An Adaptive State Estimation Method and System for Power Systems with Decoupled Noise Bias and Covariance Estimation

Abstract

This invention discloses an adaptive state estimation method and system for power systems that decouples noise bias and covariance estimation. By placing noise bias estimation and covariance estimation in two algebraically independent sequential channels, this invention completely cuts off the error positive feedback propagation path caused by the coupling between bias and covariance in traditional methods, significantly improving the numerical stability and estimation accuracy of the filter. By introducing a bias confidence mechanism, a dynamic window adaptive strategy driven by the bias change rate, and a bias estimation uncertainty correction term, high-precision independent tracking and correction of measurement noise bias and time-varying covariance are achieved, avoiding the systematic overestimation problem of covariance estimation. Furthermore, this invention can fully utilize high-precision measurement data and effectively suppress state estimation drift caused by engineering factors such as instrument zero drift and communication interference, thus enhancing the robustness, adaptability, and engineering applicability of dynamic state estimation overall.

Description

Technical Field

[0001] This invention relates to the intersection of power system state estimation and signal processing, specifically to an adaptive power system state estimation method and system that decouples noise bias and covariance estimation. Background Technology

[0002] Power system state estimation is a core function of energy management systems (EMS). By integrating multi-source measurement data such as SCADA and PMU, it acquires the voltage amplitude and phase of each node in the system in real time, providing a basis for dispatch control, fault analysis, and safety assessment. With the high proportion of renewable energy integration and the increasing complexity of load structures, the dynamic characteristics of power systems have significantly enhanced, making static state estimation insufficient to meet the requirements. Therefore, dynamic state estimation methods based on Kalman filtering have become a research hotspot.

[0003] Unscented Kalman filtering (UKF) is widely used in dynamic state estimation of power systems due to its natural adaptability to nonlinear systems. Standard UKF assumes that the measurement noise is zero-mean Gaussian noise and that its covariance matrix R is known and invariant. However, the measurement noise in real-world SCADA systems exhibits two typical characteristics that coexist. The first is systematic bias, caused by instrument range drift, A / D converter zero drift, transmission delay, etc., manifesting as a continuous deviation of the measurement noise mean from zero, with its amplitude slowly drifting with equipment aging or changes in operating conditions; this is non-zero mean noise. Systematic bias causes the Kalman filter's innovation mean to deviate from the theoretical zero value, leading to persistent bias in state estimation, which, over time, significantly reduces estimation accuracy. The second is time-varying covariance, caused by changes in communication link quality, weather interference, equipment aging, etc., where the variance of the random component of the measurement noise changes slowly over time; furthermore, impulse interference or telemetry faults can introduce heavy-tailed non-Gaussian noise. When the noise covariance deviates from the nominal value, the gain matrix of the standard UKF becomes mismatched, and the estimation accuracy decreases.

[0004] To address the aforementioned issues, the existing Sage-Husa Adaptive Kalman Filter (Sage-Husa AKF) simultaneously estimates the noise mean vector (corresponding to the bias) and covariance matrix during the filtering process using the maximum a posteriori criterion. Its fundamental flaw lies in the fact that the bias estimation formula contains the covariance matrix, and the covariance estimation formula contains the bias mean, forming a coupled and simultaneous estimation system. When both the bias and covariance change simultaneously, the bias estimation error is amplified by the covariance estimation formula, and the covariance estimation error, in turn, worsens the bias estimation, creating positive feedback error propagation. This leads to filter divergence or oscillation, limiting its practical engineering applicability. The Robust UKF based on the Maximum Correlation Entropy (MCC) criterion reduces the weight of large-bias innovations using a kernel function, exhibiting good robustness to impulse noise. However, the MCC-UKF does not explicitly estimate and compensate for the noise mean bias; its robustness essentially reduces the weight of outliers rather than eliminating the bias. In persistent system bias scenarios, the state update after weight reduction still contains bias components, failing to fundamentally solve the estimation drift caused by the bias. In addition, various extended Kalman filter variants (EKF, cubature KF, etc.) combined with noise adaptive methods have coupling problems similar to Sage-Husa, or insufficient ability to handle systematic bias.

