System and method for grid-forming converter stability analysis based on embedded operating point modeling

Abstract

The application discloses a grid-connected converter stability analysis system and method based on embedded working point modeling, and the system comprises a GFM-GCC linearization model, a converter impedance model and a stability analysis module; the method comprises the following steps: taking grid-connected small disturbance current in an actual coordinate system as input, and corresponding outputting PCC point small disturbance voltage in the actual coordinate system after disturbance; ignoring power reference value disturbance, obtaining GFM converter port impedance according to and ; and analyzing the stability of the grid-connected converter GFM-GCC control.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and more specifically to a system and method for stability analysis of grid-connected converters based on embedded operating point modeling. Background Technology

[0002] With the large-scale integration of fluctuating power sources such as wind and solar power, and the increasingly complex dynamic characteristics of loads, wide fluctuations in grid strength have become a normal operating characteristic of modern power systems. The small-signal stability of grid-connected converters (GCCs) is highly correlated with grid strength. Therefore, the robustness and adaptability of GCCs to grid strength variations are key factors affecting the safe operation of power systems.

[0003] Grid-following (GFM) control and grid-forming (GFM) control are two typical control modes of GCC. In the field of stability analysis of grid-forming converter systems, most studies are still limited to a static evaluation framework at a single operating point. However, in actual operating conditions, the system operating point often exhibits significant time-varying characteristics, and relying solely on single-point analysis is insufficient to comprehensively characterize the dynamic stability characteristics throughout the entire operating cycle. To quantify the impact of the operating point on stability, existing studies often expand the evaluation scope through discrete multi-point analysis. For example, for illumination-driven power output scenarios, discrete operating points under different illumination intensities are selected to analyze the resulting changes in impedance characteristics, thereby revealing the mechanism by which illumination variables affect system stability.

[0004] Existing stability analysis methods for grid-type converters, such as those based on a single operating point or discrete operating points, employ traditional small-signal linearization. This involves linearizing the nonlinear function at a few specific points. When the operating point shifts, continuing to use this model for analysis will introduce significant errors. In terms of stability characterization, methods based on discrete operating points struggle to provide accurate stability conclusions for operating regions outside the selected operating point. To obtain more accurate stability thresholds, the number of operating points analyzed must be increased, resulting in high computational complexity. Summary of the Invention

[0005] In view of this, the present invention provides a system and method for stability analysis of grid converters based on embedded operating point modeling, which can at least solve the problems in the prior art where the mechanism of the influence of the operating point on the model is not clear and the stability analysis under time-varying conditions is difficult.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The stability analysis system for grid converters based on embedded operating point modeling includes: GFM-GCC linearization model, converter impedance model and stability analysis module;

[0008] The GFM-GCC linearization model is used to determine the grid-connected small disturbance current in the actual coordinate system. As input, the corresponding small perturbation voltage at the PCC point in the actual coordinate system after perturbation is output. ,in, The system closed-loop transfer function is obtained through this process, which includes:

[0009] Based on real-time data obtained through the power synchronization loop and Correspondingly obtain the phase angle difference of the synchronization ring ,pass , and Real-time acquisition Small disturbance current on the converter side in the actual coordinate system These are respectively converted into small disturbance voltages at the PCC point in the control coordinate system. and small disturbance current on the converter side ;in, It is a feedforward transfer function containing PCC point voltage information. It is the feedforward transfer function containing converter current;

[0010] Simultaneously, real-time acquisition and After low-pass filtering, it passes through the reactive power loop to obtain , After adjusting the voltage loop and current loop, a small disturbance voltage reference value for the current loop is obtained. ,according to and the feedforward transfer function containing the output voltage of the bridge arm side The bridge arm outputs a small disturbance voltage in the control coordinate system. Converted to bridge arm output small disturbance voltage in real-time coordinate system Thus regulating ;

[0011] The converter impedance model is used to ignore power reference value disturbances, based on... and Obtain the dq impedance at the port of the GFM converter. ;

[0012] The stability analysis module is used to analyze the stability of a system based on the following parameters: The stability of the GFM-GCC control for the grid converter is analyzed.

[0013] Preferably, the closed-loop transfer function of the system is as follows:

[0014] ;

[0015] ;

[0016] in, Let be the transfer function of the inductor in the LC filter. Let be the transfer function of the LC filter capacitor. It is a second-order identity matrix. This is the matrix corresponding to the grid impedance. Let be the transfer function of the current loop PI regulator. This is the decoupling function in the current loop. Let be the transfer function of the low-pass filter. To calculate the relevant current operating point matrix for grid-connected converter power, To calculate the relevant voltage operating point matrix for grid-connected converter power, This is the transfer function matrix corresponding to the active power loop droop control coefficient. This is the decoupling function in the voltage loop. This is the transfer function of the voltage loop PI regulator. This is the transfer function matrix corresponding to the reactive power loop droop control coefficient. , This is the reactive power-frequency droop control coefficient; To control the disturbance of the active and reactive power reference values ​​in the coordinate system, where and They represent meritorious and ineffective contributions, respectively.

