A model-data hybrid driving based security boundary fitting method
By employing a model-data hybrid approach, combining DC power flow models and linear regression theory, the thermal stability safety domain boundary of the power system is fitted, solving the problems of low computational efficiency and large errors, and achieving high-precision safety boundary construction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA SOUTHERN POWER GRID COMPANY
- Filing Date
- 2022-10-28
- Publication Date
- 2026-04-14
AI Technical Summary
Existing technologies face problems of low computational efficiency and large errors when constructing the thermal stability security domain of power systems. This is especially true in large-scale complex systems, where DC power flow models have large errors and AC power flow calculations are burdensome.
A model-data hybrid approach is adopted to construct the initial safety boundary through a DC power flow model, and to fit the error model using linear regression theory. Combined with a data-driven linearized error expression, the accuracy of the boundary is improved.
It improves the accuracy of thermal stability safety boundaries, reduces the computation time of nonlinear models, and retains the physical meaning of safety boundaries, making it suitable for large-scale systems.
Smart Images
Figure CN115758635B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power system security domain technology, and in particular to a model-data hybrid-driven security boundary fitting method. Background Technology
[0002] In the online safety monitoring, assessment, and control of power systems, the safety domain in the injected power space where the thermal stability constraints of all transmission lines are satisfied is the most fundamental type of safety domain, hereinafter referred to as the thermal stability safety domain. With the rapid growth of electricity load and the market-based operation of electricity, the operation of the power grid is increasingly approaching its stability limit, which makes the thermal stability safety domain of great significance in analyzing the transmission limits of the system.
[0003] With the increasing maturity of wide-area measurement systems and the continuous development of big data theory, a large amount of power system data can be used to assess the transmission security of power systems. However, with the continuous increase in the scale and complexity of power systems, the power industry faces new challenges. The continuous updates of smart grids have accumulated a large amount of dispatching and operation data for dispatch centers at all levels. This accumulated historical data will help to extract important information. However, the construction of the thermal stability security domain depends on power flow calculation, and the nonlinearity of the power flow equations reduces the efficiency of the calculation. Therefore, it is urgent to use linear power flow technology to assist in the fitting and construction of the security boundary. However, mainstream research mostly uses DC power flow models with high linearity and large errors, while using point-by-point search methods based on AC power flow will bring computational burden. Using data-driven technology can effectively solve the problem that DC power flow models cannot cope with complex large systems. Summary of the Invention
[0004] To address the shortcomings of existing technologies, this invention primarily studies the boundary fitting problem of static security regions, providing an error expression for the security boundary. Based on linear regression theory, a linearized error model can be obtained through a data-driven method using partial least squares regression, which can then be used to correct the model-driven security boundary, enhancing its adaptability to large-scale systems.
[0005] The core content of this invention can be summarized as follows:
[0006] (1) A model-data hybrid-driven safety boundary fitting method is proposed. This method first uses a model-driven approach to construct the thermal stability safety domain boundary using a DC power flow model, which can preserve the physical meaning of the safety boundary.
[0007] (2) Based on model-driven, we can make full use of data-driven methods to obtain boundary error models. By superimposing model-driven safety boundaries and data-driven linear error expressions, we can fully preserve the useful physical meaning of safety boundaries and fully consider the error models hidden in the data, thereby improving the accuracy of the boundaries.
[0008] The model-data hybrid-driven safety boundary fitting method can be divided into the following parts:
[0009] (1) Construct a thermally stable security domain model under a given topology, define the thermally stable security domain in the active power injection space of nodes, give the mapping relationship between the security boundary and the active power of nodes, and obtain a model-driven security boundary model.
[0010] (2) The dataset acquired by the measurement equipment is processed, and an error dataset is constructed based on the model-driven safety boundary model. Then, the linear regression theory is used to linearize the error. The linearized error model is added to the safety boundary model, and finally the model-data hybrid-driven linearized expression of the safety boundary is obtained.
