Robust stability assessment method for phase-locked loop dominated heterogeneous multi-inverter power system

Abstract

The application discloses a kind of robust stability evaluation methods of phase-locked loop main leading isomeric multivariable converter power system, solve the problem of difficult robust stability analysis caused by isomeric converter phase-locked loop parameter coupling, parameter optimization has no reference.For: first, obtain system parameters, based on second-order phase-locked loop step-down model to construct uncertainty separation model;Then, combined with value set theory, whether the value set contains origin is judged to determine the robust stability of the system;Then calculate the multivariable stability margin K m , determine the dominant unstable oscillation frequency ω c ;Then analyze the moving trend of the value set of parameter change, determine the influence direction of parameter on system strength, introduce negative damping line under instability state to assist analysis;Finally, develop differentiated parameter optimization strategy, iterative optimization until the system meets the stability margin requirement.The application can quantitatively evaluate the robustness of the system, reveal the non-uniform parameter adjustment rule, provide accurate basis for parameter setting, effectively avoid small signal instability, and improve the robust stability of isomeric multivariable converter power system.

Description

Technical Field

[0001] This invention relates to the field of power system stability analysis and control technology, and in particular to a robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system. Background Technology

[0002] In recent years, the penetration rate of new energy sources in the power system has continued to increase. In areas with weak grid strength, the dynamic interaction between the phase-locked loop-dominated converter control system and the grid has become the core cause of low-frequency oscillations and small-signal instability in the power system.

[0003] In real-world power systems, grid-connected converters typically come from different manufacturers, resulting in significant differences in their phase-locked loop (PLL) control parameters. This leads to a heterogeneous multi-converter power system dominated by PLLs. The heterogeneity of PLL parameters makes the dynamic coupling relationships within the system extremely complex. The impact of interactions between converters with different parameter characteristics on the system's robust stability is difficult to assess accurately. Furthermore, there is a lack of scientific and effective guidelines for adjusting PLL control parameters. Improper parameter tuning can easily trigger small-signal instability in the system, seriously threatening the safe and stable operation of the power system.

[0004] Current stability analysis methods for converter power systems are mostly applicable to homogeneous converter systems with uniform parameters. They are difficult to adapt to the parameter characteristics of heterogeneous multi-converter systems, cannot effectively separate parameter uncertainties from system nominal characteristics, cannot quantitatively evaluate the robust stability margin of the system under parameter heterogeneity, and cannot formulate differentiated parameter optimization strategies for different converters. Therefore, they are difficult to solve the stability analysis and parameter optimization problems of heterogeneous multi-converter systems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a robust stability assessment method for heterogeneous multi-converter power systems dominated by phase-locked loops (PLLs). This method solves the problems of complex dynamic interaction coupling, difficulty in robust stability assessment, and lack of basis for parameter optimization caused by the heterogeneity of PLL parameters in the converter. It achieves accurate quantitative assessment of the robust stability of heterogeneous multi-converter power systems and formulates differentiated parameter adjustment strategies to improve system robust stability and avoid small-signal instability caused by improper parameter tuning.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows: A robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system includes the following steps: S1. Construct an uncertainty separation model: Obtain the network topology parameters, steady-state operating points of each converter, and phase-locked loop (PLL) control parameters of the heterogeneous multi-converter power system; determine the adjustable range of the key converters to be analyzed and their PLL control parameters; based on the second-order PLL reduced-order model, normalize the PLL proportional-integral parameters of the converters; decompose the matrix in the converter state space into a linear combination of nominal values ​​and uncertain increments; combine the AC power grid model to obtain the closed-loop characteristic equation of the system; and separate the uncertain variables of the parameters to be analyzed from the nominal information of the system through mathematical transformation, thus constructing an uncertainty separation model for the heterogeneous multi-converter power system. S2. Determining Robust Stability Based on Value Set Theory: Based on the uncertainty separation model constructed in step S1, value set theory is used to define the set of values ​​of the system characteristic polynomial in the complex plane as the value set T(s), and the mapping of the value set in the complex plane is calculated. Under the premise of nominal system stability, according to the zero mutual exclusion principle, if for all grid angular frequencies ω≥0, the value set T(jω) does not contain the origin of the complex plane, then the system is determined to be robustly stable within the parameter uncertainty range; otherwise, the system has potential instability risk. S3. Calculate the multivariable stability margin and dominant unstable oscillation frequency: Calculate the multivariable stability margin K, which characterizes the distance of the system from the instability boundary. m If K m >1, the system is robustly stable within the given parameter adjustment range, if K m ≤1 indicates a potential instability risk in the system; the frequency corresponding to the minimum point of the minimum parameter perturbation factor when calculating the multivariable stability margin is determined as the dominant unstable oscillation frequency ω of the system. c ; S4. Determine the direction of influence of a single control parameter on the system strength: based on the dominant unstable oscillation frequency ω obtained in step S3. c Fixing all uncertain parameters except the parameter to be analyzed, observe the trend of the distance between the point mapped by the system characteristic polynomial in the complex plane and the origin as the value of the parameter to be analyzed increases, i.e., the value set T(jω) c The movement trend of the parameter on the complex plane; if the distance between the mapping point and the origin decreases, the value set moves towards the origin, indicating that increasing the parameter will worsen the system stability; if the distance between the mapping point and the origin increases, the value set moves away from the origin, indicating that increasing the parameter will enhance the system stability, and the corresponding parameter adjustment direction is the direction of increased system strength; if the system is in K m For potential instability states with a value ≤1, a negative damping line is introduced for auxiliary analysis to determine the direction of the parameter's influence on the system strength. S5. Formulate and optimize differentiated parameter optimization strategies: Based on the influence direction of each phase-locked loop control parameter obtained in step S4 on the system strength, formulate a non-uniform parameter adjustment strategy and perform differentiated optimization on the phase-locked loop control parameters of each converter; after optimization, repeat steps S1-S4 until the multivariable stability margin of the system meets the preset robust stability margin requirements.

