吳昊天，趙 陽，劉子卓，張 弛，趙 舫

基于小波變換的配電變壓器差動(dòng)保護(hù)相位補(bǔ)償方法

吳昊天1，趙 陽1，劉子卓1，張 弛2，趙 舫3

(1.國網(wǎng)麗水供電公司，浙江 麗水 323000；2.浙江浙電產(chǎn)業(yè)管理有限公司，浙江 杭州 310000；3.浙江大學(xué)電氣工程學(xué)院，浙江 杭州 310027)

為降低配電變壓器故障引起的財(cái)產(chǎn)安全損失，提升電力系統(tǒng)運(yùn)行穩(wěn)定性，提出了基于小波變換的配電變壓器差動(dòng)保護(hù)相位補(bǔ)償方法。首先，通過計(jì)算線模行波電流波動(dòng)及其梯度絕對(duì)值大小，判斷配電變壓器有無故障,即創(chuàng)建保護(hù)啟動(dòng)判據(jù)。然后，依據(jù)等效線模行波差動(dòng)電流的能量比確定故障區(qū)域，并計(jì)算小波變換故障區(qū)域的初始模量反向行波差動(dòng)電流，以獲得小波變換模極大值。最后，通過構(gòu)建故障選極判據(jù)獲取故障類型，計(jì)算故障狀態(tài)下配電變壓器空載合閘時(shí)的勵(lì)磁電流，判斷勵(lì)磁涌流和內(nèi)部故障電流的變化，并結(jié)合保護(hù)輸出信號(hào)的開啟和關(guān)閉，實(shí)現(xiàn)配電變壓器的差動(dòng)保護(hù)相位補(bǔ)償。仿真實(shí)驗(yàn)表明，該方法可對(duì)區(qū)內(nèi)故障進(jìn)行有效鑒別，具有很強(qiáng)的可靠性及有效性。負(fù)載工況下，該方法相位補(bǔ)償后電壓電流的相位差一致，具有更好的穩(wěn)定性。

配電變壓器；小波變換；相位補(bǔ)償方法；故障選極；負(fù)載工況；勵(lì)磁涌流

0 引言

為了安全運(yùn)行配電變壓器，最大限度地減少故障事故，需要對(duì)配電變壓器安裝繼電保護(hù)裝置[1-3]。配電變壓器的主保護(hù)一直采用差動(dòng)保護(hù)完成，該保護(hù)的主要原理是對(duì)比配電變壓器電流的大小和相位，但由于配電變壓器各側(cè)電流互感器等許多因素影響，會(huì)造成該配電變壓器電流的大小和相位的異常。該異常產(chǎn)生的不平衡電流會(huì)影響差動(dòng)保護(hù)，使差動(dòng)保護(hù)產(chǎn)生錯(cuò)誤動(dòng)作。除此之外，還有很多可以形成不平衡電流的因素，例如三相電壓不平衡以及電機(jī)、線路等問題。若該問題得不到解決，不平衡電流就會(huì)逐漸變大，導(dǎo)致差動(dòng)保護(hù)能力降低，靈敏度不高；特別是受到勵(lì)磁涌流的干擾，導(dǎo)致保護(hù)裝置不能正常運(yùn)行。因此，尋求有效的方法，提高差動(dòng)保護(hù)靈敏度，一直是國內(nèi)外相關(guān)學(xué)者研究的重點(diǎn)方向。文獻(xiàn)[4]提出了基于綜合制動(dòng)判據(jù)的變壓器差動(dòng)保護(hù)方法，該方法存在差動(dòng)保護(hù)速度慢、靈敏度低等不足，且無法有效避開正常工作時(shí)的不平衡電流和勵(lì)磁涌流。文獻(xiàn)[5]提出了基于GOOSE網(wǎng)絡(luò)的智能變電站變壓器縱差保護(hù)方法，但該方法保護(hù)動(dòng)作延遲，容易造成差動(dòng)保護(hù)錯(cuò)誤動(dòng)作。文獻(xiàn)[6]通過帶并聯(lián)電容實(shí)現(xiàn)變壓器相位補(bǔ)償，但該方法運(yùn)算過程復(fù)雜，還存在補(bǔ)償后電壓/電流相位差高、穩(wěn)定性差的弊端。

