CN110456159B - System side harmonic impedance estimation method and system based on corrected independent random vector - Google Patents
System side harmonic impedance estimation method and system based on corrected independent random vector Download PDFInfo
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Abstract
The invention discloses a system side harmonic impedance estimation method and a system based on a modified independent random vector, wherein the method comprises the following steps: and determining weak correlation time periods through threshold screening of the normalized correlation coefficient based on the correlation analysis of the PCC point harmonic data. In the weak correlation time period, the harmonic current of the PCC point has weak correlation with the harmonic voltage source on the system side, and further, a system harmonic impedance calculation formula corresponding to any time interval in the weak correlation time period can be deduced. And taking the average value of the impedance values corresponding to all time intervals in the weak correlation period as the system side harmonic impedance value of the PCC point. According to the method, the harmonic impedance of the system side can be rapidly calculated by using fewer sample points according to the relevant characteristics of the PCC point harmonic data, the method is suitable for the condition that the background harmonic is unstable or the impedance ratio of two sides is close, and the error caused by the influence of the change of the power system on the harmonic data is reduced.
Description
Technical Field
The invention relates to the field of division of harmonic responsibility of a user side and a system side, in particular to a system side harmonic impedance estimation method and system based on a modified independent random vector.
Background
With the access of a large number of power electronic devices to a power grid, the trend of electronization of power of a power system in China gradually appears. The nonlinear loads of the public power grid are increased in types and distribution, the harmonic content is increased, the frequency is increased, the harmonic pollution problem is more serious, accidents caused by harmonic resonance and harmonic amplification are also happened occasionally, and the harmonic waves of the power grid endanger the safe and stable operation of the power grid. Harmonic suppression becomes a problem and task which needs to be solved urgently by a public power grid. Effective separation of harmonic responsibilities of a system side and a user side of a power grid public connection Point (PCC) is a premise and a difficulty of harmonic governance, and accurate estimation of harmonic impedance of the system side is required under various complex power grid environments.
However, existing harmonic impedance estimation methods typically imply the following assumptions: 1) the harmonic wave fluctuation at the system side is basically stable; 2) the user side harmonic impedance of the PCC points is much larger than the system side. In an actual system, however, a large number of harmonic sources exist in a power grid due to the access of various new energy devices, high-speed rails, charging piles and other nonlinear users, and background harmonics are increased; the user side is additionally provided with a filtering device, so that the harmonic impedance of the user side and the harmonic impedance of the system side are not far larger than each other. When the assumption is not satisfied, the harmonic impedance error calculated by the existing method is large.
Disclosure of Invention
In order to solve the influence of background harmonic wave fluctuation and impedance ratio change on the traditional method, the method performs correlation analysis on a large amount of measured harmonic data of a wind power plant, a direct current drop point and traditional nonlinear loads such as an electric arc furnace and the like, finds that the autocorrelation and the cross correlation of the harmonic voltage and the harmonic current of the PCC point are quickly attenuated, and presents obvious short correlation, and the characteristic provides a new way for the calculation of the harmonic impedance.
The invention provides a method for estimating harmonic impedance based on weak correlation of harmonic voltage and harmonic current of a public connection point, aiming at the influence of background harmonic fluctuation and impedance ratio change on two sides on the existing method in engineering practice. The method effectively inhibits the interference of background harmonic, is also suitable when the impedance ratio of two sides is close, and greatly reduces the error caused by the influence of the change of the power system on the correlation of the harmonic data. The effectiveness of the proposed inventive method is demonstrated by simulation and analytical verification of measured data.
The invention is realized by the following technical scheme:
the system side harmonic impedance estimation method based on the corrected independent random vector comprises the following steps:
A. determining weak correlation time periods by threshold screening of normalized correlation coefficients based on correlation analysis of PCC point harmonic data;
B. establishing a Norton equivalent circuit under a certain harmonic wave, establishing a circuit equation by using a kirchhoff voltage law, and performing equivalent transformation on the equation to obtain a correlation function; in the weak correlation time period determined in the step A, the harmonic current of the PCC points has weak correlation with the harmonic voltage source on the system side, namely the correlation function of the obtained equation is regarded as 0;
C. and B, based on the correlation function equation obtained in the step B and the deduced harmonic impedance calculation formula, obtaining the impedance value corresponding to any time interval in the weak correlation time period, and taking the average value of the impedance values corresponding to all time intervals in the weak correlation time period as the system side harmonic impedance value of the PCC point.
