Multi-converter transient synchronous stability evaluation method based on maximum estimation attraction domain

Abstract

The invention relates to a multi-converter transient synchronous stability evaluation method based on a maximum estimation attraction domain, and the method comprises the following steps: S1, keeping the PLL dynamic characteristics of converters, ignoring the dynamic state of a current loop, and building a multi-converter grid-connected system reduced-order mathematical model considering the transient interaction between the converters under a power grid fault; s2, constructing a maximum estimation attraction domain of the multi-converter grid-connected system based on a TS method; and S3, evaluating the transient synchronization stability of the multi-converter grid-connected system based on the maximum estimation attraction domain.

Description

Technical Field

[0001] The invention belongs to the field of transient stability analysis of power electronic power systems, and proposes a transient synchronization stability evaluation method based on a maximum estimated attraction domain for a phase-locked loop synchronous multi-converter grid-connected system under a power grid fault. Background Art

[0002] As renewable energy is transmitted over large capacity and long distances, converters are faced with the operating scenario of connecting to weak power grids. [1] At present, the grid-connected control of new energy and energy storage converters is still mainly based on the grid-following control strategy based on phase-locked-loop (PLL) synchronization. [2] Under severe grid faults, ensuring the transient synchronous stability of the converter is the basic prerequisite for achieving fault ride-through. However, during the fault, the interaction between converters and between converters and weak grids in the multi-converter grid-connected system may cause the converters to lose synchronous stability and disconnect from the grid, which seriously threatens the safe and stable operation of the power system. [3] Therefore, it is necessary to study the transient synchronization stability problem of PLL synchronous converter connected to weak grid system.

[0003] At present, related research mainly focuses on the transient synchronization stability analysis of single-converter grid-connected systems. References [4]-[6] point out that the dynamic model of the phase-locked loop and the synchronous machine rotor motion equation are similar in mathematical model, and then reveal the transient synchronization instability mechanism of the single-converter grid-connected system based on the equal area method. References [7], [8] and [9]-

[11] use the phase trajectory method, the inverse trajectory method and the Lyapunov energy function method to quantitatively analyze the transient synchronization stability of the single-converter grid-connected system. However, the above research cannot solve the transient stability problem of multi-converter access to weak grid systems, which is the main research motivation of the present invention.

[0004] In order to solve the problem of transient synchronization stability of multi-converter connected to weak grid system, references

[12] -

[13] assume that the dynamic characteristics of all converters are similar, and then aggregate the multi-converters into a single converter, and use the transient stability analysis method of single-converter grid-connected system to study its transient stability. However, in actual situations, different converters often come from different manufacturers and have different synchronization points, and their control parameters and dynamic characteristics may be significantly different.

[14] Therefore, it is necessary to study the transient synchronization stability of multi-converter grid-connected systems under the interaction of different dynamic characteristics.

[0005] Regarding the study of transient synchronization stability of multi-converter grid-connected systems taking into account converter interaction, references

[15] -

[16] analyzed the influence of converter interaction on the steady-state equilibrium point of multi-converter grid-connected systems and pointed out that under interaction, converters far away from the grid-connected point are more likely to become unstable. However, the above studies focused on the existence of the equilibrium point and did not involve the transient synchronization stability of multi-converter grid-connected systems. Reference

[17] ignored the influence of dynamic interaction and used the equal-area method to deeply study the influence of converter static interaction on the transient synchronization stability of multi-converter grid-connected systems. However, reference

[18] pointed out that dynamic interaction will deteriorate the transient synchronization stability of the converter and ignoring dynamic interaction may lead to non-conservative conclusions. Reference

[19] analyzed the influence of control parameters on the transient synchronization stability of multi-converter grid-connected systems based on the phase trajectory method, but this method can only give the transient trajectory of the system under a certain initial state and is difficult to provide global transient synchronization stability information of the system. Reference

[20] proposed a double-iteration equal-area method to construct the stability boundary of multi-converter grid-connected systems. However, the equal area method is only applicable to the transient stability analysis of a single pendulum. For the transient instability problem of multiple pendulums that may occur in a multi-converter grid-connected system, it may misjudge the transient stability of the system. Reference