[0005] In summary, existing technologies have the following common shortcomings: bias estimation and covariance estimation are coupled within the same framework, making it impossible to independently guarantee their convergence; there is a lack of systematic adaptive trade-off rules between dynamic bias tracking capability and estimation accuracy; the heterogeneous measurement bias characteristics of SCADA and PMU are not distinguished, and uniform processing leads to resource waste or accuracy loss; the statistical uncertainty of bias estimation is not corrected in covariance estimation, resulting in systematic overestimation of covariance estimation. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention places noise bias estimation and covariance estimation in two algebraically independent sequential channels, completely cutting off the error propagation path. Simultaneously, it integrates a bias confidence mechanism, a dynamic window adaptive mechanism driven by the bias change rate, a bias estimation uncertainty correction term, and differentiated bias parameters for PMU / SCADA heterogeneous measurements, constructing a highly reliable adaptive state estimation system. Differentiated bias estimation parameters are used for measurements from different sources, fully utilizing the high precision characteristics of the PMU while effectively handling the zero-drift bias of SCADA, making it suitable for multi-source measurement fusion scenarios in modern smart grids.

[0007] To achieve the above objectives, this invention provides an adaptive state estimation method for power systems that decouples noise bias and covariance estimation, comprising the following steps: S1. Construct a state-space model that decomposes measurement noise into systematic bias components and random components; S2. Obtain the bias correction information based on the actual measured vector and the predicted state value; S3. Based on the bias correction innovation and the original innovation, obtain the adaptive estimate of the measurement noise covariance matrix; S4. Based on the second-order moment statistics of the bias correction innovation and the uncertainty of the bias estimation, obtain the corrected adaptive measurement noise covariance matrix. S5. Update the power system state variables based on the bias correction information and the corrected adaptive measurement noise covariance matrix.

[0008] Preferably, S1 includes: Using the voltage amplitude and phase of each node as state variables and the state vector as input, a discrete nonlinear state-space model of the system is obtained. The state-space model consists of state transition equations and measurement equations. A nonlinear state transition function is constructed using Holt's two-parameter exponential smoothing technique, which decomposes the state prediction into two parts: a horizontal component and a trend component. The horizontal component is updated according to the horizontal smoothing coefficient, the trend component is updated according to the trend smoothing coefficient, and the horizontal component and the trend component are superimposed to obtain the state transition function. The measurement noise is decomposed into two parts: a systematic bias and a random component. The systematic bias component is a slowly time-varying non-zero mean component, and the random component is a zero-mean Gaussian distribution component.

[0009] Preferably, S2 includes: The original information is obtained based on the actual measured vector and the predicted state value; Based on the first moment statistic of the original innovation, the systematic bias of the measurement noise is extracted online using the sliding window mean method to obtain the estimated value of the systematic bias. The bias-corrected information is obtained based on the original information, the systematic bias estimate, and the bias confidence index.

[0010] Preferably, S3 includes: Using the bias correction information, calculate the underlying covariance estimator with a preset window length; Calculate the bias estimate variance correction based on the original innovation and the systematic bias estimate; An adaptive estimator of the measurement noise covariance matrix is ​​obtained based on the basic covariance estimator and the bias estimation variance correction.

[0011] Preferably, step S3 further includes: performing eigenvalue spectrum truncation projection on the adaptive estimate of the measurement noise covariance matrix, replacing eigenvalues ​​smaller than a preset threshold to obtain a positive definite matrix.

