Method for quantitatively evaluating influence of positive and negative sequence coupling on transient stability of converter

Abstract

The invention provides a method for quantitatively evaluating the influence of positive and negative sequence coupling on the transient stability of a converter, and the method comprises the following steps: constructing a nonlinear mathematical model of a VSC (Voltage Source Converter) connected to a weak network system, and enabling the adopted converter to be a network-following converter; constructing a Takagi-Sugeno fuzzification model of a VSC (Voltage Source Converter) access weak network system; according to the Takagi-Sugeno fuzzy model, constructing an energy function of the VSC accessing the weak network system; calculating a critical energy value of the energy function; defining a transient synchronous stability index to quantify a phase-locked loop synchronous transient stability margin of a transient process that the system transitions from a balance point before a fault to a balance point during an asymmetric fault period; and defining a sequence coupling coefficient gamma to quantitatively evaluate the influence of positive and negative sequence coupling on the transient synchronization stability of the system.

Description

Technical Field

[0001] The present invention belongs to the field of transient stability analysis of power electronic power systems. Aiming at the problem of transient synchronization stability of a phase-locked loop synchronous VSC connected to a weak network system under an asymmetric fault, a method for quantitatively evaluating the influence of positive and negative sequence coupling on the transient synchronization stability of a VSC connected to a weak network system is proposed. Background Art

[0002] In recent years, a large number of renewable energy sources have been connected to the grid through voltage source converters (VSCs). [1] Unlike synchronous generators, which synchronize with the grid through the actual physical rotor structure, VSCs are often synchronized with the grid through a phase-locked loop (PLL). [2] Under large disturbances such as power grid faults, weakly connected VSCs are prone to transient instability of the phase-locked loop synchronization, causing the VSC to fail to ride through the fault and trip off the grid, seriously threatening the safe and stable operation of the system. [3] Therefore, it is necessary to study the transient synchronization stability problem of VSC access to weak grid system under fault.

[0003] At present, most of the research on transient synchronization stability of VSC connected to weak grid systems focuses on symmetrical fault conditions. References [4]-[5] point out that the PLL dynamic model and the synchronous machine rotor motion equation are similar in mathematical model, and reveal the transient synchronization instability mechanism of VSC connected to weak grid systems based on the equal area method; References [6], [7] and [8]-[9] respectively use the phase trajectory method, the inverse trajectory method and the direct method to quantitatively analyze the transient synchronization stability of VSC connected to weak grid systems. References

[10] and

[11] -

[12] respectively analyze the impact of the dynamic interaction between the current inner loop and the active outer loop and PLL on the transient synchronization stability of the system under fault conditions. References

[13] -

[14] consider the use of droop control in the reactive loop of the system during the fault period, and analyze the impact of the droop coefficient on the transient synchronization stability of the VSC connected to weak grid systems based on the phase trajectory method. However, the above studies analyze the transient synchronization stability of VSC connected to weak grid systems under symmetrical grid faults. The established models and analysis methods cannot solve the transient synchronization stability of the system under asymmetrical faults.

[0004] Compared with symmetrical faults, the transient synchronization stability problem of VSC connected to weak grid system under asymmetrical fault is more complicated. According to the grid connection guidelines, VSC needs to inject double sequence current during asymmetrical fault ride-through.

[15] Therefore, under asymmetric faults, the transient synchronization stability of both positive and negative sequences of VSC connected to weak grid systems needs to be considered. In addition, under asymmetric faults, the networks are interconnected, resulting in dynamic interaction between positive and negative sequence synchronization dynamics.

[16] , which can be called positive and negative sequence coupling. Under weak network conditions, the positive and negative sequence coupling effect is further strengthened, and the dual-sequence transient synchronization behavior is complex, which makes the transient synchronization stability analysis of VSC access to weak network system during asymmetric faults face severe challenges. However, the probability of asymmetric faults in actual systems is much higher than that of symmetric faults.

[17] -

[18] Therefore, it is necessary to study the transient synchronization stability of VSC connected to the weak grid system during asymmetric faults.

[0005] In order to solve the problem of transient synchronization stability of VSC connected to weak grid system under asymmetric fault, the literature

[19] established a nonlinear reduced-order mathematical model suitable for analyzing the transient synchronization stability of VSC connected to weak grid system under asymmetric fault, and derived the analytical criterion for the existence of equilibrium point in the system during the fault. However, satisfying the static stability condition alone cannot guarantee the transient synchronization stability of the converter, which is also related to the transient synchronization process dominated by the phase-locked loop.

