Method for experimental determination of battery parameters and use thereof

Abstract

A method for experimental determination of battery parameters is disclosed. The method includes the steps of determining a plurality of round-trip battery efficiencies for a number of different pairs of charge and discharge battery C-rates / P-rates, solving a nonlinear optimization problem to obtain unidirectional efficiencies, and finding charge and discharge characteristics for the selected charge and discharge C-rates / P-rates. The obtained characteristic curve reveals the actual current / actual power to charge / discharge the battery when the battery is charged / discharged from the external source / receiving terminal at the selected current / power. The charge / discharge characteristic curve is used to determine battery charge capacity, battery energy capacity, state of charge (SOC), state of energy (SOE), state of health (SOH), and other important battery parameters. The method helps to optimize the operation of a battery energy storage device executing energy arbitrage in the day-ahead energy market.

Description

Technical Field

[0001] The present disclosure discloses a novel method for experimentally determining battery parameters and its use for calculating the SOE (State of Energy), SOC (State of Charge) and SOH (State of Health) of a given battery. The present disclosure also discusses the subsequent use of the mentioned values ​​in everyday battery applications. Thus, the technical field of the present disclosure can be seen as a device that uses hardware and software to detect electrical properties, more specifically to detect, measure or monitor the electrical condition of an accumulator or battery. Background Art

[0002] Advances in power electronics, which convert direct current to alternating current, are helping to make battery storage systems increasingly reliable. Recent breakthroughs in advanced battery storage suggest that they can deliver 50-100 million charge / discharge cycles, or more. Advanced battery systems that shave daily peaks will need at least 365 cycles per year, lasting more than 10 years and potentially up to 30 years. In addition, there is a growing demand for advanced batteries that store wind energy generated primarily during off-peak hours, as well as solar energy generated during weekday hours for use during subsequent peak periods. These renewable energy applications will require 200-300 cycles per year. And, when renewable energy is unavailable, batteries can be used for arbitrage, buying low-cost energy at night and selling it when energy prices are higher, adding an additional 100-200 cycles per year. For all of the above reasons, once installed as part of the grid, battery parameters must be determined for reliable use.

[0003] The main technical problem solved by the present invention is to provide a E A method for experimentally determining the unidirectional efficiency of a battery, wherein the term "unidirectional efficiency" refers only to the efficiency of charging or discharging the battery. The disclosed method is equally well applicable to battery cycling schemes in constant current (CC) or constant power (CP) mode. Such methods for CC mode and CP mode appear to have never been reported in the art before in the form described herein.

[0004] The unidirectional efficiency calculated in CC mode is subsequently used to determine the state of charge (SOC) vector, while the unidirectional efficiency calculated in CP mode is used to determine the state of energy (SOE) vector. 1 or the battery energy capacity C determined over time E , using either the SOC vector or the SOE vector to determine the state of health (SOH) of a given battery.

[0005] Prior art

[0006] For many reasons, even historical ones, the SOC vector or value is used more in battery management than the SOE vector. Perhaps the SOE vector was first reported and defined consistently in reference 1).

[0007] 1) Mamadou, K., Lemaire, E., Delaille, A., Riu, D., Hing, S. E., & Bultel, Y. (2012). Definition of a State-of-Energy Indicator (SoE) for Electrochemical Storage Devices: Application for Energetic Availability Forecasting. Journal of the Electrochemical Society, 159(8), A1298–A1307. doi: 10.1149 / 2.075208jes.

[0008] References 2) and 3) use more or less the same technique for SOE vector determination.

[0009] 2) The invention “METHOD FOR CALIBRATING AN ELECTROCHEMICAL BATTERY” invented by Mamadou, K. et al., with PCT patent application publication number WO2011 / 000872A1, which was subsequently granted a European patent (EP2449392B1) and a U.S. patent (US 9,075,117).

[0010] 3) The invention “DEVICE AND METHOD FOR DETERMINING A POWER STATUS ACCORDING TO DATA FROM THE PROCESSING METHOD” invented by Fernandez E. et al., with PCT patent application publication number WO2013 / 175005A1, was subsequently granted a European patent (EP2856187B1).

[0011] Reference 4) recognizes the importance of the unidirectional efficiency of charging and discharging, and provides battery system management based on the obtained SOC vector associated with the time derivative through a nonlinear model.

[0012] 4) The invention “BATTERY SYSTEM MANAGEMENT THROUGH NON-LINEAR ESTIMATION OF BATTERY STATE OF CHARGE” invented by JACRAWFORD et al., with PCT patent application publication number WO2018 / 084939A1, was subsequently granted multiple US patents.

