CN110008645A - A kind of transformer loss calculation method - Google Patents

Abstract

The invention relates to a transformer loss calculation method, comprising: S1: obtaining the B-H curve of the transformer under the actual power frequency operation state through no-load test before the transformer is put into operation; S2: establishing a J-A dynamic model, using the B-H curve Optimize the parameters of the J‑A dynamic model to obtain the J‑A dynamic model used to simulate the hysteresis loop of the transformer core under actual operating conditions; S3: Establish the transformer winding model under harmonics, and calculate the primary side impedance and transformer excitation impedance ; S4: The non-sinusoidal input is processed by Fourier decomposition, and the winding current and excitation current under real-time data are obtained by using the equivalent model of the transformer circuit; The real-time transformer winding loss is calculated by the relationship, and the real-time transformer core loss is calculated through the J-A model; the invention takes into account the rapidity and accuracy of the transformer loss calculation to realize the real-time prediction of the transformer loss.

Description

A kind of transformer loss calculation method

technical field

The invention relates to the field of power system loss prediction methods, and more particularly, to a transformer loss calculation method.

Background technique

With the gradual increase of nonlinear loads in the power system, there are a large number of harmonic currents and voltages that exceed the standard in the line, which makes the harmonic problem of the power system more and more serious. Heat generation, thereby reducing the insulation level of the transformer, reducing the service life of the transformer, and affecting the safety of the power grid in severe cases.

Reducing transformer losses and improving the energy efficiency of power supply equipment are the basis for achieving high-quality and high-efficiency power grid operation; a model that accurately and quickly calculates real-time losses of transformers can provide an important reference for the dispatching and switching of transformers during operation, as well as provide simulations for research on power quality assessment methods. module.

At present, the transformer loss calculation models at home and abroad generally use the Steinmetz equation or the static J-A model, and the nonlinearity of the transformer excitation branch impedance adopts a segmental processing, which requires a large amount of experimental data, and does not take into account a certain speed and accuracy to achieve loss. Real-time predictions.

SUMMARY OF THE INVENTION

The present invention provides a transformer loss calculation method in order to overcome the defect that the transformer loss calculation described in the above-mentioned prior art does not take into account certain rapidity and accuracy to realize the real-time prediction of the loss.

The method includes the following steps:

S1: The B-H curve of the transformer under the actual power frequency operation state is obtained through the no-load test before the transformer is put into operation; the B-H curve is the magnetization curve that characterizes the relationship between the magnetic induction intensity B and the magnetic field intensity H of the transformer core during the magnetization process;

S2: Establish a J-A dynamic model, use the B-H curve to optimize the parameters of the J-A dynamic model, and obtain the J-A dynamic model used to simulate the hysteresis loop of the transformer core under actual operating conditions;

S3: Establish the transformer winding model under harmonics, calculate the transformer primary side impedance according to the transformer nameplate parameters; use the i-L function to calculate the transformer excitation impedance;

S4: Collect and record the primary and secondary voltage and current data of the transformer, modify the primary and secondary voltage and current parameters in the transformer winding model according to the data; process the non-sinusoidal input through Fourier decomposition, and use the transformer winding model to obtain the winding current under real-time data and excitation current;

S5: Calculate the transformer winding loss through the relationship between the primary and secondary side impedance in the winding equivalent circuit and the flowing winding current, and calculate the real-time transformer core loss through the J-A model.

Preferably, the J-A dynamic model in S2 is:

where M _an =M _s (coth(H _e /a)-(a/H _e ))

B=μ _o (H+M)

