A method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit satellites

Abstract

This disclosure relates to a method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit (LEO) satellites. The method includes: analyzing actual on-orbit data during the use of the zinc-nickel battery and combining this with test data from the battery's development process to obtain characteristic quantities related to the battery's lifespan; fitting the relationship between these characteristic quantities and the battery's lifespan based on the test data, and constructing a battery lifespan model; obtaining a set of constants relating the characteristic quantities to the battery's lifespan based on the actual on-orbit data and the relationship between these characteristic quantities and the battery's lifespan; and obtaining the remaining lifespan of the zinc-nickel battery based on the battery lifespan model and the set of constants. This disclosure provides a nonlinear function description method that utilizes actual on-orbit data and test data to obtain the characteristic quantities of the zinc-nickel battery and their relationship to its lifespan, providing support for subsequent on-orbit management and risk analysis of zinc-nickel batteries for LEO satellites.

Description

Technical Field

[0001] This disclosure relates to the field of aerospace measurement and control technology, and in particular to a method for predicting the on-orbit lifespan of zinc-nickel batteries for low-orbit satellites. Background Technology

[0002] The power system is one of the key subsystems of a satellite system, undertaking the important task of powering other subsystems and the payload. Batteries are a critical product determining the satellite's lifespan, and their development is characterized by small prototypes and high lifespan requirements. With the increasing lifespan requirements for low-Earth orbit satellites year by year, the demands on the lifespan and reliability of these products are becoming increasingly stringent, making lifespan verification and on-orbit lifespan prediction increasingly difficult.

[0003] Generally, satellite batteries are long-life products, but their lifespan decreases with increasing charge-discharge cycles. The reasons for this include: natural degradation of the battery itself, such as the dissolution of the positive electrode material, self-discharge, and the formation of interfacial films; unexpected impacts from complex external environments, such as damage caused by solar ion storms and cosmic rays; cascading effects from malfunctions in other subsystems; and human error. It can be seen that the charging and discharging process of satellite batteries is not merely a simple energy storage device, but an electrochemical process closely related to changes in temperature and other factors. This poses a significant obstacle to predicting the lifespan of satellite batteries.

[0004] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0005] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0006] The purpose of this disclosure is to provide a method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit satellites, thereby overcoming, at least to some extent, one or more problems caused by limitations and defects in related technologies.

[0007] According to embodiments of this disclosure, a method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit satellites is provided, comprising:

[0008] By analyzing the actual on-orbit data during the use of the zinc-nickel battery and combining it with the test data during the development of the zinc-nickel battery, characteristic quantities related to the lifespan of the zinc-nickel battery were obtained.

[0009] Based on the test data, the relationship between the feature quantity and the lifespan of the zinc-nickel battery is fitted, and a battery lifespan model is constructed.

[0010] Based on the actual on-orbit data, the relationship between the characteristic quantities and the lifespan of the zinc-nickel battery, a set of constants relating the characteristic quantities and the lifespan of the zinc-nickel battery is obtained.

[0011] The remaining lifespan of the zinc-nickel battery is obtained based on the battery life model and the set of relational constants.

[0012] In one embodiment of this disclosure, the feature quantity includes:

[0013] The battery temperature and depth of discharge of the zinc-nickel battery.

[0014] In one embodiment of this disclosure, the relationship between the battery temperature and the lifespan of the zinc-nickel battery is as follows:

[0015] At a constant voltage, the lifespan of the zinc-nickel battery is reduced by 50% for every 10°C increase in battery temperature.

[0016] In one embodiment of this disclosure, the relationship between the depth of discharge and the lifespan of the zinc-nickel battery is as follows:

[0017] At a constant temperature, the lifespan of the zinc-nickel battery is an inverse function of the depth of discharge.

[0018] In one embodiment of this disclosure, the formula for the depth of discharge is:

[0019] DOD = Battery pack discharge capacity in ampere-hours after full charge / Rated ampere-hour capacity (1)

[0020] Where DOD stands for Depth of Discharge.

