Iterative process improvement-based power distribution network prediction auxiliary state estimation method and system

Abstract

The invention discloses a power distribution network prediction auxiliary state estimation method and system based on iteration process improvement. The method comprises the following steps: establishing a nonlinear discrete time state space model; generating a group of Sigma points through unscented transformation, substituting the Sigma points into a state transition equation, and calculating a state prediction value and a state prediction error covariance matrix at the current moment; substituting the Sigma point into a measurement equation to obtain a measurement predicted value, and calculating a Kalman gain; calculating a process noise covariance matrix at the next moment; and correcting the state prediction value and the state prediction error covariance matrix at the current moment to obtain an optimal state estimation value and an error covariance matrix thereof. According to the method, the risk that the covariance matrix loses the semi-positive qualitative property in the iteration process is avoided from the algorithm mechanism, the numerical stability and robustness of the UKF algorithm are remarkably enhanced, and reliable application in high-dimensional complex power distribution network state estimation is ensured.

Description

Technical Field

[0001] This invention belongs to the field of power grids and relates to distribution network predictive auxiliary state estimation technology, specifically to a distribution network predictive auxiliary state estimation method and system based on iterative process improvement. Background Technology

[0002] With the widespread integration of dynamic components such as distributed energy resources, electric vehicles, and energy storage systems into distribution networks, the dynamic characteristics of system operation are becoming increasingly prominent. Traditional static state estimation is no longer sufficient to meet the needs of real-time tracking and short-term prediction of system evolution trends. Therefore, Forecasting Aided State Estimation (FASE), as a standardized term for dynamic state estimation under the quasi-steady-state characteristics of distribution networks, has emerged. It establishes a model of the system state's evolution over time to predict and correct the system state at the next moment, providing key technical support for preventative control and optimized scheduling of active distribution networks.

[0003] Among the many implementation algorithms of FASE, those based on Kalman Filter (KF) and its nonlinear extensions are the most widely used. In particular, Unscented Kalman Filter (UKF) is considered an efficient tool for handling nonlinear models of distribution networks because it uses unscented transformation (UT) to approximate the probability distribution of the nonlinear function, avoiding the complex calculation of the Jacobian matrix in Extended Kalman Filter (EKF), and usually has higher estimation accuracy.

[0004] However, the standard UKF algorithm exhibits a serious numerical stability problem when applied to large-scale, high-dimensional real-world distribution network systems. This problem stems from the algorithm's update calculation of the error covariance matrix during iteration. Specifically, matrix subtraction occurs in the propagation and update steps of the covariance matrix. In an ideal infinite-precision computing environment, this operation does not violate the positive semi-definiteness of the covariance matrix. However, in practical finite-precision computer calculations, due to the accumulation of rounding errors, after multiple iterations, the calculated covariance matrix may lose its inherent positive semi-definiteness, or even exhibit negative diagonal elements (negative variance), which is physically meaningless. Once the covariance matrix loses its positive semi-definiteness, the filtering algorithm will diverge, causing the estimation process to completely fail. This deficiency severely limits the reliable application of UKF in complex distribution network FASE and is a technical bottleneck that urgently needs to be overcome in this field. Summary of the Invention

[0005] Purpose of the invention: In order to solve the problem that existing state estimation algorithms based on unscented Kalman filtering may cause the error covariance matrix to lose its positive semidefiniteness when processing high-dimensional distribution network models, thus leading to numerical instability and estimation failure, this invention provides a distribution network prediction auxiliary state estimation method and system based on an iterative process improvement.

[0006] Technical Solution: To achieve the above objectives, this invention provides a distribution network predictive auxiliary state estimation method based on an iterative process improvement, comprising the following steps:

[0007] S1: Establish a nonlinear discrete-time state-space model describing the operating characteristics of the distribution network, including state transition equations and measurement equations;

[0008] S2: Based on the state estimate and its error covariance matrix at the previous time step, generate a set of Sigma points through unscented transformation, and substitute the Sigma points into the state transition equation to calculate the state prediction and state prediction error covariance matrix at the current time step.

