CN113591801A - Power signal parameter estimation method and device - Google Patents

Power signal parameter estimation method and device Download PDF

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CN113591801A
CN113591801A CN202111002248.8A CN202111002248A CN113591801A CN 113591801 A CN113591801 A CN 113591801A CN 202111002248 A CN202111002248 A CN 202111002248A CN 113591801 A CN113591801 A CN 113591801A
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power signal
error covariance
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王康乐
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Guangdong Power Grid Co Ltd
Shaoguan Power Supply Bureau Guangdong Power Grid Co Ltd
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Shaoguan Power Supply Bureau Guangdong Power Grid Co Ltd
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Abstract

The embodiment of the invention discloses a method and a device for estimating parameters of a power signal. The method establishes a first-order central difference model, and because the first-order central difference term not only comprises the first-order term of the common Taylor expansion, but also comprises other nonlinear terms, therefore, the calculation accuracy of the first-order central difference item is high, the calculation accuracy of the fading factor obtained by solving the first-order central difference model is also high, the calculation accuracy of the first prediction error covariance matrix obtained by solving the fading factor is higher, the accuracy of the filter gain matrix obtained by solving according to the first prediction error covariance matrix is higher, and finally the estimation accuracy of the state estimation of the power signal parameters is improved, the calculation process is simple, and the robustness of the system can be improved due to the introduction of the fading factor, therefore, by the method, the calculation amount can be reduced and the estimation precision can be improved on the basis of ensuring the robustness of the algorithm.

Description

Power signal parameter estimation method and device
Technical Field
The embodiment of the invention relates to an estimation technology of power parameters, in particular to a power signal parameter estimation method and device.
Background
In the estimation algorithms for the amplitude, the frequency and the phase angle of the power signal, the extended Kalman filtering algorithm and the unscented Kalman filtering algorithm cannot estimate parameters of sudden change of the power signal due to lack of robustness. The strong tracking Kalman filtering algorithm introduces an evanescent factor, and the robustness of the algorithm is improved. However, for a nonlinear system, the nonlinear equation is linearized by using a taylor series expansion, so that the convergence speed and the estimation accuracy of the algorithm are reduced. Based on an improved strong tracking unscented Kalman filtering algorithm and a particle filtering thought, the convergence speed and the estimation precision of the algorithm are improved, but in the parameter estimation process, the sigma point needs to be selected for 3 times according to a symmetric sampling strategy, the calculation amount is large, the calculation process is complex, and the condition of parameter estimation divergence is easy to occur.
Disclosure of Invention
The invention provides a method and a device for estimating parameters of an electric power signal, which are used for reducing calculated amount and improving estimation precision on the basis of ensuring algorithm robustness.
In a first aspect, an embodiment of the present invention provides a method for estimating parameters of an electric power signal, where the method includes:
solving the nonlinear functions of the one-step prediction state vector and the one-step prediction measurement equation;
acquiring an actual power signal parameter measurement value;
establishing a first-order central difference model, and solving an elimination factor according to the first-order central difference model;
introducing the fading factor into a prediction error covariance matrix to obtain a first prediction error covariance matrix;
determining a filter gain matrix according to the first prediction error covariance matrix;
and determining state estimation according to the one-step prediction state vector, the one-step prediction measurement equation nonlinear function, the actual power signal parameter measurement value and the filter gain matrix.
Optionally, the first order central difference model is:
Figure BDA0003235906560000021
wherein the content of the first and second substances,
Figure BDA0003235906560000022
representing the first central differential derivative, μRepresenting an iteration step size;
Figure BDA0003235906560000023
and
Figure BDA0003235906560000024
is a non-linear function.
Optionally, the solving for the fading factor according to the first-order central difference model includes:
Figure BDA0003235906560000025
wherein the content of the first and second substances,
Figure BDA0003235906560000026
Nk+1＝Vk+1-AAT-βRk+1
Mk+1＝CCT
wherein λ isk+1Is a fading factor, Vk+1Is a matrix, Rk+1Is a matrix, Nk+1Is a matrix, Mk+1And the matrix A and the matrix C are obtained according to the first-order central difference model.
Optionally, the prediction error covariance matrix is:
Pk+1|k＝Fk+1|kPkFk+1|k T+Qk
wherein, Pk+1|kRepresenting the prediction error covariance matrix, QkA non-negative-definite variance matrix representing process noise;
the calculation method of the matrix A and the matrix C obtained according to the first-order central difference model is as follows:
the prediction error covariance matrix Pk+1|kCholesky decomposition was performed to obtain:
Pk+1|k＝SWSW T
then according to the first-order central difference model, a matrix A can be obtainedj，
Figure BDA0003235906560000031
Wherein j is 1 … n, n is the dimension of the state vector; a. thejRepresents the j-th column, S, of the matrix Aw,jRepresentation matrix SwColumn j, μ denotes the iteration step,
Figure BDA0003235906560000032
is the predicted state phasor at time k +1,
Figure BDA0003235906560000033
and
Figure BDA0003235906560000034
is a linear function;
f in the prediction error covariance matrixk+1|kPkFk+1|k TCholesky decomposition was performed to obtain:
Fk+1|kPkFk+1|k T＝BBT
then, according to the first-order central difference model, a matrix C can be obtainedj，
Figure BDA0003235906560000035
Wherein, BjRepresents the jth column, C, of the matrix BjRepresenting the jth column of matrix C.
