Transformer inter-turn short circuit fault recognition and positioning method based on magnetic flux leakage difference value distribution difference

Abstract

The method for transformer inter-turn short circuit fault recognition and positioning based on leakage magnetic difference value distribution difference comprises the following steps: deriving a leakage magnetic induction intensity calculation formula for transformer inter-turn short circuit fault according to Biot-Savart law; constructing a leakage magnetic difference value function representing the magnetic field generated by short circuit turn current; analyzing the leakage magnetic difference value distribution law of transformer under different working conditions, and constructing a transformer inter-turn short circuit protection criterion; analyzing the influence of inter-turn short circuit fault position and fault degree on structure function G value, and constructing a position function K value reflecting the inter-turn short circuit fault position information; taking the standard K value as the benchmark, reflecting the matching degree of the measured K value and the standard K value through the objective function, and predicting the transformer inter-turn short circuit fault position through the Beaver algorithm. The method is based on the leakage magnetic difference value distribution characteristics, analyzes the leakage magnetic difference value distribution difference of each measuring point under different working conditions, constructs a transformer inter-turn short circuit protection criterion, derives a position function K value, and realizes accurate positioning of the transformer inter-turn short circuit fault in combination with the Beaver algorithm.

Description

Technical Field

[0001] This invention relates to the field of transformer short-circuit fault diagnosis technology, specifically to a method for identifying and locating transformer inter-turn short-circuit faults based on the difference in leakage flux distribution. Background Technology

[0002] Inter-turn short-circuit faults are a typical threat to the safe operation of transformers. Inter-turn short circuits easily burn the winding insulation and exacerbate inter-turn discharge. If not detected in time, the fault will continue to expand, affecting the normal operation of the transformer. Traditional differential protection has the ability to identify inter-turn short-circuit faults and has high sensitivity to severe faults such as phase-to-phase short circuits and winding grounding. However, in early-stage faults, the number of short-circuited turns is small, and the impact on the winding port current is relatively small. Limited by the protection threshold setting principle, differential protection can only effectively identify inter-turn short-circuit faults with a fault severity of 3% or higher, making it difficult to respond effectively to these minor inter-turn short-circuit faults. Therefore, it cannot be used as a method for identifying early-stage winding faults. Inter-turn short-circuit faults cause significant distortion in the transformer's leakage flux distribution. Existing research has confirmed that diagnostic methods based on leakage flux information can effectively identify minor inter-turn short-circuit faults. However, these methods still have two shortcomings: first, they are difficult to locate inter-turn short-circuit faults, significantly increasing the difficulty of on-site maintenance; second, they lack adaptability to complex power system operating conditions, and their ability to distinguish non-winding fault factors such as no-load closing and system short circuits needs to be improved. Therefore, it is urgent to explore more accurate fault location methods and more reliable diagnostic models.

[0003] To address the issues of insufficient diagnostic capability and difficulty in locating faults during inter-turn short circuits in transformers under complex operating conditions, many scholars have utilized changes in leakage magnetic flux to achieve online identification of inter-turn short circuit faults, as documented in the literature: Deng Xiangli, Peng Yuancan, Tong Zhixiang, et al. Research on Differential Protection of Leakage Magnetic Field with Third Harmonic in Early Faults of Transformers [J]. Power System Technology, 2025. These studies demonstrate that leakage magnetic flux exhibits significant changes during inter-turn short circuit faults. However, the ability to identify minor inter-turn short circuit faults under complex operating conditions still needs improvement, and existing methods struggle to effectively locate the fault position. Summary of the Invention

[0004] To address the issues of insufficient diagnostic capability and difficulty in locating faults in transformer inter-turn short circuit faults, a method for identifying and locating transformer inter-turn short circuit faults based on the differences in leakage flux difference distribution is proposed. This method is based on the characteristics of leakage flux difference distribution, analyzes the differences in leakage flux difference distribution at various measuring points under different operating conditions, constructs a criterion for transformer inter-turn short circuit protection, derives the position function K value based on this, and combines it with the Beaver Algorithm to achieve accurate location of transformer inter-turn short circuit faults.

[0005] The technical solution adopted in this invention is as follows: A method for identifying and locating inter-turn short-circuit faults in transformers based on differences in leakage flux distribution includes the following steps: Step 1: Derive the formula for calculating the leakage magnetic flux intensity during an inter-turn short circuit fault in a transformer based on the Biot-Savart law; Step 2: Combining current data and magnetic field data, construct a leakage magnetic difference function to characterize the magnetic field generated by the short-circuit turn current; Step 3: Analyze the distribution pattern of leakage flux difference under different operating conditions of the transformer, and construct the criterion for inter-turn short circuit protection of the transformer; Step 4: Analyze the influence of the structure function G value on the location and severity of the inter-turn short-circuit fault, and construct the location function K value that reflects the location information of the inter-turn short-circuit fault; Step 5: Using the standard K value as a benchmark, apply the objective function... f ( x It reflects the degree of matching between the measured K value and the standard K value, and predicts the location of the inter-turn short circuit fault in the transformer using the beaver algorithm.

[0006] In step 1, based on the Biot-Savart law, the magnetic field generated by a single winding at a point P outside the three-phase winding is calculated, thereby obtaining the magnetic field of the three-phase winding at point P. Finally, the leakage flux calculation formula under the inter-turn short-circuit fault condition is derived, as follows: In a three-phase transformer, taking the high-voltage winding as an example, and using phase B as a reference, the spatial position of the three-phase winding is obtained. The generated x The leakage magnetic flux density in the axial direction is shown in equation (1): (1); In formula (1): For phase B winding at point Place x Structure functions in the axial direction; This refers to the number of turns in phase B winding; This refers to the magnitude of the B-phase current. For phase A winding at point Place x Structure functions in the axial direction; This refers to the number of turns in phase A winding; The magnitude of phase A current; The center distance of the core pillars; For the C-phase winding at point Place x Structure functions in the axial direction; This refers to the number of turns in the C-phase winding. This refers to the magnitude of the C-phase current. , , These represent the windings of phases A, B, and C respectively. x The flux leakage induction intensity generated in the axial direction; , In equation (1) , The equivalent substitutions represent the A-phase winding and the C-phase winding at point, respectively. Place x The axial structure function, after replacement, makes the leakage magnetic flux intensity generated by each phase winding represented with phase B as the reference. Among them, the B-phase winding is at point of x , y , z The structure function in the axial direction is shown in equation (2): (2); In formula (2): Permeability; h This refers to the winding height. L This refers to the winding thickness; r for Q The radius of the current loop where the point is located; for Q Point current element and y The included angle of the axis; d for Q Click P Distance between points .

