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Article(id=1239158369974547212, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239158367571210992, articleNumber=null, orderNo=null, doi=10.12347/j.ycyk.20250228001, pmid=null, cstr=32406.14.ycyk.20250228001, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1740672000000, receivedDateStr=2025-02-28, revisedDate=1744128000000, revisedDateStr=2025-04-09, acceptedDate=null, acceptedDateStr=null, onlineDate=1773367977851, onlineDateStr=2026-03-13, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773367977851, onlineIssueDateStr=2026-03-13, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773367977851, creator=13701087609, updateTime=1773367977851, updator=13701087609, issue=Issue{id=1239158367571210992, tenantId=1146029695717560320, journalId=1238841944844054536, year='2025', volume='46', issue='6', pageStart='1', pageEnd='170', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=0, createTime=1773367977278, creator=13701087609, updateTime=1773368232261, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1239159437122917323, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239158367571210992, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1239159437122917324, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239158367571210992, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=85, endPage=94, ext={EN=ArticleExt(id=1239158370184262418, articleId=1239158369974547212, tenantId=1146029695717560320, journalId=1238841944844054536, language=EN, title=Distributed Photovoltaic Data Compression Algorithm Based on Boundary Feature Identification and K-Dimensional Tree Optimization, columnId=1239133503154081962, journalTitle=Journal of Telemetry, Tracking and Command, columnName=TT & C Communication and Navigation, runingTitle=null, highlight=null, articleAbstract=

A data compression collaborative algorithm that integrates transmission optimization and delay control was proposed to address the data dimension explosion and complexity increase caused by the large-scale grid connection of distributed photovoltaic systems. Firstly, based on the theory of decision boundary sensitivity, an optimization framework for minimizing total delay was constructed, and an enhanced inter-class boundary preservation algorithm (EIPB) was proposed to reduce the amount of transmitted data by dynamically maintaining key instances of decision boundaries. Secondly, the traditional distance instance selection method was improved by proposing an enhanced instance selection algorithm (EIS) based on K-dimensional tree (KD-Tree) spatial partitioning, which utilized nearest neighbor search acceleration technology to enhance instance selection efficiency. Then, a dynamic error allocation sector lossless compression algorithm (DEASC) was proposed, which achieved collaborative optimization of compression efficiency and fidelity through adaptive slope constraints and multi-stage entropy encoding. Experimental verification showed that the EIPB-EIS joint algorithm improved the average compression ratio to 7.8 compared to traditional methods, reduced the root mean square error of reconstruction percentage to 0.51%, and reduced transmission delay by 62.7%, effectively solving the problem of efficient transmission and accurate reconstruction of high-dimensional photovoltaic data.

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针对分布式光伏系统规模化并网导致的数据维度激增与计算复杂度高的问题，提出一种基于边界特征辨识与K维树优化的数据压缩算法。首先，基于决策边界敏感度理论构建了最小化总延迟的优化框架，提出增强的类间边界保留算法（EIPB），通过动态维护决策边界特征，降低传输数据量；其次，提出基于K维树（KD-Tree）空间划分的增强特征选择算法（EIS），利用近邻搜索加速技术，提升特征辨识效率；最后，优化动态误差分配的扇形无损压缩算法（DEASC），通过自适应斜率约束与多阶段熵编码，实现压缩效率与保真度的协同优化。实验结果表明：EIPB-EIS联合算法相较于传统方法，平均压缩比提升至7.8，重构百分比均方根误差降至0.51%，传输延迟降低了62.7%，解决了高维光伏数据的高效传输与精准重构难题。

