CN104459458B - A kind of circuit of specific short window integrated value of utilization orientation traveling wave, which closes a floodgate, arrives fault recognition method - Google Patents

A kind of circuit of specific short window integrated value of utilization orientation traveling wave, which closes a floodgate, arrives fault recognition method Download PDF

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CN104459458B
CN104459458B CN201410467991.4A CN201410467991A CN104459458B CN 104459458 B CN104459458 B CN 104459458B CN 201410467991 A CN201410467991 A CN 201410467991A CN 104459458 B CN104459458 B CN 104459458B
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束洪春
杨竞及
高利
吕蕾
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Kunming University of Science and Technology
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Abstract

本发明涉及一种利用方向行波特定短窗积分值的线路合闸到故障识别方法,属于电力系统继电保护技术领域。当输电线路发生单相接地故障时,采用单相重合闸,利用量测端获得的合闸线模电流行波和合闸线模电压行波构造正向电流行波和反向电流行波,分别求取正向行波和反向行波的绝对值,并计算合闸后2τmin~4τmin时窗内正、反向行波绝对值的积分值之比来构建合闸到故障识别判据。若积分值之比小于设定的门槛值k,则判为合闸到无故障线路;相反若积分值之比大于k则判为合闸到故障。仿真验证表明,本方法不受故障位置、过渡电阻、故障初始相角的影响,能可靠识别合闸到故障线路的情况,避免线路遭受二次冲击。

The invention relates to a line closing-to-fault identification method using a specific short-window integral value of directional traveling waves, and belongs to the technical field of electric power system relay protection. When a single-phase ground fault occurs on the transmission line, single-phase reclosing is adopted, and the forward current traveling wave and the reverse current traveling wave are constructed by using the closing line-mode current traveling wave and closing line-mode voltage traveling wave obtained at the measuring end, respectively. Obtain the absolute value of the forward traveling wave and the reverse traveling wave, and calculate the ratio of the integral value of the absolute value of the forward traveling wave and the reverse traveling wave within the time window of 2τ min ~ 4τ min after closing to construct the criterion from closing to fault identification . If the ratio of the integral value is less than the set threshold value k, it is judged as closing to no fault line; on the contrary, if the ratio of the integral value is greater than k, it is judged as closing to fault. The simulation verification shows that this method is not affected by the fault location, transition resistance, and fault initial phase angle, and can reliably identify the situation of closing to the fault line and avoid the secondary impact on the line.

Description

一种利用方向行波特定短窗积分值的线路合闸到故障识别 方法A Line Closing-to-Fault Identification Using Specific Short Window Integral Value of Directional Traveling Wave method

技术领域technical field

本发明涉及一种利用方向行波特定短窗积分值的线路合闸到故障识别方法,属于电力系统继电保护技术领域。The invention relates to a line closing-to-fault identification method using a specific short-window integral value of directional traveling waves, and belongs to the technical field of electric power system relay protection.

背景技术Background technique

行波特征分析是行波测距与行波保护的基础,对提出新的行波测距与保护方法有着重要的指导作用。国内知名学者对行波的特性进行了研究,并在此基础上提出了新的行波测距与保护原理。但这些行波特性分析与保护原理主要针对正常运行线路中发生故障的情况,当进行合闸操作时这些保护将会出现不能正确动作的情况,因此还需要进一步研究合闸到故障的识别方法。早期采用行波极性比较式方向保护进行合闸于故障线路的识别,方法类似于一种简单的行波测距,出现了对线路末端附近故障难以识别、正反向行波在非对称故障情况下出现的极性相同问题、以及没有考虑断路器不同期合闸等问题。The analysis of traveling wave characteristics is the basis of traveling wave ranging and traveling wave protection, and plays an important guiding role in proposing new traveling wave ranging and protection methods. Well-known domestic scholars have studied the characteristics of traveling waves, and on this basis, they have proposed new traveling wave ranging and protection principles. However, these traveling wave characteristics analysis and protection principles are mainly aimed at the failure of the normal operating line. When the closing operation is performed, these protections will not operate correctly. Therefore, further research on the identification method from closing to fault is needed. . In the early stage, traveling wave polarity comparison type directional protection was used to identify the closing on the fault line. The method is similar to a simple traveling wave distance measurement. It is difficult to identify the fault near the end of the line, and the forward and reverse traveling waves are in asymmetrical faults. The problem of the same polarity in the case, and the failure to consider the problem of the non-synchronous closing of the circuit breaker.