[0007] During an inter-turn short-circuit fault in a transformer, the leakage flux distribution is composed of the superposition of magnetic fields generated by the short-circuit current and non-short-circuit current. A single-winding inter-turn short-circuit model is shown below. Figure 1 As shown, taking phase A as an example, the number of winding turns from bottom to top is as follows: N 11 , N s , N 12 When there is a short circuit between turns x The formula for calculating the axial leakage magnetic flux density is shown in equation (3): (3); In formula (3): This represents the leakage magnetic flux density along the x-axis when there is an inter-turn short-circuit fault in phase A winding. , , They represent the windings respectively. N 11 , N s , N 12 At point Placex Structure functions in the axial direction; This represents the short-circuit turn current.

[0008] Considering that changes in current do not affect the structure function G The change in flux density along the y and z axes differs from that along the x axis only in the structure function G. Equation (3) can be further simplified to obtain the expression for flux density along the x, y, and z axes as follows: (4); In equation (4): , , These represent the points of the A-phase winding at point A. along x , y , z Structure functions in the axial direction; Taking the B-phase winding of a three-phase transformer as a reference, and an inter-turn short-circuit fault occurring in the A-phase high-voltage side winding, it is possible to deduce the short circuit at a certain point in space of the three-phase transformer. of x The magnitude of the leakage magnetic flux induction intensity in the axial direction is shown in equations (5) and (6): (5); (6); In the above formula: This indicates that the three-phase transformer is at point when an inter-turn short-circuit fault occurs. along x The flux leakage induction intensity generated in the axial direction; This indicates the three-phase winding current (i.e., the non-short-circuit turn current) along... x The flux leakage induction intensity generated in the axial direction; , , , , , These represent the windings of phases A, B, C, a, b, and c at point... along x Structure functions in the axial direction.

[0009] In step 2, the magnetic field generated by the non-short-circuit turn current is calculated using the three-phase winding current data. The non-short-circuit turn current is the magnetic field generated by the non-short-circuit turn current in equation (6). The leakage magnetic difference function, which characterizes only the magnetic field generated by the short-circuit turn current, is constructed by calculating the three-phase winding current and combining it with measured magnetic field data. Equation (7) is the formula for calculating the leakage magnetic difference, which is defined as the magnetic field generated by the short-circuit turn current. The three-phase current flowing into the transformer is a through current, while the short-circuit turn current only flows at the short-circuit turn location. The three-phase current data can be directly obtained through a detection device, and the magnetic field generated by the non-short-circuit turn current can be calculated. The measured magnetic field data at a fixed measuring point can be obtained through a magnetic induction device. The non-short-circuit turn current is the current in equation (6). The calculation is performed using the three-phase winding current.

[0010] The leakage magnetic flux difference is defined as the magnetic field generated by the short-circuit turn current. The formula for calculating the leakage magnetic flux difference is shown in equation (7): (7); In equation (7): , These represent the radial and axial leakage magnetic flux differences at measuring point i, respectively. , These represent the measured radial and axial leakage magnetic flux density data at measuring point i, respectively. , These represent the calculated radial and axial leakage magnetic flux induction intensities generated by the non-short-circuit turn current at measurement point i, respectively.

[0011] The radial leakage magnetic flux inductance coefficient is expressed as... ,in: D x For amplitude correction, φ x To correct the phase angle and reduce the deviation between theory and practice; is the axial leakage magnetic flux inductance coefficient. .

[0012] In step 3, when the transformer is in an abnormal operating condition without inter-turn short-circuit faults (such as system short circuit, no-load closing), the amplitude of the leakage flux difference at each measuring point is relatively small. However, when the transformer has inter-turn short-circuit faults or when inter-turn short-circuit is superimposed with other fault conditions (inter-turn short-circuit + no-load closing, inter-turn short-circuit + external fault), the presence of the short-circuited turn will cause significant changes in the amplitude of the leakage flux difference at some measuring points. Specifically: An inter-turn short-circuit test was conducted on the high-voltage winding of phase A of the moving-mode transformer. Taking a 1.19% inter-turn short-circuit fault occurring at 51cm as an example, ... Figure 9 As shown, the solid red line represents the calculated leakage magnetic flux density generated by the three-phase current (i.e., non-turn short-circuit current) at this measuring point, and the dashed blue line represents the actual measured leakage magnetic flux density at this measuring point. Due to the presence of the short-circuited turn under the inter-turn short-circuit fault condition, the two curves begin to differ after the fault occurs at 0.05s. According to the aforementioned content, this difference is the leakage magnetic flux difference. The closer to the fault location, the more obvious the difference in the amplitude of the leakage magnetic flux difference. When there is no inter-turn short-circuit fault, the two curves almost overlap. At this time, the amplitude of the leakage magnetic flux difference is small, and the leakage magnetic flux difference under the condition without inter-turn short-circuit fault is similar.

[0013] To ensure the protection scheme has sufficient sensitivity to various operating conditions involving inter-turn short circuits, the inter-turn short circuit protection threshold is set to [value missing]. B set When any measuring point in the axial or radial direction i When the condition of equation (8) is met, it is considered that the transformer has an inter-turn short circuit fault: (8); In equation (8): , These represent the radial and axial leakage magnetic flux differences at measuring point i, respectively. , These are the radial protection threshold and the axial protection threshold.

[0014] In step 4, the analytical expression for the leakage magnetic flux difference is derived, and the influence of the structure function G value on the location and severity of the inter-turn short-circuit fault is analyzed; a position function K value containing only location information is constructed. x Taking the axial direction as an example, the analytical expressions for the leakage magnetic flux difference are shown in equations (9) and (10): (9); (10); In the above formula: This is the radial leakage magnetic flux difference. A structure function representing the short-circuited turn during an inter-turn short-circuit fault; , Indicates the height of the short-circuit turn; , Indicates the inner and outer diameters of the winding. Figure 1 It can intuitively reflect the relevant variables.

[0015] The structure function G is primarily related to the fault location. The number of short-circuit turns can only be determined by influencing... h 1. h The value of 2 affects the magnitude of the structure function G. Since the change in the structure function G value due to the number of short-circuited turns is limited, and based on data analysis, it can be considered that... G The value is not affected by the number of short-circuit turns.

[0016] Because the measuring point is installed on the symmetrical tangent plane of the transformer, the observation line... y The magnetic field component along the axial direction is extremely small, and its influence is ignored in the calculation. (Definition) x The magnetic field component along the axial direction is the radial component. z The magnetic field component along the axial direction is called the axial component, and the position function is defined in the radial and axial directions as follows: , The expression is shown in equation (11): (11); In equation (11): , These represent radial and axial position functions, respectively. This represents the axial leakage magnetic flux difference at measuring point i. This represents the maximum value of the axial leakage magnetic flux difference among all measuring points. This represents the axial structure function of the short-circuit turn at measurement point i. This represents the axial structure function of the short-circuit turn at the measuring point corresponding to the maximum value of the leakage magnetic flux difference. and They represent the first i Radial leakage magnetic flux difference and structure function at each measuring point; and These represent the radial leakage magnetic flux difference and the maximum value of the structure function at all measuring points, respectively. Due to structure function G It is mainly related to the fault location. The location function K can effectively reflect the distribution characteristics of leakage flux in inter-turn faults and is not affected by the amplitude of short-circuit turn current.

