Power transmission line parameter estimation method and device based on robust variable projection framework

Abstract

The invention provides a power transmission line parameter estimation method and equipment based on a robust variable projection framework. The method comprises the following steps: establishing a nonlinear measurement equation for power transmission line parameter estimation; a joint estimation model used for estimating the state and parameters of the power transmission line is constructed based on the nonlinear measurement equation, a target function of the joint estimation model is that the weighted sum of a measurement residual error and a parameter prior item is minimum, and the weight of the measurement residual error is obtained through calculation by adopting a Huber loss function according to the measurement residual error during last iteration; linearly increasing along with the measurement residual error; and solving the joint estimation model, converting the joint estimation model into a state estimation sub-problem and a parameter estimation sub-problem by adopting a robust variable projection framework during solving, and carrying out iterative solving until convergence to obtain estimated power transmission line parameters. The method is high in calculation efficiency and high in robustness.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power online parameter identification, in particular to a power transmission line parameter estimation method and device based on a robust variable projection framework. BACKGROUND

[0002] Modern power systems, as a national key energy infrastructure, highly depend on the accuracy of power grid models for safe, stable and economic operation. As the physical basis of power grid models, transmission line parameters directly affect the accuracy of core applications such as state estimation, power flow calculation, fault analysis and relay protection. However, in actual operation, transmission line parameters are not constant. Line aging, temperature changes, environmental corrosion and other factors can cause them to deviate from the rated value, thereby affecting the accuracy of power grid analysis.

[0003] To address the above problems, online parameter identification using widely deployed measurement devices (such as SCADA, PMU, AMI, etc.) in the power grid has become a key technology to improve the accuracy of power grid models. However, actual measurement data often contains random noise, systematic bias and abnormal bad data, which seriously affects the reliability of parameter estimation. Traditional weighted least squares and other methods perform well under Gaussian noise assumption, but when non-Gaussian noise or outliers exist, their estimation results are easily disturbed and deviate significantly.

[0004] In addition, transmission line parameters are highly coupled with system operating states in the physical model, making the parameter identification problem essentially a high-dimensional, nonlinear, non-convex joint estimation problem. Traditional methods have high computational complexity when dealing with multiple time periods and multiple types of measurements, and are sensitive to bad data, making it difficult to be widely applied in practical engineering.

[0005] Therefore, it is urgent to develop a transmission line parameter estimation method with robustness, computational efficiency and engineering practicability to cope with the challenges of parameter identification in complex measurement environments and improve the accuracy and reliability of power system analysis. SUMMARY

[0006] In view of the problems existing in the prior art, the purpose of the present application is to provide a transmission line parameter estimation method and device based on a robust variable projection framework, which has robustness and computational efficiency.

[0007] In order to achieve the above-mentioned application purpose, the present application provides the following technical scheme:

[0008] A transmission line parameter estimation method based on a robust variable projection framework, comprising:

[0009] (1) establishing a nonlinear measurement equation for transmission line parameter estimation, the nonlinear measurement equation including line power measurement, node voltage amplitude and phase angle measurement, and nonlinear measurement equation of measurement residual;

[0010] (2) Construct a joint estimation model for estimating the state and parameters of the power transmission line based on the nonlinear measurement equation, and a target function of the joint estimation model is a weighted sum of measurement residuals and parameter prior terms, and the weight of the measurement residual is calculated according to the measurement residual of the last iteration using the Huber loss function, and increases linearly with the measurement residual;

[0011] (3) Solve the joint estimation model, and when solving, convert the joint estimation model into a state estimation sub-problem and a parameter estimation sub-problem using a robust variable projection framework, and iteratively solve until convergence, to obtain the estimated power transmission line parameters.

[0012] A computer program product comprising a computer program, which, when executed by a processor, implements the above method.

[0013] A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the above method.

[0014] A computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the above method.

