A method for transient synchronization stability analysis of multiple parallel grid-connected converters

Abstract

This invention relates to a transient synchronization stability analysis method for multi-parallel grid-connected converters. First, within a multi-machine system framework, a grid-connected converter system model considering the coupling effect of the inner loop current and the phase-locked loop is constructed. Then, using the Newton-Raphson method and the equal area criterion, quantitative assessments of the existence of equilibrium points and visual analysis of transient synchronization behavior are achieved, respectively. Next, through an extended application of the Lyapunov direct method, a physically meaningful transient synchronization stability criterion is rigorously derived, revealing the key factors that easily lead to transient synchronization instability and their influencing laws. Finally, time-domain simulations using MATLAB / SIMULIN are performed to verify the accuracy of the proposed method. The proposed transient synchronization instability characteristic description method and risk quantification assessment system have significant theoretical guiding significance for the parameter optimization design of power electronic systems.

Description

Technical Field

[0001] This invention belongs to the field of power electronic system synchronization control technology, specifically relating to a transient synchronization stability analysis method for multi-parallel grid-connected converters. Background Technology

[0002] In recent years, new energy systems, represented by solar and wind power, have been extensively connected to modern power grids through power electronic devices such as grid-connected voltage source converters (VSCs). As a core device for grid connection of new energy sources, the mainstream control strategy of VSCs is grid-following mode, relying on phase-locked loops (PLLs) for grid synchronization. The dynamic characteristics of the PLL directly dominate the transient synchronization stability of grid-following converters, making the PLL-based VSC synchronization mechanism a key research subject.

[0003] Traditional transient synchronization stability analysis typically relies on the assumption of an ideal inner loop current and focuses solely on the dynamic characteristics of the phase-locked loop (PLL). While studies on transient synchronization stability of grid-connected converters based on PLLs have yielded promising results, neglecting the interaction between the inner loop current and the PLL can lead to overly optimistic conclusions. Chen Junru et al. established a system model of a single voltage source converter with current transients and a PLL, verifying the impact of converter current transients on the dynamic characteristics of the PLL. Professor Wu Chao et al. further derived a fourth-order model of a single voltage source converter system considering inner loop current control, proposing an improved equal-area method to reveal the necessity of considering inner loop current control in transient synchronization stability analysis. They also pointed out that when the inner loop current control bandwidth is insufficient, the traditional second-order PLL model leads to inaccurate stability assessment results. Therefore, especially when the inner loop current control bandwidth is small, the dynamic characteristics of the inner loop current significantly affect the transient synchronization stability of grid-connected converter systems, resulting in complex transient models, unclear instability mechanisms, and a lack of transient synchronization stability criteria, necessitating further in-depth research.

[0004] Therefore, it is necessary to construct an intuitive description method and a quantitative evaluation criterion for transient synchronous instability characteristics of grid-connected multi-parallel grid-connected converter systems that consider the coupling effect of inner loop current and phase-locked loop. Summary of the Invention

[0005] 1. Purpose of the invention

[0006] This invention aims to solve the problem of neglecting the coupling effect of inner loop current and phase-locked loop in the transient synchronization stability analysis of existing grid-connected converters. It proposes a transient synchronization stability analysis method for multiple parallel grid-connected converters to achieve a comprehensive and accurate characterization of the nonlinear dynamic characteristics of grid-connected systems with multiple parallel grid-connected converters.

[0007] 2. Technical Solution

[0008] To achieve the above objectives, the main steps include:

[0009] Step 1: Constructing a grid-connected model for multiple parallel VSCs considering inner loop current and phase-locked loop coupling effects;

[0010] Step 2: Analysis of the transient synchronous instability mechanism of a grid-connected system with multiple parallel VSCs considering the inner loop current;

[0011] Step 3: Constructing a transient synchronization stability criterion based on the approximate Lyapunov direct method;

[0012] Step 4: Case studies and time-domain simulation.

