Description:
DESCRIPTION
Technical Field
[001] This disclosure relates generally to electrochemical cells, and more particularly to a method and a system for determining an optimal NP ratio for an electrochemical cell such as a rechargeable battery cell.
BACKGROUND
[002] Rechargeable batteries are widely used in portable consumer devices, electric light vehicles (such as motorized wheelchairs, golf carts, electric bicycles, and electric forklifts), road vehicles (cars, vans, trucks, motorbikes), trains, small airplanes, tools, uninterruptible power supplies, and battery storage power stations. Some examples of the rechargeable batteries are lead–acid, nickel–cadmium (NiCd), nickel–metal hydride (NiMH), lithium-ion (Li-ion) and sodium-ion.
[003] Emerging applications of the rechargeable batteries drive the need to reduce their cost, weight, and size, and increase lifetime. Such batteries generally include one or more electrochemical cells (also referred to as “battery cells") that may accumulate and store energy through a reversible electrochemical reaction. Electrochemical cells are generally designed considering various factors that affect safety, sustainability, energy efficiency, application area, etc. For example, technical design factors such as the capacity of electrode materials, and anode to cathode ratio (NP ratio) affect energy efficiency and battery performance.
[004] An NP ratio, also known as negative positive ratio, is one of the important parameters in designing and improving performance of an electrochemical cell. In particular, the NP ratio provides for a capacity ratio between an anode and a cathode of the electrochemical cell. An optimal NP ratio enhances the capacity, cycle life, and energy output and hence improves the overall performance and lifespan of the electrochemical cell.
[005] Therefore, there is a requirement for an efficient methodology to determine an optimal NP ratio for an electrochemical cell.
SUMMARY OF THE INVENTION
[006] In an embodiment, a method of determining an optimal NP ratio for an electrochemical cell is disclosed. The method may include, receiving, by a computing device, cell data of the electrochemical cell for each of a set of NP ratios. The cell data may include cathode data, anode data, and full-cell data. In an embodiment, each of the cathode data, the anode data, and the full-cell data may be capacity-voltage data that may include capacity values for different voltage values. In an embodiment, the optimal NP ratio belongs to the set of NP ratios. The method may further include determining optimized cell data for at least one NP ratio of the set of NP ratios. The optimized cell data for a NP ratio is determined by determining two of a modified anode data based on an anode offset value, a modified cathode data based on a cathode offset value, and a modified full-cell data based on a full-cell offset value. The optimized cell data is further determined by determining delta voltage values based on the two of the modified anode data, the modified cathode data, and the modified full-cell data, and a remaining of the anode data, the cathode data, and the full-cell data. The optimized cell data is further determined by determining a sum of squares of the delta voltage values. The optimized cell data is further determined by iteratively modifying the two of the anode offset value, the cathode offset value and the full-cell offset value to determine a minimum sum of squares of the delta voltage values. The method may further include determining the optimal NP ratio for the electrochemical cell from the set of NP ratios based on the optimized cell data for each of the set of NP ratios.
[007] In another embodiment, a system of determining an optimal NP ratio for an electrochemical cell is disclosed. The system may include at least one processor and a memory communicatively coupled to the at least one processor, wherein the memory may store processor-executable instructions, which on execution may cause the at least one processor to receive cell data for the electrochemical cell and for each NP ratio of a set of NP ratios. The cell data may include cathode data, anode data, and full-cell data. In an embodiment, each of the cathode data, the anode data, and the full-cell data may be capacity-voltage data that may include capacity values for different voltage values. In an embodiment, the optimal NP ratio belongs to the set of NP ratios. The at least one processor may further determine optimized cell data for at least one NP ratio of the set of NP ratios. The at least one processor may determine the optimized cell data for a NP ratio by determining two of a modified anode data based on an anode offset value, a modified cathode data based on a cathode offset value, and a modified full-cell data based on a full-cell offset value. The at least one processor may further determine the optimized cell data by determining delta voltage values based on the two of the modified anode data, the modified cathode data, and the modified full-cell data, and a remaining of the anode data, the cathode data, and the full-cell data. The at least one processor may further determine the optimized cell data by determining a sum of squares of the delta voltage values. The at least one processor may further determine the optimized cell data by iteratively modifying the two of the anode offset value, the cathode offset value and the full-cell offset value to determine a minimum sum of squares of the delta voltage values. The at least one processor may further determine the optimal NP ratio for the electrochemical cell from the set of NP ratios based on the optimized cell data for each of the set of NP ratios.
[008] In another embodiment, an electrochemical cell is disclosed. The electrochemical cell may include an anode, a cathode, and an electrolyte disposed between the anode and the cathode. In an embodiment, an optimal NP ratio of the electrochemical cell may be determined by a computing device based on a determination of optimized cell data for each NP ratio of a set of NP ratios. In an embodiment, the optimized cell data may be determined based on cell data for the electrochemical cell received for the each NP ratio of the set of NP ratios. It should be noted that the cell data may include cathode data, anode data, and full-cell data. In an embodiment, each of the cathode data, the anode data, and the full-cell data may be capacity-voltage data including capacity values for different voltage values. In an embodiment, the optimal NP ratio belongs to the set of NP ratios. Further, the computing device may determine the optimized cell data for at least one NP ratio of the set of NP ratios based on a determination of two of a modified anode data based on an anode offset value, a modified cathode data based on a cathode offset value, and a modified full-cell data based on a full-cell offset value. Further, the computing device may determine the optimized cell data based on a determination of the delta voltage values based on the two of the modified anode data, the modified cathode data, and the modified full-cell data, and a remaining of the anode data, the cathode data, and the full-cell data. Further, the computing device may determine the optimized cell data based on a determination of a sum of squares of delta voltage values. Further, the computing device may determine the optimized cell data based on iterative modification of two of the anode offset value, the cathode offset value and the full-cell offset value to determine a minimum sum of squares for delta capacity-voltage value.
[009] Various objects, features, aspects, and advantages of the inventive subject matter will become more apparent from the following detailed description of preferred embodiments, along with the accompanying drawing figures in which like numerals represent like components.
BRIEF DESCRIPTION OF THE DRAWINGS
[010] The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles.
[011] FIG. 1 depicts a schematic of an electrochemical cell, in accordance with some embodiments of the present disclosure.
[012] FIG. 2 illustrates a block diagram of a system including an optimization (computing) device for determining an optimal NP ratio for an electrochemical cell, in accordance with some embodiments of the present disclosure.
[013] FIG. 3 is a functional block diagram of the optimization (computing) device of FIG. 2, in accordance with some embodiments of the present disclosure.
[014] FIG. 4 depicts a table including exemplary cell data corresponding to a first NP ratio from a set of NP ratios.
[015] FIG. 5A depicts a capacity-voltage graph corresponding to modified exemplary cell data of FIG. 4.
[016] FIG. 5B depicts a capacity-voltage graph corresponding to optimized cell data based on the exemplary cell data of FIG. 4.
[017] FIG. 6 depicts a table including exemplary cell data corresponding to a second NP ratio from a set of NP ratios.
[018] FIG. 7A depicts a capacity-voltage graph corresponding to modified exemplary cell data of FIG. 6.
[019] FIG. 7B depicts a capacity-voltage graph corresponding to optimized cell data based on the exemplary cell data of FIG. 6.
[020] FIG. 8 illustrates a flowchart of a methodology for determining an optimal NP ratio for an electrochemical cell, in accordance with some embodiments of the present disclosure.
[021] FIG. 9 illustrates a flowchart of a methodology for determining an optimal NP ratio for an electrochemical cell, in accordance with some other embodiments of the present disclosure.
DETAILED DESCRIPTION OF THE DRAWINGS
[022] Exemplary embodiments are described with reference to the accompanying drawings. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the scope of the disclosed embodiments. It is intended that the following detailed description be considered exemplary only, with the true scope being indicated by the following claims. Additional illustrative embodiments are listed.
