An impedance method for robustness evaluation considering uncertainty factors
By establishing an impedance model that considers uncertainties and robustness evaluation index in the grid-connected converter system, the problem of insufficient robustness of the impedance method is solved, accurate stability evaluation under uncertain conditions is achieved, and the safety and reliability of the system are improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- POWER RES INST OF STATE GRID SHAANXI ELECTRIC POWER CO LTD
- Filing Date
- 2026-04-22
- Publication Date
- 2026-08-04
AI Technical Summary
In existing technologies, the impedance method for robust assessment of grid-connected converter systems is not accurate enough, making it difficult to accurately assess system stability under uncertainties, leading to misjudgments and safety threats.
An impedance model of a grid-connected converter system is established considering uncertainties. Characteristic equations are derived through equivalent complex circuit analysis and node elimination method. Sequence impedance and generalized impedance criteria under uncertainty conditions are constructed, and robustness evaluation indicators are used for quantitative analysis, including condition number, loop gain sensitivity and confidence index.
This study improves the accuracy of robustness assessment of grid-connected converter systems using the impedance method, reveals the essential reasons for the differences in robustness of the frequency domain impedance method, and provides theoretical support and engineering guidance for stability analysis under uncertainty conditions.
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Figure CN122509104A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of impedance robustness assessment technology for grid-connected converter systems, and in particular to an impedance robustness assessment method that takes into account uncertainty factors. Background Technology
[0002] The construction of grid-connected converter systems, primarily based on renewable energy sources, is progressing steadily. The interaction between the converter and the power grid introduces complex dynamic behaviors across a wide frequency band, leading to frequent subsynchronous / supersynchronous oscillations and harmonic oscillations, which seriously threaten system safety. Existing small-disturbance stability analysis methods are mainly divided into time-domain methods and frequency-domain methods. Time-domain methods rely on precise system models, making them difficult to apply in engineering projects; frequency-domain impedance methods, due to their clear physical meaning and lack of the need for a global system model, have become the standard tool for analyzing converter-grid interactive oscillation problems.
[0003] Common impedance methods include the dq impedance method in a synchronous rotating coordinate system, the sequence impedance method in a stationary coordinate system, and the generalized impedance method in a polar coordinate system. When the system model is accurate and the uncertainty is small, different impedance methods can be mathematically converted to each other and obtain consistent stability criteria. However, in actual engineering, the grid impedance changes with the operating mode and load fluctuations, the controller parameters have tuning errors or aging drift, and changes in the converter operating point, such as output power and power factor, will also cause changes in its equivalent impedance. These uncertainties can cause the impedance method analysis results to deviate from the true stability, or even lead to misjudgments.
[0004] The academic community has proposed a series of quantitative indicators for evaluating the robustness of frequency domain methods. For example, the literature introduces the condition number as an indicator to evaluate the robustness of impedance methods; the smaller the condition number, the lower the sensitivity of the system's eigenvalues to perturbations of matrix elements. Other studies assess the robustness of the criterion by analyzing the sensitivity of the loop gain transfer function to parameter perturbations. Additionally, there are confidence indicators obtained through statistical stability margin distributions. Although these studies have proposed various indicators, the reasons for the differences in robustness derived from frequency domain methods remain unclear, and the essential differences and relationships between the various evaluation indicators lack systematic analysis. This makes it difficult to select appropriate evaluation methods based on specific scenarios in practical applications.
[0005] In summary, the accuracy of the impedance method for robust assessment of grid-connected converter systems in the existing technology needs to be improved. Summary of the Invention
[0006] This application provides an impedance-based robustness assessment method that takes into account uncertainties, in order to address the problem that the accuracy of impedance-based robustness assessment of grid-connected converter systems in the prior art needs to be improved.
[0007] On the one hand, this application provides a robustness assessment method for impedance methods that considers uncertainty factors, including the following steps: Step 1: Establish the impedance model of the grid-connected converter system under the condition of considering uncertainties, including the sequence impedance model in the stationary coordinate system and the generalized impedance model in the polar coordinate system.
[0008] Step 2: Based on the sequence impedance model and the generalized impedance model, the error propagation path is derived through equivalent complex circuit analysis and the node elimination method, resulting in characteristic equations representing the error amplification effect of different impedance criteria. Based on the characteristic equations, a system uncertainty model caused by uncertainty factors is constructed to obtain the sequence impedance criterion and the generalized impedance criterion under uncertainty conditions.
