A method for positioning a multi-electric aircraft AC bus system instability device

Abstract

The present application relates to the field of multi-electric aircraft level connection system stability diagnosis, and provides a multi-electric aircraft AC level connection system instability device positioning method, comprising obtaining the port impedance matrix or the port admittance matrix of each subsystem in the AC level connection system, and constructing a return ratio matrix; using the return ratio matrix to construct a stability margin function, determining the baseline stability margin at the instability frequency of the AC level connection system; respectively applying a preset amplitude disturbance to each matrix element in the port impedance matrix or the port admittance matrix, and determining the sensitivity of the matrix element to the stability margin; algebraically summing the sensitivity of all matrix elements in the port impedance matrix or the port admittance matrix of each subsystem, obtaining the instability participation degree of the subsystem, and positioning the subsystem with the largest instability participation degree as the leading instability device of the AC level connection system. Only relying on the dq domain port impedance spectrum, the stability determination based on the Gail circle theorem avoids the identification of the closed loop pole, and the positioning accuracy is directly verified through the collective disturbance of the device.

Description

Technical Field

[0001] This invention relates to the field of stability diagnosis technology for multi-electric aircraft cascade systems, and in particular to a method for locating unstable devices in an AC cascade system of a multi-electric aircraft. Background Technology

[0002] With the acceleration of aviation electrification, more-electric aircraft (MEA) have become a core direction for next-generation civil airliners and new military aircraft. MEA replaces traditional bleed air, hydraulic, and mechanical actuation systems with electrical equivalents, continuously increasing the number and capacity of onboard power electronic converters. This technological evolution has significantly improved aircraft energy efficiency and reliability, but it has also placed unprecedented demands on the power quality of the onboard AC bus. In an MEA system, the AC power supply and the back-end converter form a cascaded power system; however, this cascaded coupling can easily induce broadband voltage oscillations on the AC bus.

[0003] When broadband voltage oscillations occur in the AC cascaded system of a multi-electric aircraft, it is necessary to quickly and accurately locate the instability-inducing device. Among the existing location methods, one type requires obtaining the complete internal state-space model of each converter. However, due to commercial confidentiality, the internal details of commercial aircraft converters are usually not disclosed, and the overall state-space dimension is too high, resulting in the curse of dimensionality. Another type requires identifying closed-loop poles from the frequency sweep data and then calculating the residuals. The identification results are extremely sensitive to the frequency sweep resolution and signal-to-noise ratio, and under engineering test conditions, pole misidentification or drift is prone to occur.

[0004] Therefore, how to provide a method for locating unstable devices in a multi-electric aircraft AC cascade system has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] This invention provides a method for locating unstable devices in a multi-electric aircraft AC cascade system, which solves the problem that existing technologies cannot locate unstable devices based solely on the port impedance / admittance of the subsystem.

[0006] This invention provides a method for locating unstable devices in a multi-electric aircraft AC cascade system, comprising: Obtain the port impedance matrix or port admittance matrix of each subsystem in the AC cascaded system, and construct the back ratio matrix based on the port impedance matrix or port admittance matrix; Based on Gell's circle theorem, a stability margin function is constructed using the back ratio matrix to determine the instability frequency of the AC cascaded system and the baseline stability margin at the instability frequency. A perturbation of a preset magnitude is applied to each element of the port impedance matrix or port admittance matrix of each subsystem, while keeping other matrix elements unchanged. The stability margin after the perturbation is re-determined based on the port impedance matrix or port admittance matrix after the perturbation. The sensitivity of the matrix element to the stability margin is determined based on the difference between the stability margin after the perturbation and the baseline stability margin. The instability participation degree of the subsystem is obtained by algebraically summing the sensitivity of all matrix elements in the port impedance matrix or port admittance matrix of each subsystem. Determine the degree of instability participation of each subsystem, and identify the subsystem with the highest degree of instability participation as the dominant instability device in the AC cascade system.

[0007] According to the present invention, a method for locating unstable devices in a multi-electric aircraft AC cascade system is provided, wherein the multi-electric aircraft AC cascade system includes a source-side subsystem and a load-side subsystem; The acquisition of the port impedance matrix or port admittance matrix of each subsystem in the AC cascaded system includes: Obtain the port impedance matrix of the source-side subsystem, which is a three-stage generator. The port impedance matrix is ​​the closed-loop output impedance matrix of the three-stage generator. The three-stage generator includes a pre-exciter, a DC chopper, a main exciter, a rotating rectifier, and a main generator. The closed-loop output impedance matrix of the three-stage generator is obtained by sequentially establishing and cascading the two-port equivalent circuits of each component along the physical structure from the inside out. Obtain the port admittance matrix of the load-side subsystem, where the load-side subsystem is a rectifier, and the port admittance matrix is ​​the closed-loop input admittance matrix of the rectifier.

[0008] According to the present invention, a method for locating instability devices in a multi-electric aircraft AC cascade system includes obtaining the closed-loop output impedance matrix of a three-stage generator and the closed-loop input admittance matrix of a rectifier, comprising: Established based on the analysis of physical and control parameters; Alternatively, it can be obtained directly through on-site port frequency scanning tests; Alternatively, it can be obtained through a hardware-in-the-loop testing platform.

[0009] According to the present invention, a method for locating unstable devices in a multi-electric aircraft AC cascade system, wherein constructing a lag ratio matrix based on the port impedance matrix or port admittance matrix includes: In the synchronous rotating coordinate system, the closed-loop output impedance matrix of the three-stage generator is used as the source-side port impedance matrix, and the closed-loop input admittance matrix of the rectifier is used as the load-side port admittance matrix. Multiplying the load-side port admittance matrix by the source-side port impedance matrix yields the hysteresis matrix.

