Harmonic responsibility estimation method and system for multiple harmonic sources based on linear dynamic clustering

Abstract

The present invention relates to a method and system for estimating harmonic responsibility of multiple harmonic sources based on linear dynamic clustering. The method first uses harmonic monitoring data to establish an interval harmonic equation for harmonic responsibility allocation, then uses an interval linear clustering algorithm to divide typical scenarios, and uses parameterized regression to identify interval equation parameters; finally, according to the interval equation parameters, the harmonic responsibility variation range of each harmonic source in the system is quantified. The method and system are conducive to improving the accuracy of harmonic responsibility estimation.

Description

Technical Field

[0001] The invention belongs to the field of electric power systems, and in particular relates to a method and system for estimating harmonic responsibility of multiple harmonic sources based on linear dynamic clustering. Background Art

[0002] As the penetration rate of power electronic control equipment continues to increase, the harmonic pollution problem in the power system has become more serious. At the same time, the surge in various new harmonic sources has led to an increase in the number of conditions where multiple harmonic sources coexist, which has also enhanced the randomness and time-varying nature of grid harmonics, making the harmonic problem more complicated. In order to avoid disputes due to power quality issues and effectively control harmonic sources, an important prerequisite is to evaluate the harmonic responsibility of each harmonic source.

[0003] The traditional harmonic responsibility allocation method requires the use of special equipment to synchronously measure the harmonic voltage and harmonic current of multiple users, while the current harmonic monitoring system usually gives the harmonic statistical values ​​within the monitoring period, so the engineering application of the traditional method is limited. In addition, the traditional linear regression method is effective only if the equivalent harmonic impedance and the background harmonic voltage remain constant. However, when the time scale of harmonic data acquisition is long, load switching and reactive compensation equipment switching will occur in the power grid, resulting in more obvious changes in the equivalent harmonic impedance and the background harmonic voltage. Therefore, when the system operation scenario changes greatly, the use of the above method will lead to large errors in harmonic responsibility estimation. Summary of the invention

[0004] The object of the present invention is to provide a method and system for estimating harmonic responsibility of multiple harmonic sources based on linear dynamic clustering, which method and system are conducive to improving the accuracy of harmonic responsibility estimation.

[0005] To achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a method for estimating the harmonic responsibility of multiple harmonic sources based on linear dynamic clustering, which first uses harmonic monitoring data to establish an interval harmonic equation for harmonic responsibility allocation, then uses an interval linear clustering algorithm to divide typical scenarios, and uses parameterized regression to identify interval equation parameters; finally, according to the interval equation parameters, the harmonic responsibility variation range of each harmonic source in the system is quantified.

[0006] Furthermore, the specific method for establishing the interval harmonic equation for harmonic responsibility allocation is:

[0007] Assume that the harmonic voltage of order h generated at node m when harmonic source s acts alone is U sh , the hth harmonic voltage generated by other harmonic sources and background harmonic sources at node m is U 0h , then the hth harmonic voltage U at node m is mh It is expressed as:

[0008]

[0009] Among them, Z sh is the equivalent harmonic impedance between node m and harmonic source s, I sh is the hth harmonic current injected into the power grid by harmonic source s; U mh is the reference phasor, then according to formula (1), we have:

[0010]

[0011] Where β1 = Z sh cosθ s , β0=U 0h cosθ 0s ;

[0012] The maximum and minimum values ​​in a monitoring cycle are used to construct the interval harmonic voltage sample [U mh ] and interval harmonic current samples [I sh ]:

[0013]

[0014] Convert equation (2) into interval form:

[0015] [U mh ]=[β]1[I sh ]+[β]0 (4)

[0016] The harmonic responsibility calculation formula when using interval samples is:

[0017]

[0018] Assuming that there are M monitoring cycles in the evaluation period, take the average value of both sides of equation (5) to obtain the average harmonic responsibility interval in the evaluation period: The subscript o of the interval number indicates the midpoint value;

[0019]