[0021] In one embodiment of this disclosure, the process of obtaining the remaining life of the zinc-nickel battery based on the battery life model and the set of relational constants includes:

[0022] Substituting the set of relational constants into the battery life model, we obtain the average number of cycles before the first failure of the zinc-nickel battery, which is the remaining number of charge-discharge cycles of the zinc-nickel battery.

[0023] Based on the actual on-orbit data, the average number of cycles per year for the zinc-nickel battery is obtained;

[0024] The remaining lifespan of the zinc-nickel battery is obtained based on the average number of cycles before the first failure and the average number of cycles per year.

[0025] The relation constant group includes a first relation constant, a second relation constant, and a third relation constant.

[0026] In one embodiment of this disclosure, the battery life model, i.e., the formula for the average number of cycles before the first failure, is:

[0027]

[0028] Where L is the average number of cycles before the first failure, T is the battery temperature, D is the abbreviation for DOD (depth of discharge), C1 is the first constant relating the characteristic quantity to the life of the zinc-nickel battery, C2 is the second constant relating the characteristic quantity to the life of the zinc-nickel battery, C3 is the third constant relating the characteristic quantity to the life of the zinc-nickel battery, E(D) is the average depth of discharge, and E(T) is the average temperature.

[0029] In one embodiment of this disclosure, the first relational constant is a fixed value.

[0030] In one embodiment of this disclosure, the formula for the average depth of discharge is:

[0031]

[0032] Where t1 is the start time of a deep discharge and t2 is the end time of the deep discharge.

[0033] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects:

[0034] In the embodiments of this disclosure, a nonlinear function description method is provided through the above-described method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit satellites. This method utilizes actual on-orbit data and test data to obtain the characteristic quantities of zinc-nickel batteries and the relationship between these characteristic quantities and the lifespan of the zinc-nickel batteries, thus providing support for subsequent on-orbit management and risk analysis of zinc-nickel batteries for low-Earth orbit satellites. Attached Figure Description

[0035] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0036] Figure 1 This diagram illustrates the steps of a method for predicting the on-orbit lifespan of a low-Earth orbit satellite zinc-nickel battery in an exemplary embodiment of this disclosure.

[0037] Figure 2 This diagram shows the result (two years) of the discharge capacity parameters of a satellite's zinc-nickel battery after removing jump points, in an exemplary embodiment of this disclosure.

[0038] Figure 3This diagram illustrates the sampling results of a low-orbit satellite zinc-nickel battery at a certain temperature in an exemplary embodiment of this disclosure. Detailed Implementation

[0039] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0040] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0041] This example implementation provides a method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit satellites. (Reference) Figure 1 As shown, the method may include steps S101 to S104.

[0042] Step S101: By analyzing the actual on-orbit data during the use of the zinc-nickel battery and combining it with the test data during the development of the zinc-nickel battery, the characteristic quantities related to the lifespan of the zinc-nickel battery are obtained.

[0043] Step S102: Based on the test data, fit the relationship between the feature quantity and the lifespan of the zinc-nickel battery, and construct a battery lifespan model;

[0044] Step S103: Based on the actual on-orbit data, the relationship between the characteristic quantity and the lifespan of the zinc-nickel battery, obtain a set of constants relating the characteristic quantity and the lifespan of the zinc-nickel battery;

[0045] Step S104: Based on the battery life model and the set of relational constants, obtain the remaining life of the zinc-nickel battery.

[0046] Specifically, in step S101, the design life of the battery refers to the theoretical value under a specific condition (requiring an ambient temperature of 20-25℃ and a total discharge amount not exceeding the rated capacity). However, the actual life of the battery is closely related to the usage conditions. Factors such as ambient temperature, depth of discharge, and charge / discharge frequency all have varying degrees of influence on the actual life of the battery, and can even be quite serious.

[0047] During long-term use, zinc-nickel batteries undergo continuous electrochemical reactions within individual cells. These reactions lead to phenomena such as zinc migration, nickel electrode expansion and separator oxidation and degradation, and reduced electrochemical activity of electrode active materials. These phenomena result in increased charging voltage, decreased discharging voltage, and reduced capacity of the zinc-nickel battery, thus degrading its performance. In severe cases, the zinc-nickel battery pack may completely lose its ability to function.

