Systems, methods, and apparatus for state of health estimation in energy storage systems

Abstract

Systems, methods, and devices for estimating state of health (SOH) in an energy storage system are provided, where the estimation accounts for both power decay and capacity decay. The SOH estimation system includes an SOH estimation module configured to receive and determine an estimate of SOH based on: a nominal capacity input; a voltage input; a current input; a nominal open circuit voltage curve; an operating resistance model; a nominal resistance model; an operating dynamic model; and a rated discharge current. The SOH estimation module can also include an SOH aggregation module configured to receive a rated power estimate PR n and a normalized capacity estimate NC n and can be configured to determine an estimate of SOH based on the rated power estimate PR n and the normalized capacity estimate NC n .

Description

TECHNICAL FIELD

[0001] The present disclosure relates generally to energy storage system charging and discharging, and in particular to state of health estimation in energy storage systems ("ESS") and energy storage devices. BACKGROUND

[0002] The ability of an energy storage device to store charge and generate power decreases over time and usage. The state of health ("SOH") of an energy storage device is used to track this degradation, and the term is generally defined as the ratio of the current battery performance to its performance at the nameplate conditions. Several indicators can be used to estimate the SOH of an energy storage device, including capacity change, resistance change, charge throughput, and cycle count.

[0003] The most commonly used metric for estimating SOH is ampere-hour capacity, where SOH is expressed as the ratio of the total available capacity to the nameplate capacity. However, defining SOH in terms of ampere-hour capacity can be problematic, as decisions about energy storage applications are often based on the available energy measured in watt-hours (Wh). Considering available energy is especially important for secondary life applications where electric vehicle units have been repurposed for stationary use. Furthermore, the economic viability of any long-life energy storage system designed to last 10-20 years or more often depends on the amount of energy that can be delivered.

[0004] Accordingly, an accurate SOH estimation algorithm based on energy is critical for making optimal decisions in the operation, control, and maintenance of energy storage systems. New systems and methods that more accurately estimate SOH based on energy performance would be desirable. SUMMARY

[0005] According to an example embodiment, a SOH estimation system for determining an estimate of a state of health (SOH) of an energy storage device is disclosed that considers both power decay and capacity decay. In an example embodiment, the SOH estimation system includes a SOH estimation module configured to determine the estimate of the SOH of the energy storage device based on and from: a nominal capacity input representing a nominal capacity of the energy storage device; a voltage input V representing a measured voltage associated with the energy storage device; a current input I representing a measured current from / to the energy storage device; a nominal open circuit voltage (OCV) curve associated with the energy storage device; an operating resistance model associated with the energy storage device; a nominal resistance model associated with the energy storage device; an operating dynamic model associated with the energy storage device; and a rated discharge current associated with the energy storage device.

[0006] According to another example implementation, a method of determining an estimate of a state of health (SOH) of an energy storage device is disclosed that accounts for both power fade and capacity fade. In an example implementation, the method includes receiving, at an SOH estimation module, the following information (received information): a nominal capacity input representing a nominal capacity of the energy storage device; a voltage input V representing a measured voltage associated with the energy storage device; a current input I representing a measured current to / from the energy storage device; a nominal open circuit voltage (OCV) curve associated with the energy storage device; an operating resistance model associated with the energy storage device; a nominal resistance model associated with the energy storage device; an operating dynamic model associated with the energy storage device; and a rated discharge current associated with the energy storage device. The method further includes determining, at the SOH estimation module, the estimate of the SOH of the energy storage device based on all of the received information.

[0007] According to another example implementation, a normalized capacity estimation system for generating a normalized capacity estimate of an energy storage device is disclosed. In an example implementation, the normalized capacity estimation system includes: a voltage sensor for sensing a voltage associated with the energy storage device and generating a voltage signal; a current sensor for sensing a current associated with the energy storage device and generating a current signal; an operating dynamic model associated with the energy storage device; a nominal OCV curve associated with the energy storage device; a nominal capacity associated with the energy storage device; and a normalized capacity estimation module configured to: receive the voltage signal, the current signal, the operating dynamic model, and the nominal capacity, and generate a normalized capacity estimate based on the voltage signal, the current signal, the operating dynamic model, the nominal OCV curve, and the nominal capacity; wherein the normalized capacity estimate is generated from a difference between two different OCV predictions and filtered based on: (1) the difference between the two different OCV predictions and a difference threshold, and (2) a gradient of the OCV curve at the two different OCV predictions and a gradient threshold.

[0008] According to another example implementation, a power rating estimation system for generating a power rating estimate for an energy storage device is disclosed. In an example implementation, the power rating estimation system includes a power rating estimation module configured to receive: a nominal resistance model associated with the energy storage device from a nominal resistance model module; an operating resistance model associated with the energy storage device from an operating resistance model module; a rated discharge current associated with the energy storage device from a rated discharge current module; and a nominal OCV curve associated with the energy storage device from a nominal OCV curve module. In this example implementation, the power rating estimation module is configured to generate a power rating estimate based on the nominal resistance model, the operating resistance model, the rated discharge current, and the nominal OCV curve; the operating resistance model and the nominal resistance model are each based on a voltage signal from a voltage sensor and a current signal from a current sensor; and the power rating estimate is generated by: (1) predicting an operating voltage based on the operating resistance model and the rated discharge current, (2) predicting a nominal voltage based on the nominal resistance model and the rated discharge current, (3) averaging a ratio of the predicted operating voltage to the predicted nominal voltage across an entire OCV curve. BRIEF DESCRIPTION OF DRAWINGS

[0009] Additional aspects of the disclosure will be apparent upon consideration of the non-limiting implementations as described in the specification and claims, with reference to the accompanying drawings, in which like reference numerals refer to like elements, and:

[0010] Figure 1A FIG. 1 is a diagram illustrating an example energy storage unit;

[0011] Figure 1B FIG. 2 is a diagram illustrating an example energy storage module;

[0012] Figure 1C FIG. 3 is a diagram illustrating an example energy storage stack of units;

[0013] Figure 1D FIG. 4 is a diagram illustrating an example energy storage stack of modules;

[0014] Figure 1E FIG. 5 is a diagram illustrating an example energy storage group of stacks;

[0015] Figures 2A-2D FIG. 6 is a block diagram illustrating an example health state estimation system;

[0016] Figure 3 FIG. 7 is an equivalent circuit model diagram with respect to an example energy storage device;

[0017] Figure 4 FIG. 8 is a flow diagram illustrating an example method; and

[0018] Figure 5is an example cell energy output plot. DETAILED DESCRIPTION

[0019] Reference will now be made to exemplary embodiments illustrated in the drawings, and specific language will be used herein to describe the same. It will nevertheless be understood that no limitation of the scope of the disclosure is intended. Alterations and further modifications of the inventive features illustrated herein, and additional applications of the principles of the disclosure as illustrated herein, which would occur to one skilled in the relevant art, are to be considered within the scope of the disclosure.

[0020] SOH estimation system

[0021] According to example embodiments, systems, devices, and methods for providing state of health estimation in energy storage systems and / or energy storage devices are disclosed herein. Further, in example embodiments, SOH estimation systems, devices, and methods for accurately estimating the SOH of an energy storage device at one or more of a cell level, a module level, a pack level, and a group level are provided.

[0022] There are two main limitations in the prior art that are addressed by the SOH estimation system of the present disclosure. First, capacity is typically estimated jointly with other cell parameters, which often leads to unstable and inaccurate estimates. Additionally, incorrect estimates can be generated if estimates are made in cases where there is insufficient information in the measurement data. According to example embodiments, methods to address these issues are disclosed through a normalized capacity estimation method that decouples capacity and parameter estimation. Parameter model estimation and capacity estimation can be performed at different points in time as needed, resulting in more robust and accurate estimates. Additionally, the disclosed example methods incorporate model gradient information to intelligently update estimates only in cases where there is sufficient information in the measurement data.

[0023] Second, typical methods of determining the SOH of a battery are based only on capacity estimation. However, these typical methods do not account for other changes in the energy storage device. For example, these typical methods do not account for power decay. Power decay can occur as the internal impedance of an energy storage device increases over time. Particularly for high power applications, not accounting for both capacity decay and power decay can result in an inaccurate characterization of the performance of the energy storage device. Referring to Figure 5 The amount of power that can be delivered is currently limited by the ESS design. In a similar manner, the amount of charge available is limited by the battery chemistry and capacity. Over time, as the battery degrades, power decay and capacity decay will occur as Figure 5shown to reduce the total energy. The proposed method can improve SOH accuracy by considering both mechanisms. Additionally, incorporating the rated discharge current can provide a unified method for high-power and low-power / high-energy applications to estimate SOH based on power fade. Thus, the estimated SOH varies depending on the rated operating discharge current of the ESS.