发明内容Contents of the invention

本发明要解决的技术问题是提出一种利用方向行波短窗积分值的线路合闸到故障识别元件判别方法,用以提高单相重合闸线路的供电可靠性和系统并列运行的稳定性。The technical problem to be solved by the present invention is to propose a method for judging from line closing to fault identification components using the integrated value of the directional traveling wave short window, so as to improve the power supply reliability of single-phase reclosing lines and the stability of parallel operation of the system.

本发明的技术方案是:一种利用方向行波特定短窗积分值的线路合闸到故障识别方法,当输电线路发生单相接地故障时,采用单相重合闸,利用量测端获得的合闸线模电流行波和合闸线模电压行波构造正向电流行波和反向电流行波,分别求取正向行波和反向行波的绝对值,并计算合闸后2τmin~4τmin时窗内正、反向行波绝对值的积分值之比来构建合闸到故障识别判据;若积分值之比小于设定的门槛值k,则判为合闸到无故障线路;若积分值之比大于k则判为合闸到故障。The technical solution of the present invention is: a method for identifying a line from closing to fault using the specific short-window integral value of directional traveling waves. The forward traveling wave and the reverse current traveling wave are constructed by the traveling wave of the gate line mode current and the traveling wave of the closing line mode voltage, and the absolute values of the forward traveling wave and the reverse traveling wave are obtained respectively, and the 2τ min ~ The ratio of the integral value of the positive and reverse traveling wave absolute values in the 4τ min time window is used to construct the identification criterion from closing to fault; if the ratio of the integral value is less than the set threshold k, it is judged as a line from closing to fault-free ; If the ratio of the integral value is greater than k, it is judged as closing to fault.

具体步骤为:The specific steps are:

(1)被保护线路发生单相接地故障后,断开故障相,此时由被保护线路量测端M端故障相的断路器执行合闸操作,被保护线路另一端N端断路器处于断开状态,由量测端M获得三相电流行波与电压行波,将三相电压和三相电流行波分别利用式(1)、(2)进行相模变换,提取三个线模电压分量Δuα、Δuβ和Δuγ和电流分量Δiα、Δiβ和Δiγ(1) After a single-phase ground fault occurs in the protected line, disconnect the faulty phase. At this time, the circuit breaker of the faulty phase at the M terminal of the protected line performs the closing operation, and the circuit breaker at the N terminal at the other end of the protected line is in the OFF state. In the open state, the three-phase current traveling wave and voltage traveling wave are obtained from the measuring terminal M, and the three-phase voltage and three-phase current traveling waves are respectively used for phase-mode transformation by formulas (1) and (2) to extract three line-mode voltage components Δu α , Δu β and Δu γ and current components Δi α , Δi β and Δi γ :

式(1)中,ΔuA、ΔuB和ΔuC分别为三相电压,式(2)中ΔiA、ΔiB和ΔiC分别为三相电流;In formula (1), Δu A , Δu B and Δu C are the three-phase voltages respectively, and in formula (2) Δi A , Δi B and Δi C are the three-phase currents respectively;

(2)从Δuα、Δuβ、Δuγ和Δiα、Δiβ、Δiγ中选取含故障相的线模电压Δum和线模电流Δim,利用(3)、(4)式构造正向电流行波和反向电流行波 (2) From Δu α , Δu β , Δu γ and Δi α , Δi β , Δi γ , select the line-mode voltage Δu m and the line-mode current Δi m of the faulty phase, and use (3) and (4) to construct the normal traveling wave and reverse current traveling waves

式(3)和式(4)中,n表示采样点,下标m=α或β或γ,表示选取的模量;In formula (3) and formula (4), n represents the sampling point, and the subscript m=α or β or γ represents the selected modulus;

