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

Abstract

A method for locating power quality disturbance sources based on evidence fusion theory, including: determining the system coverage matrix _AL×N and the direction determination matrix B _v,N×1 based on the two criteria of disturbance power and disturbance energy; The credibility function of each influencing factor of the direction judgment result; based on the D‑S evidence theory, the uncertain disturbance direction judgment information obtained by two different criteria is fused; based on the fused disturbance direction judgment matrix and matrix algorithm, the electric energy Quality disturbance source location decision-making; based on the consistency index among multiple evidence sources, the credibility evaluation of the power quality disturbance source location results is carried out.

Description

A Power Quality Disturbance Source Location Method Based on Evidence Theory

technical field

The invention relates to a method for locating a power quality disturbance source based on evidence theory and taking monitoring reliability into account, belonging to the fields of electrical engineering and power quality.

Background technique

In recent years, with the rapid increase of sensitive equipment in the power grid and the continuous advancement of the power marketization process, the economic losses caused by power quality disturbances have increased rapidly, and people's demands for determination of responsibility have become increasingly strong. Power quality disturbance source (Power Quality Disturbance Source, PQDS) location refers to when a power quality disturbance event occurs in the target grid area, the power quality monitoring device (Power Quality Monitor, PQM) and power quality monitoring center arranged in the system detect the disturbance The signal is collected, calculated, analyzed and processed, and then the intelligent diagnosis of the exact line or position of the PQDS is realized. The rapid and accurate positioning of PQDS is the premise and basis for the power management department to find out the cause of the disturbance as soon as possible, clarify the responsibility, eliminate the source of the disturbance, and take reasonable improvement measures to ensure that the power quality meets the needs of users. One of the core advanced functions of the Network Power Quality Monitoring System (NPQMS).

At present, the research hotspots related to power quality mainly focus on the identification and processing of power quality signals, power quality evaluation indicators, power quality monitoring devices and system structures, power quality optimization and control, etc. There are few research results on PQDS positioning methods. The invention patents with the application numbers 2013104676593 and 2014101006927 proposed a voltage sag source location method based on limited power quality monitoring points and a method of locating the fault source by calculating the time difference between the power quality monitoring nodes at both ends of the fault line to detect the problem, respectively. However, its main idea is to solve the determination of specific fault locations on a small number of lines based on fault distance measurement; the invention patent with application number 2008100612549 proposes a distribution network PQDS automatic positioning method based on the principle of matrix algorithm, but its positioning accuracy is too high Relying on the reliability and completeness of the information of the disturbance direction discrimination results of the PQM of each measuring point; the invention patent with the application number 2014105375263 proposes an improved matrix positioning algorithm based on the particle swarm optimization algorithm and considering the monitoring reliability. The patent of the present invention studies various factors that affect the reliability of the PQM disturbance direction determination results, the influence degree characterization function, and the PQDS intelligent positioning method based on multiple evidence sources, and establishes a variety of characterization direction determination information credibility functions, based on evidence theory The fusion of two different disturbance direction criterion information realizes automatic and accurate positioning of PQDS when some monitoring information is wrong, and proposes to use the consistency of evidence sources to construct an evaluation function to realize the reliability evaluation of positioning results.

Contents of the invention

The present invention overcomes the problem that the accuracy of the existing PQDS positioning algorithm is heavily dependent on the reliability of the PQM disturbance direction determination results of each monitoring point in the NPQMS and the completeness of the direction determination information, and comprehensively considers the strength of the disturbance signal, the characteristics of the disturbance current, and the access of distributed power sources. As well as the influence of factors such as state estimation errors on the reliability of the determination of the disturbance direction, a PQDS automatic positioning method based on the evidence fusion theory is provided to realize that when some monitoring information in NPQMS is missing, wrong or the result of the determination of the disturbance direction is not ideal, Accurate positioning of PQDS can still be achieved, and the credibility of its positioning results can be evaluated.

