阅读说明：本技术 一种级联型电力电子变压器整体小信号建模方法 (Integral small signal modeling method for cascade power electronic transformer ) 是由 徐永海 徐少博 龙云波 刘兴旺 董旭 于 2020-12-16 设计创作，主要内容包括：本发明公开了属于电力电子技术领域的一种级联型电力电子变压器整体小信号建模方法。分别建立级联型电力电子变压器输入级、隔离级和输出级状态空间方程并将方程线性化处理,得到对应小信号模型；以输入级交直流侧电压关系方程、隔离级高低压侧功率传输方程以及输出级交直流侧电压关系方程为联系方程,修正输入级和隔离级小信号模型,进而组合形成整体信号模型。该方法在不影响模型精度的同时降低了建模过程复杂度；另一方面,当电力电子变压器输入级、隔离级、输出级采用不同拓扑结构或控制方式时,仅需调整对应部分小信号模型结构,即可组合形成新的电力电子变压器对应的小信号模型,从而避免重新建立整体小信号模型。(The invention discloses a modeling method for an integral small signal of a cascade power electronic transformer, belonging to the technical field of power electronics. Respectively establishing state space equations of an input stage, an isolation stage and an output stage of the cascaded power electronic transformer, and carrying out linearization processing on the equations to obtain corresponding small signal models; and correcting the input stage and isolation stage small signal models by taking an input stage AC-DC side voltage relation equation, an isolation stage high-low voltage side power transmission equation and an output stage AC-DC side voltage relation equation as a relation equation, and further combining to form an integral signal model. The method reduces the complexity of the modeling process while not affecting the model precision; on the other hand, when the input stage, the isolation stage and the output stage of the power electronic transformer adopt different topological structures or control modes, a new small signal model corresponding to the power electronic transformer can be formed by combining only by adjusting the corresponding small signal model structures, so that the reestablishment of the whole small signal model is avoided.)

1. A modeling method for an integral small signal of a cascade power electronic transformer is characterized by comprising the following steps:

step S1: establishing a state space equation of a high-voltage input stage of the cascade power electronic transformer, carrying out linearization processing on the equation, and deducing a corresponding small signal model;

step S2: establishing a state space equation of an intermediate isolation stage of the cascade power electronic transformer, carrying out linearization processing on the equation and deducing a corresponding small signal model;

step S3: establishing a low-voltage output stage state space equation of the cascade power electronic transformer, carrying out linearization processing on the equation, and deriving a corresponding small signal model;

step S4: correcting the small signal models of the input stage and the isolation stage by taking an input stage AC-DC side voltage relation equation, an isolation stage high-low voltage side power transmission equation and an output stage AC-DC side voltage relation equation as a relation equation; and combining to form an integral signal model of the cascaded power electronic transformer based on the corrected three-level small signal model.

2. The method for modeling an integral small signal of a cascaded power electronic transformer according to claim 1, wherein the step S1 comprises the following sub-steps:

step S11: the input current at the high-voltage alternating current side of the cascade power electronic transformer is taken as a state variable, an input stage alternating current side state space equation of the cascade power electronic transformer is established, the equation considers the influence of the equivalent impedance of an alternating current system, the filter inductance at the high-voltage alternating current side of the cascade power electronic transformer and the equivalent resistance from a power grid common point to a port circuit of the cascade power electronic transformer,

in the formula: t is a time variable, i_sdFor the active component of the input current, i_sqFor reactive components of input current, R_tThe equivalent electricity from the common point of the system equivalent resistance and the power grid to the port line of the cascade power electronic transformerSum of resistances, L_tIs the sum of the equivalent reactance and the filter inductance of the system, omega is the angular frequency of the alternating current system, u_cdIs a cascade power electronic transformer input stage port voltage active component u_cqIs a reactive component of the input stage port voltage of the cascade type power electronic transformer u_sdIs a system voltage active component, u_sqIs a system voltage reactive component;

step S12: establishing a state space equation of an input stage direct current side of the cascade power electronic transformer by taking the capacitance voltage of an input stage submodule of the cascade power electronic transformer as a state variable:

in the formula: u. of_mIs the capacitance voltage of an input stage submodule of a cascade power electronic transformer, C_mIs the capacitance value i of an input stage submodule capacitor of a cascade power electronic transformer_mInjecting current i to input stage side of input stage submodule capacitor of cascade power electronic transformer_inOutputting current for an isolation level side of an input level sub-module capacitor of the cascade power electronic transformer;

step S13: the input stage of the cascade power electronic transformer adopts voltage outer ring current inner ring double-ring control, and the state space equation of the input stage controller of the cascade power electronic transformer is established by taking the integral output quantity of the controller as a state variable:

in the formula: x is the number of₁For the output quantity, x, of the voltage outer loop integral link in the active component controller₂The output quantity, x, of the current inner loop integral link in the active component controller₃For the output of the current inner loop integral link, k, in the reactive component controller_p1Proportional gain, k, of the outer loop of the voltage_i1For voltage outer loop integral gain, k_i2Is the current inner loop integral gain, u_mrefFor sub-module capacitor voltage reference value, i_sqrefIs a reactive current component reference value;

step S14: according to the input stage controller structure of the cascade power electronic transformer, establishing a controller output equation:

in the formula: m_dFor the real component controller output, M_qFor the reactive component controller output, u_pdFor the active component of the grid common point voltage, u_pqFor reactive component of voltage at common point of the grid, k_p2Is the current inner loop proportional gain, L_fA high voltage AC side filter inductor;

step S15: constructing a phase-locked link state space equation:

in the formula, x₄The output quantity of the integral link of the phase-locked loop is theta, the output angle of the phase-locked loop is k_p3For proportional gain, k, of the phase-locked loop_i3For phase-locked loop integral gain, omega₀The angular frequency is rated for the system;

step S16: constructing an output equation of a phase-locked link:

ω＝ω₀+x₄-k_P3u_pq (6)

step S17: establishing a corresponding equation of input stage alternating current side port voltage, controller output quantity and submodule capacitor voltage according to the input stage alternating current side and direct current side power conservation of the cascade power electronic transformer; establishing a corresponding equation of input stage alternating current side current, controller output quantity and submodule capacitor input stage side injection current:

wherein N is the number of cascade modules of the input stage, I_mInjecting an average value of current into the input stage side of an input stage submodule capacitor of the cascade power electronic transformer;

step S18: establishing an equation corresponding to the voltage of a high-voltage side system, the voltage of a common point of a power grid and the voltage of an input stage port of the cascade power electronic transformer:

in the formula, R_fFor equivalent resistance, R, from the grid common point to the port line of the cascaded power electronic transformer_sIs a system equivalent resistance, L_sIs the equivalent inductance of the system;

step S19: and (3) integrating the equations (1) - (8), constructing an integral state space equation of the input stage of the cascade power electronic transformer, wherein the integral state space equation comprises the high-voltage system side equivalent impedance, the line equivalent resistance, the alternating current and direct current side electrical equation and a control equation, and performing linearization processing to obtain a corresponding small signal model:

in the formula, A_CIs an input stage system matrix, B_CFor input stage input matrix, X_CIs an input stage state variable vector, U_CA vector of variables is input for the input stage,is an input stage state variable differential vector; wherein

X_C＝[Δi_sd Δi_sq Δu_m Δx₁ Δx₂ Δx₃ Δx₄ Δθ]^T，U_C＝[Δu_sd Δu_sq Δu_mref Δi_sqrefΔi_in]^T。

3. The method for modeling an integral small signal of a cascaded power electronic transformer according to claim 1, wherein the step S2 comprises the following sub-steps:

step S21: the method comprises the following steps of (1) constructing an isolation-level low-voltage side state space equation by taking the low-voltage direct-current side capacitor voltage of a cascade power electronic transformer as a state variable:

in the formula: u. of_dcFor isolating the low-voltage side DC capacitor voltage, C_dcFor isolating the low-side DC capacitor of stage i_dinInjecting current i into the isolation side of the isolation-stage low-voltage side DC capacitor_doutOutputting current for the output stage side of the isolation stage low-voltage side direct current capacitor;

step S22: establishing a relation equation of the injection current of the isolation level side of the low-voltage direct-current capacitor, the control quantity of the isolation level and the electrical quantity of the isolation level:

in the formula: k is the primary-secondary side transformation ratio of the high-frequency transformer, f_sIs the working frequency of the high-frequency transformer,is the primary and secondary side phase shift angle, L, of the high-frequency transformer_htFor leakage inductance of high-frequency transformers, I_dinThe average value of the injection current of the isolation level side of the isolation level low-voltage side direct current capacitor is obtained;

step S23: the isolation level of the cascade power electronic transformer adopts PI single-ring constant low-voltage side direct-current voltage control, and the output quantity of the integral link of the controller is used as a state variable to construct an isolation level controller state space equation:

in the formula: x is the number of₅Integrating the output of the loop, k, for the controller_i4Integrating the gain for the controller; u. of_dcrIs a low voltage DC side voltage reference value;

step S24: according to the structure of the isolation level controller of the cascade power electronic transformer, an output equation of the isolation level controller is constructed:

in the formula: k is a radical of_p4Proportional gain for the controller;

step S25: and (3) synthesizing (10) - (13), constructing a state space equation of an isolation stage of the cascaded power electronic transformer, and performing linearization processing to obtain a corresponding small signal model:

in the formula: a. the_DFor the isolation level system matrix, B_DFor isolating the stage input matrix, X_DFor isolation level state variable vectors, U_DTo input the variable vector for the isolation stage,is an isolation stage state variable differential vector; wherein, X_D＝[Δu_dc Δx₅]^T，U_D＝[ΔU_dcr Δi_dout]^T。