[0013] The specific process of step 1 includes: in an N parallel VSC grid-connected system, defining N phase-locked loops with N dq-axis reference frames. Additionally, defining the DQ axis as the reference frame, with the grid voltage vector U... g For reference, θ g and ω g U g The phase angle and angular velocity. Taking the k-th grid converter VSC as an example. k Taking k = 1, 2, ..., N as an example, VSC under the DQ framework k Terminal voltage vector U t,k The expression is,

[0014]

[0015] In the formula, the subscript j represents the j-th VSC and j≠k, I j VSC j Output current vector, I k VSC k Output current vector, Z g =R g +jX g and Z linek =R line,k +jX line,k R represents the grid-side impedance and the line impedance, respectively. g and R line,k X represents the grid-side resistance and the line resistance, respectively. g and X line,k These represent grid-side reactance and line reactance, respectively.

[0016] Will U t,k It is decomposed into d-axis and q-axis components, and its expression is:

[0017]

[0018] In the formula, the work angle δ k =θ PLL,k -θ g U t,k Ahead of U g The resulting angular difference, δ kj =δ k -δ j VSC k and VSC j The resulting difference in work angle. It is the current vector I k The injection angle. θ I,k θ represents the current injection angle. Zlinek and θ Zg Z linek and Z g The impedance angle.

[0019] Based on Kirchhoff's voltage law and the inner-loop current control block diagram, VSC k The governing equation for the inner loop current is:

[0020]

[0021] Where the superscript "·" represents the derivative at time t, and These represent the deviations in active current and reactive current, respectively. dC,k and x qC,k e is the state variable for current loop control. d,k and e q,k K is the control variable for current loop control. pC and K iC L represents the proportional gain and integral gain of the inner-loop current PI regulator, respectively. f This refers to the filter inductor on the AC output side of the mesh converter.

[0022] According to the phase-locked loop control block diagram, VSC k The state equation of the intermediate phase-locked loop can be derived as follows:

[0023]

[0024] Among them, K pPLL and K iPLL Let Δω represent the proportional gain and integral gain of the phase-locked loop PI regulator, respectively. k Defined as the output angular frequency ω of the phase-locked loop k With ω g The difference in angular frequency.

[0025] Furthermore, combining equations (2), (4), and (5), we obtain VSC. k The sixth-order nonlinear dynamic model.

[0026]

[0027] Among them, M k For equivalent inertia, D eq,k For equivalent damping, P m,k and P e,k These are the equivalent mechanical power and equivalent electromagnetic power, respectively. d,k and y q,k The detailed expression is as follows:

[0028]

[0029] Among them, L g and L line,k Let represent the grid-side inductance and the line inductance, respectively. Clearly, the sixth-order nonlinear model exhibits nonlinear, strongly coupled, and high-order characteristics. This model fully considers the coupling effect between the dynamic characteristics of the inner loop current and the phase-locked loop, providing a theoretical basis for subsequent transient synchronization stability analysis.

[0030] The specific process of step 2 includes: analyzing the transient instability mechanism of the sixth-order nonlinear model constructed in step 1 from the two aspects of the existence of the equilibrium point and the transient synchronization behavior.

[0031] (1) Equilibrium point existence analysis: Sufficient condition U for the existence of a system equilibrium point tq,k (x1,x2,...,x N The system of equations, ∑(k=0, k=1,2,...,N), is highly nonlinear and difficult to solve analytically directly due to the influence of cross-coupling terms and current loop control. The vector x... k =(δ k ,ΔI d,k ,ΔI q,k k = 1, 2, ..., N represents VSC k State variables, including the work angle δ k and current deviation ΔI d,k ΔI q,k The Newton-Raphson method is used to numerically calculate the nonlinear equation system: (a) Initial value selection: Initialize the state variable matrix x (i) By setting the differential term on the left-hand side of the sixth-order nonlinear model to zero, the initial steady-state values ​​of the state variables can be accurately calculated, and the steady-state values ​​before the fault can be selected. (a) As initial value; (b) Taylor expansion: transform matrix U tq (x1,x2,...,x N Perform a Taylor expansion at the initial estimation point and retain the first-order terms to obtain a linearized approximation. Where the superscript i represents the current iteration number, [J(i) ] represents the Jacobian matrix of the current iteration point, and we obtain matrix x. (i) (c) Iterative solution: Update the estimate using x obtained from (b). (i+1) Use these as the initial values ​​for the next iteration. Repeat (a) and (b) until all elements in the offset matrix are less than the convergence threshold of 10. -7 The iterative calculation stops.