[0012] Preferably, S4 includes: The fundamental second-order moment estimator is calculated using the bias-corrected innovation; A bias estimate uncertainty correction term is constructed, which is used to characterize the statistical uncertainty of the bias estimate; Based on the basic second-order moment estimator and the bias estimation uncertainty correction term, the corrected adaptive measurement noise covariance matrix is ​​calculated, and the corrected adaptive measurement noise covariance matrix is ​​subjected to eigenvalue positive definite projection processing.

[0013] Preferably, S5 includes: Calculate the Kalman gain based on the corrected adaptive measurement noise covariance matrix; Update the power system state variables based on the bias correction innovation and Kalman gain; The posterior state covariance matrix is ​​updated based on the updated power system state variables and Kalman gain.

[0014] The present invention also provides an adaptive state estimation system for power systems that decouples noise bias and covariance estimation, the system being used to implement the above method, comprising: The module constructs a state-space model that decomposes measurement noise into systematic bias components and random components. The extraction module is used to obtain bias correction information based on the actual measurement vector and the state prediction value; The calculation module is used to obtain an adaptive estimate of the measurement noise covariance matrix based on the bias correction innovation and the original innovation; The correction module is used to obtain the corrected adaptive measurement noise covariance matrix based on the second-order moment statistics of the bias correction innovation and the bias estimation uncertainty. The update module is used to update the power system state variables based on the bias correction information and the corrected adaptive measurement noise covariance matrix.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention, by placing noise bias estimation and covariance estimation in two algebraically independent sequential channels, completely severs the error positive feedback propagation path caused by the coupling between bias and covariance in traditional methods, significantly improving the numerical stability and estimation accuracy of the filter. By introducing a bias confidence mechanism, a dynamic window adaptive strategy driven by the bias change rate, and a bias estimation uncertainty correction term, it achieves high-precision independent tracking and correction of measurement noise bias and time-varying covariance, avoiding the systematic overestimation problem of covariance estimation. Furthermore, this method can differentiate heterogeneous measurements such as PMU and SCADA, fully utilizing high-precision measurement data and effectively suppressing state estimation drift caused by engineering factors such as instrument zero drift and communication interference, thus enhancing the robustness, adaptability, and engineering applicability of dynamic state estimation overall. Attached Figure Description

[0016] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] Example 1 This embodiment provides an adaptive state estimation method for power systems that decouples noise bias and covariance estimation, the steps of which include: S1. Construct a state-space model that decomposes measurement noise into systematic bias components and random components.

[0021] First, using the voltage amplitude and phase of each node as state variables, a nonlinear state transition function is constructed using the Holt two-parameter exponential smoothing technique, and a measurement equation is established in conjunction with SCADA / PMU measurements.

[0022] Furthermore, the process of establishing the voltage amplitude and phase of each node as state variables includes: definition k Moment n Power system state vector at each node , ,in, Let be the voltage phase vector, with dimension . This vector uses a node in the power system as a reference node and fixes the voltage phase of that reference node to zero, while the rest... The voltage phase of each node constitutes a phase state component; The voltage amplitude vector has a dimension of n This vector contains all n The voltage amplitude of each node.

[0023] Using the state vector as input, we obtain the discrete nonlinear state-space model of the system from the state transition equations. and measurement equation ,in, A nonlinear state transition function used to describe the transition of the system state from... k Time's up The dynamic evolution pattern at any given moment; It is process noise, and follows a zero-mean Gaussian distribution; For measurement vectors; It is a nonlinear measurement function; For measuring noise.

[0024] Measurement vector The measurement scope covers five categories of observables: node voltage amplitude, node injected active power, node injected reactive power, line active power, and line reactive power. The number of measurements for each category is as follows: m 1. m 2. m 3. m 4. m 5, then the total dimension is measured. .