[0024] In an example implementation, a SOH estimation system for determining an estimate of a state of health (SOH) of an energy storage device is disclosed, which considers both power fade and capacity fade. In an example implementation, the SOH estimation system includes a SOH aggregation module that determines an estimate of the SOH of the energy storage device, the estimate of the SOH being based on a normalized capacity estimate NC n and a rated power estimate PR n .

[0025] Referring now to Figure 2A In an example implementation, the SOH estimation system 100 includes a SOH estimation module 105. In this example implementation, the SOH estimation module 105 can be configured to receive the following information (received information): a nominal capacity Q nom representing a nominal capacity of the energy storage device; a voltage input representing a measured voltage V m of the energy storage device; a current input representing a measured current I m from / to the energy storage device; a nominal open circuit voltage (OCV) curve f ocv associated with the energy storage device; an operating resistance model R T,op associated with the energy storage device; an operating dynamic model module (R0, R1, C1) associated with the energy storage device; a nominal resistance model R T,nom associated with the energy storage device; and a rated discharge current I d associated with the energy storage device. In an example implementation, the SOH estimation module 105 is configured to determine an estimate of the operating SOH of the energy storage device based on all of the received information. In an example implementation, the SOH estimation module 105 is further configured to receive and the received information further includes a temperature input T m representing a temperature associated with the energy storage device. In an example implementation, the SOH estimation module 105 is configured to output the estimated SOH. The estimated SOH takes into account a majority of the degradation mechanisms that occur within the cells of the energy storage device.

[0026] The SOH aggregation module 110

[0027] According to example embodiments, the SOH estimation module 105 can also include an SOH aggregation module 110 that determines an SOH estimate SOH of the energy storage device. In example embodiments, the SOH aggregation module 110 is configured to: receive a normalized capacity estimate NC n for each of the cells (cell 1 through cell N) in the energy storage system; receive a rated power estimate PR n for each of the cells (cell 1 through cell N) in the energy storage system; and output the SOH estimate of the energy storage device. In example embodiments, the SOH estimate incorporates both power decay and capacity decay. In example embodiments, the SOH estimate can be considered a “functional SOH estimate” in that one or both of the normalized capacity estimate and the rated power estimate, and thus the SOH estimate, reflect actual operation of the energy storage system (i.e., how the energy storage system is operated and the operating environment of the energy storage system).

[0028] In example embodiments, the SOH estimate can be determined by multiplying the minimum normalized capacity estimate (of cell 1 through cell N) by the average of the individual rated powers of the energy storage system, and then multiplying that result by 100 to get a percentage. In other words, the normalized capacity estimates and the rated power estimates of cell 1 through cell N are aggregated together to generate a single SOH value. Thus, in one example embodiment, the SOH can be calculated by:

[0029]

[0030] where PR n is the rated power estimate of the nth cell of cell 1 through cell N in the energy storage system, and NC n is the normalized capacity estimate of the nth cell of cell 1 through cell N in the energy storage system. It should be understood that PR n is unitless and represents the power decay experienced by the energy storage device. It should also be understood that NC n is unitless and represents the degree of capacity decay experienced by the energy storage device. Multiplying the normalized capacity estimate with the rated power estimate ensures that the SOH value is based on energy capacity, and not just ampere-hour capacity. In other words, in example embodiments, the SOH aggregation module 110 is configured to base the SOH estimate on the normalized capacity estimate and / or the rated power estimate. This is a distinct advantage over SOH methods that are based solely on ampere-hour capacity, as most economic and operational decisions are based on energy considerations.

[0031] In example embodiments, the normalized capacity estimate NC n may be split into a normalized charge capacity NC c,n and a normalized discharge capacity NCd,n to account for cell imbalance within the estimated SOH. Thus, in one example implementation, the SOH can be calculated by:

[0032]

[0033] The term min 1≤x≤N (NC d,x ) represents the amount of charge that can be removed from the energy storage device without over-discharging the most charged cell. The term min 1≤y≤N (NC c,y ) represents the amount of charge that can be accepted by the energy storage device without over-charging the most charged cell. The sum of the two terms represents the total available capacity that accounts for both imbalance and capacity fade. The capacity reduction due to imbalance can be recovered by balancing the energy storage device. Example methods for calculating the normalized charge capacity NC c and the normalized discharge capacity NC d are described in further detail herein.

[0034] This method of determining an SOH estimate can be applied to any energy storage device (e.g., at the cell level, module level, stack level, or group level, to a series and parallel combination of N cells). That is, the same devices, systems, and methods of determining an aggregate SOH estimate can be used regardless of whether the energy storage device is a cell, module, stack, or group. At the cell level, N = 1 and the method provides an aggregate SOH estimate for a single cell. At the module level, the module has N cells and the method provides an aggregate SOH estimate for the entire module. Similarly, at the stack level, the stack can include N cells and the method provides an aggregate SOH estimate for the entire stack of cells. Similarly, at the group level, the group can include N cells and the method provides an aggregate SOH estimate for the entire group of cells. Further, this method of determining an SOH estimate can be applied at the energy storage system level.

[0035] The normalized capacity estimation module 120

[0036] In an example embodiment, the SOH estimation system 100 further includes a normalized capacity estimation module 120. In an example embodiment, the SOH estimation module 105 may include the normalized capacity estimation module 120. In an example embodiment, the normalized capacity estimation module 120 is configured to receive nominal capacity. The normalized capacity estimation module 120 may be configured to receive nominal capacity from the nominal capacity module 140. In an example embodiment, the normalized capacity estimation module 120 is configured to receive measured voltage, measured temperature, and / or measured current. The normalized capacity estimation module 120 may be configured to receive these measured characteristics from the sensor 150. In an example embodiment, the normalized capacity estimation module 120 is configured to receive a nominal open-circuit voltage (OCV) curve. The normalized capacity estimation module 120 may be configured to receive a nominal OCV curve f from the nominal OCV curve module 160. ocv In the example implementation, the normalized capacity estimation module 120 is configured to receive an operational dynamic model. The normalized capacity estimation module 120 can also be configured to receive an operational dynamic model from the operational dynamic model module 155.

[0037] In the example implementation, the normalized capacity estimation module 120 is configured to estimate the capacity based on the received nominal capacity Q. nom Measure voltage V m,n Measuring current I m Measure temperature T m,n Nominal OCV curve f ocv The dynamic models R0, R1, and C1 are used to generate the filtered normalized capacity estimate NC for each cell from cell 1 to cell N. n In the example implementation, the filtered normalized capacity estimation (NC) n It is the nominal capacity Q nom The percentage. For example, this can be estimated by taking the filter capacity Q. f,n (Described in more detail below) Divide by the nominal capacity Q nom Determine the normalized capacity estimate (NC) of the filter n In the example implementation, the normalized capacity estimation module 120 is configured to normalize the filtered capacity estimation NC. n Provided to SOH aggregation module 110. This document further describes in detail an example method for calculating the normalized capacity estimate.

[0038] In the example implementation, the normalized capacity estimation module 120 is configured to be based on the operating dynamic model R0, R1, C1, and the measured voltage V. m and measuring current I mto predict an open circuit voltage. As described in greater detail herein, in example embodiments, the normalized capacity estimation module 120 is configured to determine a normalized capacity estimation based on the predicted open circuit voltage, a nominal capacity Q nom and a measured current I m

[0039] rated power estimation module 130

[0040] In example embodiments, the SOH estimation system 100 further includes a rated power estimation module 130. In example embodiments, the SOH estimation module 105 can include the rated power estimation module 130. In example embodiments, the rated power estimation module 130 is configured to receive a nominal open circuit voltage (OCV) curve. The rated power estimation module 130 can be configured to receive the nominal OCV curve f ocv from the nominal OCV curve module 160. In example embodiments, the rated power estimation module 130 is configured to receive an operating resistance model. The rated power estimation module 130 can be configured to receive the operating resistance model from the operating resistance model module 170. In example embodiments, the rated power estimation module 130 is configured to receive a nominal resistance model. The rated power estimation module 130 can be configured to receive the nominal resistance model from the nominal resistance model module 180. In example embodiments, the rated power estimation module 130 is configured to receive a rated discharge current. The rated power estimation module 130 can be configured to receive the rated discharge current from the rated discharge current module 190.

