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CN104950211A - Measurement method for out-of-phase interline grounding fault distance of double-circuit lines based on single-end electric quantity of single-circuit line - Google Patents

Measurement method for out-of-phase interline grounding fault distance of double-circuit lines based on single-end electric quantity of single-circuit line
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CN104950211A
CN104950211ACN201510338449.3ACN201510338449ACN104950211ACN 104950211 ACN104950211 ACN 104950211ACN 201510338449 ACN201510338449 ACN 201510338449ACN 104950211 ACN104950211 ACN 104950211A
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曾惠敏
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State Grid Fujian Electric Power Co Ltd
Maintenance Branch of State Grid Fujian Electric Power Co Ltd
State Grid Corp of China SGCC
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State Grid Fujian Electric Power Co Ltd
Maintenance Branch of State Grid Fujian Electric Power Co Ltd
State Grid Corp of China SGCC
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Abstract

The invention discloses a measurement method for the out-of-phase interline grounding fault distance of double-circuit lines based on the single-end electric quantity of a single-circuit line. According to the measurement method disclosed by the invention, the fault distance between a protective installation part of an I-circuit line of double circuits on the same tower and an out-of-phase interline grounding fault point is calculated according to the condition that the relationship between the voltage drop from the protective installation part of the I-circuit line of the double circuits on the same tower to the out-of-phase interline grounding fault point and the product of zero-sequence compensation current and positive-sequence impedance of the I-circuit line with unit length is linear, the influence of transition resistance and load current on the measurement precision of fault distance is eliminated in principle, and no dead zone for measuring the fault distance is guaranteed when a forward output has an out-of-phase interline grounding fault; the measurement method is high in measurement precision.

Description

Translated fromChinese
基于单回线路单端电气量双回线路非同名相跨线接地故障距离测量方法Measurement method of ground fault distance based on single-end electrical quantity of single-circuit line and double-circuit line with non-identical phase across line

技术领域technical field

本发明涉及电力系统继电保护技术领域,具体地说是涉及一种基于单回线路单端电气量双回线路非同名相跨线接地故障距离测量方法。The invention relates to the technical field of relay protection of electric power systems, in particular to a method for measuring the distance of grounding faults of non-identical phases across lines of double-circuit lines based on the single-end electrical quantity of single-circuit lines.