(3)提取特征量:分别计算合闸后正向电流行波绝对值和反向电流行波绝对值,得到 (3) Feature extraction: calculate the absolute value of the forward current traveling wave and the absolute value of the reverse current traveling wave after switching on respectively, and get with

(4)利用式(5)、(6)分别计算合闸后2τmin~4τminmin为行波在最短健全线路全长传播一次所用的时间,此处τmin=lmin/v)时窗内正向电流行波绝对值和反向电流行波绝对值的积分值S+和S-(4) Use formulas (5) and (6) to calculate 2τ min ~ 4τ min after closing (τ min is the time it takes for a traveling wave to propagate once in the shortest sound line, where τ min = l min /v) Integral values S + and S - of the absolute value of the forward current traveling wave and the absolute value of the reverse current traveling wave in the time window:

式(5)和(6)中t0=2τminIn formulas (5) and (6), t 0 =2τ min ;

(5)根据式(7)求取正、反向电流行波绝对值积分的比值λ(5) Calculate the ratio λ Σ of the integral of the absolute value of the forward and reverse current traveling waves according to formula (7):

λ=S+/S (7)λ = S + /S - (7)

根据积分比值λ的大小进行合闸到故障的判别:According to the size of the integral ratio λ Σ , the judgment from closing to fault is carried out:

若λ小于设定的门槛值k,则判为合闸到无故障线路;If λ Σ is less than the set threshold value k, it is judged to be closed to the fault-free line;

若λ大于或者等于k,则判为合闸到故障。If λ Σ is greater than or equal to k, it is judged as closing to fault.

利用PSCAD电磁暂态仿真软件,沿被保护线路MN每隔Nkm设置一个故障点进行全线遍历,根据计算得到的积分比值λ沿线分布规律,对门槛值k进行整定取值。Using PSCAD electromagnetic transient simulation software, set a fault point every Nkm along the protected line MN to traverse the whole line, and set the threshold value k according to the distribution law of the calculated integral ratio λ Σ along the line.

本发明的有益效果是:本方法采用方向行波积分值比较的合闸到故障识别元件能可靠识别合闸到故障线路的情况,避免线路遭受二次冲击,提高了元件识别的可靠性,速动性。本方法不受故障位置、过渡电阻、故障初始相角的影响。The beneficial effects of the present invention are: the method adopts the directional traveling wave integral value comparison of the closing-to-fault identification element to reliably identify the situation of the closing-to-fault line, avoiding secondary impact on the line, improving the reliability of element identification, and quickly Mobility. This method is not affected by fault location, transition resistance, and fault initial phase angle.

附图说明Description of drawings

图1为实施例1、2、3中的输电线路仿真系统图;Fig. 1 is the transmission line simulation system diagram in embodiment 1,2,3;

图2为全线仿真遍历所得λ沿线规律图;Fig. 2 is the regular diagram along the line of λ obtained by traversal of the whole line simulation;

图3为实施例1中含故障相的线模电压Δum曲线;Fig. 3 is the line-mode voltage Δu m curve containing fault phase in embodiment 1;

图4为实施例1中含故障相的线模电流Δim曲线;Fig. 4 is the line-mode current Δi m curve containing fault phase in embodiment 1;

图5为实施例1中正向电流行波和反向电流行波曲线;Fig. 5 is forward current traveling wave and reverse current traveling wave curve in embodiment 1;

图6为实施例1中正向电流行波绝对值和反向电流行波绝对值曲线;Fig. 6 is positive current traveling wave absolute value and reverse current traveling wave absolute value curve in embodiment 1;

图7为实施例2中含故障相的线模电压Δum曲线;Fig. 7 is the line-mode voltage Δum curve that contains fault phase in embodiment 2;

图8为实施例2中含故障相的线模电流Δim曲线;Fig. 8 is the line-mode current Δi m curve containing fault phase in embodiment 2;

图9为实施例2中正向电流行波和反向电流行波曲线;Fig. 9 is forward current traveling wave and reverse current traveling wave curve in embodiment 2;