In the formula, the magnetic field intensity H is used as the input, the magnetic induction intensity B is the output, M _s is the saturation magnetization, k is the irreversible coefficient, c is the reversible coefficient, α is the parameter characterizing the interaction between magnetic domains, and a is the magnetization curve without hysteresis Correction parameter of shape, ρ is the resistivity of the material, the unit is Ω m; d is the material size (diameter when the cylinder is, the thickness of the sheet when slicing), the unit is m, the thickness of the general distribution transformer silicon steel sheet is 0.25- 0.35mm; β is the geometric factor (16 for the cylinder, 6 for the slice, 20 for the sphere), and β=6 for the transformer; where; w is the slice width, in m; H _o is related to the domain wall The parameter of , the value is 0.0075; G is the dimensionless constant, which is independent of the size, and the value is 0.1356; μ ₀ is the vacuum permeability, t is the time, M is the magnetization, and the unit is A/m, and δ is the nail in the characteristic magnetic field. The parameters of the blocking effect of the tie effect, when dH/dt>0, δ>0; when _dH /dt<0, δ<0; _Man is the lossless magnetization, unit A/m, He is the effective magnetic field strength, unit A /m, H is the magnetic field strength, the unit is A/m.

Preferably, the specific process of optimizing the model parameters by using the B-H curve is as follows:

The particle swarm optimization algorithm was used to fit the BH curve of the silicon steel sheet obtained by S1, and five parameters of the modified JA dynamic model were obtained: saturation magnetization Ms, irreversible coefficient _k , reversible coefficient c, parameter α characterizing the interaction between magnetic domains, no The correction parameter a of the shape of the hysteresis magnetization curve, and the other parameters are set according to the actual transformer condition, and the JA dynamic model used to simulate the hysteresis loop of the transformer core under the actual operating state is obtained.

Preferably, the transformer winding model in S3 includes: primary side power supply, primary side impedance, excitation impedance, and secondary side power supply;

The primary side power supply and the primary side impedance are connected in series; the series connected primary side power supply and the primary side impedance are connected in parallel with the excitation impedance and the secondary side power supply.

Preferably, the calculation formula of the primary side impedance in S3 is:

Among them, h is the harmonic order, R is the winding inductance, and X is the winding reactance.

Preferably, the calculation process of the excitation impedance in S3 is:

_S3.1 : Suppose there is no magnetic leakage, and the magnetic field strength H on the magnetic circuit l is equal everywhere; according to the law of total current, there is a relationship between the excitation current im and the magnetic field strength H:

have to

In the formula, l is the average core magnetic circuit of the transformer, and N is the number of turns of the high-order side winding;

S3.2: According to the principle of energy disturbance, calculate the excitation energy increment provided by the outside, and the calculation formula is:

ΔW ₁ =Δe _{m Δim}

That is, ΔW ₁ =L _{eq Δim} ²

Among them, _Δim is the excitation current generated by the coil in the circuit model under the action of an external power supply at a certain time, Δλ is the flux linkage generated by the excitation current Δi; Δe _m is the voltage increment of the excitation port; L _eq is the equivalent inductance of the excitation branch;

S3.3: Calculate the energy increment generated by the magnetic field change caused by the excitation current in the magnetic field. The calculation formula is:

ΔW ₂ =∫ΔBΔH·dV

In the formula, ΔB is the magnetic induction intensity increment; ΔH is the magnetic field intensity increment

S3.4: Combine S3.1-S3.3, and obtain the relationship between the excitation current and the equivalent inductance L _eq of the excitation branch through the JA model in S2; then obtain the iL function through the Gaussian algorithm;

The i-L function is:

where a _j , b _j , c _j are different parameters, j=1,2,3,4,5,6,7,8;

S3.5: Calculate the excitation impedance according to the i-L function.

Preferably, S4 includes the following steps:

S4.1: Collect and record the primary and secondary voltage and current data of the transformer, and modify the primary and secondary voltage and current parameters in the transformer winding model according to the data;

by Fourier series The primary side non-sinusoidal voltage and secondary side non-sinusoidal current are decomposed into sinusoidal fundamental voltage and current, odd sinusoidal harmonic voltage and current, respectively.

S4.3: Input the primary side voltage source voltage up _p and the secondary side current source current i _user decomposed by _S4.1 , and set an initial value of the initial excitation current im less than 10% of the no-load excitation current (self- Set a small initial value im of the excitation current to start the calculation process, such as _{0.05A), to find the primary side current i p ,} the calculation formula is:

i _p = i _user + i _m

S4.4: Calculate the back EMF according to the primary side current, the calculation formula is:

S4.5: Find the excitation potential, the calculation formula is:

S4.6: Calculate the excitation current: the calculation formula is:

S4.7: Determine whether the excitation current converges; if it converges, go to S5; if it does not converge, go back to step S4.3.