[0010] According to the present invention, a method for locating unstable devices in a multi-electric aircraft AC cascade system, wherein the stability margin function is constructed using the backpropagation matrix based on Gell's circle theorem, includes: The center of the Gael circle is determined based on the two diagonal elements of the back-ratio matrix; The radius of the Gael circle is determined based on the two off-diagonal elements of the back-ratio matrix; Combining the center and radius of the circle, a stability margin function is constructed based on the relative position of the boundary of the Gaelic circle and the critical point on the complex plane.

[0011] According to the present invention, a method for locating unstable devices in a multi-electric aircraft AC cascade system, wherein the stability margin function is constructed based on the relative position of the Gaelic circle boundary and the critical point on the complex plane, includes: Set the gain margin and phase margin; Based on the matrix elements of the back ratio matrix and the gain margin and phase margin, construct the first auxiliary function and the second auxiliary function; The smaller of the first auxiliary function and the second auxiliary function at the same frequency point is selected as the stability margin function at that frequency point.

[0012] According to the present invention, a method for locating unstable devices in a multi-electric aircraft AC cascade system, after constructing a stability margin function based on the relative position of the Gaelic circle boundary and the critical point on the complex plane, further includes: Based on the value of the stability margin function at the instability frequency, the dominant axis of the AC cascade system is determined to be either the d-axis or the q-axis. Wherein, the d-axis and q-axis are two orthogonal coordinate axes in a synchronous rotating coordinate system, the two diagonal elements correspond to the d-axis Geil circle and the q-axis Geil circle respectively, and the two off-diagonal elements correspond to the radius of the d-axis Geil circle and the radius of the q-axis Geil circle respectively.

[0013] According to the present invention, a method for locating instability devices in a multi-electric aircraft AC cascade system includes determining the instability frequency of the AC cascade system and determining the baseline stability margin at the instability frequency, comprising: Within the engineering frequency band, multiple frequency points are sampled at logarithmic intervals to determine the value of the stability margin function at each sampling frequency point. The minimum value of the stability margin function among each sampling frequency point is selected as the baseline stability margin, and the frequency point corresponding to the minimum value is taken as the instability frequency.

[0014] According to the present invention, a method for locating unstable devices in a multi-electric aircraft AC cascade system, wherein determining the sensitivity of the matrix elements to the stability margin includes: Determine the difference between the stability margin after the disturbance and the baseline stability margin; Dividing the difference by the preset amplitude yields the sensitivity of the matrix element to the stability margin, where the preset amplitude is a dimensionless relative disturbance amplitude.

[0015] According to the present invention, a method for locating an unstable device in a multi-electric aircraft AC cascade system, after locating the subsystem with the highest degree of instability participation as the dominant unstable device in the AC cascade system, further includes: Determine the ratio of the instability participation degree of the dominant instability device to the instability participation degree of the secondary dominant instability device; The ratio is taken as the relative dominant strength of the dominant instability device and output.

[0016] According to the present invention, a method for locating unstable devices in a multi-electric aircraft AC cascade system, wherein the step of re-determining the stability margin after disturbance based on the port impedance matrix or port admittance matrix after disturbance includes: The perturbed matrix elements are combined with other unperturbed matrix elements to reconstruct the perturbed port impedance matrix or port admittance matrix. Based on the port impedance matrix or port admittance matrix after the disturbance, reconstruct the lag ratio matrix after the disturbance; Based on Gell's circle theorem, the stability margin after the perturbation is re-determined using the perturbation-adjusted back ratio matrix.

[0017] According to the present invention, a method for locating an unstable device in a multi-electric aircraft AC cascade system, after locating the subsystem with the highest degree of instability participation as the dominant unstable device in the AC cascade system, further includes: Select the verification perturbation amplitude, and apply a proportional perturbation in the same direction according to the sign direction of the sensitivity to each matrix element of the port impedance matrix or port admittance matrix of the dominant unstable device; Re-determine the measured stability margin of the system after applying the proportional disturbance, and determine the change in the measured margin; The theoretical prediction margin change is determined by summing the products of the sensitivity values ​​of each matrix element and the amplitude of the verification perturbation. Based on the measured margin change and the theoretically predicted margin change, the relative error is determined; and / or, the consistency between the ratio of the instability participation of the theoretically predicted dominant instability device to the secondary dominant instability device and the measured ratio is used as the verification index of positioning accuracy.

[0018] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the unstable device localization method of any of the above-described methods for multiple electric aircraft AC cascade systems.

[0019] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for locating unstable devices in a multi-electric aircraft AC cascade system as described above.

[0020] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the unstable device location method of any of the above-described AC cascaded multi-electric aircraft systems.

[0021] This invention provides a method for locating unstable devices in a multi-electric aircraft AC cascade system. By obtaining the port impedance matrix or port admittance matrix of each subsystem and constructing a back-ratio matrix, and since the back-ratio matrix fully characterizes the port interaction characteristics between the source and load sides of the cascaded system, the Gell circle stability margin function constructed based on this back-ratio matrix can objectively reflect the overall stability margin state of the system. On this basis, perturbations are independently applied to each port matrix element, and the sensitivity is calculated one by one. Since each matrix element belongs to a specific subsystem, the instability participation degree obtained by algebraically summing the sensitivities of all elements belonging to the same subsystem can quantitatively characterize the contribution of that subsystem to the decrease in the system's stability margin. Furthermore, by comparing the instability participation degrees of each subsystem, the subsystem with the highest participation degree can be located as the dominant unstable device. The entire location process only requires the matrix element values ​​of the port impedance matrix or port admittance matrix, without needing to obtain the internal white-box model of the subsystem. Moreover, by directly calculating the sensitivity through preset amplitude perturbations, the requirement for identifying closed-loop poles is completely avoided, resulting in stronger robustness and feasibility under engineering test conditions. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0023] Figure 1 This is a schematic diagram of the TSG–PWM cascaded system structure provided by the present invention; Figure 2 This is a flowchart illustrating the method for locating unstable devices in a multi-electric aircraft AC cascade system provided by the present invention. Figure 3 This is a schematic diagram of Gell's circle theorem provided by the present invention; Figure 4 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0025] Figure 1 This is a schematic diagram of the TSG-PWM cascaded system structure provided by the present invention. Figure 2 This is a flowchart illustrating the method for locating unstable devices in a multi-electric aircraft AC cascade system provided by the present invention.