背景技术Background technique

从测距所用电气量来划分,故障测距的方法可分为两大类:双端测距和单端测距。双端故障测距法是利用输电线路两端电气量确定输电线路故障位置的方法,它需要通过通道获取对端电气量,因此对通道的依赖性强,实际使用中还易受双端采样值同步性的影响。单端测距法是仅利用输电线路一端的电压电流数据确定输电线路故障位置的一种方法,由于它仅需要一端数据,无须通讯和数据同步设备,运行费用低且算法稳定,因此在中低压线路中获得了广泛地应用。目前,单端测距方法主要分为两类,一类为行波法,另一类为阻抗法。行波法利用故障暂态行波的传送性质进行测距,精度高,不受运行方式、过度电阻等影响,但对采样率要求很高,需要专门的录波装置,目前未获得实质性的应用。阻抗法利用故障后的电压、电流量计算故障回路的阻抗,根据线路长度与阻抗成正比的特性进行测距,测距原理简单可靠,但应用于同杆并架双回线路单相接地故障单端故障测距时,测距精度受到故障点过渡电阻和线间零序互感影响严重。同杆并架双回线路线间存在零序互感,零序互感会对零序补偿系数产生影响,进而导致阻抗法测距结果误差偏大。若同杆并架双回线路发生单相高阻接地故障,受线间零序互感和高过渡电阻综合影响,阻抗法测距结果常常超出线路全长或无测距结果,无法提供准确的故障位置信息,导致线路故障巡线困难,不利于故障快速排出和线路供电快速恢复。Divided from the electrical quantity used for distance measurement, fault location methods can be divided into two categories: double-ended ranging and single-ended ranging. The double-terminal fault location method is a method to determine the fault location of the transmission line by using the electrical quantity at both ends of the transmission line. It needs to obtain the electrical quantity of the opposite end through the channel, so it is highly dependent on the channel, and it is also vulnerable to the double-terminal sampling value in actual use. Synchronization effects. The single-ended ranging method is a method that only uses the voltage and current data at one end of the transmission line to determine the fault location of the transmission line. Because it only needs data at one end, does not require communication and data synchronization equipment, and has low operating costs and stable algorithms, it is suitable for medium and low voltage applications. It has been widely used in the line. At present, the single-ended ranging methods are mainly divided into two categories, one is the traveling wave method, and the other is the impedance method. The traveling wave method utilizes the transmission properties of fault transient traveling waves for distance measurement. It has high precision and is not affected by the operation mode and excessive resistance. application. The impedance method uses the voltage and current after the fault to calculate the impedance of the fault loop, and performs distance measurement according to the characteristic that the length of the line is proportional to the impedance. When fault location is performed at the end of the fault, the distance measurement accuracy is seriously affected by the transition resistance of the fault point and the zero-sequence mutual inductance between the lines. There is zero-sequence mutual inductance between double-circuit lines on the same pole, and the zero-sequence mutual inductance will affect the zero-sequence compensation coefficient, which will lead to large errors in the ranging results of the impedance method. If a single-phase high-resistance grounding fault occurs on a parallel double-circuit line on the same pole, due to the comprehensive influence of the zero-sequence mutual inductance and high transition resistance between the lines, the ranging result of the impedance method often exceeds the full length of the line or there is no ranging result, which cannot provide accurate fault information Location information makes it difficult to inspect line faults, which is not conducive to rapid troubleshooting and rapid restoration of line power supply.

发明内容Contents of the invention

本发明的目的在于克服已有技术存在的不足,提供一种只用到单端单回线路电气量,不需要引入另一回线路电气量,在电力系统运行方式发生较大改变时依然具有很高的测量精度,且计及线间零序互感的影响,消除了线间零序互感对测量精度的影响,消除了过渡电阻和负荷电流影响的双回线路非同名相跨线接地故障距离测量方法。The purpose of the present invention is to overcome the deficiencies in the prior art, to provide a single-ended single-circuit line electrical quantity, without introducing another circuit electrical quantity, and still have a large capacity when the power system operation mode changes greatly. High measurement accuracy, taking into account the influence of zero-sequence mutual inductance between lines, eliminating the influence of zero-sequence mutual inductance between lines on measurement accuracy, eliminating the influence of transition resistance and load current on double-circuit line non-identical phase cross-line grounding fault distance measurement method.

为完成上述目的,本发明采用如下技术方案:For accomplishing above-mentioned object, the present invention adopts following technical scheme:

基于单回线路单端电气量双回线路非同名相跨线接地故障距离测量方法,其特征在于,包括如下依序步骤:The method for measuring the distance of a grounding fault between non-identical phases and cross-lines of a double-circuit line based on the single-ended electrical quantity of a single-circuit line is characterized in that it includes the following sequential steps:

(1)保护装置测量同杆并架双回线路I回线路保护安装处的故障相电压故障相电流和零序电流其中,φ=I回线路A相、I回线路B相、I回线路C相;(1) The protection device measures the fault phase voltage at the protection installation of the I-circuit line of the double-circuit line on the same pole fault phase current and zero sequence current Wherein, φ=I loop line A phase, I loop line B phase, I loop line C phase;

(2)保护装置计算同杆并架双回线路II回线路的零序电流相角α=r1+r2-π-β;(2) The protection device calculates the zero-sequence current phase angle α=r1 +r2 -π-β of the double-circuit line II line on the same pole;