[0020] Assume that there are G operating scenarios in the evaluation period. For the kth typical scenario, k = 1, 2, ..., G, if there are M (k) monitoring cycles in this scenario, when the parameter estimation interval value is obtained After that, the average harmonic responsibility of this scenario is:

[0021]

[0022] Then the total harmonic responsibility interval within the time of concern is:

[0023]

[0024] Furthermore, the specific method of dividing the scene and identifying the interval equation parameters is:

[0025] The parameterized regression linear dynamic clustering algorithm is used to divide the harmonic source operation scenarios and identify the interval equation parameters; sh ] is a sample set X, [U mh ] is a sample set Y:

[0026]

[0027] in and x ij , y i They are [x ij ] and [y j ], p is the interval sample dimension, n is the number of samples; for [x ij ] ij Expressed as upper and lower bounds of the interval and λ j A function where λ j ∈(0,1);

[0028]

[0029] A regression model is established for the lower bound of the response, and we have:

[0030]

[0031] Among them, ε il is the error variable, substituting equation (9) into equation (10) to obtain the following equation:

[0032]

[0033] Define two parameters α jl With ω jl , let α jl =β jl (1-λ j ),ω jl =β jl λ j , formula (11) is rewritten as:

[0034]

[0035] The matrix form of formula (12) is:

[0036] Y =X PM β PMl +ε l (13)

[0037] in:

[0038]

[0039] β PMl =[β 0l α 1l ω 1l … α pl ω pl ] T ,

[0040] Y =[ y 1 y 2 … y n ]T,

[0041] ε l =[ε 1l ε 2l … ε nl ] T .

[0042] According to the least squares method, we get The calculation formula is:

[0043]

[0044] λ j The value is obtained by the following formula:

[0045]

[0046] Similarly, a regression model is established for the upper bound of the response interval, and the calculation process is the same as that of equations (13) to (18), and we get:

[0047]

[0048]

[0049]

[0050] in:

[0051] β PMu =[β 0u α 1u ω 1u … α pu ω pu ] T

[0052]

[0053] εu =[ε 1u ε 2u … ε nu ] T

[0054] In summary, sample y i The prediction interval of The calculation formula is:

[0055]

[0056] Define the interval estimation error ε i as follows:

[0057]

[0058] Among them, k represents the kth cluster; then the interval linear clustering problem is to solve the minimization optimization problem shown in equation (23):

[0059]

[0060] First, the k-means algorithm is used to initialize clustering, and the central value of the interval sample is selected as the feature for clustering. The initial sample is divided according to the k-means clustering result; the elbow method is used to determine the number of clusters, and the SSE of different cluster numbers k is calculated. The cluster number where the SSE tends to be flat is taken as the optimal cluster number, thereby obtaining the optimal cluster number;

[0061] After cluster initialization is completed, the following steps are repeated until the objective function reaches the global optimum:

[0062] 1) Keep the division of the data set unchanged, and use the PM method to establish interval regression models for each cluster; set the window length to b, divide the data of each cluster into M / b sampling windows, perform interval regression on the data of each sampling window, and calculate the R of each sampling window. 2 ;

[0063]

[0064] Setting R 2 threshold, select all R 2 The data in the sampling window greater than the threshold are used for parameter estimation; based on the selected data, the interval regression parameters of each cluster are first calculated according to equations (14) and (17): and For all samples, the prediction interval of the i-th sample in the k-th cluster is calculated according to formula (19):

[0065] 2) According to formula (23), calculate the regression error ε of the i-th sample belonging to the k-th cluster i(k) :

[0066]

[0067] Suppose the optimal clustering solution that minimizes the objective function J is P k , k=1,…,G, then P k Obtained through the following allocation criteria:

[0068]

[0069] The above two steps are repeated alternately until the clustering solution is consistent with the previous one, then the algorithm is considered to have converged and the clustering process is finished;

[0070] Finally, the harmonic responsibility interval of the harmonic source is calculated based on the identified regression parameter interval.

[0071] The present invention also provides a method and system for estimating harmonic responsibility of multiple harmonic sources based on linear dynamic clustering, including a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the above-mentioned method steps can be implemented.

