Reduction Method and System for Multi-Coupled Field Model of Interturn Short Circuit in Converter Transformer

Abstract

The present invention discloses a method and system for reducing the order of a multi-coupled field model of turn-to-turn short circuit in a converter transformer. The method first constructs a full-order turn-to-turn short circuit geometric model of the converter transformer in the turn-to-turn short circuit state, solves the transient loss distribution function of the converter transformer through the magnetic flux density and current density distribution functions of the converter transformer, constructs a multi-coupled field model of turn-to-turn short circuit in the converter transformer, establishes an nth-order single-input single-output nonlinear model, and when solving the transient temperature field and transient magnetic field, expands the nth-order single-input single-output nonlinear model, calculates the low-order model through the standard column orthogonal matrix V0, multiplies the left side of both ends of the low-order model by #imgabs0# to obtain a secondary reduced-order model, and sums the weighted m secondary reduced-order models to obtain a reduced-order model; the present invention takes into account the nonlinear problem of the iron core and the change of the thermal conductivity of the material due to temperature, and reduces the order of this nonlinear model through the multi-point quadratic method, which speeds up the simulation efficiency and reduces the simulation time consumption.

Description

Technical Field

[0001] The present invention relates to a multi-coupled field model reduction method and system, in particular to a multi-coupled field model reduction method and system for inter-turn short circuit of a converter transformer. Background Art

[0002] The converter transformer is a key device in the DC power transmission system, and its safe operation is an important factor to ensure the stability of the power grid and the power supply quality. Through the digital twin technology, the internal operation status of the converter transformer can be understood in real time, its health status can be evaluated, early warnings can be given for potential faults and defects, and targeted operation and maintenance can be carried out to reduce the probability of faults and the power outage losses caused by transformer faults. However, for the digital twin model to reflect the true state of the main body in real time, real-time and rapid calculations of multi-field coupling of electromagnetics, heat, and fluid are required, and the calculation speed of the current full-order simulation model cannot meet the real-time requirements. Summary of the Invention

[0003] Object of the Invention: The object of the present invention is to provide a multi-coupled field model reduction method for inter-turn short circuit of a converter transformer considering the nonlinear problem of the iron core, and the second object of the present invention is to provide a multi-coupled field model reduction system for inter-turn short circuit of a converter transformer with the nonlinear problem of the iron core.

[0004] Technical Solution: The multi-coupled field model reduction method for inter-turn short circuit of the converter transformer described in the present invention includes the following steps:

[0005] (1) Construct a full-order model of the electro-magnetic-thermal coupling of the converter transformer, and on this basis, simulate the inter-turn short circuit fault to construct a geometric model of the inter-turn short circuit of the converter transformer;

[0006] (2) Calculate the magnetic flux density and current density distribution functions of the converter transformer, and solve the transient loss distribution function of the converter transformer according to the magnetic flux density and current density distribution functions to construct a multi-coupled field model of the inter-turn short circuit of the converter transformer;

[0007] (3) Establish an n-order single-input single-output nonlinear model. When solving the transient temperature field and transient magnetic field, expand the n-order single-input single-output nonlinear model and obtain a standard column orthogonal matrix V0 through the Arnoldi algorithm to obtain a low-order model, and left-multiply both ends of the low-order model by V0 T to obtain a secondary reduced-order model, and weighted sum the m secondary reduced-order models obtained by expanding at m points to obtain a reduced-order model;

[0008] (4) Calculate the error between the reduced-order model and the geometric model of the inter-turn short circuit, and verify the reduced-order model; if the error does not exceed the threshold, reconstruct the sample matrix with the reduced-order model to obtain an electro-magnetic-thermal coupling reduced-order model in the state of inter-turn short circuit of the converter transformer.

[0009] Furthermore, the n - order single - input single - output non - linear model in step (3) is as follows:

[0010]

[0011] where \(b,c\in R\) n , \(f(x(t))\in R\) n is a non - linear function of \(x(t)\), \(x(t)\in R\) n is the state variable, \(u(t)\) is the input variable, and \(y(t)\) is the output variable.

