Power electronic interface power frequency transformer waveform reshaping active damping method and system

Abstract

This invention discloses a method and system for active vibration reduction of power electronic interface power frequency transformers by waveform reshaping. First, the correlation between the inverter output voltage and the vibration of the power electronic interface power frequency transformer is analyzed, and the relationship between the inverter output voltage and the vibration acceleration of the power electronic interface power frequency transformer is derived. Then, the third and fifth harmonics injected into the inverter output voltage are considered to reshape its waveform, and the effective value of the vibration acceleration of the power electronic interface power frequency transformer after waveform reshaping is obtained. Then, with minimizing the effective value of the vibration acceleration as the objective and the total voltage distortion rate as the constraint, a particle swarm optimization algorithm is used to solve for the effective values ​​and initial phases of the third and fifth harmonics, thus achieving active vibration reduction of the power electronic interface power frequency transformer. The active vibration reduction method for power electronic interface power frequency transformers of this invention effectively reduces the vibration acceleration of the power electronic interface power frequency transformer, achieving low vibration and stable operation.

Description

Technical Field

[0001] This invention relates to the field of active vibration reduction design technology for transformers, specifically to a method and system for active vibration reduction of waveform reshaping in power frequency transformers with power electronic interfaces. Background Technology

[0002] As a crucial piece of equipment in new power systems, the safe and stable operation of power electronic interface frequency transformers plays a decisive role in the safety and reliability of these systems. The vibration and noise generated during operation of these transformers negatively impact the environment and their lifespan. Reducing the vibration acceleration of power electronic interface frequency transformers promotes low-vibration operation, thereby reducing noise.

[0003] Generally, transformer vibration is related not only to the transformer's structure and parameters but also to its input excitation. Traditional power transformers typically use sinusoidal alternating current generated by a generator for input excitation, limiting the controllability of the voltage waveform. Vibration reduction methods primarily focus on the transformer's design, such as reducing the core flux density and using silicon steel sheets with low magnetostriction. These methods are easily implemented and therefore widely used. However, the input excitation of power electronic interface power frequency transformers is the inverter's output voltage, whose waveform can be controlled by algorithms. Therefore, vibration reduction design for power electronic interface power frequency transformers can address both the transformer's structure and the input excitation to achieve optimal vibration reduction. Summary of the Invention

[0004] In view of this, the purpose of this invention is to carry out active vibration reduction design for power electronic interface power frequency transformers, so as to realize the safe, low vibration and stable operation of power electronic interface power frequency transformers, and to propose a waveform reshaping active vibration reduction method and system for power electronic interface power frequency transformers.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] On the one hand, the present invention provides a method for active vibration reduction of waveform reshaping in a power frequency transformer with a power electronic interface, comprising the following steps:

[0007] Establish a vibration model for a power frequency transformer with a power electronic interface: Using Fourier analysis, the inverter output voltage is decomposed into fundamental and harmonic components. Based on the magnetostrictive effect of the core of the power frequency transformer with a power electronic interface and the magnetic field coupling relationship, a vibration model for the power frequency transformer with a power electronic interface is established, and the expression for the core vibration acceleration caused by magnetostriction is determined.

[0008] Reshaping the voltage waveform: After injecting the third and fifth harmonics into the inverter output voltage to reshape its waveform, a reference value for the inverter output voltage is obtained.

[0009] The parameters are solved using the particle swarm optimization algorithm: Based on the reference value of the inverter output voltage, the expression for the effective value of the core vibration acceleration after voltage waveform reshaping is obtained; Based on the power frequency transformer vibration model of the power electronic interface, with the minimum effective value of the core vibration acceleration as the objective and the total voltage distortion rate of the inverter output voltage as the constraint, the effective value and initial phase of the injected third and fifth harmonics are solved using the particle swarm optimization algorithm, and the optimal value of the effective value of the core vibration acceleration is output.

[0010] Preferably, in the step of establishing the vibration model of the power frequency transformer for the power electronic interface, the Fourier analysis method is used, assuming the expression for the output voltage of phase A of the inverter is as follows:

[0011]

[0012] In the formula: t is time, and N is the harmonic order. This represents the effective value of the fundamental component of the inverter output voltage. The fundamental angular frequency of the inverter output voltage; This represents the initial phase of the fundamental component of the inverter output voltage; This represents the effective value of the kth harmonic component of the inverter output voltage. This represents the initial phase of the k-th harmonic component of the inverter output voltage;

[0013] According to the law of electromagnetic induction, the magnetic flux density of the A-phase core of a power electronic interface frequency transformer is expressed as:

[0014]

[0015] In the formula, N1 represents the number of turns in the primary winding of the power electronic interface power frequency transformer, and S represents the cross-sectional area of ​​the transformer core. When the core is in an alternating magnetic field, the relationship between the magnetic field strength and magnetic flux density of the core is as follows:

[0016]

[0017] In the formula: The magnetic susceptibility of the medium; The magnetic susceptibility of the material;

[0018] Assuming the parameters of the power electronic interface power frequency transformer are symmetrical, when the power electronic interface power frequency transformer is in an alternating magnetic field, the ferromagnetic material used in the core will produce a magnetostrictive effect, which will cause the length of the material to change periodically, thus causing the core to vibrate; the magnetostrictive effect of the core is described by the magnetostriction coefficient.

[0019]

[0020] In the formula: Indicates the magnetostriction coefficient. This represents the original axial length of the iron core. Indicates the axial expansion and contraction of the iron core;

[0021] Based on the working characteristics of silicon steel sheets with iron cores and the secondary domain rotation model, the magnetostriction coefficient is expressed as:

[0022]

[0023] In the formula: and Given the magnetostriction and magnetization in the magnetic saturation state, combining equations (3) and (5) yields:

[0024]

[0025] In the formula: Representing the magnetic field coupling constant of the ferromagnetic material, substituting (1) and (2) yields:

[0026]

[0027] From the above formula, the acceleration of the iron core vibration caused by magnetostriction is:

[0028]

[0029] In the formula, It is the voltage-vibration constant. and The expression is:

[0030]

[0031] In the formula, and Indicates frequency coupling components, and These are the effective values ​​of the nth and mth harmonic components of the inverter output voltage; and The initial phases of the nth and mth harmonic components of the inverter output voltage are given.

