Disclosure of Invention
The invention aims to solve the technical problems that when background harmonic wave fluctuation is strong, the estimated system side harmonic wave impedance is not stable enough and accurate enough in the existing system side harmonic wave impedance estimation method. The invention aims to provide a system side harmonic impedance estimation method and device based on improved linear regression. The invention can construct the background harmonic voltage by utilizing the known prior information, and the influence of the fluctuation of the background harmonic voltage on the algorithm is caused by processing the constructed background harmonic voltage data, so that the estimation result is more stable and the accuracy is higher; in addition, the invention takes the difference between the minimum calculated impedance and the initial impedance as a criterion, and the algorithm can iteratively converge to obtain the optimal initial impedance no matter the set size of the initial impedance range by searching the optimal initial impedance as a final result.
The invention is realized by the following technical scheme:
In a first aspect, the present invention provides a method for estimating system-side harmonic impedance based on improved linear regression, the method comprising:
Establishing a complex domain equivalent circuit equation according to the Norton equivalent circuit under certain harmonic frequency; performing mathematical transformation on the complex number domain equivalent circuit equation and separating a real part and an imaginary part to obtain a real number domain equivalent circuit equation;
Estimating a numerical range of initial impedance of a power grid by using a short-circuit capacity method, and setting a change step length in the numerical range as a specific value of the initial impedance; sequentially bringing specific values of each initial impedance into the real number domain equivalent circuit equation to construct background harmonic waves, and sequencing and segmenting the background harmonic waves to obtain sub-data segments of each background harmonic wave; the harmonic measurement data corresponding to the background harmonic is processed identically with the background harmonic;
In the sub-data segment of each background harmonic, a linear regression equation is constructed by utilizing the background harmonic data and the measurement data; calculating the system side harmonic impedance of the sub-data segment of each background harmonic by adopting a least square method;
And calculating the accumulated difference value between the system side harmonic impedance of the sub-data segment of each background harmonic and the initial impedance of the power grid in the numerical range, and obtaining the corresponding initial impedance of the power grid when the accumulated difference value is minimum, namely the final system side harmonic impedance.
The working principle is as follows: based on the existing system side harmonic impedance estimation method, when background harmonic fluctuation is strong, the estimated system side harmonic impedance is not robust enough and not accurate enough.
The invention aims to provide a system side harmonic impedance estimation method and device based on improved linear regression. Firstly, setting initial impedance according to the short-circuit capacity of a system to construct background harmonic voltage data, processing the constructed background harmonic voltage data to reduce adverse effects of fluctuation on an algorithm, calculating harmonic impedance corresponding to a processed data segment by using a least square method, and finally obtaining the harmonic impedance of the system according to the minimum criterion of impedance difference. The invention can construct the background harmonic voltage by utilizing the known prior information, and the influence of the fluctuation of the background harmonic voltage on the algorithm is caused by processing the constructed background harmonic voltage data, so that the estimation result is more stable and the accuracy is higher; in addition, the invention takes the difference between the minimum calculated impedance and the initial impedance as a criterion, and the algorithm can iteratively converge to obtain the optimal initial impedance no matter the set size of the initial impedance range by searching the optimal initial impedance as a final result.
The system side harmonic impedance estimation method based on the improved linear regression can be suitable for accurately estimating the system side harmonic impedance only by measuring harmonic voltage and current monitoring data of points when background harmonic fluctuation in a power grid is strong. Aiming at the characteristics of high-proportion new energy distributed network access, high-power electronic distribution network and the like in a modern power system, harmonic sources are widely distributed, harmonic content is increased, harmonic presents high-frequency, wide-frequency-domain and wide-distribution characteristics, background harmonic content in the power grid is extremely high, and the method can accurately estimate system side harmonic impedance under the background and provides reference for quantification of harmonic emission responsibility.
Further, the expression of the short-circuit capacity method is:
Wherein Zux is the real part of the system side harmonic impedance and Zuy is the imaginary part of the system side harmonic impedance; s is the short-circuit capacity of the system; vN is the rated voltage of the power grid; h is the harmonic order.
