CN111563626B

CN111563626B - Power system prediction auxiliary state estimation method and system

Info

Publication number: CN111563626B
Application number: CN202010386707.6A
Authority: CN
Inventors: 金朝阳; 丁磊; 王晨
Original assignee: Shandong University
Current assignee: Shandong University
Priority date: 2020-05-09
Filing date: 2020-05-09
Publication date: 2022-04-12
Anticipated expiration: 2040-05-09
Also published as: CN111563626A

Abstract

The invention provides a method and a system for estimating a prediction auxiliary state of an electric power system, which comprises the steps of constructing a dynamic model for predicting the state of the electric power system; calculating the state estimator of the dynamic model by using a nonlinear Kalman filter; judging whether an abnormality occurs based on the number of counted new information, performing abnormality detection, and distinguishing an abnormality caused by a plurality of bad data from sudden load changes which unevenly affect all new information; identifying bad data by using a maximum innovation method according to the detected abnormal type, identifying nodes with sudden load change, and identifying nodes removed after a fault; if any bad data is identified, deleting the bad data and returning to the anomaly detection step, if any sudden load change is identified, refusing to predict and executing static estimation; if any branch is identified as a broken line, prediction is rejected, topology is updated and static estimation is performed. The invention can accurately detect and identify three abnormal types and identify abnormal positions under different power system operation conditions.

Description

Power system prediction auxiliary state estimation method and system

Technical Field

The invention belongs to the technical field of power system detection, and relates to a power system prediction auxiliary state estimation method and system.

Background

The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.

Power systems require constant monitoring of the state of the voltage phase angle and amplitude at all nodes in the network to ensure safe and economical operation. Static State Estimator (SSE) is widely used in power systems to provide accurate information based on a set of measured states.

However, the SSE method requires a full set of measurements to estimate the state and is susceptible to bad data or data loss. The shortcomings of SSE can be overcome by using a predictive aided state estimator (FASE) that uses both measurements and predictions. The method is particularly useful for power distribution systems that measure deficiencies.

Normally, the state change of the power system is slow and predictable, but after a fault occurs, a sudden change may occur due to a sudden load change or a sudden network topology change. In this case, the estimation accuracy of FASE is even lower than SSE. Therefore, it is important for FASE to detect these anomalies and distinguish them from erroneous data, since the errors are on the measurement side, and then choose to reject or reduce the weight of the erroneous data. However, the existing intelligent methods do not consider the detection of the topology change after the fault and the identification of the abnormity, and the identification result is not accurate.

Disclosure of Invention

In order to solve the problems, the invention provides a prediction auxiliary state estimation method and a system for an electric power system.

According to some embodiments, the invention adopts the following technical scheme:

a power system prediction auxiliary state estimation method comprises the following steps:

constructing a dynamic model for predicting the state of the power system;

calculating the state estimator of the dynamic model by using a nonlinear Kalman filter;

judging whether an abnormality occurs based on the number of counted new information, performing abnormality detection, and distinguishing an abnormality caused by a plurality of bad data from sudden load changes which unevenly affect all new information;

identifying bad data by using a maximum innovation method according to the detected abnormal type, identifying nodes with sudden load change, and identifying nodes removed after a fault;

if any bad data is identified, deleting the bad data and returning to the anomaly detection step, if any sudden load change is identified, refusing to predict and executing static estimation; if any branch is identified as a broken line, prediction is rejected, topology is updated and static estimation is performed.

As an alternative embodiment, the specific process of calculating the state estimator of the dynamic model by using the nonlinear kalman filter includes: and generating volume points and corresponding weights by using a volume Kalman filter, and performing prediction state and prediction measurement to obtain Kalman estimation.

As an alternative embodiment, the specific steps of judging whether an abnormality occurs based on the number of counted new information, performing abnormality detection, and distinguishing an abnormality caused by a plurality of bad data from a sudden load change unevenly affecting all new information include:

judging whether the abnormality occurs or not by counting the number of the innovation, and if the number of the innovation is larger than a preset threshold value, detecting the abnormality;

detecting the abnormality caused by single bad data in the measurement;

setting a standardized residual error threshold value to detect sudden topology change after a fault, wherein if the standardized residual error exceeds the set threshold value, the sudden topology change occurs;

detecting sudden load changes that uniformly affect all new information;

the skewness of the maximum innovation ratio and the maximum standard deviation of the measurement noise are set to distinguish the abnormal and uneven sudden load changes affecting all the innovation caused by a plurality of bad data.