[0007] Furthermore, in step S1, the formula for normalizing the proportional-integral parameters of the converter's phase-locked loop is as follows: ; In the formula, Let be the normalized uncertainties of the proportional and integral parameters of the phase-locked loop of the j-th converter, respectively. k pj0 and k ij0 These are the nominal values ​​of the proportional and integral parameters of the phase-locked loop of the j-th converter, respectively. k pj and △ k ij These represent the adjustment ranges of the proportional and integral parameters of the phase-locked loop for the j-th converter, respectively.

[0008] Furthermore, in step S1, based on the second-order phase-locked loop order reduction model, the... j The linearized state-space expression of the converter is:

[0009] In the formula For the first j The state vector increment of the converter is small. and The first j The minute increments in the port voltage and current of the converter. For the first j The rated capacity of the converter , For variables containing uncertain parameters d The state matrix and the input matrix, This is the output matrix.

[0010] Furthermore, in step S1, the formula for decomposing the matrix in the converter state space into a linear combination of nominal values ​​and uncertain increments is as follows:

[0011] In the formula , Only with parameter nominal values k pj0 and k ij0The nominal state matrix and nominal input matrix related to the steady-state operating point; , For only the range of parameter variation △ k pj and △ k ij The relevant uncertainty state matrix and uncertainty input matrix; d j =diag( d ij , d pj (Regarding the first) j The diagonal matrix of the normalized uncertain parameters of the converter.

[0012] Furthermore, in step S1, the closed-loop characteristic equation of the heterogeneous multi-converter power system is:

[0013] In the formula For the infinitesimal increment of the state variables of the entire system, A sys ( s , d ) is the characteristic matrix of the system. A sys0 This is the nominal dynamic characteristic matrix of the system. A sys1 The uncertainty dynamic gain matrix of the system; d Let be the diagonal matrix representing the system uncertainty.

[0014] Furthermore, in step S1, the formula for constructing the uncertainty separation model is:

[0015] In the formula 2 n 3D identity matrix n For the number of converters, M ( s ) represents the uncertainty separation response matrix of a heterogeneous multi-converter power system.

[0016] Furthermore, in step S2, the value set T(s) is defined as follows: T ( s )for In the set of values ​​in the complex plane, m is the dimension of the uncertain parameter to be analyzed.

[0017] Furthermore, in step S3, the multivariate stability margin K m The calculation formula is:

[0018] in, T k (j oh c To normalize uncertain variables d The range of values ​​for is expanded from [-1, 1] to [-1, 1]. k , k When the uncertainty separation model characteristic polynomial is... The set of values ​​that can be taken in the complex plane; k m (j oh c ) characterizes the frequency of the power grid oh The minimum parameter perturbation factor required for the boundary of the value set of the characteristic polynomial of the time system to touch the origin.

