A method for stability evaluation of wind power grid-connected system based on manifold and infinite singular point

Abstract

The present application relates to a kind of based on manifold and far singularity wind power grid-connected system stability evaluation method, comprising: the active power and reactive power characteristics of wind turbine before and after fault are analyzed, which is equivalent to negative impedance model, wind turbine is incorporated into power system to obtain wind power grid-connected system, system motion equation is established;The local stability domain boundary BSD of system is described in two-dimensional plane, and two-dimensional local BSD is mapped to three-dimensional unit sphere by central projection transformation, and the global BSD of wind power grid-connected system is described in combination with far singularity SAI;By analyzing SAI, the position of SAI in projection space is determined, and its relationship with system parameters is established;According to the relationship between SAI and system parameters, and in combination with system BSD change, singularity invariance criterion SIC method is proposed, and in combination with stability constraint, system parameters are optimized and adjusted;The transient stability control problem that current large-scale new energy grid-connected background power system faces is solved, and the safe and stable operation of high proportion new energy grid-connected system is guaranteed.

Description

Technical Field

[0001] This invention relates to a transient stability analysis and control technology for new energy power systems, and particularly to a transient stability analysis method for wind power grid-connected systems based on manifolds and SAIs, applicable to most modern power systems. Background Technology

[0002] Against the backdrop of energy structure transformation, the large-scale grid connection of new energy sources such as wind power has resulted in the power grid exhibiting "low inertia" operating characteristics, significantly reducing the system's resistance to disturbances and substantially increasing the risk of transient instability. Transient stability analysis is a core technology for determining whether a system can recover synchronous operation after being subjected to a large disturbance. Existing methods are mainly divided into three categories:

[0003] Time-domain simulation method: It accurately describes the dynamics of the system by solving differential algebraic equations, but it suffers from the "curse of dimensionality" in large-scale wind farms and has high computational costs.

[0004] Direct methods include energy function (EF) based methods and perturbation-based methods. EF methods rely on specific system models, and their stability domain boundary estimations are conservative, failing to accurately describe global stability characteristics. The equal-area method is suitable for single-machine equivalent scenarios, but has poor adaptability to high-dimensional systems.

[0005] Hybrid method: combines the advantages of time-domain simulation and direct method, but does not solve the problem of describing nonlinear behavior at infinity.

[0006] In existing research, while manifold topology theory can analyze the phase space structure of high-dimensional systems, traditional planar projection cannot capture the infinite extension characteristics of the boundary of stability domain (BSD). Singular perturbation theory is only applicable to local stability analysis and does not address the geometric characteristics of the global stability domain. Furthermore, there is an inherent contradiction between the "size" of the stability domain and the "dynamic response speed" of the system—simply expanding the stability domain leads to a decrease in response speed, and existing methods cannot effectively reconcile this contradiction. Specifically, with the rapid expansion of renewable energy installed capacity, the power grid exhibits low inertia characteristics, and traditional transient stability analysis methods have significant shortcomings: time-domain simulation, while capable of accurate modeling, faces "dimensional catastrophe," resulting in extremely high computational costs; the EF method relies on specific system models to construct complex energy functions, and its estimation of the BSD is conservative, failing to fully describe global stability characteristics. Simultaneously, in wind power grid systems, the stability domain is often difficult to close due to the manifold extending to infinity, leading to inaccurate transient stability margin assessments. Moreover, there is an inherent contradiction between the size of the stability domain and the system's dynamic response speed—simply expanding the stability domain easily reduces the response speed, while conversely, shrinking it may reduce the stability margin. Therefore, there is an urgent need for a transient stability analysis method that balances the accuracy of global stability domain description with dynamic response optimization. Summary of the Invention

[0007] To address the transient stability control problem faced by the power system under the current large-scale grid connection of new energy sources (represented by wind power), a transient stability analysis method for wind power grid-connected systems based on manifolds and SAIs is proposed. This method combines theoretical integrity with engineering practicality, thereby overcoming the limitations of traditional analysis methods and control strategies and ensuring the safe and stable operation of high-proportion new energy grid-connected systems.

