Method for evaluating transient synchronous stability of multi-infeed based on maximum estimated attraction region

Abstract

The application relates to a kind of multi-converter transient synchronization stability evaluation methods based on maximum estimated attraction domain, comprising the following steps: S1 retains the PLL dynamic characteristics of converter, ignores the current loop dynamics, and establishes the reduced-order mathematical model of multi-converter grid-connected system under power grid fault considering the transient interaction between converters;S2 constructs the maximum estimated attraction domain of multi-converter grid-connected system based on TS method;S3 evaluates the transient synchronization stability of multi-converter grid-connected system based on the maximum estimated attraction domain.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of power electronic power system transient stability analysis, aiming at the transient synchronization stability problem of phase-locked loop synchronization type multi-converter grid-connected system under power grid fault, a transient synchronization stability evaluation method based on maximum estimated attraction domain is proposed. BACKGROUND

[0002] With large-capacity long-distance transmission of renewable energy, converters are faced with the operation scenario of accessing weak grids [1] . The current grid-connected control of new energy and energy storage converters is mainly based on the phase-locked loop (PLL) synchronization grid-following control strategy [2] . Under serious power grid faults, ensuring the transient synchronization stability of converters is the basic prerequisite for fault ride-through, however, the interaction between converters and between converters and weak grids coexisting in multi-converter grid-connected systems during faults may lead to the successive synchronization instability and disconnection of converters, which seriously threatens the safe and stable operation of power systems [3] . Therefore, it is necessary to study the transient synchronization stability problem of PLL synchronization type converters accessing weak grid systems.

[0003] Currently, related researches mainly focus on the transient synchronization stability analysis of single-converter grid-connected systems. Literature [4]-[6] points out that the dynamic model of the phase-locked loop is similar to the mathematical model of the rotor motion equation of a synchronous machine, and then reveals the transient synchronization instability mechanism of single-converter grid-connected systems based on the equal-area method. Literature [7], [8] and [9]-

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

[0004] For the transient synchronization stability problem of multi-converter accessing weak grid systems, literature

[12] -

[13] assumes that the dynamic characteristics of all converters are relatively similar, then aggregates the multi-converter into a single converter, and uses the transient stability analysis method of single-converter grid-connected systems 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 have significant differences

[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] For the transient synchronous stability of multi-inverter grid-connected system considering the interaction of inverters, the influence of the interaction of inverters on the steady-state equilibrium point of multi-inverter grid-connected system is analyzed in

[15] -

[16] , and it is pointed out that the inverter far from the grid point is more likely to lose stability under the interaction. However, the above research focuses on the existence of equilibrium point, and does not involve the transient synchronous stability of multi-inverter grid-connected system.

[17] ignores the influence of dynamic interaction, and deeply studies the influence of static interaction of inverters on the transient synchronous stability of multi-inverter grid-connected system by using the equal-area method. However,

[18] points out that dynamic interaction will worsen the transient synchronous stability of inverters, and ignoring dynamic interaction may lead to non-conservative conclusions.

[19] analyzes the influence of control parameters on the transient synchronous stability of multi-inverter grid-connected system based on the phase trajectory method, but this method can only give the transient trajectory of the system at a certain initial state, and it is difficult to provide the global transient synchronous stability information of the system.

[20] proposes a double-iteration equal-area method to construct the stability boundary of multi-inverter grid-connected system. However, the equal-area method is only suitable for single-swing transient stability analysis, and may misjudge the transient stability of the system for the multi-swing transient instability problem that may occur in multi-inverter grid-connected system.

[21] first constructs the energy function of multi-inverter grid-connected system, and applies the nearest unstable equilibrium point method to characterize the maximum estimated attraction domain of the system. However,

[21] ignores the influence of the PLL proportionality coefficient. Since the PLL proportionality coefficient is closely related to the indefinite damping term

[22] , ignoring the PLL proportionality coefficient may lead to the maximum estimated attraction domain constructed to be too conservative, or beyond the real attraction domain boundary. Based on

[21] ,

[23] further constructs an extended energy function, and uses the LaSalle invariant set theory to characterize the maximum estimated attraction domain of multi-inverter grid-connected system. It is worth noting that the method proposed in

[23] needs to know the maximum and minimum values of the static and dynamic interaction terms of the inverter in advance. However, the range of static and dynamic interaction terms is not easy to obtain

[0006] In summary, there is still a lack of method to analyze the transient synchronous stability of multi-inverter grid-connected system considering the interaction of inverters.