[0017] In step 5, since the interference of short-circuit turns and fault current has been eliminated during the calculation of the position function K, the calculated value of the position function K remains consistent at any time within a power frequency cycle. Based on the calculation method of the position function K, the position values ​​at different fault locations can be theoretically calculated. K The value is used as the standard K value. Specifically: According to the derivation of equation (11), the position function K is the ratio of the structure function G, and the structure function G is only related to the fault location. Therefore, the position function K is only related to the fault location. Depending on the fault location, different K values ​​can be obtained. The calculation of the G value is a numerical calculation, which does not require the import of measured data in advance. Therefore, it can be used as a standard K value.

[0018] Different fault locations correspond to K The values ​​differ, especially at the measuring points closer to the fault center. K The value is relatively larger.

[0019] like Figure 8 As shown, the differences in K values ​​at different fault locations can be clearly seen. If the measured K value corresponds to the solid red line in the graph, and the dashed line represents the standard K value, it can be clearly seen that the closer to the fault location, the higher the degree of matching of the curve. This method transforms the leakage magnetic field data of the measuring points to obtain a value that accurately reflects and characterizes the fault location. K Value information.

[0020] Based on this, an analytical model for locating short-circuit faults between transformer turns is constructed. This analytical model refers to the objective function shown in equation (12), which reflects the difference between the measured K value and the standard K value. The measured leakage flux difference data is used to calculate the measured... K Values ​​and Standards K The difference in values ​​is quantified as numerical deviation.

[0021] Accurate fault location information is obtained by inverting the analytical model for locating inter-turn short-circuit faults in transformers. The objective function expression for fault location is shown in equation (12): (12); In equation (12): The height of the fault point. Indicates the location of the center of the inter-turn short circuit; Describe the objective function. , These represent the radial and axial position functions obtained from the measured leakage magnetic flux, respectively. , These are standard radial and axial position functions.

[0022] The Beaver Algorithm, a novel metaheuristic algorithm, simulates the dam-building process of beavers to ensure effective spatial search and optimal identification, exhibiting good performance. It can be used as an optimization algorithm for the objective function to achieve accurate prediction of the location of inter-turn short-circuit faults.

[0023] This invention provides a method for identifying and locating inter-turn short-circuit faults in transformers based on differences in leakage flux distribution. The technical advantages are as follows: 1) Compared with other inventions, this invention derives the transformer leakage flux calculation formula theoretically and constructs a leakage flux difference function that can reflect inter-turn short circuit fault information, which can effectively identify inter-turn short circuit fault conditions under complex operating conditions.

[0024] 2) Based on the leakage magnetic difference, this invention constructs a position function K value that reflects the location information of inter-turn short circuit faults, and further constructs an objective function that reflects the difference in fault location. With the help of the Hippo algorithm, the inter-turn short circuit fault is located, which effectively solves the problem of difficulty in locating inter-turn short circuit faults in existing methods. 3) This invention only requires leakage magnetic data from some measuring points to identify and locate inter-turn short-circuit faults. The numerical calculation process is simple, requiring no complex algorithms, and is relatively easy to implement. Attached Figure Description

[0025] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is an equivalent schematic diagram of a single winding during an inter-turn short-circuit fault. Figure 2 Equivalent diagram of a single winding Figure 3 The curves show the leakage magnetic flux difference between inter-turn short circuits at different fault locations.

[0026] Figure 4 The curves show the leakage flux difference during no-load closing at different closing angles.

[0027] Figure 5 The leakage magnetic flux difference curves are shown for different types of external faults.

[0028] Figure 6 The distribution of leakage magnetic flux difference curves between turns under different fault degrees.

[0029] Figure 7 This is a schematic diagram illustrating the influence of fault degree and fault location on the structure function G.

[0030] Figure 8 This is a schematic diagram illustrating the K-value matching in the analytical model.

[0031] Figure 9 The curves show the leakage magnetic flux density at each measuring point during the inter-turn short circuit.

[0032] Figure 10 This is a graph comparing the algorithm performance.

[0033] Figure 11 This is a flowchart of the method of the present invention. Detailed Implementation

[0034] A method for identifying and locating transformer inter-turn short-circuit faults based on the difference in leakage flux distribution is proposed. First, the formula for calculating the leakage flux induction intensity during an inter-turn short-circuit fault is derived according to Biot-Savart's law. Next, an expression for the leakage flux difference is constructed by combining measured leakage flux data and leakage flux calculated from three-phase current. Then, based on this, the distribution characteristics of the leakage flux difference at various measuring points under different operating conditions are analyzed, and a criterion for transformer inter-turn short-circuit protection is constructed by combining amplitude differences. Furthermore, the influence of the structure function G value on the location and severity of the inter-turn short-circuit fault is analyzed, and a location function K value reflecting the location information of the inter-turn short-circuit fault is constructed. Finally, using the standard K value as a benchmark, the target function is used to... f ( x This method reflects the degree of matching between the measured K value and the standard K value, and predicts the location of inter-turn short-circuit faults in transformers using the Beaver Algorithm. This approach solves the problems of insufficient adaptability to inter-turn short-circuit fault identification under complex operating conditions and difficulty in locating the faults.

[0035] S1: Calculate the value of a single winding at a point outside the winding based on the Biot-Savart law. P The generated magnetic field, in turn, yields the three-phase winding at point PThe magnetic field was analyzed, and finally, the formula for calculating leakage flux under inter-turn short-circuit fault conditions was derived. The Biot-Savart law can be used to calculate the magnetic field distribution around a solenoid, whose structure is similar to that of a transformer winding. Figure 2 As shown, a geometric model of a single winding is established. The model ignores the minute gaps between coils, treating the winding as an equivalent hollow charged cylinder, where the inner and outer diameters of the winding are respectively... a , b winding thickness The height is h .

[0036] There exists a point in space Calculate the winding in P The magnetic field generated at the point. This process neglects the influence of the iron core on the leakage magnetic field, and derives the magnetic field distribution around the winding using differential methods. Assume the number of turns in a single winding is... N The height of a certain current loop is d z Thickness d r If the current flowing through the conductor is I The current flowing through the cross-section of the current loop As shown in equation (1).

[0037] (1); In the formula, h For winding height, L This refers to the winding thickness.

[0038] Assume there is a point on the current loop Then the current element at that point As shown in equation (2).

[0039] (2); In the formula, for Q The arc vector of a point, transformed into a rectangular coordinate system, is shown in equation (3): (3); In the formula, r Let be the radius of the current loop containing point Q. for and y The included angle of the axis.

[0040] According to the Biot-Savart theorem, it can be deduced that... Q Point current element at P The magnetic induction intensity generated by the point is shown in equation (4): (4); In the formula, for Q ClickP Vector of a point , is the magnetic permeability.

[0041] Based on the cross product formula of vectors, we can derive... As shown in equation (5).

