CN110726887A - Voltage sag detection method for in-situ power system - Google Patents

Voltage sag detection method for in-situ power system Download PDF

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CN110726887A
CN110726887A CN201910864658.XA CN201910864658A CN110726887A CN 110726887 A CN110726887 A CN 110726887A CN 201910864658 A CN201910864658 A CN 201910864658A CN 110726887 A CN110726887 A CN 110726887A
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covariance matrix
state
voltage sag
calculating
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汪冬辉
刘天明
王德林
周华
裘愉涛
黄晓明
陆承宇
王松
方芳
陈明
杨涛
孙文文
戚宣威
阮黎翔
孙志达
丁峰
罗华峰
沈奕菲
潘武略
吴佳毅
肖贤贵
吴通华
姚刚
郑小江
吴哲慧
黄志华
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State Grid Zhejiang Electric Power Co Ltd
Electric Power Research Institute of State Grid Zhejiang Electric Power Co Ltd
Nari Technology Co Ltd
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State Grid Zhejiang Electric Power Co Ltd
Electric Power Research Institute of State Grid Zhejiang Electric Power Co Ltd
Nari Technology Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Abstract

The invention discloses a method for detecting voltage sag of a localized power system. The technical scheme adopted by the invention is as follows: step 1), a nonlinear system is expressed by a state equation, and a covariance matrix and a volume fraction are calculated by a Cholesky decomposition method; step 2), calculating volume points of nonlinear function propagation, calculating a predicted measurement value in the k step, and calculating an innovative covariance matrix and a cross covariance matrix; step 3), respectively updating and calculating the state covariance matrix in the k step; and 4) estimating the amplitude, the frequency and the initial phase of the signal by adopting the STCKF accurate tracking state. The method is based on the cubature Kalman filtering, can track the change process of the voltage sag in real time, and can accurately calculate the amplitude, the phase, the frequency change and the voltage sag duration of the voltage sag.

Description

Voltage sag detection method for in-situ power system
Technical Field
The invention relates to the field of power quality detection of an in-place power system, in particular to a voltage sag detection method of the in-place power system based on strong tracking cubature Kalman filtering.
Background
With the rapid development of alternating current and direct current hybrid power grids in recent years, secondary equipment of a power system is gradually on site. The voltage sag of the localized system has an increasing impact on semiconductor loads of power electronic electrical equipment, computers and the like. Localized system voltage sag is one of the most prominent problems in power quality, and may cause significant economic loss to special power utilization equipment sensitive to power quality. In order to reduce the voltage sag and provide qualified power, various compensation devices including a Dynamic Voltage Restorer (DVR), a Unified Power Quality Controller (UPQC), etc. are used in the localization system, and one of the key steps of the compensation devices is to calculate the amplitude, duration and phase jump of the voltage sag, so that it is very important to detect the voltage sag of the localization system quickly and accurately.
At present, a fundamental frequency single vector S transformation voltage sag detection method is mainly adopted for voltage sag detection. The method comprises the steps of data acquisition and counting, sequence calculation, fundamental frequency single vector S conversion and voltage sag parameter identification, and the steps are sequentially circulated to realize the real-time detection of the voltage sag. Although fundamental frequency single vector S transformation can better capture voltage sag characteristics, noise resistance is poor, and the fundamental frequency single vector S transformation is easily influenced by white noise, so that the actual change phase difference of an obtained voltage sag amplitude change signal source is increased. The voltage sag detection method using the fundamental frequency vector cannot accurately capture the frequency change and the voltage sag duration in the voltage sag process.
In summary, how to provide a voltage sag detection method with strong noise immunity, small response delay and high estimation precision is a problem to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the present invention is to overcome the above drawbacks of the prior art, and provide a localized system voltage sag detection method based on a strong tracking volume kalman filter, which is capable of tracking the voltage sag change process in real time based on the volume kalman filter, so as to accurately calculate the amplitude, phase, frequency change, and voltage sag duration of the voltage sag.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: a localized power system voltage sag detection method, comprising:
step 1), a nonlinear system is expressed by a state equation, and a covariance matrix and a volume fraction are calculated by a Cholesky decomposition method;
step 2), calculating volume points of nonlinear function propagation, calculating a predicted measurement value in the k step, and calculating an innovative covariance matrix and a cross covariance matrix;
step 3), respectively updating and calculating the state covariance matrix in the k step;
and 4) estimating the amplitude, the frequency and the initial phase of the signal by adopting the STCKF accurate tracking state.
The invention can not only be free from the influence of white noise, but also accurately detect the amplitude, the phase, the frequency change and the duration of the voltage sag, and has better real-time property and strong tracking property.