[0008] The technical solution of this invention is as follows:

[0009] A stability assessment method for wind power grid-connected systems based on manifolds and singularities at infinity includes the following steps: Step 1: Establishing the motion equations of the wind power grid-connected system: Based on the topology and control principle of the doubly-fed induction generator (DFIG), analyze the active and reactive power characteristics of the turbine before and after the fault, and convert them into an equivalent negative impedance model; connect the turbine to the power system to obtain the wind power grid-connected system; use the single-unit equivalent method to reduce the wind power grid-connected system to an equivalent single-unit infinite system, and establish the system motion equations;

[0010] Step 2: Characterize the global stability domain boundary of the wind power grid-connected system: Based on the stability domain boundary theory, the local stability domain boundary (BSD) of the system is characterized in a two-dimensional plane. The two-dimensional local BSD is mapped to a three-dimensional unit sphere through central projection transformation, and the global BSD of the wind power grid-connected system is characterized by combining the singularity at infinity (SAIs). By analyzing the SAIs, the position of the SAIs in the projection space is determined, and their relationship with the system parameters is established.

[0011] Step 3: Propose a singularity invariance criterion to improve stability: Based on the relationship between SAIs and system parameters, and combined with the changes in the system's BSD, the Singularity Invariance Criterion (SIC) method is proposed. This involves dynamically adjusting the virtual inertia and virtual damping after a fault to keep the coordinates of the SAIs constant, thereby ensuring that the boundary of the stability domain does not shrink. Then, combined with stability constraints, the system parameters are optimized and adjusted to expand the stability domain and improve the dynamic response speed.

[0012] Based on the singularity invariance criterion, a wind power grid-connected system model is built in the system modeling and simulation tool. By setting two-phase or three-phase short-circuit faults, the power angle timing curve and critical clearance time are obtained through simulation.

[0013] Furthermore, it also includes: Step 4, designing the stability index TVI and the response speed index RTVI, comparing the BSD before and after adjustment according to the SIC method, and verifying the effectiveness of this method in expanding the stability domain and improving the dynamic response.

[0014] Furthermore, step 1 specifically includes:

[0015] First, the topology of the DFIG is analyzed to lay the foundation for subsequent equivalent model establishment and stability analysis; the relationship between the stator and rotor voltages of the DFIG is as follows:

[0016] Equation (1)

[0017] in, For complex units, For time, Stator voltage, For stator resistance, For synchronous angular velocity, For stator inductance, For rotor inductance, For mutual intuition, For stator current, For stator flux linkage, subscript Indicates stator, subscript Indicates rotor, Represents integration; Definition and Simplify equation (1) to:

[0018] Equation (2)

[0019] When a fault occurs and These are the active and reactive power of DFIG, and their values ​​satisfy... , Then DFIG is equivalent to a negative impedance model; after the fault is cleared, and These are the active and reactive power of the DFIG after the fault, and their values ​​satisfy... , Therefore, DFIG can be equivalent to a negative resistance model; thus, the equivalent negative impedance of DFIG can be derived. as follows:

[0020] Equation (3)

[0021] in, Representing complex conjugation; the equivalent negative impedance model of DFIG. The replacement method is used to integrate it into the simulated power grid system; the replacement method involves replacing the synchronous generator with a DFIG of equal capacity; for the first... i The rotor motion equation of this synchronous generator is:

[0022] Equation (4)

[0023] in, For the first i The inertia constant of a synchronous generator. For the first i The damping coefficient of the synchronous generator. For the first i The rotor angle of the synchronous generator, The derivative of the rotor angle. For the first i The angular velocity of the synchronous generator. The derivative of angular velocity. For the first i The mechanical power of the synchronous generator, For the first i The electromagnetic power of the synchronous generator; for the first j The virtual rotor motion equation of the DFIG is:

[0024] Equation (5)

[0025] in, For the first j The virtual inertia of DFIG in Taiwan For the first j Virtual damping of DFIG in Taiwan For the first j The virtual rotor angle of the DFIG platform, For the first j The virtual angular velocity of the DFIG in Taiwan, For the first j The input power command value of the DFIG. For the first j The electromagnetic power of the DFIG; using the single-machine equivalent method SIME, the multi-machine system is clustered into the dominant machine group (S group) and the remaining machine group (A group), and the power angle center of the machine group is defined:

[0026] Equation (6)

[0027] in, , Let be the equivalent inertia coefficients of group S and group A, respectively. and They represent the first The generator and the first One generator, , Let S and A be the rotor angles, respectively. , The first The rotor angle of the generator and the first The rotor angle of the generator is given by the sum of the inertia of all generators. By subtracting the A group from the S group, the dynamic equations of the single-machine system can be further derived:

[0028] Equation (7)

[0029] in, For equivalent inertia, For equivalent damping, The average damping ratio of the multi-machine system. , , For equivalent mechanical power, and The first The generator and the first The electromotive force of the generator, and The first The generator and the first The electromotive force of the generator, For the first The generator and the first Conductivity between generators For the first The generator and the first Conductivity between generators , Electromagnetic power amplitude, The relative power angle, , For equivalent active power, For the first The generator and the first Conductivity between generators For equivalent reactive power, For the first The generator and the first Admittance between generators.