[0032] Preferably, in the voltage waveform reshaping step, the initial phase of the fundamental voltage is set to 0 according to equations (8) and (9). After the third and fifth harmonic voltages are injected into the inverter output voltage to reshape its waveform, the reference value of the inverter A-phase output voltage is:

[0033]

[0034] In the formula, and These are the effective values ​​of the 3rd and 5th harmonic components of the inverter output voltage; and This represents the initial phase of the 3rd and 5th harmonic components of the inverter output voltage.

[0035] Preferably, the effective value of the core vibration acceleration is expressed as:

[0036]

[0037] in

[0038]

[0039] In the formula, A2, A4, A6, A8, A 10 These represent the 2nd, 4th, 6th, 8th, and 10th order components of the vibration acceleration, respectively.

[0040] Assuming the effective value of the fundamental component of the inverter output voltage remains constant, the effective value of the core vibration acceleration is related to the effective values ​​and initial phase of the third and fifth harmonic voltages, according to the above formula.

[0041] A vibration model based on a power frequency transformer with a power electronic interface is used, with the effective value of the core vibration acceleration as the basis. With the goal of minimizing the total voltage distortion (THD) of the inverter output voltage as a constraint, the effective values ​​and initial phases of the injected third and fifth harmonic voltages are designed using a particle swarm optimization algorithm.

[0042] The constraints are:

[0043]

[0044] The optimization model is solved using the particle swarm optimization algorithm.

[0045] Suppose there exists a particle population P in a D-dimensional feasible solution space, containing I randomly distributed particles, each with its own initial velocity and initial position. The particles in the entire population iterate and optimize T times. Then:

[0046] (14)

[0047] (15)

[0048] (16)

[0049] (17)

[0050] (18)

[0051] In the formula: X id t Let X be the position vector of the i-th particle in the d-th dimension during the t-th iteration. i1 X i2 X i3 , ..., X id V represents the position of the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; id t+1 V represents the velocity of the i-th particle in the d-th dimension during the (t+1)-th iteration. id t Let V be the velocity vector of the i-th particle in the d-th dimension during the t-th iteration. i1 V i2 V i3 , ..., V id Let E be the velocity of the i-th particle in the 1st, 2nd, 3rd, ..., dth dimensions during the tth iteration; c1 and c2 are the learning factors for the individual and global extrema, respectively; r1 and r2 are the influence perturbation factors for the individual and global extrema, respectively; i t d E is the individual extreme value vector of dimension d found by the i-th particle in the t-th iteration. i1 E i2 E i3 , ..., E id G represents the individual extreme values ​​of the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; i t d G is the optimal solution vector of dimension d found by the entire population in the t-th iteration. i1 G i2 G i3 , ..., G idLet be the optimal solution for the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions;

[0052] The particle position update method is described as follows:

[0053] (19)

[0054] In the formula: X id t+1 Let X be the position of the i-th particle in the d-th dimension during the (t+1)-th iteration; i t d V represents the position of the i-th particle in the d-th dimension during the t-th iteration; id t+1 Let be the velocity of the i-th particle in the d-th dimension during the (t+1)-th iteration.

[0055] Preferably, in the step of solving for parameters using the particle swarm optimization algorithm, the algorithm flow is as follows:

[0056] ① Set the population size P to I=20, learning factors c1=0.5 and c2=0.5, maximum number of iterations T=100, set the fitness function, and set the position to X=[ , , , If the particle swarm dimension D=4, then the particle swarm dimension is 4.

[0057] ② Randomly initialize the positions and velocities of I particles in population P, calculate the fitness values ​​of all particles, and determine the individual extreme value E of each particle and the global extreme value G of population P;

[0058] ③ Use equations (18) and (19) to obtain the updated values ​​of particle velocity and position, determine whether the constraint conditions are met, and if not, set the value to be near the constraint conditions. Calculate the fitness values ​​of all particles again to determine the individual extreme values ​​of the new generation of particles and the global extreme value of the new generation of population P.

[0059] ④ Compare step ③ with step ②, and retain the value with the higher fitness; complete the update of individual extreme values ​​and global extreme values;

[0060] ⑤ Determine whether the particle swarm optimization algorithm meets the termination condition at this time. If the number of iterations exceeds T or the optimal solution of the fitness function is found, the algorithm process ends and the optimal value is output; otherwise, continue to step ③ in a loop.

[0061] On the other hand, the present invention provides a power electronic interface power frequency transformer waveform reshaping active vibration reduction system, comprising:

[0062] The module for establishing a vibration model of a power electronic interface power frequency transformer is used to decompose the inverter output voltage into fundamental and harmonic components using Fourier analysis. Based on the magnetostrictive effect and magnetic field coupling relationship of the core of the power electronic interface power frequency transformer, a vibration model of the power electronic interface power frequency transformer is established, and the expression for the core vibration acceleration caused by magnetostriction of the power electronic interface power frequency transformer is determined.

[0063] The voltage waveform reshaping module is used to inject the third and fifth harmonics into the inverter output voltage to reshape its waveform and obtain a reference value for the inverter output voltage.

[0064] The particle swarm optimization (PSO) module is used to obtain an expression for the effective value of the core vibration acceleration after voltage waveform reshaping, based on the reference value of the inverter output voltage. Using a power frequency transformer vibration model with a power electronic interface, the module aims to minimize the effective value of the core vibration acceleration, with the total voltage distortion rate of the inverter output voltage as a constraint. The PSO algorithm is then used to solve for the effective values ​​and initial phases of the injected third and fifth harmonics, outputting the optimal value of the effective core vibration acceleration.