[0009] S3: Substitute the Sigma point into the measurement equation to obtain the measurement prediction value and calculate the Kalman gain;

[0010] S4: Using the Kalman gain and measurement residual calculated in step S3, calculate the process noise covariance matrix at the next time step using the equivalent additive update formula;

[0011] S5: Using the Kalman gain and measurement residual calculated in step S3, correct the current state prediction value and state prediction error covariance matrix obtained in step S2 to obtain the optimal state estimate value and its error covariance matrix at the current time.

[0012] Furthermore, the nonlinear discrete-time state-space model in step S1 is expressed as follows:

[0013]

[0014] in, For discrete time steps; This represents the total number of system nodes. The control input vector is known. It is an m-dimensional measurement vector; It is a nonlinear state transition function; It is a nonlinear measurement function; To account for process noise, the uncertainty of the state transition model was modeled, and its covariance matrix is: ; For the measurement noise, its covariance matrix is: .

[0015] Further, step S2 includes:

[0016] A1: Optimal state estimate based on the previous time step and its error covariance matrix Generate according to the principle of symmetric sampling A set of Sigma points ;

[0017] A2: For each Sigma point As input, through the state transition function Perform nonlinear propagation to obtain the propagated set of Sigma points. ;

[0018] A3: Calculate the weighted average of the propagated Sigma points to obtain the state prediction value. ,in, Weighted by mean;

[0019] A4: Calculate the weighted covariance of the Sigma points after propagation, and add the process noise covariance to obtain the state prediction error covariance matrix. .

[0020] Furthermore, in step A4, the state prediction error covariance matrix The formula for calculation is:

[0021]

[0022] in, Here are the corresponding covariance weights, and T represents the transpose operation.

[0023] Furthermore, the expression for the equivalent additive update formula in step S4 is:

[0024]

[0025] in, and These are the process noise covariance matrices before and after the update, respectively. The Kalman gain at the current time, calculated in step S3; Let be the measurement residual at the current moment, that is, the difference between the actual measurement value and the predicted measurement value, where These are actual measured values. To pass the measurement function The measurement prediction value obtained after propagating the Sigma point; The covariance matrix of the measurement residuals; This is an operator that retains only the diagonal elements of a matrix and sets the remaining elements to zero.

[0026] Furthermore, in the equivalent additive update formula:

[0027] Covariance matrix of measurement residuals :

[0028] ;

[0029] in, This is the measurement value corresponding to the i-th Sigma point after propagation;

[0030] Kalman gain :

[0031] ;

[0032] in, Let be the cross-covariance matrix of the state and the measurement.

[0033] Furthermore, the update principle of the equivalent additive update formula includes:

[0034] Of the three components on the right side of the formula, the first term As the covariance matrix of the previous time step, it is initialized to positive semi-definite at the start of the iteration and maintains this property in subsequent iterations through an update method; the second term ,because It is a positive semi-definite matrix with rank 1. After a linear transformation, its diagonal elements must be non-negative, therefore this term is a positive diagonal semi-definite matrix; the third term It is a typical quadratic form, due to the measurement residual covariance matrix Since it is positive semi-definite, the result of the transformation must also be positive semi-definite.

[0035] Finally, the updated The linear sum of three positive semi-definite matrices results in a positive semi-definite matrix.

[0036] Furthermore, the final optimal state estimate in step S5 and its error covariance matrix The update and correction process follows the unscented Kalman filter update equation:

[0037]

[0038] By guarantee Its positive semi-definiteness ensures The positive semidefiniteness in the next iteration forms a complete numerically stable closed loop.

[0039] The present invention also provides a distribution network predictive auxiliary state estimation system based on an iterative process improvement, comprising:

[0040] The model building module is used to build a nonlinear discrete-time state-space model that describes the operating characteristics of the distribution network, including state transition equations and measurement equations.

[0041] The prediction execution module generates a set of Sigma points based on the state estimate and its error covariance matrix at the previous time step through unscented transformation, and substitutes the Sigma points into the state transition equation to calculate the state prediction value and the state prediction error covariance matrix at the current time step.

