Grid-connected system model order reduction method based on singular perturbation method and margin reduction

Abstract

The invention discloses a grid-connected system model order reduction method based on a singular perturbation method and a reduction margin, and the method comprises the steps: precisely calculating a state variable time constant through the analysis of a system characteristic value and a participation factor, and classifying variables according to a time scale separation ratio. The method comprises the following steps: approximately decoupling fast and slow subsystems of a system by using an SPM to obtain a preliminary order reduction model; the influence of the reduced-order model on the critical oscillation mode is measured by means of the MRM, key state variables are reserved through iterative optimization, and further dimension reduction of the model is achieved. According to the method, the fast and slow dynamic characteristics of the system state variables can be accurately divided, so that the order reduction model meets the error requirement, the order reduction precision and the simulation efficiency are effectively balanced, and an efficient tool is provided for analysis and control of the power electronic interface grid-connected system.

Description

Technical Field

[0001] This invention belongs to the field of power system technology, and specifically relates to a method for reducing the order of a grid-connected system model based on the singular perturbation method and the reduction margin. Background Technology

[0002] Currently, to reduce the complexity of nonlinear systems, model reduction methods are widely used to obtain lower-order models with similar dynamic characteristics and stability. Some studies have simplified VSPSU models based on doubly-fed induction machines (DFIMs) for controller design and dynamic analysis by ignoring less critical system components. However, these studies still have some limitations. Most focus on the dynamic simulation of the model without considering the impact of model simplification on system stability. In works that include stability analysis, variations in grid strength, turbine speed, and torque conditions are rarely considered. Furthermore, theoretical analysis of the time-scale characteristics of DFIM-based VSPSUs remains insufficient.

[0003] On the other hand, model order reduction methods based on control theory are now widely used in DFIM-based wind turbines, whose structure is similar to that of DFIM-based VSPSUs. However, this method does not consider the impact of model order reduction on the dynamics and stability of the DFIM itself. The Singular Perturbation Method (SPM) has also been applied to achieve DFIM-based wind turbine model order reduction. In the considered DFIM systems, SPM has proven to outperform equilibrium truncation and equilibrium residual methods. However, the impact of interactions under different time scales on the reduced model has not received sufficient attention. The degree of interaction between system state variables may vary with operating conditions. How to reduce the corresponding system model order according to different operating conditions has become a key issue. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for reducing the order of a grid-connected system model based on the singular perturbation method and the reduction margin, which can accurately divide the fast and slow dynamic characteristics of the system state variables, so that the reduced model meets the error requirements and effectively balances the order reduction accuracy and simulation efficiency.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for reducing the order of a grid-connected system model based on singular perturbation and reduced margin, comprising the following steps: Step 1: Calculate the time constant of each state variable based on the characteristic values ​​and participation factors of the VSPSU to measure its dynamic response speed; the VSPSU is a variable speed pumped storage unit. Step 2: Analyze the system's time-scale characteristics by using the time-scale separation ratio analysis, and classify the state variables into fast variables, medium-speed variables, and slow variables according to their response speed; Step 3: Approximately decouple the fast and slow subsystems using SPM and obtain a preliminary reduced-order model; the SPM is the singular perturbation method. Step 4: Compare the modes of the reduced-order model with those of the original system to identify the critical oscillation mode; set the damping ratio deviation and calculate the MRM; if the real part deviation of the critical mode is within the MRM, the reduction is complete; otherwise, reselect the state variables; the MRM is the edge of the model reduction. Step 5: Retain the fast variables that are most correlated with the critical oscillation mode, and group the dq components and control components of the same variable together; Step 6: Combine the retained fast variables with the slow variables into a new slow state variable, and then use SPM to reduce the order again; Step 7: Calculate the eigenvalues ​​of the new reduced-order model and identify the modes corresponding to the critical oscillation mode; determine whether the real part deviation of the critical oscillation mode after model reduction exceeds the MRM. If so, return to step 5; otherwise, the model reduction ends.