[0065] Preferably, in the power electronic interface power frequency transformer vibration model establishment module, the Fourier analysis method is used, assuming the expression for the inverter A-phase output voltage is as follows:

[0066]

[0067] In the formula: t is time, and N is the harmonic order. This represents the effective value of the fundamental component of the inverter output voltage. The fundamental angular frequency of the inverter output voltage; This represents the initial phase of the fundamental component of the inverter output voltage; This represents the effective value of the kth harmonic component of the inverter output voltage. This represents the initial phase of the k-th harmonic component of the inverter output voltage;

[0068] According to the law of electromagnetic induction, the magnetic flux density of the A-phase core of a power electronic interface frequency transformer is expressed as:

[0069]

[0070] In the formula, N1 represents the number of turns in the primary winding of the power electronic interface power frequency transformer, and S represents the cross-sectional area of ​​the transformer core. When the core is in an alternating magnetic field, the relationship between the magnetic field strength and magnetic flux density of the core is as follows:

[0071]

[0072] In the formula: The magnetic susceptibility of the medium; The magnetic susceptibility of the material;

[0073] Assuming the parameters of the power electronic interface power frequency transformer are symmetrical, when the power electronic interface power frequency transformer is in an alternating magnetic field, the ferromagnetic material used in the core will produce a magnetostrictive effect, which will cause the length of the material to change periodically, thus causing the core to vibrate; the magnetostrictive effect of the core is described by the magnetostriction coefficient.

[0074]

[0075] In the formula: Indicates the magnetostriction coefficient. This represents the original axial length of the iron core. Indicates the axial expansion and contraction of the iron core;

[0076] Based on the working characteristics of silicon steel sheets with iron cores and the secondary domain rotation model, the magnetostriction coefficient is expressed as:

[0077]

[0078] In the formula: and Given the magnetostriction and magnetization in the magnetic saturation state, combining equations (3) and (5) yields:

[0079]

[0080] In the formula: Representing the magnetic field coupling constant of the ferromagnetic material, substituting (1) and (2) yields:

[0081]

[0082] From the above formula, the acceleration of the iron core vibration caused by magnetostriction is:

[0083]

[0084] In the formula, It is the voltage-vibration constant. and The expression is:

[0085]

[0086] In the formula, and Indicates frequency coupling components, and These are the effective values ​​of the nth and mth harmonic components of the inverter output voltage; and The initial phases of the nth and mth harmonic components of the inverter output voltage are given.

[0087] Preferably, in the voltage waveform reshaping module, the initial phase of the fundamental voltage is set to 0 according to equations (8) and (9). After the third and fifth harmonic voltages are injected into the inverter output voltage to reshape its waveform, the reference value of the inverter A-phase output voltage is:

[0088]

[0089] In the formula, and These are the effective values ​​of the 3rd and 5th harmonic components of the inverter output voltage; and This represents the initial phase of the 3rd and 5th harmonic components of the inverter output voltage.

[0090] Preferably, the effective value of the core vibration acceleration is expressed as:

[0091]

[0092] in

[0093]

[0094] In the formula, A2, A4, A6, A8, A 10 These represent the 2nd, 4th, 6th, 8th, and 10th order components of the vibration acceleration, respectively.

[0095] Assuming the effective value of the fundamental component of the inverter output voltage remains constant, the effective value of the core vibration acceleration is related to the effective values ​​and initial phase of the third and fifth harmonic voltages, according to the above formula.

[0096] A vibration model based on a power frequency transformer with a power electronic interface is used, with the effective value of the core vibration acceleration as the basis. With the goal of minimizing the total voltage distortion (THD) of the inverter output voltage as a constraint, the effective values ​​and initial phases of the injected third and fifth harmonic voltages are designed using a particle swarm optimization algorithm.

[0097] The constraints are:

[0098]

[0099] The optimization model is solved using the particle swarm optimization algorithm.

[0100] Suppose there exists a particle population P in a D-dimensional feasible solution space, containing I randomly distributed particles, each with its own initial velocity and initial position. The particles in the entire population iterate and optimize T times. Then:

[0101] (14)

[0102] (15)

[0103] (16)

[0104] (17)

[0105] (18)

[0106] In the formula: X id t Let X be the position vector of the i-th particle in the d-th dimension during the t-th iteration. i1 X i2 X i3 , ..., X id V represents the position of the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; id t+1 V represents the velocity of the i-th particle in the d-th dimension during the (t+1)-th iteration. id t Let V be the velocity vector of the i-th particle in the d-th dimension during the t-th iteration. i1 V i2 V i3 , ..., V id Let E be the velocity of the i-th particle in the 1st, 2nd, 3rd, ..., dth dimensions during the tth iteration; c1 and c2 are the learning factors for the individual and global extrema, respectively; r1 and r2 are the influence perturbation factors for the individual and global extrema, respectively; i t d E is the individual extreme value vector of dimension d found by the i-th particle in the t-th iteration. i1 E i2 E i3 , ..., E id G represents the individual extreme values ​​of the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; i t d G is the optimal solution vector of dimension d found by the entire population in the t-th iteration.i1 G i2 G i3 , ..., G id Let be the optimal solution for the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions;

[0107] The particle position update method is described as follows:

[0108] (19)

[0109] In the formula: X id t+1 Let X be the position of the i-th particle in the d-th dimension during the (t+1)-th iteration; i t d V represents the position of the i-th particle in the d-th dimension during the t-th iteration; id t+1 Let be the velocity of the i-th particle in the d-th dimension during the (t+1)-th iteration.

[0110] Preferably, in the particle swarm optimization algorithm parameter solving module, the algorithm flow of the particle swarm optimization algorithm is as follows:

[0111] ① Set the population size P to I=20, learning factors c1=0.5 and c2=0.5, maximum number of iterations T=100, set the fitness function, and set the position to X=[ , , , If the particle swarm dimension D=4, then the particle swarm dimension is 4.

[0112] ② Randomly initialize the positions and velocities of I particles in population P, calculate the fitness values ​​of all particles, and determine the individual extreme value E of each particle and the global extreme value G of population P;

[0113] ③ Use equations (18) and (19) to obtain the updated values ​​of particle velocity and position, determine whether the constraint conditions are met, and if not, set the value to be near the constraint conditions. Calculate the fitness values ​​of all particles again to determine the individual extreme values ​​of the new generation of particles and the global extreme value of the new generation of population P.

