CN101267116B - An automatic positioning method for power quality interference source of distribution grid - Google Patents

Abstract

The present invention provides an automatic location method of distribution network power quality disturbance source, including: (A) constructing a network power quality monitor system in the distribution network; (B) constructing a rooted tree of the distribution system according to the topology of the distribution network; (C) establishing a system covering matrix according to the position relation between each node of the rooted tree and the each power quality monitor device; (D) establishing a system direction matrix according to the judging result of disturbance direction of each PQM when the disturbance is happened; (E) processing primary disturbance source location operation according to the system cover matrix and the system direction matrix. The invention provides a disturbance source location by itself, a disturbance source location method of the distribution network power quality having high efficiency.

Description

A method for automatic location of power quality disturbance source in distribution network

technical field

The invention relates to an automatic positioning method of a power quality disturbance source in a power system network.

Background technique

At present, research hotspots related to power quality in power systems mainly focus on the following aspects: identification and processing of power quality signals, power quality evaluation indicators, power quality monitoring devices and system structures, power quality control, etc. However, the location technology of the disturbance source after the power quality event is also very important, not only helps the power department and the user to determine the responsibility and the reasonable settlement of the dispute, but also plays an important role in guiding the power department to formulate power quality mitigation and control strategies .

There are few studies on the location method of power quality disturbance source, and there are mainly two types of methods:

1. A method for judging the direction of the disturbance source based on a single measuring point. According to a single power quality monitoring device (PQM) arranged in the power system, the disturbance source direction determination algorithm corresponding to various event types is studied. For example, when a voltage sag event or a harmonic event occurs in the power system, methods based on disturbance power and disturbance energy, and based on the sign of the real part of the equivalent impedance can be used to determine whether the disturbance event occurs in the forward or backward direction of the monitoring point .

The disadvantage of this method is that it can only determine the front and rear directions of the disturbance source relative to the monitoring point, and when a power quality event occurs in the power network, it cannot really realize the precise location of the disturbance source (such as locating to a specific line). ).

2. Judgment method based on disturbance direction relationship table. According to the network structure and the arrangement of PQM in the system, write out in advance the disturbance source position in the system and the disturbance direction relationship table between each PQM. When an actual disturbance event occurs in the system, the disturbance direction is determined according to the measurement data of each monitoring point, and compared with the relational table, the disturbance source can be located.

The disadvantages of this method are: it is necessary to rely on manual comparison to locate the disturbance source, and the work efficiency is low; the automatic programming calculation and analysis of the computer cannot be performed, and the automatic positioning of the disturbance source cannot be realized; in some cases, when there is a fuzzy target disturbance source , cannot achieve precise positioning.

Contents of the invention

In order to overcome the deficiencies of manual positioning, low efficiency, and inability to realize automatic positioning in the existing distribution network power quality disturbance source positioning method, the present invention provides a distribution network power quality disturbance source that automatically locates the disturbance source and has high efficiency Automatic positioning method.

The technical solution adopted by the present invention to solve its technical problems is:

An automatic precise positioning method of a power quality disturbance source, the automatic precise positioning method comprising:

(A) Established networked power quality monitoring system: install a power quality monitoring device PQM in the lines of the radial distribution system, and the PQM communicates with the regional power quality management center at high speed, and sends each power quality monitoring Real-time monitoring data or analysis results of monitoring points;

(B) According to the known distribution system topology, construct a rooted tree structure diagram commonly used in power system analysis, and identify the layout of each PQM in the system;

(C) Establishing a system coverage matrix, the system coverage matrix _AL×M is:

Among them, L is the number of nodes in the rooted tree, that is, the number of line segments in the system; M is the number of PQMs actually configured in the system, and each data a _ij of the matrix A _L×M represents the jth PQM layout point in the system The position relationship with the i-th node, if Li is located in the backward area of Mj, then set a _ij =+1; if Li is located in the forward area of Mj, then set a _ij =-1,

The backward area of Mj refers to the jth PQM layout node and the child node area of the node; the forward area of Mj refers to other node areas except the backward area;

(D) Establishing a system direction matrix, the system direction matrix B _{M × 1} is:

Among them, each data b _j of the matrix B _M×1 represents the judgment result of the direction of the disturbance source of the j-th PQM when a disturbance event occurs at the i-th line segment position in the system. If it is determined to be a backward disturbance, the disturbance source is determined Located in the backward area of the jth PQM, set b _j =+1; otherwise, if it is determined to be a forward disturbance, set b _j =-1;

(E) Perform a simple matrix multiplication operation on the aforementioned system coverage matrix and system direction matrix, and obtain the result matrix _CL×1 as:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\begin{array}{c}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right]$

The value of each element c _i in the result matrix is related to the power network topology and PQM arrangement; according to the element value of the result matrix, if the element value in the result matrix C is equal to the number of elements of the PQM quantity M arranged in the system If it is exactly 1, it is confirmed that the line segment Li corresponding to the element _ci in this row is the power quality disturbance source.

As a preferred solution: in the step (E), if the element value in the result matrix C is equal to the number of elements of the PQM quantity M arranged in the system and the number of elements is greater than 1, it means that there are fuzzy items in the result matrix, and the disturbance source exists Enter the next step among the line segments corresponding to the several elements;

The automatic precise positioning method also includes:

(F) If the judgment fuzzy item in the step (E), arrange the corresponding virtual PQM at the corresponding line segment, and write the corresponding serial number to the newly added virtual PQM in the rooted tree of the system; according to Ohm's law, Kirchhoff The law and the parameter information of the distribution line realize the calculation of the state quantity of the unarranged PQM node;

(G) build extended coverage matrix and extended direction matrix: according to the new system rooted tree structure after defining virtual PQM in (F) step, construct system extended coverage matrix and system extended direction matrix:

(G1) Construct a new system expansion coverage matrix A'_L×M' as:

Among them, M' is the sum of the number of PQM actually configured in the system and the virtual PQM defined in step (F), and the number of columns that the extended covering matrix A'_L×M' has more than the covering matrix A _L×M is equal to the rooted tree The number of virtual PQMs added in ;

(G2) Construct a new system expansion direction matrix B′ _M′×1 as:

Similarly, the number of rows more than the direction matrix _B'M'×1 in the extended direction matrix B'M _'×1 is equal to the number of virtual PQMs increased in the rooted tree;

(G3) Accurate positioning operation of disturbance source: perform matrix multiplication operation on the aforementioned system expansion coverage matrix and system expansion direction matrix, and obtain the expansion result matrix C′ _L×1 as:

${{\mathrm{<span\; class="notranslate">\; C</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; *</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\begin{array}{c}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\left[\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ {{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right]$

In the extended result matrix C′ _L×1 , it is guaranteed that the number of elements equal to the sum of the actual PQM and the virtual PQM quantity M′ is exactly 1, then it is confirmed that the line segment Li corresponding to the row element c′ _i is the power quality source of disturbance.

As another preferred solution: the step (B) comprises the following steps:

(B1) The network topology is constructed as a rooted tree structure by adopting the method of storing a distribution line segment at each node, wherein each node serial number is consistent with the corresponding line segment serial number in the topology diagram;

(B2) Distinguish between nodes configured with PQM and nodes not configured with PQM in the system, and assign serial numbers to each PQM for identification.

The technical idea of the present invention is: in the radial power distribution system, according to the system topology and PQM layout, using simple matrix definition and calculation, the purpose of automatic and precise positioning of power quality disturbance sources can be realized.

The method of the invention mainly involves the definition and operation of the matrix, the algorithm is simple, easy to be realized by computer programming, and has strong practical significance for the realization of the power quality diagnosis function in the networked power quality monitoring system.

If there are fuzzy items in the result matrix, and the disturbance source exists in the line segment corresponding to the several elements, then the newly added virtual PQM node is calculated according to Ohm's law, Kirchhoff's law and the parameter information of the distribution line. After obtaining the electrical state quantities of the nodes, according to the single-PQM-based power quality disturbance source direction determination algorithm consistent with step (D), the relative positional relationship between the disturbance source and the virtual PQM node can be determined, and the system extended coverage can be constructed Matrix and system expansion direction matrix can accurately locate the source of power quality disturbance.

