CN111581799B - Modeling method of power electronic converter with coupled inductor and charge pump unit - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及电力电子变换器建模技术,具体涉及一种含耦合电感和电荷泵单元的电力电子变换器的建模方法。The invention relates to modeling technology of a power electronic converter, in particular to a modeling method of a power electronic converter including a coupling inductor and a charge pump unit.
背景技术Background technique
电力电子变换器的建模是其设计和分析的基础。由于电力电子变换器的电路拓扑中包含的非线性原件是强非线性系统,用数学方法求解困难,无法采用经典闭环设计方法,因此首先需要对开关电路线性化建模(小信号模型)。较简单高变比拓扑可采用传统的平均开关模型法等进行建模。而相对较为复杂的可以通过状态空间平均法(SSA)进行建模。此外还有开关信号流图非线性建模法(SFG)同时保留了物理意义清晰和方程化表达易于计算的优点。但是随着电路工作状态和阶数的提升,表示拓扑电路的状态矩阵方程相应的会难以列写,给拓扑研究带来了困难。近年来,电力电子变换器多运用绕组感性元件,开关电容/电荷泵单元等还可在进一步提升增益的同时实现零纹波、软开关等优良性能,但同时也引入了准谐振等复杂的工作状态,为电力电子变换器的建模分析带来了更多挑战。The modeling of power electronic converter is the basis of its design and analysis. Since the nonlinear components contained in the circuit topology of the power electronic converter are strongly nonlinear systems, it is difficult to solve them mathematically, and the classical closed-loop design method cannot be used. Therefore, it is first necessary to model the switching circuit linearly (small signal model). Simpler high-turn-ratio topologies can be modeled using the traditional average switch model method. The relatively complex ones can be modeled by state-space averaging (SSA). In addition, the switching signal flow graph nonlinear modeling method (SFG) retains the advantages of clear physical meaning and easy calculation of equational expression. However, with the improvement of the working state and order of the circuit, the state matrix equation representing the topological circuit will be correspondingly difficult to write, which brings difficulties to the topology research. In recent years, power electronic converters have mostly used winding inductive components, switched capacitors/charge pump units, etc. can further increase the gain while achieving excellent performance such as zero ripple and soft switching, but at the same time introduce complex work such as quasi-resonance state, which brings more challenges to the modeling and analysis of power electronic converters.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于提供一种含耦合电感和电荷泵单元的电力电子变换器的建模方法。The object of the present invention is to provide a modeling method of a power electronic converter including a coupled inductor and a charge pump unit.
实现本发明目的的技术解决方案为:一种含耦合电感和电荷泵单元的电力电子变换器的建模方法,包括以下步骤:The technical solution for realizing the object of the present invention is: a modeling method of a power electronic converter containing a coupled inductor and a charge pump unit, comprising the following steps:
步骤1、构建荷泵CP单元和TIS建模模块,确定荷泵CP单元和通用TIS建模模块的模型,包括稳态模型、大信号模型和小信号模型;
步骤2、构建等效TIS-CP建模模块,根据电荷泵CP单元和通用TIS模块的连接方式,确定等效TIS-CP建模模块的大信号模型、稳态模型和小信号模型;
步骤3、根据目标电力电子变换器和等效TIS-CP建模模块的拓扑,确定等效TIS-CP建模模块外部线性网络;Step 3. Determine the external linear network of the equivalent TIS-CP modeling module according to the topology of the target power electronic converter and the equivalent TIS-CP modeling module;
步骤4、确定目标电力电子变换器等效TIS-CP模块外部线性网络的状态方程以及目标电力电子变换器等效TIS-CP模块的内部参数,包括有效匝数比、通用耦合电感的励磁电感;Step 4. Determine the state equation of the external linear network of the equivalent TIS-CP module of the target power electronic converter and the internal parameters of the equivalent TIS-CP module of the target power electronic converter, including the effective turns ratio and the excitation inductance of the general coupling inductor;
步骤5、将目标电力电子变换器等效TIS-CP模块外部线性网络状态方程以及目标电力电子变换器等效TIS-CP模块内参数,代入步骤2中建立的等效TIS-CP模块的各个模型中,得到待建模的目标电力电子变换器模型。Step 5. Substitute the external linear network state equation of the equivalent TIS-CP module of the target power electronic converter and the internal parameters of the equivalent TIS-CP module of the target power electronic converter into each model of the equivalent TIS-CP module established in
本发明与现有技术相比,其显著优点为:将含有电荷泵单元的混合型耦合电感高增益拓扑中的电荷泵单元部分事先进行了建模,并将其嵌入通用TIS建模模块生成TIS-CP建模模块对目标拓扑中的非线性部分进行统一表达,大大降低了用户的建模难度,提高了建模分析的效率。Compared with the prior art, the present invention has the remarkable advantage that the charge pump unit in the hybrid coupled inductor high-gain topology containing the charge pump unit is modeled in advance, and embedded in a general TIS modeling module to generate a TIS - The CP modeling module uniformly expresses the nonlinear part of the target topology, which greatly reduces the difficulty of modeling for users and improves the efficiency of modeling and analysis.