[0012] Furthermore, in step (3), when solving the transient magnetic field, \(A(t)\) represents the state variable \(x(t)\), represents \(dx(t) / dt\), \(\nabla\times\nu(A(t))(\nabla\times A(t))\) represents the non - linear system \(f(x(t))\), where is called the Hamiltonian operator, \(J\) s (t) is the input current density, representing the input variable \(u(t)\), \(c\) T \(A(t)\) is the obtained vector magnetic potential, representing the output variable \(y(t)\).

[0013] Furthermore, in step (3), when solving the transient temperature field, \(T(t)\) represents the state variable \(x(t)\), represents \(dx(t) / dt\), \(\nabla\cdot\lambda(T(t))\nabla T(t)\) represents the non - linear system \(f(x(t))\), \(Q(t)\) is the input heat source density, representing the input variable \(u(t)\), \(c\) T \(T(t)\) is the obtained transient temperature, representing the output variable \(y(t)\).

[0014] Furthermore, in step (3), when solving the transient magnetic field, denote \(A(t_0)=A_0\), \(f(A(t_0)) = f(A_0)\). Assume that \(f(A)\) has derivatives of any order. Expand \(f(A_0)\) at the point \(A_0\) to get:

[0015]

[0016] where \(D_0\in R\) n×n is the Jacobian matrix of \(f(A)\) at the point \(A_0\), is the Hesse tensor of \(f(A)\) at the point \(A_0\);

[0017] Assume that \(D_0\) is a non - singular matrix. Construct the Krylov subspace Obtain the standard column - orthogonal matrix \(V_0\in R\) n×q , \(q\ll n\), to get the following low - order model:

[0018]

[0019] wherein is the lower-order form of A(t). Multiply both ends of the said lower-order model on the left by to obtain a quadratic reduced-order model:

[0020]

[0021] Repeat the above steps to obtain m quadratic reduced-order models expanded at points A0 to A m and sum the weighted m quadratic reduced-order models to obtain a reduced-order model:

[0022]

[0023] wherein is the weight function of the i-th quadratic reduced-order model.

[0024] Furthermore, in the m quadratic reduced-order models expanded at points A0 to A m obtained by repeating the above steps, the method for obtaining the next expansion point A1 according to the given initial expansion point A0 is as follows:

[0025] Calculate according to the said quadratic reduced-order model Denote d = ||A(+∞) - A0||2 / ||A0||2. If ||A0||2 = 0, then take d = ||A(+∞)||2. Select a sufficiently small constant δ > 0 such that δ << d;

[0026] Calculate according to the said quadratic reduced-order model

[0027] Select t1 such that If ||A0||2 = 0 appears, then determine t1 through the inequality and the next expansion point

[0028] Calculate A2 to A m in turn according to the above steps.

[0029] Furthermore, the method for calculating the flux density and current density distribution functions of the converter transformer in step (2) is as follows: establish the transient magnetic field control equation of the converter transformer by the vector magnetic potential method, set the magnetization model of the iron core as the effective B-H curve, and use the Newton-Raphson method to solve the said magnetic field control equation to obtain the flux density and current density distribution functions of the converter transformer.

[0030] Further, step (1) includes the following steps: constructing a full-order model of the electro-magnetic-thermal coupling of the converter transformer using a single-phase four-column double-winding structure, with the coil being a continuous disk winding, setting a short-circuit area between turns to simulate the inter-turn short circuit of the converter transformer, and constructing a geometric model of the inter-turn short circuit of the converter transformer.