[0019] Furthermore, in step S4, the specific process of introducing negative damping line to assist in the analysis is as follows: by setting a damping ratio... g Calculate the complex frequency point s corresponding to the negative damping line. g ,use T ( s g )replace T (j oh c ), observe when the value of the parameter to be analyzed increases. T ( s g The movement trend of the parameter on the complex plane determines the direction of its influence on the system strength; the complex frequency point s g The calculation formula is: .

[0020] Beneficial effects: By constructing an uncertainty separation model, this invention completely separates the uncertain variables of the parameters to be analyzed in a heterogeneous multi-converter power system from the nominal information of the system, effectively decoupling the complex dynamic coupling relationship caused by parameter heterogeneity, laying a clear model foundation for subsequent stability assessment, and solving the problem that traditional methods are difficult to adapt to the characteristics of heterogeneous parameters. This invention combines value set theory and the zero mutual exclusion principle to transform the assessment of system robust stability into a value set mapping judgment on the complex plane. It can intuitively and accurately determine the robust stability of the system within the range of parameter uncertainty, breaking through the limitations of traditional methods for homogeneous converter systems and adapting to the parameter characteristics of heterogeneous multi-converter systems. This invention proposes a multivariable stability margin. K mThe index enables a quantitative assessment of the distance of the system from the instability boundary, and at the same time determines the dominant unstable oscillation frequency of the system, pointing out the core analysis direction for subsequent parameter optimization, and solving the problem that traditional methods cannot quantitatively assess the robust stability margin of heterogeneous systems. This invention accurately determines the direction of influence of each parameter on the system strength by analyzing the movement trend of the time value set of a single control parameter change in the complex plane. Furthermore, it introduces a negative damping line to assist in the analysis of potential system instability, thereby improving the accuracy of the parameter influence direction judgment. At the same time, it reveals the non-uniform parameter adjustment rules of heterogeneous systems and identifies the opposite effects that the same type of control parameters of different converters may have on the system strength. This invention formulates differentiated parameter optimization strategies based on the influence direction of each parameter, and makes non-uniform adjustments to the phase-locked loop control parameters of each converter, rather than adopting a "one-size-fits-all" adjustment method. This provides a precise basis for parameter adjustment decisions for heterogeneous multi-converter power systems, effectively improves the robustness and stability of the system, avoids small-signal instability caused by improper parameter tuning from the root, and ensures the safe and stable operation of power systems with high penetration of new energy. Attached Figure Description

[0021] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of the robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system according to an embodiment of the present invention; Figure 2 This is a block diagram of the converter grid-connected control strategy dominated by the phase-locked loop of the present invention. Figure 3 This is a block diagram of the IEEE 39-node test system in the embodiment; Figure 4 For the stability margin K in the example m A graph showing the change of (jω) with frequency; Figure 5 This is a value set distribution diagram under the critical stability condition in the embodiment; Figure 6 This is a graph showing the direction of value set movement when the normalized variables of the control parameters of different converters in the embodiment increase from -1 to 1. Figure 7 This is a comparison chart of the changes in the system's dominant eigenvalues ​​as the normalized variables of the control parameters of different converters in the embodiment increase from -1 to 1. Figure 8 The waveform of the converter terminal voltage time domain response under different parameter adjustment strategies is shown in the simulation verification of the embodiment. Detailed Implementation