In order to achieve the above object, the present invention proposes a PQDS positioning method based on evidence fusion theory, as shown in accompanying drawing 1, and its process includes the following steps:

1. Determine the system coverage matrix _AL×N and the direction determination matrix B _v,N×1 . In a power distribution network containing L line segments and N PQMs, the coverage matrix A _L×N used to represent the positional relationship between all lines and PQMs can be constructed respectively, and it can be used to represent all monitoring points when a disturbance event occurs in a certain position in the system PQM is the direction matrix B _v,N×1 of the disturbance direction determination results realized based on two different disturbance direction criteria, the disturbance power (DP) and the disturbance energy (DE). Wherein, v=1 means that the criterion is based on the disturbance power; v=2 means that it is based on the criterion of the disturbance energy. The assignment principles of each element a _ji and b _v,i in AL _×N and B _v,N×1 are shown in formulas (1) and (2).

2. Construct the credibility function representing each influencing factor of the disturbance direction determination result. Define the concept of "credibility" of PQM direction determination information, and construct a variety of reliability sub-item function indicators to describe the strength of disturbance signals, disturbance current characteristics, distributed power access, and virtual PQM state estimation errors. The degree of influence of these factors on the credibility of the results of the disturbance direction determination under different scenarios, so as to realize the fuzzy quantification of the direction determination process and results of each monitoring point.

Step 201, constructing a direction determination credibility function that characterizes the strength of the disturbance signal. The strength of the characteristic quantity of the disturbance signal can be reflected by the relative ratio of the characteristic quantity of the disturbance signal measured at the monitoring point to the signal characteristic quantity when the system is stable. Based on this, the direction judgment credibility γ _i representing the strength of the disturbance is constructed:

In the formula, E _v (i) represents the signal characteristic quantity of the i-th monitoring point when the system is stable; _Δev (i) represents the characteristic quantity of the PQM _i disturbance signal; v=1 means that the characteristic quantity is taken as the disturbance power DP; v=2 It means that the characteristic quantity is taken as the disturbance energy DE.

Step 202, constructing a direction determination credibility function that characterizes the characteristics of the disturbance current. While the disturbance caused by the unbalanced disturbance source affects the three-phase balance of the system, there will also be a certain zero-sequence current, and its amplitude is closely related to the position of the PQM relative to the disturbance point: if the disturbance point is located in the backward direction of the PQM area, the amplitude of the detected zero-sequence current is larger; if the disturbance point is located in the forward area of PQM, the zero-sequence current is smaller. Based on this, the direction determination reliability S _i that characterizes the disturbance current characteristics during unbalanced disturbance is constructed:

in,

In the formula, I ₀ (i) is the RMS value of the zero-sequence current at monitoring point i; b _i represents the result of the determination of the disturbance direction at PQM _i ; β _i is the difference between I ₀ (i) and all monitoring points I ₀ ( i) The ratio of the average value; a is a constant, and generally takes 2.2-2.5 in order to make S _i within the interval [1-0.9].

Step 203, constructing a direction determination credibility function that characterizes disturbance energy fluctuation characteristics. When the disturbance source is located, the DE fluctuation characteristics indirectly reflect the possibility of misjudgment of the disturbance direction at this point to some extent. The following principle for determining the direction of disturbance is proposed: if the initial peak value of the DE waveform is different from the sign of the final value or the sign of DE changes momentarily, the credibility of the result of the determination of the disturbance direction of the monitoring point will be reduced. Based on this, the credibility θ _i of the direction judgment result that characterizes the disturbance energy fluctuation characteristics is constructed:

In the formula, σ is the reliability value, and the value range is 0.5-0.75; DE ₀ (i) is the initial peak value of the DE waveform at the _i -th monitoring point; DE _R (i) is the final value of the DE waveform at the i-th monitoring point; sgn is a symbolic function.

Step 204, constructing a direction determination credibility function that characterizes the state estimation error of the virtual PQM point. Due to the introduction of state estimation errors, the reliability of the determination of the disturbance direction of the virtual PQM point may be reduced. According to this, the credibility _ξi of the direction judgment result representing the virtual PQM point is constructed:

in,

In the formula, U _i is the uncertainty corresponding to the confidence u; x ₁ and x ₂ are the state estimation results of the virtual PQM measuring point i based on the measuring points z ₁ and z ₂ ; is its corresponding measurement function; d _i is its relative offset; f(d _i ) is its corresponding constructor.

3. PQDS automatic positioning based on evidence fusion theory. The D-S evidence theory has the ability to deal with uncertain information. Based on the PQDS positioning of the D-S evidence theory, the combination of the uncertain disturbance direction determination information obtained according to the two different criteria of disturbance power and disturbance energy makes the disturbance source positioning more accurate and reliable. letter.