[0032] (2) Transient synchronization behavior analysis: The dynamics of the inner loop current will be directly reflected in P m,k In the middle, it is further refined into and Defined as the equivalent mechanical power when the inner loop current characteristics are ignored and considered respectively, the expressions are as follows:

[0033]

[0034] The transient synchronization behavior of a sixth-order nonlinear model is intuitively analyzed using the equal area criterion method, revealing the influence of the dynamic characteristics of the inner loop current on the transient synchronization behavior of a grid-connected system with multiple parallel grid-connected converters.

[0035] The specific process of step 3 includes: (1) Function construction and verification: Ignoring the nonlinear damping effect, candidate Lyapunov functions are constructed by combining the first integral method and the extended invariant principle.

[0036]

[0037] In the formula, δ s,k VSC k The stable equilibrium point is obtained by the Newton-Raphson method in step 2, λ. k These are undetermined parameters for adjusting the weights of the mixed terms without changing the equilibrium point location. The derivative of the candidate Lyapunov function. The expression is,

[0038]

[0039] In the formula, H k The detailed expression for the sub-block is:

[0040]

[0041] Equation (11) consists of a quadratic term plus the last term, which is determined by choosing the parameter λ. k If we make the quadratic term a positive definite term, then It is negative semi-qualitative and satisfies the extended invariance principle. When λ k When inequality (12) is satisfied, the candidate Lyapunov function V can be used to study transient synchronization stability.

[0042]

[0043] (2) Calculation of critical energy value: Using the V constructed above, the critical energy value V at the unstable equilibrium point considering nonlinear damping dissipation is derived. cr Its expression is as follows:

[0044] V cr =V k (Δω k )+V p (δ u ,Δω u )+∫D eq Δωdδ (12)

[0045] Where, δ u Represents an unstable equilibrium point, determined by Δω u D represents the angular frequency deviation at the unstable equilibrium point. eq Δω corresponds to the frictional force during the transient process, while the damping D eq The dissipation is related to the integral path of the frictional force. Since the integral term of the frictional force is difficult to calculate precisely, the triangle area approximation method is used to estimate the damping dissipation. Specifically, assuming VSC... k The integral path of the frictional force is approximately the area of ​​a triangle, the base of which corresponds to the system path from the initial point δ0 to the maximum phase angle δ. max,k The range of variation corresponds highly to the maximum angular velocity deviation Δω max,k The expression for the maximum phase angle is as follows:

[0046]

[0047] Where, δ max,k The range of values ​​for is (δ) s,k ,δ u,k Its value equation is derived from V p,k (δ0)=V p,k (δ k Determined. Define W. da,k For the system to run from δ0 to δ s,k The damping dissipates energy. At SEP, it has the minimum transient potential energy V. pmin =0 and the maximum transient kinetic energy V kmax,k V kmax,k Determined by subtracting damping dissipation from the system's initial transient energy.

[0048]

[0049] VSC k The system runs along the path from δ0 to δ s,k Damping dissipation W da,kand path from δ s,k Run to δ max,k Damping dissipation W dd,k Approximate estimation using the area of ​​a triangle,

[0050]

[0051] Based on the above analysis, consider D eq The critical energy value V for approximate dissipation cr This can be expressed as,

[0052]

[0053] Where γ = 8M k V p,k (δ0)+((δ s,k -δ0)D eq,k ) 2 Based on the above-described V and critical energy value Vc cr The analytical expression for the transient synchronization stability criterion is:

[0054]

[0055] Here, η is defined as the transient synchronization stability index, used to quantitatively evaluate transient synchronization stability. A system with η ≥ 0 is in a transiently synchronous stable state, and the larger the value of η, the better the transient synchronization stability. Conversely, a system with a smaller value is in an unstable state.