Further, the specific values of all initial impedances are brought into the real number domain equivalent circuit equation in sequence to construct background harmonics, and the background harmonics are sequenced and segmented to obtain sub-data segments of all the background harmonics; the method comprises the following steps:
sequentially bringing specific values of all initial impedances into the real number domain equivalent circuit equation, and solving corresponding real number background harmonic voltages;
And sequencing and segmenting the real background harmonic voltage to obtain sub-data segments of each background harmonic.
Further, the harmonic measurement data includes a measured harmonic voltage and a measured harmonic current.
Further, the linear regression equation is a linear regression equation taking harmonic measurement data as a known variable and system side harmonic impedance as a regression coefficient; the real linear regression equation in each sub-data segment is:
the equation is a linear regression model y=xβ+ε, where the interpretation variable X includesIs interpreted as a variable ofRegression coefficients include/>And/>Epsilon is a random error;
j is the number of the sub-data segment; p is the number of sub-data segments; Samples in the j-th sub-data segment after sequencing and segmenting the real part of the background harmonic voltage; /(I)The real part of the harmonic voltage of the PCC point is subjected to the same sequencing and segmentation according to the real part of the background harmonic voltage, and then the samples in the jth sub-data segment are sampled; /(I)Samples in the j-th sub-data segment after the real part of the harmonic current of the PCC point is segmented according to the same sequence and the background harmonic voltage,/>The method comprises the steps that samples in a j sub-data segment are segmented for the imaginary part of the PCC point harmonic current according to the same sequence according to background harmonic voltage; /(I)For the real part of the equivalent system side harmonic impedance in the j-th sub-data segment,/>The imaginary part of the system side harmonic impedance is equivalent in the j-th sub-data segment.
Similarly, the imaginary linear regression equation in each sub-data segment is:
wherein j is the number of the sub data segment, and P is the number of the sub data segment; Sequencing and segmenting an imaginary part of the background harmonic voltage to obtain samples in a j-th sub-data segment; /(I)The method comprises the steps that samples in a j sub-data segment are segmented for the PCC point harmonic voltage imaginary part according to the same sequence of the background harmonic voltage imaginary part; /(I)The real part of the PCC point harmonic current is segmented according to the same sequence according to the imaginary part of the background harmonic voltage, and then the samples in the jth sub-data segment are sampled; /(I)Respectively carrying out the same sequencing segmentation on the imaginary part of the PCC point harmonic current according to the imaginary part of the background harmonic voltage, and then carrying out the sample segmentation in the jth sub-data segment; /(I)For the real part of the equivalent system side harmonic impedance in the j-th sub-data segment,/>The imaginary part of the system side harmonic impedance is equivalent in the j-th sub-data segment.
Further, the calculating the system side harmonic impedance of the sub-data segment of each background harmonic by using the least square method includes:
the real part of the system side harmonic impedance is calculated by adopting a least square method to the linear regression equation and is as follows:
In the method, in the process of the invention,Is the real part of the system side harmonic impedance estimated in the jth sub-data segment sample,/>The imaginary part of the system side harmonic impedance estimated in the jth sub-data section sample is respectively; /(I)Is the real part estimated value of the background harmonic voltage in the jth sub-data segment sample; /(I)Is the nth sample point of the real part of the harmonic current of the PCC point in the jth sub-data section; /(I)The method is an nth sample point of the harmonic current imaginary part of the PCC point in the jth sub-data section; /(I)Is the nth sample point of the real part of the harmonic voltage of the PCC point in the jth sub-data section;
and calculating the imaginary part of the system side harmonic impedance by adopting a least square method to the linear regression equation as follows:
In the method, in the process of the invention,Is the real part of the system side harmonic impedance estimated in the jth sub-data segment sample,/>The imaginary part of the system side harmonic impedance estimated in the jth sub-data segment sample; /(I)Is the imaginary estimated value of the background harmonic voltage in the jth sub-data segment sample; /(I)Is the nth sample point of the real part of the harmonic current of the PCC point in the jth sub-data section,/>The method is an nth sample point of the harmonic current imaginary part of the PCC point in the jth sub-data section; /(I)The method is an nth sample point of the harmonic voltage imaginary part of the PCC point in the jth sub-data section;
and according to the real part of the system side harmonic impedance and the imaginary part of the system side harmonic impedance, averaging the corresponding quantities of the system side harmonic impedance to obtain the system side harmonic impedance of each sub-data segment.
