Transformer network model-based turn-to-turn fault positioning algorithm

Abstract

The invention relates to a turn-to-turn fault positioning algorithm based on a transformer network model, and belongs to the technical field of power equipment fault diagnosis. According to the algorithm, a transformer equivalent trapezoidal network model is constructed, a winding time domain state space equation is established and converted into a frequency domain equation, and a positioning factor is defined in combination with resonant frequency deviation and impedance change characteristics to quantify fault influence. The method specifically comprises the steps of establishing an inductance and capacitance matrix based on discrete distribution parameters, and deducing an impedance change relation before and after a fault; extracting reference impedance by taking the resonant frequency as reference frequency, and constructing an objective function by combining the positioning factor with the impedance residual error and the frequency residual error; a temperature compensation mechanism is introduced to correct a structure constant, high-frequency interference is suppressed by using a nonlinear function, and the number of fault segments is globally optimized in combination with a simulated annealing algorithm. According to the method, the problem that a traditional method is sensitive to parameter drift and noise is solved, the inter-turn fault positioning precision and the robustness under the complex working condition are remarkably improved through time domain-frequency domain joint analysis and a dynamic correction mechanism, and an efficient and reliable technical means is provided for early fault diagnosis of the transformer.

Description

Technical Field

[0001] The present invention relates to the field of power equipment fault detection, and particularly to an inter-turn fault location algorithm based on a transformer network model. Background Art

[0002] A transformer is a core device for the stable operation of a power system. For its inter-turn short circuit fault of the winding, due to its weak early characteristics and susceptibility to environmental interference, traditional detection methods often face problems such as low positioning accuracy and insufficient anti-interference ability. Existing technologies such as impedance analysis and frequency response analysis mostly rely on steady-state parameters or simplified models, and it is difficult to accurately capture the non-linear characteristics of winding distribution parameters (such as temperature drift, material aging), and the correlation between frequency domain characteristics and faults is insufficiently explored, resulting in ineffective identification of small inductance changes. At the same time, the influence of high-frequency noise and complex working conditions further exacerbates the risk of misjudgment, and there are significant limitations in the robustness and adaptability of existing algorithms.

[0003] Therefore, the present invention proposes an inter-turn fault location algorithm based on a transformer network model. By constructing an equivalent trapezoidal network model, it accurately characterizes the discrete distribution parameters and electromagnetic coupling characteristics of the winding, combines time-domain and frequency-domain joint analysis to extract the correlation characteristics of resonance frequency offset and impedance change, and defines a positioning factor to quantify the fault influence. This method introduces a temperature compensation mechanism and a non-linear correction function to effectively suppress environmental interference and parameter drift, and dynamically corrects the fault location through a global optimization algorithm, significantly improving the positioning accuracy and reliability under complex working conditions. This method provides a more efficient and robust solution for the rapid diagnosis and accurate positioning of transformer inter-turn faults. Summary of the Invention

[0004] An inter-turn fault location algorithm based on a transformer network model, characterized in that: an expression is obtained by simulating the network model of the equivalent winding of the transformer to establish a state time-domain equation of the winding, which is further transformed into a frequency-domain equation to obtain a reference frequency, a reference impedance is determined, and a positioning factor defined based on the reference impedance can be used as a reference for fault location, and further the inter-turn fault location is determined through relevant algorithm processing; the inter-turn fault location based on the transformer network model includes the following steps:

[0005] Step 1: Determine the calculation of the positioning factor, including:

[0006] 1) Derive the input impedance equation through a trapezoidal network. At node n1, with i(t) as the input excitation, and taking the node voltages (v n1 , v n2 ,... v nN+1 ) and induced currents (i L11 , i L22 ,... i LNN ) as state vectors to build the following expression of the time-domain space equation:

[0007]

[0008] where u represents the input vector, x and represent the state vector and its derivative, [P] is the permutation matrix, and the specific compositions of the coefficient matrices [A] and [B] are shown in Eqs. (2) and (3).

