﻿ 一种航天器太阳电池阵供电能力计算方法<sup>*</sup>
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A calculation method for power supply capability of spacecraft solar array
LI Tao, LI Wei, YANG Lei
Institute of Manned Space System Engineering, China Academy of Space Technology, Beijing 100094, China
Received: 2016-07-13; Accepted: 2016-08-26; Published online: 2016-08-31 14:46
Foundation item: National Science and Technology Major Project
Corresponding author. LI Tao, E-mail:libitpeter@126.com
Abstract: The solar array supplies power to spacecraft. Thus, it is important to predict power supply capability for spacecraft design and certification of on-orbit flight operation, and a calculation method for power supply capability of spacecraft solar array is proposed. The current versus voltage model of photovoltaic cell under standard test condition (STC) was developed using a group of ground test data, and then the parameters of the model such as photon current, cell series resistance, and cell shunt resistance were adapted to on-orbit irradiation intensity, temperature and shadow. According to Kirchhoff law, the outputs of photovoltaic cell working voltage, current, bypass diodes and block diodes in solar array were obtained, and the model of photovoltaic array was built. Simulation was performed for a typical spacecraft. Results show that this method is applicable to photovoltaic array power capability analysis under arbitrary irradiation intensity, temperature and shadow pattern, the influence of bypass diode and block diode in the solar array is analyzed accurately, and calculation accuracy is improved by 20% compared to traditional method.

1 太阳电池阵供电模型

 图 1 太阳电池阵供电能力计算流程 Fig. 1 Calculating process of solar array's power supply capability
1.1 太阳电池片在轨伏安模型

 图 2 太阳电池片等效模型[1] Fig. 2 Solar cell equivalent model[1]

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 图 3 标准测试条件下太阳电池片伏安测试数据 Fig. 3 I-V test data of solar cell under standard test condition

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1.2 太阳电池串伏安模型

 图 4 太阳电池串等效模型 Fig. 4 Solar cell string equivalent model

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 图 5 不同光强下的太阳电池片I-V曲线 Fig. 5 Solar cell I-V curves under different irradiation intensity

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1.3 太阳电池阵伏安模型

 图 6 太阳电池阵等效模型 Fig. 6 Solar cell array equivalent model

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 图 7 太阳电池串I-V曲线 Fig. 7 Solar cell string's I-V curves

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2 仿真分析 2.1 计算方法正确性验证

Saber软件可以对太阳电池片伏安模型进行仿真，但其无法根据大规模太阳电池阵在轨光强、温度和遮挡情况进行动态分析，因此使用Saber对2并4串的简单太阳电池阵进行静态计算，以验证本文方法的正确性。太阳电池片参数如表 1所示[16]，旁路二极管和隔离二极管参数如表 2所示，太阳电池电路以及遮挡阴影如图 8所示，其中电池片PV12遮挡60%，PV13遮挡20%，其他电池片无遮挡，电池阵工作温度75 ℃，温度均匀。

 参数 数值 短路点电流Isc/A 0.17123 短路点导数dsc -0.87479 开路点电压Voc/V 2.71 开路点导数doc -5000.5 最大功率点电流Im/A 0.16725 最大功率点电压Vm/V 2.41 电池片尺寸/(mm×mm) 50×38 电流温度系数a/(A·℃-1) 0.011×10-3

 参数 数值 理想因子n 1.95 二极管饱和电流Io/A 0.9×10-8

 图 8 简单太阳电池阵电路模型 Fig. 8 Simple solar array's circuit model

 图 9 太阳电池片I-V曲线 Fig. 9 I-V curves of solar cell

 图 10 太阳电池串和电池阵I-V曲线 Fig. 10 I-V curves of solar cell strings and array
2.2 航天器太阳电池阵供电能力仿真分析

 参数 数值 轨道高度/km 393 轨道倾角/(°) 42 太阳入射角(太阳矢量与轨道面夹角)/(°) 0~60 轨道环境光强/(W·m-2) 1353 太阳电池阵温度/℃ 75

 图 11 航天器几何模型与太阳电池片电路模型 Fig. 11 Spacecraft geometric model and solar cell circuit model

 图 12 不同温度下的太阳电池阵I-V曲线 Fig. 12 I-V curves of solar array at different temperatures

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 图 13 太阳帆板1输出电流 Fig. 13 Output current of solar array 1
 图 14 太阳帆板1电流与太阳入射角余弦关系 Fig. 14 Relationship between current of solar array 1 and cosine of sun incident angle

 图 15 太阳帆板2输出电流 Fig. 15 Output current of solar array 2
 图 16 太阳帆板2输出电流误差 Fig. 16 Output current error of solar array 2

 图 17 太阳帆板2遮挡阴影 Fig. 17 Shadow pattern of solar array 2

 图 18 不同阴影形状下的太阳电池阵输出电流 Fig. 18 Output currents of solar array with different shadow patterns
3 结论

1) 本文方法可以根据一组标准测试条件下太阳电池片I-V数据，结合在轨实际光强、温度和遮挡情况，推导出电池片在轨伏安模型，并根据基尔霍夫定律推导电池阵中旁路二极管、隔离二极管开关情况，进而精确计算太阳电池阵伏安模型。

2) 太阳电池阵工作温度上升，会导致最大功率点电压下降，工作点电压小于最大功率点电压，并有一定余量，可确保温度变化期间，工作点电压始终小于最大功率点电压，从而保持电池阵输出电流稳定。

3) 太阳电池阵被部分遮挡，可能导致电池阵整体无输出；利用遮挡率和太阳光夹角计算电池输出电流的方法误差较大，最大可至6.5A，其原因是电池串被部分遮挡后，无法提供母线电压，隔离二极管反向断开，导致整串无输出，遮挡率方法无法分析这种情况。

4) 太阳电池阵输出电流与阴影形状有关，遮挡面积相同而形状不同的阴影，造成电池阵伏安模型不同，本文方法可以分析任意阴影形状下的电池阵伏安模型，避免遮挡率分析方法的误差，计算精度可提高20%。

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文章信息

LI Tao, LI Wei, YANG Lei

A calculation method for power supply capability of spacecraft solar array

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(7): 1355-1363
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0600