Consider the dc voltage dynamic vsg frequency coupling impedance modeling and stability analysis method

Abstract

The application provides a DC voltage dynamic VSG frequency coupling impedance modeling and stability analysis method, and relates to the technical field of power electronic converter control. The method comprises the following steps: constructing a two-stage VSG system topology; establishing a front-stage DC voltage control model and a rear-stage VSG power control model; based on a harmonic linearization method, establishing a small-signal model considering the mirror frequency effect; deducing a conductance matrix and an impedance matrix containing a DC voltage coupling term; and verifying the system stability through a generalized Nyquist criterion and time domain simulation. The application fuses the DC voltage dynamic and the mirror frequency effect, accurately represents the frequency coupling characteristics of the VSG, avoids the calculation deviation of the traditional model, improves the stability analysis precision, is suitable for new energy power generation, AC / DC microgrid and other scenes, and has important engineering application value.

Description

Technical Field

[0001] This invention relates to the field of power electronic converter control technology, and in particular to a method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage. Background Technology

[0002] With the increasing prominence of the energy crisis and environmental problems, renewable energy and distributed generation have received widespread attention, and a large number of traditional fossil fuel power plants are being gradually replaced. Unlike traditional synchronous generators that rely on rotating parts to provide inertia for the system, the large-scale application of power electronic converters has given power systems low inertia characteristics. Although power electronic devices have a faster dynamic response in terms of active and reactive power support, the lack of physical inertia makes the frequency stability problem of power systems increasingly prominent. Currently, virtual synchronous generator (VSG) technology is used to simulate the operating characteristics of traditional synchronous generators, providing adjustable inertia, damping, and frequency and voltage support. VSGs have been widely used in photovoltaic power plants, AC / DC microgrids, wind power generation, and many other fields.

[0003] However, existing research has several limitations: First, the VSG small-signal model established in a synchronous rotating coordinate system is not applicable when the AC system is unbalanced because the steady-state operating point is no longer a constant DC value. Second, although the harmonic linearization method can overcome the above limitations, related studies do not consider the image frequency effect (MFE) and usually assume that the inner loop of the VSG is symmetrical, ignoring the close relationship between the power loop and the dq axis components. Even in a balanced system, coupling terms will lead to positive and negative sequence coupling. If the VSG is assumed to be an image frequency decoupling (MFD) system, it will cause deviations in the equivalent impedance calculation. Third, current VSG research is mostly based on the assumption of a constant DC bus voltage, ignoring the dynamic influence of DC voltage brought about by the control of the upstream converter. In wind and solar new energy power generation scenarios, VSG generally adopts a two-stage topology of front-end DC / DC converter-DC bus-back-end DC / AC inverter. The DC bus voltage is controlled by the front-end, and its dynamic process is significant. This leads to the mutual coupling of DC voltage, AC frequency, active power and reactive power control. Moreover, the DC voltage dynamics can interact with grid impedance and VSG control links, changing the system stability. However, existing VSG impedance modeling and stability analysis do not incorporate this dynamic process, and cannot accurately characterize the impact of DC dynamics on MFE and system stability. Summary of the Invention

[0004] The main objective of this invention is to provide a method for VSG frequency coupling impedance modeling and stability analysis that considers the dynamics of DC bus voltage, thereby solving problems such as low applicability of signal models, neglect of image frequency effects and positive and negative sequence coupling, and misjudgment of stability.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage, comprising the following steps: S1: System Topology Construction: Build a two-stage VSG system including a front-end DC / DC converter, a DC bus, and a rear-end DC / AC inverter. The front-end converter regulates the DC bus voltage through PI control, and the rear-end inverter adopts grid-based control. S2: Establish a front-end DC voltage control model, which includes DC side capacitor current balance equation, AC / DC power balance relationship equation and DC voltage PI control equation to characterize the coupling relationship between DC voltage dynamics and active and reactive power. S3: Establish a power control model for the subsequent VSG, which includes active power and frequency control equations, reactive power and voltage control equations, and incorporates the power deviation term caused by DC voltage dynamics; S4: Based on the harmonic linearization method, considering the image frequency effect, establish a small-signal voltage and current model that includes the fundamental frequency, positive-sequence disturbance and negative-sequence disturbance signals; S5: Combining the influence of DC voltage dynamics on the power loop and modulation voltage, derive the admittance matrix including DC voltage coupling terms; S6: By using Park transform and inverse Park transform, combined with phase angle and internal potential dynamic modeling, the VSG output impedance matrix containing DC voltage dynamics is derived. S7: The stability of the system is analyzed using the stability criterion based on the output impedance matrix, and the analysis results are verified by combining the time-domain simulation model.

[0006] In the preferred embodiment, in S1, the DC-side voltage of the two-stage VSG system topology... U dc The DC-side equivalent impedance is tracked by the upstream converter via PI control. Z dc =1 / (s C dc G dc ),in, G dc = K pd + K id / s, K pd , K id These represent the proportional and integral gain of the DC voltage control, respectively. C dc This indicates a parallel capacitor on the DC side.

[0007] In the preferred embodiment, S2 specifically includes: S21: Construct the DC-side capacitor current balance equation, the formula is: ; In the formula, Δ U dc = U dcref U dc0 , U dcref Indicates the DC voltage reference value. U dc0 This indicates the real-time value of the DC voltage. I dc1 The signal component of the equivalent current source of the preceding stage; I dc0 This refers to the DC current signal component flowing into the subsequent VSG stage; S22: Set the instantaneous active power on the AC / DC side of the subsequent VSG to be conserved, i.e., Δ P dc =Δ P e Linearization is applied near the steady-state operating point to describe the dynamic balance between DC-side power fluctuations and AC-side active power changes. The formula is: ; In the formula, Δ I dc = I dc1 - I dc0 ; u d0 , u q0 This represents the steady-state value of the dq-axis voltage; i d0 , i q0 The steady-state value of the dq-axis current; Δ u d Δ u q For the small-signal component of the dq-axis voltage; Δ i d Δ i q For the small-signal component of the dq-axis current; Δ P e The small signal component of the active power output is provided to the AC side of the subsequent VSG. S23: Obtain the DC voltage PI control equation, where the DC voltage control proportional gain is... K pd The integral gain is K idThen the signal components of the preceding current source are: ; The proportional term quickly responds to voltage deviations, the integral term eliminates steady-state errors, and the output controlled current source command stabilizes the DC bus voltage.