小波變換是一種利用不同頻率、方位及寬度有限的基函數(shù)的變換，經(jīng)傅里葉變換演變出的更為理想的數(shù)學(xué)工具[7]。它在傅里葉變換局部化理論的基礎(chǔ)上進(jìn)行了改進(jìn)，并且也攻克了許多缺點(diǎn)，如對(duì)時(shí)間及頻率分辨率具有局限性、無法同時(shí)呈現(xiàn)時(shí)域與頻域信息等。但小波變換可以做到快速呈現(xiàn)一個(gè)“時(shí)間-頻率”的窗口，該窗口可隨頻率發(fā)生改變，并自動(dòng)適應(yīng)時(shí)頻信號(hào)，對(duì)信號(hào)在高頻處時(shí)，細(xì)化時(shí)間，低頻處時(shí)細(xì)化頻率，具有多標(biāo)準(zhǔn)識(shí)別及時(shí)-頻局部化的特點(diǎn)，有效解決電壓電流的峰值突變信號(hào)和采集其特點(diǎn)，即可以精準(zhǔn)采集異樣信號(hào)及暫態(tài)情況下的不平衡電流[8-9]。

1 配電變壓器差動(dòng)保護(hù)相位補(bǔ)償

1.1 啟動(dòng)元件

線模行波電流梯度絕對(duì)值公式為

1.2 故障區(qū)域識(shí)別

基于電流能量規(guī)則[10]，等效線模行波差動(dòng)電流的能量比公式是

1.3 故障選極

根據(jù)判斷出的故障區(qū)域，利用故障選極方法判斷故障類型。

線路兩端反向行波差動(dòng)電流公式為

電壓、電流解耦獲取的線、零模量為

其中：

若配電變壓器線路在兩極運(yùn)行時(shí)，產(chǎn)生范圍內(nèi)正極接地故障，式(9)變?yōu)?/p>

相同道理，若負(fù)極接地故障，式(9)變?yōu)?/p>

若兩極短路故障，式(9)變?yōu)?/p>

1.4 小波變換的配電變壓器差動(dòng)保護(hù)流程

基于以上過程，小波變換的配電變壓器差動(dòng)保護(hù)流程為：對(duì)配電變壓器運(yùn)行差動(dòng)保護(hù)，差動(dòng)保護(hù)運(yùn)行的前提是提取、保存正極與負(fù)極配電變壓器線路電壓及電流數(shù)據(jù)，啟動(dòng)后，識(shí)別配電變壓器線路是否故障，可通過采樣數(shù)據(jù)完成，該采樣數(shù)據(jù)需采用小波變換的配電變壓器差動(dòng)保護(hù)運(yùn)行前0.5 ms及運(yùn)行后1.5 ms共2 ms“時(shí)間窗”內(nèi)的數(shù)據(jù)[17-19]。

步驟(1) 經(jīng)極模轉(zhuǎn)換電壓電流數(shù)據(jù)，獲取模量行波電流電壓。

步驟(2) 對(duì)步驟(1)所獲數(shù)據(jù)進(jìn)行小波變換，并提取變換后的模最大值。

步驟(3) 經(jīng)繼電保護(hù)設(shè)備模極大值轉(zhuǎn)換后，對(duì)等效線模行波電流進(jìn)行重新塑造。

圖1 小波變換的配電變壓器差動(dòng)保護(hù)流程圖

2 配電變壓器差動(dòng)保護(hù)相位補(bǔ)償

采用電流的相位補(bǔ)償方法為故障時(shí)配電變壓器提供差動(dòng)保護(hù)[25]。

3 實(shí)驗(yàn)分析

為了驗(yàn)證本文提出的基于小波變換的配電變壓器差動(dòng)保護(hù)相位補(bǔ)償方法在實(shí)際應(yīng)用中的可靠性及高效性，以某區(qū)域配電網(wǎng)的220 kV配電變壓器為實(shí)驗(yàn)對(duì)象，通過Matlab搭建仿真實(shí)驗(yàn)平臺(tái)，該變電站配置4臺(tái)智能變壓器，每臺(tái)變壓器部署1臺(tái)智能通信網(wǎng)關(guān)機(jī)和一個(gè)差動(dòng)保護(hù)裝置。每個(gè)差動(dòng)保護(hù)裝置有9路模擬量通道，分別采集高壓側(cè)三相電壓、高壓側(cè)三相保護(hù)電流和低壓側(cè)三相保護(hù)電流。在主、子站之間共有7 000個(gè)信息點(diǎn)表。本文利用其中一條獨(dú)立的通道來完成相關(guān)實(shí)驗(yàn)測(cè)試。配電變壓器參數(shù)設(shè)置如表1所示。