[21] first constructed the energy function of a multi-converter grid-connected system and used the nearest unstable equilibrium point method to characterize the maximum estimated attraction domain of the system. However, reference

[21] ignored the influence of the PLL proportional coefficient. Since the PLL proportional coefficient is closely related to the indeterminate damping term

[22] , therefore, ignoring the PLL proportionality coefficient may cause the constructed maximum estimated attraction domain to be too conservative or exceed the boundary of the real attraction domain. Based on reference

[21] , reference

[23] further constructed an extended energy function and used LaSalle invariant set theory to characterize the maximum estimated attraction domain of a multi-converter grid-connected system. It should be pointed out that using the method proposed in reference

[23] to construct the maximum estimated attraction domain of the system requires knowing the maximum and minimum values ​​of the static and dynamic interaction terms of the converter in advance. However, the range of the static and dynamic interaction terms is not easy to obtain.

[0006] In summary, there is still a lack of methods for analyzing the transient synchronization stability of multi-converter grid-connected systems taking into account converter interactions.

[0007] Related Literature:

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[0017]

[10] Z.Tian,Y.Tang,X.Zha,et al,"Hamilton-Based Stability Criterion andAttraction Region Estimation for Grid-Tied Inverters Under Large-SignalDisturbances,"IEEE Journal of Emerging and Selected Topics in PowerElectronics,vol.10,no.1,pp.413-423,2022.

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[0019]

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[0020]

[13] N.Shabanikia,S.A.Khajehoddin,"Weighted Dynamic AggregationModeling of Grid-Following Inverters to Analyze Renewable DG IntegratedMicrogrids,"IEEE Trans.Industrial Electronics,vol.71,no.1,pp.583-594,Jan.2024.

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[14] X.He,H.Geng,"Synchronization Stability Analysis and Enhancementof Grid-Tied Multi-Converter Systems,"2020 IEEE Industry Applications SocietyAnnual Meeting,Detroit,MI,USA,2020,pp.1-8.

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[16] X.He,H.Geng,"PLLSynchronization Stability of Grid-ConnectedMulticonverter Systems,"IEEE Trans.Industry Applications,vol.58,no.1,pp.830-842,Jan.-Feb.2022.

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[17] X.Yi,Y.Peng,Q.Zhou,et al,"Transient Synchronization StabilityAnalysis and Enhancement of Paralleled Converters Considering DifferentCurrent Injection Strategies",IEEE Trans.Sustainable Energy,vol.13,no.4,pp.1957-1968,2022.

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[19] S.Huang,J.Yao,Y.Lin,et al,"Interaction Mechanism Analysis andSynchronization Stability Control for Paralleled PLL-VSCs System duringLVRT",2023 IEEE International Conference on Power Science and Technology(ICPST),pp.426-431,2023.

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[0029]

[22] Y.Liu, J.Yao, J.pei, et al., "Transient Stability Enhancement ControlStrategy Based on Improved PLL for Grid Connected VSC during Severe GridFault," IEEE Trans.Energy Conversion, vol.36, no.1, pp.218-229, March 2021.

[0030]

[23] Summary of the invention

[0031] The purpose of the present invention is to provide a method for evaluating the transient synchronization stability of a multi-converter. The present invention retains the PLL dynamic characteristics of the converter, ignores the current loop dynamics, and establishes a nonlinear reduced-order mathematical model of the system; on this basis, the Takagi-Sugeno fuzzification method constructs the maximum estimated attraction domain of the system under asymmetric faults. Based on the maximum estimated attraction domain, the transient synchronization stability of the multi-converter grid-connected system is evaluated. The technical solution is as follows:

[0032] A method for evaluating transient synchronous stability of multi-converters based on a maximum estimated attraction region comprises the following steps:

[0033] S1 retains the PLL dynamic characteristics of the converter, ignores the current loop dynamics, and establishes a reduced-order mathematical model of a multi-converter grid-connected system taking into account transient interactions between converters under grid faults;

[0034] S2 constructs the maximum estimated attraction domain of the multi-converter grid-connected system based on the TS method, and the method is as follows:

[0035] S21 organizes the nonlinear reduced-order mathematical model of the multi-converter grid-connected system into form;

