CN102680856B

CN102680856B - Method for measuring zero sequence current of power transmission line based on magnetic sensor array

Info

Publication number: CN102680856B
Application number: CN201210154949.8A
Authority: CN
Inventors: 林顺富; 崔龙龙; 刘庆强
Original assignee: Shanghai University of Electric Power
Current assignee: Shanghai University of Electric Power
Priority date: 2012-05-16
Filing date: 2012-05-16
Publication date: 2014-09-17
Anticipated expiration: 2032-05-16
Also published as: CN102680856A

Abstract

The invention relates to a method for measuring the zero-sequence current of a power transmission line based on a magnetic sensor array, which comprises the following steps: 1) placing the magnetic sensor array under the overhead power transmission line, and collecting output signals of the magnetic field sensor array; 2) passing the signals sequentially through After the filter circuit and amplifier circuit are transmitted to the data processing equipment; 3) The data processing equipment processes the received signal to obtain the magnetic flux density information of the current-carrying wire, and obtains the zero value of the current-carrying wire by analyzing the characteristics of the magnetic flux density. sequence current. Compared with the prior art, the invention has the advantages of simplicity, low cost, low loss and the like.

Description

Measurement method of transmission line zero-sequence current based on magnetic sensor array

技术领域 technical field

本发明涉及一种输电线路零序电流的测量方法，尤其是涉及一种基于磁传感器阵列的输电线路零序电流的测量方法。The invention relates to a method for measuring the zero-sequence current of a transmission line, in particular to a method for measuring the zero-sequence current of a transmission line based on a magnetic sensor array.

背景技术 Background technique

架空配电线路中的零序电流信息对于排除像中线断线，接地不良等相关的接地故障是非常重要的。由于零序电流保护具有结构及工作原理简单，正确动作率高；在零序网络基本稳定(即中性点接地变压器的数目和位置基本不变)的条件下，保护范围比较稳定，且有连续动作的特性；对近区故障可实现快速动作；受故障过度电阻的影响较小；保护定值不受负荷电流的影响，基本不受其它中性点不接地电网短路故障的影响等特点，零序电流保护被广泛的应用到小电流接地系统或大电流接地系统中。零序电流应用到变压器零序电流差动保护中，可以大大提高变压器内部单相故障时的灵敏度。Zero-sequence current information in overhead distribution lines is very important to troubleshoot related ground faults like broken neutral, poor grounding, etc. Due to the simple structure and working principle of the zero-sequence current protection, the correct action rate is high; under the condition that the zero-sequence network is basically stable (that is, the number and position of the neutral point grounding transformer are basically unchanged), the protection range is relatively stable and there are continuous The characteristics of the action; it can realize fast action for the fault in the near area; it is less affected by the excessive resistance of the fault; Sequence current protection is widely used in small current grounding systems or large current grounding systems. Applying the zero-sequence current to the zero-sequence current differential protection of the transformer can greatly improve the sensitivity of the single-phase fault inside the transformer.

传统的零序电流测量是通过与普通电流互感器(CTs)类似的零序电流互感器来实现的。在架空线路的零序电流测量中，一般都是采用三只电流互感器接成零序电流滤过器，因此传统的零序电流互感器具有传统的电流互感器所具有的缺点，如互感器饱和；测量范围狭窄；铁磁共振、磁滞效应；测量准确度低；存在潜在的危险。电磁式电流互感器的一、二次之间靠电磁变换原理实现能量传递，因此一、二次之间总是存在着电磁联系。如果二次侧线圈由于某种原因出现了开路，一次侧的大电流完全成为励磁电流，就会在二次线圈侧感应出高电压，危及人身、设备的安全；设备安装、检修不方便，维护工作量大，安装时接线复杂，容易出错。因此，一种具有实际应用价值的新型ZSC测量技术是非常有必要的。Traditional zero-sequence current measurement is achieved by zero-sequence current transformers similar to ordinary current transformers (CTs). In the zero-sequence current measurement of overhead lines, three current transformers are generally used to form a zero-sequence current filter, so the traditional zero-sequence current transformer has the disadvantages of the traditional current transformer, such as transformer Saturation; narrow measurement range; ferromagnetic resonance, hysteresis effect; low measurement accuracy; potential danger. The primary and secondary of the electromagnetic current transformer rely on the principle of electromagnetic transformation to realize energy transfer, so there is always an electromagnetic connection between the primary and secondary. If the secondary side coil is open for some reason, the large current on the primary side becomes the excitation current completely, and high voltage will be induced on the side of the secondary coil, which will endanger the safety of people and equipment; equipment installation and maintenance are inconvenient, maintenance The workload is large, the wiring is complicated during installation, and it is easy to make mistakes. Therefore, a new type of ZSC measurement technology with practical application value is very necessary.

发明内容 Contents of the invention

本发明的目的就是为了克服上述现有技术存在的缺陷而提供一种基于磁传感器阵列的输电线路零序电流的测量方法。The object of the present invention is to provide a method for measuring the zero-sequence current of a transmission line based on a magnetic sensor array in order to overcome the above-mentioned defects in the prior art.

本发明的目的可以通过以下技术方案来实现：The purpose of the present invention can be achieved through the following technical solutions:

一种基于磁传感器阵列的输电线路零序电流的测量方法，其特征在于，包括以下步骤：A method for measuring zero-sequence current of a transmission line based on a magnetic sensor array, characterized in that it comprises the following steps:

1)将磁传感器阵列置于架空输电线路的下方，采集载流导线信号；1) Place the magnetic sensor array under the overhead transmission line to collect the current-carrying wire signal;

2)将信号依次通过RC滤波电路和三阶放大电路后传输给数据采集设备；2) The signal is transmitted to the data acquisition device after passing through the RC filter circuit and the third-order amplifier circuit in sequence;

3)数据采集设备对接收到的信号进行处理，得到载流导线的磁通密度信息，并通过分析该磁通密度的线性特征得到载流导线的零序电流。3) The data acquisition equipment processes the received signal to obtain the magnetic flux density information of the current-carrying wire, and obtains the zero-sequence current of the current-carrying wire by analyzing the linear characteristics of the magnetic flux density.

若输电线路为三相三线架空输电线路，所述的磁传感器阵列为两个磁传感器组成磁传感器阵列。If the transmission line is a three-phase three-wire overhead transmission line, the magnetic sensor array is composed of two magnetic sensors.

零序电流的计算具体如下：The calculation of zero sequence current is as follows:

1)两个磁传感器S₁和S₂的磁通量分别为B₁和B₂，B₁、B₂在空间坐标系中分解为x，y，z三个分量分别如下1) The magnetic fluxes of the two magnetic sensors S ₁ and S ₂ are B ₁ and B ₂ respectively, and B ₁ and B ₂ are decomposed into three components of x, y and z in the space coordinate system as follows

$\{\begin{matrix} {B B}_{11 x x} = = 00 \\ {B B}_{11 y the y} = = \frac{{μ μ}_{00}}{22 π π} \cdot \cdot ((\frac{{I I}_{a a}}{{l l}_{11}} \cdot &Center Dot; cos cos {θ θ}_{11}^{22} + + \frac{{I I}_{b b}}{{l l}_{11} + + {l l}_{22}} + + \frac{{I I}_{c c}}{{l l}_{11}} \cdot &Center Dot; cos cos {θ θ}_{11}^{22})) \\ {B B}_{11 z z} = = \frac{{μ μ}_{00}}{22 π π} \cdot \cdot ((\frac{{I I}_{a a}}{{l l}_{11}} \cdot \cdot sin sin {θ θ}_{11} \cdot \cdot cos cos {θ θ}_{11} + + \frac{{I I}_{c c}}{{l l}_{11}} \cdot \cdot sin sin {θ θ}_{11} \cdot \cdot cos cos {θ θ}_{11})) \end{matrix} - - - - - - ((a a 11))$

$\{\begin{matrix} {B B}_{22 x x} = = 00 \\ {B B}_{22 y the y} = = \frac{{μ μ}_{00}}{22 π π} \cdot \cdot ((\frac{{I I}_{a a}}{{l l}_{11} + + d d} \cdot \cdot cos cos {θ θ}_{22}^{22} + + \frac{{I I}_{b b}}{{l l}_{11} + + {l l}_{22} + + d d} + + \frac{{I I}_{c c}}{{l l}_{11} + + d d} \cdot &Center Dot; cos cos {θ θ}_{22}^{22})) \\ {B B}_{22 z z} = = \frac{{μ μ}_{00}}{22 π π} \cdot &Center Dot; ((\frac{{I I}_{a a}}{{l l}_{11} + + d d} \cdot &Center Dot; sin sin {θ θ}_{11} \cdot &Center Dot; cos cos {θ θ}_{11} + + \frac{{I I}_{c c}}{{l l}_{11} + + d d} \cdot &Center Dot; sin sin {θ θ}_{11} \cdot &Center Dot; cos cos {θ θ}_{11})) \end{matrix} - - - - - - ((a a 22))$