[0015] Compared with the prior art, the present application has the beneficial effects that: by introducing the Huber loss calculation function to obtain the weight and the iterative reweighting mechanism, the influence of abnormal values in the measurement data can be effectively suppressed, and stronger robustness is achieved; at the same time, the original high-dimensional and strongly coupled non-convex joint estimation problem is decomposed into two sub-problems of parameters and states for alternative solving by using the variable projection framework, the computational complexity is significantly reduced, and the calculation efficiency is improved. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is a flowchart of the power transmission line parameter estimation method based on the robust variable projection framework provided by the embodiments of the present application;

[0017] Figure 2 is a positive sequence π-type equivalent circuit model provided by the embodiments of the present application;

[0018] Figure 3 is a solution method of the joint estimation model provided by the embodiments of the present application;

[0019] Figure 4 is a line-by-line relative error distribution of the embodiments of the present application;

[0020] Figure 5 is an absolute error distribution of the embodiments of the present application;

[0021] Figure 6 This is the distribution of the relative errors of each parameter in the three algorithms of this invention under data pollution.

[0022] Figure 7 This is a structural diagram of the computer device provided in an embodiment of the present invention. Detailed Implementation

[0023] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0024] Example 1

[0025] This invention provides a method for estimating transmission line parameters based on a robust variable projection framework, such as... Figure 1 As shown, it includes the following steps:

[0026] (1) Establish nonlinear measurement equations for estimating transmission line parameters.

[0027] The nonlinear measurement equation in this embodiment is based on the transmission line. The equivalent circuit is used to establish a nonlinear measurement equation that includes line power measurement, node voltage amplitude and phase angle measurement, and measurement residuals. The parameters and states to be estimated are defined in the equation.

[0028] In power system steady-state analysis, transmission lines typically employ methods such as... Figure 2 The diagram shows the positive-sequence π-type equivalent circuit model. This model represents a circuit. It has series impedance And two parallel admittances to ground, each with a magnitude of .in, and These represent the series resistance and series reactance of the circuit, respectively. and These represent parallel conductance to ground and parallel susceptance to ground, respectively.

[0029] The parameters formed by the transmission line to be estimated are defined as follows: Typically, series impedance is converted to series admittance. The specific relationship between impedance and admittance is as follows:

[0030]

[0031] therefore, and They are respectively:

[0032]

[0033] Define state the set of voltage magnitudes and phase angles of all nodes in the network at multiple time periods i.e.

[0034]

[0035] The values of state variables are not all measurable in general. Therefore, they are treated as latent variables whose values are determined simultaneously with line parameters in the estimation process.

[0036] For any line connecting nodes and , its type equivalent model node admittance matrix is

[0037]

[0038] where denotes the series admittance of branch , and denotes the shunt admittance of half-branch. The diagonal element is the sum of branch admittances of all branches connected to node , while the off-diagonal element is the negative of the sum of branch admittances of all branches connecting nodes and .

[0039] The full measurement function is given in (5), and the full measurement function defines the mapping from state space to measurement space, where and denote the active and reactive power transmitted by the line, respectively, denotes the set of transmission lines, denotes the set of nodes.

[0040]

[0041] The calculation of the residual error is given in (6), where a selection matrix is introduced to the full measurement function. The purpose of introducing this matrix is to select only the measurement components that are actually available at time from the "full" measurement function that contains all possible measurements, to construct the residual error . If a measurement is not available at time , it is not included in the selection matrix ​The corresponding row will be all zeros, thus ensuring that the unobserved variable does not have any impact on the objective function. In the formula, represents the actual available measurement vector at time represents the measurement error / noise term at time

[0042]

[0043] For convenience, let

[0044]

[0045] In the formula, represents the amplitude of the node voltage, represents the phase angle of the node and the phase angle difference of the node and the node

[0046] For branch , the complex power flowing from node to node is

[0047]

[0048] where the branch current is determined by the line parameters and the voltages at both ends:

[0049]

[0050] Substituting equation (9) into equation (8) and separating the real and imaginary parts, we obtain the active power and the reactive power of the branch power flow:

[0051]

[0052] The measurement equipment installed at both ends of the transmission line can directly provide high-precision node voltage amplitude and phase angle information. This type of measurement has a direct linear relationship with the state variables:

[0053]

[0054] In the formula, and represent the phase angle and voltage amplitude of the directly measured voltage, respectively.

