Virtual impedance-considered grid-connected resonance risk analysis method for network construction converter

Abstract

The invention belongs to the field of stability analysis of a grid-connected system of a grid-building converter, and particularly relates to a grid-building converter grid-connected resonance risk analysis method considering virtual impedance, which comprises the following steps: S1, establishing a three-phase time domain differential equation and simplifying the equation into a single-phase equivalent time domain model; converting into a harmonic state space model of the main circuit; s2, constructing a harmonic state space model of a control system comprising an active power control loop and a reactive power control loop; s3, introducing a virtual impedance control link, and correcting the voltage amplitude reference phasor output by the reactive power control loop; deriving an expression of a modulation signal disturbance phasor; s4, obtaining a complete frequency domain admittance model YGSC of the network construction converter considering the influence of the virtual impedance; an open loop gain TGFM of the grid converter grid-connected system is constructed; and S5, drawing a Nyquist curve based on TGFM, and carrying out resonance risk determination. According to the method, the interaction dynamic characteristics of the network building converter and the power grid under the influence of the virtual impedance can be accurately represented, and the resonance risk of the grid-connected system is evaluated.

Description

Technical Field

[0001] This invention belongs to the field of stability analysis of grid-connected converter systems, and specifically relates to a method for analyzing the risk of grid resonance in grid-connected converters that considers virtual impedance. Background Technology

[0002] Driven by carbon reduction goals, new power systems are rapidly evolving towards high-proportion renewable energy and high-penetration power electronic equipment, gradually developing into regional integrated energy systems that combine energy collection, transmission, storage, and trading. With the large-scale integration of distributed photovoltaic, wind power, energy storage systems, and various power electronic converters, the grid inertia dominated by traditional synchronous generators has significantly decreased, system damping capacity has weakened, and the problem of insufficient voltage and frequency support capabilities has become increasingly prominent. Against this backdrop, grid-forming converters (GFMs), due to their ability to actively construct voltage and frequency and simulate the external characteristics of synchronous generators, have become a key technological path to improve system stability and support capabilities.

[0003] Currently, mainstream grid control strategies include droop control, Virtual Synchronous Generator (VSG), matching control, and virtual oscillator control. Among these, the VSG has attracted widespread attention due to its ability to effectively replicate the rotational inertia, primary frequency regulation characteristics, and damping characteristics of a synchronous machine. VSG-based grid converters dynamically adjust the voltage amplitude and frequency at the grid connection point through closed-loop control of active power-frequency and reactive power-voltage, thereby maintaining system stability. However, in actual grid environments, especially in medium- and low-voltage distribution networks or weak grid scenarios, lines typically exhibit a high resistance-inductance ratio (R / X ratio), leading to significant coupling between active and reactive power. This coupling effect weakens the voltage regulation capability of reactive power control, causing inverter output voltage drops, increased output current, and even overcurrent and instability in equipment under grid faults or disturbances, seriously threatening system reliability.

[0004] To alleviate power coupling issues, virtual impedance control has been widely adopted in the control architecture of grid-connected converters. This method reconstructs the equivalent impedance characteristics of the converter output port by artificially introducing virtual resistance Rv and virtual reactance Lv into the control loop. This allows for flexible adjustment of the voltage-current relationship and reduces the effective R / X ratio of the grid without adding physical passive components. In particular, the introduction of virtual negative resistance can theoretically "cancel out" line resistance, further improving power decoupling. However, the introduction of virtual impedance (especially negative resistive components) significantly alters the dynamic characteristics of the system, potentially inducing high-frequency or subsynchronous resonances, and even leading to system instability. Existing research largely focuses on optimizing steady-state power decoupling performance, lacking in-depth analysis of the dynamic stability mechanism of grid-connected converters with virtual impedance (especially virtual negative resistance) interacting with the grid in the frequency domain.

[0005] Therefore, how to accurately characterize the dynamic interaction characteristics between the grid converter and the power grid under the influence of virtual impedance, and assess the resonance risk of the grid-connected system, so as to provide theoretical support for the safe design and parameter optimization of power decoupling strategies in high R / X ratio power grids, has become an urgent problem to be solved. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, this invention provides a method for analyzing the grid resonance risk of grid-connected converters that considers virtual impedance. This method can accurately characterize the dynamic interaction characteristics between the grid-connected converter and the power grid under the influence of virtual impedance, and assess the resonance risk of the grid-connected system. This provides theoretical support for the safe design and parameter optimization of power decoupling strategies in high R / X ratio power grids.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A method for analyzing the grid-connected resonance risk of a grid-connected converter considering virtual impedance includes the following steps:

[0009] S1. Based on the main circuit topology of the grid converter, a three-phase time-domain differential equation is established according to Kirchhoff's voltage law, and simplified to a single-phase equivalent time-domain model using three-phase symmetry. On this basis, the single-phase equivalent time-domain model is converted into a harmonic state-space model of the main circuit through small-signal linearization and harmonic state-space method, which is used to characterize the dynamic relationship between AC current disturbance, AC terminal voltage disturbance and grid voltage disturbance.