The beneficial effects of the present invention are mainly manifested in: 1. Automatically locate the disturbance source with high efficiency; 2. For the disturbance source exists in several candidate line segments, but the specific line segment cannot be determined, the fuzzy items can be effectively eliminated, and accurate position.

Description of drawings

Figure 1 is a topology of a radial power distribution system;

Fig. 2 is the rooted tree structure constructed according to system topology diagram and PQM arrangement situation among the present invention;

Fig. 3 is after defining the virtual PQM among the present invention, the system of reconstruction has rooted tree structure;

Figure 4 is a schematic diagram of the method of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

Referring to Figures 1 to 4, an automatic precise positioning method for a power quality disturbance source, the automatic precise positioning method includes: (A) a networked power quality monitoring system established: installing power Quality monitoring device PQM, said PQM communicates with the regional power quality management center at high speed, and sends real-time monitoring data or analysis results of each power quality monitoring point to the management center;

(B) According to the known distribution system topology, construct a rooted tree structure diagram commonly used in power system analysis, and identify the layout of each PQM in the system;

(C) Establishing a system coverage matrix, the system coverage matrix _AL×M is:

Among them, L is the number of nodes in the rooted tree, that is, the number of line segments in the system; M is the number of PQMs actually configured in the system, and each data a _ij of the matrix A _L×M represents the jth PQM layout point in the system The position relationship with the i-th node, if Li is located in the backward area of Mj, then set a _ij =+1; if Li is located in the forward area of Mj, then set a _ij =-1, the backward area of Mj The area refers to the jth PQM layout node and the child node area of the node; the forward area of Mj refers to other node areas except the backward area;

(D) Establishing a system direction matrix, the system direction matrix B _{M × 1} is:

Among them, each data b _j of the matrix B _M×1 represents the judgment result of the direction of the disturbance source of the j-th PQM when a disturbance event occurs at the i-th line segment position in the system. If it is determined to be a backward disturbance, the disturbance source is determined Located in the backward area of the jth PQM, set b _j =+1; otherwise, if it is determined to be a forward disturbance, set b _j =-1;

(E) Perform a simple matrix multiplication operation on the aforementioned system coverage matrix and system direction matrix, and obtain the result matrix _CL×1 as:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\begin{array}{c}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right]$

The value of each element c _i in the result matrix is related to the power network topology and PQM arrangement; according to the element value of the result matrix, if the element value in the result matrix C is equal to the number of elements of the PQM quantity M arranged in the system If it is exactly 1, it is confirmed that the line segment Li corresponding to the element _ci in this row is the power quality disturbance source.

In the step (E), if the element value in the result matrix C is equal to the number of elements of the PQM quantity M arranged in the system and the number of elements is greater than 1, it means that there are fuzzy items in the result matrix, and the disturbance source exists in the corresponding In the line segment, go to the next step;

The automatic precise positioning method also includes:

(F) If the judgment fuzzy item in the step (E), arrange the corresponding virtual PQM at the corresponding line segment, and write the corresponding serial number to the newly added virtual PQM in the rooted tree of the system; according to Ohm's law, Kirchhoff The law and the parameter information of the distribution line realize the calculation of the state quantity of the unarranged PQM node;

(G) build extended coverage matrix and extended direction matrix: according to the new system rooted tree structure after defining virtual PQM in (F) step, construct system extended coverage matrix and system extended direction matrix:

(G1) Construct a new system expansion coverage matrix A'_L×M' as:

Among them, M' is the sum of the number of PQM actually configured in the system and the virtual PQM defined in step (F), and the number of columns that the extended covering matrix A'_L×M' has more than the covering matrix A _L×M is equal to the rooted tree The number of virtual PQMs added in ;

(G2) Construct a new system expansion direction matrix B′ _M′×1 as:

Similarly, the number of rows more than the direction matrix B _{M × 1} in the extended direction matrix B′ _{M′ × 1} is equal to the number of virtual PQMs increased in the rooted tree;

(G3) Accurate positioning operation of disturbance source: perform matrix multiplication operation on the aforementioned system expansion coverage matrix and system expansion direction matrix, and obtain the expansion result matrix C′ _L×1 as:

${{\mathrm{<span\; class="notranslate">\; C</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; *</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\begin{array}{c}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\left[\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ {{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right]$

In the extended result matrix C′ _L×1 , it is guaranteed that the number of elements equal to the sum of the actual PQM and the virtual PQM quantity M′ is exactly 1, then it is confirmed that the line segment Li corresponding to the row element c′ _i is the power quality source of disturbance.

