A method and system for harmonic mitigation in isolated microgrids

Abstract

This invention provides a method and system for harmonic mitigation in islanded microgrids. The method includes modeling an average model of the inverters in an islanded microgrid system with multiple inverters connected in parallel and containing nonlinear loads using the state-space averaging method; optimizing the inverter control using a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized based on the gradient descent method based on the average model of the inverters; estimating the state variables and harmonic disturbances of the islanded microgrid system using a second-order linear state observer designed based on the bandwidth tuning method; and mitigating the microgrid voltage harmonics caused by nonlinear loads using a linearized active disturbance rejection control method based on second-order sliding mode based on the estimated state variables and harmonic disturbances of the islanded microgrid system. This invention significantly improves the dynamic performance and robustness of harmonic compensation in microgrids.

Description

Technical Field

[0001] This invention belongs to the technical field of power quality stability analysis of islanded microgrid systems, and specifically relates to a harmonic mitigation method and system for islanded microgrids. Background Technology

[0002] With the continuous development of new energy sources, islanded microgrids have become an important component of distributed energy systems due to their flexibility and independence. However, the widespread integration of nonlinear loads in islanded microgrids has led to increasingly prominent voltage harmonic problems. Linearized active disturbance rejection technology, with its unique control structure, can effectively estimate and compensate for various disturbances in the system, and has thus become a voltage compensation device of great research value.

[0003] To further improve the applicability of linearized active disturbance rejection technology (ADDIR), some scholars have proposed combining linearized ADDIR with model predictive control (MMC) to achieve rapid compensation for harmonic voltages. However, in microgrid systems with an increasing number of inverters connected in parallel and more complex operating conditions, this approach becomes extremely complex, leading to increased difficulty in parameter setting. Other scholars have focused on research into disturbance observers, and have made some progress in theoretical analysis, parameter tuning, and multivariable extensions. However, some challenges remain, such as the fact that parameter tuning methods are not yet fully standardized, and their adaptability to complex nonlinear systems needs further verification. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method and system for harmonic mitigation in islanded microgrids, which solves the technical problems in the prior art.

[0005] On the one hand, the present invention provides the following technical solution: a method for harmonic mitigation in islanded microgrids, comprising:

[0006] The state-space averaging method is used to model the average model of inverters in an islanded microgrid system with multiple inverters connected in parallel and nonlinear loads.

[0007] Based on the average model of the inverter, a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized by gradient descent method are used to optimize the control of the inverter.

[0008] A second-order linear state observer based on the bandwidth tuning method is used to estimate the state variables and harmonic disturbances of an islanded microgrid system.

[0009] Based on the estimated state variables and harmonic disturbances of the islanded microgrid system, a linearized active disturbance rejection control method based on second-order sliding mode is adopted to manage the microgrid voltage harmonics caused by nonlinear loads.

[0010] Compared with existing technologies, the beneficial effects of this invention are as follows: First, this invention uses the state-space averaging method to model the average model of inverters in an islanded microgrid system with multiple inverters connected in parallel and containing nonlinear loads. This model not only effectively simplifies the complex system model with nonlinear loads, but also accurately reflects the characteristics of each inverter in the islanded microgrid. On this basis, based on the residual generator, low-frequency and high-frequency disturbance signals are accurately separated. Combined with a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized based on the gradient descent method, optimized control of each inverter is achieved, realizing the equal distribution of reactive power among multiple inverters and solving the problem of uneven distribution in traditional droop control. Then, a second-order linear state observer optimized based on the bandwidth tuning method is used to estimate the system's state variables and harmonic disturbances in real time, providing a more accurate basis for subsequent harmonic voltage compensation strategies. Finally, a linearized active disturbance rejection controller based on second-order sliding mode is used to compensate for the voltage harmonic components of the microgrid system. By quickly tracking the reference voltage and eliminating steady-state errors through the sliding surface function, the dynamic performance and robustness of harmonic compensation for the microgrid are significantly improved.

[0011] Preferably, the step of modeling the average model of inverters in an islanded microgrid system with multiple inverters connected in parallel and containing nonlinear loads using the state-space averaging method includes:

[0012] Determine the inverter i or inverter j Dynamic differential equations to the common connection point:

[0013] ;

[0014] ;

[0015] In the formula, i nond,i(j) , i nonq,i(j) Inverter i or inverter j to common load current d , q Axial components, The angular frequency of alternating current. R line,i(j) , L line,i(j) Inverter i or inverter j The line resistance and line inductance, u od,i(j) For inverters i or inverter j Output voltage d Axial components, u oq,i(j) For invertersi or inverter j Output voltage q Axial components, u pd , u pq These are the voltages at the point of common coupling. d , q Axial components;

[0016] Determine that the common load is a nonlinear load and calculate the inverter. i or inverter j Current to nonlinear load:

[0017] ;

[0018] ;

[0019] In the formula, i nond_l,i(j) , i nond_h,i(j) They represent inverters i or inverter j Current to nonlinear load d The low-frequency and high-frequency components of the axis i nonq_l,i(j) , i nonq_h,i(j) They represent inverters i or inverter j Current to nonlinear load q The low-frequency and high-frequency components of the axis i nond,i(j) , i nonq,i(j) They represent inverters i or inverter j To nonlinear load current d , q Axial components;

[0020] Based on inverter i or inverter j Dynamic differential equations to the point of common connection and inverter i or inverter j Current determination inverter to nonlinear load i and inverter j Differential equation of the circulation between them:

[0021] ; ;

[0022] ; ;

[0023] In the formula, i hd,ij , i hq,ij They represent inverters i and inverter j Circulation between d , q Axial components, R T Indicates inverter i With inverter j The sum of the line resistances, L T Indicates inverter i With inverter j The sum of the line inductances;

[0024] Based on inverter i and inverter j The differential equation of the circulating current between the two phases determines the inverter. i or inverter j Output current:

[0025] ;

[0026] ;

[0027] In the formula, i od,i(j) , i oq,i(j) They represent inverters i or inverter j Output current d , q Axial components;

[0028] Based on inverter i or inverter j Dynamic differential equations to the point of common connection and inverter i and inverter j The differential equation of the circulating current between the two phases determines the inverter. i or inverter j Average model:

[0029] ;

[0030] ;

[0031] x i(j) =( i fd,i(j) , i fq,i(j) , u od,i(j) ,u oq,i(j) ) T ; u i(j) =( u id,i(j) , u iq,i(j) ) T ;

[0032] d non_l,i(j) =( i fd,i(j) , i fq,i(j) ) T ; d non_h,i(j) =( i nond_h,i(j) , i nonq_h,i(j) ) T ;

[0033] d h_l,i(j) =( i hd,ij , i hq,ij ) T ;

[0034] In the formula, V DC,i(j) Indicates inverter i or inverter j DC terminal voltage, i fd,i(j) , i fq,i(j) They represent inverters i or inverter j The filter current d , q Axial components, u i(j) This represents the system's control input. u id,i(j) , u iq,i(j) They represent inverters i or inverter j The inverter bridge voltage d , q Axial components, d i(j) Indicates the effect of nonlinear load disturbance on the inverter i or inverter j The interference components, among which d non_l,i(j) , d non_h,i(j)These represent the low-frequency and high-frequency disturbances of the nonlinear load current, respectively. d h_l,i(j) This represents the disturbance of the nonlinear load to the circulating current between inverters. y i(j) This represents the system's output. A inv_i(j) , B inv_i(j) , C inv_i(j) , V non_h,i(j) , V non_l,i(j) , V h_l,ij They represent inverters i or inverter j The first coefficient matrix, the second coefficient matrix, the third coefficient matrix, the high-frequency disturbance input matrix, the low-frequency disturbance input matrix, and the circulating low-frequency disturbance input matrix. x i(j) Indicates the system's input quantity. express x i(j) The first derivative.

[0035] Preferably, in the inverter i or inverter j In the average model, A inv_i(j) , B inv_i(j) , C inv_i(j) , V h_l,ij , V non_h,i(j) , V non_l,i(j) They are respectively:

[0036] ; ;

[0037] ; ;

[0038] ;

[0039] In the formula, L f,i(j) , C f,i(j) , R f,i(j) They represent inverters i or inverter j The filter inductor, filter capacitor, and parasitic resistance of the filter inductor.

[0040] Preferably, the step of optimizing the control of the inverter using a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized based on the gradient descent method according to the average model of the inverter includes:

[0041] Disturbances caused by line impedance differences, load fluctuations, or other complex operating conditions in microgrid systems are uniformly classified into high-frequency disturbances and low-frequency disturbances, and the inverters in islanded microgrid systems are also classified into these categories. i Considered the controlled object G inv,i ( s ), and determine the inverter i State-space equations:

[0042] ;

[0043] In the formula, x i ( s (inverter) i The filtered inductor current signal, express x i ( s The first derivative of ) u i,i ( s (inverter) i The inverter bridge voltage signal, d i_l ( s ), d i_h ( s ) represent the low-frequency component and high-frequency component of the disturbance, respectively; y i ( s (inverter) i The output voltage signal, A inv_i , B inv_i , C inv_i , V non_h,i , V non_l,i They represent inverters i The first coefficient matrix, the second coefficient matrix, the third coefficient matrix, the high-frequency disturbance input matrix, and the low-frequency disturbance input matrix;

[0044] The low-frequency and high-frequency disturbances of the common load are converted into corresponding high-frequency and low-frequency residuals using a residual generator, allowing... u i,i ( s As the input signal for the residual generator,y i ( s As the output signal of the residual generator, when it satisfies G inv,i ( s )= C inv_i ( sI - A inv_i ) -1 B inv_i + C inv_i At that time, the residual generator expression is:

[0045] ;

[0046] ;

[0047] In the formula, n i_l ( s ), n i_h ( s ) represent the low-frequency residual and high-frequency residual of the residual generator, respectively. N i ( s ) indicates a residual separator. N i_l ( s ), N i_h ( s ) represents the transfer functions of the low-pass and high-pass filters of the residual separator. express First derivative Indicates to x i ( s ) state estimation variables, Indicates inverter i The estimated value of the output voltage signal. s Represents a complex frequency variable. I Represents the identity matrix. L i For inverters i The gain matrix;

[0048] The low-frequency components of the disturbance are transformed into the state space Z of the low-frequency residual. i_l ( s ), and the state space Z that transforms high-frequency components into high-frequency residuals. i_h ( s ), where Z i_l ( sThe expression for ) is:

[0049] ;

[0050] In the formula, express The first derivative, This represents the low-frequency disturbance residual signal. Indicates inverter i DC terminal voltage, This represents the low-frequency component of the disturbance. N i_l This represents a low-pass filter in a residual separator.