[0013] Furthermore, reference 4) discusses the use of the calculated model in grid balancing. Summary of the invention

[0014] The present invention discloses a method for experimentally determining battery parameters and its use. More specifically, a method for experimentally determining a given ambient temperature T E A method for improving the unidirectional efficiency of a battery, wherein the method comprises the following steps:

[0015] A. performing a battery cycling scheme wherein charging and discharging are performed using an external source / sink, and wherein the scheme is selected from a constant current (CC) mode or a constant power (CP) mode;

[0016] - wherein at least two C charging C rates and at least two D discharging C rates are selected for the CC mode, or

[0017] - wherein at least two C charging P rates and at least two D discharging P rates are selected for the CP mode,

[0018] Among them, all Ω C ={c1,c2,…,c c} and Ω D ={d1,d2,…,d D The set of choices of values ​​for {c, d} constitutes C×d charge-discharge cycles for all possible values ​​of {c, d} pairs, and wherein the above cycle is repeated J times, resulting in a total of C×D×J charge-discharge cycles, with the premise that:

[0019] (i) Each cycle always starts with a depleted battery,

[0020] (ii) Each charge in that CC mode or that CP mode is terminated once the declared high battery voltage limit is reached,

[0021] (iii) Each discharge in this CC mode or in this CP mode is terminated once the declared low battery voltage limit is reached,

[0022] B. Determine multiple round-trip cell efficiencies for C×d different pairs of charge and discharge C-rates or P-rates defined in step A Among them, for each executed loop, the round-trip efficiency of each loop is calculated for the selected c, d and j

[0023] - In case the CC mode is selected, the charge extracted from the battery is And the charge injected into the battery is

[0024]

[0025] Among them, these charges and is the time-dependent charging current and discharge current Obtained by numerical integration:

[0026]

[0027] During each cycle, the current and to record, or

[0028] When the CP mode is selected, the energy extracted from the battery is And the energy injected into the battery is

[0029]

[0030] Among them, these energies and is the time-dependent charging power and discharge power Obtained by numerical integration:

[0031]

[0032] During each cycle, these powers and record, and

[0033] The round trip efficiency of each cycle is The round-trip cell efficiency for the selected C and D values ​​is obtained by averaging the number of repetitions J in step A. writing:

[0034]

[0035] By solving a nonlinear optimization problem with C+D unknowns and C×D equations:

[0036] minimize

[0037] Based on the round-trip battery efficiency calculated in step B Determine the one-way efficiency, where and Indicates the one-way charging efficiency and one-way discharging efficiency respectively,

[0038] Subject to the following conditions:

[0039]

[0040] Among them, s c,d is a slack variable, and where the solution to the above optimization problem is and For each chosen value of {c,d} pair, and The product of the measured efficiency The deviation is minimal.

[0041] Based on the above, it is quite simple to calculate the unidirectional efficiency characteristics of the CC mode and the CP mode, as shown in the detailed description.

[0042] In a first embodiment, the battery unidirectional efficiency characteristic modeling method is used to determine the state of charge (SOC) vector in CC mode. In a variant, the method is used to experimentally determine the battery charge capacity C 1 In another variation, the unidirectional efficiency characteristic is used to calculate the charge capacity of the battery C 1 As a function of time, a state of health (SOH) parameter expressed as a percentage from 0 to 100% is determined.

[0043] In a second embodiment, the battery unidirectional efficiency characteristic modeling method is used to determine the energy state (SOE) vector in CP mode. In a variant, the method is used to experimentally determine the battery energy capacity C E In another variation, the unidirectional efficiency characteristic is used to calculate the energy capacity of the battery C E As a function of time, a state of health (SOH) parameter expressed as a percentage from 0 to 100% is determined. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1A , Figure 1B , Figure 2A and Figure 2B The disclosed method is depicted.

[0045] Figure 1A shows that at a given ambient temperature T E The charging unidirectional efficiency measured and calculated at three points (C=3) is and the total current (total power) drawn from the external source (i ch (p ch )) of the relationship diagram, which corresponds to the selected charging C rate (P rate), which is Figure 2A Indicated in A collection of values.

[0046] Figure 1B shows that at a given ambient temperature T E The discharge unidirectional efficiency measured and calculated at three points (D=3) The net current (net power) transmitted to the external power receiving end (i dis (p dis )) of the relationship diagram, which corresponds to the selected discharge C rate (P rate), which is Figure 2B Indicated in A collection of values.

[0047] Figure 2A represents the piecewise linear efficiency charging characteristic η obtained by interpolating and extrapolating the input measured data and recalculated according to the proposed model C The η C The function will Value and The values ​​are linked, where Value indication It represents the net current (net power) injected into the battery during charging and is written as

[0048] Similarly, Figure 2B represents the piecewise linear efficiency discharge characteristic η obtained by interpolating and extrapolating the input measured data and recalculated according to the proposed model D The η D The function will Value and The values ​​are linked, where Value indication It represents the total current (total power) drawn from the battery during discharge and is written as DETAILED DESCRIPTION

[0049] As previously mentioned, the present disclosure discloses a novel method for experimentally determining battery parameters and its use for calculating the SOE (State of Energy), SOC (State of Charge) and SOH (State of Health) of a given battery.

[0050] It is well known in the art that battery characteristics depend largely on the ambient temperature T E Therefore, the present disclosure discloses that at a given ambient temperature T EThe method is carried out as follows, which can be directly extended to a temperature dependence model by a person skilled in the art. The experimental determination of the battery parameters consists of the steps described below.

