A data-driven voltage estimation method based on non-PMU distribution network

Abstract

The present invention relates to a data-driven voltage estimation method based on a non-PMU distribution network, comprising the following steps: Step 1: Considering the DistFlow power flow model, a mapping relationship between node injection power and voltage amplitude is established; Step 2: Using historical operating data of node injection power and voltage amplitude, a partial least squares algorithm is used to fit the power flow equation to obtain voltage sensitivity matrices R and X, thereby calculating the resistance and reactance of each branch of the distribution network; Step 3: Using a method of adding a constant term and iterative regression to enhance the model regression capability, thereby achieving data-driven distribution network voltage estimation. The present invention realizes distribution network power flow model parameter identification and accelerates calculation speed.

Description

Technical Field

[0001] The present invention belongs to the technical field of voltage estimation and relates to a data-driven voltage estimation method, in particular to a data-driven voltage estimation method based on a non-PMU power distribution network. Background Art

[0002] In recent years, the continuous integration of distributed energy resources (DERs), particularly photovoltaic systems and distributed energy storage systems, as well as flexible power loads such as electric vehicles, into distribution networks has brought about numerous changes in their operation. The physical form of distribution networks is undergoing rapid transformation. Simultaneously, with the widespread adoption of large-scale phasor measurement units (PMUs) and supervisory control and data acquisition (SCADA) systems, power system measurement data is sufficient for reconstructing system models. These methods, known as data-driven approaches, can improve the efficiency and accuracy of power system analysis. Therefore, when the complete distribution network model is unknown, it is necessary to study a data-driven voltage estimation method based on non-PMU distribution networks.

[0003] The uncertainty and volatility of distributed energy resources (DERs) present new challenges to traditional voltage estimation methods. Traditional model-based approaches approximate power flow models based on the physical characteristics of the power system, resulting in linearized models. However, these approaches impose a high computational burden. Furthermore, the frequent reconfiguration of distribution networks makes it difficult to accurately model system topology and parameters.

[0004] Today, more power system measurements are available, making data-driven methods more convenient and faster than traditional voltage estimation methods. Furthermore, the training data reflects the actual operating state of the power system, so the parameters of data-driven methods more accurately account for the operating state of the power system than model-based methods.

[0005] After searching, no public documents of the prior art that are identical or similar to the present invention were found. Summary of the Invention

[0006] The purpose of the present invention is to overcome the shortcomings of the existing technology and propose a data-driven voltage estimation method based on a non-PMU distribution network. The power flow equation is fitted based on the partial least squares (PLS) algorithm, and the method of adding a constant term and iterative regression is considered to enhance the model regression capability.

[0007] The present invention solves the practical problem by adopting the following technical solutions:

[0008] A data-driven voltage estimation method based on a non-PMU distribution network includes the following steps:

[0009] Step 1: Consider the DistFlow power flow model and establish the mapping relationship between node injection power and voltage amplitude;

[0010] Step 2: Using the historical operating data of node injection power and voltage amplitude, the power flow equation is fitted based on the partial least squares algorithm to obtain the voltage sensitivity matrices R and X, thereby calculating the resistance and reactance of each branch of the distribution network;

[0011] Step 3: The method of adding constant terms and iterative regression is used to enhance the regression capability of the model and realize data-driven distribution network voltage estimation.

[0012] Moreover, the physical quantities selected by the DistFlow power flow model in step 1 include node voltage amplitude, node output active and reactive power, and transmission line active and reactive network losses. The power flow relationship can be expressed as:

[0013] P i-1,i =P i +P i,i+1 +r i-1,i l i-1,i (1)

[0014] Q i-1,i =Q i +Q i,i+1 +x i-1,i l i-1,i (2)

[0015]

[0016]

[0017] In the formula, node i-1 is the adjacent upstream node of node i, and node i+1 is the adjacent downstream node of node i. i and Q i Represents the injected active power and reactive power of node i. When the node absorbs power from the distribution network, the injected power of the node is positive. For any branch L(i-1,i), r i-1,i and x i-1,i represents L(i-1,i) resistance and reactance, P i-1,i and Q i-1,i They represent the active power and reactive power flowing from node i-1 into L(i-1,i). i-1,i Represents the square of the current flowing through L(i-1,i). V i Represents the voltage amplitude at node i. Node 0 is the balancing node of the distribution network.

