KR20210129453A - Apparatus and method of detecting bad data in power system measurement data - Google Patents

Abstract

The present invention relates to an apparatus for detecting faulty data from power system measurement data, capable of improving the speed of faulty data detection by predicting a value becoming 0 during a matrix calculation procedure, and calculating a scarce inverse matrix excluding a 0 (zero) element of a predicted gain matrix, when detecting faulty data from measurement data measured from a power system using a normalization surplus error test, and a method thereof. In accordance with an embodiment of the present invention, the faulty data detection apparatus includes: a database storing measurement data measured from a power system; and a processor calculating a measurement function and a measurement error using the measurement data, calculating a Jacobian matrix and a gain matrix, predicting a value with an element becoming 0 during a matrix calculation procedure, calculating a scarce inverse matrix of the gain matrix excluding an element having a 0 value among elements of an inverse matrix of the predicted gain matrix, calculating a covariance matrix using the calculated scarce inverse matrix, and detecting faulty data.

Description

Apparatus and method of detecting bad data in power system measurement data

The present invention relates to an apparatus and method for detecting defective data of power system measurement data, and more particularly, when detecting defective data using a normalized residual error test in measured data measured in a power system, when the element is 0 in the matrix operation process The present invention relates to an apparatus and method for detecting bad data of power system measurement data, which predicts a value to be obtained, and calculates a sparse inverse matrix by excluding a zero element of a predicted gain matrix to improve a bad data detection speed.

Estimating the state of the power system calculates the magnitude and phase of voltage, which are state variables that can represent the current state of the power system, from the measured data, and removes the bad data included in the measured data to provide an accurate database to other applications within the EMS. It is a very important function to

In general, the state of the power system can be estimated using the measurement data measured from the power system. However, the measurement data may include bad data due to various factors, and the state estimation of the power system may not be accurately performed due to the bad data. Accordingly, it is very important to determine and detect defective data included in the measurement data.

One of the methods for detecting defective data included in the measurement data is a normalized residual error test (largest normalized residual tset). The normalized residual error test is one of the methods for accurately detecting bad data, but since it detects only one bad data during one operation, it takes a lot of computation time when the measured data includes a lot of bad data.

In particular, the covariance matrix is calculated in the process of normalizing the error during the normalized residual error test. As the size of the system and the number of measurement data increase, more computation time is required to calculate the covariance matrix. Accordingly, there is a problem in that the total calculation time for estimating the state of the power system is increased.

The present invention is to solve the above-described problem, and when bad data is detected by using the normalized residual error test in the measured data measured in the power system, the value at which the element becomes 0 is predicted in the matrix operation process, and the predicted gain An object of the present invention is to provide an apparatus and method for detecting bad data of measured data that improve a bad data detection speed by calculating a sparse inverse matrix by excluding zero elements of the matrix.

In addition to the technical problems of the present invention mentioned above, other features and advantages of the present invention will be described below or will be clearly understood by those skilled in the art from such description and description.

In order to achieve the above-described object, an apparatus for detecting defective data according to an embodiment of the present invention includes a database for storing measurement data measured in a power system, a measurement function and a measurement error using the measurement data, and a Jacobian matrix and Calculates a gain matrix, predicts a value whose element becomes 0 in the process of matrix operation, excludes an element having a value of 0 among elements of the inverse of the predicted gain matrix, and calculates a sparse inverse of the gain matrix, and calculates the calculated sparseness The processor may include a processor that calculates a covariance matrix using the inverse matrix and detects bad data.

In addition, the method for detecting bad data according to an embodiment of the present invention for achieving the above-described object includes calculating a measurement function and a measurement error using measurement data measured in a power system, and calculating a Jacobian matrix and a gain matrix predicting a value of which an element becomes 0 in a matrix operation process, and calculating a sparse inverse matrix of the gain matrix by excluding an element having a value of 0 among elements of the inverse matrix of the predicted gain matrix; It may include detecting bad data by using an inverse matrix and calculating a covariance matrix.

In the apparatus and method for detecting defective data of power system measurement data according to an embodiment of the present invention, when the defective data is detected using the normalized residual error test in the measured data measured in the electric power system, the element becomes 0 in the matrix operation process. The speed of detecting bad data can be improved by predicting .

In addition, it can serve to provide an accurate database to other applications within the EMS by expanding the detection performance of bad data for real-time environment performance of power system state estimation.

In addition, other features and advantages of the present invention may be newly recognized through embodiments of the present invention.

1 is a diagram showing the configuration of a system for detecting defective data of measured data measured in a power system according to an embodiment of the present invention.
2 is a diagram illustrating an apparatus for detecting bad data according to an embodiment of the present invention.
3 is a diagram illustrating prediction of element 0 of a gain matrix according to an embodiment of the present invention.
4 is a diagram illustrating the scale of a test system for comparing the operation speed of a covariance matrix in detecting bad data using the normalized residual error test method according to an embodiment of the present invention.
5 is a diagram illustrating a comparison result of a calculation speed of a covariance matrix for detecting bad data using a normalized residual error test method according to an embodiment of the present invention.
6 is a diagram illustrating a method for detecting bad data according to an embodiment of the present invention.