[0051] Step A

[0052] In step A, it is necessary to perform a battery cycling scheme by performing experimental measurements. The battery cycling scheme is a scheme that uses an external source / receiver to perform charging and discharging. In the art, either a constant circuit (CC) cycling mode or a constant power (CP) cycling mode is usually selected. In order to perform the experiment, the following equipment was used:

[0053] (i) A professional bidirectional DC power supply, Itech IT-M3413, combined with proprietary NI LabVIEW software, was used to control and monitor the battery experiment. The characteristics of this bidirectional DC power supply are as follows:

[0054] -Output DC voltage: 0 to 150V

[0055] - Setting resolution: 1mV

[0056] -Accuracy: <0.1-U 最大

[0057] -Output DC current: -12A to 12A

[0058] - Setting resolution: 1mA

[0059] -Accuracy: <0.1-I 最大 +0.1%-I 电流

[0060] -Output power: -200W to 200W

[0061] -Setting resolution: 0.1W

[0062] - Accuracy: <0.1-P 最大

[0063] (ii) Commercial Batteries:

[0064] -NMC (lithium nickel manganese cobalt oxide) 18650

[0065] -Declared nominal capacity: 3000mAh

[0066] -Declared nominal voltage: 3.6V

[0067] -LFP (lithium iron phosphate) 18650

[0068] -Declared nominal capacity: 1500mAh

[0069] -Declared nominal voltage: 3.2V

[0070] -LCO (lithium cobalt oxide) 18650

[0071] -Declared nominal capacity: 3200mAh

[0072] -Declared nominal voltage: 3.75V

[0073] -LTO (lithium titanate) 18650

[0074] -Declared nominal capacity: 1300mAh

[0075] -Declared nominal voltage: 2.75V.

[0076] The use of the above-mentioned device is obvious to those skilled in the art.

[0077] For proper execution, at least two C charge C rates and at least two D discharge C rates are selected for the CC mode. Each selected C rate indicates a measure of the rate at which the battery is charged or discharged relative to its declared charge capacity at a constant current, typically expressed in ampere hours, i.e., in Ah. Similarly, at least two C charge P rates and at least two D discharge P rates are selected for the CP mode. Each selected P rate indicates a measure of the rate at which the battery is charged or discharged relative to its declared charge capacity at a constant power, typically expressed in watt hours, i.e., in Wh.

[0078] All Ω C ={c1,c2,…,c C} and Ω D ={d1,d2,…,d D The set of choices of values ​​for {c, d} constitutes C×D charge-discharge cycles for all possible values ​​of {c, d} pairs. To improve the progress of the model, the above cycle is repeated J times, resulting in a total of C×D×J charge-discharge cycles. For improved accuracy, J needs to be greater than 1, but the model can run even if J=1. Each cycle should satisfy the following conditions (i) to (iii) set below:

[0079] (i) each cycle always starts with a depleted battery, where depletion means that the undepleted battery is discharged until the lower voltage limit of the battery is reached, provided that the C rate or P rate of the discharged battery is equal to the discharge C rate or P rate of the cycle in step (iii), which will ensure that the cycle has the same starting and ending points in terms of current and voltage,

[0080] (ii) each charge in that CC mode or that CP mode is terminated once the declared high battery voltage limit is reached, and

[0081] (iii) Each discharge in this CC mode or this CP mode is terminated once the declared low battery voltage limit is reached.

[0082] The low / high voltage limits of the above batteries are usually declared by the manufacturer or the waste battery management system to protect the battery from irreversible damage.

[0083] A potentially simpler, more time consuming, but also less accurate change to the above conditions (i) to (iii) is to relax the starting point of the cycle described in (i), so that the battery is discharged to its lower voltage limit at any C-rate or P-rate. This means that the start and end of the cycle (ii) to (iii) will not be exactly the same in terms of measured current and measured voltage, however, the subsequent results may still be sufficiently accurate depending on the desired application.

[0084] The above cycle conditions (i) to (iii) are for charging / discharging between the voltage limits of the battery, which corresponds to the maximum possible SOC range in which CC or CP mode can be maintained. However, the battery can also be cycled within some arbitrarily narrower SOC range, provided that the SOC is determined accurately and consistently, and each charge / discharge cycle is performed within the same SOC range while maintaining CC or CP mode during the entire cycle.

[0085] Step B

[0086] In the art, it is known that the electrochemical characteristics of batteries are quite complex. During battery charging or discharging, part of the energy is converted into pure Joule heat, and part of the energy is lost in the electrochemical process, as described in reference 5).

[0087] 5) Gatta, F. M., Geri, A., Lauria, S., Maccioni, M., & Palone, F. (2015). Battery energy storage efficiency calculation including auxiliary losses: Technology comparison and operating strategies. 2015 IEEE Eindhoven Power Tech. doi: 10.1109 / ptc.2015.7232464.