[20] Reference

[21] used the phase trajectory method to analyze the transient synchronization stability of VSC connected to the weak grid during asymmetric faults, and discussed the impact of positive and negative sequence injection currents on the system stability boundary. Reference

[22] proposed an analytical criterion for positive and negative sequence transient synchronization stability from the perspective of potential energy and kinetic energy conversion, and analyzed the transient synchronization stability of VSC connected to the weak grid under three typical asymmetric faults.

[0006] It should be pointed out that the above literatures do not consider the impact of positive and negative sequence coupling on the transient synchronization stability of the system. Therefore, the transient synchronization stability problem of the grid-connected VSC system under asymmetric faults needs to be solved urgently.

[0007] Related Literature

[0008] [1] Q. Zhou, M. Shahidehpour, A. Alabdulwahab, et al, "Flexible Division and Unification Control Strategies for Resilience Enhancement in Networked Microgrids," IEEE Trans. Power Systems, vol. 35, no. 1, pp. 474-486, Jan. 2020.

[0009] [2]D.Dong,B.Wen,D.Boroyevich,and P.Mattavelli,“Analysis of phase-locked loop low-frequency stability in three-phase grid-connected powerconverters considering impedance interactions,”IEEE Trans.IndustrialElectronics,vol.62,no.1,pp.310-321,Jan.2015.

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

[0011] [4]X.Li,Z.Tian,X.Zha,et al,"An Iterative Equal Area Criterion forTransient Stability Analysis of Grid-tied Converter Systems with VaryingDamping,"IEEE Trans.Power Systems,2023,(Early Access).

[0012] [5]X.He,H.Geng,J.Xi,et al,"Resynchronization Analysis and Improvementof grid-connected VSCs during grid faults,"IEEE Journal of Emerging andSelected Topics in Power Electronics,2021,9(1):438-45.

[0013] [6]H.Wu,X.Wang,"Design-Oriented Trans ient Stability Analysis of PLL-Synchronized Voltage-Source Converters,"IEEE Trans.Power Electronics,vol.35,no.4,pp.3573-3589,Apr 2020.

[0014] [7]Q.Hu,L.Fu,F.Ma,et al."Large Signal Synchronizing Instability ofPLL-Based VSC Connected to Weak AC Grid,"IEEE Trans.Power Systems,vol.34,no.4,pp.3220-3229,Jul 2019.

[0015] [8]Y.Zhang,C.Zhang,X.Cai."Large-Signal Grid-synchronizat ionStability Analysis of PLL-based VSCs Us ing Lyapunov’s Direct Method,"IEEETrans.Power Systems,vol.37,no.1,pp.788-791,Jan.2022.

[0016] [9]Z.Zhang,R.Schuerhuber,L.Fickert,et al,"Region of Attraction’sEstimat ion for Grid Connected Converters with Phase-Locked Loop,"IEEETrans.Power Systems,vol.37,no.2,pp.1351-1362,March 2022.

[0017]

[10] Q.Hu,L.Fu,F.Ma,et al,"Analogized Synchronous-Generator Model ofPLL-Based VSC and Trans ient Synchronizing Stability of Converter DominatedPower System,"IEEE Tran.Sustainable Energy,vol.12,no.2,pp.1174-1185,April.2021.

[0018]

[11] D.Pal,B.K.Panigrahi,"Impact of DC-bus voltage control onsynchronization stabi lity of grid-tied inverters,"IEEE Trans.Circuits andSystems II:Express Briefs,vol.69,no.6,pp.2782-2786,June.2022.

[0019]

[12] X.He,H.Geng,R.Li,"Transient Stabi lity Analysis and Enhancementof Renewable Energy Conversion System During LVRT,"IEEE Trans.SustainableEnergy,vol.11,no.3,pp.1612-1623,July.2020.

[0020]

[13] X.Wang,H.Wu,X.Wang,D.L,et al,"Transient Stability Analysi s ofGrid-Following VSCs Considering Voltage-Dependent Current Injection duringFault Ride-Through,"IEEE Trans.Energy Convers ion,pp.1-13,2022.

[0021]

[14] Q.Hu,L.Fu,F.Ma,et al,"Impact of LVRT Control on TransientSynchronizing Stabi lity of PLL-Based Wind Turbine Converter Connected toHigh Impedance AC Grid,"IEEE Trans.Power Systems,pp.1-13,2022.

[0022]

[15] S.Mortazavian,Y.A.-R.I.Mohamed,"Analys is and Augmented Model-Based Control Des ign of Distributed Generat ion Converters with a FlexibleGrid-Support Controller,"IEEE Trans.Power Electronics,vol.34,no.7,pp.6369-6387,July 2019.

