CN112069655A - Loss calculation method for high-frequency high-power three-phase transformer - Google Patents

Loss calculation method for high-frequency high-power three-phase transformer Download PDF

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CN112069655A
CN112069655A CN202010774101.XA CN202010774101A CN112069655A CN 112069655 A CN112069655 A CN 112069655A CN 202010774101 A CN202010774101 A CN 202010774101A CN 112069655 A CN112069655 A CN 112069655A
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flux density
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陈彬
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China Three Gorges University CTGU
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Abstract

A method for calculating loss of high-frequency high-power three-phase transformer deduces winding current i of high-frequency three-phase transformer in connection mode of Y-Y type, Y-delta type and delta-delta type windingsLAAn expression of the amplitude of each order harmonic current component; calculating the alternating current resistance of the primary winding and the secondary winding under each order of harmonic frequency; summing the losses corresponding to the harmonic currents of each order to obtain a primary winding loss expression P of the flat copper wirewpSecondary winding loss expression Pws(ii) a Deriving core flux density BY(t)、B△(t) an expression; superposing the magnetic flux density waveforms generated by the primary winding and the secondary winding under the phase shift control to obtain the magnetic flux density B (t) waveform of the iron core under the load operation condition; under the phase shift control operation condition, the following calculation results are obtained: the core loss of the high-frequency three-phase transformer is based on the connection mode of Y-Y type, Y-delta type and delta-delta type windings. The method of the invention can realize fast loss of the high-frequency high-power three-phase transformerThe method can predict the core loss accurately, and lays a foundation for the subsequent optimization design of the core loss of the high-frequency three-phase transformer.

Description

Loss calculation method for high-frequency high-power three-phase transformer
Technical Field
The invention belongs to the field of high-frequency transformer loss prediction methods, and particularly relates to a high-frequency high-power three-phase transformer loss calculation method.
Background
A Solid State Transformer (SST) is a key component device in future renewable energy transportation and management systems. The solid-state transformer SST is composed of a rectifier on the input side, a dc converter stage and an inverter for ac voltage output. Currently, single-phase or three-phase isolated dual-active-bridge DC-DC converter (DAB-IBDC) suitable for high power transmission and satisfying power bidirectional free flow has been applied to the DC conversion stage of the solid-state transformer. Compared with a single-phase DC/DC converter topological structure, the three-phase DC/DC converter has more advantages, not only can greatly reduce the number of elements such as a high-frequency transformer, a switching device, a communication system and an auxiliary power supply, and reduce the volume, the weight and the cost of the solid-state transformer, but also can reduce a capacitance value for filtering direct current ripples, reduce circulating current power, and improve the efficiency and the power density of the solid-state transformer.
The high-frequency high-power three-phase transformer is a core electromagnetic element of the three-phase DC/DC converter, plays the roles of electrical isolation and voltage conversion, and can reduce the volume of the transformer by improving the working frequency. With the increase of working frequency and power and the reduction of transformer volume, the problems of loss and temperature rise of the high-frequency transformer become more obvious. The accurate solution of the winding and core losses is of guiding significance for the design of high-frequency high-power three-phase transformers.
The existing high-frequency winding loss calculation method can be mainly classified into two types: analytical methods and finite element methods.
1) In terms of analytical methods, the alternating current resistance under high frequency conditions is usually calculated by adopting a Dowlell equation and a corrected Ferreira formula, and the influence of skin effect and proximity effect is considered. For example, in 2009 spanish mendor technical research center i.villar, a harmonic current expression of a single-phase DC/DC converter is derived by using a fundamental wave analysis method, and ac resistance at each order of harmonic frequency is calculated by using a Dowell equation, thereby obtaining high-frequency winding loss. The current waveform of a three-phase DC/DC converter is more complicated, and the above method is not suitable depending on factors such as winding connection mode and phase shift angle.
2) And in the aspect of the finite element method, the winding loss is calculated by adopting the finite element method, the calculation precision is high, and the winding with any shape can be researched. For example, m.aminbahmani, university of charmmers industries, 2014, uses a finite element method to calculate the current density of a conductor region under a high frequency condition, so as to obtain the winding loss. However, in principle, the finite element method makes the skin depth small as the frequency increases, and the number of division units on the surface of the conductor must be smaller, which results in an increase in the amount of computation.
The existing high-frequency core loss calculation methods can also be summarized into two types: analytical methods and finite element methods.
The method comprises the following steps: in terms of analytical methods, many documents have been studied in recent years for methods for calculating the core loss of a high-frequency transformer in a single-phase DC/DC converter topology circuit. In a high-power single-phase DC/DC converter, the excitation voltage and current of a high-frequency transformer depend on a circuit topology structure and a control strategy, and are generally not standard sine waves but non-sine waves such as square waves, trapezoidal waves and the like. Various improved forms of correcting Steinmetz are deduced by Nico H.Baars, the Egyin Hotel science and technology university in 2016 according to non-sinusoidal magnetic flux density waveforms corresponding to square waves and trapezoidal waves, and the forms of the formulas are simple and convenient and are easy to use in engineering. Nils Soltau of the industry university of aachen 2014 adopts an improved generalized Steinmetz formula to calculate the core loss of the high-frequency three-phase transformer under a Y-Y type connection mode. The voltage waveform of the high-frequency three-phase transformer is related to the connection mode of three-phase windings, phase-shift control and the like, and the effectiveness of the correction formulas in the three-level and six-level step voltage and phase-shift control modes of the three-phase DC/DC converter is yet to be deeply researched.
Secondly, the step of: in the aspect of a finite element method, the North Carolina State university adopts a transient finite element method to calculate the instantaneous iron loss value of a high-frequency three-phase transformer, adopts an equivalent ellipse method to calculate the instantaneous hysteresis loss, utilizes a loss separation model to calculate the instantaneous eddy current loss and the residual loss, and can consider the possible nonuniformity of magnetic field distribution in an iron core.