Preferably, the calculation formula of the total winding loss in step S5 is:

Among them, i _ph is the current generated by the h harmonic in the primary side current i _p .

Preferably, the calculation process of the core loss in step S5 is:

_S5.1 : Add the excitation current im under different harmonic orders through iteration in S4, and substitute the following formula to obtain the input magnetic field H:

S5.2: Calculate the magnetic induction intensity B through the J-A model;

S5.3: Calculate the core loss of the transformer, the calculation formula is:

P _Fe =P _ec +P _A +P _h

P _h =∫BdH

Among them, P _Fe is the core loss, P _ec is the eddy current loss, P _A is the additional loss caused by the local eddy current between the device structures, and P _h is the hysteresis loss.

Compared with the prior art, the beneficial effects of the technical solution of the present invention are: the present invention takes into account the rapidity and accuracy of the transformer loss calculation to realize the real-time prediction of the transformer loss, and the present invention only needs to measure the actual operation B-H curve of the transformer core to form The corresponding J-A model is used to obtain the excitation impedance and BH loop under the corresponding input, which reflects the nonlinearity of the transformer core; at the same time, the influence of frequency on the J-A model can well reflect the dynamics of the model in the harmonic environment. parameters can be used for loss evaluation.

Description of drawings

FIG. 1 is a flow chart of a method for calculating transformer loss according to the present embodiment.

Figure 2 is an equivalent circuit diagram of a transformer.

Fig. 3 is the flow chart of nonlinear inductance parameter acquisition.

Detailed ways

The accompanying drawings are for illustrative purposes only, and should not be construed as limitations on this patent;

In order to better illustrate this embodiment, some parts of the drawings are omitted, enlarged or reduced, which do not represent the size of the actual product;

It will be understood by those skilled in the art that some well-known structures and their descriptions may be omitted from the drawings.

The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

This embodiment provides a method for calculating transformer loss, as shown in FIG. 1 , the method includes the following steps:

S1: Obtain the B-H curve of the transformer under the actual power frequency operating state through the no-load test before the transformer is put into operation.

S2: The transformer core model is established through matlab/Simulink, and the J-A dynamic mathematical model is shown in formula (1):

B=μ _o (H+M) (2)

M _an =M _s (coth(H _e /a)-(a/H _e )) (3)

In formulas (1) and (2), the magnetic field strength H is used as the input, the magnetic induction strength B is used as the output, M _s is the saturation magnetization, k is the irreversible coefficient, c is the reversible coefficient, α is the parameter characterizing the interaction between the magnetic domains, a is the correction parameter for the shape of the magnetization curve without hysteresis, ρ is the resistivity of the material, the unit is Ω m; d is the material size (diameter in the case of a cylinder, slice thickness in the case of a slice), the unit is m, the general distribution transformer silicon steel The thickness of the slice is 0.25-0.35mm; β is the geometric factor (16 for the cylinder, 6 for the slice, 20 for the sphere), and β=6 for the transformer; where; w is the width of the slice, in m; H _o is a parameter related to the domain wall, and takes the value of 0.0075; G is a dimensionless constant that is independent of the size, and takes the value of 0.1356. μ ₀ is the vacuum permeability, t is the time, M is the magnetization, the unit is A/m, δ is the parameter characterizing the impeding effect of the pinning effect in the magnetic field, when dH/dt>0, δ>0; when dH/dt <0, δ<0; _Man is the non-destructive magnetization, the unit is A/m, He is the effective magnetic field strength, the unit is A/m, and _H is the magnetic field strength, the unit is A/m.

