CN117952772A - Kalman filtering-based system side harmonic impedance prediction method and device - Google Patents
Kalman filtering-based system side harmonic impedance prediction method and device Download PDFInfo
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Abstract
The invention relates to a Kalman filtering-based system side harmonic impedance prediction method and a Kalman filtering-based system side harmonic impedance prediction device, wherein the method comprises the following steps: step S1: acquiring an initial noise covariance matrix and a measurement noise covariance matrix; step S2: the result obtained based on the binary regression method is used as a priori state predicted value, and the result obtained based on the covariance method is used as a measurement predicted value; step S3: the obtained reference value of the system side harmonic impedance is calculated to obtain a priori error covariance matrix; step S4: obtaining Kalman gain; step S5: updating an error covariance matrix; step S6: outputting a final predicted value of the system side harmonic impedance; step S7: and after receiving the new data and respectively updating the noise covariance matrix and the measured noise covariance matrix, returning to the step S3. Compared with the prior art, the method combines the characteristics of the binary regression method and the covariance method, has higher calculation precision when the background harmonic wave is severely fluctuated, and can calculate the side harmonic impedance of the system under the complex working condition.
Description
Technical Field
The invention relates to the field of harmonic wave management, in particular to a Kalman filtering-based system side harmonic wave impedance prediction method and device.
Background
With the rapid development of the power industry, the power load in the power grid is increasingly complex and diversified. Meanwhile, due to the large amount of use of high-precision equipment, the demand of users for electric energy quality is continuously improved. High quality power has become a hotspot in widespread concern in academia and industry. Most of the current researches on high-quality power are focused on high-quality power supply schemes, customized power equipment, compensation principles, optimal configuration and the like. High-quality power refers to high-quality power which is provided for users with higher quality, higher reliability and higher availability by using advanced customized power equipment based on power electronics, and can meet the power requirements of different users, and many students consider the high-quality power equipment as an effective way for solving the power quality problem. Among them, harmonic pollution is one of the major power quality problems.
The harmonic wave can influence the safe operation of the public power grid, so that the additional loss of the power equipment is increased, the service life is shortened, the normal operation of the electronic equipment is interfered, the misoperation is protected and the like. In addition, the cable rate of the power grid is improved, and the capacitor is used in a large amount, so that the inductive capacity coupling phenomenon is easily induced in the system, the harmonic amplification risk is further increased, the additional loss of equipment is greatly increased, the fire disaster or explosion can be caused by incorrect installation, operation and operation, and the residual charge of the capacitor can also directly threaten the personal safety. The problem of harmonic pollution also reduces the economical efficiency of the operation of the power grid, and the harmonic wave can cause advanced ageing, damage and even accidents of power equipment, so that direct economic loss is generated. As the electronic degree of the power system is improved and a large number of power loads with nonlinear characteristics are connected to the power grid, harmonic pollution is increasingly aggravated, and the harmonic pollution of the power becomes a problem to be dealt with by the power system.
In order to scientifically control the power grid harmonic wave, a 'punishment mechanism' is proposed in the electric power field. These mechanisms include rewards and penalties for harmonic sources. Harmonic sources that contribute to grid harmonics will be correspondingly penalized, while those with suppression will be rewarded. The theoretical basis of all 'reward and punishment mechanisms' is to accurately divide the pollution responsibility of each harmonic source, so a great deal of researches are developed for solving the problems of harmonic impedance calculation, harmonic contribution quantification and the like at home and abroad. The contribution degree of each harmonic source is quantized, so that the influence of a user on the power grid can be evaluated, and corresponding rewarding and punishment schemes are formulated according to the evaluation result, so that harmonic treatment work is guided. Secondly, the contribution degree of the quantized harmonic source can determine the dominant harmonic source, and the harmonic can be treated in a targeted manner. In addition, the core of harmonic contribution quantification is the harmonic impedance of the computing system side and the user side, which has a certain guiding effect on filter design, resonance prediction and the like. However, since the subsequent application of harmonic contribution quantification simply judges the pollution responsibility of each party, the parties cannot be satisfied, and thus the enthusiasm of users for participating in harmonic governance cannot be mobilized. In addition, with the sustainable development of the power grid, new characteristics such as unstable background harmonic, nonlinear load multi-source interaction influence, enhanced system side harmonic impedance time-varying property, increased harmonic emission characteristic fluctuation, improved cable rate and the like are also presented in the harmonic problem of the power system, so that brand new problems and challenges are presented in harmonic responsibility assessment, harmonic impedance calculation and the like. And (3) accurately calculating the harmonic impedance under the new background condition, so that reasonable responsibility evaluation is carried out, and the method has a guiding effect on further advancing harmonic treatment work.
