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Article(id=1190348883428475737, tenantId=1146029695717560320, journalId=1189987059142926344, issueId=1190348881494904994, articleNumber=null, orderNo=null, doi=10.19457/j.1001-2095.dqcd25690, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1710172800000, receivedDateStr=2024-03-12, revisedDate=1714924800000, revisedDateStr=2024-05-06, acceptedDate=null, acceptedDateStr=null, onlineDate=1761730889422, onlineDateStr=2025-10-29, pubDate=1752940800000, pubDateStr=2025-07-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1761730889422, onlineIssueDateStr=2025-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1761730889422, creator=13701087609, updateTime=1761730889422, updator=13701087609, issue=Issue{id=1190348881494904994, tenantId=1146029695717560320, journalId=1189987059142926344, year='2025', volume='55', issue='7', pageStart='3', pageEnd='96', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1761730888961, creator=13701087609, updateTime=1761731818083, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1190352778577936921, tenantId=1146029695717560320, journalId=1189987059142926344, issueId=1190348881494904994, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1190352778577936922, tenantId=1146029695717560320, journalId=1189987059142926344, issueId=1190348881494904994, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=64, endPage=69, ext={EN=ArticleExt(id=1190348883600442202, articleId=1190348883428475737, tenantId=1146029695717560320, journalId=1189987059142926344, language=EN, title=Improving Fan Virtual Inertia Adaptive Cooperative Control Strategy Based on STATCOM/BESS, columnId=null, journalTitle=Electric Drive, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to eliminate the problem of low inertia and large frequency fluctuation in wind power grid-connected system when power disturbance occurs，an improved virtual inertia control strategy was proposed.A cooperative control strategy of adaptive moment of inertia and damping coefficient was introduced in the main control system of wind power inverter. The energy storage static synchronous compensator（STATCOM/BESS）was used to provide the active power and reactive power required by the system. At the same time，the power output of STATCOM/BESS was adjusted according to the frequency deviation and change rate of the system. By analyzing the small signal model of virtual synchronous generator（VSG）of the fan，the setting rules of the adaptive VSG moment of inertia and damping coefficient were determined. The Matlab/Simulink simulation results show that the strategy has a more obvious effect on frequency fluctuation，and can effectively suppress the voltage drop of the fan junction point，and improve the ability of safe and stable operation of the system.

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为消除风电并网系统在功率发生扰动时呈现出低惯性和频率波动较大的问题，提出一种改进型的虚拟惯性控制策略。在风电逆变器主控系统中引入自适应变化的转动惯量和阻尼系数协同控制策略，并采用储能型静止同步无功补偿器（STATCOM/BESS）提供系统所需补偿的有功功率和无功功率，同时依据系统频率偏差量及变化率调整STATCOM/BESS的功率输出。通过分析风机VSG的小信号模型，确定自适应VSG转动惯量及阻尼系数的整定规则。通过Matlab/Simulink仿真对比结果表明，该策略抑制频率波动的效果更为明显，并且能够有效抑制风机并网点电压跌落，提高了系统安全稳定运行的能力。

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苗海东（1993—），男，硕士，助教，主要研究方向为新能源发电技术和微电网协同控制策略，Email：

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苗海东（1993—），男，硕士，助教，主要研究方向为新能源发电技术和微电网协同控制策略，Email：

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苗海东（1993—），男，硕士，助教，主要研究方向为新能源发电技术和微电网协同控制策略，Email：

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Changes of JMΣ and D in different stages

, figureFileSmall=null, figureFileBig=null, tableContent=
阶段 Δω dω/dt Δω（dω/dt） Jα JMΣ D
1 >0 >0 >0 ↑ ↑ 适当↑
2 >0 <0 <0 ↓ ↓ 适当↑
3 <0 <0 >0 ↑ ↑ 适当↑
4 <0 >0 <0 ↓ ↓ 适当↑
), ArticleFig(id=1190380224446586961, tenantId=1146029695717560320, journalId=1189987059142926344, articleId=1190348883428475737, language=CN, label=表1, caption=