[0010] S2. Based on the virtual synchronous machine control strategy, a harmonic state-space model of the control system, including an active control loop and a reactive control loop, is constructed to characterize the influence of the control strategy on the dynamic behavior of the system. Among them, the active control loop describes the dynamic response of power disturbance to angular frequency disturbance, and the reactive control loop describes the regulation relationship between voltage amplitude reference quantity and current and voltage disturbance.

[0011] S3. Based on the harmonic state-space model of the control system constructed in step S2, a virtual resistor R is introduced. v With virtual reactance L v The virtual impedance control loop is used to correct the voltage amplitude reference phasor of the reactive power control loop output; and combined with the dual closed-loop PI control structure consisting of the voltage outer loop and the current inner loop, the expression of the modulation signal disturbance phasor is derived; the modulation signal disturbance phasor is the disturbance of the AC terminal voltage of the grid converter, which is used to reflect the adjustment effect of the virtual impedance on the control output.

[0012] S4. Using the modulation signal perturbation phasor obtained in step S3 as input, substitute it into the harmonic state-space model of the main circuit constructed in step S1, and merge the harmonic state-space models of the control system and the main circuit to obtain the complete frequency domain admittance model Y of the grid converter considering the influence of virtual impedance. GSC Based on this, a grid impedance model T is introduced. g The open-loop gain T of the grid-connected converter system GFM =Y GSC ·T g It is used to characterize the frequency domain stability characteristics under the interaction between the converter and the power grid;

[0013] S5. The open-loop gain T obtained in step S4 GFM Plot its Nyquist curve and determine the resonance risk based on the Nyquist stability criterion.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] 1. Accurately characterize the impact of virtual impedance on system dynamics. Unlike traditional methods that only rely on fundamental frequency small-signal models, this approach models the main circuit and control system in a unified manner within a harmonic state-space framework. This fully reflects the dynamic adjustment effects of virtual resistance Rv and virtual reactance Lv on voltage reference quantities, modulation signals, and port current / voltage disturbances. It is particularly suitable for analyzing the multi-frequency coupling effects that may be induced after the introduction of virtual negative impedance.

[0016] 2. Achieve full-frequency domain coupling modeling of the control system and main circuit. Existing admittance models often simplify the control loop to static gain or ignore the dynamic interaction of the dual closed-loop structure. However, this scheme explicitly integrates virtual synchronous machine control, reactive / active loop, virtual impedance correction, and voltage-current dual closed-loop PI structure to construct a high-fidelity frequency domain admittance model Y. GSC This significantly improves the model's ability to reproduce actual dynamic behavior.

[0017] 3. Effectively reveals the resonance excitation mechanism under high R / X ratio power grids. Addressing the power coupling problem caused by high resistance ratios in medium- and low-voltage or weak power grids, this method introduces a power grid impedance model T... g And construct the open-loop gain T GFM =Y GSC ·T g It can clearly identify the interactive resonant frequency between the converter output admittance and the grid impedance in the frequency domain, overcoming the limitation of traditional time-domain simulation in locating the root cause of resonance.

[0018] 4. Provide a quantitative stability assessment method based on the Nyquist criterion. Unlike approaches that rely solely on simulation or empirical judgments, this method uses a T-squared criterion to assess stability. GFM The Nyquist curve, based on classical frequency domain stability theory, can be used to rigorously determine the stability of the system, providing early warning of potential resonance risks and offering a theoretical basis for setting the safety boundaries of control parameters (such as virtual impedance values).

[0019] In summary, this method can accurately characterize the dynamic interaction characteristics between grid-connected converters and the power grid under the influence of virtual impedance, and assess the resonance risk of grid-connected systems, thus providing theoretical support for the safe design and parameter optimization of power decoupling strategies in high R / X ratio power grids.

[0020] Preferably, in S1, the three-phase time-domain differential equation is:

[0021]

[0022] In the formula, L f For constructing AC filters for grid converters; i aca i acb i acc These are the alternating currents of phases a, b, and c, respectively; u aca u acb u acc These represent the AC terminal voltages of the grid converters for phases a, b, and c, respectively; u gaca u gacb u gacc denoted as phases a, b, and c of the AC grid voltage; d represents the differentiation operator; t represents time.

[0023] The single-phase equivalent time-domain model is as follows:

[0024]

[0025] In the formula u gac This refers to the AC mains voltage.

[0026] This approach, unlike traditional simplified models that ignore line parameters or use ideal power supply assumptions, establishes three-phase time-domain differential equations based on the actual main circuit structure. This truly reflects the dynamic coupling relationship between AC current and port voltage, improving the model's ability to reproduce physical processes.

[0027] 2. By utilizing three-phase symmetry, the complex three-phase system is simplified into a single-phase equivalent model, which significantly reduces the computational complexity without losing the main dynamic characteristics. This facilitates subsequent small-signal linearization and frequency domain analysis, thereby improving modeling efficiency and applicability.

[0028] Preferably, in S1, the harmonic state-space model of the main circuit is:

[0029] Δu gac =Δu ac -L f ΔSΔi ac ;

[0030] In the formula, Δu gac For AC grid voltage disturbance phasor; Δu ac Here, Δi represents the AC voltage perturbation phasor; ΔS represents the differential equivalent coefficient matrix of the time-frequency transformation; Δi represents the voltage perturbation phasor. ac This is the alternating current perturbation phasor.