上两式中I_a、I_b、I_c分别为三相电流，μ₀为空气磁导率，w为a相和b相之间的水平距离，d为磁传感器S₁和S2之间的垂直距离，l₁为磁传感器S₁与c相之间的垂直距离，l₂为b相和c相之间的垂直距离，θ₁为a相与S₁之间连线和b相与S₁之间连线的夹角，θ₂为a相与S₂之间连线和b相与S₂之间连线的夹角；In the above two formulas, I _a , I _b , and I _c are the three-phase currents, μ ₀ is the air permeability, w is the horizontal distance between phase a and phase b, and d is the distance between magnetic sensors _S1 and S2 Vertical distance, l ₁ is the vertical distance between magnetic sensor S ₁ and phase c, l ₂ is the vertical distance between phase b and phase c, θ ₁ is the connection line between phase a and S ₁ and phase b and S The angle between the line between ₁ , _θ2 is the angle between the line between phase a and _S2 and the line between phase b and _S2 ;

2)假设电力线与磁场传感器之间的距离远大于电力线之间的距离，即l₁＞＞l₂，则三条电力线的磁场效应可由位于传感器上方的等效电流I_v表示，其中，I_v和S₁之间距离为h_v，I_v在测量点S₁，S₂处所产生磁通密度的x，y，z轴分量如式(a3)和(a4)表示。2) Assuming that the distance between the power line and the magnetic field sensor is much greater than the distance between the power lines, that is, l ₁ >> l ₂ , the magnetic field effect of the three power lines can be represented by the equivalent current I _v above the sensor, where I _v and The distance between S ₁ is h _v , and the x, y, and z axis components of the magnetic flux density generated by I _v at the measurement points S ₁ and S ₂ are expressed in formulas (a3) and (a4).

$\{\begin{matrix} {B B}_{11 vx vx} = = 00 \\ {B B}_{11 vy vy} = = \frac{{μ μ}_{00} \cdot \cdot {I I}_{v v}}{22 π π {h h}_{v v}} \\ {B B}_{11 vz vz} = = 00 \end{matrix} - - - - - - ((a a 33))$

$\{\begin{matrix} {B B}_{22 vx vx} = = 00 \\ {B B}_{22 vy vy} = = \frac{{μ μ}_{00} \cdot &Center Dot; {I I}_{v v}}{22 π π (({h h}_{v v} + + d d))} \\ {B B}_{22 vz vz} = = 00 \end{matrix} - - - - - - ((a a 44))$

由(a3)、(a4)式可知，由I_v产生的磁通密度仅包含y轴分量，在零序电流测量中，可认定虚拟电流I_v与I_a，I_b，I_c在S₁，S₂处产生磁通密度的y轴分量是相同的，即B_1y＝B_1vy，B_2y＝B_2vy，将(a1)、(a2)式中的y轴分量替代到(a3)、(a4)式，可得到I_v与I_a，I_b，I_c之间的关系式(a5)；It can be seen from formulas (a3) and (a4) that the magnetic flux density generated by I _v only includes the y-axis component. In zero-sequence current measurement, it can be assumed that the virtual current I _v and I _a , I _b , and I _c are in S ₁ , the y-axis components of the magnetic flux density at S ₂ are the same, that is, B _1y = B _1vy , B _2y = B _2vy , replace the y-axis components in (a1), (a2) with (a3), ( a4) formula, the relational formula (a5) between Iv and _Ia , _Ib , _Ic can be _obtained ;

假定l₁＞＞l₂，此外，由于l₁＞＞w以及l₁+d＞＞w，则cosθ₁≈cosθ₂。因此，虚拟电流I_v可简化为(a6)式；Assuming l ₁ >>l ₂ , furthermore, since l ₁ >>w and l ₁ +d >>w, then cosθ ₁ ≈cosθ ₂ . Therefore, the virtual current I _v can be simplified as (a6) formula;

I_v＝f(I_a，I_b，I_c)＝(I_a+I_b+I_c)＝3I₀ (a6)I _v =f(I _a , I _b , I _c )=(I _a +I _b +I _c )=3I ₀ (a6)

(a6)式表明，只要得到虚拟电流I_v就可求得零序电流I₀，虚拟电流I_v可由(a7)式计算出来，(a7)式在式(a3)、(a4)的基础上得出，其中B_1vy和B_2vy可分别通过磁场传感器S₁，S₂测量出来，Formula (a6) shows that the zero-sequence current I ₀ can be obtained as long as the virtual current I _v is obtained, and the virtual current I _v can be calculated by formula (a7), which is based on formulas (a3) and (a4) It can be obtained that B _1vy and B _2vy can be measured by magnetic field sensors S ₁ and S ₂ respectively,

${I I}_{v v} = = \frac{22 πd πd \cdot &Center Dot; {B B}_{11 vy vy} \cdot &Center Dot; {B B}_{22 vy vy}}{{μ μ}_{00} (({B B}_{11 vy vy} - - {B B}_{22 vy vy}))} - - - - - - ((a a 77))$

若输电线路为三相四线架空输电线路，所述的磁传感器阵列为两个或三个磁传感器组成磁传感器阵列。If the transmission line is a three-phase four-wire overhead transmission line, the magnetic sensor array is composed of two or three magnetic sensors.

若采用两个磁传感器，零序电流的计算如下：If two magnetic sensors are used, the zero sequence current is calculated as follows:

四条电力线由一条虚拟导线等效表示，等效电流可表示如下：The four power lines are equivalently represented by a virtual wire, and the equivalent current can be expressed as follows:

I_v＝I_a+I_b+I_c+I_n＝3I₀+I_n＝I_r (a8)I _v =I _a +I _b +I _c +I _n =3I ₀ +I _n =I _r (a8)

其中，I_v为虚拟电流，I_a、I_b、I_c分别为三相电流，I₀为零序电流，I_n为中线电流，I_r为残余电流；Among them, I _v is virtual current, I _a , I _b , I _c are three-phase current respectively, I ₀ is zero-sequence current, _In is neutral current, I _r is residual current;

I_v或I_r由磁场传感器S₁、S₂测得的磁通密度计算出来，B₁、B₂的y轴分量如下式所示：I _v or I _r is calculated from the magnetic flux density measured by the magnetic field sensors S ₁ and S ₂ , and the y-axis components of B ₁ and B ₂ are shown in the following formula:

$\{\begin{matrix} {B B}_{11 y the y} = = \frac{{μ μ}_{00} {I I}_{a a}}{22 π π {l l}_{11}} {((cos cos {θ θ}_{11}))}^{22} + + \frac{{μ μ}_{00} {I I}_{b b}}{22 π π (({l l}_{11} + + {l l}_{22}))} + + \frac{{μ μ}_{00} {I I}_{c c}}{22 π π {l l}_{11}} {((cos cos {θ θ}_{11}))}^{22} + + \frac{{μ μ}_{00} {I I}_{n no}}{22 π π {l l}_{33}} \\ {B B}_{22 y the y} = = \frac{{μ μ}_{00} {I I}_{a a}}{22 π π (({l l}_{11} + + d d))} {((cos cos {θ θ}_{22}))}^{22} + + \frac{{μ μ}_{00} {I I}_{b b}}{22 π π (({l l}_{11} + + {l l}_{22} + + d d))} \\ + + \frac{{μ μ}_{00} {I I}_{c c}}{22 π π (({l l}_{11} + + d d))} {((cos cos {θ θ}_{22}))}^{22} + + \frac{{μ μ}_{00} {I I}_{n no}}{22 π π (({I I}_{33} + + d d))} \end{matrix} - - - - - - ((a a 99))$

上式，其中μ₀为空气磁导率，w为a相和b相之间的水平距离，d为磁传感器S₁和S₂之间的垂直距离，l₁为磁传感器S₁与c相之间的垂直距离，l₂为b相和c相之间的垂直距离，l₃为磁传感器S₁与n相之间的垂直距离，θ₁为a相与S₁之间连线和b相与S₁之间连线的夹角，θ₂为a相与S₂之间连线和b相与S₂之间连线的夹角；The above formula, where μ ₀ is the air permeability, w is the horizontal distance between phase a and phase b, d is the vertical distance between magnetic sensors _S1 and _S2 , _l1 is the magnetic sensor _S1 and phase c The vertical distance between, l ₂ is the vertical distance between b phase and c phase, l ₃ is the vertical distance between magnetic sensor S ₁ and n phase, θ ₁ is the connection line between a phase and S ₁ and b The angle between the line between phase and _S1 , _θ2 is the angle between the line between phase a and _S2 and the line between phase b and _S2 ;

I_v利用等式(a7)计算得到，再根据等式(a8)，利用每一线路结构所对应的I_n/I₀比值可计算出零序电流。I _v is calculated by using equation (a7), and then according to equation (a8), the zero-sequence current can be calculated by using the ratio of I _n /I ₀ corresponding to each line structure.

