A [PQ]-[ωV] Modeling Method for Wire-Modulated Hybrid Converter Systems Based on Port Impedance-Amplitude-Frequency Mapping

Abstract

This invention discloses a [PQ]-[ωV] modeling method for a grid-connected hybrid converter system based on port impedance-amplitude-frequency mapping. The method first obtains the u-i admittance model of the grid-connected converter in the dq coordinate system and the u-i impedance model of the grid-connected converter. Then, based on the steady-state operating point, it establishes a mapping relationship between the port voltage vector and amplitude-frequency domain variables, transforming the voltage in the dq coordinate system into amplitude and frequency disturbances. Next, it performs small-signal linearization on the active and reactive power of the converter around the steady-state operating point to obtain the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance, and further obtains the equivalent port [PQ]-[ωV] model. This method allows for mutual conversion and cross-validation between the two types of models, solving the problem of the two types of models being independent and lacking correlation in existing technologies.

Description

Technical Field

[0001] This invention relates to a grid-connected converter modeling method, specifically a [PQ]-[ωV] modeling method for a grid-connected hybrid converter system based on port impedance-amplitude frequency mapping, belonging to the field of microgrid and power control technology. Background Technology

[0002] Distributed generation and energy storage systems are connected to the AC grid via power electronic converters and can be classified into two types based on control characteristics: grid-following (GFL) and grid-forming (GFM). With the increasing proportion of converter-based resources, the overall inertia and damping of modern power systems have significantly decreased, leading to extremely low frequencies, increased rates of frequency change, and increased system vulnerability. To address this issue, various enhanced virtual inertia techniques have been proposed, including virtual synchronous generator (VSG) control and inertia simulation methods. Hybrid GFL / GFM systems are the mainstream form. However, improper converter controller parameter tuning and network impedance characteristics can induce oscillations during disturbances, threatening system stability. Therefore, researching modeling methods for dynamic response analysis and stability assessment is of great significance.

[0003] Existing classic small-signal linearization analysis methods for converter systems mainly include three categories: eigenvalue analysis, impedance-based methods, and [PQ]-[ωV]-based methods.

[0004] Eigenvalue analysis relies on constructing a state-space model of the system to analyze the influence of various parameters on dynamic characteristics. However, in large or complex systems, the order of the state-space matrix is ​​high, resulting in a heavy computational burden. Furthermore, the state-space model lacks intuitive physical meaning and is difficult to directly reveal the interaction mechanism between subsystems.

[0005] Impedance-based methods derive impedance models by establishing the transfer function relationship between voltage and current. They offer advantages such as clear physical meaning and strong intuitiveness, and can be combined with pole plots, the Nyquist criterion, or Bode plots for stability and harmonic resonance analysis. Impedance models describe the input-output characteristics of converters at the ui port level and have become one of the mainstream tools for converter stability analysis.

[0006] In power system research, variables such as voltage (V), frequency (f), active power (P), and reactive power (Q) often receive more attention. Studies have successively proposed P-ω modeling and [PQ]-[ωV] modeling methods to analyze the dynamic response characteristics of power and frequency, as well as the impact of key parameters on the frequency and amplitude of active power oscillations. The [PQ]-[ωV] modeling method directly uses power, voltage, and frequency as port variables, which can intuitively characterize the power oscillation and stability characteristics of the system in the low-to-mid-frequency range (from a few hertz to tens of hertz), and can serve as a standard model for studying power oscillation problems in converter systems.

[0007] However, existing [PQ]-[ωV] modeling methods have the following shortcomings:

[0008] 1. Existing [PQ]-[ωV] models focus more on grid-connected converter systems, with less research on grid-synchronized converter systems. Grid-synchronized and grid-connected converters differ fundamentally in their control structures: grid-synchronized converters track the grid phase through a phase-locked loop (PLL), and their dynamic behavior is significantly affected by the PLL parameters; while grid-connected converters autonomously establish voltage and frequency references through a power synchronization loop. Directly transplanting the [PQ]-[ωV] modeling approach from grid-connected converters to grid-synchronized converter systems cannot accurately reflect the impact of the PLL on power dynamics.

[0009] 2. Existing converter [PQ]-[ωV] models neglect inner-loop voltage and current control, thus failing to reflect the interaction between controls at different time scales and affecting model accuracy. In actual grid-connected converter systems, phase-locked loops, power control loops, voltage control loops, and current control loops operate at different time scales, and their coupling effects have a non-negligible impact on system dynamic characteristics.

[0010] 3. The relationship between the ui admittance of grid-connected converters, the impedance model of grid-connected converters, the admittance model of passive networks, and the port [PQ]-[ω V] model has not been revealed, and no research has been conducted to establish the relevant mapping relationship between the two. This results in the two types of models being independent of each other, unable to be converted into each other, and unable to be cross-validated.