[0007] Related literature:

[0008] [1] M. V. Kazemi, S. J. Sadati, S. A. Gholamian, “Adaptive frequency control of microgrid based on fractional order control and a data-driven control with stability analysis,” IEEE Trans. Smart Grid, vol. 13, no. 1, pp. 381-392, Jan. 2022.

[0009] [2] Y. Tang, Y. Li, “Common Lyapunov Function Based Stability Analysis of VSC With Limits of Phase Locked Loop,” IEEE Trans Power Systems, vol. 38, no. 2, pp. 1759-1762, Marc. 2023.

[0010] [3] M. G. Taul, X. Wang, P. Davari, et al, “An Overview of Assessment Methods for Synchronization Stability of Grid-Connected Converters Under Severe Symmetrical Grid Faults,” IEEE Trans. Power Electronics, vol. 34, no. 10, pp. 9655-9670, Oct. 2019.

[0011] [4] X. He, H. Geng, J. Xi, et al, “Resynchronization Analysis and Improvement of grid-connected VSCs during grid faults,” IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(1):438-45.

[0012] [5] R. Ma, J. Li, J. Kurth, et al, "Generalized Swing Equation and Transient Synchronous Stability With PLL-Based VSC," IEEE Trans. Energy Conversion, vol. 37, no. 2, pp. 1428-1441, June 2022.

[0013] [6] X. Li, Z. Tian, X. Zha, et al, "An Iterative Equal Area Criterion for Transient Stability Analysis of Grid-tied Converter Systems with Varying Damping," IEEE Trans. Power Systems, 2023, (Early Access).

[0014] [7] H. Wu, X. Wang, "Design-Oriented Transient Stability Analysis of PLL-Synchronized Voltage-Source Converters," IEEE Trans. Power Electronics, vol. 35, no. 4, pp. 3573-3589, Apr 2020.

[0015] [8] Q. Hu, L. Fu, F. Ma, et al, "Large Signal Synchronizing Instability of PLL-Based VSC Connected to Weak AC Grid," IEEE Trans. Power Systems, vol. 34, no. 4, pp. 3220-3229, Jul 2019.

[0016] [9] Y. Zhang, C. Zhang, X. Cai, "Large-Signal Grid-synchronization Stability Analysis of PLL-based VSCs Using Lyapunov's Direct Method," IEEE Trans. Power Systems, vol. 37, no. 1, pp. 788-791, Jan. 2022.

[0017]

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

[0018]

[11] U. Buragohain, N. Senroy, "Reduced Order DFIG Models for PLL-Based Grid Synchronization Stability Assessment," IEEE Trans. Power Systems, Early Access.

[0019]

[12] M. G. Taul, X. Wang, P. Davari, et al, "Reduced-Order and Aggregated Modeling of Large-Signal Synchronization Stability for Multi-converter Systems," IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9, no. 3, pp. 3150-3165, June 2021.

[0020]

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

[0021]

[14] X. He, H. Geng, “Synchronization Stability Analysis and Enhancement of Grid-Tied Multi-Converter Systems,” 2020 IEEE Industry Applications Society Annual Meeting, Detroit, MI, USA, 2020, pp. 1-8.

[0022]

[15] J. Zhao, M. Huang, X. Zha, “Transient Stability Analysis of Grid-Connected VSIs via PLL Interaction,” 2018 IEEE International Power Electronics and Application Conference and Exposition (PEAC), Shenzhen, China, 2018, pp. 1-6.

[0023]

[16] X. He, H. Geng, “PLL Synchronization Stability of Grid-Connected Multiconverter Systems,” IEEE Trans. Industry Applications, vol. 58, no. 1, pp. 830-842, Jan.-Feb. 2022.

[0024]

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

[0025]

[18] X. Fu, M. Huang, S. Pan, et al, "Cascading Synchronization Instability in Multi-VSC Grid-Connected System", IEEE Trans. Power Electronics, vol. 37, no. 7, pp. 7572-7576, 2022.