[0030] Furthermore, step 2 specifically includes:

[0031] According to the stability domain boundary theory, the expression for the local stability domain boundary of the system can be obtained as follows:

[0032] Equation (8)

[0033] in, Represents a stable equilibrium point The trajectory Indicates an unstable equilibrium point The trajectory Jacobian matrix The left eigenvector, It is the coefficient matrix of the quadratic terms.T For transpose;

[0034] In this way, the local BSD of equation (7) can be characterized by equation (8). Under certain conditions, the BSD represented by the manifold will exhibit non-closure or extend to infinity. SAIs are introduced, which are the equilibrium points of the system at infinity, and also the starting or ending points of the manifold. Using a transformation method, the representation of equation (7) at infinity is mapped to a finite range for analysis. Through the central projection transformation, the overall structure of the system is mapped onto the unit sphere. At this time, the distribution of SAIs on the surface of the sphere reflects the global structure of the system model. First, the unit sphere equation is established:

[0035] Equation (9)

[0036] in , , Representing three-dimensional coordinate systems respectively; the two-dimensional BSD of the single-machine system dynamic equation (7) is mapped to the unit sphere equation (9) through central projection; through the above transformation and combined with the single-machine system dynamic equation, the four singularities at infinity can be calculated. , , , The expression is:

[0037] Equation (10)

[0038] The relationship between BSD and SAIs can be derived when or As the value increases, the singularity at infinity moves clockwise along the boundary from its initial position; during this period, the stability region expands accordingly; this expansion reflects... or The addition of [something] enhances the stability of the system.

[0039] Furthermore, step 3 specifically includes:

[0040] Based on the relationship between the singularity at infinity and system parameters, and combined with the changes in the system's stability domain boundary, a singularity invariance criterion is proposed. This criterion involves dynamically adjusting the virtual inertia and virtual damping after a fault to keep the coordinates of the singularity at infinity constant, thereby ensuring that the stability domain boundary does not shrink. The core parameter adjustment relationship of the singularity invariance criterion is as follows:

[0041] Equation (11)

[0042] in, The virtual inertia and virtual damping before adjustment. Based on the adjusted virtual inertia and virtual damping, and combined with damping, overshoot, and stability constraints during adjustment, the following further derivation is obtained: and Constraints:

[0043] Equation (12)

[0044] in, To account for the electromagnetic power of the system after considering the equivalent negative impedance of DFIG; parameter adjustment and stability constraints based on the SIC method directly affect the size of the system's stability domain boundary and dynamic response characteristics.

[0045] Furthermore, step 2 specifically includes:

[0046] The transient stability index TVI is:

[0047] Equation (13)

[0048] The response speed metric RTVI is:

[0049] Equation (14)

[0050] in, The critical fault clearing time (CCT) of the adjusted system. The CCT of the system before adjustment; The adjustment time for the adjusted system. This refers to the adjustment time of the system before the adjustment.

[0051] The beneficial effects of this invention are as follows:

[0052] 1) This invention fully considers the low inertia characteristic of wind power—virtual inertia—through modeling the equivalent negative impedance of a doubly-fed induction generator (DFIG) and multi-machine dimensionality reduction. ) and damping ( The dynamic adjustment of wind power can compensate for the lack of inertial support, reduce wind curtailment, improve the absorption capacity of new energy sources, and help build a new power system based on renewable energy.

[0053] 2) By transforming the central projection, the BSD is mapped to a three-dimensional unit sphere, and SAIs are introduced to characterize the nonlinear behavior at infinity. This solves the problem that traditional planar projection cannot close the BSD. SAIs (such as spherical points A, B, E, W) together with the stable manifold of the unstable equilibrium point constitute the global BSD, which reduces the error in describing the boundary of the stable domain and provides a more accurate geometric basis for the assessment of transient stability margin.

[0054] 3) The proposed Singularity Invariance Criterion (SIC) method preserves... Constant, Realization J and D Dynamic matching – In the IEEE 39-node system, the Transient stability index (TVI) is improved by 14.84% (stability domain expansion) and the Response speed index (RTVI) is reduced by 14.93% (response speed improvement), breaking through the inherent contradiction that "expanding the stability domain will inevitably reduce the response speed" and meeting the dynamic performance requirements of practical engineering. Attached Figure Description

[0055] Figure 1 This invention provides a flowchart of a transient stability analysis method for wind power grid-connected systems based on manifolds and singularities at infinity;

[0056] Figure 2 This is a simplified diagram of the wind power grid connection system of the present invention;

[0057] Figure 3 This is a local stability domain diagram of the wind power grid-connected system of the present invention;

[0058] Figure 4-a This is a comparison diagram of the changes in work angle using different methods of the present invention;

[0059] Figure 4-b This is a comparison chart of BSD variations in different methods of the present invention. Detailed Implementation

[0060] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0061] The following is based on Figures 1-3 , Figure 4-a as well as Figure 4-b The preferred embodiments of the present invention will be described in detail below.