[0031] The reduced-order system of the multi-coupled field model for the inter-turn short circuit of the converter transformer described in the present invention includes:

[0032] A full-order model construction module, used to construct a full-order model of the electro-magnetic-thermal coupling of the converter transformer, simulate the inter-turn short circuit fault on this basis, and construct a geometric model of the inter-turn short circuit of the converter transformer;

[0033] An inter-turn short circuit multi-coupled field model construction module, used to calculate the magnetic flux density and current density distribution functions of the converter transformer, solve the transient loss distribution function of the converter transformer according to the magnetic flux density and current density distribution functions, and construct an inter-turn short circuit multi-coupled field model of the converter transformer;

[0034] A reduced-order model construction module, used to establish an nth-order single-input single-output non-linear model. When solving the transient temperature field and transient magnetic field, expand the nth-order single-input single-output non-linear model and obtain a standard column orthonormal matrix V0 through the Arnoldi algorithm to obtain a low-order model, and left-multiply both ends of the low-order model by V0 T to obtain a second-order reduced-order model, and sum the m second-order reduced-order models obtained by expanding at m points with weights to obtain a reduced-order model;

[0035] A reduced-order model verification module, used to calculate the error between the reduced-order model and the geometric model of the inter-turn short circuit, and verify the reduced-order model; if the error does not exceed the threshold, reconstruct the sample matrix with the reduced-order model to obtain an electro-magnetic-thermal coupling reduced-order model in the state of the inter-turn short circuit of the converter transformer.

[0036] The electronic device described in the present invention includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the computer program is loaded into the processor, it implements the method for reducing the order of the multi-coupled field model of the inter-turn short circuit of the converter transformer.

[0037] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows: A simulation model of the converter transformer in the fault state of inter-turn short circuit is constructed to solve the electro-magnetic-thermal distribution of the converter transformer in this fault state. Considering the non-linear problem of the iron core and the change of the thermal conductivity of the material due to temperature, which leads to the non-linear problem of the solution system, the finite element method is used to solve the transient electro-magnetic-thermal distribution of the converter transformer in the inter-turn short circuit operation state. Finally, the multi-point quadratic method is used to reduce the order of this non-linear model, and a reduced-order model of the multi-field coupling of the converter transformer is obtained. The simulation efficiency is accelerated and the simulation time is reduced through the reduced-order model, which can be better applied to the construction of the digital twin body. It can predict the working state of the converter transformer in the fault state and provide guidance for the manufacture of the transformer. Description of the Drawings

[0038] Figure 1 It is a flow chart of the model reduction method of the present invention.

[0039] Figure 2 It is a schematic diagram of the iron core and winding structure of a single-phase four-column double-winding converter transformer in an embodiment of the present invention.

[0040] Figure 3 It is a schematic diagram of the construction of the inter-turn short circuit fault point of the converter transformer in an embodiment of the present invention.

[0041] Figure 4 It is a distribution diagram of the magnetic flux density of the inter-turn short circuit model of the converter transformer in an embodiment of the present invention.

[0042] Figure 5 It is a transient distribution diagram of the temperature of the inter-turn short circuit model of the converter transformer in an embodiment of the present invention. Detailed Embodiments

[0043] The technical solution of the present invention will be further described below with reference to the drawings.

[0044] As Figure 1 shown, the method for reducing the order of the multi-coupling field model of the inter-turn short circuit of the converter transformer includes the following steps.

[0045] Step 1: Construct a full-order model of the electro-magnetic-thermal coupling of the inter-turn short circuit of a single-phase converter transformer. First, according to the actual size of the converter transformer, a simulation model is constructed using the structure of a single-phase four-column double-winding, as Figure 2 shown. The input voltage is an ultra-high voltage of 400 kV, the iron core uses a soft iron non-linear material and is stacked by 12 soft iron sheets; the primary winding is a coil with 1024 turns, and the secondary winding is a coil with 214 turns. To simplify the model, the coils of this model simulate continuous disk windings, and the primary and secondary coils are each divided into 16 disk windings, and the inner and outer layer coils are in parallel relationship.

