A method for designing leakage inductance and suppressing transformer surge current by using leakage inductance

Abstract

The application relates to a method for designing leakage inductance and suppressing transformer impulse current by using the leakage inductance, characterized in that the method comprises the following steps: obtaining a four-dimensional feasible region of a transformer capacity arc set S and a transformer leakage inductance set by four-dimensional visualization processing respectively L lp ; obtaining a fitted B-H curve according to actual test data of a core, and converting the B-H curve into a I curve; physically modeling a no-load transformer considering the leakage inductance, and establishing a mathematical model, and solving the mathematical model to obtain a magnetic flux expression considering the leakage inductance; combining the magnetic flux expression considering the leakage inductance and the I curve, and calculating the impulse current considering the leakage inductance i , and calculating the current of multiple periods to obtain a waveform of the impulse current. The application designs the leakage inductance by using a four-dimensional visualization method, and quantitatively calculates the impulse current considering the influence of the leakage inductance on the basis of traditional qualitative analysis of the impulse current, so that the impulse current at the power-on moment of the transformer is reduced.

Description

Technical Field

[0001] This application relates to the field of transformer differential protection technology in power grid systems, specifically to a method for designing leakage inductance and using leakage inductance to suppress transformer inrush current. Background Technology

[0002] Transformers are widely used, but when energized and switched on, the core can become oversaturated, randomly generating large inrush currents. This can lead to malfunctions in the differential protection of high-voltage power transformers and accidental fuse blowouts in low-voltage single-phase transformers. Research on how to quantitatively analyze and suppress these inrush currents based on a clear understanding of the underlying mechanisms has been ongoing for a long time.

[0003] The inrush current is mainly caused by magnetic flux saturation and the nonlinear characteristics of the iron core [adaptive blocking scheme for inrush current in distribution lines]. When the transformer is closed under no-load conditions, the magnetic flux in the iron core cannot change abruptly. In addition to the steady-state component, the main magnetic flux also has a transient component that decays with time. In the short time after closing, the transient component is very large. If the closing phase angle is the phase angle corresponding to the peak value of the grid input voltage, the main magnetic flux of the transformer core will be very large, and the magnetizing inductance will become very small, thereby randomly generating an inrush current that is tens of times larger than the rated current.

[0004] The article "Inrush Current of Superconducting Transformer" points out many hazards of inrush current: (1) It may cause the differential protection device of high-voltage power transformer to malfunction, causing irreparable damage to the power grid system; (2) It may cause the fuse of low-voltage single-phase transformer to blow; (3) It generates high unbalanced electromagnetic axial force, which damages the winding and transformer insulation, and reduces the service life of the transformer; (4) Because it contains a large number of harmonics, it flows into the power grid, affecting the power quality, generating overvoltage and causing resonance.

[0005] Common methods for suppressing inrush current include: the PWM mask method, which limits the inrush current to a preset value; and the use of switching strategies, which suppress inrush current by controlling the optimal closing point, which is also the most widely used method. However, for high-frequency circuits, considering the discreteness of circuit breaker closing time, controlling the closing time is difficult to achieve, and controlling the closing requires additional external circuitry, which increases operating costs.

[0006] Therefore, there is still significant room for improvement in existing transformer designs regarding the optimization of inrush current. Most researchers lack quantitative calculations of inrush current during transformer design, and their research on inrush current remains at the qualitative analysis level. Furthermore, in studies on suppressing transformer closing inrush current, no one has paid attention to the effect of the transformer's inherent leakage inductance on suppressing inrush current, often ignoring its role. However, the report "A Review of Large-Capacity High-Frequency Transformer Technology for Power Electronic Transformer Applications" points out that the transformer's structural design affects its leakage inductance, thus acknowledging its objective existence, but it fails to address the impact of leakage inductance on inrush current. Summary of the Invention

[0007] The purpose of this invention is to provide a method for designing leakage inductance and using leakage inductance to suppress transformer inrush current. The required leakage inductance is designed using a four-dimensional visualization method, and the leakage inductance is used to quantitatively calculate the inrush current considering the influence of leakage inductance based on traditional qualitative analysis of inrush current. Thus, a transformer that can suppress large inrush current can be designed according to design requirements.