Further, calculating the accumulated difference value between the system side harmonic impedance of the sub-data segment of each background harmonic and the initial impedance of the power grid in the numerical range by adopting an impedance difference function; the formula of the impedance difference function is:
Wherein Δz is the cumulative difference and Δzx is the impedance difference function of the real part; Δzy is the impedance difference function of the imaginary part; p is the number of sub-data segments, Z0ux is the real part value of the initial impedance; z0uy is the imaginary value of the initial impedance; j.epsilon.1..p.
In a second aspect, the present invention further provides a system-side harmonic impedance estimation device based on improved linear regression, which supports the system-side harmonic impedance estimation method based on improved linear regression; the device comprises:
The real number domain equivalent circuit equation construction unit is used for constructing a complex number domain equivalent circuit equation according to the Norton equivalent circuit under certain harmonic frequency; performing mathematical transformation on the complex number domain equivalent circuit equation and separating a real part and an imaginary part to obtain a real number domain equivalent circuit equation;
The background harmonic construction and segmentation processing unit is used for estimating the numerical range of the initial impedance of the power grid by using a short-circuit capacity method, and setting a change step length in the numerical range as a specific value of the initial impedance; sequentially bringing specific values of each initial impedance into the real number domain equivalent circuit equation to construct background harmonic waves, and sequencing and segmenting the background harmonic waves to obtain sub-data segments of each background harmonic wave; the harmonic measurement data corresponding to the background harmonic is processed identically with the background harmonic;
The linear regression equation construction unit is used for constructing a linear regression equation by utilizing the background harmonic data and the measurement data in the sub-data segment of each background harmonic;
A sub-data segment harmonic impedance calculation unit for calculating the system side harmonic impedance of the sub-data segment of each background harmonic by using a least square method;
And the final system side harmonic impedance optimization calculation unit is used for calculating the accumulated difference value between the system side harmonic impedance of the sub-data segment of each background harmonic and the initial impedance of the power grid in the numerical range, and the corresponding initial impedance of the power grid is the final system side harmonic impedance when the accumulated difference value is minimum.
Further, the background harmonic construction unit comprises a short-circuit capacity estimation subunit, a segmentation processing unit and a measurement data processing unit;
the short-circuit capacity estimation subunit is used for estimating the numerical range of the initial impedance of the power grid by using a short-circuit capacity method, and setting a change step length in the numerical range as a specific value of the initial impedance;
The segmentation processing unit is used for sequentially bringing specific values of all initial impedances into the real number domain equivalent circuit equation to reversely solve corresponding real number background harmonic voltages; sequencing and segmenting the real background harmonic voltage to obtain sub-data segments of each background harmonic;
And the measured data processing unit is used for processing harmonic measured data corresponding to the background harmonic in the same way along with the background harmonic.
Further, the harmonic measurement data includes a measured harmonic voltage and a measured harmonic current.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. The invention relates to a system side harmonic impedance estimation method and a device based on improved linear regression. The invention can construct the background harmonic voltage by utilizing the known prior information, and the influence of the fluctuation of the background harmonic voltage on the algorithm is caused by processing the constructed background harmonic voltage data, so that the estimation result is more stable and the accuracy is higher; in addition, the invention takes the difference between the minimum calculated impedance and the initial impedance as a criterion, and the algorithm can iteratively converge to obtain the optimal initial impedance no matter the set size of the initial impedance range by searching the optimal initial impedance as a final result.