图10为实施例2中正向电流行波绝对值和反向电流行波绝对值曲线;Fig. 10 is positive current traveling wave absolute value and reverse current traveling wave absolute value curve in embodiment 2;

图11为实施例3中含故障相的线模电压Δum曲线;Fig. 11 is the line-mode voltage Δu m curve containing fault phase in embodiment 3;

图12为实施例3中含故障相的线模电流Δim曲线;Fig. 12 is the line-mode current Δi m curve containing fault phase in embodiment 3;

图13为实施例3中正向电流行波和反向电流行波曲线;Fig. 13 is forward current traveling wave and reverse current traveling wave curve in embodiment 3;

图14为实施例3中正向电流行波绝对值和反向电流行波绝对值曲线。Fig. 14 is the curves of the absolute value of the forward current traveling wave and the absolute value of the reverse current traveling wave in Example 3.

具体实施方式detailed description

下面结合附图和具体实施方式,对本发明作进一步说明。The present invention will be further described below in combination with the accompanying drawings and specific embodiments.

实施例1:如图1所示的500kV输电线路仿真系统模型,被保护线路为MN,线路长度LPM=150km,LMN=150km,LNQ=220km,采样率为1MHz。设被保护线路N端的A相断路器处于断开状态,由被保护线路量测端M端的A相断路器执行合闸操作,分别假设线路MN无故障和距M端149km发生AG金属性接地故障,过渡电阻为0Ω,初始相角90°。Embodiment 1: 500kV transmission line simulation system model as shown in Fig. 1, the protected line is MN, the line length L PM =150km, L MN =150km, L NQ =220km, and the sampling rate is 1MHz. Assume that the A-phase circuit breaker at the N-end of the protected line is in the disconnected state, and the A-phase circuit breaker at the M-end of the protected line’s measurement end performs the closing operation, assuming that there is no fault in the line MN and an AG metallic ground fault occurs 149km away from the M-end , the transition resistance is 0Ω, and the initial phase angle is 90°.

被保护线路发生单相接地故障后,断开故障相,此时由被保护线路量测端M端故障相的断路器执行合闸操作,被保护线路另一端N端断路器处于断开状态。采集线路合闸量测端M所产生三相电流行波与三相电压行波。将三相电压和三相电流行波分别利用式(1)、(2)进行相模变换,提取三个线模电压分量Δuα、Δuβ和Δuγ和电流分量Δiα、Δiβ和ΔiγAfter a single-phase ground fault occurs on the protected line, the faulty phase is disconnected. At this time, the circuit breaker of the faulty phase at the M terminal of the protected line performs the closing operation, and the circuit breaker at the N terminal at the other end of the protected line is in the disconnected state. The three-phase current traveling wave and the three-phase voltage traveling wave generated by the closing measurement terminal M of the line are collected. The three-phase voltage and three-phase current traveling waves are transformed into phase mode using formulas (1) and (2) respectively, and three line-mode voltage components Δu α , Δu β and Δu γ and current components Δi α , Δi β and Δi γ are extracted :

式(1)中,ΔuA、ΔuB和ΔuC分别为三相电压,式(2)中ΔiA、ΔiB和ΔiC分别为三相电流;In formula (1), Δu A , Δu B and Δu C are the three-phase voltages respectively, and in formula (2) Δi A , Δi B and Δi C are the three-phase currents respectively;

从Δuα、Δuβ、Δuγ和Δiα、Δiβ、Δiγ中选取含故障相的线模电压Δum和线模电流Δim,本例中故障相为A相,因此m=ɑ,线模电压Δuɑ、Δiɑ波形如图3、4所示。将线模电压Δuɑ、Δiɑ代入(3)、(4)式构造正向电流行波和反向电流行波其波形如图5所示。From Δu α , Δu β , Δu γ and Δi α , Δi β , Δi γ select the line-mode voltage Δu m and line-mode current Δi m of the faulty phase. In this example, the faulty phase is phase A, so m=ɑ, The waveforms of the line-mode voltage Δu ɑ and Δi ɑ are shown in Figures 3 and 4. Substitute line-mode voltages Δu ɑ and Δi ɑ into equations (3) and (4) to construct forward current traveling waves and reverse current traveling waves Its waveform is shown in Figure 5.