Disclosure of Invention
The invention aims to provide a Kalman filtering-based system side harmonic impedance prediction method and device, which combine the characteristics of a binary regression method and a covariance method, have higher calculation accuracy when background harmonic fluctuation is severe, and can calculate the system side harmonic impedance under complex working conditions.
The aim of the invention can be achieved by the following technical scheme:
A Kalman filtering-based system side harmonic impedance prediction method comprises the following steps:
Step S1: acquiring an initial noise covariance matrix and a measurement noise covariance matrix;
Step S2: acquiring a system side harmonic impedance detection result obtained based on a binary regression method as a priori state predicted value, and acquiring a system side harmonic impedance detection result obtained based on a covariance method as a measurement predicted value;
Step S3: the obtained reference value of the system side harmonic impedance is calculated to obtain a priori error covariance matrix based on the priori state predicted value and the reference value;
step S4: based on the obtained prior error covariance matrix, combining the measured noise covariance matrix to obtain Kalman gain;
Step S5: updating an error covariance matrix based on the obtained Kalman gain;
Step S6: outputting a final predicted value of the system side harmonic impedance based on the updated error covariance matrix;
Step S7: and entering the next time sequence, receiving the system side harmonic impedance detection results obtained by the new binary regression method and the covariance method, respectively updating the noise covariance matrix and the measured noise covariance matrix, and returning to the step S3.
The mathematical expression of the prior error covariance matrix is as follows:
Wherein: For the prior error covariance matrix,/> For a priori error, E [ ] is the mathematical expectation,/>For a priori state predictors, x k is a reference value.
The mathematical expression of the Kalman gain is:
Wherein: k k is Kalman gain, H is measurement matrix, and R is measurement noise covariance matrix.
The mathematical expression of the error covariance matrix updated in the step S5 is as follows:
wherein: and P is the updated error covariance matrix.
The mathematical expression of the final predicted value of the system side harmonic impedance is as follows:
Wherein: Z k is a state observation value of the kth harmonic impedance, which is a final predicted value of the system-side harmonic impedance.
A system side harmonic impedance prediction device based on kalman filtering, comprising a memory, a processor and a program, wherein the processor realizes the following steps when executing the program:
Step S1: acquiring an initial noise covariance matrix and a measurement noise covariance matrix;
Step S2: acquiring a system side harmonic impedance detection result obtained based on a binary regression method as a priori state predicted value, and acquiring a system side harmonic impedance detection result obtained based on a covariance method as a measurement predicted value;
Step S3: the obtained reference value of the system side harmonic impedance is calculated to obtain a priori error covariance matrix based on the priori state predicted value and the reference value;
step S4: based on the obtained prior error covariance matrix, combining the measured noise covariance matrix to obtain Kalman gain;
Step S5: updating an error covariance matrix based on the obtained Kalman gain;
Step S6: outputting a final predicted value of the system side harmonic impedance based on the updated error covariance matrix;
Step S7: and entering the next time sequence, receiving the system side harmonic impedance detection results obtained by the new binary regression method and the covariance method, respectively updating the noise covariance matrix and the measured noise covariance matrix, and returning to the step S3.
Compared with the prior art, the invention has the following beneficial effects:
1. the binary regression method and the covariance method are combined, so that when the background harmonic wave is intense, the calculation accuracy is still higher, and the system side harmonic impedance can be calculated under the complex working condition.