[0055] (2) Construct a joint estimation model for estimating the state and parameters of the power transmission line based on the nonlinear measurement equation.

[0056] In this embodiment, the objective function of the joint estimation model is the weighted sum of the measurement residuals and the prior term of the parameters, the weight of the measurement residual is calculated by Huber loss function according to the measurement residual of the last iteration, and increases linearly with the measurement residual.

[0057] Specifically, Huber M estimation theory is introduced, and a target function based on Huber loss is designed to suppress the influence of abnormal measurement data on the estimation result; and the iterative reweighted least squares algorithm can be used to dynamically adjust the measurement residual weight in the later calculation.

[0058] The traditional weighted least squares (WLS) assumes that the measurement residual is from a Gaussian distribution, and its objective function depends on the L2 norm of the residual square. However, when the bad data deviates from the Gaussian distribution, its large residual square may affect the estimation result, causing the estimated value to deviate from the true value. To overcome this limitation, this paper applies M estimation theory and introduces Huber loss function into the objective function.

[0059] Huber loss function is a hybrid method that uses different penalty strategies for small and large residuals:

[0060]

[0061]

[0062] where, is the normalized residual normalized by the standard deviation, is the original residual of the th measurement, is a tunable threshold parameter. When the normalized residual is small (less than the threshold ), the Huber function is equivalent to the L2 norm (square loss), which retains the statistical effectiveness of WLS under Gaussian noise; when is large, the function changes to the L1 norm (absolute value loss), and its linearly increasing penalty avoids the excessive influence of outliers on the objective function.

[0063] Minimizing the objective function based on Huber function is an M estimation problem. By solving the first-order optimality condition, the iterative reweighted least squares (IRLS) algorithm can be derived. In this embodiment, in each iteration, the weight of node i at time t in the kth iteration can be calculated based on the previous iteration by formulas (14) and (15)​ :

[0064]

[0065]

[0066] where, is the normalized residual error, is the measurement residual error of node i at time t in the k-1th iteration. According to equation (15), for the suspicious measurements with larger residual errors, their corresponding weights will be reduced, thus reducing their impact on the results of the subsequent iterations in the next iteration. This process continues until the weights or the estimates converge, and the weights of all nodes can form a weight matrix:

[0067]

[0068] where "blk" means assembling the matrix in a diagonal block form, and "blkdiag" means assembling the matrices of each time period along the diagonal to form a block diagonal matrix.

[0069] Therefore, the joint estimation model is:

[0070]

[0071] The objective function in equation (17) is a comprehensive optimization model that combines robustness, prior information, and engineering constraints: the first term of the objective function is the robust weighted least squares (WLS) term, which covers all time points and available measurements. The second and third terms are the prior terms of the parameters, which incorporate prior knowledge or act as regularization to prevent overfitting. These inequality constraints in equation (17) consider various engineering requirements that must be met. is the measurement residual weight matrix of time t, is the transpose, , are the coefficients of the voltage phase angle and the voltage amplitude prior terms, respectively, , are the upper and lower bounds of the line resistance reactance ratio constraint, respectively, to avoid unreasonable impedance characteristics, , are the element-wise upper and lower bounds of the parameter vector, representing the feasible region of the prior range, is the matrix formed by the parameters of all transmission lines, represents the reference node, L represents the weighted graph Laplacian matrix of the power grid topology, and is used for voltage phase angle priori.

[0072] (3) Solving the joint estimation model.

[0073] A, problem decoupling.

[0074] It is very difficult to directly solve such a large-scale optimization problem involving joint parameters and multi-period states as in equation (17). However, this problem has a special separable structure. If the state variable is fixed, the optimization problem about the parameter becomes a partially linear problem. Conversely, if the parameter is fixed, the original problem can be decomposed into independent nonlinear optimization problems. Each problem only involves the state . Therefore, the present application uses the variable projection framework to decompose the original high-dimensional, strongly coupled, non-convex joint estimation problem into two sub-problems of parameter estimation and state estimation; by fixing one set of variables to solve the other set of variables, the problem is decoupled.