提取特征量:计算合闸后正向电流行波绝对值和反向电流行波绝对值,得到如图6所示。Extract feature quantity: calculate the absolute value of the forward current traveling wave and the absolute value of the reverse current traveling wave after closing, and get with As shown in Figure 6.

根据式(5)、(6)分别计算合闸后2τmin~4τmin时窗(1ms)内正向电流行波绝对值和反向电流行波绝对值的积分值为S+=1634.9、S=1364。According to the formulas (5) and (6), the integral values of the absolute value of the forward current traveling wave and the absolute value of the reverse current traveling wave within the time window (1ms) of 2τ min ~ 4τ min after closing are respectively calculated as S + = 1634.9, S - = 1364.

利用PSCAD电磁暂态仿真软件,沿被保护线路MN每隔1km设置一个故障点进行全线遍历,根据计算得到的积分比值λ沿线分布规律,将门槛值k整定为0.5。Using PSCAD electromagnetic transient simulation software, set a fault point every 1 km along the protected line MN to traverse the whole line, and set the threshold value k to 0.5 according to the calculated integral ratio λ Σ distribution along the line.

将S+、S的值代入式(7)λ=S+/S,计算得到正、反向电流行波绝对值积分的比值λ=S+/S=1.20,由于λ大于门槛值0.5,故判断为合闸到故障。Substitute the values of S + and S - into formula (7) λ = S + /S - , and calculate the ratio λ = S + /S - = 1.20 of the integral of the absolute value of forward and reverse current traveling waves, because λ It is greater than the threshold value of 0.5, so it is judged as closing to fault.

实施例2:如图1所示的500kV输电线路仿真系统模型,被保护线路为MN,线路长度LPM=150km,LMN=150km,LNQ=220km,采样率为1MHz。设N端的A相断路器处于断开状态,由M端的A相断路器执行合闸操作,分别假设线路MN无故障和距M端60km发生BG金属性接地故障,过渡电阻为10Ω,初始相角90°。采集线路合闸量测端M所产生三相电流行波与三相电压行波。将三相电压和三相电流行波利用式(1)、(2)进行相模变换,提取三个线模电压分量Δuα、Δuβ和Δuγ和电流分量Δiα、Δiβ和Δiγ,并选取含故障相的线模电压Δum和线模电流Δim如图7、8所示。利用(3)、(4)式构造正向电流行波和反向电流行波如图9所示。计算合闸后正向电流行波绝对值和反向电流行波绝对值,得到如图10所示。根据式(5)、(6)分别计算合闸后1ms时窗内正向电流行波绝对值和反向电流行波绝对值的积分值为S+=1241.1、S=1286.7,则正、反向电流行波绝对值积分的比值λ=S+/S=0.96,由于λ大于0.5,故判断为合闸到故障。Embodiment 2: 500kV transmission line simulation system model as shown in Fig. 1, the protected line is MN, the line length L PM =150km, L MN =150km, L NQ =220km, and the sampling rate is 1MHz. Assume that the A-phase circuit breaker at the N terminal is in the open state, and the A-phase circuit breaker at the M terminal performs the closing operation. Assume that there is no fault in the line MN and a BG metallic ground fault occurs 60km away from the M terminal, the transition resistance is 10Ω, and the initial phase angle 90°. The three-phase current traveling wave and the three-phase voltage traveling wave generated by the closing measurement terminal M of the line are collected. The three-phase voltage and three-phase current traveling waves are transformed into phase mode by formulas (1) and (2), and three line-mode voltage components Δu α , Δu β and Δu γ and current components Δi α , Δi β and Δi γ are extracted, And select the line-mode voltage Δu m and line-mode current Δi m including the fault phase as shown in Figure 7 and 8. Using (3) and (4) to construct forward current traveling wave and reverse current traveling waves As shown in Figure 9. Calculate the absolute value of the forward current traveling wave and the absolute value of the reverse current traveling wave after closing, and get with As shown in Figure 10. According to the formulas (5) and (6), the integral values of the absolute value of the forward current traveling wave and the absolute value of the reverse current traveling wave in the time window 1ms after closing are respectively calculated as S + = 1241.1, S - = 1286.7, then the positive, The ratio λ Σ = S + /S - = 0.96 of the integral of the absolute value of the traveling wave of the reverse current, since λ Σ is greater than 0.5, it is judged to be closed to fault.