[0026] like Figure 1 As shown, corresponding to the multi-electric aircraft power supply cascading scenario targeted by this invention, the system is divided into three parts: the front-end subsystem, the rear-end subsystem, and the closed-loop control link.

[0027] The front-end subsystem is a three-stage generator (source side). This three-stage generator serves as the front-end power source and employs a three-stage coaxial structure. From the inside out, it consists of a pre-exciter, a main exciter, and a main generator, equipped with a DC chopper and a rotating rectifier. Power flows as follows: the excitation current output from the pre-exciter is regulated by the DC chopper and then fed into the main exciter's excitation winding; the three-phase AC output from the main exciter is converted to DC by the rotating rectifier and fed into the main generator's excitation winding; finally, the main generator outputs three-phase AC power (a, b, and c) which flows into the AC bus.

[0028] The downstream subsystem is the PWM rectifier (load side). The PWM rectifier is the downstream load. Its three-phase input terminals are connected in parallel to the AC bus. Through the orderly switching of internal switching transistors, the three-phase AC power is rectified into DC power to supply power to the downstream load.

[0029] The control signals in the closed-loop control link flow in the following order: First, the three-phase voltage and current are sampled from the AC bus, converted to DC values ​​in the dq coordinate system via bc / dq coordinate transformation, and then the voltage signal is sent to the voltage PI controller after RMS effective value conversion, outputting the d-axis current command. q-axis current command Two current commands are sent to the current controller to complete closed-loop regulation. The output control quantity is transformed back into a three-phase modulation signal through dq / abc coordinate transformation. The modulation signal is sent to the SVPWM module to generate a PWM drive signal, which controls the switching of the rectifier transistor to achieve voltage regulation.

[0030] like Figure 2 As shown in the figure, this embodiment provides a method for locating unstable devices in a multi-electric aircraft AC cascade system. Taking a TSG with a three-phase PWM rectifier as an example, the implementation process of this method is illustrated. The method mainly includes: 201. Obtain the port impedance matrix or port admittance matrix of each subsystem in the AC cascaded system, and construct the hysteresis matrix based on the port impedance matrix or port admittance matrix.

[0031] Specifically, the AC cascaded system is first decomposed into multiple cascaded subsystems. For each subsystem, its port impedance matrix or port admittance matrix in the dq synchronous rotating coordinate system is obtained. The port admittance matrix of the load-side subsystem is multiplied by the port impedance matrix of the source-side subsystem to obtain the back-comparison matrix of the cascaded system. A unified matrix form is used to characterize the port interaction characteristics between the subsystems of the cascaded system, avoiding connection errors between different methods.

[0032] 202. Based on Gell's circle theorem, construct a stability margin function using the back ratio matrix, determine the instability frequency of the AC cascaded system, and determine the baseline stability margin at the instability frequency.

[0033] Specifically, according to Gell's circle theorem, all eigenvalues ​​of the back-ratio matrix fall within the range of the Gell's disk constructed from the matrix elements. Without precisely solving for the matrix's eigenvalues ​​or identifying closed-loop poles, a stability margin function can be directly constructed using the elements of the back-ratio matrix. The stability state of the system can be determined by the value of this stability margin function. Frequency sampling is performed within a defined engineering frequency band, and the stability margin function value corresponding to each sampled frequency point is calculated. The stability margin function value at each frequency point is also called the activity margin at that frequency point. The frequency corresponding to the minimum value of the stability margin function is determined as the instability frequency, and this minimum value is determined as the baseline stability margin. If the calculated baseline stability margin is greater than 0, it indicates that the current cascaded system is in a stable state, and no further instability device location is required; the method terminates. If the baseline stability margin is less than or equal to 0, it indicates that the system has an instability risk, and the location steps continue. By completing system stability determination and instability frequency location without closed-loop pole identification, the requirements for the quality of the frequency sweep data are reduced, improving reliability in engineering scenarios.

[0034] 203. Apply a perturbation of a preset magnitude to each element of the port impedance matrix or port admittance matrix of each subsystem, while keeping other matrix elements unchanged. Re-determine the stability margin after the perturbation based on the port impedance matrix or port admittance matrix after the perturbation. Determine the sensitivity of the matrix elements to the stability margin based on the difference between the stability margin after the perturbation and the baseline stability margin.

[0035] Specifically, the port impedance matrix or port admittance matrix is ​​a 2×2 complex matrix, where each matrix element is a complex number containing real and imaginary components. The port matrix of a single subsystem contains eight independently perturbed element components. Each element component is selected sequentially as the perturbation target, and a relative proportional perturbation of a preset amplitude is applied to the currently selected matrix element along its own complex direction, while all other element components retain their original values. This perturbation calculation is performed eight times to break the coupling symmetry between the d and q ports, ensuring calculation accuracy. The back-ratio matrix is ​​reconstructed using the perturbed port matrix, and the stability margin at the instability frequency is recalculated to obtain the perturbed stability margin. The difference between the perturbed stability margin and the baseline stability margin is calculated. Based on the ratio of this difference to the preset perturbation amplitude, the sensitivity of the current matrix element to the stability margin is obtained. After traversing all port matrix element components, the sensitivity corresponding to all matrix elements is obtained. By quantifying the impact of each port matrix element on the system's stability margin, the calculation process only involves adjusting the values ​​of the port matrix elements, without needing to obtain the internal structure and parameters of the subsystem, thus truly achieving port-level black-box implementation.

