Power distribution network parameter abnormality positioning and correction method based on residual sensitivity matrix

Abstract

The application discloses a power distribution network parameter abnormality positioning and correction method based on a residual sensitivity matrix, and the method comprises the following steps: determining the types of each branch of the power distribution network to obtain to-be-checked parameters of each branch; obtaining actual values of active power and reactive power of each branch in the power distribution network; obtaining conductance and susceptance of each branch, and calculating theoretical values of the active power and the reactive power of each branch according to the conductance, the susceptance and the to-be-checked parameter data of each branch, and calculating active power residuals and reactive power residuals of each branch; constructing a sensitivity matrix and a measurement residual vector, and establishing a normal equation through the sensitivity matrix and the measurement residual vector, and solving the normal equation to obtain line length deviation and transformer ratio deviation; and correcting the line length and the transformer ratio. The application realizes high-precision, anti-interference and stable identification of the line length and the transformer ratio.

Description

Technical Field

[0001] This invention belongs to the field of power distribution network data processing technology, specifically a method for anomaly location and correction of power distribution network parameters based on residual sensitivity matrix. Background Technology

[0002] State estimation (SE) is a core technology for real-time sensing of the operating status of power distribution networks. It uses real-time measurement data to filter out random errors and estimate state quantities such as voltage and phase angle of the system. However, the accuracy of state estimation is highly dependent on the accuracy of network parameters (such as line resistance, reactance, transformer turns ratio, etc.).

[0003] In actual engineering projects, power distribution networks are complex in structure, have numerous devices, and undergo frequent changes. Currently, network parameters are mainly derived from geographic information systems or equipment ledger databases. Due to reasons such as manual input errors, aging lines, construction rerouting, or equipment replacement without timely updates, the parameters recorded in the ledgers (especially line length and transformer turns ratio) often deviate from the actual physical parameters.

[0004] Therefore, existing parameter estimation or verification methods typically treat electrical parameters such as line resistance and reactance as variables to be identified for mathematical optimization, aiming to minimize measurement residuals. However, these methods are essentially pure mathematical fitting, and the corrected values ​​they produce often lack clear physical correspondence. For example, the algorithm might output a corrected resistance value, but it cannot clearly indicate whether the deviation stems from an error in recording the line length, a mismatch in conductor type, or a connection problem. This abstract parameter correction result is difficult to directly translate into specific maintenance instructions (such as how long of line to check or which transformer tap to adjust), resulting in low accuracy in judging and locating errors in line and transformer equipment parameters, thus limiting its practicality. Therefore, how to achieve high-precision parameter identification with clear physical meaning that can directly guide on-site verification has become a pressing technical challenge. Summary of the Invention

[0005] To address the technical problem that existing methods for determining whether the parameters of the positioning lines and transformer equipment are incorrect may have low accuracy, this invention provides a method for locating and correcting abnormal distribution network parameters based on a residual sensitivity matrix, so as to achieve high-precision, anti-interference, and stable identification of line length and transformer ratio.

[0006] The technical solution adopted in this invention is as follows: a method for anomaly location and correction of distribution network parameters based on residual sensitivity matrix, comprising: determining the type of each branch of the distribution network and obtaining the parameters to be verified for each branch, wherein, in response to the branch type being a line branch, the line length of the line branch is determined as the parameter to be verified for the branch; in response to the branch type being a transformer branch, the turns ratio of the transformer in the transformer branch is determined as the parameter to be verified for the branch; obtaining the actual values ​​of active power and reactive power of each branch in the distribution network; obtaining the conductance and susceptance of each branch, and calculating the theoretical values ​​of active power and reactive power of each branch based on the conductance, susceptance and parameter data to be verified for each branch, and calculating the theoretical values ​​of active power and reactive power of each branch. The active power residual and reactive power residual of the branch are calculated; a sensitivity matrix and a measurement residual vector are constructed, and a normal equation is established through the sensitivity matrix and the measurement residual vector. The normal equation is solved to obtain the line length deviation and the transformer ratio deviation; in response to the geographical length deviation of the line branch being greater than a preset length threshold, the line length of the line branch is corrected according to the line length deviation, and iterated until the preset first convergence condition is met; in response to the transformer ratio deviation of the transformer branch being greater than a preset ratio threshold, the transformer ratio of the transformer branch is corrected according to the transformer ratio deviation, and iterated until the second convergence condition is met.

