A single-phase transformer residual magnetic flux density measurement method based on a composite index

Abstract

This invention provides a method for measuring the residual magnetic flux density of a single-phase transformer based on a composite index, relating to the field of transformers. First, a measurement circuit is constructed containing dual voltage sources, a transformer, and a series resistor. An initial residual magnetic flux density of the core is preset using an AC voltage source. Then, a three-level DC low-voltage excitation is applied from +V→0→-V→0. The preset winding transient current and the measured winding terminal voltage are collected and integrated after normalization and integral calculations to obtain the composite index k. The relationship curve between k and the residual magnetic flux density Br is obtained through demagnetization and adjustment of the residual magnetism. A mathematical relationship between the two is constructed based on a first-order Fourier series, and the unknown coefficients are determined using polynomial regression. Finally, the same excitation is applied to the transformer with unknown residual magnetism, and the composite index is calculated and then substituted into a fitting formula to obtain the residual magnetic flux density. This invention is a non-invasive measurement method that does not require intervention in the transformer core. It offers high measurement accuracy, simple calculation logic, and wide applicability, effectively avoiding inrush current and power grid operation accidents caused by core residual magnetism.

Description

Technical Field

[0001] This invention relates to the field of transformer technology, and specifically to a method for measuring the residual flux density of a single-phase transformer based on composite indicators. Background Technology

[0002] In actual operation of power systems, the closing and commissioning of transformers, the opening and disconnection of transformers, and various tests (such as DC winding tests) are routine procedures. However, due to the inherent magnetic hysteresis characteristics of ferromagnetic materials such as cold-rolled silicon steel sheets used in the core—that is, the change in magnetic induction intensity lags behind the magnetic field intensity—the magnetic domain arrangement cannot be completely restored to its initial state after the external magnetic field disappears, and a certain amount of residual magnetic induction intensity will inevitably remain in the core.

[0003] While residual magnetism is an inherent characteristic of ferromagnetic materials, it can cause multiple hazards to transformers and power grid operation. When a transformer is re-energized under no-load or light-load conditions, if the residual magnetism in the core is aligned with the magnetic flux generated by the applied current at the moment of re-energization, it can rapidly lead to half-cycle saturation of the core, thereby generating inrush current. This inrush current peak can reach several times or even tens of times the normal steady-state operating current. On the one hand, it can impact the transformer windings, damaging the equipment itself; on the other hand, it may trigger malfunctions in relay protection devices such as transformer differential protection, causing the transformer to fail to operate normally, and in severe cases, even leading to major accidents such as power outages and grid collapse. Furthermore, core saturation also generates a large number of even-order harmonics, reducing power quality and increasing reactive power losses in the transformer, further affecting the economical and efficient operation of the power system. However, under current technology, there are technical difficulties in accurately measuring residual magnetism density due to the need for invasive detection methods and the inability to accurately measure it due to signal interference. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a method for measuring the residual flux density of a single-phase transformer based on composite indicators. This method solves the technical problems of existing transformer residual magnetism measurement methods, such as invasive operation risks, low measurement accuracy, complex calculation logic, and difficulty in engineering implementation. It achieves non-invasive, high-precision measurement of transformer residual magnetism, and the method is simple and easy to operate, which can meet the needs of practical engineering applications.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for measuring the residual flux density of a single-phase transformer based on composite indices includes the following steps: Step 1: Construct a circuit consisting of dual voltage sources, a transformer, and a resistor; AC voltage source U1, DC voltage source U2; keep the transformer measurement side unloaded; the total series resistance R includes the load resistance R1 and the preset winding resistance R2; AC voltage source U1 and DC voltage source U2 are connected in parallel and connected to the transformer and resistor respectively by closed switches S1 and S2; Step 2: Close switch S1 and connect it to AC voltage source U1 to set the initial residual magnetism density Br of the transformer core. Adjust the amplitude and polarity of Br by controlling the opening time. Step 3: Open switch S1 and close switch S2. The DC power supply U2 adopts a three-level DC low voltage of "+V→0→-V→0", and then through the circuit time constant τ= / The duration of each voltage level is determined by analysis. After applying a three-level voltage, the circuit must fully respond to satisfy the set T>>τ in order to achieve current stability. Step 4: During the entire excitation cycle of 4T, the preset winding transient current iL and the measured winding terminal voltage us are collected by the sensor to obtain the signal data required for measurement. Step 5: Normalize the collected current and voltage signals, and integrate the features of both through integral operation and maximum value normalization method to obtain the composite index k. Step 6: Demagnetize, change the remanence, and obtain the relationship curve between the composite index k and the remanent magnetic flux density; Step 7: Obtain the mathematical relationship between the composite index and the residual flux density through first-order Fourier series; and establish the unknown coefficients using a nonlinear least squares algorithm based on the trust region. Step 8: Apply a small-signal voltage excitation to the unknown residual magnetism transformer before closing the circuit and collect voltage and current signals. Calculate the composite index and then substitute it into the fitting formula to calculate the residual magnetic flux density.