2. The system side harmonic impedance estimation method and device based on improved linear regression can be suitable for accurately estimating the system side harmonic impedance only by measuring harmonic voltage and current monitoring data of points when background harmonic fluctuation in a power grid is strong. Aiming at the characteristics of high-proportion new energy distributed network access, high-power electronic distribution network and the like in a modern power system, harmonic sources are widely distributed, harmonic content is increased, harmonic presents high-frequency, wide-frequency-domain and wide-distribution characteristics, background harmonic content in the power grid is extremely high, and the method can accurately estimate system side harmonic impedance under the background and provides reference for quantification of harmonic emission responsibility.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present invention and the descriptions thereof are for illustrating the present invention only and are not to be construed as limiting the present invention.
Example 1
The system side harmonic impedance is calculated according to the sign characteristic of the fluctuation ratio of the harmonic voltage and the harmonic current of the public coupling point based on the fluctuation method in the prior art. Firstly, respectively obtaining fluctuation values of harmonic voltage and harmonic current at adjacent moments, calculating the ratio of the harmonic voltage to the fluctuation quantity of the harmonic current, and judging whether the harmonic impedance is at the system side or the user side according to the positive and negative of the real part of the ratio. However, in the actual power grid, both the system side harmonic wave and the user side harmonic wave have fluctuation, when the fluctuation amplitude of the user side is larger than that of the system side according to the ratio of the fluctuation amounts of the harmonic voltages and the currents, the estimated result is close to the system side harmonic impedance, and when the fluctuation of the system side is larger, the calculated result is close to the user side harmonic impedance, and at the moment, a relatively accurate estimated value of the system side harmonic impedance cannot be obtained through symbol discrimination.
The linear regression method obtains a circuit equation based on a harmonic source Norton equivalent circuit, obtains regression coefficients through a linear regression analysis method and known harmonic data at PCC, and calculates harmonic impedance of a system side through calculating and averaging the obtained regression coefficients for a plurality of times. The precondition of the regression method is that the random error term and the variable are in linear correlation, and the estimation error is smaller when the harmonic wave at the system side is stable. However, the system side harmonic impedance can be calculated by a binary linear regression method. The method is interfered by the collinearity of the harmonic current of the PCC point and the background harmonic voltage, and the regression result calculation method based on least square assumes that the error term is normally distributed, and when the background harmonic is non-normally distributed, the regression result has deviation. In addition, the binary linear regression method carries out regression in a real number domain, and separates a real part from an imaginary part to obtain a compound regression result which is not in a strict sense, but the regression analysis method in a complex domain is still influenced by a colinear factor. And both are solved by adopting a least square method, the influence of fluctuation of a constant term regression coefficient, namely background harmonic wave is not solved, and the estimation error of the method is larger when stronger background harmonic wave fluctuation exists in an actual power grid. The robust regression method can prevent the influence of the abnormal data on the estimation result, has robustness on the abnormal data, but the selection weight lacks theoretical support, has strong subjectivity, and the mode of determining the abnormal data according to the deviation degree is questionable.
The random independent vector method utilizes the characteristic that the covariance of two independent random vectors is zero, can inhibit the influence of system background harmonic fluctuation on an estimation result to a certain extent, and calculates the result more accurately when the harmonic emission level of a user side is higher. However, the accuracy of the calculation result of the random independent vector method depends on the relative magnitude of the system harmonic impedance at two sides of the PCC point and the relative magnitude of the harmonic current fluctuation at two sides, that is, the fluctuation of the harmonic current of the PCC point is dominated by the user side, and the harmonic voltage of the PCC point is dominated by both sides. Meanwhile, when the relation that the impedances on two sides are far larger cannot be determined, or the harmonic voltage fluctuation of the PCC point is dominated by the user side, the calculation result of the harmonic impedance of the power grid is unreliable.
The Independent Component Analysis (ICA) method only theoretically needs to assume that the harmonic source signals at two sides are independent, the capability of resisting background harmonic wave is strong, and the ICA method can obtain more accurate results only when the impedance at the user side is far greater than the impedance at the system side. However, in practice, the calculation error is small only when the harmonic impedance of the power grid side is far smaller than that of the user side, and the calculation accuracy is not high when the harmonic impedance amplitudes of the two sides are relatively close.