4. The method for modeling an integral small signal of a cascaded power electronic transformer according to claim 1, wherein the step S3 comprises the following sub-steps:

step S31: the method comprises the following steps of (1) constructing a state space equation by taking the filtering inductance current of an alternating current port of an output stage of a cascade power electronic transformer as a state variable:

in the formula: i.e. i_mdFor filtering the active component of the inductor current, i, in the output stage_mqFor filtering the reactive component of the inductor current, R, in the output stage_flIs the filter equivalent resistance, L_flIs a filter inductance, u_ldFor the active component of the voltage at the output stage port of the cascaded power electronic transformer u_lqFor reactive component of voltage at output stage port of cascade power electronic transformer u_gdIs the active component of the low-side system voltage u_gqThe voltage reactive component of the low-voltage side system;

step S32: the method comprises the following steps of (1) constructing a state space equation by taking the voltage of an alternating current port filter capacitor of an output stage of a cascade power electronic transformer as a state variable:

in the formula: c_fIs the capacitance value of the filter capacitor; i.e. i_gdAs a real component of load current i_gqIs a load current reactive component;

step S33: establishing a state space equation of an output stage alternating current side of the cascade power electronic transformer by taking the output stage alternating current load current of the cascade power electronic transformer as a state variable:

in the formula: r_LIs a load resistance, L_lIs a line equivalent inductance;

step S34: the output stage of the cascade power electronic transformer adopts voltage outer loop current inner loop PI control, and the state space equation of the input stage controller of the cascade power electronic transformer is established by taking the integral output quantity of each controller as a state variable:

in the formula: x is the number of₆For the output quantity, x, of the voltage outer loop integral link in the active component controller₇For the output quantity, x, of the voltage outer loop integral link in the reactive component controller₈The output quantity, x, of the current inner loop integral link in the active component controller₉For the output of the current inner loop integral link, k, in the reactive component controller_p5Proportional gain, k, of the outer loop of the voltage_i5For voltage outer loop integral gain, k_i6Is the current inner loop integral gain, u_gdrefIs a reference value of active component of low-voltage side system voltage, u_gqrefThe reference value is the voltage reactive component reference value of the low-voltage side system;

step S35: according to the structure of the cascade power electronic transformer output stage controller, establishing a controller output equation:

in the formula: m_ldFor the real component controller output, M_lqThe output quantity of the reactive component controller is obtained;

step S36: establishing a relation equation between the voltage of the low-voltage direct-current side of the isolation stage and the voltage of the alternating-current port of the output stage:

step S37: and (5) synthesizing (15) - (20), constructing a state space equation of an output stage of the cascaded power electronic transformer, and performing linearization processing to obtain a corresponding small signal model:

in the formula: a. the_LFor the output stage system matrix, B_LFor the input matrix of the output stage, X_LFor output stage state variable vectors, U_LFor the input variable vector of the output stage,is an output stage state variable differential vector; wherein the content of the first and second substances,

X_L＝[Δi_md Δi_mq Δi_gd Δi_gq Δu_gd Δu_gq Δx₆ Δx₇ Δx₈ Δx₉]^T，U_L＝[Δu_gdref Δu_gqref ΔR_L Δu_dc]^T。

5. the method for modeling an integral small signal of a cascaded power electronic transformer according to claim 1, wherein the step S4 comprises the following sub-steps:

step S41: establishing a relation equation of the output current of the isolation level side of the sub-module capacitor, the control quantity of the isolation level and the electrical quantity of the isolation level:

step S42: establishing a relation equation between the output current of the low-voltage direct-current capacitor output stage side and the load current:

in the formula: i is_doutThe average value of the output current of the output stage side of the low-voltage direct current capacitor is obtained;

step S43: the integral small signal model of the cascade power electronic transformer can be established by substituting the formula (22) into the formula (9), substituting the formula (23) into the formula (14) and combining the formula (9), (14) and (21)

In the formula: a. the_PIs a power electronic transformer overall system matrix, B_PFor power electronic transformers, integral input matrix, X_PIs the integral state variable vector, U, of the power electronic transformer_PA variable vector is input for the whole power electronic transformer,the differential vector is the integral state variable differential vector of the power electronic transformer; wherein

X_P＝[Δi_sd Δi_sq Δu_m Δx₁ Δx₂ Δx₃ Δx₄ Δθ Δu_dc Δx₅ Δi_md Δi_mq Δi_gd Δi_gqΔu_gd Δu_gq Δx₆ Δx₇ Δx₈ Δx₉]^T，U_P＝[Δu_sd Δu_sq Δu_mref Δi_sqref ΔU_dcr Δu_gdref Δu_gqref ΔR_L]^T。

Technical Field

The invention relates to the technical field of power electronics, in particular to a method for modeling an integral small signal of a cascade power electronic transformer.

