Power distribution network adaptive state estimation method and system based on interactive multiple models

Abstract

The invention discloses a power distribution network adaptive state estimation method and system based on interactive multiple models, and relates to the field of power system state estimation, and the method comprises the steps: building a linear model through the dynamic state estimation of a power distribution network, and converting the linear model into a nonlinear model; using an adaptive method to improve a dynamic estimator, and embedding an interactive multiple model; estimating the reconstruction state of the power distribution network through an improved self-adaptive dynamic estimator, and eliminating the nonlinear error of the sudden load change of the power distribution network; the interactive multiple model selects a matching model according to real-time measurement data, and all improved dynamic estimators are weighted. According to the method, the dynamic characteristics and uncertainty of the system are comprehensively captured, the problems of network topology structure change and load sudden change are solved, the calculation complexity of EKF and UKF is reduced, the calculation burden is reduced while high precision is kept, and the estimation precision is improved.

Description

Technical Field

[0001] The present invention relates to the field of power system state estimation, and in particular to a distribution network adaptive state estimation method and system based on interactive multiple models. Background Art

[0002] With the integration of a large number of renewable energy sources, the operation mode of the distribution network is becoming increasingly complex. The state estimation of the distribution network is very important for its optimal scheduling, safety assessment, and market competition. Currently, state estimation is divided into static state estimation (SSE) and dynamic state estimation (DSE). SSE mainly uses methods such as least squares to iterate and optimize the residual between measurement data and system models to obtain the best state estimation result. However, due to the increase in renewable energy penetration and the increase in the time-varying and nonlinear nature of the distribution network, SSE cannot obtain the distribution network state in real time to make optimal scheduling decisions.

[0003] DSE can reflect how the voltage and phase angle states of nodes in a power system change over time. Because DSE can address time-varying characteristics, it is currently widely used. The three main DSE methods include extended Kalman filtering (EKF), unscented Kalman filtering (UKF), and particle filtering (PF).

[0004] To address the nonlinearities caused by load and renewable energy fluctuations in distribution networks, extended Kalman filtering (EKF) is a commonly used method. It approximates the Kalman filtering process by linearizing nonlinear models. EKF approximates nonlinear functions through Taylor series expansion. This method works well for systems with moderately high nonlinearity, but in highly nonlinear systems, linearization errors can lead to cumulative estimation errors. Furthermore, EKF requires the calculation of the Jacobian matrix, which can be computationally complex and, in some cases, inaccurate.

[0005] The unscented Kalman filter (UKF) requires more computing resources when generating sigma points and performing nonlinear function propagation, resulting in a relatively high computational cost. The performance of the UKF depends largely on the selection of its parameters (such as the choice of sampling points). Improper parameter settings may reduce filtering performance, and the selection of these parameters often needs to be adjusted according to specific applications, which lacks flexibility. The UKF has high requirements for the accuracy of the initial state estimate and the statistical characteristics of the noise. Errors may accumulate during the estimation process, affecting the long-term estimation accuracy.

[0006] In addition, the computational complexity of the particle filter (PF) increases with the number of particles, especially in high-dimensional state spaces. This leads to a significant increase in computational complexity, limiting its application in high-dimensional systems. Particle filters may encounter the problem of particle degradation, that is, the weights of most particles are very small, resulting in insufficient samples. During the resampling process, large-weight particles are replicated multiple times and small-weight particles are discarded, which may lead to a loss of sample diversity and, in severe cases, may cause the algorithm to diverge. It is a recursive filter based on the Monte Carlo method that represents the posterior probability of random events through a set of weighted random samples (called particles) and estimates the state of the dynamic system from a noisy or incomplete observation sequence. The particle filter can be applied to any state space model. It does not rely on the assumptions of linearity and Gaussian noise of the system model, and is therefore particularly suitable for nonlinear and non-Gaussian dynamic systems. Summary of the Invention

[0007] In view of the above existing problems, the purpose of the present invention is to propose an adaptive dynamic state estimation method based on interacting multiple models (IMM) to solve the nonlinearity, time-varying and computational complexity problems of traditional methods.

[0008] IMM-DSE uses adaptive methods to improve the EKF and UKF, enabling self-optimization of the estimator model and parameters. This enhances state estimation performance in the appropriate operating environment, addressing network changes and sudden load fluctuations. Furthermore, the proposed IMM-DSE includes two improved adaptive dynamic state estimators, each suitable for different scenarios involving distribution network changes.

[0009] In order to solve the above technical problems, a distribution network adaptive state estimation method based on interactive multiple models is proposed, including:

[0010] A linear model is constructed through distribution network dynamic state estimation and converted into a nonlinear model; an adaptive method is used to improve the dynamic estimator and embed an interactive multi-model; the distribution network reconstruction state is estimated through the improved adaptive dynamic estimator and the nonlinear error caused by sudden changes in the distribution network load is eliminated; the interactive multi-model selects a matching model based on real-time measurement data and weights all improved dynamic estimators.

