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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (12): 2412-2422    DOI: 10.3785/j.issn.1008-973X.2019.12.020
Power and Electrical Engineering     
Fault identification of double-circuit transmission lines on same tower based on measuring wave impedance
Rui-kai YE(),Hao WU*(),Xing-xing DONG
Automation and Electronic Information Engineering, Sichuan University of Science and Engineering, Zigong 643000, China
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Abstract  

An algorithm for measuring wave impedance ratio braking fault identification was proposed based on S-transform, in order to improve the sensitivity and reliability of traveling wave protection on double-circuit transmission lines. S-transform was implemented to obtain the initial traveling wave phasor of the voltage of the busbar and the current of the transmission lines. Hereby, the measuring wave impedance of transmission line was calculated and the concepts of synthetical wave sum-impedance and synthetical wave differ-impedance were given. The theoretical analysis showed that, when an internal fault occured, the synthetical wave sum-impedance was smaller than the synthetical wave differ-impedance; when an external fault occured, the synthetical wave sum-impedance was much larger than the synthetical wave differ-impedance. The ratio braking coefficient was introduced, the synthetical wave sum-impedance was used as braking amount and the synthetical wave differ-impedance was taken as actuating amount, and the ratio braking protection criterion was established to identify internal and external faults. A large number of simulation results show that the algorithm has advantages of simple criterion, reliable performance, sensitive and quick response, and is less susceptible to the changes in initial fault angles, fault types, transitional resistances, and other factors.

Key words： double-circuit transmission lines on same tower      measuring wave impedance S-transform      synthetical wave sum-impedance      synthetical wave differ-impedance      fault identification     
Received: 05 October 2018      Published: 17 December 2019
CLC:  TM 773  
  TM 771  
Corresponding Authors: Hao WU     E-mail: pokagic@163.com;wuhao801212@163.com
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Rui-kai YE
Hao WU
Xing-xing DONG
Cite this article:

Rui-kai YE,Hao WU,Xing-xing DONG. Fault identification of double-circuit transmission lines on same tower based on measuring wave impedance. Journal of ZheJiang University (Engineering Science), 2019, 53(12): 2412-2422.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.12.020     OR     http://www.zjujournals.com/eng/Y2019/V53/I12/2412


基于测量波阻抗的同杆双回输电线路故障识别

为提高行波保护在同杆双回输电线路上的灵敏性与可靠性，提出一种基于S变换的测量波阻抗比率制动故障识别算法. 利用S变换获取母线电压与线路电流的初始行波相量，据此计算线路测量波阻抗，给出和波阻抗与差波阻抗概念，引入综合和波阻抗和综合差波阻抗. 理论分析表明：当发生区内故障时，综合和波阻抗小于综合差波阻抗；当发生区外故障时，综合和波阻抗远大于综合差波阻抗. 引入比率制动系数，将综合和波阻抗作为制动量，综合差波阻抗作为动作量，建立比率制动保护判据进行区内、外故障识别. 大量仿真结果表明，该算法判据简单，性能可靠，动作灵敏、迅速，基本不受故障初始角、故障类型、过渡电阻、噪声干扰等因素影响.