其中,r1=sin-1(a3b1(a3b1)2+(a1b3)2);r2=sin-1(a1b2-a2b1(a3b1)2+(a1b3)2);a1=Re(U·IφZI1);b1=Im(U·IφZI1);a2=Re(I·Iφ+ZI0-ZI1ZI1I·I0);b2=Im(I·Iφ+ZI0-ZI1ZI1I·I0);a3=b3=|Zm3ZI1I·I0|;β=Arg(Zm3ZI1I·I0);Zm为同杆并架双回线路I回线路与同杆并架双回线路II回线路之间的零序互感;ZI0为同杆并架双回线路I回线路的零序阻抗;ZI1为同杆并架双回线路I回线路的正序阻抗;φ=I回线路A相、I回线路B相、I回线路C相;的实部;的虚部;的实部;的虚部;的幅值;的相角;的反正弦函数值;的反正弦函数值;in, r 1 = sin - 1 ( a 3 b 1 ( a 3 b 1 ) 2 + ( a 1 b 3 ) 2 ) ; r 2 = sin - 1 ( a 1 b 2 - a 2 b 1 ( a 3 b 1 ) 2 + ( a 1 b 3 ) 2 ) ; a 1 = Re ( u &Center Dot; I φ Z I 1 ) ; b 1 = Im ( u &Center Dot; I φ Z I 1 ) ; a 2 = Re ( I · I φ + Z I 0 - Z I 1 Z I 1 I &Center Dot; I 0 ) ; b 2 = Im ( I &Center Dot; I φ + Z I 0 - Z I 1 Z I 1 I &Center Dot; I 0 ) ; a 3 = b 3 = | Z m 3 Z I 1 I &Center Dot; I 0 | ; β = A r g ( Z m 3 Z I 1 I · I 0 ) ; Z m is the zero-sequence mutual inductance between the I circuit of the parallel double-circuit line on the same pole and the II circuit of the parallel double-circuit line on the same pole; ZI0 is the zero-sequence impedance of the I circuit of the parallel double-circuit line on the same pole; ZI1 is The positive sequence impedance of the I-circuit line of the double-circuit line paralleled on the same pole; φ= Phase A of the I-circuit line, Phase B of the I-circuit line, and Phase C of the I-circuit line; for the real part of for the imaginary part of for the real part of for the imaginary part of for the amplitude of for the phase angle; for The arcsine function value of ; for The arcsine function value of ;

(3)保护装置计算同杆并架双回线路II回线路的零序电流其中,j为复数算子;(3) The protection device calculates the zero-sequence current of the II-circuit line of the parallel double-circuit line on the same pole Among them, j is a complex number operator;

(4)保护装置计算同杆并架双回线路I回线路的零序补偿电流(4) The protection device calculates the zero-sequence compensation current of the I-circuit line of the parallel double-circuit line on the same pole

ΔΔII·&Center Dot;==II·&Center Dot;IIφφ++ZZII00--ZZII11ZZII11II·&Center Dot;II00++ZZmm33ZZII11II·&Center Dot;IIII00

(5)保护装置计算非同名相跨线接地故障点到同杆并架双回线路I回线路保护安装处的故障距离lf(5) The protection device calculates the fault distance lf from the grounding fault point of the non-identical phase crossing line to the protection installation point of the I-circuit line of the parallel double-circuit line on the same pole:

llff==llRR((Uu··IIφφΔΔII··))ImIm((II·&Center Dot;II00++II··IIII00ΔΔII··))--ImIm((Uu··IIφφΔΔII··))ReRe((II··II00++II··IIII00ΔΔII·&Center Dot;))ReRe((ZZII11ll))ImIm((II··II00++II··IIII00ΔΔII··))--IImm((ZZII11ll))ReRe((II··II00++II··IIII00ΔΔII·&Center Dot;))

其中,l为同杆并架双回线路I回线路长度;ZI1为同杆并架双回线路I回线路的正序阻抗;φ=I回线路A相、I回线路B相、I回线路C相;的实部;的虚部;的实部;的虚部;的实部;的虚部。Among them, l is the length of the I circuit of the parallel double circuit line on the same pole; ZI1 is the positive sequence impedance of the I circuit of the parallel double circuit line on the same pole; φ=I circuit A phase, I circuit B phase, I circuit Line C phase; for the real part of for the imaginary part of for the real part of for the imaginary part of for the real part of for the imaginary part of .