[0031] This setup clearly expresses the relationship that AC terminal voltage disturbance is jointly determined by grid voltage disturbance and inductor voltage drop. Here, ΔS is the time-frequency transformation differential equivalent coefficient matrix, which reflects the dynamic interaction between different frequency components and helps to deeply understand the propagation path of multi-frequency disturbances.

[0032] Preferably, in S2, the active power control loop is used to establish the transfer function relationship between the power disturbance and the angular frequency disturbance of the grid converter, and its expression is:

[0033]

[0034] In the formula, Δω(s) is the frequency domain representation of the angular frequency disturbance; Δp(s) is the frequency domain representation of the power disturbance; ω0 is the rated angular frequency; J is the inertia coefficient; s is the Laplace operator; D p K is the damping coefficient; f This is the primary frequency modulation coefficient.

[0035] This setup differs from the traditional approach that simplifies frequency adjustment to a static droop relationship. Instead, this scheme constructs a closed-loop transfer function between Δω(s) and Δp(s) using the Laplace transform, explicitly introducing the inertia term J and the damping term D. p and the primary frequency modulation coefficient K fIt can accurately reflect the dynamic response process of the system under power disturbance, including inertial response and damping adjustment mechanism.

[0036] 2. The obtained model clearly expresses the working mechanism of "simulated inertia" and "frequency damping" in virtual synchronous machine control, and makes the influence of controller parameters on system dynamic performance clearly expressed mathematically, which helps to understand its functional contribution in power grid support.

[0037] Preferably, in S2, the transfer function of the active power control loop is also included. Converting to harmonic state-space form yields the angular frequency perturbation phasor E. Δθ Relationship with power disturbance phasor Δp:

[0038] E Δθ =-ΔS -1 (ω0(JΔS+D p I)+K ω I) -1 ΔP;

[0039] In the formula, I is the identity matrix.

[0040] Preferably, in S2, the reactive power control loop is used to establish the transfer function matrix relationship between the AC voltage amplitude reference phasor and the current voltage and current disturbance phasors, and its expression is:

[0041]

[0042] In the formula, Δu gacd_ref Here, K is the AC voltage amplitude reference phasor; K is the voltage droop coefficient of the reactive power control link; D q The variable is the reactive power control gain coefficient; Δ represents a small disturbance; the superscript s indicates that the variable is in the main circuit coordinate system; ΔS represents the differential equivalent coefficient matrix of the time-frequency transformation; u gacd with i acd Let u be the d-axis component of AC voltage and AC current, respectively. gacq with i acq These are the q-axis components of AC voltage and AC current, respectively; T q+ With T d+ These are the positive variation matrices of AC current and voltage dq, respectively; Δu gac For AC grid voltage disturbance phasor; Δi ac This is the alternating current perturbation phasor.

[0043] This setup enables: 1. Multi-frequency domain dynamic modeling of reactive power-voltage control. Unlike traditional methods that only analyze the outer loop voltage response at the fundamental frequency, this scheme employs a harmonic state-space framework, expressing the voltage amplitude reference quantity and current and voltage disturbance quantities in phasor form. It also introduces the time-frequency transformation differential equivalent coefficient matrix ΔS, which comprehensively captures the control response characteristics under disturbances at different frequencies, significantly improving the model's ability to describe the adaptability of complex power grid environments.

[0044] 2. Accurate characterization of coordinate transformation and coupling effects in reactive power control. The resulting model explicitly includes voltage and current components and positive transformation matrices in the dq coordinate system, accurately reflecting the dynamic coupling behavior of the three-phase system in the rotating coordinate system. It is particularly suitable for analyzing the cross-effects and nonlinear coupling problems caused by coordinate transformation under weak power grids or high R / X ratio conditions.

[0045] Preferably, in S3, the introduction of the virtual resistor R v With virtual reactance L v The virtual impedance control loop is configured to correct the voltage amplitude reference phasor output by the reactive power control loop as shown below:

[0046]

[0047] In the formula, E Δθ It is the angular frequency perturbation phasor.

[0048] This setup achieves two key advantages: 1. Precise dynamic correction of the voltage reference quantity by the virtual impedance. Unlike traditional methods that treat virtual impedance as a static gain or only as an equivalent at the fundamental frequency, this scheme explicitly constructs a mechanism for adjusting the voltage reference phasor by the virtual impedance under multi-frequency disturbances, accurately reflecting R... v and L v The effect of different frequencies on voltage output is particularly useful for analyzing unstable behavior that may be caused by virtual negative resistance.

[0049] 2. Revealing the suppression mechanism of virtual impedance on power coupling. The obtained model explicitly includes the compensation effect of virtual resistance and reactance terms on dq-axis voltage disturbances, by introducing... and These measures achieve an equivalent adjustment of the line resistance-inductance ratio (R / X), thereby theoretically weakening the coupling effect between active and reactive power and improving voltage support capability.

[0050] 3. Provides an integrable dynamic interface for the dual closed-loop control structure. The voltage reference quantity, corrected by the virtual impedance, can be directly used as the input of the voltage outer loop PI controller, forming a complete modulation signal generation path together with the current inner loop. This ensures that the entire control system maintains consistency in the harmonic state space, facilitating subsequent joint modeling with the main circuit model and enabling full system stability analysis.