Therefore, the loss calculation method of the high-frequency high-power three-phase transformer is provided for the topological structure of the solid-state transformer, the high-frequency winding loss and the core loss of the transformer are accurately predicted, and the design of the high-frequency high-power three-phase transformer is instructive.
Disclosure of Invention
Aiming at the high-frequency high-power three-phase transformer, the invention provides a loss calculation method of the high-frequency high-power three-phase transformer, which is a loss calculation method suitable for the high-frequency high-power three-phase transformer and provides support for the subsequent optimization design of the high-frequency high-power three-phase transformer by related formula derivation and specific parameter setting of the high-frequency high-power three-phase transformer. The method can be used for rapidly and accurately predicting the loss of the high-frequency high-power three-phase transformer and lays a foundation for the subsequent optimization design of the core loss of the high-frequency three-phase transformer.
The technical scheme adopted by the invention is as follows:
a loss calculation method for a high-frequency high-power three-phase transformer comprises the following steps:
the method comprises the following steps: deducing high-frequency three-phase transformer winding current i in the connection mode of Y-Y type, Y-delta type and delta-delta type windings by adopting a fundamental wave analysis methodLAAn expression of the amplitude of each order harmonic current component;
step two: calculating the alternating current resistance of the primary winding and the secondary winding under each order of harmonic frequency by combining a Dowlel equation; summing the losses corresponding to the harmonic currents of each order by using the superposition principle to obtain a primary winding loss expression P of the flat copper wirewpSecondary winding loss expression Pws；
Step three: according to the voltage waveforms under Y-type and delta-type connection, the relationship between the voltage and the magnetic flux density is combined to deduce the magnetic flux density B of the iron core under the corresponding excitation voltage waveformY(t)、BΔ(t) an expression;
step four: combining a winding connection mode of a high-frequency three-phase transformer, superposing magnetic flux density waveforms generated by primary and secondary windings under phase-shifting control to obtain a magnetic flux density B (t) waveform of the iron core under a load operation condition;
step five: obtaining a simplified analytical expression according to the waveform of the magnetic flux density B (t), and calculating the following parameters under the phase-shifting control operation condition: Y-Y type, Y-delta type and delta-delta type winding connection mode.
In the first step, the inductance L is deduced by adopting a fundamental wave analysis method according to an approximate equivalent circuit model of the isolated three-phase double-active full-bridge DC-DC converterσThe expansion of the corresponding voltage drop Δ U is:
Figure BDA0002617737070000031
in the formula, Δ UnAnd phinThe nth harmonic component amplitude and phase of the voltage drop Δ U, respectively; omega is angular frequency, omega-2 pi fs；
Combining the phasor diagram to obtain the inductance L in Y-Y type and delta-delta type connectionσThe calculation expression of the nth harmonic voltage amplitude of the voltage drop delta U is as follows:
Figure BDA0002617737070000032
in the formula:
Figure BDA0002617737070000033
is a VinThe nth harmonic voltage output by side inversion;
Figure BDA0002617737070000034
is a VoutSide inversion output is converted to VinSide nth harmonic voltage;
Figure BDA0002617737070000035
the phase shift angle between the gate control signals of the inversion and rectification side three-bridge arm converter is adopted.
In a Y-delta connection, the inductance LσThe calculation expression of the nth harmonic voltage amplitude of the voltage drop delta U is as follows:
Figure BDA0002617737070000036
ΔUnthe phase of (d) can be expressed as:
Figure BDA0002617737070000037
under the Y-Y type connection mode, the amplitude of the nth harmonic voltage is as follows:
Figure BDA0002617737070000041
in the formula: n is a radical ofwThe voltage transformation ratio of the primary winding and the secondary winding is obtained.
Under the Y-delta type connection mode, the amplitude of the nth harmonic voltage is as follows:
Figure BDA0002617737070000042
under the delta-delta type connection mode, the amplitude of the nth harmonic voltage is as follows:
Figure BDA0002617737070000043
due to the inductive current ILALag Δ UnIs 90, so the current through the inductor can be expressed as:
Figure BDA0002617737070000044
in the formula:
Figure BDA0002617737070000045
is a VinThe amplitude of the nth harmonic current output by the side inverter is related to the inverter output voltage and the inductance on the two sides.
Thus, the nth harmonic current magnitude can be expressed as:
Figure BDA0002617737070000046
in the second step: primary winding loss expression PwpSecondary winding loss expression Pws；
Figure BDA0002617737070000047
Figure BDA0002617737070000048
In the formula (I), the compound is shown in the specification,
Figure BDA0002617737070000051
the AC resistance coefficients of the primary winding and the secondary winding under the nth current harmonic are respectively; n represents the highest harmonic order of the non-sinusoidal current; n is a radical ofwRepresenting the turns ratio of the primary and secondary windings.
RwpDC、RwsDCThe DC resistances of the primary winding and the secondary winding are calculated as follows
Figure BDA0002617737070000052
Figure BDA0002617737070000053
In the formula, σwIs the conductivity of the winding conductor; n is a radical ofl1And Nl2Respectively the number of turns of each layer of the primary and secondary windings; m is1And m2Respectively the number of layers of the primary and secondary windings; MTL1And MTL2Respectively the average turn length of the primary and secondary windings; df1And df2The thickness of the flat copper wire is the original thickness of the secondary side flat copper wire; h isf1And hf2The width of the original secondary side flat copper wire is obtained.