[0051] Z i_h ( s The expression for ) is:

[0052] ;

[0053] In the formula, express The first derivative, This represents the high-frequency disturbance residual signal. This represents the high-frequency components of the disturbance. N i_h This represents a high-pass filter in a residual separator.

[0054] Inverter i The reactive power deviation caused by droop characteristics is defined as follows: e droop,i The reactive power deviation caused by load changes is defined as e load,i :

[0055] ;

[0056] ;

[0057] In the formula, k 1. k 2 represents the first and second deviation gain coefficients. X i In an islanded microgrid system with multiple inverters connected in parallel, the inverters are... i The collection of other connected inverters, c ij Indicates inverter i and inverter j Connect the coefficients of the matrix. n i Indicates inverter i The reactive power droop control coefficient Q i , Qj They represent inverters i Inverter j The output reactive power;

[0058] based on e droop,i , e load,i Determine virtual impedance :

[0059] ;

[0060] In the formula, s, j These represent the complex frequency variable and the imaginary unit, respectively;

[0061] By applying a low-frequency voltage compensation controller based on virtual impedance to the voltage control loop of the inverter, a voltage closed-loop control system is formed to adjust the inverter control strategy. The reference voltage control relationship and frequency control relationship of the inverter after compensation are as follows:

[0062] ;

[0063] ;

[0064] In the formula, , They represent inverters i Reference voltage and reference frequency after compensation by the low-frequency voltage compensation controller u ref,i Indicates inverter i The original given reference voltage, u ref,j Indicates inverter j The original given reference voltage, i o,i Indicates inverter i The output current, m i Indicates inverter i The active power sagging control coefficient Q n,i , P n,i They represent inverters i Rated reactive power and rated active power Indicates inverter i The rated output voltage, N i Indicates with inverter i A set that has connections between it. f n,i Indicates inverter i The rated frequency of the output,P i Indicates inverter i The actual output active power, n i , n j They represent inverters i、 Inverter j The reactive power droop control coefficient;

[0065] A high-frequency disturbance component is used as input to design a high-frequency disturbance compensation controller, so that the high-frequency residual... n i_h ( s The value is close to 0, where the high-frequency disturbance compensation controller The solution is:

[0066] ;

[0067] In the formula, , Inverter i The transfer functions of the filter inductor and filter capacitor. For inverters i Voltage controller, This represents the transfer function of the high-frequency disturbance compensator. Z i_h ( s This indicates that the high-frequency components of the disturbance are transformed into the state space of the high-frequency residual;

[0068] Introducing the gradient descent method for high-frequency disturbance compensators The parameter optimization design is used to obtain the objective function. J ( k op ):

[0069] ;

[0070] In the formula, u o,i For inverters i The output voltage, k op for High-frequency disturbance compensation gain to be optimized. N This represents the number of sample points for the mean square error of voltage deviation collected within a preset time period. The residual weighting coefficient is... n i_h ( k () represents the high-frequency residual signal;

[0071] For the objective function J ( kop Perform differentiation and iterate along the opposite direction of the gradient to compensate for the high-frequency perturbation gain. k op The optimal high-frequency disturbance compensation gain is selected using the gradient descent method to determine the high-frequency disturbance compensator, thereby suppressing high-frequency disturbances in the islanded microgrid system. i High-frequency disturbance compensation gain of +1 iteration k op,i+1 for:

[0072] ;

[0073] ;

[0074] In the formula, For gradient operators, k op,i For the process i High-frequency disturbance compensation gain after the next iteration. For learning rate, J express J ( k op ).

[0075] Preferably, the step of estimating the state variables and harmonic disturbances of the islanded microgrid system using a second-order linear state observer designed based on the bandwidth tuning method includes:

[0076] Determine the second-order dynamic equations for any inverter in an islanded microgrid system:

[0077] ;

[0078] In the formula, The rated angular frequency, L f , C f These are the inverter's filter inductor and filter capacitor, respectively. R f This is the parasitic resistance of the inverter's filter inductor. u od(q) Indicates the inverter output voltage d shaft or q Axial components, i fd(q) Indicates the inverter filter inductor current d shaft or q Axial components, u id(q) This represents the inverter bridge voltage of the inverter. d shaft or q Axial components;

[0079] The inverter's output voltageu od With harmonic disturbances h The first state variable is regarded as a second-order linear state observer. z 1. Second state variable z 2. y As the output of the observer, the inverter bridge voltage of the inverter. d Axial components u id As the input to the observer, the second-order linear state observer satisfies the following expression condition:

[0080] ;

[0081] In the formula, u od The output voltage of the inverter d Axial components, i fd Indicates the inverter filter inductor current d Axial components, i od Indicates the inverter output current d Axial components;

[0082] Determine the extended state equation of the second-order linear state observer based on the expression conditions:

[0083] ;

[0084] In the formula, k 0 represents the control gain of the input variable. u Indicates the observer input, express z The first derivative of 2, Indicates harmonic disturbance h The first derivative;

[0085] Determining the expression for a second-order linear state observer based on the extended state equation:

[0086] ;

[0087] In the formula, , They are respectively z 1. z The derivative of the estimated value of 2, , These are the first and second gain coefficients of the second-order linear state observer, respectively. express z The estimated value of 1;

[0088] The first and second gain coefficients of the second-order linear state observer are determined using the bandwidth tuning method, and the error dynamic equation between the actual state and the estimated value of the second-order linear state observer is expressed as:

[0089] ;

[0090] In the formula, e Represents the error vector. The derivative of the error vector. Z This represents the actual state of the microgrid. For the observer's estimated value, L Here is the gain matrix. A inv , B inv , C inv These represent the first coefficient matrix, the second coefficient matrix, and the third coefficient matrix, respectively.

[0091] The solution of the second-order linear state observer is determined based on the error dynamic equation, and the state variables and harmonic disturbances of the islanded microgrid system are determined based on the solution of the second-order linear state observer. for:

[0092] ;

[0093] In the formula, t To observe the state variables and harmonic disturbances of an islanded microgrid system at a specific moment. t 0 represents the initial time. Indicates equivalent time.

[0094] Preferably, the first gain coefficient of the second-order linear state observer Second gain coefficient Control gain of input variables k 0 satisfies the following constraints:

[0095] ;

[0096] ;

[0097] In the formula, s Represents a complex frequency variable. This represents the bandwidth of a second-order linear state observer. This is the rated angular frequency.

[0098] Preferably, the step of mitigating microgrid voltage harmonics caused by nonlinear loads based on estimated state variables and harmonic disturbances of the islanded microgrid system and employing a second-order sliding mode-based linearized active disturbance rejection control method includes:

[0099] The error control rate of the linearized active disturbance rejection control (ADRC) element is determined based on the estimated state variables and harmonic disturbances of the islanded microgrid system. r :

[0100] ;

[0101] In the formula, Represents the first state variable z The estimated value of 1, Represents the second state variable z The estimated value of 2, This represents the original reference voltage given by the inverter. d Axial components, k 0 represents the control gain of the input variable. This represents the bandwidth of a second-order linear state observer;

[0102] According to the error control rate r The estimated harmonic disturbances of the islanded microgrid system are fed forward into the inverter voltage control to compensate for the voltage harmonics of the microgrid. The relationship between the inverter output voltage and the reference voltage after compensation by the linearized active disturbance rejection control is as follows:

[0103] ;

[0104] In the formula, To compensate for the inverter output voltage d Transfer function of axis components, Reference voltage of d Axial components, u od ( s To compensate for the output voltage of the pre-inverter d Transfer function of axis components, s Represents a complex frequency variable;

[0105] A second-order sliding mode control is introduced to adjust the compensation voltage of the linearized active disturbance rejection (ADNR) stage. The sliding surface function of the second-order sliding mode is defined as the output voltage of the inverter after compensation by the linearized ADNR control stage. With reference voltage The difference, the sliding surface function The expression is:

[0106] ;

[0107] Differentiating the sliding surface function, we get:

[0108] ;

[0109] In the formula, i f This refers to the inverter filter inductor current. i h For inverter circulating current, C f For the inverter's filter capacitor;

[0110] The control input of a second-order sliding mode controller is designed based on the sliding surface function and the STA algorithm. u ， for:

[0111] ; ;

[0112] In the formula, u ， This is the control input for the second-order sliding mode control loop. u 1. u 2 represents the first and second control input components, respectively. , These are the first and second gain parameters of the second-order sliding mode controller, respectively. express u The first derivative of 2;

[0113] Differentiating the sliding surface function after the first derivative yields:

[0114] ;

[0115] In the formula, L f For the inverter's filter inductor V DC This represents the DC terminal voltage of the inverter. The second derivative of the reference voltage is represented. t To observe the state variables and harmonic disturbances of an isolated microgrid system at a specific moment;

[0116] The expression for the second derivative of the sliding surface function is adjusted as follows:

[0117] ;

[0118] ;

[0119] In the formula, F ( t () is a function that simultaneously incorporates the dynamics of the second-order sliding mode control system and the external reference signal. i non This represents the current from the inverter to the nonlinear load. u ref This represents the original reference voltage given by the inverter. This represents the second derivative of the original given reference voltage;

[0120] The range of values ​​for the first and second gain parameters of the second-order sliding mode controller is determined based on the expression for the second derivative of the sliding surface function.

[0121] ; ;

[0122] In the formula, c min , c max , m They represent the first, second, and third constants, respectively.

[0123] By selecting the appropriate first and second gain parameters of the second-order sliding mode controller within a certain range, the sliding surface function can be made to converge to the sliding surface in a finite time. This is to compensate for the inverter output voltage, enabling the inverter output voltage to approach the reference voltage more quickly and accurately. .

[0124] Secondly, the present invention provides the following technical solution: a harmonic mitigation system for islanded microgrids, the system comprising:

[0125] The modeling module is used to model the average model of inverters in an islanded microgrid system with multiple inverters connected in parallel and containing nonlinear loads using the state-space averaging method.