本发明的特点及技术成果:Features and technical achievements of the present invention:

本发明方法只用到单端单回线路电气量,不需要引入另一回线路电气量,故障距离测量精度不受电力系统运行方式的影响,在电力系统运行方式发生较大改变时依然具有很高的测量精度,且计及线间零序互感的影响,消除了线间零序互感对测量精度的影响。本发明方法利用集中参数建模,根据同杆并架双回线路I回线路保护安装处到非同名相跨线接地故障点的电压降与零序补偿电流和单位长度I回线路正序阻抗的乘积呈线性关系计算同杆并架双回线路I回线路保护安装处到非同名相跨线接地故障点的故障距离,原理上消除了过渡电阻和负荷电流对故障距离测量精度的影响,保护正向出口发生非同名相跨线接地故障时无故障距离测量死区,具有很高的测量精度。The method of the present invention only uses the electrical quantity of the single-ended single-circuit line, and does not need to introduce the electrical quantity of another circuit. The measurement accuracy of the fault distance is not affected by the operation mode of the power system, and it still has great advantages when the operation mode of the power system changes greatly. High measurement accuracy, and taking into account the influence of zero-sequence mutual inductance between lines, eliminates the influence of zero-sequence mutual inductance between lines on measurement accuracy. The method of the present invention utilizes centralized parameter modeling, and according to the voltage drop from the I-circuit line protection installation place of the parallel double-circuit line on the same pole to the non-identical phase cross-line grounding fault point, the zero-sequence compensation current and the positive-sequence impedance of the I-circuit line per unit length The product shows a linear relationship to calculate the fault distance from the I-circuit line protection installation point of the double-circuit line on the same pole parallel to the ground fault point of the non-identical phase cross-line. In principle, the influence of the transition resistance and load current on the fault distance measurement accuracy is eliminated, and the protection is normal There is no dead zone for fault distance measurement when a non-identical phase cross-line ground fault occurs at the exit, and it has high measurement accuracy.

附图说明Description of drawings

图1为应用本发明的同杆并架双回线路输电系统示意图。Fig. 1 is a schematic diagram of a double-circuit line power transmission system on the same pole parallel to the rack applying the present invention.

具体实施方式Detailed ways

图1为应用本发明的同杆并架双回线路输电系统示意图。图1中PT为电压互感器、CT为电流互感器,m、n为同杆并架双回线路的两端编号。保护装置测量同杆并架双回线路I回线路保护安装处的故障相电压故障相电流和零序电流其中,φ=I回线路A相、I回线路B相、I回线路C相。Fig. 1 is a schematic diagram of a double-circuit line power transmission system on the same pole parallel to the rack applying the present invention. In Figure 1, PT is a voltage transformer, CT is a current transformer, and m and n are the numbers of the two ends of the double-circuit line on the same pole. The protection device measures the fault phase voltage at the protection installation place of the I-circuit line of double-circuit lines paralleled on the same pole fault phase current and zero sequence current Wherein, φ=phase A of the I-circuit line, phase B of the I-circuit line, and phase C of the I-circuit line.