[0011] The aforementioned technical issues make it difficult for existing methods to simultaneously meet the dual requirements of fully encompassing multi-timescale control characteristics in [PQ]-[ωV] modeling of grid-connected hybrid converter systems and the inability of UI models to directly characterize power-frequency / voltage port variables. Summary of the Invention

[0012] To address the problems existing in the prior art, the present invention aims to provide a [PQ]-[ωV] modeling method for grid-connected hybrid converter systems based on port impedance-amplitude frequency mapping. This method rapidly establishes the [PQ]-[ωV] admittance / impedance model of the grid-connected converter based on the established admittance model and impedance model of the grid-connected converter and the derived correlation mapping relationship. Compared with existing research, the modeling method provided by this invention includes the characteristics of multi-timescale control loops such as voltage and current dual closed loops and power control loops, accurately reflecting the dynamic characteristics of the system over a wide frequency band. It integrates the advantages of admittance modeling and the direct characterization of power, voltage, and frequency variables by [PQ]-[ωV].

[0013] To achieve the above technical objectives, this invention provides a [PQ]-[ωV] modeling method for a hybrid converter system based on port impedance-amplitude frequency mapping, comprising: Step S1: Obtain the ui admittance model of the grid-type converter in the dq coordinate system; Step S2: Based on the steady-state operating point, establish the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and transform the voltage in the dq coordinate system into disturbances in amplitude and frequency. Step S3: Perform small-signal linearization on the active and reactive power of the converter around the steady-state operating point to obtain the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance. Step S4: Combining the ui admittance model, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance, obtain the equivalent [PQ]-[ω V] port admittance model.

[0014] The technical solution provided by this invention firstly describes the transmission relationship between voltage disturbance and current response based on the existing grid-connected converter ui admittance model. Further, by establishing the coordinate transformation relationship between the port voltage in the dq coordinate system and the voltage amplitude and angular frequency in polar coordinates, the representation of the voltage variable is converted from dq components to a more intuitive amplitude-frequency form. Finally, based on the instantaneous power definition, small-signal linearization is performed around the steady-state operating point. Combining the aforementioned ui admittance model and the voltage transformation in the dq coordinate system into amplitude and frequency disturbances, a [PQ]-[ωV] admittance matrix is ​​obtained, with power disturbance as output and voltage amplitude disturbance and angular frequency disturbance as input. This achieves a direct mapping from the ui admittance model to the [PQ]-[ωV] admittance model.

[0015] As a preferred embodiment, the expression for the admittance model of the grid-connected converter ui is: Formula 1: ; The expression for the impedance model of the grid converter ui is: Formula 2: ; In Equations 1 and 2, in Equation 1, , , ,Y fi (s) represents the admittance of the grid converter in the dq coordinate system. "~" indicates a small perturbation near the equilibrium point. To match the output current of the grid-connected converter, and These are the components of the output current on the d-axis and q-axis. For current reference quantity, and The components of the reference current on the d-axis and q-axis; To match the output voltage of the grid-connected converter, and These are the components of the output voltage on the d-axis and q-axis; It is a 2×2 transfer function matrix; , , Z mi (s) represents the impedance of the grid-type converter in the dq coordinate system. , To match the output current of the grid-connected converter, and These are the components of the output current on the d-axis and q-axis. For voltage reference quantity, and The components of the reference current on the d-axis and q-axis; For the output voltage of the grid-type converter, and These are the components of the output voltage on the d-axis and q-axis. It is a 2×2 transfer function matrix.

[0016] As a preferred embodiment, the ui admittance model can be equivalent to an ideal current source and admittance Y. fi The parallel structure of (s) is expressed as follows: Formula 3: ; Formula 4: ; Formula 5: ; Formula 6: ; The admittance matrix Y fi (s) includes the steady-state rotation matrix caused by the phase angle difference between the phase dynamics of the phase-locked loop and the phase of the physical system. and steady-state cross-coupling terms caused by angular perturbations and Its expression process is as follows: Formula 7: ; Formula 8: ; Formula 9: ; Formula 10: ; Formula 11: ; In equations 3-11, L f and C f Here, s represents the converter filter inductor and capacitor, s is the Apras operator, and ω is the rated angular frequency. , V fi D represents the voltage amplitude. d and D q This represents the duty cycle components on the d-axis and q-axis, with the subscript "0" indicating the steady-state value; G ci =G ci (s)·I, where I is a 2×2 identity matrix, G ci (s)=(k pi +k ii / s) and G PQ (s)=(k pPQ +k iPQ / s) represent the PI controller transfer functions of the current loop and power tracking control loop, respectively; G PLL (s)=(k pθ +k iθ / s) represents the transfer function of the PI controller in the phase-locked loop; the superscript " s "" represents the value of any vector from the system coordinate system after transformation to the control coordinate system; As a preferred embodiment, the impedance model of the grid converter ui can be equivalent to an ideal voltage source and impedance Z. mi The cascade structure of (s) is expressed as follows: Formula 12: ; Formula 13: ; Formula 14: ; Formula 15: ; In equations 12-15, G cv =G ci (s)G vv (s)I, G vv (s)=(k pv +kiv / s) represents the transfer function of the PI controller in the voltage control loop. G represents the transfer function of the power loop filter. VSG = diag{1 / (s(Js+D p )), n q}, where J and D p These are the inertia coefficient and damping coefficient for the control of the network-type virtual synchronous machine, respectively. Formula 16: ; Equation 17: ; Formula 18: ;

[0017] The passive network admittance model is expressed as follows: Formula 19: ; In equations 16-19, This represents the current flowing from node i to node j; and Y represents the voltage at node i and node j, respectively. ij (s) is the node admittance matrix of the passive network.