Described step (B) comprises the following steps:

(B1) The network topology is constructed as a rooted tree structure by adopting the method of storing a distribution line segment at each node, wherein each node serial number is consistent with the corresponding line segment serial number in the topology diagram;

(B2) Distinguish between nodes configured with PQM and nodes not configured with PQM in the system, and assign serial numbers to each PQM for identification.

This embodiment provides an automatic and accurate positioning method for power quality disturbance sources, which can realize the precise and automatic positioning function of power quality disturbance sources based on simple matrix definition and calculation in a radial power distribution system, as shown in Figure 4. The implementation of this method is as follows:

Step 1. Build a networked power quality monitoring system in the power distribution network. Multi-point PQM can realize high-speed communication with the power quality management center, and send real-time monitoring data or analysis results of each monitoring point to the power quality management center.

Step 2. Construct a rooted tree of the distribution system according to the topology of the distribution network:

Using the method of storing a distribution line section in each node, the network topology of the distribution system is constructed as a rooted tree structure commonly used in power system analysis. Among them, the serial number of each node is consistent with the serial number of the corresponding line segment in the topology diagram, which can clearly indicate the relationship between the nodes; the nodes configured with PQM in the system are distinguished from the nodes without PQM configured, and the serial numbers of each PQM are identified.

Fig. 1 is a topological structure diagram of a radial power distribution system, which is used to demonstrate the present invention. Among them, Li represents the serial number of the line segment in the power distribution system; the small black box on the line segment represents the PQM arranged on the line segment, and Mi represents the serial number of the PQM.

Fig. 2 is the rooted tree structure of the system constructed according to the system topology diagram and PQM arrangement shown in Fig. 1. A circle represents a line segment, and its internal label Li is consistent with the line segment number in the topology diagram. A circle with a solid line indicates that the actual PQM is arranged on this line segment, and its external label Mi is consistent with the serial number of the PQM on this line segment in the topology diagram; a circle with a dotted line indicates that no actual PQM is arranged on this line segment.

Step 3. Establish a system coverage matrix according to the positional relationship between each node in the rooted tree and the PQM:

The number of nodes in the rooted tree shown in Figure 2 is 11, that is, the number of line segments in the power distribution system is 11, and the serial numbers are L1-L11; the number of PQMs actually configured in the system is 6. Accordingly, the system coverage matrix A _11×6 can be defined. Each data a _ij of the matrix A _11×6 represents the positional relationship between the jth PQM arrangement point and the ith node in the system. If Li is located in the backward region of Mj, then let a _ij =+1; if Li is located in the forward region of Mj, then let a _ij =-1.

According to the relative positional relationship between each node in the rooted tree of the system and the PQM, the defined system coverage matrix A _11×6 can be assigned. The system coverage matrix after assignment is:

$\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccccc}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

Taking the first column value in the coverage matrix A as an example, the element value a _i1 reflects the forward or backward positional relationship between the PQM with the serial number M1 and each line segment Li in the system. According to the rooted tree structure, only line segments L2, L4 and L5 are located in the backward area of M1, and other line segments are located in the forward area of M1. Therefore, among the values in the first column of the coverage matrix A, only a ₂₁ , a ₄₁ and a ₅₁ have values of +1, and other elements have values of -1.

Step 4. Establish a system direction matrix according to the judgment results of the disturbance direction of each PQM when the disturbance occurs:

Some existing literatures have proposed some algorithms based on the real-time power quality data obtained by single PQM monitoring to determine the relative positional relationship between various power quality event disturbance sources and monitoring points. When a power quality disturbance event occurs in the power distribution system, each PQM arranged in the system can monitor the disturbance data, and based on this, the type of power quality disturbance event can be identified. When the type of event is confirmed, each PQM can determine the relative positional relationship between the disturbance source of the power quality event and the layout point of the PQM according to the corresponding algorithm.