[0051] Preferably, in S3, the expression for the modulation signal perturbation phasor is:

[0052]

[0053]

[0054]

[0055] In the formula, the superscript c indicates that the variable is a variable in the control system coordinate system; Δu ac The modulation signal perturbation phasor is consistent with the AC terminal voltage perturbation phasor of the grid converter; H i With H v These represent the interference Δi from the current signal, respectively. ac and voltage signal interference Δu gac To modulation signal interference Δu ac The gain matrix of G; i With G v These are the PI control gain coefficient matrices for the inner current loop and outer voltage loop, respectively; K id T is the decoupling coefficient matrix for the inner current loop; q With T d These are the AC current and voltage matrices, respectively; K ω The primary frequency modulation coefficient K f The corresponding parameters in the harmonic state-space model are physically identical.

[0056] This setup achieves two objectives: 1. Unified modeling of the dual-closed-loop control structure across multiple frequency domains. This is accomplished by introducing the control gain matrix G. i G v and the current inner loop decoupling coefficient matrix K id Within the harmonic state-space framework, the dynamic response of the dual closed-loop PI controller to current and voltage disturbances is explicitly expressed, which can comprehensively reflect the internal interaction mechanism of the control system.

[0057] 2. Accurately characterize the effect of virtual impedance on the control output. The resulting expression for the modulation signal disturbance explicitly includes R. v and L v The influence term indicates that the virtual impedance not only modifies the voltage reference value, but also directly participates in the dynamic feedback process of the control loop, thereby realizing the active shaping of the port impedance characteristics.

[0058] 3. Establish a dynamic interface between the control system and the main circuit. Modulation signal disturbance phasor Δu ac It is a key variable connecting the control system and the main circuit model, and its expression clearly describes the voltage disturbance Δu from the power grid in matrix form. gac and alternating current disturbance Δiac The combined effect on the converter output voltage provides a theoretical basis for subsequently substituting it into the main circuit harmonic state-space model and constructing a complete admittance model.

[0059] Preferably, in S4, the modulation signal perturbation phasor obtained in step S3 is used as input and substituted into the harmonic state-space model of the main circuit constructed in step S1. The harmonic state-space models of the combined control system and the main circuit are shown below:

[0060]

[0061] With this setup, the admittance matrix explicitly expresses the relationship between AC current disturbances and port voltage disturbances, and can comprehensively reflect the influence of virtual impedance, control parameters and filter inductance on the converter output admittance. It is especially suitable for revealing the resonant frequency points and negative damping characteristics that may occur under multi-frequency disturbances.

[0062] Preferably, in S5, the determination of resonance risk based on the Nyquist stability criterion includes: if the Nyquist curve revolves around the point (-1,0) on the complex plane, then the grid-connected system of the grid converter is determined to have resonance risk; otherwise, the system is determined to be stable. Attached Figure Description

[0063] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0064] Figure 1 This is a flowchart of the method;

[0065] Figure 2 This is a schematic diagram of the grid converter topology and control system considering virtual impedance in the embodiment.

[0066] Figure 3 This is a schematic diagram illustrating the effect of different virtual impedance values ​​on the admittance of the grid converter in the embodiment.

[0067] Figure 4 This is a schematic diagram of the resonance analysis of the grid-connected system with the grid converter in the embodiment. Detailed Implementation

[0068] The following detailed explanation illustrates the specific implementation methods:

[0069] Example:

[0070] like Figure 1 As shown, this embodiment discloses a method for analyzing the grid-connected resonance risk of a grid-connected converter considering virtual impedance, including the following steps:

[0071] S1. Based on the main circuit topology of the grid converter, a three-phase time-domain differential equation is established according to Kirchhoff's voltage law, and simplified to a single-phase equivalent time-domain model using three-phase symmetry. On this basis, the single-phase equivalent time-domain model is converted into a harmonic state-space model of the main circuit through small-signal linearization and harmonic state-space method, which is used to characterize the dynamic relationship between AC current disturbance, AC terminal voltage disturbance and grid voltage disturbance.

[0072] In practical implementation, the grid converter topology is as follows: Figure 2 As shown. Based on Kirchhoff's voltage law, the three-phase differential equations in the time domain of the main circuit of the grid converter are derived as follows:

[0073]

[0074] In the formula, L f For constructing AC filters for grid converters; i aca i acb i acc These are the alternating currents of phases a, b, and c, respectively; u aca u acb u acc These represent the AC terminal voltages of the grid converters for phases a, b, and c, respectively; u gaca u gacb u gacc denoted as phases a, b, and c of the AC grid voltage; d represents the differentiation operator; t represents time.

[0075] Because the three phases of a grid-connected converter are symmetrical, the complete characteristics of the grid-connected converter can be described by single-phase differential equations. Therefore, the above three-phase differential equations can be simplified to a single-phase equivalent time-domain model:

[0076]

[0077] In the formula i ac u ac u gac These are the phase a AC current, AC terminal voltage, and AC grid voltage, respectively. For simplicity, the subscript 'a' is omitted here.