[0007] Preferably, the conductance of the line branch satisfies the formula:

[0008] ;

[0009] in, G line For the conductance of the line branch, r 0 represents the resistance value per unit length of the line branch. x 0 represents the reactance value per unit length of the line branch. L The length of the line branch;

[0010] The susceptance of a line branch satisfies the formula:

[0011] ;

[0012] in, B line This refers to the susceptance of the line branch.

[0013] Preferably, the formula for calculating the theoretical value of active power of the line branch is:

[0014] ;

[0015] in, This represents the theoretical value of the active power of the line branch. This represents the voltage amplitude at one end of a branch line. This refers to the voltage amplitude at the other end of the line branch. This is the voltage phase difference between one end and the other end of a line branch. Pre-determine the conductivity of the line branch;

[0016] The formula for calculating the theoretical value of reactive power in a line branch is:

[0017] ;

[0018] in, This represents the theoretical value of reactive power for the line branch. Preset the susceptance of the line branch.

[0019] Preferably, the formula for calculating the theoretical value of active power in a transformer branch is:

[0020] ;

[0021] in, This represents the theoretical value of the active power of the transformer branch. k The transformer ratio of the transformer branch. This refers to the voltage amplitude at the transformer-side node of the transformer branch. This represents the voltage amplitude at the node on the other side of the transformer branch. Pre-determine the conductance of the transformer branch. Pre-determine the susceptance of the transformer branch; This is the voltage phase difference between one end and the other end of a transformer branch.

[0022] The formula for calculating the theoretical value of reactive power in a transformer branch is:

[0023] ;

[0024] in, This represents the theoretical value of reactive power in the transformer branch.

[0025] Preferably, the sensitivity matrix is: n Line 2 n The matrix of columns, the sensitivity matrix of column number s Line number j The element of the column is the first s Partial derivatives of the theoretical active power of each branch with respect to the actual value. s < n , j < n The sensitivity matrix of the first s Line number j+n The element of the column is the first s Partial derivatives of the theoretical reactive power of each branch with respect to the actual value. n This represents the number of all branches.

[0026] Preferably, the normal equation is: Solving the normal equations to obtain the line length deviation and transformer turns ratio deviation includes: solving the normal equations to obtain the deviation vector Δ. λ The formula is: ,in H The sensitivity matrix is ​​described above. H T This is the transpose of the sensitivity matrix; W For the preset weight matrix, r The measurement residual vector, wherein the measurement residual vector r For including 2 n A column vector of elements, and a measurement residual vector. r The j The element is the first j The active power residual of each branch, the first j+n The element is the first j The reactive power residual of each branch.

[0027] Preferably, the weight matrix W 2 n Line 2 n A matrix of columns, and a weight matrix. W No. j Line number j The element of the column is the first j The weight coefficients of each branch are predetermined in size, and the weight matrix is ​​defined. W No. j + n Line number j + n The element of the column is equal to the first element. j Line number j The elements of the column, wherein all diagonal elements of the matrix are 0.

[0028] Preferably, correcting the line length of a line branch based on the line length deviation includes: adding the product of the line length deviation and a preset attenuation coefficient to the line length to obtain the corrected line length, wherein the attenuation coefficient is greater than 0 and less than 1.

[0029] Correcting the transformer ratio of a transformer branch based on the transformer ratio deviation includes adding the product of the transformer ratio deviation and the attenuation coefficient to the transformer ratio to obtain the corrected transformer ratio.

[0030] Preferably, the first convergence condition is: the absolute value of the calculated line length deviation is less than a preset length threshold, or the iteration reaches a preset number of times.

[0031] Preferably, the second convergence condition is: the absolute value of the calculated transformer turns ratio deviation is less than a preset turns ratio threshold, or the iteration reaches a preset number of times.