[0011] As a preferred solution of the interactive multiple model-based adaptive state estimation method for distribution network of the present invention, wherein: the adaptive method improves the dynamic estimator including calculating the distribution network DSE linear model and converting the linear model into a nonlinear model by a preset algorithm;

[0012] The improved dynamic estimator includes an adaptive extended Kalman filter and an adaptive unscented Kalman filter.

[0013] As a preferred solution of the distribution network adaptive state estimation method based on interactive multiple models described in the present invention, the distribution network reconstruction state estimation includes: after obtaining the nonlinear model, predicting the system state, calculating the covariance matrix of the predicted state and the error, obtaining the actual measurement value of the system, modifying the predicted state, and obtaining the current estimated state;

[0014] According to the current estimation state, the adaptive extended Kalman filter calculates the transition matrix in real time through the recursive augmented least squares method, and assigns weights and estimates the noise through the improved Sage-Husa noise statistics estimator.

[0015] As a preferred solution of the adaptive state estimation method for distribution network based on interactive multiple models described in the present invention, wherein: the elimination of nonlinear errors caused by sudden changes in load of distribution network includes: adaptive unscented Kalman filtering adopts proportional combined with symmetric sampling method to obtain a group of σ points to form a σ point set, introduces proportional factors, calculates weights and assigns them to the mean and covariance;

[0016] The σ point set is used in the prediction process model, the weighted sum and covariance of each point are calculated to obtain the predicted state, the covariance matrix of the predicted state value and the actual measurement value is calculated, and the filter gain and estimated covariance matrix are calculated based on the covariance matrix;

[0017] Among them, σ points are a set of sample points representing the probability distribution of system state variables.

[0018] As a preferred solution of the distribution network adaptive state estimation method based on interactive multiple models described in the present invention, wherein: the elimination of nonlinear errors caused by sudden changes in the load of the distribution network further includes using an adaptive factor to modify the covariance matrix and adjust the filter gain;

[0019] When the measurement residuals increase due to sudden load changes, the adaptive factor controls the covariance matrix and eliminates nonlinear errors through the improved Sage-Husa noise estimator.

[0020] As a preferred solution of the adaptive state estimation method for distribution network based on interactive multiple models described in the present invention, the interactive multiple models include embedding adaptive extended Kalman filter and adaptive unscented Kalman filter into the interactive multiple models, tracking the changing state of the distribution network in an adaptive manner, initializing the input value of each filter, and defining the model that matches the operating environment as the matching model. The mixed probability used for interactive initialization is:

[0021]

[0022] in, is the mixing probability used for interaction initialization, π (i,j) is the model conversion probability, indicating that the matching model changes from i to j; is the probability of matching model i at time k, r is the number of models; i and j represent the indexes of different models, is the mixing probability normalization constant of model j, which is used to calculate the mixing probability.

[0023] After calculating the mixing probabilities, all previous time-step estimates are used to initialize the model:

[0024]

[0025]

[0026] in, k + Initialization state prediction of model j at time 1, is the k-time model i The state estimation, is the mixing probability used for interaction initialization. is the initialization state covariance matrix, For the model i The state covariance matrix at time k is, is the outer product of state deviations, is the initialization state prediction of model j at time k.

[0027] After initialization, multi-model filtering is performed, and the filter performs DSE separately, and the measurement residual of each model is obtained. The covariance matrix of Calculate the likelihood function of the matching model

[0028]

[0029] in, are the measurement residuals for each model, is the covariance matrix, is the likelihood function, which indicates the likelihood of matching the model; is the measurement matrix, T is the transposed matrix, is the covariance of the model matching i, is the normalization factor of the Gaussian distribution, is the Mahalanobis distance, which measures the measurement residual In covariance The deviation below.

[0030] As a preferred solution of the method for adaptive state estimation of distribution network based on interactive multiple models according to the present invention, the interactive multiple models further include updating the model probability according to the likelihood function:

[0031]

[0032] in, is model i in k + The updated model probability at time 1, c is the normalization constant, is the likelihood function, r is the total number of models, After the update + 1 model's mixing probability normalization constant, is the mixing probability normalization constant for model j;

[0033] Calculate the weighted sum of all filter results to get the result of IMM-DSE:

[0034]

[0035] in, It is k + The final state estimate at time 1, i is the model index, representing a model in the IMM algorithm, r is the total number of models, is the state estimation result of model i, is model i in k + The updated model probability at time 1, is the final state covariance matrix, Model i In k + The state covariance matrix at time 1, is the outer product of state deviations.

[0036] Another object of the present invention is to provide a distribution network adaptive state estimation system based on interactive multiple models.

[0037] As a preferred solution of the interactive multiple model-based distribution network adaptive state estimation system of the present invention, it is characterized by comprising a nonlinear conversion module, an improved dynamic estimation module, and an interactive multiple model module;

[0038] The nonlinear conversion module is responsible for converting the linear model constructed by the dynamic state estimation of the distribution network into a nonlinear model. By calculating the distribution network DSE linear model and using a preset algorithm to achieve linear to nonlinear conversion, it provides an accurate model basis for subsequent state estimation.