若采用三个磁传感器，零序电流的计算如下：If three magnetic sensors are used, the zero sequence current is calculated as follows:

将三相电力线看作为一条虚拟导线，中线位于虚拟导线下方，三个磁场传感器S₁、S₂、S₃垂直位于B相导线的下方，将三相电力线看作为一条虚拟导线，中线位于虚拟导线下方，等效电流可表示如下：The three-phase power line is regarded as a virtual wire, the neutral line is located under the virtual wire, and the three magnetic field sensors S ₁ , S ₂ , S ₃ are vertically located under the B-phase wire, the three-phase power line is regarded as a virtual wire, and the neutral line is located under the virtual wire Below, the equivalent current can be expressed as follows:

I_v＝I_a+I_b+I_c＝3I₀+I_n (a10)I _v =I _a +I _b +I _c =3I ₀ +I _n (a10)

S₁，S₂，S₃处的磁通密度由式(a11)表示，I_v与B_1vy，B_2vy，B_3vy之间的关系如式(a12)所示；The magnetic flux density at S ₁ , S ₂ , and S ₃ is expressed by formula (a11), and the relationship between I _v and B _1vy , B _2vy , and B _3vy is shown in formula (a12);

$\{\begin{matrix} {B B}_{11 y the y} = = \frac{{μ μ}_{00}}{22 π π} \cdot \cdot ((\frac{{I I}_{11}}{{l l}_{11}} \cdot &Center Dot; cos cos {θ θ}_{11}^{22} + + \frac{{I I}_{22}}{{l l}_{11} + + {l l}_{22}} + + \frac{{I I}_{33}}{{l l}_{11}} \cdot \cdot cos cos {θ θ}_{11}^{22} + + \frac{{I I}_{n no}}{{l l}_{33}})) \\ {B B}_{22 y the y} = = \frac{{μ μ}_{00}}{22 π π} \cdot \cdot ((\frac{{I I}_{11}}{{l l}_{11} + + {d d}_{11}} \cdot \cdot cos cos {θ θ}_{22}^{22} + + \frac{{I I}_{22}}{{l l}_{11} + + {l l}_{22} + + {d d}_{11}} \\ + + \frac{{I I}_{33}}{{l l}_{11} + + {d d}_{11}} \cdot &Center Dot; cos cos {θ θ}_{22}^{22} + + \frac{{I I}_{n no}}{{l l}_{33} + + {d d}_{11}})) \\ {B B}_{33 y the y} = = \frac{{μ μ}_{00}}{22 π π} \cdot &Center Dot; ((\frac{{I I}_{11}}{{l l}_{11} + + {d d}_{11} + + {d d}_{22}} \cdot &Center Dot; cos cos {θ θ}_{33}^{22} + + \frac{{I I}_{22}}{{l l}_{11} + + {l l}_{22} + + {d d}_{11} + + {d d}_{22}} \\ + + \frac{{I I}_{33}}{{l l}_{11} + + {d d}_{11} + + {d d}_{22}} \cdot \cdot cos cos {θ θ}_{33}^{22} + + \frac{{I I}_{n no}}{{l l}_{33} + + {d d}_{11} + + {d d}_{22}})) \end{matrix} - - - - - - ((a a 1111))$

$\{\begin{matrix} {B B}_{11 vy vy} = = \frac{{μ μ}_{00}}{22 π π} [[\frac{11}{{h h}_{v v}} {I I}_{v v} + + \frac{11}{{l l}_{33}} {I I}_{w w}]] \\ {B B}_{22 vy vy} = = \frac{{μ μ}_{00}}{22 π π} [[\frac{11}{(({h h}_{v v} + + {d d}_{11}))} {I I}_{v v} + + \frac{11}{(({l l}_{33} + + {d d}_{11}))} {I I}_{n no}]] \\ {B B}_{33 vy vy} = = \frac{{μ μ}_{00}}{22 π π} [[\frac{11}{(({h h}_{v v} + + {d d}_{11} + + {d d}_{22}))} {I I}_{v v} + + \frac{11}{(({l l}_{33} + + {d d}_{11} + + {d d}_{22}))} {I I}_{n no}]] \end{matrix} - - - - - - ((a a 1212))$

B_1y，B_2y，B_3y由磁场传感器测量得到，在零序电流测量中，可认定虚拟电流I_v，I_n与I_a，I_b，I_c，I_n在S₁，S₂，S₃处产生磁通密度的y轴分量是相同的，即B_1y＝B_1vy，B_2y＝B_2vy，B_3y＝B_3vy，式(a12)中的变量I_v，h_v，I_n是未知的，可以通过求解式(a12)得到，最终，根据等式(a10)求解出零序电流。B _1y , B _2y , and B _3y are measured by magnetic field sensors. In zero-sequence current measurement, it can be determined that virtual current I _v , _In and I _a , I _b , I _c , _In are in S ₁ , S ₂ , S The y-axis components of magnetic flux density produced at ₃ places are the same, namely B _1y =B _1vy , B _2y =B _2vy , B _3y =B _3vy , the variable I _v in the formula (a12), h _v , _In are unknown , can be obtained by solving equation (a12), and finally, solve the zero sequence current according to equation (a10).

与现有技术相比，本发明具有简单、成本低、损耗低；可以避免传统电流互感器的饱和、测量范围狭窄和铁磁共振磁，滞效应等缺点；现场使用无需接触带电线路，无需按极性接线构成零序电流滤过器，不具有像传统电流互感器二次线圈开路引起的危险，安全性高。Compared with the prior art, the present invention has the advantages of simplicity, low cost and low loss; it can avoid the shortcomings of traditional current transformers such as saturation, narrow measurement range and ferromagnetic resonance magnetic hysteresis effect; it does not need to touch live lines or press The polarity wiring constitutes a zero-sequence current filter, which does not have the danger caused by the open circuit of the secondary coil of the traditional current transformer, and has high safety.

附图说明 Description of drawings

图1为配电系统中的三相三线式架空导线分布图及ZSC测量等效图，其中(a)为分布图，(b)为等效图；Figure 1 is the distribution diagram of the three-phase three-wire overhead conductors in the power distribution system and the ZSC measurement equivalent diagram, where (a) is the distribution diagram, and (b) is the equivalent diagram;

图2为B_z，B_y与l₁的关系曲线(w＝1.5m，l₂＝0.36m，d＝1.0m，I_a＝I_b＝I_c＝200A)；Figure 2 is the relationship curve between B _z , B _y and l ₁ (w=1.5m, l ₂ =0.36m, d=1.0m, I _a =I _b =I _c =200A);

图3为B_z，B_y与l₁的关系曲线(w＝1.5m，l₂＝0.36m，d＝1.0m，I_a＝220A，I_b＝200A，I_c＝170A)；Figure 3 is the relationship curve between B _z , By _y and l ₁ (w=1.5m, l ₂ =0.36m, d=1.0m, I _a =220A, I _b =200A, I _c =170A);

图4为三相三线系统中零序电流估算值与实际值之间的比较结果(w＝1.5m，d＝1.0m，I_a＝220A，I_b＝200A，I_c＝190A)；Fig. 4 is the comparison result between the zero-sequence current estimated value and the actual value in the three-phase three-wire system (w=1.5m, d=1.0m, I _a =220A, I _b =200A, I _c =190A);

图5为三相三线系统中零序电流估算值与实际值之间的比较结果(w＝1.5m，l₁＝9m，I_a＝240A，I_b＝220A，I_c＝190A)；Fig. 5 is the comparison result between the zero-sequence current estimated value and the actual value in the three-phase three-wire system (w=1.5m, l ₁ =9m, I _a =240A, I _b =220A, I _c =190A);

图6为三相三线系统中零序电流估算值与实际值之间的比较结果(三相电流随机产生)；Fig. 6 is the comparison result between the zero-sequence current estimated value and the actual value in the three-phase three-wire system (the three-phase current is randomly generated);

图7为配电系统中的三相四线式架空导线分布图及两磁传感器的ZSC测量等效图，其中(a)为分布图，(b)为等效图；Fig. 7 is the distribution diagram of the three-phase four-wire overhead wire in the power distribution system and the ZSC measurement equivalent diagram of the two magnetic sensors, wherein (a) is the distribution diagram, and (b) is the equivalent diagram;

图8为配电系统中的三相四线式架空导线分布图及三磁传感器的ZSC测量等效图，其中(a)为分布图，(b)为等效图；Fig. 8 is the distribution diagram of the three-phase four-wire type overhead wire in the power distribution system and the ZSC measurement equivalent diagram of the three magnetic sensors, wherein (a) is the distribution diagram, and (b) is the equivalent diagram;

图9为三相四线系统中残余电流估算值和实际值之间的比较结果(采用两个磁场传感器)；Figure 9 shows the comparison between the estimated value and the actual value of the residual current in a three-phase four-wire system (using two magnetic field sensors);

图10为三相四线系统中零序电流估算值与实际值间的比较结果(采用三个磁场传感器)；Figure 10 is the comparison result between the estimated value and the actual value of the zero-sequence current in the three-phase four-wire system (using three magnetic field sensors);

图11为测试平台原理图(w＝0.032m，l₁＝0.4m，l₂＝0m，l₃＝0.285m，d₁＝0.065m，d₂＝0.065m)；Figure 11 is a schematic diagram of the test platform (w=0.032m, l ₁ =0.4m, l ₂ =0m, l ₃ =0.285m, d ₁ =0.065m, d ₂ =0.065m);

图12为三相三线系统中传感器测量零序电流值与CTS测量零序电流值的比较结果；Figure 12 is the comparison result of the zero-sequence current value measured by the sensor and the zero-sequence current value measured by the CTS in the three-phase three-wire system;

图13为三相四线系统中传感器测量零序电流值与CTS测量零序电流值的比较结果。Figure 13 is the comparison result of the zero-sequence current value measured by the sensor and the zero-sequence current value measured by the CTS in the three-phase four-wire system.