[0062] For the grid side, this invention, based on manifold theory and Singularities at Infinity (SAIs) analysis, accurately characterizes the stability domain boundary of wind power grid-connected systems, effectively overcoming the limitations of traditional methods' strong conservatism and significantly improving the system's transient stability. By dynamically adjusting virtual inertia and virtual damping parameters, the stability domain range is expanded while the system's dynamic response is accelerated, thus resolving the contradiction between stability domain expansion and response speed. This method does not require the construction of complex energy functions, has high computational efficiency, and is suitable for low-inertia grids with a high proportion of renewable energy integration, helping to enhance the grid's adaptability to various disturbances and supporting the safe grid connection of more wind power. For power companies, this invention has been verified in the IEEE 39-node system, possessing good versatility and engineering applicability, making it easy for power companies to directly apply it to the stability analysis and control of existing wind power grid-connected systems. The parameter adjustment adopts a linear proportional relationship, making operation intuitive and calculation simple, effectively reducing the technical difficulty of system operation, maintenance, and regulation. By improving the critical fault clearing time and system damping ratio, this invention helps suppress system oscillations and reduce equipment losses, thereby improving grid operating efficiency and economic benefits, and providing reliable technical support for the dispatch and management of complex grids. For new energy power generation companies, this invention establishes an equivalent model for doubly-fed induction generators, accurately matching the dynamic characteristics of wind power grid-connected systems to ensure the stability of wind power output and grid connection safety. The dynamic parameter adjustment strategy can adapt to different wind power installed capacities and operating conditions without requiring a reconstruction of the theoretical framework; only fine-tuning of equivalent parameters is needed for flexible adaptation, improving the operational resilience of new energy power generation systems. By reducing shutdowns or output fluctuations caused by transient instability, it helps improve wind power utilization efficiency, enabling new energy power generation companies to achieve more stable power output and better economic benefits. Against this backdrop, this invention proposes a transient stability analysis method for wind power grid-connected systems based on manifolds and SAIs. It achieves a global characterization of the stability domain through central projection transformation, and combined with dynamic parameter adjustment and stability constraints, effectively overcoming the limitations of traditional methods. This achievement not only provides new theoretical support for the transient stability analysis of wind power grid-connected systems but also promotes the development of power systems towards high-proportion new energy access, high stability, and efficient regulation, contributing to the construction of a clean, safe, and efficient modern energy system and promoting power system transformation and safe operation.

[0063] like Figure 1 As shown, this embodiment of the invention provides a transient stability analysis method for wind power grid-connected systems based on manifolds and SAIs, including the following steps:

[0064] Based on the topology and control principle of doubly-fed induction generator (DFIG) wind turbines, the active and reactive power characteristics of the turbines before and after a fault are analyzed, and they are equivalent to a negative impedance model. The above-mentioned wind turbines are then integrated into a traditional power system to obtain a wind power grid-connected system. Using the single-unit equivalent method, the wind power grid-connected system is reduced to an equivalent single-unit infinite bus system, and the system's equations of motion are established.

[0065] Based on the stability domain boundary theory, the local stability domain boundary (BSD) of the system is characterized in a two-dimensional plane. Through central projection transformation, the two-dimensional local BSD is mapped to a three-dimensional unit sphere, and the global BSD of the wind power grid-connected system is characterized in conjunction with stability-independent parameters (SAIs). By analyzing the SAIs, their positions in the projection space are determined, and their relationship with system parameters is established.

[0066] Based on the relationship between SAIs and system parameters, and combined with the system BSD variation, a singularity invariance criterion (SIC) method is proposed. This involves dynamically adjusting the virtual inertia and virtual damping after a fault to keep the coordinates of the SAIs constant, thereby ensuring that the stability domain boundary does not shrink. This is further combined with the damping ratio (…). Overshoot and settling time By applying stability constraints such as stability constraints, the system parameters are optimized and adjusted to expand the stability domain and improve the dynamic response speed.

[0067] Based on the singularity invariance criterion, a wind power grid-connected system model was built in MATLAB / Simulink (a system modeling and simulation tool). By setting two-phase or three-phase short-circuit faults, the power angle timing curve and critical clearance time were obtained through simulation.

