Power distribution network prediction-aided state estimation method and system based on iterative process improvement

Abstract

The application discloses a power distribution network prediction auxiliary state estimation method and system based on an improved iteration process, and the method comprises the following steps: establishing a nonlinear discrete time state space model; generating a group of Sigma points through an unscented transformation, and substituting the Sigma points into a state transition equation to calculate a state prediction value and a state prediction error covariance matrix at a current time; substituting the Sigma points into a measurement equation to obtain a measurement prediction value, and calculating a Kalman gain; calculating a process noise covariance matrix at a next time; and correcting the state prediction value and the state prediction error covariance matrix at the current time to obtain an optimal state estimation value and an error covariance matrix thereof. The application avoids the risk of losing semi-positive definiteness of the covariance matrix in the iteration process from the algorithm mechanism, significantly enhances the numerical stability and robustness of the UKF algorithm, and ensures reliable application in high-dimensional complex power distribution network state estimation.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of power grid, and relates to a power distribution network prediction aided state estimation technology, in particular to a power distribution network prediction aided state estimation method and system based on an iterative process improvement. BACKGROUND

[0002] With the wide access of dynamic elements such as distributed energy, electric vehicles and energy storage systems in the power distribution network, the dynamic characteristics of system operation are increasingly significant. The traditional static state estimation has been difficult to meet the demand for real-time tracking and short-term prediction of system evolution trend. Therefore, forecasting aided state estimation (FASE) emerges as the times require, as a standardized formulation of dynamic state estimation under the quasi-steady state characteristics of the power distribution network. It realizes the prediction and correction of the system state at the next moment by establishing a model of the evolution of the system state over time, and provides key technical support for the preventive control and optimal scheduling of the active power distribution network.

[0003] Among the many implementation algorithms of FASE, the algorithm based on Kalman filter (KF) and its nonlinear extension is most widely used. In particular, the unscented Kalman filter (UKF) is considered as an efficient tool for dealing with nonlinear models of power distribution networks, because it uses unscented transformation (UT) to approximate the probability distribution of nonlinear functions, avoids the complex calculation of the Jacobian matrix of extended Kalman filter (EKF), and usually has higher estimation accuracy.

[0004] However, the standard UKF algorithm exposes a serious numerical stability problem when applied to large-scale, high-dimensional actual power distribution network systems. The problem is caused by the update calculation of the error covariance matrix in the iterative process of the algorithm. Specifically, in the propagation and update steps of the covariance matrix, there is a subtraction operation of matrices. In an ideal infinite precision calculation environment, this operation will not destroy the positive semi-definiteness of the covariance matrix. But in the actual finite precision computer operation, due to the accumulation of rounding errors, after several iterations, the calculated covariance matrix may lose its inherent positive semi-definiteness, and even have negative diagonal elements (variance is negative), which is physically meaningless. Once the covariance matrix loses its positive semi-definiteness, the filtering algorithm will diverge, resulting in complete failure of the estimation process. This defect greatly limits the reliable application of UKF in complex power distribution network FASE, and is a technical bottleneck that needs to be overcome in the field. SUMMARY

[0005] Inventive purpose: In order to solve the problem that the existing state estimation algorithm based on unscented Kalman filter may cause the error covariance matrix to lose semi-definiteness due to matrix subtraction operation when processing high-dimensional distribution network model, thereby causing numerical instability and estimation failure, a power distribution network prediction auxiliary state estimation method and system based on iterative process improvement are provided.

[0006] Technical scheme: In order to achieve the above purpose, the present application provides a power distribution network prediction auxiliary state estimation method based on iterative process improvement, comprising the following steps:

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

[0008] S2: Based on the state estimation value and its error covariance matrix at the previous time, generate a set of Sigma points through unscented transformation, and substitute 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;

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

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

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

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

[0013]

[0014] wherein, 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, which models the uncertainty of the state transition model, and its covariance matrix is ; is the measurement noise, and its covariance matrix is .

[0015] Further, the step S2 comprises:

[0016] 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 ;

[0017] A2: taking each Sigma point as input, the state transition function is used for nonlinear propagation to obtain a set of propagated Sigma points ;

[0018] A3: weighted average is performed on the propagated Sigma points to obtain the state prediction value , wherein is the mean weight;

[0019] A4: the weighted covariance of the propagated Sigma points is calculated, and the process noise covariance is added to obtain the state prediction error covariance matrix .

[0020] Further, the calculation formula of the state prediction error covariance matrix in the step A4 is:

[0021]

[0022] wherein is the corresponding covariance weight, and T represents the transposition operation.

[0023] Further, the expression of the equivalent additive update formula in the step S4 is:

[0024]

[0025] wherein and are the process noise covariance matrices after and before the update respectively; is the Kalman gain calculated in the 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 measurement prediction value obtained by propagating the Sigma points through the measurement function ; is the covariance matrix of the measurement residual; is an operator that only retains the diagonal elements of the matrix and sets the remaining elements to zero.

[0026] ​Further, the equivalent additive update formula is:

[0027] Covariance matrix of measurement residual

[0028]

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

[0030] Kalman gain

[0031]

[0032] wherein, is the cross-covariance matrix of state and measurement.