Background

A power electronic transformer is a power electronic device that contains a power electronic converter and implements magnetic coupling through a medium (high) frequency transformer. Besides the functions of electrical isolation and voltage conversion of the traditional transformer, the direct current and direct current transformer can also provide a plug-and-play alternating current interface for renewable energy sources and energy storage, so that bidirectional controllability of energy flow is realized, and the quality of electric energy is improved. A power electronic transformer applied to a power distribution network generally comprises three parts, namely a high-voltage input stage, an intermediate isolation stage and a low-voltage side output stage. Due to the limitation of the voltage resistance of the device, the high-voltage side usually adopts a modular cascade structure. The existing research on the cascade power electronic transformer mostly focuses on the aspects of topology design, modulation strategy design, control strategy design, soft switching technology and the like, and the stability analysis, parameter optimization design and the like are still lack of deep research; in small-signal modeling, modeling analysis is mainly performed on single equipment such as a voltage source type AC/DC converter or a DC/DC converter in the related art. For the cascaded power electronic transformer, the overall structure is complex, the order of the overall small signal model is high, the modeling difficulty is high, and related researches are still lacked.

Therefore, a detailed modeling method suitable for the whole small signal of the cascade power electronic transformer is needed, the influence of the parameters of the alternating current system, the hardware parameters of the power electronic transformer and the parameters of the controller can be fully considered, the links of the alternating current system side, the high-voltage input stage, the isolation stage, the low-voltage output stage and the output filtering stage are covered, and the difficulty of the modeling process is reduced as much as possible. The model has important significance for stability performance analysis and hardware parameter and control parameter optimization of the cascade power electronic transformer in engineering application.

Disclosure of Invention

The invention aims to provide an integral small signal modeling method for a cascade power electronic transformer, which is characterized by comprising the following steps of:

step S1: establishing a state space equation of a high-voltage input stage of the cascade power electronic transformer, carrying out linearization processing on the equation, and deducing a corresponding small signal model;

step S2: establishing a state space equation of an intermediate isolation stage of the cascade power electronic transformer, carrying out linearization processing on the equation and deducing a corresponding small signal model;

step S3: establishing a low-voltage output stage state space equation of the cascade power electronic transformer, carrying out linearization processing on the equation, and deriving a corresponding small signal model;

step S4: correcting the small signal models of the input stage and the isolation stage by taking an input stage AC-DC side voltage relation equation, an isolation stage high-low voltage side power transmission equation and an output stage AC-DC side voltage relation equation as a relation equation; and combining to form an integral signal model of the cascaded power electronic transformer based on the corrected three-level small signal model.

The step S1 includes the following substeps:

step S11: the input current at the high-voltage alternating current side of the cascade power electronic transformer is taken as a state variable, an input stage alternating current side state space equation of the cascade power electronic transformer is established, the equation considers the influence of the equivalent impedance of an alternating current system, the filter inductance at the high-voltage alternating current side of the cascade power electronic transformer and the equivalent resistance from a power grid common point to a port circuit of the cascade power electronic transformer,

in the formula: t is a time variable, i_sdFor the active component of the input current, i_sqFor reactive components of input current, R_tIs the sum of the system equivalent resistance and the equivalent resistance from the common point of the power grid to the port line of the cascade power electronic transformer, L_tIs the sum of the equivalent reactance and the filter inductance of the system, omega is the angular frequency of the alternating current system, u_cdIs a cascade power electronic transformer input stage port voltage active component u_cqIs a reactive component of the input stage port voltage of the cascade type power electronic transformer u_sdIs a system voltage active component, u_sqIs a system voltage reactive component;

step S12: establishing a state space equation of an input stage direct current side of the cascade power electronic transformer by taking the capacitance voltage of an input stage submodule of the cascade power electronic transformer as a state variable:

in the formula: u. of_mIs the capacitance voltage of an input stage submodule of a cascade power electronic transformer, C_mIs the capacitance value i of an input stage submodule capacitor of a cascade power electronic transformer_mInjecting current i to input stage side of input stage submodule capacitor of cascade power electronic transformer_inOutputting current for an isolation level side of an input level sub-module capacitor of the cascade power electronic transformer;