In order to clearly explain the present invention, parts irrelevant to the description are omitted, and the same reference numerals are given to the same or similar elements throughout the specification.

Although not defined otherwise, all terms including technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the art to which the present invention belongs. Commonly used terms defined in the dictionary are additionally interpreted as having a meaning consistent with the related technical literature and the presently disclosed content, and unless defined, they are not interpreted in an ideal or very formal meaning.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those of ordinary skill in the art can easily implement them. However, the present invention may be embodied in various different forms and is not limited to the embodiments described herein.

1 is a diagram showing the configuration of a system for detecting defective data of measured data measured in a power system according to an embodiment of the present invention.

Referring to FIG. 1 , a system 1000 for detecting bad data of measured data obtained by measuring a power system according to an embodiment of the present invention may include a power system 100 and an apparatus 200 for detecting bad data.

The bad data detection apparatus 200 may collect and store measurement data measured in the power system 100 by a sensor, a phasor measurement unit (PMU), a feeder remote terminal unit (FRTU), or the like. The bad data detection apparatus 200 may detect bad data included in the measurement data measured by the power system 100 . The bad data detection apparatus 200 according to an embodiment of the present invention may detect bad data using a largest normalized residual test. When the normalized residual error test operates to detect bad data, only one bad data is detected, so the normalized residual error test must be performed several times until bad data is not detected. Accordingly, it may take a lot of time to detect all bad data. Accordingly, according to an embodiment of the present invention, in the process of calculating the inverse matrix of the gain matrix during one process of the normalized residual error test, the element 0 among the elements of the gain matrix is predicted, and the inverse of the gain matrix is excluded from the expected element. can be calculated Due to this, the detection time of bad data may be reduced.

2 is a diagram illustrating an apparatus for detecting bad data according to an embodiment of the present invention.

Referring to FIG. 2 , an apparatus 200 for detecting bad data according to an embodiment of the present invention may include a database 210 and a processor 220 .

The database 210 may store measurement data measured in the power system 100 .

The processor 220 may detect defective data among the measurement data stored in the database 210 by using the normalized residual error test.

Specifically, the processor 220 may calculate a measurement function and a measurement error to perform the normalized residual error test. The processor 220 may calculate a relational expression between the linearized state variable and the measured data in the state estimation of the power system 100 through Equation 1 .

[Equation 1]

는 선형화된 측정 데이터의 벡터이고,

는 측정 함수의 자코비안 행렬이고,

는 선형화된 상태변수이고,

는 측정 에러를 나타낼 수 있다. 상기 수학식 1은 데이터베이스(210)에 저장되어 있을 수 있고, 프로세서(220)는 선형화된 상태변수와 측정 데이터 사이의 관계식을 계산하기 위해 데이터베이스(210)로부터 수학식 1을 리드하고, 리드된 수학식 1을 통해 선형화된 상태변수와 측정 데이터 사이의 관계식을 계산할 수 있다.here,

is a vector of linearized measurement data,

is the Jacobian matrix of the measurement function,

is a linearized state variable,

may indicate a measurement error. Equation 1 may be stored in the database 210, and the processor 220 reads Equation 1 from the database 210 to calculate a relational expression between the linearized state variable and the measured data, and the read math Through Equation 1, the relational expression between the linearized state variable and the measured data can be calculated.

The processor 220 may estimate the state variable by applying the weighted least squares method. The weighted least squares method generates residuals with constant variance by minimizing the weighted sum of squares by using the correct weights when equal variance is not satisfied in linear regression analysis, that is, when the least squares assumption that the variance of the residuals is constant is violated. may be doing The processor 220 may estimate the state variable through Equation (2).

[Equation 2]

는 추정된 상태변수이고,

는 측정 함수의 자코비안 행렬이고,

은 측정 데이터의 분산 행렬이고,

는 측정 데이터와 측정함수의 오차일 수 있다. 상기 수학식 2는 데이터베이스(210)에 저장되어 있을 수 있고, 프로세서(220)는 상태변수를 추정하기 위해 데이터베이스(210)로부터 수학식 2를 리드하고, 리드된 수학식 2를 통해 상태변수를 추정할 수 있다.here,

is the estimated state variable,

is the Jacobian matrix of the measurement function,

is the variance matrix of the measurement data,

may be an error between the measurement data and the measurement function. Equation 2 may be stored in the database 210, and the processor 220 reads Equation 2 from the database 210 to estimate the state variable, and estimates the state variable through the read Equation 2 can do.

Also, the processor 220 may estimate a vector of measurement data through the estimated state variable. The processor 220 may estimate the vector of the measurement data through Equation (3).

