CN114461982B - Power transmission line protection characteristic identification and voltage sag duration estimation method - Google Patents
Power transmission line protection characteristic identification and voltage sag duration estimation method Download PDFInfo
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Abstract
The invention discloses a method for identifying the protection characteristic of a power transmission line and estimating the voltage sag duration, which comprises the steps of identifying the line protection type according to the mean value standard deviation of a sample interval, further providing a DBSCAN clustering method based on Mahalanobis distance and K nearest neighbor algorithm optimization, accurately calculating the line protection action time characteristic, and finally providing a voltage sag duration estimation method based on the protection action characteristic calculation result, so that an extremely important data support is provided for an electric energy quality researcher to evaluate the voltage sag frequency and risk of a power grid in the actual engineering, the subjective assumption and the dependence on other systems are reduced, and the defects of difficulty in implementation and large error of the existing evaluation technology are overcome. With the current cheaper price and wider application of monitoring equipment such as a power quality monitor, a fault recorder and the like, the applicability of the method is continuously improved.
Description
Technical Field
The invention relates to the technical field of voltage sag evaluation, in particular to a method for identifying the protection characteristic of a power transmission line and estimating the voltage sag duration.
Background
Voltage sags can cause sensitive equipment to trip, causing significant industrial losses. The estimation of the voltage sag frequency is an important precondition for solving the problem of voltage sag. In voltage sag frequency estimation, two single-event characteristics of voltage sag are of primary concern, one being voltage magnitude and the other being duration. The accurate voltage sag amplitude and duration estimation result is one of key bases for calculating tripping probability of sensitive equipment and industrial processes, estimating the influence degree and economic loss of sensitive users, calculating power quality indexes of stations and estimating low-voltage ride through performance of wind turbines. For the estimation of the voltage sag amplitude, the existing research is mature. However, there are drawbacks and challenges faced in estimating the voltage sag duration.
In the existing evaluation of the voltage sag duration, the known protection characteristics and fault positions are used for calculating the protection action time so as to estimate the voltage sag duration, but the methods have some defects. First, calculating the protection action time using only the fault location is inaccurate. This is because the triggering of protection is determined according to the fault electrical quantity, which depends not only on the fault location, but also on the factors of fault impedance, fault type, grid operation mode, etc., so estimating the protection action time by the existing method will cause a certain error; second, the existing method is difficult to implement in practical engineering by subjectively assuming that the protection configuration information of the line is a known quantity. This is because there is a discrepancy between the protection system and the power quality system, with obstacles in between, and no direct data connection. If the power quality personnel manually acquire the data of the protection system into the power quality system, the time is wasted, the operation is inconvenient, and the error is easy to occur; third, the protection action time characteristics obtained from the protection system may not accurately describe the actual situation. On one hand, the actual action time and the setting time are different due to uncertainty of the operating mechanism, and on the other hand, the precision of the voltage and current transformer on the protection winding is lower than that of the measurement winding, so that certain deviation may be generated in the action time calculated by data of a protection system.
Furthermore, it is feasible for an engineer having only power quality data to estimate the voltage sag duration by mining power quality history monitoring data to calculate a protection action time characteristic. At present, a large number of electric energy quality monitors are installed in a transformer substation, high-precision voltage/current waveforms are recorded, and abundant accessible historical fault data are stored. Based on the electric energy quality data drive, the protection type and the protection action time characteristic are identified, and the protection action time is calculated, so that a more reliable voltage sag duration evaluation model can be established.
Interpretation of terms:
voltage sag: the Institute of Electrical and Electronics Engineers (IEEE) defines voltage sag as a power quality phenomenon in which an effective value of a supply voltage is rapidly decreased to 0.1 to 0.9p.u., and a duration is 0.5 cycle to 1 min.
Voltage sag amplitude: and the root mean square value of the three-phase voltage in the voltage sag process is the minimum value.
Duration of voltage sag: during the voltage sag event, the voltage magnitude is less than or equal to the duration of the voltage sag threshold (0.9 times the voltage rated per unit).
And (3) rectangular sag: and in the voltage sag process, the lowest voltage amplitude does not change along with time. The waveform diagram of the voltage effective value changing along with the time is approximately rectangular.
Multi-stage temporary drop: in the voltage sag process, due to the influences of factors such as further development of faults and inconsistent protection actions at two ends, the lowest voltage amplitude generates a voltage sag event which changes in stages along with time. The waveform diagram of the voltage effective value changing along with the time is in a step shape.
Protection action time: the time interval from the detection of a fault by the protective relay to the operation of the protective action mechanism to clear the fault.
Protection action time characteristic: the functional relation between the protection action time and the fault electric quantity is manually set.
Fault Electrical Quantity (Fault Electrical Quantity, FEQ): when the power system has a short-circuit fault, a series of electrical variables detected by the relay protection system comprise current, voltage, measured impedance and the like.
Disclosure of Invention
In view of the above problems, the present invention provides a method for identifying the time characteristic of a line protection operation and evaluating the duration of a voltage sag by using the richness, high accuracy and high availability of power quality monitoring data from the viewpoint of data driving, so as to provide an extremely important data support for power quality researchers to evaluate the frequency and risk of the voltage sag of a power grid in actual engineering, reduce subjective assumptions and dependence on other systems, and make up for the defects of difficult implementation and large errors of the existing evaluation technology. The technical scheme is as follows:
a method for identifying protection characteristics of a power transmission line and estimating voltage sag duration comprises the following steps:
step 1: identifying line protection type
Calculating the fault electrical quantity and the protection action time t under each fault event according to the historical monitoring data oc Then identifying the fault type according to the zero sequence current and calculating FEQ-t oc Interval mean standard deviation to identify the protection type;
step 2: calculating a protection action time characteristic
T corresponding to certain protection type based on optimized density-based noise space clustering algorithm oc Clustering FEQ samples, and calculating a protection action time characteristic equation according to a clustering result;
and 3, step 3: assessing duration of voltage sag
Traversing all fault points of the whole network line, determining fault electrical quantity required to be calculated according to fault types and fault positions, substituting the fault electrical quantity into a protection action time characteristic equation of corresponding protection types after calculating the fault electrical quantity, calculating protection action time of the head end and the tail end of the line, and finally evaluating the voltage sag duration time according to the protection action time of the head end and the tail end of the line.