[0068] The Transient stability index (TVI) and Response speed index (RTVI) were designed. The BSD before and after adjustment according to the SIC method were compared to verify the effectiveness of the proposed method in expanding the stability domain and improving the dynamic response. The performance of the proposed method was also compared with that of the traditional Energy function (EF) method to verify its superiority.

[0069] 1. Establish the equations of motion for the wind power grid-connected system.

[0070] First, the topology of the DFIG is analyzed to lay the foundation for subsequent equivalent model establishment and stability analysis. The relationship between the stator and rotor voltages of the DFIG is as follows:

[0071] Equation (1)

[0072] in, For complex units, For time, Stator voltage, For stator resistance, For synchronous angular velocity, For stator inductance, For rotor inductance, For mutual intuition, For stator current, For stator flux linkage, subscript Indicates stator, subscript Indicates rotor, Represents integration. Definition and Simplify equation (1) to:

[0073] Equation (2)

[0074] When a fault occurs and These are the active and reactive power of DFIG, and their values ​​satisfy... , Therefore, DFIG can be equivalent to a negative impedance model. After the fault is cleared, and These are the active and reactive power of the DFIG after the fault, and their values ​​satisfy... , Therefore, the DFIG can be equivalently represented as a negative resistance model. Thus, the equivalent negative impedance of the DFIG can be derived. as follows:

[0075] Equation (3)

[0076] in, This represents the complex conjugate. The equivalent negative impedance model of the above DFIG (i.e., The replacement method was used to integrate it into the IEEE 10-machine 39-bus system. The replacement method involves replacing the traditional synchronous generator with a DFIG of equal capacity. For the first... i The rotor motion equation of this synchronous generator is:

[0077] Equation (4)

[0078] in, For the first i The inertia constant of a synchronous generator. For the first i The damping coefficient of the synchronous generator. For the first i The rotor angle of the synchronous generator, The derivative of the rotor angle. For the first i The angular velocity of the synchronous generator. The derivative of angular velocity. For the first i The mechanical power of the synchronous generator, For the first i The electromagnetic power of the synchronous generator; for the first j The virtual rotor motion equation of the DFIG is:

[0079] Equation (5)

[0080] in, For the first j The virtual inertia of DFIG in Taiwan For the first j Virtual damping of DFIG in Taiwan For the first j The virtual rotor angle of the DFIG platform, For the first j The virtual angular velocity of the DFIG in Taiwan, For the first j The input power command value of the DFIG. For the first j The electromagnetic power of the DFIG. Using the Single Machine Equivalent (SIME) method, the multi-machine system is clustered into a dominant group (S group) and a remaining group (A group), defining the group power angle center:

[0081] Equation (6)

[0082] in, , Let be the equivalent inertia coefficients of group S and group A, respectively. and They represent the first The generator and the first One generator, , Let S and A be the rotor angles, respectively. , The first The rotor angle of the generator and the first The rotor angle of the generator is given by the sum of the inertia of all generators. By subtracting the A group from the S group, the dynamic equations of the single-machine system can be further derived:

[0083] Equation (7)

[0084] in, For equivalent inertia, For equivalent damping ( (mean damping ratio of multi-machine system) ( ), For equivalent mechanical power, and The first The generator and the first The electromotive force of the generator, and The first The generator and the first The electromotive force of the generator, For the first The generator and the first Conductivity between generators For the first The generator and the first Conductivity between generators , Electromagnetic power amplitude, The relative power angle, , For equivalent active power, For the first The generator and the first Conductivity between generators For equivalent reactive power, For the first The generator and the first The admittance between the generators, and the specific structure of the equivalent single-unit system can be intuitively presented through Figure 2.

[0085] 2. Characterize the global stability domain boundary of the wind power grid-connected system

[0086] According to the stability domain boundary theory, the expression for the local stability domain boundary of the system can be obtained as follows:

[0087] (8)

[0088] in, Represents a stable equilibrium point The trajectory Indicates an unstable equilibrium point The trajectory Jacobian matrix The left eigenvector, It is the coefficient matrix of the quadratic terms. T This is a transpose.