[0088] According to the proposed method, multiple round-trip cell efficiencies for C × D different pairs of charge and discharge C-rates or P-rates defined in step A should be determined. For each executed loop, calculate the round trip efficiency of each loop for the selected c, d, and j As described below. In the case of selecting CC mode, the charge extracted from the battery is And the charge injected into the battery is The round trip efficiency of each cycle is calculated according to the following formula:

[0089]

[0090] Charge and is the time-dependent charging current and discharge current Obtained by numerical integration:

[0091]

[0092] It should be noted that during each cycle, the current is controlled by external means or by the appropriate converter itself. and Make a record.

[0093] Similarly, in the case where CP mode is selected, the energy extracted from the battery is And the energy injected into the battery is The round trip efficiency of each cycle is calculated according to the following formula:

[0094]

[0095] energy and is the time-dependent charging power and discharge power Obtained by numerical integration:

[0096]

[0097] It should be noted that during each cycle, the power and Make a record.

[0098] Once the round-trip efficiency per cycle is obtained in the desired mode (i.e., CC mode or CP mode) The repeated runs are naturally averaged. The round trips of the same repeated runs are measured and calculated. The measured and calculated round trip efficiency of each cycle is The round-trip cell efficiency for the selected C and D values ​​is averaged over the number of repetitions J in step A. writing:

[0099]

[0100] Round-trip battery efficiency is a value that reflects the historical efficiency of the battery's cycling data (i.e., the values ​​used for a particular {c,d} pair). This value has no particular purpose, as both charge and discharge data are included.

[0101] Step C

[0102] The inventive part of the present disclosure is based on the round-trip battery efficiency measured and calculated in step B. A collection of unidirectional battery efficiency and unidirectional charging efficiency and unidirectional discharge efficiency

[0103] This problem leads to a nonlinear optimization problem with C+D unknowns and CXD equations:

[0104] minimize

[0105] Subject to the following conditions:

[0106]

[0107] Among them, s c,d is a slack variable. The solution to the above optimization problem is and At least for each chosen value of {c,d} pair, and The product of the measured efficiency It is important to note that the following assumptions were used:

[0108]

[0109] Once the unidirectional charging efficiencies of all measured / selected {c,d} pairs are known and unidirectional discharge efficiency You will have a comprehensive understanding of batteries and the results can be used in daily battery operations. Figure 1A shows that at a given ambient temperature T E The charging unidirectional efficiency measured and calculated at three points and the total current (total power) drawn from the external source (i ch (p ch )), which corresponds to the selected charging C rate (P rate). Figure 1B shows that at a given ambient temperature T E The discharge unidirectional efficiency measured and calculated at three points The net current (net power) transmitted to the external power receiving end (i dis (p dis )), which corresponds to the selected discharge C rate (P rate).

[0110] The following examples discuss the one-way efficiency and application.

[0111] Example 1 - Determination of the State of Charge (SOC) Vector

[0112] If the battery is cycled in CC mode, the unidirectional efficiency obtained is and This can be used to determine the state of charge (SOC) vector. This process will be described in more detail below.

[0113] Use the charging efficiency calculated previously for the given battery in step C and discharge efficiency Define the piecewise linear efficiency characteristic η for the battery operating charge / discharge C rate range C and η D .

[0114] These efficiency characteristics are defined as:

[0115] and

[0116] in, is the net current injected into the battery during charging and is the total current drawn from the external source is a function of the total current drawn from the battery during discharge. is the net current i delivered to the external power receiving end dis function.

[0117] Function η C and η D The known current used in the battery cycle in step A is measured by i dis Although there are many different ways to use η C and η D The reconstruction (eg, spline reconstruction or similar method) is a continuous function, but this disclosure will use a simple piecewise linear interpolation, which is accurate enough for the required task.

[0118] In order to perform the required tasks, no matter which mode is used (i.e., CC mode or CP mode), some changes are made to the tags to record the same content. In CC mode, represents the c-charge value of the C-rate selected in step A and represents the unidirectional charging efficiency obtained from step C Correction value

[0119]

[0120] Similarly, represents the discharge value of the C rate selected in step A and represents the discharge efficiency obtained from step C Correction value

[0121]

[0122] Now, the above interpolation and extrapolation can be written as:

[0123]

[0124] and

[0125]

[0126] The function obtained above and η D (i dis ) is the measured total charging current for any selected and the measured discharge net current i dis A continuous function of any of Figure 2A and Figure 2B Now use these relations to calculate the state of charge (SOC) vector of the time series t, SOC = (soc0, soc1, ..., soc t-1 ,soc t ,…).