[0041] In example embodiments, the rated power estimation module 130 is configured to determine a rated power estimation based on the rated discharge current I d , the operating resistance model R T,op , the nominal resistance model R T,nom , and the nominal OCV curve f ocv As described further herein, the rated power estimation is determined by taking a ratio of a predicted terminal voltage based on the operating resistance model to a predicted terminal voltage based on the nominal resistance model.

[0042] energy storage system (ESS)

[0043] According to various example embodiments, an energy storage system (“ESS”) is a system that stores and releases electrical charge. In example embodiments, an ESS can include one or more energy storage devices, a battery management system, sensors, inverters, etc.

[0044] energy storage device

[0045] ​In example implementations, the energy storage device can include an electrochemical cell, such as a lead-acid battery, a nickel-cadmium battery, a nickel-metal hydride battery, a lithium-ion battery, a lithium-polymer battery, a zinc-air battery, or the like. In another example implementation, the energy storage device can include a flow battery. In yet another example implementation, the energy storage device can include a supercapacitor. Further, the energy storage device can include any suitable rechargeable energy storage system relevant to SOH estimation. In example implementations, the energy storage device can include a single cell, multiple cells, a stack, a module, a pack, or a pack.

[0046] Cell

[0047] In various example implementations described herein, and with reference to Figure 1A In example implementations, the ESS can include a battery cell 1, or simply a “cell.” In example implementations, the cell 1 includes a single anode and cathode separated by an electrolyte, and the cell 1 is used to store and release electrical charge. However, other cell designs can also be used, such as in a flow battery. Multiple anodes and cathodes can be joined together in parallel or series arrangements to produce cells that operate at higher voltage or current levels. In one example implementation, the cell can be the smallest measurable energy storage unit within the ESS. The current flowing through the cell 1 is denoted as I m to measure current, with positive current flowing out of the positive terminal. A typical cell can be physically arranged as a cylindrical cell, such as a 18650 and 21700 cylindrical lithium-ion format cell, a button cell, a prismatic cell, a pouch cell, or the like. In another example implementation, the cell can include a supercapacitor. Further, the cell can include any chemistry and format suitable for rechargeable energy storage relevant to SOH estimation. Generally, the cell 1 can be any rechargeable energy storage device with connection points for a single voltage measurement. The systems, methods, and devices described herein can provide improved SOH estimation of the cell 1.

[0048] Module

[0049] Further, in example implementations, and with reference to Figure 1BThe ESS may include a battery module 2, or simply a "module". Module 2 may include two or more units connected and grouped together in series or parallel arrangement, or both series and parallel arrangement. In one example embodiment, a lead-acid automotive battery includes a module consisting of six units with only two connection points for overall voltage measurement. In another example embodiment, a lithium-ion unit module includes a module with 12 units connected in series, each unit having an independent connection point for unit voltage measurement. Module 2 may be the smallest measurable unit in the ESS if the individual units are integrated into the module in a way that makes it inconvenient to measure the voltage from the individual units. The current flowing through module 2 is expressed as I. m The positive current flows out from the most positive cell terminal. Furthermore, the module can be any energy storage device comprising a group of two or more cells, having connection points for one or more voltage measurements. The systems, methods, and apparatus described herein can provide improved SOH estimation for module 2.

[0050] heap

[0051] Furthermore, in the example implementation, and referring to Figure 1C The ESS may include a battery stack 3, or simply a "stack". In an example embodiment, the stack 3 includes a plurality of cells 1 connected in series. Therefore, in an example embodiment, the stack 3 may include N cells, and the cells may be denoted as cells n, where n = 1 to N. It should be understood that N can be any positive integer. For N = 1, the stack is a single cell. For N > 1, the stack is a plurality of cells N. In another example embodiment, and referring to Figure 1D Stack 3 comprises multiple modules 2 connected in series. Therefore, in the example embodiment, stack 3 may include N modules, and these modules may be denoted as module n, where n = 1 to N. It should be understood that N can be any positive integer. For N = 1, the stack is a single module. For N > 1, the stack is multiple modules N. The current flowing through stack 3 is denoted as I. m The positive current flows out from the most positive cell or module terminal. The systems, methods, and apparatus described herein can provide improved SOH estimation for cell stack 3.

[0052] Group

[0053] Furthermore, in the example implementation, and referring to Figure 1E The ESS may include battery pack 4, or simply "pack". In an example embodiment, pack 4 includes multiple stacks 3 connected in parallel. Therefore, in an example embodiment, pack 4 may include N stacks, and the stacks may be denoted as stack n, where n = 1 to N. It should be understood that N can be any positive integer. For N = 1, the pack is a single stack. For N > 1, the pack is multiple stacks N. The current flowing through pack 4 is expressed as I.m' which is also electrically equivalent to the sum of the individual stack currents I m,1…N If one or more stacks can be connected or disconnected from the pack using contactors, circuit breakers, solid state switches, or any other suitable means of turning current on or off, the number of stacks included within the pack 4 can vary dynamically over time. The systems, methods, and devices described herein can provide improved SOH estimation of the pack 4.

[0054] Nominal capacity module 140

[0055] Referring Figure 2A In example embodiments, the SOH estimation system 100 can include a nominal capacity module 140. In this example embodiment, the nominal capacity module 140 is configured to provide a theoretical cell capacity Q nom of a new cell to the normalized capacity estimation module 120. The nominal capacity can be in ampere-hours. The nominal capacity Q nom may be a single number provided by a manufacturer, for example, by way of an energy storage device manufacturing specification sheet for a particular model. In example embodiments, the nominal capacity can be taken as the total charge over a small range of the full OCV curve. In example embodiments, the nominal capacity Q nom is constant with respect to the life of the energy storage system. However, in other example embodiments, the Q nom provided to the normalized capacity estimation module 120 can be adjusted to account for changes in temperature or other factors.

[0056] Voltage, current, and / or temperature sensors 150

[0057] In example embodiments, the SOH estimation system 100 can include voltage, current, and / or temperature sensors 150. In this example embodiment, the normalized capacity estimation module 120 is configured to receive voltage, current, and / or temperature signals. These signals can provide information representative of the voltage, current, and / or temperature of the energy storage device, respectively. In example embodiments, these signals and this information can be measured by sensors 150 associated with the energy storage device. However, as described below, in some cases, the signals can not be based on direct measurements.

[0058] In example embodiments, the normalized capacity estimation module 120 can be configured to receive a voltage signal from a voltage sensor. The voltage sensor can be any suitable type of voltage sensor, such as a resistive or capacitive voltage sensing circuit followed by a suitable filter and analog-to-digital converter. In example embodiments, a separate voltage sensor can be associated with each of the cells 1 through N of the energy storage system. In this example embodiment, each voltage sensor can be configured to measure the voltage of the associated cell and produce a voltage measurement V mVoltage measurements can be performed at any suitable interval over time, and individual measurements are denoted herein by the subscript k, which represents each time step. Therefore, sensor 150 can provide the normalized capacity estimation module 120 with a series of measurements (represented by k, representing time steps) as shown by V... m,1,k V m,2,k ...V m,N,k This represents N unit-level voltage measurements. In other words, V m,n,k It can represent the measured voltage of the nth unit at the kth time step.

[0059] In an example implementation, the normalized capacity estimation module 120 can be configured to receive a current signal from a current sensor. The current sensor can be any suitable type of current sensor, such as a resistive shunt or a magnetic Hall effect sensor, followed by a suitable filter and analog-to-digital converter. In an example implementation, a single current sensor or multiple current sensors can be associated with the energy storage device, regardless of the number of units. For example, the current sensor can measure the current going to or leaving the energy storage device. Individual current measurements can be performed at any suitable interval over time, and the current measurements are denoted herein by the subscript k, which represents each time step. Therefore, sensor 150 can provide the normalized capacity estimation module 120 with a series of current signals (represented by k) as specified by I... m,k This represents the current measurement of the energy storage unit. In other words, I m,k This can represent the measured current for an energy storage device at the k-th time step.

[0060] In an example implementation, the normalized capacity estimation module 120 can be configured to receive a temperature signal from a temperature sensor. The temperature sensor can be any suitable type, such as a resistive thermistor or thermocouple, followed by a suitable filter and analog-to-digital converter. In an example implementation, multiple temperature sensors can be associated with each of the cells 1 through N of the energy storage device, respectively. For example, each temperature sensor can measure the temperature of a specific cell. Therefore, the temperature measurement T... m This can be performed for each of the N cells at any suitable interval over time, and the temperature measurement is denoted herein by the subscript k, which represents each time step. Therefore, sensor 150 can provide the normalized capacity estimation module 120 with a series of (time steps denoted by k) such as those given by T m,1,k T m,2,k ...T m,N,k This represents the temperature measurement at the energy storage cell level. In other words, T m,n,kmay represent a measured temperature of the n-th cell at the k-th time step. In other example implementations, there can be fewer than N physical temperature sensors. In this example implementation, an interpolation or weighted average function can be used to generate N cell temperatures from fewer than N physical sensors. Further, in another example implementation, temperature measurements T m .