表1 配電變壓器參數(shù)設(shè)置

3.1 故障選極

圖2為該配電變壓器線路某處發(fā)生正極接地故障、負(fù)極接地故障以及兩極接地故障三種情況時(shí)，小波變換模極大值變化情況。

該仿真實(shí)驗(yàn)表明，可通過得到的小波變換模極大值，利用差動(dòng)電流表現(xiàn)出的不同特征對(duì)該故障類型進(jìn)行有效識(shí)別。

3.2 不同故障距離

表2為該220 kV配電變壓器的線路分別在0.4 km、80.1 km、160.5 km、203.4 km處發(fā)生故障時(shí)，原始模量反向行波差動(dòng)電流數(shù)據(jù)。

表2 不同距離下原始模量反向行波差動(dòng)電流變化

根據(jù)以上實(shí)驗(yàn)數(shù)據(jù)可知，采用本文方法可有效依據(jù)區(qū)內(nèi)故障等級(jí)對(duì)區(qū)內(nèi)故障進(jìn)行鑒別，具有很強(qiáng)的可靠性及高效性。

3.3 相位補(bǔ)償效果

實(shí)驗(yàn)驗(yàn)證，采用本文方法進(jìn)行相位補(bǔ)償可以更好地確保配電變壓器的線路電壓及電流的穩(wěn)定性。

4 結(jié)論

本文提出基于小波變換的配電變壓器差動(dòng)保護(hù)相位補(bǔ)償方法，該方法通過故障區(qū)域識(shí)別、小波變換模量反向行波差動(dòng)電流，獲得小波變換模極大值、創(chuàng)建故障選極判斷故障類型，并在配電變壓器空載合閘的狀況下，計(jì)算出相位補(bǔ)償后的差流，通過差流判斷勵(lì)磁涌流和內(nèi)部故障電流的變化，完成相位補(bǔ)償?？偨Y(jié)仿真實(shí)驗(yàn)得到以下三點(diǎn)：

(1) 根據(jù)小波變換模極大值能夠有效判斷故障類型。

(2) 由于故障距離的變大，小波變換模極大值幅值逐漸變小。

(3) 與傳統(tǒng)方法相比，本文提出的配電變壓器差動(dòng)保護(hù)相位補(bǔ)償方法，能夠保證變壓器運(yùn)行過程中電壓電流的相位差保持一致，使配電變壓器得到更好的保護(hù)。

[1] 俞斌, 胡卓然, 李黎, 等. 10 kV大容量配電變壓器差動(dòng)保護(hù)配置應(yīng)用研究[J]. 電力系統(tǒng)保護(hù)與控制, 2021, 49(22): 98-104.

YU Bin, HU Zhuoran, LI Li, et al. Differential protection configuration of a 10 kV large capacity distribution transformer[J]. Power System Protection and Control, 2021, 49(22): 98-104.

[2] 趙志新, 趙宗羅, 趙穎, 等. 基于并行化BP神經(jīng)網(wǎng)絡(luò)的配電變壓器故障快速診斷方法[J]. 浙江電力, 2021, 40(12): 82-88.

ZHAO Zhixin, ZHAO Zongluo, ZHAO Ying, et al. A fast fault diagnosis method of distribution transformer based on parallel BP neural network[J]. Zhejiang Electric Power, 2021, 40(12): 82-88.

[3] 耿俊成, 郭志民, 李曉蕾, 等. 基于LOF和SVM的配電網(wǎng)線變關(guān)系數(shù)據(jù)校驗(yàn)方法[J]. 中國測(cè)試, 2021, 47(4): 49-54.

