A method for eliminating dominant dynamics in a voltage-controlled three-phase inverter based on complex variables.

Abstract

This invention discloses a control method for eliminating dominant dynamics in a voltage-controlled three-phase inverter based on complex variables, relating to the field of distributed power grid-connected inverter control. The method includes: constructing a system model of the three-phase inverter based on a complex state space; using a discrete complex variable resonant controller to eliminate steady-state errors in signal tracking control to obtain multiple state variables; solving for the optimized state feedback control law, obtaining the dominant pole, and setting the load current feedforward gain and reference value feedforward gain accordingly; and combining the load current disturbance variable, the output voltage reference value, the system state variables, the multiple state variables under complex variable resonant control, and the control delay state variable to determine the arm voltage control quantity of the three-phase inverter. This invention constructs a reduced-order state-space model based on complex variables and designs an inverter control structure that considers control delay and includes static feedback and feedforward terms, which can eliminate the dominant slow dynamics of the system and achieve near-zero dynamic characteristics.

Description

Technical Field

[0001] This invention relates to the field of distributed power grid-connected inverter control, and in particular to a method for eliminating dominant dynamics in a voltage-controlled three-phase inverter based on complex variables. Background Technology

[0002] In recent years, renewable energy sources such as solar and wind power have developed rapidly under the support of Chinese policies. Consequently, the number of energy storage systems, such as batteries, used to promote the use of renewable energy and the future development of electrified transportation has also increased. Three-phase inverters, typically used as interface devices between renewable energy generation devices and energy storage systems and the power grid or microgrid, will see their number in the power system increase with the large-scale integration of renewable energy generation. As a core device for power processing in sustainable energy systems, the voltage control strategy of inverters is particularly important. From the perspective of the power grid, we expect inverters to effectively resist load disturbances and quickly track changes in reference values ​​under various load conditions to cooperate with upper-level control. Secondly, we expect inverters to output high-quality voltage with low total harmonic distortion (THD), reducing harmonic pollution to the power grid and damage to AC loads.

[0003] Currently, the controllers used in inverter control can be mainly divided into two categories: linear controllers and nonlinear controllers. Traditional dual-loop control schemes are widely used, but the design of control parameters becomes more difficult when the number of controllers increases. Moreover, since they are usually designed in the continuous domain, zero-pole cancellation may not hold in the discrete domain, ultimately leading to a decrease in system performance when the controller is digitally implemented. Summary of the Invention

[0004] The purpose of this invention is to provide a control method for eliminating dominant slow dynamics in a voltage-controlled three-phase inverter based on complex variables. This method achieves voltage control of the three-phase inverter using a reduced-order state-space model based on complex variables, eliminating the system's dominant slow dynamics. This allows the inverter system to respond quickly to load disturbances and sudden changes in reference values, simplifying the control logic and reducing computational load. The technical solution adopted in this invention is as follows.

[0005] On one hand, the present invention provides a method for eliminating dominant dynamics in a voltage-controlled three-phase inverter based on complex variables, comprising:

[0006] Obtain the line parameters, load current disturbance variables, and output voltage reference values ​​of the three-phase inverter with LC filter;

[0007] Based on the acquired data, a three-phase inverter was constructed. System model based on complex state space in coordinate system;

[0008] Based on the system model, a discrete complex variable resonant controller is used to eliminate the steady-state error of signal tracking control, thereby obtaining the state variables under complex variable resonant control.

[0009] The state feedback control law is determined by considering the discrete complex variable resonant control, control delay and system state feedback gain, the system dominant pole is determined based on the state feedback control law, and the load current feedforward gain and reference value feedforward gain are set according to the state feedback control law and the system dominant pole.

[0010] Based on the system state variables, the state variables under the complex variable resonant control, the control delay state variables, and the state feedback control law, the state feedback data is obtained;

[0011] The arm voltage control quantities of the three-phase inverter are determined based on the load current disturbance variable, load current feedforward gain, output voltage reference value and reference value feedforward gain, and state feedback data.

[0012] Optionally, the discrete complex variable resonant controller can be a discrete complex variable resonant controller corresponding to the fundamental frequency, or a discrete complex variable resonant controller corresponding to multiple frequencies. When driving a linear load, only the fundamental frequency CVRC is needed to ensure that the steady-state output voltage THD is very small, while making the inverter system have near-zero dynamic characteristics. When driving a nonlinear load, multiple CVRCs can be used to effectively reduce the output voltage THD. In this case, the number of closed-loop poles will increase accordingly, and the poles of the dynamic mode corresponding to the fundamental frequency CVRC will be used as the dominant poles. By configuring zero-point and dominant pole cancellation, the system can be guaranteed to have fast dynamic response performance.