[0046] Step 2: Based on the above converter transformer model, a cuboid short - circuit region is set between the turns of the 8th turn of the right - hand primary winding according to the common forms of inter - turn short - circuits to simulate the inter - turn short - circuit of the converter transformer, as Figure 3 shown. To save computing resources, the turns of the winding are not specifically drawn, but are replaced by an overall circular ring, and the specific number of turns is distinguished when inputting parameters. Finally, after constructing the geometric model of the inter - turn short - circuit of the converter transformer, the calculation of the electro - magnetic - thermal multi - physical - field coupling is carried out, and subsequent model reduction processing is completed based on this three - dimensional full - order model.

[0047] Step 3: Based on the above model, according to Maxwell's equations, the transient magnetic - field control equation of the transformer using the vector magnetic potential method is derived as

[0048]

[0049] where ν is the magnetic reluctivity, σ is the conductivity, A is the vector magnetic potential, and Js is the current density of the transformer winding.

[0050] Run the model using the magnetic - field module of the simulation software. Considering the non - linear problem of the transformer core, there is a non - linear relationship between the magnetic - field intensity H and the magnetic - induction intensity B. The magnetic reluctivity ν = H / B is not only a function of the coordinates x, y, z, but also a function of the vector magnetic potential A. Therefore, the magnetization model of the core is selected as the "effective B - H curve", and the transient solver is used for calculation. The Jacobian matrix is updated after each iteration to realize the update of the core - material characteristics, and then the "Newton - Raphson method" is used to solve the non - linear algebraic equations. As Figure 4 shown, the flux - density and current - density distribution of the transformer are finally obtained.

[0051] Specifically, it includes the following steps:

[0052] Step 3.1: Create the geometric model of the converter transformer, mainly including the core, winding, casing, air domain, and inter - turn short - circuit region, and set the relevant dimensions and parameters; add the materials of each part, the core uses soft iron, and the winding uses copper; add the relevant physical fields, including the magnetic field and solid heat transfer, and add a voltage to the coil as the excitation source in the magnetic field. Considering the non - linear problem of the transformer core, the magnetization model of the core is selected as the "effective B - H curve", and set the relevant insulation conditions and initial values.

[0053] Step 3.2: Take the core loss and winding loss as the heat sources in the heat - transfer equations of the solid parts such as the transformer core and winding, set the solid - heat - transfer module, take the "electromagnetic volume - loss density" as the heat source, and set the relevant boundary conditions and initial values.

[0054] Step 3.3: Mesh the electro-magnetic-thermal multi-physical field coupling simulation model using "free tetrahedral mesh" to obtain good meshes.

[0055] Step 3.4: Use a transient solver for calculation. Set to update the Jacobian matrix after each iteration to achieve the update of material properties, and then use the "Newton-Raphson method" to solve the non-linear algebraic equations. Finally, obtain the transient distributions of the magnetic flux density, current density, and temperature of the transformer.

[0056] Step 4: The heat sources of the transformer mainly come from the core and winding losses. Among them, the core losses of the transformer include hysteresis loss, eddy current loss, and additional loss, and its magnitude is closely related to the magnetic flux density distribution inside the core. The winding loss is mainly the Joule heat caused by the current, so it is closely related to the current density.

[0057] Therefore, first use the current density and magnetic flux density obtained in Step 3 to solve the transient loss distribution of the transformer. Take the core loss and winding loss as the heat sources in the heat transfer equations of the solid parts such as the transformer core and windings. Since the change in temperature will affect the thermal conductivity λ of the material, the thermal conductivity is not only a function of the coordinates x, y, z, but also a function of the temperature T. Use a transient solver for calculation. Set to update the Jacobian matrix after each iteration to achieve the update of the material thermal conductivity, and then use the "Newton-Raphson method" to solve the non-linear algebraic equations. Thus, build a multi-physical field coupling model for the inter-turn short circuit of the converter transformer to realize the electro-magnetic-thermal coupling analysis of the transformer. Run this model using the solid heat transfer module of the simulation software and calculate using a transient solver. As Figure 5 shown, finally obtain the transient temperature distribution of the converter transformer.