具体实施方式 Detailed ways

下面结合附图和具体实施例对本发明进行详细说明。The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

实施例Example

对于三相三线架空电力线，其零序电流的测量原理及仿真验证如下所述。配电系统中的三相三线式架空线如图1所示，在图1中，三相电流分别为I_a，I_b，I_c，磁场传感器S₁、S₂垂直位于B相导线的下方。电力线的零序电流如下：For three-phase three-wire overhead power lines, the measurement principle and simulation verification of the zero-sequence current are as follows. The three-phase three-wire overhead line in the power distribution system is shown in Figure 1. In Figure 1, the three-phase currents are I _a , I _b , and I _c , and the magnetic field sensors S ₁ and S ₂ are vertically located below the B-phase conductor . The zero-sequence current of the power line is as follows:

${I I}_{00} = = \frac{{I I}_{a a} + + {I I}_{b b} + + {I I}_{c c}}{33} - - - - - - ((11))$

忽略麦克斯韦方程组中的转移电流(接近低频)，可以证明自由空间中的磁场与流经架空线路的总电流呈线性关系。根据比奥-萨瓦定律，图1(a)中磁场传感器所在位置(S₁、S₂)处的磁通密度(B₁、B₂)可通过(2)和(3)式表达出来。在(2)、(3)式方程组中，B1，B2在空间坐标系中分解为x，y，z三个分量。Neglecting the transferred current in Maxwell's equations (near low frequencies), it can be shown that the magnetic field in free space is linear with the total current flowing through the overhead line. According to the Biot-Savat law, the magnetic flux density (B _{1 , B 2 ) at the position (S 1} _{, S 2} ₎ _of the magnetic field sensor in Figure 1(a) can be expressed by formulas (2) and (3). In (2), (3) equation group, B1, B2 are decomposed into x, y, z three components in the space coordinate system.

$\{\begin{matrix} {B B}_{11 x x} = = 00 \\ {B B}_{11 y the y} = = \frac{{μ μ}_{00}}{22 π π} \cdot &Center Dot; ((\frac{{I I}_{a a}}{{l l}_{11}} \cdot &Center Dot; cos cos {θ θ}_{11}^{22} + + \frac{{I I}_{b b}}{{l l}_{11} + + {l l}_{22}} + + \frac{{I I}_{c c}}{{l l}_{11}} \cdot &Center Dot; cos cos {θ θ}_{11}^{22})) \\ {B B}_{11 z z} = = \frac{{μ μ}_{00}}{22 π π} \cdot \cdot ((\frac{{I I}_{a a}}{{l l}_{11}} \cdot &Center Dot; sin sin {θ θ}_{11} \cdot &Center Dot; cos cos {θ θ}_{11} + + \frac{{I I}_{c c}}{{l l}_{11}} \cdot &Center Dot; sin sin {θ θ}_{11} \cdot \cdot cos cos {θ θ}_{11})) \end{matrix} - - - - - - ((22))$

$\{\begin{matrix} {B B}_{22 x x} = = 00 \\ {B B}_{22 y the y} = = \frac{{μ μ}_{00}}{22 π π} \cdot \cdot ((\frac{{I I}_{a a}}{{l l}_{11} + + d d} \cdot &Center Dot; cos cos {θ θ}_{22}^{22} + + \frac{{I I}_{b b}}{{l l}_{11} + + {l l}_{22} + + d d} + + \frac{{I I}_{c c}}{{l l}_{11} + + d d} \cdot &Center Dot; cos cos {θ θ}_{22}^{22})) \\ {B B}_{22 z z} = = \frac{{μ μ}_{00}}{22 π π} \cdot &Center Dot; ((\frac{{I I}_{a a}}{{l l}_{11} + + d d} \cdot \cdot sin sin {θ θ}_{11} \cdot &Center Dot; cos cos {θ θ}_{11} + + \frac{{I I}_{c c}}{{l l}_{11} + + d d} \cdot &Center Dot; sin sin {θ θ}_{11} \cdot \cdot cos cos {θ θ}_{11})) \end{matrix} - - - - - - ((33))$

上式中μ₀为空气磁导率，w，d，l₁，l₂，θ₁，θ₂的含义参照图1(a)。由(2)、(3)式可知，在S₁，S₂处磁通密度的x轴分量为零。In the above formula, μ ₀ is the magnetic permeability of air, and the meanings of w, d, l ₁ , l ₂ , θ ₁ and θ ₂ refer to Figure 1(a). It can be known from (2) and (3) that the x-axis component of the magnetic flux density at S ₁ and S ₂ is zero.

假设电力线与磁场传感器之间的距离远大于电力线之间的距离，即l₁＞＞l₂，则三条电力线的磁场效应可由位于传感器上方的等效电流I_v表示。载有虚拟电流I_v的等效导线如图1(b)所示，其中，I_v和S₁之间距离为h_v。I_v在测量点S₁，S₂处所产生磁通密度的x，y，z轴分量如式(4)和(5)表示。Assuming that the distance between the power lines and the magnetic field sensor is much greater than the distance between the power lines, ie l ₁ >> l ₂ , the magnetic field effect of the three power lines can be represented by the equivalent current _Iv above the sensor. The equivalent wire carrying the virtual current _Iv is shown in Figure 1(b), where the distance between _Iv and _S1 is _hv . The x, y, and z axis components of the magnetic flux density generated by _Iv at the measurement points S ₁ and S ₂ are expressed in formulas (4) and (5).

$\{\begin{matrix} {B B}_{11 vx vx} = = 00 \\ {B B}_{11 vy vy} = = \frac{{μ μ}_{00} \cdot &Center Dot; {I I}_{v v}}{22 π π {h h}_{v v}} \\ {B B}_{11 vz vz} = = 00 \end{matrix} - - - - - - ((44))$

$\{\begin{matrix} {B B}_{22 vx vx} = = 00 \\ {B B}_{22 vy vy} = = \frac{{μ μ}_{00} \cdot \cdot {I I}_{v v}}{22 π π (({h h}_{v v} + + d d))} \\ {B B}_{22 vz vz} = = 00 \end{matrix} - - - - - - ((55))$

由(4)、(5)式可知，由I_v产生的磁通密度仅包含y轴分量。在零序电流ZSC测量中，可以认为虚拟电流I_v与I_a，I_b，I_c在S₁，S₂处产生磁通密度的y轴分量是相同的，即B_1y＝B_1vy，B₂＝B_2vy。因此，可以将(2)、(3)式中的y轴分量替代到(4)、(5)式。那么，可以得到I_v与I_a，I_b，I_c之间的关系式(6)。From (4), (5) formula can know, the magnetic flux density produced by I _v only includes the y-axis component. In the zero-sequence current ZSC measurement, it can be considered that the y-axis component of the magnetic flux density generated by the virtual current I _v and I _a , I _b , and I _c at S ₁ and S ₂ is the same, that is, B _1y = B _1vy , B ₂ = B _2vy . Therefore, the y-axis components in formulas (2) and (3) can be replaced by formulas (4) and (5). Then, the relationship (6) between I _v and I _a , I _b , I _c can be obtained.

为了避免复杂的表达式(6)，可以做几个合理的假定来简化I_v的表达式。之前我们假定l₁＞＞l₂，此外，由于l₁＞＞w以及l₁+d＞＞w，则cosθ₁≈cosθ₂。因此，虚拟电流I_v可简化为(7)式。In order to avoid complicated expression (6), several reasonable assumptions can be made to simplify the expression of _Iv . Previously we assumed that l ₁ >>l ₂ , moreover, since l ₁ >>w and l ₁ +d >>w, then cosθ ₁ ≈cosθ ₂ . Therefore, the virtual current I _v can be simplified as (7) formula.

I_v＝f(I_a，I_b，I_c)＝(I_a+I_b+I_c)＝3I₀ (7)I _v =f(I _a , I _b , I _c )=(I _a +I _b +I _c )=3I ₀ (7)

(7)式表明，只要得到虚拟电流I_v就可以求得零序电流I₀。虚拟电流I_v可由(8)式计算出来，(8)式在式(4)、(5)的基础上得出，其中B_1vy和B_2vy可分别通过磁场传感器S₁，S₂测量出来。Formula (7) shows that the zero-sequence current I ₀ can be obtained as long as the virtual current I _v is obtained. The virtual current I _v can be calculated by formula (8), which is obtained on the basis of formulas (4) and (5), where B _1vy and B _2vy can be measured by magnetic field sensors S ₁ and S ₂ respectively.