[0011] To address the problems existing in the prior art, the present invention adopts the following technical solution:
[0012] A model-data-driven method for fitting safety boundaries includes the following steps:
[0013] Step 1: Obtain the topology and parameters of the specified power system, as well as the upper and lower limits of the active power output of the system nodes, and the thermal stability security domain model under the topology; that is:
[0014]
[0015] Where: P ij Let i represent the power of branch l, with the first node being i and the last node being j. S is the maximum power constraint value for branch l. B Let f(x) = P be the set of branches, and let f(x) = P be other constraints that this set must satisfy.
[0016] Step 2: Establish a first data-driven model with a mapping relationship between the safety boundary and node active power using the nodal active power injection thermal stability safety domain space method.
[0017] Step 3: Establish the safety boundary region of the first data-driven model by using the affine transformation between the power flow transmission limit in the DC power flow model and the nodal active power injection space of the first data-driven model;
[0018] Step 4: Process the dataset acquired by the measurement device through the first data-driven model safety boundary domain to construct an error dataset;
[0019] Step 5: Establish the safety boundary region of the second data-driven model by linearly fitting the error dataset using the least squares regression method.
[0020] Furthermore, in step 3, the process of establishing the security boundary domain of the first data-driven model is as follows:
[0021] 301. The first data-driven model obtains the node-branch power flow sensitivity by solving the security domain coefficient, where: for the absolute value P of the active power flow of branch l (node i-node j) in the transmission system. L,ij Performing a Taylor expansion at node k yields the following results:
[0022]
[0023] Wherein: a power transmission system branch l includes node i to node j; The power value at the expansion point. O(ΔP) is the first derivative of the Taylor expansion. k ) represents the higher-order derivative, and k represents different nodes; the node-branch power flow constraint can be expressed as:
[0024]
[0025] 302. The first data-driven model obtains the power flow sensitivity S of node k to branch l using the following formula. l,k ;
[0026]
[0027] Wherein: S l,k This is the sensitivity coefficient. For P ij For θ i The partial derivative, For θ i For P k The partial derivative of x ij Let be the impedance value of branch l.
[0028] 303. The security domain of the first data-driven model is obtained by the following formula:
[0029]
[0030] Where: α l,k S is the hyperplane coefficient of the thermally stable safety region. l,k This is the sensitivity coefficient. This represents the maximum power constraint value for branch l.
[0031] Furthermore, in step 5, the process of establishing the security boundary domain of the second data-driven model is as follows:
[0032] 501. Establish the error dataset using the following formula:
[0033]
[0034] Where: Δy is the error value of the power flow equation. Input the actual measured value of the node power. This represents the actual measured value of the branch power flow;
[0035] 502. Obtain the error equation by calculating the error dataset using the partial least squares linear regression method:
[0036] Δy=A*P+B
[0037] Where: A is the coefficient matrix, P is the node input power matrix, and B is the constant matrix.
[0038] Wherein: the error equation is expressed in matrix form, A and B are adaptive matrices, and P is the power injection vector. Therefore, the matrix expression of the power flow equation can be obtained as follows:
[0039] P L,ij =C*P+D
[0040] The error equation is obtained by the following formula: The second data-driven linear power flow model is:
[0041]
[0042] in: For branch power flow, A and C are the coefficient matrices of the physical driving model and the data driving model, respectively, and B and D are the constant matrices of the physical driving model and the data driving model, respectively.
[0043] The second data-driven model generates its security boundary using the following formula:
[0044]
[0045] in, D = 0; σ is the standard deviation, ∈ is the mean, and PLS is the regression coefficient matrix;
[0046] The safety boundary of the second data-driven model is output through the following linear power flow equation:
[0047]
[0048] Beneficial effects
[0049] Compared with the prior art, the beneficial effects of the present invention are:
[0050] The thermal stability safety domain boundary model is derived by using a linear power flow model, reducing the time required for point-by-point solutions based on nonlinear models. This also effectively preserves the physical meaning of the safety boundary, providing a reference for subsequent data-driven processes. To improve the accuracy of the linearized safety boundary, a data-driven linear fitting technique is employed, using partial least squares regression to linearly fit the errors in the dataset, ultimately yielding a more accurate safety boundary. Attached Figure Description
[0051] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.