[0078] Unlike traditional simplified models that ignore line parameters or use ideal power supply assumptions, this method establishes three-phase time-domain differential equations based on the actual main circuit structure, realistically reflecting the dynamic coupling relationship between AC current and port voltage, thus improving the model's ability to reproduce the physical process. By utilizing three-phase symmetry, the complex three-phase system is simplified into a single-phase equivalent model, significantly reducing computational complexity without sacrificing key dynamic characteristics. This facilitates subsequent small-signal linearization and frequency domain analysis, improving modeling efficiency and applicability.

[0079] To linearize and steady-state the single-phase time-domain differential equations of the grid converter, we use small-signal linearization and harmonic state-space methods to transform the single-phase differential equations of the grid converter into a harmonic state-space model of the main circuit.

[0080] Δu gac =Δu ac -L f ΔSΔi ac ;

[0081] In the formula, Δu gac For AC grid voltage disturbance phasor; Δu ac Here, Δi represents the AC voltage perturbation phasor; ΔS represents the differential equivalent coefficient matrix of the time-frequency transformation; Δi represents the voltage perturbation phasor. ac This is the alternating current perturbation phasor.

[0082] This clearly expresses the relationship that the AC terminal voltage disturbance is jointly determined by the grid voltage disturbance and the inductor voltage drop, where ΔS is the time-frequency transformation differential equivalent coefficient matrix, which reflects the dynamic interaction between different frequency components and helps to deeply understand the propagation path of multi-frequency disturbances.

[0083] S2. Based on the virtual synchronous machine control strategy, a harmonic state-space model of the control system, including an active control loop and a reactive control loop, is constructed to characterize the influence of the control strategy on the dynamic behavior of the system. The active control loop describes the dynamic response of power disturbance to angular frequency disturbance, and the reactive control loop describes the regulation relationship between voltage amplitude reference quantity and current and voltage disturbance.

[0084] In practical implementation, the active power control loop is used to establish the transfer function relationship between the power disturbance and the angular frequency disturbance of the grid converter, and its expression is:

[0085]

[0086] In the formula, Δω(s) is the frequency domain representation of the angular frequency disturbance; Δp(s) is the frequency domain representation of the power disturbance; ω0 is the rated angular frequency; J is the inertia coefficient; s is the Laplace operator; D p K is the damping coefficient; f This is the primary frequency modulation coefficient.

[0087] Unlike traditional methods that simplify frequency tuning to a static droop relationship, this scheme constructs a closed-loop transfer function between Δω(s) and Δp(s) using the Laplace transform, explicitly introducing the inertia term J and the damping term D. p and the primary frequency modulation coefficient K fThis model accurately reflects the dynamic response of the system under power disturbances, including inertial response and damping adjustment mechanisms. The resulting model clearly expresses the working mechanism of "simulated inertia" and "frequency damping" in virtual synchronous machine control, providing a clear mathematical expression of the influence of controller parameters on the system's dynamic performance, which helps to understand its functional contribution to power grid support.

[0088] The transfer function of the active control loop will also be... Converting to harmonic state-space form yields the angular frequency perturbation phasor E. Δθ Relationship with power disturbance phasor Δp:

[0089] E Δθ =-ΔS -1 (ω0(JΔS+D p I)+K ω I) -1 ΔP;

[0090] In the formula, I is the identity matrix.

[0091] In the dq coordinate system, AC power has the following relationship with AC current and voltage:

[0092]

[0093] In the formula, u gacd with i acd Let u be the d-axis component of AC voltage and AC current, respectively. gacq with i acq Let these be the q-axis components of AC voltage and AC current, respectively.

[0094] Based on the harmonic state-space model, the dq-axis components of AC voltage and AC current can be represented in matrix form, and further, the transfer matrices of angular frequency disturbance and AC voltage and current can be obtained:

[0095]

[0096]

[0097] In the formula, the superscript s indicates that the variable is in the main circuit coordinate system, and Δ represents a small disturbance. and Let dq be the steady-state phasor of the alternating current. and Let T be the steady-state phasor of the AC grid voltage along the dq axis. d+ With T d+ Let dq be the positive transformation matrix of alternating current and voltage, and ΔS represent the differential equivalent coefficient matrix of time-frequency transformation.

[0098] The reactive power control loop is used to establish the transfer function matrix relationship between the AC voltage amplitude reference phasor and the current voltage and current disturbance phasors, and its expression is:

[0099]

[0100] In the formula, Δu gacd_ref Here, K is the AC voltage amplitude reference phasor; K is the voltage droop coefficient of the reactive power control link; D q The variable is the reactive power control gain coefficient; Δ represents a small disturbance; the superscript s indicates that the variable is in the main circuit coordinate system; ΔS represents the differential equivalent coefficient matrix of the time-frequency transformation; u gacd with i acd Let u be the d-axis component of AC voltage and AC current, respectively. gacq with i acq These are the q-axis components of AC voltage and AC current, respectively; T q+ With T d+ These are the positive variation matrices of AC current and voltage dq, respectively; Δu gac For AC grid voltage disturbance phasor; Δi ac This is the alternating current perturbation phasor.