[0075] First, all time periods are combined together:

[0076]

[0077] According to equation (18), the residual and state of each time period are vertically spliced into a long vector by column stacking or block diagonal stacking for all time periods. represents the matrix assembled along the diagonal of all time points to form a block diagonal matrix. "col" represents the vertical stacking of vectors of each time period into a continuous vector or matrix. represents the residual matrix of all time periods, , represents the state change matrix and the state change at time t, , represents the state Jacobian matrix and the parameter Jacobian matrix obtained by calculating the partial derivatives of the measurement residual with respect to the state and the parameter, , represents the state Jacobian matrix and the parameter Jacobian matrix, , represents the corresponding component at time t, represents the weight matrix of all time periods.

[0078] First-order linearization of the residual gives:

[0079]

[0080] Linearize all time intervals and sum them up to get:

[0081]

[0082]

[0083] in, It represents the change in state.

[0084] The variable projection algorithm utilizes this separable structure to solve problems. Its main idea is to divide the optimization variables into two groups and then solve them through an alternating iterative process. These two groups of variables are defined as parameters. and state The variable projection algorithm is implemented in the form of a two-step alternating optimization iteration, which decomposes a large-scale joint optimization problem into two smaller subproblems.

[0085] In the first step of the k-th iteration of the variable projection algorithm, all states at each time snapshot. All are fixed at the current best estimate of the state. Up. Then, regarding the parameters... Solve the optimization problem. Since the state is fixed, the measurement function... The state in the measurement function becomes constant. This is achieved by considering the measurement function with respect to... By performing a first-order Taylor expansion, the original nonlinear problem is approximated as a large-scale linear least squares problem.

[0086]

[0087] The solution to this problem can be obtained by solving the normal equations of a large-scale linear least squares problem. This indicates the amount of parameter change. For each time interval, all time intervals are integrated. From the information, we obtain the residual. , express coefficient,, This represents the linearization constant. (Each time period) about The residual is

[0088]

[0089] In the In the next iteration, the residual is... Perform a first-order Taylor expansion, similar to equations 19 and 22, where the superscript k denotes the value of the corresponding quantity in the k-th iteration. The derivative of the residual with respect to the state and parameters is the derivative of the function h with respect to the state and parameters. Since the state is fixed, therefore... is a variable,

[0090]

[0091] where, ,

[0092] Expanding the above equation, we write it in the standard least squares form

[0093]

[0094] Thus we get = .

[0095] The parameters at the kth iteration are given by the normal equations of the linear least squares problem, as follows:

[0096]

[0097] The derivation of this formula is as follows: the objective function of the parameter subproblem in equation (17) can be equivalently written as

[0098]

[0099] From = we get = , which is substituted into the equivalent form of the objective function of the parameter subproblem, and then we take the first derivative of p and set it to zero. After some rearrangement, we get equation (23).

[0100] where, and are the prior terms of the parameters. The key step in this step is to accumulate information over time. By summing the information matrices and the gradient terms over all time slices, this process uses all available temporal data to estimate a unique, time-invariant set of parameters . This approach significantly improves the statistical robustness and accuracy of the parameter estimates.

[0101] In the second step of the variable projection iteration, the line parameters are fixed to the updated values from the previous step. Then, the optimization problem is solved for the state . Since is fixed, and the measurements at different time slices are independent, the original objective function can be decomposed into completely independent subproblems, each corresponding to a specific time slice state estimation.

[0102] For each time slice , the state estimation problem is formulated as a standard nonlinear least squares problem, which can be solved by the Gauss-Newton (GN) method. The key step of the Gauss-Newton method is to linearize the problem using the Jacobian matrix . Subsequently, the state update is determined by solving the linear system of equations (24).

[0103]

[0104] The derivation of the formula is as follows: the state estimation subproblem of equation (17) (still the first term of 17) is solved by the GN method, at the th iteration, the current state point of the time slice , the first-order Taylor expansion of the residual is made:

[0105]

[0106] Substitute the linearized residual above back into equation (17) to obtain the quadratic approximation subproblem of GN

[0107]

[0108] Take the derivative of and set the derivative to zero, and rearrange to obtain equation (24).