[023] Further, the phrases “in some embodiments”, “in accordance with some embodiments”, “in the embodiments shown”, “in other embodiments”, and the like mean a particular feature, structure, or characteristic following the phrase is included in at least one embodiment of the present disclosure and may be included in more than one embodiment. In addition, such phrases do not necessarily refer to the same embodiments or different embodiments. It is intended that the following detailed description be considered exemplary only, with the true scope being indicated by the following claims.
[024] As used herein, the term “electrochemical cell” may refer to a device that changes chemical energy to electric energy based on a chemical reaction occurring in it. An electrochemical battery also referred to as battery, may include a single electrochemical cell or a plurality of electrochemical cells. A battery may be a primary or secondary battery.
[025] As used herein, the term “NP ratio” refers a ratio of a capacity of an anode to a capacity of a cathode of an electrochemical cell. The capacity of the anode may be defined as a capacity of an anode material of an electrochemical cell based on the ingredients and their amounts in the anode material. The capacity of the cathode may be defined as a capacity of a cathode material of an electrochemical cell based on the ingredients and their amounts in the cathode material.
[026] Referring now to FIG. 1, a schematic diagram depicts an exemplary electrochemical cell 100, in accordance with some embodiments of the present disclosure. It is to be noted, the electrochemical cell 100 in the schematic diagram depicts a cylindrical cell, however, the description may not be limited to a cylindrical cell. In an embodiment, various types and configurations of electrochemical cells can be selected based on size, shape, voltage, current and other requirements, such as, but not limited to a coin cell, a cylindrical cell, a prismatic cell, Swagelok cell, a pouch cell, etc.
[027] The electrochemical cell 100 may include an anode 102 and a cathode 104, an electrolyte 106 and a separator 108. The electrochemical cell 100 may further include a housing (not shown in FIG. 1) to enclose the anode 102, the cathode 104, the electrolyte 106 and the separator 108. The anode 102 may include an anode material 105A disposed on a first current collector 110. Similarly, the cathode 104 may include a cathode material 105B disposed on a second current collector 112. The anode material 105A and the cathode material 105B may be disposed on one or both the surfaces of the first current collector 110 and the second current collector 112 respectively, depending on the design and configuration of the electrochemical cell 100.
[028] The first current collector 110 and the second current collector 112 may act as a support for the anode 105A material and cathode material 105B respectively. Further, the first current collector 110 and the second current collector 112 may act as electrical conductors between electrode and an external circuit. In an embodiment, the first current collector 110 and the second current collector 112 may be made of, but not limited to, a metal, an alloy of the metal, or a carbon-based material. Examples of the metals that may be used to make the first current collector 110 and the second current collector 112 individually, may include, but are not limited to, aluminum, nickel, titanium, stainless steel, or copper. The first current collector 110 and the second current collector 112 can be in the form of a foil, mesh, or foam.
[029] Further, the electrolyte 106 may be disposed between the anode 102 and the cathode 104. The electrolyte 106 may facilitate transport of ions between the anode 102 and the cathode 104 without allowing electrons to conduct therethrough. It may be noted that the electrolyte 106 may be a solid electrolyte or a liquid electrolyte. In an embodiment, the electrolyte 106 may be an organic liquid. In an embodiment, the electrolyte 106 may include lithium salts such as, but is not limited to, LiPF6, LiAsF6, LiBOB, LiClO4, LiBF4, and the like. The electrolyte may also contain additives that may help in reducing corrosion and enhancing electrolyte stability.
[030] During the operation, the anode 102 and the cathode 104 of the electrochemical cell 100 may be in ionic communication through the separator 108. Accordingly, the separator 108 may be ionically conducting while acting as an insulating layer to prevent a short circuit between the anode 102 and the cathode 104. In some embodiments, the separator 108 may be capable of transporting ions between the anode 102 and the cathode 104. Suitable materials for the separator 108 may include, but are not limited to, beta’-alumina, beta”-alumina, beta’-gallate, zeolite, lithium superionic conductor compounds, a polymer membrane, or combination thereof.
[031] In an embodiment, when the electrochemical cell 100 is charged, ions migrate from the cathode 104 to the anode 102 via the electrolyte 106 while the electrons migrate from the cathode 104 towards the anode 102 via an external circuit. Further, when the electrochemical cell 100 is discharged, electrons migrate from the anode 102 towards the cathode 104 via the external circuit while the ions migrate from the anode 102 towards the cathode 104 through the electrolyte 106.
[032] The electrochemical cell 100 may be in form of a prismatic battery cell, a pouch battery cell, a cylindrical battery cell, or any other shape that may consistently implement the arrangement of the anode 102, the cathode 104, the electrolyte 106 and the separator 108. The size and shape of the electrochemical cell 100 may vary based on a specific application for which the electrochemical cell 100 may be designed. In an embodiment, a plurality of electrochemical cells 100 may be stacked together and connected in series and/or parallel in order to form a battery having an increased voltage output and power density as required.
[033] Depending on the type and chemistry of the electrochemical cell 100, the anode material 105A and the cathode material 105B may be selected. In an embodiment, the electrochemical cell 100 may be a rechargeable battery cell such as a lithium-ion battery cell, a sodium-ion battery cell, and the like etc.
[034] In order to maximize capacity, cycle life, and energy output of an electrochemical cell, an optimal NP ratio may be determined while designing the electrochemical cell. An optimal NP ratio ensures efficient use of the anode material and the cathode material and reliable function of the electrochemical cell attributing for efficient battery performance.
[035] Typically, while designing an electrochemical cell, an NP ratio may be determined based on an anode material and a cathode material used in manufacturing an anode and a cathode, respectively, of the electrochemical cell. Multiple electrochemical cells of different NP ratios are generally charged and discharged through their entire cycle life to determine an optimal NP ratio out of the different NP ratios. However, this process for determining the optimal NP ratio involves various complexities and makes the process time-consuming and resource-consuming.
[036] Embodiments of the present disclosure provide a methodology to determine an optimal NP ratio for an electrochemical cell such as electrochemical cell 100 of FIG. 1. The methodology, as disclosed herein, involves an analysis of cell data obtained for a charge cycle and/or a discharge cycle of the electrochemical cell for a set of NP ratios and identify an NP ratio from the set of NP ratios as the optimal NP ratio for the electrochemical cell 100. That is, the optimal NP ratio belongs to the set of NP ratios. In an embodiment, multiple electrochemical cells (of the same type and having the same chemistry) similar to the electrochemical cell 100 of FIG. 1 may be manufactured corresponding to different NP ratios of the set of NP ratios based on a predefined amounts of the ingredients of anode material 105A and cathode material 105B used at the anode 102 and the cathode 104.
[037] Referring now to FIG. 2, a block diagram of a system 200 including an optimization device 202 for determining an optimal NP ratio for an electrochemical cell such as the electrochemical cell 100 of FIG. 1 is illustrated, in accordance with some embodiments of the present disclosure. The system 200 may include the optimization device 202, an external device 212, and a database 214 communicably couped to each other through a wired or a wireless communication network 210. The optimization device 202 may be any computing device and may include a processor 204 and a memory 206. In an embodiment, examples of processor(s) 204 may include, but are not limited to, an Intel® Itanium® or Itanium 2 processor(s), or AMD® Opteron® or Athlon MP® processor(s), Motorola® lines of processors, Nvidia®, FortiSOC™ system on a chip processors or other future processors. In an embodiment, the memory 206 may store instructions that, when executed by the processor 204, may cause the processor 204 to determine an optimal NP ratio for the electrochemical cell 100 as discussed in greater detail below. In an embodiment, the memory 206 may be a non-volatile memory or a volatile memory. Exampled of non-volatile memory include but are not limited to, a flash memory, a Read Only Memory (ROM), a programmable ROM (PROM), Erasable PROM (EPROM), and Electrically EPROM (EEPROM) memory. Further, examples of volatile memory may include but are not limited to, Dynamic Random Access Memory (DRAM), and Static Random-Access memory (SRAM).
