A method for analyzing and constructing the current safety domain of VSC connected to weak grid under asymmetric fault

Abstract

The present invention relates to a method for analyzing and constructing a current safety domain for VSC access to a weak network under an asymmetric fault, which is characterized by comprising: (1) establishing a transient synchronization stability constraint; (2) establishing a grid connection point voltage constraint; (3) establishing a maximum current constraint; (4) constructing a positive and negative sequence current safety domain: combining the above-mentioned transient synchronization stability constraint, grid connection point voltage constraint and maximum current constraint to obtain the positive and negative sequence current safety domain for VSC access to a weak network system under an asymmetric grid fault.

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 synchronous stability of VSC under weak network conditions, a current safety domain analysis and construction method for VSC access to weak network under asymmetric faults is proposed. Background Art

[0002] The proportion of new energy in the future power system will be higher and higher, and the impact of new energy power characteristics on the power system will also be greater. [1]-[2] As a key hub connecting renewable energy and the power grid, the voltage source converter (VSC) should be able to keep pace with the power grid under large disturbances such as asymmetric grid faults. However, a large number of theoretical studies and practical cases have shown that [3]-[5] Under large disturbances such as asymmetric grid faults, inappropriate current control strategies can easily lead to transient instability of weak grid connected VSC (WG-VSC) synchronized by phase locked loop (PLL). Therefore, it is particularly important to construct positive and negative sequence current safety domains that take into account transient synchronization stability constraints under WG-VSC asymmetric grid faults.

[0003] At present, domestic and foreign scholars have proposed a large number of control strategies based on different control objectives for the positive and negative sequence current injection strategy of VSC grid-connected systems under asymmetric grid faults. [6] For example, the positive and negative sequence compensation control strategy to eliminate active and reactive oscillations [7] , control strategies to suppress negative sequence current and optimal voltage support control strategies, etc. [8] However, the control strategy proposed in the above study does not consider the PLL transient synchronization stability problem of the VSC grid-connected system under weak grid conditions.

[0004] For the PLL transient synchronization stability problem of WG-VSC system, some studies have been conducted around symmetrical grid faults. References [9]-

[10] proposed a phase trajectory method based on numerical integration to analyze the transient synchronization stability of WG-VSC and the influence of PLL damping on the transient stability of the system, but this method is difficult to make an overall evaluation of the operating status of WG-VSC. Reference

[11] characterized the real attraction domain boundary of WG-VSC based on the inverse trajectory method

[12] , but this method cannot give an explicit expression of the boundary of the characterized attraction domain

[13] , so it is difficult to use the attraction domain for quantitative analysis. Reference

[14] revealed the similarity between the WG-VSC reduced-order model and the synchronous machine swing equation. Therefore, with the help of the prior theory of transient stability of the traditional synchronous machine power angle, references

[15] and

[16] respectively revealed the mechanism of system transient instability based on the equal area criterion (EAC) and the energy function method and constructed the estimated attraction domain of the system. However, references [14-16] did not consider the indeterminate damping term introduced by the proportional coefficient of the phase-locked loop, resulting in that the theoretical analysis results are not applicable when the equivalent damping is negative. To solve this problem, reference

[17] used the positive damping boundary as the attraction domain boundary based on the LaSalle invariant set theorem and obtained a more conservative estimated attraction domain; reference

[18] limited the deceleration area to the positive damping interval and proposed an improved EAC. In order to reduce the conservatism of the estimated attraction domain, some studies have begun to turn to constructing Lyapunov functions through numerical optimization methods. Reference

[19] introduced the Takagi–Sugeno (TS) method into the AC system, analyzed the transient stability of the self-synchronous VSC grid-connected system, and constructed its estimated attraction domain; reference

[20] used the Sum-of-Square Programming (SOS) method to obtain an estimated attraction domain that is closer to the actual attraction domain boundary of the WG-VSC system.

[0005] References [9]-

[20] analyze the PLL transient synchronization stability of WG-VSC based on the time domain simulation method of numerical integration [9]-

[10] and the method based on the equilibrium point attraction domain

[11] -

[20] . However, the above references all construct the stability boundary of the system in the state variable space of WG-VSC (PLL output frequency and phase angle space). However, in actual operation control, we are more concerned about how to design the current control strategy to ensure that the system maintains transient synchronization stability during power grid faults, that is, how to construct the current safety domain considering the system transient synchronization stability constraints. In addition, references [9]-

[20] mainly study the PLL transient synchronization stability problem under symmetrical power grid faults, but asymmetrical power grid faults are more common in power systems.