In the second step, the calculation formulas of the alternating current resistance coefficients of the primary winding and the secondary winding under the nth current harmonic are respectively as follows:
Figure BDA0002617737070000054
Figure BDA0002617737070000055
in the formula，m1And m2Respectively the number of layers of the primary and secondary windings; mu.s0Is the permeability of the winding material; rwpnAnd RwsnAt nth harmonic frequency nf for primary and secondary windings respectivelysA lower alternating current resistance; rwpDCAnd RwsDCRespectively are direct current resistances of the primary winding and the secondary winding; delta1And Δ2The normalized thickness of the flat copper wire winding to the skin depth of the primary and secondary windings under the fundamental frequency component is respectively expressed as follows:
Figure BDA0002617737070000056
Figure BDA0002617737070000057
in the formula (d)f1And df2The thickness of the flat copper wire is the original thickness of the secondary side flat copper wire; h isf1And hf2The width of the original secondary side flat copper wire is obtained; n is a radical ofl1And Nl2Respectively the number of turns of each layer of the primary and secondary windings; h isw1And hw2The heights of the primary winding and the secondary winding are respectively; sigmawIs the copper conductivity; mu.s0Is magnetic permeability in vacuum, mu0＝4π×10-7H/m；fsThe frequency of the sinusoidally alternating current.
In the third step, the iron core magnetic flux density B under the corresponding excitation voltage waveform is derived according to the fact that the voltages of the six-level step wave and the three-level step wave under the Y-shaped and delta-shaped connection are in a piecewise linear waveform and the relation between the voltages and the magnetic flux densityY(t)、BΔThe expression of (t) is:
Figure BDA0002617737070000061
Figure BDA0002617737070000062
in the formula: the relationship between θ and t is θ ═ ω t.
BmYThe peak magnetic flux density under the excitation of the corresponding six-level step wave in the Y-shaped connection mode is shown; b ismΔThe peak magnetic flux density under the corresponding three-level step wave excitation in the delta connection mode is shown.
The expressions of the peak magnetic densities under the voltage excitation of the six-level step wave and the three-level step wave are respectively as follows:
Figure BDA0002617737070000063
Figure BDA0002617737070000064
in the formula: k is a radical ofcIs the core lamination coefficient; n is the number of winding turns; s is the sectional area of the iron core. VinThe direct current voltage of the input side of the DC/DC converter is shown; f denotes the operating frequency of the high frequency transformer.
In the fourth step, the magnetic flux density b (t) is represented by a piecewise function:
Figure BDA0002617737070000071
in the formula: t is the working period of the high-frequency transformer; u (t) is the instantaneous voltage.
In the fifth step, the simplified analytic expressions of the Steinmetz formula and various modified Steinmetz formulas are obtained according to the fact that the waveform of the magnetic flux density B (t) is a piecewise linear waveform, and the core loss P of the high-frequency three-phase transformer in a Y-Y type, Y-delta type and delta-delta type winding connection mode under the condition of phase-shift control operation can be calculated according to the simplified analytic expressionsc。
The method comprises the following steps: the simplified analytical calculation formula of the SE method is as follows:
Pc＝kfαBm β
in the formula: b ismPeak magnetic induction; f represents the operating frequency of the high-frequency transformer; k represents a core loss constant;α represents a core loss frequency coefficient; β represents a core loss magnetic flux density coefficient.
Secondly, the step of: the simplified analytical calculation formula of the MSE method is as follows:
Figure BDA0002617737070000072
in the formula: (B)j,tj) And (B)j+1,tj+1) Respectively is the j th and j +1 th break points of the piecewise linear magnetic flux density waveform; b ismaxAnd BminRespectively, a magnetic flux density maximum value and a magnetic flux density minimum value.
Bj+1、tj+1Respectively showing the magnitude and the time of the magnetic flux density corresponding to the break point of the j +1 th magnetic flux density curve; b isj、tjRespectively showing the magnitude and the time of the magnetic flux density corresponding to the folding point of the jth magnetic flux density curve; f denotes the operating frequency of the high frequency transformer.
③: the simplified analytical calculation formula of the GSE method is as follows:
Figure BDA0002617737070000073
and T is the working period of the high-frequency transformer.
kiFor intermediate variables, there are only simplified computational expressions, which are as follows:
Figure BDA0002617737070000081
fourthly, the method comprises the following steps: the simplified analytical calculation formula of the IGSE method is:
Figure BDA0002617737070000082
fifthly: the simplified analytical calculation formula of the WcSE method is as follows:
Figure BDA0002617737070000083
in the formula: b ismPeak magnetic induction; f represents the operating frequency of the high-frequency transformer; k represents a core loss constant; α represents a core loss frequency coefficient; β represents a core loss magnetic flux density coefficient; b isj+1、tj+1Respectively showing the magnitude and the time of the magnetic flux density corresponding to the break point of the j +1 th magnetic flux density curve; b isj、tjRespectively showing the magnitude and the time of the magnetic flux density corresponding to the folding point of the jth magnetic flux density curve.
The invention discloses a loss calculation method of a high-frequency high-power three-phase transformer, which has the technical effects that:
1): on the basis of analyzing an approximate equivalent circuit model and a phasor diagram of an isolated three-phase double-active full-bridge DC-DC converter in detail, a harmonic calculation expression and a winding loss calculation method of high-frequency three-phase transformer winding current in a Y-Y type, Y-delta type and delta-delta type winding connection mode are deduced by adopting a fundamental wave analysis method. The method can be applied to the high-frequency winding loss calculation of the high-frequency high-power three-phase transformer under the phase-shift control operation mode, and has the advantages of strong adaptability, convenience, rapidness and high engineering practical value.
2): and (4) deducing an iron core magnetic flux density waveform expression under the corresponding excitation voltage waveform by combining the six-level step wave and three-level step wave voltages under Y-type and delta-type connection. The simplified analytical expressions of various modified Steinmetz formulas are obtained by combining the characteristics of the piecewise linear magnetic flux density waveform, so that the core loss of the high-frequency three-phase transformer under the running conditions of a Y-Y type, a Y-delta type and a delta-delta type winding connection mode and a phase-shifting control mode can be calculated, the method is convenient and fast, and the engineering application is facilitated.
