CN114062850B - Double-threshold power grid early fault detection method - Google Patents
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Abstract
The invention discloses a double-threshold power grid early fault detection method, which comprises the following steps: the method comprises the following steps: collecting power grid state data in real time, and arranging the data according to a time sequence to form a state matrix; step two: at each sampling time t, obtaining a non-metric matrix through data processing according to the constructed state matrix; step three: according to the constructed non-metric matrix, obtaining an early fault detection index D through feature decomposition t (ii) a Step four: based on Tracy-Widom distribution, fault detection dual-threshold gamma is calculated according to given false alarm probability and dimensionality of window matrix 1 And gamma 2 (ii) a Step five: according to the constructed early fault detection index D t With a threshold value gamma 1 And gamma 2 The magnitude relation of (2) detects the early failure of the power grid. The fault detection method can find the fault earlier, and particularly, the detection of the early fault is more accurate and advanced.
Description
Technical Field
The invention belongs to the technical field of power grid fault detection, and particularly relates to a double-threshold power grid early fault detection method.
Background
In the operation process of the power grid, the power grid is easily influenced by the external environment and the internal structure to break down. At the early stage of the fault, the influence on the power system is small, the fault characteristics are not obvious, and the fault is detected and eliminated, so that the fault can be prevented from being further expanded, the safety threat of the fault to a power grid is reduced, and the method has important significance for social and economic development.
The existing power grid fault detection method mainly comprises a model method and a data method. Wherein, the model method faces the problems of complex modeling process, difficult solving and the like; the data method is more suitable for analyzing and processing massive and various characteristic power grid state data, so that efficient fault detection is realized.
The conventional data method is mainly based on a random matrix theory, comprises an analysis method based on characteristic values of a unitary matrix and an analysis method based on characteristic values of a sample covariance matrix, and realizes fault detection by analyzing a state matrix constructed by power grid state data. When the power grid normally operates without faults, a state matrix constructed by the power grid state data is a random matrix, and the characteristic value of the matrix meets the random matrix theory; on the contrary, when the system breaks down, the running state of the power grid is changed, the randomness of the system is damaged, and the characteristic value of the state matrix no longer meets the random matrix theory.
The existing grid fault detection method based on the random matrix theory can be divided into three categories, and specifically, an average spectrum radius method is constructed based on the characteristic value characteristic of a unitary matrix; based on the sample covariance matrix, a spectral deviation method and a maximum eigenvalue method are constructed. The average spectrum radius method does not consider the random variation condition of noise, the fault detection sensitivity is reduced under the environment with low signal-to-noise ratio, and the fault detection speed is relatively slow due to the analysis operation based on the unitary matrix; the analysis method based on the sample covariance matrix shortens the calculation time and improves the operation analysis efficiency, but the fault detection precision needs to be further improved; in addition, the above methods are all single threshold methods, and the sensitivity of early fault detection, in which the fault characteristics are not obvious, is insufficient.
Disclosure of Invention
In order to overcome the defects of the existing power grid early fault detection method, the invention provides a dual-threshold power grid early fault detection method based on the principle that the maximum and minimum characteristic values of a sample covariance matrix in a random matrix theory meet Tracy-Widom distribution, and the analysis efficiency and the fault detection precision of the existing method are effectively improved.
In order to achieve the purpose, the method for detecting the early fault of the power grid comprises the following steps:
the method comprises the following steps: collecting power grid state data in real time, and arranging the data according to a time sequence to form a state matrix X;
step two: at each sampling time t, according toThe constructed state matrix X is processed by data to obtain a non-metric matrix
Step three: according to the constructed non-metric matrix
Obtaining early fault detection index D through feature decomposition t ；
Step four: based on Tracy-Widom distribution, fault detection dual-threshold gamma is calculated according to given false alarm probability and dimensionality of window matrix 1 And gamma 2 ；
Step five: according to the constructed early fault detection index D t With a threshold value gamma 1 And gamma 2 The magnitude relation of (2) detects the early fault of the power grid.
Specifically, the power grid state data in step 1 is acquired by a wide area measurement unit.
The power grid state data in the step 1 comprise one or more of node voltage, branch current, load active power and reactive power, and each state data is analyzed independently.
