CN102928714B

CN102928714B - Moonlet sun array life forecast method based on I-V curve and energy balance

Info

Publication number: CN102928714B
Application number: CN201210432124.8A
Authority: CN
Inventors: 吕琛; 陶来发; 刘红梅; 彭健; 刘一薇; 杨生胜
Original assignee: Beihang University; Lanzhou Institute of Physics of CAST; Aerospace Dongfanghong Satellite Co Ltd
Current assignee: Beihang University; Lanzhou Institute of Physics of CAST; Aerospace Dongfanghong Satellite Co Ltd
Priority date: 2012-11-02
Filing date: 2012-11-02
Publication date: 2014-08-13
Anticipated expiration: 2032-11-02
Also published as: CN102928714A

Abstract

The present invention provides a small satellite solar array life prediction method based on IV curve and energy balance, aiming at the current small satellite solar array life prediction existing damage law space environment influence factors are less, and to a large extent limited to single battery Life prediction cannot solve the problems of solar array overall life prediction and other problems. The present invention is based on space environment simulation test, considering the sun-earth distance factor, orbital shadow time, the angle between the sun's rays and the solar array normal, temperature, solar radiation, etc. The overall life prediction model of solar arrays under the influence of space environmental factors, and then partly solves the life prediction considering the important factors affecting the life of solar arrays and the generality of the overall life prediction applicable to different batches and different models of solar arrays. The IV curve is the current and voltage curve of the solar cell. The invention is based on experiments and has better model versatility and stronger engineering practicability.

Description

A Life Prediction Method of Small Satellite Solar Array Based on I-V Curve and Energy Balance

技术领域 technical field

本发明属于小卫星太阳阵预测技术领域，具体涉及一种基于I-V曲线与能量平衡的小卫星太阳阵寿命预测方法。The invention belongs to the technical field of small satellite solar array prediction, in particular to a small satellite solar array life prediction method based on I-V curve and energy balance.

背景技术 Background technique

小卫星应用于除载人航天外的所有空间领域，包括在遥感、通信、导航、技术验证、空间科学等发挥了重要的作用。电源系统是卫星的关键服务系统，负责产生、存储和为卫星整个寿命期间为整星用电负载提供稳定的不间断的能源，其供电能力、电源品质直接影响卫星的工作状态、可靠性与使用寿命。对电源系统控制的性能、可靠性有很高的要求。Small satellites are used in all space fields except manned spaceflight, including remote sensing, communication, navigation, technology verification, and space science. The power supply system is the key service system of the satellite, which is responsible for generating, storing and providing stable and uninterrupted energy for the entire satellite power load during the entire life of the satellite. Its power supply capacity and power quality directly affect the working status, reliability and use of the satellite. life. There are high requirements on the performance and reliability of the power system control.

由于不同卫星运行轨道有其明显的环境特点，导致不同轨道运行的卫星系统性能退化规律和特征有所区别。小卫星的运行轨道大部分为中低轨道，受复杂空间环境影响，如：太阳压力、电离层、带电粒子等，太阳入射角在一年中的变化范围大，小卫星进出影频繁，高低温交替变换等，太阳阵间歇性工作次数多，工作时间短，工作电流大，高低温冲击剧烈。这些因素不可避免的将对卫星的性能与寿命产生影响。最终在内部和外部因素的综合作用下，导致系统失效。图1给出了，由于小卫星各子系统失效而导致小卫星整体失效所占的比例情况。由此可知，电源系统失效占据大部分比例，且太阳阵失效是电源系统失效的最主要因素。Due to the obvious environmental characteristics of different satellite orbits, the performance degradation laws and characteristics of satellite systems in different orbits are different. Most of the orbits of small satellites are low-to-medium orbits, which are affected by complex space environments, such as: solar pressure, ionosphere, charged particles, etc. The incident angle of the sun varies in a large range throughout the year, and small satellites enter and exit frequently. Alternate transformation, etc., the solar array intermittently works more times, the working time is short, the working current is large, and the impact of high and low temperature is severe. These factors will inevitably have an impact on the performance and life of the satellite. Finally, under the combined action of internal and external factors, the system fails. Figure 1 shows the proportion of the overall failure of the small satellite due to the failure of each subsystem of the small satellite. It can be seen that the failure of the power system accounts for the majority, and the failure of the solar array is the most important factor for the failure of the power system.

然而，由于小卫星属于不可修复产品，且受质量和尺寸的限制，不能采取冗余部件的方法以提高小卫星太阳阵的可靠性，使得小卫星太阳阵寿命预测对于小卫星的设计、生产、使用起着重要指导作用。However, since small satellites are non-repairable products and are limited by quality and size, redundant components cannot be used to improve the reliability of small satellite solar arrays, making the life prediction of small satellite solar arrays very important for the design, production, Use plays an important guiding role.

目前应用于空间环境条件下小卫星太阳阵寿命预测的方法可归纳为：（一）、紫外加速寿命试验法：建立模拟空间环境下的紫外加速寿命试验装置，对太阳电池进行紫外加速寿命试验技术研究，获得太阳电池开路电压随着紫外辐照时间的变化数据。通过试验数据处理，获得太阳电池开路电压随着等效紫外辐照时间的衰减规律，采用加严判据理论，研究紫外辐射对太阳电池的损伤规律，预测紫外辐照环境下的电池寿命；（二）、热应变极值法：以试验测试为基础分析多次热循环后太阳电池板的热应变演变规律，提出以热应变极大值(或残余热应变)作为多层胶接结构的损伤参量,建立预测太阳单体电池结构寿命的数学模型等方法。其中，紫外加速寿命试验法仅仅考虑了紫外这一空间环境条件，且较其它寿命影响因素，紫外的影响相对较弱，单一开展紫外辐射对太阳阵的损伤规律研究不能很好的揭露太阳阵在复杂空间环境条件下的损伤规律；热应变极值法从通过试验建立了单体电池的数据模型，对于经试验测试，且仅考虑单体电池在温度影响下的寿命预测是有效的，对于不同批次、不同型号等太阳单体需要重新建立寿命预测模型，且无法解决太阳阵整体寿命预测问题。The methods currently applied to the life prediction of small satellite solar arrays under space environment conditions can be summarized as follows: (1) Ultraviolet accelerated life test method: establish an ultraviolet accelerated life test device under simulated space environment, and conduct ultraviolet accelerated life test technology on solar cells Research and obtain the change data of the open circuit voltage of the solar cell with the time of ultraviolet irradiation. Through the experimental data processing, the attenuation law of the open circuit voltage of the solar cell with the equivalent ultraviolet irradiation time is obtained, and the stricter criterion theory is used to study the damage law of the ultraviolet radiation to the solar cell and predict the battery life under the ultraviolet irradiation environment; ( 2) Thermal strain extremum method: based on experimental tests, the thermal strain evolution law of solar panels after multiple thermal cycles is analyzed, and the maximum value of thermal strain (or residual thermal strain) is proposed as the damage of the multi-layer bonding structure parameters, establishing a mathematical model for predicting the structural life of solar cells, etc. Among them, the ultraviolet accelerated life test method only considers the space environment condition of ultraviolet, and the influence of ultraviolet is relatively weak compared with other factors affecting the life. The law of damage under complex space environment conditions; the thermal strain extreme value method established the data model of the single battery from the test, which is effective for the life prediction of the single battery after the test and only considers the influence of temperature. Solar cells such as batches and different models need to re-establish life prediction models, and the problem of overall life prediction of solar arrays cannot be solved.

发明内容 Contents of the invention

针对当前小卫星太阳阵寿命预测存在的问题，本发明提出一种基于I-V曲线与能量平衡的小卫星太阳阵寿命预测方法，在空间环境模拟试验的基础上，构建在考虑日地距离因子、轨道地影时间、太阳光线与太阳阵法线的夹角、温度、太阳辐射等重要空间环境因素影响下的太阳阵整体寿命预测模型，进而部分解决考虑太阳阵重要寿命影响因素的寿命预测及太阳阵整体寿命预测的通用性问题。所述I-V曲线为太阳单体电池的电流与电压曲线。Aiming at the problems existing in the life prediction of the current small satellite solar array, the present invention proposes a small satellite solar array life prediction method based on the I-V curve and energy balance. The overall life prediction model of the solar array under the influence of important space environmental factors such as the earth's shadow time, the angle between the sun's rays and the normal of the solar array, temperature, and solar radiation, and then partially solve the life prediction and solar array The general problem of overall lifespan prediction. The I-V curve is the current and voltage curve of the solar cell.

本发明采用的技术方案为：一种基于I-V曲线与能量平衡的小卫星太阳阵寿命预测方法，该方法通过如下步骤实现：The technical solution adopted in the present invention is: a method for predicting the life of a small satellite solar array based on the I-V curve and energy balance, which is realized through the following steps:

步骤一、日地距离因子、轨道地影时间、太阳光线与太阳阵法线的夹角确定；Step 1. Determine the distance factor between the sun and the earth, the orbital earth shadow time, the angle between the sun's rays and the sun array normal;

根据轨道高度、降交点地方时和预测起始时间，计算每天的日地距离因子、轨道周期Te、轨道地影时间、每轨太阳光线与太阳阵法线的夹角的变化规律，得到随时间变化的定量数据，用于后续的太阳阵I-V曲线和能量平衡分析；According to the orbital altitude, the local time of the descending node, and the predicted start time, calculate the daily sun-earth distance factor, orbital period Te, orbital earth shadow time, and the angle between the sun's rays and the sun array normal in each orbit. Quantitative data of changes for subsequent solar array I-V curve and energy balance analysis;

步骤二、太阳阵I-V曲线模型确定；Step 2, determining the solar array I-V curve model;

根据太阳阵特性构建太阳阵计算模型，同时考虑太阳入射角、辐照衰减、日地因子、损失因子因素的影响，计算不同季节、不同轨道条件和不同工况下太阳阵输出电压、输出电流，以表征太阳阵输出功率实时及长期变化情况；According to the characteristics of the solar array, the calculation model of the solar array is constructed, and the influence of the sun incident angle, radiation attenuation, sun-earth factor, and loss factor is considered at the same time, and the output voltage and output current of the solar array are calculated under different seasons, different orbital conditions and different working conditions. To characterize the real-time and long-term changes in the output power of the solar array;