[0032] The beneficial effects of this invention are as follows:

[0033] This invention locks the line length (geographical length of the line) and transformer turns ratio as parameters to be verified. By establishing a mapping relationship between physical length and conductance / susceptance, the correction results directly correspond to specific equipment attributes such as actual conductor length and tap position. A parameter sensitivity matrix based on a variant of the Jacobian matrix is ​​constructed to linearize the nonlinear problem at the current operating point, thereby efficiently solving for parameter deviations using normal equations. A weight matrix proportional to the inverse of the measurement error variance is introduced to reduce the impact of large-scale measurement data on errors, significantly improving the algorithm's anti-interference capability and robustness. Based on this, by focusing on physical parameters, constructing a sensitivity matrix, and introducing weights, this invention achieves high-precision, anti-interference, and stable identification of line length and transformer turns ratio, enabling more accurate identification and location of errors in line and transformer equipment parameters while simultaneously correcting the optimal parameters for these parameters. Attached Figure Description

[0034] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent upon reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of the invention are illustrated by way of example and not limitation, and like or corresponding reference numerals denote like or corresponding parts, wherein:

[0035] Figure 1 This is a schematic flowchart illustrating the steps of a distribution network parameter anomaly location and correction method based on a residual sensitivity matrix according to an embodiment of the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0038] Figure 1 This is a schematic flowchart illustrating the steps of a distribution network parameter anomaly location and correction method based on a residual sensitivity matrix according to an embodiment of the present invention.

[0039] like Figure 1As shown, the distribution network parameter anomaly location and correction method based on residual sensitivity matrix includes steps S1 to S4.

[0040] Step S1: After determining the type of each branch of the distribution network, obtain the parameters to be verified for each branch.

[0041] Specifically, in response to the branch type being a line branch, the line length of the line branch is obtained; in response to the branch type being a transformer branch, the transformer ratio of the transformer branch is obtained; and the actual values ​​of active power and reactive power of each branch in the distribution network are obtained.

[0042] It should be noted that the actual values ​​of active power and reactive power refer to the telemetry data collected in real time and uploaded to the main station by the measuring equipment (such as feeder terminal unit or distribution transformer monitoring terminal unit) installed on each branch of the distribution network; the branch type is determined according to the network topology data of the distribution network. If the two ends of the branch are directly connected by a conductor, it is determined to be a line branch; if the two ends of the branch are connected by a transformer device, it is determined to be a transformer branch.

[0043] Existing technologies often directly correct resistance or reactance values, without a clear physical meaning. This invention distinguishes between line branches and transformer branches, locking line length and transformer turns ratio as parameters to be verified. By establishing a mapping relationship between line length and conductance / susceptance, the final correction result directly corresponds to specific physical equipment attributes (such as conductor length and tap position).

[0044] Step S2: Obtain the conductance and susceptance of each branch, and calculate the theoretical values ​​of active power and reactive power of each branch based on the conductance, susceptance and the parameter data to be checked, and calculate the active power residual and reactive power residual of each branch.

[0045] In one embodiment, the conductance of the line branch satisfies the formula:

[0046] ;

[0047] in, G line For the conductance of the line branch, r 0 represents the resistance value per unit length of the line branch. x 0 represents the reactance value per unit length of the line branch. L This refers to the length of the branch line.

[0048] The susceptance of a line branch satisfies the formula:

[0049] ;

[0050] in, B line This refers to the susceptance of the line branch.

[0051] It should be noted that the resistance value per unit length of the line branch is... r 0 and reactance value per unit length of line branch x 0 is determined based on the conductor type of the branch line (a standard parameter matched from a preset equipment parameter library).

[0052] This step aims to establish a physical mapping relationship between the geographical length of the line and the conductance / susceptance of the line branches.

[0053] It should be noted that the conductance and susceptance of each type of line branch are calculated using the above embodiments.

[0054] In one embodiment, the formula for calculating the theoretical value of active power of a line branch is:

[0055] ;

[0056] in, This represents the theoretical value of the active power of the line branch. This represents the voltage amplitude at one end of a branch line. This refers to the voltage amplitude at the other end of the line branch. This is the voltage phase difference between one end and the other end of a line branch. The conductivity of the line branch is preset.

[0057] The formula for calculating the theoretical value of reactive power in a line branch is:

[0058] ;

[0059] in, This represents the theoretical value of reactive power for the line branch. Preset the susceptance of the line branch.