[0036] 204. Summate the sensitivity of all matrix elements in the port impedance matrix or port admittance matrix of each subsystem algebraically to obtain the instability participation degree of the subsystem.

[0037] Specifically, matrix elements are grouped according to their subsystems. The sensitivities of all matrix elements corresponding to the same subsystem are algebraically summed to obtain the instability participation degree of that subsystem. The instability participation degree is a dimensionless real number, and its physical meaning is the maximum possible change in the activity margin when all matrix elements of the subsystem's port impedance matrix are synchronously amplified by 100% in their most unfavorable directions. This change is given an upper bound by the Cauchy inequality. The larger the instability participation degree, the stronger the potential contribution of that subsystem to system instability. By aggregating element-level sensitivities into subsystem-level participation degrees, the potential contribution of each subsystem to system instability is directly quantified.

[0038] 205. Determine the degree of instability participation of each subsystem, and identify the subsystem with the highest degree of instability participation as the dominant unstable device in the AC cascade system.

[0039] Specifically, by comparing the instability participation values ​​of all subsystems, the subsystem with the largest value is the device that contributes the most to system instability, which is the dominant instability device. The output dominant device can be directly used as input for parameter-level tuning methods. Only in-depth analysis of the internal parameters of one side is needed, without repeating the processing of the other subsystem, directly outputting the final positioning result and providing a clear target object.

[0040] Furthermore, based on the above embodiments, the AC cascaded system for multi-electric aircraft in this embodiment includes a source-side subsystem and a load-side subsystem; obtaining the port impedance matrix or port admittance matrix of each subsystem in the AC cascaded system includes: obtaining the port impedance matrix of the source-side subsystem, where the source-side subsystem is a three-stage generator, and the port impedance matrix is ​​the closed-loop output impedance matrix of the three-stage generator; the three-stage generator includes a pre-exciter, a DC chopper, a main exciter, a rotating rectifier, and a main generator, and the closed-loop output impedance matrix of the three-stage generator is obtained by sequentially establishing and cascading the two-port equivalent circuits of each component along the physical structure from the inside out; obtaining the port admittance matrix of the load-side subsystem, where the load-side subsystem is a rectifier, and the port admittance matrix is ​​the closed-loop input admittance matrix of the rectifier.

[0041] Specifically, first, the two-port Thevenin or Norton equivalent circuits of the pre-exciter, DC chopper, main exciter, rotating rectifier, and main generator are established separately. The equivalent circuits of each part are cascaded according to their physical connections to obtain the open-loop output impedance of the three-stage generator. Then, a voltage closed-loop PI controller, compensator, voltage forward path, and dq peak-to-RMS conversion coefficients are introduced to finally obtain the closed-loop output impedance matrix of the three-stage generator. In a synchronous rotating coordinate system, the closed-loop input admittance matrix of the PWM rectifier is established. The cascaded system structure can be found in the appendix. Figure 1 The specific implementation targets in the typical multi-electric aircraft power supply cascading scenario are aligned with actual engineering application scenarios.

[0042] Furthermore, based on the above embodiments, this embodiment obtains the closed-loop output impedance matrix of the three-stage generator and the closed-loop input admittance matrix of the rectifier by: analytically establishing them based on physical parameters and control parameters; or, directly obtaining them through on-site port frequency sweep measurement; or, obtaining them through a hardware-in-the-loop test platform.

[0043] Specifically, when the internal physical and control parameters of the subsystem are available, the corresponding port impedance or port admittance matrix can be derived and calculated using circuit principles and control theory. In the actual system environment, frequency sweep measurements are performed on the subsystem ports using a frequency sweep testing device to directly obtain the frequency domain data of the port impedance or admittance. Alternatively, a subsystem model can be built in a hardware-in-the-loop simulation platform, and the corresponding port impedance or port admittance matrix can be obtained through port frequency sweep functionality. These three methods adapt the approach to different application conditions, ensuring that the required port matrix data can be obtained regardless of whether the internal parameters of the subsystem are available, demonstrating strong engineering applicability.

[0044] Furthermore, based on the above embodiments, in this embodiment, a hysteresis matrix is ​​constructed according to the port impedance matrix or the port admittance matrix, including: in a synchronous rotating coordinate system, using the closed-loop output impedance matrix of the three-stage generator as the source-side port impedance matrix, and using the closed-loop input admittance matrix of the rectifier as the load-side port admittance matrix; multiplying the load-side port admittance matrix with the source-side port impedance matrix to obtain the hysteresis matrix.

[0045] Specifically, in the synchronous rotating coordinate system, the closed-loop output impedance matrix of the three-stage generator is used as the source-side port impedance matrix, denoted as... , is a 2×2 complex matrix. The closed-loop input admittance matrix of the rectifier is used as the load-side port admittance matrix, denoted as . It is a 2×2 complex matrix. Multiplying the load-side port admittance matrix by the source-side port impedance matrix yields the lag ratio matrix. L (s), the corresponding calculation formula is (1): (1) in, s For complex frequency variables, L(s) The lag ratio matrix of the cascaded system fully characterizes the port interaction coupling characteristics between the source and load sides. The lag ratio matrix is ​​constructed according to the standard form of impedance interaction in cascaded systems to ensure the accuracy and universality of stability determination.