不同阶段下的JMΣ和D 变化情况

, figureFileSmall=null, figureFileBig=null, tableContent=
阶段 Δω dω/dt Δω（dω/dt） Jα JMΣ D
1 >0 >0 >0 ↑ ↑ 适当↑
2 >0 <0 <0 ↓ ↓ 适当↑
3 <0 <0 >0 ↑ ↑ 适当↑
4 <0 >0 <0 ↓ ↓ 适当↑
), ArticleFig(id=1190380224538861650, tenantId=1146029695717560320, journalId=1189987059142926344, articleId=1190348883428475737, language=EN, label=Tab.2, caption=

Simulation parameter

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参数名称 参数 参数值 参数名称 参数 参数值
线路电阻 R/Ω 2.4 基础转动惯量 Jα/（kg·m2） 0.3
滤波电感 L/mH 22 阻尼系数 D0/
（N·m·s·rad-1）		 20
滤波电容 C/μF 24 转动惯量调节系数 kj 0.8
直流母
线电压		 Udc/kV 2.4 转动惯量阈值 β 2
负载电压 UL/V 600 阻尼调节系数 kd 20
转动惯量 J0/（kg·m2） 0.2 阻尼系数阈值 α 0.1
), ArticleFig(id=1190380224652107859, tenantId=1146029695717560320, journalId=1189987059142926344, articleId=1190348883428475737, language=CN, label=表2, caption=

仿真参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数名称 参数 参数值 参数名称 参数 参数值
线路电阻 R/Ω 2.4 基础转动惯量 Jα/（kg·m2） 0.3
滤波电感 L/mH 22 阻尼系数 D0/
（N·m·s·rad-1）		 20
滤波电容 C/μF 24 转动惯量调节系数 kj 0.8
直流母
线电压		 Udc/kV 2.4 转动惯量阈值 β 2
负载电压 UL/V 600 阻尼调节系数 kd 20
转动惯量 J0/（kg·m2） 0.2 阻尼系数阈值 α 0.1
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基于STATCOM/BESS提高风机虚拟惯性自适应协同控制策略
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苗海东 1 , 张庆 1 , 晏永 1 , 张丽娜 1 , 霍婷婷 1 , 韩林杰 2
电气传动 | 综合能源与现代电网 2025,55(7): 64-69
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电气传动 | 综合能源与现代电网 2025, 55(7): 64-69
基于STATCOM/BESS提高风机虚拟惯性自适应协同控制策略
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苗海东1 , 张庆1, 晏永1, 张丽娜1, 霍婷婷1, 韩林杰2
作者信息
  • 1.宁夏师范学院 物理与电子信息工程学院，宁夏 固原756000
  • 2.中广核新能源投资（深圳）有限公司宁夏分公司，宁夏 银川750000

    • 苗海东（1993—），男，硕士，助教，主要研究方向为新能源发电技术和微电网协同控制策略，Email：

Improving Fan Virtual Inertia Adaptive Cooperative Control Strategy Based on STATCOM/BESS
Haidong MIAO1 , Qing ZHANG1, Yong YAN1, Lina ZHANG1, Tingting HUO1, Linjie HAN2
Affiliations
  • 1. School of Physics and Electronic Information Engineering，Ningxia Normal University，Guyuan 756000，Ningxia，China
  • 2. CGN New Energy Investment（Shenzhen）Co.，Ltd.，Yinchuan 750000，Ningxia，China
出版时间: 2025-07-20 doi: 10.19457/j.1001-2095.dqcd25690
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摘要
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为消除风电并网系统在功率发生扰动时呈现出低惯性和频率波动较大的问题，提出一种改进型的虚拟惯性控制策略。在风电逆变器主控系统中引入自适应变化的转动惯量和阻尼系数协同控制策略，并采用储能型静止同步无功补偿器（STATCOM/BESS）提供系统所需补偿的有功功率和无功功率，同时依据系统频率偏差量及变化率调整STATCOM/BESS的功率输出。通过分析风机VSG的小信号模型，确定自适应VSG转动惯量及阻尼系数的整定规则。通过Matlab/Simulink仿真对比结果表明，该策略抑制频率波动的效果更为明显，并且能够有效抑制风机并网点电压跌落，提高了系统安全稳定运行的能力。