[0114] ④ Compare step ③ with step ②, and retain the value with the higher fitness; complete the update of individual extreme values ​​and global extreme values;

[0115] ⑤ Determine whether the particle swarm optimization algorithm meets the termination condition at this time. If the number of iterations exceeds T or the optimal solution of the fitness function is found, the algorithm process ends and the optimal value is output; otherwise, continue to step ③ in a loop.

[0116] Compared with the prior art, the beneficial effects of the present invention include at least the following:

[0117] 1) This invention considers the influence of inverter output voltage on the vibration acceleration of the power electronic interface power frequency transformer, establishes a vibration model of the power electronic interface power frequency transformer, and based on this model, injects appropriate third and fifth harmonics into the inverter output voltage to reshape the voltage waveform, obtains the expression for the effective value of vibration acceleration after voltage waveform reshaping, and then takes the minimum effective value of vibration acceleration as the objective and the total voltage distortion (THD) as the constraint condition, uses the particle swarm optimization algorithm to solve for the effective value and initial phase of the third and fifth harmonics, effectively improving the low vibration characteristics of the power electronic interface power frequency transformer.

[0118] 2) This invention starts with the input excitation of the power electronic interface power frequency transformer to carry out vibration reduction design, so as to realize low vibration and stable operation of the power electronic interface power frequency transformer.

[0119] 3) This invention can be solved using the particle swarm optimization algorithm, satisfying the requirements for output voltage THD and low vibration. Attached Figure Description

[0120] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0121] Figure 1 This is a flowchart of the active vibration reduction method for waveform reshaping of power frequency transformers using power electronic interfaces according to the present invention;

[0122] Figure 2 This is a schematic diagram of the main structure of the inverter-power electronics interface power frequency transformer of this invention;

[0123] Figure 3 This is a flowchart of the active vibration reduction system for waveform reshaping of a power frequency transformer using a power electronic interface, as described in this invention.

[0124] Figure 4 This is a block diagram of the electronic device structure of the present invention. Detailed Implementation

[0125] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the technical solutions of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the described embodiments are merely some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0126] Example 1

[0127] like Figure 1 As shown, this invention provides a method for active vibration reduction of waveform reshaping in a power frequency transformer with a power electronic interface, comprising the following steps:

[0128] Establish a vibration model for a power frequency transformer with a power electronic interface: Using Fourier analysis, the inverter output voltage is decomposed into fundamental and harmonic components. Based on the magnetostrictive effect of the core of the power frequency transformer with a power electronic interface and the magnetic field coupling relationship, a vibration model for the power frequency transformer with a power electronic interface is established, and the expression for the core vibration acceleration caused by magnetostriction is determined.

[0129] Reshaping the voltage waveform: After injecting the third and fifth harmonics into the inverter output voltage to reshape its waveform, a reference value for the inverter output voltage is obtained.

[0130] The parameters are solved using the particle swarm optimization algorithm: Based on the reference value of the inverter output voltage, the expression for the effective value of the core vibration acceleration after voltage waveform reshaping is obtained; Based on the power frequency transformer vibration model of the power electronic interface, with the minimum effective value of the core vibration acceleration as the objective and the total voltage distortion rate of the inverter output voltage as the constraint, the effective value and initial phase of the injected third and fifth harmonics are solved using the particle swarm optimization algorithm, and the optimal value of the effective value of the core vibration acceleration is output.

[0131] The most crucial aspects of this invention are the establishment of a vibration model for the power electronic interface frequency transformer and the reshaping of the voltage waveform. Using Fourier analysis and the relationship between the vibration acceleration and magnetic flux density of the power electronic interface frequency transformer, combined with the law of electromagnetic induction, a formula is derived to establish the relationship between the vibration acceleration of the power electronic interface frequency transformer and the inverter output voltage, thus establishing the correlation between transformer dimensions and electromagnetic load. Third and fifth harmonics are injected into the inverter output voltage to obtain reference values ​​for the inverter output voltage.

[0132] Inverter-Power Electronic Interface Power Frequency Transformer, etc. Figure 2 As shown, the inverter output voltage is the input excitation of the power frequency transformer at the power electronic interface. Using Fourier analysis, we assume the expression for the inverter phase A output voltage is:

[0133]

[0134] In the formula: t is time, and N is the harmonic order. This is the effective value (V) of the fundamental component of the inverter output voltage; The fundamental angular frequency (rad) of the inverter output voltage; This represents the initial phase of the fundamental component of the inverter output voltage; The effective value (V) of the kth harmonic component of the inverter output voltage; This represents the initial phase of the k-th harmonic component of the inverter output voltage.

[0135] According to the law of electromagnetic induction, the magnetic flux density of the A-phase core of a power electronic interface frequency transformer can be expressed as:

[0136]

[0137] In the formula, N1 represents the number of turns in the primary winding of the power electronic interface power frequency transformer, and S represents the cross-sectional area of ​​the transformer core. When the core is in an alternating magnetic field, the relationship between the magnetic field strength and magnetic flux density of the core is as follows:

[0138]

[0139] In the formula: The magnetic susceptibility of the medium; denoted as the magnetic susceptibility of the material.

[0140] Assuming the parameters of the power electronic interface frequency transformer are symmetrical, when the transformer is placed in an alternating magnetic field, the ferromagnetic material used in the core will exhibit a magnetostrictive effect, causing periodic changes in the material's length, which in turn leads to core vibration. The magnetostrictive effect of the core can be described by the magnetostriction coefficient.

[0141]

[0142] In the formula: Indicates the magnetostriction coefficient. This represents the original axial length of the iron core. This indicates the axial expansion and contraction of the iron core.

