Amplitude and phase feedback system, modeling method thereof and low-frequency oscillation analysis method

Abstract

The application discloses a magnitude and phase feedback system, a modeling method thereof and a low-frequency oscillation analysis method, the system comprises a forward channel and a feedback channel, the stability of the magnitude and phase feedback system is judged by the quadrant where the component composition vector flowing through the feedback channel is located, and dynamic feedback effects between a frequency change rate and a transient frequency offset, a voltage change rate and a transient voltage offset can be identified in combination with the composition vector. The amplitude and phase feedback model of "frequency change rate-transient frequency offset" (RoCoF-TFE) and "voltage change rate-transient voltage offset" (RoCoV-TV) is introduced. The application further provides a modeling method of the above-mentioned magnitude and phase feedback system and a low-frequency oscillation analysis method based on a flexible DC power transmission system. The inertia, damping and stiffness of wide-frequency oscillation and synchronous instability in the flexible DC power transmission system are comprehensively dynamically analyzed, and the relationship between inertia support and energy release is described.

Description

Technical Field

[0001] This invention relates to the fields of virtual synchronous generator control technology and flexible DC transmission system technology, specifically to an amplitude-phase feedback system and its modeling method, and a low-frequency oscillation analysis method. Background Technology

[0002] Virtual synchronous generators (VSGs) have become a popular grid-connected control strategy and are applied in modern power electronic systems. This change enables renewable energy-friendly grid integration; for example, VSG control, which mimics the dynamic characteristics of traditional synchronous generators, can provide inertia, system damping, and stiffness support to the grid. However, the prerequisite for supporting inertia, damping, and stiffness is whether the VSG can maintain stable operation in an interactive system with the grid. However, grid-connected VSG systems are susceptible to broadband oscillations and aperiodic synchronization instability (LoS) when subjected to certain disturbances. Therefore, stability issues still exist in modern power systems and require further exploration in academic and engineering practice.

[0003] To study the physical nature of instability hidden in modern power systems, different model frameworks have been established, namely impedance models, state-space models based on eigenvalue analysis, amplitude-phase motion equations (MPME) models, etc.

[0004] The aforementioned traditional models have been extensively discussed. For example, within the framework of the amplitude-phase motion equation model, the damping torque and synchronous torque do not consider the inertia of the system. To fill this gap, a new RoCoF-FD framework that incorporates the influence of the inertia component is proposed. Under this framework, the motion trajectories of RoCoF and FD can be intuitively identified. However, this framework only considers the dynamic analysis of AC frequency and lacks AC / DC hybrid dynamic analysis. Furthermore, the physical mechanisms are not clearly elucidated within the frameworks using RoCoF-TFE and RoCoV-TVE. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides an amplitude-phase feedback system and its modeling method, a low-frequency oscillation analysis method, and amplitude-phase feedback systems based on "rate of change of frequency - transient frequency shift" (RoCoF-TFE) and "rate of change of voltage - transient voltage shift" (RoCoV-TVE). These systems can analyze the stability of DC voltage, the stability of AC frequency, and the interaction behavior between DC voltage and AC frequency in flexible DC transmission systems, and elucidate their principles.

[0006] In a first aspect of the invention, an amplitude-phase feedback system is provided, the amplitude-phase feedback system including a forward channel and a feedback channel, the stability of the amplitude-phase feedback system is determined by the quadrant in which the component synthesis vector flowing through the feedback channel is located, and the dynamic feedback effect between the rate of frequency change and transient frequency offset, and the rate of voltage change and transient voltage offset can be identified by combining the synthesis vector.

[0007] Furthermore, the amplitude-phase feedback system includes a method for determining the stability of the amplitude-phase feedback system:

[0008] If the synthesized vector is located in the first quadrant, when a positive feedback effect is formed in the synchronous and oscillatory components, oscillatory instability and synchronous instability occur, and TFE will force RoCoF to increase continuously, thereby further increasing TFE;

[0009] If the synthesized vector is located in the second quadrant, oscillations occur and the system remains synchronized, resulting in a positive feedback effect on the oscillations but a negative feedback effect on the synchronization performance.

[0010] If the composite vector is located in the third quadrant, it forms negative feedback for both oscillatory stability and synchronous stability, and the system is stable.

[0011] If the synthesized vector is located in the fourth quadrant, it creates a positive feedback effect on synchronization stability. The virtual synchronizing machine will lose its synchronization tracking of the power grid and thus produce aperiodic synchronization instability deviation.

[0012] Furthermore, the amplitude-phase feedback system includes a "frequency change rate - transient frequency offset" system and a "voltage change rate - transient voltage offset" system;

[0013] The forward channel of the “frequency change rate - transient frequency offset” system includes a single integral element, and the feedback channel includes a virtual damped acceleration component, a synchronous acceleration component, and a feedback acceleration component.

[0014] The forward path of the "voltage change rate - transient voltage offset" system includes a single integrator, and the feedback path includes a dynamic coupling component and a DC dynamic component.

[0015] Furthermore, in the aforementioned "frequency change rate - transient frequency offset" system, the virtual rotor acceleration dω / dt of the virtual synchronous machine is obtained by a single integration element to obtain the relative velocity of the virtual rotor angular frequency relative to the grid angular frequency. The relative velocity is then superimposed through three feedback channels to obtain the VSG virtual rotor acceleration dω / dt.

[0016] Furthermore, in the aforementioned "voltage change rate - transient voltage offset" system, the DC voltage change rate dV dcThe transient voltage offset is obtained by integrating / dt through a single integrator. This transient voltage offset is then superimposed through two feedback channels to obtain dV. dc / dt.

[0017] In a second aspect of the invention, a modeling method for an amplitude-phase feedback system is also provided, the modeling method comprising the steps of:

[0018] (1) Based on the circuit theorem and the law of conservation of energy, establish the mathematical model of the amplitude-phase feedback system:

[0019]

[0020] In the formula, θ G1 ,θ1,θ f1 These represent the phase angles of the output voltage and current of the AC network at the sending end of the flexible DC transmission system and the virtual synchronous machine, respectively. G1 E1 is the voltage amplitude of the rectifier-side AC grid, and E2 is the voltage amplitude of the rectifier-side virtual synchronous machine. n The nominal frequency is given, j represents the imaginary unit, s is the Laplace operator, and L... f1 R f1 L g1 R g1 These represent the inductance, parasitic resistance, mains equivalent inductance, and resistance values ​​of the VSG1 output filter, respectively.

[0021] (2) Linearize the AC side dynamic model using a synchronous rotating inertia reference frame, i.e.:

[0022]

[0023] In the formula, To synchronously rotate the reference coordinate system;

[0024] (3) Considering the coupling situation, list the small-signal power equations and Kirchhoff voltage equations for the converters at both ends and the intermediate DC cable. The rotor motion equation of the virtual synchronous machine on the rectifier side is:

[0025]

[0026] In the formula, J p1 D represents the virtual inertia coefficient of the reactive power channel in the rectifier-side control algorithm. p1 J represents the virtual damping coefficient of the active power channel in the rectifier-side control algorithm. q1 D represents the virtual inertia coefficient of the reactive power channel in the rectifier-side control algorithm. q1 The virtual damping coefficient of the reactive power channel represents the rectifier-side control algorithm, Δδω1 represents the transient frequency offset of the rectifier side, and ΔP represents the rectifier-side control algorithm. ref1 ΔQ is the reference value for active power on the rectifier side. ref1ΔP1 and ΔQ1 are the active and reactive power injected into VSG1, respectively, ΔE1 is the voltage amplitude of the virtual synchro on the rectifier side, and Δω1 is the output angular frequency of the virtual synchro on the rectifier side.