[0126] The control module is used to optimize the control of the inverter by employing a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized based on the gradient descent method, according to the average model of the inverter.

[0127] The estimation module is used to estimate the state variables and harmonic disturbances of an islanded microgrid system using a second-order linear state observer designed based on the bandwidth tuning method.

[0128] The governance module is used to manage microgrid voltage harmonics caused by nonlinear loads based on the estimated state variables and harmonic disturbances of the islanded microgrid system and a linearized active disturbance rejection control method based on second-order sliding mode.

[0129] Thirdly, the present invention provides the following technical solution: a computer, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the islanded microgrid harmonic mitigation method as described above.

[0130] Fourthly, the present invention provides the following technical solution: a storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the above-described method for harmonic mitigation in islanded microgrids. Attached Figure Description

[0131] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0132] Figure 1 A flowchart of the harmonic mitigation method for islanded microgrids provided in Embodiment 1 of the present invention;

[0133] Figure 2 This is an overall flowchart of the harmonic mitigation method for islanded microgrids provided in Embodiment 1 of the present invention;

[0134] Figure 3 This is a structural block diagram of the islanded microgrid harmonic mitigation system provided in Embodiment 2 of the present invention;

[0135] Figure 4 This is a schematic diagram of the hardware structure of a computer provided for another embodiment of the present invention.

[0136] The embodiments of the present invention will be further described below with reference to the accompanying drawings. Detailed Implementation

[0137] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0138] In the description of the embodiments of the present invention, it should be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention.

[0139] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0140] In the embodiments of the present invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of the present invention according to the specific circumstances.

[0141] Example 1

[0142] In Embodiment 1 of the present invention, as Figure 1 , Figure 2 As shown, a harmonic mitigation method for islanded microgrids includes:

[0143] S1. The state-space averaging method is used to model the average model of the inverters in an islanded microgrid system with multiple inverters connected in parallel and containing nonlinear loads.

[0144] Step S1 includes:

[0145] S11. Determine the inverter i or inverter j Dynamic differential equations to the common connection point:

[0146] ;

[0147] ;

[0148] In the formula, i nond,i(j) , i nonq,i(j) Inverter i or inverter j to common load current d , q Axial components, The angular frequency of alternating current. R line,i(j) , L line,i(j) Inverter i or inverter jThe line resistance and line inductance, u od,i(j) For inverters i or inverter j Output voltage d Axial components, u oq,i(j) For inverters i or inverter j Output voltage q Axial components, u pd , u pq These are the voltages at the point of common coupling. d , q Axial components.

[0149] S12. Determine that the common load is a nonlinear load and calculate the inverter. i or inverter j Current to nonlinear load:

[0150] ;

[0151] ;

[0152] In the formula, i nond_l,i(j) , i nond_h,i(j) They represent inverters i or inverter j Current to nonlinear load d The low-frequency and high-frequency components of the axis i nonq_l,i(j) , i nonq_h,i(j) They represent inverters i or inverter j Current to nonlinear load q The low-frequency and high-frequency components of the axis i nond,i(j) , i nonq,i(j) They represent inverters i or inverter j To nonlinear load current d , q Axial components;

[0153] Specifically, when the common load is a nonlinear load, harmonic disturbances of different frequencies will be introduced. These disturbances can be divided into low-frequency disturbances and high-frequency disturbances, thus allowing the inverter to... i or inverter j The current to the nonlinear load, and simultaneously, in step S11, inond,i(j) , i nonq,i(j) Inverter i or inverter j to common load current d , q The shaft component, since the common load is a nonlinear load in step S11, therefore, i nond,i(j) , i nonq,i(j) These are respectively represented as inverters i or inverter j to common load current d , q Axial components.

[0154] S13, Inverter-based i or inverter j Dynamic differential equations to the point of common connection and inverter i or inverter j Current determination inverter to nonlinear load i and inverter j Differential equation of the circulation between them:

[0155] ; ;

[0156] ; ;

[0157] In the formula, i hd,ij , i hq,ij They represent inverters i and inverter j Circulation between d , q Axial components, R T Indicates inverter i With inverter j The sum of the line resistances, L T Indicates inverter i With inverter j The sum of the line inductances.

[0158] S14, Inverter-based i and inverter j The differential equation of the circulating current between the two phases determines the inverter. i or inverter j Output current:

[0159] ;

[0160] ;

[0161] In the formula, i od,i(j) , i oq,i(j) They represent inverters i or inverter j Output current d , q Axial components.

[0162] S15, Inverter-based i or inverter j Dynamic differential equations to the point of common connection and inverter i and inverter j The differential equation of the circulating current between the two phases determines the inverter. i or inverter j Average model:

[0163] ;

[0164] ;

[0165] x i(j) =( i fd,i(j) , i fq,i(j) , u od,i(j) , u oq,i(j) ) T ; u i(j) =( u id,i(j) , u iq,i(j) ) T ;

[0166] d non_l,i(j) =( i fd,i(j) , i fq,i(j) ) T ; d non_h,i(j) =( i nond_h,i(j) , i nonq_h,i(j) ) T ;

[0167] d h_l,i(j) =( i hd,ij ,i hq,ij ) T ;

[0168] In the formula, V DC,i(j) Indicates inverter i or inverter j DC terminal voltage, i fd,i(j) , i fq,i(j) They represent inverters i or inverter j The filter current d , q Axial components, u i(j) This represents the system's control input. u id,i(j) , u iq,i(j) They represent inverters i or inverter j The inverter bridge voltage d , q Axial components, d i(j) Indicates the effect of nonlinear load disturbance on the inverter i or inverter j The interference components, among which d non_l,i(j) , d non_h,i(j) These represent the low-frequency and high-frequency disturbances of the nonlinear load current, respectively. d h_l,i(j) This represents the disturbance of the nonlinear load to the circulating current between inverters. y i(j) This represents the system's output. A inv_i(j) , B inv_i(j) , C inv_i(j) , V non_h,i(j) , V non_l,i(j) , V h_l,ij They represent inverters i or inverter j The first coefficient matrix, the second coefficient matrix, the third coefficient matrix, the high-frequency disturbance input matrix, the low-frequency disturbance input matrix, and the circulating low-frequency disturbance input matrix. x i(j) Indicates the system's input quantity. express x i(j) The first derivative;

[0169] Specifically, by combining the formulas in steps S11-S14 above, the inverter can be derived. i or inverter j The average model;

[0170] in, A inv_i(j) , B inv_i(j) , C inv_i(j) , V h_l,ij , V non_h,i(j) , V non_l,i(j) They are respectively:

[0171] ; ;

[0172] ; ;

[0173] ;

[0174] In the formula, L f,i(j) , C f,i(j) , R f,i(j) They represent inverters i or inverter j The filter inductor, filter capacitor, and parasitic resistance of the filter inductor.

[0175] S2. Based on the average model of the inverter, a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized by gradient descent method are used to optimize the control of the inverter.

[0176] Step S2 includes:

[0177] S21. Disturbances caused by line impedance differences, load fluctuations, or other complex operating conditions in microgrid systems are uniformly classified into high-frequency disturbances and low-frequency disturbances, and the inverters in islanded microgrid systems are classified into high-frequency disturbances and low-frequency disturbances. i Considered the controlled object G inv,i ( s ), and determine the inverter i State-space equations:

[0178] ;

[0179] In the formula, x i ( s(inverter) i The filtered inductor current signal, express x i ( s The first derivative of ) u i,i ( s (inverter) i The inverter bridge voltage signal, d i_l ( s ), d i_h ( s ) represent the low-frequency component and high-frequency component of the disturbance, respectively; y i ( s (inverter) i The output voltage signal, A inv_i , B inv_i , C inv_i , V non_h,i , V non_l,i They represent inverters i The first coefficient matrix, the second coefficient matrix, the third coefficient matrix, the high-frequency disturbance input matrix, and the low-frequency disturbance input matrix.

[0180] S22. The low-frequency and high-frequency disturbances of the common load are converted into corresponding high-frequency and low-frequency residuals using a residual generator, so that... u i,i ( s As the input signal for the residual generator, y i ( s As the output signal of the residual generator, when it satisfies G inv,i ( s )= C inv_i ( sI - A inv_i ) -1 B inv_i + C inv_i At that time, the residual generator expression is:

[0181] ;

[0182] ;

[0183] In the formula,n i_l ( s ), n i_h ( s ) represent the low-frequency residual and high-frequency residual of the residual generator, respectively. N i ( s ) indicates a residual separator. N i_l ( s ), N i_h ( s ) represents the transfer functions of the low-pass and high-pass filters of the residual separator. express First derivative Indicates to x i ( s ) state estimation variables, Indicates inverter i The estimated value of the output voltage signal. s Represents a complex frequency variable. I Represents the identity matrix. L i For inverters i The gain matrix.

[0184] S23. Transform the low-frequency components of the disturbance into the state space Z of the low-frequency residual. i_l ( s ), and the state space Z that transforms high-frequency components into high-frequency residuals. i_h ( s ), where Z i_l ( s The expression for ) is:

[0185] ;

[0186] In the formula, express The first derivative, This represents the low-frequency disturbance residual signal. Indicates inverter i DC terminal voltage, This represents the low-frequency component of the disturbance. N i_l This represents a low-pass filter in a residual separator.

[0187] Z i_h ( s The expression for ) is:

[0188] ;

[0189] In the formula, express The first derivative, This represents the high-frequency disturbance residual signal. This represents the high-frequency components of the disturbance. N i_h This represents a high-pass filter in a residual separator.

[0190] It should be noted that, L i The selection criteria are as follows: , Stable and observable, and the characteristic equation The real parts of all roots are less than 0 and are concentrated in... Therefore, there exists a suitable gain matrix that makes the residual generator stable. It represents a real number less than 0.

[0191] S24, Inverter i The reactive power deviation caused by droop characteristics is defined as follows: e droop,i The reactive power deviation caused by load changes is defined as e load,i :

[0192] ;

[0193] ;

[0194] In the formula, k 1. k 2 represents the first and second deviation gain coefficients. X i In an islanded microgrid system with multiple inverters connected in parallel, the inverters are... i The collection of other connected inverters, c ij Indicates inverter i and inverter j Connect the coefficients of the matrix. n i Indicates inverter i The reactive power droop control coefficient Q i , Q j They represent inverters i Inverter j The output reactive power.