[0036] S22 builds the Takagi-Sugeno fuzzification model of the system: finds Z nonlinear functions f in A(x) r (x), each nonlinear function f in A(x)r (x) has a maximum value f rmax and the minimum value f rmin , corresponding to two IF-THEN rules, for Z nonlinear functions, corresponding to 2 Z A matrix i ; The TS fuzzy model is obtained by 2 Z IF-THEN rules are described;

[0037] S23 constructs the energy function of the system: for all matrices A i , if there exists a positive symmetric matrix M such that the linear matrix inequality holds:

[0038]

[0039] Then the Lyapunov function V(x) of the system is constructed as follows:

[0040] V(x)=x Τ Mx

[0041] S24 calculates the critical energy value V of V(x) cr =minV(x * ), where x * is the state variable corresponding to the critical establishment of the linear matrix inequality; construct the maximum estimated attraction domain of the system: Ω = {x∈R Z |V(x)≤V cr};

[0042] S3 evaluates the transient synchronization stability of the multi-converter grid-connected system based on the maximum estimated attraction region by judging the following formula: e,0 Stability of the transient process of transition to the system's small perturbation stable equilibrium point:

[0043] V(X e,0 )≤V cr

[0044] If the above formula is established, it means that X e,0 Located in the maximum estimated attraction region of the multi-converter grid-connected system, the multi-converter grid-connected system is transiently synchronously stable; if the above formula does not hold, it means that X e,0 Outside the maximum estimated attraction region of the multi-converter grid-connected system, the system may be transiently unstable or stable.

[0045] Furthermore, after step S3, it also includes quantitatively evaluating the influence of system parameters on the transient synchronization stability of the system based on the maximum estimated attraction domain. The method is: the maximum estimated attraction domain of the feasible equilibrium point of the system constructed based on the TS method is a hyperellipsoid, and its volume is calculated. By analyzing the influence of different converter PLL control parameters, main circuit parameters and system parameters on the volume of the maximum estimated attraction domain of the system, the influence of the parameters on the transient stability of the system is quantitatively analyzed.

[0046] Furthermore, for two converters, the nonlinear matrix A(x) of the two converters is expressed as follows:

[0047]

[0048] Where x1=δ1,x2=∫V tq1 dt; x3 = δ2; x4 = ∫V tq2 dt; δ1 and δ2 represent the phase angle difference between the output phase angle of converter 1 and converter 2 and the infinite grid voltage phase angle, V tq1 and V tq2 They represent the q-axis components of the grid connection point voltages of converter 1 and converter 2, respectively. p1 , k i1 and k p2 , k i2 They represent the ratio and integral coefficient of the phase-locked loop of converter 1 and converter 2 respectively; the expression of the nonlinear function in the above formula is as follows:

[0049]

[0050] The expressions of A1~A4 and B1~B4 are as follows:

[0051]

[0052] Where V g is the amplitude of the grid voltage; x 1e ,x 2e ,x 3e and x 4e are the steady-state values ​​of x1, x2, x3 and x4, respectively, and a 11 ,a 12 ,a 21 ,a 22 ,a 21 ,b 21 The expression is as follows:

[0053]

[0054] Where R F and X Fare the equivalent resistance and reactance from the grid connection point to the grid voltage; R1 and X1 are the equivalent resistance and reactance from the converter 1 outlet to the grid connection point; R2 and X2 are the equivalent resistance and reactance from the converter 2 to the grid connection point; I tdref1 , I tqref1 and I tdref2 , I tqref2 Represent the d-axis and q-axis current reference values ​​of converter 1 and converter 2 respectively.

[0055] Furthermore, Z = 4, for rule R q , the IF-THEN rules are as follows:

[0056] If f1(x) takes the minimum value, f2(z) takes the minimum value, f3(x) takes the minimum value, and f4(x) takes the minimum value, then the system is represented as a subsystem as shown below:

[0057]

[0058] Based on 2 4 IF-THEN rules, The Takagi-Sugeno fuzzy model in the region ψ can be expressed as follows:

[0059]

[0060] The function h i The expression of is as follows;

[0061]

[0062] Where F u i (f u )(i=1,2,…,2 4 ) is the membership function.