关键词： 同杆双回输电线路,  测量波阻抗,  变换,  综合和波阻抗,  综合差波阻抗,  故障识别 
Fig.1 Simplified model of double circuit lines on same tower
Fig.2 Peterson equivalent circuit model for internal fault of double lines on same tower
Fig.3 Peterson equivalent circuit model for external fault of double lines on same tower
Fig.4 Waveform of traveling wave for internal fault occurs on bus M without noise
Fig.5 Waveform of traveling wave for internal fault on bus M with noise
Fig.6 Fault identification algorithm flow of double-circuit transmission lines on same tower
序号 故障类型 l / km $\theta \,/\,(^ \circ )$ ${R_{\rm{T}}}$ / Ω ${K_{\rm{s} } }\left| { {Z_{\rm{sM} } } } \right|\,/\,({10^3}\;\Omega )$ $\left| { { { {Z} }_{ {\rm{dM} } } } } \right|\,/\,(1{0^4}\;\Omega )$ ${ { {K} }_{\rm{s} } }\left| { { { {Z} }_{ {\rm{sN} } } } } \right|\,/\,({10^3}\;\Omega )$ $\left| { { { {Z} }_{ {\rm{dN} } } } } \right|\,/\,(1{0^4}\;\Omega )$ 判断结果
1 ⅡBGG 100 90 200 1.156 1.089 1.223 1.078 区内故障
ⅠBCG 100 90 200 1.157 1.089 1.223 1.078
ⅠBCⅡAG 100 90 200 1.157 1.089 1.223 1.078
2 ⅡBGG 200 8 500 1.115 1.103 1.098 1.105 区内故障
ⅠBCG 200 8 500 1.115 1.103 1.097 1.105
ⅠBCⅡAG 200 8 500 1.115 1.103 1.097 1.105
3 ⅠAⅡBG 150 8 50 1.087 1.110 1.087 1.110 区内故障
ⅠAⅡBG 150 15 50 1.114 1.105 1.114 1.105
ⅠAⅡBG 150 45 50 1.087 1.110 1.087 1.110
ⅠAⅡBG 150 90 50 1.087 1.110 1.087 1.110
ⅠAⅡBG 150 120 50 1.159 1.088 1.159 1.088
4 ⅠABCⅡA 200 8 ? 1.087 1.110 1.087 1.110 区内故障
ⅠABCⅡA 200 15 ? 1.114 1.105 1.114 1.105
ⅠABCⅡA 200 45 ? 1.087 1.110 1.087 1.110
ⅠABCⅡA 200 90 ? 1.098 1.105 1.098 1.105
ⅠABCⅡA 200 120 ? 1.098 1.105 1.098 1.105
5 ⅡACG 250 45 0 1.087 1.112 1.106 1.101 区内故障
ⅡACG 250 45 100 1.103 1.108 1.087 1.107
ⅡACG 250 45 300 1.105 1.107 1.085 1.108
ⅡACG 250 45 600 1.105 1.107 1.084 1.108
Tab.1 Algorithm performance test results for internal fault of double-circuit transmission line on same tower
序号 故障类型 l / km $\theta \,/\,( ^ \circ )$ ${R_{\rm{T}}}$ / Ω ${{{K}}_{\rm{s}}}\left| {{Z_{\rm{sM} }}} \right|\,/\,({10^3}\;\Omega )$ $\left| {{{{Z}}_{{\rm{dM}}}}} \right|\,/\,(1{0^{ - 9}}\;\Omega )$ ${{{K}}_{\rm{s}}}\left| {{{{Z}}_{{\rm{sN}}}}} \right|\,/\,({10^3}\;\Omega )$ $\left| {{{{Z}}_{{\rm{dN}}}}} \right|\,/\,(1{0^{ - 9}}\;\Omega )$ 判断结果
1 CG 50 15 200 8.992 12.464 4.402 0.109 区外故障
BCG 50 15 200 9.055 0.135 4.396 0.208
ABCG 50 15 200 8.994 0.122 4.396 0.168
2 CG 100 120 500 8.253 0.396 4.402 2.249 区外故障
BCG 100 120 500 8.257 0.360 4.402 0.126
ABCG 100 120 500 8.257 0.110 4.402 0.138
3 AG 50 8 100 8.978 6.865 4.402 0.253 区外故障
AG 50 15 100 8.995 2.353 4.402 0.260
AG 50 45 100 9.014 0.252 4.402 0.195
AG 50 90 100 9.038 1.256 4.402 0.183
AG 50 120 100 9.007 1.411 4.401 0.244
4 AC 100 8 ? 8.184 2.354 4.402 0.152 区外故障
AC 100 15 ? 8.208 4.916 4.402 0.259
AC 100 45 ? 8.405 2.649 4.402 0.024
AC 100 90 ? 8.407 0.430 4.402 0.023
AC 100 120 ? 8.361 0.353 4.401 0.071
5 BG 50 45 0 9.050 1.126 4.406 0.069 区外故障
BG 50 45 100 9.045 3.267 4.406 0.423
BG 50 45 300 9.040 13.983 4.406 0.617
BG 50 45 600 9.037 12.736 4.406 5.109
Tab.2 Algorithm performance test results for external fault of double-circuit transmission line on same tower