附图说明Description of drawings
图1为包含通用TIS模块的开关电源等效电路示意图。Figure 1 is a schematic diagram of an equivalent circuit of a switching power supply including a general TIS module.
图2为通用TIS建模模块的大信号模型图。Figure 2 is a large signal model diagram of the general TIS modeling module.
图3为通用TIS建模模块的稳态模型图。Figure 3 is a steady-state model diagram of the general TIS modeling module.
图4为通用TIS建模模块的小信号模型图。Fig. 4 is a small signal model diagram of the general TIS modeling module.
图5为TI-CP-Boost电力电子变换器的电荷泵CP单元和通用TIS建模模块的示意图。Fig. 5 is a schematic diagram of the charge pump CP unit and the general TIS modeling module of the TI-CP-Boost power electronic converter.
图6为电荷泵CP单元的小信号模型图。Figure 6 is a small signal model diagram of the charge pump CP unit.
图7为等效TIS-CP模块的黑盒法表示图。Figure 7 is a black-box representation of an equivalent TIS-CP module.
图8为TI-CP-Boost电力电子变换器的电荷泵CP单元及其外部支路的小信号模型图。Fig. 8 is a small signal model diagram of the charge pump CP unit of the TI-CP-Boost power electronic converter and its external branches.
图9为TI-CP-Boost电力电子变换器的等效TIS-CP模块示意图。Fig. 9 is a schematic diagram of an equivalent TIS-CP module of a TI-CP-Boost power electronic converter.
图10为TI-CP-Boost电力电子变换器的大信号模型图。Figure 10 is a large signal model diagram of the TI-CP-Boost power electronic converter.
图11为TI-CP-Boost电力电子变换器的稳态模型图。Figure 11 is a steady-state model diagram of the TI-CP-Boost power electronic converter.
图12为TI-CP-Boost电力电子变换器的小信号模型图。Figure 12 is a small signal model diagram of the TI-CP-Boost power electronic converter.
图13为TI-CP-Boost电力电子变换器控制到输出的小信号传递函数模型的计算结果和仿真结果对比图。Fig. 13 is a comparison chart of calculation results and simulation results of the small signal transfer function model from control to output of the TI-CP-Boost power electronic converter.
具体实施方式Detailed ways
下面结合附图与具体实施例,进一步说明本发明方案。The solutions of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.
本发明含耦合电感和电荷泵单元的电力电子变换器的建模方法,先构建电荷泵CP单元的建模模块,然后在原有的通用TIS建模模块上增加电荷泵CP单元形成等效TIS-CP建模模块,使其能应用于含耦合电感和电荷泵单元的电力电子变换器的建模。含耦合电感和电荷泵单元的电力电子变换器的建模方法,具体包括以下步骤:The modeling method of the power electronic converter containing coupled inductors and charge pump units in the present invention first constructs the modeling module of the charge pump CP unit, and then adds the charge pump CP unit to the original general TIS modeling module to form an equivalent TIS- The CP modeling module enables it to be applied to the modeling of power electronic converters with coupled inductors and charge pump units. A modeling method for a power electronic converter with a coupled inductor and a charge pump unit, specifically including the following steps:
步骤1、构建荷泵CP单元和TIS建模模块,确定荷泵CP单元和通用TIS建模模块的模型,包括稳态模型、大信号模型和小信号模型;
图1给出了通用TIS建模模块在开关电源中的一个示例,其三个端子可部分或全部用于连接外部线性电路。所述通用TIS建模模块包括通用耦合电感原边绕组(N10)、通用耦合电感副边绕组(N20)、通用TIS模块励磁电感(Lm),一对工作在互补模式的PWM的开关,即有源开关(K(d))和互补开关(K(d′)),以及1号端子、2号端子、0号端子,所述有源开关(K(d))一端连接1号端子,另一端连接通用耦合电感的励磁电感(Lm)的一端和通用耦合电感的原边绕组(N10)一端,所述通用耦合电感的励磁电感(Lm)另一端连接0号端子和通用耦合电感的原边绕组(N10)另一端,所述通用耦合电感的副边绕组(N20)一端连接互补开关(K(d′))一端,所述互补开关(K(d′))的另一端连接2号端子。根据上述特点与目标电力电子变换器进行比对,确定通用TIS建模模块在待建模目标电力电子变换器中的接口端子位置。Figure 1 shows an example of a general-purpose TIS modeling module in a switching power supply, and its three terminals can be partially or fully used to connect external linear circuits. The general TIS modeling module includes a general coupled inductor primary winding (N 10 ), a general coupled inductor secondary winding (N 20 ), a general TIS module excitation inductance (L m ), and a pair of PWM switches working in a complementary mode , that is, the active switch (K(d)) and the complementary switch (K(d′)), as well as terminals No. 1, No. 2, and No. 0. One end of the active switch (K(d)) is connected to No. 1 terminal, and the other end is connected to one end of the magnetizing inductance (L m ) of the universally coupled inductor and one end of the primary winding (N 10 ) of the universally coupled inductor, and the other end of the magnetizing inductance (L m ) of the universally coupled inductor is connected to