By way of further limitation, a normalized residual threshold is set to detect a sudden topology change following a fault, and if the normalized residual exceeds the set threshold, the step of causing the sudden topology change comprises:

sudden topological changes will cause continuous large errors to the predicted values, two consecutive maximum information are obtained, a first threshold is selected, static estimation is performed with the measurements received at time k, and a normalized residual NR is calculated, the impact of sudden load changes on the NR of the SSE is small, the NR is usually below the first threshold; the impact of a sudden topology change on the NR of the SSE is large, the NR is usually larger than a second threshold, which is larger than the first threshold, and the sudden topology change and the sudden load change are distinguished by setting two different thresholds.

By way of further limitation, the specific process of setting the skewness of the maximum innovation ratio and the maximum standard deviation of the measurement noise to distinguish between anomalies caused by a plurality of bad data and sudden load changes that unevenly affect all innovation includes:

and setting a third threshold according to the maximum standard deviation of the measured noise, wherein if the skewness of the maximum innovation ratio is greater than the third threshold, bad data appears, and otherwise, the load change is considered to happen suddenly.

As an alternative embodiment, the step of identifying a sudden load change node comprises:

obtaining the average value of the loads, and selecting nodes with the loads larger than the average value by a certain percentage;

predicting an active power injection measured value and covariance thereof;

calculating and correcting an active power injection measurement value;

calculating a covariance of the predicted active power injection measurement value and the predicted active power injection measurement value;

and calculating an innovation vector measured by pseudo injection by using the covariance and the two active power injection measurement values, and finding the maximum element in the vector, wherein the corresponding node is the place where sudden load change occurs.

As an alternative embodiment, identifying nodes that are removed after a fault comprises the steps of:

selecting a group of one-way tidal flow measurement to cover all branches of the network;

after receiving measurement at each moment, storing the measured value into a corresponding tidal flow measurement vector;

if any fault is detected, calculating the vector change ratio of the moment and the previous moment; the corresponding branch of the element with the largest vector change ratio is identified as the removed branch.

A power system predictive assist state estimation system, comprising:

the dynamic model building module is configured to build a dynamic model for predicting the state of the power system;

a state estimation module configured to perform a state estimator calculation of the dynamic model using a non-linear Kalman filter;

an anomaly detection module configured to determine whether an anomaly has occurred based on the number of counted infotainments, perform anomaly detection, distinguish between anomalies caused by a plurality of bad data and sudden load changes that unevenly affect all infotainments;

the abnormal identification module is configured to identify bad data by using a maximum innovation method according to the detected abnormal type, identify a sudden load change node and identify a node removed after a fault;

a selection processing module configured to delete bad data and return to the anomaly detection step if any bad data is identified, and to reject prediction and perform static estimation if any sudden load change is identified; if any branch is identified as a broken line, prediction is rejected, topology is updated and static estimation is performed.

A computer readable storage medium having stored therein a plurality of instructions adapted to be loaded by a processor of a terminal device and to execute a power system prediction assistance state estimation method as described.

A terminal device comprising a processor and a computer readable storage medium, the processor being configured to implement instructions; the computer readable storage medium stores a plurality of instructions adapted to be loaded by a processor and to perform a power system predictive assistance state estimation method.

Compared with the prior art, the invention has the beneficial effects that:

the invention solves the problem of lower estimation precision of the existing FASE algorithm under the condition of sudden load change, and can realize more accurate abnormality detection and identification.

The invention overcomes the defects that the prior method can not accurately distinguish sudden load change from bad data and can not detect sudden topology change caused by faults by using the ratio (SIR) of skewness to maximum innovation. In addition, with the maximum normalized residual of the static estimator, sudden topological changes after a fault can be detected, the location of sudden loads can also be identified, and the location of branch removal after fault clearing can be identified using the change ratio of the power measurements and the dummy injection measurements, respectively.

Under the conditions of normal data and bad data, the identification result of the method is more accurate; in case of sudden load changes, it is possible to detect anomalies and reject the predicted value, which makes its estimation more accurate than other FASE methods, and in case of failure, it is possible to detect anomalies and identify the broken branch, so that a correct estimation is made.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.

FIG. 1 is a flow chart of a prior art anomaly detection method;

FIG. 2 is a flowchart of an abnormality detection method according to the present embodiment;

FIG. 3 is the average OPI of FASE and SSE under normal operation of the IEEE118 node test system;

FIG. 4 is the average skewness of FASE under normal operation of the IEEE118 node test system;

FIG. 5 is a mean normalized innovation of FASE under normal operation of the IEEE118 node test system;

FIG. 6 is the average OPI of FASE and SSE in the case of IEEE118 node test system bad data;

FIG. 7 is the average skewness of FASE in the case of bad data from IEEE118 node test system;

FIG. 8 is the average normalized innovation of FASE in the case of bad data from IEEE118 node test system;

FIG. 9 is the average OPI of FASE and SSE in the case of sudden load changes in the IEEE14 node test system;

FIG. 10 is the average skewness of FASE in the case of sudden load changes in the IEEE14 node test system;