[0022] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0023] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0024] Example 1 See Figure 1 A robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system includes the following steps: S1. Construct an uncertainty separation model: Obtain the network topology parameters, steady-state operating points of each converter, and phase-locked loop (PLL) control parameters of the heterogeneous multi-converter power system; determine the adjustable range of the key converters to be analyzed and their PLL control parameters; based on the second-order PLL reduced-order model, normalize the PLL proportional-integral parameters of the converters; decompose the matrix in the converter state space into a linear combination of nominal values ​​and uncertain increments; combine the AC power grid model to obtain the closed-loop characteristic equation of the system; and separate the uncertain variables of the parameters to be analyzed from the nominal information of the system through mathematical transformation, thus constructing an uncertainty separation model for the heterogeneous multi-converter power system. S2. Determining Robust Stability Based on Value Set Theory: Based on the uncertainty separation model constructed in step S1, value set theory is used to define the set of values ​​of the system characteristic polynomial in the complex plane as the value set T(s), and the mapping of the value set in the complex plane is calculated. Under the premise of nominal system stability, according to the zero mutual exclusion principle, if for all grid angular frequencies ω≥0, the value set T(jω) does not contain the origin of the complex plane, then the system is determined to be robustly stable within the parameter uncertainty range; otherwise, the system has potential instability risk. S3. Calculate the multivariable stability margin and dominant unstable oscillation frequency: Calculate the multivariable stability margin K, which characterizes the distance of the system from the instability boundary. m If K m >1, the system is robustly stable within the given parameter adjustment range, if K m ≤1 indicates a potential instability risk in the system; the frequency corresponding to the minimum point of the minimum parameter perturbation factor when calculating the multivariable stability margin is determined as the dominant unstable oscillation frequency ω of the system. c ; S4. Determine the direction of influence of a single control parameter on the system strength: based on the dominant unstable oscillation frequency ω obtained in step S3. c Fixing all uncertain parameters except the parameter to be analyzed, observe the trend of the distance between the point mapped by the system characteristic polynomial in the complex plane and the origin as the value of the parameter to be analyzed increases, i.e., the value set T(jω) cThe movement trend of the parameter on the complex plane; if the distance between the mapping point and the origin decreases, the value set moves towards the origin, indicating that increasing the parameter will worsen the system stability; if the distance between the mapping point and the origin increases, the value set moves away from the origin, indicating that increasing the parameter will enhance the system stability, and the corresponding parameter adjustment direction is the direction of increased system strength; if the system is in K m For potential instability states with a value ≤1, a negative damping line is introduced for auxiliary analysis to determine the direction of the parameter's influence on the system strength. S5. Formulate and optimize differentiated parameter optimization strategies: Based on the influence direction of each phase-locked loop control parameter obtained in step S4 on the system strength, formulate a non-uniform parameter adjustment strategy and perform differentiated optimization on the phase-locked loop control parameters of each converter; after optimization, repeat steps S1-S4 until the multivariable stability margin of the system meets the preset robust stability margin requirements.

[0025] It should be noted that existing technologies are mostly applicable to homogeneous converter systems with uniform parameters. There is no full-process analysis method for the heterogeneous characteristics of phase-locked loops. Stability can only be determined individually, and the integration of "evaluation-analysis-optimization" cannot be achieved. Furthermore, the parameter adjustment adopts a "one-size-fits-all" approach, which is prone to instability due to the coupling of heterogeneous parameters.

[0026] This embodiment proposes a robust stability assessment and parameter optimization method for a phase-locked loop-dominated heterogeneous multi-converter system throughout the entire process. It is the first to achieve a closed-loop implementation from uncertainty modeling to differentiated optimization, perfectly adapting to the parameter characteristics of heterogeneous converters and solving the core problem of poor adaptability of existing technologies. Breaking away from the traditional unified parameter tuning mode of isomorphic systems, a non-unified differentiated parameter adjustment strategy is proposed. This strategy can identify the opposite effects of the same type of control parameters in different converters, providing a clear direction for parameter tuning and fundamentally avoiding the small-signal instability problem caused by blind parameter tuning in existing technologies. The introduction of negative damping lines to assist in the analysis of potential system instability overcomes the shortcomings of existing technologies in the inaccurate analysis of the direction of parameter influence near the instability boundary, thereby improving the accuracy of parameter optimization.

[0027] In a specific example, in step S1, the formula for normalizing the proportional-integral parameters of the converter's phase-locked loop is: ; In the formula, Let be the normalized uncertainties of the proportional and integral parameters of the phase-locked loop of the j-th converter, respectively. k pj0 and k ij0 These are the nominal values ​​of the proportional and integral parameters of the phase-locked loop of the j-th converter, respectively. k pj and △ k ijThese represent the adjustment ranges of the proportional and integral parameters of the phase-locked loop for the j-th converter, respectively.