[0009]

[0010] Among them, as shown in (4), (5), (6), and (7), [a] in the [A] matrix includes capacitance parameters (inter-turn capacitance C s , ground capacitance C g ), [b] includes inductance parameter L ii , [c] is a zero matrix, and [d] is a set matrix; the [B] matrix includes winding resistance (R i ) and conductance (G i ).

[0011]

[0012] 2) Convert the time-domain state-space equation (1) into a frequency-domain equation (8), and calculate the frequency-domain phasors of the node voltage and the current through the inductor according to this frequency-domain system matrix. From the first node voltage v1(ω) and the input current I(ω) of the system matrix, the winding impedance Z(ω) can be obtained.

[0013] jω[A]X(ω)+[B]X(ω)=P(ω) (8)

[0014]

[0015] 3) Since the inter-turn fault significantly affects the inductance of the winding rather than the series and parallel capacitances, the inductance matrix [b] in (5) will change. For example, if an inter-turn fault occurs in the i-th section of the winding, the matrix [b] becomes [b'], as shown in (10), and the matrix [A] becomes [A'], as shown in (11). Therefore, under the fault condition, the winding impedance will change at the reference frequency.

[0016]

[0017] 4) The resonance frequency f reflects the fixed characteristics of the winding characteristics, C in is the input capacitance of the transformer, C HV is the high-voltage side capacitance of the power transformer, Z k1 is the leakage impedance, and R k1 is the leakage resistance. Taking the resonance frequency f as the reference frequency to obtain the impedance value Z f ;

[0018]

[0019] Z f Z = Z(2πf) (13)

[0020] 5) Let the impedance of the front end of the winding be Z f1 and Z f2 , and the impedances before and after the fault are defined as Z H and Z F , respectively. Define the turn - to - turn fault location factor as R FLF , and the formula is as shown in (14):

[0021]

[0022] Step 2: Determine the fault location and verify the accuracy:

[0023] 1) Considering the non - linear distribution characteristics of the winding structure, the fault location proportionality coefficient α is jointly determined by the location factor R FLF and the resonance frequency offset Δf. Define the joint equation:

[0024]

[0025] where k1 and k2 are weight coefficients determined through calibration experiments, satisfying k1 + k2 = 1 and Δf = f F - f H , where f H and f F are the resonance frequencies before and after the fault, respectively.

[0026] 2) Introduce the influence of temperature T on the winding parameters and correct the structure constant k:

[0027] k(T) = k0·(1 + γ·(T - T0)) (16)

[0028] where k0 is the structure constant at the reference temperature T0; γ is the temperature sensitivity coefficient determined by the material properties.

[0029] 3) Based on the corrected structure constant k(T), define the non - linear function of the number of fault segments i:

[0030]

[0031] where β is the non - linear distortion coefficient determined by the winding discretization model simulation; used to suppress the interference of high - frequency offset.

[0032] 4) Construct the objective function ε(i), combining the impedance residual ε Z and the frequency residual εf :

[0033] ε(i) = w Z ·|Z(i) - Z meas | + w f ·|f(i) - f meas | (18)

[0034] where w Z , w f are weight coefficients, satisfying w Z + w f = 1; Z(i) and f(i) are the theoretical calculation values when the assumed number of faulty segments is i, Z meas and f meas are the measured values. The simulated annealing algorithm is used for global optimization, and the update rule is:

[0035] i n+1 = i n + Δi·sgn(ε(i n ) - ε(i n-1 )) (19)

[0036] until ε(i) < ε Z + ε f or the maximum number of iterations is reached. Finally, i n+1 is used as the result of the number of faulty segments output. Description of the Drawings

[0037] Figure 1 is the flow chart of the method of the present invention;

[0038] Figure 2 is the transformer network model of the method of the present invention. Detailed Embodiment

[0039] The present invention will be further described in detail below with reference to the drawings:

[0040] As Figure 1 shown, an inter-turn fault location algorithm based on a transformer network model, the method includes:

[0041] 1) In Figure 2 the shown transformer network model, the input impedance equation is derived through a ladder network. With i(t) as the input excitation at node n1, and taking the node voltages (v n1 , v n2 ,... v nN+1 ) and the induced currents (i L11 , i L22 ,... i LNN ) as the state vectors, the time-domain space equation expression is constructed as follows:

[0042]

[0043] where u represents the input vector, x and represent the state vector and its derivative, [P] is the permutation matrix, and the specific compositions of the coefficient matrices [A] and [B] are shown in Eqs. (2) and (3).