[0072] Compared with the prior art, the present invention has the following beneficial effects: it provides a method and system for estimating harmonic responsibility intervals of multiple harmonic sources based on linear dynamic clustering, which can realize the harmonic responsibility allocation of multiple harmonic sources on a complex multi-node power supply network. Firstly, taking into account the harmonic impedance and the short-term fluctuation of the background harmonic voltage, an interval model for harmonic responsibility allocation is established, and the harmonic responsibility interval index is defined; the typical scenarios are divided using the interval linear clustering algorithm, and at the same time, the harmonic responsibility interval index is defined using the interval linear clustering algorithm based on R 2 The correlation data selection method identifies the interval parameters of the linear equation to ensure that the harmonic impedance change and the fluctuation of the background harmonic voltage in each scenario are maintained at a low level, thereby reducing the estimation error of the harmonic responsibility. Based on the uncertain information in the interval-type harmonic monitoring data, the operation scenarios of the harmonic source are divided to realize the harmonic responsibility sharing of multiple harmonic sources. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a flow chart of the method implementation of the embodiment of the present invention. DETAILED DESCRIPTION

[0074] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0075] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0076] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0077] like Figure 1 As shown, this embodiment provides a method for estimating the harmonic responsibility of multiple harmonic sources based on linear dynamic clustering. First, harmonic monitoring data is used to establish an interval harmonic equation for harmonic responsibility allocation. Then, an interval linear clustering algorithm is used to divide typical scenarios, and parameterized regression is used to identify interval equation parameters. Finally, according to the interval equation parameters, the harmonic responsibility variation range of each harmonic source in the system is quantified.

[0078] In this embodiment, the specific method of establishing the interval harmonic equation for harmonic responsibility allocation is:

[0079] Assume that the harmonic voltage of order h generated at node m when harmonic source s acts alone is U sh , the hth harmonic voltage generated by other harmonic sources and background harmonic sources at node m is U 0h , then the hth harmonic voltage U at node m is mh It is expressed as:

[0080]

[0081] Among them, Z sh is the equivalent harmonic impedance between node m and harmonic source s, I sh is the hth harmonic current injected into the power grid by harmonic source s; U mh is the reference phasor, then according to formula (1), we have:

[0082]

[0083] Where β1 = Z sh cosθ s , β0=U 0h cosθ 0s ;

[0084] The maximum and minimum values ​​in a monitoring cycle are used to construct the interval harmonic voltage sample [U mh] and interval harmonic current samples [I sh ]:

[0085]

[0086] Convert equation (2) into interval form:

[0087] [U mh ]=[β]1[I sh ]+[β]0 (4)

[0088] The harmonic responsibility calculation formula when using interval samples is:

[0089]

[0090] Assuming that there are M monitoring cycles in the evaluation period, take the average value of both sides of equation (5) to obtain the average harmonic responsibility interval in the evaluation period: The subscript o of the interval number indicates the midpoint value;

[0091]

[0092] Assume that there are G operating scenarios in the evaluation period. For the kth typical scenario, k = 1, 2, ..., G, if there are M (k) monitoring cycles in this scenario, when the parameter estimation interval value is obtained After that, the average harmonic responsibility of this scenario is:

[0093]

[0094] Then the total harmonic responsibility interval within the time of concern is:

[0095]

[0096] In this embodiment, the specific method of dividing the scene and identifying the interval equation parameters is:

[0097] The parameterized regression linear dynamic clustering algorithm is used to divide the harmonic source operation scenarios and identify the interval equation parameters; sh ] is a sample set X, [U mh ] is a sample set Y:

[0098]

[0099] in and x ij , y i They are [x ij ] and [y j], p is the interval sample dimension, n is the number of samples; for [x ij ] ij Expressed as upper and lower bounds of the interval and λ j A function where λ j ∈(0,1);

[0100]

[0101] A regression model is established for the lower bound of the response, and we have:

[0102]

[0103] Among them, ε il is the error variable, substituting equation (9) into equation (10) to obtain the following equation:

[0104]

[0105] Define two parameters α jl With ω jl , let α jl =β jl (1-λ j ),ω jl =β jl λ j , formula (11) is rewritten as:

[0106]

[0107] The matrix form of formula (12) is:

[0108] Y =X PM β PMl +ε l (13)

[0109] in:

[0110]

[0111] β PMl =[β 0l α 1l ω 1l … α pl ω pl ] T ,

[0112] Y =[ y 1 y 2 … y n ] T ,

[0113] ε l =[ε 1l ε 2l … ε nl ] T .