Further, the step 1 specifically includes:
step 1.1: calculating fault electrical quantity and protective action time t based on historical monitoring data oc
Calculating 4 fault electrical quantities when a fault occurs according to the three-phase voltage and current recording data: impedance Z measured between phases P Earth connection measuring impedance Z G Fault current I f And zero sequence current I 0 (ii) a And calculating the protection action time t according to the voltage amplitude change condition oc ：
In the formula, f s For the sampling frequency, N ev The total number of wave recording sampling points of the fault event, n is the serial number of the sampling point, U sag (n) is the voltage sag amplitude at sample point n;
step 1.2: determining fault type
By zero sequence current I 0 Identifying the fault type specifically as follows:
wherein, I unb The maximum unbalanced current generated by two-phase faults of a downstream line at the protection installation position is calculated according to the following formula:
in the formula (I), the compound is shown in the specification,
and &>
When two-phase faults occur at the outlets of the downstream lines, three-phase fault currents at the installation positions are protected;
repeating the step 1.1 and the step 1.2 until all fault events removed by the protection of all lines are calculated;
step 1.3: identifying the line protection type: according to the calculated electric quantity of each fault and the protective action time t under the specific fault type oc The mapping condition of (2) is judged, which fault electrical quantity the protection response is, and then the protection type is identified.
Further, the step 1.3 specifically includes:
step 1.3.1: calculating FEQ-t oc Standard deviation of interval mean
The calculation FEQ-t oc The interval is divided according to the numerical value of the fault electrical quantity, namely the fault electrical quantity is divided into M intervals in the range of the fault sample value on average, and the standard deviation of the protection action time sample of the M interval is expressed as
The calculation formula is as follows:
the mean standard deviation of all intervals was recorded as the mean standard deviation of the sample interval
The calculation formula is as follows:
wherein, t s Is the s-th guard action time sample in the m-th interval, n m Is the number of samples in the m-th interval,
is the average guard action time of the samples in the mth interval;
for the interphase fault sample cut by one circuit breaker, calculating I f -t oc And Z P -t oc Sample interval mean standard deviation of two fault electrical quantities
For a ground fault sample of a circuit breaker cut, calculate I 0 -t oc And Z G -t oc Sample interval mean value standard deviation of two fault electrical quantities>
This step is repeated until all the line breakers' FEQ-t oc Finishing the calculation of the standard deviation of the interval mean value;
step 1.3.2: identifying line protection type
According to standard deviation of sample interval mean value
Calculating the result, and judging whether the mean value standard deviation of the sample interval corresponding to a certain fault electrical quantity is greater than or equal to>
And when the circuit breaker responds to the fault electric quantity, judging the protection type of the circuit breaker configuration as follows:
measured impedance Z by corresponding fault electrical quantity P When the protection type is interphase distance protection;
impedance Z measured by corresponding fault electrical quantity as earth connection G When the protection type is the grounding distance protection;
the corresponding fault electrical quantity is fault current I f When the current is in the normal state, the protection type is interphase current protection;
is a zero-sequence current I by corresponding fault electric quantity 0 And the protection type is zero sequence current protection.
Further, the step 2 specifically includes:
step 2.1: obtaining an optimal clustering radius R and a minimum neighborhood sample number P based on a K nearest neighbor method, and then, for t oc Clustering FEQ samples to obtain a clustering number and an optimal clustering result;
step 2.2: calculating a protection action time characteristic equation
Step 2.2.1: and (3) primarily judging the protection action characteristic according to the number of the clustering clusters: when the number of the clustering clusters is 1, inverse time limit protection is performed; when the number of the clustering clusters is 2, two-stage protection is performed; when the number of the clustering clusters is 3, three-section protection is performed; when the number of the clustering clusters is 4, four-section protection is performed;
step 2.2.2: calculating an inverse time limit protection action time characteristic equation:
fitting the inverse time limit protection characteristic curve based on a least square method, specifically, using a form t = sigma X of a power equation δ + ω perform least squares fit; wherein t is protection action time, X is fault electrical quantity, and sigma, delta and omega are fitting parameters;
step 2.2.3: calculating a stage type protection action time characteristic equation:
when the number of the cluster is 1 and the protection action time t oc When the similarity or the clustering number is more than 1, calculating a protection action time characteristic equation by using a clustering center and a clustering boundary; let the time center of the protection action of each cluster be T ω ω =1,2,3,4, the maximum and minimum values of the electrical fault quantity in each cluster being respectively
And &>
Then the protection action time characteristic equation t oc (X) is calculated as follows:
step 2.2.4: repeating the step 2.2.1 to the step 2.2.3 to obtain action time characteristic equations of phase-to-phase protection and grounding protection configured for all circuit breakers of the whole network line; wherein, the action time characteristic equations of the interphase distance protection, the grounding distance protection, the interphase current protection and the zero sequence current protection are respectively t oc (Z P )，t oc (Z G )，t oc (I f ) And t oc (I 0 )。
Further, the step 2.1 specifically includes:
step 2.1.1: r candidate parameter set for calculating clustering samples based on K nearest neighbor method
The parameter R represents the radius of the clustering process, and samples at distances less than R will be clustered into a class; taking the sample s as the center of a circle, and the circle with the radius R is called the R neighborhood of the sample s; sequentially calculating average nearest neighbor distances under different K values to serve as R candidate parameter sets;
firstly, calculating a distance distribution matrix D, wherein the element of D is the distance between two samples; d is an n-order real symmetric matrix, and n is the total number of samples; each row of D is arranged in ascending order to obtain a new matrix D A (ii) a Then calculate D A The average value of the elements in column K, called
Then->
I.e. the Kth candidate parameter R K All R candidate parameters become R candidate parameter sets, R K The calculation formula is as follows:
wherein D is M (s, K) denotes the Mahalanobis distance matrix D A Elements of the middle s row and the K column; the modified mahalanobis distance between samples s and p is calculated as follows:
wherein X s And X p Electrical fault quantities, t, for sample s and sample p, respectively s And t p The action times of sample s and sample p, respectively; beta =1 to 5 is an important factor, S c Is the covariance matrix of the sample;
step 2.1.2: computing P candidate parameter sets
P is the minimum sample number in the R neighborhood, and samples larger than the P number in the R neighborhood of the sample s are clustered into a cluster; for each value of K, calculating R K The number of samples within the radius and averaging to obtain the candidate parameter P K (ii) a The calculation formula is as follows:
wherein the content of the first and second substances,
the number of samples in the R domain that are the s-th sample;
step 2.1.3: selecting the best P K And R K
Increasing the value of K from 1, K =1,2, …, n, with corresponding different P K And R K Clustering the samples by using the parameters; the number of clusters C increases with the value of K K Gradually decreased but in a certain K value interval C K Will remain unchanged; when the number of clusters C K The number of clusters C at this time when the number of clusters is kept constant for 5 consecutive times K For optimum, the first K value in the 5 consecutive K values is the optimum K value, corresponding to the parameter R K And P K Is the best;
step 2.1.4: according to the method, the FEQ-t cut off by the interphase protection and the grounding protection configured for each circuit breaker in the whole network oc And respectively carrying out optimized DBSCAN clustering on the samples to obtain the number of clustering categories, and calculating the clustering center of each category.