[0101] Unlike traditional methods that only analyze the outer-loop voltage response at the fundamental frequency, this scheme employs a harmonic state-space framework. It expresses the voltage amplitude reference quantity and the current and voltage disturbance quantities in phasor form, and introduces the time-frequency transformation differential equivalent coefficient matrix ΔS. This comprehensively captures the control response characteristics under disturbances at different frequencies, significantly improving the model's ability to describe the adaptability of complex power grid environments. The resulting model explicitly includes voltage and current components and positive transformation matrices in the dq coordinate system, accurately reflecting the dynamic coupling behavior of the three-phase system in the rotating coordinate system. It is particularly suitable for analyzing the cross-effects and nonlinear coupling problems caused by coordinate transformation under weak power grids or high R / X ratio conditions.

[0102] S3. Based on the harmonic state-space model of the control system constructed in step S2, a virtual resistor R is introduced. v With virtual reactance L v The virtual impedance control loop is used to correct the voltage amplitude reference phasor of the reactive power control loop output; and combined with the dual closed-loop PI control structure consisting of the voltage outer loop and the current inner loop, the expression of the modulation signal disturbance phasor is derived; the modulation signal disturbance phasor is the disturbance of the AC terminal voltage of the grid converter, which is used to reflect the adjustment effect of the virtual impedance on the control output.

[0103] In specific implementation, the introduction of virtual resistance R v With virtual reactance L v The virtual impedance control loop is configured to correct the voltage amplitude reference phasor output by the reactive power control loop as shown below:

[0104]

[0105] In the formula, E Δθ It is the angular frequency perturbation phasor.

[0106] Unlike traditional methods that treat virtual impedance as static gain or only as an equivalent at the fundamental frequency, this scheme explicitly constructs a virtual impedance adjustment mechanism for the voltage reference phasor under multi-frequency disturbances, which can accurately reflect R. v and L v The influence of virtual resistance on voltage output at different frequencies is particularly applicable to analyzing the instability that may be caused by virtual negative resistance. The resulting model explicitly includes the compensation effect of virtual resistance and reactance terms on dq-axis voltage disturbances, by introducing... and These measures achieve an equivalent adjustment of the line resistance-inductance ratio (R / X), thereby theoretically weakening the coupling effect between active and reactive power and improving voltage support capability. Furthermore, the voltage reference value corrected by this virtual impedance can be directly used as the input to the voltage outer-loop PI controller, forming a complete modulation signal generation path together with the current inner loop. This ensures the consistency of the entire control system in the harmonic state space, facilitating subsequent joint modeling with the main circuit model and enabling system-wide stability analysis.

[0107] Based on the corrected AC voltage amplitude reference phasor, the expression for the modulation signal perturbation phasor of the voltage and current dual closed-loop output is further derived as follows:

[0108]

[0109]

[0110]

[0111] In the formula, the superscript c indicates that the variable is a variable in the control system coordinate system; Δu ac The modulation signal perturbation phasor is consistent with the AC terminal voltage perturbation phasor of the grid converter; H i With H v These represent the interference Δi from the current signal, respectively. ac and voltage signal interference Δu gac To modulation signal interference Δu ac The gain matrix of G; i With G v These are the PI control gain coefficient matrices for the inner current loop and outer voltage loop, respectively; K id T is the decoupling coefficient matrix for the inner current loop; q With T d These are the AC current and voltage matrices, respectively; K ω The primary frequency modulation coefficient Kf The corresponding parameters in the harmonic state-space model are physically identical.

[0112] By introducing the control gain matrix G i G v and the current inner loop decoupling coefficient matrix K id Within the harmonic state-space framework, the dynamic response of the dual-closed-loop PI controller to current and voltage disturbances is explicitly expressed, comprehensively reflecting the internal interaction mechanism of the control system. The resulting expression for the modulation signal disturbance explicitly includes R... v and L v The influence term indicates that the virtual impedance not only modifies the voltage reference value but also directly participates in the dynamic feedback process of the control loop, thereby actively shaping the port impedance characteristics. Furthermore, the modulation signal perturbation phasor Δu ac It is a key variable connecting the control system and the main circuit model, and its expression clearly describes the voltage disturbance Δu from the power grid in matrix form. gac and alternating current disturbance Δi ac The combined effect on the converter output voltage provides a theoretical basis for subsequently substituting it into the main circuit harmonic state-space model and constructing a complete admittance model.

[0113] S4. Using the modulation signal perturbation phasor obtained in step S3 as input, substitute it into the harmonic state-space model of the main circuit constructed in step S1, and merge the harmonic state-space models of the control system and the main circuit to obtain the complete frequency domain admittance model Y of the grid converter considering the influence of virtual impedance. GSC Based on this, a grid impedance model T is introduced. g The open-loop gain T of the grid-connected converter system GFM =Y GSC ·T g It is used to characterize the frequency domain stability characteristics under the interaction between the converter and the power grid;

[0114] In practical implementation, the harmonic state-space model of the combined control system and the main circuit is shown below:

[0115]

[0116] In this way, the admittance matrix explicitly expresses the relationship between AC current disturbance and port voltage disturbance, and can comprehensively reflect the influence of virtual impedance, control parameters and filter inductance on converter output admittance. It is especially suitable for revealing the resonant frequency point and negative damping characteristics that may occur under multi-frequency disturbance.