[0143] Based on the working characteristics of silicon steel sheets with iron cores and the secondary domain rotation model, the magnetostriction coefficient can be expressed as:

[0144]

[0145] In the formula: and Let be the magnetostriction and magnetization under magnetic saturation. Combining (3) and (5), we get:

[0146]

[0147] In the formula: Let represent the magnetic field coupling constant of the ferromagnetic material. Substituting (1) and (2) into the equation, we get:

[0148]

[0149] From the above formula, the acceleration of the iron core vibration caused by magnetostriction can be obtained as:

[0150]

[0151] In the formula, It is the voltage-vibration constant. and The expression is:

[0152]

[0153] In the formula, and Indicates frequency coupling components, and These are the effective values ​​of the nth and mth harmonic components of the inverter output voltage; and The initial phases of the nth and mth harmonic components of the inverter output voltage are given.

[0154] Based on equations (8) and (9), the initial phase of the fundamental voltage is set to 0. After the third and fifth harmonic voltages are injected into the inverter output voltage to reshape its waveform, the reference value of the inverter phase A output voltage is:

[0155]

[0156] In the formula, and These are the effective values ​​of the 3rd and 5th harmonic components of the inverter output voltage; and This represents the initial phase of the 3rd and 5th harmonic components of the inverter output voltage.

[0157] The effective value of the core vibration acceleration can be expressed as:

[0158]

[0159] in

[0160]

[0161] In the formula, A2, A4, A6, A8, A 10 These represent the 2nd, 4th, 6th, 8th, and 10th order components of the vibration acceleration, respectively.

[0162] Assuming the effective value of the fundamental component of the inverter output voltage remains constant, the effective value of the core vibration acceleration can be obtained from the above formula as being related to the effective values ​​and initial phase of the third and fifth harmonic voltages.

[0163] Finally, based on the vibration model of the power frequency transformer with the power electronic interface, the effective value of vibration acceleration is used. With the goal of minimizing the THD of the inverter output voltage as a constraint, the effective values ​​and initial phases of the injected third and fifth harmonic voltages are designed using a particle swarm optimization algorithm.

[0164] The constraints are:

[0165]

[0166] The above is the vibration model of a power frequency transformer with a power electronic interface. Finally, the particle swarm optimization algorithm is used to solve the optimization model.

[0167] Suppose there exists a particle population P in a D-dimensional feasible solution space, containing I randomly distributed particles, each with its own initial velocity and initial position. The particles in the entire population iterate and optimize T times. Then:

[0168] (14)

[0169] (15)

[0170] (16)

[0171] (17)

[0172] (18)

[0173] In the formula: X id t Let X be the position vector of the i-th particle in the d-th dimension during the t-th iteration. i1 X i2 X i3 , ..., X id V represents the position of the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; id t+1 V represents the velocity of the i-th particle in the d-th dimension during the (t+1)-th iteration. id t Let V be the velocity vector of the i-th particle in the d-th dimension during the t-th iteration. i1 V i2 V i3 , ..., V idLet E be the velocity of the i-th particle in the 1st, 2nd, 3rd, ..., dth dimensions during the tth iteration; c1 and c2 are the learning factors for the individual and global extrema, respectively; r1 and r2 are the influence perturbation factors for the individual and global extrema, respectively; i t d E is the individual extreme value vector of dimension d found by the i-th particle in the t-th iteration. i1 E i2 E i3 , ..., E id G represents the individual extreme values ​​of the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; i t d G is the optimal solution vector of dimension d found by the entire population in the t-th iteration. i1 G i2 G i3 , ..., G id Let be the optimal solution for the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions;

[0174] The particle position update method is described as follows:

[0175] (19)

[0176] In the formula: X id t+1 Let X be the position of the i-th particle in the d-th dimension during the (t+1)-th iteration; i t d V represents the position of the i-th particle in the d-th dimension during the t-th iteration; id t+1 Let be the velocity of the i-th particle in the d-th dimension during the (t+1)-th iteration.

[0177] The algorithm flow of particle swarm optimization is as follows:

[0178] ① Set the population size P to I=20, learning factors c1=0.5 and c2=0.5, maximum number of iterations T=100, set the fitness function, and set the position to X=[ , , , If the particle swarm dimension D=4, then the particle swarm dimension is 4.

[0179] ② Randomly initialize the positions and velocities of I particles in population P, calculate the fitness values ​​of all particles, and determine the individual extreme value E of each particle and the global extreme value G of population P;

[0180] ③ Use equations (18) and (19) to obtain the updated values ​​of particle velocity and position, determine whether the constraint conditions are met, and if not, set the value to be near the constraint conditions. Calculate the fitness values ​​of all particles again to determine the individual extreme values ​​of the new generation of particles and the global extreme value of the new generation of population P.

[0181] ④ Compare step ③ with step ②, and retain the value with the higher fitness; complete the update of individual extreme values ​​and global extreme values;

[0182] ⑤ Determine whether the particle swarm optimization algorithm meets the termination condition at this time. If the number of iterations exceeds T or the optimal solution of the fitness function is found, the algorithm process ends and the optimal value is output; otherwise, continue to step ③ in a loop.

[0183] The above process is the solution process of this invention.

[0184] This invention discloses an active vibration reduction method for power electronic interface power frequency transformers, comprising establishing a mathematical relationship between the inverter output voltage and the vibration acceleration of the power electronic interface power frequency transformer, injecting third and fifth harmonics into the inverter output voltage to reshape its waveform, and using a particle swarm optimization algorithm to solve for the effective values ​​and initial phases of the third and fifth harmonic voltages when the vibration acceleration is minimized. First, the correlation between the inverter output voltage and the vibration of the power electronic interface power frequency transformer is analyzed, and the relationship between the inverter output voltage and the vibration acceleration of the power electronic interface power frequency transformer is derived. Then, considering the injection of third and fifth harmonics into the inverter output voltage to reshape its waveform, the effective value of the vibration acceleration of the power electronic interface power frequency transformer after waveform reshaping is obtained. Then, with the minimum effective value of vibration acceleration as the objective and the total voltage distortion (THD) as the constraint, the particle swarm optimization algorithm is used to solve for the effective values ​​and initial phases of the third and fifth harmonics, thus achieving active vibration reduction of the power electronic interface power frequency transformer. The active vibration reduction method for waveform reshaping of power electronic interface power frequency transformers proposed in this invention effectively reduces the vibration acceleration of power electronic interface power frequency transformers, achieving low vibration and stable operation.