Further, in step 2.2.2, in the fitting process, a suitable sample needs to be selected to determine the parameter ω, and then the parameter ω is converted into a simple power equation to be fitted linearly, specifically:
select any two samples (X) 1 ,t 1 ) And (X) 2 ,t 2 ) (ii) a X represents the value of the fault electrical quantity corresponding to the protection type, and X = Z P ,Z G ,I f ,I 0 (ii) a Get the equation
Search for samples in a sample (X) 3 ,t 3 ) So that the equation t 3 ·t 3 ＝X 1 ·X 2 If true;
get the equation
t 3 -ω＝σ(X 1 ·X 2 ) δ
By combining the above equations, the expression of ω is solved as follows:
ω＝(t 1 ·t 2 -t 3 ·t 3 )/(t 1 +t 2 -2t 3 )
converting the power function form into a linear model as shown in the following formula;
let T = T- ω, then the values of ln σ and δ are calculated by a linear fitting method, as follows:
wherein n is the total number of samples;
substituting σ, δ into t = σ X δ + omega, obtaining the action time characteristic equation t of inverse time-limit protection oc (X)。
Further, the step 3 of estimating the voltage sag duration according to the protection action time of the head end and the tail end of the line specifically includes:
protective action time t when line head end i and tail end j oc_i And t oc_j When consistent, the voltage sag duration is estimated as follows:
d sag ＝t oc_i ＝t oc_j
protective action time t when line head end i and tail end j oc_i And t oc_j When the voltage sag is inconsistent with the voltage sag, the voltage sag is a multi-stage sag, and the equivalent voltage sag duration is calculated by using a voltage loss method, as shown in the following formula:
in the formula of U sag1 For voltage amplitudes, U, below a predetermined value in the event of the multi-level voltage sag sag2 For a voltage amplitude, t, above a preset value in the event of a multi-level voltage sag oc1 ＝min(t oc_i ，t oc_j ) Is the smaller of the sum, t oc2 ＝max(t oc_i ，t oc_j )。
The invention has the beneficial effects that:
1. the invention provides a line protection type identification method based on sample interval mean value standard deviation. The mapping characteristics of fault electrical quantities and action time in monitoring data are fully mined, the protection configuration condition of the high-voltage transmission line is innovatively and effectively identified on the basis of physical-data information, and the defect that the protection information is difficult to obtain by a traditional voltage sag evaluation method is overcome.
2. The invention further provides a method for calculating the protection action time characteristic based on the optimized DBSCAN clustering and the least square method. Optimal DBSCAN clustering parameters are obtained in a self-adaptive mode through improving the Mahalanobis distance and the K nearest neighbor algorithm, a protection action time characteristic equation is obtained through the least square method or the clustering center-extreme value based on the clustering result driven by monitoring data, and key information is provided for voltage sag duration evaluation.
3. The voltage sag duration evaluation method based on line protection characteristic calculation is typical power quality data driving application, and is a new tool for estimating actual voltage sag duration due to the fact that protection system data are generally difficult to obtain and directly apply. The real protection action characteristic is obtained according to the power quality monitoring data, the subjective assumption of the traditional method and the wrong judgment of the protection action are avoided, and the estimation accuracy of the voltage sag duration can be obviously improved.
Drawings
Fig. 1 shows the mapping relationship between FEQ and toc.
Fig. 2 is a flowchart of a method for identifying the protection characteristic of the transmission line and estimating the voltage sag duration according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments. The invention provides a line protection action time characteristic identification method and a voltage sag duration evaluation method from the perspective of data driving by utilizing the richness, high precision and high availability of electric energy quality monitoring data. The technical scheme of the invention is mainly divided into 3 major steps, namely identifying the line protection type, calculating the time characteristic of the protection action and evaluating the voltage sag duration, wherein the detailed explanation of each step is as follows:
step 1: identifying line protection type
Different types of protection respond to different fault electrical quantities FEQ. To obtain the action time characteristic of the protection-corresponding FEQ, it is necessary to first determine the type of protection installed on the line. In medium and high voltage transmission line configurations, the most common protection types are inter-phase distance protection, ground distance protection, inter-phase current protection, and zero sequence current protection. The FEQ corresponding to each protection and representation in the present invention are shown in table 1.
TABLE 1 FEQ responded to by different protection types
The invention provides a method based on FEQ-t oc And (3) a protection type identification method of the interval mean standard deviation.The method comprises 3 small steps, firstly, the FEQ and the protection action time t under each fault event are calculated according to historical monitoring data oc Secondly, identifying the fault type according to the zero sequence current, and finally, calculating the FEQ-t oc Interval mean standard deviation to identify the protection type.
