CN114662437A - Modeling method of power electronic device - Google Patents

Modeling method of power electronic device Download PDF

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CN114662437A
CN114662437A CN202210341715.8A CN202210341715A CN114662437A CN 114662437 A CN114662437 A CN 114662437A CN 202210341715 A CN202210341715 A CN 202210341715A CN 114662437 A CN114662437 A CN 114662437A
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electronic device
power electronic
differential equation
single module
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王英沛
宋洁莹
刘宗烨
于弘洋
陆振纲
杨士慧
王春义
魏振
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QINGDAO POWER SUPPLY Co OF STATE GRID SHANDONG ELECTRIC POWER Co
State Grid Smart Grid Research Institute Co ltd
State Grid Shandong Electric Power Co Ltd
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QINGDAO POWER SUPPLY Co OF STATE GRID SHANDONG ELECTRIC POWER Co
State Grid Smart Grid Research Institute Co ltd
State Grid Shandong Electric Power Co Ltd
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Abstract

The invention discloses a modeling method of a power electronic device, which comprises the steps of establishing a nonlinear differential equation for a parallel part of each single module; fourier simplification is carried out on the nonlinear differential equation of the parallel part; establishing a mathematical model of the cascade part of each phase of each single module, and simplifying the nonlinear differential equation of the simplified parallel part again by using the mathematical model; the equivalent average value model of the power electronic device is obtained based on the nonlinear differential equation of the parallel part of each single module, the mathematical model of the cascade part and the external circuit after the parallel part is simplified again, so that the simulation speed of the model is remarkably improved under the condition of ensuring stable precision, the average value model can effectively simulate the external characteristics of the power electronic device, the internal dynamic characteristics are ignored, and the method has important theoretical significance and application value.

