CN101907677A - Fault phase location method for high voltage cable-overhead line hybrid line - Google Patents

Fault phase location method for high voltage cable-overhead line hybrid line Download PDF

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CN101907677A
CN101907677A CN 201010217037 CN201010217037A CN101907677A CN 101907677 A CN101907677 A CN 101907677A CN 201010217037 CN201010217037 CN 201010217037 CN 201010217037 A CN201010217037 A CN 201010217037A CN 101907677 A CN101907677 A CN 101907677A
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positioning function
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马静
王增平
林富洪
曾惠敏
叶东华
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North China Electric Power University
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Abstract

本发明公开了属于电力系统继电保护技术领域的涉及采用定位函数相位特性实现高压电缆-架空线混合线路故障测距的方法。先采集故障后混合线路系统两端的正序电气量数据,将整个混合线路等效成一等长线路;然后由混合线路系统两端的正序电气量数据推导出定位函数,根据定位函数相位的大小确定包含故障点的最小故障等分区;最后在故障等分区内再次利用定位函数的相角大小精确测出混合线路的故障距离。本发明精确测定故障位置,可缩短故障排查时间,加快恢复供电,对电力系统的安全和经济运行具有非常重要的意义。

Figure 201010217037

The invention discloses a method for realizing fault distance measurement of a high-voltage cable-overhead line mixed line by using the phase characteristic of a positioning function, which belongs to the technical field of electric power system relay protection. First collect the positive-sequence electrical quantity data at both ends of the hybrid line system after the fault, and make the entire hybrid line equivalent to a line of equal length; then deduce the positioning function from the positive-sequence electrical quantity data at both ends of the hybrid line system, and determine it according to the size of the phase of the positioning function The smallest fault equal partition including the fault point; finally, in the fault equal partition, the phase angle of the positioning function is used to accurately measure the fault distance of the hybrid line. The invention accurately measures the fault location, can shorten the troubleshooting time, accelerates the recovery of power supply, and has very important significance for the safe and economical operation of the power system.

Figure 201010217037

Description

高压电缆-架空线混合线路故障相位测距方法 Fault phase location method for high voltage cable-overhead line hybrid line

技术领域technical field

本发明涉及电力系统继电保护技术领域,具体地说是涉及采用定位函数相位特性实现高压电缆-架空线混合线路故障测距的方法。The invention relates to the technical field of electric power system relay protection, in particular to a method for realizing fault distance measurement of a high-voltage cable-overhead line hybrid line by using the phase characteristic of a positioning function.

背景技术Background technique

随着我国大中型城市建设的飞速发展和城市规划的要求,电力电缆以其占地少、人身安全保障、供电可靠性高、维护工作量小等优点得到了广泛的应用,并进一步在原有电缆、架空线路基础上发展应用越来越广泛的电缆-架空线混合线路,例如上海小洋山电缆-架空混合线路、铁路自闭贯通电缆-架空线路以及电气化铁路电缆-架空混合线路。高压电缆-架空线混合线路发生故障后能精确测距,可以缩短故障排查时间,加快恢复供电,对电力系统的安全和经济运行具有非常重要的意义。With the rapid development of large and medium-sized cities in my country and the requirements of urban planning, power cables have been widely used due to their advantages of small footprint, personal safety, high power supply reliability, and small maintenance workload. On the basis of overhead lines, cable-overhead hybrid lines are developed and applied more and more widely, such as Shanghai Xiaoyangshan cable-overhead hybrid line, railway self-closing through cable-overhead line and electrified railway cable-overhead hybrid line. After the high-voltage cable-overhead line hybrid line fails, it can accurately measure the distance, which can shorten the troubleshooting time and speed up the restoration of power supply, which is of great significance to the safe and economical operation of the power system.

相比于单独的电缆和架空线路的故障测距,高压电缆-架空线混合输电线路故障测距会面临如下新难题:①由于电缆线路和架空线路参数相差很大,其混合线路波阻抗不连续,因此,对单独应用于架空线路故障测距的阻抗法而言,混合线路是不均匀传输线路,无法直接应用于混合线路的故障测距;②行波在电缆和架空线路的连接处会发生反射,增加了反射波的识别难度;③在电缆和架空线路中的传播速度明显不一致,难以直接测距;④行波特别是反射波在经过较长的电缆线路传播后,波头幅值衰减较大,易受到干扰信号的影响,从而影响测量精度。因此,应用于单独的电缆和架空线路的故障测距的行波法也无法直接应用于混合线路的故障测距。Compared with the fault location of individual cables and overhead lines, the fault location of high-voltage cable-overhead line hybrid transmission lines will face the following new problems: ① Due to the large difference between the parameters of the cable line and the overhead line, the wave impedance of the hybrid line is discontinuous , therefore, for the impedance method applied solely to the fault location of overhead lines, hybrid lines are uneven transmission lines and cannot be directly applied to fault location of hybrid lines; ② traveling waves will occur at the connection between cables and overhead lines Reflection, which increases the difficulty of identifying reflected waves; ③The propagation speeds in cables and overhead lines are obviously inconsistent, making it difficult to measure distances directly; ④Traveling waves, especially reflected waves, after propagating through a long cable line, the amplitude of the wave head attenuates Larger, it is easily affected by interference signals, thus affecting the measurement accuracy. Therefore, the traveling wave method applied to the fault location of individual cables and overhead lines cannot be directly applied to the fault location of mixed lines.

有关高压电缆-架空线混合输电线路的故障测距逐渐引起了广大学者的关注。于玉泽、覃剑和李功新等人发表的《电缆-架空线混合线路故障测距方法综述》是针对电缆-架空线路的故障测距提出同时向故障相和非故障相注入脉冲电流,通过比较故障相和非故障相行波信号先判断连接点和故障点位置再去精确测距的方法,但脉冲发射装置以及其同步性在实际应用中比较难实现。蔡玉梅发表的《铁路自闭贯通线路故障测距方法研究》针对铁路自闭贯通电缆-架空线路的故障测距问题提出了一种比较电流行波线零模分量极性的方法进行区段精确定位的方法,但没有考虑线零模分量在故障点发生藕合的影响。吴承恩、邰能灵和郁惟镛发表的《超高压电缆-架空线混合线路故障测寻法》针对超高压电缆-架空线混合线路的故障测距提出利用故障附加负序网中故障点负序电压幅值最大这一特点构造判据先判别故障点所在电缆线路或架空线路,然后利用故障区域首末端电压、电流突变量推算出故障点,但在混合线路连接处附近高阻短路故障时,由双端电气量推算出连接点处的负序电压幅值基本相同,加上故障暂态过程的影响,在连接点附近可能无法正确判断故障区段,从而导致测距失败。束洪春和孙涛发表的《电缆-架空线混合线路故障行波测距新方法》针对电缆-架空线路的故障测距提出利用故障后附加负序网络下通过系统两端电气量推导出的电缆架空线连接点处的分布电流的大小判断故障发生区段,再使用单端行波测距装置进行精确故障测距,但在混合线路连接处附近高阻短路故障时,由两端电气量推导出的电缆架空线连接点处的分布电流大小基本相等,加上故障暂态过程的影响,在连接点附近会有测距死区,且不适用于对称性故障。The fault location of high-voltage cable-overhead line hybrid transmission lines has gradually attracted the attention of scholars. Yu Yuze, Qin Jian, and Li Gongxin published "A Review of Fault Location Methods for Cable-Overhead Line Hybrid Lines", which proposed injecting pulse currents into fault phases and non-fault phases at the same time for cable-overhead line fault location. The faulty phase and non-faulty phase traveling wave signals first determine the connection point and fault point position and then go to the method of precise distance measurement, but the pulse transmitter and its synchronization are difficult to achieve in practical applications. Cai Yumei's "Research on Fault Location Method for Railway Self-closing Through Lines" aims at the problem of fault location of railway self-closing through cables-overhead lines, and proposes a method of comparing the polarity of the zero-mode component of the current traveling wave line to accurately locate the section method, but does not consider the influence of line zero-mode component coupling at the fault point. Wu Chengen, Tai Nengling and Yu Weiyong published the "Extra-high Voltage Cable-Overhead Line Hybrid Line Fault Finding Method", aiming at the fault location of EHV cable-overhead line hybrid line, it is proposed to use the fault point in the additional negative sequence network to maximize the negative sequence voltage amplitude of the fault point. This feature constructs the criterion to first identify the cable line or overhead line where the fault point is located, and then calculates the fault point by using the voltage and current mutations at the beginning and end of the fault area. The negative-sequence voltage amplitude at the connection point is basically the same as calculated by the quantity. In addition to the influence of the fault transient process, the fault section may not be correctly judged near the connection point, resulting in the failure of ranging. Shu Hongchun and Sun Tao published "A New Method for Fault Traveling Wave Location of Cable-Overhead Line Mixed Lines", aiming at cable-overhead line fault location. The size of the distributed current at the connection point of the overhead line judges the fault area, and then uses the single-ended traveling wave distance measuring device to perform accurate fault location. The distributed current at the connection point of the cable overhead line is basically equal, and with the influence of the fault transient process, there will be a ranging dead zone near the connection point, and it is not suitable for symmetrical faults.

