A method, device and application of constructing a linear time-invariant state space model of a power system

Abstract

The application discloses a method and device for constructing a linear time-invariant state space model of a power system and application thereof, and relates to the technical field of power system power electronic stability analysis and control. The method comprises the following steps: constructing a harmonic decomposition general equation, wherein the general equation is used for converting a linear time-varying periodic general state space equation into a linear time-invariant state space equation; establishing a linear time-varying periodic state equation of a decoupling double synchronous reference coordinate system phase sequence separation link in a rotating coordinate system; setting a harmonic order for state variables and input variables in the state equation; and performing harmonic decomposition on the state equation by using the constructed general equation to obtain a linear time-invariant state space model. The method can be used for constructing a model for realizing high-precision power system stability analysis.

Description

Technical Field

[0001] This application relates to the field of power electronic stability analysis and control technology for power systems, and in particular to a method, device and application for constructing a linear time-invariant state-space model of a power system. Background Technology

[0002] Currently, small-signal modeling of power systems mainly revolves around two major theoretical frameworks: Linear Time-Periodic (LTP) and Linear Time-Invariant (LTI). For the phase sequence separation stage of decoupling dual synchronous reference coordinate systems, the industry has established LTP models and simplified LTI models. Although the LTP model can more accurately characterize system dynamics, its state matrix A(t) is a time-varying matrix, often containing... , For isochronous variables, the corresponding stability analysis theory is not mature enough, making it difficult to effectively guide control system design and control parameter optimization. Compared to the LTP model, the LTI model has outstanding engineering practicality, manifested in the following ways: concepts such as poles, zeros, bandwidth, and phase margin of the LTI system have clear physical meanings (e.g., response speed, stability), greatly simplifying the difficulty of stability analysis. The LTI model possesses an extremely mature analysis toolbox (such as frequency domain analysis, root locus, Nyquist criterion, Bode plot, etc.), significantly reducing the design threshold and debugging cycle of controllers. Although an LTI model for decoupled dual-synchronous reference coordinate system phase sequence separation has been established, the existing model has undergone unreasonable simplification, resulting in insufficient accuracy and often leading to erroneous results in stability analysis, thus limiting its application. Summary of the Invention

[0003] Therefore, it is necessary to address the issue of insufficient accuracy of existing LTI models in stability analysis by providing a method, equipment, and application for constructing a linear time-invariant state-space model of a power system. The specific technical solution is as follows: Firstly, this application proposes a method for constructing a linear time-invariant state-space model of a power system, comprising the following steps: S1: Construct a general equation for harmonic decomposition, which is used to convert the general state-space equation of linear time-varying period into a linear time-invariant state-space equation. S2: Establish a linear time-varying periodic state equation for the phase sequence separation link of the decoupled dual synchronous reference coordinate system in the rotating coordinate system. The state variables and input variables of the linear time-varying periodic state equation include the electrical quantities of the power system. S3: Set the harmonic order for the state variables and input variables in the state equation, and use the constructed general equation to perform harmonic decomposition on the state equation to obtain a linear time-invariant state-space model.

[0004] Furthermore, the process of constructing the general equation for harmonic decomposition in step S1 is as follows: The general state-space equation for linear time-varying periodicity is denoted as:

[0005] in, , Given a state vector and an input vector, , The state matrix and the input matrix are used for calculation. Perform a Fourier series expansion on the state vector, input vector, state matrix, and input matrix, and substitute them into the linear time-varying periodic general state-space equation. Based on the fourth... k Based on the principle that the first harmonic coefficients are equal, the 1st harmonic is obtained. k The state equation corresponding to the subharmonic; Based on the characteristics of the phase sequence separation stage of the decoupling dual synchronous reference coordinate system, the first... k The state equation corresponding to the second harmonic is transformed into the state variable of the third harmonic. k The state equations corresponding to the complex Fourier coefficients; For the state variable k Expanding the state equations corresponding to the complex Fourier coefficients and setting the truncation order yields the general equations for harmonic decomposition.