2. When the background harmonic wave is intense, a relatively stable result can be obtained.
Drawings
FIG. 1 is a schematic diagram of a Norton equivalent circuit for harmonic analysis at the user side and the system side;
FIG. 2 is a schematic flow chart of the main steps of the method of the present invention;
FIG. 3 is a schematic diagram of the topology of an actual wind farm system in a verification example;
fig. 4 is a schematic diagram of 5 th harmonic voltage and harmonic current at PCC points.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
Example 1
In harmonic analysis, a norton equivalent circuit is generally used as a theoretical model, and a power grid is divided into two parts of a user side and a system side from a common junction point of the user and the system, wherein the norton equivalent circuit is shown in fig. 1.
In the context of figure 1 of the drawings,A fluctuation vector value which is an equivalent harmonic current source at the system side; z s is the system side harmonic impedance; /(I)A fluctuation vector value of the equivalent harmonic current source at the user side; z c is the user side harmonic impedance; /(I)Harmonic current ripple vector values for the PCC points; /(I)Is the harmonic voltage fluctuation vector value of the PCC point. The harmonic currents at the system side and the user side jointly act on a common junction point to enable the PCC point to generate harmonic voltages and currents. Wherein Z s is mainly dependent on the system side short circuit capacity and Z c is dependent on the user side load condition, reflecting the electrical distance and the degree of coupling between the system side and the user side and the PCC point.
According to the superposition principle and fig. 1 there are:
The regression equation of the binary linear regression method is shown in formula (2).
Wherein:
Wherein: the subscripts x and y represent the real and imaginary parts of the complex signal, respectively. In formula (2), U pccxIpccx+UpccyIpccy and U pccyIpccx-UpccxIpccy are interpreted variables, and To interpret the variables, and under certain conditions may be clustered into a straight line. Z ux and Z uy are the slopes of the cluster lines, and β 1 and β 2 are the longitudinal intercepts of the cluster lines.
As can be seen from equation (3), when the background harmonic fluctuates, the longitudinal intercept of the clustering straight line also becomes unstable, thereby making it difficult for the explanatory variable to be linearly clustered with the explained variable.
To further improve the computational accuracy of the algorithm. An independent random vector covariance method is proposed by using the characteristic that background harmonic voltage and harmonic current measured on a public connecting line are in weak correlation in academic. According to the characteristic that the covariance of the weak correlation vector is approximately zero, a covariance equation is introduced. The method has certain background harmonic wave resistance capability. However, in algorithm theory, the user side harmonic impedance is required to be far greater than the system side harmonic impedance. This assumption holds for normal nonlinear users. However, if a harmonic source such as a converter station is provided with a filter, the frequency of |z c|＞＞|Zu | is not satisfied at some frequencies. Furthermore, when the background harmonic wave is severe, the calculation accuracy of the covariance method is still not ideal.
In practical application, when background harmonic wave fluctuation is severe, certain errors exist in solving results, and the invention applies the data fusion idea to calculation of harmonic impedance and provides a system side harmonic impedance prediction method based on a Kalman filtering technology.
A Kalman filtering-based system side harmonic impedance prediction method, as shown in figure 2, comprises the following steps:
Step S1: acquiring an initial noise covariance matrix and a measurement noise covariance matrix;
Step S2: acquiring a system side harmonic impedance detection result obtained based on a binary regression method as a priori state predicted value, and acquiring a system side harmonic impedance detection result obtained based on a covariance method as a measurement predicted value;
Step S3: the obtained reference value of the system side harmonic impedance is calculated based on the prior state predicted value and the reference value to obtain a prior error covariance matrix, and the mathematical expression of the prior error covariance matrix is as follows:
Wherein: For the prior error covariance matrix,/> For a priori error, E [ ] is the mathematical expectation,/>For a priori state predictors, x k is a reference value.