[0006] In Step 3 above, the transformer under no-load conditions is equivalent to a first-order RL series circuit, with a circuit time constant τ= / In this circuit, R is the total resistance of the first-order RL series circuit, and L is the nonlinear magnetizing inductance of the first-order RL series circuit. By satisfying the condition that T>>τ, the current in the preset winding is ensured to transition to a steady state, and the influence of the excitation source on the original residual magnetism of the transformer core is minimized.

[0007] In Step 3 above, the three-level DC voltage is applied to the transformer's preset winding in the sequence +V→0→-V→0. The duration of each level is T, and the excitation period is 4T. The three-level DC voltage is output from the DC voltage source U2 and is applied only to the transformer's preset winding. The transformer's measurement side is only used to acquire the terminal voltage us.

[0008] In Step 7 above, a first-order Fourier series is used to approximate the nonlinear relationship between the composite index k and the residual magnetic flux density Br, and a mathematical relationship between the two is constructed. The composite index k is obtained by integrating the transient current iL of the transformer preset winding and the terminal voltage us of the measured winding under different residual magnetic flux densities Br after signal processing. After the mathematical relationship is constructed, all unknown coefficients in the formula are determined by fitting the formula using the nonlinear least squares method based on the trust region.

[0009] In the circuit constructed in Step 1 above, AC voltage source U1 is connected in series with switch S1 as a preset unit for the initial remanent magnetization density of the transformer core, which is used to adjust the amplitude and polarity of the initial remanent magnetization Br of the core by controlling the timing of the switch opening; DC voltage source U2 is connected in series with switch S2 as an excitation unit for the measurement stage, which is used to output a three-level DC small voltage to be applied to the preset winding of the transformer, and the preset winding of the transformer is connected in series with a total resistance R, which is composed of load resistance R1 and preset winding resistance R2.

[0010] In Step 5 above, the normalization of transient current iL and terminal voltage us is a maximum value normalization process. First, the collected transient current iL and terminal voltage us are integrated, and then the integration results are processed by the maximum value normalization method. Finally, the characteristic parameters of current and voltage are integrated to obtain the composite index k.

[0011] In Step 8 above, the small-signal voltage excitation applied to the unknown residual magnetism transformer is the three-level DC small voltage in Step 3. During the excitation process, the transient current iL of the preset winding and the terminal voltage us of the measured winding are collected. After calculating the composite index k according to the method in Step 5, it is substituted into the fitting formula in Step 7 to directly solve for the residual magnetic flux density value of the transformer core.

[0012] The first-order Fourier series formula for the nonlinear relationship between the composite index k and the remanent magnetic flux density Br is as follows: ; in, B r: Initial magnetic flux density; a 0、 a 1. b 1 ω Fitting constants; k Composite index; in: ; and These are the predicted transient current in the winding and the measured terminal voltage of the winding under different residual magnetic flux densities Br, respectively.