阻尼系数  /  虚拟同步发电机  /  频率抑制  /  转动惯量  /  STATCOM/BESS器件

In order to eliminate the problem of low inertia and large frequency fluctuation in wind power grid-connected system when power disturbance occurs，an improved virtual inertia control strategy was proposed.A cooperative control strategy of adaptive moment of inertia and damping coefficient was introduced in the main control system of wind power inverter. The energy storage static synchronous compensator（STATCOM/BESS）was used to provide the active power and reactive power required by the system. At the same time，the power output of STATCOM/BESS was adjusted according to the frequency deviation and change rate of the system. By analyzing the small signal model of virtual synchronous generator（VSG）of the fan，the setting rules of the adaptive VSG moment of inertia and damping coefficient were determined. The Matlab/Simulink simulation results show that the strategy has a more obvious effect on frequency fluctuation，and can effectively suppress the voltage drop of the fan junction point，and improve the ability of safe and stable operation of the system.

damping coefficient  /  virtual synchronous generator（VSG）  /  frequency suppression  /  moment of inertia  /  STATCOM/BESS
苗海东, 张庆, 晏永, 张丽娜, 霍婷婷, 韩林杰. 基于STATCOM/BESS提高风机虚拟惯性自适应协同控制策略. 电气传动, 2025 , 55 (7) : 64 -69 . DOI: 10.19457/j.1001-2095.dqcd25690
Haidong MIAO, Qing ZHANG, Yong YAN, Lina ZHANG, Tingting HUO, Linjie HAN. Improving Fan Virtual Inertia Adaptive Cooperative Control Strategy Based on STATCOM/BESS[J]. Electric Drive, 2025 , 55 (7) : 64 -69 . DOI: 10.19457/j.1001-2095.dqcd25690
正文
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大规模的风电机组因其波动性和随机性给系统频率的控制造成很大困难，同时负载端功率突变破坏了系统的功率平衡导致频率闪变，此时风电机组惯量支撑能力不足[1]，所以强化风电机组的惯量支撑能力对新型电力系统具有重要意义[2]。
当下风电和光伏利用储能技术能够抑制有功功率的波动，以此提高了分布式能源系统并网的虚拟惯性[3-4]。虚拟同步发电机（virtual synchronous generator，VSG）技术利用转动惯量和阻尼环节，模拟同步发电机对系统进行一次调频[5]。文献[6]采用乒乓可调节控制转动惯量，根据参数值的不同抑制角速度的变化量并缩短角速度的恢复时间，但未给出两种关键参数的整定原则。文献[7]采用虚拟VSG技术提出系统电压调节和双馈风机并网频率调节方案，但是没有考虑虚拟惯性随系统频率自适应变化，从而减小频率的超调量和调整时间。文献[8]采用下垂控制和虚拟同步发电机结合的方法，引入储能技术减小系统频率波动，但未考虑系统电压波动的恢复机制。文献[9-10]采用交错协同控制，结合转动惯量、阻尼系数随时间变化减小转子角速度偏移量，但未给出具体参数的整定原则。文献[11-12]利用STATCOM/BESS与光储系统结合控制，以此增强系统的转动惯量，提高新能源电网调频能力，但是转动惯量为固定值，负荷突变会出现频率暂态过程较长问题。文献[13]研究了STATCOM/BESS对风电场和光伏有功功率平仰和无功功率补偿协同控制策略，但未给出工作模式的分区原则和转动惯量的取值。