[0048] By reviewing a large amount of relevant literature and conducting failure mechanism analysis on zinc-nickel batteries, and combining test data and actual on-orbit data, the characteristic quantities affecting the service life of zinc-nickel batteries were analyzed and obtained. Among them, the characteristic quantities affecting the service life of zinc-nickel batteries analyzed in this disclosure are battery temperature and depth of discharge.

[0049] Step S102 fits the relationship between the characteristic quantity and the lifespan of the zinc-nickel battery, and a battery lifespan model is constructed.

[0050] An analysis of the impact of battery temperature on the lifespan of nickel-zinc batteries reveals that high temperatures are the primary reason why the actual lifespan of nickel-zinc batteries fails to meet their design lifespan. For every 10°C increase in battery temperature, the charging current accepted at a constant voltage doubles, shortening the battery's lifespan due to the increased cumulative overcharge. At high temperatures, the increased float current accelerates the accumulation of overcharge, as well as grid corrosion and hydrogen generation and escape, leading to faster water loss and thus shortening the battery's lifespan. Therefore, it can be concluded that for every 10°C increase in ambient temperature, under a constant float voltage, the lifespan of a nickel-zinc battery will be shortened by 50%. Satellite battery pack measurements typically include battery temperature parameters, allowing for the extraction of temperature data over a specific time period to reflect the battery's temperature characteristics.

[0051] This paper analyzes the impact of battery temperature on the lifespan of nickel-zinc batteries. The depth of discharge (DDC) is measured by the ratio of the actual discharge capacity to the rated discharge capacity at the same discharge rate. The lifespan of nickel-zinc batteries is closely related to their DDC. With a DDC of 20%, a nickel-zinc battery can last for 2000 cycles; with a DDC of 100%, the cycle life is only 350 cycles. Therefore, deep discharge should be avoided as much as possible during use. During deep discharge of valve-regulated lead-acid (VRA) battery banks, the voltage and capacity of individual cells may become unbalanced. To eliminate this imbalance, the charging voltage must be appropriately increased for equalization charging. Equalization charging typically uses a "constant voltage, current-limited" method. This charging method and parameters are mainly determined by the characteristics of the battery. Furthermore, after deep discharge, "lagging cells" will appear in the battery bank. The more severe the over-discharge, the less likely the "lagging cells" are to recover during the next charge, which will seriously affect the battery's lifespan. To avoid over-discharge, the battery's termination voltage must be precisely set according to the discharge rate.

[0052] As mentioned earlier, the cycle life of a battery pack is mainly related to the depth of discharge and battery temperature. Cycle life can be described by setting the number of charge-discharge cycles as the independent variable and the depth of discharge and temperature as dependent variables. When constructing a battery life model, it is necessary to first choose a mathematical expression to accurately express the relationship between the variables, and then select a statistical distribution that best matches the test data. The physical characteristics of the battery are also factors to be considered when selecting the model; for example, an increase in the depth of discharge and an increase in temperature can reduce the cycle life of the battery.

[0053] Therefore, the identified characteristic quantities of the battery are the depth of discharge and the battery temperature. The depth of discharge (DOD) can be expressed as:

[0054] DOD = Battery pack discharge capacity in ampere-hours after full charge / Rated ampere-hour capacity (1)

[0055] As shown in formula (1), the depth of discharge can be expressed as the ampere-hour capacity discharged by the battery pack after full charging / rated ampere-hour capacity. After satellite launch, if no battery pack malfunctions, the rated ampere-hour capacity of the battery pack is fixed. The ampere-hour capacity discharged by the battery pack after full charging also has a measurable parameter, namely the discharged capacity of the battery pack. Therefore, the depth of discharge can be obtained by dividing the discharged capacity parameter data after full charging by the rated ampere-hour capacity.