[0044]

[0045] Among them, as shown in (4), (5), (6), and (7), [a] in the [A] matrix contains capacitance parameters (inter-turn capacitance C s , ground capacitance C g ), [b] contains inductance parameter L ii , [c] is a zero matrix, and [d] is a set matrix; the [B] matrix contains winding resistance (R i ) and conductance (G i ).

[0046]

[0047] 2) Transform the time-domain state-space equation (1) into a frequency-domain equation (8), and calculate the frequency-domain phasors of the node voltage and the current through the inductor according to this frequency-domain system matrix. From the first node voltage v1(ω) and the input current I(ω) of the system matrix, the winding impedance Z(ω) can be obtained.

[0048] jω[A]X(ω)+[B]X(ω)=P(ω) (8)

[0049]

[0050] 3) Since the inter-turn fault significantly affects the inductance of the winding rather than the series and parallel capacitances, the inductance matrix [b] in (5) will change. For example, if an inter-turn fault occurs in the i-th section of the winding, the matrix [b] becomes [b'], as shown in (10), and the matrix [A] becomes [A'], as shown in (11). Therefore, under the post-fault condition, the winding impedance will change at the reference frequency.

[0051]

[0052] 4) The resonance frequency f reflects the fixed characteristics of the winding characteristics. C in is the input capacitance of the transformer, C HV is the high-voltage side capacitance of the power transformer, Z k1 is the leakage impedance, and R k1 is the leakage resistance. Taking the resonance frequency f as the reference frequency to obtain the impedance value Z f at the reference frequency;

[0053]

[0054] Z f = Z(2πf) (13)

[0055] 5) Let the impedance of the front end of the winding be Z f1 and Z f2 , and the impedances before and after the fault are defined as Z H and Z F respectively. Define the turn - to - turn fault location factor as R FLF , and the formula is as shown in (14):

[0056]

[0057] 6) Considering the non - linear distribution characteristics of the winding structure, the fault location proportionality coefficient α is jointly determined by the location factor R FLF and the resonance frequency offset Δf. Define the combined equation:

[0058]

[0059] where k1 and k2 are weight coefficients determined by calibration experiments, satisfying k1 + k2 = 1 and Δf = f F - f H , where f H and f F are the resonance frequencies before and after the fault respectively.

[0060] 7) Introduce the influence of temperature T on the winding parameters and correct the structure constant k:

[0061] k(T)= k0·(1 + γ·(T - T0)) (16)

[0062] where k0 is the structure constant at the reference temperature T0; γ is the temperature sensitivity coefficient determined by material properties.

[0063] 8) Based on the corrected structure constant k(T), define the non - linear function of the number of fault segments i:

[0064]

[0065] where β is the non - linear distortion coefficient determined by the simulation of the winding discretization model; used to suppress the interference of high - frequency offset.

[0066] 9) Construct the objective function ε(i), combining the impedance residual ε Z and the frequency residual ε f :

[0067] ε(i)= w Z ·|Z(i)- Zmeas | + w f · | f(i) - f meas | (18)

[0068] Where w Z 、w f are weight coefficients, satisfying w Z + w f = 1; Z(i) and f(i) are the theoretical calculated values when the assumed number of fault segments is i, Z meas and f meas are measured values. The simulated annealing algorithm is used for global optimization, and the update rule is:

[0069] i n+1 = i n + Δi · sgn(ε(i n ) - ε(i n-1 )) (19)

[0070] Until ε(i) < ε Z + ε f or the maximum number of iterations is reached. Finally, i n+1 is used as the result of the output number of fault segments.