[0028] This embodiment separates the nominal values ​​of the proportional / integral parameters of the phase-locked loop from the uncertain increments through a normalization formula, thereby achieving standardized quantification of parameter fluctuations / adjustment ranges. This allows different parameters of heterogeneous converters to have a unified analysis dimension, solving the problem that existing technologies make it difficult to analyze parameter coupling separately, and laying the foundation for subsequent uncertainty modeling.

[0029] In a specific example, in step S1, based on the second-order phase-locked loop order reduction model, the... j The linearized state-space expression of the converter is:

[0030] In the formula For the first j The state vector increment of the converter is small. and The first j The minute increments in the port voltage and current of the converter. For the first j The rated capacity of the converter , For variables containing uncertain parameters d The state matrix and the input matrix, This is the output matrix.

[0031] This embodiment constructs a linearized state-space expression based on a second-order phase-locked loop reduced-order model, significantly reducing the computational load while ensuring analytical accuracy; it also incorporates the rated capacity of the converter. By incorporating engineering parameters, the model becomes more closely aligned with real-world engineering scenarios, resolving the issues of redundancy and disconnect between existing technical models and engineering practices.

[0032] In a specific example, in step S1, the formula for decomposing the matrix in the converter state space into a linear combination of nominal values ​​and uncertain increments is as follows:

[0033] In the formula , Only with parameter nominal values k pj0 and k ij0 The nominal state matrix and nominal input matrix related to the steady-state operating point; , For only the range of parameter variation △ k pj and △ k ijThe relevant uncertainty state matrix and uncertainty input matrix; d j =diag( d ij , d pj (Regarding the first) j The diagonal matrix of the normalized uncertain parameters of the converter.

[0034] This embodiment decomposes the state matrix and input matrix into a nominal part and an uncertain incremental part, thereby completely decoupling the inherent dynamic characteristics of the system from the uncertainty caused by parameter heterogeneity. It can accurately analyze the impact of parameter changes on system dynamics separately, and solves the problems of low accuracy and interference from nominal characteristics in the analysis results of existing technologies.

[0035] In a specific example, in step S1, the closed-loop characteristic equation of the heterogeneous multi-converter power system is:

[0036] In the formula For the infinitesimal increment of the state variables of the entire system, A sys ( s , d ) is the characteristic matrix of the system. A sys0 This is the nominal dynamic characteristic matrix of the system. A sys1 The uncertainty dynamic gain matrix of the system; d Let be the diagonal matrix representing the system uncertainty.

[0037] This embodiment introduces a global uncertainty diagonal matrix into the system's closed-loop characteristic equation. d It integrates the parameter uncertainties of all heterogeneous converters, and can accurately describe the overall dynamic characteristics of the system within the parameter fluctuation range. It makes up for the shortcomings of existing technologies that can only analyze nominal state and have great limitations, and makes system analysis more comprehensive.

[0038] In a specific example, in step S1, the formula for constructing the uncertainty separation model is:

[0039] In the formula 2 n 3D identity matrix n For the number of converters, M ( s ) represents the uncertainty separation response matrix of a heterogeneous multi-converter power system.

[0040] This embodiment constructs an uncertainty separation model through mathematical transformations, completely separating the system's nominal dynamic characteristics from parameter uncertainties, forming an independent uncertainty response matrix. M ( s This approach allows robust stability analysis to focus solely on the impact of parameter changes, overcoming the shortcomings of existing technologies where the coupling of parameters with nominal information leads to analytical difficulties, and providing a clear model foundation for subsequent value set analysis.

[0041] In a specific instance, in step S2, the value set T(s) is defined as follows: T ( s )for In the set of values ​​in the complex plane, m is the dimension of the uncertain parameter to be analyzed.

[0042] This embodiment defines a value set T(s) on the complex plane based on value set theory, which covers all values ​​of the system's characteristic polynomial within the range of parameter uncertainty. It can comprehensively reflect all possible dynamic states of the system. Combined with the zero mutual exclusion principle to determine stability, it avoids the problem of missing instability risk points in the single characteristic root analysis of the existing technology, and greatly improves the comprehensiveness and accuracy of robust stability determination.

[0043] In a specific instance, in step S3, the multivariate stability margin K m The calculation formula is:

[0044] in, T k (j oh c To normalize uncertain variables d The range of values ​​for is expanded from [-1, 1] to [-1, 1]. k , k When the uncertainty separation model characteristic polynomial is... The set of values ​​that can be taken in the complex plane; k m (j oh c ) characterizes the frequency of the power grid oh The minimum parameter perturbation factor required for the boundary of the value set of the characteristic polynomial of the time system to touch the origin.