[0006] For asymmetric grid faults, references

[21] and

[22] established a reduced-order mathematical model that takes into account the dynamics of the positive and negative sequence PLL and proposed corresponding stability criteria. However, references

[21] and

[22] essentially explore the issue of whether the system has a balance point under asymmetric grid faults. Therefore, the proposed stability criteria are necessary conditions for the transient synchronization stability of the system. In other words, even if the WG-VSC meets the stability criteria proposed in references

[21] and

[22] after the fault, the system may still be transiently unstable. Therefore, it is very important and necessary to further explore the transient synchronization stability of the WG-VSC system under asymmetric grid faults and construct a positive and negative sequence current safety domain to ensure the transient synchronization stability of the system.

[0007] References

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[0020]

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[0021]

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[0027]

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[0029]

[18] Y.Zhang,C.Zhang,X.Cai.Large-Signal Grid-synchronization StabilityAnalysis of PLL-based VSCs Using Lyapunovs Direct Method[J].IEEE Trans.PowerSystems,early Access.

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[0031]

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[0032]

[21] M.G. Taul, S. Golestan, X. Wang, et al. Modeling of Converter Synchronization Stability under Grid Faults: The General Case[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, early access.

[0033]

[22] X. He, C. He, S. Pan, et al. Synchronization Instability of Inverter - Based Generation During Asymmetrical Grid Faults[J]. IEEE Trans. Power Systems, early access. Summary of the Invention

[0034] The purpose of the present invention is to provide a method for analytically constructing a positive and negative sequence current safety domain under an asymmetric power grid fault. The present invention establishes an equivalent rotor motion model of a WG-VSC system under an asymmetric power grid fault, and then proposes the concept of a positive and negative sequence current safety domain of a WG-VSC system under an asymmetric power grid fault. Based on the improved equal area rule and the expressions of the steady-state grid connection point voltage and the output current of the converter, an analytical expression of the safety domain is obtained. Based on the analytical model of the current safety domain constructed by the present invention, it is possible to obtain the positive and negative sequence current safety area of ​​WG-VSC analysis under a single-phase power grid grounding fault, and provide a practical and feasible guiding basis and theoretical guarantee for the formulation of the positive and negative sequence current injection strategy during asymmetric power grid faults. The technical solution is as follows:

[0035] A method for analyzing and constructing a current safety domain of a VSC connected to a weak network under an asymmetric fault, characterized by comprising:

[0036] (1) Establish transient synchronous stability constraints:

[0037] After an asymmetric grid fault, in order to satisfy the constraint that both the positive and negative sequence phase-locked loops of the VSC grid-connected system can maintain transient synchronous stability, based on the improved equal area rule, the positive and negative sequence injection currents should meet the following conditions:

[0038]

[0039] Where R g and X g I is the equivalent resistance and reactance from the grid connection point to the infinite grid; td,1 + ,I tq,1 + and I td,1 - ,I tq,1 - is the component of positive sequence current and negative sequence current after fault on dq axis; V g,1 + ,θ g,1 + and V g,1 - ,θ g,1 - are respectively the positive sequence voltage amplitude, phase angle and negative sequence voltage amplitude, phase angle of the grid voltage after the fault, which are calculated by formula (2); δ e,0 + ,δ e,1 + and δ e,0 - ,δ e,1 - are the steady-state output phase angles of the positive-sequence phase-locked loop and the negative-sequence phase-locked loop before and after the power grid fault, respectively, and their expressions are shown in equation (3); δDL + With δ DL - The expression of is shown in formula (4);

[0040]

[0041] In formula (2), V ga,1 、V gb,1 and V gc,1 is the three-phase voltage of the power grid after the fault;

[0042]

[0043] In formula (3), I td,0 + ,I tq,0 + is the component of the positive sequence current before the fault on the dq axis, V g,0 + and θ g,0 + are respectively the positive sequence voltage amplitude and phase angle of the grid voltage before the fault;

[0044]