GENG Juncheng, GUO Zhimin, LI Xiaolei, et al. Connectivity data verification method of feeder-transformers based on LOF and SVM[J]. China Measurement & Test, 2021, 47(4): 49-54.

[4] 李梅, 唐菊生. 基于綜合制動(dòng)判據(jù)的變壓器差動(dòng)保護(hù)研究[J]. 電力科學(xué)與技術(shù)學(xué)報(bào), 2020, 35(2): 135-141.

LI Mei, TANG Jusheng. Transformer differential protection method based on the comprehensive braking criterion[J]. Journal of Electric Power Science and Technology, 2020, 35(2): 135-141.

[5] 倪傳坤, 于同偉, 鄧茂軍, 等. 基于GOOSE網(wǎng)絡(luò)的智能變電站變壓器縱差保方案[J]. 電力系統(tǒng)自動(dòng)化, 2019, 43(6): 151-155.

NI Chuankun, YU Tongwei, DENG Maojun, et al. Longitudinal differential protection of transformer in smart substation based on GOOSE network[J]. Automation of Electric Power Systems, 2019, 43(6): 151-155.

[6] 王柏峰, 張懋魯. 帶并聯(lián)電容補(bǔ)償電爐變壓器的各繞組容量計(jì)算[J]. 變壓器, 2019, 56(5): 10-12.

WANG Baifeng, ZHANG Maolu. Winding capacity calculation of furnace transformer with parallel capacitance compensation[J]. Transformer, 2019, 56(5): 10-12.

[7] 曹俊平, 黃勃, 王成珠, 等. 基于小波變換的高壓電纜混合線路故障定位方法及驗(yàn)證試驗(yàn)[J]. 浙江電力, 2021, 40(2): 14-19.

CAO Junping, HUANG Bo, WANG Chengzhu, et al. Fault location method and verification test analysis of hybrid HV cable lines based on wavelet transform[J]. Zhejiang Electric Power, 2021, 40(2): 14-19.

[8] 陶彩霞, 杜雪, 高鋒陽, 等. 基于經(jīng)驗(yàn)小波變換的混合輸電線路單相接地故障測(cè)距[J]. 電力系統(tǒng)保護(hù)與控制, 2021, 49(10): 105-112.

TAO Caixia, DU Xue, GAO Fengyang, et al. Single-phase to ground fault location of hybrid transmission lines based on empirical wavelet transform[J]. Power System Protection and Control, 2021, 49(10): 105-112.

[9] 卓放, 楊澤斌, 易皓, 等. 綜合配網(wǎng)諧波及三相不平衡評(píng)價(jià)指標(biāo)的治理設(shè)備優(yōu)化配置策略[J]. 中國電力, 2020, 53(11): 40-49.

ZHUO Fang, YANG Zebin, YI Hao, et al. Optimal allocation strategy for power quality control devices based on harmonic and three-phase unbalance comprehensive evaluation indices for distribution network[J]. Electric Power, 2020, 53(11): 40-49.

[10] 安義, 陳春, 范瑞祥, 等. 基于數(shù)據(jù)驅(qū)動(dòng)的配電變壓器容量在線校正方法[J]. 高電壓技術(shù), 2019, 45(9): 161-167.

AN Yi, CHEN Chun, FAN Ruixiang, et al. On-line correcting method of the distribution transformer capacity based on data-driven[J]. High Voltage Engineering, 2019, 45(9): 161-167.

[11] 黃家凱, 高厚磊. 輸電線路自同步電流差動(dòng)保護(hù)[J]. 電工技術(shù)學(xué)報(bào), 2019, 34(9): 1944-1951.

HUANG Jiakai, GAO Houlei. Self-synchronized current differential protection scheme for transmission line[J]. Transactions of China Electrotechnical Society, 2019, 34(9): 1944-1951.

[12]吳沛鋒, 張國云, 孔令號(hào). 基于全波電流關(guān)聯(lián)性的線路差動(dòng)保護(hù)算法[J]. 電網(wǎng)技術(shù), 2019, 43(7): 2584-2591.

WU Peifeng, ZHANG Guoyun, KONG Linghao. A new line differential protection principle based on correlation of full wave current data[J]. Power System Technology, 2019, 43(7): 2584-2591.