[0195] S25, based on e droop,i , e load,i Determine virtual impedance :

[0196] ;

[0197] In the formula, s, j These represent the complex frequency variable and the imaginary unit, respectively;

[0198] Specifically, by introducing virtual impedance Z vir,i Design a low-frequency voltage compensation controller This is to compensate for the inverter's output voltage, achieve reactive power distribution among the inverters, and reduce the inverter's output voltage. i The reactive power deviation caused by droop characteristics is defined as follows: e droop,i The reactive power deviation caused by load changes is defined as e load,i These two parameters can clearly show the deviation between the actual reactive power distribution and the ideal even distribution.

[0199] S26. By applying a low-frequency voltage compensation controller based on virtual impedance to the voltage control loop of the inverter, a voltage closed-loop control system is formed to adjust the inverter control strategy. The reference voltage control relationship and frequency control relationship of the inverter after compensation are as follows:

[0200] ;

[0201] ;

[0202] In the formula, , They represent inverters i Reference voltage and reference frequency after compensation by the low-frequency voltage compensation controller u ref,i Indicates inverter i The original given reference voltage, u ref,j Indicates inverter j The original given reference voltage, i o,i Indicates inverter i The output current, m i Indicates inverter i The active power sagging control coefficient Q n,i , P n,i They represent inverters i Rated reactive power and rated active power Indicates inverter i The rated output voltage,N i Indicates with inverter i A set that has connections between it. f n,i Indicates inverter i The rated frequency of the output, P i Indicates inverter i The actual output active power, n i , n j They represent inverters i、 Inverter j The reactive power droop control coefficient;

[0203] Specifically, through the new control relationship in step S26, more precise reactive power sharing and output voltage stability can be achieved among the inverters in the microgrid system.

[0204] S27. Design a high-frequency disturbance compensation controller using high-frequency disturbance components as input, so as to ensure high-frequency residual... n i_h ( s The value is close to 0, where the high-frequency disturbance compensation controller The solution is:

[0205] ;

[0206] In the formula, , Inverter i The transfer functions of the filter inductor and filter capacitor. For inverters i Voltage controller, This represents the transfer function of the high-frequency disturbance compensator. Z i_h ( s This indicates that the high-frequency components of the disturbance are transformed into the state space of the high-frequency residual;

[0207] S28. Introducing the gradient descent method for high-frequency disturbance compensators. The parameter optimization design is used to obtain the objective function. J ( k op ):

[0208] ;

[0209] In the formula, u o,i For inverters i The output voltage, k op for High-frequency disturbance compensation gain to be optimized. N This represents the number of sample points for the mean square error of voltage deviation collected within a preset time period. The residual weighting coefficient is... n i_h ( k () represents the high-frequency residual signal;

[0210] Specifically, to rationally design the parameters of the high-frequency disturbance compensator and minimize the impact of high-frequency disturbances on the inverter output voltage, a gradient descent method is introduced for the high-frequency disturbance compensator. The parameter optimization design transforms the objective function into that of the inverter. i Mean square error of output voltage deviation.

[0211] S29. Regarding the objective function J ( k op Perform differentiation and iterate along the opposite direction of the gradient to compensate for the high-frequency perturbation gain. k op The optimal high-frequency disturbance compensation gain is selected using the gradient descent method to determine the high-frequency disturbance compensator, thereby suppressing high-frequency disturbances in the islanded microgrid system. i High-frequency disturbance compensation gain of +1 iteration k op,i+1 for:

[0212] ;

[0213] ;

[0214] In the formula, For gradient operators, k op,i For the process i High-frequency disturbance compensation gain after the next iteration. For learning rate, J express J ( k op );

[0215] The learning rate determines the step size of parameter updates. Iteration stops when the magnitude of the gradient is infinitely close to 0. At this point, the output compensation gain is the optimal high-frequency disturbance compensation gain. Therefore, the optimal compensation gain is selected by gradient descent to design a high-frequency disturbance compensator, so as to better suppress high-frequency disturbances in the microgrid system.

[0216] S3. Use a second-order linear state observer designed based on the bandwidth tuning method to estimate the state variables and harmonic disturbances of an islanded microgrid system.

[0217] Step S3 includes:

[0218] S31. Determine the second-order dynamic equations for any inverter in an islanded microgrid system:

[0219] ;

[0220] In the formula, The rated angular frequency, L f , C f These are the inverter's filter inductor and filter capacitor, respectively. R f This is the parasitic resistance of the inverter's filter inductor. u od(q) Indicates the inverter output voltage d shaft or q Axial components, i fd(q) Indicates the inverter filter inductor current d shaft or q Axial components, u id(q) This represents the inverter bridge voltage of the inverter. d shaft or q Axial components;

[0221] Specifically, due to the second-order dynamic equation of the inverter in d shaft and q The axis is symmetric, therefore only the second-order linear state observer is derived. d The design principle of the axial direction therefore determines the inverter's output voltage. u od With harmonic disturbances h The first state variable is regarded as a second-order linear state observer. z 1. Second state variable z 2. y As the output of the observer, the inverter bridge voltage of the inverter. d Axial components u id As an observer input.

[0222] S32, Convert the inverter's output voltage u od With harmonic disturbances h The first state variable is regarded as a second-order linear state observer. z 1. Second state variable z 2. y As the output of the observer, the inverter bridge voltage of the inverter. d Axial components u idAs the input to the observer, the second-order linear state observer satisfies the following expression condition:

[0223] ;

[0224] In the formula, u od The output voltage of the inverter d Axial components, i fd Indicates the inverter filter inductor current d Axial components, i od Indicates the inverter output current d Axial components.

[0225] S33. Determine the extended state equation of a second-order linear state observer based on expression conditions:

[0226] ;

[0227] In the formula, k 0 represents the control gain of the input variable. u Indicates the observer input, express z The first derivative of 2, Indicates harmonic disturbance h The first derivative.

[0228] S34. Determine the expression for the second-order linear state observer based on the extended state equation:

[0229] ;

[0230] In the formula, , They are respectively z 1. z The derivative of the estimated value of 2, , These are the first and second gain coefficients of the second-order linear state observer, respectively. express z The estimated value of 1.

[0231] S35. The first and second gain coefficients of the second-order linear state observer are determined using the bandwidth tuning method, and the error dynamic equation between the actual state and the estimated value of the second-order linear state observer is expressed as follows:

[0232] ;

[0233] In the formula, e Represents the error vector. The derivative of the error vector. ZThis represents the actual state of the microgrid. For the observer's estimated value, L Here is the gain matrix. A inv , B inv , C inv These represent the first coefficient matrix, the second coefficient matrix, and the third coefficient matrix, respectively.

[0234] S36. Determine the solution of the second-order linear state observer based on the error dynamic equation, and determine the state variables and harmonic disturbances of the islanded microgrid system based on the solution of the second-order linear state observer. The solution of the second-order linear state observer... for:

[0235] ;

[0236] In the formula, t To observe the state variables and harmonic disturbances of an islanded microgrid system at a specific moment. t 0 represents the initial time. Indicates equivalent time;

[0237] Therefore, by rationally designing and optimizing the gain coefficient of the second-order linear state observer, it is of great significance to improve the stability and estimation accuracy of the observer.

[0238] Meanwhile, according to the principle of bandwidth tuning, the selection of the gain coefficient of the second-order linear state observer is based on making the gain coefficient of the second-order linear state observer more efficient. A inv - LC inv Even if Hurwitz stability is satisfied, , , k 0 satisfies the following constraints:

[0239] ;

[0240] ;

[0241] In the formula, s Represents a complex frequency variable. This represents the bandwidth of a second-order linear state observer. This is the rated angular frequency.

[0242] S4. Based on the estimated state variables and harmonic disturbances of the islanded microgrid system, a linearized active disturbance rejection control method based on second-order sliding mode is adopted to manage the microgrid voltage harmonics caused by nonlinear loads.

[0243] Step S4 includes:

[0244] S41. Based on the estimated state variables and harmonic disturbances of the islanded microgrid system, determine the error control rate of the linearized active disturbance rejection control element. r :

[0245] ;

[0246] In the formula, Represents the first state variable z The estimated value of 1, Represents the second state variable z The estimated value of 2, This represents the original reference voltage given by the inverter. d Axial components, k 0 represents the control gain of the input variable. This represents the bandwidth of a second-order linear state observer.

[0247] S42. Based on the error control rate r The estimated harmonic disturbances of the islanded microgrid system are fed forward into the inverter voltage control to compensate for the voltage harmonics of the microgrid. The relationship between the inverter output voltage and the reference voltage after compensation by the linearized active disturbance rejection control is as follows:

[0248] ;

[0249] In the formula, To compensate for the inverter output voltage d Transfer function of axis components, Reference voltage of d Axial components, u od ( s To compensate for the output voltage of the pre-inverter d Transfer function of axis components, s This represents a complex frequency variable.

[0250] S43. Second-order sliding mode control is introduced to adjust the compensation voltage of the linearized active disturbance rejection link. The sliding surface function of the second-order sliding mode is defined as the output voltage of the inverter after compensation by the linearized active disturbance rejection control link. With reference voltage The difference, the sliding surface function The expression is:

[0251] ;

[0252] Specifically, to improve the response speed and accuracy of linearized active disturbance rejection control, second-order sliding mode control is introduced to adjust the compensation voltage of the linearized active disturbance rejection link, thereby improving its compensation performance and stability.

[0253] S44. Differentiating the sliding surface function yields:

[0254] ;

[0255] In the formula, i f This refers to the inverter filter inductor current. i h For inverter circulating current, C f For the inverter's filter capacitor;

[0256] S45. Design the control input of a second-order sliding mode controller based on the sliding surface function and the STA algorithm. u ， for:

[0257] ; ;

[0258] In the formula, u ， This is the control input for the second-order sliding mode control loop. u 1. u 2 represents the first and second control input components, respectively. , These are the first and second gain parameters of the second-order sliding mode controller, respectively. express u The first derivative of 2;

[0259] The first control input component is used to quickly respond to changes in the sliding surface, ensuring that the system state rapidly approaches the sliding surface. The second control input component is used to eliminate steady-state errors, ensuring that the system eventually stabilizes on the sliding surface. Furthermore, the value ranges of the first and second gain parameters of the second-order sliding controller are crucial to the controller's stability and convergence. For control input u The relative degree is 2, therefore the formula in step S46 can be obtained.

