Short-circuit current zero point prediction method based on wavelet Kalman filtering

Abstract

The invention discloses a short-circuit current zero point prediction method based on wavelet Kalman filtering, and belongs to the technical field of high-voltage switches of power systems. The method comprises the following steps: monitoring and identifying a short-circuit fault current in real time, and constructing a four-dimensional current array as an observation vector by adopting a sliding window mechanism; establishing a wavelet Kalman filtering equation based on the short-circuit current expression, and dynamically estimating signal components of each layer of current parameters through a wavelet Kalman filtering algorithm; and restoring the current parameters by using a wavelet transform reconstruction technology, and predicting the current zero crossing point position. According to the method, the multi-scale analysis capability of Kalman filtering is enhanced through wavelet transform, the accuracy and rapidity of short-circuit current zero point prediction are improved, the contact ablation risk is reduced in cooperation with a phase selection breaking technology, and the breaking reliability is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of fault current phase-selective interruption, and in particular to a short-circuit current zero point prediction method based on wavelet Kalman filtering. Background Art

[0002] With the recent expansion of my country's power grid, the continued decline in equivalent impedance of the power system has led to excessive short-circuit currents, posing a significant challenge to the safe and stable operation of the grid. Phase-selective short-circuit current interruption technology involves controlling the circuit breaker's tripping operation by selecting a specific phase of the current flowing through the circuit breaker, separating the contacts at the zero point of the short-circuit current. Interrupting short-circuit currents with phase-selective interruption technology can effectively improve the reliability of switchgear, significantly contributing to enhancing the transient stability of power systems and extending the electrical life of circuit breaker arc chambers.

[0003] The core mechanism of phase-selective interrupting technology lies in precisely controlling arc energy through high-precision prediction of the short-circuit current zero-crossing point. The key challenge of phase-selective interrupting is how to quickly identify short-circuit current parameters and accurately predict the zero-crossing point within the power protection system's operating time. Summary of the Invention

[0004] In response to the technical problems existing in the above-mentioned prior art, the purpose of the present invention is to propose a short-circuit current zero point prediction method based on wavelet Kalman filtering. This method is based on the multi-resolution analysis technology of wavelet analysis and combined with the optimal estimation method of Kalman filtering. It can quickly and accurately restore the short-circuit current waveform and realize the short-circuit current zero point prediction.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A short-circuit current zero point prediction method based on wavelet Kalman filtering includes the following steps:

[0007] Step 1: Monitor current signals and identify short-circuit faults: Monitor the power system current signal in real time. When a short-circuit fault is detected, immediately collect short-circuit current time series data at a preset sampling rate.

[0008] Step 2: Use the sliding window mechanism to construct the short-circuit current time series array: the short-circuit current value v collected at that time is k Compared with the historical short-circuit current values ​​v of the previous three samples k-1 、v k-2 、v k-3 Combine into a four-dimensional array;

[0009] Step 3: Based on the power system short-circuit current expression, construct the Kalman filter equations and convert them into wavelet Kalman filter equations through wavelet transform. Use the short-circuit current time series array obtained in step 2 as the observation vector input and call the wavelet Kalman filter algorithm to estimate the signal components of each layer of the short-circuit current parameters.

[0010] It should be further explained that step 3 specifically includes the following steps:

[0011] Step 3.1: Construct the discrete expression of the power system short-circuit current as:

[0012]

[0013] Among them, a0 is the starting value of DC component attenuation; T a is the DC component decay time constant; ΔT is the sampling interval; a1 and a2 are the amplitudes of the AC cosine and sine components respectively; k is the discrete time index, indicating the number of sampling times; K is the number of sampling points; ω is the power system frequency; i noise (k) is the Gaussian white noise component;

[0014] Step 3.2: Based on the short-circuit current expression in step 3.1, establish the Kalman filter equations, and establish the state equation and observation equation of the short-circuit current, as follows:

[0015] The Kalman filter equations are expressed as:

[0016]

[0017] Where, X k is the state vector at the kth sampling time; A k,k-1 is the state transfer matrix, which represents the state transfer relationship from the k-1th sampling to the kth sampling; X k-1 is the state vector at the last sampling; Γ k,k-1 ξ k-1 is the state vector noise term; V k is the observation vector at the kth sampling time; C k is the observation transfer matrix at the kth sampling time; η k is the observation noise term.