[0039] The improved dynamic estimation module includes an adaptive extended Kalman filter unit and an adaptive unscented Kalman filter unit, which performs distribution network reconstruction state estimation and eliminates nonlinear errors caused by sudden load changes;

[0040] Predict system states and calculate the covariance matrix of predicted states and errors;

[0041] Get the actual measurement value of the system, modify the predicted state, and get the current estimated state;

[0042] The adaptive extended Kalman filter calculates the transition matrix in real time through the recursive augmented least squares method and uses the improved Sage-Husa noise statistics estimator to assign weights and estimate the noise;

[0043] Adaptive unscented Kalman filter uses proportional and symmetric sampling to obtain a set of points, calculates weights and assigns them to the mean and covariance to eliminate nonlinear errors;

[0044] The interactive multiple model module is responsible for selecting a matching model based on real-time measurement data and weighting all improved dynamic estimators;

[0045] The adaptive extended Kalman filter and the adaptive unscented Kalman filter are embedded in the interactive multi-model to track the changing state of the distribution network.

[0046] Initialize the input value of each filter and define the model that matches the operating environment as the matching model;

[0047] Calculate the mixing probability for model initialization;

[0048] Perform multi-model filtering and calculate the likelihood function of the matching model;

[0049] Update the model probability according to the likelihood function;

[0050] Calculate the weighted sum of all filter results to get the final IMM-DSE result.

[0051] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and is characterized in that when the processor executes the computer program, the steps of the distribution network adaptive state estimation method based on interactive multiple models are implemented.

[0052] A computer-readable storage medium having a computer program stored thereon, characterized in that when the computer program is executed by a processor, the steps of the distribution network adaptive state estimation method based on interactive multiple models are implemented.

[0053] Beneficial effects of the present invention: (1) The present invention integrates multiple dynamic models through an interactive multi-model framework, which can more comprehensively capture the dynamic characteristics and uncertainties of the system. This adaptive method improves the EKF and UKF, realizes the self-optimization of the model and parameters in the estimator, and enhances the state estimation performance in the corresponding operating environment, solving the problems of network topology changes and load mutations.

[0054] (2) IMM-DSE reduces the computational complexity of EKF and UKF through adaptive methods, making these methods more efficient in dealing with network changes and load mutations. Compared with the high computational complexity of particle filtering (PF), IMM-DSE reduces the computational burden while maintaining high accuracy.

[0055] (3)IMM-DSE demonstrates better estimation accuracy and convergence speed than traditional methods in the case study, especially when dealing with nonlinear and time-varying problems in the distribution network. IMM-DSE can dynamically modify the model noise statistics to cope with load fluctuations under normal conditions, thereby improving the estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0057] Figure 1 An overall flow chart of a distribution network adaptive state estimation method based on interactive multiple models provided by one embodiment of the present invention.

[0058] Figure 2 An embodiment of the present invention provides an improved IEEE 33-node distribution network based on an interactive multiple-model adaptive state estimation method for distribution networks.

[0059] Figure 3This is a state estimation result of the voltage amplitude of node 6 under load mutation conditions of the distribution network adaptive state estimation method based on interactive multiple models provided by an embodiment of the present invention.

[0060] Figure 4 This is a state estimation result of the voltage phase angle of node 6 under load mutation conditions of a distribution network adaptive state estimation method based on interactive multiple models provided by an embodiment of the present invention.

[0061] Figure 5 The present invention provides a comparison of the state estimation performance of the voltage amplitude at node 6 under load mutation of a distribution network adaptive state estimation method based on interactive multiple models provided by one embodiment of the present invention.

[0062] Figure 6 The present invention provides a comparison of the state estimation performance of the voltage phase angle of node 6 under load mutation of the distribution network adaptive state estimation method based on interactive multiple models provided by one embodiment of the present invention.

[0063] Figure 7 A system solution module diagram of a distribution network adaptive state estimation system based on interactive multiple models provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0064] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, the following detailed description of the specific embodiments of the present invention is given in conjunction with the accompanying drawings. It is obvious that the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in this field without creative work should fall within the scope of protection of the present invention.

[0065] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0066] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it individually or selectively refer to an embodiment that is mutually exclusive of other embodiments.

[0067] The present invention is described in detail with reference to schematic diagrams. For ease of illustration, cross-sectional views of device structures may be partially enlarged and not to scale when describing embodiments of the present invention. Furthermore, the schematic diagrams are merely illustrative and should not limit the scope of the present invention. Furthermore, in actual production, the three-dimensional dimensions of length, width, and depth should be included.

[0068] In the description of the present invention, it should be noted that the terms "upper, lower, inner, and outer" and other references to orientations or positional relationships are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first, second, or third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0069] In this disclosure, unless otherwise specified or limited, the terms "mounted," "connected," and "connected" should be interpreted broadly. For example, they may refer to fixed, removable, or integral connections. They may also refer to mechanical, electrical, or direct connections, indirect connections through an intermediary, or internal communication between two components. Those skilled in the art will understand the specific meanings of these terms in this disclosure.