[038] In an embodiment, the optimization device 202 may include an input/output (I/O) device 208. The I/O device 208 may comprise of variety of interface(s), for example, interfaces for data input and output devices, and the like. The I/O device 208 may facilitate inputting of instructions by a user communicating with the optimization device 202. In an embodiment, the I/O device 208 may be wirelessly connected to the optimization device 202 through wireless network interfaces such as Bluetooth®, infrared, or any other wireless radio communication known in the art. In an embodiment, the optimization device 202 may be connected to a communication pathway for one or more components of the optimization device 202 to facilitate the transmission of inputted instructions and output the results of data generated by various components such as, but not limited to, processor(s) 204 and memory 206.
[039] The database 214 may be enabled in a cloud or a physical database and may store data to be input to the optimization device 202 or data output by the optimization device 202 and/or the external device 212 in the process of determination of the optimal NP ratio. In an embodiment, data may include, but is not limited to, cell data obtained for at least a charge cycle or a discharge cycle of the electrochemical cell 100 for each NP ratio of the set of NP ratios. In an embodiment, the cell data may include cathode data, anode data, and full-cell data. Further, in an embodiment, each of the cathode data, the anode data, and the full-cell data may be capacity-voltage data comprising capacity values of the cathode, the anode or the full-cell for different voltage values.
[040] In an embodiment, the communication network 210 may be a wired or a wireless network or a combination thereof. The network 210 can be implemented as one of the different types of networks, such as but not limited to, ethernet IP network, intranet, local area network (LAN), wide area network (WAN), the internet, Wi-Fi, LTE network, CDMA network, 5G and the like. Further, network 210 can either be a dedicated network or a shared network. The shared network represents an association of the different types of networks that use a variety of protocols, for example, Hypertext Transfer Protocol (HTTP), Transmission Control Protocol/Internet Protocol (TCP/IP), Wireless Application Protocol (WAP), and the like, to communicate with one another. Further network 210 can include a variety of network devices, including routers, bridges, servers, computing devices, storage devices, and the like.
[041] In an embodiment, the optimization device 202 may receive a request for determining an optimal NP ratio for the electrochemical cell 100 from the external device 212. In an embodiment, each of the optimization device 202 and the external device 212 may be a computing device including, but is not limited to, a portable computer, a personal digital assistant, a handheld, a scanner, or a mobile device. In an embodiment, the optimization device 202 may be in-built into the external device 212 or a standalone computing device.
[042] In an embodiment, the optimization device 202 may receive cell data of the electrochemical cell 100 for each of a set of NP ratios. In an embodiment, the cell data corresponding to the electrochemical cell 100 may be stored in the database 214 and may be received by the optimization device 202 from the database 214.
[043] As stated above, the term “cell data”, as used herein, refers to capacity-voltage data obtained during a charge cycle, a discharge cycle or both the charge cycle and discharge cycle of an electrochemical cell for each of a set of NP ratios. The capacity-voltage data includes capacity values of the electrochemical cell at different voltage values during a charge cycle, a discharge cycle or both the charge cycle and the discharge cycle. The electrochemical cell may be an anode half-cell, a cathode half-cell or a full-cell. The set of NP ratios includes a plurality of NP ratios. The plurality of NP ratios of the set of NP ratios may be implemented on electrochemical cells that are designed as an anode half-cell, a cathode half-cell or a full-cell. It should be noted that the one or more electrochemical cells are of the same type or have the same chemistry. In an embodiment, the one or more electrochemical cells are the same with respect to their components and the materials used for the components except the amounts of the ingredients of the anode material and the cathode material to achieve different NP ratios. In an embodiment, the cell data includes capacity-voltage data for a full-cell (i.e., full-cell data), capacity-voltage data for anode half-cell (i.e., anode data) and capacity-voltage data for cathode half-cell (i.e., cathode data) for each NP ratio of the set of NP ratios. In an embodiment, the cell data may be considered to be optimized when the full-cell voltage value is about same as difference between cathode voltage value and anode voltage value for each or most of the capacity values.
[044] In an embodiment, an optimal NP ratio may be one of the NP ratios from the set of NP ratios. In order to determine the optimal NP ratio from the set of NP ratios, the optimization device 202 may analyze the cell data of the electrochemical cell 100 designed for each NP ratio of the set of NP ratios, separately. Analyzing the cell data of the electrochemical cell 100 designed for each NP ratio may mean analyzing cell data of multiple electrochemical cells similar to the electrochemical cell 100 of FIG. 1 i.e., of the same type and having the same chemistry and having different NP ratios of the set of NP ratios. That is, the multiple electrochemical cells may be the same with respect to their components and the materials used for the components except the amounts of the ingredients of the anode material and the cathode material to achieve different NP ratios of the set of NP ratios. Further, the multiple electrochemical cells may include anode half-cells, cathode half cells and full cells of each NP ratio of the NP ratios.
[045] In an embodiment, for a given NP ratio of the set of NP ratios, the optimization device 202 may first determine whether the cell data is optimized. Thus, the optimization device 202 may determine if a difference of the voltage values of the cathode data and the anode data is about equal to a voltage value of the full-cell data corresponding to each or most of the capacity values. For example, in case the difference of the voltage values of the cathode data and the anode data is equal to or within a predefined threshold value of the voltage value of the full-cell data corresponding to each or most of the capacity values for the given NP ratio, the optimization device 202 may determine that the cell data corresponding to the given NP ratio is optimized. Upon determining that the difference of the voltage values of the anode data and the cathode data is not equal to or outside the predefined threshold value of the voltage value of the full-cell data for the given NP ratio, the optimization device 202 may optimize the cell data. The cell data that is determined as optimized, and the cell data that is optimized by the optimization device 202 is referred to as ‘optimized cell data’ throughout the specification.
[046] In some cases, the optimization device 202 may determine that cell data corresponding to more than one NP ratio of the set of NP ratios is optimized. In such cases, the optimization device 202 may optimize cell data corresponding to the remaining NP ratios of the set of NP ratios.
[047] Thus, upon determining that the difference of voltage values of the anode data and the cathode data is not equal to or outside the predefined threshold value of the voltage value of the full-cell data for each of the remaining NP ratios, the optimization device 202 may optimize cell data corresponding to each of the remaining NP ratios. As will be described in greater detail below, the optimization of cell data for a given NP ratio may be performed by iteratively modifying the cell data such that a sum of squares of delta voltage values (i.e., a difference of the voltage value of the full-cell data and the difference of the voltage values of the cathode data and the anode data for each or most of the capacity values for the given NP ratio) is minimum.
[048] In order to optimize cell data for a given NP ratio of the set of NP ratios, the optimization device 202 may determine modified cell data corresponding to the given NP ratio. It should be noted that the term “modified cell data” may be used to represent the “cell data” in which any of the capacity and/or voltage values for the anode, the cathode, and/or the full-cell has been modified. For example, the term “modified cell data” may be used to represent the “cell data” in which two of the anode, the cathode, and the full-cell data has been modified, while one of the anode, the cathode, and the full-cell data has not been modified. In an embodiment, the optimization device 202 may determine modified cell data by determining offset voltage values corresponding to two of the cathode data, anode data or the full-cell data. The offset voltage values corresponding to the cathode data, anode data and the full-cell data are, individually, referred to as cathode offset value, anode offset value and full-cell offset value, respectively. The offset voltage values may be determined based on randomly identified two offset values for the two of the cathode capacity values, anode capacity values and/or the full-cell capacity values. Accordingly, the modified cell data may include two of the modified anode data, modified cathode data or modified full-cell data. The modified anode data may be determined based on an anode offset value and the anode data. The modified cathode data may be determined based on a cathode offset value and the cathode data. The modified full-cell data may be determined based on a full-cell offset value and full-cell data. In an embodiment, the anode offset value, the cathode offset value and the full-cell offset value, individually, may include a respective offset capacity value. In such embodiments, each of the modified anode data, the modified cathode data and the modified full-cell data may include respective capacity values modified based on the respective offset capacity values at different voltage values.
[049] Further, the optimization device 202 may determine delta voltage values based on the modified cell data. For example, the optimization device 202 may determine the delta voltage values based on the two of the modified anode data, the modified cathode data and the modified full-cell data and a remaining of the cathode data, the anode data and the full-cell data. The delta voltage values are a difference of the voltage value of the full-cell data (or modified full-cell data) and the difference of the voltage values of the cathode data (or modified cathode data) and the anode data (or modified anode data) corresponding to each or most of the capacity values.