Optionally, the method for calculating the first prediction error covariance matrix by introducing the fading factor into the prediction error covariance matrix includes:
Figure BDA0003235906560000036
wherein the content of the first and second substances,
Figure BDA0003235906560000037
representing a first prediction error covariance matrix.
Optionally, the filter gain matrix is determined according to the first prediction error covariance matrix, and the calculation method includes:
performing Cholesky decomposition on the first prediction error covariance matrix to obtain:
Figure BDA0003235906560000041
then according to the first-order central difference model, a matrix D can be obtainedj，
Figure BDA0003235906560000042
Wherein D isjRepresents the jth column of matrix D; gain filter matrix K can be obtainedk+1
Figure BDA0003235906560000043
Optionally, the determining a state estimate according to the one-step predicted state vector, the one-step predicted measurement equation nonlinear function, the actual power signal parameter measurement value, and the filter gain matrix includes:
obtaining the error of the measured value according to the difference between the actual power signal parameter measured value and the nonlinear function of the measurement equation;
and multiplying the error of the measurement value by the filter gain matrix and accumulating the error and the one-step prediction state vector to obtain the state estimation.
Optionally, the power signal parameter estimation method further includes estimating a power signal parameter according to the first prediction error covariance matrix, the filter gain matrix, and the matrix
Figure BDA0003235906560000044
And the matrix D is used for obtaining a post-test error covariance matrix.
Optionally, the first prediction error covariance matrix, the filter gain matrix, the matrix are selected based on the first prediction error covariance matrix
Figure BDA0003235906560000045
And the matrix D is used for obtaining a post-test error covariance matrix, and the calculation method comprises the following steps:
Figure BDA0003235906560000046
wherein, Pk+1Representing the post-test error covariance matrix.
In a second aspect, an embodiment of the present invention further provides an apparatus for estimating parameters of an electrical power signal, where the apparatus includes:
the prediction quantity solving module is used for solving the nonlinear functions of the one-step prediction state vector and the one-step prediction measurement equation;
the actual measurement value acquisition module is used for acquiring an actual power signal parameter measurement value;
the model establishing module is used for establishing a first-order central difference model;
the fading factor solving module is used for solving fading factors according to the first-order central difference model;
the first prediction error covariance matrix calculation module is used for introducing the fading factor into a prediction error covariance matrix to obtain a first prediction error covariance matrix;
a filter gain matrix determination module, configured to determine a filter gain matrix according to the first prediction error covariance matrix;
and the state estimation determining module is used for determining state estimation according to the one-step prediction state vector, the one-step prediction measurement equation nonlinear function, the actual power signal parameter measurement value and the filter gain matrix.
The invention provides a power signal parameter estimation method and device. The method establishes a first-order central difference model, and because the first-order central difference term not only comprises a first-order term of a common Taylor expansion but also comprises other nonlinear terms, the calculation precision of the first-order central difference term is high, the calculation precision of an extinction factor obtained by solving the first-order central difference model is also higher, the calculation precision of a first prediction error covariance matrix obtained by solving the extinction factor is also higher, the precision of a filter gain matrix obtained by solving the first prediction error covariance matrix is also higher, the estimation precision of the state estimation of the power signal parameter is finally improved, the calculation process is simple, the calculation amount is small, and the robustness of the system can be improved due to the introduction of the extinction factor, so the calculation amount is reduced on the basis of ensuring the robustness of the algorithm by the method, and the estimation precision is improved.
Drawings
Fig. 1 is a flowchart of a method for estimating parameters of an electrical signal according to a first embodiment of the present invention;
FIG. 2 is a simulation diagram of frequency tracking of an electrical signal according to a second embodiment of the present invention;
FIG. 3 is a simulation diagram of tracking voltage amplitude of an electric power signal according to a second embodiment of the present invention;
FIG. 4 is a simulation diagram of phase angle tracking of an electric power signal according to a second embodiment of the present invention;
FIG. 5 is a timing diagram illustrating a comparison of power signal parameter estimation run times according to a second embodiment of the present invention;
fig. 6 is a block diagram of a power signal parameter estimation apparatus according to a third embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some of the structures related to the present invention are shown in the drawings, not all of the structures.
