Method and system for analyzing transient stability of grid-forming multi-machine grid-connected system

Abstract

This invention discloses a transient stability analysis method and system for a multi-machine grid-connected system. First, a transient model of the system is established, and the stable equilibrium point before the fault is determined based on the power balance equation and the eigenvalues ​​of the Jacobian matrix. Using the stable equilibrium point as initial values, the fault trajectory is calculated, and an interpolation correction algorithm is introduced to eliminate discrete simulation step size errors and accurately locate the point on the fault trajectory where the potential energy derivative changes from positive to negative. Using this point as an initial value, the system iteratively searches for the minimum point of power imbalance along the gradient descent path. Solving the power balance equation using the minimum point as an initial value yields the dominant unstable equilibrium point. Finally, the energy of the dominant unstable equilibrium point is used as the critical energy to determine whether the system is stable after the fault is cleared. The method provided by this invention reduces the conservatism of the traditional energy function method for stability assessment in multi-machine systems, effectively reduces the multi-saddle point interference problem in multi-machine systems, and accurately locates the dominant unstable equilibrium point related to the fault path.

Description

Technical Field

[0001] This invention relates to the field of grid-connected power generation of new energy sources, and in particular to a transient stability analysis method and system for a grid-connected multi-machine grid-connected system. Background Technology

[0002] With a high proportion of renewable energy being integrated into the grid, problems such as low system inertia, low damping, and weak support have become particularly prominent, increasing the risk of frequency and voltage stability issues caused by power supply and demand imbalances. To improve the grid's frequency / voltage support capabilities, grid-connected renewable energy power generation equipment has become a feasible technical means.

[0003] When large-scale renewable energy sources are connected to the grid through grid-connected converters, coupling interference between equipment and between equipment and the grid intensifies, deteriorating the system's transient synchronization stability and making it more prone to synchronization instability. Among existing methods for quantitative analysis of transient stability in multi-machine grid-connected systems, the energy function method based on Lyapunov stability theory is widely used because it reveals the instability mechanism of nonlinear dynamic systems from the physical essence of energy conversion and dissipation, and can directly provide a quantitative stability margin index characterizing the system's safety level. However, most existing research focuses on constructing the energy function, while the critical energy—the core indicator determining the accuracy of stability judgment—is usually determined by the nearest unstable equilibrium point method, which iterates through all unstable equilibrium points and selects the minimum potential energy as the critical energy. Using the minimum potential energy as the critical criterion can incorrectly classify regions belonging to the stable domain as unstable, leading to overly conservative assessment results, underestimating the system's actual fault tolerance, and limiting the full utilization of the power system's transmission capacity.

[0004] CN119070365A discloses a transient stability analysis method for AC / DC systems based on VSC-HVDC. This method is highly dependent on the accuracy of the initial escape point and is easily affected by multiple saddle points in complex multi-machine systems, leading to search failure or convergence to an incorrect equilibrium point. While using the potential energy maximum point as the escape point, the discrete nature of the time-domain simulation integration, limited by the step size, often captures the maximum value among discrete points, rather than the true physical peak potential energy point. This results in inherent biases in the initial values ​​used in subsequent calculations. Furthermore, the method neglects the damping coefficient D unique to grid-type converters when constructing the energy function. The absence of a damping term leads to a conservative energy function model, ignoring the energy attenuation caused by damping during oscillations. This is severely inconsistent with the actual physical characteristics of grid-type units, resulting in overly conservative transient stability criteria and a tendency to misjudge a system that should be stable as unstable. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a transient stability analysis method and system for a grid-connected multi-machine grid system, which effectively improves the accuracy of transient stability judgment, in order to address the shortcomings of the existing technology.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a transient stability analysis method for a grid-connected multi-machine system, comprising the following steps:

[0007] A transient mathematical model of a multi-machine grid-connected grid-connected system of grid-connected converters is established. The active power loop damping parameters of the grid-connected converters are taken into account in the transient mathematical model. The power balance equation is obtained using the transient mathematical model, and the stable equilibrium node before the fault is determined by Jacobian matrix eigenvalue analysis.