[0260] S46. Differentiating the sliding surface function after the first derivative yields:

[0261] ;

[0262] In the formula, L f For the inverter's filter inductor V DC This represents the DC terminal voltage of the inverter. The second derivative of the reference voltage is represented. t This refers to the specific time at which the state variables and harmonic disturbances of an islanded microgrid system are observed.

[0263] S47. Adjust the expression for the second derivative of the sliding surface function as follows:

[0264] ;

[0265] ;

[0266] In the formula, F ( t () is a function that simultaneously incorporates the dynamics of the second-order sliding mode control system and the external reference signal. i non This represents the current from the inverter to the nonlinear load. u ref This represents the original reference voltage given by the inverter. This represents the second derivative of the original given reference voltage;

[0267] in, F ( t ) is a function that simultaneously incorporates the dynamics of the second-order sliding mode control system and the external reference signal, reflecting the difference between the system state and the external reference signal, and how these differences change over time;

[0268] S48. Determine the range of values ​​for the first and second gain parameters of the second-order sliding mode controller based on the expression of the second derivative of the sliding surface function:

[0269] ; ;

[0270] In the formula, c min , c max , m They represent the first, second, and third constants, respectively.

[0271] Specifically, due to and All are bounded, therefore there exist constants greater than 0. c min , c max , m Make The range is - m ~ m , The range is c min ~ c max , c min , c max , m Used to restrict and These boundaries are crucial for the design of second-order sliding mode controllers.

[0272] S49. By selecting the appropriate first and second gain parameters of the second-order sliding mode controller within the range of values, the sliding surface function can converge to the sliding surface in a finite time. This is to compensate for the inverter output voltage, enabling the inverter output voltage to approach the reference voltage more quickly and accurately. ;

[0273] Specifically, This determines the dynamic response speed of the second-order sliding mode control. The steady-state performance of the control is determined by selecting appropriate second-order sliding mode control parameters, which ensures that the sliding surface function converges to the sliding surface in a finite time. This allows for better control of the linearization active disturbance rejection module to compensate for the inverter's output voltage, enabling it to approach the reference voltage more quickly and accurately.

[0274] The islanded microgrid harmonic mitigation method provided in Embodiment 1 of this invention first uses the state-space averaging method to model the average model of inverters in an islanded microgrid system with multiple inverters connected in parallel and containing nonlinear loads. This model not only effectively simplifies the complex system model with nonlinear loads but also accurately reflects the characteristics of each inverter in the islanded microgrid. Based on this, a residual generator is used to accurately separate low-frequency and high-frequency disturbance signals. Combined with a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized by the gradient descent method, optimized control of each inverter is achieved, realizing the equal distribution of reactive power among multiple inverters and solving the problem of uneven distribution in traditional droop control. Then, a second-order linear state observer optimized by the bandwidth tuning method is used to estimate the system's state variables and harmonic disturbances in real time, providing a more accurate basis for subsequent harmonic voltage compensation strategies. Finally, a linearized active disturbance rejection controller based on second-order sliding mode is used to compensate for the voltage harmonic components of the microgrid system. By quickly tracking the reference voltage and eliminating steady-state errors through the sliding surface function, the dynamic performance and robustness of harmonic compensation for the microgrid are significantly improved.

[0275] Example 2

[0276] like Figure 3 As shown, in Embodiment 2 of the present invention, a harmonic mitigation system for an islanded microgrid is provided, the system comprising:

[0277] Modeling module 1 is used to model the average model of inverters in an islanded microgrid system with multiple inverters connected in parallel and containing nonlinear loads using the state-space averaging method.

[0278] Control module 2 is used to optimize the control of the inverter by using a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized by gradient descent method according to the average model of the inverter.

[0279] Estimation module 3 is used to estimate the state variables and harmonic disturbances of an islanded microgrid system using a second-order linear state observer designed based on the bandwidth tuning method.

[0280] Governance module 4 is used to govern the voltage harmonics of the microgrid caused by nonlinear loads based on the estimated state variables and harmonic disturbances of the islanded microgrid system and a linearized active disturbance rejection control method based on second-order sliding mode.

[0281] The modeling module 1 includes:

[0282] The first modeling submodule is used to determine the inverter. i or inverter j Dynamic differential equations to the common connection point:

[0283] ;

[0284] ;

[0285] In the formula, i nond,i(j) , i nonq,i(j) Inverter i or inverter j to common load current d , q Axial components, The angular frequency of alternating current. R line,i(j) , L line,i(j) Inverter i or inverter j The line resistance and line inductance, u od,i(j) For inverters i or inverter j Output voltage d Axial components, u oq,i(j) For inverters i or inverter j Output voltage q Axial components, u pd , u pq These are the voltages at the point of common coupling. d , q Axial components;

[0286] The second modeling submodule is used to determine that the common load is a nonlinear load and to calculate the inverter. i or inverter j Current to nonlinear load:

[0287] ;

[0288] ;

[0289] In the formula, i nond_l,i(j) , i nond_h,i(j) They represent inverters i or inverter j Current to nonlinear load d The low-frequency and high-frequency components of the axis i nonq_l,i(j) , i nonq_h,i(j) They represent inverters i or inverter j Current to nonlinear load q The low-frequency and high-frequency components of the axis i nond,i(j) , i nonq,i(j) They represent inverters i or inverter j To nonlinear load current d , q Axial components;

[0290] The third modeling submodule is used for inverter-based... i or inverter j Dynamic differential equations to the point of common connection and inverter i or inverter j Current determination inverter to nonlinear load i and inverter j Differential equation of the circulation between them:

[0291] ; ;

[0292] ; ;

[0293] In the formula, i hd,ij , i hq,ij They represent inverters i and inverter j Circulation between d , q Axial components,R T Indicates inverter i With inverter j The sum of the line resistances, L T Indicates inverter i With inverter j The sum of the line inductances;

[0294] The fourth modeling submodule is used for inverter-based... i and inverter j The differential equation of the circulating current between the two phases determines the inverter. i or inverter j Output current:

[0295] ;

[0296] ;

[0297] In the formula, i od,i(j) , i oq,i(j) They represent inverters i or inverter j Output current d , q Axial components;

[0298] The fifth modeling submodule is used for inverter-based... i or inverter j Dynamic differential equations to the point of common connection and inverter i and inverter j The differential equation of the circulating current between the two phases determines the inverter. i or inverter j Average model:

[0299] ;

[0300] ;

[0301] x i(j) =( i fd,i(j) , i fq,i(j) , u od,i(j) , u oq,i(j) ) T ; u i(j) =( u id,i(j) , u iq,i(j) )T ;

[0302] d non_l,i(j) =( i fd,i(j) , i fq,i(j) ) T ; d non_h,i(j) =( i nond_h,i(j) , i nonq_h,i(j) ) T ;

[0303] d h_l,i(j) =( i hd,ij , i hq,ij ) T ;

[0304] In the formula, V DC,i(j) Indicates inverter i or inverter j DC terminal voltage, i fd,i(j) , i fq,i(j) They represent inverters i or inverter j The filter current d , q Axial components, u i(j) This represents the system's control input. u id,i(j) , u iq,i(j) They represent inverters i or inverter j The inverter bridge voltage d , q Axial components, d i(j) Indicates the effect of nonlinear load disturbance on the inverter i or inverter j The interference components, among which d non_l,i(j) , d non_h,i(j) These represent the low-frequency and high-frequency disturbances of the nonlinear load current, respectively. d h_l,i(j) This represents the disturbance of the nonlinear load to the circulating current between inverters. y i(j) This represents the system's output. A inv_i(j) ,B inv_i(j) , C inv_i(j) , V non_h,i(j) , V non_l,i(j) , V h_l,ij They represent inverters i or inverter j The first coefficient matrix, the second coefficient matrix, the third coefficient matrix, the high-frequency disturbance input matrix, the low-frequency disturbance input matrix, and the circulating low-frequency disturbance input matrix. x i(j) Indicates the system's input quantity. express x i(j) The first derivative.

[0305] The control module 2 includes:

[0306] The first control submodule is used to uniformly classify disturbances caused by line impedance differences, load fluctuations, or other complex operating conditions in the microgrid system into high-frequency disturbances and low-frequency disturbances, and to control the inverters in the islanded microgrid system. i Considered the controlled object G inv,i ( s ), and determine the inverter i State-space equations:

[0307] ;

[0308] In the formula, x i ( s (inverter) i The filtered inductor current signal, express x i ( s The first derivative of ) u i,i ( s (inverter) i The inverter bridge voltage signal, d i_l ( s ), d i_h ( s ) represent the low-frequency component and high-frequency component of the disturbance, respectively; y i ( s (inverter) i The output voltage signal, A inv_i , Binv_i , C inv_i , V non_h,i , V non_l,i They represent inverters i The first coefficient matrix, the second coefficient matrix, the third coefficient matrix, the high-frequency disturbance input matrix, and the low-frequency disturbance input matrix;

[0309] The second control submodule is used to convert the low-frequency and high-frequency disturbances of the common load into corresponding high-frequency and low-frequency residuals through a residual generator, so that... u i,i ( s As the input signal for the residual generator, y i ( s As the output signal of the residual generator, when it satisfies G inv,i ( s )= C inv_i ( sI - A inv_i ) -1 B inv_i + C inv_i At that time, the residual generator expression is:

[0310] ;

[0311] ;

[0312] In the formula, n i_l ( s ), n i_h ( s ) represent the low-frequency residual and high-frequency residual of the residual generator, respectively. N i ( s ) indicates a residual separator. N i_l ( s ), N i_h ( s ) represents the transfer functions of the low-pass and high-pass filters of the residual separator. express First derivative Indicates to x i ( s ) state estimation variables, Indicates inverter i The estimated value of the output voltage signal. s Represents a complex frequency variable. I Represents the identity matrix. L i For inverters i The gain matrix;

[0313] The third control submodule is used to convert the low-frequency components of the disturbance into the state space Z of the low-frequency residual. i_l ( s ), and the state space Z that transforms high-frequency components into high-frequency residuals. i_h ( s ), where Z i_l ( s The expression for ) is:

[0314] ;

[0315] In the formula, express The first derivative, This represents the low-frequency disturbance residual signal. Indicates inverter i DC terminal voltage, This represents the low-frequency component of the disturbance. N i_l This represents a low-pass filter in a residual separator.