[0089] In this way, the local BSD of equation (7) can be characterized according to equation (8), such as Figure 3 As shown, under certain conditions, the BSD represented by the manifold will exhibit non-closure or extend to infinity. To solve this problem, this invention introduces the concept of SAIs, which are the equilibrium points of the system at infinity, and also the starting or ending points of the manifold, to describe the nonlinear dynamic behavior of the scene at infinity, thereby improving the characterization of the overall BSD. To solve the behavior problem at infinity, this invention uses a transformation method to map the performance of equation (7) at infinity to a finite range for analysis. Through the central projection transformation, the overall structure of the system is mapped onto a unit sphere, and the distribution of SAIs on the surface of the sphere reflects the global structure of the system model. First, the equation of the unit sphere is established:

[0090] Equation (9)

[0091] in , , Let each represent a three-dimensional coordinate system. The two-dimensional BSD of the single-machine system dynamic equation (7) is mapped to the unit sphere equation (9) through central projection. Through the above transformation and combined with the single-machine system dynamic equation, the four singularities at infinity can be calculated. , , , The expression is:

[0092] Equation (10)

[0093] The relationship between BSD and SAIs can be derived when (or As the value increases, the singularity at infinity moves clockwise along the boundary from its initial position. During this period, the stability region (outer boundary) expands accordingly. This expansion phenomenon reflects... (or The addition of ) enhances the stability of the system.

[0094] 3. Propose a singularity invariance criterion to improve stability.

[0095] Based on the relationship between the singularity at infinity and system parameters, and combined with the changes in the system's stability domain boundary, a singularity invariance criterion is proposed (i.e., dynamically adjusting the virtual inertia and virtual damping after a fault to keep the coordinates of the singularity at infinity constant, thereby ensuring that the stability domain boundary does not shrink). The core parameter adjustment relationship of the singularity invariance criterion is as follows:

[0096] Equation (11)

[0097] in, The virtual inertia and virtual damping before adjustment. Based on the adjusted virtual inertia and virtual damping, and combined with damping, overshoot, and stability constraints during adjustment, the following further derivation is obtained: and Constraints:

[0098] Equation (12)

[0099] in, To consider the electromagnetic power of the system after taking into account the equivalent negative impedance of DFIG, parameter adjustment and stability constraints based on the SIC method directly affect the size of the system's stability domain boundary and dynamic response characteristics.

[0100] Based on the singularity invariance criterion, a wind power grid-connected system model is built in the system modeling and simulation tool. By setting two-phase or three-phase short-circuit faults, the power angle timing curve and critical clearance time are obtained through simulation.

[0101] 4. Design stability indices and verify the effectiveness and superiority of the singularity invariance criterion.

[0102] This invention proposes the following transient stability index (TVI):

[0103] Equation (13)

[0104] The proposed Response Time Via (RTVI) metric is:

[0105] Equation (14)

[0106] in, This refers to the Critical Clearing Time (CCT) of the adjusted system. The CCT of the system before adjustment; The adjustment time for the adjusted system. The settling time of the system before adjustment is given. A comparative analysis is conducted on the proposed singularity invariance criterion and energy function method, and the results are verified through practical simulations under four different conditions. and The adjusted values ​​are shown in the table below.

[0107] Table 1 Comparison of different cases

[0108]

[0109] This invention sets a condition to ensure that the energy function remains unchanged before and after adjustment, thereby deriving the relationship between the adjusted virtual inertia and virtual damping, and determining... Then, select an appropriate virtual damping. To ensure that the BSD does not shrink before and after adjustment, the SIC method achieves stronger oscillation suppression and improved stability. Regarding the damping ratio index (RTVI), the SIC method exhibits a faster convergence speed. In Case 3, the TVI index of the SIC method is -14.93%, lower than the -7.84% of the EF method. To visually demonstrate the comparison of the two methods under different operating conditions, this invention plots the power angle time series diagram and the stability domain boundary change diagram, as shown below. Figure 4-a and 4-b As shown in the figure. In summary, the SIC method demonstrates superior performance in terms of dynamic response speed and stability domain boundary size.

[0110] The main conclusions are as follows:

[0111] 1) From the grid side perspective: This invention accurately characterizes the BSD (Boundary Stability Distance) through manifold theory and SAIs analysis, solving the problem of strong conservatism in traditional methods and significantly improving the transient stability of wind power grid-connected systems. By dynamically adjusting virtual inertia and virtual damping parameters, the stability region size is expanded and the dynamic response speed is accelerated, effectively resolving the contradiction between stability region size and response speed. This method does not require the construction of complex energy functions, has higher computational efficiency, and is applicable to low-inertia grids with a high proportion of renewable energy integration, supporting more renewable energy such as wind power to be connected to the grid and enhancing the grid's adaptability to disturbances. Based on IEEE Section 39 system verification, this invention has strong versatility and is easy to implement in engineering. Power companies can directly apply it to the stability analysis and control of existing wind power grid-connected systems. Parameter adjustment follows a linear proportional relationship, making operation intuitive and calculation simple, reducing the technical difficulty of system operation and maintenance and regulation. By improving the critical fault clearing time and damping ratio, the risk of system oscillation is reduced, equipment losses are reduced, and grid operation efficiency and economic benefits are improved, providing more reliable technical support for the dispatch and management of complex grids.

