CN112131778A - Transformer residual magnetism assessment method based on particle swarm optimization - Google Patents

Abstract

The invention relates to a particle swarm algorithm-based transformer residual magnetism assessment method, which comprises the steps of constructing an iron core static hysteresis model to obtain the iron core static hysteresis model with magnetic flux density as an input variable and magnetic field intensity as an output; and then constructing an iron core dynamic hysteresis model to obtain a magnetic field intensity calculation method of the iron core dynamic hysteresis model with eddy current loss and abnormal loss, and finally solving the established model by adopting a particle swarm algorithm. The evaluation method provided by the invention can realize the residual magnetism evaluation of the transformer, solves the problem that the residual magnetism of the transformer is difficult to accurately evaluate by the traditional method, and can monitor the running state of the transformer in the power system in real time by a power company, inhibit the occurrence of the excitation inrush current of the transformer and improve the running safety of the transformer, thereby improving the running safety of the power system and the power supply reliability of a power distribution network.

Description

Transformer residual magnetism assessment method based on particle swarm optimization

Technical Field

The invention relates to a transformer residual magnetism assessment method, in particular to a particle swarm algorithm-based transformer residual magnetism assessment method, and belongs to the technical field of operation and maintenance of power transformation equipment.

Background

The transformer is a static electric appliance based on the electromagnetic induction principle, is used for converting low voltage into high voltage, converting high voltage into low voltage and isolating an alternating current power supply, and is important electric equipment in a power system. The normal operation of the transformer is directly related to the continuous and stable operation of the power system. When the transformer is damaged due to faults, the overhaul difficulty is high, the overhaul period is long, the safe and stable operation of a power system is influenced, and economic loss and social influence are caused. In the process of switching on, operating and switching off the transformer, due to the hysteresis characteristic of the ferromagnetic material, a certain magnetic flux is left in the iron core, and the residual magnetic flux is called as the residual magnetism of the iron core. In addition, residual magnetism remains in the core after various testing operations of the transformer. The common operation mode of the transformer in the operation of the power system is that the voltage is restored again after no-load input or external fault removal, and the residual magnetism of the iron core and the closing bias magnetism act together to saturate the inner half cycle of the iron core, so that the generation of excitation inrush current is caused, and the safe and stable operation of a power grid is influenced. Therefore, measurement, calculation, estimation and inhibition of the residual magnetism of the transformer are very important, and the method has important theoretical significance and practical value.

At present, research on a remanence evaluation method of a transformer at home and abroad has a certain foundation. The experience estimation method can provide reference for transformer manufacturers to carry out ex-factory transformer tests, but the method cannot obtain accurate residual magnetism values; the direct measurement method can adopt a gauss meter to measure the residual magnetism, but the method can only test the surface magnetic property of the ferromagnetic material, and the result is not accurate; the indirect measurement method obtains the peak value of the magnetizing inrush current through a transformer energization experiment, obtains the value of the residual magnetism according to the peak value, but can only obtain the value of the residual magnetism through a preliminary experiment and cannot be applied to an actual field; the pre-magnetizing and demagnetizing method is characterized in that an external power supply is added into an iron core to excite the iron core from an original remanence value to a known remanence, and then phase selection and closing operation is carried out on the basis of the known remanence to restrain magnetizing inrush current, but equipment needed by the pre-magnetizing method of the large transformer is high in price, and large current is needed to generate magnetic flux, and the large current can certainly affect the transformer; the voltage integration method obtains a remanence value by recording a voltage value at the opening moment of the transformer, but the remanence value obtained by the method is not accurate, and noise is introduced particularly when the voltage is small.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides a particle swarm algorithm-based transformer residual magnetism assessment method, which aims to solve the problem that the traditional method is difficult to accurately assess the transformer residual magnetism, can realize the real-time monitoring of the transformer operation state in a power system, inhibit the occurrence of transformer excitation inrush current, and improve the transformer operation safety, thereby achieving the technical effects of improving the power system operation safety and improving the power distribution network power supply reliability.