[0026]

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

[0027]

[20] X. Li, Z. Tian, X. Zha, et al, "Nonlinear Modeling and Stability Analysis of Grid-Tied Paralleled-Converters Systems Based on the Proposed Dual-Iterative Equal Area Criterion", IEEE Trans. Power Electronics, vol. 38, no. 6, pp. 7746-7759, 2023.

[0028]

[21] D. Pal, B. K. Panigrahi, "Reduced-Order Modeling and Transient Synchronization Stability Analysis of Multiple Heterogeneous Grid-Tied Inverters," IEEE Trans. Power Delivery, vol. 38, no. 2, pp. 1074-1085, April 2023.

[0029]

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

[0030]

[23] X. Fu, M. Huang, C. K. Tse, et al, "Synchronization Stability of Grid-Following VSC Considering Interactions of Inner Current Loop and Parallel-Connected Converters," IEEE Trans. Smart Grid, Early Access. SUMMARY

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

[0032] A multi-converter transient synchronization stability evaluation method based on the maximum estimated attraction domain, comprising the following steps:

[0033] S1 Retain the PLL dynamic characteristics of the converter, ignore the current loop dynamics, and establish a reduced-order mathematical model of the multi-converter grid-connected system under grid fault considering the transient interaction between converters;

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

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

[0036] S22 Construct the Takagi-Sugeno fuzzy model of the system: find Z nonlinear functions f r (x) in A(x), each nonlinear function fr (x) all have a maximum f rmax and a minimum f rmin , corresponding to two IF-THEN rules, for Z nonlinear functions, corresponding to 2 Z matrices A i ; The TS fuzzy model of (1) is described by 2 Z IF-THEN rules;

[0037] S23 Construct the energy function of the system: for all matrices A i , if there exists a positive definite 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 Calculate the critical energy value V cr = min V(x * ) of V(x), where x * corresponds to the critical case of the linear matrix inequality; construct the largest estimated attraction domain of the system: Ω = {x ∈ R Z | V(x) ≤ V cr};

[0042] S3 Evaluate the transient synchronous stability of the multi-inverter grid-connected system based on the largest estimated attraction domain Determine the stability of the transient process of the system from the initial state X e,0 to the small perturbation stable equilibrium point of the system by judging the following formula:

[0043] V(X e,0 ) ≤ V cr

[0044] If the above formula is true, it means that X e,0 is located in the largest estimated attraction domain of the multi-inverter grid-connected system, and the multi-inverter grid-connected system is transiently synchronous stable; if the above formula is not true, it means that X e,0 is located outside the largest estimated attraction domain of the multi-inverter grid-connected system, and the system may be transiently unstable or stable.

[0045] Further, after step S3, the method further comprises quantitatively evaluating the influence of system parameters on the transient stability of the system based on the maximum estimated attractor domain, and the method is as follows: the maximum estimated attractor domain of the feasible equilibrium point of the system constructed based on the TS method is a hyper-ellipsoid, the volume of the hyper-ellipsoid is calculated, and the influence of different converter PLL control parameters, main circuit parameters and system parameters on the volume of the maximum estimated attractor domain of the system is analyzed, so as to quantitatively analyze the influence of the parameters on the transient stability of the system.

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

[0047]

[0048] wherein x1=δ1, x2=∫V tq1 dt; x3=δ2; x4=∫V tq2 dt; δ1 and δ2 respectively represent phase angle differences of output phase angles of the converter 1 and the converter 2 and phase angles of infinite grid voltages, V tq1 and V tq2 respectively represent q-axis components of grid-connection point voltages of the converter 1 and the converter 2. p1 , k i1 and k p2 , k i2 respectively represent proportional and integral coefficients of phase-locked loops of the converter 1 and the converter 2; and expressions of the nonlinear functions in the above formula are as follows:

[0049]

[0050] wherein expressions of A1-A4 and B1-B4 are as follows:

[0051]

[0052] wherein V g is an amplitude of grid voltages; x 1e , x 2e , x 3e and x 4e are steady-state values of x1, x2, x3 and x4, respectively, and expressions of a 11 , a 12 , a 21 , a 22 , a 21 , b 21 are as follows:

[0053]

[0054] wherein R F and X FR and X are the equivalent resistance and reactance of the point of common coupling (PCC) to the grid voltage, respectively; R1 and X1 are the equivalent resistance and reactance of the converter 1 outlet to the PCC, respectively; R2 and X2 are the equivalent resistance and reactance of the converter 2 to the PCC, respectively; I tdref1 , I tqref1 and I tdref2 , I tqref2 represent the d-axis and q-axis current reference values of the converter 1 and the converter 2, respectively.