[0046] Furthermore, based on the above embodiments, this embodiment constructs a stability margin function using the Gale circle theorem and the back-ratio matrix, including: determining the center of the Gale circle based on the two diagonal elements of the back-ratio matrix; determining the radius of the Gale circle based on the two off-diagonal elements of the back-ratio matrix; and constructing a stability margin function based on the relative position of the boundary of the Gale circle and the critical point on the complex plane by combining the center and the radius.

[0047] Specifically, the back-ratio matrix L (s) is a second-order square matrix containing two diagonal elements. and Each diagonal element corresponds to the center of a Gaelic circle. The absolute value of two off-diagonal elements is... and The absolute value of each off-diagonal element corresponds to the radius of a Gell-Robin circle. According to the Gell-Robin circle theorem, the two eigenvalues ​​of the back-bibliographic matrix... , They must fall within the corresponding Gaelic disks, satisfying the following constraints (2) and (3): (2) (3) in, , These are the eigenvalues ​​of the back ratio matrix. , These are the diagonal elements of the back-ratio matrix, corresponding to the self-impedance coupling terms on the d-axis and q-axis, respectively; , These are the off-diagonal elements of the back-ratio matrix, corresponding to the cross-axis coupling terms.

[0048] By combining the center and radius of the circle, a stability margin function is constructed based on the relative positions of the boundary of the Gell circle and the critical point on the complex plane. A basic illustration of the Gell circle theorem can be found in the appendix. Figure 3 By using Gell's circle theorem, the range of eigenvalues ​​can be directly defined using matrix elements. There is no need to solve for the eigenvalues ​​precisely. The distribution range of eigenvalues ​​can be defined simply by using matrix elements, thereby measuring the stability of the system.

[0049] like Figure 3 The diagram illustrates the basic principles of the Gell-U-Circle theorem, using the complex plane as a framework and serving as the mathematical foundation for stability determination. The diagram contains two Gell-U-Circles: the d-axis Gell-U-Circle has its center at the diagonal elements of the hysteresis matrix and its radius at the absolute values ​​of the off-diagonal elements; the q-axis Gell-U-Circle has its center at the diagonal elements of the hysteresis matrix and its radius at the absolute values ​​of the off-diagonal elements. According to the Gell-U-Circle theorem, the two eigenvalues ​​of the hysteresis matrix must lie within their respective disks. No precise solution for the eigenvalues ​​is required; the distribution boundary of the eigenvalues ​​can be determined solely through the matrix elements. Based on the relative position of this boundary and the critical stability point, a stability margin function is constructed, eliminating the need for eigenvalue solving and closed-loop pole identification, thus providing a unified computational basis for instability.

[0050] Furthermore, based on the above embodiments, this embodiment constructs a stability margin function based on the relative position of the Gaelic circle boundary and the critical point on the complex plane, including: setting a gain margin and a phase margin; constructing a first auxiliary function and a second auxiliary function according to each matrix element of the back-ratio matrix and the gain margin and phase margin; and selecting the smaller of the first auxiliary function and the second auxiliary function at the same frequency point as the stability margin function at that frequency point.

[0051] Specifically, set the gain margin. and phase margin Gain margin and phase margin are preset according to actual engineering requirements to define the stability reserve requirements that the system needs to meet. This is based on the elements of the back-ratio matrix and the gain margin. and phase margin Construct the first auxiliary function E(s) and the second auxiliary function F(s): (4) (5) The two auxiliary functions are constructed based on Gell's circle theorem and stability margin requirements. They measure the shortest distance from the Gell's circle boundary to the critical point of the complex plane from two dimensions: gain margin boundary and phase margin boundary. Based on these two auxiliary functions, the following structures are constructed: Axis stability margin function and Axis stability margin function : (6) (7) The smaller of the first auxiliary function and the second auxiliary function at the same frequency point is selected as the stability margin function, i.e., the activity margin, at that frequency point. The corresponding calculation formula is: (8) in, Angular frequency The activity margin at the location, for The value of the stability margin function corresponding to the axis. for q The value of the stability margin function corresponding to the axis. It takes into account the stability requirements of both gain reserve and phase reserve, making the evaluation of stability margin more comprehensive.

[0052] Furthermore, based on the above embodiments, this embodiment, after constructing the stability margin function based on the relative position of the Gell circle boundary and the critical point on the complex plane, further includes: determining the dominant axis of the AC cascaded system as either the d-axis or the q-axis according to the value of the stability margin function at the instability frequency; wherein the d-axis and q-axis are two orthogonal coordinate axes in a synchronous rotating coordinate system, the two diagonal elements correspond to the d-axis Gell circle and the q-axis Gell circle respectively, and the two off-diagonal elements correspond to the radii of the d-axis Gell circle and the q-axis Gell circle respectively. The axis corresponding to the auxiliary function with the smaller value at the instability frequency is the dominant axis of system instability.

[0053] Furthermore, based on the above embodiments, this embodiment determines the instability frequency of the AC cascaded system and the baseline stability margin at the instability frequency, including: sampling multiple frequency points at logarithmic intervals within the engineering frequency band, determining the value of the stability margin function at each sampling frequency point; selecting the minimum value of the stability margin function among each sampling frequency point as the baseline stability margin, and taking the frequency point corresponding to the minimum value as the instability frequency.

[0054] Specifically, the engineering frequency band is determined based on the actual operating frequency band of the more-electric aircraft power system. Logarithmic sampling of 100 or more frequency points can be used to ensure frequency coverage accuracy. The hysteresis matrix element corresponding to each sampled frequency point is calculated, and then the stability margin function value for that frequency point is calculated. The minimum value of the stability margin function among all sampled frequency points is selected as the baseline stability margin. The frequency point corresponding to the minimum value is taken as the instability frequency. The corresponding calculation formulas are (9) and (10): (9) (10) in, For the instability frequency, This represents the stability margin function value corresponding to frequency f; The instability frequency f x The corresponding baseline stability margin is the minimum value of the activity margin across the entire frequency band.