[0063] The beneficial effects of the present invention are as follows:

[0064] 1) The present invention retains the PLL dynamic characteristics of the converter, ignores the current loop dynamics with a faster response speed, and establishes a reduced-order mathematical model of a multi-converter grid-connected system taking into account transient interactions between converters under grid faults. This reduces the complexity of transient synchronization stability analysis of a multi-converter grid-connected system under grid faults.

[0065] 2) A method for constructing the maximum estimated attraction domain of a multi-converter grid-connected system taking into account the dynamic interaction between converters is proposed. Based on this maximum estimated attraction domain, the transient synchronization stability of the system can be quantitatively evaluated.

[0066] 3) The maximum estimated attraction domain constructed by the present invention can quantitatively evaluate the influence of the converter control parameters on the transient synchronization stability of the converter grid-connected system, and thus can provide a reference for the design of the converter control parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 (a) System topology diagram; (b) PLL k Control block diagram

[0068] Figure 2 Equivalent circuit of multi-converter grid-connected system

[0069] Figure 3 Electromagnetic transient simulation results of transient instability

[0070] Figure 4 Characteristic roots of the system equilibrium point

[0071] Figure 5 Ω V (X e,1 ) on the δ1-δ2 plane;

[0072] Figure 6 The volume of the maximum estimated attraction domain of the multi-converter grid-connected system varies with k p2 Trends of change

[0073] Figure 7 Electromagnetic transient simulation results under different scale parameters

[0074] Figure 8 The volume of the maximum estimated attraction domain of the multi-converter grid-connected system varies with k i2 Trends of change

[0075] Fig. 9 Electromagnetic transient simulation results under different integration parameters DETAILED DESCRIPTION

[0076] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0077] 1 Reduced-order model of multi-converter grid-connected system under fault conditions

[0078] 1.1 Description of PLL Synchronous Multi-Converter Grid-Connected System

[0079] The topology and control of the multi-converter grid-connected system according to the embodiment of the present invention are as follows: Figure 1 As shown in (a), VSC1 and VSC2 are both connected to the same point of common coupling (PCC), but have different synchronization points (POS). Figure 1 POS k (k=1,2) represents VSCk The synchronization point; V g and V tk Represent the infinite grid voltage and POS respectively k Voltage, simulates severe faults by symmetrically dropping the grid voltage; I tk For VSC k Current injected into PCC; Z Lk and Z g Respectively represent POS k The equivalent impedance between PCC and power supply point; L fk and C fk For VSC k The inductance and capacitance of the LC filter.

[0080] VSC k The control part mainly includes phase-locked loop and current inner loop control. k Track POS k The voltage to achieve VSC k Synchronous with the power grid, its control structure is as follows Figure 1 As shown in (b), k pk and k ik are the proportional and integral coefficients respectively. Figure 1 (b) It can be seen that PLL k The input is POS k The q-axis voltage V tqk , output angular frequency ω pllk and phase angle θ pllk . Current inner loop control realizes VSC k Injected current to current reference value I tdrefk and I tqrefk It should be noted that under normal circumstances, the current reference value is generated by the active and reactive outer loop control, but during a symmetrical fault, the VSC k The current reference value is directly given by the fault ride-through control strategy.

[0081] 1.2 Reduced-order mathematical model of phase-locked loop synchronous multi-converter grid-connected system

[0082] Based on the above assumptions, VSC k It can be equivalent to a current source, which injects current I tk As shown in equation (1). The equivalent circuit of the multi-converter grid-connected system is as follows Figure 2 shown.

[0083]

[0084] for Figure 2 The equivalent circuit shown in the figure can be obtained based on the superposition theorem. k The voltage of is expressed as follows:

[0085]

[0086] POS k The voltage is converted to VSC k Under its own dq coordinate axis, POS can be obtained k The q-axis voltage V tqk As shown below:

[0087]

[0088] Where δ ki =θ pllk -θ plli For PLL k and PLL i The phase angle difference; R k =R Lk +R g , X k =X Lk +X g .

[0089] Depend on Figure 1 (b) PLL can be obtained k The dynamic equation is as follows:

[0090] θ pllk =-∫(k pk V tqk +k ik ∫V tqk dt+ω0)dt (11)

[0091] Combining equations (11) and (12), the nonlinear mathematical model of the converter system can be obtained, as shown in equation (12).