Description

Modeling method of power electronic device
Technical Field
The invention relates to the field of power system simulation, in particular to a modeling method of a power electronic device.
Background
With the increasing demand for large-scale intermittent distributed renewable energy power generation and power grid integration, the traditional single-power-supply single-end alternating-current power distribution network is rapidly developing into a multi-power-supply multi-end flexible direct-current or alternating-current/direct-current hybrid power distribution network. Power Electronic Transformers (PET) are used as core devices of energy routers to realize voltage conversion and Power transmission through Power Electronic technology. Among the various types of PET topologies, multi-active bridge PET contains multiple ac and dc ports for interconnecting multiple voltage and power energy networks, and is becoming increasingly popular due to its more compact and lower cost. In recent years, high-speed equivalent modeling and simulation of various PET structures are widely concerned, and different types of modeling methods are proposed, including an average value model, a decoupling model, a mathematical mechanism model, a Thevenin equivalent model and the like, but most models have large memory requirements and long simulation time.
Disclosure of Invention
Therefore, the technical problem to be solved by the present invention is to overcome the defects of large memory requirement and long simulation time of the modeling method of the power electronic device in the prior art, thereby providing a modeling method of the power electronic device.
In order to achieve the purpose, the invention provides the following technical scheme:
the embodiment of the invention provides a modeling method of a power electronic device, wherein the power electronic device is composed of a plurality of single modules, each phase of the input end of each single module is composed of an active bridge module, the output end of each single module is composed of an active bridge module, active bridges of the same phase of the power electronic device are connected in cascade, and active bridges of the output end are connected in parallel, the method comprises the following steps: establishing a nonlinear differential equation for the parallel part of each single module; fourier simplification is carried out on the nonlinear differential equation of the parallel part; establishing a mathematical model of the cascade part of each phase of each single module, and simplifying the nonlinear differential equation of the simplified parallel part again by using the mathematical model; and obtaining an equivalent average value model of the power electronic device based on the nonlinear differential equation, the mathematical model of the cascade part and the external circuit after the parallel part of each single module is simplified again.
In one embodiment, the process of establishing a nonlinear differential equation for the parallel portion of each single module includes: for the parallel part of each single module, selecting a corresponding state variable, and establishing a state variable equation according to the circuit structure of the parallel part; obtaining the current switching signal of a switching device in an active bridge module of the parallel part of each single module, and representing the switching device by using a switching function model; and combining the switching function of the switching device and the state variable equation to obtain a nonlinear differential equation of the parallel part of each single module.
In one embodiment, the process of fourier reducing the nonlinear differential equation of the parallel portion includes: decomposing the state variable into Fourier series; carrying out Fourier transform on the switching function; and substituting the state variable after Fourier decomposition and the switching function after Fourier transformation into the nonlinear differential equation of the corresponding parallel part to obtain the nonlinear differential equation expressing the real part and the imaginary part of the state variable.
In one embodiment, the process of decomposing the state variables into a Fourier series comprises: and obtaining an average value model of the parallel parts described by the Fourier coefficients of each state variable according to the convolution characteristics of the Fourier coefficients.
In one embodiment, the state variables include: inductor current and current voltage.
In one embodiment, only the harmonics of the inductor current of a predetermined order and the dc component of the capacitor voltage are considered in the decomposition of the state variable into a fourier series.
In one embodiment, the process of establishing a mathematical model of the cascaded portion of each phase of each single module comprises: for the cascade part of each phase of each single module, on the basis of the corresponding modulation mode, acquiring on-off signals of each switching element of the bridge module of each cascade part; for each cascade part, acquiring the relation between the voltage and the current at two sides of each cascade part based on the on-off signal of the switching element and the circuit structure of the cascade part; and establishing a mathematical model of each cascade part according to the relation between the voltage and the current at the two sides of each cascade part.
In one embodiment, the mathematical model of each cascaded section is substituted into its corresponding parallel partially simplified nonlinear differential equation to reduce the preliminarily simplified nonlinear differential equation again.
In one embodiment, the equivalent average model is a four-port voltage source equivalent circuit.
In one embodiment, the modeling method of the power electronic device further includes: simulating the equivalent average model by using simulation software, and reversely solving current information of each port; the step of "establishing a non-linear differential equation for the parallel portion of each single module" is returned based on the port current information until the simulation time stops.
The technical scheme of the invention has the following advantages:
according to the modeling method of the power electronic device, the nonlinear differential equation is established for the parallel part of each single module; fourier simplification is carried out on the nonlinear differential equation of the parallel part; establishing a mathematical model of the cascade part of each phase of each single module, and simplifying the nonlinear differential equation of the parallel part again by using the mathematical model; the equivalent average value model of the power electronic device is obtained based on the nonlinear differential equation of the parallel part of each single module, the mathematical model of the cascade part and the external circuit after the parallel part is simplified again, so that the simulation speed of the model is remarkably improved under the condition of ensuring stable precision, the average value model can effectively simulate the external characteristics of the power electronic device, the internal dynamic characteristics are ignored, and the method has important theoretical significance and application value.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a topology diagram of a power electronic device according to an embodiment of the present invention;
FIG. 2 is a topology diagram of a single module provided by an embodiment of the present invention;
FIG. 3 is a flow chart of a specific example of a modeling method provided by an embodiment of the invention;
FIG. 4 is a flow chart of another specific example of a modeling method provided by an embodiment of the present invention;
fig. 5 is a schematic diagram of the conduction characteristic of the H-bridge according to the embodiment of the invention;
FIG. 6 is a flow chart of another specific example of a modeling method provided by an embodiment of the present invention;
FIG. 7 is a flow chart of another specific example of a modeling method provided by an embodiment of the present invention;
FIG. 8 is an equivalent circuit of a single module according to an embodiment of the present invention;
fig. 9 is a flowchart of another specific example of the modeling method according to the embodiment of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; the two elements may be directly connected or indirectly connected through an intermediate medium, or may be communicated with each other inside the two elements, or may be wirelessly connected or wired connected. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