Therefore, when the background harmonic wave fluctuation is strong, the system side harmonic impedance estimation methods in the prior art are not robust and accurate enough. The invention designs a system side harmonic impedance estimation method based on improved linear regression, which comprises the steps of firstly setting initial impedance according to the short-circuit capacity of a system to construct background harmonic voltage data, processing the constructed background harmonic voltage data to reduce adverse effects of fluctuation on an algorithm, calculating harmonic impedance corresponding to a processed data segment by using a least square method, and finally obtaining the required system side harmonic impedance by using an impedance difference minimum criterion. The invention can construct the background harmonic voltage by utilizing the known prior information, and the influence of the fluctuation of the background harmonic voltage on the algorithm is caused by processing the constructed background harmonic voltage data, so that the estimation result is more stable and the accuracy is higher; in addition, the invention takes the difference between the minimum calculated impedance and the initial impedance as a criterion, and the algorithm can iteratively converge to obtain the optimal initial impedance no matter the set size of the initial impedance range by searching the optimal initial impedance as a final result.
As shown in fig. 2, the system side harmonic impedance estimation method based on improved linear regression of the present invention comprises:
step A, a complex domain equivalent circuit equation is established according to a Norton equivalent circuit under certain harmonic frequency; performing mathematical transformation on the complex number domain equivalent circuit equation and separating a real part and an imaginary part to obtain a real number domain equivalent circuit equation;
Harmonic analysis typically employs the Norton equivalent circuit shown in FIG. 1, whereinAnd/>A harmonic voltage and a harmonic current that are measurable for a point of common coupling (Point of common coupling, PCC); /(I)And/>Harmonic source currents corresponding to the system side and the user side respectively; zu and Zc are respectively harmonic impedances corresponding to a system side and a user side; the following circuit equations can be written according to the superposition theorem:
Will beEquation of/>Can be obtained by the equation of (2)
Wherein the method comprises the steps ofAs background harmonic, the calculation method of the system side harmonic impedance Zu mostly needs to assume that the background harmonic is basically stable, but the modern power system is highly power-electronic, and various nonlinear loads are distributed and largely connected to the network, so that the assumption is difficult to meet, and the calculation of the system side harmonic impedance by the existing method can generate larger errors.
Since the equation of equation (2) is based on complex domain, to facilitate the processing of the background harmonic, the real and imaginary parts of the equation are separated:
The equation (3) is an equivalent circuit equation of a real number domain, and Vux in a real part expression is a real part of the background harmonic voltage; zux is the real part of the system side harmonic impedance; vuy is the imaginary part of the background harmonic voltage; zuy is the imaginary part of the system side harmonic impedance. The formula (3) can be regarded as a linear model, regression coefficients can be calculated by adopting a regression method, but the accuracy of the method is greatly influenced by background harmonic fluctuation, so the invention provides an improved regression method for calculating the side harmonic impedance of a system.
Step B, estimating a numerical range of initial impedance of the power grid by using a short-circuit capacity method, and setting a change step length in the numerical range as a specific value of the initial impedance; sequentially bringing specific values of each initial impedance into the real number domain equivalent circuit equation to construct background harmonic waves, and sequencing and segmenting the background harmonic waves to obtain sub-data segments of each background harmonic wave; the harmonic measurement data corresponding to the background harmonic is processed identically with the background harmonic;
Wherein the harmonic measurement data includes a measured harmonic voltage and a measured harmonic current.
Specifically, the specific values of all initial impedances are brought into the real number domain equivalent circuit equation in turn to construct background harmonics, and the background harmonics are sequenced and segmented to obtain sub-data segments of all the background harmonics; the method comprises the following steps:
Sequentially bringing specific values of all initial impedances into the real number domain equivalent circuit equation (formula (3)), and reversely solving corresponding real number background harmonic voltages;
And sequencing and segmenting the real background harmonic voltage to obtain sub-data segments of each background harmonic.