step S13: the input stage of the cascade power electronic transformer adopts voltage outer ring current inner ring double-ring control, and the state space equation of the input stage controller of the cascade power electronic transformer is established by taking the integral output quantity of the controller as a state variable:

in the formula: x is the number of₁For the output quantity, x, of the voltage outer loop integral link in the active component controller₂The output quantity, x, of the current inner loop integral link in the active component controller₃For the output of the current inner loop integral link, k, in the reactive component controller_p1Proportional gain, k, of the outer loop of the voltage_i1For voltage outer loop integral gain, k_i2Is the current inner loop integral gain, u_mrefFor sub-module capacitor voltage reference value, i_sqrefIs a reactive current component reference value;

step S14: according to the input stage controller structure of the cascade power electronic transformer, establishing a controller output equation:

in the formula: m_dFor the real component controller output, M_qFor the reactive component controller output, u_pdFor the active component of the grid common point voltage, u_pqFor reactive component of voltage at common point of the grid, k_p2Is the current inner loop proportional gain, L_fA high voltage AC side filter inductor;

step S15: constructing a phase-locked link state space equation:

in the formula, x₄The output quantity of the integral link of the phase-locked loop is theta, the output angle of the phase-locked loop is k_p3For proportional gain, k, of the phase-locked loop_i3For phase-locked loop integral gain, omega₀The angular frequency is rated for the system;

step S16: constructing an output equation of a phase-locked link:

ω＝ω₀+x₄-k_P3u_pq (6)

step S17: establishing a corresponding equation of input stage alternating current side port voltage, controller output quantity and submodule capacitor voltage according to the input stage alternating current side and direct current side power conservation of the cascade power electronic transformer; establishing a corresponding equation of input stage alternating current side current, controller output quantity and submodule capacitor input stage side injection current:

wherein N is the number of cascade modules of the input stage, I_mInjecting an average value of current into the input stage side of an input stage submodule capacitor of the cascade power electronic transformer;

step S18: establishing an equation corresponding to the voltage of a high-voltage side system, the voltage of a common point of a power grid and the voltage of an input stage port of the cascade power electronic transformer:

in the formula, R_fFor equivalent resistance, R, from the grid common point to the port line of the cascaded power electronic transformer_sIs a system equivalent resistance, L_sIs the equivalent inductance of the system;

step S19: and (3) integrating the equations (1) - (8), constructing an integral state space equation of the input stage of the cascade power electronic transformer, wherein the integral state space equation comprises the high-voltage system side equivalent impedance, the line equivalent resistance, the alternating current and direct current side electrical equation and a control equation, and performing linearization processing to obtain a corresponding small signal model:

in the formula, A_CIs an input stage system matrix, B_CFor input stage input matrix, X_CIs an input stage state variable vector, U_CA vector of variables is input for the input stage,is an input stage state variable differential vector; wherein

X_C＝[Δi_sd Δi_sq Δu_m Δx₁ Δx₂ Δx₃ Δx₄ Δθ]^T，U_C＝[Δu_sd Δu_sq Δu_mref Δi_sqref Δi_in]^T。

The step S2 includes the following substeps:

step S21: the method comprises the following steps of (1) constructing an isolation-level low-voltage side state space equation by taking the low-voltage direct-current side capacitor voltage of a cascade power electronic transformer as a state variable:

in the formula: u. of_dcFor isolating the low-voltage side DC capacitor voltage, C_dcFor isolating the low-side DC capacitor of stage i_dinInjecting current i into the isolation side of the isolation-stage low-voltage side DC capacitor_doutOutputting current for the output stage side of the isolation stage low-voltage side direct current capacitor;

step S22: establishing a relation equation of the injection current of the isolation level side of the low-voltage direct-current capacitor, the control quantity of the isolation level and the electrical quantity of the isolation level:

in the formula: k is the primary-secondary side transformation ratio of the high-frequency transformer, f_sIs the working frequency of the high-frequency transformer,is the primary and secondary side phase shift angle, L, of the high-frequency transformer_htFor leakage inductance of high-frequency transformers, I_dinThe average value of the injection current of the isolation level side of the isolation level low-voltage side direct current capacitor is obtained;

step S23: the isolation level of the cascade power electronic transformer adopts PI single-ring constant low-voltage side direct-current voltage control, and the output quantity of the integral link of the controller is used as a state variable to construct an isolation level controller state space equation:

in the formula: x is the number of₅Integrating the output of the loop, k, for the controller_i4Integrating the gain for the controller; u. of_dcrIs a low voltage DC side voltage reference value;

step S24: according to the structure of the isolation level controller of the cascade power electronic transformer, an output equation of the isolation level controller is constructed:

in the formula: k is a radical of_p4Proportional gain for the controller;

step S25: and (3) synthesizing (10) - (13), constructing a state space equation of an isolation stage of the cascaded power electronic transformer, and performing linearization processing to obtain a corresponding small signal model:

in the formula: a. the_DFor the isolation level system matrix, B_DFor isolating the stage input matrix, X_DFor isolation level state variable vectors, U_DTo input the variable vector for the isolation stage,is an isolation stage state variable differential vector; wherein, X_D＝[Δu_dcΔx₅]^T，U_D＝[ΔU_dcrΔi_dout]^T。