[0092]

[0093] Where x pllk =∫V tqk dt; δ k =θ pllk -θ F ; a 11 ,a 12 ,a 21 ,a 22 ,a 21 ,b 21 The expression is as follows:

[0094]

[0095] 1.3 Verification of reduced-order mathematical model and transient synchronous instability phenomenon

[0096] In order to intuitively demonstrate the transient synchronous instability phenomenon of multi-converter grid-connected system under severe grid fault. Figure 1 The multi-converter grid-connected system based on the detailed switch model is shown in Table 1. The present invention considers the balance point X of the system before the fault e,0 = = [0.42, 0, 0.44, 0]. During the fault, the voltage drops to 0.1 pu, I dqref1 and I dqref2 are adjusted to 0.15 pu and 0.15 jpu respectively, and the SEP of the system during the fault period is recorded as X e,1 The electromagnetic transient simulation results are as follows: Figure 3 shown.

[0097] Table 1

[0098]

[0099] Depend on Figure 3 The electromagnetic transient simulation results show that when the grid voltage drops to 0.1pu, the system becomes transiently unstable. Figure 4 The characteristic roots of the system equilibrium point when the grid voltage drops to 0.1 pu are given. Obviously, the characteristic roots of the system equilibrium point are all located in the left half plane, indicating that the system has a small-signal equilibrium point (SEP) during the fault period. Figure 3 The instability phenomenon shown cannot be explained by the small signal stability analysis method. Analyzing this type of transient synchronous instability problem is the main task of the present invention.

[0100] in addition, Figure 3 The simulation results show that the simulation results of the nonlinear mathematical model (12) and the detailed switch model are basically consistent, indicating that the model (12) can be used to analyze the transient synchronous stability problem of the system.

[0101] 2 Construction of the maximum estimated attraction domain of multi-converter grid-connected system

[0102] There are many existing methods for constructing the maximum estimated attraction domain of a multi-converter grid-connected system, such as the energy function method, the linear matrix inequality optimization method, the square sum programming method, and other construction methods. Existing studies have shown that the maximum estimated attraction domain of a system constructed based on the TS method has obvious advantages such as fast construction speed and low conservatism. The steps for constructing the maximum estimated attraction domain of a multi-converter grid-connected system based on the TS method are briefly introduced as follows:

[0103] Step 1: Arrange the nonlinear system into The nonlinear matrix A(x) is expressed as follows:

[0104]

[0105] The expression of the nonlinear function is as follows:

[0106]

[0107] The expressions of A1~A4 and B1~B4 are as follows:

[0108]

[0109] Step 2: For the nonlinear function in A(x), combine the maximum and minimum values ​​of the nonlinear function into a new parameter matrix. Therefore, for the four nonlinear functions, corresponding to 2 4 A matrix i ;

[0110] Step 3: All matrices A i , if there exists a positive definite symmetric matrix M such that the linear matrix inequality (16) holds:

[0111]

[0112] Then the Lyapunov function V(x) of the system can be constructed as follows:

[0113] V(x)=x Τ Mx(17)

[0114] Step 4: Calculate the critical energy value V of V(x) cr =minV(x * ), where x * is the state variable corresponding to the critical establishment of equation (10); construct the maximum estimated attraction domain of the system: Ω = {x∈R 4 |V(x)≤V cr};

[0115] Case Study

[0116] 1 Evaluation of system transient stability based on maximum estimated attraction domain

[0117] In order to illustrate the effectiveness of the maximum estimated attraction region constructed based on the TS method in quantitatively analyzing the transient synchronization stability problem of multi-converter grid-connected systems, the present invention uses Figure 3 The transient instability phenomenon shown in the figure is analyzed as an example

[0118] The present invention constructs X based on the TS method e,1 The maximum estimated attraction domain of V (X e,1 ), Figure 5 Given Ω V (X e,1) is projected on the δ1-Δω1-δ2 plane. At the moment of fault, the angular frequency jumps, so X e,0 Instantaneous jump to X e,0 '=[δ 1e,0 ,Δω1(t0 + ),δ je,0 ,Δω2(t0 + )].Depend on Figure 5 It can be seen that X e,0 'Located in Ω V (X e,1 ), it is shown that under Case-A, the system will experience transient synchronous instability. The above theoretical analysis is completely consistent with the electromagnetic transient simulation results.