Specifically, the data processing process in the second step is as follows: construction of a window matrix X using a sliding time window model t (ii) a According to the constructed window matrix X t Normalizing the state data by the row transformation of the formula (1) to obtain a non-metric matrix
Wherein the element in (1) is represented by formula;
wherein i is 1,2, …, N, N is the constructed window matrix X t The number of lines of (1) represents the collected formThe number of state variables; j is 1,2, …, T W ，T W Is a window matrix X t The number of columns of (a), i.e. the width of the sliding time window; x is a radical of a fluorine atom i,j Representing a window matrix X t The elements of (a) and (b),
is a window matrix X t The row vector of (2);
representing normalized matrix
The elements of (a) and (b),
is a matrix
The row vector of (2); mu (x) i ) Is a matrix X t Mean value of the row vectors of (a), σ (x) i ) Is a window matrix X t The standard deviation of the row vector of (a);
for normalized matrix
Of the average value of the row vectors of (a),
is a matrix
The standard deviation of the row vector of (c).
Specifically, the feature decomposition process in the third step includes: according to the constructed non-metric matrix
Calculating a sample covariance matrix S according to equation (2) t ：
Wherein
To represent
The conjugate transpose of (1);
further obtaining S by characteristic decomposition t Maximum eigenvalue λ of max,t And minimum eigenvalue λ min,t (ii) a Early failure detection index D t Calculated by the formula (3)
D t ＝λ max,t -λ min,t (3)。
Specifically, the Tracy-Widom distribution of the step four is expressed as:
for NxT W Matrix S of order t When N, T W → infinity and N/T W E [0, ∞ ]),
wherein F (x) is a Tracy-Widom cumulative distribution function, and P represents a probability.
Step four fault detection double threshold gamma 1 And gamma 2 Obtained according to the following method:
according to a given false alarm probability eta w And matrix dimensions N and T W Based on the Tracy-Widom distribution, the threshold value gamma is calculated according to the formulas (6) to (7) 1 And gamma 2 ：
Wherein a and b represent the sample covariance matrix S, respectively t The theoretical infimum and supremum of the characteristic values,
F -1 (. cndot.) represents the inverse of the Tracy-Widom cumulative distribution function.
Specifically, the early failure detection index D in the fifth step t With fault detection dual threshold gamma 1 And gamma 2 The size relationship of (2) includes:
wherein, min (gamma) 1 ,γ 2 ) Referred to as lower threshold, max (γ) 1 ,γ 2 ) Referred to as upper threshold, respectively representing gamma 1 And gamma 2 Minimum and maximum values among the above.
The early failure detection results are expressed as:
wherein, P 0 When the fault detection index is between the upper threshold value and the lower threshold value, the probability that no fault occurs in the power grid is calculated by the formula (10)
D t ＝max(γ 1 ,γ 2 ) The corresponding sampling time is the fault time.
The invention has the beneficial effects that:
1. the construction process of the double threshold takes the false alarm probability eta into account w And the influence of matrix dimension on the fault detection precision can be adjusted by adjusting the false alarm probability eta w And the width T of the sliding time window W And the threshold value is adjusted, so that higher flexibility is realized.
2. Compared with a single threshold analysis method, the method has the advantages that the lower threshold and the characteristic fuzzy processing between the upper threshold and the lower threshold can reduce the false alarm probability to a certain extent, and the method is specifically represented as follows: when the detection index is between the upper threshold and the lower threshold, the double-threshold method judges the system to be in a fault state according to a certain probability. In the single threshold method, only when the detection index is larger than the threshold value, it is determined that the system has disturbance. Therefore, the fault detection method of the invention can find the fault earlier, and particularly, the detection of the early fault is more accurate and advanced.
Drawings
Fig. 1 is a flowchart of a fault detection method according to the present invention.
Fig. 2 is a diagram of an IEEE39 node network topology.
Fig. 3 is a simulation graph of the fault detection method provided by the present invention under the condition of overload fault.
FIG. 4 is a graph of a simulation of the mean spectral radius method under overload fault.
FIG. 5 is a graph of a simulation of the spectral deviation method under overload fault.