[0117] like Figure 3 As shown, based on the derived admittance matrix of the grid converter, a Bode plot of the grid converter considering virtual impedance can be plotted to analyze the influence of virtual impedance on the admittance of the grid converter system.

[0118] Further derivation of the open-loop gain of the grid-connected converter system is as follows:

[0119] T GFM =Y GSC Z g ;

[0120] In the formula, T g This is the power grid impedance matrix. It should be noted that the power grid impedance matrix is ​​an industry standard term, referring to the equivalent impedance matrix of the power grid in the frequency domain.

[0121] S5. The open-loop gain T obtained in step S4 GFM ,like Figure 4 As shown, the Nyquist curve of the open-loop gain is plotted, and the resonance risk is determined based on the Nyquist stability criterion. The resonance risk determination based on the Nyquist stability criterion includes: if the Nyquist curve revolves around the point (-1,0) on the complex plane, then the grid-connected system of the grid-connected converter is determined to have resonance risk; otherwise, the system is determined to be stable.

[0122] Unlike traditional methods based solely on fundamental frequency small-signal models, this approach models the main circuit and control system within a unified harmonic state-space framework. This fully reflects the dynamic adjustment effects of virtual resistance Rv and virtual reactance Lv on voltage reference values, modulation signals, and port current / voltage disturbances, making it particularly suitable for analyzing multi-frequency coupling effects that may be induced by the introduction of virtual negative impedance. Furthermore, existing admittance models often simplify the control loop to static gain or neglect the dynamic interaction of the dual-closed-loop structure. This approach, however, explicitly integrates virtual synchronous machine control, reactive / active loops, virtual impedance correction, and a voltage-current dual-closed-loop PI structure to construct a high-fidelity frequency domain admittance model Y. GSC This significantly improves the model's ability to reproduce actual dynamic behavior. Furthermore, addressing the power coupling problem caused by high resistance ratios in low-voltage or weak voltage power grids, this method introduces a grid impedance model T. g And construct the open-loop gain T GFM =Y GSC ·T g This method can clearly identify the interactive resonant frequency between the converter output admittance and the grid impedance in the frequency domain, overcoming the limitation of traditional time-domain simulation in locating the root cause of resonance. Furthermore, unlike approaches that rely solely on simulation or experience to judge stability, this method plots T... GFM The Nyquist curve, based on classical frequency domain stability theory, can be used to rigorously determine the stability of the system, providing early warning of potential resonance risks and offering a theoretical basis for setting the safety boundaries of control parameters (such as virtual impedance values).