[0027] (4) By combining the equations of the circuit section and the control section, we can obtain the active power closed-loop control system model on the inverter side and the DC voltage closed-loop control system model on the rectifier side.

[0028] The main circuit model of the inverter-side converter output is as follows:

[0029]

[0030] In the formula, θ G2 ,θ2,θ f2 These are the phase angles of the receiving-end grid voltage, the output voltage phase angle of the inverter-side virtual synchronous machine, and the output current phase; E2, V G2 These represent the output voltage amplitude of the virtual synchronous machine on the inverter side and the voltage amplitude of the grid at the receiving end, respectively; L f2 L g2 R f2 R g2 These are, respectively, the inductance value of the inverter output filter, the inductance value of the grid equivalent impedance, the resistance value of the grid equivalent impedance, the parasitic resistance value of the output filter, and the resistance value of the grid equivalent impedance;

[0031] The rotor motion equation model of the virtual synchronous machine on the inverter side is as follows:

[0032]

[0033] In the formula, Δδω2 represents the transient frequency offset of the virtual synchronous machine on the inverter side, and D p2 J represents the virtual damping coefficient of the active power channel in the inverter-side virtual synchronous machine control algorithm. p2 The virtual inertia coefficient of the active channel, ΔP, represents the control algorithm of the virtual synchronous machine on the inverter side. ref2 ΔP2 is the active power reference value of the inverter-side active power control loop, ΔQ is the actual output active power of the inverter side, and ΔQ is the active power reference value of the inverter-side active power control loop. ref2 J represents the reactive power reference value of the inverter-side reactive power control loop, ΔQ2 represents the actual output reactive power of the inverter side, and J represents the reactive power of the inverter side. q2 D represents the virtual inertia coefficient of the reactive power channel in the inverter-side virtual synchronous machine control algorithm. q2 ΔE2 is the virtual damping coefficient of the reactive power channel in the inverter-side virtual synchronous machine control algorithm, and ΔE2 is the output voltage amplitude of the inverter-side virtual synchronous machine.

[0034] (5) Under the framework of “frequency change rate - transient frequency shift” and “voltage change rate - transient voltage shift”, the models of the feedback system on the rectifier side and the inverter side are built respectively.

[0035] In a third aspect of the invention, based on the flexible DC transmission system and the aforementioned amplitude-phase feedback system, a low-frequency oscillation analysis method is also provided, the analysis method comprising:

[0036] Determine the coupling relationship between the virtual inertia, virtual damping, and grid stiffness of the amplitude-phase feedback system;

[0037] Based on the coupling relationship between virtual inertia, virtual damping, and grid stiffness, determine the influence of virtual inertia, virtual damping, and grid stiffness on dynamic frequency change rate and transient frequency offset.

[0038] Based on the feedback effect of system frequency and DC voltage in the amplitude-phase feedback system, the dynamic interaction between the rectifier, DC network and inverter in the flexible DC transmission system is obtained;

[0039] By combining virtual inertia, virtual damping, and stiffness in the energy release and absorption of the system frequency oscillation, the relationship between inertia level and energy release or energy absorption is quantitatively analyzed.

[0040] By combining the released energy, we further analyze the relationship between inertial support and energy release.

[0041] Furthermore, the coupling relationship between virtual inertia, virtual damping, and grid stiffness is as follows:

[0042]

[0043] In the formula, L is the total inductance from the converter output point to the AC mains point, and k stiff The defined grid stiffness coefficient.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] 1. This invention provides an amplitude-phase feedback system, including a "rate of change of frequency-transient frequency offset" (RoCoF-TFE) system and a "rate of change of voltage-transient voltage offset" (RoCoV-TVE) system, which can analyze the stability of DC voltage, the stability of AC frequency, and the interaction behavior between DC voltage and AC frequency in flexible DC transmission systems, and elucidate their principles.

[0046] 2. This invention also provides a modeling method for amplitude-phase feedback systems, which can intuitively correlate RoCoF and TFE with frequency stability. Furthermore, the principles of DC voltage oscillations and DC voltage synchronous instability are revealed through a framework of rate of change of voltage (RoCoV)-transient voltage offset (TVE). It also allows for the identification of RoCoF and TFE, RoCoV and TVE, and their interactions, rather than simply determining dynamic stability from a single port.

[0047] 3. Furthermore, this invention also provides a low-frequency oscillation analysis method based on flexible DC transmission systems. By considering the effects of virtual inertia, virtual damping, and grid stiffness, it comprehensively discusses the dynamic interaction between the rectifier, DC network, and inverter, and quantitatively discusses the relationship between inertia level and energy release or energy absorption. In addition, the relationship between inertia support and energy release is physically elucidated. Attached Figure Description

[0048] Figure 1 This diagram illustrates the topology and control strategy of a flexible DC transmission system; in the diagram, V ref This is the reference value for DC voltage; V dc1 The DC side voltage is located near the rectifier side; PI is the proportional-integral circuit; P1 and Q1 are the power injected into VSG1; ω n Represents the nominal angular velocity; D p1 The virtual damping coefficient of the active power path representing the rectifier-side control algorithm; J p1 δω1 represents the virtual inertia coefficient of the reactive power channel in the rectifier-side control algorithm; ω1 represents the transient offset between the VSG frequency and the grid frequency; ω1 represents the VSG frequency; θ1 represents the phase angle of VSG1; Q ref1 D is the reference value for reactive power on the rectifier side. q1 The virtual damping coefficient of the reactive power channel representing the rectifier-side control algorithm; J q1 The virtual inertia coefficient represents the reactive power channel of the rectifier-side control algorithm; δ1 represents the transient offset between the VSG1 voltage amplitude and the rectifier-side grid voltage amplitude; V G1 E1 is the voltage amplitude of the AC grid on the rectifier side; E1 is the voltage amplitude at VSG1, and the corresponding parameters on the inverter side on the right can be obtained similarly; SPWM is sinusoidal pulse width modulation.

[0049] Figure 2 This is the rectifier-side DC voltage closed-loop control system in this embodiment; in the figure, Δδθ1 equals θ1 minus θ G1 And take the small signal model, θ G1 Δδθ1 is the phase angle of the AC grid on the rectifier side; Hdp is the transfer function from Δδθ1 to ΔP1 in equation (5) considering voltage, phase angle, active and reactive coupling; the subscript 0 indicates that the quantity takes the steady-state value; the mark Δ indicates that the variable is small-signalized.

[0050] Figure 3 This is the active power closed-loop control system on the inverter side in this embodiment.

[0051] Figure 4 This is a frequency dynamic decay diagram based on the physical analysis of inertia, damping, and stiffness in this embodiment. The virtual damping changes from 16000 to 56000 with a step size of 10000. In the diagram, Freq is the frequency and pu is the per-unit value.