[0009] Step 3: Quantitatively analyze the amplitude deviation of the sequence impedance criterion and the generalized impedance criterion using robustness evaluation indicators to obtain robustness evaluation results.
[0010] In one possible implementation, in step one, the uncertainties include fluctuations in the magnitude and phase angle of the grid-side impedance, perturbations of the parameters of the proportional and integral elements of the converter controller, and changes in output power and power factor.
[0011] In one possible implementation, in step one, after establishing the sequence impedance model in the stationary coordinate system, the positive sequence circuit is selected to correct the negative sequence circuit to obtain the converter sequence admittance model.
[0012] In one possible implementation, in step two, when constructing a system uncertainty model caused by uncertainty factors, the various sources of model uncertainty are divided into parameter uncertainty and dynamic uncertainty, and then the order impedance criterion and generalized impedance criterion under uncertainty conditions are obtained respectively.
[0013] In one possible implementation, in step three, the robustness evaluation metrics include: condition number metric, loop gain sensitivity metric, and confidence metric.
[0014] The condition number index refers to the maximum value of the sensitivity of the transfer function to system perturbations. The larger the condition number index, the higher the sensitivity of the model to perturbations and the worse its robustness.
[0015] The loop gain sensitivity index measures the criterion's sensitivity to parameter changes by calculating the partial derivative of the open-loop transfer function with respect to impedance parameter perturbations.
[0016] The confidence index assesses the reliability of the criterion conclusion by evaluating the stability margin distribution of the statistical impedance model within the perturbation range.
[0017] In one possible implementation, step three is followed by: Step four: Verify the effectiveness of steps one through three through simulation, including: establishing a simulation model in the MATLAB / Simulink environment, plotting the Nyquist curve and electromagnetic transient simulation waveforms under the consideration of parameter perturbation and dynamic uncertainty, analyzing the applicability and advantages and disadvantages of different evaluation indicators, and verifying the effectiveness of steps one through three.
[0018] In one possible implementation, in step four, the robustness differences between the generalized impedance criterion and the modified order impedance criterion when considering uncertainties are verified by comparing the Nyquist curve envelopes of different evaluation metrics and the voltage oscillation waveforms in electromagnetic simulations, and the selection principles for robustness evaluation metrics under different scenarios are determined.
[0019] The impedance method robustness assessment method considering uncertainty factors in this application has the following advantages: By establishing an impedance model considering uncertainties and combining it with a system uncertainty model and robustness evaluation indicators, the accuracy of the impedance-based robustness evaluation of grid-connected converter systems is improved. For the first time, the essential reasons for the differences in robustness of the frequency domain impedance method are systematically revealed from the perspective of error propagation.
[0020] By combining condition number, loop gain sensitivity, and confidence level indices, the robustness of impedance criteria can be quantitatively compared under different uncertainty scenarios.
[0021] Simulation results demonstrate that the method presented in this application can accurately assess the impact of uncertainties on the impedance method stability criterion, providing theoretical support and engineering guidance for the frequency domain stability analysis of novel power systems. Attached Figure Description
[0022] To more clearly illustrate the technical solutions in the embodiments of this application 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 this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0023] Figure 1 A schematic flowchart illustrating an impedance method robustness assessment method considering uncertainty factors, provided for an embodiment of this application; Figure 2 A control block diagram of a grid-connected converter system provided in an embodiment of this application; Figure 3 This is a schematic diagram of the equivalent complex circuit of a grid-connected converter system provided in the embodiments of this application; Figure 4 A schematic diagram of the system uncertainty model provided in the embodiments of this application; Figure 5 A schematic diagram of a sequence impedance model considering inductance uncertainty provided for an embodiment of this application; Figure 6 A schematic diagram of a generalized impedance model considering inductance uncertainty provided for an embodiment of this application; Figure 7 A schematic diagram of a transfer function model considering dynamic uncertainties provided for embodiments of this application; Figure 8 A schematic diagram of the data hierarchy of the three robustness evaluation metrics provided in the embodiments of this application; Figure 9 A schematic diagram of the amplitude deviation of the generalized impedance criterion under the dominance of the phase-locked loop, considering