[0013] In Step 6 above, the demagnetization operation of the transformer core adopts the DC decreasing demagnetization method. After reducing the residual magnetic flux density Br of the core to zero, the opening time of switch S1 is adjusted by AC voltage source U1 to obtain residual magnetic flux densities Br with different amplitudes and polarities.

[0014] The nonlinear least squares algorithm in Step 7 above is a trust region-based nonlinear least squares method. This method is used to fit the relationship curve between the composite index k and the residual magnetic flux density Br, solve and determine all the unknown coefficients in the mathematical relationship model, and the fitting error of the fitting formula is no greater than 2%.

[0015] In Step 6 above, when adjusting the residual magnetic flux density Br of the transformer core, the numerical range of -1.5T to +1.5T should be covered, and the numerical interval between two adjacent sets of residual magnetic flux density Br should not be greater than 0.1T, so as to ensure the sample size and fitting accuracy of the relationship curve.

[0016] The present invention discloses a non-invasive method for measuring the residual magnetic flux density of a single-phase transformer based on composite indicators. This method requires no physical intervention on the transformer core during measurement; it measures the residual magnetic flux density solely through the acquisition and processing of electrical signals, thus avoiding secondary damage to the transformer. Furthermore, this method is applicable to both oil-immersed and dry-type single-phase power transformers, and is suitable for measuring the residual magnetic flux density of single-phase transformers at various voltage levels, demonstrating wide applicability and strong compatibility.

[0017] The beneficial effects of this invention are as follows: 1. Non-invasive measurement with high safety and convenience: The present invention does not require any physical intervention on the transformer core. Residual magnetism measurement can be achieved simply by setting up an electrical measurement circuit and collecting electrical signals. This avoids secondary damage to the transformer caused by invasive operations. The measurement process is simple to operate, and the circuit can be reused after it is set up, which greatly improves the safety and convenience of the measurement.

[0018] 2. High measurement accuracy: This invention uses a composite index k constructed from current and voltage signals to measure remanence. Compared with single-signal measurement, this effectively reduces the impact of circuit interference and environmental factors on the measurement results. At the same time, a mathematical relationship model is constructed by first-order Fourier series, and a nonlinear least squares method based on the trust region is used for fitting, resulting in small fitting error and further improving the measurement accuracy of remanent magnetic flux density.

[0019] 3. Simple calculation logic and easy engineering implementation: The measurement steps of this invention are clear, the signal processing adopts the conventional methods of integral operation and maximum value normalization, and the mathematical modeling and fitting adopt mature algorithms. There is no need for complex calculation logic. The relevant operations can be implemented through conventional power measurement instruments and data processing modules, which makes it easy to promote and apply in engineering practice.

[0020] 4. Wide applicability and strong compatibility: The measurement method of this invention is applicable to different types of single-phase power transformers such as oil-immersed and dry-type transformers. It can be adapted to the measurement of residual magnetism of transformers with multiple voltage levels. Moreover, the excitation parameters of the three-level DC low voltage can be dynamically adjusted according to the transformer model. It has strong compatibility and can meet the measurement needs of different types of transformers in the power system.

[0021] 5. Minimal impact on the original residual magnetism of the core: This invention uses a three-level DC low voltage with an amplitude of 1%-5% of the transformer's rated voltage as the excitation source, and ensures current steady state by setting T>>τ. The excitation process minimizes the impact on the original residual magnetism of the transformer core. After the measurement is completed, the transformer can be directly switched on and put into operation without additional recovery operations. Attached Figure Description

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart illustrating the method of the present invention.

[0023] Figure 2 This is a schematic diagram of the remanent magnetization measurement circuit model of the present invention.