[0018] In this invention, the grid-connected converter is represented as a current source connected in parallel with admittance. The admittance includes contributions from the filter inductor, phase-locked loop (PLL) dynamics, and cross-coupling terms. If the contribution of the PLL dynamics is ignored, the model cannot reflect the PLL's influence on the system's low-frequency oscillation characteristics, leading to overly optimistic stability analysis results. If the contribution of the cross-coupling terms is ignored, the model cannot accurately describe the coupling between the d and q axes, affecting the prediction accuracy of wideband dynamic characteristics.

[0019] As a preferred embodiment, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables is achieved through a linear transformation matrix. Specifically, it means: Step S2-1: The voltage vector at any port can be expressed as... ,in The phase angle difference between the voltage phasor and the dq frame angle is expressed as follows: Formula 20: ; Step S2-2: Linear transformation matrix between the dq coordinate system and the amplitude-frequency domain variables Defined as the mapping matrix from voltage amplitude perturbation and frequency perturbation to voltage perturbation in the dq coordinate system, its expression is: Equation 21: , ; Equation 22: ; In equations 20-22, ω fi The angular frequency of the output voltage. , V represents the voltage amplitude, and the subscript "0" represents the steady-state value.

[0020] As a preferred embodiment, the process for establishing the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance is as follows: Step S3-1: Calculate the active and reactive power of the i-th converter. The process is as follows: Equation 23: ; Step S3-2: Perform small-signal linearization around the steady-state operating point and obtain the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance. The calculation process is as follows: Formula 24: ; Formula 25: .

[0021] As a preferred embodiment, the process of establishing the direct analytical mapping between the port power disturbance and the voltage amplitude-frequency domain disturbance is as follows: Simultaneously establishing the grid-connected converter ui admittance model, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation relationship between the power disturbance and the voltage amplitude-frequency domain disturbance, the equivalent [PQ]-[ωV] port admittance model of the grid-connected converter is calculated. The calculation process is as follows: Equation 26: ; Wherein, the equivalent port admittance matrix The transfer function matrix is ​​represented as follows: Its parsing expression is: Equation 27: .

[0022] As a preferred embodiment, the process of establishing the direct analytical mapping between the port power disturbance and the voltage amplitude-frequency domain disturbance is as follows: By combining the ui impedance model of the grid-connected converter, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance, the equivalent [PQ]-[ωV] port impedance model of the grid-connected converter is calculated. The calculation process is as follows: Equation 28: ; in, Equivalent port admittance matrix The transfer function matrix is ​​represented as follows: Its analytical expression is: Equation 29: ; ; ; In equations 28 and 29, ω mi V is the angular frequency of the output voltage. mi This indicates the voltage amplitude, and the subscript "0" indicates the steady-state value.

[0023] As a preferred embodiment, the process of establishing the direct analytical mapping between the port power disturbance and the voltage amplitude-frequency domain disturbance is as follows: Simultaneously establishing the passive network ui admittance model, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation relationship between the power disturbance and the voltage amplitude-frequency domain disturbance, the equivalent [PQ]-[ωV] port impedance model of the passive network is calculated. The calculation process is as follows: Formula 30: ; in, and This indicates the angular frequency and voltage amplitude at the point of common coupling (PCC) and the power grid; The analytical expression for the equivalent matrix is: Equation 31: ; Equation 32: ; Equation 33: ; Equation 34: , ; In equations 30-34, i gd and i gq V represents the d-axis and q-axis components of the grid-connected current. pd and V pq V represents the d-axis and q-axis components of the PCC voltage. gd and V gq These are the d-axis and q-axis components of the grid voltage, with the subscript "0" indicating the steady-state value.

[0024] In this invention, a universal steady-state phase angle is used for dq transformation. This process makes the model applicable to any dq coordinate system orientation, enhancing the model's versatility and scalability. If a coordinate system with specific axis alignment is used, such as the d-axis aligned with the voltage vector, the model is only applicable to that specific coordinate system orientation, limiting the model's applicability in different application scenarios.