[0070] Example 1, with reference to Figure 1 , which is the first embodiment of the present invention, provides a distribution network adaptive state estimation method based on interactive multiple models, comprising:

[0071] S1: Construct a linear model through dynamic state estimation of the distribution network and convert it into a nonlinear model.

[0072] Furthermore, the linear model of the distribution network DSE is calculated and converted into a nonlinear model through a preset algorithm.

[0073] Specifically, the traditional distribution network DSE linear model

[0074] The mathematical model of DSE consists of the process equation (1) and the measurement equation (2), as shown below:

[0075] x k+1 =f(x k )+ω k (1)

[0076] y k =h(x k )+v k (2)

[0077] Among them, x k+1 and xk They represent the system states at time k+1 and time k respectively, f is a function describing the dynamic process of the system, ω k is the noise vector in the process equation, y k , h and v k is the measured value, measurement function and measurement noise; f and h are usually nonlinear, ω k and v k is Gaussian white noise, as shown below:

[0078]

[0079] Among them, Q k and R k Yes k and v k The covariance matrix of δ k-j is the Kronecker-δ function, ω k and ω j The expected value of the outer product.

[0080] In an optional embodiment of the present invention, extended Kalman filtering (EKF) can be used as the most basic DSE method, which is applicable to linear models. The linearized model is expressed as:

[0081] x k+1 =F k x k +G k +ω k (4)

[0082] y k =H k x k +v k (5)

[0083] Among them F k is the state transition matrix at time k; G k is the input matrix; H k is the measurement matrix.

[0084] In an optional embodiment of the present invention, an adaptive H∞ cubature Kalman filter may be used, specifically:

[0085] Cubic Kalman Filter (CKF): The CKF is a state estimation method for nonlinear systems that approximates the probability density distribution of nonlinear functions using the cubic rule. It propagates the state mean and covariance through a set of carefully selected sampling points (called cubic points), avoiding the complexity of calculating the Jacobian matrix required in the traditional extended Kalman filter (EKF) and is suitable for high-dimensional nonlinear systems. The H∞CKF is used as one of the filters in the IMM framework, combined with the adaptive extended Kalman filter (AEKF) and the adaptive unscented Kalman filter (AUKF) to jointly handle dynamic state estimation in distribution networks.

[0086] Since the topology and load of the distribution network often change, the dynamic model is difficult to obtain by linearizing the process equation (1);

[0087] In the present invention, the Holt two-parameter exponential smoothing method is selected to replace the linearization module of the process equation, as shown in the following formula:

[0088]

[0089] Among them, the estimated state and predicted state at time k are respectively and represents; α and β are smoothing parameters. k and b k is the transition parameter.

[0090] The linearized process model is:

[0091]

[0092] F is the state transition matrix, G k is the input vector at time k, I is the identity matrix, is the state prediction value, α and β are smoothing parameters, a k and b k is the transition parameter.

[0093] Thus, the Holt two-parameter exponential smoothing method uses a recursive algorithm to calculate the state transition matrix and the input matrix, rather than simply representing them with constants. Therefore, through iteration, the function fitted by the Holt two-parameter exponential smoothing method can get closer and closer to the true nonlinear relationship.

[0094] S2: Use adaptive methods to improve the dynamic estimator and embed interactive multiple models; use the improved adaptive dynamic estimator to perform distribution network reconstruction state estimation and eliminate the nonlinear error of distribution network load mutation.

[0095] To address the time-varying and nonlinear problems of distribution networks, a DSE method based on IMM is proposed. Two dynamic estimators are improved using an adaptive method and embedded into the IMM framework.

[0096] Furthermore, the improved dynamic estimator includes an adaptive extended Kalman filter and an adaptive unscented Kalman filter.

[0097] After obtaining the nonlinear model, the system state is predicted, and the covariance matrix of the predicted state and error is calculated. The actual measurement value of the system is obtained, the predicted state is modified, and the current estimated state is obtained.

[0098] According to the current estimation state, the adaptive extended Kalman filter calculates the transition matrix in real time through the recursive augmented least squares method, and assigns weights and estimates the noise through the improved Sage-Husa noise statistics estimator.

[0099] Specifically, in the prediction step, the covariance matrix of the predicted state and its error can be calculated simultaneously. The predicted state is shown as follows:

[0100]

[0101] Among them, F k is the state transition matrix at time k; G k is the input matrix; the estimated state at time k is The predicted state at time k+1 is

[0102] The covariance matrix of the forecast errors is given by The calculation method is as follows:

[0103]

[0104] in, is the covariance of the estimation error at the previous moment t, x k+1 is the system state at time k+1, Q k is the Gaussian white noise ω in equation (3) k The covariance matrix of .

[0105] After obtaining the measurement results, the predicted state is modified through equations (10) to (12) to complete the state estimation at this time.