[0023]

[16] R.Teodorescu,C.L.Bak,F.Iov and P.C. “Impact of windpower plant reactive current injection during asymmetrical grid faults,”IETRenewable Power Generat ion,vol.7,no.5,pp.484–492,Sep.2013.

[0024]

[17] J.Jia,G.Yang,A.H.Nielsen,"A Review on Grid-Connected ConverterControl for Short-Circuit Power Provision Under Grid Unbalanced Faults,"IEEETrans.Power Delivery,vol.33,no.2,pp.649-661,April.2018.

[0025]

[18] NERC,“1,200MW fault induced solar photovoltaic resourceinterruption disturbance report–southern Cal ifornia 8 / 16 / 2016event,”Jun.2017,[Online].Available:www.nerc.com.

[0026]

[19] M.G.Taul,S.Golestan,X.Wang,et al,“Modeling of convertersynchronization stabi lity under grid faults:the general case,”IEEE Journalof Emerging and Selected Topics in Power Electronics,2020.

[0027]

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

[0028]

[21] Y.Li,C.Lin,J.Hu,et al,"PLL Synchronization Stability of Grid-Connected VSCs Under Asymmetric AC Faults,"IEEE Trans.Energy Convers ion,vol.37,no.4,pp.2438-2448,Dec.2022.

[0029]

[22] Summary of the invention

[0030] The purpose of the present invention is to disclose a method for quantitatively evaluating the impact of positive and negative sequence coupling on the transient stability of a VSC access weak network system under an asymmetric fault. First, the VSC access weak network system under an asymmetric fault is reasonably simplified to obtain its composite sequence network, and a nonlinear reduced-order mathematical model of the system is established; on this basis, the maximum estimated attraction domain of the system under an asymmetric fault is constructed through the Takagi-Sugeno fuzzification method. Based on the maximum estimated attraction domain, the present invention defines the positive and negative sequence coupling coefficients. The defined positive and negative sequence coupling coefficients can be used to quantitatively evaluate the impact of coupled positive and negative sequence coupling on the transient stability of the system's phase-locked loop synchronization. The technical solution is as follows:

[0031] A method for quantitatively evaluating the impact of positive-negative sequence coupling on transient stability of a converter comprises the following steps:

[0032] Step (1) The mathematical model of VSC access to the weak network system is organized as A(x) is a nonlinear matrix, including state variables and nonlinear functions, and a nonlinear mathematical model of VSC access to a weak grid system is constructed. The converter used is a grid-following converter.

[0033] Step (2) constructs the Takagi-Sugeno fuzzy model of VSC access to weak network system: for the nonlinear functions in the nonlinear matrix A(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 the mathematical model of the grid-following converter under asymmetric fault, there are four nonlinear functions in A(x), so The TS fuzzy model is obtained by 2 4 IF-THEN rules are described; based on 2 4 IF-THEN rules, establish Takagi-Sugeno fuzzy model in region ψ;

[0034] Step (3) constructing the Lyapunov function V(x) of the VSC access to the weak network system based on the Takagi-Sugeno fuzzy model, which is called the energy function V(x);

[0035] Step (4) Calculate the critical energy value V of the energy function V(x) cr ;

[0036] Step (5) defines the transient synchronous stability index ξ as shown in formula (9) to quantify the system from the equilibrium point X before the fault e,0 Transition to equilibrium point X during asymmetric fault e,1 The transient stability margin of the phase-locked loop synchronization during this transient process;

[0037] ξ=V(X e,0 -X e,1 ) / V cr (9)

[0038] In the formula, the larger the ξ, the smaller the transient stability margin of the VSC connected to the weak grid system, and the easier the system is to become unstable. In addition, when 0<ξ≤1, the VSC connected to the weak grid system is transiently synchronously stable; when ξ>1, the system may be transiently unstable or stable.

[0039] Step (8) defines the sequence coupling coefficient γ as shown in formula (10) to quantitatively evaluate the impact of positive and negative sequence coupling on the transient synchronization stability of the system: if γ is greater than 1, it means that the positive and negative sequence coupling will weaken the transient synchronization stability of the system; when γ is less than 1, it means that the positive and negative sequence coupling will weaken the transient synchronization stability of the system;

[0040] γ=ξ C / ξ NC (10)

[0041] Where ξ C and NC They are the transient synchronization coefficients of VSC accessing the weak grid system with positive and negative sequence coupling considered and without considering positive and negative sequence coupling, respectively.