故障情况 丢失数据 $k$ ${ { {K} }_{\rm{s} } }\left| { {Z_{\rm{sM} } } } \right|\,/\,({10^3}\;\Omega )$ $\left| {{{{Z}}_{{\rm{dM}}}}} \right|/\Omega $ ${ { {K} }_{\rm{s} } }\left| { { { {Z} }_{ {\rm{sN} } } } } \right|\,/\,({10^3}\;\Omega )$ $\left| {{{{Z}}_{{\rm{dN}}}}} \right|/\Omega $ 判断结果
故障一：
ⅠBCⅡA
l=100 km
θ=90°
RT=200 Ω 		无 0 1.157 $1.089 \times 1{0^4}$ 1.222 $1.078 \times 1{0^4}$ 区内故障
电压 峰值 $1.100$ $1.034 \times 1{0^4}$ $1.222$ $1.078 \times 1{0^4}$
电流 峰值 $1.208$ $1.071 \times 1{0^4}$ $1.222$ $1.078 \times 1{0^4}$
电压&电流 峰值 $1.100$ $1.034 \times 1{0^4}$ $1.222$ $1.078 \times 1{0^4}$
故障二：
ⅠAG
l=100 km
θ=45°
RT=100 Ω 		无 0 $1.156$ $1.089 \times 1{0^4}$ $1.223$ $1.078 \times 1{0^4}$ 区内故障
电压 5 $0.925$ $8.710 \times 1{0^3}$ $1.223$ $1.078 \times 1{0^4}$ 区内故障
10 $0.635$ $5.993 \times 1{0^3}$ $1.223$ $1.078 \times 1{0^4}$
15 $0.288$ $2.727 \times 1{0^3}$ $1.223$ $1.078 \times 1{0^4}$
电流 5 $1.413$ $9.995 \times 1{0^3}$ $1.223$ $1.078 \times 1{0^4}$ 区内故障
10 $1.675$ $9.103 \times 1{0^3}$ $1.223$ $1.078 \times 1{0^4}$
15 $1.937$ $8.219 \times 1{0^3}$ $1.223$ $1.078 \times 1{0^4}$
电压&电流 5 $1.020$ $7.636 \times 1{0^3}$ $1.223$ $1.078 \times 1{0^4}$ 区内故障
10 $0.888$ $4.380 \times 1{0^3}$ $1.223$ $1.078 \times 1{0^4}$
15 $0.444$ $2.191 \times 1{0^3}$ $1.223$ $1.078 \times 1{0^4}$
故障三：
ABG
l=100 km
θ=90°
RT=300 Ω 		无丢失 0 $8.407$ $4.879 \times 1{0^{ - 10}}$ $4.402$ $6.924 \times 1{0^{ - 12}}$ 区外故障
电压 5 $6.254$ $3.133 \times 1{0^{ - 10}}$ $4.402$ $6.924 \times 1{0^{ - 12}}$ 区外故障
10 $4.191$ $2.658 \times 1{0^{ - 10}}$ $4.402$ $6.924 \times 1{0^{ - 12}}$
15 $2.053$ $7.013 \times 1{0^{ - 11}}$ $4.402$ $6.924 \times 1{0^{ - 12}}$
电流 5 $6.306$ $3.755 \times 1{0^{ - 10}}$ $4.402$ $1.526 \times 1{0^{ - 11}}$ 区外故障
10 $4.220$ $2.519 \times 1{0^{ - 10}}$ $4.402$ $1.526 \times 1{0^{ - 11}}$
15 $2.069$ $9.998 \times 1{0^{ - 11}}$ $4.402$ $1.526 \times 1{0^{ - 11}}$
电压&电流 5 $6.302$ $3.724 \times 1{0^{ - 10}}$ $4.402$ $6.924 \times 1{0^{ - 12}}$ 区外故障
10 $4.205$ $2.296 \times 1{0^{ - 10}}$ $4.402$ $6.924 \times 1{0^{ - 12}}$
15 $2.478$ $1.122 \times 1{0^{ - 10}}$ $4.402$ $6.924 \times 1{0^{ - 12}}$
Tab.3 Performance test results of protection algorithm for double-circuit transmission line on same tower with losing traveling wave samples
故障情况 SNR/dB ${ { {K} }_{\rm{s} } }\left| { {Z_{\rm{sM} } } } \right|/({10^3}\;\Omega )$ $\left| { { { {Z} }_{ {\rm{dM} } } }} \right|/({10^3}\;\Omega )$ ${ { {K} }_{\rm{s} } }\left| { { { {Z} }_{ {\rm{sN} } } }} \right|/({10^3}\;\Omega )$ $\left| { { { {Z} }_{ {\rm{dN} } } }} \right|/({10^3}\;\Omega )$ 判断结果
ⅠAⅡBG
l=150 km
θ=90°
RT=50 Ω 		10 $2.851$ $3.649$ $1.834$ $8.220$ 区内故障
20 $2.548$ $7.176$ $2.400$ $14.310$
30 $1.110$ $9.840$ $0.892$ $10.599$
40 $0.949$ $10.756$ $0.981$ $11.227$
50 $1.055$ $10.853$ $1.146$ $11.057$
60 $1.135$ $11.154$ $1.127$ $11.202$
Tab.4 Performance test results of protection algorithm for internal fault of double-circuit transmission line on same tower under the noise with different SNR
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