CN104899353B - A kind of power quality disturbance localization method based on evidence theory - Google Patents

Abstract

A kind of power quality disturbance localization method theoretical based on evidence fusion, including：Determine system set covering theory A_L×NAnd the direction determining matrix B realized according to two kinds of criterions of power of disturbance and disturbance energy_v,N×1；Structure characterizes the reliability function of each influence factor of perturbation direction result of determination；Fusion treatment is carried out based on the uncertain disturbance direction determining information that D S evidence theories each obtain to two kinds of different criterions；Power quality disturbance locational decision is carried out based on the perturbation direction trip current after fusion and matrix algorithm；The reliability assessment of power quality disturbance positioning result is carried out based on the coincident indicator between more evidence sources.

Description

Electric energy quality disturbance source positioning method based on evidence theory

Technical Field

The invention relates to an electric energy quality disturbance source positioning method based on an evidence theory and considering monitoring reliability, and belongs to the field of electrical engineering and electric energy quality.

Background

In recent years, with the rapid increase of sensitive equipment in a power grid and the continuous promotion of the process of electric power marketization, the economic loss caused by the disturbance of the quality of electric energy is rapidly increased, and people have increasingly strong appeal for determining responsibility. The positioning of a Power Quality Disturbance Source (PQDS) means that when a Power Quality Disturbance event occurs in a target Power grid area, a Power Quality monitoring device (PQM) and a Power Quality monitoring center arranged in a system are used to collect, calculate, analyze and process a Disturbance signal, so as to realize intelligent diagnosis of an accurate line or position of the PQDS. The quick and accurate positioning of the PQDS is a precondition and a basis for a Power management department to find out disturbance reasons as soon as possible, clarify responsibilities, eliminate disturbance sources and take reasonable improvement measures so as to ensure that the Power Quality meets the requirements of users, and is also one of the core advanced functions of a Network Power Quality Monitoring System (NPQMS) in a future intelligent Power distribution Network.

Currently, research hotspots related to power quality mainly focus on the directions of identification processing of power quality signals, power quality evaluation indexes, structures of power quality monitoring devices and systems, power quality optimization and control and the like, and research results on a PQDS positioning method are few. The invention patents with application numbers of 2013104676593 and 2014101006927 respectively provide a voltage sag source positioning method based on limited power quality monitoring points and a method for positioning a fault source by calculating the time difference of monitoring problems by power quality monitoring nodes at two ends of a fault line, but the main idea is to determine the specific fault positions on a small number of lines based on a fault distance measurement mode; the invention patent with application number 2008100612549 provides a PQDS automatic positioning method for a power distribution network based on a matrix algorithm principle, but the positioning accuracy of the method excessively depends on the reliability of a disturbance direction judgment result of each measuring point PQM and the completeness of information; the invention patent with application number 2014105375263 provides a matrix positioning improvement algorithm taking monitoring reliability into account based on a particle swarm optimization algorithm. The invention researches various factors and influence degree characterization functions which influence the reliability of a PQM disturbance direction judgment result and a PQDS intelligent positioning method based on multiple evidence sources, establishes multiple characterization direction judgment information credibility functions, integrates two different disturbance direction criterion information based on an evidence theory to realize the automatic accurate positioning of the PQDS under the condition that part of monitoring information has errors, and provides the reliability evaluation of the positioning result by constructing an evaluation function by using the consistency of the evidence sources.

Disclosure of Invention

The invention aims to solve the problem that the accuracy of the existing PQDS positioning algorithm depends heavily on the reliability of the disturbance direction judgment result and the completeness of direction judgment information of each monitoring point PQM in the NPQMS, comprehensively considers the influence of factors such as disturbance signal strength, disturbance current characteristics, distributed power supply access, state estimation errors and the like on the disturbance direction judgment reliability, provides a PQDS automatic positioning method based on an evidence fusion theory, realizes the accurate positioning of PQDS under the conditions that part of monitoring information is missing or wrong in the NPQMS or the disturbance direction judgment result is not ideal, and can evaluate the reliability of the positioning result.

