery cells 122, 124, 126, 128. Battery 120 also includes at least one voltage sensor 130, 132, 134, 136; at least one current sensor 138, and at least one temperature sensor 140. Voltage sensor 130, 132, 134, 136 measures the terminal voltage (V_t) between the terminals of each battery cell. Current sensor 138 measures the amount of current (I) flowing into/out of the battery cells. Temperature sensor 140 measures the temperature (T) of the batter cells. Although FIG. 1 illustrates one current sensor and one temperature sensor, one of ordinary skill will recognize that the number of sensors included may vary. For example, a number of temperature sensors may be included in areas known to generate high temperatures.

[0033] The major task of the BMS 102 is to monitor each battery cell 122, 124, 126, 128 to make sure that operating conditions are properly maintained. As described above, the sensors can be connected either directly via a wire harness or wirelessly. Using the measured data from the sensors, the CPU can calculate the equivalent circuit model parameters. An example of a BMS is disclosed in commonly assigned International Application PCT/US2011/058503, titled "Wireless Battery Area Network for Smart Battery Management", which is incorporated by reference as if fully disclosed herein.

[0034] FIG. 2 illustrates an exemplary equivalent circuit 200. One skilled in the art will recognize that the embodiment illustrated in FIG. 2 is only exemplary and any number of other equivalent circuits, simpler and more complicated, may be used. The invention is not limited in this regard. The battery equivalent circuit 200 can represent either each individual battery cell 122, 124, 126, 128 in FIG. 1 or the entire battery 120. If the battery equivalent circuit 200 represents the battery cell 122, then the current sensor 202 measures current (I) flowing out of the battery cell 122. In an embodiment the positive terminal 204 and negative terminal 206 are the external positive and negative terminals of the battery cell 122. The voltage difference between terminals 204, 206 is the terminal voltage (V_t) measured by a voltage sensor, e.g. voltage sensor 130 of FIG. 1. Resistors 208, 210 and diodes 212, 214 of the equivalent circuit represent the internal resistance (R;⁺, R;^") of the battery 200. In the embodiment of FIG 2, the internal resistance is measured with two disctinct values which depend on the direction of the current through the battery, i.e. whether the battery is charging or discharging. R;⁺ (resistor 210) is the charging resistance, while R_; ^~ (resistor 208) is the discharging resistance. In other embodiments, internal resistance can also be represented by a single value R;. The internal voltage (V;) 211 is, pursuant to Ohm's law, the product of I and either R_; ⁺ or R_; ^~, depending on the flow direction of I.

[0035] In the embodiment of FIG. 2, the battery polarization effects are represented by polarization resistor 216 with a polaraziation resistance (R_p) and and a polarization capacitor 218 with a polarization capacitance (C_p) of an equivalent polarization RC circuit 219. The voltage 220 across RC circuit 219 is the polarization voltage (V_p) 220. The core battery cell is represented by RC circuit 225 that includes a core battery cell resistor 222 with battery cell resistance R_c and core battery cell capacitor 224 with battery cell capacitance C_c. The voltage 226 across RC circuit 225 is the open circuit voltage or battery cell voltage (V_c) 226. The open circuit voltage (OCV) of the battery 200 can be used to calculate SOC.

[0036] To estimate the unknown state variables (V_c and V_p) and the equivalent circuit model parameters (R;⁺, R;^~, R_p, C_p, R_c, and C_c), a set of mathematical equations can be solved using the measured quantities (I, V_t, and/or T) as inputs.

[0037] In general, the unknown state variables V_c and V_p can be solved using the following analog equations:

_Vt it) = _Vc it) _{+ Vp} it) ₊ R iit) ₊ uit) (Equation 1)

— -— v ( ——- i(t) +— (Equation 2) R,C, C C

^■i(t) + -^—w(t) (Equation 3) p p where: t is a continuous time variable, v_t(t) is the terminal voltage, v_c(t) is open circuit voltage; Vp(t) is the polarization voltage; R; is the internal resistance of the battery (either positive or negative depending on the direction of the current); i(t) is the measured current; u(t) is measurement error of the voltage, current and temperature sensors; and w(t) is system modelling error for the equivalent circuit model. One skilled in the art will recognize that R;-i(t) is equivalent to V; as defined above.

[0038] Alternativel , the equivalent digital representations can be used:

(Equation 4)

and

p,k

(Equation 5) c.k where k is discrete time instance; it is the value of I(t) at the time instance k; v_t,k is the value of v_t(t) at the time instance k; v_Pik is the value of v_p(t) at the time instance k; v_c,k is the value of v_c(t) at the time instance k; ¾ is the value of u(t) at the time instance k; Wk is the value of w(t) at the time instance k.