[0018] Let a0, a1, a2 be the parameters to be estimated, and use them as the state vector X in the equation system. k ,Right now:

[0019]

[0020] Determine the corresponding state transfer matrix A k,k-1 for:

[0021]

[0022] Observation vector V k The short-circuit current sequence obtained by sampling:

[0023] V k =i(k)

[0024] Determine the corresponding observation transfer matrix C k for:

[0025] C k =[1coskωΔT sinkωΔT]

[0026] i noise (k) only interferes with the sampling value of the short-circuit current, and its properties can be determined by the observation noise term η k The complete embodiment and the state vector noise term Γ k,k-1 ξ k-1 is zero.

[0027] The Kalman filter equations established based on the short-circuit current expression are:

[0028]

[0029] Step 3.3, select the adapted wavelet basis to be estimated for the state vector X k Perform three-layer simultaneous decomposition to form a multi-dimensional wavelet Kalman filter equation, as follows:

[0030] Treat the estimated state vector X with the selected wavelet basis k Perform three-layer decomposition simultaneously, and the decomposition amount is:

[0031]

[0032] Where N is the maximum scale layer of wavelet decomposition; X k-i is the Kalman filter state vector of the ki-th sampling; and They represent the high-frequency and low-frequency parts of the state vector decomposed into the i-th layer when the k-th sampling occurs; the operator H N-i , G N-i are finite length unit impulse response filters of low-pass {h(n)} and high-pass {g(n)}, respectively, which are determined by the selected wavelet basis and represent the responses from the Nth layer to the Nith layer; T N-3∣N is an orthogonal matrix, Mapped to three layers of filter banks.

[0033] After decomposition, the state equation of the Kalman filter is transformed into the state equation of the wavelet Kalman filter:

[0034]

[0035] Where, and They represent the high-frequency and low-frequency parts of the state vector decomposed into the i-th layer when the k+1th sampling is performed; A is the state transfer matrix of the wavelet Kalman filter:

[0036]

[0037] is the state vector transfer matrix of the four-dimensional matrix, and the calculation method is:

[0038]

[0039] is the state noise weight matrix of the wavelet Kalman filter, which is assumed to be zero.

[0040] Correspondingly, after decomposition, the observation equation of the Kalman filter is transformed into the observation equation of the wavelet Kalman filter:

[0041]

[0042] Where, is the observation vector of the wavelet Kalman filter, obtained by sampling in step 2; C is the observation state transfer matrix of the wavelet Kalman filter:

[0043]

[0044] is the observation vector transfer matrix of the four-dimensional matrix, and the calculation method is:

[0045]

[0046] is the observation noise weight matrix of wavelet Kalman filter, which is composed of the noise η sampled at the kith time k-i composition:

[0047]

[0048] In step 3.4, the short-circuit current time series array composed of the samples in step 2 is used as the observation vector input, and the wavelet Kalman filter algorithm is called to calculate the short-circuit current parameters a0, a1, and a2 to be estimated and decomposed into signal components of each layer. The calculation process includes the following steps:

[0049] Step 3.4.1, state vector prediction: predict the state vector at the kth sampling time based on the wavelet Kalman filter state vector at the k-1th sampling time:

[0050]

[0051] Step 3.4.2: State vector covariance prediction: Based on the wavelet Kalman filter state vector at the k-1th sampling time, the state vector covariance at the kth sampling time is predicted:

[0052]

[0053] Where, and Respectively represent the covariance of the high-frequency and low-frequency components of the state vector at the k-th sampling time; and Respectively represent the covariance of the high-frequency and low-frequency components of the state vector at the k-1th sampling time;

[0054] Step 3.4.3: Wavelet Kalman gain calculation:

[0055]

[0056] Where, and They represent the Kalman filter gains of the high-frequency and low-frequency components decomposed to the i-th layer at the k-th sampling time respectively; and They represent the observation noise covariance matrices of the high-frequency and low-frequency components decomposed into the i-th layer at the k-th sampling time.