[0045] This embodiment proposes a multivariable stability margin. K m Quantitative indicators can accurately calculate the safe distance of the system from the instability boundary and clearly define... K m The quantitative criterion of >1 / ≤1 is used to determine the dominant unstable oscillation frequency of the system. oh cIt overcomes the shortcomings of existing technologies that lack quantitative indicators and have no basis for parameter tuning, upgrading the assessment of system robustness and stability from qualitative to quantitative, and pointing out the core analytical direction for subsequent parameter optimization.

[0046] In a specific example, the process of introducing a negative damping line to assist in the analysis in step S4 is as follows: by setting a damping ratio... g Calculate the complex frequency point s corresponding to the negative damping line. g ,use T ( s g )replace T (j oh c ), observe when the value of the parameter to be analyzed increases. T ( s g The movement trend of the parameter on the complex plane determines the direction of its influence on the system strength; the complex frequency point s g The calculation formula is: .

[0047] This embodiment is for the system. K m For potential instability states ≤1, introduce a negative damping line and calculate the complex frequency point s. g ,use T ( s g ) replacement T (j oh c The analysis of the direction of parameter influence closely matches the actual dynamic characteristics of the system before instability, solving the problems of large deviations in parameter analysis and ambiguity in parameter tuning direction near the instability boundary in existing technologies. This significantly improves the accuracy of determining the direction of parameter influence, making parameter optimization of unstable systems more targeted.

[0048] The specific implementation process of the complete method according to the content of this invention is as follows: The block diagram of the phase-locked loop-dominated converter grid-connected control in a specific embodiment of the present invention is as follows: Figure 2 As shown in the figure. This embodiment is based on the IEEE 39-bus standard test system to build a simulation model, which includes 9 grid-connected converters synchronized by phase-locked loops. A simulation model is built in MATLAB / Simulink as follows. Figure 3 The simulation model is shown below. The simulation parameters are shown in Tables 1 and 2.

[0049] Table 1 Simulation verification parameters of the embodiments of the present invention

[0050] Table 2. Parameters and rated capacity of the phase-locked loop of the converter in this invention.

[0051] The robust stability of parameter adjustment in a heterogeneous system dominated by phase-locked loops was investigated using the complete method of this invention. The phase-locked loop parameters of the 2nd and 9th units were selected as the adjustment objects, and the parameter adjustment range was ±5%.

[0052] Figure 4 Examples are given k m (j oh The graph shows the variation of frequency. As can be seen from the graph, at the dominant unstable frequency... oh c At 98.026 rad / s, k m (j oh It reaches a minimum value of 0.096. This is due to the system's robust stability margin. K m <1 means that the heterogeneous multi-converter system is robustly unstable within a given range of ±5% parameter fluctuations, and there is a great risk of oscillation and instability.

[0053] Figure 5 The critical stability conditions in the embodiments are given, i.e. K m The value set distribution diagram at different times. As can be seen from the diagram, at the dominant instability frequency... oh c Below, when the parameter perturbation reaches a critical value, the parameter combination that first touches the origin of the complex plane at the boundary of the value set of the system's characteristic polynomial is: d c Based on this critical state, K m d c Converted to actual parameters, the calculated combination of key parameters leading to critical instability of the system is as follows: k i2 =9043.3, k p2 =17.9, k i9 =9958.5, k p9 =19.9. This result visually demonstrates the limiting state of the system from the instability boundary.

[0054] Figure 6 The diagram shows the direction of value set shift as the normalized variables of the control parameters for different converters in the embodiment increase from -1 to 1. As can be seen from the diagram, with the integral coefficient of the second converter... d i2 The increase of the characteristic polynomial As the distance between the point mapped onto the complex plane and the origin decreases, the representative value set shifts towards the origin, leading to decreased system stability; and as the proportional gain of the second converter... d p2 and the integral coefficient of the 9th converter d i9 proportionality coefficient d p9 An increase in the value of the mapping point increases the distance from the origin, representing a shift of the value set away from the origin, thus enhancing system stability. Therefore, even for control parameters of the same type (such as integral coefficients)... k i In heterogeneous systems, converters at different locations (such as converter 2 and converter 9) may have completely opposite effects on system stability, which reveals the non-uniformity of parameter adjustment rules in heterogeneous systems.