The expression of the short-circuit capacity method is as follows:
Wherein Zux is the real part of the system side harmonic impedance and Zuy is the imaginary part of the system side harmonic impedance; s is the short-circuit capacity of the system; vN is the rated voltage of the power grid; h is the harmonic order.
In this embodiment, a calculation process of a real part of a system-side harmonic impedance is taken as an example, and a calculation process of an imaginary part is identical to the real part. After Zux is obtained by the formula (4), a numerical range [ a, b ] is selected from the plus or minus tens of ohms of the distance Zux, and the change step delta is set, so that Z0ux = [ a, a+delta … a+n delta … b ] is respectively brought into the formula (3) to be reversely solved to obtain the background harmonic Vux. The background harmonic Vux data are sequenced from small to large and segmented, and under the condition that data points are enough, the difference between adjacent points after sequencing can be reduced, and the fluctuation of the segmented data of each sub-segment is smaller than that of the total data. Therefore, the influence of the background harmonic wave on the result can be reduced by calculating the impedance on the premise of the background harmonic wave after the sequencing and segmentation processing. Meanwhile, the harmonic measurement data Vpccx、Ipccx and Ipccy in the formula (3) are also arranged and segmented in the same order following the background harmonic Vux data.
Step C, constructing a linear regression equation by utilizing background harmonic data and measurement data in the sub-data segments of each background harmonic; calculating the system side harmonic impedance of the sub-data segment of each background harmonic by adopting a least square method; the linear regression equation is a linear regression equation taking harmonic measurement data as a known variable and system side harmonic impedance as a regression coefficient;
taking the calculation process of the real part of the harmonic impedance as an example, assuming that the total sample number is N, the segmentation number is P, and the sample size of each sub-data segment is n=n/P, the real part harmonic voltage equation of each sub-data segment can be obtained:
Wherein j is the number of the sub data segment; p is the number of sub-data segments; Samples in the j-th sub-data segment after sequencing and segmenting the real part of the background harmonic voltage; /(I)The real part of the harmonic voltage of the PCC point is subjected to the same sequencing and segmentation according to the real part of the background harmonic voltage, and then the samples in the jth sub-data segment are sampled; /(I)Samples in the j-th sub-data segment after the real part of the harmonic current of the PCC point is segmented according to the same sequence and the background harmonic voltage,/>The method comprises the steps that samples in a j sub-data segment are segmented for the imaginary part of the PCC point harmonic current according to the same sequence according to background harmonic voltage; /(I)For the real part of the equivalent system side harmonic impedance in the j-th sub-data segment,/>The imaginary part of the harmonic impedance at the equivalent system side in the j-th sub-data segment;
The equation (5)) can be regarded as a linear regression model y=xβ+ε, where the interpretation variable X is inclusive ofThe interpreted variable Y is/>Epsilon is the random error and the regression coefficients include/>And/>It should be noted that the background harmonic/>The initial impedance Z0ux set by the short-circuit capacity of the system is carried into the formula (3) to be reversely solved, and is subjected to sorting and segmentation processing, and all other known variables X, Y are respectively calculated according to/>Is arranged identically and is segmented. For the linear regression equation of the formula (5), calculating each regression coefficient by adopting a least square method, namely calculating the real part of the system side harmonic impedance by adopting the least square method as follows:
In the method, in the process of the invention,Is the real part of the system side harmonic impedance estimated in the jth sub-data segment sample,/>The imaginary part of the system side harmonic impedance estimated in the jth sub-data section sample is respectively; /(I)Is the real part estimated value of the background harmonic voltage in the jth sub-data segment sample; /(I)Is the nth sample point of the real part of the harmonic current of the PCC point in the jth sub-data section; /(I)The method is an nth sample point of the harmonic current imaginary part of the PCC point in the jth sub-data section; /(I)Is the nth sample point of the real part of the harmonic voltage of the PCC point in the jth sub-data section;
Similarly, the imaginary linear regression equation in each sub-data segment is:
wherein j is the number of the sub data segment, and P is the number of the sub data segment; Sequencing and segmenting an imaginary part of the background harmonic voltage to obtain samples in a j-th sub-data segment; /(I)The method comprises the steps that samples in a j sub-data segment are segmented for the PCC point harmonic voltage imaginary part according to the same sequence of the background harmonic voltage imaginary part; /(I)The real part of the PCC point harmonic current is segmented according to the same sequence according to the imaginary part of the background harmonic voltage, and then the samples in the jth sub-data segment are sampled; /(I)Respectively carrying out the same sequencing segmentation on the imaginary part of the PCC point harmonic current according to the imaginary part of the background harmonic voltage, and then carrying out the sample segmentation in the jth sub-data segment; /(I)For the real part of the equivalent system side harmonic impedance in the j-th sub-data segment,/>The imaginary part of the system side harmonic impedance is equivalent in the j-th sub-data segment.