[0042] Furthermore, in step (1), the method for constructing a nonlinear mathematical model of VSC access to a weak network system is as follows:

[0043] The mathematical model of VSC access to weak grid system is organized as A(x) is a nonlinear matrix. The specific expression of A(x) is as shown in formula (1). The nonlinear matrix A(x) contains two state variables x l (l=1,3) and four nonlinear functions f r (x)(r=1,...4), where x1=δ + ,x3=δ - :

[0044]

[0045] In the formula, the nonlinear function f1-f4 is as follows:

[0046]

[0047] The expression of the function g1-g2 in formula (2) is as follows:

[0048]

[0049] In the formula, δ + and δ - Respectively represent the phase angle difference between the positive sequence and negative sequence phase-locked loop output phase angle and the infinite grid voltage phase angle, x pll + and x pll - Respectively represent the q-axis integral voltage of the positive and negative sequence grid connection points; k p and k i are the proportional coefficient and integral coefficient of the phase-locked loop proportional-integral controller, V g Represents the infinite grid terminal voltage amplitude; |I t - |、|I t - | and θ I + ,θ I - are the amplitude and phase angle of the positive and negative sequence currents, respectively, and |I t + |={(I td + ) 2 +(I tq + ) 2} 1 / 2 ,|I t + |={(I td - ) 2 +(I tq - ) 2} 1 / 2 θ I + =arctan(I tq + / I td + ),θ I - =arctan(I tq- / I td - );I td + ,I tq + and I td - ,I tq - represents the positive and negative sequence d-axis and q-axis injection currents of the VSC, respectively, which are directly given by the asymmetric fault ride-through control strategy; Z e + =|Z e + |∠φ e + =Z g + K1+Z L + ,Z e - =|Z e - |∠φ e - =Z g - K3+Z L - ,Z c =|Z c |∠φ c =Z g + K2; K i =|K i |∠φ i ,i=1,2,3, K under different types of asymmetric faults i The expression of is shown in Table 1:

[0050] Table 1 K under different types of asymmetric faults i The expression

[0051]

[0052] In the table, R F Represents the grounding resistance, Z L and Z g They represent the equivalent impedances from PCC to the fault point and from the fault point to the power supply point respectively; the superscripts “+”, “-” and “0” represent positive, negative and zero-sequence impedances respectively.

[0053] Furthermore, in step (2), one of the rules R q As an example, show the IF-THEN rule:

[0054] Rule R q: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:

[0055]

[0056] Furthermore, in step (2), based on 2 4 IF-THEN rules, establish The Takagi-Sugeno fuzzy model in the region ψ is as follows:

[0057]

[0058] The function h i The expression of is as follows;

[0059]

[0060] Where F u i (f u )(i=1,2,…,2 4 ) is the membership function.

[0061] Furthermore, in step (3), an energy function of VSC accessing a weak network system is constructed as follows:

[0062] For the Takagi-Sugeno fuzzy model, that is, all matrices A in formula (5) i , if there exists a positive symmetric matrix M such that the linear matrix inequality (7) holds:

[0063]

[0064] Then the Lyapunov energy function V(x) of the system is constructed as follows:

[0065] V(x)=x Τ Mx (8)

[0066] Furthermore, in step (4), the critical energy value V of the energy function V(x) is calculated. cr =minV(x * ), where x * is the state variable corresponding to the critical establishment of equation (7).

[0067] The beneficial effects of the present invention are as follows:

[0068] 1) The present invention constructs the maximum estimated attraction domain of VSC access to a weak network system under asymmetric faults, and quantitatively analyzes the transient synchronization stability of the system based on the maximum estimated attraction domain.

[0069] 2) A method for quantitatively evaluating the impact of positive- and negative-sequence coupling on the transient stability of the VSC connected to a weak grid system is proposed. Based on this method, the impact of positive- and negative-sequence coupling on the transient synchronization stability of the system under different current injection strategies during different asymmetric faults can be analyzed, thus providing a reference for the design of positive- and negative-sequence injection currents under asymmetric fault ride-through. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1: Schematic diagram of topology and control structure of VSC access to weak network system

[0071] Figure 2: Equivalent circuit of VSC connected to weak grid system

[0072] Attached Figure 3 Dynamic block diagram of VSC access to weak network system under asymmetric fault

[0073] Figure 4 Contours of γ under different positive sequence injection currents: (a) I t - =-0.39+0.5jpu; (b)I t - =-0.42+0.5jpu;

[0074] Figure 5 Simulation results: point a1 (a) ω pll + ,(b)ω pll - ; a2 point (c) ω pll + ,(d)ω pll - ;

[0075] Figure 6 Simulation results: b1 point (a) ω pll + ,(b)ω pll - ; b2 point (c) ω pll + ,(d)ω pll - ; DETAILED DESCRIPTION