[0013] Optionally, the line parameters include: the equivalent series resistance of each phase inductor in the inverter circuit. The phase inductance L and phase capacitance C in the LC filter, and the current in each phase inductor. and capacitor voltage ;

[0014] The three-phase inverter with LC filter is in The system model based on complex state space in coordinate system is represented as follows:

[0015] ;

[0016] Among them, state variables x p = [ i L u C ] T = [ i L α + j i L β u C α + j u C β ] T , , and , These are the inductor currents. and capacitor voltage exist Components in coordinate system To represent a complex number, for The derivative;

[0017] This indicates the bridge arm voltage of the control input. This represents the load current disturbance variable. Indicates system output;

[0018] System Matrix , , , They are represented as follows:

[0019] A p = [ − R / L − 1 / L 1 / C 0 ] , B p 1 = [ 1 / L 0 ] T , B p2 = [ 0 1 / L ] T , C p = [ 0 1 ] .

[0020] Optionally, the method further includes: based on the system model based on complex state space, considering the worst-case damping case, ignoring the internal resistance of the filter inductor, discretizing the system to obtain the following analytical discrete model:

[0021] ;

[0022] Among them, the system matrix of the discretized model , , They are represented as follows:

[0023] G p = e A p T s = [ 1 − T s L T s C 1 ] , H p 1 = ∫ 0 T s e A p t d t B p 1 = [ T s L 0 ] , H p 2 = ∫ 0 T s e A p t d t B p 2 = [ 0 − T s C ] ;

[0024] Indicates the sampling period. Indicates the sampling time.

[0025] Optionally, the method of eliminating steady-state error in signal tracking control using a discrete complex variable resonant controller includes:

[0026] Let the input of the discrete complex variable resonant controller be the steady-state error: ,in The reference voltage input of the system is represented by the following complex variable resonant controller, which controls the fundamental frequency or multiple harmonics of different frequencies:

[0027] ,in, This represents the state variables of the complex variable resonant controller. This represents the center frequency of the complex variable resonant controller. For the fundamental frequency CVRC, its center frequency is the same as the voltage reference frequency; the center frequencies of other CVRC orders are determined based on the harmonic distribution.

[0028] Optionally, the method further includes obtaining, based on the analytical discrete model, the discrete-domain augmented state-space model of the system as follows:

[0029] ,

[0030] Among them, the system matrix , , , , They are represented as follows:

[0031] G = [ G p H p 1 0 2 × 1 ⋯ 0 2 × 1 0 1 × 2 0 0 ⋯ 0 − T s C p 0 e j ω T s ⋯ 0 ⋮ ⋮ ⋮ ⋱ ⋮ − T s C p 0 0 ⋯ e j ω n T s ] , H 1 = [ 0 2 × 1 1 0 ⋮ 0 ] , H 2 = [ H p 2 0 0 ⋮ 0 ] , R r = [ 0 2 × 1 0 T s ⋮ T s ] , C = [ C p T 0 0 ⋮ 0 ] .

[0032] Optionally, determining the arm voltage control quantity of the three-phase inverter based on the load current disturbance variable and load current feedforward gain, the output voltage reference value and reference value feedforward gain, and the state feedback data includes:

[0033] Based on load current disturbance variables and load current feedforward gain The load current feedforward data is obtained as follows: ;

[0034] According to the output voltage reference value and reference value feedforward gain The voltage reference feedforward data is obtained as follows: ;

[0035] Considering load current feedforward gain Reference value feedforward gain Controlling delay gain Multiple discrete complex variable resonant control gain and system state feedback gain [ k p 1 k p 2 ] Define the state feedback control rate as K = [ k p 1 k p 2 k η k c 1 ⋯ k cn ] Then the bridge arm voltage control quantity of the three-phase inverter is:

[0036] .