Example one
Fig. 1 is a flowchart of a power signal parameter estimation method according to a first embodiment of the present invention, which is applicable to estimating power signal parameters in a power system, and the method can be executed by a power signal parameter estimation device, and specifically includes the following steps:
and 110, solving the nonlinear functions of the one-step prediction state vector and the one-step prediction measurement equation.
Specifically, for the case where the state equation is linear and the measurement equation is nonlinear, the discrete system is assumed to be represented as the following equation:
Figure BDA0003235906560000061
Figure BDA0003235906560000062
wherein, formula (1) represents the linear state equation of the system, and formula (2) is the nonlinear measurement equation of the system; fk+1|kIn order to be a state transition matrix,
Figure BDA0003235906560000071
is a nonlinear function of the measurement equation;
Figure BDA0003235906560000072
representing phasors of the system, ykRepresenting a measurement of the system; k represents a discrete time variable; w is ak、vkThe statistical property of the white gaussian noise which is uncorrelated and has a mean value of zero can be expressed as:
Figure BDA0003235906560000073
wherein Q isk、RkRespectively process noise wkAnd observation noise vkOf the covariance matrix, QkIs a non-negative definite matrix, RkIs a positive definite matrix, δkjIs a kronecker-delta function.
Based on the above, for the fundamental voltage signal model, the following state equation and measurement equation can be established: specifically, the state vector is defined as:
Figure BDA0003235906560000074
the state equation for the fundamental voltage signal can be described as:
Figure BDA0003235906560000075
as can be seen from the corresponding equation (1), the established equation of state of the fundamental voltage signal does not contain the process noise wkAnd a state transition matrix Fk+1|kCan be expressed as:
Figure BDA0003235906560000076
the measurement equation for the fundamental voltage signal can be described as:
yk＝xk1sin(xk2)+vk (7)
Figure BDA0003235906560000077
in the formula xk1、xk2、xk3Respectively the voltage amplitude, phase and frequency of the selected fundamental voltage signal at the time k,
Figure BDA0003235906560000078
is a phase angle, TsIs a sampling time interval in which
Figure BDA0003235906560000079
Thus, according to the state equation, the first prediction of the state quantities at the next time k +1 is solved, i.e. first one is solvedStep prediction state phasor
Figure BDA0003235906560000081
The expression is as follows:
Figure BDA0003235906560000082
then, the specific method for solving the nonlinear function of the one-step prediction measurement equation at the moment of k +1 is as follows:
the measurement equation of the fundamental voltage signal discrete at time k can be described as:
yk＝xk,1sin(xk,2)+vk (10)
the measurement equation of the fundamental voltage signal discrete at the time K +1 can be described as follows:
yk+1＝xk+1,1sin(xk+1,2)+vk+1 (11)
compared with that in formula (2)
Figure BDA0003235906560000083
X in the above formula (11)k+1,1Can use the function
Figure BDA0003235906560000084
Is shown, i.e.
Figure BDA0003235906560000085
Then the one-step predicted state phasor obtained by equation (9) is used
Figure BDA0003235906560000086
By substituting equation (12), one-step predictive measurement equation nonlinear function at time k +1 can be obtained, i.e.
Figure BDA0003235906560000087
Wherein the noise is observed when not consideredSound vkWhen the measured value is the factor (2), the nonlinear function of the one-step prediction measurement equation is the one-step prediction measurement value.
And step 120, acquiring an actual power signal parameter measurement value.
Wherein, the actual power signal parameter measurement value at the time k +1 is set as yk+1And the actual power signal parameter measurement value at the moment K +1 can be obtained and fed back through power signal detection equipment such as a sensor. The difference between the measured value of the power signal parameter obtained by actual feedback and the nonlinear function of the one-step predicted measurement equation (i.e., the one-step predicted measurement value) obtained in step 110 is the deviation of the measurement value.
And step 130, establishing a first-order central difference model, and solving an elimination factor according to the first-order central difference model.
Wherein, the first order central difference model is:
Figure BDA0003235906560000091
wherein the content of the first and second substances,
Figure BDA0003235906560000092
denotes the first order central differential derivative, μ denotes the iteration step, and is usually taken as
Figure BDA0003235906560000093
Figure BDA0003235906560000094
And
Figure BDA0003235906560000095
is a non-linear function.
The first order central difference model is established based on a central difference theory, the central difference theory is a nonlinear filtering theory different from a traditional Taylor series expansion, and different from a first order derivative term in the Taylor series expansion, a first order term of a central difference algorithm not only comprises the first order derivative term of the Taylor series expansion, but also comprises a high order derivative term. Similar to the Taylor expansion algorithm, the central difference algorithm also employs a polynomial approximation technique for nonlinear functions.