[0045] In formula (4), k p and k i are the proportional coefficient and integral coefficient of the phase-locked loop proportional-integral control (PI);

[0046] (2) Establishing grid connection point voltage constraints:

[0047] After an asymmetric grid fault, the steady-state voltage of the positive and negative sequence grid connection points should be greater than zero, and the positive and negative sequence injection currents should meet the following conditions:

[0048]

[0049] (3) Establish maximum current constraints:

[0050] After an asymmetric grid fault, the maximum value of the steady-state VSC output current does not exceed the maximum current I m ; To meet this constraint, the positive and negative sequence injection currents should meet the following conditions:

[0051]

[0052] Where I a * ,I b * and I c * is the maximum value of the a, b and c phase currents output by the VSC, and its specific expression is as follows:

[0053]

[0054] Where I t + ,I t - and θ I - They are respectively the amplitude and phase angle of the positive sequence and negative sequence current output by the VSC after the fault. The specific expressions are as follows:

[0055]

[0056] (4) Constructing positive and negative sequence current safety domain:

[0057] Combining the above transient synchronization stability constraints, grid connection point voltage constraints and maximum current constraints, the positive and negative sequence current safety domain Ω of the VSC connected to the weak grid system under asymmetric grid fault is obtained: I as follows:

[0058]

[0059] The beneficial effects of the present invention are as follows:

[0060] 1) The VSC access weak grid system is reasonably simplified. The dynamic characteristics of the positive and negative sequence PLL are retained, the dynamics of the current inner loop with a faster response speed are ignored, and a reduced-order mathematical model of the VSC access weak grid system is established. The complexity of the transient synchronous stability analysis of VSC under weak grid conditions is reduced.

[0061] 2) A positive and negative sequence current safety domain is constructed to ensure the transient synchronous stability of the system when VSC is connected to the weak grid system under asymmetric grid faults. This safety domain provides a practical guiding basis and theoretical guarantee for the formulation of positive and negative sequence current injection strategies during asymmetric grid faults.

[0062] 3) This safety domain is conservative to a certain extent, so that system planners and dispatchers can be more confident when using this safety domain. In addition, this safety domain is independent of the control parameters of the phase-locked loop, so it has a wider range of applications and can provide a useful reference for the formulation of current injection current standards under asymmetric faults in the power grid.

[0063] 4) The positive and negative sequence current safety domain constructed by the present invention is completely resolved, so constructing the positive and negative sequence current safety domain of the system based on the method proposed by the present invention has the advantage of being less time-consuming. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 Schematic diagram of the WG-VSC system

[0065] Figure 2 Schematic diagram of the control structure of the WG-VSC system

[0066] Figure 3 Schematic diagram of improved EAC and energy conversion (a)δ e,0 + >δ e,1 + ; (b) δ e,0 + <δ e,1 +

[0067] Figure 4 Transient simulation results of negative sequence phase-locked loop under single-phase ground fault

[0068] Figure 5 Positive and negative sequence current safety region Ω under single-phase grounding fault I_SLG

[0069] Figure 6 Transient simulation results: (a) points a2 and a3; (b) point a1 DETAILED DESCRIPTION

[0070] The present invention is described below in conjunction with the accompanying drawings and embodiments.

[0071] 1. Equivalent rotor motion model of WG-VSC system

[0072] The main circuit structure of the WG-VSC system is as follows: Figure 1 As shown in the figure, V dc is the DC bus voltage; E and V t Respectively represent the VSC outlet voltage and grid connection point voltage; V g is the grid voltage, the present invention uses V g Asymmetric stacking to simulate different types of asymmetric grid faults; L f1 , L f2 and C f is the inductance and capacitance of the AC side LCL filter; Z g It represents the equivalent impedance between the grid connection point of the converter and the infinite power source, and its size can be used to characterize the strength of the power grid. The control part of the WG-VSC system includes a synchronization unit and a current control unit. The synchronization unit used in the present invention is a phase-locked loop based on a double second-order generalized integrator PLL (DSOGI-PLL).

[27] The current control unit is based on the current inner loop control in the αβ coordinate system of proportional-resonant (PR).

[30] ,like Figure 2 (b) as shown.