Accordingly, the system direction matrix B _6×1 can be defined. Each data b _j in the matrix B _6×1 indicates that when a disturbance event occurs at the line segment Li in the hypothetical system, the PQM with the serial number Mj determines the relative position relationship between the disturbance source and its front and back according to the corresponding algorithm. If it is a backward disturbance, set b _j =+1; otherwise, set b _j =-1.

In the system shown in Figure 2, assuming that power quality disturbance events occur on lines L ₄ , L ₈ , and L ₉ respectively, according to the aforementioned rules, the corresponding system direction matrices B _L4 , B _L8 , and B _L9 are assigned values in the three cases for:

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\left(\begin{array}{c}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right)$ ${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; 8</span>}}<span\; class="notranslate">\; =</span>\left(\begin{array}{c}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right)$ ${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; 9</span>}}<span\; class="notranslate">\; =</span>\left(\begin{array}{c}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right)$

Take the system direction matrix B _L4 as an example: Suppose a power quality disturbance event occurs at the line segment _L4 , each PQM arranged in the system monitors it, and determines the relationship between the disturbance source and its front and back positions. It can be seen from Figure 2 that the line segment L ₄ is only a backward area for M1 and M3, so the correct judgment result should be that only b ₁ and b ₃ in the matrix B _L4 have values of +1, and the values of other elements Both are -1.

Step 5. Carry out preliminary disturbance source location calculation according to the system coverage matrix and system direction matrix:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\begin{array}{}\end{array}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right]$

The value of each element _ci in the result matrix C _L×1 is related to the topological structure of the power distribution system and the location of the PQM, which contains the information to determine the source of the power quality disturbance. The most noteworthy information is the element value equal to the number M of PQMs arranged in the system in the result matrix _CL×1 .

According to the different situations in which the element value in the result matrix C _L×1 is equal to the number of elements M arranged in the system, there are two possible conclusions:

(1) If the element value in the result matrix C _L×1 is equal to the number of PQMs M arranged in the system and the number of elements is exactly 1, then it can be confirmed that the line segment Li corresponding to the element c _i in this row is the disturbance of the power quality event source, the automatic location algorithm of the disturbance source ends;

(2) If the element value in the result matrix C _L×1 is equal to the number of elements M arranged in the system and the number of elements is greater than 1, it means that there are fuzzy items in the result matrix, and the disturbance source exists in the line segment corresponding to these elements , but the specific line segment cannot be determined, and fuzzy items need to be further excluded to achieve precise positioning.

In the system shown in Figure 2, assuming that power quality disturbance events occur on lines L ₄ , L ₈ , and L ₉ respectively, according to the system coverage matrix A _11×6 assigned in step 3 and the system direction matrix assigned in step 4 B _L4 , B _L8 , B _L9 , the resulting matrices C _L4 , C _L8 , C _L9 can be determined respectively:

Among them, the result matrices C _L4 and C _L8 conform to the judgment conclusion (1), that is, the number of elements in the result matrices C _L4 and C _L8 whose element values are equal to the number of PQMs arranged in the system is exactly 1, such as the result matrices C _L4 and C _L8 shown in the box. At this time, the line segments _L4 and _L8 corresponding to the fourth row element c ₄ in _CL4 and the fourth row element c 8 in CL8 are determined to be the disturbance sources of the two power quality events. This shows that when a power quality disturbance event occurs on lines L ₄ and L ₈ , according to the simple matrix operation of this step, the disturbance source of the power quality event can be accurately confirmed, and the automatic location algorithm of the disturbance source ends.

However, the number of elements whose value is equal to the number of PQMs arranged in the system in the result matrix C _L9 is greater than 1, which is consistent with the judgment conclusion (2). This shows that there are 4 fuzzy items in the result matrix C _L9 , and the disturbance source exists in the line segments L3, L7, L9 and L11 corresponding to the four elements c ₃ , c ₇ , c ₉ and c ₁₁ , but the specific line segments cannot be determined , it is necessary to further exclude fuzzy items to achieve precise positioning.

Step 6. Nodes in the rooted tree structure that are not configured with actual PQM define virtual PQM:

If there are fuzzy items in the preliminary positioning calculation result in step 5, the algorithm needs to be further improved to eliminate fuzzy items to achieve precise positioning.