In order to achieve the above object, the present invention provides a PQDS positioning method based on evidence fusion theory, as shown in fig. 1, the process includes the following steps:

1. determining a system coverage matrix A_L×NAnd a direction decision matrix B_v,N×1. In a power distribution network containing L line segments and N PQMs, the method can be respectively constructed to represent all lines and PQM bitsRelational coverage matrix A_L×NAnd a direction matrix B used for representing a Disturbance direction judgment result of all monitoring points PQM when a Disturbance event occurs at a position in the system according to two different Disturbance direction criteria of Disturbance Power (DP) and Disturbance Energy (DE)_v,N×1. Wherein v-1 represents a criterion according to disturbance power; and v-2 represents the criterion according to the disturbance energy. A. the_L×NAnd B_v,N×1Each element a in_jiAnd b_v,iThe assignment principle of (2) is shown in formulas (1) and (2).

2. And constructing a reliability function representing each influence factor of the disturbance direction judgment result. Defining a concept of 'reliability' of the PQM direction judgment information, and respectively constructing and representing various reliability degree item function indexes for describing the influence degree of various factors such as disturbance signal strength, disturbance current characteristics, distributed power supply access, virtual PQM state estimation errors and the like on the reliability of the disturbance direction judgment result under different situations, thereby realizing the fuzzy quantization of the direction judgment process and the result of each monitoring point.

Step 201, constructing a direction judgment reliability function representing the strength of the disturbance signal. The intensity degree of the disturbing signal characteristic quantity can be represented by the relative ratio of the disturbing signal characteristic quantity measured by the monitoring point and the signal characteristic quantity when the system is stable. Accordingly, the direction judgment reliability gamma for representing the disturbance intensity is constructed_i：

In the formula, E_v(i) Indicating the ith monitoring point when the system is stableA signal characteristic quantity; Δ e_v(i) Represents PQM_iDisturbance signal characteristic quantity; v ═ 1 denotes taking the characteristic quantity as the disturbance power DP; v-2 denotes taking the characteristic quantity as the disturbance energy DE.

Step 202, constructing a direction judgment reliability function representing disturbance current characteristics. Disturbance caused by an unbalanced disturbance source affects the three-phase balance of a system, and simultaneously, certain zero-sequence current exists, and the amplitude of the zero-sequence current is closely related to the position of the PQM relative to a disturbance point: if the disturbance point is located in the backward region of the PQM, the detected zero sequence current amplitude is large; and if the disturbance point is located in the forward region of the PQM, the zero sequence current is smaller. Accordingly, the direction judgment credibility S of the disturbance current characteristic during representing the unbalanced disturbance is constructed_i：

Wherein,

in the formula I₀(i) The root mean square value of the zero sequence current of the monitoring point i is obtained; b_iRepresents PQM_iβ, the determination result of the direction of the disturbance_iIs I₀(i) And all monitoring points I in the system₀(i) The ratio of the average values; a is a constant such that S_iIn the range of [1 to 0.9]The interval is usually 2.2-2.5.

And step 203, constructing a direction judgment credibility function representing the fluctuation characteristics of the disturbance energy. When the disturbance source is positioned, the DE fluctuation characteristics indirectly reflect the possibility of misjudgment of the disturbance direction of the point to some extent. The following disturbance direction judgment principle is drawn up: and if the DE waveform initial peak value is different from the final value symbol or the DE symbol changes at any moment, the reliability of the monitoring point disturbance direction judgment result is reduced. Accordingly, the direction judgment result reliability theta representing the disturbance energy fluctuation characteristics is constructed_i：

In the formula, sigma is a credibility value, and the value range is 0.5-0.75; DE₀(i) Is as follows_iThe DE waveform initial peak value of each monitoring point; DE_R(i) Is the end value of the DE of the ith monitoring point; sgn is a sign function.