Step 301, building an object recognition framework. Assuming that the target distribution network has N PQMs, assign a number to each PQM to form an identification frame Θ composed of an array g _i :

Θ={g _i |i=1,2,3,...,N} (7)

Step 302, constructing a basic reliability assignment function. A comprehensive credibility function is constructed from the perspectives of γ _i , S _i , θ _i and ξ _i . Consider two points: Since S _i can participate in the reliability configuration when locating the disturbance caused by the unbalanced disturbance source, at this time S _i and θ _i may overlap and cause the probability of repetition to decrease, so the average probability of S _i and θ _i In order to avoid a rapid decrease in reliability; in order to avoid the situation that γ _i is greater than 1, the minimum value function processing method is adopted. Accordingly, the comprehensive credibility function W(i) is constructed:

In the formula, min is the minimum value function; μ is the voltage unbalance degree coefficient, because the normal voltage unbalance degree of the system ranges from 2% to 4%, take μ=0.04 as the boundary point.

According to the definition of the basic reliability assignment function, a new credibility function w(i) is obtained after W(i) is normalized. Then the basic reliability assignment function m(g _i ):

Step 303, combining the credibility of the disturbance direction determination. Using two direction criteria of disturbance power and disturbance energy, one direction judgment criterion corresponds to a basic reliability function distribution, and the basic reliability distribution function m _v under two scenarios can be defined respectively, and two sets of direction matrices B _v corresponding to _,N×1 . In this way, two sets of basic reliability distribution values m ₁ (O) and m ₂ (Γ) for the disturbance direction with sign characteristics can be obtained:

m ₁ (O):m ₁ (g ₁ )b _1,1 ,m ₁ (g ₂ )b _1,2 ,...,m ₁ (g _N )b _1,N (10)

m ₂ (Γ):m ₂ (g ₁ )b _2,1 ,m ₂ (g ₂ )b _2,2 ,...,m ₂ (g _N )b _2,N

In the formula, the focal element O,Γ∈Θ; b _v,i are the components of two sets of direction matrices B _v,N×1 ; m _v (g _i ) represents the credibility of the direction determination of PQM _i in two scenarios.

Due to the symbolic characteristics of fusion data, the traditional D-S evidence combination rules are invalid. According to the classic combination formula, the improved combination rules follow the following relationship:

in,

In the formula, m(P) is the basic reliability assignment function after fusion, and its focal element P∈Θ; K ^τ is the conflict factor.

4. Disturbance source location decision. Define the fused disturbance direction judgment matrix as M _N×1 , and its constituent elements are m(P), and obtain the disturbance location matrix C' _L×1 based on evidence fusion through matrix multiplication:

C' _L×1 ＝A _L×N *M _N×1 (12)

Each element value c' _j in the matrix C' _L×1 contains the system PQDS position information, and its unique maximum element c' _jm= max{c' _j ,j=1,2,...,L} corresponds to the PQM location The line L _jm is the line segment of the PQDS in the target distribution network.

5. Evaluation of the credibility of the disturbance source location results. In order to evaluate the credibility of the disturbance source location results, the reliability evaluation of a location result based on the consistency index among multiple evidence sources is proposed. Suppose {y ₁ ,y ₂ ,...,y _N } is a set composed of the same focal elements of O and Γ, and O(y _k ), Γ(y _k ) are their corresponding basic reliability values, then the evaluation function H _i,j :

According to the evaluation function H _i,j , the credibility of the disturbance source location results can be evaluated according to the following rules: the larger the H _i,j , the higher the reliability of the disturbance source location results; on the contrary, the higher the H _i,j Smaller, the lower the reliability of the positioning result, and when H _{i,j ≤} 0.7, it is considered that the reliability of the positioning result is not high.

The beneficial effects of the present invention are mainly manifested in: 1. Constructing a credibility function representing various factors that affect the reliability of disturbance direction discrimination; 2. Adopting the D-S combination rule to fuse the disturbance direction discrimination credibility matrix obtained from different evidence sources, Finally, the comprehensive disturbance direction discrimination result is obtained; 3. Realize the evaluation of the accuracy of the disturbance source location result based on the evidence consistency criterion. 4. In order to realize the precise location of the disturbance source when some monitoring information is wrong, a method for locating the power quality disturbance source based on the evidence theory is proposed.

Description of drawings

Fig. 1 is the specific implementation flowchart of the method of the present invention.