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

[0034] Among the three component terms on the right side of the formula, the first term is the covariance matrix at the previous moment, which is initialized as semi-definite at the beginning of iteration, and maintains this property in subsequent iterations through the update method; the second term is a diagonal semi-definite matrix, because is a semi-definite matrix with rank 1, and its diagonal elements are necessarily non-negative after linear transformation, so this term is a diagonal semi-definite matrix; the third term is a typical quadratic form, and since the measurement residual covariance matrix is semi-definite itself, the transformation result is also semi-definite;

[0035] Finally, the updated is the linear addition of three semi-definite matrices, and the result is a semi-definite matrix.

[0036] Further, the update and correction process of the final state optimal estimation value and its error covariance matrix in step S5 follows the unscented Kalman filter update equation:

[0037]

[0038] By ensuring the semi-definiteness of , the semi-definiteness of in the next round of iteration is ensured, thereby forming a complete numerical stable closed loop.

[0039] The application also provides a power distribution network prediction-aided state estimation system based on an improved iteration process, comprising:

[0040] ​​​​A model establishing module is configured to establish a nonlinear discrete-time state-space model describing operation characteristics of the power distribution network, including a state transition equation and a measurement equation;

[0041] A prediction performing module is configured to generate a set of Sigma points by means of unscented transformation based on state estimation values and error covariance matrices of a previous time point, and calculate state prediction values and state prediction error covariance matrices of a current time point by substituting the Sigma points into the state transition equation;

[0042] A filter updating module is configured to obtain measurement prediction values by substituting the Sigma points into the measurement equation, and calculate a Kalman gain;

[0043] A matrix updating module is configured to calculate a process noise covariance matrix of a next time point by means of an equivalent additive update formula using the Kalman gain and measurement residuals;

[0044] An update correcting module is configured to correct the state prediction values and the state prediction error covariance matrices of the current time point using the Kalman gain and the measurement residuals, so as to obtain optimal state estimation values and error covariance matrices of the current time point.

[0045] Beneficial effects: Compared with the prior art, the propagation process of the process noise covariance matrix is improved in the filter updating step of the prediction-aided state estimation; instead of updating the covariance by means of direct matrix subtraction which may introduce a non-semidefinite risk, an increment term which is equivalent and semidefinite is constructed to update the covariance matrix using the calculated Kalman gain and residual information. The numerical stability and robustness of the UKF algorithm are significantly enhanced by avoiding the risk of losing the semidefinite property of the covariance matrix in the iteration process from the algorithm mechanism, and the prediction-aided state estimation effect of the power distribution network is effectively guaranteed, so that the reliable application in the high-dimensional complex power distribution network state estimation is ensured. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 A schematic diagram of the mean and covariance of the linearized error-affected random variable;

[0047] Figure 2 An improved IEEE-13 node topology structure schematic diagram;

[0048] Figure 3 A weighted residual average ratio radar chart;

[0049] Figure 4 A comparison diagram of test numerical stability under an IEEE-13 node system. DETAILED DESCRIPTION

[0050] The present application will be further clarified by the following examples, which should be considered as merely illustrative of the present application and not in limitation of the present application, and which will be understood to be within the scope of the present application as defined by the appended claims. The following examples are presented to more fully illustrate the application and are not intended to limit the scope of the application. Numerous modifications of the application will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments without departing from the scope of the application. In the following examples, all temperatures are in degrees Celsius unless otherwise indicated. The examples are presented by way of explanation of the application, not limitation, and the examples do not constitute a definition of the entire scope of protection to be afforded the application.

[0051] Example 1

[0052] The present embodiment provides a power distribution network prediction-aided state estimation method based on an improved iterative process, comprising the following steps:

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

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

[0055]

[0056] wherein, is the discrete-time step; is the total number of system nodes, the n-dimensional state vector of the system, the elements of which include the voltage amplitude and phase angle of all nodes of the power distribution network; is the known control input vector, such as the transformer tap position or the capacitor switching state; is the m-dimensional measurement vector, including the node injection power, branch power flow, and other information uploaded by the SCADA system; is the nonlinear state transition function, which is essentially a system power flow calculation based on the previous time state and input ; is the nonlinear measurement function, which calculates the corresponding theoretical measurement value according to the current state ; is the process noise, which models the uncertainty of the state transition model, and its covariance matrix is ; is the measurement noise, and its covariance matrix is .

[0057] S2: Perform the prediction step of the prediction-aided state estimation: based on the state estimation value and its error covariance matrix at the previous time, 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;

[0058] Step S2 includes:

[0059] A1: Sigma point generation: based on the optimal state estimation at the previous time and its error covariance matrix , according to the symmetric sampling principle to generate a set of Sigma points ;

[0060] A2: Sigma point propagation: propagate each Sigma point as input through the state transition function nonlinearly to obtain a set of propagated Sigma points ;

[0061] A3: State prediction value calculation: weighted average of the propagated Sigma points to obtain the state prediction value , wherein is the mean weight;

[0062] A4: State prediction error covariance calculation: calculate the weighted covariance of the propagated Sigma points, and add the process noise covariance to obtain the state prediction error covariance matrix , the calculation formula is:

[0063]

[0064] wherein is the corresponding covariance weight, and T represents the transpose operation.