[0055] Further, Z = 4, for the 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, the system is expressed as a subsystem as shown in the following:

[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] In the expression of the function h i , the expression is as follows:

[0061]

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

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

[0064] 1) The present application retains the dynamic characteristics of the PLL of the converter, ignores the dynamic of the current loop with faster response speed, and establishes a reduced-order mathematical model of a multi-converter grid-connected system considering transient interaction between converters under grid faults. The complexity of transient synchronous stability analysis of the multi-converter grid-connected system under grid faults is reduced.

[0065] 2) A method for constructing the maximum estimated attraction domain of a multi-converter grid-connected system considering dynamic interaction between converters is proposed, and the transient synchronous stability of the system can be quantitatively evaluated based on the maximum estimated attraction domain.

[0066] 3) The maximum estimated attraction domain constructed in this invention can quantitatively evaluate the impact of converter control parameters on the transient synchronization stability of the converter grid-connected system, and thus can provide a reference for the design of converter control parameters. Attached Figure Description

[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 instability simulation results

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

[0071] Figure 5 Ω V (X e,1 The projection of ) onto the δ1-δ2 plane;

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

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

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

[0075] Figure 9 Electromagnetic transient simulation results under different integration parameters Detailed Implementation

[0076] The present invention will now be described in detail 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 Phase-Locked Loop Synchronous Multi-Converter Grid-Connected System

[0079] The topology and control of the multi-converter grid-connected system according to embodiments of the present invention are as follows: Figure 1 As shown in (a), VSC1 and VSC2 are connected to the same point of common coupling (PCC), but their synchronization points (POS) are different. Figure 1 POS k (k = 1, 2) represents VSCk the synchronization point; V g and V tk represent the infinite grid voltage and the POS k voltage, respectively; I tk is the current injected by the VSC k into the PCC; Z Lk and Z g represent the equivalent impedances from the POS k to the PCC and from the PCC to the source point, respectively; L fk and C fk are the inductance and capacitance of the LC filter of the VSC k .

[0080] The control part of the VSC k mainly includes a phase-locked loop (PLL) and a current inner loop control. The PLL k tracks the voltage of the POS k to realize the synchronization of the VSC k with the grid, and its control structure is shown in Fig. Figure 1 (b), in which k pk and k ik are the proportional and integral coefficients, respectively. As can be seen from Fig. Figure 1 (b), the input of the PLL k is the q-axis voltage V k of the POS tqk , and the output is the angular frequency ω pllk and the phase angle θ pllk . The current inner loop control realizes the tracking of the injected current of the VSC k to the current reference values I tdrefk and I tqrefk . It should be noted that, in normal conditions, the current reference values are generated by the active and reactive outer loop control, but during the symmetric fault, the current reference values of the VSC k are directly given by the fault ride-through control strategy.

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

[0082] Based on the above assumptions, the VSC k can be equivalent to a current source, and its injected current I tk is shown in equation (1). The equivalent circuit of the multi-converter grid-connected system is shown in Fig. Figure 2 .

[0083]

[0084] For the equivalent circuit shown in Fig. Figure 2 , based on the superposition theorem, the voltage of the POS k can be obtained, and the specific expression is as follows:

[0085]

[0086] The voltage of POS k is transformed to the dq coordinate of VSC k , and the q-axis voltage of POS k V tqk is obtained as follows:

[0087]

[0088] where δ ki = θ pllk - θ plli is the phase angle difference of PLL k and PLL i ; R k = R Lk + R g , X k = X Lk + X g .

[0089] The dynamic equation of PLL k is obtained as follows: Figure 1

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

[0091] Combining equation (11) and (12), the nonlinear mathematical model of the converter system is 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 are expressed as follows:

[0094]

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

[0096] ​To visually demonstrate the transient synchronization instability phenomenon of a multi-converter grid-connected system under severe grid faults, this invention establishes a system in PSCAD / EMTDC as follows: Figure 1 The multi-converter grid-connected system based on a detailed switching model is shown in Table 1, with detailed parameters. This invention considers the system's equilibrium point X before a fault. e,0 ==[0.42,0,0.44,0]. During the fault, the voltage dropped to 0.1 pu, I dqref1 and I dqref2 Adjust them to 0.15 pu and 0.15 jpu respectively, and denote the system's SEP during the fault period as X. e,1 The electromagnetic transient simulation results are as follows: Figure 3 As shown.