In order to achieve the above purpose, the invention provides a transformer residual magnetism assessment method based on a particle swarm optimization, which comprises the following steps:

(1) constructing an iron core static hysteresis model to obtain the iron core static hysteresis model with magnetic flux density as an input variable and magnetic field intensity as an output;

(2) constructing an iron core dynamic hysteresis model to obtain a magnetic field intensity calculation method of the iron core dynamic hysteresis model containing eddy current loss and abnormal loss;

(3) and (3) solving the iron core static hysteresis model and the iron core dynamic hysteresis model in the step (1) and the step (2) by adopting a particle swarm algorithm, and identifying parameters of different magnetic flux models by utilizing a fitness value.

Further, the core static hysteresis model in step (1) is specifically obtained by:

according to a differential equation with dM/dB:

and B ═ μ₀(H + M) to obtain a magnetic flux having a magnetic flux density B as an input and a magnetic field strength H as an outputHysteresis loop calculation, where M is magnetization, M is_irrBeing an irreversible component in the magnetization M, M_anIs magnetic hysteresis magnetization, B_eTo an effective magnetic flux density, mu₀For vacuum permeability, c is the reversible susceptibility, and α is the average field parameter characterizing the coupling inside the domain.

Further, the core dynamic hysteresis model in step (2) is specifically obtained by:

based on the iron core loss separation theory, the eddy current loss and the abnormal loss are combined with a static ferromagnetic hysteresis model to obtain:

H＝H_h+H_e+H_a

so as to obtain the magnetic field strength value of the dynamic hysteresis model containing eddy current loss and abnormal loss, thereby obtaining the hysteresis loop of the dynamic hysteresis model, wherein H is the total magnetic field strength, and H is H_hFor static magnetic field strength, H_eFor eddy current losses of magnetic field strength, H_aThe magnetic field strength is abnormally lost.

Further, the eddy current loss magnetic field intensity H_eAnd H_aThe abnormal loss magnetic field strength is specifically as follows:

wherein, W_eIs eddy current loss per unit volume, W_aFor abnormal losses, as the directional coefficient, k_eAnd k_aThe parameters are obtained by identification.

Further, the solving method of the particle swarm algorithm in the step (3) is specifically as follows:

the objective function of the particle swarm algorithm is expressed by a root mean square error, and the error is an adaptability value:

in the formula, the fitness is fitness; h_mIs the measured value of the magnetic field intensity; h_cCalculating the value of the magnetic field intensity; i is a sampling point; and Z is the total number of sampling points.

Further, during calculation, the target function is used as a fitness function, the values of 5 parameters are automatically updated through a particle swarm algorithm, 5 parameter values reaching a specified root mean square error are obtained, and the calculation process is as follows:

(1) initializing a particle swarm and determining a position initial value of each particle;

(2) calculating the fitness value of each particle according to the fitness evaluation function;

(3) updating individual extremum p of particles_idKeeping the optimal individual extremum;

(4) updating the position x of a particle_id；

(5) Judging whether an iteration stop condition is reached, if not, returning to the step (2); if yes, stopping calculation and outputting the result.

In summary, according to the transformer residual magnetism assessment method based on the particle swarm optimization, an iron core static hysteresis model with magnetic flux density as an input variable and magnetic field strength as an output is obtained by constructing the iron core static hysteresis model; and then constructing an iron core dynamic hysteresis model to obtain a magnetic field intensity calculation method of the iron core dynamic hysteresis model with eddy current loss and abnormal loss, and finally solving the established model by adopting a particle swarm algorithm. The residual magnetism of the transformer is evaluated by adopting the particle swarm optimization, the calculated hysteresis loop can be found and compared with the actually measured hysteresis loop, the error of the calculated hysteresis loop and the actually measured hysteresis loop is small, the correctness of the parameters obtained under the fitting formula is verified, and the local hysteresis loop can be directly obtained in practical application by utilizing the formula. The particle swarm algorithm is a swarm intelligence algorithm, has the advantages of being simple to operate, few in parameters needing to be adjusted, capable of achieving self-adaptive control and the like, greatly improves accuracy of an evaluation result by evaluating residual magnetism of the transformer in the technical scheme of the invention, and solves the technical problems that an evaluation method in the prior art is inaccurate in evaluation result, limited in application occasions, capable of influencing work of the transformer or introducing noise in a detection process and the like.