本文引入改进的虚拟惯性控制策略，该策略根据转子角速度及角速度的偏差量变化的大小，相对应地分别增加（或减小）转动惯量和阻尼系数的大小。同时，采用STATCOM/BESS装置给风电并网系统提供所需的有功功率和无功功率以此增强风电系统的虚拟惯性，并利用Matlab/Simulink进行仿真，验证了该策略在提高系统的频率支撑和稳定电压方面的可行性。
1 传统VSG的基本原理
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传统VSG模型转子运动方程如下式所示：
J d ω d t = M T - M e - M D = M T - M e - D ( ω - ω 0 ) d δ d t = ω - ω 0
式中：J，D，ω分别为同步发电机的转动惯量、阻尼系数和角频率；ω0为系统额定频率；MT为机械转矩；Me为电磁转矩；MD为阻尼转矩；δ为发电机功角。
VSG采用有功/频率控制[14]，控制原理如图1所示。
由图1可知，传统VSG频率特性为
Δ ω Δ P = ω 0 - ω P r e f - P = 1 J ω 0 s + D ω 0 + K a
式中：P为VSG输出有功功率；Ka为调差系数。
2 风机VSG虚拟惯量的提高
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2.1 风机的虚拟惯性
电网频率因负荷突增导致下降，风电机组和系统的惯量常数近似相同，通过控制有功功率使得风电机组将转子的部分动能转变为电能送入电网，抑制系统频率波动体现出同步发电机的工作模式。阻尼影响忽略不计，其部分动能Ek为
E k = 1 2 J M ω 2
式中：JM为风机的转动惯量；ω为风机角速度。
惯量常数H为
H = J M ω 2 2 S N
式中：SN为额定容量。
惯量常数H与旋转动能Ek成正比，电网频率出现波动后风电系统现有的惯量不足以抑制频率的波动，因此需要增强风电系统的惯性。
2.2 增强系统虚拟惯性分析
STATCOM/BESS与风机并联视为整体，通过对其恰当的控制，可实现对风电系统有功与无功快速响应，不仅增强了风电系统虚拟惯量的支撑，而且抑制了功率突变对风电系统频率的影响。
当电网频率突变时，STATCOM/BESS快速补偿有功和无功功率。其中：无功功率解决电压问题；有功功率解决风电系统频率波动和低惯性问题[15]。风电系统增强后的惯量常数为
H ∑ = E k m + E k w S N ∑
式中：Ekm为风机旋转动能；Ekw为STATCOM/BESS装置输出的风电系统所需补偿的动能；SN∑为额定容量之和。
电网频率突变导致系统功率失衡的情况下，通过合理控制使得STATCOM/BESS输出所需补偿的有功和无功，使惯量常数、虚拟惯量得到提升。
风电系统频率从ω0下降（或上升）到ω1，根据补偿的功率得到需要的动能为[16]
Δ E k ∑ = 1 2 J M ∑ ( ω 0 2 - ω 1 2 )
式中：ΔEk∑为补偿风机所需的动能；JM∑为虚拟惯量之和。
当ΔEk∑ <0（或>0）时，风电系统向电网释放（或吸收）所需电能，此时风电系统的虚拟转动惯量JM∑为
J M ∑ = 2 Δ E k ∑ ω 0 2 - ω 1 2
由式（7）可得，通过对STATCOM/BESS输出功率合理控制，虚拟转动惯量JM∑可根据频率和所需动能的变化量自适应地进行调整。
3 改进的虚拟惯量控制策略
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在频率发生波动的情况下，有两个关键性的指标用于评估系统频率的稳定性：一是频率振荡的超调量；二是频率稳定的时间。
在频率波动期间，功率和频率均为衰减振荡变化，根据变化特性将振荡过程分为四个阶段：第一阶段，当ω>ω0且大幅增加，dω/dt>0且先大幅增加后增加幅度减小，此时，转动惯量、阻尼系数需要相应地增加，避免dω/dt，Δω及ω偏差量较大；第二阶段，当ω>ω0且逐渐减小，dω/dt<0且逐渐减小，此时，转动惯量减小以便角速度可以快速恢复至额定值，阻尼系数需要进一步增大来消除角速度的偏移。转动惯量、阻尼系数在第三、四阶段的变化情况与第一、二阶段的变化情况类似，此处不再叙述。综上，本文改进的虚拟自适应协同控制策略为