FIG. 11 is the mean normalized innovation of FASE in the case of sudden changes in IEEE14 node test system load;

FIG. 12 is the average OPI of FASE and SSE in the case of sudden changes in IEEE118 node test system load;

FIG. 13 shows the average skewness of FASE in the case of sudden load changes in the IEEE118 node test system;

FIG. 14 is the mean normalized innovation of FASE in the case of sudden changes in IEEE118 node test system load;

FIG. 15 is the average OPI of FASE and SSE in the event of an IEEE14 node test system failure;

FIG. 16 is the average skewness of FASE in the case of IEEE14 node test system failure;

FIG. 17 is the average normalized innovation of FASE at time 26 in the case of IEEE14 node test system failure;

FIG. 18 is the mean normalized innovation of FASE at time 27 in the case of IEEE14 node test system failure.

The specific implementation mode is as follows:

the invention is further described with reference to the following figures and examples.

It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.

The invention provides an improved innovation analysis method, which can accurately detect and identify three abnormal types and identify the positions of the abnormal types. The defects of an existing FASE algorithm based on CKF are overcome, namely the estimation accuracy of the FASE algorithm is deteriorated in a long time after the load is suddenly changed; it is also more accurate than other FASE methods in four different power system operating scenarios, including normal operating conditions, bad data conditions, sudden load change conditions, and fault conditions. And identifying sudden load changes and fault locations based on the pseudo-injection measurements, the innovation analysis and the branch tidal current change ratio.

Specifically, the power system prediction auxiliary state estimation method comprises the following steps:

constructing a dynamic model for predicting the state of the power system;

Firstly, the construction of a system dynamic model is introduced:

the general form of the system state transition function may be expressed as,

x_k+1＝F_kx_k+g_k+q_k (1)

where x is the state vector, F is the transition matrix, g is the input vector, q is the process error vector, and the subscript k denotes the time constant.

The derivation of the parameters is determined by the system dynamics model used.

To study the performance of FASE when an anomaly occurs, a linear exponential smoothing technique of Holt, which is more accurate for short-term predictions, was employed. The parameters F and g are shown in the following equations:

F_k＝α_k(1+β_k)I (2)

wherein I is an identity matrix, α_kAnd beta_kIs a parameter in the range from 0 to 1, x_k ^-Is the predicted state at time k, the parameters a and b at time k can be calculated by the following method:

b_k＝β_k(a_k-a_k-1)+(1-β_k)b_k-1 (5)

in all simulations in this embodiment, α_k＝0.8,β_k＝0.5。

In other embodiments, the simulated data may be altered.

The mathematical formulas of the four nonlinear Kalman filters (EKF, UKF, CKF, IEKF and SKF) are shown. All of these non-linear kalman filters can be used to solve the prediction aided state estimation problem, as follows:

x_k＝f(x_k-1,k-1)+q_k-1 (6)

z_k＝h(x_k,k)+r_k (7)

σ²(q_k-1)＝Q_k-1 (8)

σ²(r_k-1)＝R_k-1 (9)

where f is the general form of the system state transition matrix detailed in (1) - (5), q is the zero-mean process error vector, z is the measurement vector, h is the nonlinear measurement function, and r is the zero-mean measurement error vector.

The process of Extended Kalman Filter (EKF) can be divided into two steps, prediction and correction, outlined as follows:

and (3) prediction:

correcting:

wherein P is_k ^-Is x_k ^-F is a Jacobian matrix of F to x, H is a Jacobian matrix of H to x, K_kIs the Kalman gain, z_kIs a measurement vector, x_k ⁺Is the final estimate of the corrected state, I is the identity matrix, P_k ⁺Is x_k ⁺The covariance matrix of (2).

By iteratively calculating x_kThe estimation formula in (13) can be refined and the most recent estimate linearized at each iteration. This modified strategy for EKF is called Iterative Extended Kalman Filter (IEKF). Another way to reduce the estimation error of EKF in the linearization process is to introduce the higher order terms of the Taylor expansion of the measurement function. The most widely used higher order EKF is the second order EKF (skf).

Unscented Kalman Filtering (UKF) is based on Unscented Transformation (UT) theory. Instead of using Taylor to expand the linearized measurement function, UKF propagates the statistical distribution of states through a nonlinear function. This feature allows the UKF to estimate the state and covariance matrices without computing the Jacobian matrix of the nonlinear function. Therefore, the UKF can improve the accuracy and speed of the FASE, especially in cases where the function is highly non-linear. The process of UKF can be divided into four steps, including Sigma point particle generation, state prediction, metrology prediction and calibration. The mathematical formula for each step is as follows.

Sigma dot particle generation a set of 2n +1 number (n is the number of states) Sigma dot particles are generated, which can be grouped into a matrix of rows as given in (15).