Figure 2 is a topology diagram of a 9-node radial distribution network.

Figure 3 is a division diagram of the PQM forward area and backward area.

detailed description

The present invention will be further described in detail below in conjunction with the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto. The overall block diagram of the PQDS positioning scheme based on the evidence fusion theory in the embodiment is shown in Figure 1, including the following steps:

1. Determine the system coverage matrix _AL×N and the direction determination matrix B _v,N×1 . In a power distribution network containing L line segments and N PQMs, the coverage matrix A _L×N used to represent the positional relationship between all lines and PQMs can be constructed respectively, and it can be used to represent all monitoring points when a disturbance event occurs in a certain position in the system The direction matrix B _v,N×1 of the disturbance direction determination results realized by PQM based on two different disturbance direction criteria, disturbance power and disturbance energy. The assignment principles of each element a _ji and b _v,i in AL _×N and B _v,N×1 are shown in formulas (1) and (2).

2. Construct the credibility function representing each influencing factor of the disturbance direction determination result. Define the concept of "credibility" of PQM direction determination information, and construct a variety of reliability sub-item function indicators to describe the strength of disturbance signals, disturbance current characteristics, distributed power access, and virtual PQM state estimation errors. The degree of influence of these factors on the credibility of the results of the disturbance direction determination under different scenarios, so as to realize the fuzzy quantification of the direction determination process and results of each monitoring point.

Step 201, constructing a direction determination credibility function that characterizes the strength of the disturbance signal. The strength of the characteristic quantity of the disturbance signal can be reflected by the relative ratio of the characteristic quantity of the disturbance signal measured at the monitoring point to the signal characteristic quantity when the system is stable. Accordingly, the direction determination credibility γ _i representing the strength of the disturbance is constructed as shown in formula (3).

Step 202, constructing a direction determination credibility function that characterizes the characteristics of the disturbance current. While the disturbance caused by the unbalanced disturbance source affects the three-phase balance of the system, there will also be a certain zero-sequence current, and its amplitude is closely related to the position of the PQM relative to the disturbance point: if the disturbance point is located in the backward direction of the PQM area, the amplitude of the detected zero-sequence current is larger; if the disturbance point is located in the forward area of PQM, the zero-sequence current is smaller. Accordingly, as shown in formula (4), the direction determination reliability S _i that characterizes the disturbance current characteristics during unbalanced disturbance is constructed.

Step 203, constructing a direction determination credibility function that characterizes disturbance energy fluctuation characteristics. When the disturbance source is located, the DE fluctuation characteristics indirectly reflect the possibility of misjudgment of the disturbance direction at this point to some extent. The following principle for determining the direction of disturbance is proposed: if the initial peak value of the DE waveform is different from the sign of the final value or the sign of DE changes momentarily, the credibility of the result of the determination of the disturbance direction of the monitoring point will be reduced. Accordingly, the credibility θ _i of the direction determination result representing the disturbance energy fluctuation characteristics is constructed as shown in formula (5).

Step 204, constructing a direction determination credibility function that characterizes the state estimation error of the virtual PQM point. Due to the introduction of state estimation errors, the reliability of the determination of the disturbance direction of the virtual PQM point may be reduced. According to this, the confidence degree _ξi of the direction judgment result representing the virtual PQM point is constructed as shown in formula (6).

3. PQDS automatic positioning based on evidence fusion theory. The D-S evidence theory has the ability to deal with uncertain information. Based on the PQDS positioning of the D-S evidence theory, the combination of the uncertain disturbance direction determination information obtained according to the two different criteria of disturbance power and disturbance energy makes the disturbance source positioning more accurate and reliable. letter.

Step 301, building an object recognition framework. Assuming that there are N PQMs in the target distribution network, assign a number to each PQM to form an identification frame Θ composed of array g _i , as shown in formula (7).

Step 302, constructing a basic reliability assignment function. A comprehensive credibility function is constructed from the perspectives of γ _i , S _i , θ _i and ξ _i . Consider two points: Since S _i can participate in the reliability configuration when locating the disturbance caused by the unbalanced disturbance source, at this time S _i and θ _i may overlap and cause the probability of repetition to decrease, so the average probability of S _i and θ _i In order to avoid a rapid decrease in reliability; in order to avoid the situation that γ _i is greater than 1, the minimum value function processing method is adopted. Accordingly, the comprehensive credibility function W(i) is constructed as shown in formula (8).