Step 204, a direction judgment reliability function for representing the virtual PQM point state estimation error is constructed, the disturbance direction judgment reliability of the virtual PQM point is possibly reduced due to the introduction of the state estimation error, and accordingly, the direction judgment result reliability ξ for representing the virtual PQM point is constructed_i：

Wherein,

in the formula of U_iThe uncertainty corresponding to the confidence coefficient u; x is the number of₁、x₂Measure point i for virtual PQM based on measure point z₁、z₂The state estimation result of (1);as its corresponding measurement function; d_iIs its relative offset; f (d)_i) Is its corresponding constructor.

3. PQDS automatic localization based on evidence fusion theory. The D-S evidence theory has the capability of processing uncertain information, and the uncertain disturbance direction judgment information obtained according to two different criteria of disturbance power and disturbance energy is combined based on the PQDS positioning of the D-S evidence theory, so that the disturbance source positioning is more accurate and credible.

Step 301, constructing an object recognition framework. Setting N PQMs for a target distribution network, and configuring one code for each PQMThe number is formed by the array g_iThe formed recognition framework Θ:

Θ＝{g_i|i＝1,2,3,...,N} (7)

step 302, a basic belief allocation function is constructed. From gamma_i、S_i、θ_iAnd ξ_iAnd comprehensively considering a plurality of angles to construct a comprehensive reliability function. Consider two points: due to S in locating disturbances caused by unbalanced disturbance sources_iCan participate in trust configuration, at which time S_i、θ_iThere may be intersections causing a decrease in the probability of duplication, and thus for S_i、θ_iCarrying out average probability processing to avoid rapid reduction of reliability; to avoid gamma_iAnd if the sum is greater than 1, adopting a minimum function processing mode. Accordingly, a comprehensive reliability function w (i) is constructed:

in the formula, min is a minimum function; mu is the voltage unbalance coefficient, and because the normal voltage unbalance range of the system is 2% -4%, the point of taking mu as 0.04 is used as a boundary point.

And (5) normalizing W (i) according to the definition of the basic credibility distribution function to obtain a new credibility function w (i). Then the basic confidence distribution function m (g)_i)：

Step 303, the perturbation direction is determined as the reliability combination. Two direction criteria of disturbance power and disturbance energy are adopted, one direction criterion corresponds to one basic belief function distribution, and basic belief distribution functions m under two situations can be respectively defined_vAnd corresponding to two sets of directional matrices B_v,N×1. Thus, two groups of disturbance direction basic confidence degree distribution values m with symbol characteristics can be obtained₁(O)、m₂()：

m₁(O):m₁(g₁)b_1,1,m₁(g₂)b_1,2,...,m₁(g_N)b_1,N(10)

m₂():m₂(g₁)b_2,1,m₂(g₂)b_2,2,...,m₂(g_N)b_2,N

Wherein, the focal element O is ∈ theta, b_v,iTwo sets of direction matrixes B_v,N×1The constituent elements of (1); m is_v(g_i) Indicating PQM under two scenarios_iThe direction of (1) determines the reliability.

Because the fused data has symbolic characteristics, the traditional D-S evidence combination rule fails. According to the classical combination formula, the improved combination rule follows the following relationship:

wherein,

wherein m (P) is the basic confidence distribution function after fusion, and focal elements P ∈ theta and K^τIs a collision factor.

4. And (5) disturbance source positioning decision. Defining the merged disturbance direction decision matrix as M_N×1The component element is m (P), and the disturbance positioning matrix C 'based on evidence fusion is obtained through matrix multiplication operation'_L×1：

C’_L×1＝A_L×N*M_N×1(12)

Matrix C'_L×1Value c 'of each element of'_jContains the system PQDS position information, the only maximum value element c'_jm＝max{c’_jJ is 1,2, …, L } corresponding to PQM on the line L_jmNamely the line segment where the PQDS is located in the target power distribution network.

5. And evaluating the reliability of the positioning result of the disturbance source. In order to evaluate the credibility of the positioning result of the disturbance source, the reliability evaluation of the positioning result of a certain time is carried out based on the consistency index among multiple evidence sources. Let { y₁,y₂,...,y_NIs a set of O and identical focal elements, O (y)_k)、(y_k) For its corresponding basic certainty value, the function H is evaluated_i,j：

According to an evaluation function H_i,jThe reliability evaluation of the disturbance source positioning result can be performed according to the following rules: h_i,jThe larger the interference source is, the higher the reliability of the positioning result of the interference source is; in contrast, H_i,jThe smaller the size, the less reliable the localization result, and when H_i,jAnd if the reliability of the positioning result is less than or equal to 0.7, the reliability of the positioning result is not high.