And (3) state prediction:

wherein X_k ^-Is to map X by f_kThe resulting matrix, W is the weight matrix, giving the weight vector, ω_mAnd W₀ ^c…W_2n ^cIs defined as follows:

W₀ ^m＝1-n/3 (20)

W_i ^m＝1/6,i＝1,2,...,2n (21)

W₀ ^c＝3-n/3 (22)

W_i ^c＝1/6,i＝1,2,...,2n (23)

measurement and prediction:

wherein z is_k ^-Is the predicted measurement vector for the measurement vector,

is the covariance of the metrology prediction,

is the covariance between the predicted state and the metrology prediction.

And (3) correction:

the volumetric kalman filter (CKF) is an efficient, accurate nonlinear filter. It is named by the sphere-radial volume rule, which is a key technology for calculating the multiple moment integral in the Bayesian filtering paradigm. Under the assumption that both process noise and measurement noise are gaussian noise, the process of CKF can be summarized into three steps:

and (3) state prediction:

where N (x; μ, P) is the sign of the Gaussian density of the variable x, with a mean of μ and a covariance of P.

Measurement and prediction:

and (3) correction:

it is often difficult to directly calculate the multiple integrals given in (32) to (36). However, they can be approximated by the sphere-radial volume rule, as explained by the following equation:

where ei is the ith column of the identity matrix, ξ i, i ═ 1,. 2n are volume points, ω i, i ═ 1,. 2n are the weights of the volume points.

The volume points generated in CKF are very similar to the Sigma points generated in UKF. However, they are different in both value and weight. For example, considering a four-state vector with 0 mean and unit covariance, expressions for volume point and sigma point particles and their corresponding weights are given in (43) - (46). It is clearly shown in (46) that one weight of the sigma point particles is below 0. According to (27), the covariance matrix

May become non-positive, which may lead to filter instability, i.e. for bounded inputs, the output of the filter may not be bounded.

ξ＝[ξ₁ ξ₂ ...ξ₈]＝[-I_4×4 I_4×4] (42)

Secondly, abnormality detection and discrimination are performed

Firstly, a traditional innovation analysis method is introduced, and an abnormality detection and distinguishing method based on a conventional innovation analysis method is provided. An implementation of the conventional innovation analysis method is given in fig. 1. Any measured innovation in the graph can be calculated by equation (47), and any skewness of the innovation can be calculated by (50).

The algorithm is divided into two steps.

Step 1: whether an anomaly has occurred is detected by checking whether the maximum innovation is greater than 3.

Step 2: bad data and sudden load changes are distinguished by checking whether the skewness of the maximum innovation is greater than 3.

The conventional innovation analysis method has two disadvantages. First, it cannot detect sudden topology changes after a fault. Second, the threshold of the second step is unreliable-it will vary in different networks and different measurement configurations. In order to overcome these two disadvantages, an improved innovation analysis method is proposed:

wherein the measured prediction of UKF and CKF

And its covariance

Is determined byDefinitions have already been given in (26), (27), (34) and (35). In EKF, IEKF and SKF

And

the definitions of (a) and (b) are given in (48) and (49), respectively.

Wherein M is_3,kRepresenting the third central moment, σ_kIs the standard deviation, the value of which can be shown as follows:

v_k＝E[τ_k] (53)

n is an n-order exponential operation.

Improved innovation analysis method the block diagram of the implementation of the proposed improved innovation analysis method is shown in fig. 2. The innovation and skewness can be calculated using the same equations set forth in (47) - (50). The algorithm includes five steps, each of which is explained as follows:

step 1: whether an abnormality occurs is detected by counting the number of new messages, and if the number of new messages is larger than a preset threshold value 3, the abnormality is detected. If this number is S_kGreater than 0 then an anomaly is detectedThus, or this is a normal case.

Step 2: by inspection of S_kThe anomaly caused by a single bad data in the measurement is detected as 1 because, in addition to bad data, a sudden load change and a sudden topology change due to a fault both cause multiple NIs to be larger than a threshold.

And step 3: a sudden topology change after a fault is detected. Sudden topological changes will result in sustained large errors to the predicted values. Thus, two consecutive maximum innovations were studied and a larger threshold 6 was chosen. A static estimate is made with the measurements received at time k and a normalized residual NR is calculated. The impact of sudden load changes on the NR of the SSE is small, typically below 6, and even the sudden switch-off of the heaviest load will only cause NR slightly above 10, whereas sudden topological changes have a significant impact on the NR of the SSE, typically above 1000, and therefore an NR threshold of 30 is set to distinguish between sudden topological changes and sudden load changes.

And 4, step 4: sudden load changes that affect all new information uniformly are detected. This sudden load change is characterized by a very small skewness. The detection threshold was chosen to be 3, as in the conventional innovation analysis method.