[0056] The specific process of step 4 includes: based on the transient synchronization stability criterion obtained in step 3, constructing a transient synchronization stability evaluation system for multi-parallel grid-connected converters, extracting key factors that easily lead to transient synchronization instability, and analyzing their influence patterns. Finally, time-domain simulation is performed using the MATLAB / SIMULIN platform to verify the accuracy and effectiveness of the proposed method. This mainly covers the coordinate transformation block, the VSC model block in dq coordinates, the outer loop voltage control block, the inner loop current control block, and the phase-locked loop module.

[0057] Based on the above steps, a transient synchronization stability analysis method for multi-parallel grid-type converters is presented.

[0058] The superior effects of this invention are as follows: Within a multi-machine system framework, a sixth-order nonlinear model of a grid-connected converter considering the coupling effect of the inner loop current and the phase-locked loop is established, enabling a more accurate characterization of the system's transient synchronization stability. Through the Newton-Raphson method and the equal-area criterion, quantitative assessments of the existence of the system's equilibrium point and visual analyses of transient synchronization behavior are achieved, verifying the necessity of the inner loop current in transient synchronization stability analysis. A Lyapunov function is constructed by combining the first integral method and the extended invariance principle, incorporating the nonlinear damping approximate dissipation into the critical energy, and a physically meaningful transient synchronization stability criterion is rigorously derived. Based on this criterion, a transient synchronization instability characteristic description method and risk quantification assessment system are proposed, revealing the key factors and mechanisms that easily induce transient synchronization instability. This provides a reliable theoretical basis for the parameter optimization design of power electronic systems and has significant guiding significance for ensuring the safe and stable operation of new power systems. Attached Figure Description

[0059] Figure 1 The diagram shows a flowchart of a transient synchronization stability analysis method for multiple parallel grid-connected converters.

[0060] Figure 2a The diagram shows the topology of an N VSC grid-connected system.

[0061] Figure 2b The image shows VSC. k Block diagram of grid-connected system control module

[0062] Figure 3a The diagram shown is the power angle diagram without considering the dynamic characteristics of the inner loop current.

[0063] Figure 3b The diagram shown is a power angle diagram considering the dynamic characteristics of the inner loop current.

[0064] Figure 4a The system path shown is from δ0 to δ s,k Damped approximate dissipation diagram

[0065] Figure 4b The system path shown is from δ s,k to δ max,k Damped approximate dissipation diagram

[0066] Figure 5 The diagram shown is a simplified representation of N parallel grid-type converters.

[0067] Figure 6 The figure shown is the attraction domain estimation diagram under different SCR variations.

[0068] Figure 7 The figure shown is a time-domain simulation diagram of scenario A.

[0069] Figure 8The following shows different Z values. line1,i Attraction domain estimation diagram under variation

[0070] Figure 9 The image shown is a time-domain simulation diagram of scenario B.

[0071] Figure 10a The figure shows a three-dimensional plot of η under different phase-locked loop PI gain variations.

[0072] Figure 10b The figure shows the stable region in the PI gain parameter space of the phase-locked loop.

[0073] Figure 11 The figure shown is a time-domain simulation diagram of scenario C.

[0074] Figure 12a The following shows different R values. g and 3D graph of η under change

[0075] Figure 12b The figure shows R g and Stable region in parameter space

[0076] Figure 13 The image shown is a time-domain simulation diagram of scenario D.