[0025] The overall nonlinear measurement function is expressed as: , , , , , , in, This indicates the voltage amplitude measurement at the i-th node; The voltage phase angle of the i-th node; Vj represents the voltage phase angle of the i-th node. j Voltage amplitude state variables of each node; Represents a node i Active power injection measurement; Represents a node i Reactive power injection measurement; Indicates from node i To the node j Branch active power flow measurement; Indicates from node i To the node j Branch reactive power flow measurement; , For elements of the node admittance matrix; , For line admittance; For ground susceptance; h ( xk The elements in the expression are measurement functions for the node voltage magnitude. Measurement function of active power injected into nodes Measurement function of reactive power injected at nodes Measurement function of active power of line and the measurement function of reactive power of the line .

[0026] The above measurement noise It is decomposed into two parts: systematic bias and random components. ,in, It is a slowly time-varying systematic bias component with a non-zero mean, which originates from engineering factors such as instrument aging, CT / PT ratio error, and communication delay. The random component follows a zero-mean Gaussian distribution, reflecting the statistical characteristics of the instrument, such as thermal noise, quantization error, and random interference.

[0027] Furthermore, the process of constructing a nonlinear state transition function using Holt's two-parameter exponential smoothing technique includes: Let the state transition function be State prediction is decomposed into horizontal components. and trend components It consists of two parts: the horizontal component reflects the basic level estimate of the state at the current moment, and the trend component describes the rate of change of the state quantity.

[0028] The horizontal components are according to Update, in which This is the horizontal smoothing coefficient, used to control the degree of trust in the current measurement information; The larger the value, the faster the horizontal component responds to new observations, resulting in strong real-time performance, but it is also sensitive to noise. The smaller the value, the stronger the smoothing effect and the higher the robustness to abnormal measurements.

[0029] The trend components are according to Update, in which This is the trend smoothing coefficient, used to control the response speed of the trend component to the rate of change of state; The larger the value, the more sensitive the trend component is to short-term slope changes, making it suitable for capturing rapid fluctuations. The smaller the value, the more gradual the change in the trend component, which is suitable for smoothing out slow-changing cyclical trends.

[0030] horizontal components and trend components The superposition of the system in Always The optimal predicted value of the state at time step: , Define it as a state transition function: .

[0031] This embodiment adjusts the smoothing parameters based on the system's operating conditions. and Perform the following adjustments under normal steady-state conditions: The range of values ​​is , The range of values ​​is It is used to smooth noise and track slow-changing trends.

[0032] Under gradually changing load conditions, set The range of values ​​is , The range of values ​​is This is used to balance smoothness and dynamic response; Under conditions of sudden load changes or after a fault, set The range of values ​​is , The range of values ​​is It is used to quickly track state steps and reduce prediction bias.

[0033] Furthermore, the process of establishing measurement equations in conjunction with SCADA / PMU measurements includes: Based on the above steps, the complete discrete nonlinear state-space model of the power system established in this embodiment can be represented by the following simultaneous equations: in, For process noise, Measurement bias for random measurement of noise components Estimation and compensation are performed using a specialized bias identification algorithm.

[0034] S2. Obtain the bias correction information based on the actual measured vector and the state prediction value.

[0035] This embodiment relies solely on the first-moment statistics of the original information, and uses online tracking of the systematic bias of measurement noise through recursion with a forgetting factor or dynamic window mean estimation.

[0036] Based on the measurement equations constructed above Using actual measurement vectors With state prediction value Calculate the original information. Here, It is a nonlinear measurement function that includes analytical expressions for node power, voltage amplitude, etc.

[0037] First-moment statistics that depend only on the new information ,in Using the window length as an example, the systematic bias of the measurement noise is extracted online using the sliding window mean method.

[0038] Combining bias confidence index Obtain new information on bias correction .

[0039] S3. Based on the bias correction innovation and the original innovation, obtain the adaptive estimate of the measurement noise covariance matrix.

[0040] Using the above bias to correct the new information The calculation window length is Basic covariance estimator , ; To eliminate bias estimates The effect of the inherent statistical error on the second moment, and the calculation of the bias estimate variance correction: .

[0041] This term approximates the uncertainty of the bias estimate by calculating the divergence of the original information from its mean within the window.