[0058] Step 5: Export the calculation results and build and verify a reduced-order model for the multi-coupling field model of the inter-turn short circuit of the converter transformer based on the obtained results using the multi-point quadratic method. Specifically, it includes the following steps:

[0059] Step 5.1: Considering that the non-linear problem of the transformer core belongs to the reduction of order processing of a non-linear system, introduce an nth-order single-input single-output non-linear system:

[0060]

[0061] where b, c ∈ R n , f(x(t)) ∈ R n is a non-linear function of x(t), x(t) ∈ R n is the state variable, u(t) is the input variable, and y(t) is the output variable.

[0062] When solving the problem of transient magnetic field, A(t) represents the state variable x(t), represents dx(t) / dt, and ▽×ν(A(t))(▽×A(t)) represents the nonlinear system f(x(t)), where is called the Hamiltonian operator, and J s (t) is the input current density, representing the input variable u(t), and c T A(t) is the obtained vector magnetic potential, representing the output variable y(t); when solving the problem of transient temperature field, T(t) represents the state variable x(t), represents dx(t) / dt, and ▽·λ(T(t))▽T(t) represents the nonlinear system f(x(t)), Q(t) is the input heat source density, representing the input variable u(t), and c T T(t) is the obtained transient temperature, representing the output variable y(t).

[0063] Taking the process of calculating the transient magnetic field as an example, let A(t0) = A0 and f(A(t0)) = f(A0). Assuming that f(A) has derivatives of any order, expand f(A0) at the point A0 to obtain:

[0064]

[0065] where D0 ∈ R n×n is the Jacobian matrix of f(A) at the point A0, is the Hesse tensor of f(A) at the point A0;

[0066] Step 5.2: Now assume that D0 is a non-singular matrix and construct the Krylov subspace Then obtain the standard column orthogonal matrix V0 ∈ R n×q (q << n) through the Arnoldi algorithm. Further, the following low-order model can be constructed from Equation (3):

[0067]

[0068] where is the low-order form of A(t);

[0069] Step 5.3: Multiply both sides of the above state equation by V0 on the left T to obtain the quadratic reduced-order model:

[0070]

[0071] Given the initial expansion point A0, according to the quadratic reduced-order model (5), the next expansion point A1 can be obtained. The specific selection process is as follows:

[0072] First step, calculate from model (5) Let \(d = \frac{\|A(+\infty)-A_0\|_2^2}{\|A_0\|_2^2}\). If \(\|A_0\|_2 = 0\), then take \(d=\|A(+\infty)\|_2\). Select a sufficiently small constant \(\delta>0\) such that \(\delta\ll d\). Generally, \(\delta = d / 5\) or \(\delta = d / 10\) is acceptable.

[0073] In the second step, calculate from the quadratic order reduction model (5)

[0074] In the third step, select \(t_1\) such that If \(\|A_0\|_2 = 0\) appears, then determine \(t_1\) through the inequality In this way, the next expansion point of the initial expansion point \(A_0\) can be selected as

[0075] Repeat the above first to third steps \(m\) times. Finally, \(m\) quadratic order reduction models with the same order can be obtained. Further confirm the weight functions corresponding to these \(m\) quadratic order reduction models In this way, the final reduced order model of multi-point weighted fitting can be obtained:

[0076]

[0077] Step 5.4: Conduct error analysis on the reduced order model obtained by the multi-point quadratic method, that is, estimate the error between the reduced order model formula (6) and the full order model:

[0078]

[0079] According to formula (7), the calculated error should be less than 0.01%. Reconstruct the sample matrix with the reduced order model, that is, obtain the transient electromagnetic reduced order model under the inter-turn short circuit state of the converter transformer. The model reduction process of the transient temperature field is similar to that of the transient magnetic field model. Finally, the reduced order model of the transient electromagnetic-thermal multi-coupled field of the converter transformer under inter-turn short circuit is obtained.