[0042] The filtering update module substitutes the Sigma point into the measurement equation to obtain the measurement prediction value and calculates the Kalman gain.

[0043] The matrix update module uses Kalman gain and measurement residuals to calculate the process noise covariance matrix at the next time step using an equivalent additive update formula.

[0044] The update and correction module uses Kalman gain and measurement residuals to correct the current state prediction value and the state prediction error covariance matrix, thereby obtaining the optimal state estimate value and its error covariance matrix at the current time.

[0045] Beneficial Effects: Compared with existing technologies, this invention improves the propagation process of the process noise covariance matrix in the filtering update step of predictive auxiliary state estimation. Instead of updating the covariance through direct matrix subtraction, which may introduce non-positive semidefinite risks, it innovatively utilizes the calculated Kalman gain and residual information to construct an equivalent and always positive semidefinite increment term to update the covariance matrix. This invention avoids the risk of the covariance matrix losing its positive semidefiniteness during iteration from an algorithmic mechanism perspective, significantly enhancing the numerical stability and robustness of the UKF algorithm. The effectiveness of predictive auxiliary state estimation for distribution networks is effectively guaranteed, ensuring reliable application in the state estimation of high-dimensional complex distribution networks. Attached Figure Description

[0046] Figure 1 A schematic diagram illustrating the effect of linearization error on the mean and covariance of a random variable;

[0047] Figure 2 A schematic diagram of the improved IEEE-13 node topology;

[0048] Figure 3 A radar chart showing the ratio of the weighted residuals to their mean values;

[0049] Figure 4 Comparison of numerical stability tests under the IEEE-13 node system. Detailed Implementation

[0050] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0051] Example 1:

[0052] This embodiment provides a distribution network prediction auxiliary state estimation method based on an iterative process improvement, including the following steps:

[0053] S1: Establish a nonlinear discrete-time state-space model describing the operating characteristics of the distribution network, including state transition equations and measurement equations;

[0054] The nonlinear discrete-time state-space model is expressed as follows:

[0055]

[0056] in, For discrete time steps; The total number of system nodes is denoted by , and the system's n-dimensional state vector contains the voltage magnitude and phase angle of all nodes in the distribution network. For known control input vectors, such as transformer tap position or capacitor switching state; It is an m-dimensional measurement vector containing information such as node injected power and branch power flow uploaded by the SCADA system; It is a nonlinear state transition function, which is essentially based on the state at the previous time step. and input System power flow calculation; It is a nonlinear measurement function, based on the current state. Calculate the corresponding theoretical measurement value; To account for process noise, the uncertainty of the state transition model was modeled, and its covariance matrix is: ; For the measurement noise, its covariance matrix is: .

[0057] S2: Perform the prediction steps for predictive auxiliary state estimation: Based on the state estimate value and its error covariance matrix at the previous time step, generate a set of Sigma points through unscented transformation (UT), and substitute the set of Sigma points into the state transition equation to calculate the state prediction value and the state prediction error covariance matrix at the current time step.

[0058] Step S2 includes:

[0059] A1: Sigma point generation: Based on the optimal state estimate of the previous time step. and its error covariance matrix Generate according to the principle of symmetric sampling A set of Sigma points ;

[0060] A2: Sigma point propagation: Propagating each Sigma point... As input, through the state transition function Perform nonlinear propagation to obtain the propagated set of Sigma points. ;

[0061] A3: Calculation of State Prediction Values: The state prediction values ​​are obtained by weighted averaging of the propagated Sigma points. ,in, Weighted by mean;

[0062] A4: Calculation of State Prediction Error Covariance: Calculate the weighted covariance of the Sigma points after propagation, and add the process noise covariance to obtain the state prediction error covariance matrix. The calculation formula is:

[0063]

[0064] in, Here are the corresponding covariance weights, and T represents the transpose operation.

[0065] This embodiment obtains Figure 1 The linearization error in the UT transformation process shown affects the mean and covariance of the random variable.