[0017] Preferably, based on the grid-connected small disturbance current in the actual coordinate system As input, the corresponding small perturbation voltage at the PCC point in the actual coordinate system after perturbation is output. The specific content includes:

[0018] ;

[0019] ;

[0020] in, This represents the small disturbance voltage of the power grid in the actual coordinate system. and These represent the equivalent inductance and equivalent resistance of the power grid, respectively. This is the rated angular frequency.

[0021] Preferably, the power synchronization loop is used to obtain real-time data. and Correspondingly obtain the phase angle difference of the synchronization ring The specific content includes:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] in, This is the active power-frequency droop control coefficient; and These represent the steady-state values ​​of the grid-connected current along the d-axis and q-axis, respectively. and These are the steady-state values ​​of the PCC voltage along the d-axis and q-axis, respectively. This represents the cutoff frequency of the low-pass filter.

[0027] Preferred, through , and Real-time acquisition Small disturbance current on the converter side in the actual coordinate system These are respectively converted into small disturbance voltages at the PCC point in the control coordinate system. and small disturbance current on the converter side The specific content includes:

[0028] ;

[0029] ;

[0030] ;

[0031] in, and These represent the steady-state values ​​of the converter-side current along the d-axis and q-axis, respectively. and These are the steady-state values ​​of the PCC voltage along the d-axis and q-axis, respectively.

[0032] Preferably, the data will be acquired in real time. and After low-pass filtering, it passes through the reactive power loop to obtain The specific content includes:

[0033] ;

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] In the formula, This represents the cutoff frequency of the low-pass filter; This is the active power-frequency droop control coefficient; and These represent the steady-state values ​​of the grid-connected current along the d-axis and q-axis, respectively. and These are the steady-state values ​​of the PCC voltage along the d-axis and q-axis, respectively.

[0039] Preferred, The specific contents of the voltage loop include:

[0040] ;

[0041] ;

[0042] ;

[0043] In the formula, It is a PI controller for voltage loop. The rated angular frequency of the power grid. This is the value of the filter capacitor.

[0044] Preferably, the reference value of the small disturbance voltage of the current loop is obtained after adjustment by the current loop. The specific content includes:

[0045] ;

[0046] ;

[0047] ;

[0048] In the formula, It is a PI controller for the current loop. This is the value of the filter inductance.

[0049] Preferred, according to and the feedforward transfer function containing the output voltage of the bridge arm side The bridge arm outputs a small disturbance voltage in the control coordinate system. Converted to bridge arm output small disturbance voltage in real-time coordinate system Thus regulating The specific content includes:

[0050] according to and Will Converted to bridge arm output small disturbance voltage in real-time coordinate system :

[0051] ;

[0052] ;

[0053] in, and These are the steady-state values ​​of the converter bridge arm voltage along the d-axis and q-axis, respectively.

[0054] according to and go through get ,according to and go through get ,in To control the small disturbance current on the converter side in the coordinate system; the specific relationship is as follows:

[0055] ;

[0056] ;

[0057] ;

[0058] In the formula and These are the filter inductor, filter resistor, filter capacitor, and damping resistor of the LC filter. This is the rated angular frequency.

[0059] The stability analysis method for grid-connected converters based on embedded operating point modeling includes the following steps:

[0060] Based on the grid-connected small disturbance current in the actual coordinate system As input, the corresponding small perturbation voltage at the PCC point in the actual coordinate system after perturbation is output. ,in, The system closed-loop transfer function is obtained through this process, which includes:

[0061] Based on real-time data obtained through the power synchronization loop and Correspondingly obtain the phase angle difference of the synchronization ring ,pass , and Real-time acquisition Small disturbance current on the converter side in the actual coordinate system These are respectively converted into small disturbance voltages at the PCC point in the control coordinate system. and small disturbance current on the converter side ;in, It is a feedforward transfer function containing PCC point voltage information. It is the feedforward transfer function containing converter current;

[0062] Simultaneously, real-time acquisition and After low-pass filtering, it passes through the reactive power loop to obtain , After adjusting the voltage loop and current loop, a small disturbance voltage reference value for the current loop is obtained. ,according to and the feedforward transfer function containing the output voltage of the bridge arm side The bridge arm outputs a small disturbance voltage in the control coordinate system. Converted to bridge arm output small disturbance voltage in real-time coordinate system Thus regulating ;

[0063] Ignoring power reference value disturbances, according to and Obtain the dq impedance at the port of the GFM converter. ;

[0064] according to The stability of the GFM-GCC control for the grid converter is analyzed.