[0006] Preferably, the sub-step of step one is as follows: Step 1.1: Constructing the VSPSU Mathematical Model: Establish the VSPSU mathematical model, clarifying the composition of the state vector and algebraic variable vector. The state vector includes stator current, equivalent internal voltage, rotor angular frequency, grid-side converter current, DC voltage of DC-link capacitor, intermediate variables related to various controllers, q-axis stator voltage integral, output PLL phase angle, output of output regulation system controller, guide vane opening, flow rate of water diversion tunnel, flow rate of pressure pipeline, and water level in surge tank. The algebraic variable vector includes d-axis and q-axis stator voltage, and d-axis and q-axis grid-side converter voltage. Step 1.2: Derive the VSPSU small-signal model: Linearize the VSPSU mathematical model at the operation point, ignore second-order and higher terms to obtain a linear model, and then derive the VSPSU small-signal model by eliminating the algebraic variable vector. Step 1.3: Analyze system stability-related parameters: Obtain eigenvalues ​​from the derived small-signal model matrix, and determine system stability based on the real parts of the eigenvalues; Using specific equations, calculate the damping ratio and frequency related to oscillation based on the eigenvalues, which involves the system attenuation rate and oscillation angular frequency; Step 1.4: Define participation factors: In system stability analysis, participation factors are introduced to identify the relationship between eigenvalues ​​and state variables. The participation factor represents the degree of participation of the state variable in a specific mode, and its definition is related to the left eigenvector, right eigenvector of the corresponding eigenvalue, and the total number of system state variables. Step 1.5: Calculate the time constant index: Due to the fast and slow nature of the system state, the system dynamics exhibit multi-timescale characteristics. In order to classify the fast and slow state variables, the time constant index is calculated by a specific formula to analyze the timescale characteristics of VSPSU. This formula involves the time constant of the corresponding characteristic value, the system decay rate, and the angular frequency.

[0007] Preferably, step 1.1: The mathematical model of VSPSU can be expressed as: (1); in and The state vector and algebraic variable vector are as follows: (2); in , These are the stator currents along the d-axis and q-axis. , The equivalent internal voltages for the d-axis and q-axis are given. The rotor angular frequency, , For the d-axis and q-axis grid-side converter currents, The DC voltage of the DC-connected capacitor. , , , This is an intermediate variable, corresponding to the rotor-side converter controller. This is an intermediate variable, corresponding to an external DC link voltage control loop. , The intermediate variable corresponds to the internal grid-side current control loop. The integral of the stator voltage along the q-axis. To output the PLL phase angle, To regulate the output of the system controller, For guide vane opening, The flow rate of the water diversion tunnel, For the flow rate of the pressure pipeline, The water level in the surge tank. , Let be the stator voltage components along the d-axis and q-axis, respectively. , For the d-axis and q-axis network-side converter voltages, , These are the d-axis and q-axis stator voltages.

[0008] Preferably, step 1.2: at the operation point Linearizing equation (1) and ignoring terms of second order and above, the corresponding linear model can be expressed as follows: (3); By eliminating The small-signal model of VSPSU is derived as follows: (4).

[0009] Preferably, step 1.3: eigenvalues ​​reflect system stability and can be obtained from the matrix. The system is stable if the real parts of all eigenvalues ​​are negative. For each eigenvalue, the damping ratio related to the oscillation can be calculated using equations (5) and (6). and frequency ; (5); (6); in The system attenuation rate, ω is the oscillation angular frequency.

[0010] Preferably, in step 1.4: In system stability analysis, participating factors can help identify the relationship between eigenvalues ​​and state variables; participating factors Represents state variables In mode The level of participation is defined as follows: (7); in and They correspond to The left and right eigenvectors; This represents the total number of system state variables.

[0011] Preferably, step 1.5: System states with different fast and slow properties cause the system dynamics to exhibit multi-timescale characteristics; how to classify fast and slow state variables is a key issue; therefore, the time constant index is calculated using the following formula to analyze the timescale characteristics of VSPSU: (8); in It corresponds to the eigenvalue time constant, The system attenuation rate, ω is the angular frequency.

[0012] Preferably, the time constants of the VSPSU system modes differ significantly; when these modes are arranged in ascending order of time constant, the formula for calculating the ratio of two adjacent constants is: (9); in It is the time constant corresponding to the eigenvalue; Assuming when hour, This can be viewed as the time-scale separation ratio (i.e., the indicator of time-scale division); in the VSPSU grid-connected system model, there are only three. Since the above requirements are met, the system state variables can be classified according to three time scales; further classified according to time scale, the state variables are divided into fast variables, medium-speed variables and slow variables, thus the system is studied as a singular perturbation system.