[0316] Z i_h ( s The expression for ) is:

[0317] ;

[0318] In the formula, express The first derivative, This represents the high-frequency disturbance residual signal. This represents the high-frequency components of the disturbance. N i_h This represents a high-pass filter in a residual separator.

[0319] The fourth control submodule is used to control the inverter. i The reactive power deviation caused by droop characteristics is defined as follows: e droop,i The reactive power deviation caused by load changes is defined as e load,i :

[0320] ;

[0321] ;

[0322] In the formula, k 1. k 2 represents the first and second deviation gain coefficients. X i In an islanded microgrid system with multiple inverters connected in parallel, the inverters are... i The collection of other connected inverters, c ij Indicates inverter i and inverter j Connect the coefficients of the matrix. n i Indicates inverter i The reactive power droop control coefficient Q i , Q j They represent inverters i Inverter j The output reactive power;

[0323] The fifth control submodule is used for... e droop,i , e load,i Determine virtual impedance :

[0324] ;

[0325] In the formula, s, j These represent the complex frequency variable and the imaginary unit, respectively;

[0326] The sixth control submodule is used to form a voltage closed-loop control system by applying a low-frequency voltage compensation controller based on virtual impedance to the inverter's voltage control loop, thereby adjusting the inverter's control strategy. The reference voltage control relationship and frequency control relationship of the inverter after compensation are as follows:

[0327] ;

[0328] ;

[0329] In the formula, , They represent inverters i Reference voltage and reference frequency after compensation by the low-frequency voltage compensation controller u ref,i Indicates inverter i The original given reference voltage, u ref,j Indicates inverter j The original given reference voltage, io,i Indicates inverter i The output current, m i Indicates inverter i The active power sagging control coefficient Q n,i , P n,i They represent inverters i Rated reactive power and rated active power Indicates inverter i The rated output voltage, N i Indicates with inverter i A set that has connections between it. f n,i Indicates inverter i The rated frequency of the output, P i Indicates inverter i The actual output active power, n i , n j They represent inverters i、 Inverter j The reactive power droop control coefficient;

[0330] The seventh control submodule is used to design a high-frequency disturbance compensation controller by taking the high-frequency disturbance component as input, so as to ensure that the high-frequency residual... n i_h ( s The value is close to 0, where the high-frequency disturbance compensation controller The solution is:

[0331] ;

[0332] In the formula, , Inverter i The transfer functions of the filter inductor and filter capacitor. For inverters i Voltage controller, This represents the transfer function of the high-frequency disturbance compensator. Z i_h ( s This indicates that the high-frequency components of the disturbance are transformed into the state space of the high-frequency residual;

[0333] The eighth control submodule is used to introduce the gradient descent method for the high-frequency disturbance compensator. The parameter optimization design is used to obtain the objective function. J ( k op ):

[0334] ;

[0335] In the formula, u o,i For inverters i The output voltage, k op for High-frequency disturbance compensation gain to be optimized. N This represents the number of sample points for the mean square error of voltage deviation collected within a preset time period. The residual weighting coefficient is... n i_h ( k () represents the high-frequency residual signal;

[0336] The ninth control submodule is used for the objective function. J ( k op Perform differentiation and iterate along the opposite direction of the gradient to compensate for the high-frequency perturbation gain. k op The optimal high-frequency disturbance compensation gain is selected using the gradient descent method to determine the high-frequency disturbance compensator, thereby suppressing high-frequency disturbances in the islanded microgrid system. i High-frequency disturbance compensation gain of +1 iteration k op,i+1 for:

[0337] ;

[0338] ;

[0339] In the formula, For gradient operators, k op,i For the process i High-frequency disturbance compensation gain after the next iteration. For learning rate, J express J ( k op ).

[0340] The estimation module 3 includes:

[0341] The first estimation submodule is used to determine the second-order dynamic equations of any inverter in an islanded microgrid system:

[0342] ;

[0343] In the formula, The rated angular frequency, L f , Cf These are the inverter's filter inductor and filter capacitor, respectively. R f This is the parasitic resistance of the inverter's filter inductor. u od(q) Indicates the inverter output voltage d shaft or q Axial components, i fd(q) Indicates the inverter filter inductor current d shaft or q Axial components, u id(q) This represents the inverter bridge voltage of the inverter. d shaft or q Axial components;

[0344] The second estimation submodule is used to estimate the inverter's output voltage. u od With harmonic disturbances h The first state variable is regarded as a second-order linear state observer. z 1. Second state variable z 2. y As the output of the observer, the inverter bridge voltage of the inverter. d Axial components u id As the input to the observer, the second-order linear state observer satisfies the following expression condition:

[0345] ;

[0346] In the formula, u od The output voltage of the inverter d Axial components, i fd Indicates the inverter filter inductor current d Axial components, i od Indicates the inverter output current d Axial components;

[0347] The third estimation submodule is used to determine the extended state equation of the second-order linear state observer based on the expression conditions:

[0348] ;

[0349] In the formula, k 0 represents the control gain of the input variable. u Indicates the observer input, express z The first derivative of 2, Indicates harmonic disturbance hThe first derivative;

[0350] The fourth estimation submodule is used to determine the expression for the second-order linear state observer based on the extended state equation:

[0351] ;

[0352] In the formula, , They are respectively z 1. z The derivative of the estimated value of 2, , These are the first and second gain coefficients of the second-order linear state observer, respectively. express z The estimated value of 1;

[0353] The fifth estimation submodule is used to determine the first and second gain coefficients of the second-order linear state observer using the bandwidth tuning method, and to express the error dynamic equation between the actual state and the estimated value of the second-order linear state observer as follows:

[0354] ;

[0355] In the formula, e Represents the error vector. The derivative of the error vector. Z This represents the actual state of the microgrid. For the observer's estimated value, L Here is the gain matrix. A inv , B inv , C inv These represent the first coefficient matrix, the second coefficient matrix, and the third coefficient matrix, respectively.

[0356] The sixth estimation submodule is used to determine the solution of the second-order linear state observer based on the error dynamic equation, and to determine the state variables and harmonic disturbances of the islanded microgrid system based on the solution of the second-order linear state observer. for:

[0357] ;

[0358] In the formula, t To observe the state variables and harmonic disturbances of an islanded microgrid system at a specific moment. t 0 represents the initial time. Indicates equivalent time.

[0359] The governance module 4 includes:

[0360] The first governance submodule is used to determine the error control rate of the linearized active disturbance rejection control (ADRC) based on the estimated state variables and harmonic disturbances of the islanded microgrid system. r :

[0361] ;

[0362] In the formula, Represents the first state variable z The estimated value of 1, Represents the second state variable z The estimated value of 2, This represents the original reference voltage given by the inverter. d Axial components, k 0 represents the control gain of the input variable. This represents the bandwidth of a second-order linear state observer;

[0363] The second governance submodule is used to determine the error control rate. r The estimated harmonic disturbances of the islanded microgrid system are fed forward into the inverter voltage control to compensate for the voltage harmonics of the microgrid. The relationship between the inverter output voltage and the reference voltage after compensation by the linearized active disturbance rejection control is as follows:

[0364] ;

[0365] In the formula, To compensate for the inverter output voltage d Transfer function of axis components, Reference voltage of d Axial components, u od ( s To compensate for the output voltage of the pre-inverter d Transfer function of axis components, s Represents a complex frequency variable;

[0366] The third governance submodule is used to introduce second-order sliding mode control to adjust the compensation voltage of the linearized active disturbance rejection (ADNR) stage. The sliding surface function of the second-order sliding mode is defined as the output voltage of the inverter after compensation by the linearized ADNR stage. With reference voltage The difference, the sliding surface function The expression is:

[0367] ;

[0368] The fourth governance submodule is used to differentiate the sliding surface function to obtain:

[0369] ;

[0370] In the formula, i f This refers to the inverter filter inductor current. i h For inverter circulating current, C f For the inverter's filter capacitor;

[0371] The fifth governance submodule is used to design the control input of a second-order sliding mode controller based on the sliding surface function and the STA algorithm. u ， for:

[0372] ; ;

[0373] In the formula, u ， This is the control input for the second-order sliding mode control loop. u 1. u 2 represents the first and second control input components, respectively. , These are the first and second gain parameters of the second-order sliding mode controller, respectively. express u The first derivative of 2;

[0374] The sixth governance submodule is used to differentiate the sliding surface function after the first derivative is obtained as follows:

[0375] ;

[0376] In the formula, L f For the inverter's filter inductor V DC This represents the DC terminal voltage of the inverter. The second derivative of the reference voltage is represented. t To observe the state variables and harmonic disturbances of an isolated microgrid system at a specific moment;

[0377] The seventh governance submodule is used to adjust the expression of the second derivative of the sliding surface function as follows:

[0378] ;

[0379] ;

[0380] In the formula, F ( t () is a function that simultaneously incorporates the dynamics of the second-order sliding mode control system and the external reference signal. i non This represents the current from the inverter to the nonlinear load.u ref This represents the original reference voltage given by the inverter. This represents the second derivative of the original given reference voltage;

[0381] The eighth governance submodule is used to determine the value range of the first and second gain parameters of the second-order sliding mode controller based on the expression of the second derivative of the sliding surface function.

[0382] ; ;

[0383] In the formula, c min , c max , m They represent the first, second, and third constants, respectively.

[0384] The ninth governance submodule is used to select the first and second gain parameters of the corresponding second-order sliding mode controller within a certain range, so that the sliding surface function can converge to the sliding surface in a finite time. This is to compensate for the inverter output voltage, enabling the inverter output voltage to approach the reference voltage more quickly and accurately. .

[0385] In other embodiments of the present invention, the present invention provides the following technical solution: a computer, including a memory 102, a processor 101, and a computer program stored in the memory 102 and executable on the processor 101, wherein the processor 101 executes the computer program to implement the islanded microgrid harmonic mitigation method as described above.

[0386] Specifically, the processor 101 may include a central processing unit (CPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of the present invention.