[0008] In the preferred embodiment, S3 specifically includes: S31: Establish the control equations for active power and frequency, with the following formulas: ; ; ; ; In the formula, J This is a virtual moment of inertia; ω v , ω n These are the VSG output angular frequency and the grid rated angular frequency, respectively. T set , T e These are the reference torque and the electromagnetic torque, respectively. T dc = This represents the torque disturbance term caused by dynamic DC voltage. D p This is the active damping coefficient; P ref , P e These are the active power reference value and the electromagnetic power, respectively. θ The phase angle of the internal potential of the VSG; S32: Reactive power and voltage control equations, the formula is: ; In the formula, K Voltage coefficient; Q ref , Q e These are the reactive power reference value and the electromagnetic power, respectively. D q This is the voltage droop factor; V 0、 V These are the rated voltage amplitude and the VSG output voltage amplitude, respectively. E m0 The magnitude of the internal potential of the VSG; Δ E ff =Δ U dc Gff / U dcref This represents the internal potential increment of DC voltage feedforward compensation. G ff = K_ ff / ( T_ ff s +1); Δ Q dc = K dc-Q Δ U dc This represents the coupling term between DC voltage deviation and reactive power. K dc-Q =0.02 represents the reactive-DC voltage coupling coefficient; The instantaneous output active and reactive power of the VSG can be expressed as: ; In the formula, v d , i d These represent the d-axis output voltage and current, respectively. v q , i q These represent the q-axis output voltage and current, respectively. The modulation wave of the VSG is determined by the active and reactive power loops, and the expression for the three-phase modulation wave is: ; In the formula, e am , e bm , e cm It is a VSG three-phase modulated wave; S33: Includes the power deviation term caused by DC voltage dynamics, specifically: The relationship between the VSG internal potential, output terminal voltage, and output current is as follows: ; in, , , The formula representing the dynamic correction of the DC voltage to the three-phase internal potential is: (12).

[0009] In the preferred embodiment, step S4 specifically includes: In the time domain, after adding a small signal disturbance, the voltage and current at the output terminal of phase A are given by the following formulas: ; ; In the formula, V 1. V p , V n These represent the amplitudes of the fundamental voltage, positive-sequence voltage disturbance, and negative-sequence voltage disturbance, respectively. I 1. I p , I n These represent the amplitudes of the fundamental current, positive-sequence current response, and negative-sequence current response, respectively. f 1 represents the fundamental frequency; φ v1 φ vp , φ vn These are the initial phase angles of the fundamental, positive-sequence, and negative-sequence voltage disturbances, respectively. φ i1 , φ ip , φ in These are the initial phase angles of the fundamental current, the positive-sequence current response, and the negative-sequence current response, respectively. In the frequency domain, the above voltage and current expressions are: ; ; in: , , , , , .

[0010] In the preferred embodiment, S5 specifically includes: The small-signal characteristics of the VSG AC port can be described by the admittance matrix. Considering the dynamic effect of DC voltage on the power loop and modulation voltage, the admittance matrix takes the following form: ; In the formula, ω 1=2 πf 1; In the fundamental admittance matrix Y PN In (s), Y pp ( s ), Y nn ( s These represent the positive-order and negative-order self-admittances, respectively. Y pn ( s ),Y np ( s ) represents the cross-coupled admittance.

[0011] In the preferred embodiment, S6 specifically includes: S61: After the Park transform, the output voltage and current in the frequency domain can be expressed as: ; ; ; ; In the formula, dc represents direct current; , The voltage frequency domain component of the dq axis; , The frequency domain components of the dq-axis current; S62: Substituting the formulas from step S61 into the instantaneous output active and reactive power formulas of the VSG, and using the frequency domain convolution theorem, the frequency domain expressions for active and reactive power, including DC voltage dynamics, can be obtained: ; ; in, The superscript "*" indicates complex conjugation; S63: Perform dynamic modeling of phase angle and internal potential to derive the basic admittance model.

[0012] In the preferred embodiment, in step S63, the phase angle θ During dynamic modeling, it is possible to θ Represented as ,in θ 1 represents the phase angle of the fundamental voltage. For small disturbances caused by disturbance voltage, frequency domain expressions for active and reactive power, which include DC voltage dynamics, are derived using the frequency domain convolution theorem.

[0013] In the preferred embodiment, in step S7, the stability verification adopts the generalized Nyquist criterion. The equivalent impedance ratio is formed by calculating the ratio of the positive-sequence equivalent input impedance, the negative-sequence equivalent input impedance to the system grid impedance, and plotting its Nyquist curve. The stability is judged by combining the real and imaginary part characteristics.

[0014] In the preferred embodiment, the relationship between the VSG internal potential, output terminal voltage, and output current includes a DC voltage dynamic correction term for the three-phase internal potential, and DC correction terms are set for the d-axis and q-axis. The transient reactive power coupling coefficient on the q-axis is... K q-dc=0.002, transient q-axis reactive power coupling correction factor K q-dc0 =0.005.