[0039] Established methods of estimating the unknown state variables, V_c and V_p, require a given set of model parameters (Ri⁺, K{, R_p, C_p, R_c, and C_c). For example, Kalman filters provide a solution for estimating unknown state variables, V_c and V_p, from noisy measured data when combined with known model parameters. However, in the example of rechargeable batteries, the model parameters are not known. Moreover, the model parameters change slowly over time depending on various factors such as operating temperature, cell aging, and SOC. Therefore, it is desirable to be able to accurately estimate and track the model parameter values in addition to the state variables.

[0040] Conventional Kalman filter approaches calculate the state variables and update the model parameters for each measured input data point, see, e.g. Plett, U.S. Patent No. 7,521 ,895. The data for V_t and I are typically measured once every n milliseconds, for example. In other words, the Kalman filter calculates and updates the model parameters once every n milliseconds, with n typically within the range of 100 to 1000. However, as described above, the state variables, V_c and V_p, change rapidly compared to the model parameters which change slowly. Therefore, there is no need to estimate the model parameters as frequently as the state variables.

[0041] Advantageously, embodiments of the present invention estimate model parameters either on the regular interval (typically every 5 to 10 minutes) or as needed based on a certain criteria. When it is time to estimate the model parameters, the algorithm collects the measured data V_t and I for the last n measurements. The particular value of n determines the time interval in which the algorithm adjusts the model parameters. In an embodiment, the equivalent circuit can be optimized through an optimization algorithm to produce, for example, a minimum root mean square error of (V_t ^est - V_t). This way, significant amount of computation can be saved.

[0042] FIG. 3 is a flow chart illustrating a method embodiment. Method 300 is a method for estimating and optimizing the equivalent circuit model parameters (Ri⁺, K{, R_p, C_p, R_c, and C_c). Terminal voltage (V_t), current (I), and temperature (T) are measured at 302. In an embodiment, V_t, I, and T are measured by a plurality of sensors within the battery, as discussed above in reference to FIG. 1. The measured values for V_t, I, and T are stored in memory at 304. A set of equivalent circuit model parameters is determined at 306. During the first iteration of method 300, the approximate values for the equivalent circuit model parameters may not be known. In this case, any values, including random values, can be used to begin the optimization algorithm. In subsequent iterations, the previously optimized set of equivalent circuit parameters is used. In this way, the equivalent circuit model parameters are refined through each iteration. [0043] Once a set of equivalent circuit model parameter values is determined, a set of state variables (e.g. estimated polarization voltage, estimated battery cell voltage, and internal voltage) are calculated using at least one of the equivalent circuit model parameters at 308. In an embodiment, equations 1, 2, 3 and/or equations 4, 5, described above, are used to calculate a set of state variables. For example, once values for Ri⁺, K{, and I are available, the internal voltage (Vj) is the product of I and R;⁺ or K{, depending on the direction of the current. In another example, once values for R_p and C_p are available, the polarization voltage (V_p) can be calculated using equation 2 and/or 4. In another example, once values for R_c and C_c are available, the battery cell voltage (V_c) can be calculated using equation 3 and/or 4. Once the values of V;, V_c, and V_p are available, the estimated terminal voltage (V_t ^est) can be calculated at 310. In an embodiment, V_t ^est can be calculated using equation 1 and/or 5.

[0044] Once an estimated terminal voltage has been calculated, an accumulated error is determined by comparing V_t ^est to V_t at 312. The accumulated error is the difference between the estimated terminal voltage and the measured terminal voltage. Instead of the instant accumulated error, a moving average of the accumulated error can be used. Further, any method of determining an error can be used, such as root mean square error. If the accumulated error is greater than a pre-defined threshold (314: Yes), then the accumulated error is too large and the equivalent circuit model parameters can be optimized.

[0045] In an embodiment, the Nelder-Mead Optimization algorithm can be used for repeatedly estimating battery equivalent circuit model parameters. The algorithm is also known as downhill simplex method. A simplex is a polytope in n dimension with n+1 vertices. For example, a simplex becomes a triangle in a two-dimensional space and, likewise, a tetrahedron in a three-dimensional space. The downhill simplex method only uses function evaluations and no derivative calculations are needed. The algorithm is illustrated in FIG. 4. The algorithm begins with a set of n+1 points, representing the vertices of the polytope. These points can be any random point on the function that is to be minimized. The simplex minimizes the function by selecting the least desirable point of the set and replacing it with another point in the multidimensional space where the function is reevaluated. The aim of the simplex is to minimize the value at the vertices. FIG. 4 depicts how a two-dimensional simplex started from a random position in a three-dimensional space eventually arrives at the minima 402 by simplex moves illustrated by triangles 404. One of skill in the art will recognize that any optimization algorithm can be used. The present invention is not limited in this regard.