And 5: the method distinguishes between anomalies caused by a plurality of bad data and sudden load changes which affect all new information unevenly. In this example, a number of simulations indicate that there is a clear threshold to distinguish between bad data and sudden load changes, i.e., SIR_th＝min(1/3,3σ_max). Here, SIR is the skewness of the maximum information ratio, σ_maxIs the maximum standard deviation of the measured noise. Simulation results show that if bad data occurs, SIR is larger than SIR_thIf a sudden load change occurs, the SIR will be less than the SIR_th。

Of course, the threshold 3 is used to distinguish between abnormal and normal conditions. Based on the central limit theorem, innovation can prove that following a standard gaussian distribution, only less than 0.3% of the data absolute values are greater than 3 according to the standard gaussian distribution, and therefore, we set 3 as the threshold for detecting anomalies.

In the present embodiment, thresholds of 6 and 30 are used to distinguish between failure cases and other abnormal cases. The thresholds are set according to the unique characteristics of the fault, which will cause very large persistent errors for CKF and SSE. These values are empirically selected based on statistical distribution of the simulation results.

And (3) identification of the abnormality:

identifying bad data in FASE is typically based on the method of max NI. The measurement with the largest NI is determined to be bad data because only one NI is greater than normal. However, both sudden load changes and failures can result in multiple NIs being greater than normal. Thus, the locations where these events occur may not be directly identifiable.

The present embodiment proposes two methods to identify the location of these two anomalies.

Firstly, the identification of sudden load change, which proposes a pseudo injection method using CKF to identify the bus where sudden load change occurs, comprises the following steps:

step a, obtaining the average value of the load, and selecting the nodes with the load more than the average value by a certain percentage.

B, calculating (54) the predicted active power injection measured value z given in the step_l ^-And its covariance P_l ^-。

Wherein h is_lIs the active power injection function corresponding to the selected node in step a.

Step c calculating (55) the corrected active power injection measurement z given in_l ⁺：

Step d-calculating z_l ^-And z_l ⁺Covariance P of_l:

E, calculating the innovation vector tau of the pseudo injection measurement_l：

Step f, finding tau_l(ii) a The corresponding node is where the sudden load change occurs.

Secondly, identifying broken lines after faults:

step A, selecting a group of unidirectional tidal flow measurement to cover all branches M of the network.

Step B, after receiving measurement at the time k, storing the measurement value belonging to the M into the vector M_kIn (1).

Step C, if any fault is detected, please calculate the variation ratio r given in (58)_m. Will r is_mThe corresponding branch of the largest element is identified as the removed branch:

r_m＝|ln(|m_k-1/m_k|)| (58)

in summary, based on the volume sphere rule and the proposed new anomaly detection and identification algorithm, a new prediction aided state estimation algorithm using CKF is proposed:

initially, find f according to (1) - (7)_kAnd Q_kFinding h according to (8) and (9)_k、R_k,.a₀＝x_-1,b₀＝0,x₀ ⁺＝x₀ ^-＝x₀,P_k0 ⁺＝Q₀Set k to 1.

When (k is more than or equal to 1)

{ step 1: generating volume points and corresponding weights according to (41) and (42).

And 2, predicting the state by using (32) and (33).

And 3, measuring and predicting by using the measurements (34) to (36).

And 4, acquiring a Kalman estimation by using the steps (37) to (39).

And 5, detecting the abnormality by using the algorithm in the figure 2.

And 6, identifying bad data by using a traditional maximum innovation method according to the detected abnormal type, identifying sudden load change nodes after the steps a to e, and identifying nodes removed after the fault by using the steps A to C.

And 7, if any bad data is identified, deleting the bad data and returning to the step 5. Otherwise, if any sudden load change is identified, the prediction is rejected and a static estimation is performed. Otherwise, if any branch is identified as being broken, prediction is rejected, topology is updated and static estimation is performed.

Step 8, outputting x_k ⁺And P_k ⁺Set k to k +1

The following product examples are also provided:

a power system predictive assist state estimation system, comprising:

The proposed CKF-based predictive aided state estimation method was tested and compared to the other four non-linear kalman filters of the IEEE14 and 118 node test systems. To ensure proper operation of the anomaly detection function, a redundant set of regular measurements and a redundant set of PMU measurements are selected in IEEE14 and 118 node test systems, where measurement redundancy means that the system can still perform state estimation if any measurements are missing.

Assuming the system is operating at quasi-steady state, some selected loads are simulated to increase gradually linearly by 20% over 50 hours. The small fluctuation of the variation is simulated by adding a random signal with a standard deviation of 3% of the variation amplitude. As the load increases, the power of the generator increases according to its participation factor, i.e. the percentage of electricity generated before the load changes. For example, if the total load is increased by 10MW and the participation factors of the two generators (GA and GB) are 0.3 and 0.7, respectively, the generated powers of GA and GB are 3MW and 7MW, respectively.