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

[0077] (1) Reduced-order mathematical model of phase-locked loop synchronous VSC connected to weak grid system under asymmetric fault

[0078] The topological structure and control block diagram of the VSC access weak network system of the present invention are shown in FIG1. abc 、v tabc 、v Fabc and v gabcRespectively represent the VSC outlet voltage, grid connection point voltage, fault point voltage and infinite grid voltage; i tabc The current injected into the grid by the VSC; L f and C f is the inductance and capacitance of the LC filter on the AC side; Z L and Z g They represent the equivalent impedance between PCC and power source and between fault point and power source respectively; the control part of the converter is mainly composed of a double second-order generalized integrator PLL (DSOGI-PLL) and a proportional-resonant (PR) current control in a two-phase stationary αβ coordinate system, as shown in Figure 1. DSOGI-PLL tracks the voltage phase angle of the positive and negative sequence PCCs and outputs the angular frequency ω of the positive and negative sequence voltages at the grid connection point. pll + ,ω pll - and phase angle θ pll + ,θ pll - ; Current control based on PR in two-phase stationary αβ coordinate system realizes VSC dual-sequence injection current to positive and negative sequence dq axis current reference value I tdqref + and I tdqref Tracking.

[0079] It should be pointed out that under asymmetric fault, the electrical quantity x abc contains positive and negative sequence components, which can be expressed as follows:

[0080]

[0081] In the formula and The electrical quantities x abc The positive and negative sequence rotating phasors of x + =x d + +jx q + , x - =x d - +jx q - ; In addition, x αβ + and x αβ - Respectively represent x α + +jx β+ and x α - +jx β - ;x dq + and x dq - Respectively represent x d + +jx q + and x d - +jx q - The present invention focuses on the transient stability problem of PLL synchronization when VSC is connected to a weak network system, so the following assumptions are considered to simplify the analysis

[0082] 1) Ignore LC filters and AC network dynamics;

[0083] 2) Ignoring the SOGI-QSG dynamics and current control dynamics, it can be assumed that the front end of the DSOGI-PLL can separate the positive and negative sequence components of the PCC voltage in real time, and that the VSC injection current can approximately track the positive and negative sequence current reference values ​​in real time;

[0084] Based on the above assumptions, the equivalent circuit model of the system is shown in FIG2 . The double-sequence current model in FIG2 is shown in formula (2):

[0085]

[0086] Where I t + and I t - In polar coordinates, it can also be expressed as I t + =|I t + |∠θ I + ,I t - =|I t - |∠θ I - ;

[0087] Based on the symmetrical component method and the equivalent circuit model shown in Figure 2, the positive and negative sequence PCC voltages under three common asymmetrical faults (SLG, DLG and LL) are and It can be uniformly expressed as follows:.

[0088]

[0089] In the above formula, “*” represents the conjugation symbol, Ki =|K i |∠φ i ,i=1,2,3, K under different fault types i The expression of is shown in the following table.

[0090] Table 1 K under different fault types i The expression

[0091]

[0092]

[0093] Transform equations (3) and (4) to PLL + and PLL - In the reference coordinate system, the q component V of the positive and negative sequence PCC voltage can be obtained tq + and V tq - . Then combined with PLL + and PLL - The control structure can be obtained under asymmetric faults. The system dynamic block diagram is shown in the attached figure. Figure 3 As shown in the figure, δ + =θ pll + -θ g ,δ - =θ pll - +θ g ,Z e + =|Z e + |∠φ e + =Z g + K1+Z L + ,Z e - =|Z e - |∠φ e - =Z g - K3+Z L - ,Z c =|Z c |∠φ c =Z g + K2;

[0094] By the attached Figure 3 It can be seen that PLL + and PLL -Input V tq + and V tq - It consists of two parts: positive and negative sequence self-influence terms and positive and negative sequence coupling terms. According to the grid connection guidelines, VSC should inject double sequence current during asymmetric faults. Therefore, during asymmetric faults, positive sequence self-influence terms, PLL + Dynamic, negative sequence self-influence term, PLL - The dynamic and positive and negative sequence coupling terms are coupled and interact with each other. Compared with the symmetrical fault, only the positive sequence self-influence term and the PLL + The dynamic interaction between VSC and weak grid under asymmetric faults will be more complicated, and the transient synchronization instability problem caused by it needs to be studied in depth.

[0095] Based on the attached Figure 3 The dynamic block diagram shown is a double-order reduced-order mathematical model of VSC connected to weak grid system suitable for transient synchronous stability analysis under asymmetric faults. It can be expressed as follows, where x = (δ + ,x pll + ,δ - ,x pll - ).