所述通用TIS建模模块大信号模型的开关信号流图如图2所示,包括一号端子电压大信号节点o v1、二号端子电压大信号节点o v2、零号端子电压大信号节点o v0、一号端子电流大信号节点o i1、二号端子电流大信号节点o i2、零号端子电流大信号节点o i0、励磁电感电压大信号节点o vLm、励磁电感电流大信号节点o iLm、一零端子电压大信号节点ov10、二零端子电压大信号节点o v20,所述一号端子电压大信号节点o v1到一零端子电压大信号节点o v10的增益为d,所述零号端子电压大信号节点o v0到一零端子电压大信号节点ov10增益为-1,所述零号端子电压大信号节点o v0到二零端子电压大信号节点o v20的增益为-1,所述一零端子电压大信号节点o v10到励磁电感电压大信号节点o vLm的增益为d,所述二零端子电压大信号节点o v20到励磁电感电压大信号节点o vLm的增益为a(1-d),所述励磁电感电压大信号节点o vLm到励磁电感电流大信号节点o iLm的增益为所述励磁电感电流大信号节点o iLm到一号端子电流大信号节点o i1的增益为d,所述励磁电感电流大信号节点o iLm到二号端子电流大信号节点o i2的增益为-ad′,所书一号端子电流大信号节点o i1到零号端子电流大信号节点o i0的增益为1,所述二号端子电流大信号节点o i2到零号端子电流大信号节点o i0的增益为1。特别的,上述各个节点之间的支路增益中,d为目标电力电子变换器占空比的大信号参数,d′=(1-d)为目标电力电子变换器主开关断开的时间段的大信号参数,a为通用TIS模块的有效匝数比,r为目标电力电子变换器耦合电感寄生电阻,Lm为目标电力电子变换器的励磁电感。The switching signal flow diagram of the large signal model of the general TIS modeling module is shown in Figure 2, including the voltage large signal node ov1 of the first terminal, the large voltage node ov2 of the second terminal, and the large signal node ov of the zero terminal 0 , no.1 terminal current large signal node oi 1 , no.2 terminal current large signal node oi 2 , zero terminal current large signal node oi 0 , exciting inductor voltage large signal node ov Lm , exciting inductor current large signal node oi Lm , A zero terminal voltage large signal node ov 10 , a zero terminal voltage large signal node ov 20 , the gain from the first terminal voltage large signal node ov 1 to a zero terminal voltage large signal node ov 10 is d, the zero The gain of terminal voltage large signal node ov 0 to zero terminal voltage large signal node ov 10 is -1, and the gain of the zero terminal voltage large signal node ov 0 to twenty terminal voltage large signal node ov 20 is -1, so The gain from the large signal node ov 10 of the zero terminal voltage to the large signal node ov Lm of the excitation inductance voltage is d, and the gain from the large signal node ov 20 of the zero terminal voltage to the large signal node ov Lm of the excitation inductance voltage is a(1 -d), the gain from the excitation inductor voltage large signal node ov Lm to the excitation inductor current large signal node oi Lm is The gain from the excitation inductor current large signal node oi Lm to the No. 1 terminal current large signal node oi 1 is d, and the gain from the excitation inductor current large signal node oi Lm to the No. 2 terminal current large signal node oi 2 is -ad ′, the gain from the No. 1 terminal current large signal node oi 1 to the No. 0 terminal current large signal node oi 0 is 1, and the gain from the No. 2 terminal current large signal node oi 2 to the No. 0 terminal current large signal node oi 0 The gain is 1. In particular, in the branch gain between the above nodes, d is the large signal parameter of the duty cycle of the target power electronic converter, and d'=(1-d) is the time period when the main switch of the target power electronic converter is off , a is the effective turns ratio of the general TIS module, r is the parasitic resistance of the coupling inductance of the target power electronic converter, and Lm is the excitation inductance of the target power electronic converter.