[050] In an embodiment, for each capacity value, a delta voltage value may be determined by determining a difference between a corresponding full-cell voltage value and a difference between a corresponding cathode voltage value and a corresponding anode voltage value. As mentioned in equation (1) below, each of the delta voltage values is a difference between a full-cell voltage value at a given capacity value and a difference between a cathode voltage value and an anode voltage value at the given capacity value.
Delta Voltage Value (at a given capacity value) = [(Cathode Voltage Value (at the given capacity value) – Anode Voltage Value (at the given capacity value)) – Full-cell Voltage Value (at the given capacity value)] … (1)
[051] In an embodiment, the optimization device 202 determines the delta voltage values corresponding to those capacity values for which the voltage values of the full-cell data and the corresponding cathode data and anode data have non-zero values.
[052] After determining the delta voltage values, the optimization device 202 may determine a sum of squares of the delta voltage values for the given NP ratio.
[053] Further, the optimization device 202 may iteratively modify two of the anode offset value, the cathode offset value and the full-cell offset value to determine modified cell data (i.e., two of the modified anode data, the modified cathode data, and modified full-cell data, respectively) for each subsequent iteration. For example, for each subsequent iteration, another modified cathode data and another modified full-cell data may be determined. Further, the optimization device 202 may, thereby, determine a sum of squares of the delta voltage values for each iteration. In this way, the optimization device 202 determines multiple sums of squares of the delta voltage values corresponding to various iterations for the given NP ratio. In an embodiment, the iterative modification may be performed by the optimization device 202 by employing an analysis tool or a simulation tool. In an embodiment, the analysis tool may be selected as, but is not limited to, a sensitivity analysis tool, a MICROSOFT Excel, MATLAB, Python, R, GAMS, and so forth.
[054] The optimization device 202 may then determine a sum of squares, which is minimum, out of the multiple sums of squares of the delta voltage values determined corresponding to various iterations. Such a sum of squares may be referred to as a minimum sum of squares of delta voltage values corresponding to the given NP ratio. The optimization device 202 may then select the modified cell data (i.e., two of the modified anode data, the modified cathode data and the modified full-cell data, and a remaining of the non-modified anode data, the non-modified cathode data, and the non-modified full-cell data) for which the sum of squares of the delta voltage values is minimum. The modified cell data selected by the optimization device 202 is referred to as ‘selected modified cell data’ or ‘optimized cell data’. Thus, for example, when a given modified cell data including modified cathode data, modified full-cell data and non-modified anode data is selected, the given modified cell data is referred to as the ‘selected modified cell data’ or the ‘optimized cell data’.
[055] In an embodiment, the optimization device 202 may further determine the ‘selected modified cell data’ or the ‘optimized cell data’ for each of the remaining NP ratios (i.e., NP ratios for which the cell data was determined as not optimized). Thus, the optimization device 202 may determine, for each NP ratio of the remaining NP ratios, a minimum sum of squares of the delta voltage values and select modified cell data for each NP ratio of the remaining NP ratios as the selected modified cell data or the optimized cell data, similar to as explained above for the given NP ratio.
[056] The optimization device 202 may then select an NP ratio (i.e., a selected NP ratio) from the set of NP ratios as the optimal NP ratio. In an embodiment, the optimization device 202 may determine the optimal NP ratio out of the set of NP ratios based on the optimized cell data for each NP ratio of the set of NP ratios. In an embodiment, the optimal NP ratio is determined based on the values of a maximum voltage (or maximum voltage value) and a minimum voltage (or minimum voltage value) of the optimized cell data for each NP ratio of the set of NP ratios. The optimization device 202 may determine the values of a maximum voltage and a minimum voltage for each of the selected modified cell data (i.e., the optimized cell data), for each NP ratio of the set of NP ratios.
[057] In order to select an NP ratio from the set of NP ratios as the optimal NP ratio, the optimization device 202 may first identify one or more NP ratios (i.e., identified NP ratios) from the set of NP ratios for which the values of the maximum voltage and the minimum voltage of the optimized cell data are within respective predefined threshold values. In an embodiment, the optimization device 202 may identify the one or more NP ratios for which the maximum voltage value and the minimum voltage value of the optimized anode data (i.e., modified/non-modified anode data) and/or the optimized cathode data (i.e., modified/non-modified cathode data) are within respective predefined threshold values.
[058] Upon determining the values of the maximum voltage and the minimum voltage of the cathode and/or anode from the optimized cell data for a given NP ratio, the optimization device 202 determines whether the values of the maximum voltage and the minimum voltage for the cathode and/or the anode are within respective predefined threshold values. In some embodiments, the optimization device 202 determines whether the values of the maximum voltage or the minimum voltage for one of optimized anode data and optimized cathode data are within the respective predefined threshold values. In an embodiment, each of the respective predefined threshold values corresponding to the anode and/or the cathode may depend on the charge cycle or discharge cycle of the electrochemical cell 100. In an embodiment, each of the respective predefined threshold values corresponding to the anode and/or cathode may be saved in the memory 206.
[059] In case the values of the maximum voltages and the minimum voltages are determined beyond the respective threshold values, it means there may be some undesired changes occurring inside the electrochemical cell (e.g., Lithium plating, irreversible phase transformations of materials etc.).
[060] As discussed, the optimization device 202 may identify one or more NP ratios from the set of NP ratios, corresponding to which the values of the maximum voltages and the minimum voltages are within the respective predefined threshold values. Such one or more NP ratios may be referred to as one or more identified NP ratios. Upon determining the one or more identified NP ratios, the optimization device 202 may select an NP ratio out of the one or more identified NP ratios as the optimal NP ratio based on the designing of the corresponding electrochemical cell in terms of the performance (capacity and cycle life of the electrochemical cell) and the cost. In these embodiments, the selected NP ratio is the optimal NP ratio.
[061] Referring now to FIG. 3, a functional block diagram of an optimization device 202 is illustrated, in accordance with some embodiments of the present disclosure. In an embodiment, the optimization device 202 may include a data receiving module 302, an analysis module 304, and a determination module 306.
[062] The data receiving module 302 may be implemented in the I/O device 208 and may receive cell data for each NP ratio of a set of NP ratios. Referring now to FIG. 4 and FIG. 6, a table 400 and 600 including exemplary cell data 402 and 602 corresponding to a first NP ratio and a second NP ratio from the set of NP ratios is shown.
[063] Cell data 402 as shown in table 400 of FIG. 4, may include full-cell data 404, anode data 406 and cathode data 408 corresponding to the first NP ratio. Similarly, cell data 602 as shown in table 600 of FIG. 6, may include full-cell data 604, anode data 606 and cathode data 608 corresponding to the second NP ratio. In an embodiment, the anode data 406 or 606 and the cathode data 408 or 608 may also be referred to as half-cell data or non-modified half-cell data. As shown, the full-cell data 404 or 604 may include full-cell capacity data (Fca1, Fca2, …, Fcan) 404A or 604A corresponding to full-cell voltage data (Fv1, Fv2, …, Fvn) 404B or 604B. Further, the anode data 406 or 606 may include anode capacity data (Aca1, Aca2, …, Acan) 406A or 606A corresponding to anode voltage data (Av1, Av2, …, Avn) 406B or 606B. Further, the cathode data 408 or 608 may include cathode capacity data (Cca1, Cca2, …, Ccan) 408A or 608A corresponding to cathode voltage data (Cv1, Cv2, …, Cvn) 408B or 608B.
[064] As will be appreciated, the exemplary full-cell data 404 or 604, anode data 406 or 606 and cathode data 408 or 608 have been depicted using annotations (Fca1, Fca2, … , Fcan), (Fv1, Fv2, … , Fvn), (Aca1, Aca2, … , Acan), (Av1, Av2, … , Avn), (Cca1, Cca2, … , Ccan) and (Cv1, Cv2, … , Cvn) for representation purpose in the table 400 or the table 600, however, such annotations are representative of respective capacity values and voltage values determined for the first NP ratio from the set of NP ratios.