Particle swarm optimization algorithm was used to fit the BH curve of the silicon steel sheet obtained in step 1, and five parameters of the modified JA dynamic model were obtained: saturation magnetization M _s , irreversible coefficient k, reversible coefficient c, parameter α characterizing the interaction between magnetic domains, no The correction parameter a of the shape of the hysteresis magnetization curve, and other parameters are set according to the actual transformer condition, and a dynamic model that can simulate the hysteresis loop of the transformer core under the actual operating state is obtained.

S3: Build the transformer winding model through matlab/Simulink; as shown in Figure 2, the winding model consists of the primary side power supply, the primary side impedance, the excitation impedance, and the secondary side power supply.

When the harmonic order is relatively low, the influence of proximity effect and skin effect on the AC winding is relatively small. For the transformer in the power network, the main analysis frequency is lower than the 23rd harmonic. In order to simplify the calculation, the present invention adopts the conventional transformer winding model, formula (2), the equivalent impedance of the primary side of the transformer winding at 50Hz is calculated from the transformer nameplate parameters. :

h is the harmonic order, the winding impedance changes with the harmonic order, R is the winding inductance, and X is the winding reactance.

As shown in Figure 3, the acquisition process of nonlinear inductance parameters is as follows:

According to the full current law

In formula (5), l is the average core magnetic circuit of the transformer, and N is the number of turns of the high-order side winding; the magnetic flux leakage is not considered (the single-frame core is regarded as a non-branched magnetic circuit), and it is considered that the magnetic field strength H on the magnetic circuit l is everywhere. are equal, so according to the full current law, there is a relationship between the excitation current _im and the magnetic field strength H:

According to the principle of energy disturbance, the coil in the circuit model generates the excitation current Δi under the action of the external power supply at a certain time to generate the flux linkage Δλ, and thus the voltage increment of the excitation port is obtained. to cancel the induced electromotive force in the coil. Then the externally provided excitation energy increment is ΔW ₁ =Δe _{m Δim} , namely:

ΔW ₁ =L _{eq Δim} ² (7)

Among them, L _eq is the equivalent inductance of the excitation branch.

In the magnetic field, the excitation current Δi causes the field quantity changes ΔB and ΔH, and the corresponding magnetic field energy increment is:

ΔW ₂ =∫ΔBΔH·dV (8)

Simultaneous equations (4) (5) (6) can be obtained through the JA model in step 2 to _{obtain the relationship between the excitation current im and the equivalent inductance L eq of} the excitation branch, and the iL function can be obtained through the matlab fitting toolbox using the Gaussian algorithm, That is, the parameter of excitation impedance Z _eq is changed by the change of excitation current _im ;

Among them, the i-L function is:

where a _j , b _j , c _j are different parameters, j=1,2,3,4,5,6,7,8;

Then calculate the excitation impedance according to the i-L function.

Collect and record the primary and secondary voltage and current data of the transformer, and modify the primary and secondary voltage and current parameters in the transformer winding model according to the data; through the Fourier series The primary side non-sinusoidal voltage and secondary side non-sinusoidal current are decomposed into sinusoidal fundamental voltage and current, odd sinusoidal harmonic voltage and current, respectively.

Input the primary side voltage source voltage up _p and the secondary side current source current i _user decomposed by _S4.1 , and set an initial value of the initial excitation current im less than 10% of the no-load excitation current (set a smaller value by yourself). The initial value of the excitation current im to start the calculation process, such as 0.05A), the primary side current i _p is _calculated by the iterative circuit model such as (9)(10)(11)(12):

i _p = i _user + i _m (9)

After iterative convergence, the primary side current _ip used to calculate the winding loss and the excitation current _im used to calculate the core loss under different harmonic orders can be obtained.

S5: Calculate the transformer winding loss through the relationship between the primary and secondary side impedance in the winding equivalent circuit and the flowing winding current, and calculate the real-time transformer core loss through the J-A model.

Calculate winding losses:

Transformer winding harmonic loss based on equation (3) can be obtained from equation (13):

h is the harmonic order, i _ph is the current generated by the h harmonic in the primary side current i _p .

The total winding loss can be calculated by formula (13) through the iterative primary side current i _p under different harmonic orders.