[0037] Optionally, the state feedback control law The methods for determining this include:

[0038] Given the following performance metrics:

[0039] J = ∑ k = 0 ∞ a 2 [ x ( k ) H Q x ( k ) + v ( k ) H r v ( k ) ] ;

[0040] Based on performance indicators The minimum value is found, and the closed-loop poles lie within a circle centered at the origin of the Z-domain complex plane with a radius of . Within the circle, with the objective as the target, solve the following discrete Riccati equation to obtain a symmetric positive definite matrix. :

[0041] ;

[0042] The optimal state feedback control law is then expressed as:

[0043] ,

[0044] in, Describes a positive definite weight matrix. This represents the weighting coefficient of the control quantity. , The superscript H indicates the complex conjugate transpose. The above state feedback ensures that the performance index J is minimized while also ensuring that the closed-loop poles fall within a circle centered at the origin with a radius of... Within the circle, ensure the dynamic performance of the system.

[0045] Optionally, the load current feedforward gain and reference value feedforward gain The setup methods include:

[0046] by As a delay factor, it is introduced As control delay state variables, the optimal state feedback control law, load current feedforward data, and voltage reference feedforward data are substituted into the discrete domain augmented state-space model of the system to obtain the closed-loop state-space model of the system, which is expressed as:

[0047] ;

[0048] in , ;

[0049] The system output is then expressed as: ;

[0050] in, for The adjoint matrix; for The determinant;

[0051] When the discrete complex variable resonant controller is a discrete complex variable resonant controller corresponding to the fundamental frequency, its control gain is: The system output is then expressed as:

[0052] ;

[0053] in, This is the transfer function from load current to output voltage; Let be the transfer function from the reference voltage to the output voltage; the outputs of the load current feedforward and the voltage reference value feedforward, considering the control delay, are expressed as follows:

[0054] ,

[0055] Z r ( z ) = T s 2 L C [ ( z − e j ω T s ) k r − T s k c ] ;

[0056] Then for and The following zero points are configurable:

[0057] ,

[0058] ;

[0059] For according to Determined system dominant poles By setting and make The corresponding load current feedforward gain Reference value feedforward gain Set them to:

[0060] ,

[0061] .

[0062] Optionally, in setting the load current feedforward gain and reference value feedforward gain If the discrete complex variable resonant controller adopts a multiple discrete complex variable resonant controller corresponding to multiple resonant frequencies:

[0063] After obtaining the state feedback gain matrix through linear quadratic optimal control, the poles of the corresponding fundamental frequency CVRC dynamic mode are taken as the dominant poles pd, so that the zeros... With the dynamic change of the dominant pole Cancel, get .

[0064] Beneficial effects

[0065] This invention employs a reduced-order state-space model based on complex variables to simplify control design and reduce the computational burden of digital control. Simultaneously, it integrates control delays such as computation and modulation as state variables into the augmented state-space equations, designing an inverter control structure that includes separate static feedback and feedforward terms. A multi-repetitive variable resonant controller is used to achieve error-free output voltage control and low total harmonic distortion (THD) under nonlinear loads. The state feedback control law is quickly determined using a linear quadratic optimal control method. Then, utilizing the designed control structure, the complex gain of the feedforward term is analytically set based on the zero-pole cancellation principle to eliminate the system's dominant slow dynamics. This enables the inverter system to respond quickly to load disturbances and reference value abrupt changes under linear or nonlinear loads, achieving near-zero dynamic characteristics for distributed power grid-connected inverter systems. Attached Figure Description

[0066] Figure 1 The diagram shown is a schematic of a three-phase LC inverter topology.

[0067] Figure 2 The diagram shown is a schematic diagram of the state space principle corresponding to the control method of the present invention.

[0068] Figure 3 The diagram shown is a schematic representation of the specific implementation process of the control method of the present invention in one embodiment. Detailed Implementation

[0069] The technical concept of this invention is as follows: On the one hand, a state-space form control structure is adopted for relatively complex system models, which allows for a more intuitive setting of the state feedback gain coefficient, thereby obtaining good steady-state and dynamic performance; on the other hand, using complex variables for control not only reduces the amount of computation, but also allows the feedforward term to offset the dominant dynamics of the system through complex gain.

[0070] The following description, in conjunction with the accompanying drawings and specific embodiments, provides further details.

[0071] Example 1

[0072] This embodiment is based on Figure 1 The technical solution for the three-phase inverter system topology with LC filter shown is introduced.

[0073] refer to Figure 3 As shown in the figure, this embodiment introduces a dominant dynamic elimination control method for voltage-controlled three-phase inverters based on complex variables, which includes:

[0074] Obtain the line parameters, load current disturbance variables, and output voltage reference values ​​of the three-phase inverter with LC filter;

[0075] Based on the acquired data, a three-phase inverter was constructed. System model based on complex state space in coordinate system;

[0076] Based on the system model, a discrete complex variable resonant controller is used to eliminate the steady-state error of signal tracking control, thereby obtaining the state variables under complex variable resonant control.