[0185] Example 2

[0186] like Figure 3 As shown, the present invention provides an active vibration reduction system for waveform reshaping of a power frequency transformer with a power electronic interface, including a vibration model establishment module for a power frequency transformer with a power electronic interface, a voltage waveform reshaping module, and a parameter solving module using a particle swarm optimization algorithm.

[0187] The vibration model establishment module for the power electronic interface power frequency transformer is used to decompose the inverter output voltage into fundamental and harmonic components using Fourier analysis. Based on the magnetostrictive effect and magnetic field coupling relationship of the core of the power electronic interface power frequency transformer, a vibration model of the power electronic interface power frequency transformer is established, and the expression for the core vibration acceleration caused by magnetostriction of the power electronic interface power frequency transformer is determined.

[0188] The voltage waveform reshaping module is used to inject third and fifth harmonics into the inverter output voltage to reshape its waveform and obtain a reference value for the inverter output voltage.

[0189] The particle swarm optimization (PSO) algorithm parameter solving module is used to obtain an expression for the effective value of the core vibration acceleration after voltage waveform reshaping based on the reference value of the inverter output voltage. Based on the power frequency transformer vibration model of the power electronic interface, with the minimum effective value of the core vibration acceleration as the objective and the total voltage distortion rate of the inverter output voltage as the constraint, the PSO optimization algorithm is used to solve for the effective value and initial phase of the injected third and fifth harmonics, and output the optimal value of the effective value of the core vibration acceleration.

[0190] Other features in this embodiment are the same as in Embodiment 1, so they will not be repeated here.

[0191] Example 3

[0192] Based on the same concept, the present invention also provides a schematic diagram of a physical structure, such as... Figure 4 As shown, the server may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840. The processor 810, communications interface 820, and memory 830 communicate with each other via the communication bus 840. The processor 810 can call logic instructions stored in the memory 830 to execute the steps of the power electronic interface power frequency transformer waveform reshaping active vibration reduction method.

[0193] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0194] Example 4

[0195] Based on the same concept, the present invention also provides a non-transitory computer-readable storage medium storing a computer program containing at least one piece of code that can be executed by a master control device to control the master control device to implement the steps of the active vibration reduction method for waveform reshaping of the power electronic interface power frequency transformer.

[0196] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive).

[0197] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as ROM or random access memory (RAM), magnetic disks, or optical disks.

[0198] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for active vibration reduction of waveform reshaping in a power frequency transformer with a power electronic interface, characterized in that, Includes the following steps: Establish a vibration model for a power frequency transformer with a power electronic interface: Using Fourier analysis, the inverter output voltage is decomposed into fundamental and harmonic components. Based on the magnetostrictive effect of the core of the power frequency transformer with a power electronic interface and the magnetic field coupling relationship, a vibration model for the power frequency transformer with a power electronic interface is established, and the expression for the core vibration acceleration caused by magnetostriction is determined. Reshaping the voltage waveform: After injecting the third and fifth harmonics into the inverter output voltage to reshape its waveform, a reference value for the inverter output voltage is obtained. The parameters are solved using the particle swarm optimization algorithm: Based on the reference value of the inverter output voltage, the expression for the effective value of the core vibration acceleration after voltage waveform reshaping is obtained; Based on the vibration model of the power frequency transformer with power electronic interface, the goal is to minimize the effective value of the core vibration acceleration, and the total voltage distortion rate of the inverter output voltage is used as the constraint. The particle swarm optimization algorithm is used to solve for the effective value and initial phase of the injected third and fifth harmonics, and output the optimal value of the effective value of the core vibration acceleration. In the steps of establishing the vibration model of the power frequency transformer with the power electronic interface, the Fourier analysis method is used, assuming the expression for the output voltage of phase A of the inverter is as follows: In the formula: t is time, and N is the harmonic order. This represents the effective value of the fundamental component of the inverter output voltage. The fundamental angular frequency of the inverter output voltage; This represents the initial phase of the fundamental component of the inverter output voltage; This represents the effective value of the kth harmonic component of the inverter output voltage. This represents the initial phase of the k-th harmonic component of the inverter output voltage; According to the law of electromagnetic induction, the magnetic flux density of the A-phase core of a power electronic interface frequency transformer is expressed as: In the formula, N1 represents the number of turns in the primary winding of the power electronic interface power frequency transformer, and S represents the cross-sectional area of ​​the transformer core. When the core is in an alternating magnetic field, the relationship between the magnetic field strength and magnetic flux density of the core is as follows: In the formula: The magnetic susceptibility of the medium; The magnetic susceptibility of the material; Assuming the parameters of the power electronic interface power frequency transformer are symmetrical, when the power electronic interface power frequency transformer is in an alternating magnetic field, the ferromagnetic material used in the core will produce a magnetostrictive effect, which will cause the length of the material to change periodically, thus causing the core to vibrate; the magnetostrictive effect of the core is described by the magnetostriction coefficient. In the formula: Indicates the magnetostriction coefficient. This represents the original axial length of the iron core. Indicates the axial expansion and contraction of the iron core; Based on the working characteristics of silicon steel sheets with iron cores and the secondary domain rotation model, the magnetostriction coefficient is expressed as: In the formula: and Given the magnetostriction and magnetization in the magnetic saturation state, combining equations (3) and (5) yields: In the formula: Representing the magnetic field coupling constant of the ferromagnetic material, substituting (1) and (2) yields: From the above formula, the acceleration of the iron core vibration caused by magnetostriction is: In the formula, It is the voltage-vibration constant. and The expression is: In the formula, and Indicates frequency coupling components, and These are the effective values ​​of the nth and mth harmonic components of the inverter output voltage; and The initial phases of the nth and mth harmonic components of the inverter output voltage are given.