[0077] Figure 14a The following shows different X values. line,k and 3D graph of η under change

[0078] Figure 14b The figure shown is X line,k and Stable region in parameter space

[0079] Figure 15 The figure shown is a time-domain simulation diagram of scenario E. Detailed Implementation

[0080] To provide a clearer understanding of the objectives, features, and advantages of this invention, the following detailed description is provided in conjunction with the accompanying drawings and specific embodiments:

[0081] Figure 1 A schematic flowchart illustrating a transient synchronization stability analysis method for multiple parallel grid-connected converters. Figure 1 As shown, it includes the following steps:

[0082] Step 1: Taking N parallel grid-connected converters connected to the grid as an example, its typical topology and control module are shown in Figure 2. A multi-parallel grid-connected converter model considering the inner loop current and phase-locked loop coupling effect is constructed. The equations of this model are not elaborated here. The main system parameters are set as shown in Table 1. In this implementation example, the design bandwidth of the inner loop current is approximately 80 times the design bandwidth of the phase-locked loop.

[0083] Table 1 Main System Parameters

[0084]

[0085] Step 2: Analyze the transient instability mechanism of the model based on the existence of the equilibrium point and transient synchronization behavior. First, use the Newton-Raphson method to determine whether an equilibrium point exists during the transient period; if no equilibrium point exists, the system is unstable. Second, use the equal area method to visually analyze the transient synchronization behavior of the model. As shown in Figure 3, S a and S d Curves I and II respectively represent the acceleration and deceleration regions. and The changes in the inner loop current verified that they cause changes in the equilibrium point and deceleration area, ultimately affecting transient synchronization behavior.

[0086] Step 3: First, combining the first integration method and the extended invariance principle, construct the candidate Lyapunov function V. In this implementation example, λ k (k=1,...,N) is set to 0.06 such that Satisfying semi-negative definiteness, V is ensured to be suitable for transient synchronous stability analysis. The critical energy value Vc at the unstable equilibrium point, considering nonlinear damped dissipation, is derived using Vc. cr The nonlinear damping dissipation is approximated using the triangle area method (as shown in Figure 4). Then, based on W and W at the unstable equilibrium point... cr Calculate the transient synchronization stability index η.

[0087] Step 4: Extract key factors that may affect the transient synchronization stability of the nonlinear system using the transient synchronization stability criterion constructed in Step 3, such as the short-circuit ratio (SCR) (a basic indicator for quantifying the strength of grid connections, SCR≈1 / X). g This experiment investigates the effects of line impedance, phase-locked loop (PLL) PI gain, line reactance, grid-side resistance, and current reference values ​​on transient synchronization stability. The specific impacts of these factors on transient synchronization stability are revealed. This experiment employs methods such as... Figure 5 The simulation is performed using the N (N=4) parallel VSCs scenario shown in Figure 2. Figure 6 The circuit model was built in MATLAB / SIMULINK. When the simulation scenario is t = 0.5s, the grid voltage U... gIt drops sharply to 0.3 pu. Unless otherwise specified, the parameter settings remain unchanged.

[0088] The attraction region is formed by the contour plot of the proposed Lyapunov function W at a fixed level W. cr An approximate estimate of the value. Figure 6 This indicates that a larger SCR increases the attraction domain, meaning a larger SCR enhances the transient synchronization stability of the system. Table 2 presents the transient synchronization stability analysis results for Case A. Decreasing SCR leads to a decrease in the stability exponent η. Under conditions A1 and A2, the calculated results for η are both greater than 0, and system A1 is more stable than system A2 (A1: η = 0.8747 > A2: η = 0.3053). Figure 7 Time-domain simulations show that the waveform oscillation amplitude under condition A2 is greater than that under condition A1, which is consistent with the theoretical results. Under condition A3, further reducing the value of SCR leads to system instability (η<0), which is consistent with the simulation results. The simulation results verify the accuracy of the theoretical analysis.

[0089] Table 2. Results of transient synchronization stability analysis under different SCR values.