[0387] The memory 102 may include a large-capacity memory for data or instructions. For example, and not limitingly, the memory 102 may include a hard disk drive (HDD), a floppy disk drive, a solid-state drive (SSD), flash memory, an optical disk drive, a magneto-optical disk drive, magnetic tape, or a Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, the memory 102 may include removable or non-removable (or fixed) media. Where appropriate, the memory 102 may be internal or external to a data processing device. In a particular embodiment, the memory 102 is non-volatile memory. In a particular embodiment, the memory 102 includes read-only memory (ROM) and random access memory (RAM). Where appropriate, the ROM may be a mask-programmed ROM, a programmable read-only memory (PROM), an erasable read-only memory (EPROM), an electrically erasable read-only memory (EEPROM), an electrically alterable read-only memory (EAROM), or flash memory, or a combination of two or more of these. Where appropriate, the RAM can be Static Random-Access Memory (SRAM) or Dynamic Random-Access Memory (DRAM). DRAM can be Fast Page Mode Dynamic Random Access Memory (FPMDRAM), Extended Data Out Dynamic Random Access Memory (EDODRAM), Synchronous Dynamic Random-Access Memory (SDRAM), etc.

[0388] The memory 102 can be used to store or cache various data files that need to be processed and / or used for communication, as well as possible computer program instructions executed by the processor 101.

[0389] The processor 101 reads and executes the computer program instructions stored in the memory 102 to implement the above-mentioned harmonic mitigation method for islanded microgrids.

[0390] In some embodiments, the computer may further include a communication interface 103 and a bus 100. For example, Figure 4 As shown, the processor 101, memory 102, and communication interface 103 are connected through bus 100 and communicate with each other.

[0391] The communication interface 103 is used to enable communication between the various modules, devices, units, and / or equipment in the embodiments of the present invention. The communication interface 103 can also enable data communication with other components such as external devices, image / data acquisition devices, databases, external storage, and image / data processing workstations.

[0392] Bus 100 includes hardware, software, or both, that couples components of a computer device together. Bus 100 includes, but is not limited to, at least one of the following: data bus, address bus, control bus, expansion bus, and local bus. For example, and not as a limitation, bus 100 may include an Accelerated Graphics Port (AGP) or other graphics bus, an Extended Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a Hyper Transport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an InfiniBand interconnect, a Low Pin Count (LPC) bus, a memory bus, a Micro Channel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local Bus (VLB) bus, or other suitable buses, or a combination of two or more of these. Where appropriate, bus 100 may include one or more buses. Although specific buses are described and illustrated in the embodiments of the present invention, the present invention is contemplated by any suitable bus or interconnect.

[0393] The computer can execute the islanded microgrid harmonic mitigation method of the present invention based on the acquired islanded microgrid harmonic mitigation system, thereby realizing harmonic mitigation of the islanded microgrid.

[0394] In some further embodiments of the present invention, in conjunction with the above-described method for mitigating harmonics in isolated microgrids, the present invention provides the following technical solution: a storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the above-described method for mitigating harmonics in isolated microgrids.

[0395] Those skilled in the art will understand that the logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can mean any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0396] More specific examples of readable media (a non-exhaustive list) include: electrical connections (electronic devices) with one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0397] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0398] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0399] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for harmonic mitigation in islanded microgrids, characterized in that, include: The state-space averaging method is used to model the average model of inverters in an islanded microgrid system with multiple inverters connected in parallel and nonlinear loads. Based on the average model of the inverter, a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized by gradient descent method are used to optimize the control of the inverter. A second-order linear state observer based on the bandwidth tuning method is used to estimate the state variables and harmonic disturbances of an islanded microgrid system. Based on the estimated state variables and harmonic disturbances of the islanded microgrid system, a linearized active disturbance rejection control method based on second-order sliding mode is adopted to manage the microgrid voltage harmonics caused by nonlinear loads. The steps for mitigating microgrid voltage harmonics caused by nonlinear loads based on estimated state variables and harmonic disturbances of the islanded microgrid system and employing a second-order sliding mode-based linearized active disturbance rejection control method include: The error control rate of the linearized active disturbance rejection control (ADRC) element is determined based on the estimated state variables and harmonic disturbances of the islanded microgrid system. r : ； In the formula, Represents the first state variable z The estimated value of 1, Represents the second state variable z The estimated value of 2, This represents the original reference voltage given by the inverter. d Axial components, k 0 represents the control gain of the input variable. This represents the bandwidth of a second-order linear state observer; According to the error control rate r The estimated harmonic disturbances of the islanded microgrid system are fed forward into the inverter voltage control to compensate for the voltage harmonics of the microgrid. The relationship between the inverter output voltage and the reference voltage after compensation by the linearized active disturbance rejection control is as follows: ； In the formula, To compensate for the inverter output voltage d Transfer function of axis components, Reference voltage of d Axial components, u od ( s To compensate for the output voltage of the pre-inverter d Transfer function of axis components, s This represents a complex frequency variable.

2. The harmonic mitigation method for islanded microgrids according to claim 1, characterized in that, The steps for modeling the average model of inverters in an islanded microgrid system with multiple inverters connected in parallel and containing nonlinear loads using the state-space averaging method include: Determine the inverter i or inverter j Dynamic differential equations to the common connection point: ； ； In the formula, i nond,i(j) , i nonq,i(j) Inverter i or inverter j to common load current d , q Axial components, The angular frequency of alternating current. R line,i(j) , L line,i(j) Inverter i or inverter j The line resistance and line inductance, u od,i(j) For inverters i or inverter j Output voltage d Axial components, u oq,i(j) For inverters i or inverter j Output voltage q Axial components, u pd , u pq These are the voltages at the point of common coupling. d , q Axial components; Determine that the common load is a nonlinear load and calculate the inverter. i or inverter j Current to nonlinear load: ； ； In the formula, i nond_l,i(j) , i nond_h,i(j) They represent inverters i or inverter j Current to nonlinear load d The low-frequency and high-frequency components of the axis i nonq_l,i(j) , i nonq_h,i(j) They represent inverters i or inverter j Current to nonlinear load q The low-frequency and high-frequency components of the axis i nond,i(j) , i nonq,i(j) They represent inverters i or inverter j To nonlinear load current d , q Axial components; Based on inverter i or inverter j Dynamic differential equations to the point of common connection and inverter i or inverter j Current determination inverter to nonlinear load i and inverter j Differential equations for the circulation between them: ； ； ； ； In the formula, i hd,ij , i hq,ij They represent inverters i and inverter j Circulation between d , q Axial components, R T Indicates inverter i With inverter j The sum of the line resistances, L T Indicates inverter i With inverter j The sum of the line inductances; Based on inverter i and inverter j The differential equation of the circulating current between the inverters determines the inverter. i or inverter j Output current: ； ； In the formula, i od,i(j) , i oq,i(j) They represent inverters i or inverter j Output current d , q Axial components; Based on inverter i or inverter j Dynamic differential equations to the point of common connection and inverter i and inverter j The differential equation of the circulating current between the inverters determines the inverter. i or inverter j Average model: ； ； x i(j) =( i fd,i(j) , i fq,i(j) , u od,i(j) , u oq,i(j) ) T ； u i(j) =( u id,i(j) , u iq,i(j) ) T ； d non_l,i(j) =( i fd,i(j) , i fq,i(j) ) T ； d non_h,i(j) =( i nond_h,i(j) , i nonq_h,i(j) ) T ； d h_l,i(j) =( i hd,ij , i hq,ij ) T ； In the formula, V DC,i(j) Indicates inverter i or inverter j DC terminal voltage, i fd,i(j) , i fq,i(j) They represent inverters i or inverter j The filter current d , q Axial components, u i(j) This represents the system's control input. u id,i(j) , u iq,i(j) They represent inverters i or inverter j The inverter bridge voltage d , q Axial components, d i(j) Indicates the effect of nonlinear load disturbance on the inverter i or inverter j The interference components, among which d non_l,i(j) , d non_h,i(j) These represent the low-frequency and high-frequency disturbances of the nonlinear load current, respectively. d h_l,i(j) This represents the disturbance of the nonlinear load to the circulating current between inverters. y i(j) This represents the system's output. A inv_i(j) , B inv_i(j) , C inv_i(j) , V non_h,i(j) , V non_l,i(j) , V h_l,ij They represent inverters i or inverter j The first coefficient matrix, the second coefficient matrix, the third coefficient matrix, the high-frequency disturbance input matrix, the low-frequency disturbance input matrix, and the circulating low-frequency disturbance input matrix. x i(j) Indicates the system's input quantity. express x i(j) The first derivative.

3. The harmonic mitigation method for islanded microgrids according to claim 2, characterized in that, In inverter i or inverter j In the average model, A inv_i(j) , B inv_i(j) , C inv_i(j) , V h_l,ij , V non_h,i(j) , V non_l,i(j) They are respectively: ； ； ； ； ； In the formula, L f,i(j) , C f,i(j) , R f,i(j) They represent inverters i or inverter j The filter inductor, filter capacitor, and parasitic resistance of the filter inductor.