[0008] Based on the system dynamic equations during the fault duration, with the stable equilibrium node as the initial value, the trajectory during the fault is obtained, the rate of change of potential energy on the trajectory during the fault is monitored, the transition interval from rising to falling potential energy is captured, and the state point where the time derivative of potential energy is exactly zero is reconstructed in the transition interval using linear interpolation, denoted as PEP.

[0009] A potential energy gradient descent system is constructed, and an iterative search is performed along the gradient descent direction starting from the state point PEP. In response to the distortion of the potential energy boundary caused by the damping coefficient, the direction of the search ray is adjusted by monitoring the changing trend of the power imbalance index within the integration window during the iteration process, so as to achieve dynamic calibration of the search path and locate the minimum point of power imbalance.

[0010] Using the minimum point of power imbalance as the initial value, the dominant unstable equilibrium point is calculated by substituting the Newton-Raphson method into the power balance equation.

[0011] Calculate the energy function value corresponding to the dominant unstable equilibrium point. This value is the critical energy. The isoenergy surface corresponding to the potential energy at the dominant unstable equilibrium point is the stability region.

[0012] This invention introduces a linear interpolation correction algorithm, eliminating the discrete errors caused by the simulation step size, providing more accurate initial values ​​for finding the dominant unstable equilibrium point, and significantly improving the accuracy of critical energy assessment. By monitoring the rate of change of potential energy affected by damping, the initial point for subsequent calculations can be detected more accurately and sensitively. By introducing a network-type second-order transient model including the damping coefficient, the dissipation mechanism of the energy function in the transient process is realistically reproduced. Furthermore, to address the distortion of the PEBS boundary caused by the introduction of the damping term, this invention proposes a new CUEP tracking scheme, which can adjust the iteration direction in a timely manner and converge to CUEP more quickly.

[0013] The transient mathematical model expression is as follows:

[0014] ;

[0015] in, Let be the power angle difference between the i-th grid-connected generating unit and the grid voltage. Let be the angular frequency difference between the i-th grid-connected generating unit and the power grid. This is the reference value for the active power output of the i-th grid-connected unit. To output electromagnetic power to the i-th grid-connected unit, Let be the active power loop damping parameters of the i-th grid-connected unit. Let be the inertia parameter of the i-th unit.

[0016] The i-th grid-type unit outputs electromagnetic power The calculation formula is:

[0017] ;

[0018] in, , These are the output voltages of the two grid-connected inverters, respectively. This is the grid voltage. , , These are the equivalent impedances between the two grid-connected inverters and the power grid. The power angle difference between the first grid-connected unit and the second grid-connected unit. , which is the power angle difference between the first grid-type unit and the second grid-type unit at the stable equilibrium point.

[0019] The power balance equation is: .

[0020] The specific implementation process of reconstructing the state point PEP where the potential energy has an exact time derivative of zero includes:

[0021] Based on the system dynamic equations during the fault duration, the fault trajectory is calculated, the rate of change of potential energy along the trajectory is monitored, and the point where the potential energy changes from an upward trend to a downward trend is found. Using the state data before and after this point, a linear interpolation method is used to reconstruct the state point where the time derivative of the potential energy is exactly zero. The specific expression of the system dynamic equations during the fault duration is as follows: ;in, The electromagnetic power output by the i-th inverter unit during the fault duration.

[0022] The specific expression is:

[0023] ;

[0024] in, This represents the grid voltage during the duration of the fault.

[0025] The steps to reconstruct the state point where the potential energy has an exact time derivative of zero include:

[0026] Step 1: Using the derivative of potential energy with respect to time Substitute each point of the fault trajectory into ,turn up The point where the sign changes from positive to negative, assuming it follows the trajectory of the fault. Moment Recorded as , Fault trajectory Moment Recorded as , , This is the integration step size;

[0027] Step Two: In The linear interpolation method is applied to obtain the interpolation time. , ,calculate Place Recorded as ,like If it is less than the set threshold, then take... The point where the fault trajectory is located at any given moment is the precise potential energy peak point. Otherwise, proceed to step three;

[0028] Step 3: If ,but replace Proceed to step one; if ,but replace Proceed to step one.

[0029] The degree of imbalance is expressed as follows: ;in This is the value of the imbalance index at the k-th integration step. Let be the output electromagnetic power at the k-th integration step.