Without loss of generality, the covariance of the process error Q is assumed to be 1 × 10^-6xI, where I is the identity matrix. The measurement error is a gaussian error, whose standard deviation is set as a certain percentage measured according to the measurement type:

SCADA P, Q (0.02) and V (0.002)

PMU amplitude of 0.002 and phase angle of 0.01

For example, if the active power injection measurement is 0.5p.u, the standard deviation of the error is set to 0.5 × 0.02 — 0.01 p.u.

Initial conditions assume a known initial state (x)_-1And x₀) Information of the first two states so that the Holt method can be used for the first prediction. The overall performance index (overall performance index) defined below was usedOPI) evaluation of FASE performance:

the intuitive explanation for the OPI is the rate of reduction of the measurement error after state estimation. Thus, a small OPI indicates good performance of FASE.

Four cases were considered in the simulation, including normal operating conditions, the presence of bad data, sudden load changes, and failures. The simulation setup was the same in all cases except that in the last three cases an exception was introduced at time 25.

Simulation results and analysis

In this section, simulation results and analysis of the IEEE14 and 118 node test system are presented for four cases of normal operation, bad data, sudden load changes, and failures. The results of these four cases are discussed separately, first the performance of the different nonlinear filters and then the results of the anomaly detection method. The results of anomaly identification are also discussed. Because of its excessively long execution time in the IEEE118 node test system, the simulation of SKF is performed only in the IEEE14 node test system. All results presented are obtained after 100 monte carlo simulations.

Normal operating conditions

The embodiment shows the simulation result of the IEEE118 node test system under the normal condition. The simulation results of the IEEE14 node test system are substantially the same as the simulation results of the IEEE118 node test system. The OPI, skewness and NI of SKF are similar to those of EKF and IEKF. Because of the similarity of these results, the present embodiment will not be described again.

The performance of the nonlinear filter is compared in that fig. 3 shows the OPI of four FASE at time 50. All FASE showed less OPI than the Steady State Estimator (SSE), demonstrating the effectiveness of Holt's method and the higher accuracy of FASE estimation at system quasi-steady state than SSE. It is also clearly shown that the OPI of CKF is lowest, about 10% in UKF, about 25% in EKF and IEKF, and about 30% in SSE. It is important to improve the estimation accuracy with CKF considering that other FASEs use the same measurements and the same prediction process.

The results in fig. 4 and 5 show that under normal operating conditions, the mean skewness and mean Normalized Innovation (NI) are within the threshold range. Therefore, it turns out that the skewness threshold in this method is 3 and the NI threshold is 3, which is correct for normal operating conditions.

Abnormality detection: table 2 lists the test results of three anomaly detection methods, including the method proposed in this embodiment, the conventional NI method, and the PS method.

Test results show that the method correctly detects 85 cases of normal operation, 14 cases of bad data and 1 case of sudden load change. Since the gaussian error of the measurements may occasionally cross the threshold, subsequent identification and elimination of these measurements will improve the estimation accuracy. In contrast, detection as a sudden load change is false detection, which will result in elimination or mitigation of prediction, and ultimately, a drop in estimation accuracy. Thus, this method has a good detection rate of 99%, whereas the traditional NI method has a good detection rate of only 85%. The threshold of the PS method for bad data is small, so that the PS method can reduce the measurement value with larger error. Thus, the PS method can be 100% correctly detected under normal operating conditions.

TABLE 2 results of anomaly detection method

Bad data

The presence of the first anomaly, i.e., bad data, was considered in the simulation study. A bad data (measurement set to 0) is introduced in the measurement 83, i.e. the active power flow between node 4 and node 5 is measured at time 26.

The performance of the nonlinear filter is compared:

in fig. 6, there is a significant decrease in both FASE and SSE. This is because after any type of estimation, the magnitude of the total error is smaller than the magnitude of the total error itself. However, the OPI quantifies the improvement in data quality, not the absolute value of the error. Therefore, bad data needs to be detected and identified because it significantly affects the state estimation.

To illustrate the effect of bad data on NI and skewness, the average skewness at different times and the average NI at time 26 are given in fig. 7 and 8, respectively. The average NI of measurement 83 is much greater than threshold 3, and the average skewness at time 26 is about 23, significantly greater than one-third of the maximum | NI | (about 45).

And (4) abnormal detection, wherein the result shows that the NI threshold value is 3, the skewness threshold value is 3, and the SIR threshold value is 1/3 in the method, so that the method is correct. The test results in table 3 show that the three methods compared in this example can detect bad data 100% accurately. Bad data is identified as a measurement 83 because its corresponding NI is uniquely greater than threshold 3.