[0008] The technical solution adopted in this invention is: a method for designing leakage inductance and using leakage inductance to suppress transformer inrush current, characterized by comprising the following steps:

[0009] S1: Cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Using these as decision variables, the objective function S(transformer capacity) is obtained. A m , A w , K ), with the cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Using the coordinate axes, the objective function for transformer capacity is S( A m , A w , K Using ) as the color scale axis, perform four-dimensional visualization processing to obtain the four-dimensional feasible region of the transformer capacity arc set S;

[0010] S2: Cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Construct the objective function for transformer leakage inductance as the decision variable. Llp ( A m , A w , K ), with the cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Using the coordinate axes, the objective function of transformer leakage inductance L lp ( A m , A w , K Using π as the color axis, four-dimensional visualization processing is performed to obtain the transformer leakage inductance set. L l The four-dimensional feasible region;

[0011] S3: Based on the actual test data of the iron core, using the magnetic field strength H of the iron core as the abscissa and the magnetic induction intensity B as the ordinate, a large-range nonlinear fitting method is used to transform it into a small-range linear fitting method to obtain the fitted BH curve, and then the BH curve is transformed into... - I Curve; where, For iron core flux, I It is the magnetizing current;

[0012] S4: Perform a physical modeling of the unloaded transformer considering leakage inductance, establish a mathematical model, and solve the mathematical model to obtain the magnetic flux considering leakage inductance. expression;

[0013] S5: Taking into account the magnetic flux of leakage inductance Expressions and - I The curve was used to calculate the inrush current considering leakage inductance. i The waveform of the inrush current is obtained by calculating the current over multiple cycles.

[0014] Furthermore, the specific steps of step S3 are as follows:

[0015] S301: Based on the actual test data of the iron core, the magnetic field strength H of the iron core is used as the horizontal axis data and the magnetic induction intensity B is used as the vertical axis data. The coordinate data are grouped in pairs in sequence to obtain N sets of coordinate data.

[0016] S302: According to the order of N sets of coordinate data, calculate a set of straight line equations for every two adjacent sets of coordinate data, and obtain N-1 sets of straight line equations;

[0017] S303: Plot the N-1 sets of linear equations sequentially to obtain the fitted BH curve, and transform the BH curve into... - I curve.

[0018] Further, in step S303, the BH curve is transformed according to the following formula. - I curve:

[0019] = B× A m

[0020] I =H l / N p

[0021] in, l The length of the magnetic circuit of the iron core. N p This refers to the number of turns on the primary side of the transformer.

[0022] Furthermore, step S3 further includes the following specific steps:

[0023] S304: Will - I The curve is transformed into a semi-logarithmic curve with the horizontal axis at a multiple of 10.

[0024] Furthermore, the mathematical model for the no-load transformer considering leakage inductance in step S4 is as follows:

[0025]

[0026] in, i p For primary side excitation current, R p For the primary winding resistance, L lp For total leakage, N p For the number of turns of the primary winding of the transformer, For iron core flux, U p For the primary side effective voltage, For the angular frequency of voltage, This is the transformer closing phase angle.

[0027] Furthermore, in step S4, the magnetic flux of leakage inductance is taken into account. The expression is:

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] in, L av is the average magnetizing inductance of the first cycle.

[0034] Furthermore, in step S5, the maximum excitation current value in the first cycle is the impulse current. i .