The technical scheme of the invention has the following beneficial technical effects:

by the particle swarm algorithm-based transformer residual magnetism assessment method, a user can monitor the running state of a transformer in a power system in real time, inhibit the occurrence of transformer excitation inrush current and improve the running safety of the transformer, so that the running safety of the power system is improved, and the power supply reliability of a power distribution network is improved.

Drawings

FIG. 1 is a waveform diagram of a shut-off overvoltage simulation;

FIG. 2 is a magnetic flux density waveform diagram;

FIG. 3 is a graph comparing a calculated current to a measured current;

fig. 4 is a graph comparing the hysteresis loop calculation result with the actual measurement result.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings in conjunction with the following detailed description. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.

The invention provides a particle swarm algorithm-based transformer residual magnetism assessment method, aiming at the defects that in the prior art, the assessment result is inaccurate, the application occasion is limited, the operation of a transformer can be influenced or noise is introduced in the detection process, and the like. The invention provides a particle swarm algorithm-based transformer residual magnetism assessment method, which comprises the steps of constructing an iron core static hysteresis model to obtain the iron core static hysteresis model with magnetic flux density as an input variable and magnetic field intensity as an output; and then constructing an iron core dynamic hysteresis model to obtain a magnetic field intensity calculation method of the iron core dynamic hysteresis model with eddy current loss and abnormal loss, and finally solving the established model by adopting a particle swarm algorithm. The evaluation method provided by the invention can realize the residual magnetism evaluation of the transformer, solves the problem that the residual magnetism of the transformer is difficult to accurately evaluate by the traditional method, and can monitor the running state of the transformer in the power system in real time by a power company, inhibit the occurrence of the excitation inrush current of the transformer and improve the running safety of the transformer, thereby improving the running safety of the power system and the power supply reliability of a power distribution network.

The technical scheme of the invention is explained in detail below, and the method for evaluating the residual magnetism of the transformer based on the particle swarm optimization comprises the following steps:

(1) constructing an iron core static hysteresis model to obtain the iron core static hysteresis model with magnetic flux density as an input variable and magnetic field intensity as an output; the method comprises the following steps:

in the core-static hysteresis model, the magnetization M includes a reversible component M_revAnd an irreversible component M_irrTwo parts are as follows:

M＝M_rev+M_irr

the relationship between these two components and the anhysteretic magnetization is derived from the physical mechanism of the magnetization process as follows:

M_rev＝c(M_an-M_irr)

in the formula, M_anIs magnetic hysteresis magnetization, and c is reversible magnetization coefficient;

magnetic hysteresis magnetization M_anExpressed as:

in the formula, H_eTo consider the magnetic field intensity after the mutual coupling action between the magnetic domains; m_sThe saturation magnetization is related to the self-characteristics and the temperature of the material; a is a parameter for representing the shape of a hysteresis-free magnetization curve;

calculating magnetic induction intensity B:

H_e＝H+αM

B＝μ₀(H+M)

in the formula, alpha and k are average field parameters for representing the internal coupling of the magnetic domain; h is the magnetic field intensity; mu.s₀Is a vacuum magnetic conductivity; is a directional coefficient;

the magnetization M can be expressed as:

M＝M_irr+c(M_an-M_irr)＝(1-c)M_irr+cM_an

upper type two-side simultaneous pair effective magnetic flux density B_eAnd (5) obtaining a derivative:

wherein, B_e＝μ₀H_e，μ₀＝4π×10^-7Obtaining:

B＝B_e-μ₀αM+μ₀M

the two sides of the upper formula simultaneously conduct on B, and the B is obtained by sorting:

for dM_an/dB_eIt is possible to obtain:

and according to B_e＝μ₀H_eObtaining:

in the above formula, dM_an/dH_eComprises the following steps:

for dM_irr/dB_eThe following can be converted:

it can therefore be deduced that:

finally, a differential equation containing dM/dB is obtained:

according to the above formula and B ═ mu₀(H + M), a hysteresis loop calculation result is obtained with the magnetic flux density B as an input and the magnetic field strength H as an output.

(2) Constructing an iron core dynamic hysteresis model to obtain a magnetic field intensity calculation method of the iron core dynamic hysteresis model containing eddy current loss and abnormal loss; the method comprises the following steps:

according to the core loss separation theory, in one magnetization period, the core loss is:

W＝W_h+W_e+W_a

in the formula, the iron core loss W is the area of an alternating current magnetic hysteresis loop; hysteresis loss W_hIs the area of a direct current magnetic hysteresis loop; w_eIs the eddy current loss;W_ais an abnormal loss;

eddy current loss W per unit volume for frequency dependent eddy current loss and anomalous loss_eComprises the following steps:

k_e＝d²/2ργ

in the formula, k_eIs the eddy current loss coefficient, and rho is the resistivity of the iron core material; d is the thickness of the silicon steel sheet; gamma is the shape factor of the iron core material; t is a time period;

abnormal loss W per unit volume_aThe expression of (a) is:

in the formula, k_aIs the abnormal loss coefficient, G is a dimensionless constant; w is the width of the silicon steel sheet; h₀Is the fluctuation coefficient inside the domain wall;

based on the iron core loss separation theory, the eddy current loss and the abnormal loss are combined with a static ferromagnetic hysteresis model to obtain:

H＝H_h+H_e+H_a

wherein H is the total magnetic field strength; h_hIs static magnetic field intensity; h_eMagnetic field strength is lost for eddy currents; h_aFor abnormal loss of magnetic field strengthDegree;

dynamic hysteresis model parameter k_eAnd k_aAfter the identification, the magnetic field strength value of the dynamic hysteresis model containing eddy current loss and abnormal loss can be obtained, and thus the hysteresis loop of the dynamic hysteresis model can be obtained.

(3) Solving the established model by adopting a particle swarm algorithm

The particle swarm optimization is an algorithm for solving the optimization of an objective function, which is inspired by the foraging phenomenon of the flying bird. Each possible solution value optimized by the objective function corresponds to a bird, i.e., a particle, in a foraging flock of birds within a certain range. All particles move to their adapted values under the control of functions and constraints, each particle initially having a certain velocity and initial position, on the basis of which all particles are searched in a space like a bird.

In the target search space of n dimension, there are d particles to form a cluster, where the ith particle is expressed as a vector of n dimension, x_i＝(x_i1，x_i2，……x_in) Is the current position of the particle; v. of_i＝(v_i1，v_i2，……v_in) Is the current velocity of the particle; p is a radical of_i＝(p_i1，p_i2，……p_in) The best position for a particle to pass through, i.e. the set of best fitness value positions through which all particles pass, the set of these positions constitutes the global best position. The closer to the center of the particle population, the smaller the value of the solution to the function, and the better the fitness.

By analyzing the characteristics of the flight tracks of the foraging activities of the bird groups, a formula for refreshing the speed and the position of the bird groups is obtained:

v_in(t)＝v_in(t-1)+c₁r_1n(t-1)(p_in(t-1)-x_in(t-1))

+c₂r_2n(t-1)(p_gj(t-1)-x_in(t-1))

x_in(t)＝x_in(t-1)+v_in(t)

in the formula, the lower subscript n represents the nth dimension of the particle, and i represents the ith micro particleParticle, t represents the t-th generation, c₁，c₂Represents a learning factor, r₁、r₂Is at [0,1 ]]Random numbers within a range.