J M ∑ = J 0                                                                                                                                     Δ ω d ω / d t   ≤ 0 J α                                                                                                                               | d ω / d t   ≤ β J α + k j | d ω / d t                         | d ω / d t   β
D = D 0                                                                                                                                     Δ ω ≤ α D 0   + k d | Δ ω                               | Δ ω α
式中：J0为系统稳定时的转动惯量；D0为系统稳定时的阻尼系数；β，α为变化的阈值（β>0，α >0）；kj为转动惯量的调节系数；kd为阻尼的调节系数；Jα为基础转动惯量。
JM∑，D的变化情况如表1所示。
综上所述，转动惯量JMΣ需根据角速度偏差量及其变化率的变化而变化，阻尼系数D只根据角速度偏差量的变化而变化，基础转动惯量Jα随着STATCOM/BESS输出的有功大小进行适当调节，所以需要调节它的工作模式，其控制原理如图2所示，本文只考虑蓄电池有足够的补偿功率的三种工作模式。
1）当|dω/dt|≤β时，装置只输出无功功率，调节并网点的电压幅值，电流内环的d，q轴电流为[17]
i d = 0 i q = i q 0
2）当|dω/dt|>β且 Δω（dω/dt）>0时，BESS释放电能，装置输出所需有功功率，增大系统的虚拟惯量，此时电流内环的d，q轴电流为
i d 0 ≤ 0 i q = i q 0
3）当|dω/dt|>β并且 Δω（dω/dt）<0时，BESS吸收电能，减小系统的虚拟惯量，此时电流内环的d，q轴电流为
i d 0 0 i q = i q 0
为了使系统能够安全稳定运行，需对JM∑参数进行合理的设计并给出取值范围。
4 参数整定分析
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由式（7）可得，JMΣ与ΔEkΣ成正比，与角频率的波动量成反比，所以Δω值影响STATCOM/BESS装置的功率输出，同时需要对虚拟惯量进行适当调整，以此来确保系统的稳定性。结合视在功率的整定方法，得到VSG的有功功率、无功功率的表达式如下式所示：
P = E U c c o s ( φ - δ ) Z - U c 2 c o s φ Z Q = E U c s i n ( φ - δ ) Z - U c 2 s i n φ Z
其中
Z = ( ω L ) 2 + R 2 φ = a r c t a n ( ω L / R )
式中：Z为线路的等效阻抗；E，Uc分别为风机的机端电压和系统电压；δ为VSG的功角；φ为VSG的阻抗角；L为线路的电感；R为等效电阻。
结合式（1），并根据传统的同步发电机小信号模型分析法[18]，令VSG的等效电阻R等于0，得到VSG电磁功率的传递函数为传统的二阶系统传递函数，表达式如下式所示：
G ( s ) = P ( s ) P r e f ( s ) = 1 ω 0 E U c Z J M s 2 + ( D + K a ω 0 ) s + 1 ω 0 E U c Z
风机虚拟同步发电机的特征根为
x 1,2 = - ( D + K a ω 0 ) ± ( D + K a ω 0 ) 2 - 4 J M E U c ω 0 Z 2 J M
根据二阶系统控制理论[19]，系统处于稳定状态时需传递函数的特征根位于坐标轴的左半平面，因此D和JM∑均应大于0。由式（16）可知，二阶系统的自然振荡角频率ωn和阻尼系数ξ为
ω n = E U c J M ω 0 Z ξ = D ω 0 Z 4 J E U c + K a Z 4 J ω 0 E U c
按照最优二阶系统的原则[20]，对虚拟同步发电机的控制器进行设计，选取ξ=0.707，根据式（17）可确定阻尼系数D的基础值，虚拟同步发电机的自然振荡频率一般在0.628~15.700 rad/s范围内，所以JM∑的取值范围为
E U c 15 . 7 2 Z ≤ J M ∑ ≤ E U c 0 . 628 2 Z
5 仿真结果分析
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STATCOM/BESS并入风机的电力系统的仿真模型如图3所示，设定电网系统额定频率为60 Hz，PL为本地可变负载，大小为5 MW，系统电压为25 kV，风电系统与火电机组并联经一条长21 km的交流输电线路给负载提供电能。系统模型仿真参数如表2所示。
5.1 并网点频率响应
在本地负载突变情况下对风电系统频率的响应进行分析，当t=5 s时，本地负载PL突增4 MW，单台风电的额定功率为3 MW。下面将分析传统/自适应虚拟惯量控制策略下的风电系统频率响应波形图，如图4所示。