[0024] Figure 3 This is a schematic diagram of the equivalent circuit of the transformer core of the present invention. Detailed Implementation

[0025] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the embodiments of this application. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0026] Example 1: like Figure 1 As shown in the figure, a method for measuring the residual magnetic flux density of a single-phase transformer based on composite indicators is presented. In this embodiment, a 10kV dry-type single-phase transformer is used as the test object, and its residual magnetic flux density is measured using the method of the present invention. The specific steps are as follows: 1. Construct the measurement circuit: Construct a measurement circuit consisting of an AC voltage source U1, a DC voltage source U2, a 10kV dry-type single-phase transformer, and a series total resistance R. The AC voltage source U1 is connected in series with switch S1, and the DC voltage source U2 is connected in series with switch S2. The two are connected in parallel and form a loop with the transformer's preset winding, load resistor R1, and preset winding resistor R2. The total series resistance R = 25Ω. The transformer's measurement side is kept unloaded and no load is connected. A current sensor is connected in series with the preset winding, and a voltage sensor is connected in parallel with the measurement winding.

[0027] like Figure 2 As shown in the diagram, in the residual magnetism measurement circuit model, AC voltage source U1 is connected in series with switch S1, DC voltage source U2 is connected in series with switch S2 and then in parallel, and then forms a series circuit with preset winding L, load resistor R1, and preset winding resistor R2; current sensor is connected in series with preset winding L to collect transient current iL; the measuring winding is kept unloaded, and voltage sensor is connected in parallel with measuring winding to collect terminal voltage us; the total series resistance R is the sum of the resistance values ​​of load resistor R1 and preset winding resistor R2.

[0028] 2. Preset initial remanent magnetization density: Close switch S1 to connect the measuring circuit to AC voltage source U1. By controlling the opening time of switch S1, set the initial remanent magnetization density Br of the transformer core to 0.5T.

[0029] 3. Apply a three-level DC low-voltage excitation: Open switch S1 and close switch S2. Apply a three-level DC low-voltage (amplitude of 0.5% of the transformer's rated voltage) from DC voltage source U2 to the preset winding: +50V→0→-50V→0. Based on the circuit time constant τ= / (L is the preset nonlinear excitation inductance of the winding, with a value of 50mH, τ=50mH / 25Ω=2ms), and the duration of each level is determined to be T=10ms (T=5τ), satisfying the condition T>>τ, that is, T is not less than 3τ.

[0030] like Figure 3 The diagram shown is an equivalent circuit diagram of a transformer core. The transformer core under no-load conditions is equivalent to a first-order RL series circuit, where R is the total series resistance in the measuring circuit, and L is the nonlinear magnetizing inductance of the transformer's preset winding. The equivalent circuit has a circuit time constant τ = / This provides a theoretical basis for the calculation and determination of the duration T of the three-level DC small voltage.

[0031] 4. Acquisition of voltage and current signals: Within the excitation period of 40ms, the transient current iL of the preset winding and the terminal voltage us of the measured winding are synchronously acquired through current and voltage sensors to eliminate environmental interference during the acquisition process and obtain effective signal data.

[0032] 5. Processing the signal to obtain the composite index k: Denoise and filter the transient current iL and terminal voltage us signals, then perform 40ms time domain integration on the preprocessed signal, normalize the maximum value of the integration result, map the result to the 0-1 interval, and integrate the current and voltage characteristic parameters by weighted summation (current weight 0.6, voltage weight 0.4) to obtain the composite index k.

[0033] 6. Obtain the k-Br relationship curve: The residual magnetism of the transformer core is reduced to zero by the DC demagnetization method. Then, the residual magnetic flux density Br is adjusted within the range of -1.5T to +1.5T by adjusting the opening time of switch S1 through AC voltage source U1. The interval between two adjacent Br sets is 0.1T, and a total of 31 sets of data are obtained. After each adjustment, steps 3-5 are repeated to obtain 31 sets of composite index k and corresponding Br values, and the k-Br relationship curve is plotted.

[0034] 7. Construct and fit a mathematical relationship model: A nonlinear mathematical relationship model between k and Br is constructed using a first-order Fourier series. The k-Br relationship curve is fitted using the nonlinear least squares method based on the trust region to determine the unknown coefficients in the model and obtain the fitting formula. The fitting error is verified to be 1.2%.