In addition, the technical features involved in the different embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Examples
An embodiment of the present invention provides a modeling method for a power electronic device, where as shown in fig. 1, the power electronic device is composed of a plurality of single modules, as shown in fig. 2, each phase of an input end of each single module is composed of an active bridge module, an output end of each single module is composed of an active bridge module, where active bridges of the same phase of the power electronic device are connected in cascade, and active bridges of the output ends are connected in parallel, and as shown in fig. 3, the modeling method includes:
step S11: a non-linear differential equation is established for the parallel portion of each single module.
Specifically, for the parallel portion of each single module, the embodiment of the present invention first selects the state variable and performs equivalence on the switching devices involved in the parallel portion by using the switching function, so as to obtain the nonlinear differential equation, as shown in fig. 4, step S11 is performed by steps S21 to S23, specifically as follows:
step S21: and selecting corresponding state variables for the parallel part of each single module, and establishing a state variable equation according to the circuit structure of the parallel part.
Specifically, taking the single module topology shown in fig. 2 as an example, starting from phase a of the parallel portion of the single module, first, the equivalent inductor current i is selectedLAnd the capacitor voltage UC1、UC2As the state variable, a state equation is written for the inductance and capacitance columns of the parallel part, as shown in formula (1), it should be noted that, in the exemplary embodiment of the present invention, only the topological structure single module shown in fig. 2 is taken as an example, and other structures may be transformed by using the same method.
Figure BDA0003572908580000061
In the formula, n: and 1 is the transformation ratio of the cascade part to the parallel part.
Step S22: and acquiring the current switching signal of the switching device in the active bridge module of the parallel part of each single module, and representing the switching device by using a switching function model.
Specifically, the switching device shown in fig. 2 is an IGBT of an anti-parallel diode, the IGBT and the anti-parallel diode are represented by a switching function model, and the switching function is obtained from the H-bridge conduction characteristic shown in fig. 5, which is only for example and not limited thereto. Thus, the alternating square wave voltage uH(t)、uL(t) and a current iLH(t)、iLL(t) available switching function s1(t)、s2(t) is represented by the formula (2).
Figure BDA0003572908580000071
Wherein,
Figure BDA0003572908580000072
in the formula,
Figure BDA0003572908580000073
are each uH(t)、uLAnd (T) the phase angle of the outward shift, T, is the single module action period.
Step S23: and combining the switching function of the switching device and the state variable equation to obtain a nonlinear differential equation of the parallel part of each single module.
Specifically, combining equations (1) to (3), a nonlinear differential equation (state equation) of the parallel portion of the single block can be obtained as shown below.
Figure BDA0003572908580000074
Step S12: and carrying out Fourier simplification on the nonlinear differential equation of the parallel part.
Specifically, in the embodiment of the present invention, the parallel portion is simplified by using fourier decomposition, and the simplification method may also be other simplification methods, which are not limited herein, as shown in fig. 6, step S12 is executed by steps S31 to S33, which are specifically as follows:
step S31: the state variables are decomposed into fourier series.
Specifically, based on the expressions (1) and (2), an average value model of the parallel part described by the fourier coefficient of each state variable is obtained according to the convolution characteristic of the fourier coefficient, as follows:
Figure BDA0003572908580000081
Figure BDA0003572908580000082
step S32: the switching function is fourier transformed.
Fourier transform of the switching function shown in equation (3) can obtain:
Figure BDA0003572908580000083
step S33: and substituting the state variable after Fourier decomposition and the switching function after Fourier transformation into the nonlinear differential equation of the corresponding parallel part to obtain the nonlinear differential equation expressing the real part and the imaginary part of the state variable.
Specifically, in order to simplify the model to meet the actual requirement, only the harmonics of the inductor current of the preset number and the dc component of the capacitor voltage are considered in the process of decomposing the state variable into the fourier series. For example, considering only the first, third and fifth harmonics of the equivalent inductor current and the dc component of the capacitor voltage, the fourier coefficients of the state variables are represented as complex numbers, i.e.:
Figure BDA0003572908580000091
substituting the Fourier decomposition state variable into the transformed differential equation to obtain a nonlinear differential equation representing the real part and the imaginary part of the state variable, as follows:
Figure BDA0003572908580000092
Figure BDA0003572908580000101
step S13: and establishing a mathematical model of the cascade part of each phase of each single module, and simplifying the nonlinear differential equation after the parallel part is simplified by using the mathematical model again.
Specifically, the establishment of the mathematical model of the cascade part in the embodiment of the present invention obtains the relationship between the voltage and the current at the two sides of the cascade part according to the on-off signal of each switching device in the cascade part based on the corresponding modulation mode, and substitutes the relationship into the state equation of the parallel part to realize equation simplification.
Specifically, as shown in fig. 7, the process of establishing a mathematical model of the cascaded portion of each phase of each single module includes:
step S41: and for the cascade part of each phase of each single module, acquiring the on-off signal of each switching element of the bridge module of each cascade part on the basis of the corresponding modulation mode.
Step S42: and for each cascade part, acquiring the relation between the voltage and the current at two sides of each cascade part based on the on-off signal of the switching element and the circuit structure of the cascade part.
Specifically, taking the H-bridge on-state table shown in table 1 as an example, according to the topology shown in fig. 2, the relationship between the voltage and the current at both sides of the cascade part can be obtained.
TABLE 1
Figure BDA0003572908580000102
Figure BDA0003572908580000111
Step S43: and establishing a mathematical model of each cascade part according to the relation between the voltage and the current at the two sides of each cascade part.
Step S14: and obtaining an equivalent average value model of the power electronic device based on the nonlinear differential equation, the mathematical model of the cascade part and the external circuit after the parallel part of each single module is simplified again.
Specifically, according to the mathematical model obtained in step S13, the mathematical model is substituted into its corresponding parallel partially simplified nonlinear differential equation to reduce the preliminarily simplified nonlinear differential equation again.
Specifically, based on the above steps, the equivalent average model of the power electronic device shown in fig. 1 and 2 obtained in the embodiment of the present invention is a four-port voltage source equivalent circuit, where the equivalent circuit of a single module is shown in fig. 8.
In one embodiment, the modeling method of the power electronic device further includes: simulating the equivalent average model by using simulation software, and reversely solving the current information of each port; the step of "establishing a non-linear differential equation for the parallel portion of each single module" is returned based on the port current information until the simulation time stops.
Specifically, steps S11 to S14 provided in the embodiment of the present invention are steps of single-step simulation modeling, and the modeling flow is as shown in fig. 9 in the whole simulation time, and after the single step is finished, step S11 is returned until the simulation time is finished.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.