FIG. 6 is a simulation graph of a sample covariance matrix maximum eigenvalue method under overload fault.
Detailed Description
The invention will be described in further detail below with reference to the figures and specific embodiments.
As shown in fig. 1, the method for detecting an early fault of a power grid provided by the present invention includes the following steps:
the method comprises the following steps: collecting power grid state data in real time, and arranging the data according to a time sequence to form a state matrix X;
step two: at each sampling time t, obtaining non-kilometers through data processing according to the constructed state matrix XSpecial matrix
Step three: according to the constructed non-metric matrix
Obtaining early failure detection index D through feature decomposition t ；
Step four: based on Tracy-Widom distribution, fault detection dual-threshold gamma is calculated according to given false alarm probability and dimensionality of window matrix 1 And gamma 2 ；
Step five: according to the constructed early fault detection index D t With a threshold value gamma 1 And gamma 2 The magnitude relation of (2) detects the early failure of the power grid.
The dual-threshold early failure detection method proposed by the present invention is described in detail below by taking the IEEE39 node network shown in fig. 2 as a specific example. The power grid state data comprise node voltage, branch current, load active power, reactive power and the like, and can be selected according to analysis requirements. Each status data was analyzed separately. The type of fault we want to detect in the example is overload.
The method comprises the following steps: setting the fault type as overload, specifically, setting the load of the No. 8 bus in the experiment to be gradually increased from a rated value at the sampling time t of 500-600. The slow increase in load causes the bus voltage to change slowly over a small range and therefore the fault signature is not apparent early in the fault.
The IEEE39 node network shown in fig. 2 contains a total of 39 buses. The voltage of each bus is selected as a measurement state variable, namely N-39. The bus voltage is sampled for 1.5s by using the existing wide area measurement unit, if the sampling interval is 1ms, 1500 sampling moments are total, and a 39 × 1500 bus voltage matrix, namely the state matrix X in the step one, is obtained.
The data processing process of the second step comprises the following steps:
construction of a window matrix X using a sliding time window model t (ii) a According to the constructed window matrix X t Normalizing the state data by the row transformation of the formula (1) to obtain a non-metric matrix
The element(s) in (b) is represented by formula (1);
wherein i is 1,2, …, N, N is the constructed window matrix X t The number of rows of (2) represents the number of the collected state variables; j-1, 2, …, T W ，T W Is X t The number of columns of (a), i.e. the width of the sliding time window; x is the number of i,j Is X t The elements of (a) and (b),
is X t A row vector of (a);
for normalized matrix
The elements of (a) and (b),
is a matrix
A row vector of (a); mu (x) i ) Is X t Mean value of the row vectors of (a), σ (x) i ) Is X t The standard deviation of the row vector of (a);
for normalized matrix
The average of the row vectors of (a) is,
is a matrix
The standard deviation of the row vector of (1).
T W Typically several tens to several hundreds, T W Since the smaller the number of samples included in the matrix, the more sensitive the matrix is to noise signals, the less the asymptotic assumption (N, T) is satisfied in order to reduce the influence of noise on the state data when detecting an early fault whose fault signature is insignificant W → infinity and N/T W E [0, infinity)), selecting larger T as much as possible W 。
In an embodiment, the sliding time window width T is determined W At each sampling time t, a 39 × 100 non-metric matrix is obtained according to the above data processing procedure
The characteristic decomposition process of the third step comprises the following steps:
computing
Sample covariance matrix S of t And further obtaining a matrix S through characteristic decomposition t Maximum eigenvalue λ of max,t Minimum eigenvalue λ min,t ；
Wherein
To represent
The conjugate transpose of (c).
Further, an early failure detection index D is calculated t
D t ＝λ max,t -λ min,t (3)
The Tracy-Widom distribution of the step four is expressed as follows:
for NxT W Matrix S of order t ，λ max,t 、λ min,t Are respectively S t The maximum and minimum eigenvalues of (2), then when N, T W → infinity and N/T W Belongs to [0, ∞ ]),
wherein F (x) is a Tracy-Widom cumulative distribution function, and P represents a probability.