The least squares solution of equation (7) is:
In the method, in the process of the invention,Is the real part of the system side harmonic impedance estimated in the jth sub-data segment sample,/>The imaginary part of the system side harmonic impedance estimated in the jth sub-data segment sample; /(I)Is the imaginary estimated value of the background harmonic voltage in the jth sub-data segment sample; /(I)Is the nth sample point of the real part of the harmonic current of the PCC point in the jth sub-data section,/>The method is an nth sample point of the harmonic current imaginary part of the PCC point in the jth sub-data section; /(I)The method is an nth sample point of the harmonic voltage imaginary part of the PCC point in the jth sub-data section;
The calculated values of the real part and the imaginary part of the harmonic impedance are obtained by the formula (6) and the formula (8), and the calculated value of the formula (6) is marked as 1, and the calculated value of the formula (8) is marked as 2 for distinguishing. And then, the corresponding amounts of the harmonic impedances in the formula (6) and the formula (8) are averaged to obtain the system side harmonic impedance of each sub-data segment.
Wherein,And/>Estimate from equation (6)/>And/>An estimate from equation (8); /(I)And (3) withThe real part and the imaginary part estimated values of the system side harmonic impedance in the jth sub-data segment are calculated by the method.
And D, calculating the accumulated difference value between the system side harmonic impedance of the sub-data segment of each background harmonic and the initial impedance of the power grid in the numerical range, and obtaining the corresponding initial impedance of the power grid when the accumulated difference value is minimum, namely the final system side harmonic impedance.
Specifically, calculating the accumulated difference value between the system side harmonic impedance of the sub-data segment of each background harmonic and the initial impedance of the power grid in the numerical range by adopting an impedance difference function; the formula of the impedance difference function is:
Wherein Δz is the cumulative difference and Δzx is the impedance difference function of the real part; Δzy is the impedance difference function of the imaginary part; p is the number of sub-data segments, Z0ux is the real part value of the initial impedance; z0uy is the imaginary value of the initial impedance; j.epsilon.1..p.
Each input of an initial impedance Z0ux and Z0uy results in an impedance difference Δz, which is therefore a binary function of Z0ux and Z0uy. The initial impedances Z0ux and Z0uy corresponding to the minimum ΔZ are the final results that are obtained, namely:
In the method, in the process of the invention,And/>The real part and the imaginary part of the system side harmonic impedance finally obtained by the method are the values of the real part and the imaginary part of the system side harmonic impedance finally obtained by the method. Since the Δz minimum exists and is unique, the selection of the initial impedance does not affect the final calculation result, but affects the calculation amount of the whole algorithm iterative process. Because the method of the invention aims to obtain the initial impedance which makes the impedance difference function delta Z minimum, if the initial impedance deviates from the true value greatly, the calculation time for converging to the minimum delta Z value is increased, the minimum delta Z value is only present, and can converge to the minimum value after iteration, so that the initial impedance value selection does not influence the accuracy of the result.