[0055] Figure 7 A comparison chart of the changes in the system's dominant eigenvalues ​​as the normalized variables of the control parameters for different converters in the embodiment increase from -1 to 1 is provided. Among them, the integral coefficient of the second converter... d i2 As the value increases, the real part of the dominant eigenvalue gradually increases and shifts to the right half-plane, causing the system damping to weaken or even become unstable. This is related to... Figure 6 The analysis results are consistent when the median set is shifted towards the origin; conversely, when... d p2 , d i9 or d p9 When the value increases, the real part of the dominant eigenvalue decreases and shifts to the left, increasing the system damping. This is also related to... Figure 6 The analysis results are consistent with those of the median set being far from the origin.

[0056] In electromagnetic simulation, by Figure 8 It can be seen that the time-domain response waveforms of the converter terminal voltage differ significantly under different parameter adjustment strategies. Specifically, (a) represents the system response under nominal parameters, where the system tends to stabilize but its strength is very weak; (b) corresponds to the critical parameter combination, where the waveform exhibits constant-amplitude oscillations, verifying... K m (c) When the parameter is adjusted by 5% in the direction closer to the origin, the voltage waveform diverges and oscillates, indicating that further deterioration of the parameters in the critical instability parameter combination will lead to system instability; (d) When the parameter is adjusted by 5% in the direction away from the origin according to the value set, the system strength increases significantly.

[0057] Therefore, this invention demonstrates significant technical advantages: it solves the challenge of robust stability assessment in heterogeneous multi-converter power systems dominated by phase-locked loops (PLLs) due to the heterogeneity of PLL parameters. By establishing an uncertainty separation model and combining it with value set theory, this invention not only quantifies the robust stability margin of the system but also intuitively reveals the non-uniform influence of heterogeneous parameters on system strength through value set movement trends. This provides a precise theoretical basis for parameter optimization in heterogeneous systems, effectively avoiding the oscillation risk caused by improper parameter tuning and improving the robust stability of heterogeneous multi-converter systems.

[0058] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system, characterized in that, Includes the following steps: S1. Construct an uncertainty separation model: Obtain the network topology parameters, steady-state operating points of each converter, and phase-locked loop (PLL) control parameters of the heterogeneous multi-converter power system; determine the adjustable range of the key converters to be analyzed and their PLL control parameters; based on the second-order PLL reduced-order model, normalize the PLL proportional-integral parameters of the converters; decompose the matrix in the converter state space into a linear combination of nominal values ​​and uncertain increments; combine the AC power grid model to obtain the closed-loop characteristic equation of the system; and separate the uncertain variables of the parameters to be analyzed from the nominal information of the system through mathematical transformation, thus constructing an uncertainty separation model for the heterogeneous multi-converter power system. S2. Determining Robust Stability Based on Value Set Theory: Based on the uncertainty separation model constructed in step S1, value set theory is used to define the set of values ​​of the system characteristic polynomial in the complex plane as the value set T(s), and the mapping of the value set in the complex plane is calculated. Under the premise of nominal system stability, according to the zero mutual exclusion principle, if for all grid angular frequencies ω≥0, the value set T(jω) does not contain the origin of the complex plane, then the system is determined to be robustly stable within the parameter uncertainty range; otherwise, the system has potential instability risk. S3. Calculate the multivariable stability margin and dominant unstable oscillation frequency: Calculate the multivariable stability margin K, which characterizes the distance of the system from the instability boundary. m If K m >1, the system is robustly stable within the given parameter adjustment range, if K m ≤1 indicates a potential instability risk in the system; the frequency corresponding to the minimum point of the minimum parameter perturbation factor when calculating the multivariable stability margin is determined as the dominant unstable oscillation frequency ω of the system. c ; S4. Determine the direction of influence of a single control parameter on the system strength: based on the dominant unstable oscillation frequency ω obtained in step S3. c Fixing all uncertain parameters except the parameter to be analyzed, observe the trend of the distance between the point mapped by the system characteristic polynomial in the complex plane and the origin as the value of the parameter to be analyzed increases, i.e., the value set T(jω) c The movement trend of the parameter on the complex plane; if the distance between the mapping point and the origin decreases, the value set moves towards the origin, indicating that increasing the parameter will worsen the system stability; if the distance between the mapping point and the origin increases, the value set moves away from the origin, indicating that increasing the parameter will enhance the system stability, and the corresponding parameter adjustment direction is the direction of increased system strength; if the system is in K m For potential instability states with a value ≤1, a negative damping line is introduced for auxiliary analysis to determine the direction of the parameter's influence on the system strength. S5. Formulate and optimize differentiated parameter optimization strategies: Based on the influence direction of each phase-locked loop control parameter obtained in step S4 on the system strength, formulate a non-uniform parameter adjustment strategy and perform differentiated optimization on the phase-locked loop control parameters of each converter; after optimization, repeat steps S1-S4 until the multivariable stability margin of the system meets the preset robust stability margin requirements.

