A residual magnetism calculation verification method based on an arc starting point algorithm

Abstract

The application provides a residual magnetism calculation verification method based on an arc starting point algorithm, comprising the following steps: collecting analog quantities of current and voltage and performing digital-analog conversion; when the collected data has an abnormal value, performing filtering processing on the sampling data by using a morphological filtering algorithm; detecting a closing period and judging whether a closing point exists, if not, returning to step S1, and if yes, executing step S4; extracting excitation inrush current waveform data and judging whether N continuous data are less than a current threshold value and the N+1th data is greater than the current threshold value, if not, returning to step S1, and if yes, outputting a mutation point and calculating a corresponding phase angle of the mutation point; and comprehensively calculating residual magnetism in a transformer core at the last time of switching off by derivation at the arc starting point. The method is simple and effective, is not affected by inaccurate magnetic flux estimation before and after magnetic saturation, requires only closing data, and can more accurately give a residual magnetism value.

Description

Technical Field

[0001] This invention belongs to the field of transformers, and in particular relates to a method for calculating and verifying residual magnetism based on the arc-starting point algorithm. Background Technology

[0002] Inrush currents pose significant hazards to power systems, causing issues such as protection malfunctions, surge current generation, and transformer damage, severely impacting the safe and stable operation of the power system. Due to the unmeasurable nature of transformer residual magnetism, the residual magnetism results obtained from both residual magnetism algorithms and demagnetizing instruments cannot be verified. This means that the residual magnetism calculation results or demagnetization effects can only be qualitatively determined by the magnitude of the inrush current, rather than quantitatively analyzed. For demagnetizing equipment, the level of residual magnetism after demagnetization directly affects the closing effect. Currently, the mainstream demagnetization principle uses alternating attenuated DC, which is time-consuming and complex. Without accurate quantitative analysis of the residual magnetism level, the expected inrush current suppression effect cannot be achieved, affecting the safe, stable, and reliable operation of the power system. For phase-selective closing control technology, the optimal closing angle is selected based on the calculated residual magnetism. Errors in the calculated residual magnetism can lead to significant errors in the optimal closing angle, resulting in poor phase-selective control. Therefore, appropriate verification and compensation of the calculated residual magnetism are necessary.

[0003] Due to the unmeasurable nature of transformer residual magnetism, current measurements are all obtained indirectly through calculation or measurement. There are two main methods for estimating residual magnetism: ① estimation using the hysteresis loop; ② calculation of the residual magnetism value using the voltage integration method. Transformers typically have their hysteresis loop measured at the factory by measuring the magnetic induction intensity curve of the transformer core under different magnetic field strengths. After obtaining the hysteresis loop curve, the residual magnetism can be estimated by measuring the intercept of the loop. The residual magnetism can also be calculated by measuring the hysteresis loop between two adjacent points and then performing numerical integration. The voltage integration method generally involves collecting the voltage value on the low-voltage side of the transformer and integrating the voltage to obtain the calculated value of the residual magnetism.

[0004] Both methods for estimating transformer residual magnetism have limitations in practical engineering applications. For many transformer manufacturers, the measurement and calculation of hysteresis curves inherently involve errors. In actual use, due to the complexity of the transient process of the transformer after switching off, the residual magnetism value predicted by this method is often unusable due to excessive error. The voltage integration method also has significant limitations in practical application because it cannot accurately represent the change in magnetic flux in the transformer core before and after oversaturation, leading to large errors in residual magnetism calculation. Summary of the Invention

[0005] The purpose of this invention is to provide a method for verifying remanence calculation based on the arc-starting point algorithm, which aims to solve the problem of large errors in existing remanence calculation methods.

[0006] This invention is implemented as follows: a method for calculating and verifying remanence based on the arc initiation point algorithm, the method comprising the following steps:

[0007] Step S1: Acquire analog quantities of current and voltage, and perform digital-to-analog conversion;

[0008] Step S2: When outliers appear in the collected data, the sampled data is filtered using a morphological filtering algorithm.

[0009] Step S3: Detect the closing cycle and determine whether a closing point has occurred. If not, return to step S1; if so, proceed to step S4.

[0010] Step S4: Extract the excitation inrush current waveform data, determine whether there are N consecutive data points less than the inrush threshold and the (N+1)th data point greater than the inrush threshold. If not, return to step S1. If so, output the abrupt change point and calculate the corresponding phase angle of the abrupt change point, and execute step S5.

[0011] Step S5: Define the point where the inrush current first appears as the arc initiation point, and φ at the arc initiation point. 饱和 =φ 稳态 +φ 暂态 The transient magnetic flux is the sum of the residual magnetic flux in the transformer core during the previous tripping and the bias magnetic field generated during the current closing, where φ 偏磁 =cos(α*π / 180), where α is the closing angle and φ 稳态 =cos(θ1*π / 180), where θ1 is the phase angle corresponding to the starting point of the arc. Combining the above three equations and through derivation, the residual magnetism remaining in the transformer core during the last trip is...