[0042] (5); From this, we can deduce... Q Point current element at P The magnetic induction intensity of the point along x , y , z The components of the axis are shown in equation (6).

[0043] (6); By performing triple integration, the magnetic flux density of a single winding at a point in space in each direction can be obtained as follows: (7); It is not difficult to find from the formula that when calculating the magnetic field at a certain point, the magnetic field at that point is proportional to the current. By simplifying the above formula, the formula for calculating the magnetic field around a single winding is obtained as shown in Equation (8) and Equation (9).

[0044] (8); (9); The spatial positions of each winding of the three-phase transformer are relatively fixed. Taking phase B as the reference, the center distance of the core columns is assumed to be... Taking the high-voltage side winding as an example, the three-phase windings are at the same point The generated x The magnetic field along the axis is shown in equation (10).

[0045] (10); Further derivation shows that each phase winding is along the same point y , z The formula for calculating the magnetic field in the axial direction states that the magnetic field at a point in the space of a three-phase transformer is the sum of the magnetic fields of each phase winding at that point, exhibiting a sinusoidal characteristic. When an inter-turn short-circuit fault occurs in the transformer, the short-circuit current will be superimposed with a leakage flux fault component in space. The single winding model during an inter-turn short circuit is as follows: Figure 1 As shown, taking phase A as an example, the number of winding turns from bottom to top is as follows: N 11 , N s , N 12Based on the analytical expression for leakage flux derived above, and considering the current flow direction, a formula for calculating spatial leakage flux when an inter-turn short circuit occurs in a single winding can be further obtained. x Taking the axial magnetic field as an example, as shown in equations (11) and (12).

[0046] (11); (12); Considering that changes in current do not affect the structure function G The changes can be further simplified to obtain: (13); (14); Similarly, it can be calculated y , z The axial magnetic field is shown in equations (15) and (16).

[0047] (15); (16); Taking the B-phase winding of a three-phase transformer as a reference, and the inter-turn short-circuit fault occurring in the A-phase high-voltage side winding as an example, we can further deduce the phenomenon of a short circuit at a certain point in space in the three-phase winding. The generated magnetic field is shown in equations (17) and (18).

[0048] (17); (18); S2: Combining current data and magnetic field data, a leakage magnetic difference function is constructed to characterize the magnetic field generated by the short-circuit turn current. When abnormal operating conditions occur, the three-phase current flowing into the transformer may change, which will indirectly affect the leakage magnetic field distribution characteristics. It is worth noting that, except for inter-turn short circuits, the three-phase current flowing into the transformer is mostly through current, which can be directly measured. The magnetic field generated by it can be obtained by combining the magnetic field analysis formula. When an inter-turn short circuit fault occurs, the short-circuit turn current only flows at the fault location. It is difficult to directly calculate the leakage magnetic distribution characteristics including the inter-turn short circuit fault through external measurable current. The leakage magnetic difference is defined as the difference between the measured leakage magnetic field and the leakage magnetic field calculated by the three-phase current, as shown in Equation (19). The leakage magnetic difference at each measuring point can be obtained.

[0049] (19); In the formula, For the first i Measured magnetic flux leakage data at each measuring point; The first phase obtained by calculating the three-phase current i Leakage magnetic field data at each measuring point; The inductance coefficient is expressed as... ,in D x For amplitude correction, φ x This is for phase angle correction, mainly to reduce the deviation caused by overly idealistic theoretical calculations.

[0050] S3: Analyze the distribution pattern of leakage flux difference under different operating conditions of the transformer and construct a criterion for identifying inter-turn short-circuit faults. The leakage flux characteristics show that the distribution of leakage flux difference is related to the location of the inter-turn short-circuit fault, with significant amplitude changes and a large fluctuation range. This means that the inter-turn short-circuit fault in the transformer induces a magnetic field across the entire spatial area through the fault current, causing changes in the magnetic field distribution at each location. A three-phase, three-limb dry-type transformer operating in the dynamic model laboratory is used as a prototype reference; the transformer parameters are shown in Table 1.

[0051]

[0052] Taking a 0.45% inter-turn short-circuit fault occurring at different locations in phase A winding as an example, six measuring points are evenly distributed along the winding height on the observation line, corresponding to 2.5cm, 22.5cm, 42.5cm, 62.5cm, 82.5cm, and 102.5cm of the winding height, respectively, and labeled as mea_1 to mea_6. The leakage magnetic flux difference at each measuring point can be obtained as follows: Figure 3 As shown. Figure 3 The data reflects the change in leakage magnetic flux difference during an inter-turn short circuit. Because the number of short-circuited turns is relatively small, the change in magnetic field caused by the change in three-phase current is small, and the change in leakage magnetic flux is primarily caused by the short-circuited turns. Since there will be a certain degree of deviation between the analytically calculated leakage magnetic flux and the actual leakage magnetic flux, a small difference in leakage magnetic flux can still be detected at each measuring point before the fault. After the inter-turn short circuit fault, amplitude changes occur at each measuring point, with the amplitude changes being more pronounced at measuring points closer to the fault point, which can be used as a basis for fault diagnosis.

[0053] When a transformer is closed under no-load conditions, the core becomes saturated due to the hysteresis characteristics and residual magnetism of the core. Under this condition, the inrush current contains a large number of harmonic and attenuation components, causing changes in the leakage flux distribution in space. This leakage flux is a superposition of transient and steady-state leakage flux, exhibiting a dynamic change. However, considering that only through-current flows through the transformer, the current change can be directly measured by a detection device. Therefore, theoretically, the leakage flux distribution in space can be directly calculated using analytical equations. The leakage flux distribution in space at the moment of maximum leakage flux under different closing angles is shown below. Figure 4 As shown in the figure, the leakage flux difference fluctuates within the mT range during no-load closing fault, and the change in leakage flux difference is limited. Compared with inter-turn short circuit, it can be basically considered that the leakage flux difference is not affected by no-load closing.

[0054] Due to various uncontrollable factors, power systems experience ground faults, phase-to-phase short circuits, and other operating conditions. These conditions cause changes in the current flowing into the three-phase windings of the transformer, thus affecting the leakage flux distribution within the transformer space. During a system short circuit, the current transient process is relatively short, so the magnetic field quickly reaches a steady state. Taking some operating conditions as examples, the leakage flux difference distribution under different external fault conditions is as follows: Figure 5 As shown. From Figure 5 It can be observed that when an external fault occurs, the fluctuation range of the leakage magnetic difference is limited. Although it exhibits different distribution characteristics under different fault conditions, the overall change range is small, and it is basically considered that the leakage magnetic difference is not affected by external faults.