the impedance criterion after perturbation, provided for embodiments of this application; Figure 10 A schematic diagram of the amplitude deviation of the phase-locked loop-dominated lower-sequence impedance criterion considering the perturbation impedance criterion provided in the embodiments of this application; Figure 11 A schematic diagram of the amplitude deviation of the generalized impedance criterion under the inner loop dominance, considering the impedance criterion after perturbation, provided for embodiments of this application; Figure 12 A schematic diagram of the amplitude deviation of the inner loop-dominated lower-order impedance criterion considering the perturbation impedance criterion provided in the embodiments of this application; Figure 13 A schematic diagram of the participation factors in each step provided in the embodiments of this application; Figure 14 This is a schematic diagram of the Nyquist curves corresponding to the two criteria under the phase-locked loop (PLL) dominance provided in the embodiments of this application. Figure 15 This application provides a schematic diagram of the Nyquist curves corresponding to the two criteria under the inner loop dominance in the embodiments of this application; Figure 16 This is a schematic diagram of the active voltage waveform for setting PLL parameters provided in an embodiment of this application; Figure 17 This is a schematic diagram of the active voltage waveform for setting the inner loop parameters in an embodiment of this application. Detailed Implementation
[0024] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0025] like Figure 1 As shown in the embodiments of this application, an impedance method robustness assessment method considering uncertainty factors is provided, including the following steps: Step 1: Establish the impedance model of the grid-connected converter system under the condition of considering uncertainties, including the sequence impedance model in the stationary coordinate system and the generalized impedance model in the polar coordinate system.
[0026] Step 2: Based on the sequence impedance model and the generalized impedance model, the error propagation path is derived through equivalent complex circuit analysis and the node elimination method, resulting in characteristic equations representing the error amplification effect of different impedance criteria. Based on the characteristic equations, a system uncertainty model caused by uncertainty factors is constructed to obtain the sequence impedance criterion and the generalized impedance criterion under uncertainty conditions.
[0027] Step 3: Quantitatively analyze the amplitude deviation of the sequence impedance criterion and the generalized impedance criterion using robustness evaluation indicators to obtain robustness evaluation results.
[0028] For example, in step one, the uncertainties include fluctuations in the amplitude and phase angle of the grid-side impedance, perturbations in the parameters of the proportional and integral elements of the converter controller, and changes in output power and power factor.
[0029] Specifically, such as Figure 2 As shown, the grid-connected converter system consists of a grid-connected converter, a filter device, and a transmission line. The DC bus voltage of the converter is... U dc The line inductance, filter inductance, and filter capacitor are respectively L line , L f and C f , , These represent the amplitude and phase angle of the power grid, respectively. An inner current loop-outer power loop control structure is adopted. The inner loop controller provides rapid regulation of the converter output current, while the outer loop controller regulates the output active and reactive power.
[0030] For example, in step one, after establishing the sequence impedance model in the stationary coordinate system, the positive sequence circuit is selected to correct the negative sequence circuit to obtain the converter sequence admittance model.
[0031] Specifically, in this embodiment, a sequence impedance model for the converter and the power grid is established in a stationary coordinate system. Both the positive and negative sequence impedances of the converter can be expressed in matrix form, and the specific expression for the sequence impedance model is as follows: .
[0032] in, Let be the admittance matrix in ordered coordinates, satisfying .
[0033] To account for frequency coupling between the converter and the power grid, a positive-sequence circuit is selected to correct the negative-sequence circuit, resulting in the corrected converter sequence admittance (i.e., the converter sequence admittance model), whose expression is as follows: .
[0034] Among them, the positive and negative sequence admittance models for the converter and the power grid are respectively and .
[0035] Specifically, in this embodiment, in step two, in order to study the impact of uncertainty on the impedance method, a method is constructed as follows: Figure 3 The equivalent complex circuit shown can be obtained by eliminating nodes G and D in the circuit using the node elimination method. The characteristic equation representing the error amplification effect of different impedance criteria is as follows: .
[0036] in, , .
[0037] Comparing the formulas, it can be seen that in subsynchronous mode, the error amplification effect of the generalized impedance criterion is small, while the error amplification effect of the positive and negative sequence impedance criterion is large; the opposite is true in high-frequency mode.