${I I}_{v v} = = \frac{22 πd πd \cdot \cdot {B B}_{11 vy vy} \cdot &Center Dot; {B B}_{22 vy vy}}{{μ μ}_{00} (({B B}_{11 vy vy} - - {B B}_{22 vy vy}))} - - - - - - ((88))$

采用虚拟等效电流I_v代替三相电流I_a，I_b，I_c，测量出虚拟电流I_v产生的磁通密度的y轴分量计算ZSC。The virtual equivalent current I _v is used to replace the three-phase currents I _a , I _b , I _c , and the y-axis component of the magnetic flux density generated by the virtual current I _v is measured to calculate ZSC.

以下面的仿真案例来验证所提出的三相三线架空电力线ZSC测量方法的准确性。The following simulation case is used to verify the accuracy of the proposed three-phase three-wire overhead power line ZSC measurement method.

在式(2)-(5)的基础上，磁通密度y，z轴分量的均方根值(RMS)与距离l₁之间的关系如图2和3所示。图2中三相电流平衡(I_a＝I_b＝I_c＝200A)，而图3中三相电流不平衡(I_a＝220A，I_b＝200A，I_c＝170A)。通常架空配电线周围的磁场强度很弱，因此磁通密度一般采用mG为单位。On the basis of formulas (2)-(5), the relationship between the root mean square value (RMS) of the magnetic flux density y and the z-axis component and the distance l ₁ is shown in Figures 2 and 3. In Fig. 2, the three-phase currents are balanced (I _a = I _b = I _c = 200A), while in Fig. 3 the three-phase currents are unbalanced (I _a = 220A, I _b = 200A, I _c = 170A). Usually the magnetic field strength around the overhead power distribution line is very weak, so the magnetic flux density is generally taken as the unit of mG.

在l₁＞＞l₂的条件下，令h_v＝l₁。图2与图3中的B_1y和B_2y由式(2)、(3)算解得，为准确值；B_1vy，B_2vy通过(4)、(5)式解得，即B_1vy，B_2vy为估算值。图2表明，在三相电流平衡的情况下，l₁大于8m时，接近于零。同时，在这种情况下由于I_a+I_b+I_c＝0，零序电流为零，并且根据公式(6)可知，虚拟等效电流为零，所以B_1vy，B_2vy都等于零。因此，假设B_1y＝B_1vy，B_2y＝B_2vy是合理的。图3表明，在满足l₁大于8m的条件下，这一假设同样适用于三相电流不平衡的情况。Under the condition that l ₁ >>l ₂ , let h _v =l ₁ . B _1y and B _2y in Fig. 2 and Fig. 3 are calculated and solved by equations (2) and (3), which are accurate values; B _1vy and B _2vy are obtained by solving equations (4) and (5), that is, B _1vy , B _2vy is an estimate. Figure 2 shows that in the case of three-phase current balance, when l ₁ is greater than 8m, it is close to zero. At the same time, since I _a +I _b +I _c =0 in this case, the zero-sequence current is zero, and according to formula (6), the virtual equivalent current is zero, so B _1vy and B _2vy are both equal to zero. Therefore, it is reasonable to assume that B _1y =B _1vy , B _2y =B _2vy . Figure 3 shows that this assumption is also applicable to the unbalanced three-phase current under the condition that l ₁ is greater than 8m.

图4表明了在w＝1.5m，d＝1.0m，I_a＝220A，I_b＝200A，I_c＝190A的条件下，l₁从4到15m变化时零序电流估算值与实际值的比较结果。可以看出，如果l₁大于10m，零序电流估算值和实际值非常接近，在l₁＝10m时两电流之差与l₁＝20m时相比变化并不大，即l₁取10m的距离就可以足够准确地估算零序电流。Figure 4 shows that under the conditions of w=1.5m, d=1.0m, _Ia =220A, _Ib =200A, _Ic =190A, the estimated value and actual value of the zero-sequence current when l ₁ changes from 4 to 15m Comparing results. It can be seen that if l ₁ is greater than 10m, the zero-sequence current estimated value is very close to the actual value, and the difference between the two currents when l ₁ = 10m does not change much compared with l ₁ = 20m, that is, l ₁ takes 10m The distance is enough to accurately estimate the zero-sequence current.

图5所示为在w＝1.5m，l₁＝9m，I_a＝240A，I_b＝220A，I_c＝190A的条件下d变化时的零序电流的估算值曲线和实际值曲线。从图5可以看出，传感器间距离d对零序电流估算误差的影响微乎其微。实际上，配电线到地之间的距离通常小于11.7m，为了确保l₁大于9m，推荐d取大约1.0m以消除噪音干扰来实现零序电流更加准确的计算。Fig. 5 shows the estimated and actual value curves of the zero-sequence current when d changes under the conditions of w=1.5m, l ₁ =9m, I _a =240A, I _b =220A, and I _c =190A. It can be seen from Figure 5 that the distance d between sensors has little influence on the estimation error of the zero-sequence current. In fact, the distance between the distribution line and the ground is usually less than 11.7m. In order to ensure that l ₁ is greater than 9m, it is recommended that d be about 1.0m to eliminate noise interference and achieve a more accurate calculation of zero-sequence current.

图6表示了在50种情况下零序电流估算值与实际值之间的比较结果，在这些情况下，三相电流(I_a，I_b，I_c)从180A到260A之间随机产生。这一仿真结果表明，在w＝1.5m，l₁＝10.0m，l₂＝0.36m，d＝1.0m的条件下，三相三线系统中零序电流的估算值与实际值非常接近。当零序电流值在2A到16A的范围内时，其估算值与实际值间的绝对误差在±1A之间。Figure 6 shows the comparison between the estimated and actual zero-sequence currents for 50 cases where the three-phase currents (I _a , I _b , I _c ) were randomly generated from 180A to 260A. The simulation results show that under the conditions of w=1.5m, l ₁ =10.0m, l ₂ =0.36m, d=1.0m, the estimated value of the zero-sequence current in the three-phase three-wire system is very close to the actual value. When the zero-sequence current value is in the range of 2A to 16A, the absolute error between the estimated value and the actual value is between ±1A.

对于三相四线架空电力线，其零序电流的测量原理如下所述。For three-phase four-wire overhead power lines, the measurement principle of the zero-sequence current is as follows.

配电系统中的三相四线式架空线如图7所示。中线电流为I_n。四条电力线由一条虚拟导线等效表示，等效电流可表示如下：The three-phase four-wire overhead line in the power distribution system is shown in Figure 7. The neutral current is _In . The four power lines are equivalently represented by a virtual wire, and the equivalent current can be expressed as follows:

I_v＝I_a+I_b+I_c+I_n＝3I₀+I_n＝I_r (9)I _v =I _a +I _b +I _c +I _n =3I ₀ +I _n =I _r (9)

其中，I_r为残余电流。与三相三线系统类似，三相四线系统中的零序电流I₀可由I_v或I_r估算得到，I_v或I_r又可以由磁场传感器S₁，S₂测得的磁通密度计算出来。Among them, I _r is the residual current. Similar to the three-phase three-wire system, the zero-sequence current _I0 in the three-phase four-wire system can be estimated by _Iv or _Ir , and _Iv or _Ir can be calculated by the magnetic flux density measured by the magnetic field sensors _S1 and _S2 come out.

B₁，B₂的y轴分量如下式所示：The y-axis components of B ₁ and B ₂ are shown in the following formula:

$\{\begin{matrix} {B B}_{11 y the y} = = \frac{{μ μ}_{00} {I I}_{a a}}{22 π π {l l}_{11}} {((cos cos {θ θ}_{11}))}^{22} + + \frac{{μ μ}_{00} {I I}_{b b}}{22 π π (({l l}_{11} + + {l l}_{22}))} + + \frac{{μ μ}_{00} {I I}_{c c}}{22 π π {l l}_{11}} {((cos cos {θ θ}_{11}))}^{22} + + \frac{{μ μ}_{00} {I I}_{n no}}{22 π π {l l}_{33}} \\ {B B}_{22 y the y} = = \frac{{μ μ}_{00} {I I}_{a a}}{22 π π (({l l}_{11} + + d d))} {((cos cos {θ θ}_{22}))}^{22} + + \frac{{μ μ}_{00} {I I}_{b b}}{22 π π (({l l}_{11} + + {l l}_{22} + + d d))} \\ + + \frac{{μ μ}_{00} {I I}_{c c}}{22 π π (({l l}_{11} + + d d))} {((cos cos {θ θ}_{22}))}^{22} + + \frac{{μ μ}_{00} {I I}_{n no}}{22 π π (({I I}_{33} + + d d))} \end{matrix} - - - - - - ((1010))$

I_v还可以利用等式(8)计算得到。那么，根据等式(9)，利用每一线路结构对应的I_n/I₀比值计算出零序电流。 _Iv can also be calculated using equation (8). Then, according to equation (9), the zero-sequence current is calculated using the ratio of I _n /I ₀ corresponding to each line structure.