[0006] The first k The process of constructing the state equation corresponding to the subharmonic is as follows: right , , , Performing a Fourier series expansion, we get:

[0007]

[0008] In the formula, N It is the highest harmonic order that is cut off. The fundamental angular frequency; , They are respectively , The m The complex Fourier coefficients corresponding to the subharmonics; , They are respectively , The n The complex Fourier coefficient matrix corresponding to the subharmonics; After unfolding , , , Substituting into the general state-space equation for linear time-varying periods, since the first... k The first harmonic coefficients are equal, thus obtaining the second harmonic coefficient. k The state equation corresponding to the subharmonic is: .

[0009] The first k The state equation corresponding to the second harmonic is transformed into the state variable of the third harmonic. k The specific content of the state equation corresponding to the complex Fourier coefficients is as follows: The phase sequence separation stage of the decoupling dual synchronous reference coordinate system mainly contains DC and second harmonic components in its state variables during operation. The p line, number h Column elements , The p line, number z Column elements Represented as a general formula: (4.1) (4.2) In the formula, , , They are respectively The amplitudes of the DC, second harmonic sine, and cosine components, , , They are respectively The amplitudes of the DC, second harmonic sine, and cosine components; Substituting equations (4.1) and (4.2) into the above... k The state equation corresponding to the second harmonic is obtained. p State variables The k Second complex Fourier coefficients The corresponding state equation is:

[0010] In the formula, , Matrix elements , The n The complex Fourier coefficients corresponding to the subharmonics; , Variables , The ( kn The complex Fourier coefficients corresponding to the first harmonic.

[0011] The first state variable k Expanding the state equations corresponding to the second complex Fourier coefficients and setting the truncation order, we obtain the following specific content of the general equation for harmonic decomposition: The expanded expression is: Setting the truncation order to 2, the corresponding state equation, i.e., the general equation for harmonic decomposition, is: .

[0012] Furthermore, the workflow of the phase sequence separation step of decoupling the dual synchronous reference coordinate system described in step S2 is as follows: The electrical quantities in the three-phase stationary coordinate system are transformed into electrical quantities in the two-phase stationary coordinate system by Clarke transformation, and then output as two signals by fundamental frequency forward rotation Park transformation and fundamental frequency reverse rotation Park transformation, respectively. The two signals are then subjected to second harmonic interference elimination and low-pass filtering to obtain positive sequence components and negative sequence components.

[0013] The linear time-varying periodic state equation described in step S2 is:

[0014] In the formula, For state vectors, The input vector; , These represent the amplitudes of the positive and negative sequence components of the input voltage. , The initial phase, and ; This represents the small-signal disturbance of the input voltage in a three-phase stationary coordinate system. Extracted for the phase sequence separation step d , q shaft voltage , Small signal perturbation components; Small-signal disturbance components of the state variable are introduced into the integral stage of the phase-locked loop PI controller. This refers to the small-signal disturbance component of the phase-locked loop output phase.

[0015] Furthermore, the specific content of step S3 is as follows: With the cutoff number set to 2, harmonic decomposition is performed on the linear time-varying periodic state equation based on the general harmonic decomposition equation, resulting in a linear time-invariant state-space model:

[0016] in, The state matrix, The input matrix is ​​denoted as .

[0017] Secondly, this application proposes an electronic device, including a memory and a processor; the memory is used to store instructions; the processor is used to operate according to the instructions to execute the method for constructing a linear time-invariant state-space model of a power system as described in this application.

[0018] Thirdly, this application proposes an application of a linear time-invariant state-space model, which is constructed based on the method for constructing a linear time-invariant state-space model of a power system described in this application, and is applied to a power electronic system under unbalanced power grid conditions.