[0013] Preferably, the specific steps of the SPM order reduction method are as follows: Step 3.1: Medium-speed state variables are slower than fast variables, but faster than slow variables; when analyzing the dynamics of slow variables, medium-speed state variables are classified into the fast subsystem; when analyzing the dynamics of medium-speed and fast variables, medium-speed state variables are classified into the slow subsystem; therefore, the VSPSU grid-connected system... m + n State variables can be divided into m Slow variables and n Fast variables; then the system model is reformulated in a singular perturbation form, as follows: (10); in and These are the slow and fast state variable vectors, respectively; the function and It consists of the system's continuous differential equations; This represents a positive singular perturbation matrix with small elements; Step 3.2: When assuming fast state variables The dynamic process can quickly reach a quasi-steady state, while the slow state vector Before the dynamic process occurs, it can be If we set it to 0, then the model in the second equation can be simplified into an algebraic equation. fast state variables The quasi-steady-state solution can be obtained from the following equation: (11); Substituting into the simplified algebraic equation, we get the original... The order system model can be simplified to The order model is as follows: (12); The MRM determination process involved in the steps includes the following steps: The Model Reduction Margin (MRM) index is used to measure the influence of state variables on critical oscillation modes in a reduced-order model; the damping ratio reflects the decay characteristics of the oscillation mode; when the allowable damping ratio deviation is ±Δζ, the absolute value of the maximum real part change of the critical oscillation mode is defined as the MRM; the following is the calculation method for MRM: (13); in For damping ratio deviation, ω is the oscillation angular frequency.

[0014] A grid-connected system model order reduction system based on singular perturbation method and reduced margin is provided, which adopts the aforementioned grid-connected system model order reduction method based on singular perturbation method and reduced margin.

[0015] The present invention can achieve the following beneficial effects: 1. Through joint analysis of eigenvalues, participation factors, and time constant indices, a time-scale classification method for state variables of VSPSU grid-connected systems was established, transforming the dynamic characteristics of the system into quantifiable indicators and providing a theoretical basis for model order reduction.

[0016] 2. By combining the Singular Perturbation Method (SPM) with the Model Reduction Margin (MRM) index, the stability error boundary of the reduced model is quantified by the damping ratio deviation, which solves the problem that the traditional SPM method does not consider the impact of changes in operating conditions on the reduction accuracy.

[0017] 3. By participating in factor screening and identifying fast variables strongly correlated with critical oscillation modes, and by forcibly classifying dq components and control components, the loss of key dynamic characteristics is avoided. Attached Figure Description

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a block diagram of the VSPSU integrated nonlinear model of the present invention; Figure 3 The μ value of the VSPSU grid-connected system of this invention; Figure 4 The figures show the stator voltage simulation results for different models of this invention. Figure 5 This is a bar chart showing the simulation time for different models of this invention. Detailed Implementation

[0019] Preferred solutions include Figures 1 to 5 As shown, a method for reducing the order of a grid-connected system model based on singular perturbation and reduced margin is described, with the following steps: Step 1: Calculate the time constant of the corresponding state variable based on the characteristic values ​​and participating factors under the given working conditions.

[0020] More specifically, step one includes the following steps: Step 1.1: The mathematical model of VSPSU can be expressed as: (1); in x and z The state vector and algebraic variable vector are as follows: (2); in , These are the stator currents along the d-axis and q-axis. , The equivalent internal voltages for the d-axis and q-axis are given. The rotor angular frequency, , For the d-axis and q-axis grid-side converter currents, The DC voltage of the DC-connected capacitor. , , , This is an intermediate variable, corresponding to the rotor-side converter controller. This is an intermediate variable, corresponding to an external DC link voltage control loop. , The intermediate variable corresponds to the internal grid-side current control loop. The integral of the stator voltage along the q-axis. To output the PLL phase angle, To regulate the output of the system controller, For guide vane opening, The flow rate of the water diversion tunnel, For the flow rate of the pressure pipeline, The water level in the surge tank. , Let be the stator voltage components along the d-axis and q-axis, respectively. , For the d-axis and q-axis network-side converter voltages, , These are the d-axis and q-axis stator voltages.

[0021] Step 1.2: At the operation point Linearizing equation (1) and ignoring terms of second order and above, the corresponding linear model can be expressed as follows: (3); By eliminating The small-signal model of VSPSU is derived as follows: (4): Step 1.3: Eigenvalues ​​reflect system stability and can be obtained from the matrix. The system is stable if the real parts of all eigenvalues ​​are negative. For the eigenvalues, the damping ratio and frequency associated with the oscillation can be calculated using equations (5) and (6), respectively.

[0022] (5); (6); in For system attenuation rate, ω is the angular frequency.

[0023] Step 1.4: In system stability analysis, participation factors can help identify the relationship between eigenvalues ​​and state variables. Participation Factors Represents state variables In mode The level of participation is defined as follows: (7); in and They correspond to The left and right eigenvectors. This represents the total number of system state variables.