[0065] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a system and method for stability analysis of grid converters based on embedded operating point modeling, which has the following beneficial effects:

[0066] This invention is an evolution of traditional stability methods under time-varying conditions. Its core feature is that by explicitly embedding the steady-state operating point variable into the linearization process, a parameterized model is established that can continuously characterize the dynamic characteristics of the system throughout the entire operating range. Stability analysis based on this model can overcome the limitations of traditional methods under time-varying conditions.

[0067] Specifically, compared to the traditional small-signal linearization used in discrete operating point analysis, this paper employs a piecewise linearization method. This method divides the nonlinear function into several intervals, approximates the nonlinear function within each interval, and then combines the resulting piecewise linearized models to form a piecewise linearized model of the nonlinear function. The advantage of this method is that it can model the nonlinear function across its entire domain, rather than just at specific points, thus avoiding the problem of large errors between the linearized model and the nonlinear function when deviating from specific points. The model established in this paper embeds the operating point variable, resulting in a piecewise linearized model when the operating point changes continuously. This process can be seen as the limiting form of the piecewise linearization method, i.e., linearizing the system at infinite operating points. The introduction of the limiting concept allows the obtained linearized model to infinitely approximate the nonlinear system, thus enabling direct analysis of the dynamic characteristics of GCC operation under time-varying conditions, and broadening its applicability.

[0068] Furthermore, based on the linearized model, the influence path of the operating point on the converter can be intuitively seen, such as the transfer function. , and Derived from the abc-dq transform, , , , This stems from power calculations. Changes in operating points such as voltage and current affect coordinate transformations and power calculations, thus impacting system stability. Attached Figure Description

[0069] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, 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.

[0070] Figure 1 This is a typical control structure for GFM control of GCC;

[0071] Figure 2 A detailed structural diagram of the GFM-GCC linearized model in the stability analysis system for grid converters based on embedded operating point modeling provided by this invention;

[0072] Figure 3 The figure shown is an experimental result diagram disclosed in the embodiment of the present invention, wherein... Figure 3 (a) and Figure 3 (b) shows the theoretical model of dq impedance and the port impedance sweep frequency measurement results of the GFM converter at the rated operating point. Detailed Implementation

[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0074] This invention provides a stability analysis system for grid converters based on embedded operating point modeling, including: a GFM-GCC linearization model, a converter impedance model, and a stability analysis module;

[0075] The GFM-GCC linearization model is used to determine the grid-connected small disturbance current in the actual coordinate system. As input, the corresponding small perturbation voltage at the PCC point in the actual coordinate system after perturbation is output. ,in, The system closed-loop transfer function is obtained through this process, which includes:

[0076] Based on real-time data obtained through the power synchronization loop and Correspondingly obtain the phase angle difference of the synchronization ring ,pass , and Real-time acquisition Small disturbance current on the converter side in the actual coordinate system These are respectively converted into small disturbance voltages at the PCC point in the control coordinate system. and small disturbance current on the converter side ;in, It is a feedforward transfer function containing PCC point voltage information. It is the feedforward transfer function containing converter current;

[0077] Simultaneously, real-time acquisition and After low-pass filtering, it passes through the reactive power loop to obtain , After adjusting the voltage loop and current loop, a small disturbance voltage reference value for the current loop is obtained. ,according to and the feedforward transfer function containing the output voltage of the bridge arm side The bridge arm outputs a small disturbance voltage in the control coordinate system. Converted to bridge arm output small disturbance voltage in real-time coordinate system Thus regulating ;

[0078] The converter impedance model is used to ignore power reference value disturbances, based on... and Obtain the dq impedance at the port of the GFM converter. ;

[0079] The stability analysis module is used to analyze the stability of a system based on the following parameters: The stability of the GFM-GCC control for the grid converter is analyzed.