The simulation results of the IEEE14 node test are substantially the same as those of the IEEE118 node test system, and SKF also has similar OPI, skewness, and NI compared to EKF and IEKF. Therefore, these results are not given here.

TABLE 3 results of anomaly detection method

Sudden change in load

IEEE14 node test System the simulation case relates to the presence of sudden load changes: the load at node 2 suddenly decreases by 40% at time 26.

Nonlinear filter performance contrasts the impact of sudden load changes on FASE for different nonlinear filters is different from the almost equal impact of bad data: as shown in fig. 9, CKF is the most influential filter, with peaks around 0.7, the UKF is also significantly affected, but much smaller, and the SSE is unaffected, since it does not use prediction, the EKF-like method is slightly affected, with peak OPI values only slightly larger than the SSE. Further, the OPI of CKF rises again after time 26, reaching a second peak at time 29, even though no further anomalies occur after time 26. Therefore, it is important to accurately detect and identify sudden load changes and take appropriate action to ensure that FASE can be accurately estimated with high performance nonlinear filters, particularly CKF.

To illustrate the effect of sudden load changes in a small network on NI and skewness, the average skewness at different times and the average NI at time 26 are given in fig. 10 and 11. Since sudden load changes of a small network like the IEEE14 node test system may affect each state more or less, the average skewness of FASE increases slightly at time 26, but still within the normal range of values, while the average NI of several measurements has exceeded the threshold of 3. These results correspond to the detection criteria given in the proposed method.

Table 4 shows the results of the anomaly detection method after 100 monte carlo simulations, indicating that this method and the conventional NI method successfully detected sudden load changes in all 100 simulations, while the PS method failed in all simulations. This is because the PS method detects an abnormality using the Z matrix defined in equation (60), and the change in the predicted state is much smaller than the change in the measured NI.

TABLE 4 results of anomaly detection method

Abnormality recognition although V₄,I_real,1-2,I_real,1-5,I_imag,1-2And I_imag,2-4The measured absolute value of five close nodes 2 is greater than 3, but the sudden negative is directly recognizedThe location where the change in charge occurs is not apparent. Calculating a pseudo-injection measurement τ for CKF_lAs shown in table 5, the data clearly shows that the load 1 at node 2 has the maximum τ_l. Thus, sudden load changes are correctly identified as being located at node 2.

TABLE 5 Innovation of pseudo-implant measurements

Load(s)	Node point	τ	_l
				1	2	1.25
2	3	0.0579
			3	4	0.0256
4	5	0.1026
			5	6	0.1595
6	9	0.2753
			7	10	0.7035
8	11	0.1135
			9	12	0.0748
10	13	0.1226
			11	14	0.1997

IEEE118 node test System Another emulation is performed in a large network of IEEE118 node test systems. The load on node 2 also suddenly decreases by 40% at time 26 in this simulation.

And comparing the performances of the nonlinear filters, wherein in the condition, the influence of the sudden load change on the estimation precision is similar to that of an IEEE14 node test system, CKF is influenced most, and EKF-type methods are influenced least. Further, the accuracy of estimation of CKF is worse than before the sudden load change until 10 times after the sudden load change, which is also similar to the previous case. Notably, the OPI level of the SSE remains unchanged. This is because the SSE is not estimated using prediction.

To summarize the effect of sudden load changes in a larger network of an IEEE118 node test system, the average skewness of NI and time 26 at different times is given in fig. 13 and 14. When the load changes suddenly, the skewness clearly exceeds the threshold of 3 at time 26. This is very similar to the skewness in the case of bad data, but the peak is around 5, less than one third of the maximum | NI |, about 30. Finally, many measurements have NI greater than the threshold of 3, which is significantly different from the bad data case where only a few data may be corrupted. The similarity of skewness to bad data cases can be explained by the fact that in larger networks, sudden load changes on any node have a significant impact on a smaller number of states, and thus on the predicted values. Thus, the effect of a sudden load change will be similar to the effect of a set of adjacent bad data with a small error.

Anomaly detection the detection result shows that the method can successfully detect all 100 sudden load changes, whereas the conventional NI method erroneously detects all them as bad data because the skewness is larger than the threshold 3. Notably, the PS method labels both the correlation measurements and the correlation predictions as outliers. Therefore, subsequent de-weighting of the measurements and predictions may not improve the estimation accuracy. Therefore, in this case, only the proposed method has a perfect abnormality detection performance, and both of the existing methods cannot detect a sudden load change.