[0030] The expression for the energy function value at the dominant unstable equilibrium point is:

[0031] ;

[0032] in, Let be the power angle value at the stable equilibrium point after the failure of the i-th inverter unit. , which is the power angle difference between the first grid-type unit and the second grid-type unit. The power angle difference between the first grid-type unit and the second grid-type unit at the stable equilibrium point.

[0033] As an inventive concept, the present invention also provides a transient stability analysis system for a grid-connected multi-machine system, including a memory, a processor, and a computer program stored in the memory; the processor executes the computer program to implement the steps of the above method.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0035] 1. This invention reconstructs the state point where the potential energy has an exact time derivative of zero by using linear interpolation, eliminating the discrete error caused by the simulation step size, providing a more accurate initial value for finding the dominant unstable equilibrium point, and helping the subsequent algorithm converge.

[0036] 2. This invention takes into account the damping parameter D unique to grid-type converters and constructs an energy function that includes damping dissipation terms, which is closer to the actual system and effectively improves the accuracy of transient stability judgment.

[0037] 3. To address the PEBS boundary distortion caused by the introduction of the damping coefficient, this invention introduces an orthogonal projection calibration method, which can monitor the changing trend of power imbalance within the integration window and adjust the direction of the search ray in real time, thereby quickly and accurately locating the minimum point of imbalance. Attached Figure Description

[0038] Figure 1 This is the control structure of a multi-machine grid-connected grid-connected converter system according to an embodiment of the present invention;

[0039] Figure 2 This is a flowchart of the transient stability analysis method for a grid-connected multi-machine grid-connected system according to an embodiment of the present invention;

[0040] Figure 3 This is a diagram showing the relationship between the equilibrium point and potential energy in an embodiment of the present invention.

[0041] Figure 4 This is a trajectory potential energy trend diagram in a fault according to an embodiment of the present invention;

[0042] Figure 5 This is a trend chart showing the change of the imbalance degree index in an embodiment of the present invention. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] Example 1

[0045] Figure 1 This is the control structure of a multi-machine grid-connected converter system according to an embodiment of the present invention. The main circuit consists of an inverter, a filter circuit, and a transformer connected in sequence, with the transformer connected to the power grid. and Let be the equivalent line impedance and grid impedance of the i-th grid-connected unit, respectively. and This is an output-side LC filter. The network-type control includes an active power loop (APC), a reactive power loop (DPC), and an inner voltage-current loop. The mathematical expression for the active power loop is shown in equation (1):

[0046]

[0047] in, Let be the angular frequency difference between the i-th grid-connected generating unit and the power grid. This is the reference value for the active power output of the i-th grid-connected unit. To output electromagnetic power to the i-th grid-connected unit, Let be the active power loop damping parameter of the i-th grid-type unit.

[0048] The specific mathematical expression for it is shown in equation (2):

[0049]

[0050] in, , These are the output voltages of the first and second inverters, respectively. This is the grid voltage. , , This is the equivalent impedance between the first and second grid-connected inverters and the power grid.

[0051] The power angle difference between the i-th grid-connected unit and the grid voltage There exists relation (2):

[0052]

[0053] Because at the equilibrium point Combining equations (1)-(3), the power balance equation at the equilibrium point is:

[0054]

[0055] Solve the equilibrium equations to find the equilibrium points of the system, and substitute these equilibrium points into the system's Jacobian matrix. As shown in equation (5):

[0056]

[0057] Find the eigenvalues ​​corresponding to each point , .like Then the equilibrium point is a saddle point; if If , then the equilibrium point is a stable equilibrium node; if If so, then the equilibrium point is an unstable equilibrium node;

[0058] Using the stable equilibrium node as the initial value, the fault trajectory is obtained by solving the second-order swing equation (6) of the grid-type inverter in fault condition using the MATLAB command "ode45":

[0059]

[0060] in, The electromagnetic power output of the i-th inverter unit during the fault duration is calculated by equation (7).

[0061]

[0062] in, This represents the grid voltage during the duration of the fault.