[0015] This invention provides a method for VSG frequency coupling impedance modeling and stability analysis that integrates DC voltage dynamics. It constructs a two-stage VSG system topology; establishes a front-stage DC voltage control model and a rear-stage VSG power control model; establishes a small-signal model considering image frequency effects based on harmonic linearization; derives the admittance and impedance matrices including DC voltage coupling terms; and verifies system stability through the generalized Nyquist criterion and time-domain simulation. This invention integrates DC voltage dynamics and image frequency effects, and the established sequence impedance model can more accurately characterize the dynamic interaction between the VSG and the power grid, reducing impedance calculation errors caused by neglecting DC dynamics, improving the accuracy of system stability boundary prediction, and enhancing the accuracy of characterizing the frequency coupling characteristics of the VSG. Considering image frequency effects and positive and negative sequence coupling characteristics, the generalized Nyquist criterion is used to determine the system stability boundary conditions. Attached Figure Description

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a schematic diagram of the new energy two-stage grid-connected (VSG) converter of the present invention; Figure 2 This is a block diagram of the VSG control considering DC voltage coupling in this invention; Figure 3 This is a graph showing the cross-coupling impedance and self-impedance amplitude of the present invention; Figure 4 These are the theoretical and simulated values ​​of the positive and negative sequence impedance of the DC voltage dynamic change system of this invention; Figure 5 This is the positive and negative sequence impedance Nyquist plot of the present invention; Figure 6 This is a waveform diagram of DC bus voltage and frequency in the DC voltage dynamic change system of the present invention; Figure 7 This is a waveform distortion rate curve of AC side current and voltage under dynamic changes of DC voltage according to the present invention; Figure 8 This is a DC-side voltage waveform diagram under different PI control parameters of the present invention; Figure 9 This is a diagram showing the distortion rate of AC side current and voltage waveforms under different PI control parameters according to the present invention. Figure 10 This invention is different K _ff Time-sequence impedance comparison curve; Figure 11 This invention is different T_ff Time-sequence impedance comparison curve. Detailed Implementation

[0017] Example 1 like Figure 1-11 As shown, a method for VSG frequency coupling impedance modeling and stability analysis integrating DC voltage dynamic processes includes the following steps: S1: System Topology Construction: Build a two-stage VSG system including a front-end DC / DC converter, a DC bus, and a back-end DC / AC inverter. The front-end converter regulates the DC bus voltage through PI control, and the back-end inverter adopts grid-based control.

[0018] S2: Establish a front-end DC voltage control model, which includes DC side capacitor current balance equation, AC / DC power balance relationship equation and DC voltage PI control equation to characterize the coupling relationship between DC voltage dynamics and active and reactive power.

[0019] S3: Establish the power control model for the subsequent VSG stage. The model includes active power and frequency control equations, reactive power and voltage control equations, and incorporates the power deviation term caused by DC voltage dynamics.

[0020] S4: Based on the harmonic linearization method, considering the image frequency effect, establish a small-signal voltage and current model that includes the fundamental frequency, positive-sequence disturbance, and negative-sequence disturbance signals.

[0021] S5: Combining the influence of DC voltage dynamics on the power loop and modulation voltage, derive the admittance matrix including DC voltage coupling terms.

[0022] S6: By using Park transformation and inverse Park transformation, combined with phase angle and internal potential dynamic modeling, the VSG output impedance matrix containing DC voltage dynamics is derived.

[0023] S7: The stability of the system is analyzed using a stability criterion based on the output impedance matrix, and the analysis results are verified by combining a time-domain simulation model.

[0024] This embodiment constructs a two-stage VSG system topology; establishes a front-stage DC voltage control model and a rear-stage VSG power control model; establishes a small-signal model considering the image frequency effect based on the harmonic linearization method; derives the admittance matrix and impedance matrix including the DC voltage coupling term; and verifies the system stability through the generalized Nyquist criterion and time-domain simulation. By integrating DC voltage dynamics and the image frequency effect, it improves the accuracy of characterizing the frequency coupling characteristics of the VSG, reduces the calculation bias of the traditional model, and enhances the accuracy of stability analysis. It is suitable for scenarios such as new energy power generation and AC / DC microgrids.

[0025] This embodiment analyzes the technical solution for VSG frequency coupling impedance modeling and stability analysis based on the dynamic process of DC voltage in steps.

[0026] Step S1: System Topology Construction: Build a two-stage system of front-end DC / DC converter - DC bus - back-end DC / AC inverter. The front-end converter regulates the DC bus voltage through PI control, and the back-end inverter uses grid-connected control (GFM) to support the grid frequency and voltage. Clarify the physical meaning of filter inductors, capacitors, damping resistors and grid-side parameters.

[0027] Step S11: As Figure 1 As shown, a two-stage grid-type (VSG) converter was constructed. Figure 1 The topology of VSG is shown on the right side. U dc The DC side voltage of the VSG is controlled by the upstream converter and is subject to dynamic processes. e a , e b , e c The internal potential of the VSG; i La , i Lb , i Lc For VSG output current; i a , i b , i c This is the grid-connected current; u a , u b , u c This refers to the output voltage of the VSG. L f , C f , R f These are the filter inductor, filter capacitor, and damping resistor, respectively. R g , L g For the grid-side resistance and inductance; u ga , u gb , u gc This refers to the grid voltage. C dc Indicates the parallel capacitor on the DC side; Δ U dcIndicates a small DC voltage deviation signal; Δ P dc This represents the active power deviation caused by dynamic DC voltage, reflecting the AC / DC power balance relationship; Δ Q dc This indicates the reactive power deviation generated dynamically by the DC voltage. Z dc =1 / (s C dc G dc ) represents the DC-side equivalent impedance, and G dc = K pd + K id / s, K pd , K id These represent the proportional gain and integral gain of the DC voltage control, respectively. The front-end converter uses PI control to convert the output voltage of the new energy source to the DC bus side, controlling the DC bus voltage to track the reference value.

[0028] Step S12: The VSG control model with DC voltage coupling is as follows Figure 2 As shown, it includes front-end DC voltage control and back-end VSG control. The active and reactive power control loops of the VSG simulate the mechanical and electrical operation principles of a real VSG, respectively.

[0029] This embodiment clarifies the connection logic of the front-end DC / DC converter, DC bus, and back-end DC / AC inverter through the above steps, quantifies core parameters such as filtering and power grid, avoids modeling deviations caused by topology ambiguity or missing parameters, and improves data accuracy.

[0030] Step S2: Front-end DC voltage control model: includes DC side capacitor current balance equation, AC / DC power balance relationship equation and PI control equation, which characterizes the coupling relationship between DC voltage dynamics and active and reactive power.

[0031] Step S21: DC-side capacitor current balance equation, the formula is: (1); In the formula, Δ U dc = U dcref U dc0 , U dcref Indicates the DC voltage reference value. U dc0 This indicates the real-time value of the DC voltage.I dc1 The signal component of the equivalent current source of the preceding stage; I dc0 This refers to the DC current signal component flowing into the subsequent VSG stage.