3): and comparing the analytic calculation result with the finite element simulation and experimental measurement result. The deviation between the analytic calculation result of the winding loss and the finite element calculation result is found to be less than 8%, the error between the IGSE and the measured value in the iron core loss analytic calculation method is the minimum, the global average relative error is 2.3%, and the rapidity and the accuracy of transformer loss calculation are considered to realize the real-time prediction of the transformer loss.
Drawings
FIG. 1(a) is a graph of steady state voltage and current waveforms for a Y-Y connected DAB3-IBDC converter;
FIG. 1(b) is a graph of steady state voltage and current waveforms for a DAB3-IBDC converter connected in a Y- Δ configuration;
FIG. 1(c) is a graph of steady state voltage and current waveforms for a DAB3-IBDC converter connected in a delta-delta configuration.
FIG. 2 is an approximate equivalent circuit diagram of a DAB3-IBDC converter.
Fig. 3 is a fundamental voltage current phasor diagram of a high-frequency high-power three-phase transformer.
FIG. 4(a) is a waveform diagram of magnetic flux density under six-step voltage wave excitation;
fig. 4(b) is a waveform diagram of magnetic flux density under the excitation of three-step voltage wave.
FIG. 5(a) is a magnetic flux density waveform diagram of a high-frequency high-power three-phase transformer core under Y-Y type connection;
FIG. 5(b) is a magnetic flux density waveform diagram of a high-frequency high-power three-phase transformer core under Y-delta connection;
fig. 5(c) is a magnetic flux density waveform diagram of a high-frequency high-power three-phase transformer core under delta-delta connection.
FIG. 6(1) is a schematic structural diagram of a high-frequency high-power three-phase transformer;
fig. 6(2) is a partially enlarged view of fig. 6 (1).
FIG. 7(a1) is a primary side current waveform diagram of the A-phase winding under Y-Y connection;
fig. 7(a2) is a graph showing the amplitude of each harmonic current at the primary side of the a-phase winding in the Y-Y connection.
FIG. 7(b1) is a primary side current waveform diagram of the A-phase winding under Y-delta connection;
FIG. 7(b2) is a graph showing the amplitude of each harmonic current at the primary side of the A-phase winding in the Y-Delta connection.
FIG. 7(c1) is a waveform diagram of the primary side current of the A-phase winding in a delta-delta connection;
fig. 7(c2) is a graph showing the amplitude of each harmonic current at the primary side of the a-phase winding in the Δ - Δ connection.
Fig. 8 is a graph of winding loss as a function of phase shift angle for different connection modes.
FIG. 9(a) is a diagram showing the result of finite element calculation of the loss density of the Y-Y connection high-frequency transformer under phase shift control;
FIG. 9(b) is a diagram showing the result of finite element calculation of the loss density of the Y-delta type connected high-frequency transformer under phase shift control;
FIG. 9(c) is a view showing the result of finite element calculation of loss density of a Δ - Δ type connected high-frequency transformer under phase shift control.
FIG. 10(a) is a graph of core loss for a six-level step voltage wave at different peak flux densities under no-load conditions;
fig. 10(b) is a core loss diagram of a three-level step voltage wave under no-load condition at different peak magnetic densities.
Fig. 11 is a schematic diagram of a core loss measurement system.
FIG. 12(a) is a graph of core loss with phase shift angle for a Y-Y connection;
FIG. 12(b) is a graph of core loss with phase shift angle for a Y-delta connection;
FIG. 12(c) is a graph of core loss with phase shift angle for a Δ - Δ connection.
Detailed Description
A loss calculation method for a high-frequency high-power three-phase transformer specifically comprises the following steps:
the first step is as follows: calculating harmonic current:
in the DAB3-IBDC converter, the high frequency three phase transformer winding currents are not sinusoidal but rather are non-sinusoidal periodic currents with respect to phase shift angle, voltage waveform, and connection scheme, as shown in fig. 1(a), 1(b), and 1 (c). The method is combined with an approximate equivalent circuit model and a phasor diagram of the DAB3-IBDC converter, and a fundamental wave analysis method is adopted to obtain a winding harmonic current analysis calculation method suitable for the high-frequency three-phase transformer. When the winding resistance of the high-frequency three-phase transformer is far smaller than the leakage inductance and the excitation inductance is far larger than the leakage inductance, the approximate equivalent circuit of the converter can be obtained according to a fundamental wave analysis method. With A phase power from VinSide transfer to VoutSide example, when uASLead uas', the approximate equivalent circuit under phase shift control is shown in FIG. 2, the phasor diagram is shown in FIG. 3, and the voltage is uas' reference vector.
In fig. 3: u. ofasIs' a VoutThe side inverting output is converted into VinThe voltage at the back side;
Figure BDA0002617737070000101
and
Figure BDA0002617737070000102
is a voltage uASAnd uas' amplitude of fundamental component; l isσTo reduce to VinLateral leakage inductance; Δ U is leakage inductance drop;
Figure BDA0002617737070000103
gamma and phi are fundamental voltages respectively
Figure BDA0002617737070000104
And
Figure BDA0002617737070000105
Δ U.
Firstly, a trigonometric function expansion of Fourier series is utilized to obtain f for fundamental frequencysA phase shift angle of
Figure BDA0002617737070000109
The original secondary side voltage is subjected to Fourier decomposition, and the result is as follows:
Figure BDA0002617737070000106
in the formula:
Figure BDA0002617737070000107
is a VinThe nth harmonic voltage output by side inversion;
Figure BDA0002617737070000108
is a VoutSide inversion output is converted to VinThe nth harmonic voltage of the side.