[0090] Case A <![CDATA[X g ]]> η Results of the proposed method Simulation results A1 0.1818 (SCR = 5.5) 0.8747(>0) Stablize Stablize A2 0.3333 (SCR = 3.0) 0.3053(>0) Stablize Stablize A4 0.6667 (SCR = 1.5) -0.1429(<0) Unstable Unstable

[0091] Keep VSC 2-4 With the impedance value remaining constant, select four different Z-axis values ​​for VSC1. line1,i (i = 1, 2, 3, 4) (Table 3). Z line1,1 Z line2,1 and Z line3,1 They have almost the same impedance angle, but different amplitudes. Z line3,1 and Z line4,1 The amplitudes are almost the same, but the impedance angles are different. Figure 8 This indicates that a smaller impedance magnitude or impedance angle will increase the attraction region, i.e., a smaller Z-axis. line1,i This will enhance the transient synchronization stability of the system. Table 3 shows the transient synchronization stability results for Case B. Figure 9 The accuracy of the proposed method's conclusions was verified through time-domain simulation.

[0092] Table 3 Different Z line1,i Transient synchronization stability analysis results under the given value

[0093] Case B <![CDATA[Z line1,i ]]> η Results of the proposed method Simulation results B1 0.19+j0.065 0.4894(>0) Stablize Stablize B2 0.1046+j0.3217 -0.0245(<0) Unstable Unstable B3 0.2508+j0.7726 -0.1698(<0) Unstable Unstable B4 0.6599+j0.4739 0.3266(>0) Stablize Stablize

[0094] Figure 10 shows the large proportional gain K. pPLL Or a smaller integral gain K iPLL This can significantly increase η, thereby improving transient synchronization stability. Table 4 presents the transient synchronization stability results for Case C. Figure 11The accuracy of the proposed method's conclusions was verified through time-domain simulation.

[0095] Table 4 Different K iPLL and K pPLL Results of transient synchronization stability under the given value

[0096] Case C <![CDATA[K iPLL ]]> <![CDATA[K pPLL ]]> η Results of the proposed method Simulation results C1 0.15 10 0.1074 Stablize Stablize C2 0.15 12 -0.0927 Unstable Unstable C3 0.50 12 0.0850 Stablize Stablize

[0097] In Case D, the grid voltage dropped sharply to 0.25 pu. Figure 12 shows the large R g or This can significantly increase η, thereby improving transient synchronization stability, while simultaneously taking R... g and The system is most prone to instability when the sum reaches its minimum value (point a in Figure 12(a)). Table 5 presents the transient synchronization stability results for Case D. Figure 13 The accuracy of the proposed method's conclusions was verified through time-domain simulation.

[0098] Table 5 Different R g and Results of transient synchronization stability under the given value

[0099]

[0100] Figure 14 shows the smaller X line,k or This can significantly increase η, thereby improving transient synchronization stability, and simultaneously take X. line,k and When the value of the constant is at its maximum (point b in Figure 14(a)), the system is most prone to instability. Table 5 presents the transient synchronization stability results for Case D. Figure 15 The accuracy of the proposed method's conclusions was verified through time-domain simulation.

[0101] Table 6 Different X line,k and Results of transient synchronization stability under the given value

[0102]

[0103] This specification uses a progressive structure to describe each case, highlighting the unique aspects of each case, while allowing cross-referencing of similar or identical parts. Case A serves as a detailed example, emphasizing the analytical methods and related conclusions for transient synchronization stability. The analytical methods for other cases (such as B, C, D, and E) are similar to Case A, and therefore described more briefly, highlighting only their key differences and results. Through specific cases, this document systematically elucidates the principles and implementation methods of the invention, aiming to aid in understanding the core ideas of the method. Those skilled in the art can modify or make equivalent substitutions to the specific implementation methods without departing from the overall concept of the invention. Furthermore, adaptive adjustments can be made to the implementation methods and application scope based on the ideas of the invention. Therefore, the content of this specification should not be construed as a limitation of the invention.