[0106]

[0107] Among them, K k+1 is the gain matrix of the Kalman filter, H k is the measurement matrix, is the estimated state at time k+1, y k+1is the measurement value at time k+1, R k is the Gaussian white noise v in formula (3) k The covariance matrix of , I is the identity matrix, is the covariance matrix of the state estimation error at time k+1.

[0108] In fact, the dynamic characteristics of the distribution network make the model obtained by the Holt method inaccurate. Therefore, the present invention proposes an adaptive EKF (AEKF) method that combines recursive enhanced least squares method and improved Sage-Husa noise estimator.

[0109] The recursive augmented least squares method uses model uncertainty to calculate the transition matrix in real time. Simultaneously, the fading memory exponential weighting method is introduced into the Sage-Husa noise statistics estimator to give more weight to new data and estimate the time-varying system noise. In the AEKF, the covariance matrix of the state transition matrix and the process noise is calculated as follows:

[0110] State transition matrix F k Calculation:

[0111]

[0112] Among them, L k is the gain matrix of the recursive enhanced least squares method at time k, and ψ is the forgetting factor (0<ψ<1).

[0113] The covariance matrix Q of the process noise k Calculation

[0114]

[0115] d k-1 =(1-φ) / (1-φ k ) (16)

[0116] Among them, Q k is the process noise covariance matrix at time k, d k-1 is the forgetting factor at time k-1, Q k-1 is the process noise covariance matrix at time k-1, K k is the Kalman gain matrix at time k, r k is the measurement residual at time k, is the covariance matrix of the state estimation error at time k. φ is another forgetting factor (0<φ<1).

[0117] According to equations (13) to (16), DSE uses F k and Q kModified with relevant information. The state transition matrix is ​​treated as an estimated variable in the AEKF to improve the performance of online parameter calculation.

[0118] It should also be noted that the adaptive unscented Kalman filter of the present invention adopts a "proportional + symmetric" sampling method to obtain σ points (i.e., a set of sample points representing the probability distribution of the system state variables). "Symmetric" means that the σ points are symmetrically distributed around the state mean to ensure that the statistical characteristics of the distribution are captured. "Proportional" means that the offset distance of the σ points is controlled by a proportional factor so that the distribution range matches the covariance scale. Among them, the σ points are a set of carefully selected sample points used to approximately describe the probability distribution of the system state variables. These points are generated by performing a specific transformation on the current estimated mean and covariance of the state variables. The main purpose is to capture the statistical characteristics of the state distribution (such as mean and covariance) in nonlinear systems so that more accurate posterior estimates can be obtained after transformation through nonlinear functions.

[0119] The details are as follows:

[0120]

[0121] Where n is the dimension of the state, is the scale factor; Represents the distribution of σ points and For Gaussian distribution, κ = 3-n; yes The ith column of ; the σ point set formed in this way is denoted by χ k express.

[0122] According to the scale factor ζ, the weight W used to calculate the average value is obtained m,i , and the weights W used to calculate the covariance c,i , as shown below:

[0123]

[0124] Among them, ζ = 2 is the optimal value of the Gaussian distribution, because it can make the unscented transform better match the fourth-order moment of the Gaussian distribution when calculating the covariance, reduce the high-order approximation error, and improve the accuracy of state estimation.

[0125] In the prediction phase, the σ point set is first applied to the process model.

[0126] χ k+1|k,i =F k χ k,i +G k (19)

[0127] Among them, χ k,i represents χ kThe i-th element of the point set (the σ point set generated by the ratio + symmetry method is recorded as χ k ), χ k+1|k,i represents χ k+1|k The i-th element of the point set, χ k+1|k The point set is obtained by substituting χ into the process model. k Obtained by point set.

[0128] The predicted state is χ k+1∣k The weighted sum of each point is as follows:

[0129]

[0130] Covariance of predicted states for:

[0131]

[0132] In the filtering stage, the filter gain and the estimated covariance matrix are given by The covariance matrix of the state value and the measurement value is obtained: As shown in the following formula:

[0133]

[0134] in, It is through y k+1∣k,i The predicted value of the calculated measured value.

[0135] The filtering process is shown in formula (23):

[0136]

[0137] During the load mutation process, the system has a strong nonlinear relationship and the deviation of the linear model is large. Therefore, the adaptive factor is used to modify and Subsequently, the filter gain is adjusted to reduce the effect of load changes. Adaptive factor τ k The definition is shown in formula (24):

[0138]

[0139] When the load mutation measurement residual increases, the adaptive factor is used to control and

[0140]

[0141] The gain matrix is ​​tuned to improve the performance of the estimator in extreme environments.

[0142] Similar to AEKF, the improved Sage-Husa noise estimator is also introduced into AUKF, which is expressed as:

[0143] d k-1 =(1-φ) / (1-φ k )(26)

[0144]

[0145] Different from the adaptive factor method, the present invention introduces an improved Sage-Husa noise estimator to calculate the covariance matrix of the model error online, thereby optimizing the system model and the estimation results in multiple scenarios.