[0061] According to another example implementation, voltage, current, and / or temperature measurements can be provided to the dynamic model estimation module 145. According to another example implementation, voltage, current, and / or temperature measurements can be provided to the resistance model estimation module 175.

[0062] Nominal OCV curve module 160

[0063] In an example implementation, the SOH estimation system 100 further includes a nominal OCV curve module 160. In an example implementation, the nominal OCV curve module 160 provides a nominal OCV curve f ocv (SOC). In an example implementation, the nominal OCV curve module 160 provides a nominal OCV curve f ocv (SOC) to the rated power estimation module 130. The nominal OCV curve represents the open circuit voltage of a new cell or module or pack as a function of state of charge. This can be provided by the manufacturer, or can be determined empirically by testing the energy storage device itself or similar energy storage devices. The nominal OCV curve can be a function, or can be a lookup table based function. Thus, in one example implementation, the nominal OCV curve is determined once and does not change over time. However, in other example implementations, the nominal OCV curve can be adjusted over time to account for changes in temperature or other factors. In an example implementation, two different OCV curves can be used, one for charging and another for discharging.

[0064] Equivalent circuit model diagram

[0065] Referring now to Figure 3 , a battery cell can be represented by an equivalent circuit model (ECM) diagram 300. Although various calculations are described herein based on the ECM diagram 300, it should be understood that similar calculations can be based on other ECMs in implementing the concepts described herein as applied to energy storage systems or energy storage devices. The ECM diagram 300 models the voltage response of a cell in operation. There are three main components in the equivalent circuit model (ECM): the open circuit voltage (V ocv), a resistor (R0), and a resistor-capacitor pair (R1 and C1). It should be noted that other ECMs can include more or different parameters.

[0066] Open-circuit voltage V ocv represents the thermodynamic potential of the cell at rest. The value of the open-circuit voltage can vary based on the state of charge of the cell. The single resistor component R0 is used to represent the ohmic losses of the cell. This resistance is the sum of the ohmic losses experienced at the two electrodes and at the electrolyte. In example embodiments, R0 = 0.1 Ohm. 0,n represents the ohmic resistance of the nth cell. The resistance (R1) and the capacitor (C1) in the ECM are used to model the time-dependent voltage drop within the cell. In example embodiments, R1 = 0.1 Ohm and C1 = 0.1 F. 1,n represents the polarization resistance of the RC pair of the nth cell. In example embodiments, R1 = 0.1 Ohm. 1,n represents the polarization capacitance of the RC pair of the nth cell. The voltage drop of this RC pair is caused by specific chemical reactions taking place within the cell and is denoted herein as V1.

[0067] Resistance model estimation module 175

[0068] According to example embodiments, the SOH estimation system 100 includes a resistance model estimation module 175. The resistance model estimation module 175 can be configured to receive voltage, current, and temperature measurements from the sensors 150. Typically, only current and voltage measurements are needed for the online estimation method. However, in other example embodiments, all three measurements can be necessary, for example when offline techniques are used. The voltage and temperature measurements can be for each of the N cells of the energy storage device. However, in other example embodiments, the temperature measurements can be determined in other ways (assumed, averaged, estimated, etc.). In example embodiments, the resistance model estimation module 175 can be configured to calculate (as further described below) an operating resistance model R T,op and provide it to the operating resistance model module 170. In example embodiments, the resistance model estimation module 175 can be configured to calculate (as further described below) a nominal resistance model R T,nom and provide it to the nominal resistance model module 180.

[0069] Dynamic model estimation module 145

[0070] According to example embodiments, the SOH estimation system 100 includes a dynamic model estimation module 145. The dynamic model estimation module 145 can be configured to receive voltage, current, and temperature measurements from the sensors 150. The voltage and temperature measurements can be for each of the N cells of the energy storage device. However, in other example embodiments, the temperature measurements can be determined in other ways (assumed, averaged, estimated, etc.). In example embodiments, the dynamic model estimation module 145 can be configured to compute (as further described below) and provide the operating dynamic model (R0, R1, and C1) to the operating dynamic model module 155.

[0071] Estimation techniques

[0072] In example embodiments, the dynamic model estimation module 145 and the resistance model estimation module 175 include offline methods for estimating the operating dynamic model (R0, R1, and C1), the nominal resistance model (R T,nom ), and the operating resistance model (R T,op ), respectively. In example embodiments, the method involves using empirical models that describe how each of these five parameters varies with temperature and open-circuit voltage. In example embodiments, a cell can be modeled by five equations:

[0073]

[0074] where subscript p represents R0, R1, C1, R T,op , R T,nom . In other words, the single equations above represent a first equation for f R0 (T, V), a second equation for f R1 (T, V), a third equation for f C1 (T, V), a fourth equation for f RT,nom (T, V), and a fifth equation for f RT,opa fifth equation for (T, V). Thus, in example embodiments, a unique parameter model is provided for each of these parameters. In this approach, hybrid pulse power characteristic (HPPC) tests are performed outside of normal operation and the output voltage, current, and temperature are recorded. The HPPC tests can be performed over a narrow voltage and OCV range or at several temperature and OCV points. When tests are performed over a range of operating conditions, the design of the experimental method described in M. Mathew, M. Mastali, J. Catton, E. Samadani, S. Janhunen, and M. Fowler, “Development of an electro-thermal model for electric vehicles using a design of experiments approach” Batteries 4(2), 2018 can be used to minimize the test time. The voltage and current data from the HPPC experiments can be used in a nonlinear regression method to determine the coefficients of the model β 0，p ...β 8，p for a particular cell n. Furthermore, any suitable method for obtaining the parameters of the model for the ECM can be used.

[0075] In example embodiments, the dynamic model estimation module 145 and / or the resistance model estimation module 175 can be configured to estimate the operating dynamic model (R0, R1, and C1) in the case of the dynamic model estimation module 145 and the nominal resistance model (R T,nom ) and the operating resistance model (R T,op ) in the case of the resistance model estimation module 175 using an online method. The online mode can also be referred to herein as a “monitoring” mode. In this example embodiment, the operation of the energy storage system is not interrupted by the updating or “generation” of the operating dynamic model and the operating resistance model. In this monitoring mode, the dynamic model estimation module 145 or the resistance model estimation module 175 is configured to update the operating dynamic model or the resistance model, for example, based on an online estimation method such as an extended Kalman filter (EKF) or a recursive least squares method (RLS). The dynamic model estimation module 145 or the resistance model estimation module 175 is configured to perform this calculation in a timely manner during the charging and discharging activities of the energy storage system. Thus, the operating dynamic model or the operating resistance model can be updated in this monitoring mode without interrupting the operation of the energy storage device. This is the fastest and most convenient method. However, any suitable online method for obtaining the parameters for the ECM can be used.

[0076] Thus, in example embodiments, the dynamic model estimation module 145 is configured to update the operating dynamic model (R0, R1, C1), and / or the resistance model estimation module 175 is configured to update the operating resistance model R T,op and / or the nominal resistance model R T,nom In example embodiments, the dynamic model estimation module 145 is configured to provide the operating dynamic model (R0, R1, C1) to the operating dynamic model module 155. In example embodiments, the resistance model estimation module 175 is configured to provide the operating resistance model to the operating resistance model module 170 and / or the nominal resistance model to the nominal resistance model module 180. In example embodiments, an estimate of the SOH of the energy storage system can be determined using the output models from the dynamic model estimation module 145 and the resistance model estimation module 175 in subsequent modules. Thus, in one example embodiment, the systems and methods disclosed herein can determine an estimate of the SOH of the energy storage system by monitoring the energy storage system during normal operation. In this example embodiment, it is not necessary to interrupt the operation of the energy storage system to determine an estimate of the SOH. However, as described herein, alternative testing methods can be employed to determine an estimate of the SOH within the scope of the present disclosure. In either case, the accuracy of the estimate of the SOH can be improved by basing the estimate on both a capacity estimate and a power rating estimate.