[0080] The present invention can be summarized into five implementation steps:

[0081] ① Build a geometric model of a single-phase four-column converter transformer according to the actual size and structure, set the relevant sizes and parameters, and add the materials of each part;

[0082] ② On the basis of the above model, set a cuboid short circuit area between the turns of the on-line winding to simulate the inter-turn short circuit of the converter transformer according to the common form of the inter-turn short circuit.

[0083] ③ Apply the finite element method, consider the nonlinear problem of the iron core, and solve the transient distribution of the electric field and magnetic field under the inter-turn short circuit state of the converter transformer;

[0084] ④ Substitute the iron loss and copper loss of the converter transformer as heat sources into the transformer heat transfer equation, and consider the problem that the change in temperature causes the thermal conductivity of the material to change, resulting in the nonlinearity of the solution system. Use the finite element method to solve the transient electromagnetic heat distribution during the operation of the converter transformer under the condition of inter-turn short circuit;

[0085] ⑤ Use the multi-point quadratic method to reduce the order of the nonlinear model of the converter transformer inter-turn short circuit, so that the error between the reduced-order model and the full-order model reaches the allowable range, and finally obtain the reduced-order model of the multi-field coupling of the converter transformer inter-turn short circuit.

[0086] The reduced-order system of the multi-coupling field model of the converter transformer inter-turn short circuit described in the present invention includes:

[0087] The full-order model construction module is used to construct the full-order model of the electro-magnetic-thermal coupling of the converter transformer, simulate the inter-turn short circuit fault on this basis, and construct the inter-turn short circuit geometric model of the converter transformer;

[0088] The inter-turn short circuit multi-coupling field model construction module is used to calculate the magnetic flux density and current density distribution functions of the converter transformer, solve the transient loss distribution function of the converter transformer according to the magnetic flux density and current density distribution functions, and construct the inter-turn short circuit multi-coupling field model of the converter transformer;

[0089] The reduced-order model construction module is used to establish an nth-order single-input single-output nonlinear model. When solving the transient temperature field and transient magnetic field, expand the nth-order single-input single-output nonlinear model and obtain the standard column orthogonal matrix V0 through the Arnoldi algorithm to obtain the low-order model, and left-multiply V0 at both ends of the low-order model T to obtain the quadratic reduced-order model, and weighted sum the m quadratic reduced-order models obtained by expanding at m points to obtain the reduced-order model;

[0090] The reduced-order model verification module is used to calculate the error between the reduced-order model and the inter-turn short circuit geometric model, and verify the reduced-order model; if the error does not exceed the threshold, use the reduced-order model to reconstruct the sample matrix to obtain the electro-magnetic-thermal coupling reduced-order model of the converter transformer under the condition of inter-turn short circuit.

[0091] The electronic device described in the present invention includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the computer program is loaded into the processor, the method for reducing the order of the multi-coupling field model of the converter transformer inter-turn short circuit is implemented.

[0092] The computer-readable storage medium may include RAM, ROM, EEPROM, CD-ROM or other optical disc storage, magnetic disk storage or other magnetic storage devices, flash memory, or any other medium that can be used to store the desired program code in the form of instructions or data structures and that can be accessed by a computer.

[0093] The processor is configured to execute the computer program stored in the memory to implement the respective steps in the methods involved in the above embodiments.