[0077] The state feedback control law is determined by considering the discrete complex variable resonant control, control delay and system state feedback gain, the system dominant pole is determined based on the state feedback control law, and the load current feedforward gain and reference value feedforward gain are set according to the state feedback control law and the system dominant pole.

[0078] Based on the system state variables, the state variables under the complex variable resonant control, the control delay state variables, and the state feedback control law, the state feedback data is obtained;

[0079] The arm voltage control quantities of the three-phase inverter are determined based on the load current disturbance variable, load current feedforward gain, output voltage reference value and reference value feedforward gain, and state feedback data.

[0080] refer to Figure 2 The control principle shown includes separate state feedback and feedforward terms in the control structure. The state feedback is used to eliminate the steady-state error of the system and ensure low total harmonic distortion (THD) of the output voltage under various load conditions. The feedforward control of the voltage reference value and load current introduces configurable zeros to cancel out the dominant poles, achieving near-zero dynamic characteristics of the system.

[0081] The specific implementation of the method in this embodiment mainly includes: (1) constructing the discrete domain complex variable state space model of the system; (2) determining the state feedback control law; and (3) setting the feedforward control gain. The following is a detailed introduction to these aspects.

[0082] I. Discrete Domain Complex Variable State-Space Model of the System

[0083] Figure 1 A voltage-controlled three-phase inverter topology with an LC filter, its The model based on complex state space in coordinate system is as follows:

[0084] ,

[0085] Among them, state variables x p = [ i L u C ] T = [ i L α + j i L β u C α + j u C β ] T , , and , These are the inductor currents. and capacitor voltage exist Components in coordinate system To represent a complex number, for The derivative;

[0086] This refers to the bridge arm voltage, which is also the control input. This represents the load current disturbance variable. Indicates system output;

[0087] System Matrix , , , This can be derived from the basic Kirchhoff's voltage and current laws, and is expressed as:

[0088] A p = [ − R / L − 1 / L 1 / C 0 ] , Bp1=[1 / L 0]T, Bp2=[0 1 / L]T, Cp=[0 1];

[0089] Considering the worst-case scenario with damping, and neglecting the internal resistance of the filter inductor, the system can be discretized to obtain the following analytical discrete model:

[0090] ,

[0091] in, G p = e A p T s = [ 1 − T s L T s C 1 ] , H p 1 = ∫ 0 T s e A p t d t B p 1 = [ T s L 0 ] , H p 2 = ∫ 0 T s e A p t d t B p 2 = [ 0 − T s C ] .

[0092] To achieve For zero steady-state error control of the under-shaft AC quantity, consider a discrete complex variable resonant controller in state-space form to eliminate the steady-state error of signal tracking control:

[0093] ;

[0094] Considering u = e = yref − Cpxp, the discrete-domain augmented state-space model of the system is expressed as:

[0095] ,

[0096] in:

[0097] G = [ G p H p 1 0 2 × 1 ⋯ 0 2 × 1 0 1 × 2 0 0 ⋯ 0 − T s C p 0 e j ω T s ⋯ 0 ⋮ ⋮ ⋮ ⋱ ⋮ − T s C p 0 0 ⋯ e j ω n T s ] , H 1 = [ 0 2 × 1 1 0 ⋮ 0 ] , H 2 = [ H p 2 0 0 ⋮ 0 ] , R r = [ 0 2 × 1 0 T s ⋮ T s ] , C = [ C p T 0 0 ⋮ 0 ] .

[0098] II. Determination of State Feedback Control Law

[0099] Introducing η=z⁻¹vc as the control delay state variable, and considering the load current feedforward gain. Reference value feedforward gain Controlling delay gain Multiple discrete complex variable resonant control gain and system state feedback gain [ k p 1 k p 2 ] Define the state feedback control rate as K = [ k p 1 k p 2 k η k c 1 ⋯ k cn ] Then the bridge arm voltage control quantity of the three-phase inverter is:

[0100] ;

[0101] Given the following performance metrics:

[0102] J = ∑ k = 0 ∞ a 2 [ x ( k ) H Q x ( k ) + v ( k ) H r v ( k ) ] ;

[0103] By solving the following discrete Riccati equation, we obtain the symmetric positive definite matrix. :

[0104] ;

[0105] The optimal state feedback control law can be obtained:

[0106] ,

[0107] in, Describes a positive definite weight matrix. This represents the weighting coefficient of the control quantity. , The superscript H indicates the complex conjugate transpose.