Step 1.1: computing FEQ and t based on historical monitoring data oc
First, 4 FEQ's, Z, at each failure are calculated P ，Z G ，I f ，I 0 。
The fault electric quantity comprises a voltage effective value, a current effective value, a voltage sag amplitude value, zero sequence current, interphase measurement impedance and grounding measurement impedance. The calculation steps are as follows:
(1) Calculating current effective value, voltage effective value, fault current and voltage sag amplitude
The invention adopts a whole-period root-mean-square calculation method to calculate the effective value. Effective value of three-phase voltage and current
The calculation is shown in formulas (1) to (2):
in which a, b and c are different, N cy The number of sampling points in one period, n is the serial number of the sampling points, u is the instantaneous value of the voltage waveform, and i is the instantaneous value of the current waveform.
Fault current I f Is calculated as the current value of the largest one phase in the three-phase current effective values, namely:
according to the national standard GBV. Pat. No./T30137-2013, voltage sag amplitude U sag And (3) calculating the voltage per unit value of the one-phase voltage with the minimum three-phase voltage according to the formula (4):
in the formula of U nom The voltage is rated effective value.
(2) Zero sequence current
According to a symmetrical component method, a zero-sequence current I flows through the protective installation 0 Is represented by equation (5):
(3) Measuring impedance
The impedance measurement is divided into interphase measurement impedance Z P And a ground measurement impedance Z G . Measuring impedance between phases, e.g. Z of two phases b, c P The calculation formula is shown in formula (6):
measuring impedance of earth of a phase, e.g. Z of a-phase G The calculation formula is shown in formula (7):
in the formula (I), the compound is shown in the specification,
is a three-phase voltage phase quantity, and>
is three-phase current phasor, K is zero-sequence compensation coefficient, and is formed from positive-sequence impedance z of power transmission line 1 And zero sequence impedance z 0 Determining, as shown in equation (8):
secondly, calculating the protection action time t according to the change situation of the voltage amplitude value oc As shown in the following formula:
in the formula, f s Is the sampling frequency, N ev The total number of wave recording sampling points of the fault event is shown, and n is the serial number of the sampling points.
Step 1.2: determining fault type
The power transmission line protection is configured with phase-to-phase protection and grounding protection, and responds to two fault types, namely phase-to-phase short-circuit fault and grounding short-circuit fault respectively. When the power system normally operates or an interphase short circuit occurs, the zero sequence current and the zero sequence voltage are very small, but when the grounding short circuit occurs, the zero sequence current is increased. Therefore, zero sequence current I 0 May be used to identify the type of fault. The invention determines the fault type according to the following formula:
wherein, I unb The maximum unbalanced current generated by two-phase faults of a downstream line at the protection installation position is calculated according to the following formula:
in the formula I l-l When two-phase fault occurs at the outlet of the downstream line, the fault current at the installation position is protected.
And repeating the steps 1.1-1.2 until all fault events removed by the protection of all lines are calculated.
Step 1.3: identifying line protection type
1) Principle of identification
For a certain circuit breaker, the configured interphase protection type can be interphase distance protection or interphase current protection, and the interphase distance protection or the interphase current protection uniquely responds to interphase measurement impedance Z P The latter being exclusively responsive to fault current I f . For the protection of the phase-to-phase currents, the circuit breaker is then dependent on the fault current I f Large and small movements and generating a unique movement time t oc Then I f Will map to t oc A value of (I) f A value of (a) hardly maps t oc A plurality of values of (a) and the action of interphase current protection and Z P Is irrelevant, therefore Z P May map a plurality of significantly different t oc Value since multiple fault events may produce the same Z P Value and different I f The value is obtained.
This law can be explained by fig. 1, fig. 1 FEQ (I) calculated for phase-to-phase fault event removed by phase-to-phase current protection f And Z p ) And t oc The composition of the scattergram, fig. 1 (a) (b) is the step current protection, fig. 1 (c) (d) is the inverse time current protection. It can be seen that regardless of the action time characteristics of the protection, I f For t oc There is a unique mapping relationship, and Z P For t oc There is a one-to-many relationship.
In contrast, for inter-phase distance protection, Z P A value of (d) maps t oc A value of (a) and I f Can map to t oc Two or more values of (a). There is an analogy law in ground protection. Thus, FEQ and t to which different protection types respond are summarized oc The mapping relationship between the two is shown in the following table:
TABLE 2 FEQ to toc mapping for different protection types
Thus, each FEQ and t is calculated for a particular fault type oc Can judge the mapping condition ofWhat FEQ the protection responds to, and thus the type of protection identified
Step 1.3.1) calculating FEQ-t oc Standard deviation of interval mean
The invention calculates FEQ-t oc Determination of FEQ-t by interval mean standard deviation oc And (5) mapping relation. The interval refers to FEQ intervals, such as Int1, int2, int3, etc. in fig. 1, and the dotted line indicates the boundary of the interval. Firstly, dividing FEQ into M intervals in the range of fault sample values, and then t of M-th interval oc Sample standard deviation is expressed as
The calculation formula is shown as (12). The mean standard deviation of all intervals is recorded as the mean standard deviation of the sample interval->
The calculation formula is shown as (13).
Wherein t is s Is the s-th t in the m-th interval oc Sample, n m Is the number of samples in the m-th interval,
is the average t of the samples in the m-th interval oc 。
For the interphase fault sample cut by one circuit breaker, calculating I f -t oc And Z P -t oc Difference between interval mean samples of two FEQ
For a ground fault sample of a circuit breaker cut, calculate I 0 -t oc And Z G -t oc Interval mean sample difference of two FEQs>
This step is repeated until FEQ-t of all line breakers oc And finishing the calculation of the standard deviation of the interval mean value.
Step 1.3.2) identification of line protection type
According to
Calculating the result, when a FEQ corresponds to->
On the smaller hand, the FEQ is the response of the circuit breaker, and the protection type of the circuit breaker configuration can be known from table 1. And judging the interphase protection and the grounding protection configured on the circuit breaker respectively. For example, if t oc -I f And t oc -I 0 Is/are>
If the calculated result is relatively small, the circuit breaker is configured with inter-phase current protection and zero sequence current protection. And traversing the breakers of the whole network, and identifying the protection types configured by all the circuit breakers.