Further, in the method for estimating the system side harmonic impedance based on the modified independent random vector, the step a of establishing the equation set comprises the following steps:
a1, obtaining an expression of an autocorrelation function of harmonic current and harmonic voltage based on PCC point harmonic data, wherein the expression is as follows:
and the expression of the cross-correlation function of the harmonic voltage and the harmonic current is:
in the formula (I), the compound is shown in the specification,
respectively representing the harmonic current and harmonic voltage of a PCC point, N representing the total number of sample points, N representing any moment of a signal sequence, k representing the time interval of two signals, E { } representing the mathematical expectation, and x representing the conjugation.
And A2, determining the weak correlation period by threshold screening of the normalized correlation coefficient. The expression of the normalized autocorrelation coefficients of the harmonic current and the harmonic voltage is:
the expression for the normalized cross-correlation coefficient of harmonic current and harmonic voltage is:
in probability theory and statistics, the correlation coefficient shows the strength and direction of a linear relationship between two random variables. The degree of attenuation of the correlation function over the time interval k is usually characterized by a normalized correlation coefficient. The sign of the normalized correlation coefficient only indicates the direction of correlation and the absolute value indicates the degree of correlation. A weak correlation may be defined when the normalized correlation coefficient is less than 0.3.
The threshold value of the correlation coefficient of the measured data is set to be 0.3, the time interval corresponding to the fact that the autocorrelation coefficient of the harmonic current at the PCC is smaller than the threshold value for the first time is recorded as k1, the time interval corresponding to the fact that the cross correlation coefficient of the harmonic voltage and the current at the PCC is smaller than the threshold value for the first time is recorded as k2, and the maximum value is recorded as kmaxFor N samples, defining the range of k values corresponding to the weak correlation period as kmax～N-1。
Further, in the method for estimating the system side harmonic impedance based on the modified independent random vector, the formula equivalent transformation in the step B includes the following steps:
b1, norton equivalent circuit diagram, column write circuit equation:
in the formula, ZuThe harmonic impedance on the system side is shown,
representing the vector values of the harmonic current sources on the system side,
vector values representing a system-side harmonic voltage source;
multiplying both ends of the formula (6) by
Then, a correlation function is calculated, and the result is as follows:
when the metrology data is a second order statistic ergodic, equation (7) is approximated as:
b2, in the weak correlation period determined in a, the cross correlation between the harmonic voltage and the harmonic current and the auto correlation between the harmonic currents are weak, so that the PCC point harmonic current can be considered to have a weak correlation with the system side harmonic voltage source, and equation (8) is considered to be 0.
In the method for estimating the system-side harmonic impedance based on the modified independent random vector, the derivation of the system harmonic impedance calculation formula in the step C includes the following steps:
c1, equation (8) is regarded as 0, and the expression of the system harmonic impedance corresponding to any time interval in the weak correlation period is deduced to be
Wherein k has a value range of kmax～N-1。
C2 for the obtained (N-k)max) Averaging the impedance to obtain harmonic impedance based on independent random vector of the correction version as follows:
on the other hand, corresponding to the method, the invention also provides a system side harmonic impedance estimation system based on the modified independent random vector, and the system comprises:
the weak correlation time interval obtaining unit is used for analyzing the correlation of the harmonic data of the PCC points, obtaining the normalized cross correlation coefficient of the harmonic current and the harmonic voltage of the PCC points and the normalized autocorrelation coefficient of the harmonic current at the PCC points, and setting a threshold value to screen and obtain a weak correlation time interval based on the cross correlation coefficient and the autocorrelation coefficient;
the relevant function obtaining unit is used for establishing a Norton equivalent circuit under certain harmonic, establishing a circuit equation based on the kirchhoff voltage law, performing equivalent transformation on the established circuit equation, and solving a relevant function of the circuit equation after the equivalent transformation;
and the harmonic impedance value calculation unit is used for deducing a harmonic impedance calculation formula on the system side of the public connection point of the power grid corresponding to any time interval in the weak correlation time period based on the correlation function obtained by the correlation function obtaining unit, and taking the mean value of the impedance values corresponding to all time intervals in the weak correlation time period as the system side harmonic impedance value of the PCC point based on the deduced harmonic impedance calculation formula.