[0055] When a transformer is under abnormal operating conditions without inter-turn short circuits (such as system short circuits or no-load closing), the amplitude of the leakage flux difference is relatively small. However, when the transformer has an inter-turn short circuit fault or a scenario where an inter-turn short circuit is superimposed on other fault conditions (inter-turn short circuit + no-load closing, inter-turn short circuit + external fault), the presence of the short-circuited turn will cause a significant change in the amplitude of the leakage flux difference, which can be observed at various measuring points. The leakage flux difference is mainly affected by the inter-turn short circuit. When operating without an inter-turn short circuit fault, the change in the leakage flux difference is relatively small. Comparing the leakage flux difference curves at the maximum leakage flux moment under the inter-turn short circuit conditions of the transformer with fault levels of 0.59%, 0.89%, and 1.19%, as shown... Figure 6 As shown. Based on the distribution characteristics of the leakage magnetic flux difference curve, it was found that the amplitude change is significant at the point of maximum leakage magnetic flux difference. To ensure that the protection scheme has sufficient sensitivity to various operating conditions containing inter-turn short circuits, the inter-turn short circuit protection threshold is set to [value missing]. B set When any measuring point in the axial or radial direction i When the condition of equation (20) is met, it is considered that the transformer has an inter-turn short circuit fault.

[0056] (20); Considering the limited number of measuring points, it cannot be guaranteed that the maximum value of leakage magnetic flux difference can be detected by the measuring points. To ensure reliable identification of inter-turn short circuits, a radial protection threshold is set based on a large amount of data measurement. B x_set The axial protection threshold is 24mT. B z_set The value is 26mT. When the leakage flux difference at a certain measuring point exceeds this threshold, it can be considered that an inter-turn short-circuit fault has occurred in the transformer. As can be seen from the figure, even if the fault severity is below 0.89%, if the fault location is near the measuring point, the measuring point may still detect a leakage flux difference exceeding the threshold, thus indicating a short-turn fault. However, for operating conditions without inter-turn short-circuit faults, such as… Figure 4 , Figure 5As shown, this ensures that the fault level cannot exceed the threshold. Theoretically, this threshold can effectively identify inter-turn short circuit faults with a fault severity of 0.89% or higher, and can partially identify inter-turn short circuit faults with a fault severity of less than 0.89%, effectively avoiding misjudgment of non-inter-turn short circuit faults.

[0057] S4: Derive the analytical expression for the leakage magnetic flux difference and construct the position function K value that reflects the fault location information. According to equation (17), the analytical expression for the leakage magnetic flux difference is shown in equation (21).

[0058] (twenty one); When an inter-turn short-circuit fault occurs, the A-phase current, although affected by the short-circuit turn coupling, experiences a small fluctuation. However, the fluctuation range is limited, and its impact on the leakage flux calculation results is negligible. Since the number of winding turns and winding current are not integral variables, they can be extracted outside the triple integral. The remaining triple integral expression is the structure function. G The number of short-circuit turns is mainly related to the location of the fault. h 1. h The value of 2 affects the structure function. G The size of the fault current. The structure function corresponding to the fault current for inter-turn short-circuit conditions with different fault locations and severity. G xs , G zs Changes such as Figure 7 As shown in the figure. It can be observed from the figure that when a fault occurs at the same location, as the severity of the fault increases, the structure function... G The variation range is extremely small, almost unable to reflect the difference in fault severity, while the structure function at different fault locations shows significant differences. Therefore, it can be inferred that the structure function... G Primarily related to the fault location, it mainly characterizes the fault location features, caused by inter-turn short circuits. h 1. h 2. Changes in numerical values ​​have almost no effect G The changes.

[0059] Considering that the observation line is located on the symmetrical tangent plane of the transformer, and is affected by the symmetrical distribution of the magnetic field, the observation line... y The magnetic field component along the axial direction is extremely small, and its influence is ignored in the calculation. (Definition) x The magnetic field component along the axial direction is the radial component. z The magnetic field component along the axial direction is called the axial component, and the position function is assumed to be respectively in the radial and axial directions. K x , K z The expression is as follows: (twenty two); In the formula, and They represent the first i Radial leakage magnetic flux difference and structure function at each measuring point and These represent the radial leakage magnetic flux difference and the maximum value of the structure function at all measuring points, respectively.

[0060] Position function K It can effectively reflect the distribution characteristics of leakage flux during inter-turn faults and is unaffected by the amplitude of short-circuit turn current. Due to the position function... K The interference from short-circuit turns and fault current has been eliminated during the calculation process. The position function calculated at any time within one power frequency cycle is... K The values ​​remain consistent. (Based on the position function) K The calculation method for the value can theoretically yield the position function corresponding to different fault locations and different numbers of fault turns. K The values ​​are calculated, and the results are shown in Table 2. Here, loc represents the fault location, and deg represents the fault severity.

[0061]

[0062] According to the data in Table 2, when the fault location is the same, the location functions corresponding to different fault degrees are... K The values ​​are the same, but the corresponding values ​​are different at different fault locations. K The values ​​differ, closer to the fault center K The values ​​are relatively larger. This method transforms the leakage magnetic field data from 6 measuring points into 12 feature quantities that can accurately reflect the fault location information. The calculation process is efficient and fast, with minimal theoretical calculation error and extremely high accuracy. It can be used as a standard fault feature for fault matching in actual fault scenarios.

[0063] S5: Calculate the K value at each measuring point, construct an objective function reflecting the degree of matching between the measured K value and the standard K value, and further predict the location of inter-turn short-circuit faults using the Beaver Algorithm. Based on the theoretically derived formula, the standard K value corresponding to different fault locations can be obtained in advance. K The measured value information is used as a matching benchmark for fault location, and the measured leakage magnetic field difference data is used to calculate the measured value. K Values ​​and Standards K The characteristic differences in the values ​​are quantified as numerical deviations, and accurate fault location information is obtained by solving the analytical model. The objective function expression for fault location is shown in equation (23). (twenty three); In the formula, The height of the fault point; K x_i , K z_iTo pass through the fault point height The standard of each measuring point obtained by calculation K Value, of which This indicates the center location of the inter-turn short circuit, with a standard based on an inter-turn short circuit severity of 0.74%. K Value calculation; K x_act_i , K z_act_i The measured leakage magnetic flux difference was calculated from the actual measured value. K value.

[0064] Standards for inter-turn short circuits at different locations K Values ​​and Measured Values K Differences in the degree of matching of values ​​can be directly reflected in the numerical solution of the analytical model. Taking the full data of the observation line as an example, for... K Value matching is the standard K Value-oriented actual measurement K The value approaches infinitely close, such as Figure 8 As shown. From Figure 8 The image clearly shows the different fault locations. K The values ​​show significant differences, according to actual measurements. K The calculated value can only correspond to one distribution scenario. The closer to the fault location, the higher the matching degree and the smaller the value of the objective function. The height corresponding to the minimum value is taken. This is the location of the fault closest to the fault point.