Step S4: based on the obtained prior error covariance matrix, combining the measured noise covariance matrix to obtain a Kalman gain, wherein the mathematical expression of the Kalman gain is as follows:
Wherein: k k is Kalman gain, H is measurement matrix, and R is measurement noise covariance matrix.
Step S5: updating an error covariance matrix based on the obtained Kalman gain, wherein the mathematical expression of the updated error covariance matrix is as follows:
wherein: and P is the updated error covariance matrix.
Step S6: based on the updated error covariance matrix, outputting a final predicted value of the system side harmonic impedance, wherein the mathematical expression of the final predicted value of the system side harmonic impedance is as follows:
Wherein: Z k is a state observation value of the kth harmonic impedance, which is a final predicted value of the system-side harmonic impedance.
Step S7: and entering the next time sequence, receiving the system side harmonic impedance detection results obtained by the new binary regression method and the covariance method, respectively updating the noise covariance matrix and the measured noise covariance matrix, and returning to the step S3.
Specifically, the kalman filter technique is one of the optimal estimation methods, and an optimal estimation value is obtained by minimizing the in-variance of an estimation error, and the principle thereof is as follows.
The state space model considering the linear discrete dynamic system is:
X(k)＝AX(k-1)+ΓW(k-1) (4)
Z(k)＝HX(k)+V(k) (5)
Wherein k is a discrete time; x (k) and Z (k) are a state variable and a measurement variable, respectively; w (k-1) and V (k) are input noise and measurement noise, respectively; Γ is the noise driving matrix; a is a state transition matrix; b is an observation matrix. Equation (4) is a state equation, and equation (5) is an observation equation.
Assuming that the input noise and the measurement noise are mutually independent, the mean value is zero, the covariance matrices are respectively Q and R, and the statistical characteristics are as follows:
when considering harmonic impedance calculations, X (k) and Z (k) can be considered as the calculation results of the two methods, respectively. The Kalman filter recurrence formula is as follows.
When the noise error is not considered, a priori predictions can be derived, which are expressed mathematically as:
in the method, in the process of the invention, A priori state predicted value for the kth time; /(I)For measuring the predicted value. However, due to the presence of input noise and measurement noise in the system, the obtained estimated values have errors, so that the noise needs to be eliminated by Kalman filtering. The final predicted value of the kalman filter at time k can be expressed as:
Where K k is the Kalman gain, and K k∈[0,H-1. It can be seen that: when K k =0, the number of times, I.e. the final predictor is equal to the a priori state predictor. When K k＝H-1,/>I.e. the final predicted value is equal to the measured predicted value. Therefore, it is necessary to find the optimal kalman gain so that the final predicted value approaches the true value x k indefinitely.
Taking the prediction error e k and the prior errorThe method comprises the following steps:
When the variance of the error is minimal, the final predicted value is closest to the true value. The covariance matrix P k of the error is:
the combination of formula (10) and formula (12) can result in:
For the convenience of calculation, let:
Wherein the method comprises the steps of
The method can obtain the following steps:
Then
The trace of the covariance matrix P k of the error is:
When a proper K k is obtained so that tr (P k) is minimum, the variance of the prediction error e k is minimum, and therefore tr (P k) is derived, and there are:
Taking out
Then there is
It should be noted that, in the practical application of the kalman filter, whether the covariance matrix Q of the input noise and the covariance matrix R of the measurement noise can be estimated correctly has a great influence on the calculation accuracy and convergence speed of the kalman filter. However, in practical engineering applications, since the true values are unknown, the values of Q and R are usually empirical values, which increases the error and reduces the convergence rate.