[0057] Step 3.4.4: State vector update: Update the state vector by measuring the residual:

[0058]

[0059] Step 3.4.5: State vector covariance update:

[0060]

[0061] Step 4: Every time a new current data is sampled, execute steps 2 and 3 for iterative calculation until the preset sampling window length is reached. The signal components of each layer are restored to short-circuit current parameters through wavelet transform reconstruction technology, and the short-circuit current zero point position is determined.

[0062] Among them, the reconstruction method of wavelet transform for the estimated parameters is:

[0063]

[0064] As can be seen from the above technical solution, the short-circuit current zero point prediction method based on wavelet Kalman filtering of the present invention combines the multi-resolution analysis technology of wavelet analysis with the optimal estimation method of Kalman filtering, which can quickly and accurately predict the zero point position of the short-circuit current, thereby shortening the arcing time of switching devices such as circuit breakers, reducing the arc erosion of switching devices, and improving the breaking capacity. The short-circuit current of the power system is mainly composed of components such as the DC attenuation component and the steady-state AC component. The parameters to be estimated in the short-circuit current expression are solved using the wavelet Kalman filtering algorithm, so that the zero point of the short-circuit current is predicted according to the short-circuit current expression, so that the switching devices such as circuit breakers can be accurately disconnected at the current zero point. The short-circuit current zero point predicted by the algorithm of the present invention can meet the accuracy requirements of the short-circuit current phase selection and disconnection control, and can achieve successful disconnection with a shorter arcing time by cooperating with power grid relay protection, circuit breakers and other devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is the short-circuit current zero point prediction method process of the present invention.

[0066] Figure 2 This is the calculation process of the short-circuit current parameters of the present invention.

[0067] Figure 3 This is the prediction effect of the algorithm proposed in this invention on the three-phase short-circuit current. DETAILED DESCRIPTION

[0068] The technical solutions in the embodiments of the present invention are further described in detail below in conjunction with the drawings of specific embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, but not all of the embodiments.

[0069] The short-circuit current zero point prediction algorithm based on wavelet Kalman provided by the present invention is as follows: Figure 1 As shown in the figure, the current signal of the power system is first monitored to identify the short-circuit fault. Then, the short-circuit current value obtained by the current sampling and the historical short-circuit current values ​​of the previous three samplings are combined into a four-dimensional array as the observation vector. The wavelet Kalman filter algorithm is called. In the process of continuous sampling and iterative calculation, the short-circuit current parameter to be estimated gradually approaches the actual short-circuit current situation, and the zero point position is calculated.

[0070] The specific implementation steps are as follows:

[0071] Step 1: Monitor the current signal at a 10kHz frequency in real time to identify short-circuit faults: Monitor the power system current signal in real time. If no fault is detected, continue monitoring. When a short-circuit fault is detected, maintain a 10kHz sampling rate to collect short-circuit current time series data.

[0072] Step 2: Use the sliding window mechanism to construct the short-circuit current time series array: the short-circuit current value v collected at that time is k Compared with the historical short-circuit current values ​​v of the previous three samples k-1 、v k-2 、v k-3 Combine into a four-dimensional array;

[0073] Step 3: Based on the power system short-circuit current expression, construct the Kalman filter equations, select the Haar wavelet to transform it into the wavelet Kalman filter equations, use the current time series array sampled in step 2 as the observation vector input, and call the wavelet Kalman filter algorithm to estimate the signal components of each layer of the short-circuit current parameters.

[0074] It should be further explained that the algorithm steps adopted in step 3 include:

[0075] Step 3.1: Construct the discrete expression of the power system short-circuit current as:

[0076]

[0077] Among them, a0 is the starting value of DC component attenuation; T a is the DC component decay time constant; ΔT is the sampling interval; a1 and a2 are the amplitudes of the AC cosine and sine components respectively; k is the discrete time index, indicating the number of sampling times; K is the number of sampling points; ω is the power system frequency; i noise (k) is the Gaussian white noise component;

[0078] Step 3.2: Establish the Kalman filter equations according to the short-circuit current expression in step 3.1, and establish the state equation and observation equation of the short-circuit current, as follows:

[0079] The Kalman filter equations are expressed as:

[0080]

[0081] Where, X k is the state vector at the kth sampling time; A k,k-1 is the state transfer matrix, which represents the state transfer relationship from the k-1th sampling to the kth sampling; X k-1 is the state vector at the last sampling; Γ k,k-1 ξ k-1 is the state vector noise term; V k is the observation vector at the kth sampling time; C k is the observation transfer matrix at the kth sampling time; η k is the observation noise term.