[0052] Figure 5 Figure (a) shows the frequency unit step response diagram in this embodiment; where Figure (a) shows the virtual inertia changing from 2000 to 10000 with a step size of 2000; and Figure (b) shows the stiffness changing from 0.3183 to 0.0796 with a step size of -0.0796.

[0053] Figure 6 This refers to the RoCoF-TFE and RoCoV-TVE frameworks proposed in this embodiment for analyzing the frequency and DC voltage stability of VSG-based flexible DC systems.

[0054] Figure (a) shows the RoCoF-TFE frame on the rectifier side, where Δα ref1 The reference acceleration represents the rectifier-side frequency; Δdω1 / dt represents the rectifier-side frequency change rate (RoCoF); ω n Represents the nominal angular velocity; Δδω1 represents the transient frequency shift (TFE) on the rectifier side; D p1 The virtual damping coefficient representing the rectifier-side control algorithm; J p1 FA1 represents the virtual inertia coefficient of the rectifier-side control algorithm; FA2 represents the component of feedback acceleration from virtual damping; FA3 represents the component of feedback acceleration from synchronization; and FA4 represents the component of feedback acceleration from reactive dynamic coupling.

[0055] Figure (b) shows the RoCoF-TFE frame on the inverter side, where Δα ref2 The reference acceleration represents the inverter-side frequency; Δdω² / dt represents the inverter-side frequency change rate (RoCoF); Δδω² represents the inverter-side transient frequency offset (TFE); D p2 The virtual damping coefficient representing the inverter-side control algorithm; J p2 FA1 represents the virtual inertia coefficient of the inverter-side control algorithm; FA2 represents the component of feedback acceleration from virtual damping; FA3 represents the component of feedback acceleration from synchronization; and FA4 represents the component of feedback acceleration from reactive dynamic coupling.

[0056] Figure (c) shows the RoCoV-TVE framework on the rectifier side, where Δα... refdc Reference acceleration of DC-side voltage; ΔdV dc / d represents the rate of change of voltage (RoCoV); ΔδV dc Represents transient voltage offset (TVE); G dcdynamic (s) represents the transfer function of the DC network dynamic feedback effect from transient voltage offset (TVE) to RoCoV; G fvc (s) represents the dynamic coupling transfer function between DC voltage and AC frequency.

[0057] Figure 7 This is the frequency response diagram of the feedback frame in this embodiment, where (a)(c)(e)(g) are... Figure 6 (b) The framework obtained, (b)(d)(f) is based on Figure 6 (a) is obtained from the framework, (h) is based on Figure 6 (c)(d) The above are all Bode plots, namely the logarithmic magnitude-frequency curve and the logarithmic phase-frequency curve.

[0058] Figure 8 In this embodiment, and Figure 7 The corresponding composite vector diagram of the feedback transfer function (FTF) in the figure, from (a) to (h) and Figure 7 (a) to (h) in the text match.

[0059] Figure 9 For this embodiment Figure 6 (c) Reconstruction diagram.

[0060] Figure 10 Figure (a) shows the oscillation instability (ORI) phenomenon of the flexible DC system based on VSG in this embodiment. Figure (b) shows the inverter-side frequency, and Figure (c) shows the rectifier-side frequency.

[0061] Figure 11 Figure 1 shows the non-periodic synchronous instability (LoS) phenomenon of the flexible DC system based on VSG in this embodiment under the influence of grid strength interference; where Figure 2(a) is the AC frequency on the inverter side, Figure 3(b) is the AC frequency on the rectifier side, Figure 4(c) is the DC voltage on the inverter side, and Figure 5(d) is the reference value and actual active power in case 3 on the rectifier side.

[0062] Figure 12 Figure (a) shows the non-periodic synchronous instability (LoS) phenomenon of the flexible DC system based on VSG in this embodiment under the step disturbance caused by the active power on the inverter side; where Figure (a) is the inverter side frequency and Figure (b) is the DC voltage.

[0063] Figure 13 Figure 1 shows the DC voltage DC side resonance diagram and the AC frequency diagram of the inverter side in this embodiment; wherein, Figure (a) shows the DC voltage and current in Case 1 of Table 7, Figure (b) shows the DC voltage and current in Case 2 of Table 7, Figure (c) shows the DC voltage and current in Case 3 of Table 7, Figure (d) shows the AC frequency in Case 1 of Table 7, Figure (e) shows the AC frequency in Case 2 of Table 7, and Figure (f) shows the AC frequency in Case 3 of Table 7. Detailed Implementation

[0064] To facilitate understanding of the present invention, a more comprehensive description of the present invention will be given below with reference to the accompanying drawings, which illustrate several embodiments of the present invention. However, the present invention can be implemented in different forms and is not limited to the embodiments described in the text. Rather, these embodiments are provided to make the disclosure of the present invention more thorough and complete.

[0065] This invention discloses an amplitude-phase feedback system and its modeling method, as well as a low-frequency oscillation analysis method based on a flexible DC transmission system. The amplitude-phase feedback system includes a forward channel and a feedback channel. The stability of the amplitude-phase feedback system is determined by the quadrant in which the component synthesis vector flowing through the feedback channel is located. Furthermore, the dynamic feedback effect between the rate of frequency change and transient frequency shift, and between the rate of voltage change and transient voltage shift can be identified by combining the synthesis vector.

[0066] The aforementioned amplitude and phase feedback system mainly includes the "Rate of Frequency Change - Transient Frequency Shift" (RoCoF-TFE) system and the "Rate of Voltage Change - Transient Voltage Shift" (RoCoV-TVE) system. The RoCoF-TFE system is divided into two types: rectifier side and inverter side, while the RoCoV-TVE system is only on the rectifier side. All three systems have forward and feedback channels.

[0067] The RoCoF-TFE system's forward path includes a single integrator, while the feedback path includes virtual damped acceleration components, synchronous acceleration components, and feedback acceleration components. Furthermore, in the RoCoF-TFE system, the VSG virtual rotor acceleration dω / dt is integrated through the single integrator to obtain the relative velocity of the virtual rotor angular frequency relative to the grid angular frequency. This relative velocity is then superimposed through the three feedback paths to obtain the VSG virtual rotor acceleration dω / dt.

[0068] The forward path of the RoCoV-TVE system includes a single integrator, while the feedback path includes a dynamic coupling component and a DC dynamic component. The dynamic coupling component represents the dynamic coupling between the DC voltage and the AC frequency, while the DC dynamic component represents the feedback effect from the TVE to RoCoV. In the RoCoV-TVE system, the rate of change of the DC voltage, dV... dc The transient voltage offset is obtained by integrating / dt through a single integrator. This offset is then superimposed through two feedback channels to obtain dV. dc / dt.

[0069] In the three amplitude-phase feedback systems mentioned above, the stability of the system can be determined based on the quadrant in which the composite vector of each component is located.

[0070] To further illustrate the above-mentioned amplitude-phase feedback system, the present invention also provides a modeling method for the amplitude-phase feedback system, specifically taking a flexible DC transmission system as an example.

[0071] like Figure 1 The diagram shows the hardware circuit topology and control strategy of the flexible DC transmission system. The mathematical model is established in three parts: the rectifier side, the inverter side, and the DC cable side.