发明内容Contents of the invention

本发明的目的在于针对缆线混合线路的特殊性和复杂性,提供一种利用定位函数相位特性实现高压电缆-架空线混合线路故障定位的测距方法,其特征在于,先采集故障后混合线路系统两端的正序电气量数据,将整个混合线路等效成一等长线路;然后由混合线路系统两端的正序电气量数据推导出定位函数,根据定位函数相位的大小确定包含故障点的最小故障等分区;最后在故障等分区内再次利用定位函数的相角大小精确测出混合线路的故障距离,具体步骤如下:The purpose of the present invention is to aim at the particularity and complexity of cable hybrid lines, and to provide a distance measuring method for realizing the fault location of high-voltage cable-overhead line hybrid lines by using the phase characteristics of the positioning function. The positive-sequence electrical quantity data at both ends of the system, the entire hybrid line is equivalent to a line of equal length; then the positioning function is derived from the positive-sequence electrical quantity data at both ends of the hybrid line system, and the minimum fault including the fault point is determined according to the phase size of the positioning function Equal partition; Finally, in the fault equal partition, the phase angle of the positioning function is used to accurately measure the fault distance of the hybrid line. The specific steps are as follows:

(1)提取故障后混合线路系统m、n两端的三相电压与电流相量,

Figure BSA00000168437600031
Figure BSA00000168437600032
分别为故障后m、n端的三相电压与电流相量,根据对称分量法分别求出m、n端的正序分量
Figure BSA00000168437600034
Figure BSA00000168437600035
(1) Extract the three-phase voltage and current phasors at both ends of the hybrid line system m and n after the fault,
Figure BSA00000168437600031
Figure BSA00000168437600032
and are the three-phase voltage and current phasors of terminals m and n after the fault respectively, and the positive sequence components of terminals m and n are obtained respectively according to the symmetrical component method
Figure BSA00000168437600034
and
Figure BSA00000168437600035

(2)将混合线路等效为一条长为lmn的长线路,则初始包含故障点的区域为(lbegin,lend)=(0,lmn);(2) The hybrid line is equivalent to a long line with a length of l mn , then the initial area containing the fault point is (l begin , l end )=(0, l mn );

(3)将包含故障点的区域为(lbegin,lend)进行Num等分;(3) Divide the area containing the fault point into Num equal parts (l begin , l end );

(4)利用系统m、n端测量到的电气量从混合线路系统两端进行推导,得出(3)所确定的区域内每一等分点处的正序电压、正序电流;(4) Use the electrical quantities measured at the m and n terminals of the system to deduce from the two ends of the mixed line system, and obtain the positive sequence voltage and positive sequence current at each equal point in the area determined in (3);

(5)由(4)推导出定位函数,并以此求出每一等分点处的定位函数的相角;(5) deduce positioning function by (4), and find out the phase angle of the positioning function at each bisection point place with this;

(6)由(5)计算的定位函数相角的大小判断等分点与故障点的位置关系:(6) The positional relationship between the bisection point and the fault point is judged by the size of the positioning function phase angle calculated in (5):

1)定位函数相角大于零,参考位置位于故障位置左侧;1) The phase angle of the positioning function is greater than zero, and the reference position is on the left side of the fault position;

2)定位函数相角小于零,参考位置位于故障位置右侧2) The phase angle of the positioning function is less than zero, and the reference position is on the right side of the fault position

3)定位函数相角等于零,参考位置和故障位置相匹配;3) The phase angle of the positioning function is equal to zero, and the reference position matches the fault position;

由此判据找到两个相邻等分点k和k+1,其定位函数相角分别大于零及小于零,则此时包含故障点的区域(lbegin,lend)=(lk,lk+1)。设定一最小等分区域阀值Δlset,重复(3)~(5)直至lend-lbegin<Δlset,则能够得出包含故障点的最小等分区域(lbeginm,lendm);Based on this criterion, two adjacent bisection points k and k+1 are found, and the phase angles of their positioning functions are respectively greater than zero and less than zero, then the area containing the fault point (l begin , l end )=(l k , l k+1 ). Set a threshold value Δl set for the minimum equal division area, repeat (3)~(5) until l end -l begin <Δl set , then the minimum equal division area (l beginm , l endm ) including the fault point can be obtained;

(7)由(6)计算的最小包含故障点的等分区确定故障位置:(7) Determine the fault location by the equal partition that contains the fault point calculated by (6):

1)确定步长Δl;1) Determine the step size Δl;

2)参考位置lmk从lbeginm开始以Δl为步长递增至lendm,计算各点处的定位函数的相角;2) The reference position l mk starts from l beginm and increases to l endm with Δl as the step size, and calculates the phase angle of the positioning function at each point;

3)寻找确定最优参考位置lmk,使其满足在lmk-Δl处定位函数相角大于零,在lmk处定位函数相角小于零;3) Find and determine the optimal reference position l mk so that the phase angle of the positioning function at l mk -Δl is greater than zero, and the phase angle of the positioning function at l mk is less than zero;

则故障位置f距m端的故障距离lmf=lmk-Δl/2。Then the fault distance from the fault position f to the terminal m is l mf =l mk -Δl/2.

在步骤(5)中,高压电缆-架空线混合线路上任何一点k处的定位函数为:In step (5), the positioning function at any point k on the high-voltage cable-overhead line hybrid line is:

ff (( ll mkmk )) == Uu &CenterDot;&Center Dot; mkmk 11 -- Uu &CenterDot;&Center Dot; nknk 11 II &CenterDot;&Center Dot; mkmk 11 ++ II &CenterDot;&Center Dot; nknk 11

其中,

Figure BSA00000168437600042
Figure BSA00000168437600043
分别为m、n端正序电气量推导出的混合线路上k点处的正序电压、正序电流。in,
Figure BSA00000168437600042
and
Figure BSA00000168437600043
are the positive sequence voltage and positive sequence current at point k on the hybrid line derived from the positive sequence electrical quantities at terminals m and n, respectively.

步骤(6)中的Δlset可以根据实际精度要求灵活进行区间大小的设定。Δl set in step (6) can flexibly set the interval size according to the actual precision requirements.

步骤(7)中的故障位置可以是位于架空线I段、中间电缆或位于架空线II段上,定位函数的相位特性都满足:当lmf>lmk时,定位函数相角大于零;当lmf<lmk时,定位函数相角小于零;当且仅当lmf=lmk时,定位函数的相角才等于零。其中,lmf、lmk分别为混合线路上故障位置f、参考位置k到架空线I段m端的距离。The fault location in step (7) can be located on the overhead line section I, the intermediate cable or on the overhead line section II, and the phase characteristics of the location function all satisfy: when lmf > lmk , the location function phase angle is greater than zero; when When l mf <l mk , the phase angle of the positioning function is smaller than zero; if and only when l mf =l mk , the phase angle of the positioning function is equal to zero. Among them, l mf and l mk are respectively the distances from the fault position f and the reference position k on the hybrid line to the end m of section I of the overhead line.

步骤(7)中的Δl可以根据实际测距精度和实际测距速度要求灵活设定。Δl in step (7) can be flexibly set according to the actual ranging accuracy and actual ranging speed requirements.

本发明利用定位函数相位特性,实现了混合线路的故障精确测距,主要具有以下优点:The present invention utilizes the phase characteristic of the positioning function to realize accurate fault distance measurement of hybrid lines, and mainly has the following advantages:

1.将混合线路等效为一等长线路进行定位,无需事先判别故障区段即可测距。1. The hybrid line is equivalent to a line of equal length for positioning, and the distance can be measured without prior identification of the fault section.