[0019] Beneficial effects: This application proposes a method, device, and application for constructing a linear time-invariant state-space model of a power system. By constructing a general harmonic decomposition equation, the linear time-varying periodic state equation of the phase sequence separation link in the decoupled dual-synchronous reference coordinate system under the rotating coordinate system is converted into a linear time-invariant state-space model. The model improves the accuracy of power system stability analysis. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating a method for constructing a linear time-invariant state-space model of a power system according to an embodiment of this application. Figure 2 This is a schematic diagram illustrating the working principle of the phase sequence separation stage of the decoupling dual synchronous reference coordinate system in the embodiments of this application. Figure 3 This is a diagram of the test system in an embodiment of this application; Figure 4 This is a d-axis positive sequence voltage diagram extracted by DDSRF-PLL after applying a negative sequence voltage under symmetrical operating conditions in the embodiments of this application; Figure 5 This is a d-axis negative sequence voltage diagram extracted by DDSRF-PLL after applying a negative sequence voltage under symmetrical operating conditions in the embodiments of this application. Figure 6 The figure shows the response curve of the positive-sequence d-axis component of the output voltage of the EMT model when Kp steps in the embodiments of this application. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0022] Example 1 This embodiment provides a method for constructing a linear time-invariant state-space model of a power system. The flowchart of the method is as follows: Figure 1As shown, it includes the following steps: S1: Construct a general equation for harmonic decomposition, which is used to convert the general state-space equation of linear time-varying period into a linear time-invariant state-space equation. It should be noted that the process of constructing the general equation for harmonic decomposition in step S1 is as follows: The general state-space equation for linear time-varying periodicity is denoted as: (1) in, , Given a state vector and an input vector, , The state matrix and the input matrix are used for calculation. and satisfy , (T is the system fundamental frequency period).

[0023] In equation (1), the first p State variables The corresponding state equation is: (2) In the formula, H and Z These represent the total number of state variables and the total number of input variables, respectively. for The p line, number h Column elements, for The p line, number z Column elements. for The Middle h One state variable, for The Middle z One input variable.

[0024] Perform a Fourier series expansion on the state vector, input vector, state matrix, and input matrix, and substitute them into the linear time-varying periodic general state-space equation. Based on the fourth... k Based on the principle that the first harmonic coefficients are equal, the 1st harmonic is obtained. k The state equations corresponding to the subharmonics are as follows: right , , , Expanding the Fourier series, we have: (3) (4) In the formula, N It is the highest harmonic order that is cut off. This is the system's fundamental angular frequency; , They are respectively , The m The complex Fourier coefficients corresponding to the subharmonics; , They are respectively , The n The complex Fourier coefficient matrix corresponding to the second harmonic.

[0025] Substituting equations (3) and (4) into the right side of equation (1), we get: (5) (6) Substituting equation (5) into the left side of equation (3), we get: (7) Substitute equations (5) and (6) into the right side of equation (1). Based on the left and right sides of equation (1), the first... k The first harmonic coefficients are equal, so the second harmonic coefficient can be obtained. k The state equation corresponding to the subharmonic is: (8) Based on the characteristics of the phase sequence separation stage of the decoupling dual synchronous reference coordinate system, the first... k The state equation corresponding to the second harmonic is transformed into the state variable of the third harmonic. k The state equations corresponding to the complex Fourier coefficients are as follows: The phase sequence separation stage of the decoupling dual synchronous reference coordinate system mainly contains DC and second harmonic components in its state variables during operation. The p line, number h Column elements , The p line, number z Column elements It can be expressed as a general formula: (9) (10) In the formula, , , They are respectively The amplitudes of the DC, second harmonic sine, and cosine components, , , They are respectively The amplitudes of the DC, 2nd harmonic sine, and cosine components.

[0026] Substituting equations (9) and (10) into equation (8), we can obtain the first... p State variables The k Second complex Fourier coefficients The corresponding state equation is: (11) In the formula, , Matrix elements , The n The complex Fourier coefficients corresponding to the subharmonics; , Variables , The ( kn The complex Fourier coefficients corresponding to the first harmonic.

[0027] For the state variable k Expanding the state equations corresponding to the second complex Fourier coefficients and setting the truncation order, we obtain the general equations for harmonic decomposition, as detailed below: Expanding equation (11) yields equation (12): (12) In equation (12), k Taking values ​​of -2, 0, and +2 respectively, the corresponding state equations are: (13).

[0028] When the truncation order is 2, the time-invariant equation corresponding to the periodic time-varying equation (2) is the above equation.