[0035] The beneficial effects of this invention are as follows: It designs a transformer with known leakage inductance using a four-dimensional visualization method, realizing the function of visually designing leakage inductance. It also quantitatively calculates the inrush current considering leakage inductance, which is different from the traditional qualitative analysis of the impact of inrush current. This overcomes the drawback of traditional transformers that only qualitatively analyze the inrush current under uncertain leakage inductance factors, without knowing its value. It largely solves the problem of transformer misoperation when used in power systems. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a design flowchart of an embodiment of the present invention;

[0038] Figure 2 This is a flowchart of the four-dimensional visualization method used in the embodiments of the present invention;

[0039] Figure 3 This is a flowchart illustrating the visualization of capacity arc sets in an embodiment of the present invention.

[0040] Figure 4 This is a schematic diagram of the visualization result of the capacity arc set in an embodiment of the present invention;

[0041] Figure 5 Leakage sensing set in an embodiment of the present invention L l Flowchart of expression derivation;

[0042] Figure 6 This is a schematic diagram of the intersection of the capacity arc set and the leakage sensing set in an embodiment of the present invention;

[0043] Figure 7 The semi-logarithmic BH curve and semi-logarithmic curve obtained by fitting in the embodiments of the present invention. -I curve;

[0044] Figure 8 Magnetization characteristics of R-type and EE-type iron cores;

[0045] Figure 9 This is the equivalent circuit model of an unloaded transformer.

[0046] Figure 10 To consider the change curve of the main magnetic flux over time when leakage inductance is taken into account, and the simulation waveform of the inrush current obtained through the magnetization curve;

[0047] Figure 11 A comparison chart of various parameters with and without considering leakage inductance;

[0048] Figure 12 The waveform of the impulse current considering leakage inductance was measured in an embodiment of the present invention. Detailed Implementation

[0049] To better understand the above-described objects, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Many specific details are set forth in the following description to provide a thorough understanding of the present invention; however, the present invention may be practiced in other ways different from those described herein, and therefore, the present invention is not limited to the specific embodiments disclosed below.

[0050] like Figure 1 As shown, this embodiment of the invention provides a method for designing leakage inductance and using leakage inductance to suppress transformer inrush current. The method steps and principles of this embodiment of the invention will now be explained in conjunction with specific transformer requirements and parameters.

[0051] The embodiments of the present invention include the following steps:

[0052] S1: Cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K As the decision variable, construct the objective function S( transformer capacity). A m , A w , K ), with the cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Using the coordinate axes, the objective function for transformer capacity is S(A m , A w , K Using ) as the color axis, perform four-dimensional visualization processing to obtain the four-dimensional feasible region of the transformer capacity arc set S.

[0053] The formula for calculating the transformer capacity arc set S is:

[0054] S = f · K f · I’ · = 0.0001K f · f · J · K cu · A w · B max · K fe · A m / 2.05 (1)

[0055] in, f For input voltage frequency, K f For voltage waveform coefficients, J Current per unit area K cu For core window utilization rate, total current I’ = JK cu A w , B max This represents the maximum amplitude of the core magnetic flux density of the transformer when it is operating in steady state under sinusoidal AC voltage. K fe For lamination coefficient, magnetic flux = B max K fe A m The sum of primary and secondary capacity and losses is U p I p + U s I s + P fecu , Up The rated voltage of the primary side of the transformer, U s This is the rated voltage on the secondary side of the transformer; I p The rated current of the primary side of the transformer, I s This is the rated current on the secondary side of the transformer; P fecu The losses of the conductor and the iron core are respectively taken as per unit value 1+1+0.05=2.05 to form the denominator of formula (1).

[0056] In this embodiment of the invention, 27P120 silicon steel sheets are used to make the iron core, with saturated magnetic flux density. B sat =1.95T, taken as the magnetic flux amplitude when the transformer is in steady-state operation. B max =1.8T; B max exist BH knee of the curve a to B sat Between the saturation point D. K f = 4.44、 f =50Hz K cu = 0.5、 K fe = 0.95 and J = 265A / cm 2 Substituting into formula (1), we get:

[0057] S = 2.45 A m A w ·1(2)

[0058] Take the cross-sectional area of ​​the iron core A m ∈[1, 60]cm 2 Iron core window area A w ∈[1, 60] cm 2 And take the rectangular coefficient K =1, to upgrade the 3D to 4D visualization, resulting in, as shown Figure 4 The arc-shaped region shown is composed of Figure 4 Therefore, the range of the capacity arc set in this embodiment of the invention is: S ∈[1000, 1100]VA. The multi-objective constraint four-dimensional visualization process used in this embodiment of the invention is as follows: Figure 2As shown, the method for solving the transformer capacity arc set is as follows: Figure 3 As shown.