[0038] For example, in step two, when constructing a system uncertainty model caused by uncertainty factors, the various sources of model uncertainty are divided into parameter uncertainty and dynamic uncertainty, and then the order impedance criterion and generalized impedance criterion under uncertainty conditions are obtained respectively.
[0039] Specifically, in this embodiment, in step two, to further describe the impact of uncertainty on the system, a system is established as follows: Figure 4 The system uncertainty model shown divides the sources of uncertainty into parametric uncertainty and dynamic uncertainty, and then obtains the order impedance criterion and generalized impedance criterion under uncertainty conditions.
[0040] The sequence impedance criterion can be expressed as: .
[0041] The order impedance criterion considering uncertainties can be expressed as: .
[0042] in, , , , .
[0043] The generalized impedance criterion can be expressed as: .
[0044] The generalized impedance criterion, considering uncertainties, can be expressed as: .
[0045] in, , , , .
[0046] For example, in step three, the robustness evaluation metrics include: condition number metric, loop gain sensitivity metric, and confidence metric.
[0047] The condition number index refers to the maximum value of the sensitivity of the transfer function to system perturbations. The larger the condition number index, the higher the sensitivity of the model to perturbations and the worse its robustness.
[0048] The loop gain sensitivity index measures the criterion's sensitivity to parameter changes by calculating the partial derivative of the open-loop transfer function with respect to impedance parameter perturbations.
[0049] The confidence index assesses the reliability of the criterion conclusion by evaluating the stability margin distribution of the statistical impedance model within the perturbation range.
[0050] Specifically, conditional number index The maximum singular value of the open-loop transfer function matrix and minimum singular value The ratio, mathematically expressed as follows: .
[0051] When the condition number index The larger the value, the higher the model's sensitivity to perturbations and the worse its robustness.
[0052] like Figure 8 The diagram shows the data hierarchy of the three robustness evaluation metrics. The first layer uses the condition number metric, the second layer adds the loop gain sensitivity metric, and the third layer further calculates the confidence metric.
[0053] For example, step three also includes: Step four: Verify the effectiveness of steps one through three through simulation, including: establishing a simulation model in the MATLAB / Simulink environment, plotting the Nyquist curve and electromagnetic transient simulation waveforms under the consideration of parameter perturbation and dynamic uncertainty, analyzing the applicability and advantages and disadvantages of different evaluation indicators, and verifying the effectiveness of steps one through three.
[0054] Specifically, with Figure 5 and Figure 6For example, the Nyquist curves of the sequence impedance model and the generalized impedance model considering inductance uncertainty are given respectively. The analysis shows that in the phase-locked loop dominant mode, the Nyquist curve of the generalized impedance criterion has a smaller deviation from inductance perturbation, and both the condition number index and the loop gain sensitivity index show that it has higher robustness; in the inner loop dominant mode, the robustness difference between the two criteria is small. Figure 7 This demonstrates the transfer function model considering dynamic uncertainties. Figures 9 to 12 The comparison of impedance criterion amplitude deviations after considering perturbation is presented. Figure 13 The participation factors for each stage are given. These figures can be used to further explain the impact of different uncertainties on the criteria in different frequency bands.
[0055] For example, in step four, by comparing the Nyquist curve envelopes of different evaluation metrics and the voltage oscillation waveforms in electromagnetic simulation, the robustness differences between the generalized impedance criterion and the modified order impedance criterion when considering uncertainty factors are verified, and the selection principles for robustness evaluation metrics under different scenarios are determined.
[0056] Specifically, to further verify the theoretical analysis, simulations were performed to plot the Nyquist curve envelopes for the two criteria, as follows: Figure 14 and Figure 15 As shown; simultaneously, in the electromagnetic transient simulation, the voltage oscillation waveforms based on the control parameters set according to two criteria are compared, as follows: Figure 16 and Figure 17 As shown in the figure. The results show that when considering uncertainties, the Nyquist curve envelope of the system based on the generalized impedance criterion for PLL parameter tuning never encircles the point (-1, j0), and the system remains stable; while the Nyquist curve of the system based on the modified sequence impedance criterion for inner loop parameter tuning encircles the point (-1, j0) under perturbation, resulting in oscillations. Electromagnetic simulation waveforms also show that the control based on the generalized impedance criterion can quickly recover stability after perturbation, while the model based on the modified sequence impedance criterion becomes unstable.