[0025] The reason why the preparation method provided by this invention can establish an accurate [PQ]-[ωV] admittance model for grid-connected converters is mainly due to the following: First, this invention directly derives the model based on the existing ui admittance model of grid-connected converters, making full use of the mature achievements of existing ui admittance modeling, without the need to reconstruct a complex internal control loop model; secondly, by establishing the coordinate transformation relationship between the dq coordinate system and the polar coordinate system, the direct conversion of the voltage variable representation is realized; in addition, based on the small-signal linearization method of instantaneous power definition, an accurate linear relationship is established between power disturbance, voltage amplitude disturbance, and frequency disturbance. In summary, this invention directly converts the existing ui admittance model into a [PQ]-[ωV] admittance model through the port admittance-amplitude-frequency mapping relationship, retaining the multi-time-scale control loop characteristics of the original model, while realizing the direct characterization of power, voltage, and frequency variables.

[0026] Compared with existing technologies, the beneficial technical effects of the technical solution provided by this invention are as follows:

[0027] 1) The technical solution provided by this invention establishes an analytical mapping relationship between the ui admittance model of the grid converter and the [PQ]-[ωV] admittance model, so that the two types of models can be converted and cross-validated, which solves the problem that the two types of models are independent and lack correlation in the prior art.

[0028] 2) In the technical solution provided by the present invention, since the ui admittance model itself includes the characteristics of multiple time-scale control loops such as phase-locked loop control, voltage and current dual closed-loop control and power control loop, there is no need to re-derive the contribution of each control loop in the [PQ]-[ω V] modeling, thus overcoming the defect of the existing [PQ]-[ω V] model that ignores the inner loop control.

[0029] 3) The [PQ]-[ω V] admittance model established by the technical solution provided by this invention directly uses power, frequency and voltage as port variables, which combines the completeness of admittance modeling with the advantage of the [PQ]-[ω V] model directly representing power, voltage and frequency variables, providing a more intuitive and effective tool for power oscillation analysis and stability assessment of grid-connected converter systems. Attached Figure Description

[0030] Figure 1 For the [PQ]-[ωV] admittance model Y fai (s) Frequency sweep verification diagram; in, Figure 1 (a) Figure 1 (b) Figure 1 (c) Figure 1 (d) represent Y fai (s) matrix four elements Y pω YpV Y Qω Y QV The frequency sweep verification diagram; Figure 2 For the [PQ]-[ωV] impedance model Z mi (s) Frequency sweep verification diagram; in, Figure 2 (a) Figure 2 (b) Figure 2 (c) Figure 2 (d) represents Z mai (s) matrix four elements Z pω Z pV Z Qω Z QV The frequency sweep verification diagram; Figure 3 The proportional gain k of the phase-locked loop pθ [0.01, 0.1] Root locus comparison chart; in, Figure 3 (a) is based on the traditional impedance model. Figure 3 (b) Based on the proposed [PQ]-[ωV] admittance model; Figure 4 The damping coefficient D p Comparison chart of root locus ∈ [700, 900]; in, Figure 4 (a) Based on the traditional impedance model, Figure 4 (b) Based on the proposed [PQ]-[ωV] impedance model; Figure 5 The diagram shows the hardware-in-the-loop experimental results for the active power waveform control. Figure 5 (a) indicates that the grid-connected converter is at k at 5s. pθ The graph showing the process of decreasing from 0.03 to 0.02. Figure 5 (b) indicates that the grid converter is at 6s D p The process diagram of reducing from 860 to 850. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the present invention more apparent, exemplary embodiments according to the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely a part of the embodiments of the present invention, and not all of the embodiments of the present invention. It should be understood that the present invention is not limited to the exemplary embodiments described herein. Based on the embodiments of the present invention described herein, all other embodiments obtained by those skilled in the art without inventive effort should fall within the protection scope of the present invention.

[0032] Example 1

[0033] This embodiment provides a [PQ]-[ωV] modeling method for a root-structured hybrid converter system based on port impedance-amplitude frequency mapping, including: Step S1: Obtain the ui admittance model of the grid-type converter in the dq coordinate system; Step S2: Based on the steady-state operating point, establish the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and transform the voltage in the dq coordinate system into disturbances in amplitude and frequency. Step S3: Perform small-signal linearization on the active and reactive power of the converter around the steady-state operating point to obtain the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance. Step S4: Combining the ui admittance model, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance, obtain the equivalent [PQ]-[ω V] port admittance model.

[0034] The technical solution provided by this invention firstly describes the transmission relationship between voltage disturbance and current response based on the existing grid-connected converter ui admittance model. Further, by establishing the coordinate transformation relationship between the port voltage in the dq coordinate system and the voltage amplitude and angular frequency in polar coordinates, the representation of the voltage variable is converted from dq components to a more intuitive amplitude-frequency form. Finally, based on the instantaneous power definition, small-signal linearization is performed around the steady-state operating point. Combining the aforementioned ui admittance model and the voltage transformation in the dq coordinate system into amplitude and frequency disturbances, a [PQ]-[ωV] admittance matrix is ​​obtained, with power disturbance as output and voltage amplitude disturbance and angular frequency disturbance as input. This achieves a direct mapping from the ui admittance model to the [PQ]-[ωV] admittance model.