Step 2: calculating protection action time characteristics
The protection action time characteristic can be expressed by an action time equation and is characterized by a functional relation between FEQ and toc. The invention provides a protection action time equation calculation method Based on an optimized DBSCAN (Density-Based Spatial Clustering of Applications with Noise Based on Density) Clustering algorithm and a least square method to obtain t oc FEQ curves, providing a basis for voltage sag duration evaluation. The method comprises 2 small steps, firstly, on the basis of identifying the protection type in the last step, t corresponding to a certain protection type is determined based on an optimized DBSCAN algorithm oc -clustering FEQ samples, and then calculating a protection action time characteristic equation according to the clustering result.
Step 2.1: t based on optimized DBSCAN algorithm oc -FEQ sample clustering
By making a pair t oc -clustering FEQ samples and determining the number of clusters, the protection action time characteristic can be obtained. However, on the premise that the number of clusters is unknown, the clustering method based on density clustering does not need the number of cluster categories, and is suitable for t oc Clustering of FEQ samples, using DBSCAN clustering algorithm as in the present invention. Firstly, 2 clustering parameters, namely an optimal clustering radius R and a minimum neighborhood sample number P, are obtained based on a K nearest neighbor method. And finally, clustering to obtain the clustering number and the optimal clustering result.
Step 2.1.1: and calculating the R candidate parameter set of the clustering sample based on the K nearest neighbor method. The parameter R represents the radius of the clustering process and samples at distances less than R will be clustered into a class. A circle with the sample s as the center and R as the radius is called the R neighborhood of the sample s. In the invention, the average nearest neighbor distances under different K values are sequentially calculated to be used as the R candidate parameter set.
First a distance distribution matrix D is calculated, the elements of D being the distance between two samples. It is clear that D is an n-th order real symmetric matrix, where n is the total number of samples. Each row of D is arranged in ascending order to obtain a new matrix D A . Then calculate D A Average value of elements in column K, called
Then->
I.e. the Kth candidate parameter R K All R candidate parameters become R candidate parameter sets, R K The calculation formula is as follows:
wherein D M (s, K) denotes the Mahalanobis distance matrix D A S rows and K columns. It should be noted that the invention uses the improved mahalanobis distance in the calculation of the sample distance, and the mahalanobis distance is used for calculating the covariance between two samplesA difference distance, which is not affected by the dimension. Meanwhile, the Mahalanobis distance is improved by adding an importance factor beta, so that the importance of the action time dimension in the clustering process is highlighted, and the clustering precision is improved. The modified mahalanobis distance between samples s and p is calculated as follows:
wherein, X s And X p Electrical fault quantities, t, for sample s and sample p, respectively s And t p The action times of sample s and sample p, respectively; beta =1 to 5 is an important factor, S c Is the covariance matrix of the samples.
Step 2.1.2: p candidate parameter sets are computed. P is the minimum number of samples in the R neighborhood. In the R neighborhood of samples s, more than P number of samples will be clustered into one cluster. For each value of K, calculating R K The number of samples within the radius and averaging to obtain the candidate parameter P K . The calculation formula is as follows:
wherein the content of the first and second substances,
the number of samples in the R domain of the s-th sample.
Step 2.1.3: optimum P selection K And R K . Increasing the value of K from 1, K =1,2, …, n, with corresponding different P K And R K The parameters cluster the samples. The number of clusters C increases with the value of K K Gradually decreased but in a certain K value interval C K Will remain unchanged. When the number of clusters C K The number of clusters C at this time when the number of clusters is kept constant for 5 consecutive times K For optimum, the first K value in the 5 consecutive K values is the optimum K value, corresponding to the parameter R K And P K Is most preferred.
Step 2.1.4: according toThe method cuts off the FEQ-t of the interphase protection and the grounding protection configured for each circuit breaker in the whole network oc And respectively carrying out optimized DBSCAN clustering on the samples to obtain the number of the clustering categories, and calculating the clustering center of each category.
Step 2.2: calculating a protection action time characteristic equation
Step 2.2.1: and preliminarily judging the protection action characteristic. The protection action characteristic can be classified into two types, one is staged protection, and the other is inverse time-limited protection. The time characteristic curve of the stage protection presents a discontinuous step-type characteristic, and the time characteristic curve of the inverse time-limit protection presents a continuous curve. Therefore, the protection operation characteristic is preliminarily determined according to the number of clusters, and the following table shows.
TABLE 3 relationship between class Cluster count and protection action time characteristics
| Number of clusters clustered | Protective action time characteristic |
| 1 | Inverse time-limit protection |
| 2 | Two-stage protection |
| 3 | Three-stage protection |
| 4 | Four-stage protection |
Step 2.2.2: method for calculating inverse time limit protection action time characteristicThe process. For the case of cluster number 1, and action time t in the sample oc When the difference is large, namely inverse time limit protection, the method is used for fitting the characteristic curve of the device based on the least square method. Since the action time characteristic of the inverse time-lag protection is in the form of a power function, the form of a power equation t = σ X is adopted δ + ω a least squares fit. In the fitting process, an appropriate sample is selected to determine the parameter ω, and then the parameter ω is converted into a simple power equation linear fitting. The method comprises the following steps:
any two samples (X) are selected 1 ,t 1 )and(X 2 ,t 2 ) (ii) a X represents the value of FEQ corresponding to the protection type, and X = Z P ,Z G ,I f ,I 0 。
Get the equation
Search for samples in a sample (X) 3 ,t 3 ) So that the equation t 3 ·t 3 ＝X 1 ·X 2 If true;
obtain the equation t 3 -ω＝σ(X 1 ·X 2 )δ；
By combining the above equations, we can solve the expression of ω as follows:
ω＝(t 1 ·t 2 -t 3 ·t 3 )/(t 1 +t 2 -2t 3 ) (17)
the power function form is converted into a linear model as shown in equation (18).