The step S3 includes the following substeps:

step S31: the method comprises the following steps of (1) constructing a state space equation by taking the filtering inductance current of an alternating current port of an output stage of a cascade power electronic transformer as a state variable:

in the formula: i.e. i_mdFor filtering the active component of the inductor current, i, in the output stage_mqFor filtering the reactive component of the inductor current, R, in the output stage_flIs the filter equivalent resistance, L_flIs a filter inductance, u_ldFor the active component of the voltage at the output stage port of the cascaded power electronic transformer u_lqFor reactive component of voltage at output stage port of cascade power electronic transformer u_gdIs the active component of the low-side system voltage u_gqThe voltage reactive component of the low-voltage side system;

step S32: the method comprises the following steps of (1) constructing a state space equation by taking the voltage of an alternating current port filter capacitor of an output stage of a cascade power electronic transformer as a state variable:

in the formula: c_fIs the capacitance value of the filter capacitor; i.e. i_gdAs a real component of load current i_gqIs a load current reactive component;

step S33: establishing a state space equation of an output stage alternating current side of the cascade power electronic transformer by taking the output stage alternating current load current of the cascade power electronic transformer as a state variable:

in the formula: r_LIs a load resistance, L_lIs a line equivalent inductance;

step S34: the output stage of the cascade power electronic transformer adopts voltage outer loop current inner loop PI control, and the state space equation of the input stage controller of the cascade power electronic transformer is established by taking the integral output quantity of each controller as a state variable:

in the formula: x is the number of₆For the output quantity, x, of the voltage outer loop integral link in the active component controller₇For the output quantity, x, of the voltage outer loop integral link in the reactive component controller₈The output quantity, x, of the current inner loop integral link in the active component controller₉For the output of the current inner loop integral link, k, in the reactive component controller_p5Proportional gain, k, of the outer loop of the voltage_i5For voltage outer loop integral gain, k_i6Is the current inner loop integral gain, u_gdrefIs a reference value of active component of low-voltage side system voltage, u_gqrefThe reference value is the voltage reactive component reference value of the low-voltage side system;

step S35: according to the structure of the cascade power electronic transformer output stage controller, establishing a controller output equation:

in the formula: m_ldFor the real component controller output, M_lqThe output quantity of the reactive component controller is obtained;

step S36: establishing a relation equation between the voltage of the low-voltage direct-current side of the isolation stage and the voltage of the alternating-current port of the output stage:

step S37: and (5) synthesizing (15) - (20), constructing a state space equation of an output stage of the cascaded power electronic transformer, and performing linearization processing to obtain a corresponding small signal model:

in the formula: a. the_LFor the output stage system matrix, B_LFor the input matrix of the output stage, X_LFor output stage state variable vectors, U_LFor the input variable vector of the output stage,is an output stage state variable differential vector; wherein the content of the first and second substances,

X_L＝[Δi_md Δi_mq Δi_gd Δi_gq Δu_gd Δu_gq Δx₆ Δx₇ Δx₈ Δx₉]^T，U_L＝[Δu_gdrefΔu_gqref ΔR_L Δu_dc]^T。

the step S4 includes the following substeps:

step S41: establishing a relation equation of the output current of the isolation level side of the sub-module capacitor, the control quantity of the isolation level and the electrical quantity of the isolation level:

step S42: establishing a relation equation between the output current of the low-voltage direct-current capacitor output stage side and the load current:

in the formula: i is_doutThe average value of the output current of the output stage side of the low-voltage direct current capacitor is obtained;

step S43: the integral small signal model of the cascade power electronic transformer can be established by substituting the formula (22) into the formula (9), substituting the formula (23) into the formula (14) and combining the formula (9), (14) and (21)

In the formula: a. the_PIs a power electronic transformer overall system matrix, B_PFor power electronic transformers, integral input matrix, X_P

Is the integral state variable vector, U, of the power electronic transformer_PA variable vector is input for the whole power electronic transformer,the differential vector is the integral state variable differential vector of the power electronic transformer; wherein