保护装置计算同杆并架双回线路II回线路的零序电流相角α=r1+r2-π-β;The protection device calculates the zero-sequence current phase angle α=r1 +r2 -π-β of the double-circuit line II line on the same pole;

其中,Zm为同杆并架双回线路I回线路与同杆并架双回线路II回线路之间的零序互感;ZI0为同杆并架双回线路I回线路的零序阻抗;ZI1为同杆并架双回线路I回线路的正序阻抗;φ=I回线路A相、I回线路B相、I回线路C相;a3=b3=|Zm3ZI1I·I0|,的幅值;β=Arg(Zm3ZI1I·I0),的相角;a2=Re(I·Iφ+ZI0-ZI1ZI1I·I0),的实部;b2=Im(I·Iφ+ZI0-ZI1ZI1I·I0),的虚部;a1=Re(U·IφZI1),的实部;b1=Im(U·IφZI1),的虚部;r1、r2为中间变量,无物理意义,且r1=sin-1(a3b1(a3b1)2+(a1b3)2),r2=sin-1(a1b2-a2b1(a3b1)2+(a1b3)2);sin-1(a3b1(a3b1)2+(a1b3)2)的反正弦函数值;的反正弦函数值。Among them, Zm is the zero-sequence mutual inductance between the I-circuit line of the parallel double-circuit line on the same pole and the II-circuit line of the parallel double-circuit line on the same pole; ZI0 is the zero-sequence impedance of the I-circuit line of the parallel double-circuit line on the same pole ; ZI1 is the positive-sequence impedance of the double-circuit line I circuit on the same pole; φ=I circuit A phase, I circuit B phase, I circuit C phase; a 3 = b 3 = | Z m 3 Z I 1 I &Center Dot; I 0 | , for the amplitude of β = A r g ( Z m 3 Z I 1 I · I 0 ) , for the phase angle; a 2 = Re ( I &Center Dot; I φ + Z I 0 - Z I 1 Z I 1 I · I 0 ) , for the real part of b 2 = I m ( I · I φ + Z I 0 - Z I 1 Z I 1 I &Center Dot; I 0 ) , for the imaginary part of a 1 = Re ( u · I φ Z I 1 ) , for the real part of b 1 = Im ( u · I φ Z I 1 ) , for the imaginary part of ; r1 , r2 are intermediate variables with no physical meaning, and r 1 = sin - 1 ( a 3 b 1 ( a 3 b 1 ) 2 + ( a 1 b 3 ) 2 ) , r 2 = sin - 1 ( a 1 b 2 - a 2 b 1 ( a 3 b 1 ) 2 + ( a 1 b 3 ) 2 ) ; sin - 1 ( a 3 b 1 ( a 3 b 1 ) 2 + ( a 1 b 3 ) 2 ) for The arcsine function value of ; for The arcsine function value of .

保护装置计算同杆并架双回线路II回线路的零序电流其中,j为复数算子。The protection device calculates the zero-sequence current of the double-circuit line II on the same pole Among them, j is a complex number operator.

保护装置计算同杆并架双回线路I回线路的零序补偿电流The protection device calculates the zero-sequence compensation current of the I-circuit line of the parallel double-circuit line on the same pole

ΔΔII··==II·&Center Dot;IIφφ++ZZII00--ZZII11ZZII11II··II00++ZZmm33ZZII11II·&Center Dot;IIII00

保护装置计算非同名相跨线接地故障点到同杆并架双回线路I回线路保护安装处的故障距离lfThe protection device calculates the fault distance lf from the grounding fault point of the non-identical phase crossing line to the protection installation point of the I-circuit line of the parallel double-circuit line on the same pole:

llff==llReRe((Uu·&Center Dot;IIφφΔΔII·&Center Dot;))ImIm((II·&Center Dot;II00++II·&Center Dot;IIII00ΔΔII·&Center Dot;))--ImIm((Uu·&Center Dot;IIφφΔΔII··))ReRe((II··II00++II··IIII00ΔΔII··))ReRe((ZZII11ll))ImIm((II··II00++II··IIII00ΔΔII··))--IImm((ZZII11ll))ReRe((II··II00++II··IIII00ΔΔII·&Center Dot;))

其中,l为同杆并架双回线路I回线路长度;ZI1为同杆并架双回线路I回线路的正序阻抗;φ=I回线路A相、I回线路B相、I回线路C相;的实部;的虚部;的实部;的虚部;的实部;的虚部。Among them, l is the length of the I circuit of the parallel double circuit line on the same pole; ZI1 is the positive sequence impedance of the I circuit of the parallel double circuit line on the same pole; φ=I circuit A phase, I circuit B phase, I circuit Line C phase; for the real part of for the imaginary part of for the real part of for the imaginary part of for the real part of for the imaginary part of .