Under the Y-Y type connection mode, the amplitude of the nth harmonic voltage is as follows:
Figure BDA0002617737070000111
in the formula: n is a radical ofwThe voltage transformation ratio of the primary winding and the secondary winding is obtained.
Under the Y-delta type connection mode, the amplitude of the nth harmonic voltage is as follows:
Figure BDA0002617737070000112
under the delta-delta type connection mode, the amplitude of the nth harmonic voltage is as follows:
Figure BDA0002617737070000113
in the equivalent circuit diagram of FIG. 2, the inductance LσThe expansion of the corresponding voltage drop Δ U is:
Figure BDA0002617737070000114
in the formula: delta UnAnd phinThe nth harmonic component magnitude and phase of the voltage drop au, respectively.
As can be seen from the phasor diagram shown in FIG. 3, the inductance L is shown in the Y-Y and Δ - Δ connectionsσThe calculation expression of the nth harmonic voltage amplitude of the voltage drop delta U is as follows:
Figure BDA0002617737070000115
similarly, the Y-delta connection medium inductance LσThe calculation expression of the nth harmonic voltage amplitude of the voltage drop delta U is as follows:
Figure BDA0002617737070000116
ΔUnthe phase of (d) can be expressed as:
Figure BDA0002617737070000121
current I due to inductanceLALag Δ UnIs 90, so the current through the inductor can be expressed as
Figure BDA0002617737070000122
In the formula:
Figure BDA0002617737070000123
is a VinThe amplitude of the nth harmonic current output by the side inverter is related to the inverter output voltage and the inductance on the two sides.
As can be seen from fig. 2, the nth harmonic current amplitude can be expressed as:
Figure BDA0002617737070000124
the second step is as follows: winding loss calculation under non-sinusoidal excitation:
calculating the current amplitude of each order of harmonic wave by adopting a formula (11), and calculating the winding loss under the single order of harmonic wave current respectively; and summing the losses corresponding to the harmonic currents of each order by using a superposition principle to further obtain the winding loss of the high-frequency three-phase transformer in the DAB3-IBDC converter, wherein the calculation formula of the winding loss is as follows:
Figure BDA0002617737070000125
Figure BDA0002617737070000126
in the formula (I), the compound is shown in the specification,
Figure BDA0002617737070000127
the AC resistance coefficients of the primary winding and the secondary winding under the nth current harmonic are respectively; rwpDC、RwsDCThe DC resistances of the primary winding and the secondary winding are calculated as follows
Figure BDA0002617737070000128
Figure BDA0002617737070000131
In the formula, σwIs the conductivity of the winding conductor; n is a radical ofl1And Nl2Respectively the number of turns of each layer of the primary and secondary windings; m is1And m2Respectively the number of layers of the primary and secondary windings; MTL1And MTL2Respectively the average turn length of the primary and secondary windings; df1And df2The thickness of the flat copper wire is the original thickness of the secondary side flat copper wire; h isf1And hf2The width of the original secondary side flat copper wire is obtained.
The calculation formula of the alternating current resistance coefficient of the primary winding and the secondary winding under the nth current harmonic is respectively as follows:
Figure BDA0002617737070000132
Figure BDA0002617737070000133
in the formula, m1And m2Respectively the number of layers of the primary and secondary windings; rwpnAnd RwsnAt nth harmonic frequency nf for primary and secondary windings respectivelysA lower alternating current resistance; rwpDCAnd RwsDCRespectively are direct current resistances of the primary winding and the secondary winding; delta1And Δ2The normalized thickness of the flat copper wire winding to the skin depth of the primary and secondary windings under the fundamental frequency component is respectively expressed as follows:
Figure BDA0002617737070000134
Figure BDA0002617737070000135
in the formula (d)f1And df2The thickness of the flat copper wire is the original thickness of the secondary side flat copper wire; h isf1And hf2The width of the original secondary side flat copper wire is obtained; n is a radical ofl1And Nl2Respectively the number of turns of each layer of the primary and secondary windings; h isw1And hw2The heights of the primary winding and the secondary winding are respectively; sigmawIs the copper conductivity; mu.s0Is magnetic permeability in vacuum, mu0＝4π×10-7H/m；fsThe frequency of the sinusoidally alternating current.
The third step: an iron core magnetic flux density expression under phase shift control:
the core loss is closely related to the magnetic flux density of the core. From the piecewise linear voltage ripples of fig. 1(a), 1(B), and 1(c), it can be seen that the magnetic flux densities corresponding to two typical voltage ripples can also be expressed by a piecewise function, based on the relationship between the voltage U and the magnetic flux density B shown in the equation (20).
Figure BDA0002617737070000136
Fig. 4(a) and 4(b) show steady-state voltage and core flux waveforms in a sinusoidal voltage wave, a six-level ladder voltage wave (Y-connection), or a three-level ladder voltage wave (Δ -connection), respectively. As can be seen from fig. 4(a) and 4(b), under six-level or three-level step voltage excitation, both the voltage and the magnetic flux density are piecewise linear waveforms, which can be expressed by piecewise linear functions. Under the condition of load operation, the three-bridge arm voltage source at two sides of the converter has a phase shift angle of
Figure BDA0002617737070000142
Two sets of non-sinusoidal voltages. Will shift the angle of phase to
Figure BDA0002617737070000143
The magnetic flux density waveforms generated by the primary and secondary windings are superposed, so that the actual magnetic flux density waveforms of the high-frequency high-power three-phase transformer core with different connection modes under the load operation condition can be obtained, as shown in fig. 5(a), 5(b) and 5(c) respectively.
The fourth step: core loss calculation under non-sinusoidal excitation:
for the core loss under sine wave excitation, the most widely used engineering is the Steinmetz formula (SE for short), as follows:
Pc＝kfαBm β (20)
in the formula: pcIs the core loss density; b ismPeak magnetic induction; f represents the operating frequency of the high-frequency transformer; k represents a core loss constant; α represents a core loss frequency coefficient; β represents a core loss magnetic flux density coefficient.