Claims

1. A transient synchronization stability analysis method for multiple parallel grid-connected converters, characterized in that... Includes the following steps: Step 1: Constructing a grid-connected model for multiple parallel VSCs considering inner loop current and phase-locked loop coupling effects; In a grid-connected system with N parallel VSCs, N phase-locked loops are defined with N dq-axis reference frames. Additionally, the DQ axis is defined as the reference frame, with the grid voltage vector U... g For reference, θ g and ω g U g The phase angle and angular velocity, with the k-th grid converter VSC k Taking k = 1, 2, ..., N as an example, VSC under the DQ framework k Terminal voltage vector U t,k The expression is, In the formula, the subscript j represents the j-th VSC and j≠k, I j VSC j Output current vector, I k VSC k Output current vector, Z g =R g +jX g and Z linek =R line,k +jX line,k R represents the grid-side impedance and the line impedance, respectively. g and R line,k X represents the grid-side resistance and the line resistance, respectively. g and X line,k These represent the grid-side reactance and the line reactance, respectively. Will U t,k It is decomposed into d-axis and q-axis components, and its expression is: In the formula, the work angle δ k =θ PLL,k -θ g U t,k Ahead of U g The resulting angular difference, δ kj =δ k -δ j VSC k and VSC j The resulting angle difference, It is the current vector I k The injection angle, θ I,k θ represents the current injection angle. Zlinek and θ Zg Z linek and Z g impedance angle, Based on Kirchhoff's voltage law and the inner-loop current control block diagram, VSC k The governing equation for the inner loop current is: Where the superscript "·" represents the derivative at time t, and These represent the deviations in active and reactive current, respectively, x. dC,k and x qC,k e is the state variable for current loop control. d,k and e q,k K is the control variable for current loop control. pC and K iC L represents the proportional gain and integral gain of the inner-loop current PI regulator, respectively. f This refers to the filter inductor on the AC output side of the mesh converter. According to the phase-locked loop control block diagram, VSC k The state equation of the intermediate phase-locked loop can be derived as follows: Among them, K pPLL and K iPLL Let Δω represent the proportional gain and integral gain of the phase-locked loop PI regulator, respectively. k Defined as the output angular frequency ω of the phase-locked loop k With ω g angular frequency difference, Furthermore, combining equations (2), (4), and (5), we obtain VSC. k The sixth-order nonlinear dynamic model, Among them, M k For equivalent inertia, D eq,k For equivalent damping, P m,k and P e,k These are the equivalent mechanical power and equivalent electromagnetic power, respectively. d,k and y q,k The detailed expression is as follows: Among them, L g and L line,k Let represent the grid-side inductance and the line inductance, respectively. This model fully considers the dynamic characteristics of the inner loop current and the coupling effect of the phase-locked loop. Subsequent transient synchronization stability analyses are all based on this model. Step 2: Analysis of the transient synchronous instability mechanism of a grid-connected system with multiple parallel VSCs considering the inner loop current; For the sixth-order nonlinear dynamic model constructed in step 1, the Newton-Raphson method and the equal area criterion are used to confirm the equilibrium point and analyze the transient synchronization behavior, respectively. The method flow is as follows: First, confirm the existence of the equilibrium point: the sufficient condition U for the existence of the system equilibrium point. tq,k (x1,x2,...,x N Given a system of equations with x = 0, k = 1, 2, ..., N, where the vector x... k =(δ k ,ΔI d,k ,ΔI q,k k = 1, 2, ..., N represents VSC k The state variables are used to numerically calculate the nonlinear equation system using the Newton-Raphson method. (a) Initial value selection: Initialize the state variable matrix x (i) By setting the differential term on the left-hand side of the sixth-order nonlinear model to zero, the initial steady-state values ​​of the state variables can be accurately calculated, and the steady-state values ​​before the fault can be selected. (a) As initial value; (b) Taylor expansion: transform matrix U tq (x1,x2,...,x N Perform a Taylor expansion at the initial estimation point and retain the first-order terms to obtain a linearized approximation. Where the superscript i represents the current iteration number, [J (i) ] represents the Jacobian matrix of the current iteration point, and we obtain matrix x. (i) (c) Iterative