However, in order to avoid errors caused by the change of the harmonic impedance at the system side due to long samples, the harmonic voltage and current data of the PCC point in a short time are generally selected, and the harmonic impedance at the system side is considered to be constant in a short time. Based on this, a super-parameter estimation method of the covariance matrix of the input noise and the measurement noise is proposed herein to determine the covariance matrix Q of the input noise and the covariance matrix R of the measurement noise, specifically as follows:
Assume that the calculation error e is:
e＝Zs-j-Zs-z (22)
Wherein Z S-j is a system side harmonic impedance calculated value; z S-z is the system side harmonic impedance true value. The variance of the error e is:
VAR(e)＝VAR(Zs-j-Zs-z) (23)
During the harmonic impedance calculation, Z S-z is constant and can be considered a constant. According to the variance operation theorem, there are:
VAR(e)＝VAR(Zs-j-Zs-z)＝VAR(Zs-j) (24)
as can be seen from equation (24), the values of the covariance matrix Q of the input noise and the covariance matrix R of the measurement noise can be determined by the variances of the binary regression method and the covariance method calculation results.
In summary, the kalman filtering is mainly divided into three parts, i.e. prediction, correction and update.
In order to further verify the feasibility of the method provided by the invention for quantifying harmonic contribution, we select a multi-wind-field system as a research case for deep analysis, and the topology structure of the multi-wind-field system is shown in fig. 3.
As can be seen from fig. 3, the grid contains a plurality of wind fields, while other complex nonlinear users are present. The study focused on a 35kV bus of the wind power plant, 5 collector wires are distributed below the bus, and 10 fans are connected below each collector wire. The 35kV grid connection point of the wind power plant is taken as a node (PCC point) which is focused, harmonic voltage and harmonic current monitoring data of the node are collected, and the data of the PCC point, namely 5 th harmonic voltage and harmonic current, within 10 minutes are shown in fig. 4.
The sampling frequency of the data is 10kHz, and the data measured every 10 cycles is subjected to fast Fourier transform, so that 300 sample data can be obtained every minute on average. In order to avoid errors caused by the fact that the harmonic impedance of the system side changes due to long samples, the harmonic data measured by the PCC point are divided into 10 time periods, each time period is 1 minute long, and at the moment, the harmonic impedance of the system side can be considered to be constant in a short time. Three calculation methods (method 1 is a binary regression method, method 2 is a covariance method, and method 3 is a method provided by the invention) are respectively adopted to calculate Z s, and the result errors are compared and analyzed.
The system side harmonic impedance is generally stable for a short period of time. The results obtained by the binary regression method and the covariance method have larger fluctuation, and the results are larger in access with the actual engineering situation. The reason for this is that there are many complex harmonic sources in the grid of the wind farm, so that the instability of the background harmonic increases considerably, leading to an increase in calculation errors. In this case, there is a large uncertainty in the result calculated using the fluctuation amount method, and the fluctuation of the calculated result is large. In contrast, the method has high stability of the calculated result and accords with the actual engineering situation.
Example 2
The embodiment specifically provides a system side harmonic impedance prediction device based on Kalman filtering, which comprises a memory, a processor and a program, wherein the processor realizes the following steps when executing the program:
Step S1: acquiring an initial noise covariance matrix and a measurement noise covariance matrix;
Step S2: acquiring a system side harmonic impedance detection result obtained based on a binary regression method as a priori state predicted value, and acquiring a system side harmonic impedance detection result obtained based on a covariance method as a measurement predicted value;
Step S3: the obtained reference value of the system side harmonic impedance is calculated to obtain a priori error covariance matrix based on the priori state predicted value and the reference value;
step S4: based on the obtained prior error covariance matrix, combining the measured noise covariance matrix to obtain Kalman gain;
Step S5: updating an error covariance matrix based on the obtained Kalman gain;
Step S6: outputting a final predicted value of the system side harmonic impedance based on the updated error covariance matrix;
Step S7: and entering the next time sequence, receiving the system side harmonic impedance detection results obtained by the new binary regression method and the covariance method, respectively updating the noise covariance matrix and the measured noise covariance matrix, and returning to the step S3.
Other portions are the same as embodiment 1, and are not repeated for the purpose of avoiding ambiguity.