The invention has the following beneficial effects: 1. constructing a credibility function representing various factors influencing the reliability of the judgment of the disturbance direction; 2. adopting a D-S combination rule to fuse disturbance direction judgment credibility matrixes obtained by different evidence sources, and finally obtaining a comprehensive disturbance direction judgment result; 3. and evaluating the accuracy of the positioning result of the disturbance source based on the evidence consistency criterion. 4. In order to realize accurate positioning of the disturbance source under the condition that part of monitoring information is wrong, an electric energy quality disturbance source positioning method based on an evidence theory is provided.

Drawings

FIG. 1 is a flow chart of an embodiment of the method of the present invention.

Fig. 2 is a topology structure diagram of a 9-node radiation type power distribution network.

Fig. 3 is a diagram of dividing the forward region and the backward region of PQM.

Detailed Description

The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited to these examples. The general block diagram of the PQDS positioning scheme based on evidence fusion theory in the embodiment is shown in fig. 1, and includes the following steps:

1. determining a system coverage matrix A_L×NAnd a direction decision matrix B_v,N×1. In a power distribution network containing L line segments and N PQMs, a coverage matrix A for representing the position relation of all lines and the PQMs can be constructed respectively_L×NAnd a direction matrix B for representing disturbance direction judgment results of all monitoring points PQM realized according to two different disturbance direction criteria of disturbance power and disturbance energy when a disturbance event occurs at a position in the system_v,N×1。A_L×NAnd B_v,N×1Each element a in_jiAnd b_v,iThe assignment principle of (2) is shown in formulas (1) and (2).

2. And constructing a reliability function representing each influence factor of the disturbance direction judgment result. Defining a concept of 'reliability' of the PQM direction judgment information, and respectively constructing and representing various reliability degree item function indexes for describing the influence degree of various factors such as disturbance signal strength, disturbance current characteristics, distributed power supply access, virtual PQM state estimation errors and the like on the reliability of the disturbance direction judgment result under different situations, thereby realizing the fuzzy quantization of the direction judgment process and the result of each monitoring point.

Step 201, constructing a direction judgment reliability function representing the strength of the disturbance signal. The intensity degree of the disturbing signal characteristic quantity can be represented by the relative ratio of the disturbing signal characteristic quantity measured by the monitoring point and the signal characteristic quantity when the system is stable. Accordingly, the direction judgment confidence level gamma representing the disturbance intensity is constructed as shown in the formula (3)_i。

Step 202, constructing a direction for characterizing the disturbance currentA confidence function is determined. Disturbance caused by an unbalanced disturbance source affects the three-phase balance of a system, and simultaneously, certain zero-sequence current exists, and the amplitude of the zero-sequence current is closely related to the position of the PQM relative to a disturbance point: if the disturbance point is located in the backward region of the PQM, the detected zero sequence current amplitude is large; and if the disturbance point is located in the forward region of the PQM, the zero sequence current is smaller. Accordingly, the direction judgment credibility S for representing the disturbance current characteristics in the unbalanced disturbance is constructed as shown in the formula (4)_i。

And step 203, constructing a direction judgment credibility function representing the fluctuation characteristics of the disturbance energy. When the disturbance source is positioned, the DE fluctuation characteristics indirectly reflect the possibility of misjudgment of the disturbance direction of the point to some extent. The following disturbance direction judgment principle is drawn up: and if the DE waveform initial peak value is different from the final value symbol or the DE symbol changes at any moment, the reliability of the monitoring point disturbance direction judgment result is reduced. Accordingly, the reliability theta of the direction judgment result representing the fluctuation characteristic of the disturbance energy is constructed as shown in the formula (5)_i。

And step 204, constructing a direction judgment reliability function for representing the virtual PQM point state estimation error, wherein the disturbance direction judgment reliability of the virtual PQM point is possibly reduced due to the introduction of the state estimation error, and accordingly, the direction judgment result reliability ξ for representing the virtual PQM point is constructed as shown in a formula (6)_i。

3. PQDS automatic localization based on evidence fusion theory. The D-S evidence theory has the capability of processing uncertain information, and the uncertain disturbance direction judgment information obtained according to two different criteria of disturbance power and disturbance energy is combined based on the PQDS positioning of the D-S evidence theory, so that the disturbance source positioning is more accurate and credible.