Specifically, the specific solving process and principle of the first-order central difference model are as follows:
assuming a non-linear function f (x) in
Figure BDA0003235906560000096
The second order central differential expansion of (a) is:
Figure BDA0003235906560000097
Figure BDA0003235906560000098
Figure BDA0003235906560000099
wherein the content of the first and second substances,
Figure BDA00032359065600000910
and
Figure BDA00032359065600000911
representing the first and second derivatives of the central difference, respectively.
To make a non-linear function
Figure BDA00032359065600000912
And
Figure BDA00032359065600000913
is divided into tables
Figure BDA00032359065600000914
And (4) performing Taylor-series expansion, wherein the expansion term is as follows:
Figure BDA00032359065600000915
Figure BDA00032359065600000916
when formulae (17) and (18) are substituted for formula (14), there are:
Figure BDA0003235906560000101
from the formula (19), in comparison with f (x)
Figure BDA0003235906560000102
First derivative of the Taylor expansion of (A)
Figure BDA0003235906560000103
Figure BDA0003235906560000104
Not only contains a first derivative term, but also contains a high-order odd number order term, and obviously intercepts when nonlinear functions are linearized
Figure BDA0003235906560000105
Ratio intercept
Figure BDA0003235906560000106
The time linearization precision is high. Therefore, since the first-order central difference term includes not only the first-order term of the common taylor expansion but also other nonlinear terms, the calculation accuracy of the first-order central difference term is relatively high, and therefore, the calculation accuracy of the fading factor calculated by the first-order central difference model is also improved.
Wherein, the fading factor lambda is solved according to a first-order central difference modelk+1The calculation method comprises the following steps:
Figure BDA0003235906560000107
wherein the content of the first and second substances,
Figure BDA0003235906560000108
Nk+1＝Vk+1-AAT-βRk+1 (22)
Mk+1＝CCT (23)
wherein β is a softening factor, typically taken to be 2; the matrix A and the matrix C are obtained according to a first-order central difference model.
The specific process of solving the matrix A and the matrix C according to the first-order central difference model is as follows:
first, the prediction error covariance matrix is:
Pk+1|k＝Fk+1|kPkFk+1|k T+Qk (24)
wherein, Pk+1|kRepresenting the prediction error covariance matrix, QkA non-negative-definite variance matrix representing process noise;
will predict the error covariance matrix Pk+1|kPerforming Cholesky decomposition, one can obtain:
Pk+1|k＝SWSW T (25)
then, the nonlinear function is processed according to a first-order central difference model, namely equation (14)
Figure BDA0003235906560000111
And
Figure BDA0003235906560000112
substitution of formula (14) yields the matrix Aj，
Figure BDA0003235906560000113
Wherein j is 1 … n, n is the dimension of the state vector; a. thejRepresents the j-th column, S, of the matrix Aw,jRepresentation matrix SwColumn j of (1);
predicting F in the error covariance matrixk+1|kPkFk+1|k TPerforming Cholesky decomposition, one can obtain:
Fk+1|kPkFk+1|k T＝BBT (27)
then, according to a first-order central difference model, the nonlinear function is processed
Figure BDA0003235906560000114
And
Figure BDA0003235906560000115
by substituting formula (14), a matrix C can be obtainedj，
Figure BDA0003235906560000116
Wherein, BjRepresents the jth column, C, of the matrix BjRepresenting the jth column of matrix C.
Wherein V in the formula (22)k+1Representing the residual variance matrix, can be found by the following equation (29):
Figure BDA0003235906560000117
therefore, the matrix A and the matrix B can be obtained through Cholesky decomposition and calculation of a first-order central difference model, and then the fading factor is obtained through solving, and the calculation process is simple. And because the calculation accuracy of the first-order central difference model algorithm is higher, the calculation accuracy of the matrix A and the matrix C obtained by the calculation of the first-order central difference model is higher, and further the calculation accuracy of the fading factors is higher.
Step 140, introducing the fading factor into the prediction error covariance matrix to obtain a first prediction error covariance matrix.
Wherein the prediction error covariance matrix is:
Pk+1|k＝Fk+1|kPkFk+1|k T+Qk (24)
wherein, Pk+1|kRepresenting the prediction error covariance matrix, QkA non-negative-definite variance matrix representing process noise;
specifically, an evanescent factor is introduced into the prediction error covariance matrix to obtain a first prediction error covariance matrix, and the specific calculation method is as follows:
Figure BDA0003235906560000126
wherein the content of the first and second substances,
Figure BDA0003235906560000127
representing a first prediction error covariance matrix. Since the accuracy of the first-order central difference model algorithm is high, the accuracy of the fading factor obtained by solving the first-order central difference model is also high, and therefore the calculation accuracy of the first prediction error covariance matrix obtained by introducing the high-accuracy fading factor into the prediction error covariance matrix is also high.
Step 150, determining a filter gain matrix according to the first prediction error covariance matrix.