[0072] First, the mathematical model can be obtained from the topology of the rectifier side:

[0073]

[0074] In equation (1), θ G1 ,θ1,θ f1 These are the phase angles of the AC network, VSG, and current, respectively, ω. n V is the nominal frequency. G1 E1 is the voltage amplitude of the rectifier-side AC grid, and E2 is the voltage amplitude of the rectifier-side virtual synchronous machine. n The nominal frequency is given, j represents the imaginary unit, s is the Laplace operator, and L is the nominal frequency. f1 R f1 L g1 R g1 These represent the inductance, parasitic resistance, mains equivalent inductance, and resistance values ​​of the VSG1 output filter, respectively.

[0075] To linearize the dynamic model on the AC side, a synchronous rotating inertia reference frame (SRIRF) is required, i.e., both sides of equation (1) are multiplied simultaneously. Right now:

[0076]

[0077] in

[0078] Using Euler expansion, equation (2) can be transformed into:

[0079] in

[0080] The instantaneous equations for active power and reactive power are:

[0081]

[0082] Linearizing equations (3) and (4) around the equilibrium point, the dynamic coupling formulas for phase angle, voltage magnitude, active power, and reactive power can be written as:

[0083]

[0084] according to Figure 1 The dynamic control block diagram of the rectifier side in the diagram can be written as follows: The dynamic swing equation of the VSG can be reduced to a small signal form:

[0085]

[0086] In the formula, J p1 D represents the virtual inertia coefficient of the reactive power channel in the rectifier-side control algorithm. p1 J represents the virtual damping coefficient of the active power channel in the rectifier-side control algorithm. q1 D represents the virtual inertia coefficient of the reactive power channel in the rectifier-side control algorithm. q1 The virtual damping coefficient of the reactive power channel represents the rectifier-side control algorithm, Δδω1 represents the transient frequency offset of the rectifier side, and ΔP represents the rectifier-side control algorithm. ref1 ΔQ is the reference value for active power on the rectifier side. ref1 ΔP1 and ΔQ1 are the active and reactive power injected into VSG1, respectively, ΔE1 is the voltage amplitude of the virtual synchronous machine on the rectifier side, and Δω1 is the output angular frequency of the virtual synchronous machine on the rectifier side.

[0087] The reference value in equation (6) comes from the outer loop of DC voltage, that is:

[0088]

[0089] If energy loss on the rectifier side is ignored, the small-signal model of energy conservation can be written as:

[0090]

[0091] According to equations (5) to (8), the rectifier-side closed-loop control system is as follows: Figure 2 As shown, DC voltage stability and DC voltage trajectory can be evaluated.

[0092] The mathematical model, namely the main circuit model of the inverter output circuit, can be obtained from the inverter-side topology:

[0093]

[0094] In the formula, θ G2 ,θ2,θ f2 These are the phase angles of the receiving-end grid voltage, the output voltage phase angle of the inverter-side virtual synchronous machine, and the output current phase; E2, V G2 These represent the output voltage amplitude of the virtual synchronous machine on the inverter side and the voltage amplitude of the grid at the receiving end, respectively; L f2 L g2 R f2 R g2 These are the inductance value of the inverter output filter, the inductance value of the grid equivalent impedance, the resistance value of the grid equivalent impedance, the parasitic resistance value of the output filter, and the resistance value of the grid equivalent impedance.

[0095] Expanding equation (9) using Euler's method, we get:

[0096]

[0097] The active and reactive power of the system transmitting data from the DC side to the onshore inverter network can be written as:

[0098]

[0099] The small-signal model of equations (10) and (11) can be written as:

[0100]

[0101] Where H 11 H 12 H 21 H 22 It represents the coupling relationship between active power, reactive power, phase angle, and voltage amplitude.

[0102] The rotor motion equation model of the inverter-side virtual synchronous machine, i.e., the dynamic swing equation of the inverter-side VSG, can be written as:

[0103]

[0104] In the formula, Δδω2 represents the transient frequency offset of the virtual synchronous machine on the inverter side, and D p2 J represents the virtual damping coefficient of the active power channel in the inverter-side virtual synchronous machine control algorithm. p2 The virtual inertia coefficient of the active channel, ΔP, represents the control algorithm of the virtual synchronous machine on the inverter side. ref2 ΔP2 is the active power reference value of the inverter-side active power control loop, ΔQ is the actual output active power of the inverter side, and ΔQ is the active power reference value of the inverter-side active power control loop. ref2 J represents the reactive power reference value of the inverter-side reactive power control loop, ΔQ2 represents the actual output reactive power of the inverter side, and J represents the reactive power of the inverter side. q2 D represents the virtual inertia coefficient of the reactive power channel in the inverter-side virtual synchronous machine control algorithm. q2 ΔE2 is the virtual damping coefficient of the reactive power channel in the inverter-side virtual synchronous machine control algorithm, and ΔE2 is the output voltage amplitude of the inverter-side virtual synchronous machine.

[0105] According to equations (12) and (13), the closed-loop active dynamic control system is as follows: Figure 3 As shown.

[0106] according to Figure 2 and Figure 3 The closed-loop control framework, the RoCoF-TFE framework on the rectifier and inverter sides, and the RoCoV-TVE framework on the rectifier side can be rearranged, such as... Figure 6 As shown.

[0107] exist Figure 6 In (a), δω(ω-ω) nTFE can be considered as the "relative velocity (RV)" of the angular frequency of the VSG's virtual rotor relative to the angular frequency of the grid, and dω / dt (RoCoF) can be seen as the acceleration of the VSG's virtual rotor, as it describes the rate of change of the dynamic frequency. Therefore, based on this idea, if a positive feedback effect (PFE) forms between RV and acceleration, RV will cause the acceleration to continuously increase, and then the acceleration will in turn affect RV, causing it to increase further. Thus, a positive feedback effect PFE is formed, leading to both RoCoF and TFE becoming increasingly larger, representing intensified oscillations or aperiodic synchronous instability. FA1, FA2, and FA3 represent the three components of the feedback acceleration from virtual damping, synchronization, and reactive power dynamic coupling, respectively. These three components can be synthesized into a vector, which can be decomposed into two orthogonal orientations: one related to oscillation-related instability (ORI) and the other related to aperiodic synchronous instability (ALoS).

[0108] It is important to note that Figure 6 The feedback framework in (a) comes from the inner loop of the VSG on the rectifier side, and its purpose is to identify frequency stability assessments on the rectifier side.

[0109] Figure 6 The architecture of the feedback framework in (b) and Figure 6 (a) is similar because it originates from the VSG control loop on the inverter side.

[0110] Figure 6 (c) is a feedback framework for evaluating the dynamic trajectory of DC voltage. Specifically, G dcdynamic (s) describes the dynamic feedback effect of the DC network from transient voltage offset (TVE) to RoCoV. It describes the interactive behavior of the DC dynamic network to the DC voltage trajectory. From Figure 6 As can be seen, the operating points of DC voltage and DC current affect the feedback path from transient voltage shift to RoCoV. This also indicates that if the DC voltage or DC current loses synchronization due to AC side loss of synchronization, it will create a local positive feedback effect on RoCoV, which is called the operating point-dependent feedback effect.