[Equation 3]

는 추정된 측정 데이터의 벡터 또는 추정된 측정 데이터와 측정함수의 오차이고,

는 측정 함수의 자코비안 행렬이고,

는 추정된 상태변수이고,

는 측정 데이터와 측정함수의 오차이고,

는

일 수 있다. 상기 수학식 3은 데이터베이스(210)에 저장되어 있을 수 있고, 프로세서(220)는 측정 데이터를 추정하기 위해 데이터베이스(210)로부터 수학식 3을 리드하고, 리드된 수학식 3을 통해 측정 데이터를 추정할 수 있다.here,

is the vector of the estimated measurement data or the error between the estimated measurement data and the measurement function,

is the Jacobian matrix of the measurement function,

is the estimated state variable,

is the error between the measurement data and the measurement function,

Is

can be Equation 3 may be stored in the database 210, and the processor 220 reads Equation 3 from the database 210 to estimate the measurement data, and estimates the measurement data through the read Equation 3 can do.

Also, the processor 220 may calculate a measurement error through Equation (4).

[Equation 4]

은 측정 데이터와 추정된 측정 데이터 간의 측정 오차이고,

는

일 수 있다. 즉,

는 측정 에러에 대한 측정 오차의 민감도를 나타내는 오차 민감도 행렬일 수 있다.here,

is the measurement error between the measurement data and the estimated measurement data,

Is

can be in other words,

may be an error sensitivity matrix indicating the sensitivity of the measurement error to the measurement error.

Also, the processor 220 may calculate the covariance matrix through Equation 5.

For example, the covariance matrix may be a matrix expressing covariance or correlation coefficients between a plurality of variable values in two or more variables.

[Equation 5]

은 공분산 행렬일 수 있다.here,

may be a covariance matrix.

Meanwhile, the operation speed of the normalized residual error test may be determined according to the time consumed in the calculation of the covariance matrix to be calculated when normalizing the measurement error. Equation 5 for calculating the covariance matrix may be the same as Equation 6.

[Equation 6]

는 이득 행렬로,

일 수 있다.

는 대칭 행렬일 수 있고, 각 행의 원소가 0이 아닌 원소의 개소가 극히 적은 희소 행렬일 수 있다. 일반적으로 희소 행렬의 역행렬은 모든 원소가 0이 아닌 원소를 가지는 밀도 행렬이 될 수 있다. 이에 따라, 수학식 6을 이용하여 공분산 행렬을 계산하는 경우, 희소 행렬의 역행렬을 계산하는 데 많은 시간이 소요될 수 있다.here,

is the gain matrix,

can be

may be a symmetric matrix, and may be a sparse matrix in which the number of non-zero elements in each row is extremely small. In general, the inverse of a sparse matrix can be a density matrix in which every element has a non-zero element. Accordingly, when calculating the covariance matrix using Equation 6, it may take a lot of time to calculate the inverse of the sparse matrix.

)과, 이득 행렬(

)의 희소성을 이용하여 이득 행렬의 역행렬을 계산하기 위해 이득 행렬의 역행렬에서 0인 원소를 예측하고, 예측된 원소를 제외하고 희소 행렬의 역행렬을 계산함으로써 희소 행렬의 역행렬을 더 빠른 시간 내에 계산하도록 할 수 있다.According to an embodiment of the present invention, the processor 220 is a Jacobian matrix (

) and the gain matrix (

) to calculate the inverse of the sparse matrix in a faster time by predicting the zero element in the inverse of the gain matrix and calculating the inverse of the sparse matrix by excluding the predicted element to calculate the inverse of the gain matrix using the sparsity of can do.

를 계산한 결과 0이 아닌 원소를 가지는 위치만을 선택하여 계산할 수 있다. 이득 행렬의 역행렬에서 0이 아닌 원소를 가지는 위치는 이득 행렬에서 0이 아닌 원소를 가지는 위치와 동일한 위치일 수 있다. 이에 따라, 전력계통(100)의 상태추정 연산 과정에서 메모리의 소모를 감소하고, 연산속도의 향상을 위해 2차원 희소 행렬을 1차원의 벡터로 표현하여 저장되어 있으므로 벡터화를 따로 수행하지 않아도 될 수 있다. That is, the processor 220 does not need to calculate all the elements of the inverse of the gain matrix in order to calculate the elements of the covariance matrix. That is, the processor 220 determines that the element position of the inverse of the gain matrix is

As a result of calculating , it can be calculated by selecting only positions that have non-zero elements. A position having a non-zero element in the inverse of the gain matrix may be the same position as a position having a non-zero element in the gain matrix. Accordingly, since the two-dimensional sparse matrix is expressed and stored as a one-dimensional vector in order to reduce memory consumption in the state estimation operation process of the power system 100 and improve the operation speed, it is not necessary to separately perform vectorization. have.