[0109] The state can be updated by the formula , where is the step factor. Since state estimation subproblems are independent of each other, they can be assigned to different computing cores or nodes and solved simultaneously. For large data sets containing hundreds or thousands of time slices, this temporal decoupling and the resulting parallel computing capability are crucial to improving computational efficiency.

[0110] In joint state parameter estimation, a large linear system of equations needs to be solved, where the coefficient matrix is symmetric positive definite. To avoid large-scale matrix decomposition, the preconditioned conjugate gradient method (PCG) is used.

[0111]

[0112] where is a block diagonal matrix constructed row by row, and is a block diagonal matrix formed by time.

[0113] B. Construction of Jacobian matrix.

[0114] The Jacobian matrix serves as a bridge between the measurement residuals and the variables to be estimated. The accurate calculation of its elements is crucial for gradient-based optimization algorithms. In the robust variable projection framework proposed in this approach, two types of Jacobian matrices should be calculated:

[0115] 1) Partial derivatives of residuals with respect to states:

[0116] According to the chain rule, the following relations can be obtained:

[0117]

[0118] The partial derivatives of residuals with respect to state variables are defined by the power flow equations. They are the partial derivatives of branch active and reactive power with respect to bus voltage magnitude and phase angle. For branch power flow measurements, the partial derivative with respect to phase angle is:

[0119]

[0120]

[0121] The partial derivatives of branch power flow with respect to voltage magnitude are:

[0122]

[0123]

[0124] The elements obtained in equations (27) to (30) are arranged into the Jacobian matrix for each time interval. Then, the matrix is obtained according to equation (18).

[0125] 2) Derivatives of residuals with respect to parameters:

[0126] Similarly, the partial derivatives of residuals with respect to states can be obtained using the chain rule. That is, the active and reactive power of branch flow are partial derivatives with respect to parameters. Since it is complex to directly take the derivative of and , the chain rule is applied in two steps. First, take the derivative of the measurement function with respect to intermediate parameters and :

[0127]

[0128]

[0129] Then, the derivative of the chain rule from to is:

[0130]

[0131] The parameter Jacobian matrix after chain operation:

[0132]

[0133] C. According to the above analysis, as shown in Figure 3 , the specific steps for solving the model are as follows:

[0134] (3-1) Initialize the parameters of the transmission line and the state of each time period, that is, set and ;

[0135] (3-2) Set the iteration number k = 0;

[0136] (3-3) According to the measurement residual of the last iteration, update the measurement residual weight matrix of each time period t using formula (6) ;

[0137] (3-4) Fix the state in the joint estimation model as the value of the state in the last iteration , so as to convert the joint estimation model into a parameter estimation sub-model, solve the parameter estimation sub-model according to formula (23), and obtain the updated parameter value of the transmission line l ;

[0138] (3-5) Fix the parameter in the joint estimation model as , so as to convert the joint estimation model into a state estimation sub-problem, then for each time period t in the state estimation sub-problem, construct a Gauss-Newton state sub-problem according to formula (24), solve to obtain the state change of each time period , and update the state as: , denotes the step factor;

[0139] (3-6) If the parameter and state change meet the convergence condition, output the current parameter as the final parameter estimation value; otherwise, = , and return to step (3-3).

[0140] The Huber M loss calculation function and the iterative reweighting mechanism are introduced, so that the influence of abnormal values in the measurement data can be effectively inhibited, and stronger robustness is achieved. Meanwhile, the original high-dimensional and strong coupling non-convex joint estimation problem is decomposed into two sub-problems of parameters and states for alternative solving by using a variable projection framework, and the calculation complexity is significantly reduced by combining with a preconditioned conjugate gradient method. In addition, the method comprehensively utilizes multi-period measurement information and internally calibrates the system state, so as to provide a more accurate physical background for parameter identification, and thus, higher parameter estimation precision than traditional methods can be obtained under a complex measurement environment.