[0042] Obtain an adaptive estimator of the measurement noise covariance matrix: , in, The predicted measurement covariance matrix represents the degree of fluctuation in the measured values ​​derived from the prior estimation of the system. The specific calculation steps are as follows.

[0043] First, take the data obtained in the previous moment... The Sigma point for predicting a state is represented as follows: Substituting into the nonlinear observation equation The corresponding predicted measurement Sigma point is obtained. : Calculate the weighted average of the predicted measurements using weighted summation. : in It is mean weight.

[0044] Finally, the matrix is ​​obtained by calculating the dispersion of each measured Sigma point relative to the mean: in This is the covariance weight. This term is used to remove the influence of system state error from the overall statistical characteristics of the observed sequence, thereby reducing measurement noise. Adaptive estimation.

[0045] To ensure numerical stability, Perform eigenvalue spectrum truncation projection, given an arbitrarily small positive number. (This can be determined based on the minimum range of the specific sensor), all those smaller than... Eigenvalue forced replacement The positive definite matrix is ​​obtained. .

[0046] The above process does not pass any covariance parameters to it, satisfies the algebraic decoupling condition, and guarantees the independent convergence of the estimates for each channel.

[0047] S4. Based on the second-order moment statistics of the bias correction innovation and the uncertainty of the bias estimation, obtain the corrected adaptive measurement noise covariance matrix.

[0048] This embodiment relies solely on the second-order moment statistics of the bias correction information, introduces a bias estimation uncertainty correction term, and adaptively updates the measurement noise covariance matrix. There is no parameter feedback between the two channels, thus achieving algebraic decoupling.

[0049] Furthermore, the above-mentioned bias correction is used to correct the new information. Calculate the fundamental second-order moment estimator: , Constructing the uncertainty correction term for bias estimation Used to approximate the bias estimate Statistical uncertainty: ; Calculate the corrected adaptive measurement noise covariance matrix and to Perform eigenvalue positive definite projection processing to obtain .

[0050] S5. Update the power system state variables based on the bias correction information and the corrected adaptive measurement noise covariance matrix.

[0051] The state update steps of the unscented Kalman filter are jointly driven by bias correction innovation and adaptive covariance, and the method includes: The calculation is based on the above adaptive covariance. Kalman gain: , in, This represents the cross-covariance matrix between the predicted state vector and the predicted measurement vector, specifically characterizing the cross-covariance during the prediction phase. The correlation between time-state estimation error and measurement estimation error.

[0052] Using the above bias to correct the new information Update power system state variables (voltage amplitude and phase): , Update the posterior state covariance matrix: , in, The predicted state covariance matrix, also known as the prior state covariance matrix, describes the state covariance in the prior state. The degree of certainty of the prior estimate of the state at time step.

[0053] The process in this embodiment is as follows: Figure 1 As shown.

[0054] Example 2 This embodiment also provides an adaptive state estimation system for power systems that decouples noise bias and covariance estimation. It includes: a construction module for constructing a state-space model that decomposes measurement noise into systematic bias components and random components; an extraction module for obtaining bias correction information based on actual measurement vectors and predicted state values; a calculation module for obtaining an adaptive estimate of the measurement noise covariance matrix based on the bias correction information and the original information; a correction module for obtaining a corrected adaptive measurement noise covariance matrix based on the second-order moment statistics of the bias correction information and the uncertainty of the bias estimation; and an update module for updating the power system state variables based on the bias correction information and the corrected adaptive measurement noise covariance matrix.

[0055] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. An adaptive state estimation method for power systems that decouples noise bias and covariance estimation, characterized in that, Includes the following steps: S1. Construct a state-space model that decomposes measurement noise into systematic bias components and random components; S2. Obtain the bias correction information based on the actual measured vector and the predicted state value; S3. Based on the bias correction innovation and the original innovation, obtain the adaptive estimate of the measurement noise covariance matrix; S4. Based on the second-order moment statistics of the bias correction innovation and the uncertainty of the bias estimation, obtain the corrected adaptive measurement noise covariance matrix. S5. Update the power system state variables based on the bias correction information and the corrected adaptive measurement noise covariance matrix.