[0077] In example embodiments, the operating dynamic model, the operating resistance model, or the nominal resistance model is generated locally, by which is meant at the physical location of the energy storage device, but in other example embodiments, the operating dynamic model, the operating resistance model, or the nominal resistance model is generated remotely, for example via processing performed by a remote workstation or a cloud server.

[0078] The operating dynamic model, the operating resistance model, or the nominal resistance model can be generated / updated at any suitable frequency. For example, the operating dynamic model, the operating resistance model, or the nominal resistance model can be generated / updated with each sample time step or on any suitable hourly, daily, or monthly schedule.

[0079] The operating resistance model module 170

[0080] In example embodiments, the SOH estimation system 100 includes the operating resistance model module 170. In example embodiments, the operating resistance model module 170 is configured to receive the updated operating resistance model from the resistance model estimation module 175 and store the model. In other words, the operating resistance model module 170 is simply a store of the total resistance R T for each cell in the ESS. In example embodiments, the total resistance R TThe function can be implemented using a look-up table. In this case, the operating resistance model module 170 is simply a storage of a look-up table for each cell in the ESS. In an example embodiment, the operating resistance model module 170 is configured to provide the stored updated operating resistance model to the rated power estimation module 130.

[0081] Nominal resistance model module 180

[0082] In an example embodiment, the SOH estimation system 100 includes a nominal resistance model module 180. In an example embodiment, the nominal resistance model module 180 is configured to receive the initial resistance model from the resistance model estimation module 175 and store these parameters. In other words, the nominal resistance model module can be configured to simply store the total resistance R0 at the beginning of life for each cell in the ESS. T This total resistance can be re-estimated one or more times during the life of the system. For example, this can be estimated at manufacturing time, during commissioning, or due to reconfiguration or maintenance performed on the ESS. In an example embodiment, the nominal resistance model module 180 is configured to provide the stored updated nominal resistance model to the rated power estimation module 130.

[0083] Operating dynamic model module 155

[0084] In an example embodiment, the SOH estimation system 100 includes an operating dynamic model module 155. In an example embodiment, the operating dynamic model module 155 is configured to receive the updated operating dynamic model from the dynamic model estimation module 145 and store these parameters. In other words, the operating dynamic model module can be configured to simply store the operating dynamic model (R0, R1, and C1) for each cell in the ESS. In an example embodiment, the operating dynamic model module 155 is configured to provide the stored updated operating dynamic model to the normalized capacity estimation module 120.

[0085] The updates to the operating resistance model in the operating resistance model module 170 and the operating dynamic model in the operating dynamic model module 155 can be done independently and at different time scales than the capacity estimation and / or rated power estimation. In one example embodiment, the time scale can be as small as less than a minute, with real-time measured data used to update the models as quickly as possible. In another example embodiment, the time scale can be large, for example, multiple days or months. This increased flexibility can allow the model updates to be scheduled when there is sufficient information in the measured data to make accurate updates, thus improving the overall accuracy of the SOH estimation.

[0086] In example implementations, the signals or data discussed herein can be communicated locally between modules, all at the energy storage system (e.g., in the battery management system). But it is within the scope of the present disclosure for one or more of the described modules to be located remotely from the energy storage device (e.g., storing and processing data in a cloud server). In example implementations, the operating resistance model, the nominal resistance model, and the operating dynamic model can be updated based on information provided to the dynamic model estimation module 145 and the resistance model estimation module 175 (but this data can be provided to the three model modules from a cloud or other source). And, in another example implementation, the resistance model estimation module 175 and the dynamic model estimation module 145 can be located remotely from the energy storage device, e.g., in the cloud. At their source, the measured data will be provided by sensors at the energy storage unit, but it is possible that this data can first be provided to a database or module remote from the energy storage system. Moreover, the various modules described herein can be combined, their functions performed in whole or in part by other modules, and / or their functions can be distributed among these or other modules.

[0087] Nominal capacity estimation module 120

[0088] In example implementations, the nominal capacity estimation module 120 is configured to receive the nominal capacity from the nominal capacity module 140, the voltage, current, and temperature measurements from the sensors 150, the nominal OCV curve f ocv (SOC), and the operating dynamic model from the operating dynamic model module 155. In example implementations, the nominal capacity estimation module 120 is configured to determine a normalized capacity estimate NC n based on the received information, and provide it to the SOH aggregation module 110.

[0089] In example implementations, for each cell, the determination of the normalized capacity estimate NC n can be made by using the values of the ohmic resistance (R 0,n ), the polarization resistance (R 1,n ), and the capacitance (C 1,n ) stored in the operating dynamic model module. In example implementations, the nominal capacity estimation module 120 first initializes (time k = 0) the values for the model circuit diagram, where the polarization voltage of the RC pair for all cells is initialized to: V 1，n = 0, and the initial open circuit voltage for all cells is initialized to V ocv，n = V m，n .

[0090] The normalized capacity estimation module 120 can next determine, at time step k, the polarization voltage of the nth cell for each unit based on the previously calculated polarization voltage, the coefficients for the ECM, and the previously measured current. For example:

[0091]

[0092] where τ 1，n = R 1，n * C 1，n , and where Δt = the change in time between sample steps k and k-1. In this example, the polarization voltage for each unit at each time step is based on the polarization voltage at the previous time step and an update based on the measured current.

[0093] Next, in example implementations, the normalized capacity estimation module 120 is configured to predict, at time step k, the open circuit voltage V ocv，n，k for the nth cell for each unit. This calculation is based on the current voltage measurement plus the polarization voltage plus the voltage drop due to the current flow through the resistance Ro of the ECM. For example,

[0094] V ocv，n，k = V m，n，k + V 1，n，k + I m R 0，n

[0095] Next, in example implementations, the normalized capacity estimation module 120 is configured to gate its calculation of an estimate of capacity so as to only do so when the energy storage system has experienced sufficient charge or discharge for a reliable calculation. Although this can be accomplished in various ways, consistent with the present disclosure, in example implementations, this is performed by looking at the OCV from k to k+W, e.g., V ocv，n，k to V ocv，n，k+W . The normalized capacity estimation module 120 can be configured to determine the minimum OCV (V ocv,min ) and the maximum OCV (V ocv,max ) between V ocv，n，k and V ocv，n，k+W . The time steps at which these estimates occur are denoted as ti and t2. In identifying these, the normalized capacity estimation module 120 can be configured to determine the OCV curve gradients at V ocv,min and V ocv,max . These gradient values are denoted herein as V dOcv,min and V dOcv,max .

[0096] In example implementations, the normalized capacity estimation module 120 is configured to compute the capacity only when conditions are suitable for computing the capacity. Although other gating criteria can be used, in one example implementation, the conditions are suitable for computing the capacity when:

[0097] i.V oce,max -V ocv,min >Δ Thres

[0098]

[0099] where Δ Thres and are configurable thresholds. The purpose of this filter or these gating thresholds is to ensure that the computation is only done when there is enough information in the data to obtain an accurate capacity estimate. In this way, the SOH can be computed in an online mode by using opportunistic monitoring of the energy storage device.

[0100] In example implementations, if the above criteria are met, the normalized capacity estimation module 120 is configured to compute the estimated capacity (for each cell n) Q e,n :

[0101]

[0102] where g soc is the inverse of the open circuit voltage curve (f ocv -1 ), η is the coulombic efficiency, and where the function f ocv is the open circuit voltage curve provided by the nominal OCV curve module 160, and it is a function of the state of charge (SOC) of each cell n.

[0103] The capacity prediction Q e,n may be filtered using an exponentially weighted moving average function to produce a filtered capacity estimate Q f,n :

[0104] Q f，n,h = (1 - λ Q ) Q f,n，h-1 + λ cap Q e，n

[0105] where λ Q is a constant smoothing factor used in the filtered capacity estimate, and where the index h denotes an estimate index, which is at a different time scale than the sampling index k. In example implementations, Q f,n may have units of Ah.

[0106] Thus, in example implementations, when (1) the difference between the maximum predicted OCV and the minimum predicted OCV is less than a threshold, when (2) the minimum predicted OCV curve gradient V dOcv,min is less than a gradient threshold, and when (3) the maximum predicted OCV curve gradient V dOcv,max is less than a gradient threshold, the filtered capacity estimate is based on the minimum predicted OCV and the maximum predicted OCV that are filtered to prevent updates to the capacity estimate.