[0073] like Figure 2 As shown in (a), the DSOGI-PLL consists of a second-order generalized integrator-quadrature signals generator (SOGI-QSG), a positive / negative-sequence calculator (PNSC), and a positive / negative-sequence phase-locked loop (PLL). + and PLL - composition

[27] SOGI-QSG can realize orthogonal phase separation and harmonic suppression of grid-connected point voltage; PNSC can obtain the components V of the positive and negative sequence voltage of the grid-connected point in the αβ coordinate system based on the output of SOGI-QSG. tαβ + and V tαβ - ; The positive and negative sequence phase-locked loop obtains the q-axis component V of the positive and negative sequence voltage of the grid connection point through dq transformation tq + and V tq - , after the proportional integral (PI) controller (k p and k i are proportional and integral coefficients respectively), and the angular frequency ω of the positive and negative sequence voltage at the output grid connection point pll + ,ω pll - and the absolute phase angle θ pll + ,θ pll - And the relative phase angle δ with the grid frequency ω0 and -ω0 as the reference axis + and δ - .

[0074] The current inner loop control based on the PR αβ coordinate system is as follows Figure 2 (b) is shown. t The current injected into the grid by the VSC, I tα and I tβ I t α and β axis components in the αβ coordinate system; and is the positive and negative sequence current setting value; k pi for and k ri They are the proportional gain of PR control and the resonant gain at the fundamental frequency respectively.

[0075] This paper focuses on the transient synchronization stability problem of WG-VSC, so the following assumptions are considered:

[0076] 1) Ignore the dynamics of the LC filter, AC network, and SOGI-QSG;

[0077] 2) The bandwidth of the PLL is usually tens of Hz. In order to achieve rapid tracking of the current reference value, the bandwidth of the current loop is much larger than the bandwidth of the phase-locked loop. Therefore, in the time scale of transient synchronous stability analysis, it can be considered that the VSC injection current can approximately track the current setting value in real time.

[0078] 3) Ignore the influence of zero-sequence components;

[0079] Depend on Figure 1 Combined with the above assumptions, we can get the positive sequence voltage at the grid connection point at d + q + The dq axis components of the coordinates V tq + and the negative sequence voltage at the grid connection point at d - q - The dq axis components of the coordinates V tq - as follows:

[0080]

[0081] Where R g and X g I is the equivalent resistance and reactance from the grid connection point to the grid; tdq + and I tdq - is the positive sequence current at d + q + The dq axis components and negative sequence current in the coordinates are - q - The dq axis components of the coordinates, and V g + ,θ g + and V g - ,θ g - are respectively the positive sequence voltage amplitude, phase angle and negative sequence voltage amplitude, phase angle of the grid voltage after the fault, which can be calculated by formula (2):

[0082]

[0083] Where V ga 、V ga and V ga is the three-phase voltage of the power grid after the fault.

[0084] Combined with Vtq + and V tq - The expression of and the structure of the positive and negative sequence phase-locked loop, the equivalent rotor motion model of the WG-VSC system is as follows:

[0085]

[0086] Where P mv + , P mv + and P ev - , P ev - are the virtual prime mover power and virtual electromagnetic power of the positive sequence PLL and negative sequence PLL respectively; J v + , D v + and J v - , D v - are the virtual inertia and virtual damping of the positive sequence PLL and negative sequence PLL respectively. In addition, by analogy with the kinetic energy and potential energy in a single-machine infinite system, the equivalent kinetic energy and potential energy of the positive and negative sequence PLL can be obtained as follows:

[0087]

[0088] From the static stability analysis, it can be seen that if the positive and negative sequence injection currents satisfy inequality (5), then the mathematical model (3) has two equilibrium points x e1 + 、x e2 + and x e1 - 、x e2 - , the specific expression is shown in (6), where x e1 + and x e1 - is a small perturbation stable equilibrium point, x e2 + and x e2 - It is a small perturbation unstable equilibrium point.

[0089]

[0090]

[0091] Since the existence of a small disturbance stable equilibrium point in the system is a prerequisite for the transient synchronous stability of the system, and the present invention focuses on the transient synchronous stability problem of the WG-VSC system under an asymmetric fault in the power grid, the following theoretical analysis and simulation verification are carried out on the premise that formula (5) is established.