[0035] As a preferred embodiment, the expression for the admittance model of the grid-connected converter ui is: Formula 1: ; The expression for the impedance model of the grid converter ui is: Formula 2: ; In Equations 1 and 2, in Equation 1, , , ,Y fi (s) represents the admittance of the grid converter in the dq coordinate system. "~" indicates a small perturbation near the equilibrium point. To match the output current of the grid-connected converter, and These are the components of the output current on the d-axis and q-axis. For current reference quantity, and The components of the reference current on the d-axis and q-axis; To match the output voltage of the grid-connected converter, and These are the components of the output voltage on the d-axis and q-axis. It is a 2×2 transfer function matrix; , , Z mi (s) represents the impedance of the grid-type converter in the dq coordinate system. , To match the output current of the grid-connected converter, and These are the components of the output current on the d-axis and q-axis. For voltage reference quantity, and The components of the reference current on the d-axis and q-axis; For the output voltage of the grid-type converter, and These are the components of the output voltage on the d-axis and q-axis. It is a 2×2 transfer function matrix.

[0036] As a preferred embodiment, the ui admittance model can be equivalent to an ideal current source and admittance Y. fi The parallel structure of (s) is expressed as follows: Formula 3: ; Formula 4: ; Formula 5: ; Formula 6: ; The admittance matrix Y fi (s) includes the steady-state rotation matrix caused by the phase angle difference between the phase dynamics of the phase-locked loop and the phase of the physical system. and steady-state cross-coupling terms caused by angular perturbations and Its expression process is as follows: Formula 7: ; Formula 8: ; Formula 9: ; Formula 10: ; Formula 11: ; In equations 3-11, L f and Cf Here, s represents the converter filter inductor and capacitor, s is the Apras operator, and ω is the rated angular frequency. , V fi D represents the voltage amplitude. d and D q This represents the duty cycle components on the d-axis and q-axis, with the subscript "0" indicating the steady-state value; G ci =G ci (s)·I, where I is a 2×2 identity matrix, G ci (s)=(k pi +k ii / s) and G PQ (s)=(k pPQ +k iPQ / s) represent the PI controller transfer functions of the current loop and power tracking control loop, respectively; G PLL (s)=(k pθ +k iθ / s) represents the transfer function of the PI controller in the phase-locked loop; the superscript " s "" represents the value of any vector from the system coordinate system after transformation to the control coordinate system; As a preferred embodiment, the impedance model of the grid converter ui can be equivalent to an ideal voltage source and impedance Z. mi The cascade structure of (s) is expressed as follows: Formula 12: ; Formula 13: ; Formula 14: ; Formula 15: ; In equations 12-15, G cv =G ci (s)G vv (s)I, G vv (s)=(k pv +k iv / s) represents the transfer function of the PI controller in the voltage control loop. G represents the transfer function of the power loop filter. VSG = diag{1 / (s(Js+D p )), n q}, where J and D p These are the inertia coefficient and damping coefficient for the control of the network-type virtual synchronous machine, respectively. Formula 16: ; Equation 17: ; Formula 18: ; The passive network admittance model is expressed as follows: Formula 19: ; In equations 16-19, This represents the current flowing from node i to node j; and Y represents the voltage at node i and node j, respectively. ij (s) is the node admittance matrix of the passive network.

[0037] In this invention, the grid-connected converter is represented as a current source connected in parallel with admittance. The admittance includes contributions from the filter inductor, phase-locked loop (PLL) dynamics, and cross-coupling terms. If the contribution of the PLL dynamics is ignored, the model cannot reflect the PLL's influence on the system's low-frequency oscillation characteristics, leading to overly optimistic stability analysis results. If the contribution of the cross-coupling terms is ignored, the model cannot accurately describe the coupling between the d and q axes, affecting the prediction accuracy of wideband dynamic characteristics.

[0038] As a preferred embodiment, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables is achieved through a linear transformation matrix. Specifically, it means: Step S2-1: The voltage vector at any port can be expressed as... ,in The phase angle difference between the voltage phasor and the dq frame angle is expressed as follows: Formula 20: ; Step S2-2: Linear transformation matrix between the dq coordinate system and the amplitude-frequency domain variables Defined as the mapping matrix from voltage amplitude perturbation and frequency perturbation to voltage perturbation in the dq coordinate system, its expression is: Equation 21: , ; Equation 22: ; In equations 20-22, ω fi The angular frequency of the output voltage. , V represents the voltage amplitude, and the subscript "0" represents the steady-state value.

[0039] As a preferred embodiment, the process for establishing the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance is as follows: Step S3-1: Calculate the active and reactive power of the i-th converter. The process is as follows: Equation 23: ; Step S3-2: Perform small-signal linearization around the steady-state operating point and obtain the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance. The calculation process is as follows: Formula 24: ; Formula 25: .