solution: Update the estimate using x obtained from (b). (i+1) Use this as the initial value for the next iteration, repeating (a) and (b) until all elements in the offset matrix are less than the convergence threshold of 10. -7 The iterative calculation stops; Then, transient synchronization behavior analysis: the dynamics of the inner loop current will be directly reflected in P. m,k In the middle, it is further refined into and Defined as the equivalent mechanical power when the inner loop current characteristics are ignored and considered respectively, the expressions are as follows: The transient synchronization behavior of a sixth-order nonlinear dynamic model is analyzed intuitively using the equal area criterion method, thereby revealing the influence of the inner loop current dynamic characteristics on the transient synchronization behavior of the grid-connected system. Step 3: Construction of Transient Synchronous Stability Criterion Based on Approximate Lyapunov Direct Method For the sixth-order nonlinear dynamic model constructed in step 1, a transient synchronization stability criterion is rigorously constructed based on the approximate Lyapunov direct method. The method flow is as follows: First, function construction and verification: Ignoring nonlinear damping effects, candidate Lyapunov functions are constructed using the first integral method and the extended invariance principle. In the formula, δ s,k VSC k The stable equilibrium point is obtained by the Newton-Raphson method in step 2, λ. k For undetermined parameters that allow for adjustable weights of mixed terms without altering the equilibrium point, the derivative of the candidate Lyapunov function is... The expression is, In the formula, H k The detailed expression for the sub-block is: Equation (11) consists of a quadratic term plus the last term, which is determined by choosing the parameter λ. k If we make the quadratic term a positive definite term, then It is negative semi-qualitative and satisfies the extended invariance principle when λ k When inequality (11) is satisfied, V can be used for transient synchronization stability studies. Secondly, the critical energy value is calculated: using the V constructed above, the critical energy value V at the unstable equilibrium point considering nonlinear damping dissipation is derived. cr Its expression is as follows: V cr =V k (See k )+V p (d u ,Here u )+∫D eq Dodd (12) Where, δ u Represents an unstable equilibrium point, determined by Δω u D represents the angular frequency deviation at the unstable equilibrium point. eq Δω corresponds to the frictional force during the transient process, while the damping D eq The dissipation is related to the integral path of the frictional force. Since the integral term of the frictional force is difficult to calculate accurately, the triangle area approximation method is used to estimate the damping dissipation. Specifically, assuming VSC k The integral path of the frictional force is approximately the area of ​​a triangle, the base of which corresponds to the system path from the initial point δ0 to the maximum phase angle δ. max,k The range of variation corresponds highly to the maximum angular velocity deviation Δω max,k The expression for the maximum phase angle is as follows: Where, δ max,k The range of values ​​for is (δ) s,k ,δ u,k Its value equation is derived from V p,k (δ0)=V p,k (δ k Determine and define W. da,k For the system to run from δ0 to δ s,k The damping dissipation energy has a minimum transient potential energy V at SEP. pmin =0 and the maximum transient kinetic energy V kmax,k V kmax,k Determined by subtracting damping dissipation from the system's initial transient energy. VSC k The grid-connected system runs along the path from δ0 to δ s,k Damping dissipation W da,k and path from δ s,k Run to δ max,k Damping dissipation W dd,k Approximate estimation using the area of ​​a triangle, Based on the above analysis, consider D eq The critical energy value of approximate dissipation V cr This can be expressed as, Where γ = 8M k V p,k (δ0)+((δ s,k -δ0)D eq,k ) 2 Based on the above-constructed V and critical energy value V cr The analytical expression for the transient synchronization stability criterion is: Here, η is defined as the transient synchronization stability index, used to quantitatively evaluate transient synchronization stability. When η ≥ 0, the system is in a transient synchronous stable state, and the larger the value of η, the better the transient synchronization stability; conversely, the system is in an unstable state. Based on the above steps, a transient synchronization stability analysis method for multi-parallel grid-type converters is presented.

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