[0063] like Figure 2 The figure shows the potential energy change curve on the trajectory during a system fault. The search is conducted along the fault trajectory to find the first point where the derivative of the potential energy with respect to time (8) changes from positive to negative. The specific steps are as follows:

[0064]

[0065] Step 1: Assume following the trajectory in the fault Moment Recorded as , Fault trajectory Moment Recorded as , . This is the integration step size.

[0066] Step Two: In The interpolation time is obtained by applying the linear interpolation method according to equation (9). ,calculate Place Recorded as .like If it is less than a certain threshold, then take The point where the fault trajectory is located at any given moment is the state point PEP. Otherwise, proceed to step three.

[0067]

[0068] Step 3: If ,but replace Proceed to step one; if ,but replace Proceed to step one.

[0069] by Starting from the initial angle of the scanning ray, determine the initial angle of the scanning ray. The calculation method is as follows:

[0070]

[0071] in, , They are respectively Place , The value of .

[0072] By integrating, the system moves along the descent direction of the potential energy gradient, searching for a path as shown in equation (11). The minimum point:

[0073]

[0074] If no result is found after integrating at a certain step size The minimum point is within the observation integration window. If a monotonically increasing trend is observed, orthogonal projection calibration is used; otherwise, stable boundary tracking is used.

[0075] The specific implementation process of the stable boundary tracking algorithm is as follows:

[0076] Step 1: Record the point corresponding to the last step of the integration window as... Starting from the stable equilibrium point after the fault, the process proceeds... ray.

[0077] Step 2: Search for the ray The specific steps for finding the first point that changes from positive to negative are the same as those for finding the escape point in the fault trajectory. Let the point found on the ray be... .

[0078] by Starting from this point, repeat the search described above. The steps to find the minimum point continue until it is found within the specified integration step. The local minimum point is denoted as . .

[0079] The specific implementation process of orthogonal projection calibration is as follows:

[0080] calculate Power gradient vector at point .

[0081]

[0082] To determine in which direction the ray should rotate to detect lower terrain, a unit vector orthogonal to the current ray direction is defined. By calculating the projection values ​​of the power gradient vector in the orthogonal directions. As shown in equation (13):

[0083]

[0084] use The positive or negative sign of the signal determines the downward slope direction of the potential energy surface along the boundary tangential direction, and the feedback dynamically adjusts the deflection angle of the next round of scanning rays. The calculation method is as follows:

[0085]

[0086] The preset rotation correction step size is used. After updating the deflection angle, the system generates a new ray for scanning. Through multiple rounds of iterative closed-loop "probe-feedback-rotation", the search path can bypass the high potential energy barrier, thus successfully capturing the minimum point of the imbalance index on the integral trajectory of the gradient descent system.

[0087] The flowchart of the above steps is as follows: Figure 2 As shown. The corresponding search process is as follows: Figure 5 As shown.

[0088] by The power balance equation is calculated with initial values. The solution obtained is consistent with a saddle point obtained from the initial solution. This solution is the dominant unstable equilibrium point.

[0089] The energy at the dominant unstable equilibrium point is calculated based on equation (11). , This is the critical energy of the system.

[0090]

[0091] Substitute the data at the fault clearing time and calculate the system energy at the fault clearing time according to equation (11). ,like If the fault is cleared, the system will be stable; if If the fault is cleared, the system will be stable.

[0092] Example 2

[0093] Embodiment 2 of the present invention provides an analysis system corresponding to Embodiment 1 above, including a memory, a processor, and a computer program stored in the memory; the processor executes the computer program in the memory to implement the steps of the method in Embodiment 1 above.

[0094] In some implementations, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.

[0095] In other implementations, the processor can be any type of general-purpose processor, such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation here.

[0096] Example 3

[0097] Embodiment 3 of the present invention provides a computer-readable storage medium corresponding to Embodiment 1 above, on which a computer program / instructions are stored. When the computer program / instructions are executed by a processor, they implement the steps of the method of Embodiment 1 above.

[0098] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.