2.以混合线路上参考位置和故障位置匹配时定位函数过零这一特征进行定位,原理上不存在伪根,克服了过渡电阻、负荷电流、采样频率、故障类型和故障点位置的影响。2. Based on the characteristic that the positioning function crosses zero when the reference position on the hybrid line matches the fault position, there is no pseudo root in principle, and the influence of transition resistance, load current, sampling frequency, fault type and fault point position is overcome.

3.所需搜索范围小,具有良好快速性。3. The required search range is small and has good rapidity.

4.该发明原理简单可靠,测距精度高。4. The principle of the invention is simple and reliable, and the ranging accuracy is high.

随着电缆-架空混合线路应用增多,电缆-架空混合线路发生故障后,故障位置精确测距可缩短故障排查时间,加快恢复供电,对电力系统的安全和经济运行具有非常重要的意义。With the increasing application of cable-overhead hybrid lines, after the cable-overhead hybrid line fails, accurate fault location measurement can shorten the troubleshooting time and speed up the restoration of power supply, which is of great significance to the safe and economical operation of the power system.

附图说明Description of drawings

图1为本发明B型混合线路连接结构;Fig. 1 is the B-type hybrid line connection structure of the present invention;

图2为架空线I段故障时混合线路的正序序网图;Fig. 2 is the positive sequence sequence network diagram of hybrid line when section I of overhead line fails;

图3为架空线I段故障时混合线路上定位函数的相位特性;Fig. 3 is the phase characteristic of the positioning function on the mixed line when the I segment of the overhead line is faulty;

图4为中间电缆线路故障时混合线路的正序序网图;Fig. 4 is the positive sequence sequence network diagram of the hybrid line when the middle cable line fails;

图5为中间电缆线路故障时混合线路上定位函数的相位特性;Fig. 5 is the phase characteristic of the positioning function on the hybrid line when the intermediate cable line is faulty;

图6为架空线II段时混合线路的正序序网图;Fig. 6 is the positive sequence sequence network diagram of the hybrid line during the overhead line II section;

图7为架空线II段故障时混合线路上定位函数的相位特性;Fig. 7 is the phase characteristic of the positioning function on the mixed line when the II section of the overhead line is faulty;

图8为负荷电流和过渡电阻对架空线Ⅰ段上25km处ABG故障测距结果的影响;Figure 8 shows the influence of load current and transition resistance on the ABG fault location results at 25km on the first section of the overhead line;

图9为过渡电阻和故障位置对中间电缆线路上AG故障测距结果的影响;Figure 9 shows the influence of transition resistance and fault location on the AG fault location results on the intermediate cable line;

图10为过渡电阻和故障位置对架空线II段上AG故障测距结果的影响;Figure 10 is the influence of transition resistance and fault location on the AG fault location results on the II section of the overhead line;

图11为负荷电流和故障位置对混合线路上ABCG故障测距结果的影响。Figure 11 shows the influence of load current and fault location on the results of ABCG fault location on hybrid lines.

具体实施方式Detailed ways

本发明提供一种利用定位函数相位特性实现高压电缆-架空线混合线路故障定位的测距方法。先采集故障后混合线路系统两端的正序电气量数据,将整个混合线路等效成一等长线路;然后由混合线路系统两端的正序电气量数据推导出定位函数,根据定位函数相位的大小确定包含故障点的最小故障等分区;最后在故障等分区内再次利用定位函数的相角大小精确测出混合线路的故障距离。下面结合附图和实施例对本发明予以进一步说明。The invention provides a distance measuring method for realizing fault location of a high-voltage cable-overhead line hybrid line by utilizing the phase characteristic of a location function. First collect the positive-sequence electrical quantity data at both ends of the hybrid line system after the fault, and make the entire hybrid line equivalent to a line of equal length; then deduce the positioning function from the positive-sequence electrical quantity data at both ends of the hybrid line system, and determine it according to the size of the phase of the positioning function The smallest fault equal partition including the fault point; finally, in the fault equal partition, the phase angle of the positioning function is used to accurately measure the fault distance of the hybrid line. The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

实施例1Example 1

如图1所示B型混合线路类型作为分析及仿真对象为例,具体是作为一个简单的双端系统,当线路上任何一点发生故障时,运用对称分量法将故障网络分解为正、负、零序网络;对于三相对称性故障或三相不称性故障,都存在正序网络,因此,在本发明中,利用正序电压、正序电流进行混合线路故障测距。As shown in Figure 1, the type B hybrid line is used as an example for analysis and simulation. Specifically, it is a simple double-ended system. When a fault occurs at any point on the line, the symmetrical component method is used to decompose the fault network into positive, negative, Zero-sequence network; for three-phase symmetry faults or three-phase asymmetry faults, there is a positive-sequence network. Therefore, in the present invention, positive-sequence voltage and positive-sequence current are used for hybrid line fault distance measurement.

假设在B型混合线路上发生故障,故障点位置有3种形式:架空线I段、中间电缆线路、架空线II段。Assuming that a fault occurs on a Type B hybrid line, the location of the fault point has three forms: overhead line section I, intermediate cable line, and overhead line section II.

一、架空线I段故障时混合线路上任一点处的定位函数及其相位特性1. The location function and its phase characteristics at any point on the hybrid line when the I section of the overhead line is faulty

图2为架空线I段故障时混合线路的正序序网图。其中,

Figure BSA00000168437600061
Figure BSA00000168437600062
Figure BSA00000168437600063
分别为m、n端的正序电压、正序电流;c节点为架空线I段和中间电缆线路的连接点;t节点为架空线II段和中间电缆线路的连接点。架空线I段故障时架空线I段内任何一点k处定位函数表达式如式(1)所示。Fig. 2 is the positive sequence sequence network diagram of the hybrid line when section I of the overhead line fails. in,
Figure BSA00000168437600061
and
Figure BSA00000168437600062
Figure BSA00000168437600063
are the positive sequence voltage and positive sequence current of terminals m and n respectively; node c is the connection point between section I of the overhead line and the middle cable line; node t is the connection point between section II of the overhead line and the middle cable line. The expression of the positioning function at any point k in the overhead line section I when the overhead line section I is faulty is shown in formula (1).

ff (( ll mkmk )) == Uu &CenterDot;&Center Dot; mkmk 11 -- Uu &CenterDot;&Center Dot; nknk 11 II &CenterDot;&Center Dot; mkmk 11 ++ II &CenterDot;&Center Dot; nknk 11 == ZZ LL 11 tanhtanh &gamma;&gamma; LL 11 (( ll mfmf -- ll mkmk )) -- -- -- (( 11 ))

Uu &CenterDot;&Center Dot; mkmk 11 == Uu &CenterDot;&Center Dot; mm 11 coshcosh &gamma;&gamma; LL 11 ll mkmk -- II &CenterDot;&Center Dot; mm 11 ZZ LL 11 sinsin &gamma;&gamma; LL 11 ll mkmk II &CenterDot;&Center Dot; mkmk 11 == II &CenterDot;&CenterDot; mm 11 coshcosh &gamma;&gamma; LL 11 ll mkmk -- Uu &CenterDot;&Center Dot; mm 11 ZZ LL 11 sinhsinh &gamma;&gamma; LL 11 ll mkmk Uu &CenterDot;&Center Dot; ntnt 11 == Uu &CenterDot;&Center Dot; nno 11 coshcosh &gamma;&gamma; LL 11 ll mm -- II &CenterDot;&Center Dot; nno 11 ZZ LL 11 sinsin h&gamma;h&gamma; LL 11 ll tntn II &CenterDot;&Center Dot; ntnt 11 == II &CenterDot;&Center Dot; nno 11 coshcosh &gamma;&gamma; LL 11 ll mm -- Uu &CenterDot;&CenterDot; nno 11 sinhsinh &gamma;&gamma; LL 11 ll tntn // ZZ LL 11 Uu &CenterDot;&CenterDot; ncnc 11 == Uu &CenterDot;&CenterDot; ntnt 11 coshcosh &gamma;&gamma; cc 11 ll ctct -- II &CenterDot;&CenterDot; ntnt 11 ZZ cc 11 sinhsinh &gamma;&gamma; cc 11 ll ctct II &CenterDot;&Center Dot; ncnc 11 == II &CenterDot;&Center Dot; ntnt 11 coshcosh &gamma;&gamma; cc 11 ll ctct -- Uu &CenterDot;&Center Dot; ntnt 11 sinhsinh &gamma;&gamma; cc 11 ll ctct // ZZ cc 11 Uu &CenterDot;&CenterDot; nknk 11 == Uu &CenterDot;&CenterDot; ncnc 11 coshcosh &gamma;&gamma; LL 11 (( ll mcmc -- ll mkmk )) -- II &CenterDot;&Center Dot; ncnc 11 ZZ LL 11 sinhsinh &gamma;&gamma; LL 11 (( ll mcmc -- ll mkmk )) II &CenterDot;&Center Dot; nknk 11 == II &CenterDot;&CenterDot; ncnc 11 coshcosh &gamma;&gamma; LL 11 (( ll mcmc -- ll mkmk )) -- Uu &CenterDot;&Center Dot; ncnc 11 ZZ LL 11 sinhsinh &gamma;&gamma; LL 11 (( ll mcmc -- ll mkmk )) -- -- -- (( 22 ))