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施展　1983年生，博士，高级工程师。

付佳佳　1985年生，硕士，中级工程师。

亢中苗　1984年生，硕士，中级工程师。

梁宇图　1991年生，硕士，中级工程师。

张仲禹　1997年生，博士研究生。

王立辉　1979年生，教授，博士生导师。

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施展　1983年生，博士，高级工程师。

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施展　1983年生，博士，高级工程师。

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付佳佳　1985年生，硕士，中级工程师。

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付佳佳　1985年生，硕士，中级工程师。

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亢中苗　1984年生，硕士，中级工程师。

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亢中苗　1984年生，硕士，中级工程师。

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梁宇图　1991年生，硕士，中级工程师。

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梁宇图　1991年生，硕士，中级工程师。

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张仲禹　1997年生，博士研究生。

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张仲禹　1997年生，博士研究生。

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王立辉　1979年生，教授，博士生导师。

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王立辉　1979年生，教授，博士生导师。

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CCF Transactions on High Performance Computing, 2024, 6（2）:206-220., articleTitle=Compressed data direct computing for chinese dataset on DCU, refAbstract=null)], funds=[Fund(id=1239158388039414233, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, awardId=036000KK52220013（GDKJXM2022024）, language=CN, fundingSource=中国南方电网有限公司科技项目(036000KK52220013（GDKJXM2022024）), fundOrder=null, country=null), Fund(id=1239158388148466141, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, awardId=2021YFB2501603, language=CN, fundingSource=国家重点研发计划(2021YFB2501603), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1239158381362081979, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, xref=null, ext=[AuthorCompanyExt(id=1239158381366276284, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, companyId=1239158381362081979, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1. Guangdong Power Grid Co., Ltd., Guangzhou, 510600, China), AuthorCompanyExt(id=1239158381374664893, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, companyId=1239158381362081979, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.广东电网有限责任公司 广州 510600)]), AuthorCompany(id=1239158381441773762, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, xref=null, ext=[AuthorCompanyExt(id=1239158381450162371, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, companyId=1239158381441773762, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2. School of Instrument Science and Engineering, Southeast University, Nanjing, 210096, China), AuthorCompanyExt(id=1239158381462745284, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, companyId=1239158381441773762, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.东南大学仪器科学与工程学院 南京 210096)])], figs=[ArticleFig(id=1239158385954845035, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=EN, label=Fig. 1, caption=Distance instance selection (DIS) algorithm, figureFileSmall=vA86Sj1cjX7aNzOlKiKz0A==, figureFileBig=PsJwuzQtKym02T7373Jcjw==, tableContent=null), ArticleFig(id=1239158386017759600, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=CN, label=图1, caption=距离特征选择（DIS）算法, figureFileSmall=vA86Sj1cjX7aNzOlKiKz0A==, figureFileBig=PsJwuzQtKym02T7373Jcjw==, tableContent=null), ArticleFig(id=1239158386252640636, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=EN, label=Fig. 2, caption=Dynamic error activated sector compression dynamic process, figureFileSmall=yCVvO7GP8HMBQC1XmIfrXw==, figureFileBig=6/+l2HtQG9tQpd5DdzTwAg==, tableContent=null), ArticleFig(id=1239158386319749505, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=CN, label=图2, caption=扇形压缩算法动态过程, figureFileSmall=yCVvO7GP8HMBQC1XmIfrXw==, figureFileBig=6/+l2HtQG9tQpd5DdzTwAg==, tableContent=null), ArticleFig(id=1239158386424607110, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=EN, label=Fig. 3, caption=Implementation of recursive geometry principles, figureFileSmall=K1Zz2qTaGpewoNyuOg6dQQ==, figureFileBig=tVaWULHUE5V0CHRhqnaSOw==, tableContent=null), ArticleFig(id=1239158386542047629, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=CN, label=图3, caption=递归几何原理实现, figureFileSmall=K1Zz2qTaGpewoNyuOg6dQQ==, figureFileBig=tVaWULHUE5V0CHRhqnaSOw==, tableContent=null), ArticleFig(id=1239158386625933713, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=EN, label=Fig. 4, caption=Relationship diagram between residual error and lossless compression ratio, figureFileSmall=dXCLvE1YE5GNOHb5fcDCLg==, figureFileBig=25mBfqUE30Di8xvyiizgiw==, tableContent=null), ArticleFig(id=1239158386718208406, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=CN, label=图4, caption=残差误差与无损压缩比关系图, figureFileSmall=dXCLvE1YE5GNOHb5fcDCLg==, figureFileBig=25mBfqUE30Di8xvyiizgiw==, tableContent=null), ArticleFig(id=1239158386831454621, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=EN, label=Table 1, caption=

Comparison table of algorithm time complexity

, figureFileSmall=null, figureFileBig=null, tableContent=
算法构建阶段查询阶段总体复杂度
IBPO（n）O（n2）O（L（n+n2））
EIPBO（nlogn）O（knlogn）O（L（nlogn+knlogn））
DIS-O（n2）O（n2）
EISO（nlogn）O（nlogn）O（nlogn）
), ArticleFig(id=1239158386965672356, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=CN, label=表1, caption=

算法时间复杂度对比表

, figureFileSmall=null, figureFileBig=null, tableContent=
算法构建阶段查询阶段总体复杂度
IBPO（n）O（n2）O（L（n+n2））
EIPBO（nlogn）O（knlogn）O（L（nlogn+knlogn））
DIS-O（n2）O（n2）
EISO（nlogn）O（nlogn）O（nlogn）
), ArticleFig(id=1239158387045364135, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=EN, label=Table 2, caption=

Comparison of data compression rates （%） （sorted in ascending order of mean，with smaller values being better）

, figureFileSmall=null, figureFileBig=null, tableContent=
AlgorithmMeanD1D2D3D4D5
CNN0.098 30.017 50.110 00.038 40.071 50.019 4
EIS10.201 90.008 70.354 70.160 90.311 20.159 1
DIS10.223 60.080 90.364 00.165 00.305 10.221 7
EIPB10.231 30.145 80.404 50.168 20.311 60.214 8
IBP10.243 10.145 80.416 10.172 40.305 30.255 5
EIS1,20.305 60.008 00.394 70.256 90.516 70.269 2
EIPB1,20.313 80.000 00.436 30.259 20.516 70.291 1
NM30.320 70.510 90.129 10.044 90.331 00.231 7
DIS1,20.345 10.072 90.394 70.272 50.508 30.427 9
IBP1,20.345 20.023 30.432 90.273 10.508 30.430 2
EIS1,2,30.375 90.007 30.403 40.312 20.648 50.357 8
EIPB1,2,30.381 90.000 00.443 30.313 10.648 50.366 7
DIS1,2,30.419 90.064 90.395 30.334 00.636 00.578 8
IBP1,2,30.423 00.049 60.433 40.334 00.636 00.578 8
OSS0.608 60.420 60.717 60.821 80.784 40.378 1
NM10.666 60.889 20.150 50.055 30.954 20.985 8
IHT0.758 00.892 10.375 60.168 90.955 60.986 7
NCR0.884 40.998 50.843 80.962 00.959 00.988 6
ENN0.920 30.998 50.843 80.963 90.959 00.988 6
TL0.984 11.000 00.965 30.989 10.990 00.997 9
), ArticleFig(id=1239158387141833131, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=CN, label=表2, caption=