[0029] S2: Establish a linear time-varying periodic state equation for the phase sequence separation link of the decoupled dual synchronous reference coordinate system in the rotating coordinate system. The state variables and input variables of the linear time-varying periodic state equation include the electrical quantities of the power system. It should be noted that the working principle diagram of the phase sequence separation stage for decoupling the dual synchronous reference coordinate system is as follows: Figure 2 As shown, the specific content is as follows: Voltage or current in a three-phase stationary coordinate system (hereinafter referred to as electrical quantities) abc Electrical quantities transformed into two-phase stationary coordinates by Clarke transformation . The output signal is processed by Park transform, which involves forward and reverse rotation of the fundamental frequency. , .in, Include abc DC component corresponding to the middle positive sequence component and abc The second harmonic component corresponding to the negative sequence component; Include abc DC component corresponding to the middle negative sequence component and abc The second harmonic component corresponding to the middle positive sequence component. The second harmonic component in the middle can be derived from... Multiply by the second harmonic forward Park transform matrix. The second harmonic component in the middle can be derived from... Multiply by the frequency-inverted Park transform matrix. Therefore, from The result after subtracting the second harmonic component ,from The result after subtracting the second harmonic component It contains only a DC component. , Output after low-pass filter , Thus completed abc Middle order components Negative order components Extraction. In the image, and These are the Clarke transform and Park transform matrices, respectively, as shown in Equation (14). The LPF (Low Pass Filter) is a low-pass filter, and its transfer function is shown in Equation (15).

[0030] When the input signal is the three-phase voltage at point PCC, the extracted It can be used as the input of a phase-locked loop (PLL), and the output of the PLL... Provides a reference angle for the Park transform. and For the proportional and integral coefficients of the phase-locked loop PI controller, The rated angular frequency of the power grid. This refers to the grid angular frequency detected by the phase-locked loop.

[0031] , (14) (15) In the formula, The phase of the phase-locked loop output. This is the cutoff angular frequency of the filter. It is an identity matrix.

[0032] It should be noted that the linear time-varying periodic state equation of the phase sequence separation element in the decoupling dual-synchronization reference coordinate system in the rotating coordinate system is: (16) In the formula, For state vectors, The input vector. , These represent the amplitudes of the positive and negative sequence components of the input voltage. , The initial phase, and . This represents the small-signal disturbance of the input voltage in the abc coordinate system. Extracted for the phase sequence separation step d , q shaft voltage , Small signal perturbation components; Small-signal disturbance components of the state variable are introduced into the integral stage of the phase-locked loop PI controller. This refers to the small-signal disturbance component of the phase-locked loop output phase.

[0033] , , , steady-state value , , , satisfy: (17) In subsequent derivation, use directly , To represent the state and input variables, the small perturbation symbol "Δ" is no longer written.

[0034] S3: Set the harmonic order for the state variables and input variables in the state equation, and use the constructed general equation to perform harmonic decomposition on the state equation to obtain a linear time-invariant state-space model.

[0035] It should be noted that the specific content of step S3 is as follows: Considering a cutoff of 2, the corresponding LTI model can be obtained by applying the obtained general equation to each line of equation (16) for harmonic decomposition.

[0036] Taking the first row of equation (16) as an example, we give... The derivation process of the LTI state equation.