In order to calculate the core loss under non-sinusoidal excitation, many scholars have developed on the basis of the SE formula. Several SE-based correction methods are reported in the literature, such as Steinmetz correction formula (MSE), generalized Steinmetz formula (GSE), modified generalized Steinmetz formula (IGSE), Steinmetz form factor formula (WcSE), and the like. These SE correction methods improve the accuracy of core loss calculation under non-sinusoidal voltage wave excitation to some extent. However, the working mode of the high-frequency three-phase transformer is more complex, and no literature clearly indicates which method is most suitable for solving the core loss of the high-frequency three-phase transformer. Therefore, a simplified analytical calculation formula of the correction method is derived by combining the core magnetic flux density waveform diagrams given in fig. 5(a), fig. 5(b) and fig. 5(c), and as shown in table 1, the core losses of different phase shift angles and different winding connection modes can be directly calculated by using the loss coefficients under sinusoidal excitation.
TABLE 1 iron core loss calculation expression
Figure BDA0002617737070000141
Figure BDA0002617737070000151
In Table 1, (B)j,tj) Is the jth break point of the piecewise linear magnetic flux density waveform; b ismaxAnd BminRespectively as the maximum value and the minimum value of the magnetic flux density; k is a radical ofiThe expression of (a) is as follows:
Figure BDA0002617737070000152
the fifth step: the method comprises the following steps:
1) a high-frequency high-power three-phase transformer test model;
aiming at three high-frequency three-phase transformers with the rated capacity of 15kW, the voltage level of 500V/500V and the working frequency of 5kHz, the winding loss and the core loss are obtained by adopting methods of analytical calculation, finite element simulation and experimental measurement, and the accuracy of the analytical calculation method is verified by comparing the analytical calculation value with a simulated value and a measured value. The winding connection modes of the high-frequency three-phase transformer are Y-Y type, Y-delta and delta-delta respectively, the topological structure of the iron core of the high-frequency three-phase transformer is three-phase five-column type (three-frame type), the structural schematic diagram is shown in fig. 6(1) and fig. 6(2), and the main structural parameters are shown in table 2.
TABLE 2 high-frequency three-phase transformer core loss and winding loss comparison
Geometric dimension Y-Y type connection Y-delta type connection Connection of the delta-delta type
(A/B/C/D)mm 18/40/43/68.28 18/34/77/81.64 18/50/52/73.56
(A/B/C/D1)/mm 18/40/43/36.64 18/34/77/43.32 18/50/52/39.28
m1×N l1 3×8 2×13 4×10
m2×N l2 4×6 4×15 5×8
(df1×hf1)/mm 1×4 1×5 1×4
(df2×hf2)/mm 1×4 1×4 1×4
2) And (3) calculating the winding loss:
the phase shift angles at both sides of the original secondary side are taken as
Figure BDA0002617737070000161
For example, the primary side current i of the phase A winding of the high-frequency three-phase transformer is obtained by simulationLAThe current waveform and the spectral characteristics thereof are shown in fig. 7(a1), fig. 7(a2), fig. 7(b1), fig. 7(b2), fig. 7(c1), and fig. 7(c 2). By using the given harmonic current expression, the amplitude of each order harmonic current component of the current on the primary side of the A-phase winding can be calculated.
And calculating the high-frequency winding loss under different phase shift angles according to a given winding loss expression under non-sinusoidal wave excitation, wherein the value range of the phase shift angle is pi/24-pi/2. Fig. 8 compares the total loss of the primary and secondary windings of three high-frequency three-phase transformers with the change of the phase shift angle in different winding connection modes. The solid line represents the analytical calculations and the dashed line represents the simulated values. FIG. 9(a), FIG. 9(b) and FIG. 9(c) show three high frequency three-phase transformers at phase shifting angles
Figure BDA0002617737070000162
And (5) a lower loss density simulation result. As can be seen from fig. 9(a), 9(b) and 9(c), the loss density distribution of the primary and secondary windings in the three connection modes is approximately the same, wherein the loss density of the Y- Δ connection is the largest, and the Δ - Δ connection is the smallest after the Y-Y connection, which is mainly caused by the fact that the leakage magnetic field in the primary and secondary isolation channels is too large due to the asymmetric winding structure of the Y- Δ connection.
3) Calculating the iron core loss:
simplified analytical calculations incorporating the various modified SE equations of Table 1, and the loss coefficient C of the nanocrystalline materialm＝4.74×10-5Core loss was calculated at a frequency of 5kHz and a peak magnetic induction of 0.1 to 1T, with α being 1.57 and β being 1.95, as shown in fig. 10(a) and 10 (b). The simulation value is used as a reference, the concept of global average relative error AUD is introduced to carry out error analysis on various SE formulas, and the result is shown in Table 3. As can be seen from table 3, the AUD value between the analytic value obtained by the IGSE formula and the simulated value in the analytic calculation method is the minimum. Therefore, the method for calculating the core loss of the high-frequency three-phase transformer by adopting the IGSE simplified calculation analytic formula is more preciseAnd (8) determining.
TABLE 3 Global mean relative error comparison of calculated values to simulated values
Method of producing a composite material SE MSE GSE IGSE WcSE
Six step wave AUD (%) 8.46 3.16 18.42 2.21 5.59
Three step wave AUD (%) 8.29 2.93 16.71 2.07 4.72
In order to research the influence rule of the phase shift angle on the core loss, the peak magnetic density B of the core magnetic flux waveform under a six-level step voltage wave (Y-type connection) or a three-level step voltage wave (delta-type connection) is usedmYAnd BmΔKeeping the phase shift angle at 0.5T, the value interval of the phase shift angle is pi/24-pi/2, and the step length is pi/24. And calculating the change rule of the iron core loss along with the phase shift angle under different winding connection modes by adopting a magnetic density waveform expression and an iron core loss density expression given in tables 2-4 and a transient finite element calculation method. The phase shift angles at both sides of the original secondary side are taken as
Figure BDA0002617737070000171
For example, fig. 9(a), 9(b), and 9(c) show the core loss density simulation results of three high-frequency three-phase transformers under the phase-shift control mode. Fig. 12(a), 12(b) and 12(c) compare the core loss analysis calculation results and finite element simulation results with the phase shift angle under different winding connection modes.