Figure BSA00000168437600066
Figure BSA00000168437600067
可由式(2)算得;其中,
Figure BSA00000168437600068
分别为m、n端正序电气量,推导出的架空线I段上k点处的正序电压、正序电流;lmf、lmk分别为架空线I段内故障位置f、参考位置k距m端的距离;lct为中间电缆线路的长度;lmc、lnt分别架空线I段和架空线II段的长度;ZL1、rL1分别为架空线I段和架空线II段的波阻抗、传播常数;Zc1、rc1分别为中间电缆线路的波阻抗、传播常数。
Figure BSA00000168437600066
and
Figure BSA00000168437600067
Can be calculated by formula (2); where,
Figure BSA00000168437600068
and are the positive- sequence electrical quantities at terminals m and n, respectively, and the derived positive-sequence voltage and positive- sequence current at point k on section I of the overhead line; m-terminal distance; l ct is the length of the middle cable line; l mc and l nt are the lengths of overhead line section I and overhead line section II respectively; Z L1 and r L1 are the wave impedance of overhead line section I and overhead line section II respectively , propagation constant; Z c1 , r c1 are the wave impedance and propagation constant of the intermediate cable line respectively.

架空线I段故障时中间电缆线路内任何一点处的定位函数如式(3)所示。The positioning function at any point in the intermediate cable line when the I section of the overhead line is faulty is shown in formula (3).

ff (( ll mkmk )) == Uu &CenterDot;&Center Dot; mkmk 11 -- Uu &CenterDot;&Center Dot; nknk 11 II &CenterDot;&CenterDot; mkmk 11 ++ II &CenterDot;&CenterDot; nknk 11 == -- ZZ cc 11 22 sinhsinh &gamma;&gamma; cc 11 ll ckck coshcosh &gamma;&gamma; LL 11 ll fcfc ++ ZZ cc 11 ZZ LL 11 coshcosh &gamma;&gamma; cc 11 ll ckck sinsin &gamma;&gamma; LL 11 ll fcfc ZZ cc 11 coshcosh &gamma;&gamma; cc 11 ll ckck coshcosh &gamma;&gamma; LL 11 ll fcfc ++ ZZ LL 11 sinhsinh &gamma;&gamma; cc 11 ll ckck sinsin &gamma;&gamma; LL 11 ll fcfc -- -- -- (( 33 ))

Uu &CenterDot;&Center Dot; ntnt 11 == Uu &CenterDot;&Center Dot; nno 11 coshcosh &gamma;&gamma; LL 11 ll tntn -- II &CenterDot;&CenterDot; nno 11 ZZ LL 11 sinsin &gamma;&gamma; LL 11 ll tntn II &CenterDot;&CenterDot; ntnt 11 == II &CenterDot;&CenterDot; nno 11 coshcosh &gamma;&gamma; LL 11 ll tntn -- Uu &CenterDot;&Center Dot; nno 11 sinhsinh &gamma;&gamma; LL 11 ll tntn // ZZ LL 11 Uu &CenterDot;&Center Dot; mcmc 11 == Uu &CenterDot;&Center Dot; mm 11 coshcosh &gamma;&gamma; LL 11 ll mcmc -- II &CenterDot;&Center Dot; mm 11 ZZ LL 11 sinsin h&gamma;h&gamma; LL 11 ll mcmc II &CenterDot;&Center Dot; mcmc 11 == II &CenterDot;&CenterDot; mm 11 coshcosh &gamma;&gamma; LL 11 ll mcmc -- Uu &CenterDot;&CenterDot; mm 11 sinhsinh &gamma;&gamma; LL 11 ll mcmc // ZZ LL 11 Uu &CenterDot;&CenterDot; mkmk 11 == Uu &CenterDot;&CenterDot; mcmc 11 coshcosh &gamma;&gamma; cc 11 (( ll mkmk -- ll mcmc )) -- II &CenterDot;&CenterDot; mcmc 11 ZZ cc 11 sinhsinh &gamma;&gamma; cc 11 (( ll mkmk -- ll mcmc )) II &CenterDot;&CenterDot; mkmk 11 == II &CenterDot;&CenterDot; mcmc 11 coshcosh &gamma;&gamma; cc 11 (( ll mkmk -- ll mcmc )) -- Uu &CenterDot;&Center Dot; mcmc 11 ZZ cc 11 sinhsinh &gamma;&gamma; cc 11 (( ll mkmk -- ll mcmc )) Uu &CenterDot;&CenterDot; nknk 11 == Uu &CenterDot;&CenterDot; ncnc 11 coshcosh &gamma;&gamma; cc 11 (( ll ctct ++ ll mcmc -- ll mkmk )) -- II &CenterDot;&Center Dot; ntnt 11 ZZ cc 11 sinhsinh &gamma;&gamma; cc 11 (( ll ctct ++ ll mcmc -- ll mkmk )) II &CenterDot;&Center Dot; nknk 11 == II &CenterDot;&CenterDot; ntnt 11 coshcosh &gamma;&gamma; cc 11 (( ll ctct ++ ll mcmc -- ll mkmk )) -- Uu &CenterDot;&CenterDot; ntnt 11 ZZ cc 11 sinhsinh &gamma;&gamma; cc 11 (( ll ctct ++ ll mcmc -- ll mkmk )) -- -- -- (( 44 ))

其中,lfc为架空线I段内故障位置f距c节点的距离;lmk、lck分别为中间电缆线路内所选参考位置k距m端、c节点的距离;

Figure BSA00000168437600073
Figure BSA00000168437600074
分别为m、n端正序电气量推导出的中间电缆线路上k点处的正序电压、正序电流,且由式(4)算得。Among them, l fc is the distance from fault position f to node c in section I of the overhead line; l mk and l ck are the distances from selected reference position k in the middle cable line to m end and node c respectively;
Figure BSA00000168437600073
and
Figure BSA00000168437600074
are the positive sequence voltage and positive sequence current at point k on the intermediate cable line derived from the positive sequence electrical quantities at terminals m and n, respectively, and are calculated by formula (4).