[0059] S2: Cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Construct the objective function for transformer leakage inductance as the decision variable. L l ( A m , A w , K ), with the cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Using the coordinate axes, the objective function of transformer leakage inductance L l ( A m , A w , K Using π as the color axis, four-dimensional visualization processing is performed to obtain the transformer leakage inductance set. L l The four-dimensional feasible region.

[0060] The formula for calculating the leakage inductance of a non-concentric transformer is as follows:

[0061] L l = L LP '+ L LS + L LPS (3)

[0062] in, L LP 'Leakage inductance calculated from the primary side to the secondary side,' L LS For leakage inductance of the secondary winding, L LPS 'For the mutual leakage inductance between the primary and secondary windings.'

[0063] Leakage inductance from primary side to secondary side L LP The formula for calculating ' is:

[0064] L LP ' = ( U s / Up ) 2 L LP = (230 / 480) 2 L LP (4)

[0065] (5)

[0066] (6)

[0067] in, U s The effective voltage on the secondary side of the transformer, U p This is the effective voltage on the primary side of the transformer. L LP This is a primary sensation of leakage. The permeability of free space, h p For the length of the primary winding, N p This refers to the number of turns in the primary winding. L MLTP The average turn length of the primary winding. b p The primary and secondary windings are thicker. L For winding length, R For the winding radius, k is the winding magnetic flux density coefficient.

[0068] Leakage inductance of the secondary winding L LS The calculation formula is as follows:

[0069] (7)

[0070] in, h s For the secondary winding length, N s The number of turns in the secondary winding. L MLTS The average turn length of the secondary winding. b s For the secondary winding thickness, b s = b p .

[0071] Mutual leakage inductance between primary and secondary windings L LPS The formula for calculating ' is:

[0072] (8)

[0073] in,h c It is the length of the outer cylindrical core of the primary winding and the long winding.

[0074] Table 1 describes the parameters of each structure in the embodiments of the present invention, and Table 2 shows the design parameters of the transformer to be designed in the embodiments of the present invention.

[0075] Table 1. Description of structural parameters in embodiments of the present invention

[0076]

[0077] Substituting the relevant parameters from Table 1 into formulas (3) to (8), we obtain the leakage sensing set. L l The expression, based on the capacity arc set S, uses the leakage sensing set... L l Given the constraint ∈ [35, 80mH], the result is obtained using a four-dimensional visualization method. Figure 6 Visualization methods such as Figure 2 As shown, leakage sensing set L l The expression derivation process is as follows: Figure 5 As shown. Figure 6 The center of the "○"-shaped area represents the leakage inductance of the transformer designed in this invention, with a value of 44 mH. Figure 6 Read the corresponding text A m , A w , K Record the information in Table 2, and construct the transformer according to Table 2:

[0078] Table 2 Design parameters of the transformer to be designed in the embodiments of the present invention

[0079]

[0080] like Figure 2 As shown, the four-dimensional visualization method used in this embodiment of the invention includes the following steps:

[0081] (1) Constructing the start and end points and step size of the decision variables: In the example of this invention, the decision variables are determined by the cross-sectional area of ​​the iron core, Am∈[1,60]cm. 2 The area of ​​the iron core window, Aw, ∈ [1, 60] cm² 2 The rectangular coefficients K∈[1,2.5] have step sizes of (60-1) / 200, (60-1) / 200, and (2.5-1) / 200, respectively.