[0056] Furthermore, for batteries, cycle life can be described by setting the number of charge-discharge cycles as the independent variable and the depth of discharge and battery temperature as dependent variables. When constructing a battery life model, a mathematical expression must first be chosen to accurately represent the relationship between the variables, and then one that best matches the statistical distribution of the test data must be selected. Other physical characteristics are also factors to consider when choosing a model; for example, increased depth of discharge and higher temperature can reduce the battery's cycle life. Various relationship types are commonly used to analyze cycle life test data. Among these, more than one, such as exponential relationships, inverse power relationships, and the Arrhenius equation, can agree with the test data. The Arrhenius equation, in particular, agrees best with the cycle life test data, indicating that electrochemical degradation is the fundamental cause limiting operational life. That is:

[0057]

[0058] Where L is the average number of cycles before the first failure, T is the battery temperature, D is the depth of discharge, and C1, C2, and C3 are constants determined by fitting multi-level decay curves. Specifically, C1 is the first constant relating the characteristic quantity to the lifespan of the zinc-nickel battery, C2 is the second constant relating the characteristic quantity to the lifespan of the zinc-nickel battery, and C3 is the third constant relating the characteristic quantity to the lifespan of the zinc-nickel battery.

[0059] In step S103, in order to determine the failure model of a zinc-nickel battery for a certain satellite, it is necessary to obtain the parameter values ​​of C1, C2, and C3. For this purpose, the test data of the zinc-nickel battery and some basic laws of zinc-nickel battery life decay are used to fit the curve.

[0060] Generally speaking, the C1 parameter needs to be obtained from the battery's experimental data, that is, from the test data.

[0061] At a given battery temperature, battery life is an inverse function of the depth of discharge. Taking a nickel-metal hydride (NiMH) battery as an example, if the lifespan of a NiMH battery at 50% depth of discharge is 100 units, then the lifespan of a NiMH battery at 25% depth of discharge will be approximately 200 units; that is:

[0062]

[0063]

[0064] but:

[0065] It can be known that:

[0066] Finally, we get C3 = 4ln2.

[0067] Under normal circumstances (around 10°C), for every 10°C increase in ambient temperature, the battery life will be shortened by 50% under constant float voltage charging; that is:

[0068]

[0069]

[0070] but:

[0071] When T is 10℃:

[0072] Finally, we get C2 = -2ln2.

[0073] In step S104, for the battery life model, the formula (4) described above mainly applies to the case where the discharge depth is fixed. In practical applications, especially for low-Earth orbit satellites, the discharge depth is different almost every orbit. Therefore, in order to meet the needs of practical applications, formula (4) needs to be improved. For low-Earth orbit satellites, as long as there are no sudden problems, it can be assumed that their discharge depth fluctuates within a certain range. To more accurately simulate the discharge depth, the average discharge depth and the average temperature are introduced:

[0074]

[0075] Where E(D) is the average depth of discharge.

[0076] After obtaining the average number of cycles L before the first failure of the zinc-nickel battery using formula (2), which is the remaining charge and discharge cycle of the zinc-nickel battery, and then obtaining the average number of cycles per year of the zinc-nickel battery based on the actual data in orbit, the remaining lifespan of the zinc-nickel battery can be obtained.

[0077] Based on the above-mentioned method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit (LEO) satellites, a nonlinear function description method is provided. This method uses actual on-orbit data and test data to obtain the characteristic quantities of the zinc-nickel batteries and the relationship between these characteristic quantities and the battery lifespan, providing support for subsequent on-orbit management and risk analysis of LEO satellite zinc-nickel batteries.

[0078] In one embodiment, the characteristic quantities include the battery temperature and depth of discharge of the zinc-nickel battery. Specifically, by reviewing a large amount of relevant literature and conducting failure mechanism analysis on zinc-nickel batteries, and combining test data and actual on-orbit data, characteristic quantities affecting the service life of zinc-nickel batteries were analyzed and obtained. Among them, the characteristic quantities affecting the service life of zinc-nickel batteries analyzed in this disclosure are battery temperature and depth of discharge.

[0079] In one embodiment, the relationship between battery temperature and the lifespan of the zinc-nickel battery is as follows: at a constant voltage, for every 10°C increase in battery temperature, the lifespan of the zinc-nickel battery is shortened by 50%. Specifically, at high temperatures, the increase in float charge current accelerates the accumulation of charge, and also accelerates grid corrosion and hydrogen generation and escape, thus accelerating water loss from the zinc-nickel battery and shortening its lifespan. Specifically, for every 10°C increase in ambient temperature, the lifespan of the zinc-nickel battery will be shortened by 50% under a constant float charge voltage.