[065] Referring back to FIG. 3, the analysis module 304 may first determine, separately, whether the cell data is optimized (i.e., whether a difference of the cathode voltage data 408B and the anode voltage data 406B is equal to or within the predefined threshold value of a full-cell voltage data 414B corresponding to each capacity value). As stated above, if the determination is positive (i.e., if the difference is equal to or within the predefined threshold value of the full-cell delta voltage value), then the analysis module 304 may determine the cell data to be optimized cell data and proceed to analyze cell data for a subsequent NP ratio of the set of NP ratios. However, if the determination is negative (i.e., if the difference is not equal to or not within the predefined threshold value of the full-cell delta voltage value), then the analysis module 304 may first optimize the cell data for the given NP ratio of the set of NP ratios prior to analyzing cell data for the subsequent NP ratio of the set of NP ratios.
[066] Upon determining that the cell data is not optimized (i.e., the difference of the cathode voltage data (408B, 608B) and the anode voltage data (406B, 606B)is not equal to a full-cell voltage data (404B, 604B), the analysis module 304 may then iteratively modify the cell data received for each NP ratio (including the first NP ratio and the second NP ratio) of the set of NP ratios until the data is optimized. The determination of optimized cell data by the analysis module 304 has been discussed in accordance with the exemplary cell data 402 corresponding to the first NP ratio. It is to be noted that similar processing may be performed for the exemplary cell data 602 corresponding to the second NP ratio and other NP ratios in the set of NP ratios to determine optimized cell data for each of the NP ratios for which the cell data is not optimized.
[067] Referring again to FIG. 4, the exemplary cell data 402 may be modified to determine modified cell data 403 by modifying, for example, full-cell data 404 based on a full-cell offset value 422 and cathode data 408 based on a cathode offset value 424. It should be noted that, as discussed above, any two of the anode data, cathode data or the full-cell data may be modified using respective offset value to generate the modified cell data. Accordingly, the analysis module 304 may determine modified cell data 403 from cell data 402 by modifying full-cell data 404 and by modifying cathode data 408 based on the corresponding offset values 422, 424. The cathode data 408 that has been modified using the cathode offset value 424 is represented as modified cathode data 412. Similarly, the full-cell data 404 that has been modified using the full-cell offset value 422 is represented as modified full-cell data 414. Further, since the anode data 406 is not modified it may be referred to as the non-modified anode data. As will be appreciated, the modified cathode data 412, the modified full-cell data 414, as well as the corresponding non-modified anode data may be referred to as modified cell data 403.
[068] In an embodiment, the full-cell offset value 422 and the cathode offset value 424 may be initialized as ‘a1’ and ‘b1’ respectively for the first NP ratio as depicted in table 400. In an embodiment, the full-cell offset value 422 and the cathode offset value 424 may be initialized as random positive numeric values.
[069] Accordingly, in order to determine modified cell data 403 for the first NP ratio, the full-cell offset value 422 may be added to or subtracted from each capacity value of the full-cell capacity data 404A and the cathode offset value 424 may be added to or subtracted from each capacity value of the cathode capacity data 408A. Thus, for example, mFca1 is equal to Fca1 + a1, while mCca1 is equal to Cca1 + b1.
[070] As can be seen in table 400, the modified cathode data 412 includes modified cathode capacity data 412A depicted using annotations (mCca1, mCca2, …, mCcan). Further, the modified full-cell data 414 includes modified full-cell capacity data 414A depicted using annotations (mFca1, mFca2, …, mFcan). It is to be noted that the annotations in the table 400 are for representation purpose, however, such annotations are representative of respective modified capacity values determined for the first NP ratio from the set of NP ratios.
[071] Referring back to FIG. 3, I analysis module 304 may then determine modified cathode voltage data 412B for the modified cathode capacity 412A based on the cathode voltage data 408B. In an embodiment, the modified cathode voltage values (mCvn) are generated for the modified cathode capacity values (mCca1) in the modified cathode data 412 by replicating cathode voltage values (Cvn) corresponding to original cathode capacity values (Ccan) in the cathode voltage data 408B. For example, mCv1 corresponding to mCca1 is equal to Cv1 corresponding to Cca1. Further, the analysis module 304 may determine modified full-cell voltage data 414B for the modified full-cell capacity 414A based on the full-cell voltage data 404B. In an embodiment, the modified full-cell voltage values (mFvn) are generated for the modified full-cell capacity values (mFca1) in the modified full-cell data 414 by replicating full-cell voltage values (Fvn) corresponding to the original full-cell capacity values (Fcan) in the full-cell voltage data 404B. As will be appreciated, the exemplary modified full-cell voltage data 414B and modified cathode voltage data 412B have been depicted using annotations (mFv1, mFv2, … , mFvn) and (mCv1, mCv2, … , mCvn) for representation purpose in the table 400, however, such annotations are representative of respective modified voltage values determined by the analysis module 304.
[072] The analysis module 304 may then determine delta voltage values 416 for different capacity values. For example, delta voltage value (?n) at a given capacity is determined by determining a difference between the modified full-cell voltage values from the modified full-cell voltage data 414B at the given capacity and a difference of the modified cathode voltage values from the modified cathode voltage data 412B at the given capacity and the anode voltage values from the anode voltage data 406B in accordance to equation (2) (analogous to equation (1)) given below. It should be noted that table 400 depicts the delta voltage values 416 for each capacity value as (?1, ?2, … ?n) for representation purpose, however, such annotations are representative of respective delta voltage values determined by the analysis module 304 based on equation (2) below.
Delta Voltage Value (at a given capacity value) = [(Modified Cathode Voltage Value (at the given capacity value) – Anode Voltage Value (at the given capacity value)) – Modified Full-cell Value (at the given capacity value)] … (2)
[073] It should be noted that, in an embodiment, the delta voltage values 416 may not be determined for a given capacity value if no corresponding voltage value exists in one of: the anode voltage data 406B for the given capacity value in the anode capacity data 406A, or, the modified cathode voltage data 412B for the given capacity value in the modified cathode capacity data 412A, or the modified full-cell voltage data 414B for the given capacity value in the modified full-cell capacity data 414A.
[074] Further, the analysis module 304 may determine a square of each of the delta voltage values 418. The analysis module 304 may then determine a sum of squares of the delta voltage values 420 by adding each of the squares of delta voltage values 418.
[075] The above description provides determination of a sum of squares of the delta voltage values 420 for the first NP ratio for one iteration in which the full-cell offset value 422 and the cathode offset value 424 have been initialized as ‘a1’ and ‘b1’ respectively. However, the analysis module 304 may iteratively modify the full-cell offset value 422 and the cathode offset value 424 in each of subsequent iterations and accordingly may determine a sum of squares of the delta voltage values 420 for each of the corresponding subsequent iterations. In this way, the analysis module 304 may determine multiple sums of squares of the delta voltage values 420 corresponding to various iterations for the first NP ratio. The analysis module 304 may then determine a minimum sum of squares of the delta voltage values out of the multiple sums of squares for the first NP ratio. Further, the modified cell data for an iteration for which the minimum sum of squares of the delta voltage values is determined may be referred to a selected modified cell data or the optimized cell data. The determination of an optimal NP ratio may be performed based on further analysis of the selected modified cell data or the optimized cell data.
[076] Similar to the exemplary embodiment described with respect to cell data 402 corresponding to first NP ratio of the set of NP ratios, it is to be noted that the analysis module 304 may determine a sum of squares of the delta voltage values 620 for the cell data 602 corresponding to the second NP ratio. As depicted in table 600, the sum of squares of the delta voltage values 620 may be determined for a first iteration in which the full-cell offset value 622 and the cathode offset value 624 have been initialized as ‘a2’ and ‘b2’ respectively. Further, the sum of squares of the delta voltage values 620 may be determined for various iterations and a minimum sum of squares of the delta voltage values 620 is determined. Further, the iteration for which the minimum sum of squares of the delta voltage values is determined for the second NP ratio, the modified cell data for that particular iteration may be determined as a selected modified cell data or the optimized cell data for the second NP ratio.