)의 대각선의 원소만이 필요할 수 있다. 이에 따라, 프로세서(220)는 수학식 6을 기초로 공분산 행렬의 대각선의 원소를 추출할 수 있다. 즉, 프로세서(220)는 수학식 7을 통해 공분산 행렬의 원소를 계산할 수 있다.To perform the normalized residual error test, the covariance matrix (

) may only be needed on the diagonal of Accordingly, the processor 220 may extract the diagonal element of the covariance matrix based on Equation (6). That is, the processor 220 may calculate the elements of the covariance matrix through Equation (7).

[Equation 7]

,

는 자코비안 행렬에서 0이 아닌(non-zero) 원소이고,

는 이득 행렬의 역행렬의 원소일 수 있다.where m is the number of measured data, n is the number of state variables,

,

is a non-zero element in the Jacobian matrix,

may be an element of the inverse of the gain matrix.

The processor 220 may detect bad data included in the measurement data set by using the covariance matrix.

After estimating the state of the power system 100 , the processor 220 may calculate a measurement error vector between each measurement data and a measurement function calculated using the estimated state variable. The processor 220 may calculate a measurement error vector through Equation (8).

[Equation 8]

는 i번째 측정 데이터와 측정 함수 사이의 측정 오차이고,

는 i번째 측정 데이터이고,

는 i번째 측정 데이터의 측정 함수이고,

는 추정된 상태변수 벡터일 수 있다.here,

is the measurement error between the i-th measurement data and the measurement function,

is the i-th measurement data,

is the measurement function of the i-th measurement data,

may be an estimated state variable vector.

The processor 220 may perform normalization on the calculated measurement error. The processor 220 may normalize the measurement error through Equation (9).

[Equation 9]

는 정규화된 측정 오차이고,

는 i번째 측정 데이터에 대한 공분산일 수 있다.here,

is the normalized measurement error,

may be a covariance with respect to the i-th measurement data.

When the normalized measurement error value is greater than or equal to a certain size, the processor 220 may determine that the data set includes bad data, and may determine that the data having the measurement error value is bad data and remove it.

를 만족하는 측정 데이터가 있을 경우 불량 데이터가 측정 데이터 셋에 포함된 것이므로, 측정 데이터 셋에서 k번째 측정 데이터를 제거할 수 있다.For example, the processor 220 may select one of the normalized measurement error values.

If there is measurement data that satisfies , the k-th measurement data can be removed from the measurement data set because the bad data is included in the measurement data set.

를 만족하는 측정 데이터가 없을 경우 불량 데이터가 측정 데이터 셋에 포함되지 않은 것이므로, 불량 데이터 처리를 종료할 수 있다.On the other hand, the processor 220 of the normalized measurement error value

When there is no measurement data that satisfies , since the bad data is not included in the measurement data set, the processing of the bad data can be terminated.

3 is a diagram illustrating prediction of element 0 when calculating an inverse of a gain matrix using the sparsity of a Jacobian matrix according to an embodiment of the present invention.

)과, 이득 행렬(

)의 희소성을 이용하여 이득 행렬의 역행렬 계산에서 계산할 필요가 없는 0인 원소를 예측할 수 있다. 프로세서(220)는 0인 것으로 예측된 원소를 제외하고 희소 행렬의 역행렬을 계산할 수 있다.3, the processor 220 is a Jacobian matrix (

) and the gain matrix (

) can be used to predict elements that are zero, which do not need to be calculated in the inverse of the gain matrix. The processor 220 may calculate the inverse of the sparse matrix by excluding the element predicted to be zero.

)에서

를 계산한 결과 0이 아닌 원소를 가지는 위치를 선택할 수 있다. 여기서, 자코비안 행렬의 0이 아닌 원소는 행렬의 원소 기호

로 나타낼 수 있다.For example, the processor 220 has six measurement data and three state variables in the Jacobian matrix (

)at

As a result of calculating , a position with a non-zero element can be selected. where the nonzero element of the Jacobian matrix is the element symbol of the matrix

can be expressed as

The processor 220 may calculate the elements of the covariance matrix through Equation (7).

[Equation 7]

,

는 자코비안 행렬에서 0이 아닌(non-zero) 원소이고,

는 이득 행렬의 역행렬의 원소일 수 있다.where m is the number of measured data, n is the number of state variables,

,

is a non-zero element in the Jacobian matrix,

may be an element of the inverse of the gain matrix.

를 계산한 결과 이득 행렬의 역행렬 계산에서 0이 아닌 원소를 가지는 위치만을 선택하여 이득 행렬의 희소 역행렬의 원소 위치를 선택할 수 있다. 이득 행렬의 역행렬에서 0이 아닌 원소를 가지는 위치는 이득 행렬에서 0이 아닌 원소를 가지는 위치와 동일한 위치일 수 있다.The processor 220

As a result of calculating , it is possible to select the element position of the sparse inverse matrix of the gain matrix by selecting only positions having non-zero elements in the inverse matrix calculation of the gain matrix. A position having a non-zero element in the inverse of the gain matrix may be the same position as a position having a non-zero element in the gain matrix.