[0060] It should be noted that the voltage amplitude and voltage phase difference are current state quantities calculated based on the distribution network state estimation program; the theoretical value refers to the power value that should be calculated according to the branch power transmission equation in physics, assuming that the current line geographical length is completely accurate. It should also be noted that the theoretical values ​​of active and reactive power for each line branch are calculated using the above embodiments.

[0061] In one embodiment, the formula for calculating the theoretical value of active power in a transformer branch is:

[0062] ;

[0063] in, This represents the theoretical value of the active power of the transformer branch. kThe transformer ratio of the transformer branch. This refers to the voltage amplitude at the transformer-side node of the transformer branch. This represents the voltage amplitude at the node on the other side of the transformer branch. Pre-determine the conductance of the transformer branch. Pre-determine the susceptance of the transformer branch; It represents the voltage phase difference between one end and the other end of a transformer branch.

[0064] The formula for calculating the theoretical value of reactive power in a transformer branch is:

[0065] ;

[0066] in, This represents the theoretical value of reactive power in the transformer branch.

[0067] In one embodiment, the sensitivity matrix is n Line 2 n The matrix of columns, the sensitivity matrix of column number s Line number j The element of the column is the first s The partial derivatives of the theoretical active power of each branch with respect to the actual value. s < n , j < n The sensitivity matrix of the first s Line number j+n The element of the column is the first s Partial derivatives of the theoretical reactive power of each branch with respect to the actual value. n This represents the number of all branches.

[0068] It should be noted that the parameter sensitivity matrix is ​​essentially a variant of the Jacobian matrix, which physically characterizes the degree of influence of small disturbances in the parameter to be verified (i.e., line geographical length or transformer turns ratio) on the theoretical value of branch power. By constructing this matrix, the nonlinear power equation can be linearized near the current operating point, thereby using a system of linear equations to solve for parameter deviations. It should also be noted that the theoretical values ​​of active and reactive power for each transformer branch are calculated using the above embodiment.

[0069] Step S3: Construct the sensitivity matrix and measurement residual vector, and establish a normal equation using the sensitivity matrix and measurement residual vector. Solve the normal equation to obtain the line length deviation and transformer turns ratio deviation.

[0070] In one embodiment, the normal equation is: Solving the normal equations to obtain the line length deviation and transformer turns ratio deviation includes: solving the normal equations to obtain the deviation vector Δ. λ The formula is: ,in H The sensitivity matrix is ​​described above. H T This is the transpose of the sensitivity matrix; W For the preset weight matrix, r The measurement residual vector, wherein the measurement residual vector r For including 2 n A column vector of elements, and a measurement residual vector. r The j The element is the first j The active power residual of each branch, the first j+n The element is the first j The reactive power residual of each branch.

[0071] It should be noted that the measurement residual vector r The construction follows the "work-first, no-work-later" arrangement rule, that is, the first vectors... n Each element corresponds to the active power residual of all branches, and then... n Each element corresponds to the reactive power residual of all branches; correspondingly, the active power residual is equal to the actual active power value obtained in step S2 minus the calculated theoretical active power value, and the reactive power residual is equal to the actual reactive power value minus the theoretical reactive power value.

[0072] In one embodiment, the weight matrix W 2 n Line 2 n A matrix of columns, and a weight matrix. W No. j Line number j The element of the column is the first j The weight coefficients of each branch are predetermined in size, and the weight matrix is ​​defined. W No. j + n Line number j + n The element of the column is equal to the first element. j Line number j The elements of the column, wherein all diagonal elements of the matrix are 0.

[0073] It should be noted that the weight matrix WThe weight matrix is ​​used to quantify the reliability of different measurement data. The values ​​of the elements on the diagonal are proportional to the measurement accuracy of the corresponding measurement equipment (usually the reciprocal of the measurement error variance). The purpose of introducing the weight matrix is ​​to reduce the interference of measurement data with large errors on the calculation results of line geographical length deviation and transformer turns ratio deviation when solving the normal equation, and to improve the robustness of parameter identification.

[0074] Step S4: Correct the line length and correct the transformer turns ratio.