The objective function of the particle swarm algorithm is expressed by a root mean square error, and the error is an adaptability value:

in the formula, the fitness is fitness; h_mIs the measured value of the magnetic field intensity; h_cCalculating the value of the magnetic field intensity; i is a sampling point; and Z is the total number of sampling points.

During calculation, the target function is used as a fitness function, the values of 5 parameters are automatically updated through a particle swarm algorithm, 5 parameter values reaching a specified root mean square error are obtained, and the calculation process is as follows:

(1) initializing a particle swarm and determining a position initial value of each particle;

(2) calculating the fitness value of each particle according to the fitness evaluation function;

(3) updating individual extremum p of particles_idKeeping the optimal individual extremum;

(4) updating the position x of a particle_id

(5) Judging whether an iteration stop condition is reached, if not, returning to the step (2); if yes, stopping calculation and outputting the result.

The overvoltage simulation oscillogram for estimating the residual magnetism of the transformer by the above estimation method and the comparison between the calculated result and the actual measurement result are further explained by combining the attached drawings.

The residual magnetism of the iron core is evaluated by calculating the hysteresis loop of the iron core after the cutoff overvoltage of the transformer occurs. The input is a trapping overvoltage simulation waveform, as shown in fig. 1, where the reference voltage phase is selected to be 90 degrees, where the trapping overvoltage occurs when the current is at a maximum. At this time, the problem of the shut-off overvoltage is the most serious.

The magnetic flux density waveform obtained by integrating the cut-off overvoltage is shown in fig. 2, and an alternating current component and a direct current component in the magnetic flux density waveform are used as the input of the core dynamic hysteresis model, so that the exciting current is obtained by calculation.

Fig. 3 is a comparison of the calculated current versus the measured current under external excitation for the shut-off overvoltage, wherein the calculated current for the first and final iteration are given separately. The current of the second cycle is shown in the figure, and the calculated current is larger than the measured current as can be seen from the result of the first iteration, which is caused by the reason that the initial magnetic flux density is larger than the actual magnetic flux density. And then, adjusting alternating current components and direct current components in the magnetic flux density, wherein the current obtained by the last iterative calculation is well matched with the actually measured current.

Therefore, an iron core dynamic hysteresis model and a particle swarm algorithm are applied to calculating a hysteresis loop under the interception overvoltage, and the lowest point of the hysteresis loop is a remanence value. Because the direct current hysteresis loop is difficult to measure under the condition of complete direct current, the direct current hysteresis loop is obtained by actually measuring at a lower frequency. The results of the parameter identification of the model at a frequency of 25Hz and a magnetic flux density of 1.4T are shown in Table 1.

TABLE 1 model parameter identification results

The measured hysteresis loop is compared with the calculated hysteresis loop as shown in fig. 4. The actually measured magnetic hysteresis loop is matched with the magnetic hysteresis loop obtained by calculation, and the correctness of the model and the method provided by the text is verified.

In summary, the invention relates to a particle swarm algorithm-based transformer residual magnetism assessment method, which comprises the steps of constructing an iron core static hysteresis model to obtain the iron core static hysteresis model with magnetic flux density as an input variable and magnetic field intensity as an output; and then constructing an iron core dynamic hysteresis model to obtain a magnetic field intensity calculation method of the iron core dynamic hysteresis model with eddy current loss and abnormal loss, and finally solving the established model by adopting a particle swarm algorithm. The evaluation method provided by the invention can realize the residual magnetism evaluation of the transformer, and solves the technical problems that the evaluation method in the prior art has inaccurate evaluation result, limited application occasions, influences on the work of the transformer or introduces noise in the detection process and the like. By adopting the evaluation method, the power company can monitor the running state of the transformer in the power system in real time, inhibit the occurrence of the excitation inrush current of the transformer and improve the running safety of the transformer, so that the running safety of the power system is improved, and the power supply reliability of a power distribution network is improved.

