CN110442895B - High-frequency transformer electromagnetic transient equivalent modeling method considering capacitance effect - Google Patents
High-frequency transformer electromagnetic transient equivalent modeling method considering capacitance effect Download PDFInfo
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Abstract
The invention designs An electromagnetic transient equivalent modeling method (An electromagnetic transient equivalent modeling method for high-frequency transformer configuration effect) considering capacitance effect. The method comprises six steps, according to equivalent parameters of magnetic coupling of the transformer and capacitance effect representing between conductors, a backward Euler method discretizes inductance, a capacitance expression and electrical two-port equivalent conditions, and provides an electromagnetic transient modeling method of the single-phase double-winding high-frequency transformer considering the capacitance effect. The equivalent modeling method provided by the invention provides a new idea for designing a high-frequency transformer module with kilohertz order in offline simulation software.
Description
Technical Field
The invention relates to an electromagnetic transient equivalent modeling method of a high-frequency transformer considering a capacitance effect, and belongs to the field of modeling and simulation of power equipment.
Background
The high-power DC-DC converter containing the high-frequency transformer magnetic coupling can realize flexible transmission and control of large-scale direct current energy, simultaneously ensures electrical isolation of two sides of the system, and becomes core equipment for constructing a direct current power grid together with a high-voltage direct current circuit breaker, a direct current cable, a direct current converter valve and the like. The high-frequency transformer can realize the electrical isolation and the voltage grade conversion of two sides of the system, and is a key link for manufacturing the magnetic coupling DC-DC converter.
Under the condition of meeting the switching loss limit of a power electronic switching device and the insulation requirement of a transformer, the volume of the transformer can be greatly reduced by improving the working frequency. For DC-DC converters with bridge topology, the operating frequency of the high frequency transformer can reach thousands to tens of kilohertz. As the operating frequency increases, the capacitive effects associated with the internal structure of the transformer will not be negligible. The existing classic three-capacitor characterization model is simple in structure and few in capacitance parameters, and is widely applied to the fields of transformer dynamic circuit analysis, transformer port characteristic numerical simulation and the like. However, in the currently used electromagnetic transient simulation software, there is no high-frequency transformer module that is completely packaged and represents the capacitive effect. The invention provides a single-phase double-winding high-frequency transformer electromagnetic transient equivalent modeling method considering a capacitance effect on the basis of a discretization trapezoidal numerical integration method aiming at an equivalent modeling scene of a high-frequency transformer.
Disclosure of Invention
The invention provides an electromagnetic transient equivalent modeling method of a single-phase double-winding high-frequency transformer considering capacitance effect, which comprises the following steps:
step 1: deducing to obtain a self-inductance parameter and a mutual inductance parameter which are related to the voltage-current relationship of the transformer according to a leakage reactance per unit value and an excitation current per unit value obtained by a standard transformer experiment; according to the measurement of the parasitic capacitance of the existing experiment, the equivalent parameter of the lumped capacitance of the winding layer is obtained, so that the equivalent parameter of the transformer which is magnetically coupled and reflects the influence of the parasitic capacitance is determined;
step 2: firstly, discretizing an inductor by using a trapezoidal integration method, and converting a differential-voltage expression of current into a current-voltage expression related to a historical voltage value at the previous moment so as to convert the current-voltage expression into an electromagnetic transient phenomenon of a simulation transformer at a discrete time point;
and step 3: then designing a circuit reflecting the port current-voltage expression in the step 2, namely a decoupled controlled current source equivalent circuit, wherein the transformation ratio is contained in the conductance parameter;
and 4, step 4: and (3) discretizing the capacitor obtained in the step (1) by utilizing a trapezoidal integration method again to obtain a form that the equivalent historical current source and the equivalent conductance at the previous moment are connected in parallel, and accessing the equivalent circuit obtained in the step (3) to further obtain a corrected transformer two-port equivalent circuit.
And 5: and adding the obtained equivalent model of the transformer into the whole system simulation network, and solving the whole circuit network by electromagnetic transient simulation software to obtain the voltage and current values of the two ports of the transformer.
Step 6: and reversely solving the voltage value and the current value of the port, and further updating the equivalent historical current source and the equivalent historical voltage source.
Drawings
Fig. 1 is a schematic diagram of a single-phase double-winding transformer.
Fig. 2 is an equivalent circuit of the transformer operating in load.
Fig. 3 is a source-containing pi-type equivalent circuit of the transformer proposed by the present invention.
Fig. 4 is a decoupling controlled current source equivalent circuit of the transformer proposed by the present invention.
Fig. 5 is a two-port equivalent circuit of the transformer in consideration of the capacitance effect according to the present invention.
Detailed Description
The invention provides an electromagnetic transient equivalent modeling method of a high-frequency transformer considering capacitance effect, which takes a single-phase double-winding transformer as an example and combines the attached drawings to further explain the simulation steps of the invention in detail.
FIG. 1 is a schematic diagram of a single-phase double-winding transformer, which is composed of two windings wound on the same core, the windings are interconnected through alternating magnetic flux, 1,2,3 and 4 are four terminals externally connected with the transformer, U1,U2Is the port voltage, I1,I2Is a port current, L11、L12And L12The self-inductance of the primary winding, the self-inductance of the secondary winding and the mutual inductance of the windings are realized. The same name ends are marked on the figure.
The parameters of the transformer shown in fig. 1 are known: rated capacity S, primary winding/secondary winding rated voltage U1:U2Fundamental frequency fbase. Per unit value of leakage reactance XLExcitation current I0. (the parameters are set for yield and measured under ideal experimental conditions.)