[0082] Let a0, a1, a2 be the parameters to be estimated, and use them as the state vector X in the equation system.k ,Right now:

[0083]

[0084] Determine the corresponding state transfer matrix A k,k-1 for:

[0085]

[0086] Observation vector V k The short-circuit current sequence obtained by sampling:

[0087] V k =i(k)

[0088] Determine the corresponding observation transfer matrix C k for:

[0089] C k =[1coskωΔT sinkωΔT]

[0090] i noise (k) only interferes with the sampling value of the short-circuit current, and its properties can be determined by the observation noise term η k The complete embodiment and the state vector noise term Γ k,k-1 ξ k-1 is zero.

[0091] The Kalman filter equations established based on the short-circuit current expression are:

[0092]

[0093] Step 3.3, select Haar wavelet to estimate the state vector X k Perform three-layer simultaneous decomposition and transform the Kalman filter equation in step 3.2 into a multi-dimensional wavelet Kalman filter equation, as follows:

[0094] The state vector X is transformed into k Perform three-layer decomposition simultaneously, and the decomposition amount is:

[0095]

[0096] Where N is the maximum scale layer of wavelet decomposition; X k-i is the Kalman filter state vector of the ki-th sampling; and They represent the high-frequency and low-frequency parts of the state vector decomposed into the i-th layer at the k-th sampling time; T N-3∣N is an orthogonal matrix, Mapped to the three layers of the filter bank; operator H N-i , G N-iThey are the finite length unit impulse response filters of the Haar wavelet low-pass {h(n)} and high-pass {g(n)}, representing the response from the Nth layer to the Nith layer:

[0097]

[0098] After decomposition, the state equation of the Kalman filter is transformed into the state equation of the wavelet Kalman filter:

[0099]

[0100] Where, and They represent the high-frequency and low-frequency parts of the state vector decomposed into the i-th layer when the k+1th sampling is performed; A is the state transfer matrix of the wavelet Kalman filter:

[0101]

[0102] is the state vector transfer matrix of the four-dimensional matrix, and the calculation method is:

[0103]

[0104] is the state noise weight matrix of the wavelet Kalman filter, which is assumed to be zero.

[0105] Correspondingly, after decomposition, the observation equation of the Kalman filter is transformed into the observation equation of the wavelet Kalman filter:

[0106]

[0107] Where, is the observation vector of the wavelet Kalman filter, obtained by sampling in step 2; C is the observation state transfer matrix of the wavelet Kalman filter:

[0108]

[0109] is the observation vector transfer matrix of the four-dimensional matrix, and the calculation method is:

[0110]

[0111] is the observation noise weight matrix of wavelet Kalman filter, which is composed of the noise η sampled at the kith time k-i composition:

[0112]

[0113] Step 3.4: Take the short-circuit current time series array composed of the samples in step 2 as the observation vector input, and call the wavelet Kalman filter algorithm to calculate the short-circuit current parameters a0, a1, and a2 to be estimated and decompose them into signal components of each layer. The calculation process is as follows: Figure 2 As shown, the following steps are included:

[0114] Step 3.4.1, state vector prediction: predict the state vector at the kth sampling time based on the wavelet Kalman filter state vector at the k-1th sampling time:

[0115]

[0116] Step 3.4.2: State vector covariance prediction: Based on the wavelet Kalman filter state vector at the k-1th sampling time, the state vector covariance at the kth sampling time is predicted:

[0117]

[0118] Where, and Respectively represent the covariance of the high-frequency and low-frequency components of the state vector at the k-th sampling time; and Respectively represent the covariance of the high-frequency and low-frequency components of the state vector at the k-1th sampling time;

[0119] Step 3.4.3: Wavelet Kalman gain calculation:

[0120]

[0121] Where, and They represent the Kalman filter gains of the high-frequency and low-frequency components decomposed to the i-th layer at the k-th sampling time respectively; and They represent the observation noise covariance matrices of the high-frequency and low-frequency components decomposed into the i-th layer at the k-th sampling time.