[0119] Based on the above analysis, it can be seen that for the transient synchronous stability problem of the multi-converter grid-connected system, the transient synchronous stability of the system can be effectively evaluated by constructing the maximum estimated attraction domain of the system.

[0120] 2 Quantitative evaluation of the influence of converter control parameters on the transient stability of the system based on the maximum estimated attraction region

[0121] The larger the volume of the maximum estimated attraction domain of the converter system's feasible equilibrium point, the more initial states can stably transition to the feasible equilibrium point. Therefore, the size of the maximum estimated attraction domain volume of the equilibrium point can reflect the strength of the system's transient synchronization stability. The maximum estimated attraction domain of the system's feasible equilibrium point constructed based on the TS method is a hyperellipsoid, and its volume Vol can be calculated based on formula (18).

[0122]

[0123] Where λ i is the characteristic root of the positive definite matrix M, and Γ is the gamma function.

[0124] Next, the influence of different converter PLL control parameters on the system's maximum estimated attraction domain volume will be analyzed to quantitatively analyze the impact of the above parameters on the system's transient stability.

[0125] 2.1 Analysis of the influence of phase-locked loop proportional coefficient on transient stability

[0126] In order to analyze the influence of PLL proportional system on system transient stability, the fault voltage drops to 0.115 pu, k p1 =10, k i1 =50, k i2 =200. Figure 6 Compared with k p2 The changing trend of the maximum estimated attraction domain volume of the multi-converter system connected to the grid when it increases from 4 to 24.

[0127] Depend on Figure 6 It can be seen that the proportional coefficient k of PLL2 is p2 The larger the value is, the larger the volume of the multi-converter grid-connected system is, indicating that increasing the proportional coefficient of PLL2 will enhance the transient synchronization stability of the system. Figure 7 Compared with k p2 The electromagnetic transient simulation results of the multi-converter grid-connected system when k is equal to 5 and 20 respectively. It can be seen from the figure that when k p2 When it increases from 5 to 20, the system changes from transient instability to transient synchronous stability. The simulation results show that increasing the proportional coefficient of the PLL of a converter in the multi-converter grid-connected system can enhance the transient synchronous stability of the system.

[0128] 2.1 Analysis of the influence of phase-locked loop integral coefficient on transient stability

[0129] In order to analyze the influence of PLL integration system on the transient stability of the system, the fault voltage drops to 0.115 pu, k p1 =10, k i1 =50, k p2 =20. Figure 8 Compared with k i2 Variation trend of the maximum estimated attraction domain volume of the multi-converter grid-connected system when it increases from 50 to 200.

[0130] For multi-converter grid-connected systems, Figure 8 The red solid line shows that k i2 The influence on the transient synchronization stability of the multi-converter grid-connected system is not a simple monotonic relationship. On the contrary, when k i When it increases to a certain value, continue to increase k i2 The transient synchronous stability of the system may be enhanced. This is significantly different from the case of a single-converter system and needs to be paid attention to.

[0131] To further verify the theoretical analysis results, Fig. 9 Given k i2 The electromagnetic transient simulation results of the system when is equal to 50 and 120. Fig. 9 It can be clearly seen that when k i2 When k is equal to 50, the system can maintain transient synchronous stability. i2 If it increases to 120, the converter cannot keep pace with the grid and the system becomes transiently unstable. Figure 7 As shown in the blue waveform, if k i2 When it continues to increase to 200, the system can maintain transient synchronous stability. Figure 7 and Fig. 9 The simulation results show that if only the integral coefficient of the PLL of a converter in the parallel system is increased, the transient synchronization stability of the system may be deteriorated. Figure 8 The theoretical analysis results are completely consistent, verifying the effectiveness of the theoretical analysis.