[0092] 2. Positive and negative sequence current feasible region

[0093] It can be seen from the equivalent rotor motion model (3) that the virtual prime mover power, virtual electromagnetic power, virtual inertia and virtual damping will affect the transient synchronization stability of the positive and negative sequence PLL, and among these influencing factors, only the virtual prime mover power determined by the positive and negative sequence injection current is fully controllable and can be quickly adjusted. Therefore, selecting appropriate positive and negative sequence injection currents is the key to maintaining the transient synchronization stability of the WG-VSC system under asymmetric grid faults. However, in the current research and specific applications of asymmetric fault crossing, there are few literatures that explore how to set the positive and negative sequence injection currents from the perspective of ensuring the transient stability of the system. An important innovative work of the present invention is to construct a feasible domain of positive and negative sequence currents to ensure the transient stability of the system.

[0094] In this section, the present invention will give the definition of the feasible domain of positive and negative sequence current of the WG-VSC system under asymmetric grid fault, and then give the analytical boundary of the feasible domain based on the modified equal area method. It should be pointed out that the subscript "0" in the following text represents the system parameters before the fault, and the subscript "1" represents the system parameters during the fault.

[0095] 2.1 Definition of the feasible region of positive and negative sequence current

[0096] The definition of the feasible domain of positive and negative sequence current is: the set of positive and negative sequence currents corresponding to all operating points that meet the constraints (I)-(III) under the asymmetric fault of the power grid:

[0097] (I) Both positive and negative sequence phase locked loops can be operated at the working point x before the fault. e,0 + (δ e,0 + ,0),x e,0 - (δ e,0 - ,0) Stable transition to the equilibrium point x after the fault e,1 + (δ e,1 + ,0),x e,1 - (δ e,1 - ,0);

[0098] (II) The steady-state positive and negative sequence d-axis voltages after the fault are greater than zero;

[0099] (III) The maximum amplitude of the VSC steady-state injection current after the fault does not exceed the maximum current I allowed by the inverter m ;

[0100] The feasible domain of positive and negative sequence current is denoted as Ω I , the formula is:

[0101]

[0102] 2.2 Construction of the feasible region of positive and negative sequence current

[0103] 2.2.1, Constraint (I), Transient Synchronous Stability Constraint

[0104] It can be seen from equation (3) that positive-sequence PLL and negative-sequence PLL have the same transient characteristics, so the transient synchronization stability analysis results of positive-sequence PLL are also applicable to negative-sequence PLL. Therefore, by analyzing the transient synchronization stability of positive-sequence PLL, the feasible range of positive-sequence and negative-sequence currents that meet constraint (I) is obtained.

[0105] Given the similarity between the positive sequence PLL dynamic equation and the traditional synchronous machine rotor motion equation, a natural idea is to use the traditional EAC method to analyze the transient synchronization stability of the positive sequence PLL. Considering that the damping coefficient is the premise for using the EAC method to analyze the transient synchronization stability of the traditional single machine infinite system, when analyzing the transient synchronization stability problem of the positive sequence PLL based on the EAC method, the positive and negative properties of the virtual damping should be discussed first.

[0106] From the formula (3), D v + From the expression, we can see that the positive damping region Ω of the positive sequence PLL pos + and negative damping region Ω neg + as follows:

[0107]

[0108] Where δ DL + The expression is as follows:

[0109]

[0110] Obviously, the virtual damping D v + In the region {-π≤δ + -θ g,1 + ≤π}. Therefore, it may not be appropriate to directly use the classical EAC method to analyze the transient synchronization stability of the positive sequence PLL. For this reason, the present invention uses the system equivalent kinetic energy E ke + and the equivalent potential energy Epe + The transient process of the system is analyzed from the perspective of mutual transformation, and an improved EAC is proposed. e,0 + In Ω pos + Internal and delta e,0 + In Ω pos + The following two situations are introduced in detail:

[0111] A)δ e,0 + In Ω pos + Inner (|δ e,1 + -δ e,0 + |≤δ DL + )

[0112] For δ e,0 + In Ω pos + In the case of e,0 + With δ e,1 + The position relationship is analyzed in the following three cases:

[0113] 1)δ e,0 + =δ e,1 + (P mv,1 + =V g,1 + sin(δ e,0 + -θ g,1 + ))

[0114] In this case, x e,0 + and x e,1 + Similarly, during a grid fault, the positive-sequence PLL must be transiently synchronous and stable.