[0018] Ignoring the branch network loss, the DistFlow power flow model can be simplified as:

[0019]

[0020]

[0021]

[0022] β(i) represents the set of node i and its downstream nodes. Based on formulas (5)-(7), we have:

[0023]

[0024] Where, L i R represents the set of branches on the path from node 0 to node i. n represents the number of nodes in the distribution network excluding the balancing node. ij Represents the set L i ∩L j The sum of the resistances of all branches in the circuit. X ij Represents the set L i ∩L j The sum of the reactances of all branches within a circuit.

[0025] The matrix expression of formula (8) is:

[0026]

[0027]

[0028] Where R and X represent the voltage sensitivity matrix. Since the voltage of the balancing node in the distribution network is always equal to 1, in the present invention, V0 = [1,…,1] T n×1 .

[0029] Moreover, the specific steps of step 2 include:

[0030] (1) The goal of the PLS algorithm in the present invention is to perform regression between I and J. The expression of I and J is:

[0031]

[0032] Where t represents the number of groups in the training dataset.

[0033] (2) The PLS algorithm divides the model into an external model and an internal model;

[0034] The external model transforms the original data into the latent variable space to obtain mutually orthogonal score vectors; the internal model establishes a linear relationship between the score vectors;

[0035] The external model is:

[0036]

[0037] Where w1 and u1 are the score vectors of the first principal component of I and J respectively, f1 and g1 represent the load of the first principal component, and H1 and G1 are the residual matrices.

[0038] The internal model is:

[0039] u1=b1w1+h1 (13)

[0040] Where b1 represents the regression coefficient and h1 represents the minimization of modeling error.

[0041] After extracting the first principal component, the same method is used to extract the second principal component from the residuals. This process is repeated until all principal components are extracted. The number of principal components is determined through cross-validation. Next, based on the external and internal models, the relationship between I and J is established to obtain the voltage sensitivity matrices R and X, which are then used to calculate the resistance and reactance of each branch of the distribution network.

[0042] Moreover, the specific steps of step 3 include:

[0043] (1) Adding a constant term to formula (9), we can get:

[0044]

[0045] Where C is an n×1 dimensional constant term matrix.

[0046] Based on the above derivation, using historical operating data, and ignoring network losses, we perform parameter regression on formula (14) to obtain the voltage sensitivity matrices R and X, thereby calculating the resistance and reactance of each branch of the distribution network.

[0047] (2) Based on the branch impedance and formulas (4)-(6), the loss of each branch is calculated. When considering the network loss, formulas (5) and (6) can be expressed as:

[0048]

[0049]

[0050] (3) Substituting equations (15) and (16) for equations (5) and (6), and regressing the line impedance based on PLS again, more accurate resistance and reactance can be obtained.

[0051] (4) The distribution network control system can calculate the voltage sensitivity matrices R and X, and estimate the node voltage according to formula (14) and the node injection power.

[0052] Advantages and beneficial effects of the present invention:

[0053] 1. The present invention proposes a data-driven voltage estimation method based on a non-PMU distribution network. This method does not require phase angle measurement and is based only on historical measurement data, including voltage amplitude and node injection power, to achieve distribution network power flow model parameter identification and accelerate the calculation speed.

[0054] 2. The present invention proposes an algorithm based on partial least squares (PLS) to solve the collinearity problem of actual operation data and make it more accurate.