[0024] Step 1.5: System states with different fast and slow properties cause the system dynamics to exhibit multi-timescale characteristics. How to classify fast and slow state variables is a key issue. Therefore, the time constant index is calculated using the following formula to analyze the timescale characteristics of VSPSU: (8); in It corresponds to the eigenvalue time constant, For system attenuation rate, ω is the angular frequency.

[0025] Step 2: Analyze the time-scale characteristics of the system based on the separation ratio of the time scale, and classify the state variables according to their relative speed.

[0026] The time constants of the VSPSU system modes differ significantly. When these modes are arranged in ascending order of time constant, the formula for calculating the ratio of two adjacent constants is: (9); in It corresponds to the eigenvalue The time constant.

[0027] Assuming when hour, This can be considered as the time-scale separation ratio (i.e., the indicator of time-scale division). In the VSPSU grid-connected system model, there are only three... Meeting the above requirements, the system state variables can be classified according to three time scales. Further classification by time scale divides the state variables into fast variables, medium-speed variables, and slow variables, thus allowing the system to be studied as a singularly perturbated system.

[0028] Step 3: Apply SPM to approximate decoupling of the fast and slow subsystems, and obtain a preliminary reduced-order model. The specific steps of the SPM reduction method used in Steps 3 and 6 are as follows: Step 3.1: Medium-speed state variables are slower than fast variables, but faster than slow variables. When analyzing the dynamics of slow variables, medium-speed state variables are classified as part of the fast subsystem. When analyzing the dynamics of both medium-speed and fast variables, medium-speed state variables are classified as part of the slow subsystem. Therefore, the VSPSU grid-connected system... m + n State variables can be divided into m Slow variables and n Fast variables. The system model is then reformulated in a singular perturbation form, as follows: (10); in and These are the slow and fast state variable vectors, respectively. (Function) and It consists of the system's continuous differential equations. This represents a positive singular perturbation matrix with small elements.

[0029] Step 3.2: When assuming fast state variables The dynamic process can quickly reach a quasi-steady state, while the slow state vector Before the dynamic process occurs, it can be If we set it to 0, then the model described in the second equation can be simplified to an algebraic equation.

[0030] fast state variables The quasi-steady-state solution can be obtained from the following equation: (11): Substituting into the simplified algebraic equation, we get the original... The order system model can be simplified to The order model is as follows: (12); The state variables of the reduced-order models obtained under different conditions using SPM and the reduction strategy proposed in this invention are shown below: Table 1. Reduced-order models obtained by SPM under different SCR conditions.

[0031] Table 2. Reduced-order models obtained by SPM at different turbine speeds and torques.

[0032] Table 3. Order reduction models obtained using the proposed order reduction strategy under different SCR conditions.

[0033] Step 4: After calculating the modes of the reduced-order model and comparing them with the modes of the original system, the critical oscillation mode can be identified. Then, the damping ratio deviation is set, and the MRM of the system is calculated using the formula. If the real part deviation of the critical oscillation mode after model reduction is within the MRM, the model reduction is complete. Otherwise, the state variables need to be reselected for model reduction.

[0034] The MRM determination process involved in the steps includes the following steps: The Model Reduction Margin (MRM) metric is used to measure the impact of state variables on critical oscillatory modes in a reduced-order model. The damping ratio reflects the decay characteristics of the oscillation mode. The absolute value of the maximum real part change of the critical oscillation mode is defined as MRM when the allowable damping ratio deviation is ±Δζ. The calculation method for MRM is as follows: (13); in For damping ratio deviation, ω is the oscillation angular frequency.

[0035] Step 5: Retain the fast variables that represent the largest participants associated with the critical oscillation mode. It is important to note that the dq and control components of the same variable should be grouped together. Otherwise, they may degrade the system's dynamic characteristics.

[0036] Step six combines the variables retained in step five with the slow variables from step two to form a new set of slow state variables. SPM is then applied to achieve model dimensionality reduction.

[0037] Step 7: Calculate the eigenvalues ​​of the new reduced-order model and identify the modes corresponding to the critical oscillation mode. Determine whether the real part deviation of the critical oscillation mode after model reduction exceeds the MRM. If so, return to Step 5; otherwise, the model reduction ends.

[0038] Appendix Figure 4The stator voltage simulation results are shown, with appendix. Figure 5 The simulation times for different models are shown, with the reduced-order model taking significantly less time than the original model.