[0146] S3: Interactive multi-model selection based on real-time measurement data matching model, and all improved dynamic estimators are weighted.

[0147] The present invention uses an interacting multiple model (IMM) framework to deal with the DSE problem of the distribution network.

[0148] IMM uses measurement data to identify estimators that are more suitable for current operations and assigns them higher weights. In IMM-DSE, AEKF and AUKF are embedded in IMM to track the changing state of the distribution network in an adaptive manner, as follows:

[0149] The adaptive extended Kalman filter and the adaptive unscented Kalman filter are embedded in the interactive multi-model to track the changing state of the distribution network in an adaptive manner. The input value of each filter is initialized, and the model matching the operating environment is defined as the matching model. The mixed probability for interactive initialization is:

[0150]

[0151]

[0152] in, is the mixing probability used for interaction initialization, π (i,j) is the model conversion probability, indicating that the matching model changes from i to j; is the probability of matching model i at time k, r is the number of models; i and j represent the indices of different models. is the mixing probability normalization constant of model j, which is used to calculate the mixing probability.

[0153] After calculating the mixing probabilities, all previous time-step estimates are used to initialize the model:

[0154]

[0155] is the initialization state prediction of model j at time k+1, is the state estimate of model i at time k, is the mixing probability used for interaction initialization. is the initialization state covariance matrix, is the state covariance matrix of model i at time k, is the outer product of state deviations, is the initialization state prediction of model j at time k.

[0156] After initialization, multi-model filtering is performed, and the filter performs DSE separately, and the measurement residual of each model is obtained. The covariance matrix of Compute the likelihood function for the matching model:

[0157]

[0158] in, are the measurement residuals for each model, is the covariance matrix, is the likelihood function, which indicates the likelihood of matching the model; is the measurement matrix, T is the transposed matrix, is the covariance of the model matching i. is the normalization factor of the Gaussian distribution. is the Mahalanobis distance, which measures the measurement residual In covariance The deviation below.

[0159] Specifically, update the model probability according to the likelihood function:

[0160]

[0161] in, is the updated model probability of model i at time k+1. c is the normalization constant, is the likelihood function, r is the total number of models, is the mixed probability normalization constant of the updated i+1 model, is the mixing probability normalization constant for model j.

[0162] Calculate the weighted sum of all filter results to get the result of IMM-DSE:

[0163]

[0164] in, It is k + The final state estimate at time 1, i is the model index, representing a model in the IMM algorithm, ris the total number of models, is the state estimation result of model i, is the updated model probability of model i at time k+1. is the final state covariance matrix, The state covariance matrix of model i at time k+1, is the outer product of state deviations.

[0165] The IMM algorithm achieves multi-model interaction through the above four steps. Combining the advantages of AEKF and AUKF estimators, IMM-DSE can handle the complexity and time-varying problems in the distribution network state estimation process.

[0166] In summary, the adaptive dynamic state estimation method of the present invention proposes an adaptive dynamic state estimation (DSE) method based on an interactive multiple model (IMM), which can adapt to the nonlinear and time-varying problems in the distribution network caused by renewable energy and load uncertainty.

[0167] The improved extended Kalman filter (EKF) and unscented Kalman filter (UKF) of the present invention improve the existing extended Kalman filter (EKF) and unscented Kalman filter (UKF) through adaptive technology, realize self-optimization of the model and parameters in the estimator, and enhance the state estimation performance.

[0168] The IMM-DSE framework of the present invention proposes an IMM-DSE framework including two improved adaptive dynamic state estimators, which are respectively suitable for different scenarios of distribution network changes to improve the accuracy and robustness of state estimation.

[0169] Example 2, reference Figure 2-Figure 6 The second embodiment of the present invention provides a distribution network adaptive state estimation method based on interactive multiple models. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through experiments.

[0170] The present invention uses the improved IEEE 33-node distribution network for example analysis. Nodes 18 and 33 are connected to distributed photovoltaics, and nodes 19 and 23 are connected to electric vehicle charging piles. The system is equipped with various measuring devices, such as Figure 2 shown.

[0171] The performance of IMM-DSE, UKF, and EKF is compared under the condition of sudden load changes in the distribution network. In order to compare the performance of different DSE methods, 50 consecutive sampling points are selected for estimation. According to the characteristics of the distribution network, the smoothing parameters in the Holt method are selected as α = 0.82, β = 0.36, and the forgetting factors are selected as ψ = 0.91 and φ = 0.77. The system error covariance is initialized as Q = diag(10-3 ).

[0172] When distributed photovoltaics were activated at the 10th sampling point, the load on nodes 18 and 33 decreased by 70%. At the 20th sampling point, the load on nodes 19 and 23 increased by 50% due to the activation of the charging piles.

[0173] The case analysis uses three DSE methods and one SSE method for comparison. The SSE method uses the weighted least squares (WLS) method. The state estimation results are as follows: Figure 3 and Figure 4 As shown in the figure, the relative error of state estimation is as follows Figure 5 and Figure 6 shown.