[0065] The embodiment obtains Figure 1 the mean and covariance of the linearization error affecting random variables in the UT transformation process.

[0066] S3: Perform filter update step of prediction aided 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 containing matrix subtraction operation, the Kalman gain and measurement residual calculated in step S3 are used to calculate the process noise covariance matrix of the next time through the equivalent additive update formula, so as to fundamentally ensure that it always maintains semi-definiteness in the iteration process;

[0068] The expression of the equivalent additive update formula is:

[0069]

[0070] wherein and are the process noise covariance matrices after and before updating, respectively; is the Kalman gain of 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 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.

[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 the measurement residual calculated in step S3, the state prediction value and the state prediction error covariance matrix of the current time in step S2 are corrected to obtain the optimal state estimation value and its error covariance matrix of the current time.

[0082] the final optimal state estimation value and its error covariance matrix The update correction process of the final optimal state estimation value

[0083]

[0084] Although the update of the final optimal state estimation value contains subtraction, due to the covariance update equivalence in Joseph form, as long as the final optimal state estimation value is semi-positive definite, the updated final optimal state estimation value will also remain semi-positive definite. The present application ensures the semi-positive definiteness of the final optimal state estimation value and the semi-positive definiteness of the final optimal state estimation value in the next round of iteration, thereby forming a complete numerical stable closed loop.

[0085] Embodiment 2:

[0086] Based on the method of embodiment 1, the present embodiment provides a power distribution network prediction-aided state estimation system based on an improved iteration process, comprising:

[0087] a model establishment module for establishing a nonlinear discrete-time state space model describing the operating characteristics of the power distribution network, including a state transition equation and a measurement equation;

[0088] a prediction execution module for generating a set of Sigma points through unscented transformation based on the state estimation value and its error covariance matrix of the previous time, and substituting the Sigma points into the state transition equation to calculate the state prediction value and the state prediction error covariance matrix of the current time;

[0089] a filter update module for substituting the Sigma points into the measurement equation to obtain the measurement prediction value, and calculating the Kalman gain;

[0090] a matrix update module for calculating the process noise covariance matrix of the next time through the equivalent additive update formula using the Kalman gain and the measurement residual;

[0091] an update correction module for correcting the state prediction value and the state prediction error covariance matrix of the current time using the Kalman gain and the measurement residual to obtain the optimal state estimation value and its error covariance matrix of the current time.

[0092] Embodiment 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 radar chart, respectively, showing the estimation performance of each node for each phase.

[0100] The radar chart shows the performance of the four estimation methods. It can be seen from Figure 3 that the estimation performance of the method representing the present application is concentrated in the center of the radar chart, and the average value of the weighted residual error ratio is the best among the four methods. In this estimation example, the adjustment of the parameters can improve the estimation performance of the UKF algorithm. From the analysis of the results shown, gradually expanding parameters will make it more advantageous to estimate the node parameters.

[0101] The numerical stability of the state estimator refers to the fact that as the estimation time increases, the state estimation gradually becomes independent of the initial state value, and the mean square error of the estimation gradually becomes independent of the original estimation mean square error matrix. In order to verify the numerical stability of the method of the present application in the test system, Figure 4 the comparison of the RMSE estimation accuracy of the Monte Carlo test is described, which is a 24-hour test for one day, with an estimation every 5 minutes, and a total of 288 test results. The prediction-aided state estimation based on UKF still uses the three tuning parameters described above for comparison. At 15:55, the UKF estimation of the parameter fails due to the unavailability of the square root covariance, forcing the estimation process to stop. When a specific parameter is selected in the UKF estimation algorithm, the error covariance matrix often has the possibility of losing its positive semi-definiteness during the propagation process, leading to estimation failure, which is a manifestation of poor numerical stability. In this simple model of a small system, the amount of data and uncertainty are relatively small. By optimizing the parameters of the UKF, the numerical stability can be improved to avoid estimation failure, but when the system size continues to expand, the traditional UKF is limited by the error propagation of the algorithm itself and is difficult to ensure the positive semi-definiteness 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 operating 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 the 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; 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 after propagating the Sigma points through the measurement function ; and 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. 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; The update principle of the equivalent additive update formula includes: Among the three terms on the right side of the equation, the first term is the covariance matrix at the previous time, which is initialized to be positive semi-definite at the beginning of iteration and remains this property in the following iterations through the update method; the second term is a rank-1 positive semi-definite matrix, which is diagonal positive semi-definite after linear transformation because is a rank-1 positive semi-definite matrix, and its diagonal elements are non-negative after linear transformation; the third term is a typical quadratic form, which is also positive semi-definite because is positive semi-definite by itself. Finally, the updated is the linear sum of three positive semidefinite matrices, the result is a positive semidefinite matrix.

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, The 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 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.

6. 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 operating 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 filtering 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 the equivalent additive update formula, calculating the process noise covariance matrix of the next time; An updating correcting module for, using the Kalman gain and measurement residual, and 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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