Let T = T- ω, then the values of ln σ and δ are calculated by a linear fitting method, as follows:
where n is the total number of samples.
Step 2.2.2.7: substituting σ, δ into t = σ X δ + omega, obtaining the action time characteristic equation t of inverse time-limit protection oc (X)。
Step 2.2.3: and calculating a stage type protection action time characteristic equation. When the number of clusters is 1 and the action time t is oc And when the similarity is close or the clustering number is more than 1, calculating a protection action time characteristic equation by using the clustering center and the clustering boundary. Let t of each cluster oc The centre being T ω ω =1,2,3,4, FEQ maximum and minimum in each cluster being respectively
And &>
Then the protection action time characteristic equation t oc (X) is calculated as>
Step 2.2.4: repeating the steps 2.2.1-2.2.3 to obtain action time characteristic equations of interphase protection and grounding protection configured for all circuit breakers of the whole network circuit, wherein the action time characteristic equations of the interphase distance protection, the grounding distance protection, the interphase current protection and the zero sequence current protection are respectively t oc (Z P )，t oc (Z G )，t oc (I f ) And t oc (I 0 )。
And step 3: assessing duration of voltage sag
The voltage sag duration is important information in the estimation of the voltage sag frequency, and a fault point method is generally adopted for evaluation. The fault point method is to traverse all fault points of the whole network line and calculate the voltage sag duration caused by each fault point in turn. The steps of calculating the voltage sag duration caused by each fault point are as follows:
step 3.1: determining the FEQ required to be calculated according to the fault type and the fault position
Each fault point has four fault types, namely single-phase grounding, two-phase short circuit, two-phase grounding and three-phase short circuit. And determining the FEQ required to be calculated according to the protection type identification result of the line where the fault point is positioned, as shown in the following table.
TABLE 4 FEQ required for calculation for different fault types and protection types
Step 3.2: calculating FEQ to obtain protection action time t oc
After the FEQ required to be calculated is determined according to the table 4, the FEQ at the protection installation positions at two ends of the line is calculated according to the expressions (3) to (8) and the expressions (22) to (31), and the FEQ is substituted into the action time characteristic equation t of the corresponding protection oc (Z P )，t oc (Z G )，t oc (I f ) And t oc (I 0 ) Calculating the protection action time t of the head end i and the tail end j of the line oc_i And t oc_j . If the protection is only installed on the single end of the line, only the protection action time of the single end is calculated.
When a three-phase short circuit f occurs on the line i-j, the per unit distance value of the f point from the head end i of the off-line is set as l, the distance of the f point from the tail end j of the line is set as (1-l), and Z f For fault transition impedance, the formula of the three-phase current value and the voltage value of the node m = i, j at the protection installation site can be represented by the following formula:
in the formula
And &>
Representing the pre-fault voltages at node m and fault point f, respectively. Z is a linear or branched member mf Representing the mutual impedance between node m and fault point f, Z ff The self-impedance of the fault point is represented and calculated by the following formula respectively: />
Wherein Z ii 、Z jj And Z ij Self-and mutual impedances of nodes i, j, respectively, z ij Is the impedance per unit length of line ij.
And when the fault f is an asymmetric short circuit, calculating according to a symmetric component method. When a single-phase fault occurs at the point f, taking the phase a as a reference phase, the three-phase current value and voltage value formulas of the node m = i, j at the protection installation site can be represented by the following formulas:
wherein
For the twiddle factor, superscript (0), (1), (2) denotes zero sequence, positive sequence and negative sequence, and/or>
And
the pre-fault voltages at node m and fault f, respectively.
When a two-phase interphase fault occurs at point f, the following steps are provided:
when a two-phase grounding fault occurs at the point f, the following conditions are provided:
in the formula, Z Δ 、Z ∑ 、Z Π0 、Z Π1 And Z Π2 For the combined resistance change, the calculation formula is as follows:
step 3.3: estimating voltage sag duration
Protection action time t when two ends (i end and j end) of the line are connected oc_i And t oc_j When consistent, the voltage sag duration is estimated as follows:
d sag ＝t oc_i ＝t oc_j (32)
when the protection action time of the two ends of the line is inconsistent, the voltage sag is a multi-stage sag, and the equivalent voltage sag duration is calculated by using a voltage loss method, as shown in the following formula:
in the formula of U sag1 For the multi-stage voltage sag eventLower voltage amplitude in the element, U sag2 For higher voltage amplitudes, t, in the event of such a multistage voltage sag oc1 Is t oc_i And t oc_j The smaller of the two, t oc2 Is t oc_i And t oc_j The larger one.
In summary, the general flow chart of the method of the present invention is shown in fig. 2.