According to Ohm's law, Kirchhoff's law and the parameter information of the distribution line, the state quantities of the undistributed PQM nodes can be calculated. In this way, it can be considered that corresponding virtual PQMs are arranged at these line segments, and corresponding serial numbers can be programmed for these newly added virtual PQMs in the system rooted tree. The rooted tree structure of the system that defines the virtual PQM is shown in Figure 3. An external label M′i is added outside the dotted circle in the original system rooted tree structure, indicating the serial number of the virtual PQM defined by this node.

Step 7. Construct an extended coverage matrix and an extended direction matrix, and eliminate fuzzy items to achieve accurate positioning of disturbance sources:

According to the new rooted tree structure of the system after the virtual PQM is defined in step 6, the system expansion coverage matrix A'_L×M' and the system expansion direction matrix B'_M'×1 can be constructed. The number L of line segments in the system has not changed, but the number of PQMs has increased from the original number M of actual configured PQMs to the sum of the number of actual configured PQMs and virtual PQMs M′. Therefore, the number of columns of the system extension coverage matrix A′ _L×M′ and the number of rows of the system extension direction matrix B′ _M′×1 are both increased from the original M to the current M′:

In addition, the meanings and element assignment basis of the other symbols in the system extension coverage matrix A′ _L×M′ and the system extension direction matrix B′ _M′×1 are completely consistent with the system coverage matrix and the system direction matrix. The system expansion coverage matrix A′ _{11 × 10} in the system shown in Fig. 2 and the system expansion direction matrix B′ _L9 when power quality disturbance events occur on the assumption line L ₉ are respectively:

${\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccccccccc}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$ ${{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; 9</span>}}<span\; class="notranslate">\; =</span>\left(\begin{array}{c}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right)$

According to the constructed system expansion coverage matrix and system expansion direction matrix, the same simple matrix multiplication operation as in step 5 is performed to obtain the expansion result matrix C′ _L×1 as:

${{\mathrm{<span\; class="notranslate">\; C</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; *</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\begin{array}{c}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\left[\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ {{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right]$

Accordingly, the extended result matrix C′ _L9 of the system shown in Fig. 2 is:

It can be seen that in the extended result matrix _C′L9 , the number of elements whose element value is equal to the sum M′ of the actual PQM and virtual PQM is exactly 1, and it can be confirmed that the line segment L9 corresponding to the element _c9 in this row is the power quality disturbance source. The fuzzy items in the result of step 5 are eliminated, the disturbance source of the power quality in the system is determined, and the automatic location algorithm of the disturbance source ends.

Through the above invention, in the radial power distribution system, according to the system topology and PQM layout, the automatic and precise positioning of the power quality disturbance source can be realized by using simple matrix definition and calculation.

The implementation of the present invention mainly involves the definition and operation of the matrix. The algorithm is simple, easy to realize by computer programming, and has strong practical significance for the realization of the power quality diagnosis function in the networked power quality monitoring system.

Claims (3)

1. the automatic accurate positioning method in an electrical energy power quality disturbance source, described automatic accurate positioning method comprises:

(A) set up networked electric energy quality monitoring system: equipment for monitoring power quality PQM is installed in the circuit of radial pattern distribution system, described PQM all with the high-speed communication of regional quality of power supply administrative center, and send the real-time Monitoring Data or the analysis result of each electric energy quality monitoring point to administrative center;

(B) according to the network topology structure of known distribution system, make up the rooted tree structure chart of an electric power system, and identify the deployment scenarios of each PQM in the system;

(C) set up system and cover matrix, described system covers matrix and is:

Wherein, L is the number of nodes in the rooted tree, also is the line segment quantity in the system; M is the PQM quantity of actual disposition in the system, matrix A _{L * M}Each data a _IjJ the position relation that PQM arranges node M j and i node Li if Li is positioned at the back to the zone of Mj, then makes a in the expression system _Ij=+1; If Li is positioned at the forward region of Mj, then make a _Ij=-1,

Described Mj's is back to the zone, is meant that j PQM arranges the child node zone of node and this node; The forward region of described Mj is meant and removes the back to extra-regional other node regions;