本发明方法只用到单端单回线路电气量,不需要引入另一回线路电气量,故障距离测量精度不受电力系统运行方式的影响,在电力系统运行方式发生较大改变时依然具有很高的测量精度,且计及线间零序互感的影响,消除了线间零序互感对测量精度的影响。The method of the present invention only uses the electrical quantity of the single-ended single-circuit line, and does not need to introduce the electrical quantity of another circuit. The measurement accuracy of the fault distance is not affected by the operation mode of the power system, and it still has great advantages when the operation mode of the power system changes greatly. High measurement accuracy, and taking into account the influence of zero-sequence mutual inductance between lines, eliminates the influence of zero-sequence mutual inductance between lines on measurement accuracy.

本发明方法利用集中参数建模,根据同杆并架双回线路I回线路保护安装处到非同名相跨线接地故障点的电压降与零序补偿电流和单位长度I回线路正序阻抗的乘积呈线性关系计算同杆并架双回线路I回线路保护安装处到非同名相跨线接地故障点的故障距离,原理上消除了过渡电阻和负荷电流对故障距离测量精度的影响,保护正向出口发生非同名相跨线接地故障时无故障距离测量死区,具有很高的测量精度。The method of the present invention utilizes centralized parameter modeling, and according to the voltage drop from the I-circuit line protection installation place of the double-circuit parallel line on the same pole to the non-identical phase cross-line grounding fault point, the zero-sequence compensation current and the positive-sequence impedance of the I-circuit line per unit length The product has a linear relationship to calculate the fault distance from the I-circuit line protection installation point of the double-circuit line on the same pole to the non-same-named phase cross-line grounding fault point. In principle, the influence of transition resistance and load current on the fault distance measurement accuracy is eliminated, and the protection is normal. There is no dead zone for fault distance measurement when a non-identical phase cross-line ground fault occurs at the exit, and it has high measurement accuracy.

以上所述仅为本发明的较佳具体实施例,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 descriptions are only preferred specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto, any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention , should be covered within the protection scope of the present invention.

Claims (1)

Wherein, <math> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>=</mo> <msup> <mi>sin</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mn>3</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>=</mo> <msup> <mi>sin</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>Re</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow></math> <math> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>=</mo> <mo>|</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>|</mo> <mo>;</mo> <mi>&beta;</mi> <mo>=</mo> <mi>A</mi> <mi>r</mi> <mi>g</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow></math>Zmzero sequence mutual inductance between the circuit I of the double-circuit line on the same tower and the circuit II of the double-circuit line on the same tower is achieved; zI0Zero sequence impedance of I-loop circuit of double-loop circuit on the same tower; zI1The positive sequence impedance of the I-loop line of the double-loop line on the same tower is obtained; phase A of I loop line and phase B of I loop lineAnd a C phase of the I loop circuit;is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe amplitude of (d);is composed ofThe phase angle of (d);is composed ofThe arcsine function value of (1);is composed ofThe arcsine function value of (a).
<math> <mrow> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow></math>
<math> <mrow> <msub> <mi>l</mi> <mi>f</mi> </msub> <mo>=</mo> <mi>l</mi> <mfrac> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mrow> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mrow> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>Re</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> <mrow> <mi>Re</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mo>)</mo> </mrow> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mi>I</mi> <mi>m</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mo>)</mo> </mrow> <mi>Re</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow></math>
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