Compared with the prior art, the invention has the following advantages and beneficial effects:
existing methods are often based on the following assumptions: 1) the harmonic wave fluctuation at the system side is basically stable; 2) the user side harmonic impedance of the PCC points is much larger than the system side. On the basis of correlation analysis, the weak correlation time interval is determined by screening the time interval k to estimate the harmonic impedance, only the self attribute of the measured data is relied on, the self characteristic of the system is reflected, the error caused by the influence of the fluctuation of background harmonic and the impedance ratio change at two sides on the source data correlation is weakened, and the application range is wider.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention;
FIG. 1 is a Norton equivalent circuit diagram of the present invention;
FIG. 2 is a schematic diagram of the system-side harmonic impedance estimation system based on the modified independent random vector according to the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflicting with each other.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described and thus the scope of the present invention is not limited by the specific embodiments disclosed below.
Example one
The system side harmonic impedance estimation method based on the corrected independent random vector comprises the following steps:
A. determining weak correlation time periods by threshold screening of normalized correlation coefficients based on correlation analysis of PCC point harmonic data;
B. establishing a Norton equivalent circuit under a certain harmonic wave, establishing a circuit equation by using a kirchhoff voltage law, and performing equivalent transformation on the equation to obtain a correlation function; in the weak correlation time period determined in the step A, the harmonic current of the PCC points has weak correlation with the harmonic voltage source on the system side, namely the correlation function of the obtained equation is regarded as 0;
C. and B, deriving a system harmonic impedance calculation formula corresponding to any time interval in the weak correlation time period based on the correlation function equation obtained in B, and taking the mean value of impedance values corresponding to all time intervals in the weak correlation time period as the system side harmonic impedance value of the PCC according to the method of the invention based on the derived harmonic impedance calculation formula.
Further, in the method for estimating the system side harmonic impedance based on the modified independent random vector, the step a of establishing the equation set comprises the following steps:
a1, obtaining an expression of an autocorrelation function of harmonic current and harmonic voltage based on PCC point harmonic data, wherein the expression is as follows:
and the expression of the cross-correlation function of the harmonic voltage and the harmonic current is:
in the formula (I), the compound is shown in the specification,
respectively representing the harmonic current and harmonic voltage of a PCC point, N representing the total number of sample points, N representing any moment of a signal sequence, k representing the time interval of two signals, E { } representing the mathematical expectation, and x representing the conjugation.
And A2, determining the weak correlation period by threshold screening of the normalized correlation coefficient. The expression of the normalized autocorrelation coefficients of the harmonic current and the harmonic voltage is:
the expression for the normalized cross-correlation coefficient of harmonic current and harmonic voltage is:
in probability theory and statistics, the correlation coefficient shows the strength and direction of a linear relationship between two random variables. The degree of attenuation of the correlation function over the time interval k is usually characterized by a normalized correlation coefficient. The sign of the normalized correlation coefficient only indicates the direction of correlation and the absolute value indicates the degree of correlation. A weak correlation may be defined when the normalized correlation coefficient is less than 0.3.
The threshold value of the correlation coefficient of the measured data is set to be 0.3, the time interval corresponding to the fact that the autocorrelation coefficient of the harmonic current at the PCC is smaller than the threshold value for the first time is recorded as k1, the time interval corresponding to the fact that the cross correlation coefficient of the harmonic voltage and the current at the PCC is smaller than the threshold value for the first time is recorded as k2, and the maximum value is recorded as kmaxFor N samples, defining the range of k values corresponding to the weak correlation period as kmax～N-1。
Further, in the method for estimating the system side harmonic impedance based on the modified independent random vector, the formula equivalent transformation in the step B includes the following steps:
b1, norton equivalent circuit diagram, column write circuit equation:
in the formula, ZuThe harmonic impedance on the system side is shown,
representing the vector values of the harmonic current sources on the system side,
vector values representing a system-side harmonic voltage source;
multiplying both ends of the formula (6) by
Then, a correlation function is calculated, and the result is as follows:
when the metrology data is a second order statistic ergodic, equation (7) is approximated as:
b2, in the weak correlation period determined in a, the cross correlation between the harmonic voltage and the harmonic current and the auto correlation between the harmonic currents are weak, so that the PCC point harmonic current can be considered to have a weak correlation with the system side harmonic voltage source, and equation (8) is considered to be 0.