[0080] In one embodiment, the relationship between the depth of discharge and the lifespan of the zinc-nickel battery is such that, at a constant temperature, the lifespan of the zinc-nickel battery is an inverse function of the depth of discharge.

[0081] Specifically, during deep discharge of valve-regulated lead-acid (VRA) battery packs, the voltage and capacity of individual cells may become unbalanced. To eliminate this imbalance, the charging voltage must be appropriately increased for equalization charging. Equalization charging typically employs a "constant voltage, current-limiting" method. This charging method and parameters are primarily determined by the battery's characteristics. At a depth of discharge of 20%, a zinc-nickel battery can have a cycle life of up to 2000 cycles; at a depth of discharge of 100%, the cycle life is only 350 cycles. Therefore, deep discharge should be avoided as much as possible during use.

[0082] In one embodiment, the formula for the depth of discharge is:

[0083] DOD = Battery pack discharge capacity in ampere-hours after full charge / Rated ampere-hour capacity (1)

[0084] Here, DOD stands for Depth of Discharge. Specifically, the depth of discharge can be expressed as the ampere-hour capacity discharged by the battery pack after a full charge divided by its rated ampere-hour capacity. After satellite launch, assuming no battery pack malfunctions, the rated ampere-hour capacity of the battery pack is fixed. The ampere-hour capacity discharged by the battery pack after a full charge is also a measurable parameter in orbit, i.e., the battery pack's discharged capacity. Therefore, the depth of discharge can be obtained by dividing the discharged capacity after a full charge by the rated ampere-hour capacity.

[0085] In one embodiment, the process of obtaining the remaining lifespan of the zinc-nickel battery based on the battery lifespan model and the set of relational constants includes: substituting the set of relational constants into the battery lifespan model to obtain the average number of cycles before the first failure of the zinc-nickel battery, i.e., the remaining charge-discharge cycles of the zinc-nickel battery; obtaining the average number of cycles per year of the zinc-nickel battery based on the actual on-orbit data; and obtaining the remaining lifespan of the zinc-nickel battery based on the average number of cycles before the first failure and the average number of cycles per year; wherein the set of relational constants includes a first relational constant, a second relational constant, and a third relational constant.

[0086] Specifically, the depth of discharge and battery temperature are calculated separately, and then these are input into the battery life model to obtain the remaining number of charge-discharge cycles of the battery, thereby obtaining the remaining life of the battery.

[0087] In one embodiment, the battery life model, i.e., the formula for the average number of cycles before the first failure, is:

[0088]

[0089] Where L is the average number of cycles before the first failure, T is the battery temperature, D is the abbreviation for DOD (depth of discharge), C1 is the first constant relating the characteristic quantity to the lifespan of the zinc-nickel battery, C2 is the second constant relating the characteristic quantity to the lifespan of the zinc-nickel battery, C3 is the third constant relating the characteristic quantity to the lifespan of the zinc-nickel battery, E(D) is the average depth of discharge, and E(T) is the average temperature. Specifically, increased depth of discharge and higher temperature can reduce the cycle life of the battery. Various relationship types commonly used to analyze lifespan test data can express this relationship. Among these relationship types, such as exponential relationships, inverse power relationships, and the Arrhenius formula, more than one can agree well with the test data. The Arrhenius formula agrees best with the lifespan test data, indicating that chemical degradation is the fundamental cause limiting the working life.

[0090] E(D) represents the average depth of discharge. Specifically, for low-Earth orbit satellites, as long as no sudden problems occur, the depth of discharge can be considered to fluctuate within a certain range. To more accurately simulate the depth of discharge, the average value of the depth of discharge and the average value of the temperature are introduced to obtain formula (2). After obtaining the average number of cycles L before the first failure of the zinc-nickel battery through formula (2), i.e. the remaining charge and discharge cycles of the zinc-nickel battery, the average number of cycles per year of the zinc-nickel battery can be obtained based on the actual data in orbit, and thus the remaining lifespan of the zinc-nickel battery can be obtained.