图2所示的通用TIS模块大信号模型也可由通用TIS模块大信号状态变量组成的方程组表示如下:The large-signal model of the general TIS module shown in Figure 2 can also be expressed by a system of equations composed of large-signal state variables of the general TIS module as follows:
其中,一号端子电压大信号v1,二号端子电压大信号v2,零号端子电压大信号v0,一号端子电流大信号i1,二号端子电流大信号i2,零号端子电流大信号i0,励磁电感电压大信号vLm,励磁电感电流大信号iLm,目标电力电子变换器占空比的大信号参数d,通用TIS模块的有效匝数比a,目标电力电子变换器耦合电感寄生电阻r,目标电力电子变换器的励磁电感Lm。Among them, the large voltage signal v 1 of
所述通用TIS建模模块稳态模型开关信号流图如图3所示,包括一号端子电压节点o V1、二号端子电压节点o V2、零号端子电压节点o V0、一号端子电流节点o I1、二号端子电流节点o I2、零号端子电流节点o I0、辅助节点o 1、励磁电感电压节点o VLm、励磁电感电流节点o ILm,所述一号端子电压节点o V1到励磁电感电压节点o VLm的增益为D,所述零号端子电压节点o V0到励磁电感电压节点o VLm的增益为-(D+aD′),所述零号端子电压节点o V0到辅助节点o 1的增益为-a,所述二号端子电压节点o V2到辅助节点o 1的增益为a,所述二号端子电压节点o V2到励磁电感电压节点o VLm的增益为aD′,所述励磁电感电压节点o VLm到励磁电感电流节点o ILm的增益为所述励磁电感电流节点o ILm到一号端子电流节点I1的增益为D,所述励磁电感电流节点o ILm到二号端子电流节点o I2的增益为-aD′,所书一号端子电流节点o I1到零号端子电流节点o I0的增益为1,所述二号端子电流节点o I2到零号端子电流节点o I0的增益为1。特别的,上述各个节点之间的支路增益中,D为目标电力电子变换器占空比的稳态参数,D′=(1-D)为目标电力电子变换器主开关断开的时间段的稳态参数,a为通用TIS模块的有效匝数比,r为目标电力电子变换器耦合电感寄生电阻。The general TIS modeling module steady-state model switch signal flow diagram is shown in Figure 3, including the first terminal voltage node o V 1 , the second terminal voltage node o V 2 , the zero terminal voltage node o V 0 , and the first terminal voltage node o
图3所示的通用TIS模块稳态模型也可由通用TIS模块稳态状态变量组成的方程组表示如下:The steady-state model of the general TIS module shown in Figure 3 can also be expressed by a system of equations composed of the steady-state state variables of the general TIS module as follows:
其中,励磁电感电流VLm,励磁电感电流ILm,一号端子电压V1,二号端子电压V2,零号端子电压V0,一号端子电流I1,二号端子电流I2,零号端子电流I0,目标电力电子变换器占空比的稳态参数D,通用TIS模块的有效匝数比a,目标电力电子变换器耦合电感寄生电阻r。Among them, the exciting inductor current V Lm , the exciting inductor current I Lm , the voltage of the first terminal V 1 , the voltage of the second terminal V 2 , the voltage of the zero terminal V 0 , the current of the first terminal I 1 , the current of the second terminal I 2 , zero No. terminal current I 0 , the steady-state parameter D of the duty cycle of the target power electronic converter, the effective turns ratio a of the general TIS module, and the parasitic resistance r of the coupling inductor of the target power electronic converter.
所述通用TIS建模模块小信号模型开关信号流图如图4所示,包括一号端子电压小信号节点二号端子电压小信号节点零号端子电压小信号节点一号端子电流小信号节点二号端子电流小信号节点零号端子电流小信号节点励磁电感电压小信号节点励磁电感电流小信号节点占空比小信号节点所述一号端子电压小信号节点到励磁电感电压小信号节点的增益为D,所述零号端子电压小信号节点到励磁电感电压小信号节点的增益为-(D+aD′),所述二号端子电压小信号节点到励磁电感电压小信号节点的增益为aD′,所述占空比小信号节点到励磁电感电压小信号节点的增益为V1+(a-1)V0-aV2,所述占空比小信号节点到一号端子电流小信号节点的增益为ILm,所述占空比小信号节点到二号端子电流小信号节点的增益为-aILm,所述励磁电感电压小信号节点到励磁电感电流小信号节点的增益为所述励磁电感电流小信号节点到一号端子电流小信号节点的增益为D,所述励磁电感电流小信号节点到二号端子电流小信号节点的增益为aD′,所述一号电流端子小信号节点到零号端子电流小信号节点的增益为1,所述二号端子电流小信号节点到零号端子电流小信号节点的增益为1。The general TIS modeling module small-signal model switch signal flow diagram is shown in Figure 4, including the first terminal voltage small-
图4所示的通用TIS模块小信号模型也可由通用TIS模块小信号状态变量组成的方程组表示如下:The small-signal model of the general TIS module shown in Figure 4 can also be expressed by a system of equations composed of small-signal state variables of the general TIS module as follows:
其中,TIS模块小信号状态变量包含:一号端子电压小信号二号端子电压小信号零号端子电压小信号一号端子电流小信号二号端子电流小信号零号端子电流小信号励磁电感电压小信号励磁电感电流小信号目标电力电子变换器占空比的稳态参数D,通用TIS模块的有效匝数比a,目标电力电子变换器耦合电感寄生电阻r,目标电力电子变换器的励磁电感Lm,目标电力电子变换器励磁电流平均值ILm。Among them, the small signal state variables of the TIS module include:
图5给出了TI-CP-Boost电力电子变换器中的电荷泵CP单元和通用TIS建模模块的示意图。所述电荷泵CP单元包括电容(CP)和一对二极管,即充电二极管(DC)和放电二极管(DO),以及C端子、O端子和P端子,所述电容(CP)一端连接C号端子,另一端连接充电二极管(DC)的阴极和放电二极管(DO)的阳极,所述充电二极管(DC)另一端连接P号端子,所述放电二极管(DO)另一端连接O号端子。根据上述特点与目标电力电子变换器进行比对,确定电荷泵CP单元在待建模目标电力电子变换器中的接口端子位置。Figure 5 shows a schematic diagram of the charge pump CP unit and the general TIS modeling module in the TI-CP-Boost power electronic converter. The charge pump CP unit includes a capacitor (C P ) and a pair of diodes, namely a charging diode (D C ) and a discharging diode (D O ), as well as a C terminal, an O terminal and a P terminal, and one end of the capacitor (C P ) Connect to terminal C, the other end is connected to the cathode of charging diode (D C ) and the anode of discharging diode (D O ), the other end of charging diode (D C ) is connected to terminal P, and the discharging diode (D O ) is connected to One end is connected to terminal O. According to the above characteristics, it is compared with the target power electronic converter to determine the interface terminal position of the charge pump CP unit in the target power electronic converter to be modeled.