[0012] φ 剩磁 =φ 饱和磁通 -cos(θ1*π / 180)-cos(α*π / 180).

[0013] A further technical solution of the present invention is: in step S1, the analog quantities of voltage and current collected are converted from digital to analog by an AD chip.

[0014] A further technical solution of the present invention is: in step S2, the morphological filtering algorithm adopts a combination of morphological opening operation followed by morphological closing operation, or a combination of morphological closing operation followed by morphological opening operation.

[0015] A further technical solution of the present invention is as follows: In step S2, in the morphological filtering algorithm, let the original signal be I(n), where (n = 1, 2, ..., N); define the structuring element as G(m), where (m = 1, 2, ..., M; and N ≥ M); define the erosion and dilation operations of I(n) with respect to G(m) as follows:

[0016] (I!G)(n)=min[I(n+m)-G(m)],m∈0,1,…,M-1.

[0017]

[0018] The opening and closing operations of U(n) with respect to G(m) are defined as follows:

[0019]

[0020]

[0021] A further technical solution of the present invention is that the collected current and voltage data are output after undergoing two processes of corrosion and expansion.

[0022] A further technical solution of the present invention is: taking the magnetic flux at 100% of the rated voltage level. The value is taken as the saturation magnetic flux of the transformer core.

[0023] A further technical solution of the present invention includes step S6: displaying the remanence value calculated in step S5 through a display module.

[0024] The beneficial effects of this invention are: by accurately calculating the residual magnetism remaining in the core at the time of the last circuit breaker tripping through the arc initiation point, and then displaying the residual magnetism value through a visualization process, it can be used to verify the demagnetization effect or the residual magnetism calculation effect. This method is simple and effective, and is not affected by inaccurate magnetic flux prediction before and after magnetic saturation. The only required data is the closing data, which can provide a relatively accurate residual magnetism value. Attached Figure Description

[0025] Figure 1 This is a flowchart of the method of the present invention;

[0026] Figure 2 This is a schematic diagram of the voltage-magnetic flux-inrush current relationship in the algorithm of this invention;

[0027] Figure 3 This is a schematic diagram of arc-start point detection in the algorithm of this invention;

[0028] Figure 4 This is a comparison chart of the filtering effects for arc-start point detection in the algorithm of this invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0030] This invention provides a method for verifying remanence calculation based on the arc initiation point algorithm, the method comprising the following steps:

[0031] Step S1: Acquire analog quantities of current and voltage, and perform digital-to-analog conversion;

[0032] Step S2: When outliers appear in the collected data, the sampled data is filtered using a morphological filtering algorithm.

[0033] Step S3: Detect the closing cycle and determine whether a closing point has occurred. If not, return to step S1; if so, proceed to step S4.

[0034] Step S4: Extract the excitation inrush current waveform data, determine whether there are N consecutive data points less than the inrush threshold and the (N+1)th data point greater than the inrush threshold. If not, return to step S1. If so, output the abrupt change point and calculate the corresponding phase angle of the abrupt change point, and execute step S5.

[0035] Step S5: Define the point where the inrush current first appears as the arc initiation point, and φ at the arc initiation point. 饱和 =φ 稳态 +φ 暂态 The transient magnetic flux is the sum of the residual magnetic flux in the transformer core during the previous tripping and the bias magnetic field generated during the current closing, where φ 偏磁 =cos(α*π / 180), where α is the closing angle and φ 稳态 =cos(θ1*π / 180), where θ1 is the phase angle corresponding to the starting point of the arc. Combining the above three equations and through derivation, the residual magnetism remaining in the transformer core during the last trip is...

[0036] φ 剩磁 =φ 饱和磁通 -cos(θ1*π / 180)-cos(α*π / 180).

[0037] Prior to step S1, the analog quantities of voltage and current collected are converted from digital to analog using an AD chip.

[0038] Preferably, in step S2, the morphological filtering algorithm uses a combination of morphological opening operation followed by morphological closing operation, or a combination of morphological closing operation followed by morphological opening operation.

[0039] Preferably, in step S2, in the morphological filtering algorithm, let the original signal be I(n), where (n = 1, 2, ..., N); define the structuring element as G(m), where (m = 1, 2, ..., M; and N ≥ M), and define the erosion and dilation operations of I(n) with respect to G(m) as follows:

[0040] (I!G)(n)=min[I(n+m)-G(m)],m∈0,1,…,M-1.

[0041]

[0042] The opening and closing operations of U(n) with respect to G(m) are defined as follows:

[0043]

[0044]

[0045] Prior to this, the collected current and voltage data are output after undergoing two processes of corrosion and expansion.