[0037] A The element in the first row and first column of (t) ,correspond , , .Will p =1, q Substituting 1 into equation (15), we get right The contribution of the LTI state equation is: (18) A The element in the first row and second column of (t) Corresponding coefficient , , .Will p =1, q Substituting 2 into equation (13), we get right The contribution of the LTI state equation is: (19) A The element in the 1st row and 3rd column of (t) Corresponding coefficient , , .Will p =1, q Substituting 3 into equation (13), we get right The contribution of the LTI state equation is: (20) A The element in the 1st row and 4th column of (t) Corresponding coefficient , , .Will p =1, q Substituting 4 into equation (13), we get right The contribution of the LTI state equation is: (twenty one) A The element in the 1st row and 5th column of (t) Corresponding coefficient , , .Will p =1, q Substituting 5 into equation (13), we get right The contribution of the LTI state equation is: (twenty two) A The element in row 1, column 6 of (t) Corresponding coefficient , , .Will p =1, q Substituting 6 into equation (15), we get right The contribution of the LTI state equation is: (twenty three) Synthetic equations (18)~(23), state matrix The first row of elements is the state variable. The contribution of the LTI state equation is: (twenty four) Following the derivation process of equation (24), the input matrix can be obtained. The first row of elements is the state variable. The contribution of the LTI state equation is: (25) Combining equations (24) and (25), we obtain The LTI state equation is: (26) Following the derivation process of equation (26), we can obtain the LTI model corresponding to equation (16), namely equation (27). Wherein, the state vector is... The input vector is The state matrix is The input matrix is .

[0039] (27) in and The elements are as follows:

[0040] For each row of elements, we have: (1)

[0041] (2)

[0042]

[0043] ⑶.

[0044] ⑷.

[0045] ⑸.

[0046]

[0047] ⑹.

[0048] ⑺.

[0049] ⑻.

[0050]

[0051] ⑼.

[0052] ⑽.

[0053] ⑾.

[0054]

[0055] 12.

[0056] 13.

[0057] 14.

[0058]

[0059] 12.

[0060] 13.

[0061] 14.

[0062]

[0063] 18.

[0064]

[0065] For each row of elements, we have: (1)

[0066] (2)

[0067] ⑶.

[0068] ⑷.

[0069] ⑸.

[0070] ⑹.

[0071] ⑺.

[0072] ⑻.

[0073] ⑼.

[0074] ⑽.

[0075] ⑾.

[0076] ⑿.

[0077] ⒀.

[0078] ⒁.

[0079] ⒂.

[0080] 13.

[0081] 14.

[0082] 18.

[0083] Example 2 This embodiment designs a test system to verify the LTI model constructed in this application, the details of which are as follows: 1. Overview of the testing system To verify the LTI model constructed in this invention, this invention employs... Figure 3 The system shown was tested. In the figure, an ideal three-phase voltage source with adjustable positive and negative sequence components is grounded through a resistor, and a decoupling dual synchronous reference coordinate system phase sequence separation link (DDSRF-PLL) separates the phase sequence of the three-phase voltage output by the power supply.

[0084] Table 1 lists the parameters of the test loop and the DDSRF-PLL. A test loop was constructed based on the MATLAB / Simulink platform. Figure 2 The electromagnetic transient simulation model of the phase sequence separation link of the decoupled dual synchronous reference coordinate system is shown, and the small signal model represented by equation (27) is implemented based on MATLAB. In order to simulate the asymmetrical operation of the AC system, according to the GB / T15543-2008 standard, the short-term negative sequence voltage imbalance during normal operation of the power grid is set to not exceed 4%, and the negative sequence voltage amplitude of the AC system is taken as 27.6V.

[0085] Table 1. Main circuit and control system parameters of the phase-locked loop positive and negative sequence separation algorithm for decoupling dual synchronous reference coordinate systems.

[0086] To verify the accuracy and effectiveness of this invention, the following two tests were conducted. Test 1: A negative-sequence voltage disturbance was introduced, and the consistency of the time-domain response of the electromagnetic transient model (EMT model), the LTP model, the direct simplified LTI model, and the LTI model of this invention was compared. Test 2: By setting a sudden change in control parameters to excite the dominant oscillation mode of the system, the consistency of the oscillation frequency obtained from the time-domain simulation with the eigenvalue analysis results of the LTP model, the direct simplified LTI model, the simplified LTI model, and the LTI model of this invention was compared.