[0123] This method can accurately characterize the dynamic interaction characteristics between grid-connected converters and the power grid under the influence of virtual impedance, and assess the resonance risk of grid-connected systems, thus providing theoretical support for the safe design and parameter optimization of power decoupling strategies in high R / X ratio power grids.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1.A method for grid-connected resonance risk analysis of a network-forming converter considering virtual impedance, characterized in that, The method comprises the following steps: S1, based on the main circuit topology of the grid-connected converter, three-phase time-domain differential equations are established according to Kirchhoff's voltage law, and a single-phase equivalent time-domain model is simplified by using three-phase symmetry; on this basis, the single-phase equivalent time-domain model is converted into a harmonic state space model of the main circuit by small signal linearization and harmonic state space method, which is used to represent the dynamic relationship between AC current disturbance, AC terminal voltage disturbance and grid voltage disturbance; S2, based on the virtual synchronous machine control strategy, a harmonic state space model of the control system including active control loop and reactive control loop is constructed, which is used to depict the influence of the control strategy on the dynamic behavior of the system; wherein the active control loop describes the dynamic response of power disturbance to angular frequency disturbance, and the reactive control loop describes the adjustment relationship of voltage amplitude reference quantity to current and voltage disturbance; S3、On the basis of the harmonic state space model of the control system constructed in step S2, a virtual impedance control link composed of a virtual resistance R v and a virtual reactance L v is introduced to modify the voltage amplitude reference phasor output by the reactive power control loop; and in combination with the double closed-loop PI control structure composed of the voltage outer loop and the current inner loop, an expression of a modulation signal disturbance phasor is derived; the modulation signal disturbance phasor is a disturbance quantity of the AC terminal voltage of the grid-connected converter and is used to reflect the adjustment of the virtual impedance on the control output. S4, taking the modulated signal disturbance phasor obtained in step S3 as input, substituting into the harmonic state space model of the main circuit constructed in step S1, merging the harmonic state space models of the control system and the main circuit, thereby obtaining a complete frequency domain admittance model Y of the grid-connected converter considering the influence of the virtual impedance GSC ; on this basis, the grid impedance model T g is introduced, and the open-loop loop gain T GFM of the grid-connected converter system is constructed = Y GSC ·T g , which is used to represent the frequency domain stability characteristics of the interaction between the converter and the grid; S5, based on the open loop gain T obtained in step S4 GFM The Nyquist curve is plotted and the risk of resonance is determined according to the Nyquist stability criterion. 2.The method of claim 1, wherein the method further comprises: determining a virtual impedance of the grid-connected converter; and determining the grid-connected converter resonance risk based on the virtual impedance. In S1, the three-phase time-domain differential equations are: In the formula, L f is a grid-connected converter AC filter; i aca , i acb , i acc is the a, b, c phase AC current; u aca , u acb , u acc is the a, b, c phase grid-connected converter AC terminal voltage; u gaca , u gacb , u gacc is the a, b, c phase AC grid voltage; d is a derivative operator; t is time; The single-phase equivalent time-domain model is: wherein u gac is the alternating mains voltage. 3.The method of claim 2, wherein the method further comprises: determining a virtual impedance of the grid-connected converter; and determining the grid-connected converter resonance risk based on the virtual impedance. In S1, the harmonic state space model of the main circuit is: Δu gac = Δu ac - L f ΔSΔi ac ; where Δu gac is the AC grid voltage disturbance phasor; Δu ac is the AC voltage disturbance phasor; ΔS represents the differential equivalent coefficient matrix of the time-frequency transform; Δi ac is the AC current disturbance phasor. 4.The method of claim 3, wherein the method further comprises: determining a virtual impedance of the grid-connected converter; and determining the grid-connected converter resonance risk based on the virtual impedance. In S2, the active control loop is used to establish the transfer function relationship between the power disturbance of the grid-connected converter and the angular frequency disturbance, and its expression is: where Δω(s) is the frequency domain representation of the angular frequency disturbance; Δp(s) is the frequency domain representation of the power disturbance quantity; ω0is the rated angular frequency; J is the inertia coefficient; s is the Laplace operator; D p is the damping coefficient; K f is the primary frequency modulation coefficient. 5.The method of claim 4, wherein the method further comprises: determining a virtual impedance of the grid-connected converter; and determining the grid-connected converter resonance risk based on the virtual impedance. In S2, the transfer function of the active control loop Transformed into the harmonic state-space form, the angular frequency disturbance phasor E Δθ The relationship between the power disturbance phasor Δp: E Δθ = - ΔS -1 (ω0(JΔS+D p I)+K ω I) -1 ΔP; Wherein, I is a unit matrix. 6.The method of claim 5, wherein the method further comprises: determining a virtual impedance of the grid-connected converter; and determining the grid-connected converter resonance risk based on the virtual impedance. In S2, the reactive control loop is used to establish the transfer function matrix relationship between the AC voltage amplitude reference phasor and the current voltage, current disturbance phasor, and its expression is: where Δu gacd_ref is the AC voltage amplitude reference phasor; K is the voltage droop coefficient of the reactive power control loop; D q is the reactive power control gain coefficient; Δ denotes a small perturbation; the superscript s indicates that the variable is in the primary circuit coordinate system; ΔS represents the differential equivalent coefficient matrix of the time-frequency transformation; u gacd and i acd are the d-axis components of the AC voltage and AC current, respectively; u gacq and i acq are the q-axis components of the AC voltage and AC current, respectively; T q+ and T d+ are the dq positive transformation matrices of the AC current and voltage, respectively; Δu gac is the AC grid voltage disturbance phasor; Δi ac is the AC current disturbance phasor. 7.The method of claim 6, wherein the method further comprises: determining a virtual impedance of the grid-connected converter; and determining the grid-connected converter resonance risk based on the virtual impedance. In S3, the introduction by the virtual resistance R v and the virtual reactance L v The virtual impedance control link is composed of a virtual resistance R and a virtual reactance L. The voltage amplitude reference phasor output by the reactive power control loop is modified as follows: In the formula, E Δθ is the angular frequency perturbation phasor. 8.The method of claim 7, wherein the method further comprises: determining a virtual impedance of the grid-connected converter; and determining the grid-connected converter resonance risk based on the virtual impedance. In S3, the expression of the modulation signal disturbance phasor is: wherein the superscript c indicates that the variable is in the coordinate system of the control system; Δu ac is the modulation signal disturbance phasor, which is consistent with the network-forming converter AC terminal voltage disturbance phasor; H i and H v respectively represent the gain matrix from the current signal disturbance Δi ac and the voltage signal disturbance Δu gac to the modulation signal disturbance Δu ac ; G i and G v are respectively the PI control gain coefficient matrix of the current inner loop and the voltage outer loop; K id is the current inner loop decoupling coefficient matrix; T q and T d are respectively the AC current and voltage matrix; K ω is the primary frequency modulation coefficient K f is the corresponding parameter in the harmonic state space model, and the two are consistent in physical meaning. 9.The method of claim 8, wherein the method further comprises: determining a virtual impedance of the grid-connected converter; and determining the grid-connected converter resonance risk based on the virtual impedance. In S4, the modulation signal disturbance phasor obtained in step S3 is taken as input and substituted into the harmonic state space model of the main circuit constructed in step S1, and the harmonic state space models of the control system and the main circuit are combined as follows: 10.The method of claim 9, wherein the method further comprises: determining a virtual impedance of the grid-connected converter; and determining the grid-connected converter resonance risk based on the virtual impedance. In S5, the resonance risk judgment according to the Nyquist stability criterion comprises: if the Nyquist curve surrounds the point (-1, 0) on the complex plane, it is judged that the grid-connected converter grid-connected system has resonance risk; otherwise, it is judged that the system is stable.

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