[0111] Based on the aforementioned amplitude-phase feedback system and its modeling method, this invention also proposes a low-frequency oscillation analysis method based on a flexible DC transmission system. The analysis method includes: determining the coupling relationship between the virtual inertia, virtual damping, and grid stiffness of the amplitude-phase feedback system; judging the influence of virtual inertia, virtual damping, and grid stiffness on the dynamic frequency change rate and transient frequency offset based on the coupling relationship between virtual inertia, virtual damping, and grid stiffness; obtaining the dynamic interaction between the rectifier, DC network, and inverter of the flexible DC transmission system based on the feedback effect of the system frequency and DC voltage in the amplitude-phase feedback system; quantitatively analyzing the relationship between inertia level and energy release or absorption by combining the energy release and absorption of virtual inertia, virtual damping, and stiffness in system frequency oscillations; and further analyzing the relationship between inertia support and energy release by combining the released energy.

[0112] Before we begin the analysis, let's define the grid stiffness:

[0113]

[0114] Where L is the total inductance from the converter output point to the AC mains point, and k stiff Let L be the grid stiffness as defined. As previously studied in theoretical analysis and simulation, L (grid inductance) has a greater impact on the synchronous instability of the system than R (grid resistance), and plays an important role in grid stiffness.

[0115] The process of frequency dynamic decay is as follows Figure 4 As shown. The physical essence of inertia is the ability of a system to resist further motion and change of state variables to maintain its original state when disturbed. The physical essence of damping is to reduce fluctuations in state variables around the equilibrium point; these fluctuations manifest as dissipation losses. Stiffness generally refers to the ability of a system to maintain synchronization when disturbed.

[0116] It can be seen that these three physical quantities have similar effects, namely, maintaining the stability of the system at the original equilibrium point. It can also be seen from the swing equation of VSG, as shown in equations (6) and (14), that inertia, damping and stiffness are all contained in a single active balance equation, which shows that the three quantities are coupled with each other.

[0117] Table 2. Effects of inertia, damping, and stiffness on dynamic RoCoF and TFE (see Table 2). Figure 4 )

[0118]

[0119] Table 2 shows the effects of inertia, damping, and stiffness on dynamic RoCoF(dω / dt) and TFE(δω), which are compared with... Figure 4The transient response shown is relevant. Within one oscillation cycle, the dynamic frequency can typically be divided into four parts: I, II, III, and IV.

[0120] It can be seen that RoCoF and TFE have the same sign in regions I and III, but opposite signs in regions II and IV. This indicates that they have a positive feedback effect (PFE) in regions I and III, and a negative feedback effect (NFE) in regions II and IV. The frequency motion trajectories in regions II and IV are close to the nominal equilibrium point, while the motion trajectories in regions I and III are far from the nominal equilibrium point, which also proves this phenomenon.

[0121] Inertia and damping have similar effects on frequency dynamics and trajectory because their goal is to impede changes in the state variable to maintain the original state at the last moment. As a result, their effects appear to be good in regions I and III, but poor in regions II and IV. However, stiffness always returns the frequency to the initial nominal equilibrium point, thus maintaining synchronous operation. Therefore, it has a good effect in all four regions.

[0122] Specifically, the main reason for the coupling of stiffness, inertia and damping is that oscillation-related instability (ORI) is essentially synchronous instability with a fixed oscillation period.

[0123] Specifically, transient frequency oscillations are typically caused by active power imbalances and the release and absorption of energy. Inertia, damping, and stiffness play crucial roles in energy release and absorption. Therefore, the root cause hidden in the frequency oscillations of a system is closely related to the system's inertia level, damping, and stiffness.

[0124] Figure 5 By considering the effects of virtual damping constant, virtual inertia factor and stiffness, the unit step response at frequency is shown.

[0125] Figure 4 It also demonstrates the unit step response with virtual damping varying from 16000 to 56000 in steps of 10000. Figure 5 (a) The virtual inertia changes from 2000 to 10000 with a step size of 2000; Figure 5 (b) The stiffness changes from 0.3183 to 0.0796, with a step size of -0.0796.

[0126] so, Figure 4 and Figure 5The unit step response under different virtual damping coefficient values ​​is shown. It can be seen that a higher virtual damping level results in lower overshoot, shorter settling time, smaller average rates of frequency change (RoCoF) and transient frequency offset (TFE), higher inertia, and stronger oscillation suppression ability (OSA). However, it is important to note that the effect of Dp on the synchronous tracking capability (STA) of the VSG is not yet determined. This is because while a higher Dp leads to faster response decay, it also results in a slower recovery speed. Therefore, it is difficult to determine the relationship between the virtual damping value and STA.

[0127] Specifically, the larger the Dp, the higher the inertia level because a larger Dp results in smaller average RoCoF and TFE. The frequency characteristics exhibited are the same as those of inertia. Damping and stiffness are decoupled because the damping effect is orthogonal to the stiffness effect.

[0128] The effects of increasing the virtual inertia level on the unit step response at frequency can be summarized as follows: higher overshoot, longer settling time, larger average TFE, higher inertia level, worse OSA, worse STA, and reduced stiffness. However, its effect on the average RoCoF is uncertain, because the average RoCoF is related not only to the oscillation frequency but also to the oscillation amplitude. Therefore, it can be inferred that the virtual inertia factor affects not only the inertia level but also the damping characteristics, OSA, and STA.

[0129] Table 3. Influence of inertia, damping, and stiffness on oscillation suppression capability, synchronization tracking capability, and stiffness level.

[0130]

[0131]

[0132] It is important to note that in Table 3, a positive sign indicates a positive correlation between the quantity and the index, meaning that the larger or higher the quantity, the larger, higher, or longer the corresponding index. A negative sign indicates a negative correlation between the quantity and the index.

[0133] In fact, the energy of the VSG, which provides inertia and damping support on the inverter side, originates from the DC side of the system. This invention elaborates in detail the relationship between the released energy, the nominal DC voltage, and the inertia support capability.

[0134] Assume the initial nominal DC voltage is V nom The energy release rate of a DC capacitor can then be described as:

[0135]

[0136] As can be seen from (15), as the energy released by the DC-side capacitor increases, Vnom The rate of decrease is much faster, indicating a reduction in inertia support capacity due to the slower rate of active power release. Furthermore, at the same level of active power release, the rate of voltage change is higher, which is detrimental to the stability of the system's DC side.

[0137] The initial value of the energy stored in the DC capacitor is:

[0138]

[0139] Two dynamic processes of energy release are presented, illustrating the relationship between inertia and energy. One dynamic process is the release of stored energy from E... nom Released into (1-1 / x)E nom Another dynamic process is that the stored energy changes from (1-1 / x)E. nom Released into (1-2 / x)E nom (x≥3). It can be seen that the energy released in the two dynamic processes is the same. However, the changes in transient voltage are different, i.e.

[0140]

[0141] Where V' and V” represent the final state voltages of the first and second dynamic processes, respectively. The transient voltage offsets between these two processes are represented by ΔV1 and ΔV2, respectively, i.e.:

[0142] ΔV1=V nom -V′<ΔV2=V′-V″ (18)

[0143] As can be seen from (18), when the voltage is low, more voltage is sacrificed to provide the same inertia support.