[0141] Example description:

[0142] In order to simulate the data-driven analysis scene in the modern smart grid, a time series measurement data set containing 24 time sections is constructed. In each time section, a uniform random disturbance in the interval of [-10%, +10%] is applied to the system reference load to simulate the natural fluctuation of the daily load. Then, an accurate power flow calculation is performed to obtain the true state of the network at each operating point, such as node voltage, injected power, etc. Finally, Gaussian white noise obeying a normal distribution is added to the true values to generate pseudo-measurement data. The noise standard deviation is set according to industry experience as follows:

[0143] Node voltage amplitude (V):

[0144] Node active / reactive power injection (P / Q):

[0145] In order to estimate the accuracy of the multi-dimensional quantification algorithm, the following evaluation indexes are used, including absolute error (AE), relative error (RE), and root mean square error (RMSE) as the core of macro evaluation. As shown in equations (35)-(38):

[0146] (35)

[0147] (36)

[0148] (37)

[0149] (38)

[0150] In order to estimate the accuracy of the multi-dimensional quantification algorithm, the following evaluation indexes are used, including absolute error (AE), relative error (RE), and root mean square error (RMSE) as the core of macro evaluation.

[0151] ​Table 1. Comparison of overall root mean square error (RMSE) of four line parameters estimation under different methods

[0152] The line-by-line relative error distribution and absolute error distribution of the embodiments of the present application are shown in Figure 4 , 5 and Table 1. The data show that, in the estimation of all four parameters of the line type model, the method in this paper has the optimal performance in both absolute error and relative error root mean square error (RMSE) indicators. In particular, in the estimation of line reactance , the relative error RMSE of the method in this paper is only 0.0794%, which is significantly lower than the traditional joint state estimation (JSE) and weighted least squares method (WLS).

[0153] Table 2. Comparison of overall root mean square error (RMSE) of line parameter estimation with bad data

[0154] The relative error of each parameter of the embodiments of the present application under the addition of bad data is shown in Figure 6 and Table 2. Comparison shows that under the harsh condition of introducing 5% bad data, the method in this paper still maintains the optimal estimation accuracy. The absolute error and relative error RMSE of each parameter are significantly lower than the traditional WLS and JSE methods, especially in the estimation of weakly measurable parameters such as ground admittance. This shows that the method in this paper not only can achieve accurate estimation in ideal environment, but also has excellent performance stability under bad measurement conditions, effectively overcoming the inherent defect of traditional methods that are sensitive to bad data.

[0155] In order to more accurately quantify the impact of bad data, Table 3 calculates the RMSE growth rate of each algorithm from the pure Gaussian noise environment to the bad data pollution environment, i.e. the performance degradation rate.

[0156] Table 3. Performance degradation analysis

[0157] The performance degradation rate analysis of Table 3 further quantifies the robustness of each algorithm from a dynamic perspective. The data shows that when the measurement environment changes from pure to polluted, the RMSE growth rate of the method in this paper on all parameters is much lower than the two comparison methods, and its degradation rate is generally less than one third of WLS and one half of JSE. This result powerfully proves that the robust framework constructed in this paper can effectively absorb the impact of bad data and overcome the shortcomings of traditional methods.

[0158] Embodiment two

[0159] The embodiment of the present application also provides a computer program product, such as an app on a mobile phone, a tablet computer, an installation program on a computer, etc., which comprises computer programs / instructions, and the computer programs / instructions are executed by a processor to implement the method in the embodiment one. The code for executing the computer executable program of the present application can be written in one or more programming languages or combinations thereof, including object oriented programming languages such as Java, Smalltalk, C++, and conventional procedural programming languages such as "C" language or similar programming languages. The program code can be executed entirely on a user computer, partially on a user computer, as an independent software package, partially on a user computer and partially on a remote computer, or entirely on a remote computer or server. In the case involving a remote computer, the remote computer can be connected to the user computer through any kind of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (for example, through the Internet by using an Internet service provider).