[0127] At a certain time t, each vector element soc t can be related to the previous soc known in the time interval Δt that occurred just before time t t-1 value, by using the relation and The calculation is done using the following definitions:

[0128]

[0129] Example 2 - Battery Charge Capacity C I Determination

[0130] The data obtained in Example 1 and the experimentally determined battery parameters expressed in steps A to C are used here to experimentally determine the battery charge capacity CI For the described task, perform steps D and E below:

[0131] Step D

[0132] First, it is necessary to select K different C rates and perform K complete charge and discharge cycles in constant current constant voltage mode. In order to improve the accuracy of the method, K needs to be greater than 1, but this process can be performed even if K = 1. The premise or conditions are as follows:

[0133] (i) The selected C rate remains constant within the same charge and discharge cycles,

[0134] (ii) the cycling starts with either a fully depleted battery or a fully charged battery, wherein fully depleting means discharging the battery until the discharge current drops below a defined low cutoff value while maintaining the voltage of the battery at a low voltage limit, and fully charging means charging the battery until the charge current drops below a defined low cutoff value while maintaining the voltage of the battery at a high voltage limit, and

[0135] (iii) Each charge is terminated when the battery is fully charged, and each discharge is terminated when the battery is fully exhausted, as defined in (ii).

[0136] Step E

[0137] For each complete cycle performed in step D, the charge efficiency characteristic η C And discharge efficiency characteristics η D The obtained results are corrected for the recorded current and To obtain current and These values ​​are time-integrated to obtain K injected charges and K extracted charges Wherein the acquired charges are averaged to calculate the newly defined average battery charge capacity:

[0138]

[0139] Example 3 - Determination of State of Health (SOH) Parameters

[0140] The results obtained in the previous examples can be used to determine the state of health (SOH) parameter expressed as a percentage of 0-100%. That is, SOH is a time-dependent parameter defined as parameter Corresponding to the average battery charge capacity C determined for the first time according to the process of Example 2 when the battery is newI ,and is the value C newly determined during the battery life according to the same process I .

[0141] Now, the teachings of embodiments 1 to 3 for the constant current (CC) mode can be simply rewritten for the constant power (CP) mode, thereby providing a power / energy method instead of a current / charge method.

[0142] Example 4 - Determination of the State of Energy (SOE) Vector

[0143] If the battery cycle is performed in CP mode, the unidirectional efficiency obtained is and can be used to determine the state of energy (SOE) vector. This process is described in more detail below.

[0144] Use the charging efficiency calculated in step C for the given battery and discharge efficiency Define the piecewise linear efficiency characteristic η for the battery operating charge / discharge rate range P C and η D .

[0145] These efficiency characteristics are defined as:

[0146] and

[0147] in, is the net power injected into the battery during charging and is the total power drawn from external sources is a function of the total power extracted from the battery during discharge. is the net power p delivered to the external receiving end dis function.

[0148] Function η C and η D The known current used in the battery cycle in step A is calculated by comparing the measured power p dis Although there are many different ways to use η C and η D The reconstruction (eg, spline reconstruction or similar method) is a continuous function, but this disclosure will use a simple piecewise linear interpolation, which is accurate enough for the required task.

[0149] In order to perform the required tasks, some changes are made to the tags to record the same content regardless of the mode used (i.e., CC mode or CP mode). In CP mode, represents the c charge value of the P rate selected in step A and represents the unidirectional charging efficiency obtained from step C Correction value

[0150]

[0151] Similarly, represents the discharge value of the P rate selected in step A and represents the discharge efficiency obtained from step C Correction value

[0152]

[0153] Now, the above interpolation and extrapolation can be written as:

[0154]

[0155] and

[0156]

[0157] The function obtained above and η D (p dis ) is the measured total charging power for any selected and the measured discharge net power p dis A continuous function of any of Figure 2A and Figure 2B Now use these relations to calculate the state of energy (SOE) vector of the time series t, SOE = (soe0, soe1,…, soe t-1 ,soe t ,…).

[0158] At a certain time t, each vector element soe t can be related to the previous soe known in the time interval Δt that occurred just before time t t-1 value, by using the relation and The calculation is done using the following definitions:

[0159]

[0160] Example 5 - Battery Energy Capacity C E Determination

[0161] The data obtained in Example 4 and the experimentally determined battery parameters expressed in steps A to C are used here to experimentally determine the battery energy capacity CE For the described task, perform steps D and E below:

[0162] Step D

[0163] First, it is necessary to select K different P rates and perform K complete charge and discharge cycles in constant current constant voltage mode. In order to improve the accuracy of the method, K needs to be greater than 1, but this process can be performed even if K = 1. The premise or conditions are as follows:

[0164] (i) The selected P rate remains constant within the same charge and discharge cycles,

[0165] (ii) the cycling starts with either a fully depleted battery or a fully charged battery, wherein fully depleting means discharging the battery until the discharge current drops below a defined low cutoff value while maintaining the voltage of the battery at a low voltage limit, and fully charging means charging the battery until the charge current drops below a defined low cutoff value while maintaining the voltage of the battery at a high voltage limit, and

[0166] (iii) Each charge is terminated when the battery is fully charged, and each discharge is terminated when the battery is fully exhausted, as defined in (ii).