[0075] Specifically, in response to a geographical length deviation of a line branch exceeding a preset length threshold, the line length of the line branch is corrected based on the line length deviation, and this process is iterated until a preset first convergence condition is met. Similarly, in response to a transformer ratio deviation of a transformer branch exceeding a preset ratio threshold, the transformer ratio of the transformer branch is corrected based on the transformer ratio deviation, and this process is iterated until a second convergence condition is met.

[0076] In one embodiment, the first convergence condition is: the absolute value of the calculated line length deviation is less than a preset length threshold, or the iteration reaches a preset number of times. In one embodiment, the second convergence condition is: the absolute value of the calculated transformer ratio deviation is less than a preset ratio threshold, or the iteration reaches a preset number of times.

[0077] It should be noted that setting a preset length threshold (e.g., 0.1m) and a preset ratio threshold (e.g., 0.001) is to determine whether the parameter correction is accurate enough; while setting a preset number of iterations is to prevent the algorithm from failing to converge and getting stuck in an infinite loop under certain extreme data conditions, thereby ensuring the effectiveness and stability of the calculation process.

[0078] In one embodiment, correcting the line length of a line branch based on the line length deviation includes: adding the product of the line length deviation and a preset attenuation coefficient to the line length to obtain the corrected line length, wherein the attenuation coefficient is greater than 0 and less than 1.

[0079] Correcting the transformer ratio of a transformer branch based on the transformer ratio deviation includes adding the product of the transformer ratio deviation and the attenuation coefficient to the transformer ratio to obtain the corrected transformer ratio.

[0080] It should be noted that the attenuation coefficient (also known as damping factor or step size factor) is used to control the magnitude of parameter correction in a single iteration. Since the normal equation is based on linearization approximation, direct full correction may cause the calculation results to oscillate or even diverge around the true value. Introducing the attenuation coefficient (with a value between 0 and 1) can smooth the iteration process and ensure that the algorithm can stably approximate the actual geographical length of the line and the transformer ratio.

[0081] Furthermore, for any line branch, if the absolute value of the line length deviation corresponding to the line branch is less than a preset length threshold before the iteration, then the parameters of the line branch are determined to be normal; otherwise, the parameters of the line branch are determined to be abnormal. If the parameters of the line branch are abnormal, the corrected line length obtained from the last iteration is output.

[0082] For any transformer branch, if the absolute value of the transformer ratio deviation corresponding to that transformer branch is less than a preset ratio threshold before any iteration, then the parameters of that transformer branch are determined to be normal; otherwise, the parameters of that transformer branch are determined to be abnormal. If the parameters of that transformer branch are abnormal, the corrected line length obtained from the last iteration is output.

[0083] In the description of this specification, "multiple" or "several" means at least two, such as two, three or more, unless otherwise explicitly specified.

[0084] While this specification has shown and described numerous embodiments of the invention, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Many modifications, alterations, and alternatives will occur to those skilled in the art without departing from the spirit and essence of the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in the practice of this invention.

Claims

1. A method for locating and correcting anomalies in distribution network parameters based on residual sensitivity matrices, characterized in that, include: After determining the type of each branch in the distribution network, the parameters to be verified for each branch are obtained. For example, in response to the branch type being a line branch, the line length of the line branch is determined as the parameter to be verified for the branch; in response to the branch type being a transformer branch, the transformer ratio of the transformer branch is determined as the parameter to be verified for the branch; and the actual values ​​of active power and reactive power of each branch in the distribution network are obtained. Obtain the conductance and susceptance of each branch, and calculate the theoretical values ​​of active power and reactive power of each branch based on the conductance, susceptance and the parameter data to be checked, and calculate the active power residual and reactive power residual of each branch. Construct a sensitivity matrix and a measurement residual vector, and establish a normal equation using the sensitivity matrix and the measurement residual vector. Solve the normal equation to obtain the line length deviation and the transformer turns ratio deviation. In response to the geographical length deviation of the line branch being greater than the preset length threshold, the line length of the line branch is corrected according to the line length deviation, and the process is iterated until the preset first convergence condition is met. In response to the transformer ratio deviation of the transformer branch being greater than the preset ratio threshold, the transformer ratio of the transformer branch is corrected according to the transformer ratio deviation, and the process is iterated until the second convergence condition is met. The sensitivity matrix is: n Line 2 n The matrix of columns, the sensitivity matrix of column number s Line number j The element of the column is the first s The partial derivatives of the theoretical active power of each branch with respect to the actual value. s < n , j < n The sensitivity matrix of the first s Line number j+n The element of the column is the first s Partial derivatives of the theoretical reactive power of each branch with respect to the actual value. n The number of all branches; The normal equation is: Solving the normal equations to obtain the line length deviation and transformer turns ratio deviation includes: Solve the normal equation to obtain the deviation vector Δ λ The formula is: ,in H The sensitivity matrix is ​​described above. H T This is the transpose of the sensitivity matrix; This is a preset weight matrix; r The measurement residual vector, wherein the measurement residual vector r For including 2 n A column vector of elements, and a measurement residual vector. r The j The element is the first j The active power residual of each branch, the first j+n The element is the first j The reactive power residual of each branch.