[0052] Figure 1 The flowchart of the static security domain boundary fitting method provided by the present invention is shown below.
[0053] Figure 2 The fitting results of the safety boundary provided by this invention show that errors occur in the boundary fitting due to the omission of higher-order terms during Taylor expansion, and the results are highly dependent on the selection of initial values, leading to significant errors. A model-data hybrid-driven model can effectively fit these errors, avoiding excessive errors caused by ignoring higher-order terms or improper initial value selection. The results demonstrate that the hybrid-driven approach is effective and can significantly improve the accuracy of the thermally stable safety boundary. Detailed Implementation
[0054] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.
[0055] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0056] As introduced in the background section, existing DC power flow models cannot meet the needs of stability analysis when the power grid operation is approaching the stability limit, and their neglect of nonlinear parts in the model also greatly reduces the accuracy of the model. In order to solve the above technical problems, this application proposes a safety boundary fitting method based on model-data hybrid driving. Combining the advantages of model-driven and data-driven methods, it not only retains the physical meaning of the safety boundary, but also fully fits the linear model of the error, thereby improving the accuracy while still ensuring linear expression.
[0057] like Figure 1-2 As shown, this invention provides a model-data driven safety boundary fitting method. This method acquires a large amount of power grid operation data, uses a DC power flow model to obtain an error sample set, and then employs linear regression to perform regression analysis on the error samples to obtain a linear error model, thereby improving the accuracy of the model-based safety boundary. Specifically, it includes the following steps:
[0058] Step 1: Obtain the topology and parameters of the specified power system, as well as the upper and lower limits of the active power output of the system nodes, and the thermal stability security domain model under the topology; that is:
[0059]
[0060] Where: P ij Let i represent the power of branch l, with the first node being i and the last node being j. S is the maximum power constraint value for branch l. B Let f(x) = P be the set of branches, and let f(x) = P be other constraints that this set must satisfy.
[0061] Step 2: Establish a first data-driven model with a mapping relationship between the safety boundary and node active power using the nodal active power injection thermal stability safety domain space method.
[0062] Step 3: Establish the safety boundary region of the first data-driven model by using the affine transformation between the power flow transmission limit in the DC power flow model and the nodal active power injection space of the first data-driven model;
[0063] Step 4: Process the dataset acquired by the measurement device through the first data-driven model safety boundary domain to construct an error dataset;
[0064] Step 5: Establish the safety boundary region of the second data-driven model by linearly fitting the error dataset using the least squares regression method.
[0065] The process of establishing the security boundary domain of the first data-driven model:
[0066] 301. The first data-driven model obtains the node-branch power flow sensitivity by solving the security domain coefficient, where: for the absolute value P of the active power flow of branch l (node i-node j) in the transmission system. L,ij Performing a Taylor expansion at node k yields the following results:
[0067]
[0068] Wherein: a power transmission system branch l includes node i to node j; The power value at the expansion point. O(ΔP) is the first derivative of the Taylor expansion. k ) represents the higher-order derivative, and k represents different nodes; the node-branch power flow constraint can be expressed as:
[0069]
[0070] 302. The first data-driven model obtains the power flow sensitivity S of node k to branch l using the following formula. l,k ;
[0071]
[0072] Wherein: S l,k This is the sensitivity coefficient. For P ij For θ i The partial derivative, For θ i For P k The partial derivative of x ij Let be the impedance value of branch l.
[0073] 303. The security domain of the first data-driven model is obtained by the following formula:
[0074]
[0075] Where: α l,k S is the hyperplane coefficient of the thermally stable safety region. l,k This is the sensitivity coefficient. This represents the maximum power constraint value for branch l. The second data-driven model's safety boundary domain establishment process is as follows:
[0076] 501. Establish the error dataset using the following formula:
[0077]
[0078] Where: Δy is the error value of the power flow equation. Input the actual measured value of the node power. This represents the actual measured value of the branch power flow;
[0079] 502. Obtain the error equation by calculating the error dataset using the partial least squares linear regression method:
[0080] Δy=A*P+B
[0081] Where: A is the coefficient matrix, P is the node input power matrix, and B is the constant matrix;
[0082] The error equation is expressed in matrix form, where A and B are adaptive matrices, and P is the power injection vector. The matrix expression of the power flow equation is as follows:
[0083] P L,ij =C*P+D
[0084] The error equation is obtained by the following formula: The second data-driven linear power flow model is:
[0085]
[0086] in: For branch power flow, A and C are the coefficient matrices of the physical driving model and the data driving model, respectively, and B and D are the constant matrices of the physical driving model and the data driving model, respectively.