[0055] After calculation, the sign of the baseline stability margin is first determined. If the minimum value of the full-band activity margin is greater than 0, the system is stable, and the method terminates. If it is less than or equal to 0, subsequent positioning steps are performed. By scanning the entire frequency band, the position with the lowest system stability margin is found, accurately pinpointing the frequency point most prone to instability.

[0056] Furthermore, based on the above embodiments, the sensitivity of the matrix element to the stability margin in this embodiment includes: determining the difference between the stability margin after the disturbance and the baseline stability margin; dividing the difference by a preset amplitude to obtain the sensitivity of the matrix element to the stability margin, wherein the preset amplitude is a dimensionless relative disturbance amplitude.

[0057] Specifically, select small perturbation amplitude ,like Select the port matrix element to be calculated and proportionally perturb that element along its own complex direction. The remaining 7 port matrix elements retain their original values. The perturbed new elements are then used. Together with other unperturbed elements, they are reassembled into a perturbed port impedance matrix. Port admittance matrix Then, following the methods described above for constructing auxiliary functions and stability margin functions, the activity margin at the instability frequency is recalculated to obtain the activity margin after the disturbance. The port element-level sensitivity of this element is calculated and stored using a numerical difference method. : (11) in, Let X be the sensitivity of the port element to the stability margin, with subscript X as the index. , , The activity margin of port element X after perturbation. Baseline activity margin, For the dimensionless relative perturbation amplitude, a small quantity is selected to ensure the first-order approximation accuracy of the numerical difference. The physical meaning is: the first-order change in the activity margin when the matrix elements are scaled up by 100%.

[0058] After completing the sensitivity calculation for all 8 port elements, output the corresponding sensitivity array: (12) Element-level sensitivity is obtained through numerical difference, a calculation process that is intuitive and simple, requiring no analytical differentiation, and is suitable for applications involving black-box port data. Performing perturbation calculations eight times in a loop breaks the coupling symmetry between the d and q ports, ensuring calculation accuracy.

[0059] Furthermore, based on the above embodiments, after identifying the subsystem with the largest instability participation as the dominant instability device in the AC cascade system, this embodiment further includes: determining the ratio of the instability participation of the dominant instability device to the instability participation of the secondary dominant instability device; and outputting the ratio as the relative dominance of the dominant instability device.

[0060] Specifically, for subsystems By summing the sensitivities of the four elements of its port impedance matrix, the instability participation degree of the subsystem can be obtained. : (12) in, It is a dimensionless real number, and its physical meaning is: when the four matrix elements of the port impedance matrix of subsystem k are simultaneously amplified by 100% in their respective most unfavorable directions, the activity margin is... The maximum possible change (the upper bound given by the Cauchy inequality). The larger the value, the greater the potential contribution of the subsystem to instability.

[0061] Based on the above formulas, the sensitivity sets of TSG and PWM can be obtained as (13) (14): (13) (14) Next, determine the dominant instability device and define the dominant instability device. The subsystem with the highest instability participation: (15) Simultaneously outputs the dominant instability device With secondary dominant instability device Instability participation ratio As a relative dominant strength, quantifying the instability contribution potential and dominance of each subsystem can be directly used as a quantitative reference for prioritizing stability rectification.

[0062] Furthermore, based on the above embodiments, this embodiment redetermines the stability margin after disturbance based on the port impedance matrix or port admittance matrix after disturbance. This includes: reconstructing the port impedance matrix or port admittance matrix after disturbance using the disturbed matrix elements and other undisturbed matrix elements, adjusting only the value of the currently disturbed single matrix element, while keeping the original values ​​of all other matrix elements unchanged. Based on the port impedance matrix or port admittance matrix after disturbance, reconstructing the back-ratio matrix after disturbance according to the same matrix multiplication rules as the baseline calculation. Based on Gell's circle theorem, using the back-ratio matrix after disturbance, redetermining the stability margin after disturbance according to the same Gell's circle margin calculation rules as the baseline calculation. The stability margin before and after disturbance uses completely consistent calculation methods. The stability assessment and positioning stages share the same set of Gell's circle mathematical systems, avoiding the connection errors caused by different calculation methods, and ensuring greater accuracy in sensitivity calculation.

[0063] Furthermore, based on the above embodiments, after identifying the subsystem with the highest instability participation as the dominant unstable device in the AC cascade system, this embodiment further includes: selecting the verification perturbation amplitude; applying a proportional perturbation in the same direction according to the sign direction of the sensitivity to each matrix element of the port impedance matrix or port admittance matrix of the dominant unstable device; re-determining the measured stability margin of the system after applying the proportional perturbation, and determining the measured margin change; determining the theoretical predicted margin change based on the sum of the products of the sensitivity values ​​of each matrix element and the verification perturbation amplitude; determining the relative error based on the measured margin change and the theoretical predicted margin change; and / or using the consistency between the theoretically predicted ratio of the instability participation of the dominant unstable device and the secondary dominant unstable device and the measured ratio as the verification index of the positioning accuracy.

[0064] Specifically, the verification perturbation amplitude can be selected from small percentages such as 0.1%, 0.3%, and 0.5%. For each element of the subsystem's k-port impedance matrix... According to its sensitivity symbol Apply proportional perturbation in the same direction This causes all four elements to shift synchronously in the direction of increasing M.

[0065] The activity margin of the system after the disturbance is recalculated as described above. The measured margin change was obtained. ;according to First-order prediction based on computational theory.

[0066] Calculate the relative error (16): (16) in, The relative error of the positioning result. This represents the measured margin change. This represents the margin change obtained based on the first-order sensitivity prediction.