[0082] (2) Determine the lattice size and construct the lattice: In the example of this invention, the number of lattices is 200*200*200, and the size of the lattice is [(60-1) / 200]*[(60-1) / 200]*[(2.5-1) / 200].

[0083] (3) Determine the slice range, quantity, and color bar range: In this example, the slice range is the capacity per-unit value range [0, 1], the quantity is 1000, that is, the step size is 1 / 1000, and the color bar range is consistent with the capacity per-unit value range.

[0084] (4) Multi-objective and constraint selection: The constraints selected in this invention example are: capacity arc set S∈[1000, 1100VA] and leakage sensing set. L l ∈[35, 80mH].

[0085] (5) Obtain the capacity range from the capacity expression A and consider the constraint S∈[1000, 1100VA] to obtain the capacity arc set S. 1k Let this be dataset ①; and calculate the global range of leakage inductance values ​​using the leakage inductance expression H, while considering the constraints. L l The target leakage sensing region is obtained from [35, 80mH], denoted as dataset ②.

[0086] Capacity arc set S 1k The solution process is shown in the figure. Figure 3 Based on formula (2), let the rectangular coefficient K =1, set the capacity arc set S Increasing to four dimensions, we obtain the capacity arc set S in A m ∈[1, 60], A w The sum of the global sets when K ∈ [1, 60] and K ∈ [1, 2.5] is then used to select the constraint range [1000, 1100] of the capacity arc set S in this embodiment of the invention, and finally obtain the capacity arc set. S 1k The plot (Am, Aw, K) is denoted as dataset ① and fed into the database. Figure 2 middle.

[0087] Leakage collection L l The solution process is as follows Figure 5 As shown, the final leak detection set will be obtained. L l Let's call this dataset ② and send it in. Figure 2 middle.

[0088] (6) Take the intersection or union of dataset ① and dataset ②. In this invention example, the capacity arc set S is taken. 1k and target leakage fieldL l The intersection of.

[0089] (7) Draw a four-dimensional visualization graphic to obtain the following: Figure 6 The visualization shown is shown in the image.

[0090] (8) Set the relevant identifier attributes of the graphic.

[0091] S3: Based on the actual test data of the iron core, using the magnetic field strength H of the iron core as the abscissa and the magnetic induction intensity B as the ordinate, a large-range nonlinear fitting method is used to transform it into a small-range linear fitting method to obtain the fitted BH curve, and then the BH curve is transformed into... - I Curve; where, For iron core flux, I This is the excitation current. The specific operating method is as follows:

[0092] S301: Based on the actual test data of the iron core, the magnetic field strength H of the iron core is used as the horizontal axis data and the magnetic induction intensity B is used as the vertical axis data. The coordinate data are grouped in pairs in sequence to obtain N sets of coordinate data.

[0093] S302: Following the order of N sets of coordinate data, calculate a set of straight line equations for every two adjacent sets of coordinate data, resulting in N-1 sets of straight line equations.

[0094] S303: Plot the N-1 sets of linear equations sequentially to obtain a multi-piece polyline for fitting the BH data, and then convert the multi-piece BH polyline into a multi-piece polyline. - I A broken line. Generally speaking, the larger the value of N, the higher the fitting accuracy, but the greater the computational load. Considering both computational load and fitting accuracy, the preferred value of N is 20-40. Compared to other fitting methods, the fitting method described in this embodiment of the invention is simpler when calculating the impact current.

[0095] To facilitate data observation, step S304 can also be performed: - I The curve is transformed into a semi-logarithmic curve with the horizontal axis at a multiple of 10.

[0096] The test data of the 27Q120 type oriented silicon steel sheet selected in the embodiments of the present invention are shown in Table 3:

[0097] Table 3 Test data of 27Q120 type oriented silicon steel sheet

[0098]

[0099] Since it is difficult to determine the equation of the magnetization curve by fitting high-order curves when the magnetization curve data is large and discrete, this embodiment of the invention uses a method of converting large-range nonlinear fitting into small-range linear fitting to obtain the magnetization curve, which can effectively reduce the amount of calculation of quantized impact current.