在图7中，利用零序电流和中线电流之间的估算关系仅使用两个磁场传感器就可以获取零序电流。为了得到更加准确的结果，可以将三相电力线看作为一条虚拟导线，中线位于虚拟导线下方，如图8所示，这种情况必须需要三个磁场传感器。三相电流分别为I_a，I_b，I_c，中线电流为I_n。磁场传感器(S₁，S₂，S₃)垂直位于B相导线的下方。将三相电力线看作为一条虚拟导线，中线位于虚拟导线下方，等效电流可表示如下：In Figure 7, the zero-sequence current can be acquired using only two magnetic field sensors using the estimated relationship between the zero-sequence current and the neutral current. In order to obtain more accurate results, the three-phase power line can be regarded as a virtual wire, and the neutral wire is located below the virtual wire, as shown in Figure 8. In this case, three magnetic field sensors must be required. The three-phase currents are I _a , I _b , I _c , and the neutral current is _In . Magnetic field sensors (S ₁ , S ₂ , S ₃ ) are located vertically below the phase B conductor. Considering the three-phase power line as a virtual wire, the neutral wire is located below the virtual wire, and the equivalent current can be expressed as follows:

I_v＝I_a+I_b+I_c＝3I₀+I_n (11)I _v ＝I _a +I _b +I _c ＝3I ₀ +I _n (11)

图8中S₁，S₂，S₃处的磁通密度由式(12)表示。I_v与B_1vy，B_2vy，B_3vy之间的关系如式(13)所示。The magnetic flux density at S ₁ , S ₂ , and S ₃ in Fig. 8 is expressed by formula (12). The relationship between I _v and B _1vy , B _2vy , and B _3vy is shown in formula (13).

$\{\begin{matrix} {B B}_{11 y the y} = = \frac{{μ μ}_{00}}{22 π π} \cdot \cdot ((\frac{{I I}_{11}}{{l l}_{11}} \cdot \cdot cos cos {θ θ}_{11}^{22} + + \frac{{I I}_{22}}{{l l}_{11} + + {l l}_{22}} + + \frac{{I I}_{33}}{{l l}_{11}} \cdot &Center Dot; cos cos {θ θ}_{11}^{22} + + \frac{{I I}_{n no}}{{l l}_{33}})) \\ {B B}_{22 y the y} = = \frac{{μ μ}_{00}}{22 π π} \cdot \cdot ((\frac{{I I}_{11}}{{l l}_{11} + + {d d}_{11}} \cdot \cdot cos cos {θ θ}_{22}^{22} + + \frac{{I I}_{22}}{{l l}_{11} + + {l l}_{22} + + {d d}_{11}} \\ + + \frac{{I I}_{33}}{{l l}_{11} + + {d d}_{11}} \cdot \cdot cos cos {θ θ}_{22}^{22} + + \frac{{I I}_{n no}}{{l l}_{33} + + {d d}_{11}})) \\ {B B}_{33 y the y} = = \frac{{μ μ}_{00}}{22 π π} \cdot \cdot ((\frac{{I I}_{11}}{{l l}_{11} + + {d d}_{11} + + {d d}_{22}} \cdot \cdot cos cos {θ θ}_{33}^{22} + + \frac{{I I}_{22}}{{l l}_{11} + + {l l}_{22} + + {d d}_{11} + + {d d}_{22}} \\ + + \frac{{I I}_{33}}{{l l}_{11} + + {d d}_{11} + + {d d}_{22}} \cdot \cdot cos cos {θ θ}_{33}^{22} + + \frac{{I I}_{n no}}{{l l}_{33} + + {d d}_{11} + + {d d}_{22}})) \end{matrix} - - - - - - ((1212))$

$\{\begin{matrix} {B B}_{11 vy vy} = = \frac{{μ μ}_{00}}{22 π π} [[\frac{11}{{h h}_{v v}} {I I}_{v v} + + \frac{11}{{l l}_{33}} {I I}_{w w}]] \\ {B B}_{22 vy vy} = = \frac{{μ μ}_{00}}{22 π π} [[\frac{11}{(({h h}_{v v} + + {d d}_{11}))} {I I}_{v v} + + \frac{11}{(({l l}_{33} + + {d d}_{11}))} {I I}_{n no}]] \\ {B B}_{33 vy vy} = = \frac{{μ μ}_{00}}{22 π π} [[\frac{11}{(({h h}_{v v} + + {d d}_{11} + + {d d}_{22}))} {I I}_{v v} + + \frac{11}{(({l l}_{33} + + {d d}_{11} + + {d d}_{22}))} {I I}_{n no}]] \end{matrix} - - - - - - ((1313))$

B_1y，B_2y，B_3y由磁场传感器测量得到，在ZSC测量中，可以认为虚拟电流I_v，I_n与I_a，I_b，I_c，I_n在S₁，S₂，S₃处产生磁通密度的y轴分量是相同的，即B_1y＝B_1vy，B_2y＝B_2vy，B_3y＝B_3vy。式(13)中的变量I_v，h_v，I_n是未知的，可以通过求解式(13)得到。最终，根据等式(11)求解出零序电流。B _1y , B _2y , _B _3y are measured by magnetic field sensors. In ZSC measurement, it can be considered that the virtual current I _v , In and I _a , I _b , I _c , _In are at S ₁ , S ₂ , S ₃ The y-axis components of the resulting magnetic flux density are the same, ie B _1y =B _1vy , B _2y =B _2vy , B _3y =B _3vy . The variables I _v , h _v , In in formula (13 ₎ are unknown and can be obtained by solving formula (13). Finally, the zero-sequence current is solved according to equation (11).

以下面的仿真案例来验证所提出的三相四线架空电力线ZSC测量方法的准确性。The following simulation case is used to verify the accuracy of the proposed three-phase four-wire overhead power line ZSC measurement method.

对于采用两个传感器的三相四线系统，残余电流可以通过所提出的测量方法直接获取，然后，根据公式(9)，利用I_n/I₀比值可以计算出零序电流。这一比值主要受电力线结构影响，在多接地配电系统中，I_n/I₀比值可取为3.9。For a three-phase four-wire system with two sensors, the residual current can be directly obtained by the proposed measurement method, and then, according to Equation (9), the zero-sequence current can be calculated using the ratio I _n /I ₀ . This ratio is mainly affected by the structure of the power line. In a multi-ground power distribution system, the ratio of I _n /I ₀ can be taken as 3.9.

图9比较了采用两个磁场传感器时的残余电流估算值和实际值。在w＝1.22m，l₁＝10.0m，l₂＝0.36m，l₃＝9.0m，d＝1.0m的条件下对50种不同情况进行了仿真。在仿真中电流I_a，I_b，I_c在180A和260A之间随机变化，中线电流I_n的幅值和相角分别在0-20A和0-180°范围内随机变化。Figure 9 compares the estimated and actual residual current values using two magnetic field sensors. Fifty different cases were simulated under the conditions of w=1.22m, l ₁ =10.0m, l ₂ =0.36m, l ₃ =9.0m, d=1.0m. In the simulation, the currents I _a , I _b , and I _c vary randomly between 180A and 260A, and the amplitude and phase angle _of the neutral current In vary randomly within the range of 0-20A and 0-180°, respectively.

从图9中可以看出，残余电流估算值接近于其实际值。当残余电流在1A到25A范围内时，残余电流估算值与实际值之间的绝对误差也在±1A范围内。It can be seen from Figure 9 that the residual current estimate is close to its actual value. When the residual current is in the range of 1A to 25A, the absolute error between the estimated value and the actual value of the residual current is also in the range of ±1A.

采用三个磁场传感器的情况下零序电流估算值与实际值的比较结果如图10所示，图10中仿真条件和电流变化与图9相同，这一结果表明由这一方法估算的零序电流值与实际值非常接近。三相四线系统中零序电流估算值与实际值间的误差比三相三线系统两者间误差要大一些。当零序电流在5A到24A范围内时，零序电流估算值与实际值间的绝对误差在±2A范围内。The comparison results of the zero-sequence current estimate and the actual value in the case of three magnetic field sensors are shown in Figure 10. The simulation conditions and current changes in Figure 10 are the same as those in Figure 9. This result shows that the zero-sequence current estimated by this method The current value is very close to the actual value. The error between the estimated value and the actual value of the zero-sequence current in the three-phase four-wire system is larger than that in the three-phase three-wire system. When the zero-sequence current is in the range of 5A to 24A, the absolute error between the estimated value and the actual value of the zero-sequence current is in the range of ±2A.

基于上述输电线路零序电流的测量方法本发明搭建了一套测量平台以通过实验验证所提出的测量方法的准确性与可行性。测试系统的原理图如图11所示。Based on the measurement method for the zero-sequence current of the transmission line, the present invention builds a measurement platform to verify the accuracy and feasibility of the proposed measurement method through experiments. The schematic diagram of the test system is shown in Figure 11.

本测试系统由三相电压源，磁场传感器，平行导线，电流互感器(CTs)以及负荷组成。测试系统中电流频率为50HZ，使用两个可变的负荷箱调节零序电流的幅值，采用电流互感器取得参考电流进行验证。实验数据通过基于Lab-View的数据采集系统(图11所示)采集得到。由于实验室空间的限制，图11所示的测试平台中的距离l₁，l₃，w与实际现场中的值相比有成比例的减小。The test system consists of a three-phase voltage source, a magnetic field sensor, parallel wires, current transformers (CTs) and a load. The current frequency in the test system is 50HZ, two variable load boxes are used to adjust the amplitude of the zero-sequence current, and a current transformer is used to obtain a reference current for verification. The experimental data is collected by the Lab-View-based data acquisition system (shown in Figure 11). Due to the limitation of laboratory space, the distances l ₁ , l ₃ , w in the test platform shown in Fig. 11 are proportionally reduced compared with the values in the actual field.