[0046] Preferably, the magnetic flux at 100% of the rated voltage level is taken. The value is taken as the saturation magnetic flux of the transformer core.

[0047] Preferredly, it also includes step S6: displaying the remanence value calculated in step S5 through a display module.

[0048] This invention automatically captures the voltage and current waveforms of the transformer during circuit breaker closing. Based on the mechanism theory of transformer inrush current generation, it obtains the accurate value of the transformer's transient magnetic flux through an arc-starting point algorithm. Then, by subtracting the calculated value from the bias magnetism generated during closing, the accurate value of the residual magnetism can be obtained. Finally, the calculated residual magnetism value is displayed through a visualization module for comparison with the estimated residual magnetism value. It is particularly important to note that the process from circuit breaker closing to the occurrence of inrush current requires a delay of no more than half a cycle. During this time, the transient magnetic flux composed of the residual magnetism reserved from the previous opening and the bias magnetism generated by the current closing will decay for no more than half a cycle. This decay is related to the transformer's structure and wiring circuit, but under normal circumstances, it has little impact on the residual magnetism value. The difference between the transient residual magnetism value calculated by the arc-starting point algorithm and the bias magnetism can be considered as the residual magnetism remaining in the transformer core during the previous opening.

[0049] like Figure 2As shown, when a transformer is closed under no-load conditions, the magnetic flux is classified into steady-state flux and transient flux based on its attenuation characteristics. The transient flux mainly consists of the residual magnetism left after the previous opening and the bias magnetism generated during closing. The residual magnetism is the magnetic flux remaining on the transformer core after the previous opening, while the bias magnetism is the magnetic flux generated on the core at a specific closing angle when the transformer is closed. The steady-state flux is the magnetic flux induced on the transformer core by the applied AC voltage. The total flux is the sum of these three values. The saturation flux is determined by the transformer core; the saturation flux of each transformer is determined during manufacturing. When the total flux is less than or equal to the saturation flux, such as... Figure 2 Points a, b, c, and d in the diagram do not experience inrush current. Current surges only when the total magnetic flux is greater than or equal to the saturation flux. The current threshold is defined as follows: Scanning the current waveform data confirms the presence of current; values ​​exceeding this threshold are considered current-containing, while values ​​below it are considered current-free.

[0050] The point at which the inrush current first occurs is defined as the arc initiation point, i.e. Figure 2 Point a in the equation, the arc-starting point algorithm is based on the excitation inrush current generation mechanism. When the total magnetic flux of the transformer core exceeds the saturation magnetic flux, excitation inrush current will occur. The magnetic flux expression when the transformer is closed is shown below:

[0051] φ 总 =φ 稳态 +φ 暂态 (1)

[0052] In the above formula, the steady-state magnetic flux is the magnetic flux induced by the sinusoidal voltage applied to each winding of the transformer, and the transient magnetic flux is the sum of the magnetic flux remaining in the transformer core when the circuit was opened last time and the bias magnetism generated when the circuit was closed this time.

[0053] The sliding window method for detecting arc initiation points is susceptible to interference from harmonics, abnormal data, and sampling accuracy, leading to inaccurate arc initiation point detection and consequently, significant errors in the calculation results. To address the interference in the sampled data, a morphological filtering algorithm is used. Morphological opening and closing operations are a pair of dual transformations; morphological opening suppresses positive impulse noise in the signal, while morphological closing suppresses negative impulse noise. Due to statistical bias in morphological opening and closing operations, their filtering effect is not very good when used alone; therefore, a combination of opening-closing or closing-opening filtering methods is usually employed. The effectiveness of morphological filtering also depends on the size and shape of the structuring element, which is generally selected based on the characteristics of the signal. Let the original signal be I(n), where (n = 1, 2, ..., N); define the structuring element as G(m), where (m = 1, 2, ..., M; and N ≥ M). Define the erosion and dilation operations of I(n) with respect to G(m) as follows:

[0054] (I!G)(n)=min[I(n+m)-G(m)],m∈0,1,…,M-1.

[0055]

[0056] The opening and closing operations of U(n) with respect to G(m) are defined as follows:

[0057]

[0058]

[0059] The collected voltage data was processed through two erosion and expansion steps before output. The structuring element G(m) was set to [1,1,1,1,1] and [0,0.0711,1,0.0711,0] respectively for flattened structuring element filtering and sinusoidal structuring element filtering. The filtered data from these two methods were compared and verified. The comparison graph after filtering is shown below. Figure 4 As shown, the original signal contains significant harmonics, leading to substantial errors in detecting the arc starting point, with only 20 arc starting points identified. After filtering, when using both flattened structuring element filtering and sinusoidal structuring element filtering for arc starting point detection, both methods detected 43 arc starting points, demonstrating consistent results and indirectly verifying the accuracy of the algorithm.