Wherein, a filter gain matrix is determined according to the first prediction error covariance matrix, and the specific calculation method comprises the following steps:
firstly, Cholesky decomposition is performed on the first prediction error covariance matrix, and the following results can be obtained:
Figure BDA0003235906560000121
then, according to a first-order central difference model, the nonlinear function is processed
Figure BDA0003235906560000122
And
Figure BDA0003235906560000123
a matrix D can be obtained by substituting formula (14)j，
Figure BDA0003235906560000124
Wherein D isjRepresents the jth column of matrix D; thus, a gain filter matrix K can be obtained from the matrix Dk+1
Figure BDA0003235906560000125
The first-order central difference model algorithm has high calculation accuracy, so that the matrix D obtained by using the first-order central difference model and the first prediction error covariance matrix have high calculation accuracy, and further the technical accuracy of the gain filtering matrix is high.
And step 160, determining state estimation according to the one-step prediction state vector, the one-step prediction measurement equation nonlinear function, the actual power signal parameter measurement value and the filter gain matrix.
The calculation accuracy of the first-order central difference model algorithm is high, and the calculation accuracy of the fading factor obtained by solving the first-order central difference model is also high, so that the calculation accuracy of the first prediction error covariance matrix obtained by calculating the fading factor is high, the calculation accuracy of the filter gain matrix obtained by solving the first prediction error covariance matrix is high, and the calculation accuracy of state estimation is improved finally.
Specifically, determining the state estimation according to the one-step prediction state vector, the one-step prediction measurement equation nonlinear function, the actual power signal parameter measurement value and the filter gain matrix specifically includes:
obtaining the error of the measured value according to the difference between the actual measured value of the power signal parameter and the nonlinear function of the measurement equation, i.e. obtaining the error of the measured value
Figure BDA0003235906560000131
The measured value of the power signal parameter is compared with the measured value of the power signal parameter obtained by solving the nonlinear function of the measurement equation to obtain the deviation of the measured value and the measured value, and then the deviation of the measured value is adjusted to improve the state estimation calculation accuracy.
And multiplying the error of the measured value by the filter gain matrix and accumulating the error and the one-step prediction state vector to obtain the state estimation.
Wherein the state estimation at the time of K +1
Figure BDA0003235906560000132
The calculation formula of (2) is as follows:
Figure BDA0003235906560000133
wherein the content of the first and second substances,
Figure BDA0003235906560000134
can be obtained from equation (9) in step 110,
Figure BDA0003235906560000135
can be determined from equation (13) in step 110 byk+1Can be measured from the actual power signal, Kk+1Can be obtained according to the formula (33) in the step 150.
On the basis of the technical scheme, the state estimation method can be used for correcting or adjusting the parameters of the power signals by combining the parameters actually measured by the power system so as to meet the requirements of parameter precision, errors and the like. The method and the device can also be used for monitoring or monitoring the power signal parameters of the power system in real time, for example, the electric wave states of the parameters such as the amplitude, the frequency and the phase angle of the voltage of the power system at the current time node are monitored in real time, so that a change oscillogram of the power signal parameters is provided for power system workers in time, the workers can observe the change of the parameters conveniently and visually, and the efficiency of monitoring or monitoring the power parameters of the power system is improved.
In the technical solution of this embodiment, the working principle of the power signal parameter estimation method is as follows: firstly, solving a one-step prediction state vector and a one-step prediction measurement equation nonlinear function; acquiring an actual power signal parameter measurement value; then, establishing a first-order central difference model, and solving an elimination factor according to the first-order central difference model; introducing an evanescence factor into the prediction error covariance matrix to obtain a first prediction error covariance matrix; determining a filter gain matrix according to the first prediction error covariance matrix; and finally, determining state estimation according to the one-step prediction state vector, the one-step prediction measurement equation nonlinear function, the actual electric power signal parameter measurement value and the filter gain matrix. Therefore, the calculation accuracy of the first-order central difference model algorithm is high, so that the calculation accuracy of an extinction factor obtained by using the first-order central difference model is higher, the calculation accuracy of a first prediction error covariance matrix obtained by using the extinction factor is higher, the accuracy of a filter gain matrix obtained by using the first prediction error covariance matrix is higher, and finally the estimation accuracy of the state estimation of the power signal parameters is improved.