[0112] 2) From the perspective of new energy power generation companies: This invention constructs an equivalent model for doubly-fed induction generators, accurately adapting to the dynamic characteristics of wind power grid-connected systems, ensuring the stability of wind power output and grid connection security. The dynamic parameter adjustment strategy can adapt to different wind power installed capacities and operating conditions without reconstructing the theoretical framework; it only requires fine-tuning the equivalent parameters, thus improving the flexibility and adaptability of new energy power generation systems. This method can reduce downtime or output fluctuations caused by transient instability, improve wind power utilization, and help new energy power generation companies achieve more stable power output and higher economic benefits.

[0113] The above-described embodiments are merely one implementation of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention should be determined by the appended claims.

Claims

1. A stability assessment method for wind power grid-connected systems based on manifolds and singularities at infinity, characterized in that, The process includes the following steps: Step 1: Establish the motion equations of the wind power grid-connected system: Based on the topology and control principle of the doubly-fed induction generator (DFIG), analyze the active and reactive power characteristics of the turbine before and after the fault, and convert them into an equivalent negative impedance model; connect the turbine to the power system to obtain the wind power grid-connected system; use the single-unit equivalent method to reduce the wind power grid-connected system to an equivalent single-unit infinite system, and establish the system motion equations; Step 2: Characterize the global stability domain boundary of the wind power grid-connected system: Based on the stability domain boundary theory, the local stability domain boundary (BSD) of the system is characterized in a two-dimensional plane. The two-dimensional local BSD is mapped to a three-dimensional unit sphere through central projection transformation, and the global BSD of the wind power grid-connected system is characterized by combining the singularity at infinity (SAIs). By analyzing the SAIs, the position of the SAIs in the projection space is determined, and their relationship with the system parameters is established. Step 3: Propose a singularity invariance criterion to improve stability: Based on the relationship between SAIs and system parameters, and combined with the changes in the system's BSD, the Singularity Invariance Criterion (SIC) method is proposed. This involves dynamically adjusting the virtual inertia and virtual damping after a fault to keep the coordinates of the SAIs constant, thereby ensuring that the boundary of the stability domain does not shrink. Then, combined with stability constraints, the system parameters are optimized and adjusted to expand the stability domain and improve the dynamic response speed. Based on the singularity invariance criterion, a wind power grid-connected system model is built in the system modeling and simulation tool. By setting two-phase or three-phase short-circuit faults, the power angle timing curve and critical clearance time are obtained through simulation.

2. The stability assessment method for wind power grid-connected systems based on manifolds and singularities at infinity as described in claim 1, characterized in that, It also includes: Step 4, designing the stability index TVI and the response speed index RTVI, comparing the BSD before and after adjustment according to the SIC method, and verifying the effectiveness of this method in expanding the stability domain and improving the dynamic response.