磁场传感器是一种单轴的感应线圈传感器，电感为0.15H，并且有高达80KHz的频带宽。此线圈传感器的直径为8mm。与导线和磁场传感器之间的距离相比，传感器的尺寸可以忽略不计。每一个磁场传感器的输出都通过一个三阶放大电路进行放大。放大电路的总增益大约为2000。在放大电路之前有RC滤波电路，其截止频率为1.2KHz。每一路放大电路的输出由NI DAQ数据采集设备进行采样。由线圈传感器和电子元器件构成的磁场传感器电路板已经在实验室完成校准，其误差大约为1％。电压对于磁通密度的因数为3.3×10⁵(V/G)。为了消除有限导线的边缘效应，磁场传感器安装在垂直于平行导线的板子上，这一板子位于导线的中间位置，推荐采用易携的激光垂直测量仪器以确保传感器可以方便安装。在测试中，零序电流估算值通过由磁场传感器测出的磁通密度计算得到，参考值由灵敏度为100mV/A，精确度为0.5％的Fluke电流传感器测量得到。对每个信号进行快速傅立叶变换(FFT)可获取到一些基本分量。The magnetic field sensor is a single-axis induction coil sensor with an inductance of 0.15H and a frequency bandwidth of up to 80KHz. The diameter of this coil sensor is 8mm. The size of the sensor is negligible compared to the distance between the wire and the magnetic field sensor. The output of each magnetic field sensor is amplified by a third-stage amplifier circuit. The total gain of the amplifier circuit is about 2000. There is an RC filter circuit before the amplifier circuit, and its cutoff frequency is 1.2KHz. The output of each amplifier circuit is sampled by a NI DAQ data acquisition device. The magnetic field sensor circuit board, which consists of a coil sensor and electronic components, has been calibrated in the laboratory to an error of about 1%. The factor of voltage to magnetic flux density is 3.3×10 ⁵ (V/G). In order to eliminate the edge effect of limited wires, the magnetic field sensor is installed on a board perpendicular to the parallel wires. This board is located in the middle of the wires. It is recommended to use a portable laser perpendicular measuring instrument to ensure that the sensor can be easily installed. In the test, the zero-sequence current estimation value is calculated by the magnetic flux density measured by the magnetic field sensor, and the reference value is measured by the Fluke current sensor with a sensitivity of 100mV/A and an accuracy of 0.5%. Performing a Fast Fourier Transform (FFT) on each signal yields some fundamental components.

图12和13分别表示了三相三线和三相四线系统中本文所提出的测量方法与CTs测量方法的对比结果。在测试过程中，通过调节负荷箱阻抗零序电流从0到6A变化。对于图12所示的三相三线系统的情况，中性导线断开并且只采用了两个磁场传感器进行测量。对于图13所示的三相四线系统的情况，采用了三个磁场传感器进行测量。Figures 12 and 13 show the comparison results between the measurement method proposed in this paper and the CTs measurement method in three-phase three-wire and three-phase four-wire systems, respectively. During the test, the zero-sequence current was varied from 0 to 6A by adjusting the load box impedance. For the case of the three-phase three-wire system shown in Figure 12, the neutral conductor is disconnected and only two magnetic field sensors are used for measurements. For the case of the three-phase four-wire system shown in Figure 13, three magnetic field sensors are used for measurement.

从图12和13中可以看出，三相三线和三相四线系统的测量相对误差分别低于5％和7％。实验结果表明，在三相三线和三相四线系统中，本文所提出的测量方法都可以较准确地计算出零序电流。It can be seen from Figures 12 and 13 that the measurement relative errors of the three-phase three-wire and three-phase four-wire systems are lower than 5% and 7%, respectively. The experimental results show that the measurement method proposed in this paper can calculate the zero-sequence current more accurately in the three-phase three-wire and three-phase four-wire systems.

在采用两个磁场传感器测量三相四线系统的情况下，测量得零序电流的准确度主要受I_n/I₀这一比值的影响。导致测量误差的一个主要不确定性因素就是传感器没有垂直放置在中间的配电线下方。在实际现场中，1.0m的偏差就会引起大约5％的误差。0.5m的偏差会引起大约1％的误差。现场可以采用便利的激光垂直测量仪器来放置传感器阵列。这样，在实际现场测量中可以避免这一主要的测量不确定性因素。In the case of using two magnetic field sensors to measure a three-phase four-wire system, the accuracy of the measured zero-sequence current is mainly affected by the ratio I _n /I ₀ . A major source of uncertainty in measurement errors is that the sensor is not placed vertically below the distribution line in between. In the actual field, a deviation of 1.0m will cause an error of about 5%. A deviation of 0.5m will cause an error of about 1%. The sensor array can be placed in the field using a convenient laser plumb gauge. In this way, this major measurement uncertainty factor can be avoided in actual field measurements.

基于磁传感器阵列的ZSC的测量方法简单、成本低、损耗低；可以避免传统电流互感器的饱和、测量范围狭窄和铁磁共振磁，滞效应等缺点；现场使用无需接触带电线路，无需按极性接线构成零序电流滤过器，不具有像传统电流互感器二次线圈开路引起的危险，安全性高。The ZSC measurement method based on the magnetic sensor array is simple, low in cost, and low in loss; it can avoid the shortcomings of traditional current transformers such as saturation, narrow measurement range, and ferromagnetic resonance magnetic hysteresis effect; it does not need to touch live lines for field use, and does not need to press poles The positive wiring constitutes a zero-sequence current filter, which does not have the danger caused by the open circuit of the secondary coil of the traditional current transformer, and has high safety.

Claims

1. a measuring method for the power transmission line zero-sequence electric current based on array of magnetic sensors, is characterized in that, comprises the following steps:

1) array of magnetic sensors is placed in to the below of overhead transmission line, gathers array of magnetic sensors output signal;

2) by signal successively by being transferred to data processing equipment after filtering circuit and amplifying circuit;

3) data processing equipment is processed to the received signal, obtains the magnetic flux density information of current carrying conductor, and by analyzing the feature of this magnetic flux density, obtains the zero-sequence current of current carrying conductor;

If transmission line of electricity is phase three-wire three overhead transmission line, described array of magnetic sensors is that two Magnetic Sensors form array of magnetic sensors;

The calculating of zero-sequence current is specific as follows:

301) two Magnetic Sensor S ₁and S ₂magnetic flux density be respectively B ₁and B ₂, B ₁, B ₂in space coordinates, be decomposed into x, y, tri-components of z are as follows respectively

\{\begin{matrix} B_{1 x} = 0 \\ B_{1 y} = \frac{μ_{0}}{2 π} \cdot (\frac{I_{a}}{l_{1}} \cdot {\cos θ}_{1}^{2} + \frac{I_{b}}{l_{1} + l_{2}} + \frac{I_{c}}{l_{1}} \cdot {\cos θ}_{1}^{2}) \\ B_{1 z} = \frac{μ_{0}}{2 π} \cdot (\frac{I_{a}}{l_{1}} \cdot {\sin θ}_{1} \cdot {\cos θ}_{1} + \frac{I_{c}}{l_{1}} \cdot {\sin θ}_{1} \cdot {\cos θ}_{1}) \end{matrix} - - - (1)

\{\begin{matrix} B_{2 x} = 0 \\ B_{2 y} = \frac{μ_{0}}{2 π} \cdot (\frac{I_{a}}{l_{1} + d} \cdot {\cos θ}_{2}^{2} + \frac{I_{b}}{l_{1} + l_{2} + d} + \frac{I_{c}}{l_{1} + d} \cdot {\cos θ}_{2}^{2}) \\ B_{2 z} = \frac{μ_{0}}{2 π} \cdot (\frac{I_{a}}{l_{1} + d} \cdot {\sin θ}_{1} \cdot {\cos θ}_{1} + \frac{I_{c}}{l_{1} + d} \cdot {\sin θ}_{1} \cdot {\cos θ}_{1}) \end{matrix} - - - (2)

I in upper two formulas _a, I _b, I _cbe respectively three-phase current, μ ₀for air permeability, w is the horizontal range between a phase and b phase, and d is Magnetic Sensor S ₁and S ₂between vertical range, l ₁for Magnetic Sensor S ₁with the vertical range between c phase, l ₂for the vertical range between b phase and c phase, θ ₁for a phase and S ₁between line and b phase and S ₁between the angle of line, θ ₂for a phase and S ₂between line and b phase and S ₂between the angle of line;

302) suppose that the distance between line of electric force and Magnetic Sensor is greater than the distance between line of electric force, i.e. l ₁>>l ₂, the magnetic field effect of three line of electric force can be by the equivalent current I that is positioned at sensor top _vrepresent, wherein, I _vand S ₁between distance be h _v, I _vat measurement point S ₁, S ₂place produces the x of magnetic flux density, _y, z axle component represents suc as formula (3) and (4);