[077] Similarly, a sum of squares of the delta voltage values may be determined for each of the other NP ratios from the set of NP ratios for which the cell data is not optimized. Further, a selected modified cell data (or an optimized cell data) for each of the other NP ratios from the set of NP ratios may also be determined.
[078] In an embodiment, the iterative modification of the offset values for one or more NP ratios of the set of NP ratios may be performed by employing an analysis technique such as, but is not limited to, a sensitivity analysis, a what-if analysis, and so forth. Further, the initial offset values for the one or more NP ratios of the set of NP ratios may be initialized as random positive numeric values and iteratively and randomly modified in every iteration until a minimum sum of squares of the delta voltage values is determined. In an embodiment, the two selected offset values may be decimal number, real numbers, whole numbers, etc.
[079] Referring now to FIG. 5A, a capacity-voltage graph 500A corresponding to the modified cell data 403 in table 400 of FIG. 4 is depicted. The graph 500A may be plotted by plotting voltage data values on y-axis with respect to capacity values on the x-axis of the modified full-cell data 414, the anode data 406 and the modified cathode data 412. It is to be noted that, from the graph 500A, plot 502 represents the modified cathode data 412 (e.g., cathode data 408 modified with the cathode offset value 424), plot 504 represents the modified full-cell data 414 (e.g., full-cell data 404 modified with the full-cell offset value 422) and plot 506 represents the non-modified anode data 406 for the first NP ratio.
[080] In FIG. 5B, graph 500B shows a portion of the capacity-voltage graph 500A of FIG. 5A. Accordingly, plots 508, 510 and 512 of FIG. 5B are portions of plot 502, plot 504 and 506, respectively, of FIG. 5A. It should be noted that the graph 500B shows plots 508, 510 and 512 only for those capacity values for which the corresponding voltage values exists in the non-modified anode data 406, the modified cathode data 412 and the modified full-cell data 414 of table 400 of FIG. 4. Further, a difference between the modified cathode data 412 data and the non-modified anode data 406 is represented by plot 514. The graph 500B shows that the plot 510 (representing the modified full-cell data 414) and the plot 514 (representing the difference between the modified cathode data 412 data and the non-modified anode data 406) may seem to be about overlapping. As used herein, the term “about overlapping” or “about overlap” may mean that a plot is overlapping another plot by more than 95 percent. Referring to FIG. 5B and FIG. 4, an about overlap of the modified full-cell data 414 and the difference between the modified cathode data 412 data and the non-modified anode data 406 may depict that modified cell data 403 for the first NP ratio for that particular iteration has yielded a minimum sum of squares of the delta voltage value 420. Accordingly, the modified cell data as represented in FIGS. 5A and 5B corresponding to the first NP ratio is optimized.
[081] Similarly, referring now to FIG. 7A, a capacity-voltage graph 700A corresponding to the modified cell data 603 of FIG. 6 for the second NP ratio is depicted. The graph 700A may be plotted by plotting voltage data values on y-axis with respect to capacity values on the x-axis of the modified full-cell data 614, the anode data 606 and the modified cathode data 612. It is to be noted that, from the graph 600A, plot 702 represents the modified cathode data 612, plot 704 represents the modified full-cell data 614 and plot 706 represents the non-modified anode data 606 for the second NP ratio.
[082] In FIG. 7B, graph 700B shows a portion of the capacity-voltage graph 700A of FIG. 7A. Accordingly, plots 708, 710 and 712 of FIG. 7B are portions of plot 702, plot 704 and 706, respectively, of FIG. 7A. It should be noted that the graph 700B shows plots 708, 710 and 712 only for those capacity values for which the corresponding voltage values exists in the non-modified anode data 606, the modified cathode data 612 and the modified full-cell data 614 of table 600 of FIG. 6. Further, a difference between the modified cathode data 612 data and the non-modified anode data 606 is represented by plot 714 in FIG. 7B. The graph 700B shows that the plot 710 (representing the modified full-cell data 614) and the plot 714 (representing the difference between the modified cathode data 612 data and the non-modified anode data 606) may seem to be about overlapping. Referring to FIG. 7B and FIG. 6, an about overlap of the modified full-cell data 614 and the difference between the modified cathode data 612 data and the non-modified anode data 606 may depict that modified cell data 603 for the second NP ratio for that particular iteration has yielded a minimum sum of squares of the delta voltage value 620. Accordingly, the modified cell data as represented in FIGS. 7A and 7B corresponding to the second NP ratio is optimized.
[083] Referring back to FIG. 3, the determination module 306 may determine an optimal NP ratio, based on the determination of the optimized cell data for each NP ratio of the set of NP ratios.
[084] In particular, the determination module 306 may determine the optimal NP ratio by identifying one or more NP ratios from the set of NP ratios based on the optimized cell data and then by selecting the optimal NP ratio from among the one or more identified NP ratio based on design considerations of the electrochemical cell in terms of the performance and the cost. In an embodiment, each of the one or more NP ratios may correspond to an NP ratio of the set of NP ratios that is identified based on the determination of maximum voltage values and minimum voltage values of the optimized anode data (i.e., modified/non-modified anode data) and/or optimized cathode data (i.e., modified/non-modified cathode data). For example, the determination module 306 may identify the one or more NP ratios for which the maximum voltage value and the minimum voltage value of the optimized anode data and/or the optimized cathode data (i.e., modified/non-modified cathode data) are within respective predefined threshold values.
[085] Referring to FIG. 5B and FIG. 7B, the graphs 500B and 700B depicts the values of a maximum anode voltage (520, 720), and a minimum anode voltage (518, 718) of the non-modified anode data (406, 606) and a maximum cathode voltage (522, 722) and a minimum cathode voltage (524, 724) of the modified cathode data (412, 612) corresponding to the optimized cell data (i.e., selected modified cell data for which the sum of squares of the delta voltage values is minimum) for the first and the second NP ratios, respectively.
[086] The determination module 306 may determine whether the values of the maximum anode voltage (520, 720) and the minimum anode voltage (518, 718) and/or the maximum cathode voltage (522, 722) and the minimum cathode voltage (524, 724) are within respective predefined threshold values. In an embodiment, the respective predefined threshold values may be saved in the memory 206. A similar determination may be made for the optimized cell data of each NP ratio of the set of NP ratios.
[087] For example, the determination module 306 may determine that the value of the maximum cathode voltage (Cmax1) (FIG. 5B) is not within the respective predefined threshold value. Accordingly, the determination module 306 may not identify the first NP ratio from the set of NP ratios. The determination module 306 may identify the second NP ratio, from the set of NP ratios, upon determining that the values of the maximum anode voltage 720 and/or the minimum anode voltage 718 and the values of the maximum cathode voltage 722 and/or the minimum cathode voltage 724 are within the respective predefined threshold values. In particular, the determination module 306 may determine that the values of the maximum cathode voltage 722 and the minimum cathode voltage 724 of the modified cathode data 612 corresponding to the optimized cell data are within the predefined cathode threshold values for the cathode half-cell. Further, the determination module 306 may determine that the values of the maximum anode voltage 720 and the minimum anode voltage 718 of the non-modified anode data 606 corresponding to the optimized cell data are within the predefined anode threshold values for the anode half-cell. Accordingly, the second NP ratio, may be identified. That is, the second NP ratio is one of the identified NP ratios. In an embodiment, the determination module 306 may then select the second NP ratio as the optimal NP ratio based on the based on the designing of the corresponding electrochemical cell in terms of the performance (capacity and cycle life of the electrochemical cell) and the cost.
[088] Referring now to FIG. 8, a flowchart 800 of a methodology for determining an optimal NP ratio for an electrochemical cell 100 is illustrated, in accordance with some embodiments of the present disclosure. In an embodiment, the method 800 may include a plurality of steps that may be performed by the processor 204 to determine an optimal NP ratio for an electrochemical cell and the various modules of the optimization device 202. It should be appreciated that the steps of the flowchart have been explained in conjugation with the exemplary embodiments of FIGS. 4-7B.