Further, the specific content of step 1) is as follows:
1) the state equation of a nonlinear system is expressed by the following equation:
wherein x iskIs a state vector, zkTo measure the vector, wk-1、vkProcess noise and measurement noise, respectively; f (x)k-1) Expressed as a function of a nonlinear equation of state, h (x)k) Representing a nonlinear observation equation function;
2) covariance matrix was calculated using Cholesky decomposition:
Sk-1＝chol(Pk-1)，
wherein chol (. cndot.) refers to Cholesky decomposition coefficient, Sk-1Is the Cholesky matrix decomposition result; pk-1Representing a covariance matrix;
3) the volume fraction is calculated as follows:
Xi,k-1＝xk-1+Sk-1ξi，
the volume point xiiAnd corresponding weight omegaiCalculated by the following formula:
Figure BDA0002200904950000031
Figure BDA0002200904950000032
where i is 1,2, …, 2n, n is a status number, [1 ═ 1]Is all permutations, vector 1]i＝[1 0 … 0]T。
Further, the specific content of step 2) is as follows:
calculate the volume point of the nonlinear function propagation:
X* i,k＝f(Xi,k-1)，
calculating a prediction state and prediction error covariance matrix:
Figure BDA0002200904950000034
in the formula, Qk-1A covariance matrix representing process noise, m represents the dimension of the state variable,a weighted mean representing the predicted state;
the Cholesky decomposition results were calculated:
Sk/k-1＝chol(P* k/k-1)，
calculate the volume point of the nonlinear function propagation:
Zi,k＝h(Xi,k)，
calculating the predicted measurement value of the k step:
respectively calculating an innovation covariance matrix and a cross covariance matrix:
Figure BDA0002200904950000037
Figure BDA0002200904950000038
in the formula, RKA covariance matrix representing the measurement noise.
Further, the specific content of step 3) is as follows: after obtaining a new measurement value, the state matrix and covariance matrix in the k-th step are respectively updated as:
Figure BDA0002200904950000041
Kk＝Pxz,k/Pzz,k，
in the formula, KkIs a Kalman filter gain matrix, Pxz，kRepresenting the cross-covariance of the state values and the observed values, Pzz，kAn autocovariance representing the observed value;
calculating a state covariance matrix:
Pk＝Pk/k-1-KkPzz,kKT k，
in the formula, Pk/k-1Representing a state covariance matrix.
Further, the specific content of step 4) is as follows:
accurate tracking of states using STCKF
Figure BDA0002200904950000042
Wherein λ iskThe calculation formula of (a) is as follows:
Figure BDA0002200904950000043
NK+1＝V0,k+1-HkQkHk T-βRk+1，
Hk＝P* xz,k/P* k/k-1，
Figure BDA0002200904950000044
γk＝zk-h(xk)，
Figure BDA0002200904950000045
wherein R isKRepresenting process noise variance, lambda is an fading factor of a strong tracking algorithm, tr (-) represents trace-solving operation, gamma represents a residual error of an observed value, and beta is a coefficient for adjusting the fading factor; v0，k+1Representing the product of the residual vector and the residual transposed vector in the k-th calculation process; v0，kRepresenting the product of the residual vector and the residual transposed vector in the calculation process of the step (k-1); ρ represents a weakening factor, typically taken to be 0.95; l represents a signal length; hkThe variable name is expressed, and the actual meaning is not realized;to representTransposing;
the voltage signal in the power system is represented by the following equation:
Figure BDA0002200904950000051
in the formula, ω represents an angular frequency,
the estimated signal amplitude, frequency, and initial phase are:
Figure BDA0002200904950000052
Figure BDA0002200904950000053
Figure BDA0002200904950000054
wherein u isqAnd udCalculated from the following formula:k denotes the kth sampling point, T denotes the sampling interval, x1、x2、x3Respectively represent 1 st, 2 nd and 3 rd state variables;
in the formula, A,
Figure BDA0002200904950000056
f represents the signal amplitude, initial phase, frequency, u, respectivelyqAnd udThere is no practical meaning as an intermediate variable for the calculation.
Furthermore, the performance of the STCKF is evaluated by adopting three indexes of overshoot, response time and total error.
Compared with the prior art, the invention has the following advantages:
the method can accurately detect the amplitude, phase, frequency change and duration of the voltage sag under the condition of considering the influence of white noise, has smaller response delay and higher precision estimation, and meets the requirement of dynamic voltage compensation of the power system on voltage sag detection.