In the method for estimating the system-side harmonic impedance based on the modified independent random vector, the derivation of the system harmonic impedance calculation formula in the step C includes the following steps:
c1, equation (8) is regarded as 0, and the expression of the system harmonic impedance corresponding to any time interval in the weak correlation period is deduced to be
Wherein k has a value range of kmax～N-1。
C2 for the obtained (N-k)max) Averaging the impedance to obtain harmonic impedance based on independent random vector of the correction version as follows:
based on the principle of the above embodiments, the embodiment discloses a specific implementation manner:
a simulation model is built according to the Noton equivalent circuit in the figure 1, and specific parameters are set as follows.
1) Harmonic current at user side
Is of an amplitude of 100A and,
the amplitude makes 20% sinusoidal fluctuation and +/-15% random fluctuation relative to the initial value in the whole estimation time period; system side harmonic source current
The amplitude being the current at the user side
N times the amplitude (n is 0.3, 0.5, 0.8, 1.0, 1.2), random fluctuations of ± 15% with respect to the amplitude magnitude are made throughout the estimation period.
The phase angle has an initial value of-30 degrees,
the phase angle is initially 30 deg., plus random perturbations of relative phase angle magnitude + -10%.
2) System side impedance ZuAnd is constantly (5+ j10) omega. Setting two impedance conditions, i.e. user side impedance ZcRespectively (5+ j10) omega and (20+ j40) omega, and the effect of impedance ratio on algorithm error is contrasted and analyzed. ZuAnd ZcAdding 10% sinusoidal fluctuations throughout the estimation period.
100 data are simulated, recursion calculation is carried out on 40 data in each time period, the mean value of 61 sections of data is used as the error value of the impedance amplitude value and the phase angle of one-time operation, the program runs for 100 times, and the root mean square value of the operation result of 100 times is used as the error result of the method. Meanwhile, the calculation results of the method herein and other methods are compared. (method 1 is a fluctuation amount method, method 2 is a complex ICA method, method 3 is an independent vector covariance method, method 4 is a binary regression method, and method 5 is a text method).
The present embodiment is divided into 2 scenes. In scenario 1, the system-side impedance ZuIs (5+ j10) omega, the user-side impedance ZcAt (20+ j40) Ω, and a side impedance ratio of 4, the RMS error of the amplitude and phase angle of the harmonic impedance of the system is shown in tables 1 and 2, respectively.
Table 1 impedance magnitude error user side impedance/system measured impedance ═ 4
Table 2 impedance phase angle error user side impedance/system measured impedance is 4
In scenario 2, the system-side impedance ZuIs (5+ j10) omega, the user-side impedance ZcAt (5+ j10) Ω, the impedance ratio on both sides is 1, and the RMS error of the amplitude and phase angle of the harmonic impedance of the system is shown in tables 3 and 4, respectively.