[0115] 2)δ e,0 + >δ e,1 + (P mv,1 + <V g,1 + sin(δ e,0 +-θ g,1 + ))

[0116] like Figure 3 As shown in (a), during normal operation, the system operating point is at point A (δ + =δ e,0 + , P mv,0 =P ev,0 ). After the fault occurs, the virtual prime mover power and virtual electromagnetic power change, the working point jumps from point A to point B1, and the system equivalent potential energy curve changes. At this time, the system potential energy E at point B1 is pe,1 + (B1) greater than the minimum potential energy E pe,1 + (C1), so the working point will decelerate from point B1 to point C1, and the system will convert potential energy into kinetic energy. The deceleration area S of this process dec1 is equal to the kinetic energy converted from potential energy, so S dec1 It can be specifically expressed as follows:

[0117]

[0118] When the working point moves to point C1, although it reaches the minimum potential energy point, Δω pll + <0, so the working point will continue to move toward point D1, and the system will gradually convert the kinetic energy accumulated during deceleration into potential energy. When the working point does not cross point D1 (the working point will not move to the negative damping area Ω neg + In the case of the maximum acceleration area S accmax1 is equal to the maximum kinetic energy that the system can release, that is, the potential energy difference between points D1 and C1. accmax1 As shown below:

[0119]

[0120] Obviously, when S dec1 ≤S accmax1 When the system passes through point D1 and enters Ω neg - The kinetic energy accumulated during the deceleration process will be completely released before the working point moves back and forth around c1, and under the action of positive damping, it will eventually stabilize at point c1, and the system will be transiently synchronously stable. Otherwise, the working point will pass point D1 and enter Ω neg - The positive sequence PLL may become transiently unstable. Therefore, the modified EAC criterion can be obtained, that is, the sufficient condition to ensure the transient synchronization stability of the positive sequence PLL is as follows:

[0121]

[0122] In the formula

[0123] 3)δ e,0 + <δ e,1 + :P mv,1 + >V F + +sin(δ e,0 + -θ g + )

[0124] like Figure 3 As shown in (b), in this case, the acceleration area S of the system acc2 is equal to the potential energy difference between point B2 and C2, and the maximum deceleration area is equal to S decmax2 is equal to the potential energy difference between points D2 and C2. The modified EAC criterion is S acc2 ≤S decmax2 , so the sufficient conditions to ensure the transient synchronization stability of the positive sequence PLL are as follows:

[0125]

[0126] In the formula Combining cases 1), 2) and 3), we can see that when δ e,0 + Located in Ω pos + When the positive sequence PLL is in transient state, the conditions for stable synchronization are as follows:

[0127]

[0128] B)δ e,0 + In Ω pos + Outside (|δ e,1 + -δ e,0 + |>δ DL + )

[0129] δ e,0 + Located in Ω pos + It shows that after the fault occurs, the operating point of the system is in the negative damping area Ω neg -Therefore, the positive sequence PLL may be temporarily unstable. In addition, when the injected current satisfies equation (16), the voltage drop of the current on the impedance is zero, and the positive sequence PLL is globally stable. Therefore, δ e,0 + In Ω pos + To ensure the transient synchronization stability of the positive sequence PLL, I td + and I tq + The formula (16) must be satisfied.

[0130]

[0131] Combining situations A) and B), it can be seen that in order to ensure the transient synchronization stability of the positive-sequence PLL, the positive-sequence injection current should meet the following conditions:

[0132]

[0133] Based on the above analysis, the feasible range of negative-sequence current corresponding to ensuring transient synchronization stability of negative-sequence PLL is as follows:

[0134]

[0135] Where A3, A4 and δ DL - The expression is as follows:

[0136]

[0137]

[0138] 2.2.2, Constraint (II), Grid-connected point voltage constraint

[0139] After the fault, the steady-state voltage of the positive and negative sequence grid-connected points only has the d-axis voltage, so constraint (II) can be expressed as follows:

[0140]

[0141] Where V t + and V t + are the amplitudes of the positive-sequence grid-connected point voltage and the negative-sequence grid-connected point voltage, respectively.