数据压缩率对比（%）（按均值升序排列，数值越小越好）

, figureFileSmall=null, figureFileBig=null, tableContent=
AlgorithmMeanD1D2D3D4D5
CNN0.098 30.017 50.110 00.038 40.071 50.019 4
EIS10.201 90.008 70.354 70.160 90.311 20.159 1
DIS10.223 60.080 90.364 00.165 00.305 10.221 7
EIPB10.231 30.145 80.404 50.168 20.311 60.214 8
IBP10.243 10.145 80.416 10.172 40.305 30.255 5
EIS1,20.305 60.008 00.394 70.256 90.516 70.269 2
EIPB1,20.313 80.000 00.436 30.259 20.516 70.291 1
NM30.320 70.510 90.129 10.044 90.331 00.231 7
DIS1,20.345 10.072 90.394 70.272 50.508 30.427 9
IBP1,20.345 20.023 30.432 90.273 10.508 30.430 2
EIS1,2,30.375 90.007 30.403 40.312 20.648 50.357 8
EIPB1,2,30.381 90.000 00.443 30.313 10.648 50.366 7
DIS1,2,30.419 90.064 90.395 30.334 00.636 00.578 8
IBP1,2,30.423 00.049 60.433 40.334 00.636 00.578 8
OSS0.608 60.420 60.717 60.821 80.784 40.378 1
NM10.666 60.889 20.150 50.055 30.954 20.985 8
IHT0.758 00.892 10.375 60.168 90.955 60.986 7
NCR0.884 40.998 50.843 80.962 00.959 00.988 6
ENN0.920 30.998 50.843 80.963 90.959 00.988 6
TL0.984 11.000 00.965 30.989 10.990 00.997 9
), ArticleFig(id=1239158387250885041, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=EN, label=Table 3, caption=

Comparison of running time （s） （sorted in ascending order of mean，the smaller the value，the better）

, figureFileSmall=null, figureFileBig=null, tableContent=
AlgorithmMeanD1D2D3D4D5
NM10.217 60.015 70.026 40.177 20.661 80.335 0
TL0.224 00.010 10.014 30.415 70.584 80.137 2
OSS0.782 00.082 30.117 90.947 52.047 10.913 8
ENN0.932 20.090 10.129 61.701 42.733 40.871 4
NCR0.949 90.126 90.139 50.939 92.757 01.044 2
IHT1.930 40.243 10.232 55.713 32.864 41.388 7
EIS32.255 10.067 30.060 05.541 13.931 43.879 7
EIPB32.258 00.068 10.060 85.543 63.940 13.884 2
EIS23.198 60.067 10.063 58.613 26.917 05.015 1
EIPB23.201 20.067 80.064 38.615 06.925 65.018 1
EIS14.555 70.078 60.104 710.188 112.510 57.201 3
EIPB14.557 70.079 30.105 610.189 812.516 37.203 7
DIS368.158 30.612 10.117 954.992 4262.792 635.251 2
IBP368.161 20.612 80.118 854.994 5262.801 735.255 0
CNN84.135 54.014 89.617 4116.067 8154.872 229.234 2
DIS2113.726 30.736 60.265 3101.608 8530.278 465.490 9
IBP2113.728 90.737 30.266 1101.610 6530.286 665.494 6
DIS1221.974 01.680 02.491 7184.048 51 205.309123.500
IBP1221.976 11.680 62.492 5184.050 01 205.315123.503
), ArticleFig(id=1239158387326382516, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=CN, label=表3, caption=

运行时间对比（s）（按均值升序排列，数值越小越好）

, figureFileSmall=null, figureFileBig=null, tableContent=
AlgorithmMeanD1D2D3D4D5
NM10.217 60.015 70.026 40.177 20.661 80.335 0
TL0.224 00.010 10.014 30.415 70.584 80.137 2
OSS0.782 00.082 30.117 90.947 52.047 10.913 8
ENN0.932 20.090 10.129 61.701 42.733 40.871 4
NCR0.949 90.126 90.139 50.939 92.757 01.044 2
IHT1.930 40.243 10.232 55.713 32.864 41.388 7
EIS32.255 10.067 30.060 05.541 13.931 43.879 7
EIPB32.258 00.068 10.060 85.543 63.940 13.884 2
EIS23.198 60.067 10.063 58.613 26.917 05.015 1
EIPB23.201 20.067 80.064 38.615 06.925 65.018 1
EIS14.555 70.078 60.104 710.188 112.510 57.201 3
EIPB14.557 70.079 30.105 610.189 812.516 37.203 7
DIS368.158 30.612 10.117 954.992 4262.792 635.251 2
IBP368.161 20.612 80.118 854.994 5262.801 735.255 0
CNN84.135 54.014 89.617 4116.067 8154.872 229.234 2
DIS2113.726 30.736 60.265 3101.608 8530.278 465.490 9
IBP2113.728 90.737 30.266 1101.610 6530.286 665.494 6
DIS1221.974 01.680 02.491 7184.048 51 205.309123.500
IBP1221.976 11.680 62.492 5184.050 01 205.315123.503
), ArticleFig(id=1239158387443823036, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=EN, label=Table 4, caption=

Comparison of compression performance of distributed photovoltaic dataset

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RMSEPRDLossy CRLossless CR
D14.421 30.476 149.433 42.221 2
D24.423 10.477 289.554 62.215 7
D34.5370.512 449.640 62.225 1
D44.8130.550 217.660 82.106 1
D54.5780.534 287.537 72.116 1
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分布式光伏数据集的压缩性能比较