架空线I段故障时架空线II段内任何一点处的定位函数如式(5)所示。The positioning function at any point in the overhead line section II when the overhead line section I fails is shown in formula (5).

ff (( ll mkmk )) == Uu &CenterDot;&CenterDot; mkmk 11 -- Uu &CenterDot;&Center Dot; nknk 11 II &CenterDot;&CenterDot; mkmk 11 ++ II &CenterDot;&Center Dot; nknk 11 == -- ff 11 ff 22 -- -- -- (( 55 ))

式中In the formula

ff 11 == ZZ LL 11 ZZ cc 11 22 sinhsinh &gamma;&gamma; cc 11 ll ctct coshcosh &gamma;&gamma; LL 11 ll fcfc coshcosh &gamma;&gamma; LL 11 ll tktk ++ ZZ cc 11 ZZ LL 11 22 coshcosh &gamma;&gamma; cc 11 ll ctct sinsin &gamma;&gamma; LL 11 (( ll fcfc ++ ll tktk )) ++

ZZ LL 11 33 sinhsinh &gamma;&gamma; LL 11 ll fcfc sinhsinh &gamma;&gamma; cc 11 ll ctct sinhsinh &gamma;&gamma; LL 11 ll tktk

ff 22 == ZZ LL 11 ZZ cc 11 coshcosh &gamma;&gamma; cc 11 ll ctct coshcosh &gamma;&gamma; LL 11 (( ll fcfc ++ ll tktk )) ++ ZZ LL 11 22 sinhsinh &gamma;&gamma; LL 11 ll fcfc sinhsinh &gamma;&gamma; cc 11 ll ctct coshcosh &gamma;&gamma; LL 11 ll tktk ++

ZZ cc 11 22 sinhsinh &gamma;&gamma; cc 11 ll ctct coshcosh &gamma;&gamma; LL 11 ll fcfc sinhsinh &gamma;&gamma; LL 11 ll tktk

其中,lfc为架空线I段内故障位置f距c节点的距离;lmk、ltk分别为架空线II段内所选参考位置k距m端、t节点的距离;

Figure BSA00000168437600086
分别为m、n端正序电气量推导出的架空线II段上k点处的正序电压、正序电流,且由式(6)算得。Among them, l fc is the distance from fault location f to node c in section I of the overhead line; l mk and l tk are the distances from the selected reference position k to node m and node t in section II of the overhead line, respectively; and
Figure BSA00000168437600086
are the positive sequence voltage and positive sequence current at point k on the overhead line section II derived from the positive sequence electrical quantities at terminals m and n, respectively, and are calculated by formula (6).

Uu &CenterDot;&Center Dot; nknk 11 == Uu &CenterDot;&CenterDot; nno 11 coshcosh &gamma;&gamma; LL 11 (( ll mcmc ++ ll ctct ++ ll tntn -- ll mkmk )) -- II &CenterDot;&CenterDot; nno 11 ZZ LL 11 sinhsinh &gamma;&gamma; LL 11 (( ll mcmc ++ ll ctct ++ ll tntn -- ll mkmk )) II &CenterDot;&CenterDot; nknk 11 == II &CenterDot;&Center Dot; nno 11 coshcosh &gamma;&gamma; LL 11 (( ll mcmc ++ ll ctct ++ ll mm -- ll mkmk )) -- Uu &CenterDot;&Center Dot; nno 11 ZZ LL 11 sinhsinh &gamma;&gamma; LL 11 (( ll mcmc ++ ll ctct ++ ll tntn -- ll mkmk )) Uu &CenterDot;&Center Dot; mcmc 11 == Uu &CenterDot;&Center Dot; mm 11 coshcosh &gamma;&gamma; LL 11 ll mcmc -- II &CenterDot;&Center Dot; mm 11 ZZ LL 11 sinhsinh &gamma;&gamma; LL 11 ll mcmc II &CenterDot;&Center Dot; mcmc 11 == II &CenterDot;&Center Dot; mm 11 coshcosh &gamma;&gamma; LL 11 ll mcmc -- Uu &CenterDot;&Center Dot; mm 11 sinhsinh &gamma;&gamma; LL 11 ll mcmc // ZZ LL 11 Uu &CenterDot;&Center Dot; mtmt 11 == Uu &CenterDot;&Center Dot; mcmc 11 coshcosh &gamma;&gamma; cc 11 ll ctct -- II &CenterDot;&Center Dot; mcmc 11 ZZ cc 11 sinhsinh &gamma;&gamma; cc 11 ll ctct II &CenterDot;&Center Dot; mtmt 11 == II &CenterDot;&Center Dot; mcmc 11 coshcosh &gamma;&gamma; cc 11 ll ctct -- Uu &CenterDot;&Center Dot; mcmc 11 ZZ cc 11 sinhsinh &gamma;&gamma; cc 11 ll ctct Uu &CenterDot;&Center Dot; mkmk 11 == Uu &CenterDot;&Center Dot; mtmt 11 coshcosh &gamma;&gamma; LL 11 (( ll mkmk -- ll ctct -- ll mcmc )) -- II &CenterDot;&Center Dot; mtmt 11 ZZ LL 11 sinhsinh &gamma;&gamma; LL 11 (( ll mkmk -- ll ctct -- ll mcmc )) II &CenterDot;&Center Dot; mkmk 11 == II &CenterDot;&CenterDot; mtmt 11 coshcosh &gamma;&gamma; LL 11 (( ll mkmk -- ll ctct -- ll mcmc )) -- Uu &CenterDot;&Center Dot; mtmt 11 ZZ LL 11 sinhsinh &gamma;&gamma; LL 11 (( ll mkmk -- ll ctct -- ll mcmc )) -- -- -- (( 66 ))

架空线I段故障时混合线路上定位函数相位特性如图3所示。在混合线路上,当lmf>lmk时,定位函数相角大于零;当lmf>lmk时,定位函数相角大于零;当lmf<lmk时,定位函数相角小于零;当且仅当lmf=lmk时,定位函数的相角才等于零。其中,lmf、lmk分别为混合线路上故障位置f、参考位置k到架空线I段m端的距离。Figure 3 shows the phase characteristics of the positioning function on the hybrid line when the I section of the overhead line is faulty. On the hybrid line, when lmf > lmk, the phase angle of the positioning function is greater than zero; when l mf > l mk , the phase angle of the positioning function is greater than zero; when l mf < l mk , the phase angle of the positioning function is smaller than zero; when and The phase angle of the positioning function is equal to zero only when l mf =l mk . Among them, l mf and l mk are respectively the distances from the fault position f and the reference position k on the hybrid line to the end m of section I of the overhead line.

二、中间电缆线路故障时混合线路上任一点处的定位函数及其相位特性2. The location function and its phase characteristics at any point on the hybrid line when the intermediate cable line is faulty

图4为中间电缆线路故障时混合线路的正序序网图。则中间电缆线路故障时架空线I段内任何一点处定位函数表达式如式(7)所示。Fig. 4 is the positive sequence sequence network diagram of the hybrid line when the intermediate cable line is faulty. Then the expression of the positioning function at any point in section I of the overhead line when the intermediate cable line is faulty is shown in formula (7).

ff (( ll mkmk )) == Uu &CenterDot;&CenterDot; mkmk 11 -- Uu &CenterDot;&Center Dot; nknk 11 II &CenterDot;&CenterDot; mkmk 11 ++ II &CenterDot;&CenterDot; nknk 11 == -- ZZ cc 11 ZZ LL 11 sinhsinh &gamma;&gamma; cc 11 ll cfcf coshcosh &gamma;&gamma; LL 11 ll ckck ++ ZZ LL 11 22 coshcosh &gamma;&gamma; cc 11 ll cfcf sinhsinh &gamma;&gamma; LL 11 ll ckck ZZ LL 11 coshcosh &gamma;&gamma; cc 11 ll cfcf coshcosh &gamma;&gamma; LL 11 ll ckck ++ ZZ cc 11 sinhsinh &gamma;&gamma; cc 11 ll cfcf sinsin &gamma;&gamma; LL 11 ll ckck -- -- -- (( 77 ))

其中,分别为m、n端正序电气量推导出的架空线I段上k点处的正序电压、正序电流,且由式(2)算得;lcf为中间电缆线路内故障位置f距c节点的距离;lmk、lck分别为架空线I段内所选参考位置k距m端、c节点的距离。in, and are the positive-sequence voltage and current at point k on the overhead line section I deduced from the positive-sequence electrical quantities at terminals m and n, respectively, and are calculated by formula (2); l mk , l ck are the distances from the selected reference position k in section I of the overhead line to terminal m and node c, respectively.

中间电缆线路故障时中间电缆线路内任何一点处定位函数表达式如式(8)所示。The expression of the positioning function at any point in the middle cable line when the middle cable line is faulty is shown in formula (8).

ff (( ll mkmk )) == Uu &CenterDot;&CenterDot; mkmk 11 -- Uu &CenterDot;&Center Dot; nknk 11 II &CenterDot;&Center Dot; mkmk 11 ++ II &CenterDot;&Center Dot; nknk 11 == ZZ cc 11 tanhtanh &gamma;&gamma; cc 11 (( ll mfmf -- ll mkmk )) -- -- -- (( 88 ))

其中,lmf、lmk分别为中间电缆线路内故障位置f、所选参考位置k距m端的距离;

Figure BSA00000168437600094
Figure BSA00000168437600095
分别为m、n端正序电气量推导出的中间电缆线路上k点处的正序电压、正序电流,且由式(4)算得。Among them, l mf and l mk are respectively the fault position f in the intermediate cable line, the distance between the selected reference position k and the end m;
Figure BSA00000168437600094
and
Figure BSA00000168437600095
are the positive sequence voltage and positive sequence current at point k on the intermediate cable line derived from the positive sequence electrical quantities at terminals m and n, respectively, and are calculated by formula (4).