[0040] As a preferred embodiment, the process of establishing the direct analytical mapping between the port power disturbance and the voltage amplitude-frequency domain disturbance is as follows: Simultaneously establishing the grid-connected converter ui admittance model, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation relationship between the power disturbance and the voltage amplitude-frequency domain disturbance, the equivalent [PQ]-[ωV] port admittance model of the grid-connected converter is calculated. The calculation process is as follows: Equation 26: ; Wherein, the equivalent port admittance matrix The transfer function matrix is ​​represented as follows: Its parsing expression is: Equation 27: .

[0041] As a preferred embodiment, the process of establishing the direct analytical mapping between the port power disturbance and the voltage amplitude-frequency domain disturbance is as follows: By combining the ui impedance model of the grid-connected converter, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance, the equivalent [PQ]-[ωV] port impedance model of the grid-connected converter is calculated. The calculation process is as follows: Equation 28: ; in, Equivalent port admittance matrix The transfer function matrix is ​​represented as follows: Its analytical expression is: Equation 29: ; ; ; In equations 28 and 29, ω mi V is the angular frequency of the output voltage. mi This indicates the voltage amplitude, and the subscript "0" indicates the steady-state value.

[0042] As a preferred embodiment, the process of establishing the direct analytical mapping between the port power disturbance and the voltage amplitude-frequency domain disturbance is as follows: Simultaneously establishing the passive network ui admittance model, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation relationship between the power disturbance and the voltage amplitude-frequency domain disturbance, the equivalent [PQ]-[ωV] port impedance model of the passive network is calculated. The calculation process is as follows: Formula 30: ; in, and This indicates the angular frequency and voltage amplitude at the point of common coupling (PCC) and the power grid; The analytical expression for the equivalent matrix is: Equation 31: ; Equation 32: ; Equation 33: ; Equation 34: , ; In equations 30-34, i gd and i gq V represents the d-axis and q-axis components of the grid-connected current. pd and V pq V represents the d-axis and q-axis components of the PCC voltage. gd and V gq These are the d-axis and q-axis components of the grid voltage, with the subscript "0" indicating the steady-state value.

[0043] Example 2

[0044] This embodiment uses the model obtained by the modeling method provided in Embodiment 1 to verify the correctness of the analytical mapping relationship. The process is as follows: First, the Bode plot of the theoretical port [PQ] - [ωV] model is compared with the frequency scan measurement results. A current interference source is connected in parallel at the inverter terminal to inject an interference signal. This interference source will excite the grid-connected inverter circuit, resulting in power and voltage responses; For grid-connected converters, in order to obtain Y fai (s), two different sets of current interference signals are injected sequentially, and Y is calculated. fai (s), the process is as follows: Formula 35: ; In Equation 35, subscripts 1 and 2 represent the first and second disturbance injections, respectively. The power can be calculated according to Equation 14, and ΔV and Δω can be obtained through a phase-locked loop.

[0045] Figure 1The frequency response results of the [PQ]-[ωV] admittance model of the grid-connected converter are shown, where the black curve represents the theoretical model and the red dots represent the measured data. It can be seen that the measured results are in high agreement with the theoretical results, which verifies the effectiveness of the proposed [PQ]-[ωV] modeling method for grid-connected converters based on the port admittance-amplitude-frequency mapping relationship.

[0046] For grid converters, in order to obtain Z mai (s), two different sets of current interference signals are injected sequentially, and Z is calculated. mai (s), the process is as follows: Equation 36: ; In Equation 36, the subscripts 1 and 2 represent the first and second perturbation injections, respectively.

[0047] Figure 2 The frequency response results of the [PQ]-[ωV] impedance model of the grid-connected converter are shown, where the black curve represents the theoretical model and the red dots represent the measured data. It can be seen that the measured results are in high agreement with the theoretical results, which verifies the effectiveness of the proposed [PQ]-[ωV] modeling method for grid-connected converters based on the port admittance-amplitude-frequency mapping relationship.

[0048] Example 3

[0049] This embodiment uses model (18) obtained by the modeling method provided in Embodiment 1 and dq impedance model (2) existing in the prior art to perform stability analysis on a single grid-connected converter system and a single grid-connected converter system, in order to verify the accuracy of the proposed admittance [PQ] - [ωV] mapping relationship. The results are as follows: Figure 3 and Figure 4 As shown.

[0050] Figure 3 The root locus of the phase-locked loop (PLL) proportional coefficient kpθ ∈ [0.01, 0.1] for the grid-connected converter is shown under both the dq impedance model and the [PQ] - [ωV] model. It can be seen that increasing the PLL proportional coefficient kpθ will increase the characteristic root λ. 1，2 Shifting to the left helps improve system stability. When the proportionality constant kpθ increases from 0.02 to 0.03, the system transitions from unstable to stable. Furthermore, based on the dq impedance model and the proposed [PQ]-[ωV] model, the root locus trends are essentially consistent, and the stability regions of the system parameters are also the same.