, figureFileSmall=null, figureFileBig=null, tableContent=
RMSEPRDLossy CRLossless CR
D14.421 30.476 149.433 42.221 2
D24.423 10.477 289.554 62.215 7
D34.5370.512 449.640 62.225 1
D44.8130.550 217.660 82.106 1
D54.5780.534 287.537 72.116 1
), ArticleFig(id=1239158387640955337, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=EN, label=Table 5, caption=

Comparison of running time of various algorithms（s）

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算法MeanD1D2D3D4D5
EIS0.078 60.0750.0800.0810.0790.078
EIPB0.079 30.0760.0820.0830.0800.076
DEASC0.001 20.0010.0010.0010.0020.001
DIS1.680 01.6501.7001.7201.6901.660
IBP1.680 61.6551.7101.7251.6951.658
), ArticleFig(id=1239158387741618636, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=CN, label=表5, caption=

各算法的运行时间对比（s）

, figureFileSmall=null, figureFileBig=null, tableContent=
算法MeanD1D2D3D4D5
EIS0.078 60.0750.0800.0810.0790.078
EIPB0.079 30.0760.0820.0830.0800.076
DEASC0.001 20.0010.0010.0010.0020.001
DIS1.680 01.6501.7001.7201.6901.660
IBP1.680 61.6551.7101.7251.6951.658
), ArticleFig(id=1239158387825504722, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=EN, label=Table 6, caption=

Comparison of the performance of the algorithm proposed in this article with other compression algorithms

, figureFileSmall=null, figureFileBig=null, tableContent=
算法LossyCRLosslessCRPRDRMSE
傅里叶分解17.440.476 140.8-20.914
DCT压缩27.900.477 282.930.571
神经网络18.27-1.170.914
SPIHT（分层树集分割算法）8.40-6.580.646
Cubic Hermitian（三次埃尔米特插值）2-6.6-0.9-9.60.716
Burrows-Wheeler-3.07-0.651
JODC Scheme（联合正交分解与偏码方案）-2.28-0.452
本文综合算法7.82.110.510.318
), ArticleFig(id=1239158387905196501, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239158369974547212, language=CN, label=表6, caption=

本文所提算法与其他压缩算法的性能比较

, figureFileSmall=null, figureFileBig=null, tableContent=
算法LossyCRLosslessCRPRDRMSE
傅里叶分解17.440.476 140.8-20.914
DCT压缩27.900.477 282.930.571
神经网络18.27-1.170.914
SPIHT（分层树集分割算法）8.40-6.580.646
Cubic Hermitian（三次埃尔米特插值）2-6.6-0.9-9.60.716
Burrows-Wheeler-3.07-0.651
JODC Scheme（联合正交分解与偏码方案）-2.28-0.452
本文综合算法7.82.110.510.318
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基于边界特征辨识与K维树优化的分布式光伏数据压缩算法
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施展 1 , 付佳佳 1 , 亢中苗 1 , 梁宇图 1 , 张仲禹 2 , 王立辉 2
遥测遥控 | 测控通信与导航 2025,46(6): 85-94
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遥测遥控 | 测控通信与导航 2025, 46(6): 85-94
基于边界特征辨识与K维树优化的分布式光伏数据压缩算法
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施展1, 付佳佳1, 亢中苗1, 梁宇图1, 张仲禹2, 王立辉2
作者信息
  • 1.广东电网有限责任公司 广州 510600
  • 2.东南大学仪器科学与工程学院 南京 210096

    • 施展　1983年生，博士，高级工程师。

    付佳佳　1985年生，硕士，中级工程师。

    亢中苗　1984年生，硕士，中级工程师。

    梁宇图　1991年生，硕士，中级工程师。

    张仲禹　1997年生，博士研究生。

    王立辉　1979年生，教授，博士生导师。

Distributed Photovoltaic Data Compression Algorithm Based on Boundary Feature Identification and K-Dimensional Tree Optimization
Zhan SHI1, Jiajia FU1, Zhongmiao KANG1, Yutu LIANG1, Zhongyu ZHANG2, Lihui WANG2
Affiliations
  • 1. Guangdong Power Grid Co., Ltd., Guangzhou, 510600, China
  • 2. School of Instrument Science and Engineering, Southeast University, Nanjing, 210096, China
doi: 10.12347/j.ycyk.20250228001
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摘要
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针对分布式光伏系统规模化并网导致的数据维度激增与计算复杂度高的问题，提出一种基于边界特征辨识与K维树优化的数据压缩算法。首先，基于决策边界敏感度理论构建了最小化总延迟的优化框架，提出增强的类间边界保留算法（EIPB），通过动态维护决策边界特征，降低传输数据量；其次，提出基于K维树（KD-Tree）空间划分的增强特征选择算法（EIS），利用近邻搜索加速技术，提升特征辨识效率；最后，优化动态误差分配的扇形无损压缩算法（DEASC），通过自适应斜率约束与多阶段熵编码，实现压缩效率与保真度的协同优化。实验结果表明：EIPB-EIS联合算法相较于传统方法，平均压缩比提升至7.8，重构百分比均方根误差降至0.51%，传输延迟降低了62.7%，解决了高维光伏数据的高效传输与精准重构难题。

分布式光伏  /  数据压缩  /  延迟优化  /  类间边界保留  /  动态误差分配

A data compression collaborative algorithm that integrates transmission optimization and delay control was proposed to address the data dimension explosion and complexity increase caused by the large-scale grid connection of distributed photovoltaic systems. Firstly, based on the theory of decision boundary sensitivity, an optimization framework for minimizing total delay was constructed, and an enhanced inter-class boundary preservation algorithm (EIPB) was proposed to reduce the amount of transmitted data by dynamically maintaining key instances of decision boundaries. Secondly, the traditional distance instance selection method was improved by proposing an enhanced instance selection algorithm (EIS) based on K-dimensional tree (KD-Tree) spatial partitioning, which utilized nearest neighbor search acceleration technology to enhance instance selection efficiency. Then, a dynamic error allocation sector lossless compression algorithm (DEASC) was proposed, which achieved collaborative optimization of compression efficiency and fidelity through adaptive slope constraints and multi-stage entropy encoding. Experimental verification showed that the EIPB-EIS joint algorithm improved the average compression ratio to 7.8 compared to traditional methods, reduced the root mean square error of reconstruction percentage to 0.51%, and reduced transmission delay by 62.7%, effectively solving the problem of efficient transmission and accurate reconstruction of high-dimensional photovoltaic data.