中间电缆线路故障时架空线II段内任何一点处的定位函数如式(9)所示。The positioning function at any point in the overhead line II section when the intermediate cable line is faulty is shown in formula (9).

ff (( ll mkmk )) == Uu &CenterDot;&Center Dot; mkmk 11 -- Uu &CenterDot;&Center Dot; nknk 11 II &CenterDot;&Center Dot; mkmk 11 ++ II &CenterDot;&Center Dot; nknk 11 == -- ZZ cc 11 ZZ LL 11 sinhsinh &gamma;&gamma; cc 11 ll tftf coshcosh &gamma;&gamma; LL 11 ll tktk ++ ZZ LL 11 22 coshcosh &gamma;&gamma; cc 11 ll tftf sinhsinh &gamma;&gamma; LL 11 ll tktk ZZ LL 11 coshcosh &gamma;&gamma; cc 11 ll tftf coshcosh &gamma;&gamma; LL 11 ll tktk ++ ZZ cc 11 sinhsinh &gamma;&gamma; cc 11 ll tftf sinsin &gamma;&gamma; LL 11 ll tktk -- -- -- (( 99 ))

其中,ltf为中间电缆线路内故障位置f距t节点的距离;lmk、ltk分别为架空线II段内所选参考位置k距m端、t节点的距离;

Figure BSA00000168437600097
分别为m、n端正序电气量推导出的架空线II段上k点处的正序电压、正序电流,且由式(6)算得。Among them, l tf is the distance from the fault position f in the intermediate cable line to the node t; l mk and l tk are the distances from the selected reference position k in the section II of the overhead line to the m terminal and the node t;
Figure BSA00000168437600097
and are the positive sequence voltage and positive sequence current at point k on the overhead line section II derived from the positive sequence electrical quantities at terminals m and n, respectively, and are calculated by formula (6).

中间电缆线路故障时混合线路上定位函数相位特性如图5所示。在混合线路上,当lmf>lmk时,定位函数相角大于零;当lmf<lmk时,定位函数相角小于零;当lmf=lmk时,定位函数的相角才等于零。其中,lmf、lmk分别为混合线路上故障位置f、参考位置k到架空线I段m端的距离。Figure 5 shows the phase characteristics of the positioning function on the hybrid line when the intermediate cable line is faulty. On the hybrid line, when l mf >l mk , the phase angle of the positioning function is greater than zero; when l mf <l mk , the phase angle of the positioning function is less than zero; when l mf =l mk , the phase angle of the positioning function is equal to zero . Among them, l mf and l mk are respectively the distances from the fault position f and the reference position k on the hybrid line to the end m of section I of the overhead line.

三、架空线II段故障时混合线路任一点处的定位函数及其相位特性3. The location function and its phase characteristics at any point of the mixed line when the second section of the overhead line is faulty

图6为架空线II段时混合线路的正序序网图。则架空线II段故障时架空线I段内任何一点处定位函数表达式如式(10)所示。Fig. 6 is the positive sequence network diagram of the mixed line in the second section of the overhead line. Then the expression of the positioning function at any point in the I section of the overhead line when the section II of the overhead line is faulty is shown in formula (10).

ff (( ll mkmk )) == Uu &CenterDot;&Center Dot; mkmk 11 -- Uu &CenterDot;&Center Dot; nknk 11 II &CenterDot;&Center Dot; mkmk 11 ++ II &CenterDot;&Center Dot; nknk 11 == ff 33 ff 44 -- -- -- (( 1010 ))

ff 33 == ZZ LL 11 ZZ cc 11 22 sinhsinh &gamma;&gamma; cc 11 ll ctct coshcosh &gamma;&gamma; LL 11 ll tftf coshcosh &gamma;&gamma; LL 11 ll ckck ++ ZZ cc 11 ZZ LL 11 22 coshcosh &gamma;&gamma; cc 11 ll ctct sinsin &gamma;&gamma; LL 11 (( ll tftf ++ ll ckck ))

++ ZZ LL 11 33 sinhsinh &gamma;&gamma; LL 11 ll tftf sinhsinh &gamma;&gamma; cc 11 ll ctct sinhsinh &gamma;&gamma; LL 11 ll ckck

ff 44 == ZZ LL 11 ZZ cc 11 coshcosh &gamma;&gamma; cc 11 ll ctct coshcosh &gamma;&gamma; LL 11 (( ll tftf ++ ll ckck )) ++ ZZ LL 11 22 sinhsinh &gamma;&gamma; LL 11 ll tftf sinhsinh &gamma;&gamma; cc 11 ll ctct coshcosh &gamma;&gamma; LL 11 ll ckck ++

ZZ cc 11 22 sinhsinh &gamma;&gamma; cc 11 ll ctct coshcosh &gamma;&gamma; LL 11 ll tftf sinhsinh &gamma;&gamma; LL 11 ll ckck

其中,ltf为架空线II段内故障位置f距t节点的距离;lmk、lck分别为架空线I段内所选参考位置k距m端、c节点的距离;

Figure BSA00000168437600106
Figure BSA00000168437600107
分别为m、n端正序电气量推导出的架空线I段上k点处的正序电压、正序电流,且由式(2)算得;Among them, l tf is the distance from fault location f to node t in the section II of the overhead line; l mk and l ck are the distances from the selected reference position k to the m terminal and node c in the section I of the overhead line, respectively;
Figure BSA00000168437600106
and
Figure BSA00000168437600107
are the positive sequence voltage and positive sequence current at point k on section I of the overhead line deduced from the positive sequence electrical quantities at terminals m and n respectively, and are calculated by formula (2);

架空线II段故障时中间电缆线路内任何一点处定位函数表达式如式(11)所示。The expression of the positioning function at any point in the intermediate cable line when the second section of the overhead line is faulty is shown in formula (11).

ff (( ll mkmk )) == Uu &CenterDot;&CenterDot; mkmk 11 -- Uu &CenterDot;&CenterDot; nknk 11 II &CenterDot;&CenterDot; mkmk 11 ++ II &CenterDot;&Center Dot; nknk 11 == -- ZZ cc 11 22 sinhsinh &gamma;&gamma; cc 11 ll tktk coshcosh &gamma;&gamma; LL 11 ll tftf ++ ZZ cc 11 ZZ LL 11 coshcosh &gamma;&gamma; cc 11 ll tftf sinsin &gamma;&gamma; LL 11 ll tktk ZZ cc 11 coshcosh &gamma;&gamma; cc 11 ll tftf coshcosh &gamma;&gamma; LL 11 ll tktk ++ ZZ LL 11 sinhsinh &gamma;&gamma; cc 11 ll tftf sinsin &gamma;&gamma; LL 11 ll tktk -- -- -- (( 1111 ))

其中,lmk、ltk为中间电缆线路内所选参考位置k距m端、t节点的距离;ltf为架空线II段内故障位置f距t节点的距离;

Figure BSA00000168437600109
Figure BSA000001684376001010
分别为m、n端正序电气量推导出的中间电缆线路上k点处的正序电压、正序电流,且由式(4)算得。Among them, l mk and l tk are the distances from the selected reference position k in the intermediate cable line to the m terminal and the node t; l tf is the distance from the fault position f to the node t in the section II of the overhead line;
Figure BSA00000168437600109
and
Figure BSA000001684376001010
are the positive sequence voltage and positive sequence current at point k on the intermediate cable line derived from the positive sequence electrical quantities at terminals m and n, respectively, and are calculated by formula (4).

架空线II段故障时架空线II段内任何一点处的定位函数如式(12)所示。The positioning function of any point in the second section of the overhead line when the second section of the overhead line is faulty is shown in formula (12).

ff (( ll mkmk )) == Uu &CenterDot;&Center Dot; mkmk 11 -- Uu &CenterDot;&Center Dot; nknk 11 II &CenterDot;&Center Dot; mkmk 11 ++ II &CenterDot;&Center Dot; nknk 11 == ZZ LL 11 tanhtanh &gamma;&gamma; LL 11 (( ll mfmf -- ll mkmk )) -- -- -- (( 1212 ))

其中,lmf、lmk分别为架空线II段内故障位置f、所选参考位置k距m端的距离;

Figure BSA000001684376001012
分别为m、n端正序电气量推导出的架空线II段上k点处的正序电压、正序电流,且由式(6)算得。Among them, l mf and l mk are respectively the fault position f in the section II of the overhead line, the distance from the selected reference position k to the end m;
Figure BSA000001684376001012
and are the positive sequence voltage and positive sequence current at point k on the overhead line section II derived from the positive sequence electrical quantities at terminals m and n, respectively, and are calculated by formula (6).