Step four fault detection double threshold gamma 1 And gamma 2 Obtained according to the following method:
according to a given false alarm probability eta w And matrix dimensions N and T W Based on the Tracy-Widom distribution, the threshold value gamma is calculated according to the formulas (6) to (7) 1 And gamma 2 ：
Wherein a and b represent the sample covariance matrix S, respectively t Theoretical infimum and supremum of characteristic values, and
F -1 (. represents Tracy-Widom)The inverse of the distribution function is accumulated.
Wherein the false alarm probability eta w The fault probability is set according to actual analysis requirements, false alarm probability is increased when the false alarm probability is too high, false alarm probability is possibly too low, and false alarm is possibly missed, so that eta is obtained when higher fault detection probability is pursued in engineering practice w Should be relatively large. Determining false alarm probability eta in an embodiment w Obtaining double threshold value gamma based on Tracy-Widom distribution calculation 1 ＝2.9962，γ 2 ＝2.4230。
In step five, according to D t And gamma 1 And gamma 2 Detects whether the system has a fault.
Early failure detection index D t With fault detection dual threshold gamma 1 And gamma 2 The size relationship of (2) includes:
wherein, min (gamma) 1 ,γ 2 ) Referred to as lower threshold, max (γ) 1 ,γ 2 ) Referred to as upper threshold, respectively representing gamma 1 And gamma 2 Minimum and maximum values among the above.
Further, the early fault detection condition in step five is represented as:
wherein, P 0 When the fault detection index is between the upper threshold value and the lower threshold value, the probability that no fault occurs to the power grid is calculated by the formula (10).
The moment of failure is D t ＝max(γ 1 ,γ 2 ) The corresponding sampling instant. The power grid protection device can immediately respond and execute corresponding fault protectionAnd (5) operating.
The probability judgment between the upper threshold and the lower threshold is called as "feature fuzzy" processing, wherein the "feature fuzzy" is relative to the determined state feature (fault/normal) of the power grid, and in the engineering practice, when the fault detection index is between the upper threshold and the lower threshold, whether the power grid has a fault is judged according to the probability, and at the moment, an engineer can determine whether to take protective measures according to experience.
FIG. 3 is a graph of the double threshold early fault detection method of the present invention under a set overload fault condition D t Curve line.
As can be seen from FIG. 3, in the normal state, D t ＜min(γ 1 ,γ 2 ) And from the time t being 500, the bus voltage changes slowly as the load of node 8 increases, and at t 1 At the moment of time, satisfy
Then, D t Between the upper and lower thresholds to t 2 At the moment of time, satisfy
Therefore, the system can be judged to be at t through the double-threshold method 2 An overload fault occurs at a moment of time, and t 1 ～t 2 In P 0 The grid state is determined to be normal with a probability of 0.07, i.e. 1-P 0 And judging that the power grid state is abnormal by the probability of 0.93.
In order to verify the effectiveness of the fault detection method provided by the invention, the method provided by the invention is compared with three single threshold methods, and the method specifically comprises the following steps: mean Spectral Radius (MSR), spectral skewness, and sample covariance matrix Maximum Eigenvalue (MESCM). Simulation curves of the three methods under overload fault are respectively shown in fig. 4, fig. 5 and fig. 6. Wherein, the detection index of the MSR method is MSR, and the threshold value is Inner Radius; the detection index of the spectrum deviation method is d S The threshold value is
The detection index of the MESCM method is the most of the matrixLarge eigenvalue lambda max The threshold is γ. In the above single-threshold method, the intersection point of the detection index and the threshold is the fault time.
As can be seen from fig. 4, when detecting an overload fault with insignificant fault characteristics, the detection index of the MSR method does not have an intersection point with the threshold, that is, the MSR method fails; in FIGS. 5 and 6, both the spectral skewness method and the MESCM method are performed at t > t 2 The fault is detected at the moment, and compared with a double-threshold method, the fault is detected when t is t 2 The time for detecting faults is relatively lagged by the spectrum deviation method and the MESCM method.
The fault detection performance of the fault detection method based on the double threshold and the fault detection performance of the fault detection method based on the three single thresholds are summarized in table 1.
TABLE 1
As can be seen from table 1, compared with the single threshold method, the dual-threshold early fault detection method provided by the present invention can detect a fault earlier, and the calculation time is less.