Claims

1. An inter-turn fault location algorithm based on a transformer network model, characterized in that: The time-domain equation of the winding state is obtained by establishing an expression through the network model of the equivalent winding of the simulation transformer, and further transformed into a frequency-domain equation to obtain the reference frequency, and the reference impedance is determined. The positioning factor defined based on the reference impedance can be used as a reference for fault location, and the inter-turn fault location is further determined by processing through relevant algorithms; The inter-turn fault location based on the transformer network model includes the following steps: Step 1: Determine the calculated positioning factor, including: 1) Derive the input impedance equation through a ladder network. Taking i(t) as the input excitation at node n1, and using the node voltages (v n1 , v n2 ,... v nN+1 ) and the induced currents (i L11 , i L22 ,... i LNN ) as the state vectors, the time-domain space equation expression is constructed as follows: where \(u\) represents the input vector, \(x\) and represent the state vector and its derivative, \([P]\) is the permutation matrix, and the specific compositions of the coefficient matrices \([A]\) and \([B]\) are shown in Eqs. (2) and (3); Among them, as shown in (4), (5), (6), and (7), [a] in the [A] matrix includes capacitance parameters (inter-turn capacitance C s , ground capacitance C g ), [b] includes inductance parameter L ii , [c] is a zero matrix, and [d] is a set matrix; the [B] matrix includes winding resistance (R i ) and conductance (G i ); 2) Transform the time-domain state-space equation (1) into the frequency-domain equation (8), and calculate the frequency-domain phasors of the node voltage and the current through the inductor according to the frequency-domain system matrix; from the first node voltage v1(ω) and the input current I(ω) of the system matrix, the winding impedance Z(ω) can be obtained; jω[A]X(ω)+[B]X(ω)=P(ω) (8) 3) Since the inter-turn fault significantly affects the inductance of the winding rather than the series and parallel capacitances, the inductance matrix [b] in (5) will change; for example, if an inter-turn fault occurs in the i-th section of the winding, the matrix [b] becomes [b'], as shown in (10), and the matrix [A] becomes [A'], as shown in (11); therefore, under the fault condition, the winding impedance will change at the reference frequency; 4) The resonant frequency f reflects the fixed characteristics of its winding characteristics, C in is the input capacitance of the transformer, C HV is the high-voltage side capacitance of the power transformer, Z k1 is the leakage impedance, R k1 is the leakage resistance; taking the resonant frequency f as the reference frequency to obtain the impedance value Z f ; Z f = Z(2πf) (13) 5) Let the impedance of the front end of the winding be \(Z\) and the impedance of the rear end be \(Z\). f1 and \(Z\) f2 . The impedances before and after the fault are defined as \(Z\) H and \(Z\) F respectively. Define the inter-turn fault location factor as \(R\) FLF . The formula is as shown in (14): Step 2: Determine the fault location and verify the accuracy: 1) Considering the non-linear distribution characteristics of the winding structure, the fault location proportionality coefficient α is jointly determined by the positioning factor R FLF and the resonance frequency offset Δf, and a joint equation is defined as follows: wherein, k1 and k2 are weight coefficients determined through calibration experiments, satisfying k1 + k2 = 1 and Δf = f F -f H , where f H and f F are the resonance frequencies before and after the fault, respectively; 2) Introduce the influence of temperature T on the winding parameters and correct the structure constant k: k(T)=k0·(1+γ·(T-T0)) (16) In the formula, k0 is the structure constant at the reference temperature T0; γ is the temperature sensitivity coefficient, which is determined by the material properties; 3) Based on the corrected structure constant k(T), define the non-linear function of the number of fault segments i: where β is the non-linear distortion coefficient, which is determined by the simulation of the discrete winding model; used to suppress the interference of high-frequency offset; 4) Construct the objective function ε(i), combining the impedance residual ε Z and the frequency residual ε f : ε(i) = w Z ·|Z(i) - Z meas | + w f ·|f(i) - f meas | (18) where w Z , w f are weight coefficients, satisfying w Z + w f = 1; Z(i) and f(i) are theoretical calculated values when the assumed number of faulty segments is i, Z meas and f meas are measured values; the simulated annealing algorithm is used for global optimization, and the update rule is: i n+1 = i n + Δi·sgn(ε(i n ) - ε(i n-1 )) (19) until ε(i) < ε Z + ε f or reach the maximum number of iterations; finally, i n+1 as the result of the number of faulty segments output.

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