2. The adaptive state estimation method for power systems based on decoupling noise bias and covariance estimation according to claim 1, characterized in that, S1 includes: Using the voltage amplitude and phase of each node as state variables and the state vector as input, a discrete nonlinear state-space model of the system is obtained. The state-space model consists of state transition equations and measurement equations. A nonlinear state transition function is constructed using Holt's two-parameter exponential smoothing technique, which decomposes the state prediction into two parts: a horizontal component and a trend component. The horizontal component is updated according to the horizontal smoothing coefficient, the trend component is updated according to the trend smoothing coefficient, and the horizontal component and the trend component are superimposed to obtain the state transition function. The measurement noise is decomposed into two parts: a systematic bias and a random component. The systematic bias component is a slowly time-varying non-zero mean component, and the random component is a zero-mean Gaussian distribution component.

3. The adaptive state estimation method for power systems based on decoupling noise bias and covariance estimation according to claim 1, characterized in that, S2 includes: The original information is obtained based on the actual measured vector and the predicted state value; Based on the first moment statistic of the original innovation, the systematic bias of the measurement noise is extracted online using the sliding window mean method to obtain the estimated value of the systematic bias. The bias-corrected information is obtained based on the original information, the systematic bias estimate, and the bias confidence index.

4. The adaptive state estimation method for power systems based on decoupling noise bias and covariance estimation according to claim 1, characterized in that, S3 includes: Using the bias correction information, calculate the underlying covariance estimator with a preset window length; Calculate the bias estimate variance correction based on the original innovation and the systematic bias estimate; An adaptive estimator of the measurement noise covariance matrix is ​​obtained based on the basic covariance estimator and the bias estimation variance correction.

5. The adaptive state estimation method for power systems based on decoupling noise bias and covariance estimation according to claim 4, characterized in that, S3 further includes: performing eigenvalue spectrum truncation projection on the adaptive estimate of the measurement noise covariance matrix, replacing eigenvalues ​​smaller than a preset threshold to obtain a positive definite matrix.

6. The adaptive state estimation method for power systems based on decoupling noise bias and covariance estimation according to claim 1, characterized in that, S4 includes: The fundamental second-order moment estimator is calculated using the bias-corrected innovation; A bias estimate uncertainty correction term is constructed, which is used to characterize the statistical uncertainty of the bias estimate; Based on the basic second-order moment estimator and the bias estimation uncertainty correction term, the corrected adaptive measurement noise covariance matrix is ​​calculated, and the corrected adaptive measurement noise covariance matrix is ​​subjected to eigenvalue positive definite projection processing.

7. The adaptive state estimation method for power systems based on decoupling noise bias and covariance estimation according to claim 1, characterized in that, S5 includes: Calculate the Kalman gain based on the corrected adaptive measurement noise covariance matrix; Update the power system state variables based on the bias correction innovation and Kalman gain; The posterior state covariance matrix is ​​updated based on the updated power system state variables and Kalman gain.

8. An adaptive state estimation system for a power system that decouples noise bias and covariance estimation, said system being used to implement the method described in any one of claims 1-7, characterized in that, include: The module constructs a state-space model that decomposes measurement noise into systematic bias components and random components. The extraction module is used to obtain bias correction information based on the actual measurement vector and the state prediction value; The calculation module is used to obtain an adaptive estimate of the measurement noise covariance matrix based on the bias correction innovation and the original innovation; The correction module is used to obtain the corrected adaptive measurement noise covariance matrix based on the second-order moment statistics of the bias correction innovation and the bias estimation uncertainty. The update module is used to update the power system state variables based on the bias correction information and the corrected adaptive measurement noise covariance matrix.

Images