[0055] 3. This invention improves the accuracy of power flow model parameter identification by adding a constant term and iterative regression. For some independent variables that remain constant, the constant term absorbs their influence, enhancing the model's regression capabilities. Network losses are calculated based on the resistance and reactance obtained from the initial regression. A second regression yields even more accurate resistance and reactance values. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is a simplified radial power distribution network schematic diagram of the present invention;

[0057] Figure 2 The improved IEEE33 node topology diagram of the present invention;

[0058] Figure 3 A relative error curve diagram of branch resistance and branch reactance of the present invention;

[0059] Figure 4 2 is a graph showing the relative error of node voltages according to the present invention. DETAILED DESCRIPTION

[0060] The embodiments of the present invention are further described below in conjunction with the accompanying drawings:

[0061] A data-driven voltage estimation method based on a non-PMU distribution network includes the following steps:

[0062] Step 1: Consider the DistFlow power flow model and establish the mapping relationship between node injection power and voltage amplitude;

[0063] The present invention realizes voltage estimation of radial distribution network based on DistFlow model. In radial distribution network, the system power flow equation established in the form of branches may be more intuitive.

[0064] The physical quantities selected by the DistFlow power flow model in step 1 include node voltage amplitude, node output active and reactive power, and transmission line active and reactive network losses. Figure 1 shown.

[0065] The power flow relationship can be expressed as:

[0066] Pi-1,i =P i +P i,i+1 +r i-1,i l i-1,i (1)

[0067] Q i-1,i =Q i +Q i,i+1 +x i-1,i l i-1,i (2)

[0068]

[0069]

[0070] In the formula, node i-1 is the adjacent upstream node of node i, and node i+1 is the adjacent downstream node of node i. i and Q i Represents the injected active power and reactive power of node i. When the node absorbs power from the distribution network, the injected power of the node is positive. For any branch L(i-1,i), r i-1,i and x i-1,i represents L(i-1,i) resistance and reactance, P i-1,i and Q i-1,i They represent the active power and reactive power flowing from node i-1 into L(i-1,i). i-1,i Represents the square of the current flowing through L(i-1,i). V i Represents the voltage amplitude at node i. Node 0 is the balancing node of the distribution network.

[0071] Ignoring the branch network loss, the DistFlow power flow model can be simplified as:

[0072]

[0073]

[0074]

[0075] β(i) represents the set of node i and its downstream nodes. Based on formulas (5)-(7), we have:

[0076]

[0077] Where, L i R represents the set of branches on the path from node 0 to node i. n represents the number of nodes in the distribution network excluding the balancing node. ij Represents the set L i ∩L j The sum of the resistances of all branches in the circuit. X ijRepresents the set L i ∩L j The sum of the reactances of all branches within a circuit.

[0078] The matrix expression of formula (8) is:

[0079]

[0080]

[0081] Where R and X represent the voltage sensitivity matrix. Since the voltage of the balancing node in the distribution network is always equal to 1, in the present invention, V0 = [1,…,1] T n×1 .

[0082] Step 2: Using the historical operating data of node injection power and voltage amplitude, the partial least squares (PLS) algorithm is used to fit the power flow equation to obtain the voltage sensitivity matrices R and X, thereby calculating the resistance and reactance of each branch of the distribution network.

[0083] The specific steps of step 2 include:

[0084] In order to obtain R and X in formula (9), the present invention uses the historical operating data of the node injection power and voltage amplitude to fit the power flow equation based on the partial least squares algorithm.

[0085] The components and residual matrices of PLS ​​have many excellent properties, one of which is that the components are mutually orthogonal, which, to a certain extent, eliminates multiple linear correlations. The essence of the partial least squares regression algorithm is to decompose the independent variable data matrix according to the covariance maximization criterion while also decomposing the dependent variable data matrix. It also establishes the regression relationship equation between the corresponding explanatory latent variables and the response latent variables, fully embodying the basic idea of ​​partial least squares regression.

[0086] (1) The goal of the PLS algorithm in the present invention is to perform regression between I and J. The expression of I and J is:

[0087]

[0088] Where t represents the number of groups in the training dataset.

[0089] (2) The PLS algorithm divides the model into an external model and an internal model;

[0090] The external model transforms the original data into the latent variable space to obtain mutually orthogonal score vectors; the internal model establishes a linear relationship between the score vectors;

[0091] The external model is:

[0092]

[0093] Where w1 and u1 are the score vectors of the first principal component of I and J respectively, f1 and g1 represent the load of the first principal component, and H1 and G1 are the residual matrices.