Claims (10)

1. A modeling method of a power electronic device, wherein the power electronic device is composed of a plurality of single modules, each phase of an input end of each single module is composed of one active bridge module, and an output end of each single module is composed of one active bridge module, wherein active bridges of the same phase of the power electronic device are connected in cascade, and active bridges of the output ends are connected in parallel, the method comprising:
establishing a nonlinear differential equation for the parallel part of each single module;
fourier simplification is carried out on the nonlinear differential equation of the parallel part;
establishing a mathematical model of the cascade part of each phase of each single module, and simplifying the nonlinear differential equation of the parallel part again by using the mathematical model;
and obtaining an equivalent average value model of the power electronic device based on the nonlinear differential equation, the mathematical model of the cascade part and the external circuit after the parallel part of each single module is simplified again.
2. A method of modelling a power electronic device according to claim 1, wherein the process of establishing a non-linear differential equation for the parallel portion of each single module comprises:
for the parallel part of each single module, selecting a corresponding state variable, and establishing a state variable equation according to the circuit structure of the parallel part;
obtaining the current switching signal of the switching device in the active bridge module of the parallel part of each single module, and representing the switching device by using a switching function model;
and combining the switching function of the switching device and the state variable equation to obtain a nonlinear differential equation of the parallel part of each single module.
3. A method of modelling a power electronic device according to claim 2, wherein the process of fourier reducing the non-linear differential equation of the parallel portion comprises:
decomposing the state variable into Fourier series;
carrying out Fourier transform on the switching function;
and substituting the state variable after Fourier decomposition and the switching function after Fourier transformation into the nonlinear differential equation of the corresponding parallel part to obtain the nonlinear differential equation expressing the real part and the imaginary part of the state variable.
4. A method of modelling a power electronic device according to claim 3, wherein the process of decomposing the state variables into a fourier series comprises:
and obtaining an average value model of the parallel parts described by the Fourier coefficients of each state variable according to the convolution characteristics of the Fourier coefficients.
5. Method for modelling a power electronic device according to claim 4, characterized in that said state variables comprise: inductor current and current voltage.
6. A method of modelling a power electronic device according to claim 5 wherein only the harmonics of the inductor current of a predetermined order and the DC component of the capacitor voltage are taken into account in the decomposition of the state variables into a Fourier series.
7. A method of modelling a power electronic device according to claim 1, wherein said process of establishing a mathematical model of the cascaded part of each phase of each single module comprises:
for the cascade part of each phase of each single module, on the basis of the corresponding modulation mode, acquiring on-off signals of each switching element of the bridge module of each cascade part;
for each cascade part, acquiring the relation between the voltage and the current at two sides of each cascade part based on the on-off signal of the switching element and the circuit structure of the cascade part;
and establishing a mathematical model of each cascade part according to the relation between the voltage and the current at the two sides of each cascade part.
8. A method of modelling a power electronic device according to claim 7,
and substituting the mathematical model of each cascade part into the corresponding nonlinear differential equation after the parallel part is simplified so as to simplify the nonlinear differential equation after the preliminary simplification again.
9. A method of modelling a power electronic device according to claim 1, wherein the equivalent mean model is a four-port voltage source equivalent circuit.
10. The modeling method of a power electronic device according to claim 9, further comprising:
simulating the equivalent average model by using simulation software, and reversely solving the current information of each port;
and returning the step of establishing a nonlinear differential equation for the parallel part of each single module based on the port current information until the simulation time stops.
CN202210341715.8A 2022-03-30 2022-03-30 Modeling method of power electronic device Pending CN114662437A (en)

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