4 is a diagram illustrating the scale of a test system for comparing the operation speed of a covariance matrix in detecting bad data using the normalized residual error test method according to an embodiment of the present invention.

Referring to FIG. 4 , when calculating the inverse matrix of the gain matrix according to an embodiment of the present invention, a position having an element of 0 that does not need to be calculated is predicted, and only other elements are used except for the element at the predicted position. You can check the operation speed when calculating the inverse matrix.

When calculating the inverse matrix of the gain matrix according to an embodiment of the present invention, when calculating the inverse matrix using only other elements, excluding the zero element, to compare the covariance matrix operation time for detecting bad data according to the scale A test system of any size may be used.

For example, when calculating the inverse matrix using the first system (IEEE 14), the test system consists of 14 busbars and 20 lines, and a total of 82 measurement data can be used. Here, the measurement data of the test system may be the voltage magnitude and injection power of all busbars calculated through the tidal current calculation, and the line tidal current power. There are a total of 27 state variables in the test system. The Jacobian matrix used in the calculation process has a size of 82×27 dimensions, the gain matrix has a size of 27×27 dimensions, and the covariance matrix has a size of 82×82 dimensions. may be a matrix of

In addition, when calculating the inverse matrix using the second system (IEEE 30), the test system consists of 30 busbars and 41 lines, and a total of 172 measurement data can be used. Here, the measurement data of the test system may be the voltage magnitude and injection power of all busbars calculated through the tidal current calculation, and the line tidal current power. There are a total of 81 state variables in the test system. The Jacobian matrix used in the calculation process has a size of 172×81, the gain matrix has a size of 81×81, and the covariance matrix has a size of 172×172. may be a matrix of

In addition, when calculating the inverse matrix using the third system (IEEE 57), the test system consists of 57 busbars and 80 lines, and a total of 331 measurement data can be used. Here, the measurement data of the test system may be the voltage magnitude and injection power of all busbars calculated through the tidal current calculation, and the line tidal current power. There are a total of 113 state variables in the test system. The Jacobian matrix used in the calculation process has a size of 331×113 dimensions, the gain matrix has a size of 113×113 dimensions, and the covariance matrix has a size of 331×331 dimensions. may be a matrix of

In addition, when calculating the inverse matrix using the fourth system (IEEE 118), the test system consists of 118 busbars and 186 lines, and a total of 726 measurement data can be used. Here, the measurement data of the test system may be the voltage magnitude and injection power of all busbars calculated through the tidal current calculation, and the line tidal current power. There are a total of 235 state variables in the test system. The Jacobian matrix used in the calculation process has a size of 726×235, the gain matrix has a size of 235×235, and the covariance matrix has a size of 726×726. may be a matrix of

In addition, when calculating the inverse matrix using the fifth system (IEEE 300), the test system consists of 300 busbars and 411 lines, and a total of 1,722 measurement data can be used. Here, the measurement data of the test system may be the voltage magnitude and injection power of all busbars calculated through the tidal current calculation, and the line tidal current power. There are a total of 599 state variables in the test system. The Jacobian matrix used in the calculation process has a size of 1722×599, the gain matrix has a size of 599×599, and the covariance matrix has a size of 1722×1722. may be a matrix of

In addition, when calculating the inverse matrix using the 6th system (KEPCO 2191), the test system consists of 2,191 busbars and 3,563 lines, and a total of 13,699 measured data can be used. Here, the measurement data of the test system may be the voltage magnitude and injection power of all busbars calculated through the tidal current calculation, and the line tidal current power. There are a total of 4,381 state variables in the test system. The Jacobian matrix used in the calculation process has a size of 13,699×4,381 dimensions, the gain matrix has a size of 4,381×4,381 dimensions, and the covariance matrix has a size of 13,699×13,699 dimensions. may be a matrix of

Accordingly, according to an embodiment of the present invention, it is possible to check the operation speed when calculating the inverse matrix by using only other elements except for the element 0 in the inverse matrix calculation of the gain matrix as the system scale increases.

5 is a diagram illustrating a comparison result of a calculation speed of a covariance matrix for detecting bad data using a normalized residual error test method according to an embodiment of the present invention.

Referring to FIG. 5 , (a) shows the operation execution time when the covariance matrix is calculated according to an embodiment of the present invention, and (b) is the operation execution time when the covariance matrix is calculated through the conventional technique. can indicate

A conventional technique may be to perform a normalized residual error test using forward/backward substitution. In addition, the x-axis may represent the size of the system, and the y-axis may represent time (seconds).

When calculating the covariance matrix according to an embodiment of the present invention, when calculating the covariance matrix, when calculating the inverse of the gain matrix, predicting an element of 0 that does not need calculation, and performing the operation except for the predicted element, forward/backward The computation time can be reduced compared to performing the normalized residual error test using the substitution method. In addition, as the size of the system increases, the difference in the calculation time for detecting bad data may gradually increase.