[0094] The internal model is:

[0095] u1=b1w1+h1 (13)

[0096] Where b1 represents the regression coefficient and h1 represents the minimization of modeling error.

[0097] After extracting the first principal component, we use the same method to extract the second principal component from the residuals. This process is repeated until all principal components are extracted. The number of principal components is determined through cross-validation. Next, based on the external and internal models, the relationship between I and J is established to obtain the voltage sensitivity matrices R and X, which are then used to calculate the resistance and reactance of each branch of the distribution network.

[0098] Step 3: In order to improve the accuracy of power flow model parameter identification, the method of adding constant terms and iterative regression is adopted to enhance the model regression capability and realize data-driven distribution network voltage estimation.

[0099] In order to improve the accuracy of power flow model parameter identification, this paper proposes a voltage estimation method based on precision improvement. Formula (9) is improved by adding a constant term and iterative regression method to enhance the model regression capability. The specific description is as follows:

[0100] The specific steps of step 3 include:

[0101] During the distribution network parameter identification process, the values ​​of some independent variables may remain unchanged, resulting in the regression parameters of these independent variables not being regressed. The influence of these independent variables can be absorbed by using a constant term.

[0102] (1) Adding a constant term to formula (9), we can get:

[0103]

[0104] Where C is an n×1 dimensional constant term matrix.

[0105] Based on the above derivation, using historical operating data, and ignoring network losses, we perform parameter regression on formula (14) to obtain the voltage sensitivity matrices R and X, thereby calculating the resistance and reactance of each branch of the distribution network.

[0106] (2) Then, the loss of each branch is calculated based on the branch impedance and formulas (4)-(6). Taking into account the network loss, formulas (5) and (6) can be expressed as:

[0107]

[0108]

[0109] (3) Then, replace formulas (5) and (6) with formulas (15) and (16), and regress the line impedance based on PLS again to obtain more accurate resistance and reactance.

[0110] (4) In this way, the distribution network control system can calculate more accurate voltage sensitivity matrices R and X, and estimate the node voltage according to formula (14) and the node injection power.

[0111] The accuracy and effectiveness of the present invention are verified by using specific examples below:

[0112] 1. Example Settings

[0113] The example of this invention analyzes the improved IEEE33 node system. The network topology is as follows: Figure 2 As shown in Figure 2, three microgrids participate in voltage control, located at nodes 8, 26, and 28 of the system. Nodes 11 and 22 are equipped with biomass power generation devices. When the microgrid power is positive, it injects power into the distribution network; when the power is negative, it absorbs power from the distribution network.

[0114] 2. Simulation analysis

[0115] The case study uses Monte Carlo simulations based on operational measurement data from the distribution system. Parameters are regressed using a training dataset, and the accuracy of voltage estimation is tested using a newly generated test dataset. The training dataset size is 3000, and the training dataset size is 500. In the Monte Carlo simulation, load loss is calculated by multiplying a preset load loss by a coefficient randomly drawn from a uniform distribution. The active and reactive losses are in the intervals [0.8, 1.2] and [0.15, 0.25], respectively. The load fluctuation range is random. Based on the load consumption, the voltage fluctuation range is [0.97, 1.01]. Figure 3 is the calculation error of branch resistance and reactance. For any branch L(i-1,i), the branch number is i. Figure 3 As shown in Figure 2, the maximum error values ​​of resistance and reactance are -2.294% for branch L(4,5) and -0.077% for branch L(24,25), respectively. Based on the newly generated test data set, the voltage estimation error is as follows: Figure 4As shown in Figure 2, the relative error of each bus node voltage is within a reasonable range. Figure 3 and Figure 4 The shown errors demonstrate the effectiveness of the proposed data-driven voltage estimation method.

[0116] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can 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 can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0117] 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 produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. 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.

[0118] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work 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 The function specified in one or more boxes.