[0096]

[0097] In the above formula, x pll + =∫V tq + dt,x pll - =∫V tq - dt,

[0098] It should be pointed out that there is a local asymptotically stable equilibrium point, i.e., a feasible equilibrium point, in the VSC access weak network system during a fault, which is the prerequisite for the transient synchronization stability of the system. Regarding the existence conditions of the feasible equilibrium point of the VSC access weak network system, the present invention assumes that during a fault, there is a feasible equilibrium point X in the VSC access weak network system. e =(δ e + ,0,δ e - ,0), and δ e + and δ e - They are denoted as X e1 and X e3 .

[0099] Normally, the positive sequence impedance is the same as the negative sequence impedance, and the zero sequence impedance is greater than the positive sequence impedance. To simplify the analysis, the positive sequence, negative sequence, and zero sequence impedances are considered equal.

[0100] (2) Maximum estimated attraction domain of VSC access to weak grid system under asymmetric fault

[0101] First, the mathematical model (5) of VSC access to weak grid system is organized as A(x) is a nonlinear matrix. The specific expression of A(x) is shown in the following formula. As can be seen from the following formula, the matrix A(x) contains two state variables x l (l=1,3) and four nonlinear functions f r (x)(r=1,...4), where x1=δ + ,x3=δ - .

[0102]

[0103] The nonlinear function f1-f4 in the above formula is as shown below.

[0104]

[0105] The expression of the function g1-g2 in formula (D2) is as follows:

[0106]

[0107] In the above formula

[0108] For VSC access to weak network system In the region ψ={x∈R 4 |x lmin ≤x l ≤x lmax}, each nonlinear f in A(x) r (x) has a maximum value f rmax and the minimum value f rmin , corresponding to two IF-THEN rules. Therefore, The TS fuzzy model can be obtained by 2 4 The following is a description of one of the IF-THEN rules, q As an example, show the IF-THEN rule:

[0109] Rule R q : If f1(x) takes the minimum value f 1min 、f2(x) takes the minimum value f 2min 、f3(x) takes the minimum value f 3min 、f4(x) takes the minimum value f 4min, then the system can be represented as a subsystem as shown below:

[0110]

[0111] Based on 2 4 IF-THEN rules, The TS fuzzy model in the region ψ can be expressed as follows:

[0112]

[0113] The function h i The expression of is as follows;

[0114]

[0115] Where F u i (f u )(i=1,2,…,2 4 ) is the membership function

[0116] For all matrices A i , if there exists a positive symmetric matrix M such that the linear matrix inequality (12) holds, then is an estimated attraction domain of the VSC access weak network system, where v(x) is a Lyapunov function of the system, v(x) = x T Mx, is the boundary of region ψ.

[0117]

[0118] Obviously, the larger the area ψ is, the larger the estimated attraction domain Ω of the VSC access to the weak network system is. Therefore, the area ψ can be gradually expanded (increasing x lmax , reduce x lmin ) until there is no matrix M that makes equation (12) true. At this time, the region ψ reaches its maximum, and the corresponding estimated attraction domain is the LEDA of the WG-VSC system.

[0119] Based on the above analysis, the present invention proposes the following algorithm for constructing VSC access to weak network system LEDA based on TS method, referred to as Algorithm 1.

[0120]

[0121]

[0122] Based on Algorithm 1, the feasible balance point X of VSC access to the weak grid system during the fault period is obtained e,1After LEDA is set, the system can be judged by formula (13) from the equilibrium point X before the fault e,0 Transition to X e,1 The stability of this transient process.

[0123] V(X e,0 -X e,1 )≤V cr (13)

[0124] Specifically, if formula (13) holds, it means that X e,0 Located in X e,1 In LEDA, the system is transiently stable; if equation (13) does not hold, it means that X e,0 Located in X e,1 In addition to LEDA, due to the conservatism of LEDA, strictly speaking, the system may be transiently unstable or stable.

[0125] (3) Quantitative evaluation of the impact of positive-negative sequence coupling on the transient stability of VSC-connected weak grid systems

[0126] In order to quantitatively evaluate the impact of positive and negative sequence coupling terms on the transient synchronous stability of the system, the following sequence coupling coefficient γ is defined.

[0127] γ=ξ C / ξ NC (14)

[0128] Where ξ C and NC are the transient synchronization coefficients of the WG_VSC system when positive and negative sequence coupling are considered and when positive and negative sequence coupling is not considered. It can be seen from the above formula that when γ is greater than 1, sequence coupling will weaken the transient synchronization stability of the system; when γ is less than 1, sequence coupling will enhance the transient synchronization stability of the system.