Calculate core loss:

Add the excitation current _im under different harmonic orders obtained through iteration, and substitute it into formula (5) (6) to obtain the input magnetic field strength H, and obtain the magnetic induction strength B required to calculate the core loss through formula (1) (2) (3) .

According to the theory of loss separation, transformer core loss can be divided into three parts, eddy current loss, hysteresis loss and additional loss caused by local eddy current between equipment structures:

P _Fe =P _ec +P _A +P _h (14)

Among them, P _Fe is the core loss, P _ec is the eddy current loss, P _A is the additional loss caused by the local eddy current between the device structures, and P _h is the hysteresis loss.

Under the condition of uniform penetration of the magnetic field, the classical eddy current loss can be obtained by solving Maxwell's equation, which is expressed as:

During the movement of the magnetic domain wall, microscopic local eddy currents will appear near the magnetic domain wall, causing eddy current loss, which is expressed as:

The size of the hysteresis loss per cycle is the area enclosed by the hysteresis B-H curve. The hysteresis loss per unit volume of core can be calculated by calculating the area of the hysteresis loop:

Ph = _∫BdH (17)

The total core loss data of the transformer can be obtained by adding the three losses.

The terms describing the positional relationship in the accompanying drawings are only used for exemplary illustration, and should not be construed as a limitation on this patent;

Obviously, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the embodiments of the present invention. For those of ordinary skill in the art, changes or modifications in other different forms can also be made on the basis of the above description. There is no need and cannot be exhaustive of all implementations here. Any modification, equivalent replacement and improvement made within the spirit and principle of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (9)