Claims

1. A method for reducing the order of a multi-coupled field model of turn-to-turn short circuit in a converter transformer, characterized in that It includes the following steps: (1) Construct a full-order model of the electro-magnetic-thermal coupling of the converter transformer. Based on it, simulate the inter-turn short-circuit fault and construct a geometric model of the inter-turn short-circuit of the converter transformer; (2) Calculate the magnetic flux density and current density distribution functions of the converter transformer. Solve the transient loss distribution function of the converter transformer according to the magnetic flux density and current density distribution functions, and construct a multi-coupled field model of the inter-turn short-circuit of the converter transformer; (3) Establish an nth-order single-input single-output nonlinear model. When solving the transient temperature field and transient magnetic field, expand the nth-order single-input single-output nonlinear model and obtain the standard column orthogonal matrix V0 through the Arnoldi algorithm to get a low-order model. Multiply the left side of both ends of the low-order model by to obtain a quadratic reduced-order model, and sum the weighted m quadratic reduced-order models obtained by expanding at m points to obtain a reduced-order model; (4) Calculate the error between the reduced-order model and the geometric model of the inter-turn short-circuit, and verify the reduced-order model; if the error does not exceed the threshold, reconstruct the sample matrix with the reduced-order model to obtain an electro-magnetic-thermal coupled reduced-order model in the state of inter-turn short-circuit of the converter transformer; The nth-order single-input single-output non-linear model described in step (3) is: where \(b, c\in R\) n , \(f(x(t))\in R\) n is a non - linear function of \(x(t)\), \(x(t)\in R\) n is the state variable, \(u(t)\) is the input variable, and \(y(t)\) is the output variable; In step (3), when solving the transient magnetic field, A(t) represents the state variable x(t), represents dx(t) / dt, represents the nonlinear system f(x(t)), where is called the Hamiltonian operator, J s (t) is the input current density, representing the input variable u(t), c T A(t) is the vector magnetic potential obtained by solving, representing the output variable y(t); Denote A(t0) = A0, f(A(t0)) = f(A0), assuming that f(A) has derivatives of any order, expand f(A0) at the point A0, and we get: where \(D_0\in\mathbb{R}\) n×n is the Jacobian matrix of \(f(A)\) at the point \(A_0\), is the Hesse tensor of \(f(A)\) at the point \(A_0\); Assume that D0 is a non-singular matrix, and construct a Krylov subspace Obtain a standard column orthonormal matrix V0 ∈ R through the Arnoldi algorithm n×q , q << n, to obtain the following low-order model: wherein is the low-order form of A(t), and multiply both ends of the low-order model on the left by to obtain a quadratic reduced-order model: Repeat the above steps to obtain m quadratic reduced-order models expanded at points A0 to A m and perform a weighted sum of the m quadratic reduced-order models to obtain a reduced-order model: Among them is the weight function of the i-th second-order reduced model.

2. The method for reducing the order of the multi-coupled field model of the turn-to-turn short circuit of a converter transformer according to claim 1, wherein In step (3), when solving the transient temperature field, T(t) represents the state variable x(t), represents dx(t) / dt, represents the nonlinear system f(x(t)), Q(t) is the input heat source density, represents the input variable u(t), c T T(t) is the transient temperature obtained by solving, represents the output variable y(t).

3. The method for reducing the order of the multi-coupled field model of the turn-to-turn short circuit of a converter transformer according to claim 1, wherein, Repeating the above steps to obtain m quadratic reduced-order models expanded at points A0 to A m Among them, the method for obtaining the next expansion point A1 based on the given initial expansion point A0 in the m quadratic reduced-order models expanded at points is as follows: Calculate according to the secondary order reduction model Let \(d = \frac{\left\lVert A(+\infty)-A_0\right\rVert_2}{\left\lVert A_0\right\rVert_2}\). If \(\left\lVert A_0\right\rVert_2 = 0\), then take \(d=\left\lVert A(+\infty)\right\rVert_2\). Select a sufficiently small constant \(\delta>0\) such that \(\delta\ll d\). Calculate according to the secondary order reduction model Select t1 such that If ||A0||2 = 0 occurs, then through the inequality to determine t1, the next expansion point Calculate A2 to A in sequence according to the above steps m .