[0108] The aforementioned state feedback ensures that the performance index J is minimized while allowing the closed-loop poles to fall within a circle centered at the origin with a radius of . Within the circle, the dynamic performance of the system is ensured.

[0109] Once the state feedback control law K is determined, the closed-loop characteristic equation of the system can be obtained, and then the dominant pole of the system can be determined.

[0110] III. Setting the feedforward control gain

[0111] Substituting the state feedback control law and the feedforward control law into the open-loop state-space equations of the system, we can obtain the closed-loop state-space equations of the system:

[0112] ,

[0113] in , ; and thus the system output can be obtained:

[0114] ,

[0115] in, for The adjoint matrix; for The determinant of the system is the closed-loop characteristic equation of the system.

[0116] Taking the baseband CVRC as an example, the system output can be obtained as follows:

[0117] ,

[0118] in This is the transfer function from load current to output voltage; Let be the transfer function from the reference voltage to the output voltage; the outputs of the load current feedforward and the voltage reference value feedforward, considering the control delay, are expressed as follows:

[0119] ,

[0120] Z r ( z ) = T s 2 L C [ ( z − e j ω T s ) k r − T s k c ] ;

[0121] It can be seen that for and The following zero points are configurable:

[0122] ,

[0123] ;

[0124] For according to Determined system dominant poles At this time, by setting and make The corresponding load current feedforward gain Reference value feedforward gain Set them to:

[0125] ,

[0126] ;

[0127] This completely eliminates the dominant pole of the system.

[0128] It should be noted that when a linear load is applied, only the base frequency CVRC needs to be engaged to ensure that the THD of the steady-state output voltage is very small, while also giving the inverter system near-zero dynamic characteristics.

[0129] When operating with a nonlinear load, multiple CVRC circuits can be implemented to effectively reduce the output voltage THD. In this case, the number of closed-loop poles will increase accordingly. After obtaining the state feedback gain matrix through linear quadratic optimal control, the poles of the corresponding base-frequency CVRC dynamic mode are taken as the dominant poles. Simply canceling out this pole is sufficient to ensure the system has a fast dynamic response performance. At this point... The configurable zero point is the same as when using a single CVRC, and can still be set resolvingly. Eliminate the dominant dynamic. However, At this point, it may be impossible to configure the zero point parsably, but fortunately... The setting pattern is similar to that when using a single CVRC, therefore it can be determined numerically. The value is chosen to eliminate the dominant dynamics, so that the system can obtain better dynamic performance.

[0130] Example 2

[0131] This embodiment introduces a computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements the dominant dynamic elimination control method for voltage-controlled three-phase inverters based on complex variables as described in Embodiment 1.

[0132] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0133] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0134] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0135] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0136] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for eliminating dominant dynamics in a voltage-controlled three-phase inverter based on complex variables, comprising: Obtain the line parameters, load current disturbance variables, and output voltage reference values ​​of the three-phase inverter with LC filter; Based on the acquired data, a three-phase inverter was constructed. System model based on complex state space in coordinate system; Based on the system model, a discrete complex variable resonant controller is used to eliminate the steady-state error of signal tracking control, thereby obtaining the state variables under complex variable resonant control. The state feedback control law is determined by considering the discrete complex variable resonant control, control delay and system state feedback, the system dominant pole is determined based on the state feedback control law, and the load current feedforward gain and reference value feedforward gain are set according to the state feedback control law and the system dominant pole. Based on the system state variables, the state variables under the complex variable resonance control, the control delay state variables, and the state feedback control law, the state feedback data is obtained; The arm voltage control quantities of the three-phase inverter are determined based on the load current disturbance variable, the load current feedforward gain, the output voltage reference value and the reference value feedforward gain, and the state feedback data. Among them, the load current feedforward gain and reference value feedforward gain The setup methods include: by As a delay factor, it is introduced As control delay state variables, the state feedback control law, load current feedforward data, and voltage reference feedforward data are substituted into the discrete domain augmented state-space model of the system: ,in, Represents the augmented state variable. Indicates the system's reference voltage input. This indicates the bridge arm voltage of the control input. This represents the load current disturbance variable. , , , , For the system matrix; The closed-loop state-space model of the system is obtained as follows: ； in, For state feedback control law, system matrix , ; The system output is then expressed as: ;in, for The adjoint matrix; for The determinant; When the discrete complex variable resonant controller is a discrete complex variable resonant controller corresponding to the fundamental frequency, its control gain is: The system output is then expressed as: ； in, This is the transfer function from load current to output voltage; Let be the transfer function from the reference voltage to the output voltage; the outputs of the load current feedforward and the voltage reference value feedforward, considering the control delay, are expressed as follows: ， ； in, The sampling period for the system discretization. and These are the phase inductance and phase capacitance in an LC filter, respectively. To control the delay gain, For system state feedback gain, This represents the center frequency of the complex variable resonant controller; Then for and The following zero points are configurable: ， ； For according to Determined system dominant poles By setting and make The corresponding load current feedforward gain Reference value feedforward gain Set them to: ， 。 2. The method according to claim 1, characterized in that, The discrete complex variable resonant controller (CVRC) is either a discrete complex variable resonant controller corresponding to the fundamental frequency, or a multiple discrete complex variable resonant controller corresponding to multiple frequencies. When the load is linear, a base-frequency CVRC is used; when the load is nonlinear, a multiple CVRC is used, and the poles of the corresponding base-frequency CVRC dynamic mode are taken as the dominant poles. .