2. The robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system according to claim 1, characterized in that, In step S1, the formula for normalizing the proportional-integral parameters of the phase-locked loop of the converter is as follows: ； In the formula, Let be the normalized uncertainties of the proportional and integral parameters of the phase-locked loop of the j-th converter, respectively. k pj0 and k ij0 These are the nominal values ​​of the proportional and integral parameters of the phase-locked loop of the j-th converter, respectively. k pj and △ k ij These represent the adjustment ranges of the proportional and integral parameters of the phase-locked loop for the j-th converter, respectively.

3. The robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system according to claim 1, characterized in that, In step S1, based on the second-order phase-locked loop order reduction model, the... j The linearized state-space expression of the converter is: In the formula For the first j The state vector increment of the converter is small. and The first j The minute increments in the port voltage and current of the converter. For the first j The rated capacity of the converter , For variables containing uncertain parameters δ The state matrix and the input matrix, This is the output matrix.

4. The robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system according to claim 1, characterized in that, In step S1, the formula for decomposing the matrix in the converter state space into a linear combination of nominal values ​​and uncertain increments is as follows: In the formula , Only with parameter nominal values k pj0 and k ij0 The nominal state matrix and nominal input matrix related to the steady-state operating point; , For only the range of parameter variation △ k pj and △ k ij The relevant uncertainty state matrix and uncertainty input matrix; δ j =diag( δ ij , δ pj (Regarding the first) j The diagonal matrix of the normalized uncertain parameters of the converter.

5. The robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system according to claim 1, characterized in that, In step S1, the closed-loop characteristic equation of the heterogeneous multi-converter power system is: In the formula For the infinitesimal increment of the state variables of the entire system, A sys ( s , δ ) is the characteristic matrix of the system. A sys0 This is the nominal dynamic characteristic matrix of the system. A sys1 The uncertainty dynamic gain matrix of the system; δ Let be the diagonal matrix representing the system uncertainty.

6. The robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system according to claim 1, characterized in that, In step S1, the formula for constructing the uncertainty separation model is: In the formula 2 n 3D identity matrix n For the number of converters, M ( s ) represents the uncertainty separation response matrix of a heterogeneous multi-converter power system.

7. The robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system according to claim 6, characterized in that, In step S2, the value set T(s) is defined as follows: T ( s )for In the set of values ​​in the complex plane, m is the dimension of the uncertain parameter to be analyzed.

8. The robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system according to claim 1, characterized in that, In step S3, multivariate stability margin K m The calculation formula is: in, T k (j ω c To normalize uncertain variables δ The range of values ​​for is expanded from [-1, 1] to [-1, 1]. k , k When the uncertainty separation model characteristic polynomial is... The set of values ​​that can be taken in the complex plane; k m (j ω c ) characterizes the frequency of the power grid ω The minimum parameter perturbation factor required for the boundary of the characteristic polynomial of the time system to touch the origin.

9. The robust stability assessment method for a phase-locked loop-dominated heterogeneous multi-converter power system according to claim 1, characterized in that, In step S4, the specific process of introducing a negative damping line to assist in the analysis is as follows: by setting a damping ratio... ζ Calculate the complex frequency point s corresponding to the negative damping line. g ,use T ( s g )replace T (j ω c ), observe when the value of the parameter to be analyzed increases. T ( s g The movement trend of the parameter on the complex plane determines the direction of its influence on the system strength; the complex frequency point s g The calculation formula is: 。

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