The above embodiments are merely used to illustrate the present invention, and are not to be taken as limitations of the present invention, the applied objects are not limited to IEEE39 node network, the set fault type is not limited to overload, and changes and modifications to the above embodiments are within the scope of the claims of the present invention as long as they are within the scope of the present invention.
Claims (4)
1. A double-threshold power grid early fault detection method is characterized by comprising the following steps:
the method comprises the following steps: collecting power grid state data in real time, and arranging the data according to a time sequence to form a state matrix X;
step two: at each sampling time t, obtaining a non-metric matrix through data processing according to the constructed state matrix X
Step three: according to the constructed non-decimeter matrix
Obtaining early failure detection index D through feature decomposition t ；
Step four: based on Tracy-Widom distribution, fault detection dual-threshold gamma is calculated according to given false alarm probability and dimensionality of window matrix 1 And gamma 2 ；
Step five: according to the constructed early fault detection index D t And a threshold value gamma 1 And gamma 2 The size relation of the grid fault detection module is used for detecting the early fault of the power grid;
the data processing process of the second step is as follows: construction of a window matrix X using a sliding time window model t (ii) a According to the constructed window matrix X t Normalizing the state data by the row transformation of the formula (1) to obtain a non-metric matrix
Wherein the element in (1) is represented by formula;
wherein i is 1,2, …, N, N is the constructed window matrix X t The number of rows of (2) represents the number of the collected state variables; j-1, 2, …, T W ，T W Is a window matrix X t The number of columns of (a), i.e. the width of the sliding time window; x is the number of i,j Representing a window matrix X t The elements of (a) and (b),
is a window matrix X t A row vector of (a);
representing normalized matrix
The elements of (a) and (b),
is a matrix
A row vector of (a); mu (x) i ) Is a matrix X t Mean value of the row vectors of (a), σ (x) i ) Is a window matrix X t The standard deviation of the row vector of (a);
for normalized matrix
The average of the row vectors of (a) is,
is a matrix
The standard deviation of the row vector of (a);
the characteristic decomposition process of the third step comprises the following steps: according to the constructed non-metric matrix
Calculating a sample covariance matrix S according to equation (2) t ：
Wherein
To represent
The conjugate transpose of (1);
further obtaining S through characteristic decomposition t Maximum eigenvalue λ of max,t And minimum eigenvalue λ min,t (ii) a Early failure detection index D t Calculated by the formula (3)
D t ＝λ max,t -λ min,t (3)
The Tracy-Widom distribution of the step four is expressed as follows:
for NxT W Matrix S of order t When N, T W → infinity and N/T W E [0, ∞ ]),
wherein F (x) is a Tracy-Widom cumulative distribution function, and P represents probability;
step four fault detection double threshold gamma 1 And gamma 2 Obtained according to the following method:
according to a given false alarm probability eta w And matrix dimensions N and T W Based on the Tracy-Widom distribution, the threshold value gamma is calculated according to the formulas (6) to (7) 1 And gamma 2 ：
Wherein a and b represent the sample covariance matrix S, respectively t Feature(s)The theoretical infimum and supremum of values,
F -1 (. -) represents the inverse of the Tracy-Widom cumulative distribution function;
early fault detection index D in step five t With fault detection dual threshold gamma 1 And gamma 2 The size relationship of (2) includes:
wherein, min (gamma) 1 ,γ 2 ) Referred to as lower threshold, max (γ) 1 ,γ 2 ) Referred to as upper threshold, respectively representing gamma 1 And gamma 2 Minimum and maximum values of (d);
the early fault detection result in the step five is represented as:
wherein, P 0 When the fault detection index is between the upper threshold value and the lower threshold value, the probability that no fault occurs in the power grid is calculated by the formula (10)
2. The method as claimed in claim 1, wherein the grid state data of the first step is collected by a wide area measurement unit.
3. The method as claimed in claim 1, wherein the grid state data of the first step includes one or more of node voltage, branch current, load active power and reactive power, and each state data is analyzed separately.
4. A dual-threshold grid early fault detection method as claimed in claim 1, wherein in step five, D t ＝max(γ 1 ,γ 2 ) The corresponding sampling time is the fault time.
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