[0087] The second data-driven model generates its security boundary region using the following formula:
[0088]
[0089] in, D = 0; σ is the standard deviation, ∈ is the mean, and PLS is the regression coefficient matrix;
[0090] The second data-driven model's safety boundary domain is output through the following linear power flow equations:
[0091]
[0092] To better explain the mechanism of the boundary method proposed in this invention, the following sections describe two aspects: the boundary fitting of the first driving model safety boundary domain based on DC power flow and the error fitting of the first data-driven safety domain.
[0093] 1. Boundary Fitting Based on DC Power Flow
[0094] For any branch l in the system, its thermal stability constraint can be expressed as follows:
[0095]
[0096] Replacing the branch current in the above formula with the branch power flow yields the thermal stability safety constraint described by the branch power flow:
[0097]
[0098] Considering that reactive power in a transmission network is generally balanced locally, and the reactive power transmitted on branches is much smaller than the active power, the impact of reactive power on branches can be ignored. Therefore, a thermal stability security constraint inequality describing the active power flow of branches can be established, as shown in the following equation. Generally,
[0099]
[0100] Power system thermal stability safety domain Ω THSR Defined in the node-injected power space, it is the set of all operating points (complex power injections) that satisfy the system's thermal stability safety constraints. The thermal stability safety domain is determined by the system's network topology and does not change with the operating points; for ease of description, it can be abbreviated as Ω. THSR (h), where h represents a certain predetermined network topology.
[0101]
[0102] For high-voltage transmission systems, the following assumptions hold:
[0103] (1) The resistance of a transmission line is much smaller than its reactance, i.e., G ij ≈0.
[0104] (2) Under steady-state operation, the branch angle of the line is very small, therefore, sinθ ij ≈θ ij cosθ ij ≈1.
[0105] (3) Under steady-state operation, the voltage amplitude of the node is approximately maintained at 1.0 pu.
[0106] (4) Ignoring the impact of transformers and grounding branches on active power distribution, for nodes without grounding branches, the sum of elements in their row and column is zero. Therefore, we have...
[0107] Under the above assumptions, the active power flow equations of the power system can be simplified to the following equation:
[0108]
[0109] By rearranging, the above equation can be transformed into the matrix shown below.
[0110] P=Bθ (6)
[0111] Correspondingly, the active power flow of branch l can be calculated by the following formula:
[0112]
[0113] The solution for the safety domain coefficient depends on the node-branch power flow sensitivity. For the absolute value of the active power flow P of branch l (node i - node j) in the transmission system... L,ij Performing a Taylor expansion at node k yields the following results:
[0114]
[0115] Ignoring the influence of higher-order terms (second order and above), the branch power flow constraint can be expressed as:
[0116]
[0117] Furthermore, this invention reveals an approximate relationship between branch power flow and node power, and the power flow sensitivity S of node k to branch l. l,k This provides the basis for solving the hyperplane coefficients of the safety region boundary, and the specific solution is as follows:
[0118]
[0119] The hyperplane coefficients of the thermally stable safe region can be obtained as follows:
[0120]
[0121] For actual large power grid operation and dispatching, the impact of changes in active power injection at the balancing node on the active power flow of branches must be taken into account; therefore, a sharing factor is introduced:
[0122]
[0123] The quasi-steady-state active power sensitivity considering the equilibrium node is obtained as follows:
[0124]
[0125] As can be seen from the above derivation process and results, when the influence of reactive power and node voltage is ignored, the sensitivity of branch active power flow to node active power injection is a constant determined by the network structure parameters and is independent of the specific node injection.