架空线II段故障时混合线路上定位函数相位特性如图7所示。在混合线路上,当lmf>lmk时,定位函数相角大于零;当lmf<lmk时,定位函数相角小于零;当且仅当lmf=lmk时,定位函数的相角才等于零。其中,lx、lmk分别为混合线路上故障位置f、参考位置k到架空线I段m端的距离。Figure 7 shows the phase characteristics of the positioning function on the hybrid line when the second section of the overhead line is faulty. On the hybrid line, when l mf >l mk , the phase angle of the positioning function is greater than zero; when l mf <l mk , the phase angle of the positioning function is smaller than zero; if and only when l mf =l mk , the phase angle of the positioning function The angle is equal to zero. Among them, lx and lmk are the distances from the fault position f and the reference position k on the hybrid line to the m end of section I of the overhead line respectively.

四、算法具体步骤Fourth, the specific steps of the algorithm

综上所述,无论故障位置是位于架空线I段或中间电缆,还是位于架空线II段上,定位函数的相位特性都满足:当lmf>lmk时,定位函数相角大于零;当lmf<lmk时,定位函数相角小于零;当lmf=lmk时,定位函数的相角等于零。因此,利用混合线路上参考位置与故障位置匹配时定位函数相角等于零这一特征进行故障测距。具体测距算法步骤如下:To sum up, no matter whether the fault location is located on the I section of the overhead line or the intermediate cable, or on the II section of the overhead line, the phase characteristics of the location function are all satisfied: when l mf >l mk , the phase angle of the location function is greater than zero; when When l mf <l mk , the phase angle of the positioning function is smaller than zero; when l mf =l mk , the phase angle of the positioning function is equal to zero. Therefore, the phase angle of the location function is equal to zero when the reference position on the hybrid line matches the fault position for fault location. The specific ranging algorithm steps are as follows:

(1)提取故障后混合线路系统两端(m、n端)的三相电压与电流相量,

Figure BSA00000168437600111
Figure BSA00000168437600112
Figure BSA00000168437600113
分别为故障后m、n端的三相电压与电流相量。根据对称分量法分别求出m、n端的正序分量
Figure BSA00000168437600114
Figure BSA00000168437600115
(1) Extract the three-phase voltage and current phasors at both ends (m, n) of the hybrid line system after the fault,
Figure BSA00000168437600111
Figure BSA00000168437600112
and
Figure BSA00000168437600113
are the three-phase voltage and current phasors of terminals m and n after the fault, respectively. According to the symmetrical component method, the positive sequence components of the m and n terminals are calculated respectively
Figure BSA00000168437600114
and
Figure BSA00000168437600115

(2)将混合线路等效为一条长为lx的长线路,则初始包含故障点的区域为(lbegin,lend)=(0,lx);(2) the hybrid line is equivalent to a long line with a length of lx, then the initial area containing the fault point is (l begin , l end )=(0, lx);

(3)将包含故障点的区域为(lbegin,lend)进行n等分;(3) divide the area containing the fault point into n equal parts (l begin , l end );

(4)利用系统m、n端测量到的电气量从两端进行推导,得出(3)所确定的区域内每一等分点处的正序电压、正序电流;(4) Use the electrical quantities measured at the m and n terminals of the system to deduce from both ends, and obtain the positive sequence voltage and positive sequence current at each equal point in the area determined by (3);

(5)由(4)推导出定位函数,并以此求出每一等分点处的定位函数的相角;(5) deduce positioning function by (4), and find out the phase angle of the positioning function at each bisection point place with this;

(6)由(5)计算的定位函数相角的大小判断等分点与故障点的位置关系:(6) The positional relationship between the bisection point and the fault point is judged by the size of the positioning function phase angle calculated in (5):

1)定位函数相角大于零,参考位置位于故障位置左侧;1) The phase angle of the positioning function is greater than zero, and the reference position is on the left side of the fault position;

2)定位函数相角小于零,参考位置位于故障位置右侧;2) The phase angle of the positioning function is less than zero, and the reference position is on the right side of the fault position;

3)定位函数相角等于零,参考位置和故障位置匹配时;3) When the phase angle of the positioning function is equal to zero and the reference position matches the fault position;

由此判据找到两个相邻等分点k和k+1,其定位函数相角分别大于零及小于零,则此时包含故障点的区域(lbegin,lend)=(lk,lk+1)。设定一最小等分区域阀值Δlset,重复(3)~(5)直至lend-lbegin<Δlset,则能够得出包含故障点的最小等分区域(lbeginm,lendm);Based on this criterion, two adjacent bisection points k and k+1 are found, and the phase angles of their positioning functions are respectively greater than zero and less than zero, then the area containing the fault point (l begin , l end )=(l k , l k+1 ). Set a threshold value Δl set for the minimum equal division area, repeat (3)~(5) until l end -l begin <Δl set , then the minimum equal division area (l beginm , l endm ) including the fault point can be obtained;

(7)由(6)计算的最小包含故障点的等分区确定故障位置:(7) Determine the fault location by the equal partition that contains the fault point calculated by (6):

4)确定步长Δl;4) Determine the step size Δl;

5)参考位置lmk从lbeginm开始以Δl为步长递增至lendm,计算各点处的定位函数的相角;5) The reference position l mk starts from l beginm and increases to l endm with Δl as the step size, and calculates the phase angle of the positioning function at each point;

6)寻找确定最优参考位置lmk,使其满足在lmk-Δl处定位函数相角大于零,在lmk处定位函数相角小于零;则故障位置f距m端的故障距离lmf=lmk-Δl/2。6) Find and determine the optimal reference position l mk , so that it satisfies that the phase angle of the positioning function at l mk -Δl is greater than zero, and the phase angle of the positioning function at l mk is less than zero; then the fault distance from the fault position f to the m terminal is l mf = l mk -Δl/2.

本发明搜索范围为

Figure BSA00000168437600121
(其中,
Figure BSA00000168437600122
表示比χ大且最接近的整数,l=lmc+lct+lnt),为提高测距精度Δl取足够小且Num合理取较大值时,
Figure BSA00000168437600123
很小。The search scope of the present invention is
Figure BSA00000168437600121
(in,
Figure BSA00000168437600122
Indicates the closest integer larger than χ, l=l mc +l ct +l nt ), when Δl is small enough to improve the ranging accuracy and Num is reasonably large,
Figure BSA00000168437600123
very small.

表1:采样频率和故障位置对AG故障测距结果的影响Table 1: Effect of sampling frequency and fault location on AG fault location results

Figure BSA00000168437600124
Figure BSA00000168437600124

五、计算结果及分析5. Calculation results and analysis

利用PSCAD仿真软件搭建缆线混合模型,不同故障点和采样频率对A相金属性接地故障测距结果的影响情况如表1所示。Using PSCAD simulation software to build a cable hybrid model, the influence of different fault points and sampling frequencies on the distance measurement results of phase A metallic ground faults is shown in Table 1.

结果表明,不同的采样频率下,本算法均能够准确测距,本发明针对混合线路的测距克服了故障位置受采样频率的影响。The results show that the algorithm can measure the distance accurately under different sampling frequencies, and the invention overcomes the influence of the sampling frequency on the fault location for the distance measurement of the hybrid line.

混合线路连接点附近A相经高阻接地故障时测距结果如表2所示。Table 2 shows the distance measurement results when phase A near the connection point of the hybrid line passes through a high-impedance ground fault.

表2:混合线路连接点附近高阻故障时本发明的测距结果Table 2: Ranging results of the present invention when a high-impedance fault near the hybrid line connection point

Figure BSA00000168437600131
Figure BSA00000168437600131

结果表明,在连接点附近0.5km处高阻接地故障时,最大相对测距误差不超过-1.191%。因此,本发明无测距死区,测距精确度高。The results show that the maximum relative ranging error does not exceed -1.191% when there is a high-resistance ground fault at 0.5km near the connection point. Therefore, the present invention has no ranging dead zone, and the ranging accuracy is high.