4. The harmonic mitigation method for islanded microgrids according to claim 1, characterized in that, The step of optimizing the control of the inverter using a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized based on the gradient descent method according to the average model of the inverter includes: Disturbances caused by line impedance differences, load fluctuations, or other complex operating conditions in microgrid systems are uniformly classified into high-frequency disturbances and low-frequency disturbances, and the inverters in islanded microgrid systems are also classified into these categories. i Considered the controlled object G inv,i ( s ), and determine the inverter i State-space equations: ； In the formula, x i ( s (inverter) i The filtered inductor current signal, express x i ( s The first derivative of ) u i,i ( s (inverter) i The inverter bridge voltage signal, d i_l ( s ), d i_h ( s ) represent the low-frequency component and high-frequency component of the disturbance, respectively; y i ( s (inverter) i The output voltage signal, A inv_i , B inv_i , C inv_i , V non_h,i , V non_l,i They represent inverters i The first coefficient matrix, the second coefficient matrix, the third coefficient matrix, the high-frequency disturbance input matrix, and the low-frequency disturbance input matrix; The low-frequency and high-frequency disturbances of the common load are converted into corresponding high-frequency and low-frequency residuals using a residual generator, allowing... u i,i ( s As the input signal for the residual generator, y i ( s As the output signal of the residual generator, when it satisfies G inv,i ( s )= C inv_i ( sI - A inv_i ) -1 B inv_i + C inv_i At that time, the residual generator expression is: ； ； In the formula, n i_l ( s ), n i_h ( s ) represent the low-frequency residual and high-frequency residual of the residual generator, respectively. N i ( s ) indicates a residual separator. N i_l ( s ), N i_h ( s ) represents the transfer functions of the low-pass and high-pass filters of the residual separator. express First derivative Indicates to x i ( s ) state estimation variables, Indicates inverter i The estimated value of the output voltage signal. s Represents a complex frequency variable. I Represents the identity matrix. L i For inverters i The gain matrix; The low-frequency components of the disturbance are transformed into the state space Z of the low-frequency residual. i_l ( s ), and the state space Z that transforms high-frequency components into high-frequency residuals. i_h ( s ), where Z i_l ( s The expression for ) is: ； In the formula, express The first derivative, This represents the low-frequency disturbance residual signal. Indicates inverter i DC terminal voltage, This represents the low-frequency component of the disturbance. N i_l This represents a low-pass filter in a residual separator. Z i_h ( s The expression for ) is: ； In the formula, express The first derivative, This represents the high-frequency disturbance residual signal. This represents the high-frequency components of the disturbance. N i_h This represents a high-pass filter in a residual separator. Inverter i The reactive power deviation caused by droop characteristics is defined as follows: e droop,i The reactive power deviation caused by load changes is defined as e load,i : ； ； In the formula, k 1. k 2 represents the first and second deviation gain coefficients. X i In an islanded microgrid system with multiple inverters connected in parallel, the inverters are... i The collection of other connected inverters, c ij Indicates inverter i and inverter j Connect the coefficients of the matrix. n i Indicates inverter i The reactive power droop control coefficient Q i , Q j They represent inverters i Inverter j The output reactive power; based on e droop,i , e load,i Determine virtual impedance : ； In the formula, s, j These represent the complex frequency variable and the imaginary unit, respectively; By applying a low-frequency voltage compensation controller based on virtual impedance to the voltage control loop of the inverter, a voltage closed-loop control system is formed to adjust the inverter control strategy. The reference voltage control relationship and frequency control relationship of the inverter after compensation are as follows: ； ； In the formula, , They represent inverters i Reference voltage and reference frequency after compensation by the low-frequency voltage compensation controller u ref,i Indicates inverter i The original given reference voltage, u ref,j Indicates inverter j The original given reference voltage, i o,i Indicates inverter i The output current, m i Indicates inverter i The active power sagging control coefficient Q n,i , P n,i They represent inverters i Rated reactive power and rated active power Indicates inverter i The rated output voltage N i Indicates with inverter i A set that has connections between it. f n,i Indicates inverter i The rated frequency of the output, P i Indicates inverter i The actual output active power, n i , n j They represent inverters i、 Inverter j The reactive power droop control coefficient; A high-frequency disturbance component is used as input to design a high-frequency disturbance compensation controller, so that the high-frequency residual... n i_h ( s The value is close to 0, where the high-frequency disturbance compensation controller The solution is: ； In the formula, , Inverter i The transfer functions of the filter inductor and filter capacitor. For inverters i Voltage controller, This represents the transfer function of the high-frequency disturbance compensator. Z i_h ( s This indicates that the high-frequency components of the disturbance are transformed into the state space of the high-frequency residual; Introducing the gradient descent method for high-frequency disturbance compensators The parameter optimization design is used to obtain the objective function. J ( k op ): ； In the formula, u o,i For inverters i The output voltage, k op for High-frequency disturbance compensation gain to be optimized. N This represents the number of sample points for the mean square error of voltage deviation collected within a preset time period. The residual weighting coefficient is... n i_h ( k () represents the high-frequency residual signal; For the objective function J ( k op Perform differentiation and iterate along the opposite direction of the gradient to compensate for the high-frequency perturbation gain. k op The optimal high-frequency disturbance compensation gain is selected using the gradient descent method to determine the high-frequency disturbance compensator, thereby suppressing high-frequency disturbances in the islanded microgrid system. i High-frequency disturbance compensation gain of +1 iteration k op,i+1 for: ； ； In the formula, For gradient operators, k op,i For the process i High-frequency disturbance compensation gain after the next iteration. For learning rate, J express J ( k op ).

5. The harmonic mitigation method for islanded microgrids according to claim 1, characterized in that, The steps for estimating the state variables and harmonic disturbances of an islanded microgrid system using a second-order linear state observer designed based on the bandwidth tuning method include: Determine the second-order dynamic equations for any inverter in an islanded microgrid system: ； In the formula, The rated angular frequency, L f , C f These are the inverter's filter inductor and filter capacitor, respectively. R f This is the parasitic resistance of the inverter's filter inductor. u od(q) Indicates the inverter output voltage d shaft or q Axial components, i fd(q) Indicates the inverter filter inductor current d shaft or q Axial components, u id(q) This represents the inverter bridge voltage of the inverter. d shaft or q Axial components; The inverter's output voltage u od With harmonic disturbances h The first state variable is regarded as a second-order linear state observer. z 1. Second state variable z 2. y As the output of the observer, the inverter bridge voltage of the inverter. d Axial components u id As the input to the observer, the second-order linear state observer satisfies the following expression condition: ； In the formula, u od The output voltage of the inverter d Axial components, i fd Indicates the inverter filter inductor current d Axial components, i od Indicates the inverter output current d Axial components; Determine the extended state equation of the second-order linear state observer based on the expression conditions: ； In the formula, k 0 represents the control gain of the input variable. u Indicates the observer input, express z The first derivative of 2, Indicates harmonic disturbance h The first derivative; Determining the expression for a second-order linear state observer based on the extended state equation: ； In the formula, , They are respectively z 1. z The derivative of the estimated value of 2, , These are the first and second gain coefficients of the second-order linear state observer, respectively. express z The estimated value of 1; The first and second gain coefficients of the second-order linear state observer are determined using the bandwidth tuning method, and the error dynamic equation between the actual state and the estimated value of the second-order linear state observer is expressed as: ； In the formula, e Represents the error vector. The derivative of the error vector. Z This represents the actual state of the microgrid. For the observer's estimated value, L Here is the gain matrix. A inv , B inv , C inv These represent the first coefficient matrix, the second coefficient matrix, and the third coefficient matrix, respectively. The solution of the second-order linear state observer is determined based on the error dynamic equation, and the state variables and harmonic disturbances of the islanded microgrid system are determined based on the solution of the second-order linear state observer. for: ； In the formula, t To observe the state variables and harmonic disturbances of an islanded microgrid system at a specific moment. t 0 represents the initial time. Indicates equivalent time.

6. The harmonic mitigation method for islanded microgrids according to claim 5, characterized in that, in, The first gain coefficient of the second-order linear state observer Second gain coefficient Control gain of input variables k 0 satisfies the following constraints: ； ； In the formula, s Represents a complex frequency variable. This represents the bandwidth of a second-order linear state observer. This is the rated angular frequency.

7. The harmonic mitigation method for islanded microgrids according to claim 1, characterized in that, The steps of mitigating microgrid voltage harmonics caused by nonlinear loads based on estimated state variables and harmonic disturbances of the islanded microgrid system and employing a second-order sliding mode-based linearized active disturbance rejection control method further include: A second-order sliding mode control is introduced to adjust the compensation voltage of the linearized active disturbance rejection (ADNR) stage. The sliding surface function of the second-order sliding mode is defined as the output voltage of the inverter after compensation by the linearized ADNR control stage. With reference voltage The difference, the sliding surface function The expression is: ； Differentiating the sliding surface function, we get: ； In the formula, i f This refers to the inverter filter inductor current. i h For inverter circulating current, C f For the inverter's filter capacitor; The control input of a second-order sliding mode controller is designed based on the sliding surface function and the STA algorithm. u ， for: ； ； In the formula, u ， This is the control input for the second-order sliding mode control loop. u 1. u 2 represents the first and second control input components, respectively. , These are the first and second gain parameters of the second-order sliding mode controller, respectively. express u The first derivative of 2; Differentiating the sliding surface function after the first derivative yields: ； In the formula, L f For the inverter's filter inductor, V DC This represents the DC terminal voltage of the inverter. The second derivative of the reference voltage is represented. t To observe the state variables and harmonic disturbances of an isolated microgrid system at a specific moment; The expression for the second derivative of the sliding surface function is adjusted as follows: ； ； In the formula, F ( t () is a function that simultaneously incorporates the dynamics of the second-order sliding mode control system and the external reference signal. i non This represents the current from the inverter to the nonlinear load. u ref This represents the original reference voltage given by the inverter. This represents the second derivative of the original given reference voltage; The range of values ​​for the first and second gain parameters of the second-order sliding mode controller is determined based on the expression for the second derivative of the sliding surface function. ； ； In the formula, c min , c max , m They represent the first, second, and third constants, respectively. By selecting the appropriate first and second gain parameters of the second-order sliding mode controller within a certain range, the sliding surface function can be made to converge to the sliding surface in a finite time. This is to compensate for the inverter output voltage, enabling the inverter output voltage to approach the reference voltage more quickly and accurately. .

8. A harmonic mitigation system for an islanded microgrid, wherein the system employs the harmonic mitigation method for an islanded microgrid as described in claim 1, characterized in that, The system includes: The modeling module is used to model the average model of inverters in an islanded microgrid system with multiple inverters connected in parallel and containing nonlinear loads using the state-space averaging method. The control module is used to optimize the control of the inverter by employing a low-frequency voltage compensation controller and a high-frequency disturbance compensation controller optimized based on the gradient descent method, according to the average model of the inverter. The estimation module is used to estimate the state variables and harmonic disturbances of an islanded microgrid system using a second-order linear state observer designed based on the bandwidth tuning method. The governance module is used to manage microgrid voltage harmonics caused by nonlinear loads based on the estimated state variables and harmonic disturbances of the islanded microgrid system and a linearized active disturbance rejection control method based on second-order sliding mode.

9. A computer comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the islanded microgrid harmonic mitigation method as described in any one of claims 1 to 7.

10. A storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the islanded microgrid harmonic mitigation method as described in any one of claims 1 to 7.

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