[0107] In example implementations, the normalized capacity estimation module 120 can also be configured to estimate a normalized capacity NC n for each cell. f,n This can be done by dividing the filtered capacity estimate Q nom of the nth cell by the nominal capacity Q n For example:

[0108]

[0109] In example implementations, the normalized capacity NC c,n can be decomposed into two smaller terms: a normalized charge capacity estimate NC d,n and a normalized discharge capacity estimate NC c,n . Splitting the normalized capacity into charge and discharge components allows for the incorporation of cell imbalances when estimating SOH. These two terms can be calculated as follows:

[0110]

[0111] At a particular point in the operation of the energy storage system, the term NC d,n represents the total normalized charge that the cell can accept, while the term NC ocv,n,k can be taken at any time step k and used to calculate both NC c,n and NC d,n . This time step k can be chosen to correspond to V ocv,n,max or V ocv,n,min . However, any suitable time step k can be chosen within the estimation window. For each cell, the sum of NC c,n and NC d,n will equal NC n . Thus, in this disclosure, at any point, the normalized capacity NC n can be replaced by the combination of the normalized charge capacity NC c,n and the normalized discharge capacity NC d,n .

[0112] In example implementations, the normalized capacity estimation module 120 is configured to estimate the nominal capacity NC n to the SOH aggregation module 110.

[0113] In example implementations, one of the advantages of the disclosed state of health estimation system is that it decouples the estimation of capacity from other model parameter estimations. This is in contrast to existing methods where one or more model parameters can be estimated simultaneously with capacity on the same time scale. Joint estimation can lead to instability issues as there is typically not enough information in the data to provide accurate estimates for each parameter. The disclosed SOH estimation system 100 allows for estimation of parameter models on a different time scale than capacity and only when there is sufficient measurement information, providing more stable and accurate estimates.

[0114] Another advantage of the disclosed SOH estimation technique is the ability to estimate the operating resistance model and the operating dynamic model offline (testing) or online (monitoring), where the analysis is performed locally at the energy storage system or remotely from the energy storage system.

[0115] Another advantage of the disclosed SOH estimation technique is the ability to estimate capacity without the need for full charge-discharge cycles. In example implementations, when there is sufficient information in the measurement data rather than requiring a full charge-discharge cycle from 100% SOC to 0% SOC, an accurate capacity estimate can be determined during partial cycles by intelligently updating the capacity estimate.

[0116] In contrast to typical capacity estimation techniques that can ignore OCV swings as a variable, in example implementations, the SOH estimation system 100 is configured to estimate capacity using cumulative charge, OCV swings, and OCV curve gradient. Ignoring OCV swings increases the chance of introducing errors as small OCV swings can not have enough information available in the data to estimate capacity correctly. By incorporating both OCV swings and OCV curve gradient, a more intelligent and robust capacity estimate can be obtained.

[0117] Rated discharge current module 190

[0118] In example implementations, the SOH estimation system 100 also includes a rated discharge current module 190. The rated discharge current module can be configured to estimate the rated discharge current I dProvided to the rated power estimation module 130. In an example implementation, the rated discharge current may correspond to the nameplate discharge current of the design (regardless of the level to which the SOH estimation system is applied, such as a cell, energy storage device, ESS, etc.). For example, the rated discharge current may be based on the design (or "nameplate") rating for a cell. However, the rated discharge current may be based on the physical limitations of one or more other designs of the energy storage device or energy storage system (e.g., busbars, BMS limitations, overcurrent protection devices, etc.). Therefore, different ESSs will have different rated discharge currents based on their specific design and application. In an example implementation, the most limiting factor may dominate the rated discharge current.

[0119] Rated power estimation module 130

[0120] In an example implementation, the SOH estimation system 100 further includes a rated power estimation module 130. In this example implementation, the rated power estimation module 130 is configured to receive an operating resistance model R for each cell in the energy storage device. T,op The rated power estimation module 130 can receive an operating resistance model from the operating resistance model module 170. In an example embodiment, the rated power estimation module 130 is configured to receive the nominal OCV curve f. ocv (SOC). The rated power estimation module 130 can receive the nominal OCV curve from the nominal OCV curve module 160. In the example embodiment, the rated power estimation module 130 is configured to receive the nominal resistance model R for each cell in the stack. T,nom The rated power estimation module 130 can receive a nominal resistance model from the nominal resistance model module 180. In an example embodiment, the rated power estimation module 130 is configured to receive the rated discharge current I of the energy storage system. d The rated power estimation module 130 can receive the rated discharge current from the rated discharge current module 190.

[0121] Furthermore, in the example implementation, the rated power estimation module 130 is configured to generate a rated power estimate PR based on the received operating resistance model, nominal OCV curve, nominal resistance model, and rated discharge current. n In one example implementation, this is accomplished through the following steps. First, the SOC region can be divided into a total of B equal-sized segments between 0 and 100%. The midpoint of these segments is determined by the SOC. b This indicates that b includes consecutive integers between 1 and B. For example, where B = 10, SOC1 = 5, SOC2 = 15, ..., SOC... 10 =95).

[0122] Next, the rated power estimation module 130 is configured to determine a time- weighted average of the discharge power by summing B individual power segments across the SOC operating range

[0123]

[0124] where f ocv is a function representing the OCV value at a specified state of charge, and R T,op,n and R T,nom,n ) are each based on R T are calculated from an SOC lookup table. In an example implementation, for each SOC segment b = 1 to B, the rated power estimation module 130 calculates a numerator representing the OCV minus the operating resistance (or, stated another way, a numerator representing the OCV minus the voltage drop due to the operating resistance). In an example implementation, for each SOC segment b = 1 to B, the rated power estimation module 130 also calculates a denominator representing the OCV minus the nominal resistance (or, stated another way, a denominator representing the OCV minus the voltage drop due to the nominal resistance). In an example implementation, the numerator is divided by the denominator to provide the rated power at that SOC. The rated power estimation module 130 is also configured to average the individual rated powers by summing the individual rated powers and dividing by B to form a rated power prediction PR e,n .

[0125] Next, the rated power estimation module 130 can be configured to filter the rated power prediction using an exponentially weighted moving average function to produce a rated power estimate:

[0126] PR n，h = (1 - λ pr ) PR n,h-1 + λ pr PR e，n

[0127] where λ pr is a constant smoothing factor used in filtering the rated power prediction. In an example implementation, the value of λ pr may range from 0.01 to 0.1, although any suitable range can be used. The smoothing factor is configured to give a greater weight to the previously calculated rated power than to the current rated power. The filter provides a weighting of the previously calculated PR n at time h - 1 to the current PR e,n , where h is the current sample and h - 1 is the previous sample.

[0128] In this way, the rated power estimation module 130 is configured to generate a rated power estimate PR nIn example implementations, the rated power estimation module 130 is configured to determine a rated power estimate PR n provided to the SOH aggregation module 110. Thus, in example implementations, the rated power estimate PR n allows high power applications to more naturally account for the impact of cell resistance than low power applications. In another example implementation, the rated power estimate PR n can be based on multiple current values, generating multiple SOH values. It also accurately accounts for the change in power on the OCV curve as the voltage changes during discharge. It can also incorporate ohmic and polarization resistance components for more accurate steady state power estimation.

[0129] Another advantage of the disclosed SOH estimation techniques is the flexibility of the method to predict SOH over a range of temperatures and / or at a current temperature. This allows SOH to account for real world performance limiting factors, such as low temperature, and thereby more closely predict the actual energy that can be delivered from the battery during operation.

[0130] Method

[0131] Figure 4 is a flowchart illustrating an example method 400 of estimating a state of health of an energy storage device. The example method includes measuring one or more currents associated with an energy storage system to determine a measured current (401). For example, the sensor 150 can measure a current associated with the energy storage system to determine a measured current (see, e.g., current measurement I M , I M,1…N .) The current can be measured using a current measurement circuit.

[0132] According to various example implementations, the method can also include measuring one or more voltages associated with the energy storage system to determine a measured voltage (402) (see, e.g., voltage measurement V M , V M,1…N .) The voltage can be measured using a voltage measurement circuit. Further, the method 400 can also include measuring one or more temperatures associated with the energy storage system to determine a measured temperature (403).

[0133] In example implementations, the method further includes determining, at the dynamic model estimation module 145, an operating dynamic model for each of the N cells of the energy storage device based on the voltage input V, the current input I, and / or the temperature input T (404).

[0134] In example implementations, the method further includes determining, at the resistance model estimation module 175, an operating resistance model for each of the N cells of the energy storage device based on the voltage input V, the current input I, and / or the temperature input T (405).

[0135] In example implementations, the method further includes determining, at the resistance model estimation module 175, a nominal resistance model for each of the N cells of the energy storage device based on the voltage input V, the current input I, and / or the temperature input T (406).