In the technical solution of this embodiment, a method for estimating parameters of an electric power signal is provided, where the method includes: solving the nonlinear functions of the one-step prediction state vector and the one-step prediction measurement equation; acquiring an actual power signal parameter measurement value; establishing a first-order central difference model, and solving an elimination factor according to the first-order central difference model; introducing an evanescence factor into the prediction error covariance matrix to obtain a first prediction error covariance matrix; determining a filter gain matrix according to the first prediction error covariance matrix; and determining state estimation according to the one-step prediction state vector, the one-step prediction measurement equation nonlinear function, the actual power signal parameter measurement value and the filter gain matrix. The method obtains the fading factor by establishing a first-order central difference model and solving the fading factor by using the first-order central difference model, and because the first-order central difference term not only comprises the first-order term of the common Taylor expansion but also comprises other nonlinear terms, the calculation precision of the first-order central difference term is high, the calculation precision of the fading factor obtained by solving the first-order central difference model is higher, the calculation precision of a first prediction error covariance matrix obtained by solving the fading factor is higher, the precision of a filter gain matrix obtained by solving according to the first prediction error covariance matrix is higher, the estimation precision of the state estimation of the power signal parameter is improved finally, the calculation process is simple, the calculated amount is less, and the robustness of the system can be improved due to the introduction of the fading factor, so the method can realize that the robustness of the algorithm is ensured, the calculation amount is reduced, and the estimation precision is improved.
On the basis of the above technical solution, optionally, the method for estimating parameters of an electric power signal further includes obtaining a first prediction error covariance matrix, a filter gain matrix, and a matrix
Figure BDA0003235906560000155
And a matrix D, obtaining a post-test error covariance matrix.
The calculation accuracy of the first-order central difference model algorithm is high, the calculation accuracy of the first prediction error covariance matrix and the filter gain matrix obtained by indirectly solving according to the first-order central difference model is also improved, and the matrix
Figure BDA0003235906560000151
The sum matrix D is also calculated according to the first-order central difference model, so that the calculation accuracy of the post-test error covariance matrix is improved.
Optionally, the first prediction error covariance matrix, the filter gain matrix, the matrix
Figure BDA0003235906560000152
And a matrix D, obtaining a post-test error covariance matrix, wherein the calculation method comprises the following steps:
Figure BDA0003235906560000153
wherein, Pk+1A post-test error covariance matrix is represented,
Figure BDA0003235906560000154
the covariance matrix for the first prediction error can be obtained from equation (30), Kk+1For the filter gain matrix, the matrix can be obtained from equation (33), the matrix D can be obtained from equation (32), and the matrix D can be obtained from
Figure BDA0003235906560000161
Can be obtained according to formula (31).
Example two
Fig. 2 is a simulation diagram of a power signal frequency tracking provided in the second embodiment of the present invention, fig. 3 is a simulation diagram of a power signal voltage amplitude tracking provided in the second embodiment of the present invention, fig. 4 is a simulation diagram of a power signal phase angle tracking provided in the second embodiment of the present invention, and fig. 5 is a comparison timing diagram of power signal parameter estimation operation time provided in the second embodiment of the present invention. On the basis of the first embodiment, for example, simulation analysis is performed according to the power signal parameter estimation method, which includes the following steps:
for the fundamental voltage signal model, the following equation of state and measurement can be established:
define the state vector as:
Figure BDA0003235906560000162
the state equation for the fundamental voltage signal can be described as:
Figure BDA0003235906560000163
the measurement equation for the fundamental voltage signal can be described as:
yk＝xk1sin(xk2)+vk
in the formula xk1、xk2、xk3Are each a selected radicalThe voltage amplitude, phase and frequency of the wave voltage signal at time k,
Figure BDA0003235906560000164
is a phase angle of
Figure BDA0003235906560000165
TsFor sampling time intervals, sampling time intervals T s1/9600 seconds.
The parameters are set as follows: the amplitude of the voltage signal is represented by a standard value, the initial operating frequency of the system is set to be 50Hz, and an initial state vector is set
Figure BDA0003235906560000166
Error covariance matrix P0＝I3×3The test signals are as follows:
Figure BDA0003235906560000171
wherein, w1＝2πf1、w2＝2πf2(ii) a Suppose that the frequency, amplitude, phase angle are at time f 0.4s1＝50Hz、A1＝1.0pu、
Figure BDA0003235906560000172
Respectively mutated to f1＝50.5Hz、A2＝2.0pu、
Figure BDA0003235906560000173
ykThe signal-to-noise ratio of (1) is 40dB, and the harmonic amplitude B is 0.04 pu.
Based on the above parameters, the matlab simulation software is used for simulation, so that the frequency tracking diagram of the power signal shown in fig. 2, the amplitude tracking diagram of the power signal shown in fig. 3, and the phase angle tracking diagram of the power signal shown in fig. 4 can be obtained, and as can be seen from fig. 2 to 3, the frequency, the amplitude and the phase angle of the power signal can be quickly tracked by using the power signal parameter estimation algorithm provided by the embodiment of the invention. Figure 4 shows the time required for a single iteration using the power signal parameter estimation algorithm. As can be seen from fig. 4, the single iteration operation time of the power signal parameter estimation algorithm provided in the embodiment of the present invention is 0.32s, the time required by the STF algorithm is 0.26s, and the time required by the ASST-SUKF algorithm is 0.6s, which shows that the time required by the algorithm operation provided in the present invention is reduced by about 45% compared with the operation time of the ASST-SUKF algorithm, and is close to the calculation time of the STF algorithm. Therefore, the power signal parameter estimation provided by the embodiment of the invention can shorten the calculation time and reduce the calculation workload.
