Method for determining stability of power system and unified power quality conditioner

Abstract

The application discloses a kind of stability determination method of power system and unified power quality conditioner.Therein, the method includes: in power system, after injecting disturbance current corresponding to predetermined disturbance frequency to point of common coupling, obtaining point of common coupling voltage signal, grid-side current signal and load-side current signal;Determine the source impedance of grid-side and the load impedance of load-side;According to source impedance and load impedance, determine the return rate matrix;According to return rate matrix, determine the first eigenvalue and the second eigenvalue;Determine the first Nyquist curve corresponding to the first eigenvalue, and the second Nyquist curve corresponding to the second eigenvalue;According to Nyquist curve, determine the stability result of power system at predetermined disturbance frequency.The application solves the technical problem that there is strong limitation when determining whether power system is stable in related technology, and it is difficult to accurately evaluate the true stability degree.

Description

Technical Field

[0001] This invention relates to the field of power systems, and more specifically, to a method for determining the stability of a power system and a unified power quality regulator. Background Technology

[0002] Against the backdrop of global energy transition, the large-scale integration of renewable energy sources such as wind and solar power into the power grid has led to a significant increase in the degree of power electronics in the power system. New energy generating units rely on converters for grid connection; their rapid dynamic response characteristics interact with the impedance characteristics of the weak power grid, easily triggering broadband oscillations and posing a serious challenge to the stable operation of the power system. Among existing technologies, impedance analysis, with its clear physical concepts and ability to quantify stability margins, has become the core method for analyzing source-grid interaction stability. However, many optimization opportunities and technical challenges remain to be addressed to better cope with the complex and ever-changing operating conditions of the current power system.

[0003] Currently, when analyzing the source-grid interaction stability of power systems, traditional single-ended measurement methods can only obtain electrical information at a single node, making it difficult to accurately capture the complex impact of the coupling between various components on stability. Regarding the application of stability criteria, while the traditional Bode diagram phase margin method is widely used, it has limitations. The phase margin index obtained by analyzing the open-loop frequency characteristics of the system is difficult to accurately assess the actual stability of the system when facing the complex interaction between the rapid dynamic response of converters and the weak impedance characteristics of the grid in highly electronic power systems. These shortcomings of existing technologies significantly reduce the effectiveness of power system stability analysis in the context of large-scale integration of new energy sources into the grid, making it difficult to meet the requirements for ensuring the safe and stable operation of the power system.

[0004] There is currently no effective solution to the above problems. Summary of the Invention

[0005] This invention provides a method for determining the stability of a power system and a unified power quality regulator, which at least solves the technical problem in related technologies that have strong limitations in determining whether a power system is stable and make it difficult to accurately assess the true degree of stability.

[0006] According to one aspect of the present invention, a method for determining the stability of a power system is provided, comprising: applying a unified power quality conditioner; in a power system, after injecting a disturbance current corresponding to a predetermined disturbance frequency into a point of common coupling (PCC), acquiring a PCC voltage signal, a grid-side current signal, and a load-side current signal, wherein the PCC is an electrical coupling node between the grid side and the load side, and the unified power quality conditioner is configured with the predetermined disturbance frequency; determining the source impedance of the grid side and the load impedance of the load side based on the PCC voltage signal, the grid-side current signal, and the load-side current signal; and determining a hysteresis matrix based on the source impedance and the load impedance, wherein the hysteresis matrix characterizes the stability of the power system. The impedance interaction strength and phase coupling relationship between the grid side and the load side are described; based on the hysteresis matrix, a first eigenvalue and a second eigenvalue are determined, wherein the first eigenvalue reflects the feedback response capability of the grid side to fluctuations on the load side, and the second eigenvalue reflects the reverse coupling capability of the load side to fluctuations on the grid side; based on the first eigenvalue and the second eigenvalue, a first Nyquist curve corresponding to the first eigenvalue and a second Nyquist curve corresponding to the second eigenvalue are determined, wherein the Nyquist curve represents the complex response trajectory of the hysteresis matrix at a specific frequency; based on the first Nyquist curve and the second Nyquist curve, the stability result of the power system at the predetermined disturbance frequency is determined.

[0007] Optionally, determining the stability result of the power system at the predetermined disturbance frequency based on the first Nyquist curve and the second Nyquist curve includes: determining a target critical point corresponding to a target Nyquist curve, wherein the target Nyquist curve includes at least one of the following: a first Nyquist curve and a second Nyquist curve; determining whether the target Nyquist curve encloses the target critical point; and determining the stability result based on the enclosed result.