[0039] As can be seen from the above technical solution, by using the present invention to reduce the order of the model of the power electronic interface grid-connected system, it is not only possible to accurately divide the fast and slow dynamic characteristics of each state variable of the system, but also to enable the reduced order model of the power electronic interface grid-connected system to meet the error requirements, and finally achieve a balance between the order reduction accuracy and simulation efficiency.

[0040] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for reducing the order of a grid-connected system model based on singular perturbation and reduced margin, characterized in that... Includes the following steps: Step 1: Calculate the time constant of each state variable based on the characteristic values ​​and participation factors of the VSPSU to measure its dynamic response speed; the VSPSU is a variable speed pumped storage unit. Step 2: Analyze the system's time-scale characteristics by using the time-scale separation ratio analysis, and classify the state variables into fast variables, medium-speed variables, and slow variables according to their response speed; Step 3: Approximately decouple the fast and slow subsystems using SPM and obtain a preliminary reduced-order model; the SPM is the singular perturbation method. Step 4: Compare the modes of the reduced-order model with those of the original system to identify the critical oscillation mode; set the damping ratio deviation and calculate the MRM; if the real part deviation of the critical mode is within the MRM, the reduction is complete; otherwise, reselect the state variables; the MRM is the edge of the model reduction. Step 5: Retain the fast variables that are most correlated with the critical oscillation mode, and group the dq components and control components of the same variable together; Step 6: Combine the retained fast variables with the slow variables into a new slow state variable, and then use SPM to reduce the order again; Step 7: Calculate the eigenvalues ​​of the new reduced-order model and identify the modes corresponding to the critical oscillation mode; determine whether the real part deviation of the critical oscillation mode after model reduction exceeds the MRM. If so, return to step 5; otherwise, the model reduction ends.

2. The method for reducing the order of a grid-connected system model based on singular perturbation and reduced margin as described in claim 1, characterized in that: The sub-steps of step one are: Step 1.1: Constructing the VSPSU Mathematical Model: Establish the VSPSU mathematical model, clarifying the composition of the state vector and algebraic variable vector. The state vector includes stator current, equivalent internal voltage, rotor angular frequency, grid-side converter current, DC voltage of DC-link capacitor, intermediate variables related to various controllers, q-axis stator voltage integral, output PLL phase angle, output of output regulation system controller, guide vane opening, flow rate of water diversion tunnel, flow rate of pressure pipeline, and water level in surge tank. The algebraic variable vector includes d-axis and q-axis stator voltage, and d-axis and q-axis grid-side converter voltage. Step 1.2: Derive the VSPSU small-signal model: Linearize the VSPSU mathematical model at the operation point, ignore second-order and higher terms to obtain a linear model, and then derive the VSPSU small-signal model by eliminating the algebraic variable vector. Step 1.3: Analyze system stability-related parameters: Obtain eigenvalues ​​from the derived small-signal model matrix, and determine system stability based on the real parts of the eigenvalues; Using specific equations, calculate the damping ratio and frequency related to oscillation based on the eigenvalues, which involves the system attenuation rate and oscillation angular frequency; Step 1.4: Define participation factors: In system stability analysis, participation factors are introduced to identify the relationship between eigenvalues ​​and state variables. The participation factor represents the degree of participation of the state variable in a specific mode, and its definition is related to the left eigenvector, right eigenvector of the corresponding eigenvalue, and the total number of system state variables. Step 1.5: Calculate the time constant index: Due to the fast and slow nature of the system state, the system dynamics exhibit multi-timescale characteristics. In order to classify the fast and slow state variables, the time constant index is calculated by a specific formula to analyze the timescale characteristics of VSPSU. This formula involves the time constant of the corresponding characteristic value, the system decay rate, and the angular frequency.

3. The method for reducing the order of a grid-connected system model based on the singular perturbation method and reduced margin as described in claim 2, characterized in that: Step 1.1: The mathematical model of VSPSU can be expressed as: （1）； in and The state vector and algebraic variable vector are as follows: （2）； in , These are the stator currents along the d-axis and q-axis, respectively. , These are the equivalent internal voltages along the d-axis and q-axis, respectively. The rotor angular frequency, , These represent the grid-side converter currents on the d-axis and q-axis, respectively. These are the DC voltages of the DC-linked capacitors, respectively. , , , This is an intermediate variable, corresponding to the rotor-side converter controller. This is an intermediate variable, corresponding to an external DC link voltage control loop. , The intermediate variable corresponds to the internal grid-side current control loop. The integral of the stator voltage along the q-axis. To output the PLL phase angle, To regulate the output of the system controller, For guide vane opening, The flow rate of the water diversion tunnel, For the flow rate of the pressure pipeline, The water level in the surge tank. , These are the stator voltage components along the d-axis and q-axis, respectively. , These are the d-axis and q-axis grid-side converter voltages, respectively. , These are the stator voltages along the d-axis and q-axis, respectively.