[0144] This also indicates that releasing the same amount of energy implies obtaining the same inertia support effect, but the inertia support capability decreases as the voltage level decreases. On the other hand, when the voltage drop level is the same, the amount of energy released can be assessed through two voltage change processes, namely, from V... nom Decrease to (1-1 / x)V nom , and from (1-1 / x)V nom Decrease to (1-2 / x)V nom The energy changes corresponding to these two processes can be written as:

[0145]

[0146] Here, ΔE1 and ΔE2 represent the energy released in these two processes.

[0147] From equation (19), we can see that ΔE1 < ΔE2, meaning that the energy released in the first process is less than that released in the second process. It can be seen that under the same voltage change, a lower voltage level requires more energy to provide the same voltage support. As the DC capacitor continues to discharge, the voltage support capability also decreases.

[0148] For flexible DC transmission systems using VSG control, this method reveals the physical nature of broadband oscillation stability of frequency and dynamic DC voltage.

[0149] With the help of G dcdynamic (s) and G fvc The composite vector of (s), the dynamic interaction between transient voltage offset (TVE) and rate of change of voltage (RoCoV) can be accurately evaluated. Figure 7 Showing Figure 6 The frequency response of the feedback transfer function (FTF) in the feedback framework proposed in [the paper] is presented. Three FTFs are given to identify the feedback effects of the system's frequency and DC voltage, namely:

[0150]

[0151] in To determine the FTF of the rectifier-side frequency motion trajectory, To determine the FTF of the frequency motion trajectory on the inverter side, To determine the FTF of the DC voltage trajectory in a DC network. It is important to note that the colored points in each Bode plot indicate the critical frequency for different conditions, which depends on the zero-crossing points of the corresponding open-loop transfer function, such as... Figure 2 and 3 As shown. The system parameters and general parameters for each case are shown in Tables 4 and 5.

[0152] According to Figure 7 The phase and amplitude information collected can be used to obtain, for example... Figure 8 The synthesized vector shown is used to identify the rate of change of frequency (RoCoF) and transient frequency shift (TFE), as well as the dynamic feedback effect between RoCoV and TVE.

[0153] It is important to note that Figure 7 The system parameters of (a), (c), (e), and (g) are respectively related to... Figure 7 (b), (d), (f), and (h) are the same.

[0154] Table 4 Figure 8 System parameters in (a) and (b)

[0155]

[0156]

[0157] Table 5 Figure 8 System parameters of (c) and (d)

[0158] Scenario 1 (Blue) <![CDATA[L g :7 changed from 0 millihenries to 75 millihenries]]> 500 megawatts Scenario 2 (Red) <![CDATA[L g From 70 millihenries to 77.5 millihenries 500 megawatts Situation 3 (Yellow) <![CDATA[L g From 70 millihertz to 80 millihertz 500 megawatts

[0159] Table 6 Figure 8 System parameters of (e), (f)

[0160] Scenario 1 (Blue) <![CDATA[P ref It increased by 2% P nom ]]> 500 megawatts Scenario 2 (Red) <![CDATA[P ref It increased by 5% P nom ]]> 500 megawatts Scenario 3 (Green) <![CDATA[P ref It increased by 10% P nom ]]> 500 megawatts

[0161] Table 7 Figure 8 Parameters of (g) and (h)

[0162]

[0163] Table 4 provides the following information: Figure 8 The system parameters in cases (a) and (b) are shown, with OP representing the operating point. This case study investigates the oscillation mechanism of a flexible DC transmission system caused by weak damping. Table 5 presents the system parameters under the condition of loss of synchronization due to grid inductive disturbance. Table 6 presents the active power reference disturbance and discusses the physical nature of synchronization instability (LoS) caused by active power disturbance. In Table 6, “P… nom "" indicates the nominal active power, which is equal to 500 megawatts. Table 7 gives the system parameters under the condition of DC-side resonance to illustrate the impact of DC-side resonance on AC dynamic frequency.

[0164] If the synthesized vector is located in the first quadrant, when it forms a positive feedback effect (PFE) in the synchronizing and oscillating components, both oscillating instability (OI) and synchronizing instability (LoS) will occur, meaning that the transient frequency shift (TFE) will force the rate of frequency change (RoCoF) to increase continuously, thereby further increasing the transient frequency shift (TFE).

[0165] If the synthesized vector is located in the second quadrant, oscillatory instability (OI) will occur, but the system can still remain synchronized. It has a positive feedback effect (PFE) on oscillations, but a negative feedback effect (NFE) on synchronization instability (LoS), because the accelerations are opposite for phase angles but the accelerations are the same for transient frequency shifts (TFE).

[0166] If the composite vector is located in the third quadrant, the system is stable because it provides negative feedback for both oscillatory and synchronous stability.

[0167] If the composite vector is located in the fourth quadrant, it creates a positive feedback effect (PFE) on synchronization stability, meaning that the system will lose synchronization and thus produce aperiodic synchronization instability.

[0168] Specifically, by comparing the system parameters in Tables 4 and 7 with... Figure 9 The theoretical analysis of the composite vector in the middle leads to the following conclusions regarding the stability of flexible DC transmission systems:

[0169] ① A small grid inductance results in weaker system damping, thus increasing the risk of frequency oscillation-related instability (ORI). A larger virtual damping factor results in a lower risk of ORI.

[0170] Furthermore, the higher the operating point (OP) of active power, the greater the risk of oscillation-related instability (ORI).

[0171] When D p As it decreases, OP increases, L g When the value decreases, it creates a positive feedback effect (PFE), which in turn triggers oscillation-related instability (ORI).

[0172] ②When a disturbance causes frequency oscillation on the inverter side, frequency oscillation on the rectifier side may not necessarily occur, because the DC network decouples the AC grids on both sides of the flexible DC system to a certain extent.

[0173] Moreover, the dynamic frequency on the rectifier side depends more on the feedback transfer function (TFT) on the rectifier side than on the inverter side.

[0174] ③ When L g When it changes from 70 mH to 77.5 mH and 80 mH, it forms a PFE for synchronization, which means that if L g If it is large enough, the Virtual Synchronous Generator (VSG) will be unable to keep pace with the AC network. Because L g The increase means the power grid weakens, which is related to Figure 5 (c) is consistent with the results in Table 2.

[0175] ④ The higher the OP, the greater the active power disturbance increment, which means a lower synchronization stability margin and a higher risk of synchronization instability (LoS) of the system.

[0176] ⑤ Synchronous instability (LoS) on the inverter side will not lead to synchronous instability (LoS) on the rectifier side. This is because the synchronous performance on the rectifier side depends more on the feedback transfer function (FTF) of the rectifier-side converter characteristics than on the inverter-side converter characteristics.

[0177] ⑥ Figure 8 The vector diagram in (h) and Table 7 show that DC-side resonance and low-damped DC voltage oscillations occur due to LC resonant interactions.

[0178] from Figure 8 From (g), it can be deduced that no oscillation occurred within the bandwidth of the DC resonance. The results indicate that DC-side resonance does not necessarily lead to high-frequency oscillations of the inverter-side AC frequency.