[0046] Since the equations used to optimize the equivalent circuit model parameters are linear equations, only two (n+1) parameters may be optimized at a time. Referring again to FIG. 3, the internal resistance parameters Ri⁺ and K{ are optimized at 316. The polarization RC circuit parameters R_p and C_p are optimized at 318. The battery cell RC circuit parameters are optimized at 320. After all the parameters are optimized, the method 300 returns to 310 where a new value for the estimated terminal voltage is calculated based on at least one of the optimized equivalent circuit model parameter values. At 312, the new estimated terminal voltage value is compared to the measured value stored in the memory. If the accumulated error is still greater than a predefined threshold (314: Yes), the optimizations at 316, 318, and 320 are repeated. However, if the accumulated error between the estimated terminal voltage and the measured terminal voltage is less than a pre-defined threshold (314: No), the equivalent circuit parameter values are output for use in other calculations at 322.

[0047] The method 300 will periodically monitor the changes in the measured parameters at 324 to determine if the equivalent circuit model parameters need to be updated. The decision of whether to update the equivalent circuit model parameters at 326 can be based on any criteria of interest. For example, the update may be triggered by the expiration of a set period of time, e.g. 5 minutes. Alternatively, the update may be triggered by a recalculation of the estimated terminal voltage that leads to an accumulated error greater than the pre-defined threshold. This can happen, for example, with changes in any of the measured parameters. If an update is not determined to be required (326: No) the method 300 continues to monitor the measured parameter values. If an update is required (326: Yes), the method 300 returns to step 308 where the previous set of equivalent circuit model parameters are used to calculate new values for the state variables and begin a new iteration of the optimization procedure.

[0048] The goal of method 300 is to update the slowly varying model parameters less frequently and more accurately using the optimization algorithm. More accurate model parameters that closely follow the true values would lead to a more accurate state variable estimation.

[0049] The claims, as originally presented and as they may be amended, encompass variations, alternatives, modifications, improvements, equivalents, and substantial equivalents of the embodiments and teachings disclosed herein, including those that are presently unforeseen or unappreciated, and that, for example, may arise from applicants/patentees and others.

Claims

What is claimed is:

1. A method for optimizing a set of equivalent circuit model parameters of a battery, comprising :

measuring a terminal voltage, a current, and a temperature from the battery;

storing the measured terminal voltage, measured current, measured temperature and a current time stamp;

determining a set of equivalent circuit model parameters;

calculating a set of estimated state variables based on at least one of the equivalent circuit model parameters; and

optimizing the set of equivalent circuit model parameters based on at least one of the estimaited state variables.

2. The method of claim 1 , wherein the set of equivalent circuit model parameters comprise a positive internal resistance (R;⁺), a negative internal resistance (Ri ), a polarization resistance (R_p), a polarization capacitance (C_p), a battery cell resistance (RJ, and a battery cell capacitance (C_o), and

wherein the set of state variables comprises an estimated internal voltage (V;), an estimated polarization voltage (V_p), an estimated battery cell voltage (V_c), and an estimated terminal voltage (V_t ^est).

3. The method of claim 2, further comprising:

calculating an accumulated error which is the difference between the estimated terminal voltage and the measured terminal voltage, wherein the estimated terminal voltage is equal to the sum of the estimated polarization voltage, the estimated battery cell voltage, and the internal voltage, and wherein the accumulated error is compared to a pre-defined threshold.

4. The method of claim 3, wherein calculating a set of equivalent circuit model parameters comprises:

on a condition that the accumulated error is greater than a pre-defined threshold, optimizing a set of the equivalent circuit model parameters so that the accumulated error is minimized by iteratively applying a mathematical optimization algorithm.

5. The method of claim 4, wherein optimizing a set of the equivalent circuit model parameters comprises:

optimizing a first parameter set of the equivalent circuit model parameters that comprises Ri⁺ and K{ so that the accumulated error calculated from the first parameter set is minimized.

6. The method of claim 5, wherein updating the equivalent circuit model parameters comprises:

optimizing a second parameter set that comprises R_p, and C_p so that the accumulated error calculated from the first and second parameter set is minimized.

7. The method of claim 6, wherein updating the equivalent circuit model parameters comprises:

optimizing a third parameter set comprising R_c, and C_c so that the accumulated error calculated from the first, second, and third parameter set is minimized.

8. The method of claim 7, further comprising:

determining whether an update the equivalent circuit model parameters is required; and on a condition that an update of the equivalent circuit model parameters is required; updating the equivalent circuit model parameters by repeating the optimizing of the the first, second, and third parameter sets.