[0032] Step S22: Establish the AC / DC power balance relationship of the subsequent VSG.

[0033] Assuming that the instantaneous active power on the AC / DC side of the subsequent VSG is conserved, i.e., Δ P dc =Δ P e Linearization is performed near the steady-state operating point, and the expression expands to the product of voltage and current, as shown in the formula: (2); In the formula, Δ I dc = I dc1 - I dc0 ; u d0 , u q0 This represents the steady-state value of the dq-axis voltage; i d0 , i q0 The steady-state value of the dq-axis current; Δ u d Δ u q For the small-signal component of the dq-axis voltage; Δ i d Δ i q For the small-signal component of the dq-axis current; Δ P e This provides the small signal component of the active power output to the AC side of the subsequent VSG stage.

[0034] Formula (2) describes the dynamic balance between DC power fluctuations and AC active power changes, revealing the energy basis of AC-DC coupling.

[0035] Step S23: DC voltage PI control equation, set the DC voltage control proportional gain to... K pd The integral gain is K id Then the signal components of the preceding current source are: (3); The proportional term quickly responds to voltage deviations, the integral term eliminates steady-state errors, and the output controlled current source command stabilizes the DC bus voltage.

[0036] This embodiment improves the accuracy of quantifying the coupling relationship between DC voltage deviation and active and reactive power by balancing capacitor current, balancing AC and DC power, and using PI control equations. It incorporates the dynamic process of DC voltage into the modeling, thus solving the problem of stability misjudgment caused by the assumption of constant DC voltage in traditional models.

[0037] Step S3: Post-stage VSG power control model: Establish active power and frequency control equations, reactive power and voltage control equations, incorporate the power deviation term caused by DC voltage dynamics, and simulate the mechanical and electrical characteristics of a traditional synchronous generator.

[0038] Step S31: Active power and frequency control, the formulas are as follows: (4); (5); (6); (7); In the formula, J This is a virtual moment of inertia; ω v , ω n These are the VSG output angular frequency and the grid rated angular frequency, respectively. T set , T e These are the reference torque and the electromagnetic torque, respectively. T dc = This represents the torque disturbance term caused by dynamic DC voltage. D p This is the active damping coefficient; P ref , P e These are the active power reference value and the electromagnetic power, respectively. θ The phase angle of the VSG internal potential. Formulas (4)-(6) can accurately reflect the dynamic influence of DC voltage fluctuations on AC side torque, avoiding torque calculation deviations caused by ignoring DC dynamics.

[0039] Step S32: Reactive power and voltage control, the formula is: (8); In the formula, K Voltage coefficient; Q ref , Q e These are the reactive power reference value and the electromagnetic power, respectively. D qThis is the voltage droop factor; V 0、 V These are the rated voltage amplitude and the VSG output voltage amplitude, respectively. E m0 The magnitude of the internal potential of the VSG; Δ E ff =Δ U dc G ff / U dcref This represents the internal potential increment of DC voltage feedforward compensation. G ff = K_ ff / ( T_ ff s +1); Δ Q dc = K dc-Q Δ U dc This represents the coupling term between DC voltage deviation and reactive power. K dc-Q =0.02 represents the reactive power-DC voltage coupling coefficient. By incorporating the reactive power coupling term induced by DC voltage dynamics and the feedforward compensation term, the interference of DC dynamics on reactive power control is suppressed, thereby improving voltage stability.

[0040] The instantaneous output active and reactive power of the VSG can be expressed as: (9); In the formula, v d , i d These represent the d-axis output voltage and current, respectively. v q , i q These represent the q-axis output voltage and current, respectively.

[0041] The modulation wave of the VSG is determined by the active and reactive power loops, and the expression for the three-phase modulation wave is: (10); In the formula, e am , e bm , e cm It is a VSG three-phase modulated wave.

[0042] The relationship between the VSG internal potential, output terminal voltage, and output current is as follows: (11); in, , , The expression representing the dynamic correction of the DC voltage to the three-phase internal potential is as follows: (12).

[0043] This embodiment suppresses the interference of DC voltage fluctuations on power control by using the torque disturbance term in the active / frequency control equation and the internal potential correction term and reactive coupling term in the reactive / voltage control equation, thereby improving the voltage amplitude and frequency stability and enhancing the dynamic response accuracy of power control.

[0044] Step S4: Modeling the dynamic coupling of image frequency effect and DC voltage: Based on the harmonic linearization method, considering the image frequency effect, establish a small-signal model of voltage and current to characterize the frequency domain characteristics of the fundamental, positive-sequence disturbance and negative-sequence disturbance signals.

[0045] In the time domain, after adding a small signal disturbance, the voltage and current at the output terminal of phase A can be expressed as: (13); (14); In the formula, V 1. V p , V n These represent the amplitudes of the fundamental voltage, positive-sequence voltage disturbance, and negative-sequence voltage disturbance, respectively. I 1. I p , I n These represent the amplitudes of the fundamental current, positive-sequence current response, and negative-sequence current response, respectively. f 1 represents the fundamental frequency; φ v1 φ vp , φ vn These are the initial phase angles of the fundamental, positive-sequence, and negative-sequence voltage disturbances, respectively. φ i1 , φ ip , φ in These are the initial phase angles of the fundamental current, positive-sequence current response, and negative-sequence current response, respectively.

[0046] In the frequency domain, the above voltage and current expressions can be written as: (15); (16); in: , , , , , .

[0047] This embodiment characterizes the propagation characteristics of positive and negative sequence signals and disturbances at different frequencies based on the harmonic linearization method, adapts to balanced and unbalanced systems, and improves the accuracy of capturing the mutual influence of positive and negative sequence signals caused by the image frequency effect.

[0048] Step S5: Derive the admittance matrix containing DC voltage coupling terms to reflect the cross-coupling of positive and negative sequence signals and the impact of DC dynamics on AC side current.