[089] At step 802, the method 800 may include receiving cell data of an electrochemical cell for each NP ratio of a set of NP ratios. In an embodiment, cell data includes cathode data, anode data, and full-cell data for a cathode half-cell, an anode half-cell and a full-cell respectively, for each NP ratio of a set of NP ratios. The cell data is received for at least one of a charge cycle or a discharge cycle of the electrochemical cell. In an embodiment, each of the cathode data, the anode data, and the full-cell data may include capacity values for different voltage values for each NP ratio of the set of NP ratios. Table 400 and 600 depict exemplary cell data 402 and 602 received for a first NP ratio and a second NP ratio of the set of NP ratios.
[090] Further, at step 804, the method 800 may include determining whether the cell data is optimized for each NP ratio of the set of NP ratios. As discussed above, the cell data is considered to be optimized, for a given NP ratio, if a voltage value of the full-cell data is equal to or is within a predefined threshold of a difference of the voltage values of the cathode data and the anode data. In case, at step 804, the voltage value of the full-cell data is determined equal to or within the predefined threshold of the difference of the voltage values of the cathode data and the anode data for one or more NP ratios of the set of NP ratios, the cell data for the one or more NP ratio may identified as optimized cell data. Upon identifying the one or more NP ratios having optimized cell data, the method 800 may include performing the step 820. As will be described in detail below, at step 820, the method 800 may include identifying one or more NP ratios from the set of NP ratios.
[091] However, upon determining that the cell data is not optimized (i.e., if the voltage value of the full-cell data is not equal to or not within the predefined threshold of the difference of the voltage values of the cathode data and the anode data) for one or more of the set of NP ratios at step 804, the method 800 may include optimizing the cell data at step 805. In particular, at step 805, the method 800 may include optimizing cell data for each of those NP ratios of the set of NP ratios for which the cell data is not optimized. As will be described in detail below, the cell data may be optimized by performing steps 806 – 819. The method 800, at step 806, may include initializing two of a cathode offset value, an anode offset value or a full-cell offset value for an NP ratio of the set of NP ratios. According to the exemplary embodiments of FIG. 4-7A, a cathode offset value (424, 624) and a full-cell offset value (422, 622) may be initialized. In an embodiment, the two of the anode offset value, the cathode offset value or the full-cell offset value may be initialized as any random positive number.
[092] The method, at step 808, may include determining two of a modified anode data, a modified cathode data or a modified full-cell data based on the respective two of the anode offset value, the cathode offset value, or the full-cell offset value and a remaining of the anode data (i.e., non-modified anode data), the cathode data (i.e., non-modified cathode data), or the full-cell data (i.e., non-modified full-cell data). According to the exemplary embodiments of FIG. 4-7A, a modified cathode data (412, 612) and a modified full-cell data (414, 614) may be determined based on the respective cathode offset value (424, 624) and the full-cell offset value (422, 622), respectively. In an embodiment, each of the modified anode data, the modified cathode data or the modified full-cell data may be determined based on the anode offset value, the cathode offset value, or the full-cell offset value respectively. According to the exemplary embodiments of FIG. 4-7A, a modified cathode data (412, 612) and a modified full-cell data (414, 614) may be determined based on the respective cathode offset value (424, 624) and the full-cell offset value (422, 622) respectively. In an embodiment, the respective cathode offset value (424, 624) and the full-cell offset value (422, 622) may be added to or subtracted from the cathode capacity data (408A, 608A) or the full-cell capacity data (404A, 604A), respectively, to determine the respective modified cathode capacity data (412A, 612A) and the modified full-cell capacity data (414A, 614A).
[093] Further, the method 800, at step 810, may include determining delta voltage values by determining a difference between the modified/non-modified full-cell voltage values and a difference between the modified/non-modified cathode voltage values and the modified/non-modified anode voltage values corresponding to different capacity values as per equation (1) or equation (2) mentioned above. According to the exemplary embodiments of FIG. 4-7A, the delta voltage values (416, 616) may be determined.
[094] Further, the method 800, at step 812, may include determining a square of each of the delta voltage values for each of the capacity value. Accordingly, as shown in the exemplary embodiments of FIG. 4-7A, squares of delta voltage values (418, 618) may be determined by squaring the value of each of the delta voltage values (416, 616).
[095] The method 800, at step 814, may include determining a sum of squares of the delta voltage values. Accordingly, as shown in the exemplary embodiments of FIG. 4-7A, a sum of the squares of delta voltage values (420, 620) may be determined by adding each of the squares of the delta voltage values (418, 618). In an embodiment, the sum of squares of the delta voltage values may be determined for at least a charge cycle or a discharge cycle of the electrochemical cell.
[096] At step 816, the method 800 may include repeating the steps 808-814 by modifying the two of the anode offset value offset, the cathode offset value or the full-cell offset value randomly for each repetition or iteration. In an embodiment, the iterative modification of two of the anode offset value offset, the cathode offset value or the full-cell offset value may be performed based on an analysis methodology, such as, but is not limited to, what-if analysis methodology, and a simulation tool. Accordingly, multiple sums of squares of delta voltage values may be determined for multiple iterations.
[097] The method 800, at step 818, may include determining a sum of squares that is minimum (i.e., a minimum sum of squares) out of the multiple sums of squares.
[098] Further, at step 819, the method 800 may include selecting the modified cell data corresponding to the iteration for which the minimum sum of the squares of the delta voltage values is determined, as optimized cell data.
[099] As stated above, the method 800 may perform the steps 806-819 for each of those NP ratios of the set of NP ratios for which the cell data is not optimized so as to determine optimized cell data.
[0100] At step 820, the method 800 may include identifying one or more NP ratios from the set of NP ratios. The one or more NP ratios may identified based a maximum voltage value and a minimum voltage value of the anode and/or cathode voltages in the optimized cell data for each NP ratio of the set of NP ratios. In an embodiment, the one or more NP ratios, corresponding to which the maximum voltage values and minimum voltage values of anode/cathode in the optimized cell data are determined to be within respective predefined threshold values, are identified from the set of NP ratios. Such one or more NP ratios may be referred to as identified one or more NP ratios.
[0101] At step 822, the method 800 may include selecting an NP ratio from the one or more identified NP ratios based on the designing of the corresponding electrochemical cell in terms of the performance (capacity and cycle life of the electrochemical cell) and the cost. In these embodiments, the selected NP ratio is the optimal NP ratio.
[0102] Referring now to FIG. 9, a flowchart 900 of a methodology for determining an optimal NP ratio for an electrochemical cell (e.g., the electrochemical cell 100 of FIG. 1) is illustrated, in accordance with some embodiments of the present disclosure. In an embodiment, the method 900 may include a plurality of steps that may be performed by the processor 204 to determine an optimal NP ratio for the electrochemical cell 100.
[0103] At step 902, the method 900 may include receiving cell data of an electrochemical cell for each of a set of NP ratios. In an embodiment, cell data includes cathode data, anode data, and full-cell data for a cathode half-cell, an anode half-cell and a full-cell respectively, for each NP ratio of a set of NP ratios. The cell data is received for at least one of a charge cycle or a discharge cycle of the electrochemical cell. In an embodiment, each of the cathode data, the anode data, and the full-cell data may be capacity-voltage data that may include capacity values for different voltage values.
[0104] Further, at step 903, the method 900 may include determining optimize cell data for at least one NP ratio of the set of NP ratios. In particular, the method 900 may include the steps of 904 – 910 to determine the optimize cell data for each of the at least one NP ratio of the set of NP ratios. At step 904, the method 900 may include determining two of a modified anode data, a modified cathode data or a modified full-cell data based on an anode offset value, a cathode offset value or a full-cell offset value, respectively, for each of the at least one NP ratio of the set of NP ratios. In an embodiment, each of the at least one NP ratio is a NP ratio for which the cell data is not optimized. In other words, the at least one ratio is such NP ratio for which the difference of the voltage values of the cathode data and the anode data is determined not equal to or not within the predefined threshold of the voltage value of the full-cell data corresponding to each capacity value.
[0105] Further, at step 906, the method 900 may include determining delta voltage values for each of the at least one NP ratio based on the two of the modified anode data, the modified cathode data, and the modified full-cell data, and a remaining of the anode data (i.e., non-modified anode data), the cathode data (i.e., non-modified cathode data), and the full-cell data (i.e., non-modified full-cell data).