[0100] In Table 3, each pair of adjacent data sets defines a linear function. For example, the data sets H=2, B=0.025 and H=3, B=0.059 yield the linear function B=0.0125H. Table 3 contains 40 data sets, resulting in 39 linear functions. Integrating these linear clusters yields the curve. Since the magnetic field strength ranges from 2 (A / m) to 10053 (A / m), the horizontal axis is logarithmically transformed using the semilogx function in MATLAB for easier data observation. BH Curve and semi-logarithm -I The curve ultimately yields the following result: Figure 7 The graph shown.

[0101] from Figure 7 As can be seen, as the magnetic field strength increases, the magnetic induction intensity initially increases slowly in segment 0A, then increases rapidly in segment AB, and then the rate of increase slows down in segment BC until there is no significant increase in segment CD. Segment BD is the main cause of the inrush current.

[0102] The embodiment of this invention designs a gapless, fully oriented transformer core, specifically an R-type core. However, gap-incompletely oriented cores also exist in practice. The magnetization characteristics of these two types of transformer cores are different, as detailed below. Figure 8 As shown.

[0103] like Figure 8 As shown, line ① is the magnetization line of the R-type iron core, line ② is the magnetization line of the EE-type iron core with air gap partial orientation, curve ③ is the experimentally measured hysteresis loop of the air gap-free fully oriented iron core, i.e., the R-type iron core, and curve ④ is the experimentally measured magnetization loop of the air gap-partially oriented iron core, i.e., the EE-type iron core. Dividing the magnetization lines into two segments, M and N, segment N is the segment that causes the inrush current. It is easy to see that, under the same magnetic induction intensity B, the magnetic field strength H of line ② is greater, i.e., the inrush current is larger.

[0104] S4: Perform a physical modeling of the unloaded transformer considering leakage inductance, establish a mathematical model, and solve the mathematical model to obtain the magnetic flux considering leakage inductance. expression.

[0105] When a transformer is closed under no-load conditions, because the main magnetic flux of the transformer core cannot change abruptly, the flux has both a steady-state component and a free component that decays over time. At the instant the transformer is closed under no-load conditions, the free component is very large, causing the magnetic flux of the core to be in a supersaturated state, resulting in the generation of inrush current. This embodiment of the invention uses an R-type single-phase non-concentric winding transformer for illustration.

[0106] Since this is an unloaded transformer, and the research objective is the instantaneous inrush current, the leakage inductance and magnetizing inductance are not significantly different in value. Therefore, leakage inductance is considered, while secondary and minor losses are ignored. The equivalent T-type circuit of the transformer in this case is as follows: Figure 9 As shown in Table 4, which presents the physical model parameters of the transformer physical model used in this embodiment of the invention:

[0107] Table 4 Physical Model Parameter Table of Embodiments of the Invention

[0108]

[0109] A mathematical model was established based on Kirchhoff's voltage law and Faraday's law of electromagnetic induction:

[0110] (9)

[0111] in, i p For primary side excitation current, R p For the primary winding resistance, L lp For total leakage, N p For the number of turns of the primary winding of the transformer, For iron core flux, U p For the primary side effective voltage, For the angular frequency of voltage, This is the transformer closing phase angle.

[0112] In formula (9), , , L av is the average excitation inductance of the first cycle. Solving equation (9) yields:

[0113] (10)

[0114] Solving formula (10) yields the magnetic flux considering leakage inductance. expression:

[0115] (11)

[0116] (12)

[0117] (13)

[0118] (14)

[0119] (15)

[0120] in, This represents the maximum magnetic flux of the transformer when it is operating in steady state. For iron core flux Compared to the phase shift angle of the input AC voltage, T is the decay time constant, and C is a constant.