[0060] The starting point of the inrush current during this closing operation is defined as the arc initiation point of that phase. At the arc initiation point, equation (1) can be expressed as:

[0061] φ 饱和 =φ 稳态 +φ 暂态 (1)

[0062] In the above formula, the steady-state magnetic flux is the magnetic flux induced by the sinusoidal voltage applied to each winding of the transformer, while the transient magnetic flux is the magnetic flux remaining in the transformer core during the previous tripping, the value of the bias magnetism generated during the current closing, and the attenuated magnetic flux value. Generally, the magnetic flux at 100% of the rated voltage level is taken as... The saturation magnetic flux of the transformer core is taken as a multiple. Let the closing angle be α. The bias magnetic field in the above formula is calculated using the closing angle:

[0063] φ 偏磁 =cos(α*π / 180) (2)

[0064] Since the steady-state magnetic flux is calculated through voltage integration and is also a periodic component, the steady-state magnetic flux at this point can be calculated using the phase angle corresponding to that point. The angle corresponding to point a is θ1, and the steady-state magnetic flux at this point can be expressed as:

[0065] φ 稳态=cos(θ1*π / 180) (3)

[0066] By combining equations (1), (2), and (3), the residual magnetism remaining in the transformer core at the time of the last circuit breaker trip can be accurately calculated using the arc-starting point algorithm. Its expression is as follows:

[0067] φ 剩磁 =φ 饱和磁通 -cos(θ1*π / 180)-cos(α*π / 180)

[0068] The above formula can accurately calculate the residual magnetism from the previous circuit breaker trip.

[0069] It provides several voltage and current acquisition channels. After digital-to-analog conversion using a high-precision AD chip, the high-precision digital quantity is input into the arc starting point algorithm to calculate the steady-state magnetic flux. The difference between the digital flux and the bias magnetic flux generated when the circuit is closed is used to obtain the accurate residual magnetic value. Finally, the calculated residual magnetic value is displayed through the display module.

[0070] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for verifying remanence calculation based on the arc initiation point algorithm, characterized in that, The method includes the following steps: Step S1: Acquire analog quantities of current and voltage, and perform digital-to-analog conversion; Step S2: When outliers appear in the collected data, the sampled data is filtered using a morphological filtering algorithm. Step S3: Detect the closing cycle and determine whether a closing point has occurred. If not, return to step S1; if so, proceed to step S4. Step S4: Extract the excitation inrush current waveform data, determine whether there are N consecutive data points less than the inrush threshold and the (N+1)th data point greater than the inrush threshold. If not, return to step S1. If so, output the abrupt change point and calculate the corresponding phase angle of the abrupt change point, and execute step S5. Step S5: Define the point where the inrush current first appears as the arc initiation point, and φ at the arc initiation point. 饱和 =φ 稳态 +φ 暂态 The transient magnetic flux is the sum of the residual magnetic flux in the transformer core during the previous tripping and the bias magnetic field generated during the current closing, where φ 偏磁 =cos(α*π / 180), where α is the closing angle and φ 稳态 =cos(θ1*π / 180), where θ1 is the phase angle corresponding to the starting point of the arc. Combining the above three equations and through derivation, the residual magnetism remaining in the transformer core at the time of the last circuit breaker trip is φ. 剩磁 =φ 饱和磁通 -cos(θ1*π / 180)-cos(α*π / 180); Step S6: Display the remanence value calculated in step S5 through the display module.

2. The method for remanence calculation and verification based on the arc-starting point algorithm according to claim 1, characterized in that, In step S1, the analog quantities of voltage and current collected are converted from digital to analog using an AD chip.

3. The method for remanence calculation and verification based on the arc initiation point algorithm according to claim 1, characterized in that, In step S2, the morphological filtering algorithm uses either a combination of morphological opening operation followed by morphological closing operation, or a combination of morphological closing operation followed by morphological opening operation.

4. The method for remanence calculation and verification based on the arc initiation point algorithm according to claim 3, characterized in that, In step S2, in the morphological filtering algorithm, let the original signal be I(n), where (n = 1, 2, ..., N); define the structuring element as G(m), where (m = 1, 2, ..., M; and N ≥ M); define the erosion and dilation operations of I(n) with respect to G(m) as follows: (I!G)(n)=min[I(n+m)-G(m)],m∈0,1,…,M-1. The opening and closing operations of U(n) with respect to G(m) are defined as follows:

5. The method for remanence calculation and verification based on the arc initiation point algorithm according to claim 4, characterized in that, The collected current and voltage data are output after undergoing two processes of corrosion and expansion.

6. The method for remanence calculation and verification based on the arc initiation point algorithm according to claim 1, characterized in that, Take the magnetic flux at 100% of the rated voltage level The value is taken as the saturation magnetic flux of the transformer core.

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