[0087] Test 1: 0.5s ago Figure 3 Only a positive sequence voltage is applied during the process, and a 4% negative sequence voltage is applied at 0.5s. Figure 4 and Figure 5 The electromagnetic transient model (pure solid line), the LTP model (solid line with triangles), the direct simplified LTI model (solid line with circles), and the LTI model of this invention (solid line with crosses) are given. Simulation results comparison. It can be seen that although the direct simplified LTI model can correctly extract the steady-state voltage (…),… However, the simulation results are completely inadequate to characterize the transient response of the system after the disturbance, and the simulated waveforms are severely distorted. In contrast, the LTP model and the LTI model of this invention show good agreement with the simulation results of the EMT model throughout the entire transient process, verifying the effectiveness of the LTI model of this invention.

[0088] Test 2: Setting the proportional coefficient of the phase-locked loop PI controller The electromagnetic transient model simulation results show that the value jumps from 10 to 0.01 at 2.5s. Figure 6 As shown. It can be seen that, Oscillations and divergences occur, indicating system instability. The oscillation period is 26.265ms, corresponding to an oscillation frequency of 38.073Hz.

[0089] Other parameters remain unchanged, when Table 2 shows the dominant characteristic index (eigenvalue) and corresponding oscillation frequency calculated by the LTP model, the direct simplified LTI model, and the LTI model of this invention.

[0090] Table 2 When K p Oscillation modes of each model at 0.01

[0091] As shown in Table 2, the real part of the dominant characteristic index calculated by the LTP model is positive, and the imaginary part gives an oscillation frequency of 11.914 Hz. Considering the inherent problem of the LTP model, the oscillation frequency given by the model may differ from the actual oscillation frequency by an integer multiple of the fundamental frequency (50 Hz), we correct its calculation result to... Hz, thus the oscillation frequency given by the LTP model is consistent with the frequency obtained from the time-domain simulation. It is worth noting that, to date, there is no systematic method to accurately obtain the actual oscillation frequency. This invention obtains it through trial and error by comparing EMT simulation results.

[0092] The dominant eigenvalues ​​obtained by the direct simplified LTI model have negative real parts, indicating that this method determines the system to be stable. This contradicts the EMT simulation results, so the oscillation frequencies predicted by this model are not listed in Table 2.

[0093] For the LTI model of this invention, the dominant eigenvalues ​​can be found in Table 2. The corresponding oscillation frequency is 38.086 Hz, which is consistent with the frequency obtained from the EMT time-domain simulation. It is evident that the LTI model proposed in this invention meets the required analysis accuracy and directly provides the accurate oscillation frequency, avoiding the problem that the frequency represented by the imaginary part of the LTP model differs from the actual oscillation frequency by an integer multiple of the fundamental frequency.

[0094] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for constructing a linear time-invariant state-space model of a power system, characterized in that, Includes the following steps: S1: Construct a general equation for harmonic decomposition, which is used to convert the general state-space equation of linear time-varying period into a linear time-invariant state-space equation. S2: Establish a linear time-varying periodic state equation for the phase sequence separation link of the decoupled dual synchronous reference coordinate system in the rotating coordinate system. The state variables and input variables of the linear time-varying periodic state equation include the electrical quantities of the power system. S3: Set the harmonic order for the state variables and input variables in the linear time-varying periodic state equation, and use the constructed general equation to perform harmonic decomposition to obtain a linear time-invariant state-space model.

2. The method for constructing a linear time-invariant state-space model of a power system according to claim 1, characterized in that, The process of constructing the general equation for harmonic decomposition in step S1 is as follows: The general state-space equation for linear time-varying periodicity is denoted as: in, , Given a state vector and an input vector, , The state matrix and the input matrix are used for calculation. Perform a Fourier series expansion on the state vector, input vector, state matrix, and input matrix, and substitute them into the linear time-varying periodic general state-space equation. Based on the fourth... k Based on the principle that the first harmonic coefficients are equal, the 1st harmonic is obtained. k The state equation corresponding to the subharmonic; Based on the characteristics of the phase sequence separation stage of the decoupling dual synchronous reference coordinate system, the first... k The state equation corresponding to the second harmonic is transformed into the state variable of the third harmonic. k The state equations corresponding to the complex Fourier coefficients; For the state variable k Expanding the state equations corresponding to the complex Fourier coefficients and setting the truncation order yields the general equations for harmonic decomposition.