[0121] because Therefore , Substituting into formula (11), we get:

[0122] (16)

[0123] S5: Taking into account the magnetic flux of leakage inductance expressions and - I The curve was used to calculate the inrush current considering leakage inductance. i The current for multiple cycles is calculated to obtain the waveform of the impulse current. The maximum excitation current value in the first cycle is the impulse current.

[0124] Considering the inrush current under extreme conditions, the closing angle is selected. The initial remanence is Then formula (16) becomes:

[0125] (17)

[0126] It can be seen from formula (10) that From steady-state components and free components that decay over time Composition. Quantitative calculation of the steady-state maximum magnetic flux in embodiments of the present invention. And substitute the data from Table 4 into the magnetic flux. In the expression:

[0127]

[0128]

[0129] Since large transient inrush currents only occur in the first few cycles after the transformer is energized, the peak value of the inrush current in the first cycle in which the maximum inrush current occurs is calculated. The maximum magnetic flux and magnetic induction intensity are calculated as follows:

[0130]

[0131]

[0132] The maximum magnetic flux density is mapped to Figure 7 The obtained fitted curve was used to obtain the corresponding magnetic field strength through the piecewise linear equation, and the impact current was further calculated:

[0133] H max = 114500 (A / m)

[0134]

[0135] To more intuitively and quantitatively analyze the inrush current of leakage inductance, the inrush current of the first 7 cycles can be quantitatively calculated, and mathematical modeling tools can be used to plot the current as shown below. Figure 10 The image shows a visualization of the inrush current considering the effect of leakage inductance. From... Figure 10 It can be observed that when the transformer is unloaded, the inrush current considering leakage inductance can reach 58A in the first cycle, but it rapidly decreases to 0.34A in the second cycle. The decay rate is very fast, and it basically stabilizes after the sixth cycle. The calculated value is basically consistent with the simulation value.

[0136] To clearly understand the effect of leakage inductance in suppressing inrush current, the total leakage inductance in formula (10) is ignored. L lp Then, following a similar method to solving for the flux considering leakage inductance, the flux neglecting leakage inductance is calculated, and the inrush current neglecting leakage inductance is obtained through step S5. The inrush current neglecting leakage inductance and the inrush current considering leakage inductance are plotted together to obtain... Figure 11 .pass Figure 11 It is evident that leakage inductance has a suppressive effect on inrush current. In the first cycle with the largest inrush current, the inrush current considering leakage inductance is 60A, while the inrush current ignoring leakage inductance is 220A.

[0137] To verify the reliability of the experimental results, the inrush current waveform considering leakage inductance was measured using a Tektronix-A622 AC current probe with a 10A range (i.e., 100mV / A). Figure 12 As shown. From Figure 12 It can be seen from this:

[0138] (1) Considering the leakage inductance, the maximum amplitude of the second peak current of the inrush current is 50mV, corresponding to a current amplitude of 0.5A, which is consistent with the simulation results of the aforementioned derived formula. Figure 10 The peak value of the second cycle is similar to 0.4A;

[0139] (2) The experimental waveforms of the third, fourth, and fifth cycles are also similar to the calculation and simulation results;

[0140] (3) The waveforms in the sixth and seventh cycles have become stable and are close to the simulation results;

[0141] (4) Due to the randomness of the closing time and sampling time, coupled with the interference of residual magnetism and switching devices at the moment of closing, the peak current in the first cycle has an error compared with the calculation result. However, the error is within a reasonable range. Furthermore, by observing the experimental waveforms of the second, third, fourth, and fifth cycles, the waveform changes according to an exponential decay, which is consistent with the calculation result. Therefore, the peak current calculation result of the first cycle is also reliable.

[0142] In summary, the embodiments of the present invention have the following advantages: low computational load, simple method, and relatively accurate calculation results. They can effectively estimate the specific value of the inrush current and confirm that leakage inductance has a significant suppressive effect on the transformer closing inrush current. They can provide a reference for the study of quantifying transformer inrush current and provide valuable reference formulas for researchers who use inrush current as the optimization target, thereby designing transformers with smaller inrush current.