[0049] The small-signal characteristics of the VSG AC port can be described by the admittance matrix. Considering the dynamic effect of DC voltage on the power loop and modulation voltage, the admittance matrix takes the following form: (17); In the formula, ω 1=2 πf 1; In the fundamental admittance matrix Y PN In (s), Y pp ( s ), Y nn ( s These represent the positive-order and negative-order self-admittances, respectively. Y pn ( s ), Y np ( s ) represents the cross-coupled admittance.

[0050] This embodiment demonstrates the modulation effect of DC voltage on frequency coupling through positive / negative sequence self-admittance, cross-coupling admittance, and DC voltage coupling admittance. This improves the completeness of the characterization logic of frequency coupling characteristics, reduces the impedance calculation deviation caused by neglecting coupling relationships in traditional models, and improves the calculation accuracy.

[0051] Step S6: Through Park transformation and inverse Park transformation, combined with phase angle and internal potential dynamic modeling, derive the VSG output impedance matrix and clarify the modulation mechanism of DC voltage on impedance parameters.

[0052] Step S61: Frequency domain characteristics after Park transform After the Park transform, the output voltage and current in the frequency domain can be expressed as: (18); (19); (20); (twenty one); In the formula, dc represents direct current; , The voltage frequency domain component of the dq axis; , For the dq-axis current frequency domain components.

[0053] Step S62: Consider the power frequency domain characteristics of DC voltage dynamics.

[0054] Substituting equations (18)-(21) into equation (9) and using the frequency domain convolution theorem, we can obtain the frequency domain expressions for active and reactive power, which include DC voltage dynamics: (twenty two); (twenty three); in, The superscript "*" indicates complex conjugation.

[0055] Step S63: Dynamic modeling of phase angle and internal potential.

[0056] S631: Phase Angle θ dynamics based on Figure 2 The active power controller of the VSG, phase angle θ It can be represented as: (twenty four); In the formula, In the frequency domain, the phase angle θ for: (25); in, This indicates the DC voltage feedforward correction term.

[0057] To analyze phase angle perturbation can θ Represented as ,in θ 1 represents the phase angle of the fundamental voltage. This is a small disturbance caused by the disturbance voltage. Therefore, from equation (25), we can obtain Δ in the frequency domain. θ for: (26); because For small perturbations, for sin θ Approximation processing: (27); Substituting equation (26) into equation (27) above, we can obtain the sin in the frequency domain. θ expression.

[0058] (28); Among them, cos θ 1 represents the steady-state cosine value of the work angle.

[0059] S632: Internal potential amplitude E m dynamics VSG-based reactive power controller, internal potential amplitude E m It can be represented as: (29); In the formula, .

[0060] Substituting equation (23) into equation (29) above, in the frequency domain... E m for: (30); in, This indicates steady-state DC deviation correction.

[0061] Set the d-axis and q-axis reference voltages as follows: (31); in, , representing the DC correction term for the d-axis reference voltage; Table q-axis reference voltage DC correction term, K q-dc =0.002 (transient q-axis reactive coupling coefficient), quantifying the slight influence of DC reactive deviation on the q-axis reference voltage.

[0062] Consider Δ θ At that time, the output voltage in the synchronous rotating coordinate system is: (32); Where, Δ v d1,dc Δ v q1,dc This indicates the DC correction for the steady-state voltage of the dq axis. , , K q-dc0 =0.005.

[0063] Based on equations (18)-(21) and (32), the output voltage in the frequency domain is derived: (33); (34); Similarly, the output current can be expressed as: (35); (36)

[0064] Combining the voltage given by equation (32), the output of the voltage loop (i.e., the input of the inner current loop) can be obtained: (37); in, k pv This is the proportional gain of the voltage controller.

[0065] Similarly, the output of the inner current loop can be expressed as: (38); in, G i ( s ) is the transfer function of the PI current regulator; K d This is a decoupling term. Therefore, the frequency domain can be derived. C d , C q The expressions are shown in equations (47)-(48).

[0066] According to the inverse Park transformation, in the stationary coordinate system c abc It can be represented as: (39); in, (40); and c d1 and c q1 It can be represented as: (41); Right now: (42).

[0067] Based on equations (26) and (47)-(48), the frequency domain can be derived. c d1、 c q1The expression for the internal potential in the frequency domain is given by equations (49)-(50). Further, the internal potential in the frequency domain is obtained, as shown in equation (51). Subsequently, based on equations (11) and (51), the impedance expression can be derived, as shown in equations (56), (57), (60), and (63), where: (43); The relationship between voltage and current is as follows: (44); (45)

[0068] The fundamental admittance model can be derived from the output impedance matrix: (46); (47); (48); (49); (50); (51).

[0069] Step S64: Consider the dynamic impedance matrix derivation of DC voltage.

[0070] Combining the internal potential relationship in equation (11), the dq-axis variables are transformed to the abc stationary coordinate system through the inverse Park transformation, ultimately deriving the VSG output impedance matrix that includes DC voltage dynamics. The impedance matrix elements include positive-sequence self-impedance. Z pp (s) Negative sequence self-impedance Z nn (s), cross-coupling impedance Z pn (s), Z np (s), I 1* indicates the positive-sequence current complex conjugate (reflecting the effect of current phase on impedance). G i1 The 1 in the text refers to ( s -j w 1), G i2 The 2 in the text refers to ( s +j w 1) The specific form is as follows: (52); (53); (54); (55); Z pp (s)= A 1 / B 1(56) Z pn (s)= A 2 / B 2(57) (58); (59); Z np (s)= A 3 / B 3(60) (61); (62).

[0071] Z nn (s)= A 4 / B 4(63).

[0072] This embodiment combines the above steps with Park transform, power frequency domain characteristics, and internal potential dynamic modeling to clarify the calculation logic of positive / negative sequence self-impedance and cross-coupling impedance, thereby improving the accuracy of impedance calculation, reducing the deviation between theoretical impedance and simulation value, and providing accurate impedance basis for stability analysis.

[0073] Step S7: Stability Criterion Analysis and Verification: The stability of the equivalent impedance is analyzed using the generalized Nyquist criterion. A time-domain simulation model is built using Matlab / Simulink. By changing the grid inductance, PI control parameters, and feedback function parameters, the accuracy of the model under different operating conditions is verified, and the DC voltage fluctuation, frequency stability, and waveform distortion rate are evaluated.