[0066] S3: Perform the filtering update step for predictive auxiliary state estimation: Substitute the Sigma point into the measurement equation to obtain the measurement prediction value, and calculate the Kalman gain;

[0067] S4: Update the process noise covariance matrix: Instead of using the traditional update method that includes matrix subtraction, the process noise covariance matrix at the next moment is calculated using the Kalman gain and measurement residual calculated in step S3 through the equivalent additive update formula, thereby fundamentally ensuring that it always maintains positive semidefiniteness during the iteration process.

[0068] The equivalent additive update formula is expressed as follows:

[0069]

[0070] in, and These are the process noise covariance matrices before and after the update, respectively. The Kalman gain at the current time, calculated in step S3; Let be the measurement residual at the current moment, that is, the difference between the actual measurement value and the predicted measurement value, where These are actual measured values. To pass the measurement function The measurement prediction value obtained after propagating the Sigma point; The covariance matrix of the measurement residuals; This is an operator that retains only the diagonal elements of the matrix and sets the remaining elements to zero. This formula converts the subtraction term in the traditional update into an addition term equivalent to the addition term through Kalman gain and residual information, thereby eliminating the source of non-semidefinite risk in the algorithm flow.

[0071] In the equivalent additive update formula:

[0072] Covariance matrix of measurement residuals :

[0073] ;

[0074] in, This is the measurement value corresponding to the i-th Sigma point after propagation;

[0075] Kalman gain :

[0076] ;

[0077] in, Let be the cross-covariance matrix of the state and the measurement.

[0078] The numerical stability of the equivalent additive update formula lies in the application of the closure property of positive semi-definite matrices. The principle includes:

[0079] Of the three components on the right side of the formula, the first term As the covariance matrix of the previous time step, it is initialized to positive semi-definite at the start of the iteration and maintains this property in subsequent iterations through the update method of this invention; the second term ,because It is a positive semi-definite matrix with rank 1. After a linear transformation, its diagonal elements must be non-negative, therefore this term is a positive diagonal semi-definite matrix; the third term It is a typical quadratic form, due to the measurement residual covariance matrix Since it is positive semi-definite, the result of the transformation must also be positive semi-definite.

[0080] Finally, the updated The result is a linear sum of three positive semi-definite matrices, and mathematically it is strictly guaranteed to be a positive semi-definite matrix, thus avoiding the risk of the covariance matrix losing its positive semi-definiteness due to rounding errors and other issues in numerical calculations.

[0081] S5: Using the Kalman gain and measurement residual calculated in step S3, correct the current state prediction value and state prediction error covariance matrix obtained in step S2 to obtain the optimal state estimate value and its error covariance matrix at the current time.

[0082] Final optimal state estimate and its error covariance matrix The update and correction process follows the standard unscented Kalman filter update equation:

[0083]

[0084] Among them, although The update involves subtraction, but due to the equivalence of the Joseph form of covariance update, as long as It is semi-positive definite, after the update. It will also remain positive semi-definite, and this invention ensures that Its positive semi-definiteness ensures The positive semidefiniteness in the next iteration forms a complete numerically stable closed loop.

[0085] Example 2:

[0086] Based on the method of Embodiment 1, this embodiment provides a distribution network predictive auxiliary state estimation system based on an iterative process improvement, including:

[0087] The model building module is used to build a nonlinear discrete-time state-space model that describes the operating characteristics of the distribution network, including state transition equations and measurement equations.

[0088] The prediction execution module generates a set of Sigma points based on the state estimate and its error covariance matrix at the previous time step through unscented transformation, and substitutes the Sigma points into the state transition equation to calculate the state prediction value and the state prediction error covariance matrix at the current time step.

[0089] The filtering update module substitutes the Sigma point into the measurement equation to obtain the measurement prediction value and calculates the Kalman gain.

[0090] The matrix update module uses Kalman gain and measurement residuals to calculate the process noise covariance matrix at the next time step using an equivalent additive update formula.

[0091] The update and correction module uses Kalman gain and measurement residuals to correct the current state prediction value and the state prediction error covariance matrix, thereby obtaining the optimal state estimate value and its error covariance matrix at the current time.