3. The method for constructing a linear time-invariant state-space model of a power system according to claim 2, characterized in that, The first k The process of constructing the state equation corresponding to the subharmonic is as follows: right , , , Performing a Fourier series expansion, we get: In the formula, N It is the highest harmonic order that is cut off. The fundamental angular frequency; , They are respectively , The m The complex Fourier coefficients corresponding to the subharmonics; , They are respectively , The n The complex Fourier coefficient matrix corresponding to the subharmonics; After unfolding , , , Substituting into the general state-space equation for linear time-varying periods, since the first... k The first harmonic coefficients are equal, thus obtaining the second harmonic coefficient. k The state equation corresponding to the subharmonic is: 。 4. The method for constructing a linear time-invariant state-space model of a power system according to claim 3, characterized in that, The first k The state equation corresponding to the second harmonic is transformed into the state variable of the third harmonic. k The specific content of the state equation corresponding to the complex Fourier coefficients is as follows: Based on the characteristics of the phase sequence separation stage of the decoupled dual synchronous reference coordinate system, which includes DC and second harmonic components in its state variables during operation, the following will be implemented: The p line, number h Column elements , The p line, number z Column elements Represented as a general formula: (4.1) (4.2) In the formula, , , They are respectively The amplitudes of the DC, second harmonic sine, and cosine components, , , They are respectively The amplitudes of the DC, second harmonic sine, and cosine components; Substituting equations (4.1) and (4.2) into the above... k The state equation corresponding to the second harmonic is obtained. p State variables The k Second complex Fourier coefficients The corresponding state equation is: In the formula, , Matrix elements , The n The complex Fourier coefficients corresponding to the subharmonics; , Variables , The kn The complex Fourier coefficients corresponding to the second harmonic.

5. The method for constructing a linear time-invariant state-space model of a power system according to claim 4, characterized in that, The first state variable k Expanding the state equations corresponding to the second complex Fourier coefficients and setting the truncation order, we obtain the following specific content of the general equation for harmonic decomposition: The expanded expression is denoted as: Setting the truncation order to 2, the corresponding state equation, i.e., the general equation for harmonic decomposition, is: 。 6. The method for constructing a linear time-invariant state-space model of a power system according to claim 5, characterized in that, The workflow of the phase sequence separation step of decoupling the dual synchronous reference coordinate system described in step S2 is as follows: The electrical quantities in the three-phase stationary coordinate system are transformed into electrical quantities in the two-phase stationary coordinate system by Clarke transformation, and then output as two signals by fundamental frequency forward rotation Park transformation and fundamental frequency reverse rotation Park transformation, respectively. The two signals are then subjected to second harmonic interference elimination and low-pass filtering to obtain positive sequence components and negative sequence components.

7. The method for constructing a linear time-invariant state-space model of a power system according to claim 6, characterized in that, The linear time-varying periodic state equation described in step S2 is: In the formula, For state vectors, The input vector; , These represent the amplitudes of the positive and negative sequence components of the input voltage. , The initial phase, and ; This represents the small-signal disturbance of the input voltage in a three-phase stationary coordinate system. Extracted for the phase sequence separation step d , q shaft voltage , Small signal perturbation components; Small-signal disturbance components of the state variable are introduced into the integral stage of the phase-locked loop PI controller. This refers to the small-signal disturbance component of the phase-locked loop output phase.

8. The method for constructing a linear time-invariant state-space model of a power system according to claim 7, characterized in that, The specific content of step S3 is as follows: With the cutoff number set to 2, harmonic decomposition is performed on the linear time-varying periodic state equation based on the general harmonic decomposition equation, resulting in a linear time-invariant state-space model: in, The state matrix, The input matrix is ​​denoted as .

9. An electronic device, characterized in that, It includes a memory and a processor; the memory is used to store instructions; the processor is used to operate according to the instructions to perform the method according to any one of claims 1-8.

10. An application of a linear time-invariant state-space model for a power system, characterized in that, The linear time-invariant state-space model is constructed based on the method described in any one of claims 1-8 and is applied to power electronic systems under unbalanced power grid conditions.

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