以标准状态的I-V曲线特征点为参数，考虑多种环境因素对太阳阵寿命的影响，计算太阳阵的输出特性；利用公式（Equ.1）太阳阵I-V曲线的计算机解析模型，得到不同条件下的太阳阵的I-V特性曲线；该模型在光照强度小于2个太阳常数时，有很高的精确性；太阳同步轨道小卫星的光照情况满足这一条件：Taking the characteristic points of the I-V curve of the standard state as parameters, and considering the influence of various environmental factors on the life of the solar array, the output characteristics of the solar array are calculated; using the formula (Equ.1) computer analytical model of the I-V curve of the solar array, the The I-V characteristic curve of the solar array; this model has high accuracy when the illumination intensity is less than 2 solar constants; the illumination conditions of small satellites in sun-synchronous orbit meet this condition:

$\{\begin{matrix} I I = = {Isc Isc}^{' '} ((11 - - {C C}_{11} \times \times {{exp exp [[V V / / (({C C}_{22} \times \times {V V}_{ov ov}' '))]] - - 11}})) \\ {C C}_{11} = = [[11 - - (({I I}_{mp mp}^{' '} / / {Isc Isc}^{' '}))]] \times \times {{exp exp [[- - {V V}_{mp mp}^{' '} / / (({C C}_{22} \times \times {V V}_{ov ov}^{' '}))]]}} \\ {C C}_{22} = = [[(({V V}_{mp mp}^{' '} / / {V V}_{ov ov}^{' '})) - - 11]] / / 11 n no ((11 - - {I I}_{mp mp}^{' '} / / {Isc Isc}^{' '})) \end{matrix} - - - - - - ((Equ Equivalent . . 11))$

式中：In the formula:

I——输出电流，单位为A；I——output current, the unit is A;

Isc'——太阳阵短路电流，典型参数或实测值，单位为A；Isc'——solar array short-circuit current, typical parameter or measured value, unit is A;

C₁——公式系数1；C ₁ —— formula coefficient 1;

V——太阳阵输出电压，单位为V；V——the output voltage of solar array, the unit is V;

C₂——公式系数2；C ₂ —— formula coefficient 2;

V_ov'——太阳阵开路电压，典型参数或实测值，单位为V；V _ov '—— solar array open circuit voltage, typical parameter or measured value, unit is V;

I_mp'——太阳阵最佳工作点输出电流，典型参数或实测值，单位为A；I _mp '——the output current of the best operating point of the solar array, typical parameters or measured values, in A;

V_mp'——太阳阵最佳工作点输出电压，典型参数或实测值，单位为V；V _mp '——the output voltage of the best working point of the solar array, typical parameters or measured values, the unit is V;

太阳阵开路电压和最佳工作点输出电压计算模型如下：The calculation model of the solar array open circuit voltage and the output voltage of the optimal operating point is as follows:

$\{\begin{matrix} {V V}_{ov ov}' ' = = (({V V}_{ov ov} + + {β β}_{VBOL VBOL} \times \times ((T T - - 2525)))) \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times {N N}_{s the s} \times \times {K K}_{VRAD VRAD} \\ {V V}_{mp mp}' ' = = (({V V}_{mp mp} + + {β β}_{VBOL VBOL} \times \times ((T T - - 2525)))) \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times {N N}_{s the s} \times \times {K K}_{VRAD VRAD} \end{matrix} - - - - - - ((Equ Equivalent . . 22))$

式中：In the formula:

V_ov——单体太阳电池开路电压，单位为V；V _ov - the open circuit voltage of a single solar cell, in V;

V_mp——单体太阳电池最佳工作点电压，单位为V；V _mp - the best operating point voltage of a single solar cell, in V;

β_VBOL——单体太阳电池寿命初期电压温度系数，单位为V/℃；β _VBOL ——Voltage temperature coefficient at the beginning of life of a single solar cell, in V/°C;

K_VRAD——太阳阵开路电压辐照衰降因子；K _VRAD — solar array open circuit voltage radiation attenuation factor;

T——阳阵温度，单位为℃；T——The sun array temperature, the unit is ℃;

太阳阵短路电流和最佳工作点电流计算模型如下：The calculation model of solar array short-circuit current and optimal working point current is as follows:

$\{\begin{matrix} Isc Isc' ' = = ((Isc Isc + + {α α}_{I I} \times \times ((T T - - 2525)))) \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times 0.98 0.98 {\times \times N N}_{p p} \times \times cos cos θ θ ((t t)) \times \times {F f}_{rd rd} \times \times {K K}_{IRAD IRAD} \\ {I I}_{mp mp}' ' = = (({I I}_{mp mp} + + {α α}_{I I} \times \times ((T T - - 2525)))) \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times {N N}_{p p} \times \times cos cos θ θ ((t t)) \times \times {F f}_{rd rd} \times \times {K K}_{IRAD IRAD} \end{matrix} - - - - - - ((Equ Equivalent . . 33))$

I_SC——单体太阳电池短路电流，单位为A；I _SC ——Short-circuit current of single solar cell, unit is A;

I_mp——单体太阳电池最佳工作点电流，单位为A；I _mp - the best working point current of a single solar cell, in A;

α_I—单体太阳电池电流温度系数，单位为A/℃；α _I —the current temperature coefficient of a single solar cell, in A/°C;

θ(t)—— 一圈轨道内太阳光线与太阳阵法线方向的夹角，单位为度；θ(t)——The angle between the sun's rays and the normal direction of the sun array in one orbit, in degrees;

T—太阳阵温度，单位为℃；T—solar array temperature, unit is ℃;

K_IRAD—太阳阵短路电流辐照衰降因子；K _IRAD — solar array short-circuit current radiation attenuation factor;

F_rd——日地距离因子；F _rd ——sun-earth distance factor;

利用“太阳阵开路电压及短路电流辐照衰降因子计算模型”预测LEO轨道辐射环境对卫星太阳电池输出参数衰减的影响，在该模型中Isc即为K_IRAD，Vov即为K_VRAD；Use the "solar array open circuit voltage and short circuit current radiation attenuation factor calculation model" to predict the impact of LEO orbital radiation environment on the output parameter attenuation of satellite solar cells. In this model, Isc is K _IRAD and Vov is K _VRAD ;

A.模型输入参数定义如下：A. The model input parameters are defined as follows:

电池类型：单结GaAs太阳电池；石英玻璃盖片厚度：120μm；轨道高度：300km~3000km；倾角：只针对99°；时间单位：月；Cell type: single-junction GaAs solar cell; thickness of quartz glass cover: 120μm; orbital height: 300km~3000km; inclination: only for 99°; time unit: month;

B.模型输出参数定义如下：B. Model output parameters are defined as follows:

最大输出功率P_max、短路电流I_sc、开路电压V_ov，其输出形式：给出P_max、I_sc和V_ov经过m个月后，P_max、I_sc和V_ov为初始值的百分比，即给出P_max、I_sc和V_ov关于时间month的函数；Maximum output power P _max , short-circuit current I _sc , open-circuit voltage V _ov , the output form: after m months of given P _max , I _sc and V _ov , P _max , I _sc and V _ov are the percentages of the initial values, That is, the functions of P _max , I _sc and V _ov with respect to time month are given;

以下为该太阳阵开路电压及短路电流辐照衰降因子的计算模型：The following is the calculation model of the open circuit voltage and short circuit current radiation attenuation factor of the solar array:

不同轨道高度位移损伤剂量计算如下：x为轨道高度，month为在轨月数，y为计算得到的位移损伤剂量；The displacement damage dose at different orbital heights is calculated as follows: x is the orbital height, month is the number of months in orbit, and y is the calculated displacement damage dose;

当300km<=x<=600km时，计算公式为：When 300km<=x<=600km, the calculation formula is:

y＝14（A₀+A₁·x+A₂·x²+A₃·x³+A₄·x⁴+A₅·x⁵）·month （Equ.4）y＝14(A ₀ +A ₁ ·x+A ₂ ·x ² +A ₃ ·x ³ +A ₄ ·x ⁴ +A ₅ ·x ⁵ )·month (Equ.4)

其中，A0=-5.72637E6，A1=69074.68933，A2=-329.19032，Among them, A0=-5.72637E6, A1=69074.68933, A2=-329.19032,

A3=0.77634，A4=-9.13546E-4，A5=4.49106E-7A3=0.77634, A4=-9.13546E-4, A5=4.49106E-7

当600km<x<=1000km时，计算公式为：When 600km<x<=1000km, the calculation formula is:

y＝14（A₀+A₁·x+A₂·x²+A₃·x³+A₄·x⁴）·month （Equ.5）y＝14（A ₀ +A ₁ x+A ₂ x ² +A ₃ x ³ +A ₄ x ⁴ ）month (Equ.5)

其中，A0=-5.80893E7，A1=321272.30685，A2=-663.23216，A3=0.59526，A4=-1.77968E-4当1000km<x<=3000km时，计算公式为：Among them, A0=-5.80893E7, A1=321272.30685, A2=-663.23216, A3=0.59526, A4=-1.77968E-4 When 1000km<x<=3000km, the calculation formula is:

y＝14（A₀+A₁·x+A₂·x²+A₃·x³+A₄·x⁴+A₅·x⁵）·month （Equ.6）y＝14(A ₀ +A ₁ x+A ₂ x ² +A ₃ x ³ +A ₄ x ⁴ +A ₅ x ⁵ ) month (Equ.6)

其中，A0=5.01219E8，A1=-1.76649E6，A2=2453.54778，Among them, A0=5.01219E8, A1=-1.76649E6, A2=2453.54778,

A3=-1.65135，A4=5.32602E-4，A5=-5.18233E-8A3=-1.65135, A4=5.32602E-4, A5=-5.18233E-8

GaAs/Ge太阳电池的Pmax、Isc和Voc的计算模型为：The calculation model of Pmax, Isc and Voc of GaAs/Ge solar cell is:

最大输出功率衰减，即Pmax的计算模型：The maximum output power attenuation, that is, the calculation model of Pmax:

P_max=1.0-C×log10(1+(y/Dx)) （Equ.7）P _max =1.0-C×log10(1+(y/Dx)) (Equ.7)

其中，C=0.242，Dx=3.47e9，y为计算得到的位移损伤剂量；Among them, C=0.242, Dx=3.47e9, y is the calculated displacement damage dose;

短路电流衰减，即Isc的计算模型：Short-circuit current attenuation, that is, the calculation model of Isc:

K_IRAD=Isc=1.0-C×log10(1+(y/Dx)) （Equ.8）K _IRAD =Isc=1.0-C×log10(1+(y/Dx)) (Equ.8)

其中，C=0.213，Dx=8.3e19Among them, C=0.213, Dx=8.3e19

开路电压衰减，即Voc的计算模型：Open circuit voltage attenuation, that is, the calculation model of Voc:

K_VRAD=Vov=1.0-C×log10(1+(y/Dx)) （Equ.9）K _VRAD =Vov=1.0-C×log10(1+(y/Dx)) (Equ.9)

其中，C=0.07，Dx=1.8e9Among them, C=0.07, Dx=1.8e9

步骤三、太阳阵能量平衡计算模型确定；Step 3, determining the solar array energy balance calculation model;

在进行能量平衡计算时，根据在轨数据或地面提供的数据对能量平衡的临界状态进行实时监控，如果太阳阵提供能量的多余电量Q_residual(c)由正值转变为零，则表明太阳阵已处于严重损伤状态，且Q_residual(c)的计算式为：When calculating the energy balance, the critical state of the energy balance is monitored in real time according to the on-orbit data or the data provided by the ground. If the excess power Q _residual (c) provided by the solar array changes from a positive value to zero, it indicates that the solar array Has been seriously injured, and the calculation formula of Q _residual (c) is:

${Q Q}_{residual residual} ((c c)) = = {I I}_{SA SA} ((c c)) \times \times ((Te Te - - te te)) - - {I I}_{load load__mean mean} ((c c)) \times \times ((Te Te - - te te)) - - 1.02 1.02 \times \times {&Integral; &Integral;}_{00}^{te te} {I I}_{d d} ((t t)) \times \times dt dt - - - - - - ((Equ Equivalent . . 1010))$

其中：in:

Q_residual(c)——在轨第c圈太阳阵可提供的多余电量，单位为C；Q _residual (c)——the excess power that can be provided by the solar array on the cth ring in orbit, the unit is C;

te——阴影期时间，单位为s；te——shadow period time, unit is s;

I_SA(c)——在轨第c圈方阵电流箝位点电流值，单位为A；I _SA (c)——the current value of the current clamping point of the c-th circle square array on the track, the unit is A;

I_{load_mean}(c)——光照期负载电流I_load(A)，其为在轨第c圈负载电流每周期的平均值，单位为A；I _{load_mean} (c)——the load current I _load (A) during the light period, which is the average value of the load current per cycle of the c-th circle on the rail, and the unit is A;

I_d(t)——阴影期，蓄电池放电电流，单位为A；I _d (t)——shade period, battery discharge current, unit is A;

根据指定时期太阳阵I-V曲线的方程，在给出相应的光照区母线电压V_{S_bus}及太阳阵隔离二极管和供电线缆压降之和V_{s_dioline}时，得到该指定时期I-V曲线上太阳阵工作电压箝位点V_op1处的电流值I_{s_op1}；由能量平衡计算可知，该指定时期的太阳阵提供能量的多余电量Q_residual(c)可表示为：According to the equation of the IV curve of the solar array in the specified period, when the bus voltage V _{S_bus} of the corresponding illumination area and the sum of the voltage drop of the solar array isolation diode and the power supply cable V _{s_dioline} are given, the working voltage clamp of the solar array on the IV curve of the specified period can be obtained The current value I _{s_op1} at the point V _op1 ; it can be seen from the energy balance calculation that the excess power Q _residual (c) provided by the solar array in the specified period can be expressed as:

${Q Q}_{s the s - - residual residual} ((c c)) = = {I I}_{s the s__opl opl} ((c c)) \times \times ((Te Te - - te te)) - - {I I}_{s the s__load load__mean mean} ((c c)) \times \times ((Te Te - - te te)) - - 1.02 1.02 \times \times {&Integral; &Integral;}_{00}^{te te} {I I}_{d d} ((t t)) \times \times dt dt - - - - - - ((Equ Equivalent . . 1111))$

式中：In the formula:

I_{s_op1}——指点时期I-V曲线上太阳阵工作电压箝位点V_op1处的电流值，单位为A；I _{s_op1} ——the current value at the solar array operating voltage clamp point V _op1 on the IV curve during the pointing period, the unit is A;

I_{s_load_mean}——指定时期光照区负载电流/在轨所有负载电流数据的平均值，单位为A；I _{s_load_mean} ——the average value of the load current in the illuminated area/all load current data on the track during the specified period, the unit is A;

I_d(t)——指定周期蓄电池在阴影区的放电电流值，单位为A；I _d (t)——the discharge current value of the battery in the shaded area for a specified period, in A;

太阳阵工作电压点输出功率计算模型如下；The calculation model of the output power at the operating voltage point of the solar array is as follows;

P_sA(t)＝V_bus(t)Iop1(t)， I_sa(t)＝I_op1(t)P _sA (t) = V _bus (t) I op1 (t), I _sa (t) = I _op1 (t)

进一步可得：Further available:

P_{s_op1}(c)＝V_{s_bus}(c)I_{s_op1}(c)P _{s_op1} (c)＝V _{s_bus} (c)I _{s_op1} (c)

V_{s_op1}(c)＝V_{s_bus}(c)+V_{s_dioline} （Equ.12）V _{s_op1} (c)＝V _{s_bus} (c)+V _{s_dioline} (Equ.12)

式中：In the formula:

t――第c圈轨道周期内时刻，从0<t<Te，其中，Te为轨道周期，单位为s；t——the moment in the orbital period of the cth circle, from 0<t<Te, where Te is the orbital period, and the unit is s;

P_SA——太阳阵输出功率，单位为W；P _SA - the output power of the solar array, in W;

P_{s_op1}(c)——第c圈太阳阵输出为箝位点V_{s_op1}时输出功率，单位为W；P _{s_op1} (c)——the output power when the output of the c-circle solar array is the clamping point V _{s_op1} , the unit is W;

I_{s_op1}(c)——第c圈I-V曲线上太阳阵工作电压箝位点V_{s_op1}时电流值，单位为A；I _{s_op1} (c)——the current value at the clamping point V _{s_op1} of the working voltage of the solar array on the IV curve of the cth circle, the unit is A;

V_{s_bus}——光照区母线电压，单位为V；V _{s_bus} —— bus voltage in the lighting area, the unit is V;

V_{s_dioline}——太阳阵隔离二极管和供电线缆压降之和，单位为V；V _{s_dioline} ——the sum of the voltage drop of the solar array isolation diode and the power supply cable, the unit is V;

对于在轨电源系统，由于电源控制器使得光照期母线电压始终保持为定值，因而，可以认为：在电源控制器正常工作的前提下，光照期母线电压始终不变；同时，在得到V_{s_dioline}值后，可够通过上述建立的I-V曲线得到指定时期箝位点电流值I_{s_op}(c)，以用于能量平衡计算；For the on-rail power supply system, since the power controller keeps the bus voltage at a constant value during the light period, it can be considered that: under the premise of normal operation of the power controller, the bus voltage during the light period is always constant; at the same time, after obtaining V _{s_dioline} After the value is obtained, the clamp point current value I _{s_op} (c) of the specified period can be obtained through the IV curve established above for energy balance calculation;

如果系统预测得到某指定时期Q_residual(c)=0，则说明此时太阳阵已到寿；If the system predicts that Q _residual (c)=0 for a specified period, it means that the solar array has reached its end of life at this time;

其中，进行蓄电池组放电电流计算时，蓄电池组的放电电流取决于蓄电池组的放电功率、放电调节器效率、蓄电池组供电线路损耗因子、电池组电压因素；Among them, when calculating the discharge current of the battery pack, the discharge current of the battery pack depends on the discharge power of the battery pack, the efficiency of the discharge regulator, the loss factor of the power supply line of the battery pack, and the voltage factor of the battery pack;

阴影区，蓄电池组放电电流为：In the shaded area, the discharge current of the battery pack is:

${I I}_{d d} ((t t)) = = \frac{(({I I}_{load load} ((t t)) - - {I I}_{SA SA} ((t t)))) \times \times {V V}_{bus bus}}{{η η}_{BDR BDR} \cdot \cdot {η η}_{line line} \cdot &Center Dot; {V V}_{bat bat} ((t t))}$

式中：In the formula:

I_load(t)――在轨负载电流需求随时间变化的函数；η_BDR――放电调节器效率；I _load (t) - the function of the current demand of the on-rail load with time; η _BDR - the efficiency of the discharge regulator;

n_ine――蓄电池组供电线路损耗因子；n _ine —— loss factor of power supply line of battery pack;

V_bat(t)――蓄电池组放电电压；基于在轨第c圈轨道蓄电池放电初压和放电终压值，可以近似地认为V_bat(t)由放电初压至放电终压线性变化；V _bat (t)——the discharge voltage of the battery pack; based on the initial discharge pressure and final discharge voltage value of the track battery on the cth circle of the track, it can be approximately considered that V _bat (t) changes linearly from the initial discharge pressure to the final discharge pressure;

V_bus：放电时母线电压，单位为V；V _bus : bus voltage during discharge, unit is V;

其中：阴影区太阳阵I_SA(t)电流为零，V_bat(t)是一个被积函数，该函数是由蓄电池在轨放电初压和放电终压确定的线性函数。Among them: the solar array I _SA (t) current in the shaded area is zero, and V _bat (t) is an integrand function, which is a linear function determined by the initial discharge voltage and the final discharge voltage of the battery on the rail.