[0008] Optionally, determining the stability result based on the enclosure result includes: if the enclosure result is enclosure, determining the stability result as a stable result indicating that the power system is unstable at the predetermined disturbance frequency; and / or, if the enclosure result is not enclosure, determining the stability result as a stable result indicating that the power system is stable at the predetermined disturbance frequency, and determining a stability index based on the distance between a neighboring point in the target Nyquist curve and the target critical point, wherein the neighboring point is the point in the target Nyquist curve closest to the target critical point.

[0009] Optionally, determining the source impedance on the grid side and the load impedance on the load side based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal includes: acquiring the common coupling point voltage signal, the grid-side current signal, and the load-side current signal corresponding to multiple disturbance injections; determining grid-side parameters and load-side parameters based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal corresponding to multiple disturbance injections, and the correspondence between voltage, current, and impedance, wherein... The grid-side parameters include the grid-side d-axis impedance characteristic parameters, the grid-side d-axis impedance coupling characteristic parameters, the grid-side q-axis impedance coupling characteristic parameters, and the grid-side q-axis impedance characteristic parameters. The load-side parameters include the load-side d-axis impedance characteristic parameters, the load-side d-axis impedance coupling characteristic parameters, the load-side q-axis impedance coupling characteristic parameters, and the load-side q-axis impedance characteristic parameters. Based on the grid-side parameters, the source impedance is determined, and based on the load-side parameters, the load impedance is determined.

[0010] Optionally, determining the source impedance of the grid side and the load impedance of the load side based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal includes: transforming the common coupling point voltage signal, the grid-side current signal, and the load-side current signal to a two-phase rotating coordinate system to obtain the common coupling point two-phase voltage signal, the grid-side two-phase current signal, and the load-side two-phase current signal; performing a fast Fourier transform on the common coupling point two-phase voltage signal, the grid-side two-phase current signal, and the load-side two-phase current signal to obtain the common coupling point frequency domain voltage signal, the grid-side frequency domain current signal, and the load-side frequency domain current signal in the frequency domain; and determining the source impedance of the grid side and the load impedance of the load side based on the common coupling point frequency domain voltage signal, the grid-side frequency domain current signal, and the load-side frequency domain current signal.

[0011] Optionally, determining the hysteresis matrix based on the source impedance and the load impedance includes: performing a ratio calculation between the source impedance and the load impedance to determine the hysteresis matrix.

[0012] According to one aspect of the present invention, a unified power quality conditioner is provided, comprising: an acquisition module, configured to acquire a common coupling point voltage signal, a grid-side current signal, and a load-side current signal in a power system after injecting a disturbance current corresponding to a predetermined disturbance frequency into a common coupling point, wherein the common coupling point is an electrical coupling node between the grid side and the load side, and the unified power quality conditioner is configured with the predetermined disturbance frequency; a first determination module, configured to determine the source impedance of the grid side and the load impedance of the load side based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal; and a second determination module, configured to determine a hysteresis matrix based on the source impedance and the load impedance, wherein the hysteresis matrix characterizes the relationship between the grid side and the load. The third determining module is used to determine a first eigenvalue and a second eigenvalue based on the hysteresis matrix, wherein the first eigenvalue reflects the feedback response capability of the grid side to fluctuations on the load side, and the second eigenvalue reflects the reverse coupling capability of the load side to fluctuations on the grid side; the fourth determining module is used to determine a first Nyquist curve corresponding to the first eigenvalue and a second Nyquist curve corresponding to the second eigenvalue based on the first eigenvalue and the second eigenvalue, wherein the Nyquist curve represents the complex response trajectory of the hysteresis matrix at a specific frequency; the fifth determining module is used to determine the stability result of the power system at the predetermined disturbance frequency based on the first Nyquist curve and the second Nyquist curve.

[0013] According to one aspect of the present invention, a power system is provided, comprising: a unified power quality conditioner, a grid side, and a load side, wherein the unified power quality conditioner performs the method described above, and the unified power quality conditioner is connected between the grid side and the load side.

[0014] According to one aspect of the present invention, an electronic device is provided, comprising: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured to execute the instructions to implement the power system stability determination method as described in any of the preceding claims.

[0015] According to one aspect of the present invention, a computer-readable storage medium is provided, wherein when the instructions in the computer-readable storage medium are executed by a processor of an electronic device, the electronic device is enabled to perform the power system stability determination method as described in any of the preceding claims.