As can be seen from fig. 12(a), 12(b), and 12(c), the core loss of the high-frequency three-phase transformer decreases as the phase shift angle increases, mainly because the magnetic flux density generated by the primary and secondary windings is superimposed to obtain the actual magnetic flux density waveform, and the actual magnetic flux density peak value decreases as the phase shift angle increases. Secondly, the core loss under Y-Y type connection is minimum, and the delta-delta type connection is maximum after Y-delta type connection. When the phase shift angle is larger than pi/3, the iron core loss reduction trend of the Y-Y type and the delta-delta type connection modes is increased; the core loss under Y-delta connection is slowly reduced when the phase shift angle is less than pi/6, and the core loss is obviously reduced when the phase shift angle is more than pi/6.

Claims (8)

1. A loss calculation method for a high-frequency high-power three-phase transformer is characterized by comprising the following steps:
the method comprises the following steps: deducing the winding current i of the high-frequency three-phase transformer in the connection mode of Y-Y type, Y-delta type and delta-delta type windings by adopting a fundamental wave analysis methodLAAn expression of the amplitude of each order harmonic current component;
step two: calculating the alternating current resistance of the primary winding and the secondary winding under each order of harmonic frequency by combining a Dowlel equation; summing the losses corresponding to the harmonic currents of each order by using the superposition principle to obtain a primary winding loss expression P of the flat copper wirewpSecondary winding loss meterExpression Pws；
Step three: according to the voltage waveforms under Y-type and delta-type connection and the relation between voltage and magnetic flux density, the magnetic flux density B of the iron core under the corresponding excitation voltage waveform is deducedY(t)、B△(t) an expression;
step four: combining a winding connection mode of a high-frequency three-phase transformer, superposing magnetic flux density waveforms generated by primary and secondary windings under phase-shifting control to obtain a magnetic flux density B (t) waveform of the iron core under a load operation condition;
step five: obtaining a simplified analytical expression according to the waveform of the magnetic flux density B (t), and calculating the following parameters under the phase-shifting control operation condition: the core loss of the high-frequency three-phase transformer is based on the connection mode of Y-Y type, Y-delta type and delta-delta type windings.
2. The loss calculation method of the high-frequency high-power three-phase transformer according to claim 1, characterized in that: in the first step, the inductance L is deduced by adopting a fundamental wave analysis method according to an approximate equivalent circuit model of the isolated three-phase double-active full-bridge DC-DC converterσThe expansion of the corresponding voltage drop Δ U is:
Figure FDA0002617737060000011
in the formula, Δ UnAnd phinThe nth harmonic component amplitude and phase of the voltage drop Δ U, respectively; omega is angular frequency, omega-2 pi fs；
Combining with the phasor diagram, the inductance L in the Y-Y type and delta-delta type connection can be obtainedσThe calculation expression of the nth harmonic voltage amplitude of the voltage drop delta U is as follows:
Figure FDA0002617737060000012
in the formula:
Figure FDA0002617737060000013
is a VinThe nth harmonic voltage output by side inversion;
Figure FDA0002617737060000014
is a VoutSide inversion output is converted to VinSide nth harmonic voltage;
Figure FDA0002617737060000015
the phase shift angle between gate control signals of the inverter and rectifier side three-bridge arm converter is adopted;
in a Y-delta connection, the inductance LσThe calculation expression of the nth harmonic voltage amplitude of the voltage drop delta U is as follows:
Figure FDA0002617737060000021
ΔUnthe phase of (d) can be expressed as:
Figure FDA0002617737060000022
under the Y-Y type connection mode, the amplitude of the nth harmonic voltage is as follows:
Figure FDA0002617737060000023
in the formula: n is a radical ofwThe voltage transformation ratio of the primary winding and the secondary winding is obtained;
under the Y-delta type connection mode, the amplitude of the nth harmonic voltage is as follows:
Figure FDA0002617737060000024
under the delta-delta type connection mode, the amplitude of the nth harmonic voltage is as follows:
Figure FDA0002617737060000025
due to the inductive current ILALag Δ UnIs 90 deg., so the current through the inductor can be expressed as:
Figure FDA0002617737060000026
in the formula:
Figure FDA0002617737060000027
is a VinThe nth harmonic current amplitude of the side inversion output is related to the inversion output voltage and the inductance on the two sides;
thus, the nth harmonic current magnitude can be expressed as:
Figure FDA0002617737060000031
3. the loss calculation method of the high-frequency high-power three-phase transformer according to claim 1, characterized in that: in the second step: primary winding loss expression PwpSecondary winding loss expression Pws；
Figure FDA0002617737060000032
Figure FDA0002617737060000033
In the formula (I), the compound is shown in the specification,
Figure FDA0002617737060000034
the AC resistance coefficients of the primary winding and the secondary winding under the nth current harmonic are respectively; n represents non-positiveThe highest harmonic order of the string current; n is a radical ofwRepresenting the turns ratio of the primary winding and the secondary winding;
RwpDC、RwsDCthe DC resistances of the primary winding and the secondary winding are calculated as follows
Figure FDA0002617737060000035
Figure FDA0002617737060000036
In the formula, σwIs the conductivity of the winding conductor; n is a radical ofl1And Nl2Respectively the number of turns of each layer of the primary and secondary windings; m is1And m2Respectively the number of layers of the primary and secondary windings; MTL1And MTL2Respectively the average turn length of the primary and secondary windings; df1And df2The thickness of the flat copper wire is the original thickness of the secondary side flat copper wire; h isf1And hf2The width of the original secondary side flat copper wire is obtained.