X_P＝[Δi_sd Δi_sq Δu_m Δx₁ Δx₂ Δx₃ Δx₄ Δθ Δu_dc Δx₅ Δi_md Δi_mq Δi_gdΔi_gq Δu_gd Δu_gq Δx₆ Δx₇ Δx₈ Δx₉]^T，U_P＝[Δu_sd Δu_sq Δu_mref Δi_sqref ΔU_dcr Δu_gdref Δu_gqref ΔR_L]^T。

The invention has the beneficial effects that:

on one hand, the complexity of the modeling process is reduced under the condition of not influencing the model precision; on the other hand, when the input stage, the isolation stage and the output stage of the power electronic transformer adopt different topological structures or control modes, the corresponding small signal model structures of the new power electronic transformer can be combined and formed only by adjusting the small signal model structures of the corresponding parts, so that the reestablishment of the whole small signal model of the power electronic transformer is avoided.

Drawings

FIG. 1 is a cascaded power electronic transformer topology;

FIG. 2 is a small-signal modeling equivalent circuit diagram of a cascaded power electronic transformer;

FIG. 3 is a control block diagram of an input stage of a cascaded power electronic transformer;

FIG. 4 is a phase locked loop control block diagram;

FIG. 5 is a block diagram of control of an isolation stage of a cascaded power electronic transformer;

FIG. 6 is a control block diagram of the output stage of the cascaded power electronic transformer;

FIG. 7 is a cascaded power electronic transformer topology with L filters for the low voltage output stage;

FIG. 8 is a block diagram of output stage control using constant power grid connection control;

fig. 9 is a flowchart for establishing a small signal model of a cascaded power electronic transformer.

Detailed Description

The invention provides an integral small signal modeling method for a cascade power electronic transformer, which is further explained by combining the attached drawings and specific embodiments.

Fig. 1 is a topological structure diagram of a cascaded power electronic transformer, which comprises an input stage, an isolation stage and an output stage, wherein the input stage adopts an H-bridge cascaded structure, the isolation stage adopts a double-active-bridge structure, the output stage adopts a three-phase three-wire inverter structure, and a filtering link adopts an LC filter.

Starting from fig. 2, the small-signal modeling equivalent circuit diagram of the cascaded power electronic transformer of the invention is specifically as follows:

and establishing a state space equation of the input stage alternating current side of the cascade power electronic transformer by taking the input current of the high voltage alternating current side of the cascade power electronic transformer as a state variable.

Establishing a state space equation of an input stage direct current side of the cascade power electronic transformer by taking the capacitance voltage of an input stage submodule of the cascade power electronic transformer as a state variable:

the input stage of the cascade power electronic transformer adopts voltage outer loop and current inner loop double loop control, as shown in fig. 3, and the state space equation of the input stage controller of the cascade power electronic transformer is established by taking each integral output quantity of the controller as a state variable:

according to the input stage controller structure of the cascade power electronic transformer, establishing a controller output equation:

constructing a phase-locked link state space equation:

constructing an output equation of a phase-locked link:

ω＝ω₀+x₄-k_P3u_pq (6)

wherein the phase locked loop control block diagram is shown in figure 4.

Establishing a corresponding equation of input stage alternating current side port voltage, controller output quantity and submodule capacitor voltage according to the input stage alternating current side and direct current side power conservation of the cascade power electronic transformer; establishing a corresponding equation of input stage alternating current side current, controller output quantity and submodule capacitor input stage side injection current:

establishing an equation corresponding to the voltage of a high-voltage side system, the voltage of a common point of a power grid and the voltage of an input stage port of the cascade power electronic transformer:

and (3) synthesizing the models (1) to (8), constructing an input stage state space equation of the cascade power electronic transformer, and performing linearization processing to obtain a corresponding small signal model:

wherein the state variable matrix is X_C＝[Δi_sd Δi_sq Δu_m Δx₁ Δx₂ Δx₃ Δx₄ Δθ]^T

Disturbance variable matrix is U_C＝[Δu_sd Δu_sq Δu_mref Δi_sqref Δi_in]^T,

And (2) constructing an isolation-level low-voltage side state space equation by taking the low-voltage direct-current side capacitor voltage of the cascade power electronic transformer as a state quantity:

establishing a relation equation of the injection current of the isolation level side of the low-voltage direct-current capacitor, the control quantity of the isolation level and the electrical quantity of the isolation level:

the isolation level of the cascaded power electronic transformer adopts PI single-loop constant low-voltage side direct-current voltage control, and as shown in FIG. 5, an isolation level controller state space equation is constructed by taking the integral output quantity of the controller as a state quantity:

according to the structure of the isolation level controller of the cascade power electronic transformer, an output equation of the isolation level controller is constructed:

and (3) synthesizing (10) - (13), constructing a state space equation of an isolation stage of the cascaded power electronic transformer, and performing linearization processing to obtain a corresponding small signal model:

wherein the state variable matrix is X_D＝[Δu_dcΔx₅]^TThe disturbance variable matrix is U_D＝[ΔU_dcrΔi_dout]^T。