[0051] Figure 4 The damping coefficient D of the grid converter is shown in both the dq impedance model and the [PQ] - [ωV] model.p The root locus corresponding to ∈[700, 900]. It can be seen that increasing the damping coefficient D... p It will cause the characteristic root λ 1，2 Shifting to the left helps improve system stability. When the damping coefficient D p When the value is increased from 850 to 860, the system changes from unstable to stable. Furthermore, based on the dq impedance model and the proposed [PQ]-[ωV] model, the root locus trends are basically consistent, and the stability regions of the system parameters are also the same.

[0052] Furthermore, to verify the accuracy of the stability analysis, this invention also conducted tests on grid-connected systems with grid-connected converters and grid-connected systems with cross-connected converters. The results are as follows: Figure 5 As shown. Figure 5 (a) shows the hardware-in-the-loop control results of the active power waveform of the grid converter as kpθ decreases from 0.03 to 0.02 (at the 5th second). As can be seen from the figure, the active power gradually disperses, which indicates that the system is unstable, which is consistent with the stability prediction results. Figure 5 (b) demonstrates the effect of the grid converter on the damping coefficient D. p The active power waveform during the decrease from 860 to 850 (at the 6th second) is shown in the control hardware-in-the-loop experimental results. As can be seen from the figure, the active power gradually disperses, indicating system instability, which is consistent with the stability prediction results. The above analysis verifies the correctness of the derived analytical mapping relationship between the grid converter and the system.

Claims

1. A method for modeling [PQ]-[ωV] of a hybrid converter system based on port impedance-amplitude frequency mapping, characterized in that, include: Step S1: Obtain the ui admittance model of the grid-type converter in the dq coordinate system, obtain the ui impedance model of the grid-type converter in the dq coordinate system, and obtain the passive network admittance model. Step S2: Based on the steady-state operating point, establish the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and transform the voltage in the dq coordinate system into disturbances in amplitude and frequency. Step S3: Perform small-signal linearization on the active and reactive power of the converter around the steady-state operating point to obtain the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance. Step S4: Combining the ui admittance model, ui impedance model, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation relationship between the power disturbance and the voltage amplitude-frequency domain disturbance, obtain the equivalent [PQ]-[ωV] port admittance model of the grid converter, the equivalent [PQ]-[ωV] port impedance model of the grid converter, and the passive network [PQ]-[ωV] port admittance model.

2. The [PQ]-[ωV] modeling method for a hybrid converter system based on port impedance-amplitude frequency mapping according to claim 1, characterized in that: The expression for the admittance model of the grid-connected converter ui is: Formula 1: ; The expression for the impedance model of the grid converter ui is: Formula 2: ; In Equations 1 and 2, in Equation 1, , , ,Y fi (s) represents the admittance of the grid converter in the dq coordinate system. The "~" symbol indicates a small perturbation near the equilibrium point. To match the output current of the grid-connected converter, and These are the components of the output current on the d-axis and q-axis. For current reference quantity, and The components of the reference current on the d-axis and q-axis; To match the output voltage of the grid-connected converter, and These are the components of the output voltage on the d-axis and q-axis; It is a 2×2 transfer function matrix; , , Z mi (s) represents the impedance of the grid-type converter in the dq coordinate system. , To match the output current of the grid-connected converter, and These are the components of the output current on the d-axis and q-axis. For voltage reference quantity, and The components of the reference current on the d-axis and q-axis; For the output voltage of the grid-type converter, and These are the components of the output voltage on the d-axis and q-axis; It is a 2×2 transfer function matrix.

3. The [PQ]-[ωV] modeling method for a hybrid converter system based on port impedance-amplitude frequency mapping according to claim 2, characterized in that: The u-i admittance model of the grid-connected converter can be equivalent to an ideal current source and an admittance Y fi The parallel structure of (s) is expressed as: Formula 3: ; Formula 4: ; Formula 5: ; Formula 6: ; The admittance matrix ω = 2πf, where f is the rated frequency of 50Hz, and Y fi (s) includes the steady-state rotation matrix caused by the phase angle difference between the phase dynamics of the phase-locked loop and the phase of the physical system. and steady-state cross-coupling terms caused by angular perturbations and Its expression process is as follows: Formula 7: ; Formula 8: ; Formula 9: ; Formula 10: ; Formula 11: ; In equations 3-11, L f and C f Here, s represents the converter filter inductor and capacitor, s is the Apras operator, and ω is the rated angular frequency. , V fi D represents the voltage amplitude. d and D q This represents the duty cycle components on the d-axis and q-axis, with the subscript "0" indicating the steady-state value; G ci =G ci (s)·I, where I is a 2×2 identity matrix, G ci (s)=(k pi +k ii / s) and G PQ (s)=(k pPQ +k iPQ / s) represent the PI controller transfer functions of the current loop and power tracking control loop, respectively; G PLL (s)=(k pθ +k iθ / s) represents the transfer function of the PI controller in the phase-locked loop; the superscript " s "" represents the value of any vector from the system coordinate system after transformation to the control coordinate system; The networked converter u-i impedance model can be equivalent to an ideal voltage source and impedance Z mi The series structure of (s) is expressed as: Formula 12: ; Formula 13: ; Formula 14: ; Formula 15: ; In equations 12-15, G cv =G ci (s)G vv (s)I, G vv (s)=(k pv +k iv / s) represents the transfer function of the PI controller in the voltage control loop. G represents the transfer function of the power loop filter. VSG = diag{1 / (s(Js+D p )), n q }, where J and D p These are the inertia coefficient and damping coefficient for the control of the network-type virtual synchronous machine, respectively. Formula 16: ; Formula 17: ; Formula 18: ; The passive network admittance model is expressed as follows: Formula 19: ; In equations 16-19, This represents the current flowing from node i to node j; and Y represents the voltage at node i and node j, respectively. ij (s) is the node admittance matrix of the passive network.