[0092] Example 3:

[0093] To verify the effectiveness of the method of the present invention in improving the numerical stability of predictive auxiliary state estimation in distribution networks, the following simulation experiment was conducted in this embodiment:

[0094] Classic UKF-based predictive-aided state estimation methods with different scaling parameters are presented, and three tuning parameters are set for comparison. , and For simple testing, a standard IEEE-13 node three-phase distribution network without DG access was used, with the following topology: Figure 2 As shown.

[0095] In addition to choosing RMSE as the parameter for comparison of estimation results, the average weighted residuals were also used as the evaluation parameter:

[0096]

[0097]

[0098] In the formula: S H and S M These are the average weighted residuals of the estimation error and measurement error, respectively; m is the number of Monte Carlo simulations. It is the standard deviation of the measurement noise in the t-th simulation of the i-th measurement. S is the measurement data from the t-th simulation of the i-th measurement. H and S M The ratio is related to the strength of the state estimation result. The smaller the ratio, the better the state estimation effect. If the ratio is greater than 1, the state estimation is not as effective as the measurement. This represents the total measurement dimension of the system, i.e., the total number of measurement points in the distribution network; Indicates the first The system state estimation vector obtained from the simulation calculation; Indicates the first The system's true state vector is set in this simulation; Indicates the first In this simulation, based on the state estimation vector The first, obtained by calculation using a nonlinear measurement function The estimated value of each measurement; Indicates the first In this simulation, based on the true state vector The first, obtained by calculation using a nonlinear measurement function The theoretical true value of a measurement.

[0099] This embodiment involved 200 Monte Carlo experiments. Figure 3 S was shown H / SM The radar chart (%) shows the estimation results for each phase at each node.

[0100] The radar chart illustrates the performance of the four estimation methods. From Figure 3 As can be seen, the estimation effect of the method of this invention is concentrated in the center of the radar chart, and the performance of the weighted residual mean ratio is the best among the four methods. In this estimation example, Adjusting the parameters can improve the estimation performance of the UKF algorithm. Analysis of the presented results shows that gradually expanding the range... The parameters will make the estimation of node parameters more favorable.

[0101] The numerical stability of a state estimator refers to the gradual desensitization of the state estimate to the initial state values ​​and the gradual desensitization of the mean square error of the estimate to the mean square error matrix of the original estimate as the estimation time increases. To verify the numerical stability of the method of this invention in this test system, Figure 4 A comparison of the RMSE estimation accuracy of the Monte Carlo test is described. This test lasted 24 hours, with estimations performed every 5 minutes, accumulating 288 test results. The UKF-based predictive auxiliary state estimation still uses the aforementioned three tuning parameters for comparison. At 15:55, the parameters... The UKF estimation failed because the square root covariance was unavailable, forcing the estimation process to stop. When specific parameters are selected in the UKF estimation algorithm, the error covariance matrix often loses its positive semidefiniteness during propagation, leading to estimation failure, which reflects poor numerical stability. In this simple model of a small system, the amount of data and uncertainty are relatively small. Optimizing the UKF parameters can improve numerical stability and avoid estimation failures. However, as the system scales up, the traditional UKF algorithm, limited by error propagation itself, struggles to ensure the positive semidefiniteness of the error covariance matrix.

Claims

1. A power distribution network forecast-aided state estimation method based on an improved iterative process, characterized by, The method comprises the following steps: S1: establishing a nonlinear discrete-time state space model describing the operation characteristics of the power distribution network, including a state transition equation and a measurement equation; S2: based on the state estimation value and error covariance matrix of the previous time, generating a set of Sigma points through unscented transformation, and substituting the Sigma points into the state transition equation to calculate the state prediction value and state prediction error covariance matrix of the current time; S3: substituting the Sigma points into the measurement equation to obtain the measurement prediction value, and calculating the Kalman gain; S4: using the Kalman gain and measurement residual calculated in step S3, and through an equivalent additive update formula, calculating the process noise covariance matrix of the next time; S5: using the Kalman gain and measurement residual calculated in step S3, and correcting the state prediction value and state prediction error covariance matrix of the current time in step S2 to obtain the optimal state estimation value and error covariance matrix of the current time.