所述电荷泵CP单元的模型的开关信号流图如图6所示,包括P端子电压节点C端子电压节点电荷泵电容电压节点P端子电流节点o iP,C端子电流节点o iC,O端子电流节点o iO。所述P端子电压节点到电荷泵电容电压节点的增益为1,所述C端子电压节点到电荷泵电容电压节点的增益为-1,所述电荷泵电容电压节点到C端子电流节点o iC的增益为sCP,所述C端子电流节点o iC到P端子电流节点o iP的增益为1,所述O端子电流节点o iO到P端子电流节点o iP的增益为-1。由于其大信号模型和稳态模型的模型结构和小信号模型是一样的,要得到其大信号模型和稳态模型和稳态模型仅需将其中的小信号变量(如)替换为大信号变量(如vp)或者稳态变量(如Vp)即可,故这里仅在附图中给出其小信号模型。The switch signal flow diagram of the model of the charge pump CP unit is shown in Figure 6, including the P terminal voltage node C terminal voltage node Charge Pump Capacitor Voltage Node The P terminal current node oi P , the C terminal current node oi C , and the O terminal current node oi O . The P terminal voltage node to the charge pump capacitor voltage node with a gain of 1, the C terminal voltage node to the charge pump capacitor voltage node with a gain of -1, the charge pump capacitor voltage node The gain to the C-terminal current node oi C is sCP, the gain of the C-terminal current node oi C to the P -terminal current node oi P is 1, and the gain of the O-terminal current node oi O to the P-terminal current node oi P is -1. Since the model structure of its large-signal model and steady-state model is the same as that of the small-signal model, to obtain its large-signal model, steady-state model and steady-state model, only the small-signal variables (such as ) can be replaced by a large-signal variable (such as v p ) or a steady-state variable (such as V p ), so only the small-signal model is given in the accompanying drawings.
图6所示的电荷泵CP单元小信号模型也可由电荷泵CP单元小信号状态变量组成的方程组表示如下:The small-signal model of the charge pump CP unit shown in Figure 6 can also be expressed by a system of equations composed of small-signal state variables of the charge pump CP unit as follows:
其中,电荷泵CP单元小信号状态变量包含:P端子电压小信号C号端子电压小信号电荷泵电容电压小信号P端子电流小信号C端子电流小信号O端子电流小信号电荷泵电容CP。Among them, the small signal state variable of the charge pump CP unit includes: P terminal voltage small signal C terminal voltage small signal Charge pump capacitor voltage small signal P terminal current small signal C terminal current small signal O terminal current small signal Charge pump capacitor C P .