[0035] 8. Measurement of transformer with unknown residual magnetism: For the 10kV dry-type single-phase transformer with unknown residual magnetism before closing, repeat steps 3-5, apply a three-level DC small voltage excitation with the same parameters, collect and process the signal to obtain the composite index k=0.35, substitute it into the fitting formula, and calculate the residual magnetic flux density Br=0.32T of the transformer core.

[0036] The measurement process in this embodiment is a non-invasive operation, without any physical intervention on the transformer core. The measurement error is only 1.2%, and the transformer can be directly switched on and put into operation after the measurement is completed, which verifies the high accuracy and convenience of the method of the present invention.

[0037] Example 2 This embodiment uses a 35kV oil-immersed single-phase transformer as the test object. The difference from Embodiment 1 is that the amplitude of the three-level DC small voltage is 1000V, 2.86% of the transformer's rated voltage, the circuit time constant τ = 4ms, the duration of each level is T = 16ms, T = 4τ, the integration method of the composite index k is the product method, the adjustment interval of the residual magnetic flux density Br is 0.05T, and the fitting error of the fitting formula is 0.8%. After measurement, the composite index k of the unknown residual magnetism transformer is 0.62. Substituting this into the fitting formula, the residual magnetic flux density Br = 0.85T is obtained, thus achieving high-precision non-invasive measurement.

[0038] The scope of protection of this invention is not limited to the above embodiments. For those skilled in the art, this invention can be modified and altered in various ways. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for measuring the residual flux density of a single-phase transformer based on composite indices, characterized in that, Includes the following steps: Step 1: Construct a circuit consisting of dual voltage sources, a transformer, and a resistor; AC voltage source U1, DC voltage source U2; keep the transformer measurement side unloaded; the total series resistance R includes the load resistance R1 and the preset winding resistance R2; AC voltage source U1 and DC voltage source U2 are connected in parallel and connected to the transformer and resistor respectively by closed switches S1 and S2; Step 2: Close switch S1 and connect it to AC voltage source U1 to set the initial residual magnetism density Br of the transformer core. Adjust the amplitude and polarity of Br by controlling the opening time. Step 3: Open switch S1 and close switch S2. The DC power supply U2 adopts a three-level DC low voltage of "+V→0→-V→0", and then through the circuit time constant τ= / The duration of each voltage level is determined by analysis. After applying a three-level voltage, the circuit must fully respond to satisfy the set T>>τ in order to achieve current stability. Step 4: During the entire excitation cycle of 4T, the preset winding transient current iL and the measured winding terminal voltage us are collected by the sensor to obtain the signal data required for measurement. Step 5: Normalize the collected current and voltage signals, and integrate the features of both through integral operation and maximum value normalization method to obtain the composite index k. Step 6: Demagnetize, change the remanence, and obtain the relationship curve between the composite index k and the remanent magnetic flux density; Step 7: Obtain the mathematical relationship between the composite index and the residual flux density through first-order Fourier series; and establish the unknown coefficients using a nonlinear least squares algorithm based on the trust region. Step 8: Apply a small-signal voltage excitation to the unknown residual magnetism transformer before closing the circuit and collect voltage and current signals. Calculate the composite index and then substitute it into the fitting formula to calculate the residual magnetic flux density.

2. The method for measuring the residual flux density of a single-phase transformer based on composite indices according to claim 1, characterized in that, In Step 3, the transformer under no-load conditions is equivalent to a first-order RL series circuit, with a circuit time constant τ= / In this circuit, R is the total resistance of the first-order RL series circuit, and L is the nonlinear magnetizing inductance of the first-order RL series circuit. By satisfying the condition that T>>τ, the current in the preset winding is ensured to transition to a steady state, and the influence of the excitation source on the original residual magnetism of the transformer core is minimized.

3. The method for measuring the residual flux density of a single-phase transformer based on composite indices according to claim 1, characterized in that, In Step 3, the three-level DC voltage is applied to the preset winding of the transformer in the sequence of +V→0→-V→0. The duration of each level is T, the excitation period is 4T, the three-level DC voltage is output by DC voltage source U2, and is only applied to the preset winding of the transformer. The transformer measurement side is only used to collect the terminal voltage us.