According to the definition of the basic reliability distribution function, W(i) is normalized to obtain a new credibility function w(i), then the basic reliability distribution function m(g _i ) can be obtained as shown in formula (9).

Step 303, combining the credibility of the disturbance direction determination. Using two direction criteria of disturbance power and disturbance energy, one direction judgment criterion corresponds to a basic reliability function distribution, and the basic reliability distribution function m _v under two scenarios can be defined respectively, and two sets of direction matrices B _v corresponding to _,N×1 . In this way, as shown in formula (10), two sets of basic reliability distribution values m ₁ (O) and m ₂ (Γ) for the disturbance direction with sign characteristics can be obtained.

Due to the symbolic characteristics of fusion data, the traditional D-S evidence combination rules are invalid. According to the classic combination formula, the improved combination rule is shown in formula (11).

4. Disturbance source location decision. The fused disturbance direction judgment matrix is defined as M _N×1 , and its constituent element is m(P), and the disturbance location matrix C' _L×1 based on evidence fusion is obtained through matrix multiplication as shown in formula (12). Each element value c' _j in C' _L×1 contains the system PQDS position information, and its unique maximum element c' _jm= max{c' _j ,j=1,2,...,L} corresponds to the line where the PQM is located L _jm is the line segment of PQDS in the target distribution network.

5. Evaluation of the credibility of the disturbance source location results. In order to evaluate the credibility of the disturbance source location results, the reliability evaluation of a location result based on the consistency index among multiple evidence sources is proposed. Suppose {y ₁ ,y ₂ ,...,y _N } is a set composed of the same focal elements of O and Γ, and O(y _k ), Γ(y _k ) are their corresponding basic reliability values, then it can be constructed as Evaluation function H _i,j shown in formula (13).

Accordingly, the credibility evaluation of the PQDS positioning results can be carried out according to the following rules: the larger the H _i,j , the higher the reliability of the disturbance source positioning results; on the contrary, the smaller the H _i,j , the more reliable the positioning results The lower the reliability, and when H _i,j ≤0.7, the positioning result is considered to be less reliable.

Taking the 9-node 10.5KV distribution network system as shown in Fig. 2 as an example for simulation, the implementation process of the present invention is further described. The system is equipped with 7 PQMs and 2 virtual PQMs, and a distributed power supply DG is connected. Build a system simulation model through the power system module of MATLAB/simulink simulation software. The line _L7 is set as the disturbance point, and three typical voltage sag disturbances are respectively simulated: single-phase ground short circuit, induction motor starting and capacitor switching.

According to step 2, the γ _i , S _i , θ _i , ξ _i and the fused reliability m(P) values of three different disturbances of single-phase grounding, capacitor switching, and induction motor are calculated respectively, as shown in Table 1.

Table 1 Various reliability values

Since capacitor switching and induction motor starting are both balanced disturbance sources, there is no need to calculate the value of S _i for the disturbance caused by capacitor switching and induction motor starting.

According to the structural information and PQM layout information of the distribution network shown in Figure 2, the system coverage matrix can be obtained according to step 1 as follows:

In the formula, the value ±1 corresponds to the backward area and forward area of each PQM, respectively. Taking PQM ₃ as an example, it shows the method of dividing the entire network area into a forward area and a backward area according to the power flow direction of the distribution network, as shown in Figure 3.

Follow steps 4 and 5 to make disturbance source location decisions and evaluate the reliability of the location results. Multiply the direction determination matrix M _N×1 formed by the reliability m(P) and the coverage matrix _AL×N , and calculate the evaluation function H _{i, j} The positioning results of the PQDS positioning method based on evidence fusion are shown in Table 2.

Table 2 The positioning results of the PQDS positioning method based on evidence fusion

The evaluation function H _i,j =0.7 is taken as the cut-off point, and if H _i,j <0.7, it is considered that 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 proposed in the present invention can still make accurate judgments on the locations of different types of PQDS, and the positioning results are highly reliable. In some cases, although the number of misjudgments is large, the consistency among the evidence is high, making the H _i,j value high.

As mentioned above, the present invention can be better realized. The above-described embodiments are only typical embodiments of the present invention, and are not used to limit the scope of the present invention. The scope of protection required by the claims of the present invention is covered.

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.