Further, table 1 and table 2 show an algorithm convergence time and an algorithm estimation accuracy, respectively, using the power signal parameter estimation algorithm (hereinafter, abbreviated as CDSTF algorithm).
TABLE 1 Algorithm convergence time
Algorithm Amplitude value Frequency of Phase angle
STF 0.495 0.465 0.606
ASST-SUKF 0.455 0.453 0.525
CDSTF 0.433 0.443 0.495
TABLE 2 Algorithm estimation accuracy
Algorithm Amplitude value Frequency of Phase angle
STF 0.0024 0.0032 0.5113
ASST-SUKF 0.0016 0.0021 0.3625
CDSTF 0.0015 0.0019 0.3597
As can be seen from the data in tables 1 and 2, the CDSTF algorithm provided by the invention has obviously better convergence speed and estimation precision than the STF algorithm, but is equivalent to the ASST-SUKF algorithm.
EXAMPLE III
Fig. 6 is a block diagram of a power signal parameter estimation apparatus according to a third embodiment of the present invention. The embodiment of the present invention provides an electric power signal parameter estimation apparatus, where the apparatus 100 includes:
the prediction quantity solving module 10 is used for solving a one-step prediction state vector and a one-step prediction measurement equation nonlinear function;
an actual measurement value obtaining module 20, configured to obtain an actual power signal parameter measurement value;
a model establishing module 30, configured to establish a first-order central difference model;
an extinction factor solving module 40, configured to solve an extinction factor according to the first-order central difference model;
a first prediction error covariance matrix calculation module 50, configured to introduce the fading factor into a prediction error covariance matrix to obtain a first prediction error covariance matrix;
a filter gain matrix determination module 60 for determining a filter gain matrix from the first prediction error covariance matrix;
and a state estimation determining module 70, configured to determine a state estimation according to the one-step predicted state vector, the one-step predicted measurement equation nonlinear function, the actual power signal parameter measurement value, and the filter gain matrix.
The technical scheme of the embodiment provides the power signal parameter estimation device. The device comprises a pre-measurement solving module, a pre-measurement calculating module and a pre-measurement calculating module, wherein the pre-measurement solving module is used for solving a one-step prediction state vector and a one-step prediction measurement equation nonlinear function; the actual measurement value acquisition module is used for acquiring an actual power signal parameter measurement value; the model establishing module is used for establishing a first-order central difference model; the fading factor solving module is used for solving fading factors according to the first-order central difference model; the first prediction error covariance matrix calculation module is used for introducing an fading factor into the prediction error covariance matrix to obtain a first prediction error covariance matrix; a filter gain matrix determination module for determining a filter gain matrix according to the first prediction error covariance matrix; and the state estimation determining module is used for determining state estimation according to the one-step prediction state vector, the one-step prediction measurement equation nonlinear function, the actual power signal parameter measurement value and the filter gain matrix. Therefore, by establishing a first-order central difference model, the first-order central difference model is utilized to obtain an extinction factor, the first-order central difference term not only comprises a first-order term of a common Taylor expansion formula, but also comprises other nonlinear terms, so the calculation precision of the first-order central difference term is high, the calculation precision of the extinction factor obtained by the first-order central difference model is higher, the calculation precision of a first prediction error covariance matrix obtained by the extinction factor is higher, the precision of a filter gain matrix obtained by the first prediction error covariance matrix is higher, and finally the estimation precision of the state estimation of the power signal parameter is improved, the calculation process is simple, the calculation amount is small, and the robustness of the system can be improved due to the introduction of the extinction factor, so the method can realize that the robustness of the algorithm is ensured, the calculation amount is reduced, and the estimation precision is improved.
It is to be noted that the foregoing is only illustrative of the preferred embodiments of the present invention and the technical principles employed. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, although the present invention has been described in greater detail by the above embodiments, the present invention is not limited to the above embodiments, and may include other equivalent embodiments without departing from the spirit of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims (10)

1. A method of power signal parameter estimation, comprising:
solving the nonlinear functions of the one-step prediction state vector and the one-step prediction measurement equation;
acquiring an actual power signal parameter measurement value;
establishing a first-order central difference model, and solving an elimination factor according to the first-order central difference model;
introducing the fading factor into a prediction error covariance matrix to obtain a first prediction error covariance matrix;
determining a filter gain matrix according to the first prediction error covariance matrix;
and determining state estimation according to the one-step prediction state vector, the one-step prediction measurement equation nonlinear function, the actual power signal parameter measurement value and the filter gain matrix.