[0074] Step S71: Nyquist criterion for system impedance.

[0075] The generalized Nyquist method has been widely used for the stability analysis of asymmetric impedance matrices. Considering the off-diagonal elements in the admittance matrix, the impedance ratio can be expressed as: (64); Nyquist functions of equivalent positive and negative sequence impedances: Nyq_p(h)=Z inveq,p(h) / ( Z gp + Zdc (65); Nyq_n(h)=Z inveq,n(h) / ( Z gn + Z dc (66).

[0076] Take the real part (amplitude) and imaginary part (phase angle) of the positive and negative impedances: Real_Hp(h)=real(Nyq_p(h))(67); Imag_Hp(h)=imag(Nyq_p(h))(68); Real_Hn(h)=real(Nyq_n(h))(69); Imag_Hn(h)=imag(Nyq_n(h))(70); in, Indicates the positive-sequence equivalent input impedance; Indicates the negative-sequence equivalent input impedance; This indicates the impedance of the AC-side power grid.

[0077] Step S72: Simulation verification results are as follows Figure 3-11 As shown.

[0078] To verify the correctness of the proposed model and the impact of DC voltage dynamics on VSG characteristics, a time-domain simulation model was built based on Matlab / Simulink, with default settings. G ff In the function K _ff , T _ff They are 8 and 0.8 (low frequency band, when) T _ff As the impedance decreases, the corresponding impedance curve changes in the mid-to-high frequency range (details will not be elaborated here). The PI control parameters are 0.48 and 3, respectively. The system parameters are shown in Table 1, and the DC voltage control parameters are shown in Table 2.

[0079] Table 1 VSG System Parameter Table

[0080] Table 2 DC Voltage Control Parameter Table

[0081] In this embodiment, the system stability, AC / DC voltage and current stability, frequency stability, and control parameters are verified. The system stability under different power grids and control parameters is comprehensively verified, and key indicators such as DC voltage fluctuation, frequency characteristics, and waveform distortion rate are clarified to ensure that the AC side current / voltage distortion rate meets the power system requirements. At the same time, the sensitivity of key parameters is analyzed in detail.

[0082] 1. Verify system stability, such as Figure 3 The figure shows the cross-coupling impedance and self-impedance amplitude curves. Taking the low-frequency band as an example, Figure 3 (a) shows the cross-coupling impedance Z pn and Z np Amplitude characteristics across the entire frequency domain. Both exhibit amplitude in the low-frequency range, indicating a dynamic interaction between positive and negative sequences within this frequency band.

[0083] Figure 3 (b) gives the self-impedance Z pp and Z pn , Z np Compare the curves in the low-frequency range. Z pn , Z np amplitude and Z pp The numerical magnitudes are comparable, indicating that the voltage component generated by the negative sequence disturbance through the coupling path ( Z pn I n The voltage component generated by the positive sequence disturbance ( Z pp I p The impact of ) cannot be ignored, and similarly Z np I p The impact of voltage components generated by negative sequence disturbances cannot be ignored; therefore, the influence of frequency coupling must be considered in the stability analysis.

[0084] Figure 4 The comparison curves of theoretical and simulated values ​​of the positive and negative sequence impedances of the system considering dynamic changes in DC voltage are presented. The solid lines represent the theoretical values ​​of the positive and negative sequence impedance magnitudes and phase angles, while the circles represent the simulated values. Figure 4 It can be seen that the positive and negative sequence impedance theory and the simulation values ​​basically coincide, indicating that the system model built is feasible and reliable, and control analysis can be carried out on the basis of this model.

[0085] To comprehensively evaluate the applicability of the established impedance model under different grid strengths and to deeply analyze the impact of DC voltage dynamics on the stability boundary, the following steps were taken: L g The parameters of the system are compared and studied by varying the power grid from a weak grid (20e-3H) to a strong grid (5e-3H). The generalized Nyquist criterion is used to analyze the stability of the system. If the Nyquist curve of the system transfer function encloses the point (-1, j0), the system is unstable. Figure 5 Comparison curves of the Nyquist stability analysis of the positive and negative sequence impedances of the system are presented. The red curve represents the Nyquist curve of the positive sequence impedance system and its mirror image, while the blue dashed line represents the Nyquist curve of the negative sequence impedance system and its mirror image. Figures (a) and (b) show the Nyquist plots of the positive and negative sequence impedances considering dynamic changes in DC voltage, while figures (c) and (d) show the Nyquist plots of the positive and negative sequence impedances without considering dynamic changes in DC voltage. Figures (a) and (c) show that when... L g When the impedance is 20e-3H (reduced to 6e-3H), the Nyquist curves of the positive and negative sequence impedances of the system do not include the point (-1, j0), indicating that the system is stable. At this time, the grid impedance itself is relatively large, which dominates the damping characteristics of the system; Figure (b) shows that when L g At 5e-3H, under strong grid conditions, the interaction between the internal control dynamics of the VSG (especially the coupling of DC voltage dynamics through the power loop and the mirror frequency effect) and the grid impedance is intensified, forming a strong positive feedback path. The Nyquist curve of the system's positive sequence impedance contains the point (-1, j0), indicating that the system is unstable. Figure (d) shows that ignoring DC voltage dynamics can easily lead to misjudgment of system stability, affecting the stable operation of the system. Figures (c) and (d) show that when the grid strength is high, the system's inherent damping is small. If DC voltage dynamics are ignored, the established model will not be able to accurately predict the instability risk caused by the front-stage-back-stage coupling, thus overestimating the system's stability margin and bringing safety hazards to system design in engineering practice.

[0086] II. Verify the stability of AC / DC voltage, current, and frequency, such as Figure 6-7 As shown.

[0087] like Figure 6 As shown, the DC bus voltage and frequency curves are given when the system is stable after considering the dynamic changes of DC voltage. It can be seen from the figure that when the DC bus voltage is stable, the fluctuation range is 700±5V and the fluctuation rate is 0.714%; when the system load changes, the fluctuation range is 700±10V and the fluctuation rate is 1.43%; the stable frequency variation range of the system is between 50±0.02Hz.