其中，所述的太阳阵温度通过太阳阵温度模型计算如下：Wherein, the described solar array temperature is calculated as follows by the solar array temperature model:

太阳阵温度随卫星进出影状态的变化而变化，地影区，太阳阵温度逐渐下降，直至降至出影前的最低温度；光照期，太阳阵温度从出影后迅速上升，直至达到光照期的温度平衡点，此后温度保持不变直至卫星进入下一轨道圈的地影期，周而复始；The temperature of the solar array changes with the state of the satellite entering and leaving the shadow. In the shadow area, the temperature of the solar array gradually drops until it reaches the lowest temperature before the shadow; The temperature equilibrium point, after which the temperature remains constant until the satellite enters the earth shadow period of the next orbit circle, and the cycle repeats;

太阳阵温度变化的简化模型如下：The simplified model of solar array temperature variation is as follows:

在地影期内，太阳阵温度从光照期的最高平衡温度线性下降至地影期最低温度，出影后，太阳阵温度在8分钟内从地影期最低温度上升至60℃，在20分钟内从60℃上升至光照期最高平衡温度，直至下次进影；During the earth shadow period, the temperature of the solar array decreases linearly from the highest equilibrium temperature in the light period to the lowest temperature in the earth shadow period. Rise from 60°C to the highest equilibrium temperature during the light period, until the next image-taking;

光照期的最高平衡温度、地影期最低温度的默认值分别为：The default values of the maximum equilibrium temperature in the light period and the minimum temperature in the shadow period are:

光照期的最高平衡温度T_SAS；地影期最低温度T_SAE。The highest equilibrium temperature T _SAS in the light period; the lowest temperature T _SAE in the earth shadow period.

本发明的优点为：The advantages of the present invention are:

（1）、多寿命影响因素综合：本发明以试验为基础，综合考虑日地距离因子、轨道地影时间、太阳光线与太阳阵法线的夹角、温度、太阳辐射等重要空间环境因素影响下的太阳阵整体寿命预测模型；(1) Synthesis of multi-life influencing factors: the present invention is based on experiments, and comprehensively considers the influence of important space environment factors such as the distance factor between the sun and the earth, the orbital shadow time, the angle between the sun's rays and the normal line of the sun array, temperature, and solar radiation. The overall life prediction model of the solar array under ;

（2）、模型通用性：对于太阳同步轨道小卫星太阳阵，包括：Si及GaAs各类型太阳电池阵的整体寿命预测，避免了只能对特定单体电池进行寿命预测的局限；(2) Model versatility: For sun-synchronous orbit small satellite solar arrays, including: the overall life prediction of Si and GaAs various types of solar cell arrays, avoiding the limitation that only specific single cells can be used for life prediction;

（3）、工程实用性：本申请的太阳阵寿命预测方法属于物理模型与数据驱动相结合的方法。在建模过程中采取了部分简化方式，同时，模型所需要的数据基于现有的小卫星所采集的参数，容易获取，简化了寿命预测模型的复杂度及数据获取困难等问题，进而具有更强的工程实用性。(3) Engineering practicability: The solar array life prediction method of this application belongs to the method of combining physical model and data-driven. Partial simplification is adopted in the modeling process. At the same time, the data required by the model is based on the parameters collected by the existing small satellites, which is easy to obtain, which simplifies the complexity of the life prediction model and the difficulty of data acquisition, and thus has a better Strong engineering practicability.

附图说明 Description of drawings

图1为各子系统失效导致小卫星失效比列分配关系图；Figure 1 is a distribution relationship diagram of the proportion of small satellite failure caused by the failure of each subsystem;

图2为太阳阵寿命预测流程图；Figure 2 is a flow chart of solar array life prediction;

图3为小卫星太阳电池特征参数衰减计算流程图；Fig. 3 is the flow chart of calculating the attenuation of characteristic parameters of small satellite solar cells;

图4为太阳阵年日地距离因子变化规律曲线图；Figure 4 is a curve diagram of the variation law of the solar array's annual sun-earth distance factor;

图5为太阳入射角年变化规律曲线图；Figure 5 is a graph showing the annual variation of the solar incidence angle;

图6为HY-1B小卫星太阳阵I-V曲线图；Figure 6 is the I-V curve of the HY-1B small satellite solar array;

图7为太阳阵提供多余电量随时间变化曲线图。Figure 7 is a graph showing the variation of excess electricity provided by the solar array over time.

具体实施方式Detailed ways

下面结合附图和实施例对本发明进行详细说明。The present invention will be described in detail below in conjunction with the accompanying drawings and embodiments.

一种基于I-V曲线与能量平衡的小卫星太阳阵寿命预测方法，该方法通过如下步骤实现：A small satellite solar array life prediction method based on I-V curve and energy balance, the method is realized through the following steps:

根据轨道高度、降交点地方时和预测起始时间，调用STK软件，计算每天的日地距离因子、轨道周期Te、轨道地影时间、每轨太阳光线与太阳阵法线的夹角的变化规律，得到随时间变化的定量数据，用于后续的太阳阵I-V曲线和能量平衡分析。According to the orbital altitude, the local time of the descending node and the predicted start time, call the STK software to calculate the daily sun-earth distance factor, orbital period Te, orbital earth shadow time, and the variation law of the angle between the sun's rays and the sun array normal every day , to obtain quantitative data over time for subsequent solar array I-V curve and energy balance analysis.

根据太阳阵特性构建太阳阵计算模型，同时考虑太阳入射角、辐照衰减、日地因子、损失因子等因素的影响，计算不同季节、不同轨道条件和不同工况下太阳阵输出电压、输出电流，以表征太阳阵输出功率实时及长期变化情况。Build a solar array calculation model according to the characteristics of the solar array, and consider the influence of solar incident angle, radiation attenuation, sun-earth factor, loss factor and other factors to calculate the output voltage and output current of the solar array under different seasons, different orbital conditions and different working conditions , to represent the real-time and long-term changes of the output power of the solar array.

以标准状态的I-V曲线特征点为参数，考虑多种环境因素对太阳阵寿命的影响，计算太阳阵的输出特性。利用Equ.1太阳阵I-V曲线的计算机解析模型，可以得到不同条件下的太阳阵的I-V特性曲线。该模型在光照强度小于2个太阳常数时，有很高的精确性。太阳同步轨道小卫星的光照情况满足这一条件：Taking the characteristic points of the I-V curve in the standard state as parameters, considering the influence of various environmental factors on the life of the solar array, the output characteristics of the solar array are calculated. Using the computer analysis model of the I-V curve of Equ.1 solar array, the I-V characteristic curve of the solar array under different conditions can be obtained. The model has high accuracy when the light intensity is less than 2 solar constants. The illumination conditions of small satellites in sun-synchronous orbit meet this condition:

式中：In the formula:

I——太阳阵输出电流，单位为A；I——the output current of the solar array, the unit is A;

ISC′——太阳阵短路电流，典型参数或实测值，单位为A；ISC'——solar array short-circuit current, typical parameter or measured value, unit is A;

C₁——公式系数1；C ₁ —— formula coefficient 1;

C₂——公式系数2；C ₂ —— formula coefficient 2;

V_ov'_____阵开路电压，典型参数或实测值，单位为V；V _ov '_____ array open circuit voltage, typical parameters or measured values, the unit is V;

I_mp′——太阳阵最佳工作点输出电流，典型参数或实测值，单位为A；I _mp ′——the output current of the best operating point of the solar array, typical parameters or measured values, in A;

V_mp'——太阳阵最佳工作点输出电压，典型参数或实测值，单位为V。V _mp '—the output voltage of the best working point of the solar array, typical parameters or measured values, the unit is V.

（1）太阳阵典型特征点参数计算模型；(1) Calculation model of typical characteristic point parameters of solar array;

（1.1）太阳阵开路电压和最佳工作点输出电压：(1.1) Solar array open circuit voltage and output voltage at the best operating point:

式中：In the formula:

V_ov——单体太阳电池开路电压（QJ 1019－1995规定的AM0，25℃），单位为V；V _ov - the open circuit voltage of a single solar cell (AM0 specified in QJ 1019-1995, 25°C), in V;

V_mp——单体太阳电池最佳工作点电压（QJ 1019－1995规定的AM0，25℃），单位为V；V _mp - the best working point voltage of a single solar cell (AM0 specified in QJ 1019-1995, 25°C), the unit is V;

β_VBOL——单体太阳电池寿命初期电压温度系数(太阳电池的温度改变1℃时，其输出电压的变化值)，单位为V/℃；β _VBOL ——Voltage temperature coefficient of the initial life of a single solar cell (when the temperature of the solar cell changes by 1°C, the change value of its output voltage), the unit is V/°C;

T——太阳阵温度，单位为℃。T——solar array temperature, unit is ℃.

（1.2）太阳阵短路电流和最佳工作点电流计算模型：(1.2) Calculation model of solar array short-circuit current and optimal working point current:

I_SC——单体太阳电池短路电流（QJ 1019－1995规定的AM025℃条件），单位为A；I _SC ——Short-circuit current of a single solar cell (AM025°C condition specified in QJ 1019-1995), unit is A;

I_mp——单体太阳电池最佳工作点电流（QJ 1019－1995规定的AM0，25℃条件），单位为A；I _mp - the best working point current of a single solar cell (AM0 specified in QJ 1019-1995, at 25°C), in A;

α_I——单体太阳电池电流温度系数(太阳电池的温度改变1℃时，其输出电流的变化值)，单位为A/℃；α _I ——The current temperature coefficient of a single solar cell (when the temperature of the solar cell changes by 1°C, the change value of its output current), the unit is A/°C;

θ(t)——一圈轨道内太阳光线与太阳阵法线方向的夹角，单位为度；θ(t)——the angle between the sun's rays and the normal direction of the sun array in one circle of orbit, the unit is degree;

T——太阳阵温度，单位为℃；T——solar array temperature, unit is ℃;

K_IRAD——太阳阵短路电流辐照衰降因子；K _IRAD — solar array short-circuit current radiation attenuation factor;

F_rd——日地距离因子。F _rd ——Sun-Earth distance factor.

（2）太阳阵开路电压及短路电流辐照衰降因子计算模型；(2) Calculation model of solar array open circuit voltage and short circuit current radiation attenuation factor;

本模型用于预测LEO轨道辐射环境对卫星太阳电池输出参数衰减的影响，模型中Isc即为K_IRAD，Vov即为K_VRAD。This model is used to predict the influence of LEO orbital radiation environment on the attenuation of satellite solar cell output parameters. In the model, Isc is K _IRAD and Vov is K _VRAD .