\{\begin{matrix} B_{1 vx} = 0 \\ B_{1 vy} = \frac{μ_{0} \cdot I_{v}}{{2 πh}_{v}} \\ B_{1 vz} = 0 \end{matrix} - - - (3)

\{\begin{matrix} B_{2 vx} = 0 \\ B_{2 vy} = \frac{μ_{0} \cdot I_{v}}{2 π (h_{v} + d)} \\ B_{2 vz} = 0 \end{matrix} - - - (4)

From (3), (4) formula, by I _vthe magnetic flux density producing only comprises y axle component, in zero sequence current measurement, can assert virtual current I _vwith I _a, I _b, I _cat S ₁, S ₂the y axle component that place produces magnetic flux density is identical, i.e. B _1y=B _1vy, B _2y=B _2vy, the y axle component in (1), (2) formula is substituted into (3), (4) formula, can obtain I _vwith I _a, I _b, I _cbetween relational expression (5);

\{\begin{matrix} I_{v} = \frac{d \cdot [l_{1} I_{b} + (I_{a} + I_{c}) (l_{1} + l_{2})] \cdot [(l_{1} + d) I_{b} + (I_{a} + I_{c}) (l_{1} + l_{2} + d)]}{(l_{1} + d) (l_{1} + l_{2} + d) [l_{1} I_{b} + (l_{1} + l_{2}) (I_{a} + I_{c})] - l_{1} (l_{1} + l_{2}) [(l_{1} + d) I_{b} + (I_{a} + I_{c}) (l_{1} + l_{2} + d)]}, when {\cos θ}_{1,2} \approx 1 \\ I_{v} = \frac{(I_{a} {\cos θ}_{i}^{2} + I_{b} + I_{c} {\cos θ}_{i}^{2}) \cdot [{\cos θ}_{i}^{2} (I_{a} + I_{c}) (l_{1} + d) + I_{b} (l_{1} + d {\cos θ}_{i})]}{(l_{1} + d) (l_{1} + d {\cos θ}_{i}) (I_{a} {\cos θ}_{i}^{2} + I_{b} + I_{c} {\cos θ}_{i}^{2}) - l_{1} [{\cos θ}_{i}^{2} (I_{a} + I_{c}) (l_{1} + d) + I_{b} (l_{1} + d {\cos θ}_{i})]}, when l_{1} > > l_{2}, i = 1 or 2 \\ I_{v} = I_{a} + I_{b} + I_{c}, when {\cos θ}_{1,2} \approx 1, l_{1} > > l_{2} \end{matrix} - - - (5)

Suppose l ₁>>l ₂, in addition, due to l ₁>>w and l ₁+ d>>w, cos θ ₁≈ cos θ ₂; Therefore, virtual current I _vcan be reduced to (6) formula;

I _v＝f(I _a,I _b,I _c)＝(I _a+I _b+I _c)＝3I ₀ (6)

(6) formula shows, as long as obtain virtual current I _vjust can try to achieve zero-sequence current I ₀, virtual current I _vcan be calculated by (7) formula, (7) formula draws on the basis of formula (3), (4), wherein B _1vyand B _2vycan pass through respectively Magnetic Sensor S ₁, S ₂measure;

I_{v} = \frac{2 πd \cdot B_{1 vy} \cdot B_{2 vy}}{μ_{0} (B_{1 vy} - B_{2 vy})} - - - (7)

。

2. the measuring method of a kind of power transmission line zero-sequence electric current based on array of magnetic sensors according to claim 1, it is characterized in that, if transmission line of electricity is three-phase and four-line overhead transmission line, described array of magnetic sensors is two or three Magnetic Sensors composition array of magnetic sensors.

3. the measuring method of a kind of power transmission line zero-sequence electric current based on array of magnetic sensors according to claim 2, is characterized in that, if adopt two Magnetic Sensors, and being calculated as follows of zero-sequence current:

Article four, line of electric force is equivalently represented by a virtual wires, and equivalent current can be expressed as follows:

I _v＝I _a+I _b+I _c+I _n＝3I ₀+I _n＝I _r (8)

Wherein, I _vfor virtual current, I _a, I _b, I _cbe respectively three-phase current, I ₀for zero-sequence current, I _nfor current in middle wire, I _rfor aftercurrent;

I _vor I _rby Magnetic Sensor S ₁, S ₂the magnetic flux density recording is calculated, B ₁, B ₂y axle component be shown below:

\{\begin{matrix} B_{1 y} = \frac{μ_{0} I_{a}}{{2 πl}_{1}} {({\cos θ}_{1})}^{2} + \frac{μ_{0} I_{b}}{2 π (l_{1} + l_{2})} + \frac{μ_{0} I_{c}}{{2 πl}_{1}} {({\cos θ}_{1})}^{2} + \frac{μ_{0} I_{n}}{{2 πl}_{3}} \\ B_{2 y} = \frac{μ_{0} I_{a}}{2 π (l_{1} + d)} {({\cos θ}_{2})}^{2} + \frac{μ_{0} I_{b}}{2 π (l_{1} + l_{2} + d)} \\ + \frac{μ_{0} I_{c}}{2 π (l_{1} + d)} {({\cos θ}_{2})}^{2} + \frac{μ_{0} I_{n}}{2 π (l_{3} + d)} \end{matrix} - - - (3)

Above formula, wherein μ ₀for air permeability, w is the horizontal range between a phase and b phase, and d is Magnetic Sensor S ₁and S ₂between vertical range, l ₁for Magnetic Sensor S ₁with the vertical range between c phase, l ₂for the vertical range between b phase and c phase, l ₃for Magnetic Sensor S ₁with the vertical range between n phase, θ ₁for a phase and S ₁between line and b phase and S ₁between the angle of line, θ ₂for a phase and S ₂between line and b phase and S ₂between the angle of line;

I _vutilize equation (7) to calculate, then according to equation (8), utilize the corresponding I of each line construction _n/ I ₀ratio can calculate zero-sequence current.

4. the measuring method of a kind of power transmission line zero-sequence electric current based on array of magnetic sensors according to claim 3, is characterized in that, if adopt three Magnetic Sensors, and being calculated as follows of zero-sequence current:

See three-phase power line as a virtual wires, center line is positioned at virtual wires below, three Magnetic Sensor S ₁, S ₂, S ₃vertically be positioned at the below of B phase conductor, see three-phase power line as a virtual wires, center line is positioned at virtual wires below, and equivalent current can be expressed as follows:

I _v＝I _a+I _b+I _c＝3I ₀+I _n (10)

S ₁, S ₂, S ₃the magnetic flux density at place is represented by formula (11), I _vwith B _1vy, B _2vy, B _3vybetween relation suc as formula shown in (12);

\{\begin{matrix} B_{1 y} = \frac{μ_{0}}{2 π} \cdot (\frac{I_{1}}{l_{1}} \cdot {\cos θ}_{1}^{2} + \frac{I_{2}}{l_{1} + l_{2}} + \frac{I_{3}}{l_{1}} \cdot {\cos θ}_{1}^{2} + \frac{I_{n}}{l_{3}}) \\ B_{2 y} = \frac{μ_{0}}{2 π} \cdot (\frac{I_{1}}{l_{1} + d_{1}} \cdot {\cos θ}_{2}^{2} + \frac{I_{2}}{l_{1} + l_{2} + d_{1}} \\ + \frac{I_{3}}{l_{1} + d_{1}} \cdot {\cos θ}_{2}^{2} + \frac{I_{n}}{l_{3} + d_{1}}) \\ B_{3 y} = \frac{μ_{0}}{2 π} \cdot (\frac{I_{1}}{l_{1} + d_{1} + d_{2}} \cdot {\cos θ}_{3}^{2} + \frac{I_{2}}{l_{1} + l_{2} + d_{1} + d_{2}} \\ + \frac{I_{3}}{l_{1} + d_{1} + d_{2}} \cdot {\cos θ}_{3}^{2} + \frac{I_{n}}{l_{3} + d_{1} + d_{2}}) \end{matrix} - - - (11)

\{\begin{matrix} B_{1 vy} = \frac{μ_{0}}{2 π} [\frac{1}{h_{v}} I_{v} + \frac{1}{l_{3}} I_{n}] \\ B_{2 vy} = \frac{μ_{0}}{2 π} [\frac{1}{(h_{v} + d_{1})} I_{v} + \frac{1}{(l_{3} + d_{1})} I_{n}] \\ B_{3 vy} = \frac{μ_{0}}{2 π} [\frac{1}{(h_{v} + d_{1} + d_{2})} I_{v} + \frac{1}{(l_{3} + d_{1} + d_{2})} I_{n}] \end{matrix} - - - (12)

B1 _y, B2 _y, B3 _yby Magnetic Sensor, measured, in zero sequence current measurement, can assert virtual current I _v, I _nwith I _a, I _b, I _c, I _nat S ₁, S ₂, S ₃the y axle component that place produces magnetic flux density is identical, i.e. B _1y=B _1vy, B _2y=B _2vy, B _3y=B _3vy, the variable I in formula (12) _v, h _v, I _nbe unknown, can obtain by solving formula (12), final, according to equation (10), solve zero-sequence current.