The system side harmonic impedance estimation method based on the improved linear regression can be suitable for accurately estimating the system side harmonic impedance only by measuring harmonic voltage and current monitoring data of points when background harmonic fluctuation in a power grid is strong. Aiming at the characteristics of high-proportion new energy distributed network access, high-power electronic distribution network and the like in a modern power system, harmonic sources are widely distributed, harmonic content is increased, harmonic presents high-frequency, wide-frequency-domain and wide-distribution characteristics, background harmonic content in the power grid is extremely high, and the method can accurately estimate system side harmonic impedance under the background and provides reference for quantification of harmonic emission responsibility.
Example 2
As shown in fig. 3, the difference between this embodiment and embodiment 1 is that the present invention further provides a system-side harmonic impedance estimation device based on improved linear regression, which supports the system-side harmonic impedance estimation method based on improved linear regression described in embodiment 1; the device comprises:
The real number domain equivalent circuit equation construction unit is used for constructing a complex number domain equivalent circuit equation according to the Norton equivalent circuit under certain harmonic frequency; performing mathematical transformation on the complex number domain equivalent circuit equation and separating a real part and an imaginary part to obtain a real number domain equivalent circuit equation;
The background harmonic construction and segmentation processing unit is used for estimating the numerical range of the initial impedance of the power grid by using a short-circuit capacity method, and setting a change step length in the numerical range as a specific value of the initial impedance; sequentially bringing specific values of each initial impedance into the real number domain equivalent circuit equation to construct background harmonic waves, and sequencing and segmenting the background harmonic waves to obtain sub-data segments of each background harmonic wave; the harmonic measurement data corresponding to the background harmonic is processed identically with the background harmonic;
The linear regression equation construction unit is used for constructing a linear regression equation by utilizing the background harmonic data and the measurement data in the sub-data segment of each background harmonic;
A sub-data segment harmonic impedance calculation unit for calculating the system side harmonic impedance of the sub-data segment of each background harmonic by using a least square method;
And the final system side harmonic impedance optimization calculation unit is used for calculating the accumulated difference value between the system side harmonic impedance of the sub-data segment of each background harmonic and the initial impedance of the power grid in the numerical range, and the corresponding initial impedance of the power grid is the final system side harmonic impedance when the accumulated difference value is minimum.
As a further implementation, the background harmonic construction unit includes a short-circuit capacity estimation subunit, a segmentation processing unit, and a measurement data processing unit;
the short-circuit capacity estimation subunit is used for estimating the numerical range of the initial impedance of the power grid by using a short-circuit capacity method, and setting a change step length in the numerical range as a specific value of the initial impedance;
The segmentation processing unit is used for sequentially bringing specific values of all initial impedances into the real number domain equivalent circuit equation to reversely solve corresponding real number background harmonic voltages; sequencing and segmenting the real background harmonic voltage to obtain sub-data segments of each background harmonic;
And the measured data processing unit is used for processing harmonic measured data corresponding to the background harmonic in the same way along with the background harmonic.
As a further implementation, the harmonic measurement data includes a measured harmonic voltage and a measured harmonic current.
The execution process of each unit is performed according to the steps of the system side harmonic impedance estimation method based on improved linear regression described in embodiment 1, and the details of this embodiment are not repeated.
According to the Norton equivalent circuit under certain harmonic frequency, a complex domain equivalent circuit equation is established, mathematical transformation is carried out on the equation, and a real-number domain equivalent circuit equation of a real part and an imaginary part is obtained; determining a numerical range of initial impedance according to the short-circuit capacity of the system, setting a change step length in the range as a specific value of the initial impedance, sequentially bringing each initial impedance into a corresponding real number domain equivalent circuit equation, solving the corresponding real number background harmonic voltage reversely, sequencing and segmenting the part of background harmonic voltage, and carrying out the same treatment on corresponding measurement data along with the background harmonic; and in the obtained sub-data segment of each background harmonic, a regression equation is established by utilizing the constructed background harmonic data and the measured harmonic voltage and current data, and the system side harmonic impedance of the sub-data segment is calculated by adopting a least square method. Obtaining system side harmonic impedance calculated by all sub-data segments; and according to the accumulated difference between the obtained impedance calculated value and the initial impedance, obtaining the initial impedance corresponding to the minimum value as a final result.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.