2. The active vibration reduction method for waveform reshaping of power frequency transformers using power electronic interfaces according to claim 1, characterized in that, In the voltage waveform reshaping step, the initial phase of the fundamental voltage is set to 0 according to equations (8) and (9). After the third and fifth harmonic voltages are injected into the inverter output voltage to reshape its waveform, the reference value of the inverter A-phase output voltage is: In the formula, and These are the effective values ​​of the 3rd and 5th harmonic components of the inverter output voltage; and This represents the initial phase of the 3rd and 5th harmonic components of the inverter output voltage.

3. The active vibration reduction method for waveform reshaping of power frequency transformers using power electronic interfaces according to claim 2, characterized in that, The effective value of the core vibration acceleration is expressed as: in In the formula, A2, A4, A6, A8, A 10 These represent the 2nd, 4th, 6th, 8th, and 10th order components of the vibration acceleration, respectively. Assuming the effective value of the fundamental component of the inverter output voltage remains constant, the effective value of the core vibration acceleration is related to the effective values ​​and initial phase of the third and fifth harmonic voltages, according to the above formula. A vibration model based on a power frequency transformer with a power electronic interface is used, with the effective value of the core vibration acceleration as the basis. With the goal of minimizing the total voltage distortion (THD) of the inverter output voltage as a constraint, the effective values ​​and initial phases of the injected third and fifth harmonic voltages are designed using a particle swarm optimization algorithm. The constraints are: The optimization model is solved using the particle swarm optimization algorithm. Suppose there exists a particle population P in a D-dimensional feasible solution space, containing I randomly distributed particles, each with its own initial velocity and initial position. The particles in the entire population iterate and optimize T times. Then: (14) (15) (16) (17) (18) In the formula: X id t Let X be the position vector of the i-th particle in the d-th dimension during the t-th iteration. i1 X i2 X i3 , ..., X id V represents the position of the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; id t+1 V represents the velocity of the i-th particle in the d-th dimension during the (t+1)-th iteration. id t Let V be the velocity vector of the i-th particle in the d-th dimension during the t-th iteration. i1 V i2 V i3 , ..., V id Let E be the velocity of the i-th particle in the 1st, 2nd, 3rd, ..., dth dimensions during the tth iteration; c1 and c2 are the learning factors for the individual and global extrema, respectively; r1 and r2 are the influence perturbation factors for the individual and global extrema, respectively; i t d E is the individual extreme value vector of dimension d found by the i-th particle in the t-th iteration. i1 E i2 E i3 , ..., E id G represents the individual extreme values ​​of the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; i t d G is the optimal solution vector of dimension d found by the entire population in the t-th iteration. i1 G i2 G i3 , ..., G id Let be the optimal solution for the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; The particle position update method is described as follows: (19) In the formula: X id t+1 Let X be the position of the i-th particle in the d-th dimension during the (t+1)-th iteration; i t d V represents the position of the i-th particle in the d-th dimension during the t-th iteration; id t+1 Let be the velocity of the i-th particle in the d-th dimension during the (t+1)-th iteration.

4. The active vibration reduction method for waveform reshaping of power frequency transformers using power electronic interfaces according to claim 3, characterized in that, In the step of solving for parameters using the particle swarm optimization algorithm, the algorithm flow is as follows: ① Set the population size P to I=20, learning factors c1=0.5 and c2=0.5, maximum number of iterations T=100, set the fitness function, and set the position to X=[ , , , If the particle swarm dimension D=4, then the particle swarm dimension is 4. ② Randomly initialize the positions and velocities of I particles in population P, calculate the fitness values ​​of all particles, and determine the individual extreme value E of each particle and the global extreme value G of population P; ③ Use equations (18) and (19) to obtain the updated values ​​of particle velocity and position, determine whether the constraint conditions are met, and if not, set the value to be near the constraint conditions. Calculate the fitness values ​​of all particles again to determine the individual extreme values ​​of the new generation of particles and the global extreme value of the new generation of population P. ④ Compare step ③ with step ②, and retain the value with the higher fitness; complete the update of individual extreme values ​​and global extreme values; ⑤ Determine whether the particle swarm optimization algorithm meets the termination condition at this time. If the number of iterations exceeds T or the optimal solution of the fitness function is found, the algorithm process ends and the optimal value is output; otherwise, continue to step ③ in a loop.

5. A waveform reshaping active vibration reduction system for power frequency transformers with power electronic interfaces, characterized in that, include: The module for establishing a vibration model of a power electronic interface power frequency transformer is used to decompose the inverter output voltage into fundamental and harmonic components using Fourier analysis. Based on the magnetostrictive effect and magnetic field coupling relationship of the core of the power electronic interface power frequency transformer, a vibration model of the power electronic interface power frequency transformer is established, and the expression for the core vibration acceleration caused by magnetostriction of the power electronic interface power frequency transformer is determined. The voltage waveform reshaping module is used to inject the third and fifth harmonics into the inverter output voltage to reshape its waveform and obtain a reference value for the inverter output voltage. The particle swarm optimization (PSO) module is used to obtain an expression for the effective value of the core vibration acceleration after voltage waveform reshaping, based on the reference value of the inverter output voltage. Using a power frequency transformer vibration model with a power electronic interface, the module aims to minimize the effective value of the core vibration acceleration, with the total voltage distortion rate of the inverter output voltage as a constraint. The PSO algorithm is then used to solve for the effective values ​​and initial phases of the injected third and fifth harmonics, outputting the optimal value of the effective core vibration acceleration. In the power electronic interface power frequency transformer vibration model establishment module, using the Fourier analysis method, it is assumed that the expression for the inverter A-phase output voltage is as follows: In the formula: t is time, and N is the harmonic order. This represents the effective value of the fundamental component of the inverter output voltage. The fundamental angular frequency of the inverter output voltage; This represents the initial phase of the fundamental component of the inverter output voltage; This represents the effective value of the kth harmonic component of the inverter output voltage. This represents the initial phase of the k-th harmonic component of the inverter output voltage; According to the law of electromagnetic induction, the magnetic flux density of the A-phase core of a power electronic interface frequency transformer is expressed as: In the formula, N1 represents the number of turns in the primary winding of the power electronic interface power frequency transformer, and S represents the cross-sectional area of ​​the transformer core. When the core is in an alternating magnetic field, the relationship between the magnetic field strength and magnetic flux density of the core is as follows: In the formula: The magnetic susceptibility of the medium; The magnetic susceptibility of the material; Assuming the parameters of the power electronic interface power frequency transformer are symmetrical, when the power electronic interface power frequency transformer is in an alternating magnetic field, the ferromagnetic material used in the core will produce a magnetostrictive effect, which will cause the length of the material to change periodically, thus causing the core to vibrate; the magnetostrictive effect of the core is described by the magnetostriction coefficient. In the formula: Indicates the magnetostriction coefficient. This represents the original axial length of the iron core. Indicates the axial expansion and contraction of the iron core; Based on the working characteristics of silicon steel sheets with iron cores and the secondary domain rotation model, the magnetostriction coefficient is expressed as: In the formula: and Given the magnetostriction and magnetization in the magnetic saturation state, combining equations (3) and (5) yields: In the formula: Representing the magnetic field coupling constant of the ferromagnetic material, substituting (1) and (2) yields: From the above formula, the acceleration of the iron core vibration caused by magnetostriction is: In the formula, It is the voltage-vibration constant. and The expression is: In the formula, and Indicates frequency coupling components, and These are the effective values ​​of the nth and mth harmonic components of the inverter output voltage; and The initial phases of the nth and mth harmonic components of the inverter output voltage are given.