[0065] The Beaver Optimization Algorithm, by simulating the dam-building activities of beavers, ensures efficient spatial search and optimal identification. By optimizing the objective function using the Beaver Algorithm, the location of inter-turn short-circuit faults in transformers can be predicted. The beaver's dam-building process exhibits unique social behavior, requiring collective division of labor to ensure optimal location and dam integrity, demonstrating outstanding foresight and planning capabilities. The dam-building process is mainly divided into an exploration phase and a development phase, described in detail below: (1) Population initialization: The Beaver Algorithm is a population-based optimization algorithm. Each dimension j of each individual beaver represents a type of building material, and its value represents the decision variable. Initially, each beaver has a randomly combined set of materials, which initializes the population across the entire search space. The formula is: (twenty four); In the formula, Indicates the first i The first one held by the beaver j Various building materials; , They represent the first j The upper and lower bounds of the property changes of a material; Represents a random number between 0 and 1.

[0066] (2) Iteration factor: The construction of the beaver dam involves material collection and area exploration (exploration phase) and dam construction and maintenance (development phase). Initially, the focus is on the exploration phase, gradually shifting towards the development phase as time progresses. While transforming this process into a mathematical one, the possibility of area exploration is maintained throughout. An iteration factor is introduced when choosing between the exploration and development phases, with the following formula: (25); At each iteration, a random number r in the range [0,1] is generated, and this is used to determine whether the population has entered the development phase. r < m ) or exploration phase ( r > m The iteration factor can enhance the randomness of the algorithm and prevent premature convergence.

[0067] (3) Exploration phase: The exploration phase primarily involves two behaviors of the beavers: gathering and exploration. During this phase, the population is divided into two groups to perform different behaviors. Gatherers randomly choose another gatherer to accompany them and have a chance to learn from their companion, collecting better materials. This mutual learning behavior among gatherers can be represented by the following formula: (26); In the formula, Indicates the first t During the nth iteration i The beaver's first j One material; The function is a characteristic function; the function value is 1 when the logic inside the parentheses is true, and 0 otherwise. , Represents a random number between 0 and 1.

[0068] Prospectors will also randomly select another prospector and have a chance to learn from their companion, actively exploring different materials. Their behavioral pattern can be represented by the following formula: (27); In the formula, Indicates the first t During the nth iteration i The beaver's first j One material; , This represents a random number between 0 and 1; the last term in the formula represents the beaver's random exploration of new materials. These are random numbers generated by a Gaussian distribution with a mean of 0 and a variance of 1.

[0069] (4) Development stage: After collecting a certain amount of materials, beavers gradually shift their focus to construction and maintenance. At this point, all members of the population participate in the construction process and no longer venture into new areas to search for materials. This stage is equivalent to the development stage, involving a fine-grained search near the optimal solution. The population update formula is expressed as follows: (28); In the formula, Indicates the first t In the nth iteration, the optimal individual in the population corresponds to the th... j Each material is updated after each iteration. , Represents a random number between 0 and 1.

[0070] The optimal individual is updated in each iteration, as shown in the following equation: (29); To verify the effectiveness of the proposed method for identifying and locating inter-turn short-circuit faults in transformers, this paper simulates different fault conditions in a dynamic model laboratory. On one hand, it determines whether an inter-turn short-circuit fault has occurred in the transformer using leakage flux difference information; on the other hand, after confirming an inter-turn short-circuit fault, it locates the fault position. Regarding the measurement accuracy issue, existing fiber optic sensors with a measurement range of 0.1~10mT and a measurement accuracy of 0.01mT can meet the requirements for transformer leakage flux measurement.

[0071] When a transformer experiences an inter-turn short-circuit fault, the leakage flux difference will change significantly due to the mismatch between the calculated and measured leakage flux of the three-phase current. An inter-turn short-circuit test was conducted on the A-phase high-voltage winding of a moving-model transformer. Taking a 1.19% inter-turn short-circuit fault occurring at 51cm as an example, the leakage flux at each measuring point is as follows: Figure 9 As shown, after an inter-turn short-circuit fault occurs within 50ms, the leakage flux changes. The leakage flux calculated from the three-phase current does not include the leakage flux generated by the short-circuit turn, resulting in a significant amplitude difference between the calculated leakage flux and the actual leakage flux at the measurement point. From... Figure 9 As can be seen, the closer the measuring point is to the fault location, the more obvious the change in leakage flux. The change amplitude at some measuring points has exceeded the protection threshold, which can effectively identify it as an inter-turn short circuit. To further verify the effectiveness of the protection scheme, multiple sets of inter-turn short circuit experiments were conducted, and the amplitude change after the fault was calculated at each measuring point. The protection action is shown in Table 3.

[0072]

[0073] Among them, fault conditions a , b These represent the A-phase high-voltage winding of the transformer at different winding heights. a Occurred at cm bThe percentage of inter-turn short circuit faults indicates a 0.89% fault, and other cases follow the same logic. For example, 51,0.89 indicates an inter-turn short circuit fault of 0.89% at a winding height of 51cm; in the operation status, 0 indicates no operation and 1 indicates operation. x i Indicates radial first i Leakage magnetic flux difference at each measuring point z i Indicates the axial first i Leakage magnetic flux difference at each measuring point.

[0074] Table 3 shows that the maximum leakage flux detected at each measuring point changes with the fault location, and all exhibit the same trend: the closer the measuring point is to the fault location, the greater the change in leakage flux; and as the fault severity increases, the difference in leakage flux detected at each measuring point increases. The leakage flux difference at each measuring point can be comprehensively evaluated, and the protection threshold can be used to effectively identify transformer inter-turn short-circuit faults with a fault severity of 0.89% or higher.

[0075] No-load closing is a special operating condition during normal transformer operation. Under this condition, the current has a non-periodic component, which affects the magnetic field distribution characteristics and magnitude, potentially causing changes in the leakage flux difference. No-load closing experiments were conducted on a moving-model transformer, using phase A as a reference, under different closing angles. The no-load closing condition with inter-turn short-circuit faults was also considered. The comprehensive evaluation of the leakage flux difference under various conditions for diagnosing inter-turn short-circuit faults is shown in Table 4. Among these, the fault conditions... a , b , c Representative transformer c ° closing angle, the A-phase high voltage winding at the winding height a Occurred at cm b Inter-turn short-circuit fault of % fault severity a , b A value of 0 indicates no short-turn fault.

[0076]

[0077] Table 4 shows that the leakage flux difference under no-load closing conditions fluctuates to some extent, but the fluctuation range is small. The degree of change in leakage flux difference at each measuring point is similar, and there is no obvious amplitude difference between the measuring points. In the no-load closing experiment with inter-turn short circuit faults, the changes in leakage flux difference at each measuring point are more obvious. Compared with no-load closing only, there is a significant inconsistency in the maximum leakage flux at each measuring point. For inter-turn short circuit faults with a fault rate below 0.89%, the leakage flux difference is larger when the fault location is close to the measuring point, so it can be partially identified. For inter-turn short circuit faults with a fault rate above 0.89%, it can be effectively identified, and misjudgment can be avoided under no-load closing conditions.