The above functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Claims (10)
1. A Kalman filtering-based system side harmonic impedance prediction method is characterized by comprising the following steps:
Step S1: acquiring an initial noise covariance matrix and a measurement noise covariance matrix;
Step S2: acquiring a system side harmonic impedance detection result obtained based on a binary regression method as a priori state predicted value, and acquiring a system side harmonic impedance detection result obtained based on a covariance method as a measurement predicted value;
Step S3: the obtained reference value of the system side harmonic impedance is calculated to obtain a priori error covariance matrix based on the priori state predicted value and the reference value;
step S4: based on the obtained prior error covariance matrix, combining the measured noise covariance matrix to obtain Kalman gain;
Step S5: updating an error covariance matrix based on the obtained Kalman gain;
Step S6: outputting a final predicted value of the system side harmonic impedance based on the updated error covariance matrix;
Step S7: and entering the next time sequence, receiving the system side harmonic impedance detection results obtained by the new binary regression method and the covariance method, respectively updating the noise covariance matrix and the measured noise covariance matrix, and returning to the step S3.
2. The method for predicting system-side harmonic impedance based on kalman filtering according to claim 1, wherein the mathematical expression of the a priori error covariance matrix is:
Wherein: For the prior error covariance matrix,/> For a priori error, E [ ] is the mathematical expectation,/>For a priori state predictors, x k is a reference value.
3. The method for predicting system-side harmonic impedance based on kalman filtering according to claim 2, wherein the mathematical expression of the kalman gain is:
Wherein: k k is Kalman gain, H is measurement matrix, and R is measurement noise covariance matrix.
4. The method for predicting harmonic impedance at system side based on kalman filtering as recited in claim 3, wherein the mathematical expression of the error covariance matrix updated in step S5 is:
wherein: and P is the updated error covariance matrix.
5. The method for predicting the harmonic impedance of a system side based on kalman filtering as recited in claim 4, wherein the mathematical expression of the final predicted value of the harmonic impedance of the system side is:
Wherein: Z k is a state observation value of the kth harmonic impedance, which is a final predicted value of the system-side harmonic impedance.
6. The system side harmonic impedance prediction device based on Kalman filtering comprises a memory, a processor and a program, and is characterized in that the processor executes the program to realize the following steps:
Step S1: acquiring an initial noise covariance matrix and a measurement noise covariance matrix;
Step S2: acquiring a system side harmonic impedance detection result obtained based on a binary regression method as a priori state predicted value, and acquiring a system side harmonic impedance detection result obtained based on a covariance method as a measurement predicted value;
Step S3: the obtained reference value of the system side harmonic impedance is calculated to obtain a priori error covariance matrix based on the priori state predicted value and the reference value;
step S4: based on the obtained prior error covariance matrix, combining the measured noise covariance matrix to obtain Kalman gain;
Step S5: updating an error covariance matrix based on the obtained Kalman gain;
Step S6: outputting a final predicted value of the system side harmonic impedance based on the updated error covariance matrix;
Step S7: and entering the next time sequence, receiving the system side harmonic impedance detection results obtained by the new binary regression method and the covariance method, respectively updating the noise covariance matrix and the measured noise covariance matrix, and returning to the step S3.
7. The kalman filter-based system-side harmonic impedance prediction apparatus according to claim 6, wherein the mathematical expression of the a priori error covariance matrix is:
Wherein: For the prior error covariance matrix,/> For a priori error, E [ ] is the mathematical expectation,/>For a priori state predictors, x k is a reference value.
8. The kalman filter-based system side harmonic impedance prediction device according to claim 7, wherein the mathematical expression of the kalman gain is:
Wherein: k k is Kalman gain, H is measurement matrix, and R is measurement noise covariance matrix.
9. The kalman filter-based system side harmonic impedance prediction apparatus according to claim 8, wherein the mathematical expression of the updated error covariance matrix in step S5 is:
wherein: and P is the updated error covariance matrix.
10. The method for predicting system-side harmonic impedance based on kalman filtering according to claim 9, wherein the mathematical expression of the final predicted value of the system-side harmonic impedance is:
Wherein: Z k is a state observation value of the kth harmonic impedance, which is a final predicted value of the system-side harmonic impedance.
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