2. The method of claim 1, wherein, The nonlinear discrete-time state space model in step S1 is expressed as follows: ； where, is the discrete time step; is the total number of system nodes; is the known control input vector; is the m-dimensional measurement vector; is the nonlinear state transition function; is the nonlinear measurement function; is the process noise, modeling the uncertainty of the state transition model, whose covariance matrix is ; is the measurement noise, whose covariance matrix is .

3. The method of claim 2, wherein, Step S2 comprises: A1: based on the optimal state estimation of the last time and the error covariance matrix thereof , a set of Sigma points is generated according to the symmetric sampling principle ; A2: each Sigma point is propagated through the state transition function As input, the state transition function is applied to each Sigma point to obtain the propagated Sigma point set ; A3: Weighted average of the propagated Sigma points to obtain the state prediction wherein is the mean weight; A4: Calculate the weighted covariance of the propagated Sigma points and add the process noise covariance to obtain the state prediction error covariance matrix .

4. The method of claim 3, wherein, The state prediction error covariance matrix in step A4 is calculated as ； wherein, are the corresponding covariance weights, T denotes the transpose operation.

5. The method of claim 4, wherein, The expression of the equivalent additive update formula in step S4 is: ； wherein, and are the updated and pre-updated process noise covariance matrices, respectively; is the Kalman gain at the current time calculated in step S3; is the measurement residual at the current time, i.e. the difference between the actual measurement value and the predicted measurement value, wherein, is the actual measurement value, is the predicted measurement value obtained by the measurement function after propagating the Sigma points; is the covariance matrix of the measurement residual; is an operator that only retains the diagonal elements of a matrix and sets the remaining elements to zero.

6. The method of claim 5, wherein, In the equivalent additive update formula: Covariance matrix of measurement residuals : ； wherein, is the measurement value corresponding to the i-th propagated Sigma point. kalman gain : ； wherein, is the cross-covariance matrix of states and measurements.

7. The method of claim 6, wherein the method is based on an iterative process improvement of power distribution network forecast-assisted state estimation. The update principle of the equivalent additive update formula comprises: Of the three components on the right side of the formula, the first term As the covariance matrix of the previous time step, it is initialized to positive semi-definite at the start of the iteration and maintains this property in subsequent iterations through an update method; the second term ,because It is a rank-1 positive semi-definite matrix. After a linear transformation, its diagonal elements must be non-negative; therefore, this term is a diagonal positive semi-definite matrix. The third term... It is a typical quadratic form, due to the measurement residual covariance matrix Since it is positive semi-definite, the result of the transformation must also be positive semi-definite. Finally, the updated is the linear sum of three positive semidefinite matrices, the result is a positive semidefinite matrix.

8. The method of claim 7, wherein, the final state optimal estimate value in the step S5 and its error covariance matrix The update correction process of the final state optimal estimate value in the step S5 follows the unscented Kalman filter update equation: ； By guaranteeing positive semi-definiteness, it is ensured positive semi-definiteness in the next iteration, forming a complete numerically stable closed loop.

9. An improved power distribution network forecast aided state estimation system based on an iterative process, characterized by, The system for implementing the method of claim 1 comprises: A model establishing module for establishing a nonlinear discrete-time state space model describing the operation characteristics of the power distribution network, including a state transition equation and a measurement equation; A prediction executing module for, based on the state estimation value and error covariance matrix of the previous time, generating a set of Sigma points through unscented transformation, and substituting the Sigma points into the state transition equation to calculate the state prediction value and state prediction error covariance matrix of the current time; A filter updating module for substituting the Sigma points into the measurement equation to obtain the measurement prediction value, and calculating the Kalman gain; A matrix updating module for, using the Kalman gain and measurement residual, and through an equivalent additive update formula, calculating the process noise covariance matrix of the next time; An update correcting module for, using the Kalman gain and measurement residual, correcting the state prediction value and state prediction error covariance matrix of the current time to obtain the optimal state estimation value and error covariance matrix of the current time.

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