[0160] Embodiment three

[0161] Figure 7 is a structural schematic diagram of a computer device provided by the embodiment of the present application, and the embodiment of the present application provides services for the implementation of the method in the above embodiment one of the present application. As shown in the figure, the device can include a memory 301 storing computer executable programs; a processor 302 coupled with the memory 301; and the processor 302 invokes the computer executable programs stored in the memory 301, and is used for executing the steps in the method described in the embodiment one. Figure 7

[0162] The memory 301 can include a computer system readable medium in the form of volatile memory, such as random access memory (RAM) and / or cache memory. The device can further include other removable / non removable, volatile / non volatile computer system storage media. For example, the memory 301 can be used to read and write non removable, non volatile magnetic media (commonly referred to as "hard disk drive"). The program / utility, having a set of (at least one) program modules, can be stored in, for example, the memory 301, which includes an operating system, one or more application programs, other program modules, and program data, each of which can include an implementation of a network environment or a combination of some of these examples. The computer executable programs of the program modules generally perform the functions and / or methods in the embodiments described in the present application.

[0163] The processor 302 performs various function applications and data processing by running the programs stored in the memory 301, such as implementing the method provided by the embodiment one of the present application.​

[0164] The code of a computer program can be written in one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like, and / or conventional procedural programming languages, such as the "C" programming language or similar programming languages.

[0165] Embodiment Four

[0166] The embodiment of the application provides a storage medium containing a computer executable program, which is used for executing the method of the embodiment one when executed by a computer processor.

[0167] The storage medium of the embodiment of the application can adopt any combination of one or more computer readable mediums. The computer readable medium can be a computer readable signal medium or a computer readable storage medium. The computer readable storage medium can be, for example but not limited to, an electronic, magnetic, optical, electromagnetic, infrared or semiconductor system, device or apparatus, or any combination of the above. More specific examples (a non-exhaustive list) of the computer readable storage medium include an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read only memory (ROM), an erasable programmable read only memory (EPROM or flash memory), an optical fiber, a portable compact disk read only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this document, the computer readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus or device.

[0168] Of course, the storage medium containing a computer executable program provided by the embodiment of the application is not limited to the method operation as above, and can also execute the related operation in the method provided by any embodiment of the application.

[0169] It should be understood that the above embodiments and the description in the specification are only the principles, main features and advantages of the application, and the application can have various changes and improvements without departing from the spirit and scope of the application. These changes and improvements all fall within the scope of the application.

Claims

1. A method for estimating transmission line parameters based on a robust variable projection framework, characterized in that, include: (1) Establish nonlinear measurement equations for transmission line parameter estimation, wherein the nonlinear measurement equations include nonlinear measurement equations for line power measurement, node voltage amplitude and phase angle measurement, and measurement residuals; (2) Based on the nonlinear measurement equation, a joint estimation model for estimating the state and parameters of the transmission line is constructed. The objective function of the joint estimation model is to minimize the weighted sum of the measurement residuals and the prior terms of the parameters. The weight of the measurement residuals is calculated using the Huber loss function based on the measurement residuals in the previous iteration and increases linearly with the measurement residuals. (3) Solve the joint estimation model. When solving, the joint estimation model is converted into a state estimation subproblem and a parameter estimation subproblem using a robust variable projection framework. The solution is iteratively solved until convergence, and the estimated transmission line parameters are obtained.

2. The transmission line parameter estimation method based on a robust variable projection framework according to claim 1, characterized in that, The nonlinear measurement equation specifically includes: Parameters of the transmission line: , Status of transmission lines: , Full measurement function: , Power measurement equation: , Equations for voltage amplitude and phase angle measurement: , Measurement residuals: , In the formula, Indicates transmission line The parameters, They represent transmission lines l The series resistance, series reactance, parallel conductance to ground, and parallel susceptance to ground are... Indicates transmission line l The preceding and following nodes, This indicates the state of the transmission line during time period t. , , Let represent the voltage, voltage amplitude, and voltage phase angle of node i during time period t, respectively. , Let represent the active power and reactive power during time period t, respectively. , They represent transmission lines l Series conductance and series susceptance , Let i and j represent the voltage amplitudes at nodes i and j respectively during time period t. This represents the phase angle difference between nodes i and j. and This represents the voltage phase angle and voltage amplitude directly measured during time period t. This represents the measurement residual for time period t. Represents the full measurement function. This represents the selection matrix. A row is 1 if the measured component is actually available during time period t, and 0 otherwise. express The actual measurement vector available at any given time. Represents a collection of transmission lines. Represents a set of nodes.