[0136] In example implementations, estimation of the operational resistance model, the nominal resistance model, and the operational dynamic model can be done on three independent time scales.

[0137] In example implementations, the method further includes determining, at the normalized capacity estimation module 120, a normalized capacity estimate for each of the N cells of the energy storage device based on the nominal capacity input, the voltage input V, the current input I, the temperature input T, the nominal OCV, and the operational dynamic model (406).

[0138] In example implementations, the method further includes determining, at the rated power estimation module, a rated power estimate for each of the N cells of the energy storage device based on the operational resistance model, the nominal OCV, the nominal resistance model, and the rated discharge current (408).

[0139] In example implementations, the method further includes determining, at the SOH aggregation module, an estimate of the operational SOH of the energy storage device based on the rated power estimate and the normalized capacity estimate (410).

[0140] Example implementations of the systems, methods, and devices described herein can be implemented in hardware, software, firmware, or some combination of hardware, software, and firmware. For example, Figure 2A the block diagrams and modules or combinations of modules, and Figure 4 the methods can be implemented in hardware, software, firmware, or some combination of hardware, software, and firmware. For example, Figure 4 the methods can be implemented in the cloud. The firmware or software modules can be implemented within a single device or distributed across multiple devices in communication with one another via a suitable wired or wireless network. For example, Figure 2A the SOH aggregation module 110, the normalized capacity estimation module 120, and / or the rated power estimation module 130 can be implemented in hardware, software, firmware, or some combination of hardware, software, and firmware.

[0141] In accordance with various example implementations, the systems, methods, and devices of the present disclosure are suitable in the context of cell-level, device-level, ESS-level, and in the context of individual cells, individual modules, cell stacks, module stacks, and / or groups. Referring now to Figure 2A Briefly, by way of example, in the context of individual cell SOH estimation, module SOH estimation, stack SOH estimation, and group SOH estimation, the following inputs can be used to produce a normalized capacity (NCn,1…N ) estimated and rated power (PR n,1…N ) estimated: voltage measurement (V m,1…N ), temperature measurement (Tm,1...N), nominal capacity (Q nom ), nominal OCV curve (f ocv ), nominal resistance model (R T,nom ), operating resistance model (R T,op ), current measurement (I m ), operating dynamic model (R0, R1 and C1) and rated discharge current (I d ). Normalized capacity (NC n,1…N ) estimated and rated power (PR n,1…N ) estimated in turn can be used to generate SOH estimates.

[0142] Referring now to Figure 2B , in one example implementation, n represents a single cell, and the energy storage device can have N cells. In this example implementation, as shown in Figure 2B , cell voltage, cell current, and cell temperature are inputs, while nominal capacity, operating resistance model, nominal resistance model, operating dynamic model, rated discharge current, and nominal OCV curve represent a cell of the energy storage device. For clarity, Figure 2A schematic blocks 140, 150, 155, 160, 170, 180, and 190 are designated 140B, 150B, 155B, 160B, 170B, 180B, and 190B to reflect the "cell" of interest in Figure 2B , which is otherwise functionally similar to Figure 2A .

[0143] Referring now to Figure 2C , in another example implementation, n represents a single module, and the energy storage device has N modules. In this example implementation, as shown in Figure 2C , module voltage, module current, and module temperature are inputs, while nominal capacity, operating resistance model, nominal resistance model, operating dynamic model, rated discharge current, and nominal OCV curve represent a module of the energy storage device, rather than a cell. For clarity, Figure 2A schematic blocks 140, 150, 155, 160, 170, 180, and 190 are designated 140C, 150C, 155C, 160C, 170C, 180C, and 190C to reflect the "module" of interest in Figure 2C , which is otherwise functionally similar to Figure 2A .

[0144] Referring now to Figure 2DIn another example implementation, n represents a single pack, and the energy storage device can have N packs. In this example implementation, as shown in FIG. 1C, the pack voltage, pack current, and pack temperature are inputs, and the nominal capacity, operational resistance model, nominal resistance model, operational dynamic model, rated discharge current, and nominal OCV curve represent the pack, rather than the cell, of the energy storage device. For clarity, the schematic blocks 140, 150, 155, 160, 170, 180, and 190 are designated 140D, 150D, 155D, 160D, 170D, 180D, and 190D to reflect the “pack” of interest in Figure 2D Figure 2A Figure 2D Figure 2A

[0145] In an example implementation, the SOH estimation system can be used in the context of stationary energy storage applications for generating SOH estimates for ESS. In another example implementation, the SOH estimation system can be used in the context of secondary life applications for batteries. For example, a battery pack in a vehicle can no longer be able to meet the vehicle’s energy demands, but can provide sufficient energy capacity and power for alternative functions such as stationary energy storage applications. In another example implementation, the SOH estimation system can be used in the context of electric vehicles (e.g., passenger vehicles, delivery vehicles, autonomous vehicles, etc.). In another example implementation, the SOH estimation system can be used in the context of special vehicles such as electric forklifts or golf carts. In another example implementation, the SOH estimation system can be used in the context of trains or long-haul trucks (e.g., a fuel cell or other energy source charges the energy storage device on the train or truck). In another example implementation, the SOH estimation system can be used in the context of airplanes. In another example implementation, the SOH estimation system can be used in the context of test devices (e.g., in a laboratory) to estimate the SOH of one or more energy storage devices within a more controlled environment.

[0146] ​​​​In the present disclosure, the following terms will be used. The singular forms “a,” “one,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to an item includes a reference to one or more items. The term “a” means one, two, or more and is generally applicable to the selection of part or all of a quantity. The term “plurality” means two or more of an item. The term “about” means quantities, dimensions, sizes, formulations, parameters, shapes and other characteristics need not be exact, but can be approximated and / or larger or smaller, reflecting accepted tolerances, conversion factors, rounding off, measurement error and other factors which are factors in many real world measurements, and the like, as well as other factors known to those skilled in the art. The term “substantially” means leaving out that need be exact with respect to the recited characteristic, parameter or value, but allows deviations or variations, including for example, tolerances, measurement error, measurement accuracy limitations and other factors which are factors in many real world implementations, as well as other factors known to those skilled in the art. Numerical data can be expressed or presented herein in a range format. It is to be understood that such a range format is used merely for convenience and brevity and thus should be interpreted flexibly to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges within that range as if each numerical value and sub-range is explicitly recited. As an illustration, a numerical range of “about 1 to 5” should be interpreted to include not only the explicitly recited values of about 1 to about 5, but also include individual values and sub-ranges within the indicated range, such as 1, 1.1, 1.2, 1.3, 1.4, 1.5, 2, 2.2, 2.4, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 4, 4.1, 4.2, 4.3, 4.4, 4.5, 5, and 5.1, and so forth, as well as 1 to 2.2, 2.4 to 3.2, 4 to 5.4, 3 to 3.1, and 4.9 to 5, and so forth. The same principle applies to ranges reciting only one numerical value (e.g., “greater than about 1”) and should apply regardless of the width of the range or the characteristics being described. For convenience, multiple items can be presented in a common list. However, these lists should be construed as though each member of the list is individually identified as a separate and unique member. Thus, for example, a list of items should be construed as though each item had been individually recited individually and disjunctively. Furthermore, where the terms “and” and “or” are used in conjunction with a list of items, they are intended to mean an even broader set of alternatives, i.e., each item in the list can be used individually or in combination with one or more other items in the list. The term “alternatively” refers to a choice of one of two or more alternatives, and is not intended to limit the choice to only those listed alternatives or only one of the listed alternatives at a time, unless the context clearly dictates otherwise.

[0147] It should be understood that the particular implementations shown in the figures and described herein are meant to be illustrative only and are not intended to be limiting in any way. Moreover, the connection lines shown in the various figures contained herein are intended to represent example functional relationships and / or physical couplings between the various elements. It should be noted that many alternatives or equivalents to the examples of apparatus and methods described herein can be employed, and that the examples described herein are meant to be illustrative only and are not intended to be limiting in any way.

[0148] Those skilled in the art will appreciate that the mechanisms of the present disclosure can be suitably configured in any of a number of ways. It should be understood that the mechanisms described herein with reference to the figures are merely one illustrative implementation of the present disclosure and are not intended to limit the scope of the present disclosure as described above.