最大输出功率P_max、短路电流I_sc、开路电压V_ov（输出形式：给出P_max、I_sc和V_ov经过m个月后，P_max、I_sc和V_ov为初始值的百分比，即给出P_max、I_sc和V_ov关于时间month的函数）；Maximum output power P _max , short-circuit current I _sc , open-circuit voltage V _ov (output form: after giving P _max , I _sc and V _ov after m months, P _max , I _sc and V _ov are the percentages of the initial values, namely Give P _max , I _sc and V _ov as a function of time month);

以下为该计算模型的计算式：The calculation formula of the calculation model is as follows:

（2.1）不同轨道高度位移损伤剂量计算(2.1) Calculation of displacement damage dose at different track heights

x为轨道高度，month为在轨月数，y为计算得到的位移损伤剂量（质子位移损伤剂量）。x is the orbit height, month is the number of months in orbit, and y is the calculated displacement damage dose (proton displacement damage dose).

y＝14（A₀+A₁·x+A₂·x²+A₃·x³A₄·x⁴+A₅·x⁵）·month （Equ.6）y＝14（A ₀ +A ₁ x+A ₂ x ² +A ₃ x ³ A ₄ x ⁴ +A ₅ x ⁵ ）month（Equ.6）

（2.2）GaAs/Ge太阳电池的Pmax、Isc和Voc的计算模型(2.2) Calculation model of Pmax, Isc and Voc of GaAs/Ge solar cells

最大输出功率衰减（Pmax的计算模型）：Maximum output power attenuation (calculation model of Pmax):

P_max=1.0-C×log10(1+(y/Dx)) （Equ.7）P _max =1.0-C×log10(1+(y/Dx)) (Equ.7)

其中，C=0.242，Dx=3.47e9，y为计算得到的位移损伤剂量。Among them, C=0.242, Dx=3.47e9, y is the calculated displacement damage dose.

短路电流衰减（Isc的计算模型）：Short-circuit current decay (calculation model of Isc):

其中，C=0.213，Dx=8.3e19Among them, C=0.213, Dx=8.3e19

开路电压衰减（Voc的计算模型）：Open circuit voltage attenuation (calculation model of Voc):

其中，C=0.07，Dx=1.8e9Among them, C=0.07, Dx=1.8e9

（3）太阳阵温度模型；(3) Solar array temperature model;

太阳阵温度随卫星进出影状态的变化而变化。地影区，太阳阵温度逐渐下降，直至降至出影前的最低温度；光照期，太阳阵温度从出影后迅速上升，直至达到光照期的温度平衡点，此后温度保持不变直至卫星进入下一轨道圈的地影期，周而复始。The temperature of the solar array changes with the state of the satellite entering and leaving the shadow. In the shadow area, the temperature of the solar array gradually drops until it drops to the lowest temperature before the shadow; during the light period, the temperature of the sun array rises rapidly after the shadow, until it reaches the temperature equilibrium point of the light period, and then the temperature remains unchanged until the satellite enters The earth shadow period of the next orbital circle repeats itself.

在地影期内，太阳阵温度从光照期的最高平衡温度线性下降至地影期最低温度，出影后，太阳阵温度在8分钟内从地影期最低温度上升至60℃，在20分钟内从60℃上升至光照期最高平衡温度，直至下次进影。During the earth shadow period, the temperature of the solar array decreases linearly from the highest equilibrium temperature in the light period to the lowest temperature in the earth shadow period. It rises from 60°C to the highest equilibrium temperature during the light period until the next time the film is taken.

步骤三、太阳阵能量平衡计算模型；Step 3, solar array energy balance calculation model;

（1）能量平衡计算；(1) Calculation of energy balance;

根据在轨数据或地面提供的数据对能量平衡的临界状态进行实时监控，如果太阳阵提供能量的多余电量Q_esidual(c)由正值转变为零，则表明太阳阵已处于严重损伤状态，且Q_esidual(c)的计算式为：The critical state of the energy balance is monitored in real time according to the on-orbit data or the data provided by the ground. If the excess power Q _esidual (c) provided by the solar array changes from a positive value to zero, it indicates that the solar array has been seriously damaged, and The calculation formula of Q _esidual (c) is:

其中：in:

te——阴影期时间，单位为s；te——shadow period time, unit is s;

I_{load_mean}(c)——光照期负载电流I_load(A)（在轨第c圈负载电流每周期的平均值），单位为A；I _{load_mean} (c)——the load current I _load (A) during the light period (the average value of the load current per cycle of the c-th circle on the rail), the unit is A;

由‘太阳阵工作电压点输出功率计算模型’可知，根据指定时期太阳阵I-V曲线的方程，在给出相应的光照区母线电压V_{s_bus}及太阳阵隔离二极管和供电线缆压降之和V_{s_dioline}时，可以得到该指定时期I-V曲线上太阳阵工作电压箝位点V_op1处的电流值I_{s_opl}。由能量平衡计算可知，该指定时期的太阳阵提供能量的多余电量Q_esidual(c)可表示为：According to the "solar array operating voltage point output power calculation model", according to the equation of the solar array IV curve in a specified period, the bus voltage V _{s_bus} of the corresponding illumination area and the sum of the voltage drop of the solar array isolation diode and power supply cable V _{s_dioline} are given. , the current value I _{s_opl} at the solar array operating voltage clamping point V _op1 on the IV curve of the specified period can be obtained. From the calculation of energy balance, it can be seen that the excess electricity Q _esidual (c) provided by the solar array in the specified period can be expressed as:

式中：In the formula:

I_{s_op1}——指点时期I-V曲线上太阳阵工作电压箝位点V_op1处的电流值；I _{s_op1} ——the current value at the solar array operating voltage clamp point V _op1 on the IV curve during the pointing period;

I_{s_load_mean}——指定时期光照区负载电流/在轨所有负载电流数据的平均值；I _{s_load_mean} ——the average value of the load current in the illumination area/all load current data on the track during the specified period;

I_d(t)——指定周期蓄电池在阴影区的放电电流值；I _d (t)——the discharge current value of the battery in the shaded area for a specified period;

如果系统预测得到某指定时期Q_residual(c)=0，则说明此时太阳阵已到寿。If the system predicts that Q _residual (c)=0 for a specified period, it means that the solar array has reached its end of life at this time.

（2）太阳阵工作电压点输出功率计算模型；(2) Calculation model of solar array working voltage point output power;

P_SA(t)＝V_bus(t)I_op1(t)， I_SA(t)＝I_op1(t)P _SA (t)＝V _bus (t)I _op1 (t), I _SA (t)＝I _op1 (t)

进一步可得：Further available:

式中：In the formula:

t――第c圈轨道周期内时刻，从0<t<Te（其中，Te为轨道周期），单位为s；t——the moment in the orbital period of the cth circle, from 0<t<Te (where Te is the orbital period), the unit is s;

P_{s_OP1}(c)——第c圈太阳阵输出为箝位点V_{s_op1}时输出功率，单位为W；P _{s_OP1} (c)——the output power when the output of the c-th circle solar array is clamping point V _{s_op1} , the unit is W;

I_{s_opl}(c)——第c圈I-V曲线上太阳阵工作电压箝位点V_{s_op1}时电流值，单位为A；I _{s_opl} (c)——the current value at the solar array operating voltage clamp point V _{s_op1} on the IV curve of the cth circle, the unit is A;

对于在轨电源系统，由于电源控制器使得光照期母线电压始终保持为定值，因而，可以认为：在电源控制器正常工作的前提下，光照期母线电压始终不变；同时，在得到Vs_dioline值后，可够通过上述建立的I-V曲线得到指定时期箝位点电流值I_{s_op1}(c)，以用于能量平衡计算。For the on-rail power supply system, since the power controller keeps the bus voltage at a constant value during the light period, it can be considered that: under the premise of normal operation of the power controller, the bus voltage during the light period is always constant; at the same time, after obtaining the value of Vs_dioline Afterwards, the clamping point current value I _{s_op1} (c) in a specified period can be obtained through the IV curve established above, and used for energy balance calculation.

（3）蓄电池放电电流计算；(3) Calculation of battery discharge current;

蓄电池组的放电电流取决于蓄电池组的放电功率、放电调节器效率、蓄电池组供电线路损耗因子、电池组电压等因素。The discharge current of the battery pack depends on factors such as the discharge power of the battery pack, the efficiency of the discharge regulator, the loss factor of the power supply line of the battery pack, and the voltage of the battery pack.

式中：In the formula:

I_load(t)――在轨负载电流需求随时间变化的函数；I _load (t) - function of the current demand of the on-rail load changing with time;

η_BDR――放电调节器效率η _BDR ――discharge regulator efficiency

η_line――蓄电池组供电线路损耗因子η _line ――The loss factor of the battery power supply line

其中：阴影区太阳阵I_SA(t)电流为零，V_bat(t)是一个被积函数，该函数是由蓄电池在轨放电初压和放电终压确定的线性函数。本专利仅考虑太阳阵的寿命预测问题，即假定蓄电池及电源控制器工作状态一切正常或蓄电池及电源控制器性能衰退对太阳阵不产生影响，因而，此处蓄电池在轨放电初压和放电终压可用定值处理。Among them: the solar array I _SA (t) current in the shaded area is zero, and V _bat (t) is an integrand function, which is a linear function determined by the initial discharge voltage and the final discharge voltage of the battery on the rail. This patent only considers the life prediction problem of the solar array, that is, assuming that the working status of the battery and the power controller is normal or the performance degradation of the battery and the power controller does not affect the solar array, therefore, here, the initial pressure and the final discharge of the battery on the rail Pressure can be fixed value processing.