[0119] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

Claims

1. A data-driven voltage estimation method based on a non-PMU distribution network, characterized by: The following steps are involved: Step 1: Consider the DistFlow power flow model and establish a mapping relationship between node injection power and voltage amplitude; Step 2: Using the historical operating data of node injection power and voltage amplitude, the power flow equation is fitted based on the partial least squares algorithm to obtain the voltage sensitivity matrices R and X, thereby calculating the resistance and reactance of each branch of the distribution network; Step 3: Adding constant terms and iterative regression methods are used to enhance the model regression capability and realize data-driven distribution network voltage estimation; The physical quantities selected by the DistFlow power flow model in step 1 include node voltage amplitude, node output active and reactive power, and transmission line active and reactive network losses. The power flow relationship is expressed as follows: P i-1,i =P i +P i,i+1 +r i-1,i l i-1,i (1) Q i-1,i =Q i +Q i,i+1 +x i-1,i l i-1,i (2) In the formula, node i-1 is the adjacent upstream node of node i, and node i+1 is the adjacent downstream node of node i; P i and Q i Represents the injected active power and reactive power of node i. When the node absorbs power from the distribution network, the injected power of the node is positive. For any branch L(i-1,i), r i-1,i and x i-1,i represents L(i-1,i) resistance and reactance, P i-1,i and Q i-1,i They represent the active power and reactive power flowing from node i-1 into L(i-1,i); l i-1,i Represents the square of the current flowing through L(i-1,i); V i represents the voltage amplitude at node i; node 0 is the balancing node of the distribution network; Ignoring the branch network loss, the DistFlow power flow model is simplified to: β(i) represents the set of node i and its downstream nodes; based on formulas (5)-(7), we have: Where, L i represents the set of branches on the path from node 0 to node i; n represents the number of nodes in the distribution network excluding the balancing node; R ij Represents the set L i ∩L j The sum of the resistances of all branches in the circuit; X ij Represents the set L i ∩L j The sum of the reactances of all branches within the circuit; The matrix expression of formula (8) is: Where R and X represent the voltage sensitivity matrix. Since the voltage of the balancing node in the distribution network is always equal to 1, we have V0 = [1,…,1] T n×1 ; The specific steps of step 3 include: (1) Add a constant term to formula (9), and we get: Where C is an n×1 dimensional constant term matrix; Based on the above derivation, using historical operating data, and ignoring network losses, we perform parameter regression on formula (14) to obtain the voltage sensitivity matrix R and X, thereby calculating the resistance and reactance of each branch of the distribution network; (2) Based on the branch impedance and formulas (4)-(6), the loss of each branch is calculated. When considering the network loss, formulas (5) and (6) are expressed as: (3) Replace formulas (5) and (6) with formulas (15) and (16), and regress the line impedance based on the partial least squares algorithm again to obtain more accurate resistance and reactance; (4) The distribution network control system calculates the voltage sensitivity matrices R and X, and estimates the node voltage according to formula (14) and the node injection power.

2. The data-driven voltage estimation method based on a non-PMU distribution network according to claim 1, characterized in that: The specific steps of step 2 include: (1) The goal of the partial least squares algorithm is to perform regression between I and J; I and J are expressed as: Where t represents the number of groups in the training data set; (2) The partial least squares algorithm divides the model into an external model and an internal model; The external model transforms the original data into the latent variable space to obtain mutually orthogonal score vectors; the internal model establishes a linear relationship between the score vectors; The external model is: Where w1 and u1 are the score vectors of the first principal component of I and J respectively, f1 and g1 represent the load of the first principal component, H1 and G1 are the residual matrices; The internal model is: u1=b1w1+h1 (13) Where b1 represents the regression coefficient; h1 represents the minimization of modeling error; After extracting the first principal component, the second principal component is extracted from the residual using the same method; this process is repeated until all principal components are extracted; the number of principal components is obtained through cross-validation; then, based on the external model and the internal model, the relationship between I and J is established to obtain the voltage sensitivity matrices R and X, thereby calculating the resistance and reactance of each branch of the distribution network.

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