[0080] To further implement the above technical solution, the system closed-loop transfer function is as follows:

[0081] ;

[0082] ;

[0083] in, Let be the transfer function of the inductor in the LC filter. Let be the transfer function of the LC filter capacitor. It is a second-order identity matrix. This is the matrix corresponding to the grid impedance. Let be the transfer function of the current loop PI regulator. This is the decoupling function in the current loop. Let be the transfer function of the low-pass filter. To calculate the relevant current operating point matrix for grid-connected converter power, To calculate the relevant voltage operating point matrix for grid-connected converter power, This is the transfer function matrix corresponding to the active power loop droop control coefficient. This is the decoupling function in the voltage loop. This is the transfer function of the voltage loop PI regulator. This is the transfer function matrix corresponding to the reactive power loop droop control coefficient. To control the disturbance of the active and reactive power reference values ​​in the coordinate system, where and They represent meritorious and ineffective contributions, respectively.

[0084] The following section will explain the GFM-GCC linearization model in detail:

[0085] In this embodiment, physical quantities with subscript 0 represent their steady-state values, and physical quantities with Δ represent small perturbations of that physical quantity.

[0086] 1) Linearization of power synchronization loop and coordinate transformation:

[0087] ;

[0088] in:

[0089] ;

[0090] ;

[0091] GFM control , and Linearized expression for coordinate transformation:

[0092] ;

[0093] in:

[0094] ;

[0095] ;

[0096] ;

[0097] 2) Small-signal model of reactive power loop controller:

[0098] ;

[0099] in:

[0100] ;

[0101] ;

[0102] ;

[0103] 3) Small-signal model of the GFM voltage loop:

[0104] ;

[0105] Among them, H PI-DU H decpl-U The transfer function matrices for the voltage loop PI regulator and the decoupling stage are shown below:

[0106] ;

[0107] ;

[0108] 4) Small-signal model of the GFM current loop:

[0109] ;

[0110] Among them, H PI-DI H decpl-I The transfer function matrices for the current loop PI regulator and the decoupling stage are shown below:

[0111] ;

[0112] ;

[0113] 5) Filtering circuit and main circuit:

[0114] ;

[0115] in:

[0116] ;

[0117] ;

[0118] ;

[0119] By combining the above steps and neglecting small grid disturbance voltages, the closed-loop transfer function of the GFM converter system, from the power reference disturbance to the output small disturbance current, can be derived under disturbance conditions. Based on the closed-loop transfer function model, the system's zero-pole distribution can be characterized, thereby revealing the mechanism by which changes in operating conditions affect system stability. Furthermore, the zeros and poles of the closed-loop transfer function can also be used to identify the system's oscillation frequency.

[0120] Figure 3 (a) and Figure 3 (b) Presents the theoretical model of the dq impedance of the GFM converter at its rated operating point and the results of port impedance sweep frequency measurement. Figure 3 As can be seen, the frequency sweep measurement results are in complete agreement with the established model, verifying the accuracy of the above small-signal model. Furthermore, the output impedance amplitude of the GFM-GCC is relatively small, approaching 0dB after 5Hz, exhibiting significant voltage source characteristics. When connected to a high-voltage power grid, the connection impedance between the converter and the power grid is too small, posing a risk of instability due to "two voltage sources directly connected in parallel".

[0121] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A stability analysis system for grid-connected converters based on embedded operating point modeling, characterized in that, include: GFM-GCC linearization model, converter impedance model, and stability analysis module; The GFM-GCC linearization model is used to determine the grid-connected small disturbance current in the actual coordinate system. As input, the corresponding small perturbation voltage at the PCC point in the actual coordinate system after perturbation is output. ,in, The system closed-loop transfer function is obtained through this process, which includes: Based on real-time data obtained through the power synchronization loop and Correspondingly obtain the phase angle difference of the synchronization ring ,pass , and Real-time acquisition Small disturbance current on the converter side in the actual coordinate system Each of these is converted into a small disturbance voltage at the PCC point in the control coordinate system. and small disturbance current on the converter side ;in, It is a feedforward transfer function containing PCC point voltage information. It is the feedforward transfer function containing converter current; Simultaneously, real-time acquisition and After low-pass filtering, it passes through the reactive power loop to obtain , After adjusting the voltage loop and current loop, a small disturbance voltage reference value for the current loop is obtained. ,according to and the feedforward transfer function containing the output voltage of the bridge arm side The bridge arm outputs a small disturbance voltage in the control coordinate system. Converted to bridge arm output small disturbance voltage in real-time coordinate system Thus regulating ; The system closed-loop transfer function is as follows: ； ； in, Let be the transfer function of the inductor in the LC filter. Let be the transfer function of the LC filter capacitor. It is a second-order identity matrix. This is the matrix corresponding to the grid impedance. Let be the transfer function of the current loop PI regulator. This is the decoupling function in the current loop. Let be the transfer function of the low-pass filter. To calculate the relevant current operating point matrix for grid-connected converter power, To calculate the relevant voltage operating point matrix for grid-connected converter power, This is the transfer function matrix corresponding to the active power loop droop control coefficient. This is the decoupling function in the voltage loop. This is the transfer function of the voltage loop PI regulator. This is the transfer function matrix corresponding to the reactive power loop droop control coefficient. To control the disturbance of the active and reactive power reference values ​​in the coordinate system, where and They represent merit and no merit, respectively; The converter impedance model is used to ignore power reference value disturbances, based on... and Obtain the GFM converter port impedance ; The stability analysis module is used to analyze the stability of a system based on the following parameters: The stability of the GFM-GCC control for the grid converter is analyzed.