[0179] The fundamental reason is that the Virtual Synchronous Generator (VSG) control behaves like a low-pass filter, which can filter out high-frequency oscillation components.

[0180] Therefore, the high-frequency DC-side resonance will not interact with the AC frequency.

[0181] ⑦ From Figure 9 As can be seen, the operating points of DC voltage and DC current affect the oscillation characteristics and synchronization tracking capability.

[0182] When the AC frequency on the inverter side experiences aperiodic synchronous instability (LoS), the DC voltage is affected by synchronous instability (LoS), causing the DC voltage to lose synchronization and fail to maintain the nominal DC voltage. This will be discussed in detail in the simulation verification below.

[0183] With V dc0 A continuous decrease in the operating point can cause a local positive feedback effect, leading to aperiodic synchronous instability (LoS) of the DC voltage. Voltage change rate (RoCoV) (dV) dc An increase in / dt) will inevitably cause the DC voltage to deviate continuously, and subsequently, this deviation will lead to a change in the voltage rate of change (RoCoV)(dV). dc The increase of / dt) results in a positive feedback loop (PFE) on the DC voltage, causing the DC voltage to lose synchronization.

[0184] It is important to note that the virtual synchronous generator (VSG) control loop on the rectifier side dynamic frequency will form local positive feedback, such as... Figure 9 As shown, this will also negatively impact the DC voltage. However, the AC frequency on the rectifier side is not necessarily affected by the synchronization instability (LoS) of the DC voltage and the AC frequency on the inverter side. This is because whether divergent oscillations or aperiodic synchronization deviations occur in the AC dynamics depends on the feedback framework of the virtual synchronous generator (VSG) control loop on the rectifier side. In fact, although the synchronization instability (LoS) of the DC voltage will cause a deviation through the outer loop proportional-integral (PI) controller, the active power will track the reference active power well through the PI controller.

[0185] Finally, to verify the amplitude and phase feedback system and its modeling method of frequency change rate-transient frequency shift (RoCoF-TFE) and voltage change rate-transient voltage shift (RoCoV-TVE) proposed in this invention, as well as the low-frequency oscillation analysis method based on flexible DC transmission system, simulation experiments were conducted, and the results are as follows.

[0186] like Figure 8As shown in (a), a negative feedback effect (NFE) is formed to suppress frequency oscillations on the inverter side, but the NFE is relatively weak. Therefore, the simulation shows weakly damped oscillations.

[0187] For cases 3 and 4, since the internal feedback path between RoCoF and TFE is positive, a positive feedback effect (PFE) is formed, resulting in divergent oscillations. However, the AC frequency on the rectifier side is usually stable because it forms a negative feedback effect (NFE), such as... Figure 8 As shown in (b).

[0188] Figure 10 The fluctuation in (b) refers to the oscillation at the synchronous frequency (50Hz), rather than the low-frequency oscillation caused by the AC frequency on the inverter side.

[0189] Table 8 System Operating Parameters

[0190]

[0191]

[0192] from Figure 10 As shown in (c), the DC voltage fluctuated, which is consistent with the corresponding frequency behavior. The underlying reason is that the rate of change of frequency (RoCoF) can be inferred from the feedback framework to have the same behavior as the transient frequency shift (TFE). Then, RoCoF (acceleration) behaves similarly to active power.

[0193] Therefore, frequency and active oscillations on the same side will occur simultaneously. From Figure 10 From (a) and (b), it can be deduced that the active power on the rectifier side does not oscillate, but the active power on the inverter side does oscillate. Therefore, the oscillation on the inverter side will reflect the DC voltage oscillation of the DC network, due to active power balance and energy conservation.

[0194] Figure 11 This study demonstrates the aperiodic synchronization instability (LoS) phenomenon in a flexible DC system based on a virtual synchronous generator (VSG) under grid inductive interference. To investigate the impact of grid inductance on the system's grid stiffness and synchronization tracking capability, the operating point and other system parameters were kept consistent.

[0195] It can be seen that when L g When the inverter changes from 70 millihenries to 75 millihenries, the virtual synchronous generator (VSG) on the inverter side can maintain synchronization.

[0196] When L g Synchronization was lost when switching from 70 mAh to 77.5 mAh and then to 80 mAh.

[0197] When L gAt 80 millihenries, the synchronization instability (LoS) is more severe than at 77.5 millihenries.

[0198] This indicates that L g The larger the voltage, the weaker the grid stiffness, and the worse the synchronization tracking capability of the virtual synchronous generator (VSG). The frequency on the rectifier side can remain stable because the dynamic performance of the rectifier side is reliable for the system parameters on the rectifier side.

[0199] The three fundamental reasons supporting stable frequency operation on the rectifier side are: ① The DC network decouples the AC frequency dynamics between the two sides. ② The synchronous instability (LoS) of the DC voltage cancels out the AC frequency on the inverter side, thus preventing synchronous instability (LoS) on the rectifier side. ③ Due to appropriate system parameters, the system provides a negative feedback effect (NFE) with synchronization capability on the rectifier side.

[0200] Figure 12 Simulation results for the inverter-side frequency and DC voltage are shown. It can be seen that the system can maintain synchronization when nominal active power disturbances of 2% and 5% occur. If the nominal active power increases by 10%, the virtual synchronizing machine will lose synchronization tracking with the grid. Furthermore, when the nominal active power increases by 10%, DC voltage synchronization instability (LoS) also occurs. The fundamental reason is that the AC frequency on the rectifier side can remain stable; due to active power balance and energy conservation, LoS will be reflected in the DC voltage of the DC network. The simulation results match the theoretical analysis results under the feedback framework.

[0201] Figure 13 The values ​​represent the DC voltage and frequency on the inverter side. It can be seen that high-frequency resonance causes DC voltage fluctuations, but the frequency does not fluctuate. Figure 13 The small frequency fluctuations visible in the simulation are essentially fundamental frequency fluctuations, rather than caused by high-frequency DC resonant resonance. The simulation effectively validates the theoretical analysis.

[0202] Compared with existing technologies, the modeling method based on the RoCoF-TFE feedback framework proposed in this invention can intuitively correlate RoCoF and TFE with frequency stability; through the RoCoV-TVE framework, the principles of DC voltage oscillation and DC voltage synchronous instability can be revealed. Furthermore, this invention comprehensively discusses the dynamic interaction between the rectifier, DC network, and inverter by considering the effects of virtual inertia, virtual damping, and grid stiffness; it can identify RoCoF, TFE, RoCoV, and TVE and their interactions, rather than judging dynamics from only one port; it quantitatively discusses the relationship between inertia level and energy release or energy absorption; and it also physically elucidates the relationship between inertia support and energy release.

[0203] The above embodiments are preferred implementations of the present invention. In addition, the present invention can be implemented in other ways. Any obvious substitutions without departing from the concept of the present technical solution are within the protection scope of the present invention.

[0204] To facilitate understanding by those skilled in the art of the improvements of this invention over the prior art, some of the accompanying drawings and descriptions have been simplified, and for clarity, some other elements have been omitted from this application. Those skilled in the art should realize that these omitted elements may also constitute the content of this invention.