[0167] Step E

[0168] For each complete cycle performed in step D, the charge efficiency characteristic η C And discharge efficiency characteristics η D The results obtained are corrected for the recorded power and To gain power and These values ​​are time-integrated to obtain the K injected energies and K extracted energies Among them, the obtained energies are averaged to calculate the newly defined average battery energy capacity:

[0169]

[0170] Example 6 - Determination of State of Health (SOH) Parameters

[0171] The results obtained in the previous Examples 4 and 5 can be used to determine the state of health (SOH) parameter expressed as a percentage of 0-100%. That is, SOH is a time-dependent parameter defined as parameter Corresponding to the average battery energy capacity C determined for the first time according to the process of Example 5 when the battery is newE ,and is the value C newly determined during the battery life according to the same process E .

[0172] Example 7 - Energy charging capability one hour in advance

[0173] There are many possible uses for the aforementioned data. However, when charging at a given P rate, the site usually estimates the one-hour ahead energy charging capability for the instantaneous SOE. This approach is often used when it is necessary to maximize profits by performing energy arbitrage. Battery storage is a price taker and cannot influence market prices, which are known or predicted in advance. The simplest objective function of the proposed model is:

[0174] maximize

[0175] Where λt is the hourly market price, is energy sold on the market, and is the energy purchased on the market for the selected time Δt. Example 4 relates the actual value to the actual battery value calculated and modeled previously, writing:

[0176]

[0177] and

[0178] Without further elaboration, a person skilled in the art will immediately recognize that the maximization result takes into account the obtained efficiency characteristic η C and η D . Therefore, the optimization algorithm may recommend extending the charge / discharge time to non-peak energy price hours if this will result in higher overall profits due to lower charge / discharge rates and therefore less energy losses. The model should also respect some constraints, such as the maximum charge / discharge rate P that the battery can withstand without being damaged. More complex models will include battery amortization, SOH calculations, and other relevant parameters in order to obtain the total cost of energy arbitrage performed using the modeled battery pack.

[0179] Example 8 - Temperature Variation

[0180] Figure 2A and Figure 2B Indicates that for a given battery pack at a certain constant ambient temperature T E The one-way efficiency characteristic η determined under C and η D Both figures show the measured pairs as solid dots; and Or in CC mode and Extrapolation and interpolation are shown using dashed and solid lines, while the “ideal cell” is shown using a dashed line, where the one-way efficiency and The cell has a unidirectional efficiency of 100%. and

[0181] Ambient temperature T E The change of the one-way efficiency η C and η D Slight changes occur and produce Figure 2A and Figure 2B The curve series presented are different curve sequences. Such variations are fully described in the prior art section citing reference 1).

[0182] Therefore, those skilled in the art will conduct experiments through reasonable experimental work to obtain a series of curves η C , η D , these curves depend, among other things, on the cell temperature T, like any other electrochemical process. Bat Or simply depends on the ambient temperature T E .

[0183] In short, these findings apply mutatis mutandis to all embodiments discussed previously.

[0184] Industrial Applicability

[0185] The industrial applicability of the present disclosure is obvious. That is, the present disclosure discloses a novel method for experimentally determining battery parameters and its use for calculating the SOE (state of energy), SOC (state of charge) and SOH (state of health) of a given battery. The present disclosure also discusses the subsequent use of said values ​​in everyday battery applications.

[0186] Definitions and Abbreviations

[0187] T E – ambient temperature,

[0188] T Bat – Measured battery temperature

[0189] CC – Constant Current Mode,

[0190] CP – Constant Power Mode,

[0191] C – the total number of different charge values ​​used to cycle the battery for the purpose of determining the unidirectional efficiency, (indicated as C rate for CC and P rate for CP),

[0192] D – the total number of different discharge values ​​used to cycle the battery for the purpose of determining the unidirectional efficiency, (indicated as C rate for CC and P rate for CP),

[0193] J – Number of cycles repeated for the purpose of determining unidirectional efficiency

[0194] Ω C ={c1, c2, ..., c C} – the set of selected C values,

[0195] Ω D ={d1, d2, ..., d D} – the set of selected D values,

[0196] – measured round-trip efficiency per cycle,

[0197] - the average round-trip cell efficiency of J repetitions,

[0198] – the calculated (discrete) unidirectional charging efficiency corresponding to the c-charging C-rate (or P-rate),

[0199] – the calculated (discrete) unidirectional discharge efficiency corresponding to the d-discharge C-rate (or P-rate),

[0200] -Round trip efficiency per cycle in CC mode,

[0201] - the charge injected into the battery,

[0202] - the charge extracted from the battery,

[0203] - recorded charging current,

[0204] - recorded discharge current,

[0205] -Round trip efficiency per cycle in CP mode,

[0206] - the power injected into the battery,

[0207] - the power extracted from the battery,

[0208] - recorded charging power,

[0209] - recorded discharge power,

[0210] η C -Piecewise linear efficiency charging characteristics,

[0211] η D -Piecewise linear efficiency discharge characteristics,

[0212] In CC mode:

[0213] - the net current injected into the battery during charging,

[0214] - the total current drawn from the external source,

[0215] – the total current drawn from the battery during discharge,

[0216] i dis - the net current delivered to the external receiving terminal,

[0217] In CP mode:

[0218] - the net power injected into the battery during charging,

[0219] - the total power drawn from external sources,

[0220] - the total power extracted from the battery during discharge,

[0221] p dis - the net power delivered to the external receiving terminal,

[0222] c – Charge value for the selected C-rate or P-rate

[0223] - represents CC mode

[0224] - represents CC mode

[0225] -Represents CP mode

[0226] -Represents CP mode

[0227] d – Discharge value for the selected C-rate or P-rate

[0228] - represents CC mode

[0229] - represents CC mode

[0230] -Represents CP mode

[0231] -Represents CP mode

[0232] SOC=(soc0,soc1,…,soc t-1 , soc t , …) – state of charge vector,

[0233]

[0234] SOE=(soc0, soe1,..., soe t-1 , soe t , …) – energy state vector,

[0235]

[0236] K – the number of cycles at different C rates (P rates) to determine the battery capacity.

[0237] - Measured average battery charge capacity,

[0238] - Measured average battery energy capacity,

[0239] -Time integral of the kth cycle

[0240] – Time integral of the kth cycle

[0241] -Time integral of the kth cycle

[0242] – Time integral of the kth cycle

[0243] – the state of health at a later time t based on the change in the battery’s charge capacity over time,

[0244] – The state of health at a later time t based on the change in the battery’s energy capacity over time.

[0245] λ t –Hourly market prices

Claims

1. A method for experimentally determining a given ambient temperature T E The method for calculating the unidirectional efficiency of the battery is as follows: The method comprises the following steps: A. performing a battery cycling scheme wherein charging and discharging are performed using an external source / sink, and wherein the scheme is selected from a constant current CC mode or a constant power CP mode; - wherein at least two C-charge C-rates and at least two D-discharge C-rates are selected for said CC mode, wherein each C-rate indicates a measure of the rate at which a battery is charged or discharged relative to its declared charge capacity at a constant current, or - wherein at least two C charging P rates and at least two D discharging P rates are selected for said CP mode, wherein said P rates indicate a measure of the rate at which a battery is charged or discharged relative to its declared energy capacity at constant power, - Among them, all Ω C ={c1,c2,…,c C } and Ω D ={d1,d2,…,d D The set of choices of values ​​for {c, d} constitutes C×D charge-discharge cycles for all possible values ​​of {c, d} pairs, and wherein the cycle is repeated J times, resulting in a total of C×D×J charge-discharge cycles, with the premise that: (i) each cycle always starts with a depleted battery, wherein depletion means that the undepleted battery is discharged until the lower voltage limit of the battery is reached, provided that the discharge battery C rate or P rate is equal to the discharge C rate or P rate of the cycle in step (iii), which will ensure that the cycles have the same starting and ending points in terms of current and voltage, (ii) each charge in said CC mode or said CP mode is terminated once the declared high battery voltage limit is reached, (iii) each discharge in said CC mode or said CP mode is terminated once the declared low battery voltage limit is reached, B. Determine multiple round-trip cell efficiencies for C×D different pairs of charge and discharge C-rates or P-rates defined in step A Among them, for each executed loop, the round-trip efficiency of each loop is calculated for the selected c, d and j - In case the CC mode is selected, the charge extracted from the battery is And the charge injected into the battery is Among them, the charge and is the time-dependent charging current and discharge current Obtained by numerical integration: During each cycle, the current and to record, or - In case the CP mode is selected, the energy extracted from the battery is and the energy injected into the battery is Among them, the energy and is the time-dependent charging power and discharge power (t) obtained by numerical integration: During each cycle, the power and record, and The round trip efficiency of each cycle is The round-trip cell efficiency for the selected C and D values ​​is obtained by averaging the number of repetitions J in step A. writing: By solving a nonlinear optimization problem with C+D unknowns and C×D equations: Minimize Based on the round-trip battery efficiency calculated in step B Determine the one-way efficiency, where and Indicates the one-way charging efficiency and one-way discharging efficiency respectively, Subject to the following conditions: Among them, s c,d is a slack variable, and where the solution to the above optimization problem is and For each chosen value of {c,d} pair, and The product of the measured efficiency The deviation is minimal.

2. The method for modeling the battery unidirectional efficiency characteristics according to claim 1 is used to determine the state of charge SOC vector in CC mode, wherein: Perform the following steps: D. Use the charging efficiency calculated in step C for the given battery and discharge efficiency Define the piecewise linear efficiency characteristic η for the battery operating charge / discharge C rate range C and η D , where the efficiency characteristic is defined as: and in, is the net current injected into the battery during charging and is the total current drawn from the external source is a function of the total current drawn from the battery during discharge. is the net current i delivered to the external power receiving end dis The function of E. Wherein, the function η C and η D The known current used in the battery cycle in step A is calculated by comparing the actual current i dis The values ​​are interpolated or extrapolated, preferably linearly interpolated, wherein represents the c-charge value for the C-rate selected in step A, and represents the unidirectional charging efficiency obtained from step C Correction value: in, represents the d discharge value for the C rate selected in step A, and represents the discharge efficiency obtained from step C Correction value: Among them, the interpolation and the extrapolation are written as: and F. Among them, for the selected measured total charging current and the measured discharge net current i dis Any of the above obtained and η D (i dis ) to calculate the state of charge SOC vector for time series t, SOC = (SOC0, soc1, ..., soc t-1 ,soc t ,…), where each vector element soc at a certain time t t are all about the previous SOC known in the time interval Δt that occurred just before the time t t-1 value, by using the relation and Calculated from the definition:

3. The battery unidirectional efficiency characteristic modeling method according to claims 1 and 2 is used to experimentally determine the battery charging capacity C in CC mode I Uses in, among which, Perform the following steps: G. Select K number of different C-rates to perform K complete charge-discharge cycles in constant current constant voltage mode, with the premise that: (i) The selected C rate remains constant within the same charge and discharge cycles, (ii) the cycling starts with either a fully depleted battery or a fully charged battery, wherein fully depleting means discharging the battery until the discharge current drops below a defined low cutoff value while maintaining the voltage of the battery at a low voltage limit, and fully charging means charging the battery until the charge current drops below a defined low cutoff value while maintaining the voltage of the battery at a high voltage limit, and (iii) each charge is terminated when the battery is fully charged and each discharge is terminated when the battery is fully exhausted, as defined in (ii), and H. For each complete cycle performed in step G, the charge efficiency characteristic η is used in step E. C And discharge efficiency characteristics η D The obtained results are corrected for the recorded current and To obtain current and Will and Integrate over time to obtain K injected charges and K extracted charges The obtained charges are averaged to calculate the battery charging capacity:

4. The method for modeling the battery unidirectional efficiency characteristics according to claim 1 is used in determining the energy state SOE vector in CP mode, wherein: Perform the following steps: D. Use the charging efficiency calculated in step C for the given battery and discharge efficiency Define the piecewise linear efficiency characteristic η for the battery operating charge / discharge rate range P C and η D , where the efficiency characteristic is defined as: and in, is the net power injected into the battery during charging and is the total power drawn from the external source is a function of the total power extracted from the battery during discharge is the net power p delivered to the external power receiving end dis The function of E. Wherein, the function η C and η D The known power used in the battery cycle in step A is calculated by p dis The values ​​are interpolated or extrapolated, preferably linearly interpolated, wherein represents the c-charge value of the P rate selected in step A, and represents the unidirectional charging efficiency obtained from step C Correction value: in, represents the d discharge value of the P rate selected from step A, and represents the discharge efficiency obtained from step C Correction value: Among them, the interpolation and the extrapolation are written as: and F. Among them, for the selected measured total charging power and the measured discharge net power p dis Any of the above obtained and η D (p dis ) to calculate the energy state SOE vector for time series t, SOE=(soe0,soe1,…,soe t-1 ,soe t ,…), where each vector element soe at a certain time t t are all about the previous soe known in the time interval Δt that occurred just before the time t t-1 value, by using the relation and Calculated from the definition:

5. The battery unidirectional efficiency characteristic modeling method according to claims 1 and 4 is used to experimentally determine the battery energy capacity C in CP mode E Uses in, among which, Perform the following steps: G. Select K different P rates to perform K complete charge-discharge cycles in constant current constant voltage mode, with the premise that: (i) The selected P rate remains constant within the same charge and discharge cycles, (ii) a cycle starts with either a fully depleted battery or a fully charged battery, wherein fully depleting means discharging the battery until the discharge current drops below a defined low cutoff value while maintaining the voltage of the battery at a low voltage limit, and fully charging means charging the battery until the charge current drops below a defined low cutoff value while maintaining the voltage of the battery at a high voltage limit, and (iii) each charge is terminated when the battery is fully charged and each discharge is terminated when the battery is fully exhausted, as defined in (ii), and H. For each complete cycle performed in step G, the charge efficiency characteristic η is used in step E. C And discharge efficiency characteristics η D The results obtained are corrected for the recorded power and To gain power and Will and Perform time integration to obtain the energy of K injections and K extracted energies The obtained energies are averaged to calculate the battery energy capacity:

6. Use of the battery unidirectional efficiency characteristic modeling method according to claim 4, wherein: The SOE vector for time series t is used to estimate the energy charging capability for one hour ahead for the instantaneous SOE when charging at a given P rate.

7. The method for modeling the battery unidirectional efficiency characteristics according to claim 3 is used to determine the health state SOH parameter expressed as a percentage of 0-100%, wherein: The SOH parameter over time is defined as And among them, corresponds to the average battery charge capacity C determined for the first time when the battery is new. I ,and is the newly determined value C during the battery life cycle I .

8. The method for modeling the battery unidirectional efficiency characteristics according to claim 5 is used to determine the health state SOH parameter expressed as a percentage of 0-100%, wherein: The SOH parameter over time is defined as And among them, corresponds to the average battery energy capacity C determined for the first time when the battery is new E ,and is the newly determined value C during the battery life cycle E .

9. Use of the battery unidirectional efficiency characteristic modeling method according to any one of claims 2 to 8, wherein: For different ambient temperatures T E Execute the method.

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