Distributed photovoltaics  /  Data compression  /  Delay optimization  /  Preservation of inter class boundaries  /  Dynamic error allocation
施展, 付佳佳, 亢中苗, 梁宇图, 张仲禹, 王立辉. 基于边界特征辨识与K维树优化的分布式光伏数据压缩算法. 遥测遥控, 2025 , 46 (6) : 85 -94 . DOI: 10.12347/j.ycyk.20250228001
Zhan SHI, Jiajia FU, Zhongmiao KANG, Yutu LIANG, Zhongyu ZHANG, Lihui WANG. Distributed Photovoltaic Data Compression Algorithm Based on Boundary Feature Identification and K-Dimensional Tree Optimization[J]. Journal of Telemetry, Tracking and Command, 2025 , 46 (6) : 85 -94 . DOI: 10.12347/j.ycyk.20250228001
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0　引言
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随着“双碳”目标的推进，分布式光伏（PVs）装机容量激增。大规模分布式光伏系统与配电网的深度耦合使得传统电力系统数据分析面临多维挑战。海量分布式光伏节点产生的多模态时序数据呈现出典型的高维耦合特性，发电功率、辐照度、组件温度等物理量间存在强非线性关联，秒级采样导致的TB级数据流使系统面临维度灾难；云层遮挡引发的辐照度跳变可导致功率输出分钟级波动，设备功率衰减特性与运行工况形成复杂耦合；边缘计算通过近源数据处理缓解了传输压力，验证了边缘计算在配网多源数据处理中的有效性[1]，但现有边缘网关受限于经典架构的计算资源[2]，难以支撑复杂压缩算法的实时需求[3]。因此，亟须研发具有特征适应性的智能压缩算法，以支撑电能质量在线监测中的暂态特征捕捉、组件健康状态评估中的微弱故障识别，以及功率预测模型中的关键模式提取。
国内外针对光伏数据压缩已有相关研究。洪杨等[4]利用模糊加权CNN（卷积神经网络）揭示变量间非线性关联，混合神经网络在处理高维数据时展现出优势[5]；Yang等[6]通过扩散模型有效捕捉随机波动特征，使光伏出力呈现多尺度不确定性，提出了一种新的多时间尺度优化调度策略；袁天梦等[7]构建的优化调度框架需依赖精准数据支撑；郑伟烁等[8]指出在线监测技术对数据完整性的依赖；Oswald等[9]提出的智能压缩机制可提升模式识别效率。现有研究在应对上述挑战时面临三重瓶颈：首先，传统主成分分析方法[10]及其稳健改进算法[11]在处理高维光伏数据时难以保持局部几何结构，导致关键状态信息丢失；其次，田征等[12]改进的分段线性逼近算法虽提升计算效率，但对光伏数据的非平稳特性敏感，易在波动剧烈时段产生累积误差，王少军等[13]在FPGA（现场可编程门阵列）实现中验证了算法动态适应性不足的问题；最后，现有压缩机制缺乏基于时空特征的自适应调节能力[14]，胡满等[15]提出的稀疏学习方法为动态平衡提供了新思路，但难以平衡压缩比与重构精度间的动态博弈关系。边缘计算通过近源数据处理缓解了传输压力，Modupe等[16]论证了边缘计算对实时数据处理的变革性影响，但现有系统受限于分布式守时架构的同步精度[17]和多站数据融合效率[18]，难以在有限算力下实现复杂压缩算法的实时部署。这要求新型压缩算法必须兼顾谱变异特征保持[19]与智能资源调度能力，以满足新型电力系统对光伏数据多维度应用需求[20]。
针对上述问题，本研究提出融合特征保持与计算加速的协同压缩算法，主要创新点如下：①提出增强型类间边界保留算法（EIPB），通过KD-Tree空间划分实现边界特征的快速选择，相较传统欧氏距离计算效率提升2.3倍；②设计增强距离特征选择算法（EIS），引入动态误差分配机制，在5个标准数据集上实现平均7.8的压缩比，同时均方根偏差百分比PRD=0.51%；③构建动态误差分配的扇形无损压缩算法（DEASC），通过自适应斜率约束与多级熵编码的协同优化，在TI C2000系列DSP上实现仅1.2 μs/点的处理延迟，满足电网实时性要求。
1　数据压缩算法
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分布式光伏系统等边缘设备的信息聚合研究，主要集中在各类数据压缩方法上[21]，包括距离特征选择（DIS）算法[22]、跨类边界保留（IPB）算法以及K维树（KD-Tree）等[23]。这些方法旨在优化数据处理效率，同时确保信息的完整性与准确性。
1.1　DIS算法
在数据管理和处理需求不断增加的背景下，DIS成为解决数据传输和存储挑战的重要方法[24]。DIS算法是一种用于数据压缩的方法[25]，它通过多轮次的迭代过程将原始数据集处理为多个较小的压缩数据集[26]。给定原始数据集，其中xi∈ℝd为D维特征向量，yi∈{1，...，C}为类别标签，DIS算法通过以下步骤生成压缩数据集DR。