Claims

1. An amplitude-phase feedback system, characterized in that, The amplitude-phase feedback system includes a forward channel and a feedback channel. The stability of the amplitude-phase feedback system is determined by the quadrant in which the component synthesis vector flowing through the feedback channel is located. Furthermore, the dynamic feedback effect between the rate of frequency change and transient frequency shift, and between the rate of voltage change and transient voltage shift can be identified by combining the synthesis vector. The system includes a method for determining the stability of the amplitude-phase feedback system: If the synthesized vector is located in the first quadrant, when a positive feedback effect is formed in the synchronous and oscillatory components, oscillatory instability and synchronous instability occur, and TFE will force RoCoF to increase continuously, thereby further increasing TFE; If the synthesized vector is located in the second quadrant, oscillations occur and the system remains synchronized, resulting in a positive feedback effect on the oscillations but a negative feedback effect on the synchronization performance. If the composite vector is located in the third quadrant, it forms negative feedback for both oscillatory stability and synchronous stability, and the system is stable. If the synthesized vector is located in the fourth quadrant, it creates a positive feedback effect on synchronization stability. The virtual synchronizing machine will lose its synchronization tracking of the power grid and thus produce aperiodic synchronization instability deviation.

2. The amplitude-phase feedback system according to claim 1, characterized in that, The amplitude and phase feedback system includes a "frequency change rate - transient frequency offset" system and a "voltage change rate - transient voltage offset" system; The forward channel of the "frequency change rate - transient frequency offset" system includes a single integral element, and the feedback channel includes a virtual damped acceleration component, a synchronous acceleration component, and a feedback acceleration component. The forward path of the "voltage change rate - transient voltage offset" system includes a single integrator, and the feedback path includes a dynamic coupling component and a DC dynamic component.

3. The amplitude-phase feedback system according to claim 2, characterized in that, In the aforementioned "frequency change rate - transient frequency offset" system, the virtual synchronous machine's virtual rotor acceleration d The relative velocity of the virtual rotor angular frequency with respect to the grid angular frequency is obtained by a single integration stage. This relative velocity is then superimposed through three feedback channels to obtain the VSG virtual rotor acceleration d. / dt.

4. The amplitude-phase feedback system according to claim 2, characterized in that, In the "voltage change rate - transient voltage offset" system, the DC voltage change rate d / dt is used to obtain the transient voltage offset through a single integration stage. The transient voltage offset is then superimposed through two feedback channels to obtain d. / dt.

5. A modeling method for an amplitude-phase feedback system according to any one of claims 1-4, characterized in that, The modeling method includes the following steps: (1) Based on the circuit theorem and the law of conservation of energy, establish the mathematical model of the amplitude-phase feedback system: （1）； In the formula, These represent the phase angles of the output voltage and current of the AC network at the sending end of the flexible DC transmission system and the virtual synchronous machine, respectively. G1 E1 represents the voltage amplitude of the AC grid on the rectifier side, and E2 represents the voltage amplitude of the virtual synchronous machine on the rectifier side. The nominal frequency is given, j represents the imaginary unit, s is the Laplace operator, and L... f1 R f1 L g1 R g1 These represent the inductance, parasitic resistance, mains equivalent inductance, and resistance values ​​of the VSG1 output filter, respectively. (2) Linearize the AC side dynamic model using a synchronous rotating inertia reference frame, i.e.: （2）； To synchronously rotate the reference coordinate system; (3) Considering the coupling situation, list the small-signal power equations and Kirchhoff voltage equations for the converters at both ends and the intermediate DC cable. The oscillation equation for the virtual synchronous machine rotor motion on the rectifier side is as follows: （6）； In the formula, The virtual inertia coefficient representing the reactive power channel of the rectifier-side control algorithm. The virtual damping coefficient of the active power channel represents the rectifier-side control algorithm. The virtual inertia coefficient representing the reactive power channel of the rectifier-side control algorithm. The virtual damping coefficient of the reactive power channel represents the rectifier-side control algorithm. This represents the transient frequency shift on the rectifier side. P ref1 Reference value for active power on the rectifier side Q ref1 This is the reference value for reactive power on the rectifier side. P1, Q1 represents the active power and reactive power injected into VSG1, respectively. E1 represents the voltage amplitude of the virtual synchronous machine on the rectifier side. ω1 is the output angular frequency of the virtual synchronizer on the rectifier side; (4) By combining the equations of the circuit part and the control part, we can obtain the active power closed-loop control system model on the inverter side and the DC voltage closed-loop control system model on the rectifier side. The main circuit model of the inverter-side converter output is as follows: （9）； In the formula, These are the phase angles of the receiving-end grid voltage, the output voltage phase angle of the inverter-side virtual synchronous machine, and the output current phase; E2, V G2 These represent the output voltage amplitude of the virtual synchronous machine on the inverter side and the voltage amplitude of the grid at the receiving end, respectively; L f2 L g2 R f2 R g2 These are, respectively, the inductance value of the inverter output filter, the inductance value of the grid equivalent impedance, the resistance value of the grid equivalent impedance, the parasitic resistance value of the output filter, and the resistance value of the grid equivalent impedance; The rotor motion equation model of the virtual synchronous machine on the inverter side is as follows: （13）； In the formula, This represents the transient frequency offset of the virtual synchronous machine on the inverter side. The virtual damping coefficient of the active power channel represents the control algorithm of the virtual synchronous machine on the inverter side. The virtual inertia coefficient of the active power channel represents the control algorithm of the virtual synchronous machine on the inverter side. P ref2 This is the reference value for the active power of the inverter-side active power control loop. P2 represents the actual active power output on the inverter side. Q ref2 This is the reactive power reference value for the inverter-side reactive power control loop. Q2 represents the actual reactive power output on the inverter side. The virtual inertia coefficient of the reactive power channel in the inverter-side virtual synchronous machine control algorithm. This represents the virtual damping coefficient of the reactive power channel in the inverter-side virtual synchronous machine control algorithm. E2 is the output voltage amplitude of the virtual synchronous machine on the inverter side; (5) Under the framework of "frequency change rate - transient frequency shift" and "voltage change rate - transient voltage shift", the models of the feedback system on the rectifier side and the inverter side are built respectively.

6. A low-frequency oscillation analysis method, based on a flexible DC transmission system and the amplitude-phase feedback system according to any one of claims 1-4, characterized in that, The analytical method includes: Determine the coupling relationship between the virtual inertia, virtual damping, and grid stiffness of the amplitude-phase feedback system; Based on the coupling relationship between virtual inertia, virtual damping, and grid stiffness, determine the influence of virtual inertia, virtual damping, and grid stiffness on dynamic frequency change rate and transient frequency offset. Based on the feedback effect of system frequency and DC voltage in the amplitude-phase feedback system, the dynamic interaction between the rectifier, DC network and inverter in the flexible DC transmission system is obtained; By combining virtual inertia, virtual damping, and stiffness in the energy release and absorption of the system frequency oscillation, the relationship between inertia level and energy release or energy absorption is quantitatively analyzed. By combining the released energy, we further analyze the relationship between inertial support and energy release.

7. The low-frequency oscillation analysis method according to claim 6, characterized in that, The coupling relationship between virtual inertia, virtual damping, and grid stiffness is as follows: （14） In the formula, L is the total inductance from the converter output point to the AC mains point, and k stiff The defined grid stiffness coefficient.

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