[0099] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0100] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0101] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0102] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0103] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A transient stability analysis method for a grid-connected multi-machine parallel system, characterized in that, Includes the following steps: A transient mathematical model of a multi-machine grid-connected grid-connected system of grid-connected converters is established. The active power loop damping parameters of the grid-connected converters are taken into account in the transient mathematical model. The power balance equation is obtained using the transient mathematical model, and the stable equilibrium node before the fault is determined by Jacobian matrix eigenvalue analysis. Based on the system dynamic equations during the fault duration, with the stable equilibrium node as the initial value, the trajectory during the fault is obtained, the rate of change of potential energy on the trajectory during the fault is monitored, the transition interval from rising to falling potential energy is captured, and the state point where the time derivative of potential energy is exactly zero is reconstructed in the transition interval using linear interpolation, denoted as PEP. A potential energy gradient descent system is constructed, and an iterative search is performed along the gradient descent direction starting from the state point PEP. In response to the distortion of the potential energy boundary caused by the damping coefficient, the direction of the search ray is adjusted by monitoring the changing trend of the power imbalance index within the integration window during the iteration process, so as to achieve dynamic calibration of the search path and locate the minimum point of power imbalance. Using the minimum point of power imbalance as the initial value, the dominant unstable equilibrium point is calculated by substituting the Newton-Raphson method into the power balance equation. Calculate the energy function value corresponding to the dominant unstable equilibrium point. This value is the critical energy. The isoenergy surface corresponding to the potential energy at the dominant unstable equilibrium point is the stability region.

2. The transient stability analysis method for a grid-connected multi-machine parallel system according to claim 1, characterized in that, The transient mathematical model expression is as follows: ； in, Let be the power angle difference between the i-th grid-connected generating unit and the grid voltage. Let be the angular frequency difference between the i-th grid-connected generating unit and the power grid. This is the reference value for the active power output of the i-th grid-connected unit. To output electromagnetic power to the i-th grid-connected unit, Let be the active power loop damping parameters of the i-th grid-connected unit. Let be the inertia parameter of the i-th unit.

3. The transient stability analysis method for a grid-connected multi-machine parallel system according to claim 2, characterized in that, The i-th grid-type unit outputs electromagnetic power The calculation formula is: ； in, , These are the output voltages of the two grid-connected inverters, respectively. This is the grid voltage. , , These are the equivalent impedances between the two grid-connected inverters and the power grid.

4. The transient stability analysis method for a grid-connected multi-machine parallel system according to claim 3, characterized in that, The power balance equation is: .

5. The transient stability analysis method for a grid-connected multi-machine grid-connected system according to claim 3, characterized in that, The specific expression of the system dynamic equations during the fault duration is as follows: ;in, The electromagnetic power output by the i-th inverter unit during the fault duration.

6. The transient stability analysis method for a grid-connected multi-machine parallel system according to claim 5, characterized in that, The specific expression is: ； in, This represents the grid voltage during the duration of the fault.

7. The transient stability analysis method for a grid-connected multi-machine grid-connected system according to claim 5, characterized in that, The steps to reconstruct the state point where the potential energy has an exact time derivative of zero include: Step 1: Using the derivative of potential energy with respect to time Substitute each point of the fault trajectory into ,turn up The point where the sign changes from positive to negative, assuming it follows the trajectory of the fault. Moment Recorded as , Fault trajectory Moment Recorded as , , This is the integration step size; Step Two: In The linear interpolation method is applied to obtain the interpolation time. , ,calculate Place Recorded as ,like If it is less than the set threshold, then take... The point where the fault trajectory is located at any given moment is the state point. Otherwise, proceed to step three; Step 3: If ,but replace Proceed to step one; if ,but replace Proceed to step one.

8. The transient stability analysis method for a grid-connected multi-machine grid-connected system according to claim 3, characterized in that, The degree of imbalance is expressed as follows: ;in This is the value of the imbalance index at the k-th integration step. Let be the output electromagnetic power at the k-th integration step.

9. The transient stability analysis method for a grid-connected multi-machine parallel system according to claim 3, characterized in that, The expression for the energy function value at the dominant unstable equilibrium point is: ； in, Let be the power angle value at the stable equilibrium point after the failure of the i-th inverter unit. , The power angle difference between the first grid-connected unit and the second grid-connected unit. , The power angle difference between the first grid-type unit and the second grid-type unit at the stable equilibrium point.

10. A transient stability analysis system for a grid-connected multi-machine parallel system, comprising a memory, a processor, and a computer program stored in the memory; characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 9.

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