2. The method for locating and correcting distribution network parameter anomalies based on residual sensitivity matrix according to claim 1, characterized in that, The conductance of a line branch satisfies the formula: ； in, G line For the conductance of the line branch, r 0 represents the resistance value per unit length of the line branch. x 0 represents the reactance value per unit length of the line branch. L The length of the line branch; The susceptance of a line branch satisfies the formula: ； in, B line This refers to the susceptance of the line branch.

3. The method for locating and correcting distribution network parameter anomalies based on residual sensitivity matrix according to claim 2, characterized in that, The formula for calculating the theoretical value of active power of a line branch is: ； in, This represents the theoretical value of the active power of the line branch. This represents the voltage amplitude at one end of a branch line. This refers to the voltage amplitude at the other end of the line branch. This is the voltage phase difference between one end and the other end of a line branch. Pre-determine the conductivity of the line branch; The formula for calculating the theoretical value of reactive power in a line branch is: ； in, This represents the theoretical value of reactive power for the line branch. Preset the susceptance of the line branch.

4. The method for locating and correcting distribution network parameter anomalies based on residual sensitivity matrix according to claim 1, characterized in that, The formula for calculating the theoretical value of active power in a transformer branch is: ； in, This represents the theoretical value of the active power of the transformer branch. k The transformer ratio of the transformer branch. This refers to the voltage amplitude at the transformer-side node of the transformer branch. This represents the voltage amplitude at the node on the other side of the transformer branch. Pre-determine the conductance of the transformer branch. Pre-determine the susceptance of the transformer branch; This is the voltage phase difference between one end and the other end of a transformer branch. The formula for calculating the theoretical value of reactive power in a transformer branch is: ； in, This represents the theoretical value of reactive power in the transformer branch.

5. The method for locating and correcting distribution network parameter anomalies based on residual sensitivity matrix according to claim 1, characterized in that, The weight matrix W 2 n Line 2 n A matrix of columns, and a weight matrix. W No. j Line number j The element of the column is the first j The weight coefficients of each branch are predetermined in size, and the weight matrix is ​​defined. W No. j + n Line number j + n The element of the column is equal to the first element. j Line number j The elements of the column, wherein all diagonal elements of the matrix are 0.

6. The method for locating and correcting distribution network parameter anomalies based on residual sensitivity matrix according to claim 1, characterized in that, Correcting the line length of a line branch based on the line length deviation includes: adding the product of the line length deviation and a preset attenuation coefficient to the line length to obtain the corrected line length, wherein the attenuation coefficient is greater than 0 and less than 1. Correcting the transformer ratio of a transformer branch based on the transformer ratio deviation includes adding the product of the transformer ratio deviation and the attenuation coefficient to the transformer ratio to obtain the corrected transformer ratio.

7. The method for locating and correcting distribution network parameter anomalies based on residual sensitivity matrix according to claim 1, characterized in that, The first convergence condition is: the absolute value of the calculated line length deviation is less than the preset length threshold, or the iteration reaches the preset number of times.

8. The method for locating and correcting distribution network parameter anomalies based on residual sensitivity matrix according to claim 1, characterized in that, The second convergence condition is: the absolute value of the calculated transformer turns ratio deviation is less than the preset turns ratio threshold, or the iteration reaches the preset number of times.

Images