4. The method for measuring the residual flux density of a single-phase transformer based on composite indices according to claim 3, characterized in that, In Step 7, a first-order Fourier series is used to approximate the nonlinear relationship between the composite index k and the residual magnetic flux density Br, and a mathematical relationship between the two is constructed. The composite index k is obtained by integrating the transient current iL of the preset winding of the transformer under different residual magnetic flux densities Br and the terminal voltage us of the measured winding after signal processing. After the mathematical relationship is constructed, all unknown coefficients in the formula are determined by fitting the formula using the nonlinear least squares method based on the trust region.

5. The method for measuring the residual flux density of a single-phase transformer based on composite indices according to claim 1, characterized in that, In the circuit constructed in Step 1, the AC voltage source U1 is connected in series with the switch S1 as a preset unit for the initial remanent magnetization density of the transformer core. It is used to adjust the amplitude and polarity of the initial remanent magnetization Br of the core by controlling the timing of the switch opening. The DC voltage source U2 is connected in series with the switch S2 as an excitation unit for the measurement stage. It is used to output a three-level DC small voltage to be applied to the preset winding of the transformer. The preset winding of the transformer is connected in series with a total resistance R, which is composed of the load resistance R1 and the preset winding resistance R2.

6. The method for measuring the residual flux density of a single-phase transformer based on composite indices according to claim 4, characterized in that, In Step 5, the normalization of transient current iL and terminal voltage us is a maximum value normalization process. First, the collected transient current iL and terminal voltage us are integrated, and then the integration results are processed by the maximum value normalization method. Finally, the characteristic parameters of current and voltage are integrated to obtain the composite index k.

7. The method for measuring the residual flux density of a single-phase transformer based on composite indices according to claim 3, characterized in that, In Step 8, the small-signal voltage excitation applied to the unknown residual magnetism transformer is the three-level DC small voltage in Step 3. During the excitation process, the transient current iL of the preset winding and the terminal voltage us of the measured winding are collected. After calculating the composite index k according to the method in Step 5, it is substituted into the fitting formula in Step 7 to directly solve for the residual magnetic flux density value of the transformer core.

8. The method for measuring the residual flux density of a single-phase transformer based on composite indices according to claim 6, characterized in that, The first-order Fourier series formula for the nonlinear relationship between the composite index k and the residual magnetic flux density Br is as follows: ； in, B r: Initial magnetic flux density; a 0、 a 1. b 1 ω Fitting constants; k Composite index; in: ； Predict the transient current in the winding; : Measure the terminal voltage of the winding; T: The period during which each level of the small-signal voltage excitation is applied.

9. The method for measuring the residual flux density of a single-phase transformer based on composite indices according to claim 1, characterized in that, In Step 6, the demagnetization operation of the transformer core adopts the DC decreasing demagnetization method. After reducing the residual magnetic flux density Br of the core to zero, the opening time of switch S1 is adjusted by AC voltage source U1 to obtain residual magnetic flux densities Br with different amplitudes and polarities.

10. The method for measuring the residual flux density of a single-phase transformer based on composite indices according to claim 1, characterized in that, The nonlinear least squares algorithm in Step 7 is a trust region-based nonlinear least squares method. This method is used to fit the relationship curve between the composite index k and the residual magnetic flux density Br, solve and determine all the unknown coefficients in the mathematical relationship model, and the fitting error of the fitting formula is no greater than 2%.

11. The method for measuring the residual flux density of a single-phase transformer based on composite indices according to claim 1, characterized in that, In Step 6, when adjusting the residual magnetic flux density Br of the transformer core, the value range of -1.5T to +1.5T is covered, and the numerical interval between two adjacent sets of residual magnetic flux density Br is no greater than 0.1T, so as to ensure the sample size and fitting accuracy of the relationship curve.

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