4. The method for reducing the order of a grid-connected system model based on singular perturbation and reduced margin as described in claim 3, characterized in that: Step 1.2: At the operation point Linearizing equation (1) and ignoring terms of second order and above, the corresponding linear model can be expressed as follows: （3）； By eliminating The small-signal model of VSPSU is derived as follows: （4）。 5. The method for reducing the order of a grid-connected system model based on singular perturbation and reduced margin as described in claim 4, characterized in that: In step 1.3, eigenvalues ​​reflect system stability and can be obtained from the matrix. The system is stable if the real parts of all eigenvalues ​​are negative. For each eigenvalue, the damping ratio related to the oscillation can be calculated using equations (5) and (6). and frequency ; （5）； （6）； in For system attenuation rate, ω is the oscillation angular frequency.

6. The method for reducing the order of a grid-connected system model based on singular perturbation and reduced margin as described in claim 5, characterized in that: Step 1.4: In system stability analysis, participating factors can help identify the relationship between eigenvalues ​​and state variables; participating factors Represents state variables In mode The level of participation is defined as follows: （7）； in and They correspond to The left and right eigenvectors; This represents the total number of system state variables.

7. The method for reducing the order of a grid-connected system model based on singular perturbation and reduced margin as described in claim 6, characterized in that: Step 1.5: System states with different fast and slow properties cause the system dynamics to exhibit multi-timescale characteristics; A key issue is how to classify fast and slow state variables; therefore, the time constant index is calculated using the following formula to analyze the time-scale characteristics of VSPSU: （8）； in It corresponds to the eigenvalue time constant, For system attenuation rate, ω is the angular frequency.

8. The method for reducing the order of a grid-connected system model based on singular perturbation and reduced margin as described in claim 1, characterized in that: The time constants of the VSPSU system modes differ significantly; when these modes are arranged in ascending order of time constant, the formula for calculating the ratio of two adjacent constants is: （9）； in It corresponds to the eigenvalue The time constant; Assuming when hour, This can be considered as the time-scale separation ratio; in the VSPSU grid-connected system model, there are only three. To meet the above requirements, the system state variables are classified according to three time scales; further classified by time scale, the state variables are divided into fast variables, medium-speed variables, and slow variables.

9. The method for reducing the order of a grid-connected system model based on singular perturbation and reduced margin as described in claim 1, characterized in that: The specific steps of the SPM order reduction method used are as follows: Step 3.1: Medium-speed state variables are slower than fast variables, but faster than slow variables; when analyzing the dynamics of slow variables, medium-speed state variables are classified into the fast subsystem; when analyzing the dynamics of medium-speed and fast variables, medium-speed state variables are classified into the slow subsystem; therefore, the VSPSU grid-connected system... m + n State variables can be divided into m Slow variables and n Fast variables; then the system model is reformulated in a singular perturbation form, as follows: （10）； in and These are the slow and fast state variable vectors, respectively; the function and It consists of the system's continuous differential equations; This represents a positive singular perturbation matrix with small elements; Step 3.2: When assuming fast state variables The dynamic process can quickly reach a quasi-steady state, while the slow state vector Before the dynamic process occurs, it can be If we set it to 0, then the model in the second equation can be simplified into an algebraic equation. fast state variables The quasi-steady-state solution can be obtained from the following equation: （11）； Substituting into the simplified algebraic equation, we get the original... The order system model can be simplified to The order model is as follows: （12）； The MRM determination process involved in the steps includes the following steps: The model reduction margin index is used to measure the influence of state variables on the critical oscillation mode in the reduced-order model; the damping ratio reflects the decay characteristics of the oscillation mode; when the allowable damping ratio deviation is ±Δζ, the absolute value of the maximum real part change of the critical oscillation mode is defined as MRM; the following is the calculation method of MRM: （13）； in For damping ratio deviation, ω is the oscillation angular frequency.

10. A grid-connected system model order reduction system based on singular perturbation method and reduced margin, characterized in that: The method for reducing the order of a grid-connected system model based on the singular perturbation method and the reduction margin, as described in any one of claims 1-9, is adopted.

Images