4. The method for reducing the order of the multi-coupled field model of the turn-to-turn short circuit of a converter transformer according to claim 1, wherein The method for calculating the magnetic flux density and current density distribution functions of the converter transformer described in step (2) is: Establish a transient magnetic field control equation of the converter transformer using the vector magnetic potential method, set the magnetization model of the iron core as the effective B-H curve, and use the Newton-Raphson method to solve the magnetic field control equation to obtain the magnetic flux density and current density distribution functions of the converter transformer.

5. The method for reducing the order of the multi-coupled field model of the turn-to-turn short circuit of a commutation transformer according to claim 1, wherein Step (1) includes the following steps: Adopt the structure of single-phase four-column double-winding to construct a full-order model of the electro-magnetic-thermal coupling of the converter transformer. The coil is a continuous disk-type winding, and a short-circuit area is set between the turns to simulate the inter-turn short-circuit of the converter transformer, and construct a geometric model of the inter-turn short-circuit of the converter transformer.

6. A reduced-order system of a multi-coupled field model for turn-to-turn short circuit of a converter transformer, characterized in that, It includes: A full-order model construction module for constructing a full-order model of the electro-magnetic-thermal coupling of the converter transformer, simulating the inter-turn short-circuit fault on this basis, and constructing a geometric model of the inter-turn short-circuit of the converter transformer; An inter-turn short-circuit multi-coupled field model construction module for calculating the magnetic flux density and current density distribution functions of the converter transformer, solving the transient loss distribution function of the converter transformer according to the magnetic flux density and current density distribution functions, and constructing a multi-coupled field model of the inter-turn short-circuit of the converter transformer; The reduced-order model construction module is used to establish an nth-order single-input single-output nonlinear model. When solving the transient temperature field and transient magnetic field, the nth-order single-input single-output nonlinear model is expanded and the standard column orthogonal matrix V0 is obtained through the Arnoldi algorithm to obtain a reduced-order model. Multiply the left side of the reduced-order model by to obtain a quadratic reduced-order model, and the reduced-order model is obtained by weighted summation of the m quadratic reduced-order models expanded at m points; A reduced-order model verification module for calculating the error between the reduced-order model and the geometric model of the inter-turn short-circuit, and verifying the reduced-order model; if the error does not exceed the threshold, reconstruct the sample matrix with the reduced-order model to obtain an electro-magnetic-thermal coupled reduced-order model in the state of inter-turn short-circuit of the converter transformer; In the reduced-order model construction module, the nth-order single-input single-output non-linear model is: where \(b, c\in R\) n , \(f(x(t))\in R\) n is a non - linear function of \(x(t)\), \(x(t)\in R\) n is the state variable, \(u(t)\) is the input variable, and \(y(t)\) is the output variable; When solving the transient magnetic field, A(t) represents the state variable x(t), represents dx(t) / dt, represents the nonlinear system f(x(t)), where is called the Hamiltonian operator, J s (t) is the input current density, representing the input variable u(t), c T A(t) is the vector magnetic potential obtained by solving, representing the output variable y(t); Denote A(t0) = A0, f(A(t0)) = f(A0), assuming that f(A) has derivatives of any order, expand f(A0) at the point A0, and get: where \(D_0\in\mathbb{R}\) n×n is the Jacobian matrix of \(f(A)\) at point \(A_0\), is the Hesse tensor of \(f(A)\) at point \(A_0\); Assume that D0 is a non-singular matrix, and construct the Krylov subspace Obtain the standard column orthonormal matrix V0 ∈ R through the Arnoldi algorithm n×q , q << n, to obtain the following low-order model: wherein is the low-order form of A(t), and multiply both ends of the low-order model by to obtain a second-order reduced model: Repeat the above steps to obtain m quadratic reduced-order models expanded at points A0 to A m and obtain a reduced-order model by weighted summation of the m quadratic reduced-order models: wherein is the weight function of the i-th second-order reduced model.

7. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it realizes the method for reducing the order of the multi-coupled field model of the inter-turn short-circuit of the converter transformer according to any one of claims 1-5.

Images