[0129] Taking the influence of positive-negative sequence coupling (hereinafter referred to as sequence coupling) on ​​the transient synchronous stability of the system under different positive-sequence injection currents as an example, it is explained how to quantitatively evaluate the influence of sequence coupling on the transient synchronous stability of the system based on the defined sequence coupling coefficient.

[0130] 4(a) and (b) show the positive sequence injection current polar coordinate space when α=0.56 and the negative sequence injection current I t - =-0.39+0.5jpu and -0.42+0.5jpu, the contour lines of the sequence coupling coefficient γ. In the blue area of ​​the figure, γ<1, indicating that in this area, sequence coupling will enhance the transient synchronization stability of the system.

[0131] The following conclusions can be drawn from Figure 4: 1) During an asymmetric fault, when the VSC positive sequence reactive injection current is less than zero, sequence coupling will weaken the transient synchronization stability of the system; when the VSC positive sequence reactive injection current is greater than zero and the positive sequence active injection current is within a certain range, sequence coupling will enhance the transient synchronization stability of the system. 2) If sequence coupling weakens the PLL-Syn stability of the system, the greater the amplitude of the positive sequence injection current, the greater the degree of weakening of the system PLL-Syn transient stability by sequence coupling.

[0132] In order to verify the effectiveness of the above scheme, a full-order switching model of VSC access to a weak grid system under asymmetric faults was built in the PSCAD / EMPDC platform. The system parameters are shown in Table 2.

[0133] Table 2 System parameters

[0134]

[0135] In Figure 4(a), the positive-sequence active injection current corresponding to points a1 and a2 is zero, and the positive-sequence reactive injection current is -0.2pu and -0.1pu respectively. Figure 5 shows the transient simulation results of the working conditions corresponding to points a1 and a2 when and without considering the influence of sequence coupling. Point a1 corresponds to the working condition where the VSC positive-sequence reactive injection current is less than zero. It can be seen from Figures 5(a) and (b) that if the sequence coupling is ignored, the system transient synchronization is stable under the working condition corresponding to point a1. However, after taking into account the influence of sequence coupling, the system exhibits transient synchronization instability dominated by the negative sequence, indicating that when the positive-sequence reactive injection current is less than zero, sequence coupling will weaken the transient synchronization stability of the VSC connected to the weak grid system.

[0136] In addition, it can be seen from Figures 5(c) and (d) that if the amplitude of the positive sequence current is reduced from 0.2pu corresponding to point a1 to 0.1pu corresponding to point a2, the system can still maintain transient synchronous stability even if the influence of sequence coupling is taken into account. This shows that the smaller the amplitude of the positive sequence injection current, the weaker the degree of deterioration of the transient synchronous stability of the system due to sequence coupling. The simulation results are completely consistent with the theoretical analysis results based on Figure 4, verifying the effectiveness of the above scheme.

[0137] In Figure 4(b), the positive-sequence reactive injection current corresponding to points b1 and b2 is 0.2pu, and the positive-sequence active injection current is 0pu and 0.2pu respectively. Figure 6 shows the transient simulation results of the working conditions corresponding to points b1 and b2 when the sequence coupling effect is considered and not considered. It can be seen from Figure 6 that under the action of positive and negative sequence coupling, the system changes from transient synchronous instability dominated by negative sequence to transient synchronous stability. This shows that when the positive-sequence active injection current is within a certain range, if a positive positive-sequence reactive current is injected, the positive-negative sequence coupling will enhance the transient synchronous stability of the WG-VSC system, which is completely consistent with the theoretical analysis results in Figure 4.