实施例3:如图1所示的500kV输电线路仿真系统模型,被保护线路为MN,线路长度LPM=150km,LMN=150km,LNQ=220km,采样率为1MHz。设N端的A相断路器处于断开状态,由M端的A相断路器执行合闸操作,分别假设线路MN无故障和距M端90km发生CG金属性接地故障,过渡电阻为10Ω,初始相角90°。采集线路合闸量测端M所产生三相电流行波与三相电压行波。将三相电压和三相电流行波利用式(1)、(2)进行相模变换,提取三个线模电压分量Δuα、Δuβ和Δuγ和电流分量Δiα、Δiβ和Δiγ,并选取含故障相的线模电压Δum和线模电流Δim如图11、12所示。利用(3)、(4)式构造正向电流行波和反向电流行波如图13所示。计算合闸后正向电流行波绝对值和反向电流行波绝对值,得到如图14所示。根据式(5)、(6)分别计算合闸后1ms时窗内正向电流行波绝对值和反向电流行波绝对值的积分值为S+=181.0、S=1083.4,则正、反向电流行波绝对值积分的比值λ=S+/S=0.1671,由于λ小于0.5,故判断为合闸到无故障线路。Embodiment 3: 500kV transmission line simulation system model as shown in Fig. 1, the protected line is MN, the line length L PM =150km, L MN =150km, L NQ =220km, and the sampling rate is 1MHz. Assume that the A-phase circuit breaker at the N terminal is in the open state, and the A-phase circuit breaker at the M terminal performs the closing operation. Assume that there is no fault in the line MN and a CG metallic ground fault occurs 90km away from the M terminal. The transition resistance is 10Ω, and the initial phase angle 90°. The three-phase current traveling wave and the three-phase voltage traveling wave generated by the closing measurement terminal M of the line are collected. The three-phase voltage and three-phase current traveling waves are transformed into phase mode by formulas (1) and (2), and three line-mode voltage components Δu α , Δu β and Δu γ and current components Δi α , Δi β and Δi γ are extracted, And select the line-mode voltage Δu m and line-mode current Δi m including the fault phase as shown in Figures 11 and 12. Using (3) and (4) to construct forward current traveling wave and reverse current traveling waves As shown in Figure 13. Calculate the absolute value of the forward current traveling wave and the absolute value of the reverse current traveling wave after closing, and get with As shown in Figure 14. According to the formulas (5) and (6), the integral values of the absolute value of the forward current traveling wave and the absolute value of the reverse current traveling wave in the time window 1ms after closing are respectively calculated as S + = 181.0, S - = 1083.4, then the positive, The ratio λ Σ = S + /S - = 0.1671 of the integral of the absolute value of the traveling wave of the reverse current, since λ Σ is less than 0.5, it is judged to be closed to the fault-free line.

上面对本发明的具体实施方式作了详细说明,但是本发明并不限于上述实施方式,在本领域普通技术人员所具备的知识范围内,还可以在不脱离本发明宗旨的前提下作出各种变化。The specific embodiments of the present invention have been described in detail above, but the present invention is not limited to the above-mentioned embodiments, and various changes can also be made without departing from the gist of the present invention within the scope of knowledge possessed by those of ordinary skill in the art. .