[0106] Further, at step 908, the method 900 may include determining a sum of squares of the delta voltage values for each of the at least one NP ratio of the set of NP ratios.
[0107] Further, at step 910, the method 900 may include repeating the steps 904-910 by iteratively modifying the two of the anode offset value, the cathode offset value or the full-cell offset value to determine a sum of squares of delta voltage values for each iteration. Accordingly, multiple sums of squares of delta voltage values may be determined for multiple iterations.
[0108] At step 910, the method 900 may further include determining a minimum sum of squares out of the multiple sums of squares of delta voltage values corresponding to various iterations.
[0109] Further, at step 912, the method 900 may include determining an optimal NP ratio for the electrochemical cell from the set of NP ratios based on the optimized cell data for each of the set of NP ratios. As discussed above, in an embodiment, selecting the optimal NP ratio for the electrochemical cell from the set of NP ratios may be based on the maximum and minimum voltage values for the anode and/or cathode in the optimized cell data for each NP ratio of the set of NP ratios. In particular, the optimal NP ratio for the electrochemical cell corresponds to an NP ratio of the set of NP ratios that is selected based on a maximum voltage value and a minimum voltage value of at least one of the anode data or the modified anode data, and the cathode data or the modified cathode data for each NP ratio of the set of NP ratios.
[0110] It is intended that the disclosure and examples be considered as exemplary only, with a true scope of disclosed embodiments being indicated by the following claims.
, Claims:CLAIMS
I/We Claim:
1. A method (900) of determining an optimal NP ratio for an electrochemical cell (100), the method (900) comprising:
receiving (902), by a computing device (202), cell data (402, 602) of the electrochemical cell (100) for each of a set of NP ratios, wherein the cell data (402, 602) comprises cathode data (408, 608), anode data (406, 606), and full-cell data (404, 604), wherein each of the cathode data (408, 608), the anode data (406, 606), and the full-cell data (404, 604) is capacity-voltage data comprising capacity values for different voltage values, and wherein the optimal NP ratio belongs to the set of NP ratios;
determining (903), by the computing device (202) and for at least one NP ratio of the set of NP ratios, optimized cell data by:
determining (904), by the computing device (202), two of a modified anode data based on an anode offset value, a modified cathode (412, 612) data based on a cathode offset value (424, 624), and a modified full-cell data (414, 614) based on a full-cell offset value (422, 622);
determining (906), by the computing device (202), delta voltage values (416, 616) based on the two of the modified anode data, the modified cathode data (412, 612), and the modified full-cell data (414, 614), and a remaining of the anode data (406, 606), the cathode data (408, 608), and the full-cell data (414, 614);
determining (908), by the computing device (202), a sum of squares (420, 620) of the delta voltage values (416, 616); and
iteratively modifying (910), by the computing device (202), the two of the anode offset value, the cathode offset value (424, 624) and the full-cell offset value (422, 622) to determine a minimum sum of squares of the delta voltage values (416, 616); and
determining (912), by the computing device (202), the optimal NP ratio for the electrochemical cell (100) from the set of NP ratios based on the optimized cell data for each of the set of NP ratios.

2. The method (900) of claim 1, wherein the optimal NP ratio for the electrochemical cell (100) corresponds to an NP ratio of the set of NP ratios that is selected based on a maximum voltage value (520, 522, 720, 722) and a minimum voltage value (518, 524, 718, 724) of at least one of the anode data (406, 606) or the modified anode data, and the cathode data (408, 608) or the modified cathode data (412, 612) for each NP ratio of the set of NP ratios.

3. The method (900) of claim 2, wherein the NP ratio is selected corresponding to which the maximum voltage value (720, 722) and the minimum voltage value (718, 724) are within respective predefined threshold values.

4. The method (900) of claim 1, wherein the minimum sum of squares of the delta voltage values (416, 616) is determined for at least one of a charge cycle of the electrochemical cell (100) or a discharge cycle of the electrochemical cell (100).

5. The method (900) of claim 1, wherein each of the delta voltage values (416, 616) is a difference between a full-cell voltage value (404B, 604B) at a given capacity and a difference between a cathode voltage value (408B, 608B) and an anode voltage value (406B, 606B) at the given capacity.

6. A system (200) for determining an optimal NP ratio for an electrochemical cell (100), the system (200) comprising:
at least one processor (204); and
a memory (206) communicatively coupled to the at least one processor (204), wherein the memory (206) stores processor-executable instructions, which, on execution, causes the at least one processor (204) to:
receive (902) cell data (402, 602) for the electrochemical cell (100) and for each of a set of NP ratios, wherein the cell data (402, 602) comprises cathode data (408, 608), anode data (406, 606), and full-cell data (404, 604), wherein each of the cathode data (408, 608), the anode data (406, 606), and the full-cell data (404, 604) is capacity-voltage data comprising capacity values for different voltage values;
determine (903), for at least one NP ratio of the set of NP ratios, optimized cell data by:
determining (904) two of a modified anode data based on an anode offset value, a modified cathode data (412, 612) based on a cathode offset value (424, 624), and a modified full-cell data (414, 614) based on a full-cell offset value (422, 622);
determining (906) the delta voltage values (416, 616) based on the two of the modified anode data, the modified cathode data (412, 612), and the modified full-cell data (414, 614), and a remaining of the anode data (406, 606), the cathode data (408, 608), and the full-cell data (414, 614);
determining (908) a sum of square (420, 620) of the delta voltage values (416, 616); and
iteratively modifying (910) the two of the anode offset value, the cathode offset value (424, 624) and the full-cell offset value (422, 622) to determine a minimum sum of square of the delta voltage values (416, 616); and
determine (912) the optimal NP ratio for the electrochemical cell (100) from the set of NP ratios based on the optimized cell data for each of the set of NP ratios.

7. The system (200) of claim 6, wherein the system (200) employs an analysis tool or a simulation tool to perform the iterative modification.

8. The system (200) of claim 6, wherein the optimal NP ratio for the electrochemical cell (100) is determined based on a selected NP ratio, and wherein the selected NP ratio corresponds to an NP ratio of the set of NP ratios based on a maximum voltage value (720, 722) and a minimum voltage value (718, 724) of at least one of the anode data (406, 606) or the modified anode data, and the cathode data (408, 608) or the modified cathode data (412, 612).

9. The system (200) of claim 8, wherein the optimal NP ratio for the electrochemical cell (100) is determined based on a selected NP ratio, and wherein the selected NP ratio corresponds to the NP ratio of the set of NP ratios for which the maximum voltage value (718, 724) and the minimum voltage value (718, 724) are within respective predefined threshold values.

10. An electrochemical cell (100), comprising:
an anode (102), a cathode (104) and an electrolyte (106) disposed between the anode (102) and the cathode (104), wherein an optimal NP ratio of the electrochemical cell (100) is determined by a computing device (202) based on:
determination of optimized cell data for each NP ratio of a set of NP ratios based on cell data (402, 602) for the electrochemical cell (100) received for each NP ratio of the set of NP ratios, wherein the cell data (402, 602) comprises cathode data (408, 608), anode data (406, 606), and full-cell data (404, 604), and wherein each of the cathode data (408, 608), the anode data (406, 606), and the full-cell data (404, 604) is capacity-voltage data comprising capacity values for different voltage values,
wherein the optimized cell data for at least one NP ratio of the set of NP ratios is determined based on:
determination of two of a modified anode data based on an anode offset value, a modified cathode data (412, 612) based on a cathode offset value (424, 624), and a modified full-cell data (414, 614) based on a full-cell offset value (422, 622);
determination of the delta voltage values (416, 616) based on the two of the modified anode data, the modified cathode data (412, 612), and the modified full-cell data (414, 614), and a remaining of the anode data (406, 606), the cathode data (408, 608), and the full-cell data (404, 604);
determination of a sum of squares (420, 620) of the delta voltage values (416, 616); and
iterative modification of two of the anode offset value, the cathode offset value (424, 624) and the full-cell offset value (422, 622) to determine a minimum sum of squares of the delta voltage values (416, 616).