9. The method of claim 4, further comprising:

on a condition that the accumulated error is less than a pre-defined threshold, monitoring the terminal voltage, current, and temperature of the battery.

10. The method of claim 4, wherein the optimization algorithm is an iterative Nelder-Mead algorithm.

11. An electronic device comprising:

a battery;

a plurality of sensors;

a processor; and

a computer-readable storage medium configured to store program instructions capable of instructing the processor to:

receive a measured terminal voltage, a measured current, and a measured temperature from at least one of the plurality of sensors;

store the measured terminal voltage, measured current, measured temperature, and a current time stamp;

determine a set of equivalent circuit model parameters;

calculate a set of estimated state variables based on at least one of the equivalent circuit model parameters; and

optimize the set of equivalent circuit model parameters based on at least one of the estimated state variables.

12. The electronic device of claim 11, wherein the set of equivalent circuit model parameters comprise a positive internal resistance (R;⁺), a negative internal resistance (RD, a polarization resistance (R_p), a polarization capacitance (C_p), a battery cell resistance (R_c), and a battery cell capacitance (C_c), and wherein the set of state variables comprises an estimated internal voltage (V;), an estimated polarization voltage (V_p), an estimated battery cell voltage (V_c), and an estimated terminal voltage (V_t ^est).

13. The electronic device of claim 12, wherein the program instructions are further capable of instructing the processor to:

calculate an accumulated error which is the difference between the estimated terminal voltage and the measured terminal voltage, wherein the estimated terminal voltage is equal to the sum of the estimated polarization voltage, the estimated battery cell voltage, and the internal voltage, and wherein the accumulated error is compared to a pre-defined threshold.

14. The electronic device of claim 13, wherein the program instructions are further capable of instructing the processor to:

on a condition that the accumulated error is greater than a pre-defined threshold, optimize a set of the equivalent circuit model parameters so that the accumulated error is minimized by iteratively applying a mathematical optimization algorithm.

15. The electronic device of claim 14, wherein the program instructions are further capable of instructing the processor to:

optimizing a first parameter set of the equivalent circuit model parameters that comprises Ri⁺ and K{ so that the accumulated error calculated from the first parameter set is minimized;

optimizing a second parameter set that comprises R_p, and C_p so that the accumulated error calculated from the first and second parameter set is minimized; and

16. The electronic device of claim 15, wherein the program instructions are further capable of instructing the processor to:

determine whether an update the equivalent circuit model parameters is required; and on a condition that an update of the equivalent circuit model parameters is required; update the equivalent circuit model parameters by repeating the optimizing of the the first, second, and third paramter sets.

17. The electronic device of claim 16, wherein the program instructions are further capable of instructing the processor to:

on a condition that the accumulated error is less than a pre-defined threshold, monitor the terminal voltage, current, and temperature of the battery.

18. A system for optimizing equivalent circuit model parameters for a battery comprising: a battery that comprises:

at least one battery cell; and

a plurality of sensors in communication with each other and in electrical contact with the at least one battery cell, wherein at least one of the plurality of sensors includes a first communication interface; and

a battery management device that comprises:

a processor;

a second communication interface; and

a computer readable memory configured to store program instructions capable of instructing the processor to:

determine a set of equivalent circuit model parameters; wherein the set of equivalent circuit model parameters comprise a positive internal resistance (Ri⁺), a negative internal resistance (RD, a polarization resistance (R_p), a polarization capacitance (C_p), a battery cell resistance (R_c), and a battery cell capacitance (C_c);

calculate a set of estimated state variables based on at least one of the equivalent circuit model parameters, wherein the set of estimated state variables comprises an estimated internal voltage (V;), an estimated polarization voltage (V_p), an estimated battery cell voltage (V_c), and an estimated terminal voltage (V_t ^est);

calculate an accumulated error which is the difference between the estimated terminal voltage and the measured terminal voltage, wherein the estimated terminal voltage is equal to the sum of the estimated polarization voltage, the estimated battery cell voltage, and the internal voltage, and wherein the accumulated error is compared to a pre-defined threshold;

on a condition that the accumulated error is greater than a pre-defined threshold, optimize a set of the equivalent circuit model parameters based on at least one of the estimated state variables so that the accumulated error is minimized by iteratively applying a mathematical optimization algorithm; and on a condition that the accumulated error is less than a pre-defined threshold, monitoring the terminal voltage, current, and temperature of the battery.

19. The system of claim 18, wherein the first and second communication interfaces are wireless interfaces.

20. The system of claim 18, wherein the first and second communication interfaces are wired interfaces.