Drawings
FIG. 1a is a graph of a time varying frequency signal with 30dB of white Gaussian noise added thereto according to an embodiment of the present invention;
FIG. 1b is a graph of the voltage sag detection results of FIG. 1a using strong tracking volume Kalman filtering (STCKF);
FIG. 1c is a graph of signal source phase angle variation tracking of FIG. 1 a;
FIG. 1d is a graph of the phase transition occurrence time and voltage sag duration of FIG. 1 a;
FIG. 2a is a graph of a time varying frequency signal with 30dB of white Gaussian noise added according to another embodiment of the present invention;
fig. 2b is a graph of the frequency tracking performance of fig. 2 a.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
The embodiment provides a method for detecting voltage sag of an in-place system based on strong tracking cubature Kalman filtering, which comprises the following steps:
step 1), a nonlinear system is expressed by a state equation, and a covariance matrix and a volume fraction are calculated by a Cholesky decomposition method;
step 2), calculating volume points of nonlinear function propagation, calculating a predicted measurement value in the k step, and calculating an innovative covariance matrix and a cross covariance matrix;
step 3), respectively updating and calculating the state covariance matrix in the k step;
and 4) estimating the amplitude, the frequency and the initial phase of the signal by adopting the STCKF accurate tracking state.
The invention can not only be free from the influence of white noise, but also accurately detect the amplitude, the phase, the frequency change and the duration of the voltage sag, and has better real-time property and strong tracking property.
The specific content of step 1) is as follows:
1) the state equation of a nonlinear system is expressed by the following equation:
Figure BDA0002200904950000061
wherein x iskIs a state vector, zkTo measure the vector, wk-1、vkProcess noise and measurement noise, respectively; f (x)k-1) As a function of a nonlinear equation of state, h (x)k) Is a nonlinear observation equation function.
2) Covariance matrix was calculated using Cholesky decomposition:
Sk-1＝chol(Pk-1)，
wherein chol (. cndot.) refers to Cholesky decomposition coefficient, Sk-1Is the Cholesky matrix decomposition result; pk-1Is a covariance matrix.
3) The volume fraction calculation is calculated as follows:
Xi,k-1＝xk-1+Sk-1ξi，
the volume point xiiAnd corresponding weight omegaiCalculated by the following formula:
Figure BDA0002200904950000071
Figure BDA0002200904950000072
where i is 1,2, …, 2n, n is a status number, [1 ═ 1]Is all permutations, vector 1]i＝[1 0 … 0]T。
The specific content of step 2) is as follows:
calculate the volume point of the nonlinear function propagation:
X* i,k＝f(Xi,k-1)，
calculating a prediction state and prediction error covariance matrix:
Figure BDA0002200904950000073
Figure BDA0002200904950000074
in the formula, Qk-1A covariance matrix representing process noise, m represents the dimension of the state,
Figure BDA0002200904950000075
representing a weighted average of the prediction states.
The Cholesky decomposition results were calculated:
Sk/k-1＝chol(P* k/k-1)，
calculate the volume point of the nonlinear function propagation:
Zi,k＝h(Xi,k)，
calculating the predicted measurement value of the k step:
Figure BDA0002200904950000081
respectively calculating an innovation covariance matrix and a cross covariance matrix:
Figure BDA0002200904950000082
Figure BDA0002200904950000083
in the formula, RKA covariance matrix representing the measurement noise.
The specific content of step 3) is as follows: after obtaining a new measurement value, the state matrix and covariance matrix in the k-th step are respectively updated as:
Figure BDA0002200904950000084
Kk＝Pxz,k/Pzz,k，
in the formula, KkIs a Kalman filter gain matrix, Pxz，kA cross-covariance matrix, P, representing state values and observed valueszz，kAn autocovariance matrix representing the observed values.
Calculating a state covariance matrix:
Pk＝Pk/k-1-KkPzz,kKT k。
in the formula, Pk/k-1Representing a state covariance matrix.
The specific content of the step 4) is as follows:
accurate tracking of states using STCKF
Figure BDA0002200904950000085
Wherein λ iskIs calculated as follows：
NK+1＝V0,k+1-HkQkHk T-βRk+1
Figure BDA0002200904950000087
Hk＝P* xz,k/P* k/k-1
Figure BDA0002200904950000088
γk＝zk-h(xk)，
Wherein R isKRepresenting process noise variance, lambda is an fading factor of a strong tracking algorithm, tr (-) represents trace-solving operation, gamma represents a residual error of an observed value, and beta is a coefficient for adjusting the fading factor; v0，k+1Representing the product of the residual vector and the residual transposed vector in the k-th calculation process; v0，kRepresenting the product of the residual vector and the residual transposed vector in the calculation process of the step (k-1); ρ represents a weakening factor; l represents a signal length; hkThe variable name is expressed, and the actual meaning is not realized;
Figure BDA0002200904950000092
to represent
Figure BDA0002200904950000093
The transposing of (1).