Claims (6)
1. A method for identifying protection characteristics of a power transmission line and estimating voltage sag duration is characterized by comprising the following steps:
step 1: identifying line protection type
Calculating fault electrical quantity and protection action time t under each fault event according to historical monitoring data oc Then, the fault type is identified according to the zero sequence current, and the FEQ-t is calculated oc Interval mean standard deviation to identify the protection type;
step 2: calculating protection action time characteristics
T corresponding to certain protection type based on optimized density-based noise space clustering algorithm oc Clustering FEQ samples, and calculating a protection action time characteristic equation according to a clustering result;
and step 3: assessing voltage sag duration
Traversing all fault points of the whole network line, determining fault electric quantity required to be calculated according to fault types and fault positions, substituting the fault electric quantity into a protection action time characteristic equation of corresponding protection types after calculating the fault electric quantity, calculating protection action time of the head end and the tail end of the line, and finally evaluating voltage sag duration time according to the protection action time of the head end and the tail end of the line; the specific process of the step 3 is as follows:
step 3.1: determining the FEQ required to be calculated according to the fault type and the fault position
Each fault point has four fault types, namely single-phase grounding, two-phase short circuit, two-phase grounding and three-phase short circuit; determining the FEQ required to be calculated by combining the protection type identification result of the line where the fault point is located, specifically:
recognition resultWhen the two-phase short circuit or three-phase short circuit fault occurs during the protection of the inter-phase distance, the FEQ required to be calculated is the inter-phase measurement impedance Z P ；
When the identification result is grounding distance protection, if single-phase grounding or two-phase grounding fault occurs, the FEQ needing to be calculated is grounding measurement impedance Z G ；
When the identification result is interphase current protection, if two-phase short circuit or three-phase short circuit fault occurs, the FEQ needing to be calculated is the fault current I f ；
When the identification result is zero sequence current protection, if single-phase grounding or two-phase grounding fault occurs, the FEQ needing to be calculated is the zero sequence current I 0 ；
Step 3.2: calculating FEQ to obtain protection action time t oc
Calculating the FEQ of the protection installation positions at two ends of the line after determining the FEQ to be calculated, and substituting the FEQ into an action time characteristic equation t of corresponding protection oc (Z P )，t oc (Z G )，t oc (I f ) And t oc (I 0 ) Calculating the protection action time t of the head end i and the tail end j of the line oc_i And t oc_j (ii) a The method specifically comprises the following steps:
when a three-phase short circuit f occurs on the line i-j, the per unit distance value of the f point from the head end i of the off-line is set as l, the distance of the f point from the tail end j of the line is set as (1-l), and Z f For fault transition impedance, the three-phase current value and voltage value formula of the node m = i, j at the protection installation is represented by the following formula:
in the formula (I), the compound is shown in the specification,
and &>
Respectively representing the voltage before the fault of the node m and the voltage before the fault of the fault point f; z mf Representing the mutual impedance between node m and fault f, Z ff The self-impedance of the fault point is represented and calculated by the following formula respectively: />
Wherein Z is ii 、Z jj And Z ij Self-and mutual impedances, z, of nodes i, j, respectively ij Impedance per unit length of line ij;
when the fault f is an asymmetric short circuit, calculating according to a symmetric component method; when a single-phase fault occurs at the point f, taking the phase a as a reference phase, the three-phase current value and voltage value formula of the node m = i, j at the protection installation site is represented by the following formula:
wherein α = e j120 The degree is a rotation factor, the superscripts (0), (1) and (2) represent zero sequence, positive sequence and negative sequence,
and &>
Pre-fault voltages at node m and fault point f, respectively;
when a two-phase interphase fault occurs at point f, the following steps are provided:
when a two-phase grounding fault occurs at point f, the following steps are provided:
in the formula, Z Δ 、Z ∑ 、Z П0 、Z П1 And Z Π2 For the combined resistance change, the calculation formula is as follows:
step 3.3: estimating voltage sag duration
Protective action time t when line head end i and tail end j oc_i And t oc_j When consistent, the voltage sag duration is estimated as follows:
d sag ＝t oc_i ＝t oc_j
protective action time t when line head end i and tail end j oc_i And t oc_j When the voltage sag is inconsistent with the voltage sag, the voltage sag is a multi-stage sag, and the equivalent voltage sag duration is calculated by using a voltage loss method, as shown in the following formula:
in the formula of U sag1 For voltage amplitudes, U, below a predetermined value in the event of the multi-level voltage sag sag2 For a voltage amplitude, t, above a preset value in the event of a multi-stage voltage sag oc1 ＝min(t oc_i ，t oc_j ) Is the smaller one of, t oc2 ＝max(t oc_i ，t oc_j )。
2. The method for identifying the protection characteristic of the power transmission line and estimating the voltage sag duration according to claim 1, wherein the step 1 specifically comprises:
step 1.1: calculating fault electrical quantity and protective action time t based on historical monitoring data oc
Calculating 4 fault electrical quantities when a fault occurs according to the three-phase voltage and current recording data: impedance Z measured between phases P And a ground measurement impedance Z G Fault current I f And zero sequence current I 0 (ii) a And calculating the protection action time t according to the voltage amplitude change condition oc ：
In the formula (f) s For the sampling frequency, N ev The total number of wave recording sampling points of the fault event, n is the serial number of the sampling point, U sag (n) is the voltage sag amplitude at sample point n;
step 1.2: determining fault type
By zero sequence current I 0 Identifying the fault type specifically as follows:
wherein, I unb The maximum unbalanced current generated by two-phase faults of a downstream line at the protection installation position is calculated according to the following formula:
in the formula (I), the compound is shown in the specification,
and &>
When two-phase faults occur at the outlets of the downstream lines, three-phase fault currents at the installation positions are protected; repeating the step 1.1 and the step 1.2 until all fault events removed by the protection of all lines are calculated;
step 1.3: identifying the line protection type: according to the electric quantity of each fault and the protection action time t under the specific fault type oc The mapping condition of (2) is judged, which fault electrical quantity the protection response is, and then the protection type is identified.
3. The method for identifying the protection characteristic of the power transmission line and estimating the voltage sag duration according to claim 2, wherein the step 1.3 specifically comprises:
step 1.3.1: calculating FEQ-t oc Standard deviation of interval mean
The calculation FEQ-t oc The interval is divided according to the numerical value of the fault electrical quantity, namely the fault electrical quantity is divided into M intervals in the range of the fault sample value on average, and the standard deviation of the protection action time sample of the M interval is expressed as
The calculation formula is as follows:
the average standard deviation of all intervals is recorded as the standard deviation of the mean value of the sample interval
The calculation formula is as follows:
wherein, t s Is the s-th guard action time sample in the m-th interval, n m Is the number of samples in the m-th interval,
is the average guard action time of the samples in the mth interval;
for the interphase fault sample cut by one circuit breaker, calculating I f -t oc And Z P -t oc Sample interval mean standard deviation of two fault electrical quantities
For a ground fault sample of a circuit breaker cut, calculate I 0 -t oc And Z G -t oc Sample interval mean standard deviation of two fault electrical quantities>
This step is repeated until all the line breakers' FEQ-t oc Finishing the calculation of the standard deviation of the interval mean value;
step 1.3.2: identifying line protection type
According to standard deviation of mean value of sample interval
Calculating the result, and when the mean value standard deviation of a sample interval corresponding to a certain fault electric quantity is greater than or equal to>
And when the circuit breaker responds to the fault electric quantity, judging the protection type of the circuit breaker configuration as follows:
impedance Z measured by corresponding fault electrical quantity as phase-to-phase P When the protection type is interphase distance protection;
impedance Z is measured for grounding by corresponding fault electrical quantity G When the protection type is the grounding distance protection;
is set as fault current I by corresponding fault electrical quantity f When the current is in the normal state, the protection type is interphase current protection;
is a zero-sequence current I by corresponding fault electric quantity 0 And the protection type is zero sequence current protection.