[0097] Table 1

[0098]

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

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

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

[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, and the sum-of-squares programming method. Existing research shows that constructing the maximum estimated attraction domain of a system based on the TS method has significant advantages, including 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 described below:

[0103] Step 1: Rearrange the nonlinear system as follows The form is given by the following expression for the nonlinear matrix A(x);

[0104]

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

[0106]

[0107] The expression of A1-A4 and B1-B4 is as follows:

[0108]

[0109] Step 2: For the nonlinear function in A(x), the maximum and minimum values of the nonlinear function are combined into a new parameter matrix. Therefore, for 4 nonlinear functions, 2 4 matrix A i is obtained.

[0110] Step 3: All matrix A i , if there is a positive definite symmetric matrix M that makes the linear matrix inequality (16) hold:

[0111]

[0112] 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 cr of V(x) = min V(x * ), where x * is the state variable corresponding to the criticality of formula (10); Construct the maximum estimated attraction domain of the system: Ω = {x ∈ R 4 |V(x)≤V cr};

[0115] Case analysis

[0116] 1. Evaluate the transient stability of the system based on the maximum estimated attraction domain

[0117] To illustrate the effectiveness of the maximum estimated attraction domain constructed based on the TS method in quantitatively analyzing the transient synchronization stability problem of the multi-inverter grid-connected system, the transient instability phenomenon shown in the figure is taken as an example for specific analysis Figure 3

[0118] The maximum estimated attraction domain of X e,1 is constructed based on the TS method, denoted as Ω V (X e,1 ), Figure 5 Ω V (X e,1 ​The projection of X onto the δ1-Δω1-δ2 plane. At the instant the fault occurs, the angular frequency jumps, therefore, 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 known that X e,0 Located in Ω V (X e,1 Furthermore, this indicates that under Case-A conditions, 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 synchronization stability problem of multi-converter grid-connected systems, the transient synchronization stability of the system can be effectively evaluated by constructing the maximum estimated attraction domain of the system.

[0120] 2. Quantitative evaluation of the impact of converter control parameters on the transient stability of the system based on the maximum estimated attraction domain.

[0121] The larger the volume of the maximum estimated attraction domain of the feasible equilibrium point of the converter system, the more initial states can stably transition to that feasible equilibrium point. Therefore, the size of the maximum estimated attraction domain of the equilibrium point can reflect the strength of the system's transient synchronous stability. 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 Vol can be calculated based on equation (18).

[0122]

[0123] In the formula λ i Γ is the eigenvalue of the positive definite matrix M, and Γ is the gamma function.

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

[0125] 2.1 Analysis of the Influence of the Proportional Coefficient of the Phase-Locked Loop on Transient Stability

[0126] To analyze the impact of the PLL proportional system on the transient stability of the system, a fault voltage drop to 0.115 pu and k were selected. p1 =10, k i1 =50, k i2 =200. Figure 6 Comparison of k p2 The changing trend of the maximum estimated attraction domain volume of the multi-converter grid-connected system when the value increases from 4 to 24.

[0127] Depend onFigure 6 It can be seen that the proportional coefficient k of PLL2 p2 The larger the value, the larger the volume of the multi-converter grid-connected system, indicating that increasing the proportional coefficient of PLL2 will enhance the transient synchronization stability of the system. Figure 7 Comparison of k p2 The electromagnetic transient simulation results of the multi-converter grid-connected system are given when k is equal to 5 and 20, respectively. As can be seen from the figure, when k... p2 When the coefficient is increased from 5 to 20, the system changes from transient instability to transient synchronous stability. This simulation result demonstrates that increasing the proportional gain (PLL) of a single converter in a multi-converter grid-connected system can enhance the system's transient synchronous stability.

[0128] 2.1 Analysis of the Influence of Phase-Locked Loop Integral Coefficients on Transient Stability

[0129] To analyze the impact of the PLL integral system on the transient stability of the system, a fault voltage drop to 0.115 pu and k were selected. p1 =10, k i1 =50, k p2 =20. Figure 8 Comparison of k i2 The changing trend of the maximum estimated attraction domain volume of the multi-converter grid-connected system when the value increases from 50 to 200.