The method comprises the following steps of (1) constructing a state space equation by taking the filtering inductance current of an alternating current port of an output stage of a cascade power electronic transformer as a state quantity:

the method comprises the following steps of (1) constructing a state space equation by taking the voltage of an alternating current port filter capacitor of an output stage of a cascade power electronic transformer as a state quantity:

establishing a state space equation of an output stage alternating current side of the cascade power electronic transformer by taking the output stage alternating current load current of the cascade power electronic transformer as a state variable:

the output stage of the cascade power electronic transformer is controlled by a voltage outer loop current inner loop PI, and as shown in fig. 6, the state space equation of the input stage controller of the cascade power electronic transformer is established by taking each integral output quantity of the controller as a state variable:

according to the structure of the cascade power electronic transformer output stage controller, establishing a controller output equation:

establishing a relation equation between the voltage of the low-voltage direct-current side of the isolation stage and the voltage of the alternating-current port of the output stage:

and (5) synthesizing (15) - (20), constructing a state space equation of an output stage of the cascaded power electronic transformer, and performing linearization processing to obtain a corresponding small signal model:

wherein the state variable matrix is X_L＝[Δi_md Δi_mq Δi_gd Δi_gq Δu_gd Δu_gq Δx₆ Δx₇ Δx₈Δx₉]^T

Disturbance variable matrix is Delta U_L＝[Δu_gdref Δu_gqref ΔR_L Δu_dc]^T。

Establishing a relation equation of the output current of the isolation level side of the sub-module capacitor, the control quantity of the isolation level and the electrical quantity of the isolation level:

establishing a relation equation between the output current of the low-voltage direct-current capacitor output stage side and the load current:

the integral small-signal model of the cascade power electronic transformer can be established by bringing the formula (22) into the formula (9), bringing the formula (23) into the formula (14) and combining the formula (9), (14) and the formula (20).

Wherein the state variable matrix is

X_P＝[Δi_sd Δi_sq Δu_m Δx₁ Δx₂ Δx₃ Δx₄ Δθ Δu_dc Δx₅ Δi_md Δi_mq Δi_gdΔi_gq Δu_gd Δu_gq Δx₆ Δx₇ Δx₈ Δx₉]^T

Disturbance variable matrix of ΔU_P＝[Δu_sd Δu_sq Δu_mref Δi_sqref ΔU_dcr Δu_gdref Δu_gqref ΔR_L]^T。

For changing the partial topological structure or the controller form of the cascade power electronic transformer, the modeling method only needs to modify the corresponding partial small signal model and does not need to modify all the small signal models.

The output stage controller is changed from constant voltage control to load operation to constant power control grid-connected operation, a corresponding control block diagram is shown in fig. 8, a filter is changed from LC filtering to L filtering, a corresponding topology is shown in fig. 7, and the output stage is modeled again on the basis of the existing small signal model.

The method comprises the following steps of (1) constructing a state space equation by taking the filtering inductance current of an alternating current port of an output stage of a cascade power electronic transformer as a state quantity:

in the formula: i.e. i_ldFor the active component of the grid-connected current i_lqIs a reactive component of the grid-connected current.

The output stage of the cascade power electronic transformer adopts a constant power current single-ring PI control, and the state space equation of the input stage controller of the cascade power electronic transformer is established by taking the integral output quantity of each controller as a state variable:

in the formula: x is the number of₁₀The output quantity, x, of an integral link in an active component controller₁₁Is the output quantity of an integral link in a reactive component controller, P_refAs active power reference value, Q_refIs a reactive power reference value.

According to the structure of the cascade power electronic transformer output stage controller, establishing a controller output equation:

establishing a relation equation between the voltage of the low-voltage direct-current side of the isolation stage and the voltage of the alternating-current port of the output stage:

and (5) synthesizing (25) - (28), constructing a state space equation of an output stage of the cascaded power electronic transformer, and performing linearization processing to obtain a corresponding small signal model:

wherein the state variable is X_L1＝[Δi_ld Δi_lq Δx₁₀ Δx₁₁]^TThe disturbance variable is U_L1＝[ΔP_ref ΔQ_refΔu_dc]^T。

And replacing the part of the formula (21) related to the formula (24) with a formula (29), thus forming a novel cascade power electronic transformer whole small-signal model.

Fig. 9 is a flowchart for establishing a small signal model of a cascaded power electronic transformer.

The present invention is not limited to the above embodiments, and any changes or substitutions that can be easily made by those skilled in the art within the technical scope of the present invention are also within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.