[0142] Substituting equation (8) into equation (21), the feasible range of positive and negative sequence injection current corresponding to constraint (II) is obtained as follows:

[0143] 2.2.3, Constraint (III), Maximum injection current constraint

[0144] In steady state, Itd,1 + and I tq,1 + The positive sequence current vector I of the synthetic forward rotation t + , whose amplitude is I t + and phase angle θ I + As shown in formula (23); td,1 - and I tq,1 - Synthesize the negative sequence current vector I t - , whose amplitude is I t - and phase angle θ I - As shown in formula (). The space vector I of the inverter output current synthesis t For I t + with I t - The resultant vector of t + with I t - During one rotation, I t The trajectory of the endpoints is an ellipse: the projection of the ellipse on the abc axis is the abc phase current output by the VSC.

[0145]

[0146] Obviously, the maximum projection of the ellipse on the abc axis is the amplitude I of the abc three-phase current injected into the grid by the VSC. a * ,I b * and Ic * To derive Ia * ,I b * and Ic * The analytical expression of I t By projecting the abc coordinate axis, we can get the steady-state three-phase current injected into the grid by the VSC under the asymmetric fault of the grid as follows:

[0147]

[0148] After combining and simplifying equation (24), the amplitude of the abc three-phase current output of the VSC in steady state is obtained as follows:

[0149]

[0150] Therefore, to ensure that constraint (III) holds, the positive and negative sequence injection currents should satisfy the following conditions:

[0151]

[0152] Combining equations (17), (18), (22) and (26), we can obtain the feasible region Ω of the positive and negative sequence current of the WG-VSC system under the asymmetric fault of the power grid: I as follows:

[0153]

[0154] 3. Positive and negative sequence current safety domain of VSC connected to weak grid system under single-phase grounding fault

[0155] After the A phase ground fault, the grid voltage can be expressed as follows:

[0156]

[0157] Where k represents the voltage drop degree of the power grid, k∈[0,1).

[0158] Substituting equation (28) into equation (2), the amplitude and phase angle of the positive and negative sequence voltages of the power grid after the fault are as follows:

[0159]

[0160] Considering that when WG-VSC is operating normally, there is usually no negative sequence current injection, that is, δ e,0 - = 0. Then we can get |δ e,1 - -δ e,0 - |As follows:

[0161]

[0162] From formula (30), we can know that |δ e,1 - -δ e,0 - | is within (π, 3π / 2), and δ DL - is approximately equal to π / 2, so after the A phase ground fault, equation (31) holds true

[0163]

[0164] Combined with V in formula (29) g,1 + ,θ g,1 + The positive and negative sequence current safety region Ω of the system under single-phase grounding fault can be obtained by using formula (31): I_SLG As follows:

[0165]

[0166] From equation (32), we can see that the relative phase angle δ of the positive sequence PLL output before the fault is e,0 + The larger the value (the larger the power of the virtual prime mover), the more serious the voltage drop (the smaller k), and the larger the equivalent impedance (the weaker the grid strength), the smaller the positive and negative sequence current safety domain of the system. These analysis results are consistent with the existing research results. Therefore, the following will not specifically analyze the effects of the above four parameters on Ω I impact.

[0167] In addition, compared with the existing research, the incremental findings are: Under single-phase fault, Ω I_SL The cross section on the 2D negative sequence current subspace is just a straight line, denoted as Ω I_SLG - This is because the phase angle of the negative sequence voltage of the power grid after the fault is π, resulting in δ e,0 - It is located in the negative damping region. It also shows that under single-phase fault, the negative sequence phase-locked loop is very prone to transient instability. To illustrate this point, Figure 4 Given k = 0.5, the positive sequence current injection is zero, (I td,1 - ,I tq,1 - ) are the transient simulation results under (0.05, 0) and (0.05, -0.5) respectively. The detailed system parameters are shown in Table 1.

[0168] Table A1 System parameters

[0169] Table A1 System parameters

[0170]

[0171] Depend on Figure 4 It can be seen that when a single-phase grounding fault occurs on the grid side, even if the negative-sequence d-axis injection current is only 0.05pu after the fault, the negative-sequence PLL is transiently unstable; however, when (I td,1 - ,I tq,1 - ) is (0.05, -0.5), located at Ω I_SLG - The simulation results show that: 1) the negative sequence phase-locked loop is very easy to become unstable under single-phase fault, which requires special attention; 2) the Ω constructed by the present invention I_SLG - is correct.