6. The active vibration reduction system for waveform reshaping of power frequency transformers with power electronic interfaces according to claim 5, characterized in that, In the voltage waveform reshaping module, the initial phase of the fundamental voltage is set to 0 according to equations (8) and (9). After the third and fifth harmonic voltages are injected into the inverter output voltage to reshape its waveform, the reference value of the inverter A-phase output voltage is: In the formula, and These are the effective values ​​of the 3rd and 5th harmonic components of the inverter output voltage; and This represents the initial phase of the 3rd and 5th harmonic components of the inverter output voltage.

7. The active vibration reduction system for waveform reshaping of power frequency transformers with power electronic interface according to claim 6, characterized in that, The effective value of the core vibration acceleration is expressed as: in In the formula, A2, A4, A6, A8, A 10 These represent the 2nd, 4th, 6th, 8th, and 10th order components of the vibration acceleration, respectively. Assuming the effective value of the fundamental component of the inverter output voltage remains constant, the effective value of the core vibration acceleration is related to the effective values ​​and initial phase of the third and fifth harmonic voltages, according to the above formula. A vibration model based on a power frequency transformer with a power electronic interface is used, with the effective value of the core vibration acceleration as the basis. With the goal of minimizing the total voltage distortion (THD) of the inverter output voltage as a constraint, the effective values ​​and initial phases of the injected third and fifth harmonic voltages are designed using a particle swarm optimization algorithm. The constraints are: The optimization model is solved using the particle swarm optimization algorithm. Suppose there exists a particle population P in a D-dimensional feasible solution space, containing I randomly distributed particles, each with its own initial velocity and initial position. The particles in the entire population iterate and optimize T times. Then: (14) (15) (16) (17) (18) In the formula: X id t Let X be the position vector of the i-th particle in the d-th dimension during the t-th iteration. i1 X i2 X i3 , ..., X id V represents the position of the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; id t+1 V represents the velocity of the i-th particle in the d-th dimension during the (t+1)-th iteration. id t Let V be the velocity vector of the i-th particle in the d-th dimension during the t-th iteration. i1 V i2 V i3 , ..., V id Let E be the velocity of the i-th particle in the 1st, 2nd, 3rd, ..., dth dimensions during the tth iteration; c1 and c2 are the learning factors for the individual and global extrema, respectively; r1 and r2 are the influence perturbation factors for the individual and global extrema, respectively; i t d E is the individual extreme value vector of dimension d found by the i-th particle in the t-th iteration. i1 E i2 E i3 , ..., E id G represents the individual extreme values ​​of the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; i t d G is the optimal solution vector of dimension d found by the entire population in the t-th iteration. i1 G i2 G i3 , ..., G id Let be the optimal solution for the i-th particle in the t-th iteration along the 1st, 2nd, 3rd, ..., d-th dimensions; The particle position update method is described as follows: (19) In the formula: X id t+1 Let X be the position of the i-th particle in the d-th dimension during the (t+1)-th iteration; i t d V represents the position of the i-th particle in the d-th dimension during the t-th iteration; id t+1 Let be the velocity of the i-th particle in the d-th dimension during the (t+1)-th iteration.

8. The active vibration reduction system for waveform reshaping of power frequency transformers with power electronic interface according to claim 7, characterized in that, The algorithm flow of the particle swarm optimization algorithm in the parameter solving module is as follows: ① Set the population size P to I=20, learning factors c1=0.5 and c2=0.5, maximum number of iterations T=100, set the fitness function, and set the position to X=[ , , , If the particle swarm dimension D=4, then the particle swarm dimension is 4. ② Randomly initialize the positions and velocities of I particles in population P, calculate the fitness values ​​of all particles, and determine the individual extreme value E of each particle and the global extreme value G of population P; ③ Use equations (18) and (19) to obtain the updated values ​​of particle velocity and position, determine whether the constraint conditions are met, and if not, set the value to be near the constraint conditions. Calculate the fitness values ​​of all particles again to determine the individual extreme values ​​of the new generation of particles and the global extreme value of the new generation of population P. ④ Compare step ③ with step ②, and retain the value with the higher fitness; complete the update of individual extreme values ​​and global extreme values; ⑤ Determine whether the particle swarm optimization algorithm meets the termination condition at this time. If the number of iterations exceeds T or the optimal solution of the fitness function is found, the algorithm process ends and the optimal value is output; otherwise, continue to step ③ in a loop.

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