首先，进行边界特征筛选，计算所有特征的类别间边界隶属度：
其中，表示xi的k近邻集合，为指示函数。
然后进行迭代原型选择，每轮迭代选择边界隶属度最高的特征作为原型：
其中，W为当前工作数据集。将加入DR后从移除，并更新剩余特征的边界隶属度。
当缩减数据集满足或剩余特征的边界隶属度低于阈值τ时终止。
图1所示为DIS算法的特征选择过程。第一轮（Level-1）选出的原型特征以方块表示，其筛选依据边界隶属度最大化准则。第二轮（Level-2）原型特征以三角形表示，用于增强缩减数据集在特征空间中的覆盖密度。未在任何阶段被选为原型的特征用圆形表示，继续保留在工作数据集中，并可能在后续阶段中被选中。图中虚线区域表示某特征因接近不同类别的特征而被选为原型，而实线区域则反映两个密切相关的特征因互相关联而同时被选为原型。
DIS算法的时间复杂度主要集中于近邻搜索与边界隶属度计算。对于N个d维数据点，每轮迭代需计算次欧氏距离，其复杂度为，其中T=[αN]。
1.2　跨类边界保留(IBP)算法
针对DIS算法存在的类间不平衡问题，IBP通过集成随机过采样机制增强类代表性。设原始数据集类别分布为，IBP强制每个类在缩减集中满足最小特征数约束：
其中，，β∈（0,1）为类别覆盖率参数。
第一步，边界增强选择，融合边界隶属度与类间距离：
其中为异类特征集，λ为平衡因子。
第二步，进行冗余抑制，基于阈值ϵ的集合运算移除重复特征：
IBP使kNN（k近邻算法）分类错误率降低，但时间复杂度仍为，未解决DIS的固有效率瓶颈。
2　基于边界特征辨识与K维树的优化算法
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针对IBP与DIS算法的高计算复杂度问题，本文提出基于KD-Tree的增强型算法EIPB与EIS。核心创新在于将空间划分树结构引入特征选择流程，实现时间复杂度从O（n2）到O（nlogn）的优化。
2.1　增强型类间边界保留算法(EIPB)
传统的IBP算法对特征选择进行了优化，重点在于边界的保持，同时附加了过采样步骤。本文提出的EIPB算法在IBP的类平衡约束基础上，引入KD-Tree加速边界特征搜索，并设计动态过采样机制。KD-树的空间划分能力加速了原型识别过程，使算法能够在不完全遍历所有特征的情况下高效地选择出具有代表性的特征。算法的数学模型如下：
对工作数据集递归划分，在最坏情况下，生成平衡二叉树：
对特征xi，查找k近邻的时间复杂度降为：
对少数类c的补偿特征数为：
其中，D代表原始数据集，Dworking初始化为D；L表示特征选择的层数；m为RandomOverSampler（随机过采样器）函数的最小特征数；qkd用于定义每个特征的最近邻居数量与工作数据集总特征数的比率。输出结果为EIPB[1,L]，即简化后的数据集。EIPB通过以下步骤来生成一系列具有预设层级的精简数据集：
初始化：算法接收原始数据集（D），并确定特征选择的层级数（L）、过采样函数的最小特征数（m）以及定义每个特征最近邻居数量的比例（qkd）。
输出准备：根据不同的层级（L），算法输出一系列简化的数据集，标记为EIPB[1,L]。
工作数据集创建：创建原始数据集（D）的副本Dworking，以在算法执行过程中对其进行修改。
层级迭代与特征选择：对于每一个层级（l），算法初始化一个空集（EIPBl）以存储该层级的原型选出的特征。
KD-树构建：从工作数据集（Dworking）创建KD-树（KDworking），以便实现高效的特征选择。
最近邻搜索：对于每个特征（d），算法通过KDworking查找其最多kkd个最近邻（N）。
原型选择：检查每个邻近特征（n）与当前特征的类别是否不同。如果不同，则将邻居（n）识别为原型并添加到当前层级的简化数据集中。
唯一性验证：处理完所有特征后，算法去除EIPBl中的重复条目，以确保数据集的唯一性。
过采样：对数据集中的每个类别（c）进行过采样，以确保各类的平衡表示，满足指定的最小特征数（m）。
工作数据集更新：从工作数据集中移除已选择的特征，以避免后续迭代中的冗余。
2.2　K维树改进的增强特征选择(EIS)
原始的DIS算法主要关注于高效的特征选择，特别是边界的保持。EIS算法通过引入KD-树结构来改进此过程。与EIPB不同，EIS专注于特征选择而省略了过采样过程。EIS算法与EIPB算法的主要区别在于EIS不包含每类的过采样步骤，重点在于特征选择流程。
算法将DIS的全局搜索改进为基于KD-Tree的局部搜索，去除过采样步骤以专注边界保持。设数据维度d=100，KD-Tree将距离计算量缩减为：
KD-Tree划分导致的近似误差上界为：
其中，δ为划分超平面偏移量。
EIS算法的输入参数包括：D表示原始数据集；L表示特征选择的层数；qkd参数用于定义每个特征的最近邻居数量与工作数据集总特征数的比率。输出结果为EIS[1,L]，即经过简化处理后得到的数据集。
原始的IBP和DIS算法依赖于欧几里得距离函数，需要对数据集中每一个特征与其余n-1个特征进行比较，因而具有O（n2）的时间复杂度。引入KD-Tree后，EIPB和EIS算法通过优化原型搜索过程，将时间复杂度从二次降至近线性。构建KD-Tree的时间通常为O（nlogn），尽管在最坏情况下可能增加至O（n2），但在分布良好的数据集中很少出现。构建完成后，KD-Tree允许在平均O（logn）时间内进行原型搜索，与欧几里得距离方法相比，显著提高了效率。通过理论推导得到的算法改进效果见表1。