[0088] like Figure 7As shown in the figure, the waveform distortion rate of the AC side current and voltage is given when the DC voltage is stable after considering the dynamic changes of DC voltage. As can be seen from the figure, the waveform distortion rate of the AC bus current is 1.6% and the voltage waveform distortion rate is 0.63% when the system is running stably. Figure 6 , 7 This indicates that the key parameters on both the AC and DC sides can meet the requirements for power system operation.

[0089] III. Verify the impact of control parameters.

[0090] First, we compare and analyze the effects of different PI control parameters on the AC and DC side voltage and current of the system. Figure 8 The DC bus voltage conditions are given for P=0.8, I=8, P=0.48, I=3, P=1, and I=16. The total system load decreases from 8200W to 5000W in 1.5 seconds and increases from 5000W to 7000W in 2.5 seconds. It can be seen that the DC voltage fluctuation amplitude of the system remains basically consistent during stable operation. Figure 9 The distortion rates of AC side current and voltage waveforms are given when the PI control parameters are P=0.8, I=8 and P=1, I=16. Figure 6 With P=0.48 and I=3, the results show that within a certain range, the dynamic impact of DC voltage on system stability is small and the sensitivity is low.

[0091] Figure 10 In the middle, setting T _ff A constant value of 0.8 was used to verify the differences. K _ff Comparison curves of positive and negative sequence impedance amplitudes and phase angles of the system; Figure 11 In the middle, setting K _ff The value is constant at 8, and the differences are verified. T _ff Comparison curves of the positive and negative sequence impedance amplitudes and phase angles of the system.

[0092] Figure 10 In (a), as K _ff As the DC voltage feedforward compensation increases, it suppresses the coupling oscillation between DC dynamics and the power loop, reduces energy transfer resistance, and the amplitude of the positive sequence impedance at the starting point of 1Hz is continuously decreasing (the amplitude changes from negative to positive). At the same time, phase compensation cancels the inductive lag, causing the phase angle to rise and achieving "resistive dominance".

[0093] Figure 10 In (b), the negative-sequence signal and the positive-sequence signal are symmetrical about the fundamental frequency and are coupled by the mirror frequency effect (MFE). K _ffWhen the value increases, the compensation effect on the positive sequence side acts "in reverse" on the negative sequence side through the MFE, so that although the amplitude shows an increasing trend (away from the horizontal axis), the change is significantly smaller than that of the positive sequence. The phase compensation effect acts synchronously on the negative sequence side, causing the negative sequence impedance phase angle to rise continuously (the positive phase angle range expands), but the phase angle increment is smaller than that of the positive sequence side, reflecting the asymmetry of the MFE coupling.

[0094] like Figure 11 As shown in (a), the starting point is 1Hz. T _ff As it continues to decrease, G ff The low-pass filter function has a faster response speed, and the feedforward compensation can quickly track the dynamics of DC voltage, cancel reactive coupling terms, weaken AC-DC coupling strength, and the positive sequence impedance amplitude moves from negative values ​​towards the horizontal axis (continuously decreasing). T _ff Further reduction leads to excessively fast compensation response, introducing high-frequency noise, enhancing the resistive component of the positive-sequence impedance, and increasing positively after its amplitude exceeds zero; in the positive-sequence impedance phase angle curve, T _ff As the voltage decreases, the timeliness of the feedforward compensation improves, promptly offsetting the phase lag caused by the dynamic DC voltage, thus gradually raising the phase angle.

[0095] like Figure 11 As shown in (b), the negative-sequence impedance is associated with the positive-sequence impedance through mirror frequency coupling (MFE): T _ff As the impedance decreases continuously, the magnitude of the negative sequence impedance increases slowly (moving away from the horizontal axis); in the negative sequence impedance phase angle, T _ff As the phase angle decreases, the initial value of the phase angle increases slowly at 1 Hz, from 8° to 25°, and the coupling strength is weaker than the positive sequence impedance effect.

[0096] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for modeling and analyzing the frequency coupling impedance of a DC voltage dynamic VSG, characterized in that, Includes the following steps: S1: System Topology Construction: Build a two-stage VSG system including a front-end DC / DC converter, a DC bus, and a rear-end DC / AC inverter. The front-end converter regulates the DC bus voltage through PI control, and the rear-end inverter adopts grid-based control. S2: Establish a front-end DC voltage control model, which includes DC side capacitor current balance equation, AC / DC power balance relationship equation and DC voltage PI control equation to characterize the coupling relationship between DC voltage dynamics and active and reactive power. S3: Establish a power control model for the subsequent VSG, which includes active power and frequency control equations, reactive power and voltage control equations, and incorporates the power deviation term caused by DC voltage dynamics; S4: Based on the harmonic linearization method, considering the image frequency effect, establish a small-signal voltage and current model that includes the fundamental frequency, positive-sequence disturbance and negative-sequence disturbance signals; S5: Combining the influence of DC voltage dynamics on the power loop and modulation voltage, derive the admittance matrix including DC voltage coupling terms; S6: By using Park transform and inverse Park transform, combined with phase angle and internal potential dynamic modeling, the VSG output impedance matrix containing DC voltage dynamics is derived. S7: The stability of the system is analyzed using the stability criterion based on the output impedance matrix, and the analysis results are verified by combining the time-domain simulation model.

2. The method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage as described in claim 1, characterized in that, In S1, the DC-side voltage of the two-stage VSG system topology U dc The DC-side equivalent impedance is tracked by the front-end converter via PI control to obtain the reference value. Z dc =1 / (s C dc G dc ),in, G dc = K pd + K id / s, K pd , K id These represent the proportional and integral gain of the DC voltage control, respectively. C dc This indicates a parallel capacitor on the DC side.