[0078] When an external fault occurs in a transformer, the three-phase current will change significantly, causing a change in the leakage flux difference. In this case, the protection will not operate. In extreme cases, during the period when the external fault is not isolated, the increased current may damage the insulation, leading to an inter-turn short circuit fault. In this case, the protection should operate. Experiments were conducted on a moving-model transformer under different external fault conditions, considering the external fault condition with inter-turn short circuits. The comprehensive response of the leakage flux difference to the diagnostic effect of inter-turn short circuit faults under various conditions is shown in Table 5. Among them, the fault conditions... a , b , d Represents the appearance outside the transformer area d Type of fault, phase A high voltage winding at winding height a Occurred at cm b Inter-turn short circuit fault of a certain degree. a , b A value of 0 indicates no short-turn fault. d The numbers 1 to 9 represent fault types AN, BN, CN, AB, AC, BC, ABN, ACN, and BCN, respectively.

[0079]

[0080] Table 5 shows that the leakage flux difference fluctuates to some extent under external fault conditions, but the fluctuation range is small, similar to the leakage flux fluctuation during no-load closing. This is mainly due to the deviation between the calculated leakage flux and the actual leakage flux, and there is no obvious amplitude difference between the measuring points. In the external fault experiment with inter-turn short circuit faults, the leakage flux difference at each measuring point changes significantly, and it can effectively operate on inter-turn short circuit faults of 0.89% or higher.

[0081] The above experiments show that the leakage magnetic flux difference at each measuring point can effectively diagnose inter-turn short circuit faults, and is not affected by through currents such as external faults or no-load closing. It can effectively identify inter-turn short circuit faults.

[0082] Existing methods for locating inter-turn short circuits divide the fault location into three regions, which fails to provide accurate location of the fault. To verify the effectiveness of our proposed method in locating transformer inter-turn short circuit faults, we use the benchmark functions shown in Table 6 for algorithm performance testing. In the table, f 1. Used to test the algorithm's local search capability. f 2. This is used to test the global search capability of the algorithm and compare its performance with traditional algorithms (Sparrow Algorithm, SSA) and newer algorithms (Aurora Algorithm, PLO).

[0083]

[0084] Depend on Figure 10It can be seen that the BO algorithm performs better in both global and local search results, and can meet the requirements of rapid and accurate location of inter-turn short-circuit faults.

[0085] To verify the effectiveness of locating the inter-turn short-circuit fault position of the transformer, inter-turn short-circuit tests of different degrees were set at different locations of the A-phase winding, and the protection operation results are shown in Table 7.

[0086]

[0087] As shown in Table 7, the method proposed in this paper can locate inter-turn short-circuit faults, and the degree of fault has almost no impact on the location effect. The location error is within 3cm. Therefore, this protection scheme can effectively locate the location of inter-turn short-circuit faults.

[0088] To verify the effectiveness of the protection in locating inter-turn short-circuit faults under complex operating conditions, inter-turn short-circuit faults of different locations and severity were set in the A-phase winding and simultaneously existed with no-load closing or external fault conditions. The protection operation under complex operating conditions is shown in Table 8.

[0089]

[0090] As can be seen from Table 8, when an inter-turn short-circuit fault occurs in the winding under complex operating conditions, the position function... K The value can still effectively locate the fault location, with an error range within 3cm. The location effect is basically unaffected by complex working conditions, which shows that the method of the present invention is feasible in the identification and location of short circuit faults between turns of transformer windings.

Claims

1. A method for identifying and locating inter-turn short-circuit faults in transformers based on differences in leakage flux distribution, characterized in that... Includes the following steps: Step 1: Derive the formula for calculating the leakage magnetic flux intensity during an inter-turn short circuit fault in a transformer based on the Biot-Savart law; Step 2: Combining current data and magnetic field data, construct a leakage magnetic difference function to characterize the magnetic field generated by the short-circuit turn current; Step 3: Analyze the distribution pattern of leakage flux difference under different operating conditions of the transformer, and construct the criterion for inter-turn short circuit protection of the transformer; Step 4: Analyze the influence of the structure function G value on the location and severity of the inter-turn short-circuit fault, and construct the location function K value that reflects the location information of the inter-turn short-circuit fault; Step 5: Using the standard K value as a benchmark, the objective function reflects the degree of matching between the measured K value and the standard K value, and the Beaver algorithm is used to predict the location of the inter-turn short circuit fault in the transformer.

2. The method for identifying and locating transformer inter-turn short-circuit faults based on leakage flux difference distribution as described in claim 1, characterized in that: In step 1, based on the Biot-Savart law, the magnetic field generated by a single winding at a point P outside the three-phase winding is calculated, thereby obtaining the magnetic field of the three-phase winding at point P. Finally, the leakage flux calculation formula under the inter-turn short-circuit fault condition is derived, as follows: In a three-phase transformer, for the high-voltage side winding, taking phase B as the reference, the position of the three-phase winding at a point in space is obtained. The generated x The leakage magnetic flux density in the axial direction is shown in equation (1): （1）； In formula (1): For phase B winding at point Place x Structure functions in the axial direction; This refers to the number of turns in phase B winding; This refers to the magnitude of the B-phase current. For phase A winding at point Place x Structure functions in the axial direction; This refers to the number of turns in phase A winding; The magnitude of phase A current; The center distance of the core pillars; For the C-phase winding at point Place x Structure functions in the axial direction; This refers to the number of turns in the C-phase winding. This refers to the magnitude of the C-phase current. , , These represent the windings of phases A, B, and C respectively. x The leakage magnetic flux intensity generated in the axial direction; , In equation (1) , The equivalent substitutions represent the A-phase winding and the C-phase winding at point, respectively. Place x The axial structure function, after replacement, makes the leakage magnetic flux intensity generated by each phase winding represented with phase B as the reference. Among them, the B-phase winding is at point of x , y , z The structure function in the axial direction is shown in equation (2): （2）； In formula (2): Permeability; h This refers to the winding height; L For winding thickness; r for Q The radius of the current loop where the point is located; for Q Point current element and y The included angle of the axis; d for Q Click P Distance between points .

3. The method for identifying and locating transformer inter-turn short-circuit faults based on leakage flux difference distribution as described in claim 2, characterized in that: During an inter-turn short-circuit fault in a transformer, the leakage flux distribution is composed of the superposition of magnetic fields generated by the short-circuit current and non-short-circuit current. For phase A, the number of winding turns from bottom to top is... N 11 , N s , N 12 When there is a short circuit between turns x The formula for calculating the axial leakage magnetic flux density is shown in equation (3): （3）； In formula (3): This represents the leakage magnetic flux density along the x-axis when there is an inter-turn short-circuit fault in phase A winding. , , They represent the windings respectively. N 11 , N s , N 12 At point Place x Structure functions in the axial direction; Indicates the short-circuit turn current; Considering that changes in current do not affect the structure function G The change in flux density along the y and z axes differs from that along the x axis only in the structure function G. Equation (3) can be further simplified to obtain the expression for flux density along the x, y, and z axes as follows: （4）； In equation (4): , , These represent the points of the A-phase winding at point A. along x , y , z Structure functions in the axial direction.