[0174] Comparing the various methods revealed that the static state estimation (SSE) method cannot handle sudden changes in system load, and the results of weighted least squares-static state estimation (WLS-SSE) are not accurate enough. The extended Kalman filter (EKF), unscented Kalman filter (UKF), and the interactive multiple model (IMM) method proposed in this paper performed relatively well.

[0175] The UKF is the most sensitive method, with performance dropping sharply at the beginning. However, due to the increased nonlinearity, the UKF recovers state estimation accuracy more quickly and maintains it over time compared to the EKF. In the IMM-DSE method, the adaptive Kalman filter (AUKF) leverages measurement errors to adjust the covariance matrix of the model noise in real time using adaptive factors. Ultimately, the filter gain can be adjusted to respond to sudden load changes, improving filter accuracy.

[0176] Therefore, the estimation accuracy and convergence speed of IMM-DSE are better than those of traditional methods. Table 1 summarizes the relative errors of various state estimation methods.

[0177] Table 1 Relative errors of various state estimation methods

[0178]

[0179] From the results, it can be seen that IMM-DSE can modify the model noise statistics to cope with load fluctuations under normal circumstances, thereby improving the estimation accuracy.

[0180] Embodiment 3, the third embodiment of the present invention, is different from the first two embodiments in that:

[0181] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0182] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0183] More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic devices), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering, or processing in another suitable manner as necessary, and then stored in a computer memory.

[0184] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0185] Example 4, reference Figure 7 , which is the fourth embodiment of the present invention, provides a distribution network adaptive state estimation system based on interactive multiple models, including a nonlinear conversion module, an improved dynamic estimation module, and an interactive multiple model module;

[0186] The nonlinear conversion module is responsible for converting the linear model constructed by the dynamic state estimation of the distribution network into a nonlinear model. By calculating the distribution network DSE linear model and using the preset algorithm to achieve linear to nonlinear conversion, it provides an accurate model basis for subsequent state estimation.

[0187] Improved dynamic estimation module, including adaptive extended Kalman filter unit and adaptive unscented Kalman filter unit, to perform distribution network reconstruction state estimation and eliminate nonlinear errors caused by sudden load changes;

[0188] Specifically, the system state is predicted and the covariance matrix of the predicted state and error is calculated;

[0189] Get the actual measurement value of the system, modify the predicted state, and get the current estimated state;

[0190] The adaptive extended Kalman filter calculates the transition matrix in real time through the recursive augmented least squares method and uses the improved Sage-Husa noise statistics estimator to assign weights and estimate the noise;

[0191] The adaptive unscented Kalman filter uses proportional and symmetric sampling to obtain a set of points, calculates weights and assigns them to the mean and covariance to eliminate nonlinear errors.

[0192] Interactive multiple model module, responsible for selecting the matching model based on real-time measurement data and weighting all improved dynamic estimators;

[0193] Specifically, the adaptive extended Kalman filter and the adaptive unscented Kalman filter are embedded in the interactive multi-model to track the changing state of the distribution network;

[0194] Initialize the input value of each filter and define the model that matches the operating environment as the matching model;

[0195] Calculate the mixing probability for model initialization;

[0196] Perform multi-model filtering and calculate the likelihood function of the matching model;

[0197] Update the model probability according to the likelihood function;

[0198] Calculate the weighted sum of all filter results to get the final IMM-DSE result.

[0199] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. An adaptive state estimation method for distribution networks based on interactive multiple models, characterized by: include, A linear model is constructed through dynamic state estimation of the distribution network and converted into a nonlinear model; Improve dynamic estimators using adaptive methods, embedding interactive multiple models; An improved adaptive dynamic estimator is used to estimate the state of distribution network reconstruction and eliminate the nonlinear error of sudden load changes in the distribution network; Interactive multi-modeling selects matching models based on real-time measurement data and weights all improved dynamic estimators.

2. The method for adaptive state estimation of a distribution network based on interactive multiple models according to claim 1, wherein: The adaptive method for improving the dynamic estimator includes calculating a linear model of the distribution network DSE and converting the linear model into a nonlinear model using a preset algorithm; The improved dynamic estimator includes an adaptive extended Kalman filter and an adaptive unscented Kalman filter.

3. The method for adaptive state estimation of a distribution network based on interactive multiple models according to claim 2, wherein: The distribution network reconstruction state estimation includes, after obtaining the nonlinear model, predicting the system state, calculating the covariance matrix of the predicted state and the error, obtaining the actual measurement value of the system, modifying the predicted state, and obtaining the current estimated state; According to the current estimation state, the adaptive extended Kalman filter calculates the transition matrix in real time through the recursive augmented least squares method, and assigns weights and estimates the noise through the improved Sage-Husa noise statistics estimator.