Step 301, constructing an object recognition framework. The target power distribution network is provided with N PQMs, and each PQM is provided with a serial number to form an array g_iThe formed recognition framework theta is shown as formula (7).

Step 302, a basic belief allocation function is constructed. From gamma_i、S_i、θ_iAnd ξ_iAnd comprehensively considering a plurality of angles to construct a comprehensive reliability function. Consider two points: due to S in locating disturbances caused by unbalanced disturbance sources_iCan participate in trust configuration, at which time S_i、θ_iThere may be intersections causing a decrease in the probability of duplication, and thus for S_i、θ_iCarrying out average probability processing to avoid rapid reduction of reliability; to avoid gamma_iAnd if the sum is greater than 1, adopting a minimum function processing mode. Accordingly, a comprehensive reliability function w (i) is constructed as shown in equation (8).

Normalizing W (i) according to the definition of the basic credibility distribution function to obtain a new credibility function w (i), and obtaining a basic credibility distribution function m (g) as shown in a formula (9)_i)。

Step 303, the perturbation direction is determined as the reliability combination. Two direction criteria of disturbance power and disturbance energy are adopted, one direction criterion corresponds to one basic belief function distribution, and basic belief distribution functions m under two situations can be respectively defined_vAnd corresponding to two sets of directional matrices B_v,N×1. Thus, as shown in equation (10), two groups of disturbance direction basic reliability assignment values m with sign characteristics can be obtained₁(O)、m₂()。

Because the fused data has symbolic characteristics, the traditional D-S evidence combination rule fails. According to the classical combination formula, the improved combination rule is shown as formula (11).

4. And (5) disturbance source positioning decision. Defining the merged disturbance direction decision matrix as M_N×1The disturbance positioning matrix C 'based on evidence fusion is obtained through matrix multiplication operation shown in a formula (12)'_L×1。C’_L×1Value c 'of each element of'_jContains the system PQDS position information, the only maximum value element c'_jm＝max{c’_jJ is 1,2, …, L } corresponding to PQM on the line L_jmNamely the line segment where the PQDS is located in the target power distribution network.

5. And evaluating the reliability of the positioning result of the disturbance source. For evaluating disturbance sourcesAnd the credibility of the positioning result provides the reliability evaluation of the positioning result at a certain time based on the consistency index among the multiple evidence sources. Let { y₁,y₂,...,y_NIs a set of O and identical focal elements, O (y)_k)、(y_k) For the corresponding basic confidence value, an evaluation function H as shown in formula (13) can be constructed_i,j。

Accordingly, the reliability evaluation of the PQDS positioning result can be performed according to the following rules: h_i,jThe larger the interference source is, the higher the reliability of the positioning result of the interference source is; in contrast, H_i,jThe smaller the size, the less reliable the localization result, and when H_i,jAnd if the reliability of the positioning result is less than or equal to 0.7, the reliability of the positioning result is not high.

The 9-node 10.5KV power distribution network system with a topological structure shown in FIG. 2 is taken as an example for simulation, and the implementation process of the invention is further explained. The system is provided with 7 PQMs, 2 virtual PQMs and one distributed power supply DG. And (3) building a system simulation model through an MATLAB/simulink simulation software power system module. Setting a line L₇Three typical voltage sag disturbances, namely single-phase grounding short circuit, induction motor starting and capacitor switching, are simulated respectively as disturbance points.

Respectively calculating the gamma of three different disturbances of single-phase grounding, capacitor switching and induction motor according to the step 2_i、S_i、θ_i、ξ_iAnd post-fusion confidence m (P) values, as shown in Table 1.