[0126] 2. Data-driven error fitting
[0127] However, when performing Taylor expansion of equation (9), the effects of the second and higher-order terms are ignored, and the accuracy of the expansion is only high at the expansion point. To solve this problem, a data-driven method is needed to fit the error boundary.
[0128] Let the samples in the dataset be... Using Equation (8) to construct error samples as follows:
[0129]
[0130] In partial least squares linear regression, the error equation can be obtained through regression techniques:
[0131] Δy=A*P+B (15)
[0132] For ease of representation, we use matrix form, where A and B are adaptive matrices, and P is the power injection vector. Therefore, the matrix expression of the power flow equations can be obtained as follows:
[0133] P L,ij =C*P+D (16)
[0134] Therefore, the linear power flow model is:
[0135]
[0136] Furthermore, the new security boundary is:
[0137]
[0138] in, D = 0. σ is the standard deviation, ∈ is the mean, and PLS is the regression coefficient matrix.
[0139] The final model-data jointly driven linear power flow equations are as follows:
[0140]
[0141] The accuracy of the linearization model of the error determines the accuracy of the linearization model driven by data-physical fusion.
Claims
1. A model-data driven method for fitting safety boundaries, characterized in that: Includes the following steps: Step 1: Obtain the topology and parameters of the specified power system, as well as the upper and lower limits of the active power output of the system nodes, and the thermal stability security domain model under the topology; that is: in: Indicates a branch l The power of the first node is i The last node is j , branch road l Maximum power constraint value, For branch road collection, f ( x )= P Other constraints that this set must satisfy; Step 2 uses the nodal active power injection thermal stability safety domain space method to establish a first data-driven model with a mapping relationship between safety boundaries and nodal active power; Step 3: Establish the safety boundary region of the first data-driven model by utilizing the affine transformation between the power flow transmission limit in the DC power flow model and the nodal active power injection space of the first data-driven model; the process of establishing the safety boundary region of the first data-driven model is as follows: Step 301: The first data-driven model obtains the node-branch power flow sensitivity by solving the security domain coefficients, where: for transmission system branches... l in node i to node j The absolute value of the meritorious tidal current At the node k Performing a Taylor expansion at that point, we can obtain... Among them: power transmission system branches l Including nodes i -node j； The power value at the expansion point. The first derivative of the Taylor expansion, For higher-order derivatives, k Different nodes are represented; the node-branch power flow constraint can be expressed as: Step 302: The first data-driven model obtains nodes using the following formula. k For branch roads l Current sensitivity ; in: This is the sensitivity coefficient. for right The partial derivative, for right The partial derivative, branch road l The impedance value; Step 303: The first data-driven model obtains its security domain using the following formula: in: For the thermal stability safety region hyperplane coefficient, This is the sensitivity coefficient. This represents the maximum power constraint value for branch l; Step 4: Process the dataset acquired by the measurement device through the first data-driven model safety boundary domain to construct an error dataset; Step 5: Establish the safe boundary region of the second data-driven model by linearly fitting the error dataset using the least squares regression method, wherein: the process of establishing the safe boundary region of the second data-driven model is as follows: Step 501 establishes the error dataset using the following formula: in: This represents the error value of the power flow equation. Input the actual measured value of the node power. This represents the actual measured value of the branch power flow; Step 502: Calculate the error equation using the partial least squares linear regression method to obtain the error dataset. Where: A is the coefficient matrix, P is the node input power matrix, and B is the constant matrix; The error equation is expressed in matrix form, where A and B are adaptive matrices, and P is the power injection vector. Therefore, the matrix expression of the power flow equation can be obtained as follows: The error equation is obtained by the following formula: The second data-driven linear power flow model is: in: For branch power flow, A and C are the coefficient matrices of the physical driving model and the data driving model, respectively, and B and D are the constant matrices of the physical driving model and the data driving model, respectively. The second data-driven model generates its security boundary using the following formula: in, , , D=0; Standard deviation The mean, This is the regression coefficient matrix; The safety boundary of the second data-driven model is output through the following linear power flow equation: 。