3. The method according to claim 1, characterized in that, The line parameters include: the equivalent series resistance of each phase inductor in the inverter circuit. The phase inductance L and phase capacitance C in the LC filter, and the current in each phase inductor. and capacitor voltage ; The three-phase inverter with LC filter is in The system model based on complex state space in coordinate system is represented as follows: ； Among them, state variables , , and , These are the inductor currents. and capacitor voltage exist Components in coordinate system To represent a complex number, for The derivative; Control input bridge arm voltage Load current disturbance variable express, Indicates system output; System Matrix , , , They are represented as follows: ， ， ， 。 4. The method according to claim 3, characterized in that, it further... include: Based on the system model based on complex state space, ignoring the internal resistance of the filter inductor, the system is discretized to obtain the following analytical discrete model: Among them, the system matrix of the discretized model , , They are represented as follows: ， ， ； Indicates the sampling period. Indicates the sampling time.

5. The method according to claim 4, characterized in that, The method of eliminating steady-state error in signal tracking control using a discrete complex variable resonant controller includes: Let the input of the discrete complex variable resonant controller be the steady-state error: The following complex variable resonant controller is used to control the fundamental frequency or multiple harmonics of different frequencies: ,in, This represents the state variables of the complex variable resonant controller.

6. The method according to claim 5, characterized in that, The system's discrete-domain augmented state-space model, by considering the effect of the discrete complex variable resonant controller, yields its system matrix based on the analytical discrete model. , , , , They are represented as follows: ， ， ， ， 。 7. The method according to claim 6, characterized in that, The determination of the bridge arm voltage control quantities of the three-phase inverter based on the load current disturbance variable and load current feedforward gain, the output voltage reference value and reference value feedforward gain, and the state feedback data includes: Based on load current disturbance variables and load current feedforward gain Then the load current feedforward data is ; According to the output voltage reference value and reference value feedforward gain Then the voltage reference feedforward data is ; Considering load current feedforward gain Reference value feedforward gain Controlling delay gain Multiple discrete complex variable resonant control gain Define the state feedback control law as Then the bridge arm voltage control quantity of the three-phase inverter is: 。 8. The method according to claim 7, characterized in that, The state feedback control law The methods for determining this include: Given the following performance metrics: ； Based on performance indicators The minimum value is found, and the closed-loop poles lie within a circle centered at the origin of the Z-domain complex plane with a radius of . Within the circle, with the objective as the target, solve the following discrete Riccati equation to obtain a symmetric positive definite matrix. : ； The optimal state feedback control law is expressed as: ， in, Describes a positive definite weight matrix. This represents the weighting coefficient of the control quantity. , The superscript H indicates the complex conjugate transpose.

9. The method according to claim 8, characterized in that, in Set the load current feedforward gain and reference value feedforward gain If the discrete complex variable resonant controller adopts a multiple discrete complex variable resonant controller corresponding to multiple resonant frequencies: After obtaining the state feedback gain matrix through linear quadratic optimal control, the poles of the corresponding fundamental frequency CVRC dynamic mode are taken as the dominant poles. To make zero point With the dynamic change of the dominant pole Cancel, get .

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