实施例1如下：Embodiment 1 is as follows:

本发明是一种基于I-V曲线与能量平衡的小卫星太阳阵寿命预测方法，所述的寿命预测方法是把太阳阵性能衰退过程视为能量平衡的衰退过程，从而，在综合考虑了小卫星运行空间环境因素（包括：日地距离因子、轨道地影时间、太阳光线与太阳阵法线的夹角、温度、太阳辐射等）影响下，建立具有较好通用性的太阳阵综合寿命预测模型。图2所示为本发明的寿命预测方法的总体流程图，具体实施步骤如下：The present invention is a small satellite solar array life prediction method based on the I-V curve and energy balance. The life prediction method regards the solar array performance decline process as the energy balance decline process, thus, taking into account the small satellite operation Under the influence of space environmental factors (including: the distance between the sun and the earth, the orbital shadow time, the angle between the sun's rays and the normal of the sun array, temperature, solar radiation, etc.), a comprehensive life prediction model for solar arrays with good versatility is established. Fig. 2 shows the overall flowchart of the life prediction method of the present invention, and concrete implementation steps are as follows:

根据轨道高度、降交点地方时和预测起始时间，调用STK软件，计算日地距离因子、轨道周期、轨道地影时间、轨道太阳光线与太阳阵法线的夹角的变化规律，得到随时间变化的定量数据，用于后续的太阳阵I-V曲线和能量平衡分析。According to the orbital altitude, the local time of the descending node and the predicted start time, call the STK software to calculate the sun-earth distance factor, orbital period, orbital earth shadow time, and the angle between the orbiting sun's rays and the sun array normal, and obtain Quantitative data of changes for subsequent solar array I-V curve and energy balance analysis.

步骤二、太阳阵I-V曲线模型；Step 2, solar array I-V curve model;

（1）太阳阵开路电压及短路电流辐照衰降因子计算模型；(1) Calculation model of solar array open circuit voltage and short circuit current radiation attenuation factor;

图3给出的是LEO轨道辐射环境对太阳电池特征参数衰减影响的定量计算流程。结合图3，首先，根据小卫星轨道高度计算位移损伤剂量随时间的变化函数y=f(month)（其中，相应参数参见Equ.4~Equ.6）。Figure 3 shows the quantitative calculation process of the influence of the LEO orbital radiation environment on the attenuation of solar cell characteristic parameters. Combined with Fig. 3, firstly, the function y=f(month) of the displacement damage dose over time is calculated according to the orbital height of the small satellite (see Equ.4~Equ.6 for the corresponding parameters).

其次，利用公式Equ.8-9分别计算太阳阵开路电压辐照衰降因子随时间的变化函数K_VRAD=gv(month)与太阳阵短路电流辐照衰降因子随时间的变化函数K_IRAD=gI(month)。Secondly, use the formula Equ.8-9 to calculate the time-varying function K _VRAD =gv(month) of the solar array open-circuit voltage radiation decay factor and the time-varying function of the solar array short-circuit current radiation decay factor K _IRAD = gI(month).

（2）太阳阵典型特征点参数计算模型；(2) Calculation model of solar array typical feature point parameters;

对于计算公式Equ.2-3，其中，V_ov，V_op，β_VBOL，I_SC，I_mp，α_I，N_p N_s皆为已知参数数据；θ(t)，F_rd通过上述步骤已计算得到；K_IRAD，K_VRAD为month的函数；由太阳阵温度模型获得光照期太阳阵的温度数据。把上述参数数据及函数带入Equ.2可得太阳阵开路电压和最佳工作点输出电压、太阳阵短路电流和最佳工作点电流，可表示如下：For the calculation formula Equ.2-3, among them, V _ov , V _op , β _VBOL , I _SC , I _mp , α _I , N _p N _s are all known parameter data; θ(t), F _rd go through the above steps It has been calculated; K _IRAD and K _VRAD are functions of month; the temperature data of the solar array during the photoperiod is obtained from the solar array temperature model. Bring the above parameter data and functions into Equ.2 to get the solar array open-circuit voltage and the output voltage of the best working point, the solar array short-circuit current and the best working point current, which can be expressed as follows:

$\{\begin{matrix} {V V}_{ov ov}' ' = = {V V}_{ov ov} ((month month)) \\ {V V}_{mp mp}' ' = = {V V}_{mp mp} ((month month)) \end{matrix}$ $\{\begin{matrix} Isc Isc' ' = = Isc Isc ((month month)) \\ {I I}_{mp mp}' ' = = {I I}_{mp mp} ((month month)) \end{matrix}, - - - - - - ((Equ Equivalent . . 1414))$

把公式Equ.14带入Equ.1，分别计算公式系数C₁，C₂，进而可建立太阳阵I-V曲线随时间变化的规律，可表示为：Bring the formula Equ.14 into Equ.1, calculate the coefficients C ₁ and C ₂ of the formula respectively, and then establish the law of the IV curve of the solar array changing with time, which can be expressed as:

I＝V(month) （Equ.15）I＝V(month) （Equ.15）

将I-V曲线上的三个特征点即开路电压点（V_oc'）、短路电流点（I_SC'）和最大功率点(I_mp',V_mp')用不同条件下的光照、温度及辐照损失系数进行修正后，代入此解析表达式，即可得到不同条件下的太阳阵的I-V特性曲线。The three characteristic points on the IV curve, that is, the open circuit voltage point (V _oc '), the short circuit current point (I _SC ') and the maximum power point (I _mp ', V _mp ') are used under different conditions of light, temperature and radiation After correction according to the loss coefficient, the IV characteristic curve of the solar array under different conditions can be obtained by substituting this analytical expression.

由V_{s_bus}，V_{s_dioline}值通过Equ.12计算V_{s_op1}值，由公式Equ.15计算得到相应的I_{s_op1}值，进而建立I_{s_opl}与时间month之间的函数关系；Calculate the V _{s_op1} value from the V _{s_bus} and V _{s_dioline} values through Equ.12, and calculate the corresponding I _{s_op1} value from the formula Equ.15, and then establish the functional relationship between I _{s_opl} and time month;

对于Equ.13中的参数η_BDR，η_line，V_bus为已知量，在阴影区I_SA(t)为零，I_load(t)利用已有小卫星在轨负载电流数据的均值做近似处理，即I_load(t):＝I_{load_mean}(c)，其中，‘:＝’表示‘定义为’，I_SA(t)＝0A。For the parameter η _BDR in Equ.13, η _line and V _bus are known quantities, and I _SA (t) is zero in the shaded area, and I _load (t) is approximated by the average value of the existing small satellite in-orbit load current data Processing, that is, I _load (t):=I _{load_mean} (c), wherein ':=' means 'defined as', and I _SA (t)=0A.

蓄电池放电电流计算：阴影期，蓄电池放电电流I_d(t)公式中的V_bat(t)作为一个被积函数。该函数是由蓄电池在轨放电初压和放电终压确定的线性函数，且其放电初压恒定，放电终压由已有小卫星蓄电池放电终压均值近似。Calculation of battery discharge current: during the shadow period, V _bat (t) in the formula of battery discharge current I _d (t) is used as an integral function. This function is a linear function determined by the initial discharge pressure and final discharge pressure of the battery on orbit, and the initial discharge pressure is constant, and the final discharge pressure is approximated by the average discharge final pressure of the existing small satellite battery.

对于Equ.11Te，te已知，V_{s_op1}及积分项通过上述描述可求，I_{S_load_mean}(c)利用已有小卫星光照期负载电流均值近似。把上述参数，带入Equ.11，由于I_{S_load_mean}(c)×(Te-te)及近似为常数项，而I_{s_op1}(c)由Equ.12及Equ.15确定，因而，I_{s_op1}(c)可表示为：I_{s_op1}(c)＝I_{s_op1}(month)，最终，得到Q_{S_residual}(c)＝Q_{S_residual}(month)，即得到太阳阵提供能量的多余电量随时间变化的函数，从而可确定太阳阵寿命。For Equ.11Te, te is known, V _{s_op1} and The integral item can be obtained through the above description, and I _{S_load_mean} (c) is approximated by the mean value of the load current during the illumination period of the existing small satellite. Bring the above parameters into Equ.11, because I _{S_load_mean} (c)×(Te-te) and It is approximately a constant term, and I _{s_op1} (c) is determined by Equ.12 and Equ.15. Therefore, I _{s_op1} (c) can be expressed as: I _{s_op1} (c)=I _{s_op1} (month), and finally, Q _{S_residual} ( c)=Q _{S_residual} (month), that is, to obtain the function of the excess electricity provided by the solar array with time, so that the life of the solar array can be determined.

实施例2如下：Embodiment 2 is as follows:

本实施例以我国航天HY-1B小卫星太阳阵为对象，通过本实施例的详细阐述，进一步说明本发明的实施过程及工程应用过程。This embodiment takes my country Aerospace HY-1B small satellite solar array as an object, through the detailed elaboration of this embodiment, further illustrates the implementation process and engineering application process of the present invention.

小卫星轨道高度645km、降交点地方时15:00PM±30min——根据轨道高度、降交点地方时和预测起始时间，调用STK软件，计算日地距离因子F_rd、轨道周期、轨道地影时间、轨道太阳光线与太阳阵法线的夹角θ(t)的变化规律，得到随时间变化的定量数据，用于后续的太阳阵输出功率计算和能量平衡分析。The orbital height of the small satellite is 645km, the local time of the descending node is 15:00PM±30min——according to the orbital altitude, the local time of the descending node and the predicted start time, call the STK software to calculate the sun-earth distance factor F _rd , orbital period, and orbital shadow time , The change law of the included angle θ(t) between the orbiting sun's rays and the normal line of the solar array, and obtain quantitative data that changes with time, which will be used for subsequent solar array output power calculations and energy balance analysis.

F_rd=[1033 1.023 1.008 0.991 0.977 0.968 0.968 0.976 0.991 1.008 1.024 1.033]（一年中每个月的日地距离因子，如图4所示）；轨道周期：Te＝100.8min；轨道地影时间：te＝33.5217min分钟；太阳入射角θ(t)具有周期性，如图5所示为太阳入射角年变化规律曲线。F _rd =[1033 1.023 1.008 0.991 0.977 0.968 0.968 0.976 0.991 1.008 1.024 1.033] (the sun-earth distance factor for each month of the year, as shown in Figure 4); orbital period: Te＝100.8min; orbital shadow time: te=33.5217min; the solar incidence angle θ(t) is periodic, as shown in Figure 5, the annual variation curve of the solar incidence angle.