TABLE 1 confidence values of the various classes

Because the capacitor switching and the induction motor starting are both balance disturbance sources, the disturbance caused by the capacitor switching and the induction motor starting does not need to calculate S_iNumerical values.

According to the structural information and the PQM arrangement information of the power distribution network shown in the attached figure 2, the system coverage matrix obtained according to the step 1 is as follows:

in the formula, the value ± 1 corresponds to the backward region and the forward region of each PQM, respectively. With PQM₃For example, a method for dividing the whole network area into a forward area and a backward area according to the power flow direction of the distribution network is shown, as shown in fig. 3.

Performing disturbance source positioning decision and evaluating the reliability of the positioning result according to the steps 4 and 5, and forming a direction decision matrix M by using M (P) of confidence level_N×1And the coverage matrix A_L×NMultiply and calculate the merit function H_i,jThe positioning results of the obtained evidence fusion based PQDS positioning method are shown in table 2.

TABLE 2 location results of evidence fusion based PQDS location method

Taking an evaluation function H_i,j0.7 is the cut-off point, if H_i,jIf the reliability of the positioning result is less than 0.7, the reliability of the positioning result is not high. The simulation results in table 2 show that, in the case of multiple misjudgments, the method provided by the present invention can still make accurate judgments on the positions of different PQDS, and the credibility of the positioning results is high. In some cases, the number of misjudgments is large, but the evidences have high consistency, so that H is_i,jThe value is higher.

The present invention is well-adapted to carry out the foregoing description, and the foregoing embodiments are merely exemplary embodiments of the present invention and are not intended to limit the scope of the invention, i.e., the equivalent variations and modifications made according to the present invention are covered by the scope of the appended claims.

Claims (1)

1. A method for positioning a power quality disturbance source based on an evidence fusion theory, wherein the power quality disturbance source is called PQDS for short, comprises the following steps:

step 1, determining a system coverage matrix A_L×NAnd a direction decision matrix B_v,N×1(ii) a In a power distribution network containing L line segments and N power quality monitoring devices, the power quality monitoring devices are called PQM for short, and a coverage matrix A for representing the position relationship between all lines and the PQM is respectively constructed_L×NAnd all monitoring points PQM are used for representing the sum of disturbance power when a disturbance event occurs at a certain position in the systemDirection matrix B of disturbance direction judgment results realized by two different disturbance direction criteria of disturbance energy_v,N×1The disturbance power is DP for short and the disturbance energy is DE for short; wherein v-1 represents a criterion according to disturbance power; v-2 represents criterion according to disturbance energy; a. the_L×NAnd B_v,N×1Each element a in_jiAnd b_v,iThe assignment principle of (A) is shown in formulas (1) and (2);

step 2, establishing a reliability function representing each influence factor of the disturbance direction judgment result; defining a concept of 'reliability' of the PQM direction judgment information, and respectively constructing and representing various reliability degree item function indexes for describing the influence degree of various factors of disturbance signal strength, disturbance current characteristics, distributed power supply access and virtual PQM state estimation errors on the reliability of the disturbance direction judgment result under different situations, thereby realizing the fuzzy quantization of the direction judgment process and result of each monitoring point;

step 201, constructing a direction judgment reliability function representing the strength of a disturbance signal; the intensity degree of the disturbing signal characteristic quantity can be represented by a relative ratio of the disturbing signal characteristic quantity measured by the monitoring point and the signal characteristic quantity when the system is stable; accordingly, the direction judgment reliability gamma for representing the disturbance intensity is constructed_i：

<mrow> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mn>0</mn> <mo>&lt;</mo> <mo>|</mo> <mfrac> <mrow> <msub> <mi>&amp;Delta;e</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>E</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> <mo>&lt;</mo> <mn>0.01</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>|</mo> <mfrac> <mrow> <msub> <mi>&amp;Delta;e</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>E</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mn>0.01</mn> <mo>&amp;le;</mo> <mo>|</mo> <mfrac> <mrow> <msub> <mi>&amp;Delta;e</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>E</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> <mo>&amp;le;</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