[0138] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for quantitatively evaluating the impact of positive-negative sequence coupling on the transient stability of a converter, comprising the following steps: Step (1) The mathematical model of VSC access to the weak network system is organized as A(x) is a nonlinear matrix, including state variables and nonlinear functions, and a nonlinear mathematical model of VSC access to a weak grid system is constructed. The converter used is a grid-following converter. Step (2) constructs the Takagi-Sugeno fuzzy model of VSC access to weak network system: for the nonlinear functions in the nonlinear matrix A(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 the mathematical model of the grid-following converter under asymmetric fault, there are four nonlinear functions in A(x), so The TS fuzzy model is obtained by 2 4 IF-THEN rules are described; based on 2 4 IF-THEN rules, establish Takagi-Sugeno fuzzy model in region ψ; Step (3) constructing the Lyapunov function V(x) of the VSC access to the weak network system based on the Takagi-Sugeno fuzzy model, which is called the energy function V(x); Step (4) Calculate the critical energy value V of the energy function V(x) cr ; Step (5) defines the transient synchronous stability index ξ as shown in formula (9) to quantify the system from the equilibrium point X before the fault e,0 Transition to equilibrium point X during asymmetric fault e,1 The transient stability margin of the phase-locked loop synchronization during this transient process; ξ=V(X e,0 -X e,1 ) / V cr (9) In the formula, the larger the ξ, the smaller the transient stability margin of the VSC connected to the weak grid system, and the easier the system is to become unstable. In addition, when 0<ξ≤1, the VSC connected to the weak grid system is transiently synchronously stable; when ξ>1, the system may be transiently unstable or stable. Step (8) defines the sequence coupling coefficient γ as shown in formula (10) to quantitatively evaluate the impact of positive and negative sequence coupling on the transient synchronization stability of the system: if γ is greater than 1, it means that the positive and negative sequence coupling will weaken the transient synchronization stability of the system; when γ is less than 1, it means that the positive and negative sequence coupling will weaken the transient synchronization stability of the system; c = x C / x NC (10) Where ξ C and NC They are the transient synchronization coefficients of VSC accessing the weak grid system with positive and negative sequence coupling considered and without considering positive and negative sequence coupling, respectively.

2. The method for quantitatively evaluating the impact of positive and negative sequence coupling on the transient stability of a converter according to claim 1 is characterized in that: In step (1), the method for constructing a nonlinear mathematical model of VSC access to a weak network system is as follows: The mathematical model of VSC access to weak grid system is organized as A(x) is a nonlinear matrix. The specific expression of A(x) is as shown in formula (1). The nonlinear matrix A(x) contains two state variables x l (l=1,3) and four nonlinear functions f r (x)(r=1,...4), where x1=δ + ,x3=δ - : In the formula, the nonlinear function f1-f4 is as follows: The expression of the function g1-g2 in formula (2) is as follows: In the formula, δ + and δ - Respectively represent the phase angle difference between the positive sequence and negative sequence phase-locked loop output phase angle and the infinite grid voltage phase angle, x pll + and x pll - Respectively represent the q-axis integral voltage of the positive and negative sequence grid connection points; k p and k i are the proportional coefficient and integral coefficient of the phase-locked loop proportional-integral controller, V g Represents the infinite grid terminal voltage amplitude; |I t - |、|I t - | and are the amplitude and phase angle of the positive and negative sequence currents, respectively, and |I t + |={(I td + ) 2 +(I tq + ) 2 } 1 / 2 ,|I t + |={(I td - ) 2 +(I tq - ) 2 } 1 / 2 ; θ I + =arctan(I tq + / I td + ),θ I - =arctan(I tq - / I td - );I td + ,I tq + and I td - ,I tq - represents the positive and negative sequence d-axis and q-axis injection currents of the VSC, respectively, which are directly given by the asymmetric fault ride-through control strategy; Z e + =|Z e + |∠φ e + =Z g + K1+Z L + ,Z e - =|Z e - |∠φ e - =Z g - K3+Z L - ,Z c =|Z c |∠φ c =Z g + K2; K i =|K i |∠φ i ,i=1,2,3, K under different types of asymmetric faults i The expression is shown in Table 1: Table 1 K under different types of asymmetric faults i The expression In the table, R F Represents the grounding resistance, Z L and Z g They represent the equivalent impedances from PCC to the fault point and from the fault point to the power supply point respectively; the superscripts "+", "-" and "0" represent positive, negative and zero-sequence impedances respectively.

3. The method for quantitatively evaluating the impact of positive and negative sequence coupling on the transient stability of a converter according to claim 2, characterized in that: In step (2), one of the rules R q Take the IF-THEN rule as an example: Rule R q :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:

4. The method for quantitatively evaluating the impact of positive and negative sequence coupling on the transient stability of a converter according to claim 3 is characterized in that: In step (2), based on 2 4 IF-THEN rules, establish The Takagi-Sugeno fuzzy model in the region ψ is 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.

5. The method for quantitatively evaluating the impact of positive and negative sequence coupling on the transient stability of a converter according to claim 4, characterized in that: In step (3), the energy function of VSC accessing the weak network system is constructed as follows: For the Takagi-Sugeno fuzzy model, that is, all matrices A in formula (5) i , if there exists a positive symmetric matrix M such that the linear matrix inequality (7) holds: Then the Lyapunov energy function V(x) of the system is constructed as follows: V(x)=x Τ Mx (8)。 6. The method for quantitatively evaluating the impact of positive and negative sequence coupling on the transient stability of a converter according to claim 5, characterized in that: In step (4), the critical energy value V of the energy function V(x) is calculated cr =minV(x * ), where x * is the state variable corresponding to the critical condition of equation (7).

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