2.3　扇形无损压缩算法(EIS)
为突破传统压缩算法在光伏时序数据中的效率低下问题，本文提出一种基于动态误差分配的扇形无损压缩算法（Dynamic Error-Allocated Sector Compression，DEASC）。该算法通过融合自适应斜率约束与多阶段压缩策略，在保证最大重建误差εmax的前提下，实现平均压缩比提升35%。算法的数学模型如下：
定义压缩区间，设时序数据序列，当前压缩区间起点为Sstart，终点候选点为Send。允许的上下界斜率Ut和Lt，由下式动态更新：
若后续数据点St+1满足，则当前区间可扩展至t+1，否则触发压缩存储。
DEASC引入三级压缩机制，第一级压缩为粗粒度筛选，基于KD-Tree划分数据空间，识别高波动区域。第二级压缩为动态误差分配，按区域波动强度调整局部ε为：
其中，σj为第i子区域的标准差。
第三级压缩为熵编码优化，对斜率差值ΔU进行霍夫曼编码：
如图2所示，算法首先固定第一个数据点S1作为起始点。对于紧接着的数据点S2，计算其与ε相加减后的两个边界值。然后，围绕这两个边界值绘制两条具有不同斜率（U1，L1）的线段1。
如果随后的数据点S3位于这两条线段构成的区域内，算法则去除S2，以S3为基准继续绘制新的边界斜率（U2，L2）。通过比较新旧斜率，保留能够涵盖更多数据点的斜率组合（U1，L2）。若下一个数据点S4超出了这些斜率定义的范围，则将S3固定下来，用于后续的存储，并以此为新的起点重复上述过程。
通过此方法，算法能够有效减少存储需求，将两个连续保留数据点之间的时间间隔存储为每个数据点的字段长度（length）。
数据的解压缩过程则通过线性插值完成。采用扇形算法对分布式光伏数据进行不同ε值下的压缩与解压缩实验，所得残差分布以零为中心，最大值受ε值限制。
扇形算法通常需要存储所有数据点的斜率并计算其在当前样本上的投影。为了简化计算并降低实施复杂度，提出了一种简单的递归几何方法来实施扇形算法，其中只估算存储最严格的斜率及其投影。如图3所示，S1是当前的起始样本，SN-1是当前考虑是否删除的样本，SN是下一个样本，而“Len”是从当前起始样本到当前样本SN-1的持续时间。为了决定是否保留SN-1，需要计算从当前起点S1到SN-1±ε在SN处的斜率值，即SNUB和SNLB。计算方法由如下公式给出。
3　实验验证
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将原始数据集加载并使用Min Max Scaler（最小最大缩放器）函数规范化至0~1范围，形成工作数据集；对原始数据集应用kNN进行5折交叉验证，记录结果；从表1中选择一种数据压缩算法进行评估。通过比较分析EIPB和EIS算法与IBP、DIS算法及其他基准算法在数据压缩效率上的性能。
3.1　数据压缩性能
基于五组分布式光伏数据集的实验表明，EIPB与EIS算法在压缩效率与特征保留能力方面有更好的表现。算法生成的不同子序列级别的压缩数据集与前一级或前一轮压缩数据集合并，提高了相邻数据类别间决策边界的特征密度。例如，EIS1,2表示EIS1与EIS2合并的数据集。
如表2所示，EIPB1的平均压缩率为0.231 3%，较原始IBP1算法降低4.9%，在多级组合压缩场景中表现更好。例如，EIPB1,2的压缩率较IBP1,2降低9.1%，验证了类间边界保留机制对数据冗余消除的有效性。
EIS算法在动态特征选择方面表现突出，其单级压缩率较传统DIS算法降低9.7%，在D1数据集上达到0.008 7%的极值。并且EIS在多级压缩中仍有较好的表现，EIS1,2,3组合的压缩率较DIS同级别组合降低10.5%。
两类改进算法的特性差异表明了其适配不同应用场景：EIPB因注重类别边界完整性，在D3数据集上的压缩误差较EIS降低4.6%，更适合需高保真度的故障诊断场景；而EIS凭借动态误差分配机制，在D4数据集上的压缩速度提升32%，更适用于实时监控系统。进一步发现，当压缩层级增至三级时，EIPB与EIS的压缩率差异收敛至0.48%，表明深度压缩下算法性能趋于均衡，此时可基于硬件资源约束进行弹性选择。
3.2　运行时间分析
通过对计算效率进行对比分析。如表3所示，EIPB与EIS算法在运行时间指标上较原始算法呈现数量级优势。EIPB1在D1数据集上的运行时间仅为0.079 3 s，相较IBP1的1.680 6 s，计算效率提升达21.2倍；在数据规模最大的D4数据集上，EIPB1耗时12.516 3 s，较IBP1的1 205.315 2 s缩短96.0%，验证了基于KD-Tree的加速机制对高维数据处理的有效性。
EIS算法在动态特征筛选中展现出更显著的优势，其D3数据集处理时间从DIS1的184.048 5 s降至10.188 1 s，效率提升94.5%。EIPB与EIS算法间的性能差异呈现规律性收敛特征：在基础压缩层级（Level1）中，两者运行时间差异不足1.2%；随着压缩层级增加至Level3，差异收敛至3.5%以内。
结果表明，两类改进算法通过不同的优化路径实现了计算效率的协同提升，EIPB侧重全局空间划分加速，EIS侧重局部搜索优化，二者在压缩效率与计算速度间形成平衡。
3.3　扇形算法压缩性能
前述研究主要关注在特定约束条件下提高压缩比。然而，对于分布式光伏数据，需要综合考虑有损和无损压缩性能。如图4所示，基于48小时光伏时序数据的实验表明，当残差误差阈值设定为2.1，对应动态范围0.1%时，压缩效率达到最优平衡点（CR=7.8），较传统单一模式提升32.6%。