4. The method for identifying transmission line protection characteristics and estimating voltage sag duration according to claim 1, wherein the step 2 specifically comprises:
step 2.1: obtaining an optimal clustering radius R and a minimum neighborhood sample number P based on a K nearest neighbor method, and then, for t oc Clustering FEQ samples to obtain a clustering number and an optimal clustering result;
step 2.2: calculating a protection action time characteristic equation
Step 2.2.1: and (3) performing preliminary judgment on the protection action characteristic according to the number of the clustered clusters: when the number of the clustering clusters is 1, inverse time limit protection is performed; when the number of the clustering clusters is 2, two-stage protection is performed; when the number of the clustering clusters is 3, three-section protection is performed; when the number of the clustering clusters is 4, four-section protection is performed;
step 2.2.2: calculating an inverse time limit protection action time characteristic equation:
fitting the inverse time-lag protected characteristic curve based on least square method, specifically, using the form t = sigma X of power equation δ + ω perform least squares fit; wherein t is protection action time, X is fault electrical quantity, and sigma, delta and omega are fitting parameters;
step 2.2.3: calculating a stage type protection action time characteristic equation:
when the number of the cluster is 1 and the protection action time t oc When the similarity is close or the clustering number is more than 1, calculating a protection action time characteristic equation by using a clustering center and a clustering boundary; let the time center of the protection action of each cluster be T ω ω =1,2,3,4, the maximum and minimum values of the electrical fault quantity in each cluster being respectively
And &>
Then the protection action time characteristic equation t oc (X) is calculated as follows:
step 2.2.4: repeating the step 2.2.1 to the step 2.2.3 to obtain action time characteristic equations of phase-to-phase protection and grounding protection configured for all circuit breakers of the whole network line; wherein, the action time characteristic equations of the interphase distance protection, the grounding distance protection, the interphase current protection and the zero sequence current protection are respectively t oc (Z P )，t oc (Z G )，t oc (I f ) And t oc (I 0 )。
5. The method for identifying transmission line protection characteristics and estimating voltage sag duration according to claim 4, wherein the step 2.1 specifically comprises:
step 2.1.1: r candidate parameter set for calculating clustering samples based on K nearest neighbor method
The parameter R represents the radius of the clustering process, and samples with distances smaller than R are to be clustered into a class; taking the sample s as a circle center, and the circle with the radius R is called the R neighborhood of the sample s; sequentially calculating average nearest neighbor distances under different K values to serve as R candidate parameter sets;
firstly, calculating a distance distribution matrix D, wherein the element of D is the distance between two samples; d is an n-order real symmetric matrix, and n is the total number of samples; each row of D is arranged in ascending order to obtain a new matrix D A (ii) a Then calculate D A Average value of elements in column K, called
Then->
I.e. the Kth candidate parameter R K All R candidate parameters become R candidate parameter sets, R K The calculation formula is as follows:
wherein D is M (s, K) denotes the Mahalanobis distance matrix D A Elements of middle s rows and K columns; the modified mahalanobis distance between samples s and p is calculated as follows:
wherein, X s And X p Electrical fault quantities, t, for samples s and p, respectively s And t p The action times of sample s and sample p, respectively; beta =1 to 5 is an important factor, S c Is the covariance matrix of the sample;
step 2.1.2: computing P candidate parameter sets
P is the minimum sample number in the R neighborhood, and samples with the number larger than P in the R neighborhood of the samples s are clustered into a cluster; for each value of K, calculating R K The number of samples within the radius and averaging to obtain the candidate parameter P K (ii) a The calculation formula is as follows:
wherein the content of the first and second substances,
the number of samples in the R domain that are the s-th sample;
step 2.1.3: selecting the best P K And R K
Increasing the value of K from 1, K =1,2, …, n, with corresponding different P K And R K Clustering the samples by using the parameters; the number of clusters C increases with the value of K K Gradually decreased but in a certain K value interval C K Will remain unchanged; when the number of clusters C K The number of clusters C at this time when the number of clusters is kept constant for 5 consecutive times K For optimum, the first K value in the 5 consecutive K values is the optimum K value, corresponding to the parameter R K And P K Is the best;
step 2.1.4: according to the method, the interphase protection and the grounding are configured for each circuit breaker of the whole networkProtecting excised FEQ-t oc And respectively carrying out optimized DBSCAN clustering on the samples to obtain the number of clustering categories, and calculating the clustering center of each category.
6. The method for identifying the protection characteristic of the power transmission line and estimating the voltage sag duration according to claim 4, wherein in the step 2.2.2, in the fitting process, a proper sample is selected to determine the parameter ω, and then the parameter ω is converted into a simple power equation linear fitting, specifically:
select any two samples (X) 1 ,t 1 ) And (X) 2 ,t 2 ) (ii) a X represents the value of the fault electrical quantity corresponding to the protection type, and X = Z P ,Z G ,I f ,I 0 ；
Get the equation
Search for samples in a sample (X) 3 ,t 3 ) Such that equation t 3 ·t 3 ＝X 1 ·X 2 Establishing;
get the equation
t 3 -ω＝σ(X 1 ·X 2 ) δ
By combining the above equations, the expression of ω is solved as follows:
ω＝(t 1 ·t 2 -t 3 ·t 3 )/(t 1 +t 2 -2t 3 )
converting the power function form into a linear model as shown in the following formula;
let T = T- ω, then the values of ln σ and δ are calculated by a linear fitting method, as follows:
wherein n is the total number of samples;
substituting σ, δ into t = σ X δ + omega, obtaining the action time characteristic equation t of inverse time-limit protection oc (X)。
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