4. The [PQ]-[ωV] modeling method for a hybrid converter system based on port impedance-amplitude frequency mapping according to claim 3, characterized in that: The mapping relationship between the port voltage vector and the amplitude-frequency domain variables is achieved through a linear transformation matrix. Specifically, it means: Step S2-1: The voltage vector at any port can be expressed as... ,in The phase angle difference between the voltage phasor and the dq frame angle is expressed as follows: Formula 20: ; Step S2-2: Linear transformation matrix between the dq coordinate system and the amplitude-frequency domain variables Defined as the mapping matrix from voltage amplitude perturbation and frequency perturbation to voltage perturbation in the dq coordinate system, its expression is: Equation 21: , ; Equation 22: ; In equations 20-22, ω fi The angular frequency of the output voltage. , V represents the voltage amplitude, and the subscript "0" represents the steady-state value.

5. The [PQ]-[ωV] modeling method for a hybrid converter system based on port impedance-amplitude frequency mapping according to claim 4, characterized in that: The process of establishing the correlation between the amplitude-frequency domain perturbation and the voltage perturbation is as follows: Step S3-1: Calculate the active and reactive power of the i-th converter. The process is as follows: Equation 23: ; Step S3-2: Perform small-signal linearization around the steady-state operating point and obtain the correlation between the power disturbance and the voltage amplitude-frequency domain disturbance. The calculation process is as follows: Formula 24: ; Formula 25: .

6. The [PQ]-[ωV] modeling method for a hybrid converter system based on port impedance-amplitude frequency mapping according to claim 5, characterized in that: The process of establishing the direct analytical mapping between the port power disturbance and the voltage amplitude-frequency domain disturbance is as follows: Simultaneously establish the grid-connected converter ui admittance model, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation relationship between the power disturbance and the voltage amplitude-frequency domain disturbance. Then, calculate the equivalent [PQ]-[ωV] port admittance model of the grid-connected converter. The calculation process is as follows: Equation 26: ; Wherein, the equivalent port admittance matrix The transfer function matrix is ​​represented as follows: Its parsing expression is: Equation 27: .

7. The [PQ]-[ωV] modeling method for a hybrid converter system based on port impedance-amplitude frequency mapping according to claim 5, characterized in that: The process of establishing the direct analytical mapping between the port power disturbance and the voltage amplitude-frequency domain disturbance is as follows: By combining the ui impedance model of the grid-connected converter, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation relationship between the power disturbance and the voltage amplitude-frequency domain disturbance, the equivalent [PQ]-[ωV] port impedance model of the grid-connected converter is calculated. The calculation process is as follows: Formula 28: , in, Equivalent port admittance matrix The transfer function matrix is ​​represented as follows: Its analytical expression is: Equation 29: ; ； ； In formulas 28 and 29, ω mi is the angular frequency of the output voltage, V mi denotes the voltage amplitude, the subscript "0" denotes the steady-state value.

8. The [PQ]-[ωV] modeling method for a hybrid converter system based on port impedance-amplitude frequency mapping according to claim 5, characterized in that: The process of establishing the direct analytical mapping between the port power disturbance and the voltage amplitude-frequency domain disturbance is as follows: Simultaneously establish the passive network ui admittance model, the mapping relationship between the port voltage vector and the amplitude-frequency domain variables, and the correlation relationship between the power disturbance and the voltage amplitude-frequency domain disturbance, and calculate the equivalent [PQ]-[ωV] port impedance model of the passive network. The calculation process is as follows: Formula 30: , in, and This indicates the angular frequency and voltage amplitude at the point of common coupling (PCC) and the power grid; The analytical expression for the equivalent matrix is: Equation 31: ; Equation 32: ; Equation 33: ; Equation 34: , ; In equations 30-34, i gd and i gq V represents the d-axis and q-axis components of the grid-connected current. pd and V pq V represents the d-axis and q-axis components of the PCC voltage. gd and V gq These are the d-axis and q-axis components of the grid voltage, with the subscript "0" indicating the steady-state value.

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