6 is a diagram illustrating a method for detecting bad data according to an embodiment of the present invention.

Referring to FIG. 6 , the processor 220 may calculate a measurement function and a measurement error based on the measurement data collected from the power system 100 ( S100 ).

The processor 220 may calculate a relational expression between the linearized state variable and the measured data in the state estimation of the power system 100 through Equation 1 .

[Equation 1]

는 선형화된 측정 데이터의 벡터이고,

는 측정 함수의 자코비안 행렬이고,

는 선형화된 상태변수이고,

는 측정 에러를 나타낼 수 있다. here,

is a vector of linearized measurement data,

is the Jacobian matrix of the measurement function,

is a linearized state variable,

may indicate a measurement error.

The processor 220 may estimate the state variable by applying the weighted least squares method. The processor 220 may estimate the state variable through Equation (2).

[Equation 2]

는 추정된 상태변수이고,

는 측정 함수의 자코비안 행렬이고,

은 측정 데이터의 분산 행렬이고,

는 측정 데이터와 측정함수의 오차일 수 있다.here,

is the estimated state variable,

is the Jacobian matrix of the measurement function,

is the variance matrix of the measurement data,

may be an error between the measurement data and the measurement function.

The processor 220 may estimate a vector of measurement data through the estimated state variable. The processor 220 may estimate the vector of the measurement data through Equation (3).

[Equation 3]

는 추정된 측정 데이터의 벡터 또는 추정된 측정 데이터와 측정함수의 오차이고,

는 측정 함수의 자코비안 행렬이고,

는 추정된 상태변수이고,

는 측정 데이터와 측정함수의 오차이고,

는

일 수 있다.here,

is the vector of the estimated measurement data or the error between the estimated measurement data and the measurement function,

is the Jacobian matrix of the measurement function,

is the estimated state variable,

is the error between the measurement data and the measurement function,

Is

can be

The processor 220 may calculate a measurement error through Equation (4).

[Equation 4]

은 측정 데이터와 추정된 측정 데이터 간의 측정 오차이고,

는

일 수 있다. 즉,

는 측정 에러에 대한 측정 오차의 민감도를 나타내는 오차 민감도 행렬일 수 있다.here,

is the measurement error between the measurement data and the estimated measurement data,

Is

can be in other words,

may be an error sensitivity matrix indicating the sensitivity of the measurement error to the measurement error.

를 계산한 결과 0이 아닌 원소를 가지는 위치만을 선택하여 계산할 수 있다. 이득 행렬의 역행렬에서 0이 아닌 원소를 가지는 위치는 이득 행렬에서 0이 아닌 원소를 가지는 위치와 동일한 위치일 수 있다. The processor 220 may predict an element of 0 in the inverse of the gain matrix to calculate the inverse of the gain matrix, and may calculate the inverse of the gain matrix by excluding the predicted element of 0 ( S200 ). The processor 220 is the processor 220 is the element position of the inverse of the gain matrix is

As a result of calculating , it can be calculated by selecting only positions that have non-zero elements. A position having a non-zero element in the inverse of the gain matrix may be the same position as a position having a non-zero element in the gain matrix.

)과, 이득 행렬(

)의 희소성을 이용하여 이득 행렬의 역행렬을 계산하기 위해 이득 행렬의 역행렬에서 0인 원소를 예측하고, 예측된 원소를 제외하고 희소 행렬의 역행렬을 계산함으로써 희소 행렬의 역행렬을 더 빠른 시간 내에 계산하도록 할 수 있다.The processor 220 is a Jacobian matrix (

) and the gain matrix (

) to calculate the inverse of the sparse matrix in a faster time by predicting the zero element in the inverse of the gain matrix and calculating the inverse of the sparse matrix by excluding the predicted element to calculate the inverse of the gain matrix using the sparsity of can do.

The processor 220 may calculate a covariance matrix of the measurement data ( S300 ). The processor 220 may detect bad data included in the measurement data set by using the covariance matrix. The processor 220 may calculate the covariance matrix through Equation (8).

[Equation 6]

는 이득 행렬로,

일 수 있다.

는 대칭 행렬일 수 있고, 각 행의 원소가 0이 아닌 원소의 개소가 극히 적은 희소 행렬일 수 있다. 일 수 있다. here,

is the gain matrix,

can be

may be a symmetric matrix, and may be a sparse matrix in which the number of non-zero elements in each row is extremely small. can be

)의 대각선의 원소만이 필요할 수 있다. 이에 따라, 프로세서(220)는 수학식 9를 통해 공분산 행렬의 원소를 계산할 수 있다.To perform the normalized residual error test, the covariance matrix (

) may only be needed on the diagonal of Accordingly, the processor 220 may calculate the elements of the covariance matrix through Equation (9).