[0057] In summary, by combining error propagation analysis and three robustness evaluation indices, the method proposed in this invention can effectively evaluate the robustness of the frequency domain impedance method under uncertainty conditions, guide the selection of control parameters for new power systems, and has significant theoretical and engineering application value.
[0058] This application's embodiments improve the accuracy of impedance-based robustness assessment of grid-connected converter systems by establishing an impedance model considering uncertainties and combining it with a system uncertainty model and robustness evaluation indicators. For the first time, it systematically reveals the essential reasons for differences in robustness of the frequency domain impedance method from the perspective of error propagation.
[0059] By combining condition number, loop gain sensitivity, and confidence level indices, the robustness of impedance criteria can be quantitatively compared under different uncertainty scenarios.
[0060] Simulation results demonstrate that the method presented in this application can accurately assess the impact of uncertainties on the impedance method stability criterion, providing theoretical support and engineering guidance for the frequency domain stability analysis of novel power systems.
[0061] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.
[0062] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.
Claims
1. A robustness assessment method for impedance methods considering uncertainty factors, characterized in that, Includes the following steps: Step 1: Establish the impedance model of the grid-connected converter system under the condition of considering uncertainties, including the sequence impedance model in the stationary coordinate system and the generalized impedance model in the polar coordinate system. Step 2: Based on the sequence impedance model and the generalized impedance model, the error propagation path is derived through equivalent complex circuit analysis and the node elimination method, resulting in the characteristic equation representing the error amplification effect of different impedance criteria. Based on the characteristic equation, a system uncertainty model caused by uncertainty factors is constructed to obtain the sequence impedance criterion and the generalized impedance criterion under uncertainty conditions. Step 3: Quantitatively analyze the amplitude deviation of the sequence impedance criterion and the generalized impedance criterion using robustness evaluation indicators to obtain robustness evaluation results.
2. The impedance method robustness assessment method considering uncertainty factors according to claim 1, characterized in that, In step one, the uncertainties include fluctuations in the amplitude and phase angle of the grid-side impedance, perturbations in the parameters of the proportional and integral elements of the converter controller, and changes in output power and power factor.
3. The impedance method robustness assessment method considering uncertainty factors according to claim 1, characterized in that, In step one, after establishing the sequence impedance model in the stationary coordinate system, the positive sequence circuit is selected to correct the negative sequence circuit, thus obtaining the converter sequence admittance model.
4. The impedance method robustness assessment method considering uncertainty factors according to claim 1, characterized in that, In step two, when constructing a system uncertainty model caused by uncertainty factors, the sources of uncertainty in various models are divided into parameter uncertainty and dynamic uncertainty, and then the order impedance criterion and generalized impedance criterion under uncertainty conditions are obtained respectively.
5. The impedance method robustness assessment method considering uncertainty factors according to claim 1, characterized in that, In step three, the robustness evaluation metrics include: condition number metric, loop gain sensitivity metric, and confidence metric. The condition number index refers to the maximum value of the sensitivity of the transfer function to system perturbations. The larger the condition number index, the higher the sensitivity of the model to perturbations and the worse its robustness. The loop gain sensitivity index measures the criterion's sensitivity to parameter changes by calculating the partial derivative of the open-loop transfer function with respect to impedance parameter perturbations. The confidence index assesses the reliability of the criterion conclusion by evaluating the stability margin distribution of the statistical impedance model within the perturbation range.
6. The impedance method robustness assessment method considering uncertainty factors according to claim 1, characterized in that, Step three also includes: Step four: Verify the effectiveness of steps one through three through simulation, including: establishing a simulation model in the MATLAB / Simulink environment, plotting the Nyquist curve and electromagnetic transient simulation waveforms under the consideration of parameter perturbation and dynamic uncertainty, analyzing the applicability and advantages and disadvantages of different evaluation indicators, and verifying the effectiveness of steps one through three.
7. The impedance method robustness assessment method considering uncertainty factors according to claim 6, characterized in that, In step four, by comparing the Nyquist curve envelopes of different evaluation indices and the voltage oscillation waveforms in electromagnetic simulation, the robustness differences between the generalized impedance criterion and the modified order impedance criterion when considering uncertainties are verified, and the selection principles for robustness evaluation indices under different scenarios are determined.