[0114] According to the least squares method, we get The calculation formula is:

[0115]

[0116] λ j The value is obtained by the following formula:

[0117]

[0118] Similarly, a regression model is established for the upper bound of the response interval, and the calculation process is the same as that of equations (13) to (18), and we get:

[0119]

[0120]

[0121]

[0122] in:

[0123] β PMu =[β 0u α 1u ω 1u … α pu ω pu ] T

[0124]

[0125] ε u =[ε 1u ε 2u … ε nu ] T

[0126] In summary, sample y i The prediction interval of The calculation formula is:

[0127]

[0128] Define the interval estimation error ε i as follows:

[0129]

[0130] Among them, krepresents the kth cluster; then the interval linear clustering problem is to solve the minimization optimization problem shown in equation (23):

[0131]

[0132] First, the k-means algorithm is used to initialize clustering, and the central value of the interval sample is selected as the feature for clustering. The initial sample is divided according to the k-means clustering result; the elbow method is used to determine the number of clusters, and the SSE of different cluster numbers k is calculated. The cluster number where the SSE tends to be flat is taken as the optimal cluster number, thereby realizing the selection of the optimal cluster number;

[0133] After cluster initialization is completed, the following steps are repeated until the objective function reaches the global optimum:

[0134] 1) Keep the division of the data set unchanged, and use the PM method to establish interval regression models for each cluster; set the window length to b, divide the data of each cluster into M / b sampling windows, perform interval regression on the data of each sampling window, and calculate the R of each sampling window. 2 ;

[0135]

[0136] Setting R 2 The threshold is 0.9, and all R 2 The data in the sampling window greater than the threshold are used for parameter estimation; based on the selected data, the interval regression parameters of each cluster are first calculated according to equations (14) and (17): and For all samples, the prediction interval of the i-th sample in the k-th cluster is calculated according to formula (19):

[0137] 2) According to formula (23), calculate the regression error ε of the i-th sample belonging to the k-th cluster i(k) :

[0138]

[0139] Suppose the optimal clustering solution that minimizes the objective function J is P k , k=1,…,G, then P k Obtained through the following allocation criteria:

[0140]

[0141] The above two steps are repeated alternately until the clustering solution is consistent with the previous one, then the algorithm is considered to have converged and the clustering process is finished;

[0142] Finally, the harmonic responsibility interval of the harmonic source is calculated based on the identified regression parameter interval.

[0143] This embodiment also provides a method and system for estimating harmonic responsibility of multiple harmonic sources based on linear dynamic clustering, including a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the above-mentioned method steps can be implemented.