[0149] However, it is to be understood that the detailed description and specifically the examples are given by way of illustration only and are not intended to limit the scope of the present disclosure in any way. Numerous changes and modifications within the scope of the present disclosure can be made and will be apparent to those skilled in the art and it is intended to include all such modifications as fall within the scope of the present disclosure. The corresponding structures, materials, acts, and equivalents of all elements as described in the claims are meant to include any structures, materials, or acts for performing the functions in combination with other claimed requirements protection elements. The scope of the present disclosure should be determined by the appended claims and their legal equivalents, rather than by the examples given above. For example, the operations recited in any method claims can be performed in any order and are not limited to the order presented in the claims. Furthermore, no element, component, or method step described herein is necessary or essential to the practice of the present disclosure, unless specifically described as "critical" or "essential."

Claims

1. A SOH estimation system for determining an estimate of a state of health (SOH) of an energy storage device, the SOH estimation system accounting for both power decay and capacity decay, the SOH estimation system comprising: a SOH estimation module configured to receive and determine an estimate of the SOH of the energy storage device based on: a nominal capacity input representing a nominal capacity of the energy storage device; a voltage input V representing a measured voltage associated with the energy storage device; a current input I representing a measured current from / to the energy storage device; a nominal open circuit voltage (OCV) curve associated with the energy storage device; an operating resistance model associated with the energy storage device; a nominal resistance model associated with the energy storage device; an operating dynamic model associated with the energy storage device, wherein the operating dynamic model comprises a model parameter based on the current input I associated with the energy storage device; and a rated discharge current associated with the energy storage device, wherein the rated discharge current is associated with the power decay.

2. The SOH estimation system according to claim 1, wherein the SOH estimation module is further configured to receive a temperature input representing a temperature associated with the energy storage device and further determine an estimate of the SOH of the energy storage device based thereon.

3. A SOH estimation system for determining an estimate of a state of health (SOH) of an energy storage device, the SOH estimation system accounting for both power decay and capacity decay, the SOH estimation system comprising: a SOH estimation module configured to receive and determine an estimate of the SOH of the energy storage device based on: a nominal capacity input representing a nominal capacity of the energy storage device; a voltage input V representing a measured voltage associated with the energy storage device; a current input I representing a measured current from / to the energy storage device; a nominal open circuit voltage (OCV) curve associated with the energy storage device; an operating resistance model associated with the energy storage device; a nominal resistance model associated with the energy storage device; an operating dynamic model associated with the energy storage device; and a rated discharge current associated with the energy storage device. wherein the SOH estimation module further comprises an SOH aggregation module configured to receive N power rating estimates PR n and N normalized capacity estimates NC n from the energy storage device, and determine an estimate of the SOH of the energy storage device based on the power rating estimates PR n and normalized capacity estimates NC n , wherein the estimate of the SOH of the energy storage device is an aggregated estimate of the energy storage device.

4. A SOH estimation system for determining an estimate of a state of health (SOH) of an energy storage device, the SOH estimation system accounting for both power decay and capacity decay, the SOH estimation system comprising: a SOH estimation module configured to receive and determine an estimate of the SOH of the energy storage device based on: a nominal capacity input representing a nominal capacity of the energy storage device; a voltage input V representing a measured voltage associated with the energy storage device; a current input I representing a measured current from / to the energy storage device; a nominal open circuit voltage (OCV) curve associated with the energy storage device; an operating resistance model associated with the energy storage device; a nominal resistance model associated with the energy storage device; an operating dynamic model associated with the energy storage device; and a rated discharge current associated with the energy storage device; wherein the SOH estimation module further comprises a SOH aggregation module configured to receive a rated power estimate PR n and a normalized capacity estimate NC n for each of the n cells in the energy storage device, and determine an estimate of the SOH of the energy storage device based on the rated power estimate PR n and the normalized capacity estimate NC n , wherein the estimate of the SOH of the energy storage device is an aggregate estimate of the energy storage device, wherein the energy storage device comprises N cells.

5. The SOH estimation system according to claim 4, wherein The SOH estimation module also includes a normalized capacity estimation module configured to determine the normalized capacity estimate NC for each of the N cells of the energy storage device based on the nominal capacity input, the voltage input V, the current input I, a temperature input T, the nominal OCV, and the operating dynamics model n .

6. The SOH estimation system according to claim 4, wherein The SOH estimation module also includes a rated power estimation module configured to determine the rated power estimate PR for each of the N cells of the energy storage device based on the operating resistance model, the nominal OCV, the nominal resistance model, and the rated discharge current n .

7. A method of determining an estimate of a state of health (SOH) of an energy storage device, the method accounting for both power decay and capacity decay, the method comprising: receiving, at an SOH estimation module, the following received information: a nominal capacity input representing a nominal capacity of the energy storage device; a voltage input V representing a measured voltage associated with the energy storage device; a current input I representing a measured current from / to the energy storage device; a nominal open circuit voltage (OCV) curve associated with the energy storage device; an operating resistance model associated with the energy storage device; a nominal resistance model associated with the energy storage device; an operating dynamic model associated with the energy storage device, wherein the operating dynamic model comprises model parameters based on the current input associated with the energy storage device; and a rated discharge current associated with the energy storage device, wherein the rated discharge current is associated with the power decay; and determining, at the SOH estimation module, the estimate of the SOH of the energy storage device based on all of the received information.

8. The method of claim 7, further comprising receiving, at the SOH estimation module, the following additional received information: a temperature input T representing a temperature associated with the energy storage device.

9. The method of claim 7, wherein, the SOH estimation module further comprises an SOH aggregation module, the method further comprising: receiving, at the SOH aggregation module, a rated power estimate and a normalized capacity estimate; and determining the estimate of the SOH of the energy storage device based on the rated power estimate and the normalized capacity estimate.

10. A method of determining an estimate of a state of health (SOH) of an energy storage device, the method accounting for both power decay and capacity decay, the method comprising: receiving, at an SOH estimation module, the following received information: a nominal capacity input representing a nominal capacity of the energy storage device; a voltage input V representing a measured voltage associated with the energy storage device; a current input I representing a measured current from / to the energy storage device; a nominal open circuit voltage (OCV) curve associated with the energy storage device; an operating resistance model associated with the energy storage device; a nominal resistance model associated with the energy storage device; an operating dynamic model associated with the energy storage device; and a rated discharge current associated with the energy storage device; and determining, at the SOH estimation module, the estimate of the SOH of the energy storage device based on all of the received information, wherein the SOH estimation module further comprises an SOH aggregation module; receiving, at the SOH aggregation module, a rated power estimate and a normalized capacity estimate; and determining the estimate of the SOH of the energy storage device based on the rated power estimate and the normalized capacity estimate, ​ wherein the estimate of the SOH of the energy storage device is an aggregate estimate of the energy storage device, wherein the energy storage device comprises N cells.

11. A method of determining an estimate of a state of health (SOH) of an energy storage device, the method accounting for both power decay and capacity decay, the method comprising: receiving the following received information at an SOH estimation module: a nominal capacity input representing a nominal capacity of the energy storage device; a voltage input V representing a measured voltage associated with the energy storage device; a current input I representing a measured current from / to the energy storage device; a nominal open circuit voltage (OCV) curve associated with the energy storage device; an operating resistance model associated with the energy storage device; a nominal resistance model associated with the energy storage device; an operating dynamic model associated with the energy storage device; and a rated discharge current associated with the energy storage device; and determining, at the SOH estimation module, the estimate of the SOH of the energy storage device based on all of the received information; wherein the SOH estimation module further comprises a normalized capacity estimation module, the method further comprising: determining, at the normalized capacity estimation module, a normalized capacity estimate for each of the N cells of the energy storage device based on the nominal capacity input, the voltage input V, the current input I, the nominal OCV, and the operating dynamic model.

12. A method of determining an estimate of a state of health (SOH) of an energy storage device, the method accounting for both power decay and capacity decay, the method comprising: receiving the following received information at an SOH estimation module: a nominal capacity input representing a nominal capacity of the energy storage device; a voltage input V representing a measured voltage associated with the energy storage device; a current input I representing a measured current from / to the energy storage device; a nominal open circuit voltage (OCV) curve associated with the energy storage device; an operating resistance model associated with the energy storage device; a nominal resistance model associated with the energy storage device; an operating dynamic model associated with the energy storage device; and a rated discharge current associated with the energy storage device; and determining, at the SOH estimation module, the estimate of the SOH of the energy storage device based on all of the received information; wherein the SOH estimation module further comprises a rated power estimation module, the method further comprising: determining, at the rated power estimation module, a rated power estimate for each of the N cells of the energy storage device based on the operating resistance model, the nominal OCV, the nominal resistance model, and the rated discharge current.

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