The voltage signal in the power system is represented by the following equation:
Figure BDA0002200904950000094
in the formula, ω represents an angular frequency,
the estimated signal amplitude, frequency, and initial phase are:
Figure BDA0002200904950000095
Figure BDA0002200904950000096
Figure BDA0002200904950000097
wherein u isqAnd udCalculated from the following formula:
Figure BDA0002200904950000098
k denotes the kth sampling point, T denotes the sampling interval, x1、x2、x3Respectively representing 1 st, 2 nd and 3 rd state variables.
In the formula, A,
Figure BDA0002200904950000099
f represents the signal amplitude, initial phase, frequency, u, respectivelyqAnd udThere is no practical meaning as an intermediate variable for the calculation.
The invention adopts three indexes of overshoot, response time and total error to evaluate the performance of STCKF.
Application example
It should be noted that, according to the IEEE-1159 power quality standard, the voltage sag matlab simulation test method provided in the application example of the present invention is based on the PQD including voltage sag, expansion, interruption, transient harmonics, notches, and spikes, and only the problems of voltage sag, frequency deviation, and the like are discussed here. The sampling frequency of all investigated signals was 6400Hz, i.e. 128 samples per cycle.
1. Voltage sag identification
The voltage sag signal source with phase jump is shown as the following formula
Figure BDA0002200904950000101
In order to make the simulation test condition closer to the field reality, 30dB white gaussian noise is added on the time-varying frequency signal as shown in fig. 1 a. The voltage sag detection result of Strong Tracking Cubature Kalman Filter (STCKF) is shown in fig. 1b, and it is obvious that STCKF can not only immediately track the change of signal amplitude, but also has faster tracking speed than CKF. Phase angle variation tracking of signal sources as shown in fig. 1c, STCKF is able to accurately identify the process of phase angle transitioning from 0 degrees to 30 degrees at 0.1s and then back to 0 degrees at 0.2 s. And the phase transition occurrence time and the voltage sag duration are accurately indicated by the decay factor as shown in fig. 1 d.
In order to compare the effects of the two methods, the invention introduces three voltage sag detection quantization indexes of overshoot, duration and comprehensive error. Table I shows that STCKF has 7% overshoot at the beginning of the sag, 1.83% overshoot at the end of the sag, and a smaller overshoot compared to STCKF. In addition, the response delay of the STCKF at the beginning and the end of the pause is relatively small, which shows that the strong tracking performance of the STCKF is better. The amplitude and phase errors of the STCKF sum are 0.46% and 2.27%, respectively, and the amplitude and phase errors of the CKF sum are 1.58% and 5.68%, respectively, which shows that the estimation error of the STCKF is significantly smaller than the CKF.
TABLE I overshoot and duration in phase tracking
Figure BDA0002200904950000102
2. Frequency estimation
To compensate for voltage sags, dynamic voltage compensators (DVRs) require frequency to synthesize a specified voltage, and therefore it is important to accurately obtain frequency variations. The nominal frequency of the power system is 50HZ, while the actual frequency at which the system operates is typically slightly variable. The time-varying frequency signal is given by the following equation.
Figure BDA0002200904950000111
In order to make the simulation test condition closer to the field reality, 30dB of white Gaussian noise is added on the time-varying frequency signal as shown in FIG. 2a, and the frequency of the signal jumps from 50HZ to 52HZ at 0.1 s. The STCKF performance in frequency tracking is clearly better than CKF as shown in fig. 2 b. The overshoot and response time indices of table II indicate that both STCKF and CKF can accurately estimate frequency, while the STCKF response time is less than CKF. And the total error of the STCKF is only 0.28 percent, which shows that the performance of the STCKF is better.
TABLE II overclocking and response time for frequency tracking
Figure BDA0002200904950000112
Matlab simulation results show that compared with CKF, the method has smaller total error and higher response speed.
Finally, it is also noted that the above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (6)

1. A method for detecting a voltage sag in a localized power system, comprising:
step 1), a nonlinear system is expressed by a state equation, and a covariance matrix and a volume fraction are calculated by a Cholesky decomposition method;
step 2), calculating volume points of nonlinear function propagation, calculating a predicted measurement value in the k step, and calculating an innovative covariance matrix and a cross covariance matrix;
step 3), respectively updating and calculating the state covariance matrix in the k step;
and 4) estimating the amplitude, the frequency and the initial phase of the signal by adopting the STCKF accurate tracking state.