步骤2、构建等效TIS-CP建模模块,根据电荷泵CP单元和通用TIS模块的连接方式,确定等效TIS-CP建模模块的大信号模型、稳态模型和小信号模型;
等效TIS-CP建模模块如图7和9所示,包含电荷泵CP单元和通用TIS建模模块的所有组件,其中电荷泵CP单元的输出二极管DO复用为通用TIS建模模块的互补开关(K(d′)),其外部可引出4个端子,分别为0号端子、1号端子、2号端子和P端子。构建目标变换器的等效TIS-CP建模模块,即将事先建好的电荷泵CP单元的模型嵌入通用TIS建模模块得到目标变换器。此操作应结合电荷泵CP单元和通用TIS建模模块的端口连接方式,分析电荷泵CP单元中P端子电流iP对通用TIS建模模块中的1端子电流i1和0端子电流i0的影响;分析电荷泵CP单元C端子电压vC和通用TIS建模模块中的1端子电压v1和0端子电压v0的关系。The equivalent TIS-CP modeling module is shown in Figures 7 and 9, which contains all components of the charge pump CP unit and the general TIS modeling module, where the output diode D O of the charge pump CP unit is multiplexed as the general TIS modeling module The complementary switch (K(d')) can lead out 4 terminals, which are terminal 0,
由于电荷泵CP单元的C端子在嵌套后将存在于TIS-CP建模模块的内部,因此可将电荷泵CP单元的C端子电压vC用通用TIS建模模块中的1端子电压v1和0端子电压v0表示,将C端子电流iC用电荷泵电容电流icp表示,进而可将C端子删去。由于在等效TIS-CP模块中电荷泵CP单元的O端子和通用TIS建模模块的2号端子为同一端子,因此可将它们合并,即统一为2号端子。根据上述分析结果修改电荷泵CP单元模型和通用TIS建模模块各自模型中相应的方程,并将电荷泵CP单元模型和通用TIS建模模块的大信号模型、稳态模型和小信号模型中的方程分别联立,即可得到目标变换器的等效TIS-CP建模模块的大信号模型、稳态模型和小信号模型。Since the C terminal of the charge pump CP unit will exist inside the TIS-CP modeling module after nesting, the C terminal voltage v C of the charge pump CP unit can be used by the 1 terminal voltage v 1 in the general TIS modeling module and 0 terminal voltage v 0 , the C terminal current i C is expressed by the charge pump capacitance current i cp , and then the C terminal can be deleted. Since the O terminal of the charge pump CP unit in the equivalent TIS-CP module and the No. 2 terminal of the general TIS modeling module are the same terminal, they can be merged, that is, unified as No. 2 terminal. According to the above analysis results, the corresponding equations in the respective models of the charge pump CP unit model and the general TIS modeling module are modified, and the large-signal model, steady-state model and small-signal model of the charge pump CP unit model and the general TIS modeling module are By combining the equations separately, the large-signal model, steady-state model and small-signal model of the equivalent TIS-CP modeling module of the target converter can be obtained.
步骤3、根据目标电力电子变换器和等效TIS-CP建模模块的拓扑,确定等效TIS-CP建模模块外部线性网络;Step 3. Determine the external linear network of the equivalent TIS-CP modeling module according to the topology of the target power electronic converter and the equivalent TIS-CP modeling module;
所述等效TIS-CP模块外部线性网络包括目标电力电子变换器中除了等效TIS-CP模块中组件之外的所有组件。确定等效TIS-CP建模模块外部线性网络时,将等效TIS-CP建模模块与目标电力电子变换器进行拓扑比对,确定等效TIS-CP建模模块在待建模目标电力电子变换器的接口位置,包括0号端子、1号端子、2号端子和P端子;确定等效TIS-CP建模模块的接口位置后,即得到四个端子包围的等效TIS-CP建模模块,其余部分即为等效TIS-CP建模模块外部线性网络。The external linear network of the equivalent TIS-CP module includes all components in the target power electronic converter except the components in the equivalent TIS-CP module. When determining the external linear network of the equivalent TIS-CP modeling module, compare the topology of the equivalent TIS-CP modeling module with the target power electronic converter, and determine that the equivalent TIS-CP modeling The interface position of the converter, including
步骤4、确定目标电力电子变换器等效TIS-CP模块外部线性网络的状态方程以及目标电力电子变换器等效TIS-CP模块的内部参数,包括有效匝数比、通用耦合电感的励磁电感;Step 4. Determine the state equation of the external linear network of the equivalent TIS-CP module of the target power electronic converter and the internal parameters of the equivalent TIS-CP module of the target power electronic converter, including the effective turns ratio and the excitation inductance of the general coupling inductor;
设有效匝数比为a,通用耦合电感的励磁电感为Lm以,寄生阻抗参数为r1、r2和r0,其中r1为1号端子支路寄生阻抗之和、r2为2号端子支路寄生阻抗之和、r0为零号端子支路寄生阻抗之和,则有效匝数比a、通用耦合电感的励磁电感Lm的计算公式为:Assuming that the effective turns ratio is a, the magnetizing inductance of the general coupling inductor is L m or more, and the parasitic impedance parameters are r 1 , r 2 and r 0 , where r 1 is the sum of the parasitic impedance of the No. 1 terminal branch, and r 2 is 2 The sum of the parasitic impedance of the number terminal branch, r 0 is the sum of the parasitic impedance of the zero terminal branch, then the calculation formula of the effective turns ratio a and the excitation inductance L m of the general coupling inductor is:
式中,N10为通用TIS模块1号端子和0号端子之间的耦合电感匝数,N20为通用TIS模块2号端子和0号端子之间的耦合电感匝数,在计算N10和N20时,若实际绕组同名端顺接则取‘+’,反接则取‘-’,N1为目标电力电子变换器的变压器原边绕组匝数,L1为目标电力电子变换器的变压器原边绕组电感量。In the formula, N 10 is the number of coupling inductor turns between
步骤5、将目标电力电子变换器等效TIS-CP模块外部线性网络状态方程以及目标电力电子变换器等效TIS-CP模块内参数,代入步骤2中建立的等效TIS-CP模块的各个模型中,得到待建模的目标电力电子变换器模型;Step 5. Substitute the external linear network state equation of the equivalent TIS-CP module of the target power electronic converter and the internal parameters of the equivalent TIS-CP module of the target power electronic converter into each model of the equivalent TIS-CP module established in
步骤6、根据目标电力电子变换器的稳态模型求得稳态解,再将稳态解代入目标电力电子变换器的小信号模型中,即得此电力电子变换器的小信号传递函数。Step 6. Obtain the steady-state solution according to the steady-state model of the target power electronic converter, and then substitute the steady-state solution into the small-signal model of the target power electronic converter to obtain the small-signal transfer function of the power electronic converter.