In the formula, E_v(i) Representing the signal characteristic quantity of the ith monitoring point when the system is stable; Δ e_v(i) Represents PQM_iDisturbance signal characteristic quantity; v ═ 1 denotes taking the characteristic quantity as the disturbance power DP; v-2 represents taking the characteristic quantity as disturbance energy DE;

step 202, constructing a direction judgment reliability function representing disturbance current characteristics; disturbance caused by an unbalanced disturbance source affects the three-phase balance of a system, and simultaneously, certain zero-sequence current exists, and the amplitude of the zero-sequence current is closely related to the position of the PQM relative to a disturbance point: if the disturbance point is located in the backward region of the PQM, the detected zero sequence current amplitude is large; if the disturbance point is located in the forward region of the PQM, the zero sequence current is small; accordingly, the direction judgment credibility S of the disturbance current characteristic during representing the unbalanced disturbance is constructed_i：

<mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>&lt;</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <mn>0.01</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>a</mi> </mrow> </msup> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>&gt;</mo> <mn>0.01</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>&gt;</mo> <mn>0.01</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>~</mo> <mn>0.9</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>&lt;</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <mn>0.01</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

Wherein,

in the formula I₀(i) The root mean square value of the zero sequence current of the monitoring point i is obtained; b_iRepresents PQM_iβ, the determination result of the direction of the disturbance_iIs I₀(i) And all monitoring points I in the system₀(i) The ratio of the average values; a is a constant such that S_iIn the range of [1 to 0.9]Taking 2.2-2.5 in the interval;

step 203, constructing a direction judgment credibility function representing disturbance energy fluctuation characteristics; when the disturbance source is positioned, the DE fluctuation characteristics indirectly reflect the possibility of misjudgment of the disturbance direction of the point to some extent; the following disturbance direction judgment principle is drawn up: if the DE waveform initial peak value is different from the final value symbol or the DE symbol changes at any moment, the reliability of the monitoring point disturbance direction judgment result is reduced; accordingly, the direction judgment result reliability theta representing the disturbance energy fluctuation characteristics is constructed_i：

<mrow> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mi>DE</mi> <mn>0</mn> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mi>DE</mi> <mi>R</mi> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;sigma;</mi> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mi>DE</mi> <mn>0</mn> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mi>DE</mi> <mi>R</mi> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

In the formula, sigma is a credibility value, and the value range is 0.5-0.75; DE₀(i) The DE waveform initial peak value is the ith monitoring point; DE_R(i) Is the end value of the DE of the ith monitoring point; sgn is a sign function;

step 204, constructing a direction judgment reliability function representing a virtual PQM point state estimation error; due to introduction of state estimation errors, ghostThe disturbance direction judgment reliability of the PQM point is possibly reduced, and accordingly, the direction judgment result reliability ξ representing the virtual PQM point is constructed_i：

<mrow> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mn>0</mn> <mo>&lt;</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <mo>&amp;lsqb;</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>f</mi> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

Wherein,

in the formula of U_iThe uncertainty corresponding to the confidence coefficient u; x is the number of₁、x₂Measure point i for virtual PQM based on measure point z₁、z₂The state estimation result of (1);as its corresponding measurement function; d_iIs its relative offset; f (d)_i) For its corresponding constructor;

step 3, automatically positioning PQDS based on evidence fusion theory; the D-S evidence theory has the capability of processing uncertain information, and the uncertain disturbance direction judgment information obtained according to two different criteria of disturbance power and disturbance energy is combined based on the PQDS positioning of the D-S evidence theory, so that the disturbance source positioning is more accurate and credible;

step 301, constructing a target identification framework; the target power distribution network is provided with N PQMs, and each PQM is provided with a serial number to form an array g_iThe formed recognition framework Θ:

Θ＝{g_i|i＝1,2,3,...,N} (7)

step 302, constructing a basic credibility distribution function; from gamma_i、S_i、θ_iAnd ξ_iComprehensively considering a plurality of angles, and constructing a comprehensive reliability function; consider two points: due to S in locating disturbances caused by unbalanced disturbance sources_iCan participate in trust configuration, at which time S_i、θ_iThere may be intersections causing a decrease in the probability of duplication, and thus for S_i、θ_iCarrying out average probability processing to avoid rapid reduction of reliability; to avoid gamma_iIf the value is larger than 1, adopting a minimum function processing mode; accordingly, a comprehensive reliability function w (i) is constructed:

<mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> <mn>2</mn> </mfrac> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>*</mo> <mi>min</mi> <mo>{</mo> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <mo>,</mo> <mn>1</mn> <mo>}</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>&amp;mu;</mi> <mo>&amp;GreaterEqual;</mo> <mn>0.04</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>*</mo> <mi>min</mi> <mo>{</mo> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <mo>,</mo> <mn>1</mn> <mo>}</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>&amp;mu;</mi> <mo>&lt;</mo> <mn>0.04</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>

in the formula, min is a minimum function; mu is a voltage unbalance coefficient, and because the normal voltage unbalance range of the system is 2% -4%, the point of taking mu as 0.04 is a boundary point;

normalizing W (i) according to the definition of the basic credibility distribution function to obtain a new credibility function w (i); then the basic confidence distribution function m (g)_i)：

303, judging a reliability combination according to the disturbance direction; two direction criteria of disturbance power and disturbance energy are adopted, one direction criterion corresponds to one basic belief function distribution, and basic belief distribution functions m under two situations are respectively defined_vAnd corresponding to two sets of directional matrices B_v,N×1(ii) a Thus, two groups of disturbance direction basic reliability distribution values m with symbol characteristics are obtained₁(O)、m₂()：

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>O</mi> <mo>)</mo> </mrow> <mo>:</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;Gamma;</mi> <mo>)</mo> </mrow> <mo>:</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>

Wherein, the focal element O is ∈ theta, b_v,iTwo sets of direction matrixes B_v,N×1The constituent elements of (1); m is_v(g_i) Indicating PQM under two scenarios_iThe direction of (1) determines the reliability;

as the fusion data has symbolic characteristics, the traditional D-S evidence combination rule fails; according to the classical combination formula, the improved combination rule follows the following relationship:

wherein,

wherein m (P) is the basic confidence distribution function after fusion, and focal elements P ∈ theta and K^τIs a conflict factor;

step 4, disturbance source positioning decision; defining the merged disturbance direction decision matrix as M_N×1The component element is m (P), and the disturbance positioning matrix C 'based on evidence fusion is obtained through matrix multiplication operation'_L×1：

C’_L×1＝A_L×N*M_N×1(12)

Matrix C'_L×1Value c 'of each element of'_jContains the system PQDS position information, the only maximum value element c'_jm＝max{c’_jJ is 1,2, …, L } corresponding to PQM on the line L_jmThe PQDS is a line segment of a target power distribution network;

step 5, evaluating the reliability of the positioning result of the disturbance source; in order to evaluate the credibility of the positioning result of the disturbance source, the reliability evaluation of the positioning result of a certain time is carried out based on the consistency index among the multiple evidence sources; let { y₁,y₂,...,y_NIs a set of O and identical focal elements, O (y)_k)、(y_k) For its corresponding basic certainty value, the function H is evaluated_i,j：

<mrow> <msub> <mi>H</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mi>exp</mi> <mo>{</mo> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>&amp;lsqb;</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>O</mi> <mo>(</mo> <msub> <mi>y</mi> <mi>k</mi> </msub> <mo>)</mo> <mo>-</mo> <mi>&amp;Gamma;</mi> <mo>(</mo> <msub> <mi>y</mi> <mi>k</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>

According to an evaluation function H_i,jThe reliability evaluation of the disturbance source positioning result can be performed according to the following rules: h_i,jThe larger the interference source is, the higher the reliability of the positioning result of the interference source is; in contrast, H_i,jThe smaller the size, the less reliable the localization result, and when H_i,jAnd if the reliability of the positioning result is less than or equal to 0.7, the reliability of the positioning result is not high.