[0143] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing leakage inductance and using leakage inductance to suppress transformer inrush current, characterized in that, Includes the following steps: S1: Cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Using these as decision variables, the objective function S(transformer capacity) is obtained. A m , A w , K ), with the cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Using the coordinate axes, the objective function for transformer capacity is S( A m , A w , K Using ) as the color scale axis, perform four-dimensional visualization processing to obtain the four-dimensional feasible region of the transformer capacity arc set S; S2: Cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Construct the objective function for transformer leakage inductance as the decision variable. L lp ( A m , A w , K ), with the cross-sectional area of ​​the iron core A m Window area A w and rectangular coefficient K Using the coordinate axes, the objective function of transformer leakage inductance L lp ( A m , A w , K Using π as the color axis, four-dimensional visualization processing is performed to obtain the transformer leakage inductance set. L lp The four-dimensional feasible region; S3: Based on the actual test data of the iron core, using the magnetic field strength H of the iron core as the abscissa and the magnetic induction intensity B as the ordinate, a large-range nonlinear fitting method is used to transform it into a small-range linear fitting method to obtain the fitted BH curve, and then the BH curve is transformed into... - I Curve; where, For iron core flux, I It is the magnetizing current; S4: Perform a physical modeling of the unloaded transformer considering leakage inductance, establish a mathematical model, and solve the mathematical model to obtain the magnetic flux considering leakage inductance. expression; S5: Taking into account the magnetic flux of leakage inductance Expressions and - I The curve was used to calculate the inrush current considering leakage inductance. i The waveform of the inrush current is obtained by calculating the current over multiple cycles.

2. The method for designing leakage inductance and suppressing transformer inrush current using leakage inductance according to claim 1, characterized in that, The specific steps of step S3 are as follows: S301: Based on the actual test data of the iron core, the magnetic field strength H of the iron core is used as the horizontal axis data and the magnetic induction intensity B is used as the vertical axis data. The coordinate data are then grouped in pairs in sequence to obtain N sets of coordinate data. S302: According to the order of N sets of coordinate data, calculate a set of straight line equations for every two adjacent sets of coordinate data, and obtain N-1 sets of straight line equations; S303: Plot the N-1 sets of linear equations sequentially to obtain the fitted BH curve, and transform the BH curve into... - I curve.

3. The method for designing leakage inductance and using leakage inductance to suppress transformer inrush current according to claim 2, characterized in that, In step S303, the BH curve is transformed according to the following formula. - I curve: = B× A m I =H l / N p in, l The length of the magnetic circuit of the iron core. N p This refers to the number of turns on the primary side of the transformer.

4. The method for designing leakage inductance and suppressing transformer inrush current using leakage inductance according to claim 2, characterized in that, The specific steps of step S3 also include: S304: Will - I The curve is transformed into a semi-logarithmic curve with the horizontal axis at a multiple of 10.

5. The method for designing leakage inductance and suppressing transformer inrush current using leakage inductance according to claim 3, characterized in that, The mathematical model for the unloaded transformer considering leakage inductance in step S4 is as follows: in, i p For primary side excitation current, R p For the primary winding resistance, L lp For total leakage, N p For the number of turns of the primary winding of the transformer, For iron core flux, U p For the primary side effective voltage, For the angular frequency of voltage, This is the transformer closing phase angle.

6. The method for designing leakage inductance and suppressing transformer inrush current using leakage inductance according to claim 5, characterized in that, In step S4, the magnetic flux considering leakage inductance is taken into account. The expression is: in, L av This is the average magnetizing inductance for the first cycle.

7. The method for designing leakage inductance and suppressing transformer inrush current using leakage inductance according to claim 6, characterized in that, In step S5, the maximum excitation current value in the first cycle is the impulse current. i .

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