[13]翁漢琍, 李昊威, 邢家維, 等. 采用S變換相位差及能量相對(duì)熵的換流變零序差動(dòng)保護(hù)新判據(jù)[J]. 電力自動(dòng)化設(shè)備, 2019, 39(9): 27-33.

WENG Hanli, LI Haowei, XING Jiawei, et al. Novel criterion adopting S-transform phase angle difference and energy relative entropy for zero-sequence differential protection of converter transformer[J]. Electric Power Automation Equipment, 2019, 39(9): 27-33.

[14]朱妍, 陸于平, 黃濤. 計(jì)及諧波頻率特征的含風(fēng)電配電網(wǎng)充分式電流幅值差動(dòng)保護(hù)[J]. 電力系統(tǒng)自動(dòng)化, 2020, 44(16): 171-179.

ZHU Yan, LU Yuping, HUANG Tao. Sufficient current amplitude differential protection considering frequency characteristic of harmonics for distribution network with wind power[J]. Automation of Electric Power Systems, 2020, 44(16): 171-179.

[15]安義, 朱志杰, 王華云, 等. 一種配電變壓器熱評(píng)估方法[J]. 電測(cè)與儀表, 2019, 56(4): 54-60.

AN Yi, ZHU Zhijie, WANG Huayun, et al. A thermal evaluation method of distribution transformers[J]. Electrical Measurement & Instrumentation, 2019, 56(4): 54-60.

[16] 吳曉文, 魏慧杰, 周年光, 等. 半消聲室內(nèi)干式配電變壓器的噪聲與振動(dòng)特性研究[J]. 電力科學(xué)與技術(shù)學(xué)報(bào), 2019, 34(3): 190-195.

WU Xiaowen, WEI Huijie, ZHOU Nianguang, et al. Noise and vibration analysis of dry-type distribution transformer in semi-anechoic room[J]. Journal of Electric Power Science and Technology, 2019, 34(3): 190-195.

[17] 吳建章, 梅飛, 陳暢, 等. 基于經(jīng)驗(yàn)小波變換的電力系統(tǒng)諧波檢測(cè)方法[J]. 電力系統(tǒng)保護(hù)與控制, 2020, 48(6): 136-143.

WU Jianzhang, MEI Fei, CHEN Chang, et al. Harmonic detection method in power system based on empirical wavelet transform[J]. Power System Protection and Control, 2020, 48(6): 136-143.

[18] 孫德娟, 孫士云, 范小紅, 等. 基于勵(lì)磁電感計(jì)算的雙饋風(fēng)電場(chǎng)送出變差動(dòng)保護(hù)[J]. 電工技術(shù)學(xué)報(bào), 2020, 35(2): 395-407.

SUN Dejuan, SUN Shiyun, FAN Xiaohong, et al. Doubly-fed wind farm outgoing transformer differential protection based on excitation inductance calculation[J]. Transactions of China Electrotechnical Society, 2020, 35(2): 395-407.

[19] 石吉銀. 基于暫態(tài)負(fù)荷的變壓器保護(hù)一次電流檢驗(yàn)方法[J]. 中國電力, 2021, 54(5): 148-155.

SHI Jiyin. Primary current test method for transformer protection based on transient load[J]. Electric Power, 2021, 54(5): 148-155.

[20] 王永進(jìn), 樊艷芳, 李自乾. 基于突變量能量波形特征的特高壓直流輸電線路單端保護(hù)方法[J]. 電力系統(tǒng)保護(hù)與控制, 2019, 47(21): 55-61.

WANG Yongjin, FAN Yanfang, LI Ziqian. Single-end protection method for UHVDC transmission line based on characteristics of sudden energy waveform[J]. Power System Protection and Control, 2019, 47(21): 55-61.

[21] HUANG Bingqi. Analysis of debugging method in RCS-978 ratio differential protection[J]. Integrated Circuit Application, 2019, 36(9): 98-99.

[22] ANDERSEN K K, FRIJLINK M E, HOFF L. A numerical optimization method for transducer transfer functions by the linearity of the phase spectrum[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2019, 66(1): 71-78.