2. The on-site power system voltage sag detection method according to claim 1, wherein the specific content of step 1) is as follows:
1) the state equation of a nonlinear system is expressed by the following equation:
Figure FDA0002200904940000011
wherein x iskIs a state vector, zkTo measure the vector, wk-1、vkProcess noise and measurement noise, respectively; f (x)k-1) As a function of a nonlinear equation of state, h (x)k) Is a nonlinear observation equation function;
2) covariance matrix was calculated using Cholesky decomposition:
Sk-1＝chol(Pk-1)，
wherein chol (. cndot.) refers to Cholesky decomposition coefficient, Sk-1Is the Cholesky matrix decomposition result; pk-1Is a covariance matrix;
3) the volume fraction is calculated as follows:
Xi,k-1＝xk-1+Sk-1ξi，
the volume point xiiAnd corresponding weight omegaiCalculated by the following formula:
Figure FDA0002200904940000012
Figure FDA0002200904940000013
where i is 1,2, …, 2n, n is a status number, [1 ═ 1]Is all permutations, vector 1]i＝[1 0 … 0]T。
3. The on-site power system voltage sag detection method according to claim 2, wherein the specific content of step 2) is as follows:
calculate the volume point of the nonlinear function propagation:
X* i,k＝f(Xi,k-1)，
calculating a prediction state and prediction error covariance matrix:
Figure FDA0002200904940000021
Figure FDA0002200904940000022
in the formula, Qk-1A covariance matrix representing process noise, m represents the dimension of the state variable,
Figure FDA0002200904940000023
a weighted mean representing the predicted state;
the Cholesky decomposition results were calculated:
Sk/k-1＝chol(P* k/k-1)，
calculate the volume point of the nonlinear function propagation:
Zi,k＝h(Xi,k)，
calculating the predicted measurement value of the k step:
Figure FDA0002200904940000024
separately computing innovation covariance matrix and cross covariance matrix
Figure FDA0002200904940000025
In the formula, RKA covariance matrix representing the measurement noise.
4. The on-site power system voltage sag detection method according to claim 3, wherein the specific content of step 3) is as follows: after obtaining a new measurement value, the state matrix and covariance matrix in the k-th step are respectively updated as:
Figure FDA0002200904940000031
Kk＝Pxz,k/Pzz,k，
in the formula, KkIs a Kalman filter gain matrix, Pxz，kRepresenting the cross-covariance of the state values and the observed values, Pzz，kAn autocovariance representing the observed value;
calculating a state covariance matrix:
Pk＝Pk/k-1-KkPzz,kKT k，
in the formula, Pk/k-1Is a state covariance matrix.
5. The on-site power system voltage sag detection method according to claim 4, wherein the specific content of step 4) is as follows:
accurate tracking of states using STCKF
Figure FDA0002200904940000032
Wherein λ iskThe calculation formula of (a) is as follows:
Figure FDA0002200904940000033
NK+1＝V0,k+1-HkQkHk T-βRk+1
Figure FDA0002200904940000034
Hk＝P* xz,k/P* k/k-1
γk＝zk-h(xk)，
Figure FDA0002200904940000036
wherein R isKRepresenting process noise variance, lambda is an fading factor of a strong tracking algorithm, tr (-) represents trace-solving operation, gamma represents a residual error of an observed value, and beta is a coefficient for adjusting the fading factor; v0，k+1Representing the product of the residual vector and the residual transposed vector in the k-th calculation process; v0，kRepresenting the product of the residual vector and the residual transposed vector in the calculation process of the step (k-1); ρ represents a weakening factor; l represents a signal length; hkThe variable name is expressed, and the actual meaning is not realized;
Figure FDA0002200904940000041
to represent
Figure FDA0002200904940000042
Transposing;
the voltage signal in the power system is represented by the following equation:
Figure FDA0002200904940000043
in the formula, ω represents an angular frequency;
the estimated signal amplitude, frequency, and initial phase are:
Figure FDA0002200904940000044
Figure FDA0002200904940000045
Figure FDA0002200904940000046
wherein u isqAnd udCalculated from the following formula:
Figure FDA0002200904940000047
k denotes the kth sampling point, T denotes the sampling interval, x1、x2、x3Respectively represent 1 st, 2 nd and 3 rd state variables;
in the formula, A,
Figure FDA0002200904940000048
f represents the signal amplitude, initial phase, frequency, u, respectivelyqAnd udThere is no practical meaning as an intermediate variable for the calculation.
6. The localized power system voltage sag detection method of any one of claims 1 to 5, wherein the STCKF performance is evaluated by using three indexes, namely overshoot, response time and total error.
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