3. The transmission line parameter estimation method based on a robust variable projection framework according to claim 1, characterized in that, The joint estimation model is as follows: , , , In the formula, This represents the measurement residual for time period t, where T represents the total number of time periods. This represents the measurement residual weight matrix for time period t. Indicates transpose. , These represent the coefficients of the a priori terms for voltage phase angle and voltage amplitude, respectively. Let these represent the voltage amplitude matrix and voltage phase angle matrix for time period t, respectively. , They represent the lines respectively. Upper and lower bounds of the resistance-reactance ratio constraint. They represent transmission lines l The series resistance, series reactance, and parallel conductance to ground are all factors in the series resistance, series reactance, and parallel conductance to ground. , These represent the element-wise upper and lower bounds of the parameter vector, respectively. Parameters representing all transmission lines The resulting matrix This indicates the state of the transmission line during time period t. L represents the balance node, i.e., the reference node, and L represents the weighted graph Laplace matrix of the power grid topology.

4. The transmission line parameter estimation method based on a robust variable projection framework according to claim 1, characterized in that, The weights of the measurement residuals are specifically as follows: , , , In the formula, This represents the measurement residual weight matrix at time t during the k-th iteration. This represents assembling the matrix along the diagonal for time interval t to form a block diagonal matrix. This indicates retrieving the diagonal elements. This represents the weight of node i in time period t during the k-th iteration. This indicates Huber's losses. Represents the standardized residual. This represents the measurement residual of node i in time period t during the (k-1)th iteration. Indicates the threshold parameter. Represents a symbolic function. This represents the residual threshold.

5. The method for estimating transmission line parameters based on a robust variable projection framework according to claim 1, characterized in that, Step (3) specifically includes: (3-1) Initialize the parameters of the transmission line and the status of each time period; (3-2) Set the iteration count k=0; (3-3) Update the measurement residual weight matrix for each time period t based on the measurement residual from the previous iteration. ; (3-4) Fix the state in the joint estimation model to the value of the state at the time of the last iteration. This transforms the joint estimation model into a parameter estimation sub-model. Solving the parameter estimation sub-model yields the updated transmission line. l parameter values ; (3-5) Fix the parameters in the joint estimation model to This transforms the joint estimation model into a state estimation subproblem. Then, for each time interval t in the state estimation subproblem, a Gaussian-Newton state subproblem is constructed, and the state change for each time interval is obtained by solving it. And update the status to: , Indicates the step size factor; (3-6) If the changes in parameters and state both satisfy the convergence condition, then the current parameters are set to... Output as the final parameter estimate; otherwise, = Then return to step (3-3).

6. The transmission line parameter estimation method based on a robust variable projection framework according to claim 5, characterized in that, The parameter value The following formula is used to update the result: , In the formula, The Jacobian matrix represents the parametric matrix, specifically the partial derivative of the measurement residuals with respect to the parameters. express transpose, The weighted matrix represents the prior terms. Indicates time period The linearization constant term, This represents the prior value of the parameter. The preset parameter is used in the first iteration estimation, and the result of the previous iteration estimation is used as the new parameter in each subsequent iteration estimation. .

7. The method for estimating transmission line parameters based on a robust variable projection framework according to claim 5, characterized in that, The state change amount for each time period The following formula is used to calculate: , In the formula, The state Jacobian matrix is ​​represented by the partial derivative of the measurement residuals with respect to the state. express transpose, The coefficients of the voltage phase angle prior are represented by I, which represents the identity matrix. Indicates the state as The parameters are The residual, These are the parameters for all time periods of all transmission lines during the k-th iteration.

8. The transmission line parameter estimation method based on a robust variable projection framework according to claim 5 or 6, characterized in that, For large-scale matrices, a preprocessing conjugate gradient method is used for solving the problem.

9. A computer program product, comprising a computer program, characterized in that: When the computer program is executed by a processor, it implements the method of any one of claims 1-8.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: The processor executes the computer program to implement the method as described in any one of claims 1-8.

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