[0172] Figure 5The most serious single-phase grounding fault (k = 0) is given, and (I td,1 - ,I tq,1 - ) is (0.05, -0.5), Ω I_SLG Section Ω on the 2-dimensional positive-sequence current subspace I_SLG + , denoted as the positive sequence current safety region.

[0173] Depend on Figure 5 It can be clearly seen that: when the inverter has not reached its maximum output current limit, for the positive-sequence current, appropriately increasing the positive-sequence reactive injection current can increase the maximum positive-sequence active injection current of the inverter, as shown by points a2 and a3 in the figure.

[0174] against Figure 5 Security DomainΩ I_SLG + Points a1, a2 and a3 in the figure have specific working conditions (I td,1 + , I tq,1 + ) are (-0.14, 0.5), (0.74, 0.5) and (0.74, 0.2), Figure 6 The transient simulation results are given.

[0175] from Figure 6 (a) and (b) show that: 1) Ω I_SLG + The system is transiently stable at the operating points a1 and a2 on the boundary, Ω I_SLG + The system is transiently unstable at the operating point a3 outside the boundary, which verifies Figure 5 The Ω I_SLG + 2) After the fault, when the positive sequence reactive current injection current increases from 0.2pu at point a3 to 0.5pu at point a2, the system changes from transient instability to transient synchronous stability, which is consistent with Figure 5 The conclusions of the theoretical analysis are consistent.

Claims

1. A method for analyzing and constructing a current safety domain for VSC access to a weak grid under an asymmetric fault, characterized in that include: (1) Establish transient synchronous stability constraints: After an asymmetric grid fault, in order to satisfy the constraint that both the positive and negative sequence phase-locked loops of the VSC grid-connected system can maintain transient synchronous stability, based on the improved equal area rule, the positive and negative sequence injection currents should meet the following conditions: Where R g and X g I is the equivalent resistance and reactance from the grid connection point to the infinite grid; td,1 + ,I tq,1 + and I td,1 - ,I tq,1 - is the component of positive sequence current and negative sequence current after fault on dq axis; V g,1 + ,θ g,1 + and V g,1 - ,θ g,1 - are respectively the positive sequence voltage amplitude, phase angle and negative sequence voltage amplitude, phase angle of the grid voltage after the fault, which are calculated by formula (2); δ e,0 + , δ e,1 + and δ e,0 - , δ e,1 - are the steady-state output phase angles of the positive-sequence phase-locked loop and the negative-sequence phase-locked loop before and after the power grid fault, respectively, and their expressions are shown in equation (3); δ DL + With δ DL - The expression of is shown in formula (4); In formula (2), V ga,1 、V gb,1 and V gc,1 is the three-phase voltage of the power grid after the fault; In formula (3), I td,0 + ,I tq,0 + is the component of the positive sequence current before the fault on the dq axis, V g,0 + and θ g,0 + are respectively the positive sequence voltage amplitude and phase angle of the grid voltage before the fault; In formula (4), k p and k i are the proportional coefficient and integral coefficient of the phase-locked loop proportional-integral control (PI); (2) Establishing grid connection point voltage constraints: After an asymmetric grid fault, the steady-state voltage of the positive and negative sequence grid connection points should be greater than zero, and the positive and negative sequence injection currents should meet the following conditions: (3) Establish maximum current constraints: After an asymmetric grid fault, the maximum value of the steady-state VSC output current does not exceed the maximum current I m ; To meet this constraint, the positive and negative sequence injection currents should meet the following conditions: Where I a * ,I b * and I c * is the maximum value of the a, b and c phase currents output by the VSC, and its specific expression is as follows: Where I t + ,I t - and θ I + ,θ I - They are respectively the amplitude and phase angle of the positive sequence and negative sequence current output by the VSC after the fault. The specific expressions are as follows: (4) Constructing positive and negative sequence current safety domain: Combining the above transient synchronization stability constraints, grid connection point voltage constraints and maximum current constraints, the positive and negative sequence current safety domain Ω of the VSC connected to the weak grid system under asymmetric grid fault is obtained: I as follows:

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