4. The method for identifying and locating transformer inter-turn short-circuit faults based on leakage flux difference distribution as described in claim 3, characterized in that: Taking the B-phase winding of a three-phase transformer as a reference, for an inter-turn short-circuit fault in the A-phase high-voltage side winding, the spatial short-circuit fault of the three-phase transformer at a certain point can be deduced. of x The magnitude of the leakage magnetic flux induction intensity in the axial direction is shown in equations (5) and (6): （5）； （6）； In the above formula: This indicates that the three-phase transformer is at point when there is an inter-turn short circuit fault. along x The leakage magnetic flux intensity generated in the axial direction; This indicates the three-phase winding current, i.e., the non-short-circuit turn current along... x The leakage magnetic flux intensity generated in the axial direction; , , , , , These represent the windings of phases A, B, C, a, b, and c at point... along x Structure functions in the axial direction.

5. The method for identifying and locating transformer inter-turn short-circuit faults based on leakage flux difference distribution as described in claim 4, characterized in that: In step 2, the magnetic field generated by the non-short-circuit turn current is calculated using the three-phase winding current data. The non-short-circuit turn current is the magnetic field generated by the non-short-circuit turn current in equation (6). Calculated using three-phase winding current; Based on measured magnetic field data, a leakage magnetic difference function is constructed to characterize only the magnetic field generated by the short-circuit turn current. Equation (7) is the formula for calculating the leakage magnetic difference, which is defined as the magnetic field generated by the short-circuit turn current. The three-phase current flowing into the transformer is a through current. The short-circuit turn current only flows at the short-circuit turn location. The three-phase current data can be directly obtained through the detection device, and the magnetic field generated by the non-short-circuit turn current can be calculated. The measured magnetic field data at a fixed measuring point can be obtained through the magnetic induction device. The non-short-circuit turn current is the value in equation (6). Calculated using three-phase winding current; The leakage magnetic flux difference is defined as the magnetic field generated by the short-circuit turn current. The formula for calculating the leakage magnetic flux difference is shown in equation (7): （7）； In equation (7): , These represent the radial and axial leakage magnetic flux differences at measuring point i, respectively. , These represent the measured radial and axial leakage magnetic flux density data at measuring point i, respectively. , These represent the calculated data of radial and axial leakage magnetic induction intensity generated by the non-short-circuit turn current at measuring point i, respectively. The radial leakage magnetic flux inductance coefficient is expressed as... ,in: D x For amplitude correction, φ x For phase angle correction; is the axial leakage magnetic flux inductance coefficient. .

6. The method for identifying and locating transformer inter-turn short-circuit faults based on leakage flux difference distribution as described in claim 5, characterized in that: In step 3, when the transformer is in an abnormal operating condition without inter-turn short circuit faults, the amplitude of leakage magnetic flux difference at each measuring point is small; however, when the transformer has inter-turn short circuit faults or inter-turn short circuits superimposed with other fault conditions, such as inter-turn short circuits and no-load closing, or inter-turn short circuits and external faults, the presence of short-circuited turns will cause significant amplitude changes in the leakage magnetic flux difference at some measuring points.

7. The method for identifying and locating transformer inter-turn short-circuit faults based on leakage flux difference distribution as described in claim 6, characterized in that: To ensure the protection scheme has sufficient sensitivity to various operating conditions involving inter-turn short circuits, the inter-turn short circuit protection threshold is set to [value missing]. B set When any measuring point in the axial or radial direction i When the condition of equation (8) is met, it is considered that the transformer has an inter-turn short circuit fault: （8）； In equation (8): , These represent the radial and axial leakage magnetic flux differences at measuring point i, respectively. , These are the radial protection threshold and the axial protection threshold.

8. The method for identifying and locating transformer inter-turn short-circuit faults based on leakage flux difference distribution as described in claim 7, characterized in that: In step 4, the analytical expression for leakage flux difference is derived, and the influence of the structure function G value on the location and degree of inter-turn short circuit fault is analyzed. Construct the position function K value that contains only location information; x The analytical expressions for the leakage magnetic flux difference along the axial direction are shown in equations (9) and (10): （9）； （10）； In the above formula, This is the radial leakage magnetic flux difference. A structure function representing the short-circuited turn during an inter-turn short-circuit fault; , Indicates the height of the short-circuit turn; , This indicates the inner and outer diameters of the winding.

9. The method for identifying and locating transformer inter-turn short-circuit faults based on leakage flux difference distribution as described in claim 8, characterized in that: The structure function G is related to the fault location; the number of short-circuit turns affects... h 1. h The value of 2 thus affects the magnitude of the structure function G. Since the change in the value of the structure function G due to the number of short-circuited turns is limited, based on data analysis, it can be considered that... G The value is not affected by the number of short-circuit turns; Because the measuring point is installed on the symmetrical tangent plane of the transformer, the observation line... y The magnetic field component along the axial direction is extremely small, and its influence is ignored in the calculation. (Definition) x The magnetic field component along the axial direction is the radial component. z The magnetic field component along the axial direction is called the axial component, and the position function is defined in the radial and axial directions as follows: , The expression is shown in equation (11): （11）； In equation (11): , These represent radial and axial position functions, respectively. This represents the axial leakage magnetic flux difference at measuring point i. This represents the maximum value of the axial leakage magnetic flux difference among all measuring points. This represents the axial structure function of the short-circuit turn at measurement point i. The axial structure function of the short-circuit turn at the measuring point corresponding to the maximum value of the leakage magnetic flux difference; and They represent the first i Radial leakage magnetic flux difference and structure function at each measuring point; and These represent the radial leakage magnetic flux difference and the maximum value of the structure function at all measuring points, respectively. Due to structure function G The location function K is related to the fault location and can effectively reflect the distribution characteristics of leakage flux in inter-turn faults, and is not affected by the amplitude of short-circuit turn current.

10. The method for identifying and locating transformer inter-turn short-circuit faults based on leakage flux difference distribution differences according to claim 9, characterized in that: In step 5, since the interference of short-circuit turns and fault current has been eliminated during the calculation of the position function K, the calculated value of the position function K remains consistent at any time within a power frequency cycle. Based on the calculation method of the position function K, the values ​​of different fault locations are calculated. K The value is used as the standard K value; specifically as follows: A fault location analysis model for transformer inter-turn short circuit is constructed. The fault location analysis model refers to the objective function shown in equation (12), which reflects the difference between the measured K value and the standard K value. The measured leakage flux difference data is used to calculate the measured value. K Values ​​and Standards K The difference in values ​​is quantified as numerical deviation; Accurate fault location information is obtained by solving the analytical model for locating inter-turn short-circuit faults in transformers; the objective function expression for fault location is shown in equation (12): （12）； In equation (12): The height of the fault point. Indicates the location of the center of the inter-turn short circuit; Describe the objective function. , These represent the radial and axial position functions obtained from the measured flux leakage magnetic field calculations, respectively. , These are standard radial and axial position functions.

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