3. The method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage as described in claim 1, characterized in that, S2 specifically includes: S21: Construct the DC-side capacitor current balance equation, the formula is: ； In the formula, Δ U dc = U dcref U dc0 , U dcref Indicates the DC voltage reference value. U dc0 This indicates the real-time value of the DC voltage. I dc1 The signal component of the equivalent current source of the preceding stage; I dc0 This refers to the DC current signal component flowing into the subsequent VSG stage; S22: Set the instantaneous active power on the AC / DC side of the subsequent VSG to be conserved, i.e., Δ P dc =Δ P e Linearization is applied near the steady-state operating point to describe the dynamic balance between DC-side power fluctuations and AC-side active power changes. The formula is: ； In the formula, Δ I dc = I dc1 - I dc0 ; u d0 , u q0 This represents the steady-state value of the dq-axis voltage; i d0 , i q0 The steady-state value of the dq-axis current; Δ u d Δ u q For the small-signal component of the dq-axis voltage; Δ i d Δ i q For the small-signal component of the dq-axis current; Δ P e The small signal component of the active power output is provided to the AC side of the subsequent VSG. S23: Obtain the DC voltage PI control equation, where the DC voltage control proportional gain is... K pd The integral gain is K id Then the signal components of the preceding current source are: ； The proportional term quickly responds to voltage deviations, the integral term eliminates steady-state errors, and the output controlled current source command stabilizes the DC bus voltage.

4. The method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage as described in claim 1, characterized in that, Specifically, S3 includes: S31: Establish the control equations for active power and frequency, with the following formulas: ； ； ； ； In the formula, J This is a virtual moment of inertia; ω v , ω n These are the VSG output angular frequency and the grid rated angular frequency, respectively. T set , T e These are the reference torque and the electromagnetic torque, respectively. T dc = This represents the torque disturbance term caused by dynamic DC voltage. D p This is the active damping coefficient; P ref , P e These are the active power reference value and the electromagnetic power, respectively. θ The phase angle of the internal potential of the VSG; S32: Reactive power and voltage control equations, the formula is: ； In the formula, K Voltage coefficient; Q ref , Q e These are the reactive power reference value and the electromagnetic power, respectively. D q This is the voltage droop factor; V 0、 V These are the rated voltage amplitude and the VSG output voltage amplitude, respectively. E m0 The magnitude of the internal potential of the VSG; Δ E ff =Δ U dc G ff / U dcref This represents the internal potential increment of DC voltage feedforward compensation. G ff = K_ ff / ( T_ ff s +1); Δ Q dc = K dc-Q Δ U dc This represents the coupling term between DC voltage deviation and reactive power. K dc-Q =0.02 represents the reactive-DC voltage coupling coefficient; The instantaneous output active and reactive power of the VSG can be expressed as: ； In the formula, v d , i d These represent the d-axis output voltage and current, respectively. v q , i q These represent the q-axis output voltage and current, respectively. The modulation wave of the VSG is determined by the active and reactive power loops, and the expression for the three-phase modulation wave is: ； In the formula, e am , e bm , e cm It is a VSG three-phase modulated wave; S33: Includes the power deviation term caused by DC voltage dynamics, specifically: The relationship between the VSG internal potential, output terminal voltage, and output current is as follows: ； in, , , The formula representing the dynamic correction of the DC voltage to the three-phase internal potential is: (12)。 5. The method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage as described in claim 1, characterized in that, S4 specifically includes: In the time domain, after adding a small signal disturbance, the voltage and current at the output terminal of phase A are given by the following formulas: ； ； In the formula, V 1. V p , V n These represent the amplitudes of the fundamental voltage, positive-sequence voltage disturbance, and negative-sequence voltage disturbance, respectively. I 1. I p , I n These represent the amplitudes of the fundamental current, positive-sequence current response, and negative-sequence current response, respectively. f 1 represents the fundamental frequency; φ v1 φ vp , φ vn These are the initial phase angles of the fundamental, positive-sequence, and negative-sequence voltage disturbances, respectively. φ i1 , φ ip , φ in These are the initial phase angles of the fundamental current, the positive-sequence current response, and the negative-sequence current response, respectively. In the frequency domain, the above voltage and current expressions are: ； ； in: , , , , , .

6. The method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage as described in claim 1, characterized in that, S5 specifically includes: The small-signal characteristics of the VSG AC port can be described by the admittance matrix. Considering the dynamic effect of DC voltage on the power loop and modulation voltage, the admittance matrix takes the following form: ； In the formula, ω 1=2 πf 1; In the fundamental admittance matrix Y PN In (s), Y pp ( s ), Y nn ( s These represent the positive-order and negative-order self-admittances, respectively. Y pn ( s ), Y np ( s ) represents the cross-coupled admittance.

7. The method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage as described in claim 1, characterized in that, S6 specifically includes: S61: After the Park transform, the output voltage and current in the frequency domain can be expressed as: ； ； ； ； In the formula, dc represents direct current; , The voltage frequency domain component of the dq axis; , The frequency domain components of the dq-axis current; S62: Substituting the formulas from step S61 into the instantaneous output active and reactive power formulas of the VSG, and using the frequency domain convolution theorem, the frequency domain expressions for active and reactive power, including DC voltage dynamics, can be obtained: ； ； in, The superscript "*" indicates complex conjugation; S63: Perform dynamic modeling of phase angle and internal potential to derive the basic admittance model.

8. The method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage as described in claim 7, characterized in that, In S63, the phase angle θ During dynamic modeling, it is possible to θ Represented as ,in θ 1 represents the phase angle of the fundamental voltage. For small disturbances caused by disturbance voltage, frequency domain expressions for active and reactive power, which include DC voltage dynamics, are derived using the frequency domain convolution theorem.

9. The method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage as described in claim 1, characterized in that, In S7, the stability verification adopts the generalized Nyquist criterion. The equivalent impedance ratio is formed by calculating the ratio of the positive-sequence equivalent input impedance, the negative-sequence equivalent input impedance and the system grid impedance, and its Nyquist curve is plotted. The stability is judged by combining the real part and the imaginary part characteristics.

10. The method for modeling and stability analysis of dynamic VSG frequency coupling impedance considering DC voltage as described in claim 1, characterized in that, The relationship between the VSG internal potential, output terminal voltage, and output current includes a DC voltage dynamic correction term for the three-phase internal potential, with DC correction terms set for the d-axis and q-axis. The transient reactive power coupling coefficient on the q-axis is also included. K q-dc =0.002, transient q-axis reactive power coupling correction factor K q-dc0 =0.005.

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