实施例Example
为了验证本发明方案的有效性,以TI-CP-Boost电力电子变换器为建模对象,详述本发明方案的建模步骤。In order to verify the validity of the scheme of the present invention, the modeling steps of the scheme of the present invention are described in detail by taking the TI-CP-Boost power electronic converter as the modeling object.
图5所示的TI-CP-Boost电力电子变换器的主要参数如下,输入电压Vg=120V、负载电阻R=200Ohm、输出电容Co=47uF、开关频率为f=50kHz、励磁电感为L1=56uH、变压器等效漏感(副边)Llk=0.56μH、变压器原副边匝数比n=0.5、电荷泵电容Cp=1uF。对上述含耦合电感和电荷泵单元的电力电子变换器进行建模方法,实施步骤如下:The main parameters of the TI-CP-Boost power electronic converter shown in Figure 5 are as follows, input voltage Vg=120V, load resistance R=200Ohm, output capacitor Co=47uF, switching frequency f=50kHz, excitation inductance L 1 = 56uH, transformer equivalent leakage inductance (secondary side) L lk =0.56μH, transformer primary and secondary turns ratio n=0.5, charge pump capacitance Cp=1uF. The above-mentioned power electronic converter with coupled inductor and charge pump unit is modeled, and the implementation steps are as follows:
步骤1、分析待建模的目标电力电子变换器结构,识别出目标拓扑中的通用电荷泵CP单元和通用TIS建模模块。
步骤2、分析电荷泵CP单元和通用TIS模块的连接方式,将事先建好的电荷泵CP单元的模型嵌入通用TIS建模模块得到目标电力电子变换器的等效TIS-CP建模模块。
TI-CP-Boost电力电子变换器中的电荷泵CP单元及其和通用TIS建模模块相连接的外部支路大信号模型如图8所示。根据电荷泵CP单元和通用TIS建模模块相连的支路可以得到两个模块的变量之间有如下关系:The large-signal model of the charge pump CP unit in the TI-CP-Boost power electronic converter and its external branch connected to the general TIS modeling module is shown in Figure 8. According to the branch connected between the charge pump CP unit and the general TIS modeling module, the following relationship between the variables of the two modules can be obtained:
i0c=-niP i 0c =-ni P
i1c=-(n+1)iP i 1c =-(n+1)i P
iO=i2c i O =i 2c
vLmcp=-a(1-d)vcp v Lmcp =-a(1-d)v cp
vC=(n+1)v1-nv0 v C =(n+1)v 1 -nv 0
其中i0cp、i1cp和i2cp分别为电荷泵CP单元所引起的通用TIS建模模块的0端子电流分量、1端子电流分量和2端子电流分量,vLmcp为电荷泵CP单元所引起的通用TIS建模模块的励磁电感电压分量。Among them, i 0cp , i 1cp and i 2cp are the 0-terminal current component, 1-terminal current component and 2-terminal current component of the general TIS modeling module caused by the charge pump CP unit, v Lmcp is the general TIS current component caused by the charge pump CP unit The magnetizing inductance voltage component of the TIS modeling module.