步骤二、太阳阵I-V曲线模型；Step 2, solar array I-V curve model;

由于HY-1B小卫星的轨道高度为645km，依据公式Equ.5计算位移损伤剂量y随时间month变化规律:y=f(month)。利用公式Equ.8-9分别计算太阳阵开路电压辐照衰降因子随时间的变化函数K_VRAD=gv(month)与太阳阵短路电流辐照衰降因子随时间的变化函数K_IRAD=gI(month)。Since the orbital height of the HY-1B small satellite is 645km, the displacement damage dose y is calculated according to the formula Equ.5. Use the formula Equ.8-9 to calculate the variation function K _VRAD =gv(month) of solar array open-circuit voltage radiation attenuation factor with time and the variation function K _IRAD =gI( month).

对于计算公式Equ.2-3，其中，V_ov＝2.65V，V_mp＝2.32V，β_VBOL＝-6.7mV/°C，I_SC＝0.396A，I_mp＝0.375A，a_I＝0.014mA/cm²°C，N_p＝114，N_s＝18,T＝82°C（由太阳阵温度模型可知，光照期，太阳阵温度可迅速上升至平衡温度，因而，此处以最高平衡温度T_SAS＝82°C作为HY-1B小卫星太阳阵温度）；θ(t)，F_rd由步骤一给出，且K_VRAD=gv(month)，K_IRAD=gI(month)。进而，分别建立形如Equ.14的表达式，把得到的表达式带入Equ.1，并最终建立HY-1B小卫星太阳阵I-V曲线随时间变化的规律，图6为HY-1B小卫星太阳阵寿命周期内某一给定时刻的I-V曲线。For the calculation formula Equ.2-3, V _ov =2.65V, V _mp =2.32V, β _VBOL =-6.7mV/°C, I _SC =0.396A, I _mp =0.375A, a _I =0.014mA /cm ² °C, N _p ＝114, N _s ＝18, T＝82°C (from the solar array temperature model, it can be seen that the temperature of the solar array can rise rapidly to the equilibrium temperature during the light period, so here, the highest equilibrium temperature T _SAS ＝82°C as HY-1B small satellite solar array temperature); θ(t), F _rd is given by step 1, and K _VRAD =gv(month), K _IRAD =gI(month). Furthermore, the expressions in the form of Equ.14 are respectively established, and the obtained expressions are brought into Equ.1, and finally the law of the IV curve of the HY-1B small satellite solar array changing with time is established. Figure 6 shows the HY-1B small satellite The IV curve at a given moment in the life cycle of a solar array.

由V_{s_bus}＝29.3V，V_{s_dioine}＝2.0 V值通过Equ.12计算V_{s_op1}＝31.3V值，由公式Equ.15计算得到相应的I_{s_op1}值，进而建立I_{s_op1}与时间month之间的函数关系I_{s_opl}=I_{s_opl}(month)；Calculate the value of V s_op1 = 31.3V from V _{s_bus} = 29.3V, V _{s_dioine} = 2.0 V through Equ.12, and calculate the corresponding I _{s_op1} value from the formula Equ.15, _and then establish the functional relationship between I _{s_op1} and time month I _{s_opl} = I _{s_opl} (month);

对于Equ.13中的参数η_BOR＝0.92，η_line=0.9673，V_bus＝28.6V为已知量，I_load(t)，在阴影区I_sA(t)=0A，经计算得： I_load(t):＝I_{load_mean}(c)＝9.0A，其中，‘:＝’表示‘定义为’。For the parameter η _BOR =0.92 in Equ.13, η _line =0.9673, V _bus =28.6V is a known quantity, I _load (t), in the shaded area I _sA (t)=0A, calculated as follows: I _load (t):=I _{load_mean} (c)=9.0A, where ':=' means 'defined as'.

阴影期，蓄电池放电电流I_d(t)公式中的V_bat(t)作为一个被积函数。该函数是由蓄电池在轨放电初压和放电终压确定的线性函数，且其放电初压恒定，放电终压由已有小卫星蓄电池放电终压均值近似，且放电初压为1.383 V*18（蓄电池组串联单体蓄电池个数）=24.8940V，放电终压均值21.6V。During the shadow period, V _bat (t) in the battery discharge current I _d (t) formula is used as an integrand. This function is a linear function determined by the initial discharge pressure and final discharge pressure of the battery on orbit, and the initial discharge pressure is constant, and the final discharge pressure is approximated by the average discharge final pressure of the existing small satellite battery, and the initial discharge pressure is 1.383 V*18 (The number of single batteries in series in the battery pack) = 24.8940V, and the average value of the final discharge voltage is 21.6V.

把Te＝100.8min， te＝33.5217min，及通过计算得到的V_{s_op1}及I_{S_load_mean}(c)＝11.4A带入Equ.11，由于I_{S_load_mean}(c)×(Te-te)及近似为常数项，而I_{s_op1}(c)由Equ.12及Equ.15确定，因而，I_{s_op1}(c)可表示为：I_{s_op1}(c)＝I_{s_op1}(month)，由此，Equ.11转化为Q_{S_residual}(c)＝Q_{S_residual}(month)，即得到太阳阵提供能量的多余电量随时间变化的函数，图7所示为多余电量随时间的变化曲线。由图可知，多余电量随着日地距离因子，太阳入射角等周期影响因素的综合作用下，呈现明显的周期性，且多余电量持续减少，与水平线相交处即为太阳阵使用寿命终止位置。Put Te=100.8min, te=33.5217min, and the calculated V _{s_op1} and I _{S_load_mean} (c)=11.4A is brought into Equ.11, because I _{S_load_mean} (c)×(Te-te) and Approximated as a constant term, and I _{s_op1} (c) is determined by Equ.12 and Equ.15, therefore, I _{s_op1} (c) can be expressed as: I _{s_op1} (c)=I _{s_op1} (month), thus, Equ.11 Transformed into Q _{S_residual} (c)=Q _{S_residual} (month), that is, the function of the excess power provided by the solar array over time can be obtained. Figure 7 shows the curve of the excess power over time. It can be seen from the figure that the excess power shows an obvious periodicity under the combined effect of the sun-earth distance factor, the sun incident angle and other periodic factors, and the excess power continues to decrease, and the intersection with the horizontal line is the end of the service life of the solar array.

Claims

1. A small satellite solar array life prediction method based on I-V curve and energy balance, characterized in that: the method is realized through the following steps:

Step 1. Determine the distance factor between the sun and the earth, the orbital earth shadow time, the angle between the sun's rays and the sun array normal;

According to the orbital altitude, the local time of the descending node, and the predicted start time, calculate the daily sun-earth distance factor, orbital period Te, orbital earth shadow time, and the angle between the sun's rays and the sun array normal in each orbit. Quantitative data of changes for subsequent solar array I-V curve and energy balance analysis;

Step 2, the solar array I-V curve model is determined;

Build a solar array calculation model according to the characteristics of the solar array, and consider the influence of the sun's incident angle, radiation attenuation, sun-earth distance factor, and loss factor at the same time, and calculate the output voltage and output current of the solar array under different seasons, different orbital conditions, and different working conditions , to represent the real-time and long-term changes of the output power of the solar array;

Taking the characteristic points of the I-V curve of the standard state as parameters, and considering the influence of various environmental factors on the life of the solar array, the output characteristics of the solar array are calculated; using the formula (Equ.1) computer analysis model of the I-V curve of the solar array, the The I-V characteristic curve of the solar array; this model has high accuracy when the illumination intensity is less than 2 solar constants; the illumination conditions of small satellites in sun-synchronous orbit meet this condition:

\{\begin{matrix} I I = = {I I}_{SC SC}^{' '} \times \times ((11 - - {C C}_{11} \times \times {{exp exp [[V V / / (({C C}_{22} \times \times {V V}_{ov ov}^{' '}))]] - - 11}})) \\ {C C}_{11} = = [[11 - - (({I I}_{mp mp}^{' '} / / {I I}_{SC SC}^{' '}))]] \times \times {{exp exp [[- - {V V}_{mp mp}^{' '} / / (({C C}_{22} \times \times {V V}_{ov ov}^{' '}))]]}} \\ {C C}_{22} = = [[(({V V}_{mp mp}^{' '} / / {V V}_{ov ov}^{' '})) - - 11]] / / ln ln ((11 - - {I I}_{mp mp}^{' '} / / {I I}_{SC SC}^{' '})) \end{matrix} - - - - - - ((Equ Equivalent . . 11))

In the formula:

I——the output current of the solar array, the unit is A;

I _SC '——solar array short-circuit current, typical parameter or measured value, unit is A;

C ₁ —— formula coefficient 1;

V——the output voltage of solar array, the unit is V;

C ₂ —— formula coefficient 2;

V _ov '—— solar array open circuit voltage, typical parameter or measured value, unit is V;

I _mp '——the output current of the best operating point of the solar array, typical parameters or measured values, in A;

V _mp '——the output voltage of the best working point of the solar array, typical parameters or measured values, the unit is V;

The calculation model of the solar array open circuit voltage and the output voltage of the optimal operating point is as follows:

\{\begin{matrix} {V V}_{ov ov}^{' '} = = (({V V}_{ov ov} + + {β β}_{VBOL VBOL} \times \times ((T T - - 2525)))) \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times Ns NS \times \times {K K}_{VRAD VRAD} \\ {V V}_{mp mp}^{' '} = = (({V V}_{mp mp} + + {β β}_{VBOL VBOL} \times \times ((T T - - 2525)))) \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times Ns NS \times \times {K K}_{VRAD VRAD} \end{matrix} - - - - - - ((Equ Equivalent . . 22))

In the formula:

V _ov - the open circuit voltage of a single solar cell, in V;

V _mp - the best operating point voltage of a single solar cell, in V;

β _VBOL ——Voltage temperature coefficient at the beginning of life of a single solar cell, in V/°C;

K _VRAD — solar array open circuit voltage radiation attenuation factor;

T——solar array temperature, unit is ℃;

N _s is known parameter data;

The calculation model of solar array short-circuit current and optimal working point current is as follows:

\{\begin{matrix} {I I}_{SC SC}^{' '} (({I I}_{SC SC} + + {α α}_{I I} \times \times ((T T - - 2525)))) \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times {N N}_{P P} \times \times cos cos θ θ ((t t)) \times \times {F f}_{rd rd} \times \times {K K}_{IRAD IRAD} \\ {I I}_{mp mp}^{' '} = = (({I I}_{mp mp} + + {α α}_{I I} ((T T - - 2525)))) \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times 0.98 0.98 \times \times {N N}_{P P} \times \times cos cos θ θ ((t t)) \times \times {F f}_{rd rd} \times \times {K K}_{IRAD IRAD} \end{matrix} - - - - - - ((Equ Equivalent . . 33))

I _SC ——Short-circuit current of single solar cell, unit is A;

I _mp - the best working point current of a single solar cell, in A;

α _I ——the current temperature coefficient of a single solar cell, in A/℃;

θ(t)——the angle between the sun's rays and the normal direction of the sun array in one circle of orbit, the unit is degree;

T——solar array temperature, unit is ℃;

K _IRAD — solar array short-circuit current radiation attenuation factor;

F _rd ——sun-earth distance factor;

N _p is known parameter data;

Use the "solar array open circuit voltage and short circuit current radiation attenuation factor calculation model" to predict the impact of LEO orbital radiation environment on the output parameter attenuation of satellite solar cells. In this model, Isc is K _IRAD and Vov is K _VRAD ;

A. The model input parameters are defined as follows:

Cell type: single-junction GaAs solar cell; thickness of quartz glass cover: 120μm; orbital height: 300km～3000km; inclination: only for 99°; time unit: month;

B. The model output parameters are defined as follows:

Maximum output power P _max , short-circuit current I _sc , open-circuit voltage V _ov , and its output form: after m months of given P _max , I _sc and V _ov , P _max , I _sc and V _ov are the percentages of the initial values, That is, the functions of P _max , I _sc and V _ov with respect to time month are given;

The following is the "solar array open circuit voltage and short circuit current radiation attenuation factor calculation model":

The displacement damage dose at different orbital heights is calculated as follows: x is the orbital height, month is the number of months in orbit, and y is the calculated displacement damage dose;

When 300km<=x<=600km, the calculation formula is:

y＝14(A ₀ +A ₁ x+A ₂ x ² +A ₃ x ³ +A ₄ x ⁴ +A ₅ x ⁵ )month (Equ.4)

Among them, A0=-5.72637E6, A1=69074.68933, A2=-329.19032,

A3=0.77634, A4=-9.13546E-4, A5=4.49106E-7

When 600km<x<=1000km, the calculation formula is:

y＝14(A ₀ +A ₁ x+A ₂ x ² +A ₃ x ³ +A ₄ x ⁴ )month (Equ.5)

Among them, A0=-5.80893E7, A1=321272.30685, A2=-663.23216, A3=0.59526, A4=-1.77968E-4

When 1000km<x<=3000km, the calculation formula is:

y＝14(A ₀ +A ₁ x+A ₂ x ² +A ₃ x ³ +A ₄ x ⁴ +A ₅ x ⁵ )month (Equ.6)

Among them, A0=5.01219E8, A1=-1.76649E6, A2=2453.54778,

A3=-1.65135, A4=5.32602E-4, A5=-5.18233E-8

The calculation model of Pmax, Isc and Voc of GaAs/Ge solar cell is:

The maximum output power attenuation, that is, the calculation model of Pmax:

P _max ＝1.0-C×log10(1+(y/Dx)) (Equ.7)

Among them, C=0.242, Dx=3.47e9, y is the calculated displacement damage dose;

Short-circuit current attenuation, that is, the calculation model of Isc:

K _IRAD ＝Isc＝1.0-C×log10(1+(y/Dx)) (Equ.8)

Among them, C=0.213, Dx=8.3e19

Open circuit voltage attenuation, that is, the calculation model of Voc:

K _VRAD ＝Vov＝1.0-C×log10(1+(y/Dx)) (Equ.9)

where C=0.07, Dx=1.8e9

Step 3, determining the solar array energy balance calculation model;

When calculating the energy balance, the critical state of the energy balance is monitored in real time according to the on-orbit data or the data provided by the ground. If the excess power Q _residual (c) provided by the solar array changes from a positive value to an arbitrary value less than or equal to zero, It indicates that the solar array has been seriously damaged, and the calculation formula of Q _residual (c) is:

{Q Q}_{residual residual} ((c c)) = = {I I}_{SA SA} ((c c)) \times \times ((Te Te - - te te)) - - {I I}_{load load__mean mean} ((c c)) \times \times ((Te Te - - te te)) - - 1.02 1.02 \times \times {&Integral; &Integral;}_{00}^{te te} {I I}_{d d} ((t t)) \times \times dt dt - - - - - - ((Equ Equivalent . . 1010))

in:

Q _residual (c)——the excess power that can be provided by the solar array on the cth ring in orbit, the unit is C;

Te is the orbital period, the unit is s;

te——shadow period time, unit is s;

I _SA (c)——the current value of the current clamping point of the c-th circle square array on the track, the unit is A;

I _{load_mean} (c)——the load current I _load (A) during the light period, which is the average value of the load current per cycle of the c-th circle on the rail, and the unit is A;

I _d (t)——shade period, battery discharge current, unit is A;

According to the equation of the IV curve of the solar array in the specified period, when the bus voltage V _{s_bus} of the corresponding illumination area and the sum of the voltage drop of the solar array isolation diode and the power supply cable V _{s_dioline} are given, the working voltage clamp of the solar array on the IV curve of the specified period can be obtained The current value I _{s_op1} at the point V _op1 ; from the energy balance calculation, the excess power Q _residual (c) provided by the solar array in the specified period can be expressed as:

{Q Q}_{S S__residual residual} ((c c)) = = {I I}_{s the s__op op 11} ((c c)) \times \times ((Te Te - - te te)) - - {I I}_{S S__load load__mean mean} ((c c)) \times \times ((Te Te - - te te)) - - 1.02 1.02 \times \times {&Integral; &Integral;}_{00}^{te te} {I I}_{d d} ((t t)) \times \times dt dt - - - - - - Equ Equivalent . . 1111

In the formula:

I _{s_op1} ——the current value at the solar array operating voltage clamp point V _op1 on the IV curve during the pointing period, the unit is A;

I _{s_load_mean} ——the average value of the load current in the illuminated area/all load current data on the track during the specified period, the unit is A;

I _d (t)——the discharge current value of the battery in the shaded area for a specified period, in A;

The calculation model of solar array working voltage point output power is as follows:

P _SA (t) = V _bus (t) I _op1 (t), I _SA (t) = I _op1 (t)

Further available:

P _{s_op1} (c)＝V _{s_bus} (c)I _{s_op1} (c)

V _{s_op1} (c)＝V _{s_bus} (c)+V _{s_dioline} (Equ.12)

In the formula:

t——the moment in the orbital period of the cth circle, 0<t<Te, where Te is the orbital period, and the unit is s;

P _SA - the output power of the solar array, in W;

P _{s_op1} (c)——the output power when the output of the c-th circle solar array is clamping point V _{s_op1} , the unit is W;

I _{s_op1} (c)——the current value at the clamping point V _{s_op1} of the working voltage of the solar array on the IV curve of the cth circle, the unit is A;

V _{s_bus} —— bus voltage in the lighting area, the unit is V;

V _{s_dioline} ——the sum of the voltage drop of the solar array isolation diode and the power supply cable, the unit is V;

For the on-rail power supply system, since the power controller keeps the bus voltage at a constant value during the light period, it can be considered that: under the premise of the normal operation of the power controller, the bus voltage during the light period is always constant; at the same time, after obtaining V _{s_dioline} After the value is obtained, the clamping point current value I _{s_op1} (c) of the specified period can be obtained through the IV curve established above for energy balance calculation;

If the system predicts that Q _residual (c)=0 in a specified period, it means that the solar array has reached the end of its life at this time;

Among them, when calculating the discharge current of the battery pack, the discharge current of the battery pack depends on the discharge power of the battery pack, the efficiency of the discharge regulator, the loss factor of the power supply line of the battery pack, and the voltage factor of the battery pack;

In the shaded area, the discharge current of the battery pack is:

{I I}_{d d} ((t t)) = = \frac{(({I I}_{load load} ((t t)) - - {I I}_{SA SA} ((t t)))) \times \times {V V}_{bus bus}}{{η η}_{BDR BDR} \cdot \cdot {η η}_{line line} \cdot \cdot {V V}_{bat bat} ((t t))} - - - - - - ((Equ Equivalent . . 1313))

In the formula:

I _load (t) - function of the current demand of the on-rail load changing with time;

η _BDR ——discharge regulator efficiency;

η _line ——loss factor of power supply line of battery pack;

V _bat (t)——the discharge voltage of the battery pack; based on the initial discharge pressure and final discharge voltage value of the track battery on the cth circle of the track, it can be approximately considered that V _bat (t) changes linearly from the initial discharge pressure to the final discharge pressure;

V _bus : bus voltage during discharge, unit is V;

Among them: the solar array I _SA (t) current in the shaded area is zero, and V _bat (t) is an integrand function, which is a linear function determined by the initial discharge voltage and the final discharge voltage of the battery on the rail.

2. a kind of small satellite solar array life prediction method based on I-V curve and energy balance according to claim 1, is characterized in that: described solar array temperature is calculated as follows by solar array temperature model:

The temperature of the solar array changes with the state of the satellite entering and leaving the shadow. In the shadow area, the temperature of the solar array gradually drops until it reaches the lowest temperature before the shadow; The temperature equilibrium point, after which the temperature remains constant until the satellite enters the earth shadow period of the next orbital circle, and the cycle repeats;

The simplified model of solar array temperature variation is as follows:

During the earth shadow period, the temperature of the solar array decreases linearly from the highest equilibrium temperature in the light period to the lowest temperature in the earth shadow period. Rise from 60°C to the highest equilibrium temperature during the light period, until the next image-taking;

The default values of the maximum equilibrium temperature in the light period and the minimum temperature in the shadow period are:

The highest equilibrium temperature T _SAS in the light period; the lowest temperature T _SAE in the earth shadow period.