2. The power signal parameter estimation method according to claim 1, wherein the first order central difference model is:
Figure FDA0003235906550000011
wherein the content of the first and second substances,
Figure FDA0003235906550000012
denotes the first central differential derivative, μ denotes the iteration step,
Figure FDA0003235906550000013
and
Figure FDA0003235906550000014
is a non-linear function.
3. The power signal parameter estimation method according to claim 1, wherein the solving of the fading factor according to the first-order central difference model is calculated by:
Figure FDA0003235906550000015
wherein the content of the first and second substances,
Figure FDA0003235906550000016
Nk+1＝Vk+1-AAT-βRk+1
Mk+1＝CCT
wherein λ isk+1Is a fading factor, Vk+1Is a matrix, Rk+1Is a matrix, Nk+1Is a matrix, Mk+1And the matrix A and the matrix C are obtained according to the first-order central difference model.
4. The power signal parameter estimation method of claim 3, wherein the prediction error covariance matrix is:
Pk+1|k＝Fk+1|kPkFk+1|k T+Qk
wherein, Pk+1|kRepresenting the prediction error covariance matrix, QkA non-negative-definite variance matrix representing process noise;
the calculation method of the matrix A and the matrix C obtained according to the first-order central difference model is as follows:
the prediction error covariance matrix Pk+1|kCholesky decomposition was performed to obtain:
Pk+1|k＝SWSW T
then according to the first-order central difference model, a matrix A can be obtainedj，
Figure FDA0003235906550000021
Wherein j is 1 … n, n is the dimension of the state vector; a. thejRepresents the j-th column, S, of the matrix Aw,jRepresentation matrix SwColumn j, μ denotes the iteration step,
Figure FDA0003235906550000022
is the predicted state phasor at time k +1,
Figure FDA0003235906550000023
and
Figure FDA0003235906550000024
is a linear function;
f in the prediction error covariance matrixk+1|kPkFk+1|k TCholesky decomposition was performed to obtain:
Fk+1|kPkFk+1|k T＝BBT
then, according to the first-order central difference model, a matrix C can be obtainedj，
Figure FDA0003235906550000025
Wherein, BjRepresents the jth column, C, of the matrix BjRepresenting the jth column of matrix C.
5. The power signal parameter estimation method according to claim 1, wherein the step of introducing the fading factor into the covariance matrix of prediction errors to obtain a first covariance matrix of prediction errors is performed by:
Figure FDA0003235906550000035
wherein the content of the first and second substances,
Figure FDA0003235906550000036
representing a first prediction error covariance matrix.
6. The power signal parameter estimation method according to claim 1, wherein the filter gain matrix is determined according to the first prediction error covariance matrix by:
performing Cholesky decomposition on the first prediction error covariance matrix to obtain:
Figure FDA0003235906550000031
then according to the first-order central difference model, a matrix D can be obtainedj，
Figure FDA0003235906550000032
Wherein D isjRepresents the jth column of matrix D; gain filter matrix K can be obtainedk+1
Figure FDA0003235906550000033
7. The method of claim 1, wherein determining the state estimate based on the one-step predicted state vector, the one-step predicted metrology equation nonlinear function, the actual power signal parameter measurements, and the filter gain matrix comprises:
obtaining the error of the measured value according to the difference between the actual power signal parameter measured value and the nonlinear function of the measurement equation;
and multiplying the error of the measurement value by the filter gain matrix and accumulating the error and the one-step prediction state vector to obtain the state estimation.
8. The power signal parameter estimation method of claim 6, further comprising estimating the power signal parameter based on the first prediction error covariance matrix, the filter gain matrix, the matrix
Figure FDA0003235906550000034
And the matrix D is used for obtaining a post-test error covariance matrix.
9. The power signal parameter estimation method of claim 8, wherein the first prediction error covariance matrix, the filter gain matrix, and the matrix are selected according to the first prediction error covariance matrix
Figure FDA0003235906550000041
And the matrix D is used for obtaining a post-test error covariance matrix, and the calculation method comprises the following steps:
Figure FDA0003235906550000042
wherein, Pk+1Representing the post-test error covariance matrix.
10. An electric power signal parameter estimation device, comprising:
the prediction quantity solving module is used for solving the nonlinear functions of the one-step prediction state vector and the one-step prediction measurement equation;
the actual measurement value acquisition module is used for acquiring an actual power signal parameter measurement value;
the model establishing module is used for establishing a first-order central difference model;
the fading factor solving module is used for solving fading factors according to the first-order central difference model;
the first prediction error covariance matrix calculation module is used for introducing the fading factor into a prediction error covariance matrix to obtain a first prediction error covariance matrix;
a filter gain matrix determination module, configured to determine a filter gain matrix according to the first prediction error covariance matrix;
and the state estimation determining module is used for determining state estimation according to the one-step prediction state vector, the one-step prediction measurement equation nonlinear function, the actual power signal parameter measurement value and the filter gain matrix.
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