It is to be understood that the above-described embodiments of the present invention are merely illustrative of or explaining the principles of the invention and are not to be construed as limiting the invention. Therefore, any modification, equivalent replacement, improvement and the like made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. Further, it is intended that the appended claims cover all such variations and modifications as fall within the scope and boundaries of the appended claims or the equivalents of such scope and boundaries.

Claims (6)

1. A transformer residual magnetism assessment method based on particle swarm optimization is characterized by comprising the following steps:

(1) constructing an iron core static hysteresis model to obtain the iron core static hysteresis model with magnetic flux density as an input variable and magnetic field intensity as an output;

(2) constructing an iron core dynamic hysteresis model to obtain a magnetic field intensity calculation method of the iron core dynamic hysteresis model containing eddy current loss and abnormal loss;

(3) and (3) solving the iron core static hysteresis model and the iron core dynamic hysteresis model in the step (1) and the step (2) by adopting a particle swarm algorithm, and identifying parameters of different magnetic flux models by utilizing a fitness value.

2. The transformer residual magnetism assessment method according to claim 1, characterized in that said core static hysteresis model in step (1) is obtained by specifically:

according to a differential equation with dM/dB:

and B ═ μ₀(H + M) to obtain a hysteresis loop calculation result with the magnetic flux density B as input and the magnetic field strength H as output, wherein M is magnetization, and M is magnetization_irrBeing an irreversible component in the magnetization M, M_anIs magnetic hysteresis magnetization, B_eFor effective magnetic flux density, H_eFor eddy current losses of magnetic field strength, mu₀For vacuum permeability, c is the reversible susceptibility, and α is the average field parameter characterizing the coupling inside the domain.

3. The transformer residual magnetism assessment method according to claim 1, characterized in that said core dynamic hysteresis model in step (2) is obtained by specifically: based on the iron core loss separation theory, the eddy current loss and the abnormal loss are combined with a static ferromagnetic hysteresis model to obtain:

H＝H_h+H_e+H_a

so as to obtain the magnetic field strength value of the dynamic hysteresis model containing eddy current loss and abnormal loss, thereby obtaining the hysteresis loop of the dynamic hysteresis model, wherein H is the total magnetic field strength, and H is H_hFor static magnetic field strength, H_eFor eddy current losses of magnetic field strength, H_aThe magnetic field strength is abnormally lost.

4. Transformer residual magnetism assessment method according to claim 3, characterized in that said eddy current loss magnetic field strength H_eAnd abnormal loss magnetic field intensity H_aThe method specifically comprises the following steps:

wherein, W_eIs eddy current loss per unit volume, W_aFor abnormal losses, as the directional coefficient, k_eAnd k_aThe parameters are obtained by identification.

5. The transformer residual magnetism assessment method according to claim 1, wherein the solving method of the particle swarm optimization in the step (3) is specifically as follows:

the objective function of the particle swarm algorithm is expressed by a root mean square error, and the error is an adaptability value:

in the formula, the fitness is fitness; h_mIs the measured value of the magnetic field intensity; h_cCalculating the value of the magnetic field intensity; i is a sampling point; and Z is the total number of sampling points.

6. The transformer residual magnetism assessment method according to claim 5, characterized in that, during calculation, the objective function is used as a fitness function, the values of 5 parameters are automatically updated by a particle swarm algorithm, 5 parameter values reaching a specified root mean square error are obtained, and the calculation flow is as follows:

(1) initializing a particle swarm and determining a position initial value of each particle;

(2) calculating the fitness value of each particle according to the fitness evaluation function;

(3) updating individual extremum p of particles_idKeeping the optimal individual extremum;

(4) updating the position x of a particle_id；

(5) Judging whether an iteration stop condition is reached, if not, returning to the step (2); if yes, stopping calculation and outputting the result.

Images