由图4可知，t=5 s时，本地负载PL突增4 MW，造成系统在本地负载突增的瞬间电源输出的有功功率低于有功功率的需求，导致风电系统频率跌落。此时引入改进的虚拟惯性控制策略后风电系统频率由传统VSG控制下的59.82 Hz提升至59.97 Hz，提升效果达到0.15 Hz，稳定响应时间由0.37 s缩短至0.16 s，提升效果达到0.19 s，可见引入该策略相比于传统虚拟惯量控制缩短了风电系统频率响应时间，提高了风电系统频率的稳定性。
5.2 STATCOM/BESS的功率和控制电流输出
STATCOM/BESS采集并联节点的频率偏差，实时地对系统缺少的有功、无功进行定量补偿，以此来提高风机系统的虚拟惯性。图5a所示为装置输出的有功功率，图5b所示为装置输出的无功功率，图5c所示为装置的控制电流。
由图5a可知，当系统频率与额定值偏差较大时，其有功出力增加，为风机提供有功功率，增大系统的虚拟转动惯量；当频率与额定值偏差较小时，其有功出力减小，减小系统的虚拟转动惯量。
由图5b可知，当系统频率与额定值相等时，其无功出力为零，在t=5 s时，风机并网点电压因本地负载突增导致跌落，其无功出力瞬间增大来抑制电压的降落，随着功率波动的减缓，输出的无功功率也随之减小，最后输出无功功率达到稳定。
由图5c可知，当系统频率与额定值相等时，其STATCOM/BESS装置有功、无功电流为零，在t=5 s时，无功电流为正值，STATCOM/BESS装置向电网释放无功功率；同时刻，有功电流值为负值，STATCOM/BESS装置向电网释放有功功率，其后电流值为正值，STATCOM/BESS装置吸收系统多余的有功功率。
5.3 风机并网点及装置直流母线电压变化情况
为了确保风机并网点电压的稳定和装置稳定工作，STATCOM/BESS装置与系统进行双向有功功率、无功功率的释放和吸收，以此调整系统的无功和有功的基本分布。图6a所示为风电系统并网点电压变化情况，图6b所示为STATCOM/BESS装置直流母线侧电压变化情况。
由图6a可知，当负载突变时，因STATCOM/BESS装置给系统输出补偿的无功功率，使得风机并网点电压在跌落至0.98（标幺值）后快速恢复到额定值。同时，STATCOM/BESS装置直流母线侧电压出现波动后又快速恢复到额定值，保证了STATCOM/BESS装置能够正常工作，提高了系统对新能源并入电网的电压控制能力，系统频率得到了安全可靠的保障。
6 结论
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1）STATCOM/BESS装置依据电网系统频率的偏差量及变化率调节有功出力的大小，以此改善风电系统虚拟惯量自适应调节的效果。
2）改进型的虚拟惯性控制策略通过引入自适应变化的转动惯量和阻尼系数，抑制了风电系统频率的偏差量和变化率，根据小信号模型确定了阻尼惯量和阻尼系数的整定原则。
3）电网负载突变的情况下，改进型的虚拟自适应协同控制策略抑制风电系统频率波动的效果更为明显，而且STATCOM/BESS装置提供了所需补偿的无功功率，使风机并网点电压跌落后能够快速恢复到电压额定值，更好地提高了风电系统安全稳定运行的能力。
基金
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  • 宁夏自然科学基金项目(2023AAC03339)
  • 宁夏自然科学基金项目(2022AAC03302)
  • 宁夏自然科学基金项目(2022AAC03335)
  • 宁夏自然科学基金项目(2022AAC03319)
  • 宁夏重点研发项目(2020BEB04040)
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2025年第55卷第7期
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doi: 10.19457/j.1001-2095.dqcd25690
  • 接收时间：2024-03-12
  • 首发时间：2025-10-29
  • 出版时间：2025-07-20
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  • 收稿日期：2024-03-12
  • 修回日期：2024-05-06
基金
宁夏自然科学基金项目(2023AAC03339)
宁夏自然科学基金项目(2022AAC03302)
宁夏自然科学基金项目(2022AAC03335)
宁夏自然科学基金项目(2022AAC03319)
宁夏重点研发项目(2020BEB04040)
作者信息
    1.宁夏师范学院 物理与电子信息工程学院，宁夏 固原756000
    2.中广核新能源投资（深圳）有限公司宁夏分公司，宁夏 银川750000
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