1. a transformer loss calculation method, is characterized in that, described method comprises the following steps: S1: Obtain the B-H curve of the transformer under the actual power frequency operating state through the no-load test before the transformer is put into operation; S2: Establish a J-A dynamic model, use the B-H curve to optimize the parameters of the J-A dynamic model, and obtain the J-A dynamic model used to simulate the hysteresis loop of the transformer core under actual operating conditions; S3: Establish the transformer winding model under harmonics, and calculate the transformer primary side impedance and transformer excitation impedance; S4: Collect and record the primary and secondary voltage and current data of the transformer, modify the primary and secondary voltage and current parameters in the transformer winding model according to the data; process the non-sinusoidal input through Fourier decomposition, and use the transformer winding model to obtain the winding current under real-time data and excitation current; S5: Calculate the transformer winding loss through the relationship between the primary and secondary side impedance in the winding equivalent circuit and the flowing winding current, and calculate the real-time transformer core loss through the J-A model. 2. transformer loss calculation method according to claim 1, is characterized in that, the J-A dynamic model in S2 is: M _an =M _s (coth(H _e /a)-(a/H _e )) B=μ _o (H+M) In the formula, the magnetic field intensity H is used as the input, the magnetic induction intensity B is the output, M _s is the saturation magnetization, k is the irreversible coefficient, c is the reversible coefficient, α is the parameter characterizing the interaction between magnetic domains, and a is the magnetization curve without hysteresis Correction parameters for shape, ρ is the resistivity of the material, in Ω m; d is the size of the material, in m; β is the geometric factor; where; w is the slice width, in m; H _o is related to the domain wall The parameter G is a dimensionless constant that is independent of size; μ ₀ is the vacuum permeability, t is the time, M is the magnetization, the unit is A/m, and δ is the parameter that characterizes the impeding effect of the pinning effect in the magnetic field, when dH /dt>0, δ>0; when dH/dt<0, δ<0; M _an is the non-destructive magnetization, the unit is A/m, He is the effective magnetic field strength, the unit is A/m, _H is the magnetic field strength, the unit A/m. 3. transformer loss calculation method according to claim 2, is characterized in that, the concrete process that utilizes B-H curve to optimize model parameter is: The particle swarm optimization algorithm was used to fit the BH curve of the silicon steel sheet obtained by S1, and five parameters of the modified JA dynamic model were obtained: saturation magnetization Ms, irreversible coefficient _k , reversible coefficient c, parameter α characterizing the interaction between magnetic domains, no The correction parameter a of the shape of the hysteresis magnetization curve, and the other parameters are set according to the actual transformer condition, and the JA dynamic model used to simulate the hysteresis loop of the transformer core under the actual operating state is obtained. 4. The transformer loss calculation method according to claim 1, wherein the transformer winding model in S3 comprises: primary side power supply, primary side impedance, excitation impedance, and secondary side power supply; The primary side power supply and the primary side impedance are connected in series; the series connected primary side power supply and the primary side impedance are connected in parallel with the excitation impedance and the secondary side power supply. 5. transformer loss calculation method according to claim 1, is characterized in that, the calculation formula of primary side impedance in S3 is: Among them, h is the harmonic order, R is the winding inductance, and X is the winding reactance. 6. transformer loss calculation method according to claim 1 is characterized in that, the calculation process of excitation impedance in S3 is: _S3.1 : Suppose there is no magnetic leakage, and the magnetic field strength H on the magnetic circuit l is equal everywhere; according to the law of total current, there is a relationship between the excitation current im and the magnetic field strength H: have to In the formula, l is the average core magnetic circuit of the transformer, and N is the number of turns of the high-order side winding; S3.2: According to the principle of energy disturbance, calculate the excitation energy increment provided by the outside, and the calculation formula is: ΔW ₁ =Δe _{m Δim} That is, ΔW ₁ =L _{eq Δim} ² Among them, _Δim is the excitation current generated by the coil in the circuit model under the action of an external power supply at a certain time, Δλ is the flux linkage generated by the excitation current Δi; Δe _m is the voltage increment of the excitation port; L _eq is the equivalent inductance of the excitation branch; S3.3: Calculate the energy increment generated by the magnetic field change caused by the excitation current in the magnetic field. The calculation formula is: ΔW ₂ =∫ΔBΔH·dV In the formula, ΔB is the magnetic induction intensity increment; ΔH is the magnetic field intensity increment; S3.4: Combine S3.1-S3.3, and obtain the relationship between the excitation current and the equivalent inductance L _eq of the excitation branch through the JA model in S2; then obtain the iL function through the Gaussian algorithm; The i-L function is: where a _j , b _j , c _j are different parameters, j=1,2,3,4,5,6,7,8; S3.5: Calculate the excitation impedance according to the i-L function. 7. The transformer loss calculation method according to claim 1, wherein S4 comprises the following steps: S4.1: Collect and record the primary and secondary voltage and current data of the transformer, and modify the primary and secondary voltage and current parameters in the transformer winding model according to the data; by Fourier series Decompose the primary side non-sinusoidal voltage and secondary side non-sinusoidal current into sinusoidal fundamental voltage and current, odd sinusoidal harmonic voltage and current respectively; S4.2: Input the primary side voltage source voltage up _p and the secondary side current source current i _user decomposed by _S4.1 , and set an initial value of the initial excitation current im less than 10% of the no-load excitation current, find The primary side current i _p , the calculation formula is: i _p = i _user + i _m S4.3: According to the primary side current, calculate the back EMF, the calculation formula is: S4.4: Find the excitation potential, the calculation formula is: S4.5: Calculate the excitation current: The calculation formula is: S4.7: Determine whether the excitation current converges; if it converges, go to S5; if not, go back to step S4.2. 8. The transformer loss calculation method according to claim 7, wherein the calculation formula of the total winding loss in step S5 is: Among them, i _ph is the current generated by the h harmonic in the primary side current i _p . 9. transformer loss calculation method according to claim 8, is characterized in that, the calculation process of iron core loss in step S5 is: _S5.1 : Add the excitation current im under different harmonic orders through iteration in S4, and substitute the following formula to obtain the input magnetic field H: S5.2: Calculate the magnetic induction intensity B through the J-A model; S5.3: Calculate the core loss of the transformer, the calculation formula is: P _Fe =P _ec +P _A +P _h P _h =∫BdH Among them, P _Fe is the core loss, P _ec is the eddy current loss, P _A is the additional loss caused by the local eddy current between the device structures, and P _h is the hysteresis loss.