[Equation 7]

,

는 자코비안 행렬에서 0이 아닌(non-zero) 원소이고,

는 이득 행렬의 역행렬의 원소일 수 있다.where m is the number of measured data, n is the number of state variables,

,

is a non-zero element in the Jacobian matrix,

may be an element of the inverse of the gain matrix.

After estimating the state of the power system 100 , the processor 220 may calculate a measurement error vector between each measurement data and a measurement function calculated using the estimated state variable. The processor 220 may calculate a measurement error vector through Equation (8).

[Equation 8]

는 i번째 측정 데이터와 측정 함수 사이의 측정 오차이고,

는 i번째 측정 데이터이고,

는 i번째 측정 데이터의 측정 함수이고,

는 추정된 상태변수 벡터일 수 있다.here,

is the measurement error between the i-th measurement data and the measurement function,

is the i-th measurement data,

is the measurement function of the i-th measurement data,

may be an estimated state variable vector.

The processor 220 may normalize the measurement data (S400). Normalization may be performed on the calculated measurement error. The processor 220 may normalize the measurement error through Equation (9).

[Equation 9]

는 정규화된 측정 오차이고,

는 i번째 측정 데이터에 대한 공분산일 수 있다.here,

is the normalized measurement error,

may be a covariance with respect to the i-th measurement data.

The processor 220 may determine the bad data based on the size of the normalized measurement error value (S500). When the normalized measurement error value is greater than or equal to a certain size, the processor 220 may determine that the data set includes bad data, and may determine that the data having the measurement error value is bad data and remove it.

를 만족하는 측정 데이터가 있을 경우 불량 데이터가 측정 데이터 셋에 포함된 것이므로, 측정 데이터 셋에서 k번째 측정 데이터를 제거할 수 있다.For example, the processor 220 may select one of the normalized measurement error values.

If there is measurement data that satisfies , the k-th measurement data can be removed from the measurement data set because the bad data is included in the measurement data set.

를 만족하는 측정 데이터가 없을 경우 불량 데이터가 측정 데이터 셋에 포함되지 않은 것이므로, 불량 데이터 처리를 종료할 수 있다.On the other hand, the processor 220 of the normalized measurement error value

When there is no measurement data that satisfies , since the bad data is not included in the measurement data set, the processing of the bad data can be terminated.

As described above, according to an embodiment of the present invention, when bad data is detected using the normalized residual error test in the measured data measured in the power system, the value at which the element becomes 0 is predicted in the matrix operation process, and the predicted gain It is possible to realize an apparatus and method for detecting bad data of measurement data, which improves the speed of detecting bad data by calculating a sparse inverse matrix by excluding zero elements of the matrix.

Those skilled in the art to which the present invention pertains should understand that the present invention may be embodied in other specific forms without changing the technical spirit or essential characteristics thereof, so the embodiments described above are illustrative in all respects and not restrictive. only do The scope of the present invention is indicated by the following claims rather than the detailed description, and all changes or modifications derived from the meaning and scope of the claims and their equivalent concepts should be construed as being included in the scope of the present invention. .

100: power system
200: bad data detection device
210: database
220: processor

Claims (24)

a database for storing measurement data measured in the power system;
The measurement function and measurement error are calculated using the measurement data, the Jacobian matrix and the gain matrix are calculated, the value of which the element becomes 0 in the matrix operation process is predicted, and the value among the elements of the inverse matrix of the predicted gain matrix is and a processor for calculating a sparse inverse matrix of the gain matrix excluding an element equal to 0, calculating a covariance matrix using the calculated sparse inverse matrix, and detecting bad data.
According to claim 1,
The processor calculates a vector of linearized measurement data in the state estimation of the power system through the following equation,
[Equation]

is a vector of linearized measurement data,

is the Jacobian matrix of the measurement function,

is a linearized state variable,

is a bad data detection device that is a measurement error.
3. The method of claim 2,
The processor estimates the state variable through the following equation,
[Equation]

is the estimated state variable,

is the Jacobian matrix of the measurement function,

is the variance matrix of the measurement data,

is a bad data detection device that is the error between the measurement data and the measurement function.
4. The method of claim 3,
The processor estimates a vector of measurement data through the estimated state variable, and the vector of the measurement data is estimated through the following equation,
[Equation]

is the vector of the estimated measurement data or the error between the estimated measurement data and the measurement function,

is the Jacobian matrix of the measurement function,

is the estimated state variable,

is the error between the measurement data and the measurement function,

Is

Bad data detection device.
5. The method of claim 4,
The processor calculates a measurement error between the measurement data and the estimated measurement data, and the measurement error between the measurement data and the estimated measurement data is calculated through the following equation,
[Equation]

is the measurement error between the measurement data and the estimated measurement data,

is the sensitivity of the measurement error to the measurement error,

Bad data detection device.
6. The method of claim 5,
The processor uses the sparsity of the Jacobian matrix to predict an element of 0 that does not need to be calculated when calculating the inverse of the gain matrix.