Step 1: FIG. 2 shows the transformer in on-load operationEquivalent circuit of the line, LA，LBFor leakage inductance, the magnitude of the leakage flux of the transformer is reflected, LmFor exciting inductance, reflecting the magnitude of the main flux of the transformer, C1,C2,C3The equivalent capacitance parameter reflects the parasitic capacitance effect between the inner conductors of the transformer, wherein the ideal transformer transformation ratio is n: 1.
The equivalent inductance parameter of the transformer shown in fig. 2 can be calculated according to equations (1) and (2).
The parasitic capacitance parameter of the transformer shown in fig. 2 can be calculated according to equation (3), i.e., by calculating the electrostatic energy stored between the winding layer and the winding and the magnetic core.
Step 2: according to the superposition theorem, the relationship between the port voltage and the current when the capacitance is not considered is calculated. According to the relationship between the KCL and KVL column write voltage and current, as shown in formula (4.a), the inductance matrix is inverted and then written into the form of formula (4. b).
And (3) performing trapezoidal numerical integration on the primary side current and the secondary side current at the time t, and expressing the integrated current in the form of the sum of a historical current source and the current increment, namely the formula (5).
Wherein the content of the first and second substances,
and step 3: decoupled controlled source equivalence is performed. FIG. 3 is a source-containing pi-type time-varying equivalent circuit of a transformer, Y1,Y2,Y3Is a variable resistor, Jh1,Jh2Is a time varying current source. The port voltage current relationship shown in fig. 3 is:
i1＝V1×Y1+J1+Y2×(V1-V2)＝(Y1+Y2)×V1-Y2×V2+J1
i2＝V2×Y3+J2-Y2×(V1-V2)＝-Y2V1+(Y2+Y3)×V2+J2
(6.a)
comparing the formula (5) and the formula (6.b), the values of the admittance and the current source in fig. 3 are:
as a further preference of the present invention, the decoupled controlled source equivalence is performed at step 3, as shown in FIG. 4, Y1',Y2', is a variable resistance, Jh1',Jh2' is a time varying current source. The port voltage current relationship shown in fig. 4 is:
i1＝V1×Y1'+J1'
i2＝V2×Y2'+J2' (8.a)
comparing the equation (5) and the equation (8.b), the values of the resistor and the current source in fig. 4 are:
if the port voltage and the port current are directly converted into the node voltage and current relationship according to the constraint relationship in the step 2, the obtained node admittance matrix is shown in a formula (10), the self-admittance of some nodes has a negative value, and the physical meaning of the node admittance matrix is that a negative impedance branch is included between the nodes when only the transformer branch is considered, and the node admittance matrix cannot be realized in simulation software. And if the decoupling controlled source equivalence is carried out in the step 3, the Y parameters are all positive values, and the condition of a negative impedance branch cannot occur.
And 4, discretizing three equivalent parasitic capacitances on the basis of considering the capacitance effect, wherein the three equivalent parasitic capacitances are shown in a formula (11).
Equivalent history current source GEQi(i ═ 1,2,3) and equivalent conductance JEQi(i is 1,2) is connected in parallel, and is connected into the equivalent circuit obtained in the step 3, and then the two-port equivalent of the transformer after correction is obtainedThe circuit is shown in fig. 5.
And 5: after the equivalent model of the transformer is obtained, the equivalent model is added into the whole system simulation network, and then the whole circuit network is solved by electromagnetic transient simulation software to obtain the voltage values of the two ports of the transformer.
Step 6: the port voltage value is substituted into the formula (4) to solve the port current of the energy storage element L, the port current value is substituted into the formula (10.b) to solve the port voltage of the capacitor C, and then the equivalent historical current source value is updated.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (1)
1. An electromagnetic transient equivalent modeling method of a single-phase double-winding high-frequency transformer considering capacitance effect is characterized by comprising the following steps: according to equivalent parameters of magnetic coupling of the transformer and capacitance effect between the characteristic conductors, a backward Euler method discretizes equivalent conditions of inductance, a capacitance expression and an electrical two-port, and provides an electromagnetic transient modeling method of a single-phase double-winding high-frequency transformer considering the capacitance effect, which comprises the following steps of 1: deducing to obtain a self-inductance parameter and a mutual inductance parameter which are related to the voltage-current relationship of the transformer according to a leakage reactance per unit value and an excitation current per unit value obtained by a standard transformer experiment; according to the measurement of the parasitic capacitance of the existing experiment, the equivalent parameter of the lumped capacitance of the winding layer is obtained, so that the equivalent parameter of the transformer which is magnetically coupled and reflects the influence of the parasitic capacitance is determined; step 2: firstly, discretizing an inductor by using a trapezoidal integration method, and converting a differential-voltage expression of current into a current-voltage expression related to a historical voltage value at the previous moment so as to convert the current-voltage expression into an electromagnetic transient phenomenon of a simulation transformer at a discrete time point; and step 3: then designing a circuit reflecting the port current-voltage expression in the step 2, namely a decoupled controlled current source equivalent circuit, wherein the transformation ratio is contained in the conductance parameter; and 4, step 4: discretizing the capacitor obtained in the step 1 by utilizing a trapezoidal integration method again to obtain a form that an equivalent historical current source and an equivalent conductance at the previous moment are connected in parallel, and accessing the equivalent circuit obtained in the step 3 to obtain a corrected transformer two-port equivalent circuit; and 5: after obtaining the equivalent model of the transformer, adding the equivalent model into the whole system simulation network, and then solving the whole circuit network by electromagnetic transient simulation software to obtain the voltage and current values of two ports of the transformer; step 6: and reversely solving the voltage value and the current value of the port, and further updating the equivalent historical current source and the equivalent historical voltage source.
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