负荷电流和过渡电阻对架空线I段上25km处AB两相短路故障测距结果的影响情况如图8所示。其中,过渡电阻取0~60Ω,m侧系统电源相角取-90°~90°,结果表明,相对测距误差在-0.4%~0.4%之间,具有很高的测距精度,因此,本发明针对混合线路的测距克服了负荷电流和过渡电阻的影响。The influence of load current and transition resistance on the results of AB two-phase short-circuit fault location at 25km on section I of the overhead line is shown in Figure 8. Among them, the transition resistance ranges from 0 to 60Ω, and the phase angle of the m-side system power supply ranges from -90° to 90°. The results show that the relative ranging error is between -0.4% and 0.4%, which has a high ranging accuracy. Therefore, The invention overcomes the influence of load current and transition resistance for distance measurement of hybrid lines.

过渡电阻和故障位置对中间电缆线路上A相接地故障测距结果的影响情况如图9所示。其中,过渡电阻取0~60Ω,故障位置取70~100km,结果表明,相对测距误差在-0.6%~1.18%之间,具有很高的测距精度,因此,本发明针对混合线路的测距克服了过渡电阻和故障位置的影响。The influence of transition resistance and fault location on the distance measurement results of phase A ground fault on the intermediate cable line is shown in Figure 9. Among them, the transition resistance is 0-60Ω, and the fault location is 70-100km. The results show that the relative ranging error is between -0.6% and 1.18%, which has a very high ranging accuracy. The distance overcomes the effects of transition resistance and fault location.

过渡电阻和故障位置对架空线II段上A相接地故障测距结果的影响情况如图10所示。其中,过渡电阻取0~300Ω,故障位置取100~170km,结果表明,相对测距误差在-0.5%~1.3%之间,具有很高的测距精度,因此,本发明针对混合线路的测距克服了过渡电阻和故障位置的影响。The influence of transition resistance and fault location on the distance measurement results of phase A ground fault on the II section of the overhead line is shown in Figure 10. Among them, the transition resistance is 0-300Ω, and the fault location is 100-170km. The results show that the relative ranging error is between -0.5% and 1.3%, which has a very high ranging accuracy. Therefore, the present invention is aimed at the measurement of mixed lines. The distance overcomes the effects of transition resistance and fault location.

负荷电流和故障位置对混合线路上ABCG故障测距结果的影响情况如图11所示。其中,m侧系统电源相角取-90°~90°,故障位置取0~170km,结果表明,本发明相对测距误差在-0.3%~0.72%之间,具有很高的测距精度,因此,本发明针对混合线路的测距克服了负荷电流和故障位置的影响。综上结果表明,该方法针对混合线路的测距具有很高的准确性和有效性。The influence of load current and fault location on the results of ABCG fault location on hybrid lines is shown in Figure 11. Among them, the phase angle of the system power supply on the m side is -90°~90°, and the fault location is 0~170km. The results show that the relative ranging error of the present invention is between -0.3%~0.72%, which has very high ranging accuracy. Therefore, the present invention overcomes the influence of load current and fault location for distance measurement of hybrid lines. The above results show that the method has high accuracy and effectiveness for ranging of mixed lines.

以上所述,仅为本发明较佳的具体实施方式,但本发明的保护范围并不局限于此,任何熟悉本技术领域的技术人员在本发明揭露的技术范围内,可轻易想到的变化或替换,都应涵盖在本发明的保护范围之内。The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed in the present invention can easily think of changes or Replacement should be covered within the protection scope of the present invention.

Claims (2)

1. A distance measuring method for realizing fault location of a high-voltage cable-overhead line hybrid line by utilizing location function phase characteristics is characterized in that positive sequence electrical quantity data at two ends of a fault-behind hybrid line system are collected first, and the whole hybrid line is equivalent to an equal-length line; then deducing a positioning function from positive-sequence electrical quantity data at two ends of the hybrid line system, and determining a minimum fault partition containing a fault point according to the size of the phase of the positioning function; and finally, accurately measuring the fault distance of the hybrid line in the fault equal partition by using the phase angle of the positioning function again.
2. The distance measurement method for realizing the fault location of the high-voltage cable-overhead line hybrid line by using the phase characteristic of the location function according to claim 1, is characterized by comprising the following specific steps of:
(1) extracting three-phase voltage and current phasors at two ends of m and n of the mixed line system after the fault,
Figure FSA00000168437500011
Figure FSA00000168437500012
and
Figure FSA00000168437500013
respectively obtaining the three-phase voltage and current phasors of m and n ends after the fault according to a symmetrical component method
Figure FSA00000168437500014
And
Figure FSA00000168437500016
(2) the mixed line is equivalent to a length of lmnThe area initially including the fault point is (l)begin,lend)=(0,lmn);
(3) The area containing the failure point is (l)begin,lend) Num equal division is carried out;
(4) deducing electrical quantities measured by m and n ends of the system from two ends of the mixed line system to obtain (3) positive sequence voltage and positive sequence current at each equal division point in the determined area;
(5) deducing a positioning function according to the step (4), and solving the phase angle of the positioning function at each equally divided point;
(6) judging the position relation between the equal points and the fault points according to the size of the positioning function phase angle calculated in the step (5):
1) the phase angle of the positioning function is larger than zero, and the reference position is positioned on the left side of the fault position;
2) the phase angle of the positioning function is smaller than zero, and the reference position is located on the right side of the fault position;
3) the phase angle of the positioning function is equal to zero, and the reference position is matched with the fault position;
finding two adjacent equant points k and k +1 by the criterion, wherein the positioning function phase angle is respectively larger than zero and smaller than zero, and then the area (l) containing the fault pointbegin,lend)=(lk,lk+1) Setting a minimum equal division area threshold delta lsetRepeating (3) to (5) until lend-lbegin<ΔlsetThen the smallest equally divided region (l) containing the failure point can be foundbeginm,lendm);
(7) Determining the fault position by the calculated equal partition with the minimum fault point:
1) determining a step length delta l;
2) reference position lmkFrom lbeginmStart to increment to l in steps of Δ lendmCalculating the phase angle of the positioning function at each point;
3) finding and determining an optimal reference position lmkSo that it satisfies atmkThe phase angle of the localization function is greater than zero at lmkThe phase angle of the positioning function is less than zero;
the fault location f is a fault distance l from end mmf=lmk-Δl/2;
In step (5), the positioning function at any point k on the high-voltage cable-overhead line hybrid line is:
<math><mrow><mi>f</mi><mrow><mo>(</mo><msub><mi>l</mi><mi>mk</mi></msub><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><msub><mover><mi>U</mi><mo>&CenterDot;</mo></mover><mrow><mi>mk</mi><mn>1</mn></mrow></msub><mo>-</mo><msub><mover><mi>U</mi><mo>&CenterDot;</mo></mover><mrow><mi>nk</mi><mn>1</mn></mrow></msub></mrow><mrow><msub><mover><mi>I</mi><mo>&CenterDot;</mo></mover><mrow><mi>mk</mi><mn>1</mn></mrow></msub><mo>+</mo><msub><mover><mi>I</mi><mo>&CenterDot;</mo></mover><mrow><mi>nk</mi><mn>1</mn></mrow></msub></mrow></mfrac></mrow></math>
wherein,
Figure FSA00000168437500022
and
Figure FSA00000168437500023
positive sequence voltage and positive sequence current at k point on the mixed line are derived for the positive sequence electric quantities of the m end and the n end respectively;
delta l in step (6)setFlexibly setting the interval size according to the actual precision requirement;
the fault position in the step (7) can be located on an overhead line I section, an intermediate cable or an overhead line II section, and the phase characteristics of the positioning function meet the following conditions: when l ismf>lmkWhen the positioning function phase angle is larger than zero; when l ismf<lmkWhen the positioning function phase angle is less than zero; when l ismf=lmkThe phase angle of the positioning function is equal to zero; wherein lmf、lmkRespectively the distances from a fault position f and a reference position k on the hybrid line to the end m of the section I of the overhead line;
and (4) flexibly setting delta l in the step (7) according to the requirements of the actual distance measurement precision and the actual distance measurement speed.
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