4. The loss calculation method of the high-frequency high-power three-phase transformer according to claim 3, characterized in that: in the second step, the calculation formulas of the alternating current resistance coefficients of the primary winding and the secondary winding under the nth current harmonic are respectively as follows:
Figure FDA0002617737060000037
Figure FDA0002617737060000038
in the formula, m1And m2Respectively the number of layers of the primary and secondary windings; mu.s0Is the permeability of the winding material; rwpnAnd RwsnAt nth harmonic frequency nf for primary and secondary windings respectivelysA lower alternating current resistance; rwpDCAnd RwsDCRespectively are direct current resistances of the primary winding and the secondary winding; delta1And Δ2The normalized thickness of the flat copper wire winding to the skin depth of the primary and secondary windings under the fundamental frequency component is respectively expressed as follows:
Figure FDA0002617737060000041
Figure FDA0002617737060000042
in the formula (d)f1And df2The thickness of the flat copper wire is the original thickness of the secondary side flat copper wire; h isf1And hf2The width of the original secondary side flat copper wire is obtained; n is a radical ofl1And Nl2Respectively the number of turns of each layer of the primary and secondary windings; h isw1And hw2The heights of the primary winding and the secondary winding are respectively; sigmawIs the copper conductivity; mu.s0Is magnetic permeability in vacuum, mu0＝4π×10-7H/m；fsThe frequency of the sinusoidally alternating current.
5. The loss calculation method of the high-frequency high-power three-phase transformer according to claim 1, characterized in that: in the third step, the iron core magnetic flux density B under the corresponding excitation voltage waveform is derived according to the fact that the voltages of six-level step waves and three-level step waves under the Y-type and delta-type connection are piecewise linear waveforms and the relation between the voltages and the magnetic flux densityY(t)、B△The expression of (t) is:
Figure FDA0002617737060000043
Figure FDA0002617737060000051
in the formula: the relation between theta and t is theta-t;
BmYthe peak magnetic flux density under the excitation of the corresponding six-level step wave in the Y-shaped connection mode is shown; b ismΔThe peak magnetic flux density under the corresponding three-level step wave excitation in a delta-type connection mode is shown;
the expressions of the peak magnetic densities under the voltage excitation of the six-level step wave and the three-level step wave are respectively as follows:
Figure FDA0002617737060000052
Figure FDA0002617737060000053
in the formula: k is a radical ofcIs the core lamination coefficient; n is the number of winding turns; s is the sectional area of the iron core; vinThe direct current voltage of the input side of the DC/DC converter is shown; f denotes the operating frequency of the high frequency transformer.
6. The loss calculation method of the high-frequency high-power three-phase transformer according to claim 1, characterized in that: in the fourth step, the magnetic flux density b (t) is represented by a piecewise function:
Figure FDA0002617737060000054
in the formula: t is the working period of the high-frequency transformer; u (t) is the instantaneous voltage.
7. The loss calculation method of the high-frequency high-power three-phase transformer according to claim 1, characterized in that: in the fifth step, the simplified analytic expressions of the Steinmetz formula and various modified Steinmetz formulas are obtained according to the fact that the waveform of the magnetic flux density B (t) is a piecewise linear waveform, and the core loss P of the high-frequency three-phase transformer of the Y-Y type, the Y-delta type and the delta-delta type winding connection modes under the phase-shifting control operation condition can be calculated according to the simplified analytic expressionsc。
8. The loss calculation method of the high-frequency high-power three-phase transformer according to claim 7, characterized in that: in the fifth step, the first step is that,
the method comprises the following steps: the simplified analytical calculation formula of the SE method is as follows:
Pc＝kfαBm β
in the formula: b ismPeak magnetic induction; f represents the operating frequency of the high-frequency transformer; k represents a core loss constant; α represents a core loss frequency coefficient; β represents a core loss magnetic flux density coefficient;
secondly, the step of: the simplified analytical calculation formula of the MSE method is as follows:
Figure FDA0002617737060000061
in the formula: (B)j,tj) And (B)j+1,tj+1) Respectively is the j th and j +1 th break points of the piecewise linear magnetic flux density waveform; b ismaxAnd BminThe maximum value and the minimum value of the magnetic flux density are respectively;
Bj+1、tj+1respectively showing the magnitude and the time of the magnetic flux density corresponding to the break point of the j +1 th magnetic flux density curve; b isj、tjRespectively showing the magnitude and the time of the magnetic flux density corresponding to the folding point of the jth magnetic flux density curve; f represents the operating frequency of the high-frequency transformer;
③: the simplified analytical calculation formula of the GSE method is as follows:
Figure FDA0002617737060000062
t is the working period of the high-frequency transformer;
kifor intermediate variables, the calculation expression is as follows:
Figure FDA0002617737060000063
fourthly, the method comprises the following steps: the simplified analytical calculation formula of the IGSE method is:
Figure FDA0002617737060000071
fifthly: the simplified analytical calculation formula of the WcSE method is as follows:
Figure FDA0002617737060000072
in the formula: b ismPeak magnetic induction; f represents the operating frequency of the high-frequency transformer; k represents a core loss constant; α represents a core loss frequency coefficient; β represents a core loss magnetic flux density coefficient; b isj+1、tj+1Respectively showing the magnitude and the time of the magnetic flux density corresponding to the break point of the j +1 th magnetic flux density curve; b isj、tjRespectively showing the magnitude and the time of the magnetic flux density corresponding to the folding point of the jth magnetic flux density curve.
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