同时考虑到在通用TIS建模模块中端子电流有如下关系:At the same time, it is considered that the terminal current has the following relationship in the general TIS modeling module:
i0=i1+i2 i 0 =i 1 +i 2
可将电荷泵CP单元和通用TIS建模模块的大信号模型方程修改后联立得到等效TIS-CP建模模块的大信号模型如下:The large signal model equation of the charge pump CP unit and the general TIS modeling module can be modified and combined to obtain the large signal model of the equivalent TIS-CP modeling module as follows:
步骤3、分析待建模的目标电力电子变换器拓扑,将目标电力电子变换器划分为等效TIS-CP建模模块和等效TIS-CP建模模块外部线性网络两个部分,构建由目标开关变换等效TIS-CP模块和目标电力电子变换器等效TIS-CP模块外部线性网络组成的目标电力电子变换器TIS-CP等效电路,如图9所示;Step 3. Analyze the topology of the target power electronic converter to be modeled, divide the target power electronic converter into two parts: the equivalent TIS-CP modeling module and the external linear network of the equivalent TIS-CP modeling module, and construct the The target power electronic converter TIS-CP equivalent circuit composed of the switch conversion equivalent TIS-CP module and the target power electronic converter equivalent TIS-CP module external linear network is shown in Figure 9;
步骤4、确定目标电力电子变换器等效TIS-CP模块外部线性网络的状态方程。根据TIS-CP-Boost变换器中的等效TIS-CP模块外部线性网络,得到外部线性网络的状态方程如下:Step 4. Determine the state equation of the external linear network of the equivalent TIS-CP module of the target power electronic converter. According to the equivalent TIS-CP module external linear network in the TIS-CP-Boost converter, the state equation of the external linear network is obtained as follows:
其中负载阻抗Zout为:where the load impedance Z out is:
以及目标电力电子变换器等效TIS-CP模块的内部参数,包括有效匝数比a、通用耦合电感的励磁电感Lm如下:And the internal parameters of the equivalent TIS-CP module of the target power electronic converter, including the effective turns ratio a, and the excitation inductance L m of the general coupling inductor are as follows:
式中,N10为TIS-CP-Boost电力电子变换器等效TIS-CP模块端子1和0之间的耦合电感匝数,N20为TIS-CP-Boost电力电子变换器等效TIS-CP模块端子2和0之间的耦合电感匝数,N1为TIS-CP-Boost电力电子变换器的变压器原边绕组匝数,L1为TIS-CP-Boost开关建模的电力电子变换器的变压器原边绕组电感量。In the formula, N 10 is the number of coupling inductance turns between
步骤5、将目标电力电子变换器等效TIS-CP模块外部线性网络状态方程以及目标电力电子变换器等效TIS-CP模块内参数,代入等效TIS-CP模块稳态模型、大信号模型或小信号模型中,得到待建模的目标电力电子变换器的稳态模型、大信号模型或小信号模型。Step 5. Substitute the external linear network state equation of the equivalent TIS-CP module of the target power electronic converter and the internal parameters of the equivalent TIS-CP module of the target power electronic converter into the steady-state model, large signal model or In the small-signal model, a steady-state model, a large-signal model or a small-signal model of the target power electronic converter to be modeled is obtained.
如图10所示的TIS-CP-Boost电力电子变换器的大信号模型,也可由方程组的形式表述如下:The large signal model of the TIS-CP-Boost power electronic converter shown in Figure 10 can also be expressed in the form of equations as follows:
如图11所示的TIS-CP-Boost电力电子变换器的稳态模型,也可由方程组的形式表述如下:The steady-state model of the TIS-CP-Boost power electronic converter shown in Figure 11 can also be expressed in the form of equations as follows:
由稳态模型方程可以求得稳态解表达式如下:The steady-state solution expression can be obtained from the steady-state model equation as follows:
Vcp=nVg V cp = nV g
如图12所示的TIS-CP-Boost电力电子变换器的小信号模型,也可由方程组的形式表述如下:The small-signal model of the TIS-CP-Boost power electronic converter shown in Figure 12 can also be expressed in the form of equations as follows:
其中增益Zout的表达式为:The expression of the gain Z out is:
步骤6、根据目标电力电子变换器的稳态模型求得稳态解,再将稳态解代入目标电力电子变换器的小信号模型中,即得此变换器的小信号传递函数可用于进一步的分析和计算。Step 6. Obtain the steady-state solution according to the steady-state model of the target power electronic converter, and then substitute the steady-state solution into the small-signal model of the target power electronic converter, that is, the small-signal transfer function of the converter can be used for further analysis and calculation.
将步骤5中求得的稳态解代入TIS-CP-Boost电力电子变换器的小信号模型即可求得该变换器的控制到输出的小信号传递函数如下:Substituting the steady-state solution obtained in step 5 into the small-signal model of the TIS-CP-Boost power electronic converter, the small-signal transfer function from control to output of the converter can be obtained as follows:
将本实例中的仿真参数代入上式,可得TI-CP-Boost的小信号传递函数为:Substituting the simulation parameters in this example into the above formula, the small signal transfer function of TI-CP-Boost can be obtained as:
图13展示了通过此建模方法计算得到的TI-CP-Boost电力电子变换器控制到输出的频域特性伯德图和通过仿真得到的控制到输出的频域特性伯德图的对比,可见二者有很高的匹配度,仿真结果验证了此建模方法的正确性。Figure 13 shows the comparison between the Bode diagram of the frequency domain characteristics of the TI-CP-Boost power electronic converter from control to output calculated by this modeling method and the Bode diagram of the frequency domain characteristics of control to output obtained through simulation. It can be seen that The two have a high degree of matching, and the simulation results verify the correctness of this modeling method.
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