在有损压缩域，压缩比与残差阈值呈显著正相关（R2=0.93），阈值每增加1个单位，CR提升1.2倍。而在无损压缩域，过低阈值（<1.5）因元数据开销导致CR下降18.7%，过高阈值（>5.0）则因残差位宽膨胀使CR降低14.3%。实验进一步表明，EIPB算法残差方差较基准方法降低39.2%，有效缓解高位宽问题，验证了类间边界约束对压缩稳定性的提升。
该优化机制在TIC2000系列DSP硬件平台上实现1.2 μs/点的处理速度，较纯有损模式延迟仅增加7.8%。这为光伏数据压缩提供新的研究点，通过动态调节残差阈值，可在信息熵保持与计算资源消耗间实现帕累托最优。
为量化算法对数据可用性的影响，基于kNN分类器构建了压缩-分类联合评估框架。实验表明，当残差误差阈值控制在光伏信号动态范围的0.3%~0.7%时，EIPB与EIS算法在压缩效率与分类精度间达到帕累托最优。如表4所示，该条件下算法平均实现7.86的有损压缩比，重构百分比均方根误差（PRD）与均方根误差（RMSE）分别为0.51%与4.61。RMSE和PRD是常用的有损压缩评价指标，具体计算公式如下。
其中，x'（n）为有损压缩后的重构样本，x（n）为原始样本，n为光伏记录的样本个数。
有损压缩比（Lossy CR）定义为有损压缩前后的数据大小比率，平均为7.86，数据量减少至原始大小的约12.7%。这表明算法在显著减少数据量的同时保留了数据的可用性。无损压缩比（Lossless CR）衡量无损压缩下的数据缩减程度，平均为2.11，压缩后数据量为原始数据的约47.4%。
为全面评估算法性能，在Texas Instruments TDA4VM处理器上（主频1.8 GHz）进行的软件运行时测试表明，EIPB和EIS算法相较原始版本具有显著优势。基于TI C2000系列DSP（型号TMS320F 28379D）部署的DEASC实现了硬件级加速。
如表5所示，其平均处理延迟为1.2 μs/点，满足光伏数据采集系统≤5 μs的实时性要求。上述结果验证了本文提出的三级优化的有效性：EIPB/EIS算法解决软件计算瓶颈，DEASC实现硬件级加速，三者协同工作使系统整体延迟降低62.7%。
表6比较了传统有损和无损压缩算法与本文算法。传统算法如DCT、傅里叶变换和神经网络可实现较高的有损CR，但通常伴随着较大的PRD和高实现复杂性，因此不适用于低功耗需求的光伏设备。在有损压缩算法中，SPIHT和Cubic Hermite插值的有损CR相似，但PRD也较高。在无损压缩算法中，JODC Scheme和Burrows Wheeler变换实现了2.28和3.07的压缩比，但其复杂性较高。
实验结果表明，提出的综合算法同时生成有损和增量无损数据流，支持混合数据传输，并具有较低的计算复杂性，更适用于分布式光伏发电系统。
4　结束语
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针对分布式光伏系统高维时序数据的传输效率与计算资源约束难题，提出融合特征保持与计算加速的压缩框架，主要取得以下创新：①提出基于KD-Tree空间划分的增强型类间边界保留算法（EIPB），通过动态近邻搜索机制将传统IBP算法的特征选择效率提升2.3倍，在D1-D5数据集上实现平均压缩比7.8，同时PRD=0.51±0.04%，较基准方法提升62.7%；②设计增强距离特征选择算法（EIS），引入动态误差分配策略，在TI C2000系列DSP硬件平台上实现1.2 μs/点的处理延迟，较传统DIS算法计算耗时降低94.5%，同时将类别模糊度控制在1.8%以内；③构建扇形无损压缩算法（DEASC）的混合压缩，通过自适应斜率约束与多级熵编码的协同优化，在2.1残差阈值下达到压缩效率拐点，无损压缩比达2.11。研究成果为大规模光伏电力系统的边缘智能计算提供了一种高效的数据压缩方法，具有较高的工程应用价值。
基金
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  • 中国南方电网有限公司科技项目(036000KK52220013（GDKJXM2022024）)
  • 国家重点研发计划(2021YFB2501603)
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2025年第46卷第6期
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doi: 10.12347/j.ycyk.20250228001
  • 接收时间：2025-02-28
  • 首发时间：2026-03-13
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  • 收稿日期：2025-02-28
  • 修回日期：2025-04-09
基金
中国南方电网有限公司科技项目(036000KK52220013（GDKJXM2022024）)
国家重点研发计划(2021YFB2501603)
作者信息
    1.广东电网有限责任公司 广州 510600
    2.东南大学仪器科学与工程学院 南京 210096
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