TABLE 6 results of anomaly detection method

Fault of

The last embodiment is a fault condition. The transient nature of the network response to faults is not studied, since the state estimator updates its estimate much more slowly (intervals of about a few minutes) than the transient. It is assumed that the topology of the network changes after clearing the fault due to the disconnection of one branch. In this case, in the IEEE14 node test system, when the leg 6 connecting the node 3 and the node 4 is removed, the topology change occurs at the time 26. If the topology changes are not updated in time, the state estimator will not be able to produce a correct estimate of the state. The present embodiment does not give the results of the IEEE118 bus test system due to the similarity of the results.

The nonlinear filter performs in contrast as shown in fig. 15, after the fault clears, the OPI of the state estimator is much greater than 1, indicating that the estimate is much worse than the metrology. However, persistent errors caused by topology errors, which result in persistent interference with measured innovation and its skewness, can be used to detect topology changes, as shown in fig. 16 to 18, where the skewness of CKF drops sharply from a normal value around 1 to around 0.1 at time 26, then returns to 1 at time 27, and then increases further above 4 after time 28, as shown in fig. 17, where several measured NI are much larger than threshold 3 at time 27, as shown in fig. 1, and some NI are still larger than threshold 3.

TABLE 7 results of anomaly detection method

Anomaly identification to identify the branch removed, the change ratio calculation of the branch flow at time 26 is as listed in table 8. Leg 6 is successfully identified as the removed leg because of its r_mIs the largest.

Table 814 node tests branch change ratio after system failure

As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims

1. A power system prediction auxiliary state estimation method is characterized in that: the method comprises the following steps:

constructing a dynamic model for predicting the state of the power system;

if any bad data is identified, deleting the bad data and returning to the anomaly detection step, if any sudden load change is identified, refusing to predict and executing static estimation; if any branch is identified as a broken line, rejecting the prediction, updating the topology and performing a static estimation;

the specific steps of judging whether the abnormality occurs or not based on the number of the counted new information, carrying out abnormality detection, and distinguishing the abnormality caused by a plurality of bad data from sudden load changes which unevenly affect all new information comprise:

detecting the abnormality caused by single bad data in the measurement;

detecting sudden load changes that uniformly affect all new information;

setting skewness of the maximum innovation ratio and the maximum standard deviation of the measurement noise so as to distinguish the abnormal load change which is caused by a plurality of bad data and influences all innovation suddenly in a non-uniform way;

bad data is identified using the maximum innovation method: since only one average normalized innovation NI is greater than normal, the measurement with the largest average normalized innovation NI is determined to be bad data;

the step of identifying the sudden load change node includes:

predicting an active power injection measured value and covariance thereof;

calculating and correcting an active power injection measurement value;

calculating an innovation vector measured by pseudo injection by using the covariance and the two active power injection measurement values, and finding out the maximum element in the vector, wherein the corresponding node is the place where sudden load change occurs;

identifying nodes that are removed after a fault comprises the steps of:

2. The method of estimating the predictive assist state of an electric power system according to claim 1, wherein: the specific process of utilizing the nonlinear Kalman filter to calculate the state estimator of the dynamic model comprises the following steps: and generating volume points and corresponding weights by using a volume Kalman filter, and performing prediction state and prediction measurement to obtain Kalman estimation.

3. The method of estimating the predictive assist state of an electric power system according to claim 1, wherein: setting a normalized residual threshold to detect a sudden topology change after a fault, the step of, if the normalized residual exceeds the set threshold, causing the sudden topology change to occur comprising:

4. The method of estimating the predictive assist state of an electric power system according to claim 1, wherein: the specific process of setting the skewness of the maximum innovation ratio and the maximum standard deviation of the measurement noise to distinguish the abnormality caused by a plurality of bad data and the sudden load change which unevenly influences all the innovation comprises the following steps:

5. A power system prediction auxiliary state estimation system is characterized in that: the method comprises the following steps:

a selection processing module configured to delete bad data and return to the anomaly detection step if any bad data is identified, and to reject prediction and perform static estimation if any sudden load change is identified; if any branch is identified as a broken line, rejecting the prediction, updating the topology and performing a static estimation;

detecting the abnormality caused by single bad data in the measurement;

detecting sudden load changes that uniformly affect all new information;

the step of identifying the sudden load change node includes:

predicting an active power injection measured value and covariance thereof;

calculating and correcting an active power injection measurement value;

identifying nodes that are removed after a fault comprises the steps of:

6. A computer-readable storage medium characterized by: a plurality of instructions stored therein, the instructions adapted to be loaded by a processor of a terminal device and to perform a power system prediction assistance state estimation method according to any one of claims 1-4.

7. A terminal device is characterized in that: the system comprises a processor and a computer readable storage medium, wherein the processor is used for realizing instructions; a computer readable storage medium for storing a plurality of instructions adapted to be loaded by a processor and to perform a power system prediction assistance state estimation method according to any one of claims 1-4.