A device for detecting bad data that selects a position having a non-zero element as a result of calculating , and calculates a sparse inverse matrix of a gain matrix by using a non-zero element.
6. The method of claim 5,
The processor calculates the covariance matrix through the following equation,
[Equation]

m is the number of measured data, n is the number of state variables,

,

is a non-zero element in the Jacobian matrix,

is an element of the inverse of the gain matrix, a bad data detection device.
7. The method of claim 6,
The processor calculates a measurement error vector between the measurement function using the measurement data and the estimated state variable, and the measurement error vector is calculated through the following equation,
[Equation]

is the measurement error between the i-th measurement data and the measurement function,

is the i-th measurement data,

is the measurement function of the i-th measurement data,

is an estimated state variable vector, a bad data detection device.
9. The method of claim 8,
The processor performs normalization on the calculated measurement error, and the normalization is performed through the following equation,
[Equation]

is the normalized measurement error,

is the covariance of the i-th measurement data, a bad data detection device.
According to claim 1,
The processor determines that the data set includes bad data when the normalized measurement error is equal to or greater than a predetermined size, and determines that the measured data having the normalized measurement error equal to or greater than the predetermined size is defective data.
According to claim 1,
The processor determines that the bad data is not included in the dataset when the normalized measurement error is less than a predetermined size.
According to claim 1,
The gain matrix is a symmetric matrix and is a sparse matrix.
calculating a measurement function and a measurement error using the measurement data measured in the power system;
calculating a Jacobian matrix and a gain matrix;
predicting a value in which an element becomes 0 in a matrix operation process, and calculating a sparse inverse matrix of the gain matrix excluding an element having a value of 0 among elements of an inverse matrix of the predicted gain matrix; and
A method for detecting bad data, comprising: calculating a covariance matrix using the calculated sparse inverse matrix and detecting bad data.
14. The method of claim 13,
The step of calculating the measurement function and measurement error,
In estimating the state of the power system, a vector of linearized measurement data is calculated through the following equation,
[Equation]

is a vector of linearized measurement data,

is the Jacobian matrix of the measurement function,

is a linearized state variable,

is a measurement error, bad data detection method.
15. The method of claim 14,
The step of calculating the measurement function and measurement error,
Estimate the state variable through the following equation,
[Equation]

is the estimated state variable,

is the Jacobian matrix of the measurement function,

is the variance matrix of the measurement data,

is the error data detection method between the measurement data and the measurement function.
16. The method of claim 15,
The step of calculating the measurement function and measurement error,
A vector of measurement data is estimated through the estimated state variable, and the vector of the measurement data is estimated through the following equation,
[Equation]

is the vector of the estimated measurement data or the error between the estimated measurement data and the measurement function,

is the Jacobian matrix of the measurement function,

is the estimated state variable,

is the error between the measurement data and the measurement function,

Is

A method for detecting bad data.
17. The method of claim 16,
The step of calculating the measurement function and measurement error,
A measurement error between the measurement data and the estimated measurement data is calculated, and the measurement error between the measurement data and the estimated measurement data is calculated through the following equation,
[Equation]

is the measurement error between the measurement data and the estimated measurement data,

is the sensitivity of the measurement error to the measurement error,

A method for detecting bad data.
18. The method of claim 17,
Calculating the sparse inverse of the gain matrix comprises:
In order to predict the zero element that does not need to be calculated when calculating the inverse of the gain matrix using the sparsity of the Jacobian matrix.

A method for detecting bad data that selects a position having a non-zero element as a result of calculating
18. The method of claim 17,
The step of detecting the bad data includes:
Calculate the covariance matrix through the following equation,
[Equation]

m is the number of measured data, n is the number of state variables,

,

is a non-zero element in the Jacobian matrix,

is a bad data detection method that is an element of the inverse of the gain matrix.
18. The method of claim 17,
The step of detecting the bad data includes:
A measurement error vector between the measurement functions is calculated using the measurement data and the estimated state variable, and the measurement error vector is calculated through the following equation,
[Equation]

is the measurement error between the i-th measurement data and the measurement function,

is the i-th measurement data,

is the measurement function of the i-th measurement data,

is an estimated state variable vector, a bad data detection method.
21. The method of claim 20,
The step of detecting the bad data includes:
Normalization is performed on the calculated measurement error, and the normalization is performed through the following equation,
[Equation]

is the normalized measurement error,

is the covariance of the i-th measurement data, the bad data detection method.
14. The method of claim 13,
The step of detecting the bad data includes:
When the normalized measurement error is greater than or equal to a certain size, it is determined that the dataset contains defective data, and the measurement data having the normalized measurement error greater than or equal to a certain size is determined as defective data.
14. The method of claim 13,
The step of detecting the bad data includes:
A bad data detection method that determines that the dataset does not contain bad data when the normalized measurement error is less than a certain size.
14. The method of claim 13,
The step of detecting the bad data includes:
wherein the gain matrix is a symmetric matrix and a sparse matrix.

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