[0130] For multi-converter grid-connected systems, by Figure 8 As shown by the solid red line, k i2 The impact on the transient synchronization stability of multi-converter grid-connected systems is not a simple monotonic relationship. Instead, when k... i When k increases to a certain value, continue increasing k. i2 This may enhance the transient synchronization stability of the system. This differs significantly from the case of a single-converter system and requires attention.

[0131] To further verify the results of the theoretical analysis, Figure 9 Given k i2 Electromagnetic transient simulation results of the system when the voltage is 50 and 120. From... Figure 9 It can be clearly seen that when k i2 When k equals 50, the system can maintain transient synchronization and stability. i2 Increasing the value to 120 will cause the converter to lose synchronization with the grid, resulting in system transient instability. However, due to... Figure 7 As shown in the blue waveform, if k i2 If the number is increased to 200, the system can maintain transient synchronization and stability. Figure 7 and Figure 9 The simulation results show that increasing only the integral coefficient of the PLL of a single converter in a parallel system may worsen the transient synchronization stability of the system. This is consistent with the results based on...Figure 8 The theoretical analysis results are consistent with the experimental results, which verifies the validity of the theoretical analysis.

Claims

1. A method for evaluating the transient synchronous stability of a multi-converter based on the maximum estimated attraction domain, 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 that considers transient interactions between converters under grid fault conditions. S2 constructs the maximum estimated attraction region of a multi-converter grid-connected system based on the TS method, as follows: S21 reorganizes the nonlinear reduced-order mathematical model of the multi-converter grid-connected system as follows: The form; S22 constructs the Takagi-Sugeno fuzzy model of the system: find the Z nonlinear functions f in A(x). r (x), each nonlinear function f in A(x) r (x) all have a maximum value f. rmax and minimum value f rmin This corresponds to two IF-THEN rules. For Z nonlinear functions, it corresponds to 2. Z Matrix A i ; The TS fuzzy model is obtained through 2 Z Describe each IF-THEN rule; S23 Constructs the energy function of the system: for all matrices A i If there exists a positive definite symmetric matrix M such that the linear matrix inequality holds: The Lyapunov function V(x) of the system is then constructed as follows: V(x)=x Τ Mx S24 calculates the critical energy value V(x). cr =minV(x) * ), where x * Let be the state variables corresponding to the critical validity of the linear matrix inequality; construct the maximum estimated attraction region 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 domain: The system is determined by judging the following formula based on its initial state X. e,0 Stability of the transient process transitioning to a stable equilibrium point under small disturbances: V(X e,0 )≤V cr If the above formula holds true, it means X e,0 Within 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 equation does not hold, it indicates that X... e,0 Located outside the maximum estimated attraction domain of a multi-converter grid-connected system, the system may be transiently unstable or stable.

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

3. The method for evaluating the transient synchronization 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; In the formula, 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 phase angle of the infinite grid voltage, respectively. tq1 and V tq2 Let k 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 Let represent the proportional-integral coefficients of the phase-locked loops of converter 1 and converter 2, respectively; the expression for the nonlinear function in the above formula is as follows: The expressions for A1~A4 and B1~B4 in the formula are as follows: In the formula V g It is the amplitude of the grid voltage; x 1e ,x 2e ,x 3e and x 4e These 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: In the formula R F and X F R1 and X1 are the equivalent resistance and reactance from the grid connection point to the grid voltage, respectively; R2 and X2 are the equivalent resistance and reactance from the outlet of converter 1 to the grid connection point, respectively; I tdref1 I tqref1 and I tdref2 I tqref2 These represent the d-axis and q-axis current reference values ​​for converter 1 and converter 2, respectively.

4. The method for evaluating the transient synchronization stability of multiple converters according to claim 3, characterized in that, Z=4, for rule R q The IF-THEN rule is 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 It is represented as a subsystem as shown below: Based on 2 4 One IF-THEN rule, The Takagi-Sugeno fuzzy model within the region ψ can be represented as follows: In the formula, the function h i The expression is as follows; In the formula F u i (f u (i = 1, 2, ..., 2) 4 ) is the membership function.

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