(D) set up the system orientation matrix, described system orientation matrix B _{M * 1}For:

Wherein, matrix B _{M * 1}Each data b _jWhen disturbance event took place in i line segment position in the expression supposing the system, the disturbing source direction determining result of j PQM if be judged to be the back to disturbance, promptly determined disturbing source and is positioned at the back to the zone of j PQM, then makes b _j=+1; Otherwise,, then make b if be judged to be the forward direction disturbance _j=-1;

(E) aforesaid system covering matrix and system orientation matrix are carried out simple matrix multiplication operation, obtain matrix of consequence C _{L * 1}For:

$C_{L\&times;1}=A_{L\&times;M}*B_{M\&times;1}=\begin{array}{cc}\begin{array}{c}{L}_1\\ L_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ L_i\end{array}\left[\begin{array}{c}{c}_1\\ c_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ c_i\end{array}\right]& \end{array}$

Each element c in the described matrix of consequence _iValue and electric power networks topological structure and PQM arrange related; According to the element value of matrix of consequence,, then confirm this row element c if the element number of the PQM quantity M that element value equals to arrange in the system among the matrix of consequence C is 1 just _iCorresponding line segment Li is the electrical energy power quality disturbance source.

2. the automatic accurate positioning method in electrical energy power quality disturbance as claimed in claim 1 source, it is characterized in that: in described step (E), if the element number of the PQM quantity M that element value equals to arrange in the system among the matrix of consequence C is greater than 1, then there be fuzzy in the ecbatic matrix, disturbing source is present among the line segment of described element correspondence, enters next step;

Described automatic accurate positioning method also comprises:

(F) if judging in the step (E) to exist blurs item, corresponding line segment place is arranged corresponding virtual PQM, and in system's rooted tree, newly-increased virtual PQM is write corresponding sequence number; According to the parameter information of Ohm's law, Kirchhoff's law and distribution line, realize that the quantity of state of not arranging the PQM node calculates;

(G) make up expansion and cover matrix and propagation direction matrix: according to the new system's rooted tree structure behind the defining virtual PQM in (F) step, the constructing system expansion covers matrix and system extension direction matrix:

(G1) the system extension covering matrix A that structure is new ' _{L * M '}For:

Wherein, M ' is the quantity summation of the PQM and the middle virtual PQM that defines of step (F) of actual disposition in the system, M ' _jFor j PQM after the expansion arranges node, expansion covering matrix A ' _{L * M '}Than covering matrix A _{L * M}The virtual PQM number that the columns that has more equals to increase in the rooted tree;

(G2) make up new system extension direction matrix B ' _{M ' * 1}For:

Equally, the propagation direction matrix B ' _{M ' * 1}Analogy is to matrix B _{M * 1}The virtual PQM number that the line number that has more equals to increase in the rooted tree;

(G3) the accurate location computing of disturbing source: aforesaid system extension covering matrix and system extension direction matrix are carried out matrix multiplication operation, and matrix of consequence C ' is expanded _{L * 1}For:

${C^{\&prime;}}_{L\&times;1}={A^{\&prime;}}_{L\&times;M^{\&prime;}}*{B^{\&prime;}}_{M^{\&prime;}\&times;1}=\begin{array}{cc}\begin{array}{c}{L}_1\\ L_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ L_i\end{array}\left[\begin{array}{c}{c^{\&prime;}}_1\\ {c^{\&prime;}}_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {c^{\&prime;}}_i\end{array}\right]& \end{array}$

Described spreading result Matrix C ' _{L * 1}In, guarantee that the element number that element value equals actual arrangement PQM and virtual PQM quantity summation M ' is 1 just, then confirm this row element c ' _iCorresponding line segment Li is the electrical energy power quality disturbance source.

3. the automatic accurate positioning method in electrical energy power quality disturbance as claimed in claim 1 or 2 source is characterized in that:

Described step (B) may further comprise the steps:

(B1) adopt each node to store the method for a distribution line segment, this network topology structure is configured to the rooted tree structure, wherein each node ID is consistent with corresponding line segment sequence number in the topological structure;

(B2) node of configuration PQM in the system is distinguished with the node that does not dispose PQM, and identified for each PQM volume sequence number.

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