Claims

1. A method for evaluating transient synchronous stability of multi-converters based on a maximum estimated attraction region, comprising the following steps: S1 retains the PLL dynamic characteristics of the converter, ignores the current loop dynamics, and establishes a reduced-order mathematical model of a multi-converter grid-connected system taking into account transient interactions between converters under grid faults; S2 constructs the maximum estimated attraction domain of the multi-converter grid-connected system based on the TS method, and the method is as follows: S21 organizes the nonlinear reduced-order mathematical model of the multi-converter grid-connected system into form; S22 builds the Takagi-Sugeno fuzzification model of the system: finds Z nonlinear functions f in A(x) r (x), each nonlinear function f in A(x) r (x) has a maximum value f rmax and the minimum value f rmin , corresponding to two IF-THEN rules, for Z nonlinear functions, corresponding to 2 Z A matrix i ; The TS fuzzy model is obtained by 2 Z IF-THEN rules are described; S23 constructs the energy function of the system: for all matrices A i , if there exists a positive symmetric matrix M such that the linear matrix inequality holds: Then the Lyapunov function V(x) of the system is constructed as follows: V(x)=x Τ Mx S24 calculates the critical energy value V of V(x) cr =minV(x * ), where x * is the state variable corresponding to the critical establishment of the linear matrix inequality; construct the maximum estimated attraction domain of the system: Ω = {x∈R Z |V(x)≤V cr }; S3 evaluates the transient synchronization stability of multi-converter grid-connected systems based on the maximum estimated attraction region: By judging the following formula, we can judge that the system is in the initial state X e,0 Stability of the transient process of transition to the system's small perturbation stable equilibrium point: V(X e,0 )≤V cr If the above formula holds, it means that X e,0 Located in the maximum estimated attraction region of the multi-converter grid-connected system, the multi-converter grid-connected system is transiently synchronously stable; if the above formula does not hold, it means that X e,0 Outside the maximum estimated attraction region of the multi-converter grid-connected system, the system may be transiently unstable or stable.

2. The method for evaluating transient synchronous stability of multiple converters according to claim 1, characterized in that: After step S3, it also includes quantitatively evaluating the influence of system parameters on the transient synchronization stability of the system based on the maximum estimated attraction domain. The method is as follows: the maximum estimated attraction domain of the feasible equilibrium point of the system constructed based on the TS method is a hyperellipsoid, and its volume is calculated. By analyzing the influence of different converter PLL control parameters, main circuit parameters and system parameters on the volume of the maximum estimated attraction domain of the system, the influence of the parameters on the transient stability of the system is quantitatively analyzed.

3. The method for evaluating transient synchronous stability of multiple converters according to claim 1, characterized in that: For two converters, the nonlinear matrix A(x) of the two converters is expressed as follows; Where x1=δ1,x2=∫V tq1 dt; x3 = δ2; x4 = ∫V tq2 dt; δ1 and δ2 represent the phase angle difference between the output phase angle of converter 1 and converter 2 and the infinite grid voltage phase angle, V tq1 and V tq2 They represent the q-axis components of the grid connection point voltages of converter 1 and converter 2, respectively. p1 , k i1 and k p2 , k i2 They represent the ratio and integral coefficient of the phase-locked loop of converter 1 and converter 2 respectively; the expression of the nonlinear function in the above formula is as follows: The expressions of A1~A4 and B1~B4 are as follows: Where V g is the amplitude of the grid voltage; x 1e ,x 2e ,x 3e and x 4e are the steady-state values ​​of x1, x2, x3 and x4, respectively, and a 11 ,a 12 ,a 21 ,a 22 ,a 21 ,b 21 The expression is as follows: Where R F and X F are the equivalent resistance and reactance from the grid connection point to the grid voltage; R1 and X1 are the equivalent resistance and reactance from the converter 1 outlet to the grid connection point; R2 and X2 are the equivalent resistance and reactance from the converter 2 to the grid connection point; I tdref1 , I tqref1 and I tdref2 , I tqref2 Represent the d-axis and q-axis current reference values ​​of converter 1 and converter 2 respectively.

4. The method for evaluating transient synchronous stability of multiple converters according to claim 3, characterized in that: Z = 4, for rule R q , the IF-THEN rules are as follows: If f1(x) takes the minimum value, f2(z) takes the minimum value, f3(x) takes the minimum value, and f4(x) takes the minimum value, then the system is represented as a subsystem as shown below: Based on 2 4 IF-THEN rules, The Takagi-Sugeno fuzzy model in the region ψ can be expressed as follows: The function h i The expression of is as follows; Where F u i (f u )(i=1,2,…,2 4 ) is the membership function.

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