4. The method for adaptive state estimation of a distribution network based on interactive multiple models according to claim 3, wherein: The method for eliminating the nonlinear error of the sudden change of the load of the distribution network includes: adopting the adaptive unscented Kalman filter to obtain a group of σ points by using the proportional combined with symmetric sampling method to form a σ point set, introducing a proportional factor, calculating the weight and assigning it to the mean value and covariance; The σ point set is used in the prediction process model, the weighted sum and covariance of each point are calculated to obtain the predicted state, the covariance matrix of the predicted state value and the actual measurement value is calculated, and the filter gain and estimated covariance matrix are calculated based on the covariance matrix; Among them, σ points are a set of sample points representing the probability distribution of system state variables.

5. The method for adaptive state estimation of a distribution network based on interactive multiple models according to claim 4, characterized in that: Eliminating the nonlinear error of the sudden change of the load of the distribution network also includes using an adaptive factor to modify the covariance matrix and adjust the filter gain; When the measurement residuals increase due to sudden load changes, the adaptive factor controls the covariance matrix and eliminates nonlinear errors through the improved Sage-Husa noise estimator.

6. The method for adaptive state estimation of a distribution network based on interactive multiple models according to claim 5, characterized in that: The interactive multi-model includes embedding an adaptive extended Kalman filter and an adaptive unscented Kalman filter into the interactive multi-model, tracking the changing state of the distribution network in an adaptive manner, initializing the input value of each filter, and defining the model that matches the operating environment as the matching model. The mixed probability used for interactive initialization is: in, is the mixing probability used for interaction initialization, π (i,j) is the model transition probability, indicating that the matching model changes from i to j; is the probability of matching model i at time k, r is the number of models; i and j represent the indexes of different models, is the mixing probability normalization constant of model j, used to calculate the mixing probability; After calculating the mixing probabilities, all previous time-step estimates are used to initialize the model: in, is the initialization state prediction of model j at time k+1, is the state estimate of model i at time k, is the mixing probability used for interaction initialization, is the initialization state covariance matrix, is the state covariance matrix of model i at time k, is the outer product of state deviations, is the initialization state prediction of model j at time k; After initialization, multi-model filtering is performed, and the filter performs DSE separately, and the measurement residual of each model is obtained. The covariance matrix of Calculate the likelihood function of the matching model in, are the measurement residuals for each model, is the covariance matrix, is the likelihood function, which indicates the likelihood of matching the model; is the measurement matrix, T is the transposed matrix, is the covariance of the model matching i, is the normalization factor of the Gaussian distribution, is the Mahalanobis distance, which measures the measurement residual In covariance The deviation below.

7. The method for adaptive state estimation of a distribution network based on interactive multiple models according to claim 6, characterized in that: The interactive multiple model further includes updating the model probability according to the likelihood function: in, is model i in k + The updated model probability at time 1, c is the normalization constant, is the likelihood function, r is the total number of models, After the update + 1 model's mixing probability normalization constant, is the mixing probability normalization constant for model j; Calculate the weighted sum of all filter results to get the result of IMM-DSE: in, It is k + The final state estimate at time 1, i is the model index, representing a model in the IMM algorithm, r is the total number of models, is the state estimation result of model i, is model i in k + The updated model probability at time 1, is the final state covariance matrix, Model i In k + The state covariance matrix at time 1, is the outer product of state deviations.

8. A system using the distribution network adaptive state estimation method based on interactive multiple models according to any one of claims 1 to 7, characterized in that: Including nonlinear transformation module, improved dynamic estimation module, interactive multiple model module; The nonlinear conversion module is responsible for converting the linear model constructed by the dynamic state estimation of the distribution network into a nonlinear model. By calculating the distribution network DSE linear model and using a preset algorithm to achieve linear to nonlinear conversion, it provides an accurate model basis for subsequent state estimation. The improved dynamic estimation module includes an adaptive extended Kalman filter unit and an adaptive unscented Kalman filter unit, which performs distribution network reconstruction state estimation and eliminates nonlinear errors caused by sudden load changes; Predict system states and calculate the covariance matrix of predicted states and errors; Get the actual measurement value of the system, modify the predicted state, and get the current estimated state; The adaptive extended Kalman filter calculates the transition matrix in real time through the recursive augmented least squares method and uses the improved Sage-Husa noise statistics estimator to assign weights and estimate the noise; Adaptive unscented Kalman filter uses proportional and symmetric sampling to obtain a set of points, calculates weights and assigns them to the mean and covariance to eliminate nonlinear errors; The interactive multiple model module is responsible for selecting a matching model based on real-time measurement data and weighting all improved dynamic estimators; The adaptive extended Kalman filter and the adaptive unscented Kalman filter are embedded in an interactive multi-model to track the changing state of the distribution network. The input value of each filter is initialized, and the model that matches the operating environment is defined as the matching model. The mixing probability is calculated for model initialization. Multi-model filtering is performed to calculate the likelihood function of the matching model. The model probability is updated according to the likelihood function. The weighted sum of all filter results is calculated to obtain the final IMM-DSE result.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the distribution network adaptive state estimation method based on interactive multiple models according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the distribution network adaptive state estimation method based on interactive multiple models according to any one of claims 1 to 7 are implemented.

Images