Claims (1)

1. a kind of circuit of specific short window integrated value of utilization orientation traveling wave, which closes a floodgate, arrives fault recognition method, it is characterised in that:When defeated When singlephase earth fault occurs for electric line, using single-pole reclosing, the closing line mould current traveling wave obtained using measuring end and conjunction Brake cable mode voltage traveling wave constructs forward current traveling wave and reverse current traveling wave, and the absolute of direct wave and backward-travelling wave is asked for respectively Value, and calculate 2 τ after combined floodgatemin~4 τmin, τminPropagated once time used in the most short total track length that perfects for traveling wave, when window The ratio between integrated value of interior forward and reverse traveling wave absolute value arrives Fault Identification criterion to build to close a floodgate;If the ratio between integrated value is less than setting Threshold value k, then be judged to close a floodgate arrive fault-free circuit;It is judged to close a floodgate if the ratio between integrated value is more than k and arrives failure;
Concretely comprise the following steps:
(1) protected circuit occurs after singlephase earth fault, failure phase is disconnected, now by protected circuit measuring end M ends failure The breaker of phase performs closing operation, and protected circuit other end N-terminal breaker is off, and three are obtained by measuring end M Phase current traveling wave and voltage traveling wave, are utilized respectively formula (1), (2) by three-phase voltage and three-phase current traveling wave and carry out phase-model transformation, carry Take three line mode voltage component Δ uα、ΔuβWith Δ uγWith current component Δ iα、ΔiβWith Δ iγ
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&amp;Delta;</mi> <msub> <mi>u</mi> <mi>&amp;alpha;</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;u</mi> <mi>&amp;beta;</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;u</mi> <mi>&amp;gamma;</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&amp;Delta;</mi> <msub> <mi>u</mi> <mi>A</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;u</mi> <mi>B</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;u</mi> <mi>C</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&amp;Delta;</mi> <msub> <mi>i</mi> <mi>&amp;alpha;</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;i</mi> <mi>&amp;beta;</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;i</mi> <mi>&amp;gamma;</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&amp;Delta;</mi> <msub> <mi>i</mi> <mi>A</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;i</mi> <mi>B</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;i</mi> <mi>C</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
In formula (1), Δ uA、ΔuBWith Δ uCΔ i in respectively three-phase voltage, formula (2)A、ΔiBWith Δ iCRespectively three-phase current;
(2) from Δ uα、Δuβ、ΔuγWith Δ iα、Δiβ、ΔiγThe middle line mode voltage Δ u for choosing the phase containing failuremWith line mould electric current Δ im, utilize (3), (4) formula construction forward current traveling waveWith reverse current traveling wave
<mrow> <msubsup> <mi>i</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;Delta;u</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> <msub> <mi>Z</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </mfrac> <mo>+</mo> <msub> <mi>&amp;Delta;i</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>i</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;Delta;u</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> <msub> <mi>Z</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </mfrac> <mo>-</mo> <msub> <mi>&amp;Delta;i</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
In formula (3) and formula (4), n represents sampled point, subscript m=α or β or γ, represents the modulus chosen;
(3) characteristic quantity is extracted:Forward current traveling wave absolute value and reverse current traveling wave absolute value after closing a floodgate are calculated respectively, are obtainedWith
(4) 2 τ after closing a floodgate are calculated respectively using formula (5), (6)min~4 τminWhen window in forward current traveling wave absolute value and reversely electricity The integrated value S of popular ripple absolute value+And S-
<mrow> <msup> <mi>S</mi> <mo>+</mo> </msup> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>&amp;tau;</mi> <mi>min</mi> </msub> </mrow> </msubsup> <mo>|</mo> <msubsup> <mi>i</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>|</mo> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msup> <mi>S</mi> <mo>-</mo> </msup> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>&amp;tau;</mi> <mi>min</mi> </msub> </mrow> </msubsup> <mo>|</mo> <msubsup> <mi>i</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>|</mo> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
T in formula (5) and (6)0=2 τmin
(5) the ratio λ that forward and reverse current traveling wave absolute value is integrated is asked for according to formula (7)
λ=S+/S- (7)
According to integration ratio λSize carry out close a floodgate to failure differentiation:
If λLess than the threshold value k of setting, then it is judged to close a floodgate and arrives fault-free circuit;
If λMore than or equal to k, then it is judged to close a floodgate and arrives failure.
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