[0067] To predict Ratio and Measured The consistency of the ratio serves as a verification indicator for equipment sorting. The higher the consistency between the predicted ratio and the measured ratio, the more accurate the positioning result of the equipment sorting.

[0068] This invention provides a black-box-friendly, closed-loop pole identification-free, self-consistent with commonly used stability assessment methods in engineering, and directly verifiable accuracy method for locating unstable devices. It relies solely on the eight elements of the dq-domain port impedance matrix, completely independent of internal information such as subsystem physical parameters, control structures, and parameter sets. It can be directly integrated with engineering testing facilities such as HIL platforms and frequency sweep test benches, requiring only on-site frequency sweep data for implementation. Sensitivity is obtained by applying a small, proportional perturbation to the eight port matrix elements and then recalculating in the frequency domain, completely avoiding the pole identification process and significantly improving robustness under engineering test conditions. The output dominant device can be directly used as input for parameter-level tuning method research, requiring only in-depth analysis of the internal parameters on the dominant device side, without needing to repeatedly process the other subsystem.

[0069] Figure 4 A schematic diagram of the physical structure of an electronic device is provided. like Figure 1As shown, the electronic device may include: a processor 410, a communications interface 420, a memory 430, and a communication bus 440, wherein the processor 410, the communications interface 420, and the memory 430 communicate with each other through the communication bus 440. The processor 410 can call logic instructions in the memory 430 to execute a method for locating unstable devices in a multi-electric aircraft AC cascade system. This method includes: obtaining the port impedance matrix or port admittance matrix of each subsystem in the AC cascade system; constructing a back-ratio matrix based on the port impedance matrix or port admittance matrix; constructing a stability margin function using the back-ratio matrix based on Gell's circle theorem to determine the instability frequency of the AC cascade system and the baseline stability margin at the instability frequency; and processing each matrix element in the port impedance matrix or port admittance matrix of each subsystem. A perturbation of a preset amplitude is applied while keeping other matrix elements unchanged. The stability margin after the perturbation is re-determined based on the port impedance matrix or port admittance matrix after the perturbation. The sensitivity of the matrix elements to the stability margin is determined based on the difference between the stability margin after the perturbation and the baseline stability margin. The instability participation of each subsystem is obtained by algebraically summing the sensitivity of all matrix elements in the port impedance matrix or port admittance matrix of each subsystem. The instability participation of each subsystem is determined, and the subsystem with the largest instability participation is identified as the dominant instability device in the AC cascade system.

[0070] Furthermore, the logical instructions in the aforementioned memory 430 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0071] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the instability device localization method for a multi-electric aircraft AC cascade system provided by the above methods. The method includes: obtaining the port impedance matrix or port admittance matrix of each subsystem in the AC cascade system; constructing a back ratio matrix based on the port impedance matrix or port admittance matrix; constructing a stability margin function using the back ratio matrix based on Gell's circle theorem; determining the instability frequency of the AC cascade system; and determining the baseline stability at the instability frequency. Margin; apply a perturbation of a preset amplitude to each element of the port impedance matrix or port admittance matrix of each subsystem, keeping other matrix elements unchanged, and redetermine the stability margin after perturbation based on the perturbed port impedance matrix or port admittance matrix. Determine the sensitivity of the matrix element to the stability margin based on the difference between the stability margin after perturbation and the baseline stability margin. Summate the sensitivities of all matrix elements in the port impedance matrix or port admittance matrix of each subsystem algebraically to obtain the instability participation degree of the subsystem. Determine the instability participation degree of each subsystem, and locate the subsystem with the largest instability participation degree as the dominant instability device in the AC cascade system.

[0072] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method for locating unstable devices in a multi-electric aircraft AC cascade system provided by the methods described above. This method includes: obtaining the port impedance matrix or port admittance matrix of each subsystem in the AC cascade system; constructing a back-ratio matrix based on the port impedance matrix or port admittance matrix; constructing a stability margin function using the back-ratio matrix based on Gell's circle theorem; determining the instability frequency of the AC cascade system; and determining the baseline stability margin at the instability frequency; and respectively determining the port impedance matrix of each subsystem. Each element in the impedance matrix or port admittance matrix is ​​perturbed by a preset amplitude, while keeping other matrix elements unchanged. The stability margin after the perturbation is re-determined based on the perturbed port impedance matrix or port admittance matrix. The sensitivity of the matrix element to the stability margin is determined based on the difference between the perturbed stability margin and the baseline stability margin. The instability participation of each subsystem is obtained by algebraically summing the sensitivities of all matrix elements in the port impedance matrix or port admittance matrix of each subsystem. The instability participation of each subsystem is determined, and the subsystem with the largest instability participation is identified as the dominant instability device in the AC cascade system.

[0073] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0074] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for locating unstable devices in a multi-electric aircraft AC cascade system, characterized in that, include: Obtain the port impedance matrix or port admittance matrix of each subsystem in the AC cascaded system, and construct the back ratio matrix based on the port impedance matrix or port admittance matrix; Based on Gell's circle theorem, a stability margin function is constructed using the back ratio matrix to determine the instability frequency of the AC cascaded system and the baseline stability margin at the instability frequency. A perturbation of a preset magnitude is applied to each element of the port impedance matrix or port admittance matrix of each subsystem, while keeping other matrix elements unchanged. The stability margin after the perturbation is re-determined based on the port impedance matrix or port admittance matrix after the perturbation. The sensitivity of the matrix element to the stability margin is determined based on the difference between the stability margin after the perturbation and the baseline stability margin. The instability participation degree of the subsystem is obtained by algebraically summing the sensitivity of all matrix elements in the port impedance matrix or port admittance matrix of each subsystem. Determine the degree of instability participation of each subsystem, and identify the subsystem with the highest degree of instability participation as the dominant instability device in the AC cascade system.

2. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to claim 1, characterized in that, The multi-electric aircraft AC cascade system includes a source-side subsystem and a load-side subsystem; The acquisition of the port impedance matrix or port admittance matrix of each subsystem in the AC cascaded system includes: Obtain the port impedance matrix of the source-side subsystem, which is a three-stage generator. The port impedance matrix is ​​the closed-loop output impedance matrix of the three-stage generator. The three-stage generator includes a pre-exciter, a DC chopper, a main exciter, a rotating rectifier, and a main generator. The closed-loop output impedance matrix of the three-stage generator is obtained by sequentially establishing and cascading the two-port equivalent circuits of each component along the physical structure from the inside out. Obtain the port admittance matrix of the load-side subsystem, where the load-side subsystem is a rectifier, and the port admittance matrix is ​​the closed-loop input admittance matrix of the rectifier.

3. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to claim 2, characterized in that, Obtain the closed-loop output impedance matrix of the three-stage generator and the closed-loop input admittance matrix of the rectifier, including: Established based on the analysis of physical and control parameters; Alternatively, it can be obtained directly through on-site port frequency scanning tests; Alternatively, it can be obtained through a hardware-in-the-loop testing platform.

4. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to claim 1, characterized in that, The step of constructing the lag ratio matrix based on the port impedance matrix or port admittance matrix includes: In the synchronous rotating coordinate system, the closed-loop output impedance matrix of the three-stage generator is used as the source-side port impedance matrix, and the closed-loop input admittance matrix of the rectifier is used as the load-side port admittance matrix. Multiplying the load-side port admittance matrix by the source-side port impedance matrix yields the hysteresis matrix.

5. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to claim 1, characterized in that, The method of constructing a stability margin function based on Gell's circle theorem and using the back-ratio matrix includes: The center of the Gael circle is determined based on the two diagonal elements of the back-ratio matrix; The radius of the Gael circle is determined based on the two off-diagonal elements of the back-ratio matrix; Combining the center and radius of the circle, a stability margin function is constructed based on the relative position of the boundary of the Gaelic circle and the critical point on the complex plane.

6. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to claim 5, characterized in that, The stability margin function constructed based on the relative position of the Gaelic circle boundary and the critical point on the complex plane includes: Set the gain margin and phase margin; Based on the matrix elements of the back ratio matrix and the gain margin and phase margin, construct the first auxiliary function and the second auxiliary function; The smaller of the first auxiliary function and the second auxiliary function at the same frequency point is selected as the stability margin function at that frequency point.

7. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to claim 5, after constructing the stability margin function based on the relative position of the Gaelic circle boundary and the critical point on the complex plane, further includes: Based on the value of the stability margin function at the instability frequency, the dominant axis of the AC cascade system is determined to be either the d-axis or the q-axis. Wherein, the d-axis and q-axis are two orthogonal coordinate axes in a synchronous rotating coordinate system, the two diagonal elements correspond to the d-axis Geil circle and the q-axis Geil circle respectively, and the two off-diagonal elements correspond to the radius of the d-axis Geil circle and the radius of the q-axis Geil circle respectively.

8. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to claim 1, characterized in that, Determining the instability frequency of the AC cascaded system and determining the baseline stability margin at the instability frequency includes: Within the engineering frequency band, multiple frequency points are sampled at logarithmic intervals to determine the value of the stability margin function at each sampling frequency point. The minimum value of the stability margin function among each sampling frequency point is selected as the baseline stability margin, and the frequency point corresponding to the minimum value is taken as the instability frequency.

9. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to claim 1, characterized in that, Determining the sensitivity of the matrix elements to the stability margin includes: Determine the difference between the stability margin after the disturbance and the baseline stability margin; Dividing the difference by the preset amplitude yields the sensitivity of the matrix element to the stability margin, where the preset amplitude is a dimensionless relative disturbance amplitude.

10. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to claim 1, characterized in that, After identifying the subsystem with the highest instability participation as the dominant instability device in the AC cascade system, the system further includes: Determine the ratio of the instability participation degree of the dominant instability device to the instability participation degree of the secondary dominant instability device; The ratio is taken as the relative dominant strength of the dominant instability device and output.

11. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to claim 1, characterized in that, The step of re-determining the stability margin after the disturbance based on the port impedance matrix or port admittance matrix after the disturbance includes: The perturbed matrix elements are combined with other unperturbed matrix elements to reconstruct the perturbed port impedance matrix or port admittance matrix. Based on the port impedance matrix or port admittance matrix after the disturbance, reconstruct the lag ratio matrix after the disturbance; Based on Gell's circle theorem, the stability margin after the perturbation is re-determined using the perturbation-adjusted back ratio matrix.

12. The method for locating unstable devices in a multi-electric aircraft AC cascade system according to any one of claims 1-11, characterized in that, After identifying the subsystem with the highest instability participation as the dominant instability device in the AC cascade system, the system further includes: Select the verification perturbation amplitude, and apply a proportional perturbation in the same direction according to the sign direction of the sensitivity to each matrix element of the port impedance matrix or port admittance matrix of the dominant unstable device; Re-determine the measured stability margin of the system after applying the proportional disturbance, and determine the change in the measured margin; The theoretical prediction margin change is determined by summing the products of the sensitivity values ​​of each matrix element and the amplitude of the verification perturbation. Based on the measured margin change and the theoretically predicted margin change, the relative error is determined; and / or, the consistency between the theoretically predicted ratio of the instability participation of the dominant instability device and the secondary dominant instability device and the measured ratio is used as the verification index of positioning accuracy.

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