[0091] In one embodiment, the first relational constant is a fixed value. Specifically, the C1 parameter is typically obtained from experimental data of the battery, i.e., from test data.

[0092] In one embodiment, the formula for the average depth of discharge is:

[0093]

[0094] Where t1 is the start time of a deep discharge and t2 is the end time of the deep discharge.

[0095] Specifically, in the process of calculating the average discharge depth, for each high-depth discharge peak, a polynomial fitting method can be used to obtain the fitting relationship curve f(D) curve of the high-depth discharge peak. For the f(D) curve, the mean value is calculated by formula (3).

[0096] The following simulation examples further illustrate this embodiment.

[0097] Discharge depth calculation:

[0098] The discharge parameters of a certain satellite from 00:0:00 on January 1, 2013 to 00:0:00 on January 1, 2015 were normalized after removing jump points. Figure 2 .

[0099] The satellite's orbital period is approximately 107 minutes, and the data from the two years totals about 9,825 orbits.

[0100] from Figure 2 It can be seen that the measured values ​​of the discharge capacity parameter of a certain satellite over two years contain 9 high-depth discharge peaks, with low-depth discharge peaks in the middle. Given the large difference in mean and variance between the two sets of data, and the fact that the discharge depth of the low-depth discharge peak is less than 1%, only the mean of the high-depth discharge peak is calculated when calculating the mean discharge depth. If the discharge depth of the low-depth discharge peak is not calculated, then the corresponding time needs to be subtracted when calculating the cycle period. According to the calculation, the satellite had approximately 941 non-discharge cycles in 2013 (including low-depth discharge peaks), and approximately 843 non-discharge cycles in 2014 (same as above). For each high-depth discharge peak, a polynomial fitting method can be used to obtain the fitting relationship curve f(D) curve of the high-depth discharge peak. For the f(D) curve, the mean is calculated using formula (3).

[0101] The fitting results are as follows:

[0102] The fitting result of the first high-depth discharge peak is as follows Figure 2 The fitting results for the first high-depth discharge peak and the second high-depth discharge peak are as follows: Figure 2 The second high-depth discharge peak in the middle.

[0103] According to formula (2), the average discharge depth of the first high-depth discharge peak is 14.32%; the average discharge depth of the second high-depth discharge peak is 14.25%.

[0104] The fitting results for the third high-depth discharge peak are as follows: Figure 2 The fitting results for the third and fourth high-depth discharge peaks are as follows: Figure 2 The fourth high-depth discharge peak in the middle.

[0105] According to formula (2), the average discharge depth of the third high-depth discharge peak is 13.5%; the average discharge depth of the fourth high-depth discharge peak is 13.15%.

[0106] The fitting results for the fifth high-depth discharge peak are as follows: Figure 2 The fitting results for the fifth and sixth high-depth discharge peaks are as follows: Figure 2 The 6th high-depth discharge peak in the middle.

[0107] According to formula (2), the average discharge depth of the fifth high-depth discharge peak is 14.36%; the average discharge depth of the sixth high-depth discharge peak is 13.64%.

[0108] The fitting results for the seventh high-depth discharge peak are as follows: Figure 2 The fitting results for the 7th and 8th high-depth discharge peaks are as follows: Figure 2 The 8th high-depth discharge peak in the middle.

[0109] According to formula (2), the average discharge depth of the seventh high-depth discharge peak is 13.54%; the average discharge depth of the eighth high-depth discharge peak is 13.32%.

[0110] The fitting results for the ninth high-depth discharge peak are as follows: Figure 2 The 9th high-depth discharge peak in the middle.

[0111] According to formula (2), the average depth of discharge is 14.43%.

[0112] Based on the above calculations, the discharge depths of the nine high-depth discharge peaks are: 14.32%, 14.25%, 13.5%, 13.15%, 14.36%, 13.64%, 13.54%, 13.32%, and 14.43%. The average discharge depth in 2013 was 13.81% (the first four peaks were in 2013), and the average discharge depth in 2014 was 13.83%.