Table 3 impedance magnitude error user side impedance/system measured impedance ═ 1
Table 4 impedance phase angle error user side impedance/system measured impedance is 1
Example two
Referring to fig. 2, the present invention further provides a system side harmonic impedance estimation system based on modified independent random vectors, the system includes:
the weak correlation time interval obtaining unit is used for analyzing the correlation of the harmonic data of the PCC points, obtaining the normalized cross correlation coefficient of the harmonic current and the harmonic voltage of the PCC points and the normalized autocorrelation coefficient of the harmonic current at the PCC points, and obtaining the weak correlation time interval through threshold value screening based on the cross correlation coefficient and the autocorrelation coefficient;
the relevant function obtaining unit is used for establishing a Norton equivalent circuit under certain harmonic, establishing a circuit equation based on the kirchhoff voltage law, performing equivalent transformation on the established circuit equation, and solving a relevant function of the circuit equation after the equivalent transformation;
and the harmonic impedance value calculation unit is used for deducing a harmonic impedance calculation formula on the system side of the public connection point of the power grid corresponding to any time interval in the weak correlation time period based on the correlation function obtained by the correlation function obtaining unit, and taking the mean value of the impedance values corresponding to all time intervals in the weak correlation time period as the system side harmonic impedance value of the PCC point based on the deduced harmonic impedance calculation formula.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (6)
1. The system side harmonic impedance estimation method based on the modified independent random vector is characterized by comprising the following steps:
step A: analyzing the correlation of the harmonic data of the PCC points to obtain a normalized cross correlation coefficient of the harmonic current and the harmonic voltage of the PCC points and a normalized autocorrelation coefficient of the harmonic current, and setting a threshold value for screening to obtain a weak correlation time period based on the cross correlation coefficient and the autocorrelation coefficient;
and B: establishing a Norton equivalent circuit under a certain harmonic wave, establishing a circuit equation based on kirchhoff voltage law, performing equivalent transformation on the established circuit equation, and solving a correlation function of the circuit equation after the equivalent transformation;
and C: b, deducing a harmonic impedance calculation formula of the PCC point system side corresponding to any time interval in the weak correlation time period based on the correlation function obtained in the step B, obtaining impedance values corresponding to all time intervals in the weak correlation time period based on the deduced harmonic impedance calculation formula, and taking the mean value of the impedance values corresponding to all time intervals in the weak correlation time period as the harmonic impedance value of the PCC point system side;
the step B comprises the following steps:
step B1: according to the norton equivalent circuit diagram, the circuit equation of the column-writing norton equivalent circuit:
in the formula, ZuThe harmonic impedance on the system side is shown,
representing the vector values of the harmonic current sources on the system side,
vector values representing system-side harmonic voltage sources；
Multiplying both ends of the formula (4) by
Then, a correlation function is calculated, and the result is:
when the metrology data is a second order statistic ergodic, equation (5) is transformed to:
step B2: in the weak correlation period determined in step a, equation (6) is regarded as 0.
2. The method according to claim 1, wherein the correlation function of the equivalent transformed circuit equation is regarded as 0 in the weak correlation period.
3. The method according to claim 1, wherein the step a further comprises normalizing the cross-correlation coefficient and the autocorrelation coefficient.
4. The method for estimating system-side harmonic impedance based on modified independent random vectors according to claim 1, wherein the step a specifically comprises:
step A1: based on PCC point harmonic data, the expression of the autocorrelation function of the harmonic current and the harmonic voltage is obtained as follows:
the expression for the cross-correlation function of harmonic voltage and harmonic current is:
wherein the content of the first and second substances,
respectively representing harmonic current and harmonic voltage of a PCC point, N represents the total number of sample points, N represents any moment of a signal sequence, k represents the time interval of two signals, E { } represents mathematical expectation, and x represents the conjugation;
step A2: and obtaining a correlation coefficient based on a cross-correlation function of the harmonic voltage and the harmonic current and an autocorrelation function of the harmonic current, setting a threshold value to screen the correlation coefficient, and determining a weak correlation time period.
5. The method according to claim 4, wherein a threshold value of the correlation coefficient of the measured data is set; recording a time interval corresponding to the fact that the autocorrelation coefficient of the harmonic current at the PCC is smaller than the threshold for the first time as k1, recording a time interval corresponding to the fact that the cross correlation coefficient of the harmonic voltage and the current at the PCC is smaller than the threshold for the first time as k2, and recording the maximum value as kmax(ii) a For N samples, defining the k value range corresponding to the weak correlation time period as kmax～N-1。
6. The system side harmonic impedance estimation method based on the modified independent random vector as claimed in claim 1, wherein a calculation formula of the system side harmonic impedance of the grid public connection point corresponding to any time interval in the weak correlation period is derived based on the correlation function obtained in step B, and specifically includes:
step C1: the formula (6) is regarded as 0, and an expression for deducing the system harmonic impedance corresponding to any time interval in the weak correlation time interval is as follows:
wherein the value range of k is kmax～N-1；
Step C2: for the obtained N-kmaxAveraging the impedance to obtain harmonic impedance based on independent random vector of the correction version as follows:
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