2. The stability analysis system for grid converters based on embedded operating point modeling according to claim 1, characterized in that, Based on the grid-connected small disturbance current in the actual coordinate system As input, the corresponding small perturbation voltage at the PCC point in the actual coordinate system after perturbation is output. The specific content includes: ； ； in, This represents the small disturbance voltage of the power grid in the actual coordinate system. and These represent the equivalent inductance and equivalent resistance of the power grid, respectively. This is the rated angular frequency.

3. The stability analysis system for grid converters based on embedded operating point modeling according to claim 1, characterized in that, Based on real-time data obtained through the power synchronization loop and Correspondingly obtain the phase angle difference of the synchronization ring The specific content includes: ； ； ； ； ； in, This is the active power-frequency droop control coefficient; and These represent the steady-state values ​​of the grid-connected current along the d-axis and q-axis, respectively. and These are the steady-state values ​​of the PCC voltage along the d-axis and q-axis, respectively. This represents the cutoff frequency of the low-pass filter.

4. The stability analysis system for grid converters based on embedded operating point modeling according to claim 1, characterized in that, pass , and Real-time acquisition Small disturbance current on the converter side in the actual coordinate system These are respectively converted into small disturbance voltages at the PCC point in the control coordinate system. and small disturbance current on the converter side The specific content includes: ； ； ； in, and These represent the steady-state values ​​of the converter-side current along the d-axis and q-axis, respectively. and These are the steady-state values ​​of the PCC voltage along the d-axis and q-axis, respectively.

5. The stability analysis system for grid converters based on embedded operating point modeling according to claim 1, characterized in that, Real-time acquisition and After low-pass filtering, it passes through the reactive power loop to obtain The specific content includes: ； ； ； ； ； In the formula, This represents the cutoff frequency of the low-pass filter; This is the active power-frequency droop control coefficient; and These represent the steady-state values ​​of the grid-connected current along the d-axis and q-axis, respectively. and These are the steady-state values ​​of the PCC voltage along the d-axis and q-axis, respectively.

6. The stability analysis system for grid-connected converters based on embedded operating point modeling according to claim 1, characterized in that, The specific contents of the voltage loop include: ； ； ； In the formula, It is a PI controller for voltage loop. The rated angular frequency of the power grid. This is the value of the filter capacitor.

7. The stability analysis system for grid converters based on embedded operating point modeling according to claim 5, characterized in that, The reference value for the small disturbance voltage of the current loop is obtained after adjustment by the current loop. The specific content includes: ； ； ； In the formula, It is a PI controller for the current loop. This is the value of the filter inductance.

8. The stability analysis system for grid converters based on embedded operating point modeling according to claim 1, characterized in that, according to and the feedforward transfer function containing the output voltage of the bridge arm side The bridge arm outputs a small disturbance voltage in the control coordinate system. Converted to bridge arm output small disturbance voltage in real-time coordinate system Thus regulating The specific content includes: according to and Will Converted to bridge arm output small disturbance voltage in real-time coordinate system : ； ； in, and These are the steady-state values ​​of the converter bridge arm voltage along the d-axis and q-axis, respectively. according to and go through get ,according to and go through get ,in To control the small disturbance current on the converter side in the coordinate system; the specific relationship is as follows: ； ； ； In the formula, and These are the filter inductor, filter resistor, filter capacitor, and damping resistor of the LC filter. This is the rated angular frequency.

9. A method for stability analysis of grid-connected converters based on embedded operating point modeling, based on the stability analysis system for grid-connected converters based on embedded operating point modeling as described in any one of claims 1-8, characterized in that, Includes the following steps: Based on the grid-connected small disturbance current in the actual coordinate system As input, the corresponding small perturbation voltage at the PCC point in the actual coordinate system after perturbation is output. ,in, Obtained through the system closed-loop transfer function; Ignoring power reference value disturbances, according to and Obtain the GFM converter port impedance ; according to The stability of the GFM-GCC control for the grid converter is analyzed.

Images