[0113] Battery temperature calculation:

[0114] After normalizing a certain temperature parameter of a battery from a satellite between 00:0:00 on January 1, 2013 and 00:0:00 on January 1, 2015, the following data is obtained: Figure 3 As shown.

[0115] The average battery temperature at the coordinate point corresponding to the discharge peak was taken as 8.83.

[0116] Calculation of charge and discharge cycles

[0117] According to formula (4), the average number of cycles L before the first failure of the zinc-nickel battery is between 62,000 and 59,800.

[0118] Based on the data above, if the satellite's orbital period is 107 minutes, then the satellite has approximately 4912 cycles per year. Furthermore, based on the number of battery cycles over two years, it can be determined that the battery cycles approximately 4020 times over two years with an average depth of discharge between 13.15% and 14.43%. Therefore, at a temperature of 10°C and a 30% depth of discharge, the minimum lifespan of a zinc-nickel low-Earth orbit satellite battery, capable of approximately 40,000 cycles, is calculated to be between 14.63 and 15.16 years. This is essentially close to the design lifespan given by the developer.

[0119] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0120] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit satellites, characterized in that, The method includes: By analyzing the actual on-orbit data during the use of the zinc-nickel battery and combining it with the test data during the development of the zinc-nickel battery, characteristic quantities related to the lifespan of the zinc-nickel battery were obtained. Based on the test data, the relationship between the feature quantity and the lifespan of the zinc-nickel battery is fitted, and a battery lifespan model is constructed; wherein, the feature quantity includes: the battery temperature and depth of discharge of the zinc-nickel battery; Based on the actual on-orbit data, the relationship between the characteristic quantities and the lifespan of the zinc-nickel battery, a set of constants relating the characteristic quantities and the lifespan of the zinc-nickel battery is obtained. Based on the battery life model and the set of relational constants, the remaining life of the zinc-nickel battery is obtained; The process of obtaining the remaining lifespan of the zinc-nickel battery based on the battery lifespan model and the set of relational constants includes: Substituting the set of relational constants into the battery life model, we obtain the average number of cycles before the first failure of the zinc-nickel battery, which is the remaining number of charge-discharge cycles of the zinc-nickel battery. Based on the actual on-orbit data, the average number of cycles per year for the zinc-nickel battery is obtained; The remaining lifespan of the zinc-nickel battery is obtained based on the average number of cycles before the first failure and the average number of cycles per year. The relation constant group includes a first relation constant, a second relation constant, and a third relation constant; The battery life model, i.e., the formula for the average number of cycles before the first failure, is as follows: Where L is the average number of cycles before the first failure, T is the battery temperature, D is the abbreviation for DOD (depth of discharge), C1 is the first constant relating the characteristic quantity to the life of the zinc-nickel battery, C2 is the second constant relating the characteristic quantity to the life of the zinc-nickel battery, C3 is the third constant relating the characteristic quantity to the life of the zinc-nickel battery, E(D) is the average depth of discharge, and E(T) is the average temperature.

2. The method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit satellites according to claim 1, characterized in that, The relationship between the battery temperature and the lifespan of the zinc-nickel battery is as follows: At a constant voltage, the lifespan of the zinc-nickel battery is reduced by 50% for every 10°C increase in battery temperature.

3. The method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit satellites according to claim 1, characterized in that, The relationship between the depth of discharge and the lifespan of the zinc-nickel battery is as follows: At a constant temperature, the lifespan of the zinc-nickel battery is an inverse function of the depth of discharge.

4. The method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit satellites according to claim 1, characterized in that, The formula for the depth of discharge is: DOD = Battery pack discharge capacity in ampere-hours after full charge / Rated ampere-hour capacity (1) Where DOD stands for Depth of Discharge.

5. The method for predicting the on-orbit lifespan of zinc-nickel batteries for low-Earth orbit satellites according to claim 1, characterized in that, The first relational constant is a fixed value.

6. The method for predicting the on-orbit lifespan of a low-orbit satellite zinc-nickel battery according to claim 5, characterized in that, The formula for the average depth of discharge is: Where t1 is the start time of a deep discharge and t2 is the end time of the deep discharge.

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