[0144] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0145] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0146] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0147] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0148] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A method for estimating harmonic responsibility of multiple harmonic sources based on linear dynamic clustering, characterized in that: Firstly, the harmonic monitoring data is used to establish the interval harmonic equation for harmonic responsibility allocation. Then, the interval linear clustering algorithm is used to divide the typical scenarios, and the parameters of the interval equation are identified by parametric regression. Finally, the harmonic responsibility variation range of each harmonic source in the system is quantified according to the parameters of the interval equation. The specific method to establish the interval harmonic equation for harmonic responsibility allocation is: Assume that the harmonic voltage of order h generated at node m when harmonic source s acts alone is U sh , the hth harmonic voltage generated by other harmonic sources and background harmonic sources at node m is U 0h , then the hth harmonic voltage U at node m is mh It is expressed as: U mh =U sh +U 0h =Z sh I sh +U 0h (1) Among them, Z sh is the equivalent harmonic impedance between node m and harmonic source s, I sh is the hth harmonic current injected into the power grid by harmonic source s; U mh is the reference phasor, then according to formula (1), we have: where β1 = Z sh cosθ s , β0 = U 0h cosθ 0s ; The maximum and minimum values ​​in a monitoring cycle are used to construct the interval harmonic voltage sample [U mh ] and interval harmonic current samples [I sh ]: Convert equation (2) into interval form: [U mh ]=[β]1[I sh ]+[β]0 (4) The harmonic responsibility calculation formula when using interval samples is: Assuming that there are M monitoring cycles in the evaluation period, take the average value of both sides of equation (5) to obtain the average harmonic responsibility interval in the evaluation period: The subscript o of the interval number indicates the midpoint value; Assume that there are G operating scenarios in the evaluation period. For the kth typical scenario, k = 1, 2, ..., G, if there are M (k) monitoring cycles in this scenario, when the parameter estimation interval value is obtained After that, the average harmonic responsibility of this scenario is: Then the total harmonic responsibility interval within the time of concern is: The specific method of dividing the scene and identifying the parameters of the interval equation is: The parameterized regression linear dynamic clustering algorithm is used to divide the harmonic source operation scenarios and identify the interval equation parameters; sh ] is a sample set X, [U mh ] is a sample set Y: in With x ij ,y i They are [x ij ] and [y j ], D is the interval sample dimension, n represents the number of samples; for [x ij ] ij Expressed as upper and lower bounds of the interval and λ j A function where λ j ∈(0,1); A regression model is established for the lower bound of the response, and we have: Among them, ε il is the error variable, substituting equation (9) into equation (10) to obtain the following equation: Define two parameters α jl With ω jl , let α jl =β jl (1-λ j ),ω jl =β jl λ j , formula (11) is rewritten as: The matrix form of formula (12) is: Y=X PM b PMl +e l (13) in: b PMl =[β 0l a 1l oh 1l …a Dl oh Dl ] T , Y=[y1 y2…y n ] T , e l =[e 1l e 2l ...he nl ] T According to the least squares method, we get The calculation formula is: λ j The value is obtained by the following formula: Similarly, a regression model is established for the upper bound of the response interval, and the calculation process is the same as that of equations (13) to (18), and we get: in: b PMu =[β 0u a 1u oh 1u …a Du oh Du ] T e u =[e 1u e 2u ...he nu ] T In summary, sample y i The prediction interval of The calculation formula is: Define the interval estimation error ε i as follows: Among them, k represents the kth cluster; then the interval linear clustering problem is to solve the minimization optimization problem shown in equation (23): First, the k-means algorithm is used to initialize clustering, and the central value of the interval sample is selected as the feature for clustering. The initial sample is divided according to the k-means clustering result; the elbow method is used to determine the number of clusters, and the SSE of different cluster numbers k is calculated. The cluster number where the SSE tends to be flat is taken as the optimal cluster number, thereby obtaining the optimal cluster number; After cluster initialization is completed, the following steps are repeated until the objective function reaches the global optimum: 1) Keep the division of the data set unchanged, and use the PM method to establish interval regression models for each cluster; set the window length to b, divide the data of each cluster into M / b sampling windows, perform interval regression on the data of each sampling window, and calculate the R of each sampling window. 2 ; Setting R 2 threshold, select all R 2 The data in the sampling window greater than the threshold are used for parameter estimation; based on the selected data, the interval regression parameters of each cluster are first calculated according to equations (14) and (17): and For all samples, the prediction interval of the i-th sample in the k-th cluster is calculated according to formula (19): 2) According to formula (23), calculate the regression error ε of the i-th sample belonging to the k-th cluster i(k) : Suppose the optimal clustering solution that minimizes the objective function J is P k , k=1,…,G, then P k Obtained through the following allocation criteria: The above two steps are repeated alternately until the clustering solution is consistent with the previous one, then the algorithm is considered to have converged and the clustering process is finished; Finally, the harmonic responsibility interval of the harmonic source is calculated based on the identified regression parameter interval.

2. A multi-harmonic source harmonic responsibility estimation system based on linear dynamic clustering, characterized in that: The method comprises a memory, a processor and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps as claimed in claim 1 can be implemented.

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