[0122] Step 3.4.4: State vector update: Update the state vector by measuring the residual:

[0123]

[0124] Step 3.4.5: State vector covariance update:

[0125]

[0126] Step 4: Each time a new current data point is sampled, steps 2 and 3 are iterated until the sampling window length reaches 3ms, i.e., the number of iterations reaches 30. After the calculation is completed, the signal components of each layer are restored to short-circuit current parameters through wavelet reconstruction using Haar wavelets. Based on the short-circuit current expression, the short-circuit current zero point position is determined using a binary search method, providing guidance for phase selection and interruption of the switchgear.

[0127] Among them, the reconstruction method of wavelet transform for the estimated parameters is:

[0128]

[0129] Figure 3 The prediction method proposed in the present invention is used to record and verify the short-circuit current in the power grid. After sampling the short-circuit current signal, the wavelet Kalman filter algorithm is used to obtain the coefficients of the short-circuit current expression, so that the parameters such as the attenuation DC component, the attenuation time constant, the steady-state AC component amplitude, etc. can be obtained, the short-circuit current waveform can be restored, and the position of the zero point can be calculated. The method only takes 3ms to complete the accurate prediction of the current zero point. The error between the predicted value obtained by the prediction method of the present invention and the true value is less than 0.1ms. It is proved that the short-circuit current zero point predicted by the method of the present invention can meet the accuracy requirements of the short-circuit current phase selection and disconnection control, and can achieve successful disconnection with a shorter arcing time by cooperating with power grid relay protection, circuit breakers and other devices.

[0130] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. The present invention is subject to various modifications and variations. Any modifications, equivalent substitutions, improvements, etc. made without departing from the technical principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A short-circuit current zero point prediction method based on wavelet Kalman filtering, characterized in that: The method comprises the following steps: Step 1: Monitor current signals and identify short-circuit faults: Monitor the power system current signal in real time. When a short-circuit fault is detected, immediately collect short-circuit current time series data at a preset sampling rate. Step 2: Use the sliding window mechanism to construct the short-circuit current time series array: the short-circuit current value v collected at that time is k Compared with the historical short-circuit current values ​​v of the previous three samples k-1 、v k-2 、v k-3 Combine into a four-dimensional array; Step 3: Based on the power system short-circuit current expression, construct the Kalman filter equations and convert them into wavelet Kalman filter equations through wavelet transform. Use the short-circuit current time series array obtained in step 2 as the observation vector input and call the wavelet Kalman filter algorithm to estimate the signal components of each layer of the short-circuit current parameters. Step 4: Every time a new current data is sampled, execute steps 2 and 3 for iterative calculation until the preset sampling window length is reached. The signal components of each layer are restored to short-circuit current parameters through wavelet transform reconstruction technology, and the short-circuit current zero point position is determined.

2. The short-circuit current zero point prediction method based on wavelet Kalman filtering according to claim 1 is characterized in that: Step 3 specifically includes the following steps: Step 3.1: Construct a discrete expression for the power system short-circuit current: Among them, a0 is the starting value of DC component attenuation; T a is the DC component decay time constant; ΔT is the sampling interval; a1 and a2 are the amplitudes of the AC cosine and sine components respectively; k is the discrete time index, indicating the number of sampling times; K is the number of sampling points; ω is the power system frequency; i noise (k) is the Gaussian white noise component; Step 3.2: Establish the Kalman filter equations according to the short-circuit current expression in step 3.1, and establish the state equation and observation equation of the short-circuit current; The Kalman filter equations established based on the short-circuit current expression are: Step 3.3: Select an adaptive wavelet basis to perform three-layer simultaneous decomposition on the short-circuit current parameters a0, a1, and a2 to form a multi-dimensional wavelet Kalman filter equation; Step 3.4: Use the short-circuit current time series array composed of samples in step 2 as the observation vector input, call the wavelet Kalman filter algorithm to calculate the short-circuit current parameters a0, a1, and a2 to be estimated and decompose them into signal components of each layer.

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