[23] 余曉, 呂飛鵬, 張國星, 等. 循環(huán)神經(jīng)網(wǎng)絡(luò)輸電線路雙端故障測(cè)距方法[J]. 中國測(cè)試, 2021, 47(9): 119-125.

YU Xiao, Lü Feipeng, ZHANG Guoxing, et al. Two-terminal fault location algorithm for transmission lines based on recurrent neural network[J]. China Measurement & Test, 2021, 47(9): 119-125.

[24]曾志輝, 肖宇. 基于變異系數(shù)與高階累積量的小電流接地故障選線[J]. 電力系統(tǒng)保護(hù)與控制, 2020, 48(13): 99-109.

ZENG Zhihui, XIAO Yu. Small current grounding fault selection based on coefficient of variation and high order cumulant[J]. Power System Protection and Control, 2020, 48(13): 99-109.

[25] HASHEMI S M, SANAYE-PASAND M. Current-based out-of-step detection method to enhance line differential protection[J]. IEEE Transactions on Power Delivery, 2019, 34(2): 448-456.

[26] TOKI A, KASUMOVI M, PEJI M, et al. Determination of single-phase transformer saturation characteristic by using Nelder–Mead optimization method[J]. Electrical Engineering, 2021(1): 1-13.

[27] WANG J, TONG J, FAN X, et al. A dynamic differential phase analysis method for wireless sensing[J]. IEEE Transactions on Vehicular Technology, 2019, 68(8): 7723-7732.

[28] WANG J, WANG Y, ZHAO G, et al. Location protection method for mobile crowd sensing based on local differential privacy preference[J]. Peer-to-Peer Networking and Applications, 2019(1): 1-13.

[29] AFRASIABI S, AFRASIABI M, PARANG B, et al. Integration of accelerated deep neural network into power transformer differential protection[J]. IEEE Transactions on Industrial Informatics, 2020, 16(2): 865-876.

Phase compensation method of distribution transformer differential protection based on wavelet transform

WU Haotian1, ZHAO Yang1, LIU Zizhuo1, ZHANG Chi2, ZHAO Fang3

(1. State Grid Lishui Power Supply Company, Lishui 323000, China; 2. Zhejiang Electric Industrial Company, Hangzhou 310000 , China; 3. College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China)

To reduce the safety loss of property caused by a distribution transformer fault and improve the operational stability of power system, a phase compensation method of distribution transformer differential protection based on wavelet transform is proposed. First, considering the fluctuation of line mode traveling wave current and the absolute value of its gradient, it is judged whether there is a fault in the distribution transformer. That is, a protection startup criterion is created. Secondly, it determines the fault area according to the energy ratio of the equivalent line mode traveling wave differential current, calculates the initial modulus of reversing the traveling wave differential current under the fault area of the wavelet transform, and obtains the maximum value of the wavelet transform modulus. Finally, by creating a fault pole selection criterion to obtain the fault type, the excitation current is calculated when the distribution transformer is closed without the load in a fault state. Also the changes of excitation inrush current and internal fault current are judged, and the phase compensation of differential protection of the distribution transformer is realized in combination with the opening and closing of the protection output signal. Simulation results show that this method can effectively identify faults in the area, has strong reliability and effectiveness, and under load conditions, the phase difference of voltage and current after phase compensation is consistent. It also has better stability.

distribution transformer; wavelet transform; phase compensation method; fault pole selection; load condition; excitation inrush current

10.19783/j.cnki.pspc.211604

國家重點(diǎn)研發(fā)計(jì)劃資助(2017YFB0903100)

This work is supported by the National Key Research and Development Program of China (No. 2017YFB0903100).

2021-11-26；

2021-12-29

吳昊天(1987—)，男，學(xué)士，工程師，主要研究方向?yàn)殡姎夤こ碳捌渥詣?dòng)化；E-mail: tianhaowu1987@163.com

趙 陽(1987—)，男，學(xué)士，工程師，主要研究方向?yàn)殡姎夤こ碳捌渥詣?dòng)化；

劉子卓(1987—)，男，學(xué)士，工程師，主要研究方向?yàn)殡姎夤こ碳捌渥詣?dòng)化。

(編輯 張愛琴)