3. The stability assessment method for wind power grid-connected systems based on manifolds and singularities at infinity as described in claim 1, characterized in that, Step 1 specifically includes: First, the topology of the DFIG is analyzed to lay the foundation for subsequent equivalent model establishment and stability analysis; the relationship between the stator and rotor voltages of the DFIG is as follows: Equation (1) in, For complex units, For time, Stator voltage, For stator resistance, For synchronous angular velocity, For stator inductance, For rotor inductance, For mutual intuition, For stator current, For stator flux linkage, subscript Indicates stator, subscript Indicates rotor, Represents integration; Definition and Simplify equation (1) to: Equation (2) When a fault occurs and These are the active and reactive power of DFIG, and their values ​​satisfy... , Then DFIG is equivalent to a negative impedance model; after the fault is cleared, and These are the active and reactive power of the DFIG after the fault, and their values ​​satisfy... , Therefore, DFIG can be equivalent to a negative resistance model; thus, the equivalent negative impedance of DFIG can be derived. as follows: Equation (3) in, Representing complex conjugation; the equivalent negative impedance model of DFIG. The replacement method is used to integrate it into the simulated power grid system; the replacement method involves replacing the synchronous generator with a DFIG of equal capacity; for the first... i The rotor motion equation of this synchronous generator is: Equation (4) in, For the first i The inertia constant of a synchronous generator. For the first i The damping coefficient of the synchronous generator. For the first i The rotor angle of the synchronous generator, The derivative of the rotor angle. For the first i The angular velocity of the synchronous generator. The derivative of angular velocity. For the first i The mechanical power of the synchronous generator, For the first i The electromagnetic power of the synchronous generator; for the first j The virtual rotor motion equation of the DFIG is: Equation (5) in, For the first j The virtual inertia of DFIG in Taiwan For the first j Virtual damping of DFIG in Taiwan For the first j The virtual rotor angle of the DFIG platform, For the first j The virtual angular velocity of the DFIG in Taiwan, For the first j The input power command value of the DFIG. For the first j The electromagnetic power of the DFIG; using the single-machine equivalent method SIME, the multi-machine system is clustered into the dominant machine group (S group) and the remaining machine group (A group), and the power angle center of the machine group is defined: Equation (6) in, , Let be the equivalent inertia coefficients of group S and group A, respectively. and They represent the first The generator and the first One generator, , Let S and A be the rotor angles, respectively. , The first The rotor angle of the generator and the first The rotor angle of the generator is given by the sum of the inertia of all generators. By subtracting the A group from the S group, the dynamic equations of the single-machine system can be further derived: Equation (7) in, For equivalent inertia, For equivalent damping, The average damping ratio of the multi-machine system. , , For equivalent mechanical power, and The first The generator and the first The electromotive force of the generator, and The first The generator and the first The electromotive force of the generator, For the first The generator and the first Conductivity between generators For the first The generator and the first Conductivity between generators , Electromagnetic power amplitude, The relative power angle, , For equivalent active power, For the first The generator and the first Conductivity between generators For equivalent reactive power, For the first The generator and the first Admittance between generators.

4. The stability assessment method for wind power grid-connected systems based on manifolds and singularities at infinity as described in claim 1, characterized in that, Step 2 specifically includes: According to the stability domain boundary theory, the expression for the local stability domain boundary of the system can be obtained as follows: Equation (8) in, Represents a stable equilibrium point The trajectory Indicates an unstable equilibrium point The trajectory Jacobian matrix The left eigenvector, It is the coefficient matrix of the quadratic terms. T For transpose; In this way, the local BSD of equation (7) can be characterized by equation (8). Under certain conditions, the BSD represented by the manifold will exhibit non-closure or extend to infinity. SAIs are introduced, which are the equilibrium points of the system at infinity, and also the starting or ending points of the manifold. Using a transformation method, the representation of equation (7) at infinity is mapped to a finite range for analysis. Through the central projection transformation, the overall structure of the system is mapped onto the unit sphere. At this time, the distribution of SAIs on the surface of the sphere reflects the global structure of the system model. First, the unit sphere equation is established: Equation (9) in , , Representing three-dimensional coordinate systems respectively; the two-dimensional BSD of the single-machine system dynamic equation (7) is mapped to the unit sphere equation (9) through central projection; through the above transformation and combined with the single-machine system dynamic equation, the four singularities at infinity can be calculated. , , , The expression is: Equation (10) The relationship between BSD and SAIs can be derived when or As the value increases, the singularity at infinity moves clockwise along the boundary from its initial position; during this period, the stability region expands accordingly; this expansion reflects... or The addition of [something] enhances the stability of the system.

5. The stability assessment method for wind power grid-connected systems based on manifolds and singularities at infinity as described in claim 3, characterized in that, Step 3 specifically includes: Based on the relationship between the singularity at infinity and system parameters, and combined with the changes in the system's stability domain boundary, a singularity invariance criterion is proposed. This criterion involves dynamically adjusting the virtual inertia and virtual damping after a fault to keep the coordinates of the singularity at infinity constant, thereby ensuring that the stability domain boundary does not shrink. The core parameter adjustment relationship of the singularity invariance criterion is as follows: Equation (11) in, The virtual inertia and virtual damping before adjustment. Based on the adjusted virtual inertia and virtual damping, and combined with damping, overshoot, and stability constraints during adjustment, the following further derivation is obtained: and Constraints: Equation (12) in, To account for the electromagnetic power of the system after considering the equivalent negative impedance of DFIG; parameter adjustment and stability constraints based on the SIC method directly affect the size of the system's stability domain boundary and dynamic response characteristics.

6. The stability assessment method for wind power grid-connected systems based on manifolds and singularities at infinity as described in claim 1, characterized in that, Step 2 specifically includes: The transient stability index TVI is: Equation (13) The response speed metric RTVI is: Equation (14) in, The critical fault clearing time (CCT) of the adjusted system. The CCT of the system before adjustment; The adjustment time for the adjusted system. This refers to the adjustment time of the system before the adjustment.

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