[0016] In this embodiment of the invention, applied to a unified power quality conditioner (UPQC), in a power system, after injecting a disturbance current corresponding to a predetermined disturbance frequency into the point of common coupling (PCC), the voltage signal of the PCC, the grid-side current signal, and the load-side current signal are obtained. The PCC is the electrical coupling node between the grid side and the load side. The unified power quality conditioner is configured with a predetermined disturbance frequency. Based on the PCC voltage signal, the grid-side current signal, and the load-side current signal, the source impedance of the grid side and the load impedance of the load side are determined. Based on the source impedance and the load impedance, a hysteresis matrix is ​​determined, where the hysteresis matrix represents the relationship between the grid side and the load side. The impedance interaction strength and phase coupling relationship between the load and load sides are determined. Based on the hysteresis matrix, a first eigenvalue and a second eigenvalue are determined, where the first eigenvalue reflects the feedback response capability of the grid side to fluctuations on the load side, and the second eigenvalue reflects the reverse coupling capability of the load side to fluctuations on the grid side. Based on the first eigenvalue and the second eigenvalue, a first Nyquist curve corresponding to the first eigenvalue and a second Nyquist curve corresponding to the second eigenvalue are determined, where the Nyquist curve represents the complex response trajectory of the hysteresis matrix at a specific frequency. Based on the first Nyquist curve and the second Nyquist curve, the stability result of the power system at a predetermined disturbance frequency is determined. By employing an online dual-ended impedance detection method based on a unified power quality regulator (UPQC), a disturbance current is injected at the common coupling point, and electrical response signals from the grid side and the load side are acquired simultaneously. A hysteresis matrix is ​​constructed, and a dual Nyquist curve is plotted based on its eigenvalues. This achieves the goal of high-precision quantitative characterization and closed-loop stability discrimination of the impedance interaction characteristics between the grid side and the load side. Thus, it realizes the technical effect of wide-band system stability self-diagnosis without changing the original power quality regulation function of the UPQC. This solves the technical problem in related technologies that have strong limitations in determining whether a power system is stable and make it difficult to accurately assess the true degree of stability. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0018] Figure 1 This is a flowchart of a method for determining the stability of a power system according to an embodiment of the present invention;

[0019] Figure 2 This is a schematic diagram of the UPQC main circuit topology provided by an optional embodiment of the present invention;

[0020] Figure 3 This is a flowchart of a two-terminal impedance measurement process provided by an optional embodiment of the present invention;

[0021] Figure 4This is an equivalent diagram of parallel-side injection provided by an optional embodiment of the present invention;

[0022] Figure 5 This is a block diagram of the UPQC series-side control provided by an optional embodiment of the present invention;

[0023] Figure 6 This is a block diagram of the parallel side control of UPQC provided by an optional embodiment of the present invention. Detailed Implementation

[0024] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0025] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "including" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0026] Example 1

[0027] According to an embodiment of the present invention, an embodiment of a method for determining the stability of a power system is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0028] Figure 1 This is a flowchart of a power system stability determination method according to an embodiment of the present invention, such as... Figure 1 As shown, the method includes the following steps:

[0029] Step S102: In the power system, after injecting a disturbance current corresponding to a predetermined disturbance frequency into the common coupling point, the voltage signal of the common coupling point, the grid-side current signal, and the load-side current signal are obtained. The common coupling point is the electrical coupling node between the grid side and the load side, and a predetermined disturbance frequency is set in the unified power quality regulator.

[0030] The common coupling point (PCC) refers to the interface node where the grid side and the load side are electrically connected in a power system. It is a shared measurement reference point for voltage and current, enabling global observation of the system's interactive state and avoiding impedance estimation errors caused by measurement location offsets. For example, in a new energy grid-connected system, the PCC point can be the boundary between the photovoltaic inverter, wind power converter, and weak grid, and its electrical characteristics directly determine the system stability.

[0031] The predetermined disturbance frequency refers to a specific frequency point preset and stored within the unified power quality regulator. Multiple predetermined disturbance frequencies can be used to cover the risk frequency bands of subsynchronous (e.g., 5–30Hz) and supersynchronous (e.g., 60–150Hz) oscillations. This enables precise excitation and response capture of wide-band oscillation modes. For example, traditional methods only detect power frequency or a single frequency point, while this solution can simultaneously identify multimodal oscillation risks through multi-frequency disturbances.

[0032] Among them, disturbance current refers to a periodic current signal with controllable amplitude and known frequency actively injected by a unified power quality regulator. It can be used as a probe to stimulate the system impedance response without affecting the normal operation of the system. For example, by injecting small signal disturbances such as 10Hz, 80Hz, and 120Hz, the system can be safely excited dynamically without triggering protection actions.

[0033] Among them, voltage and current signals refer to the three-phase instantaneous electrical quantities collected from the common coupling point, the grid side, and the load side, respectively. They can provide complete input and output response data of the system under disturbance excitation. For example, after the three signals are sampled synchronously, the excitation response relationship can be constructed, providing the original data basis for subsequent impedance modeling.

[0034] In this step, the unified power quality regulator injects multi-frequency disturbance current into the PCC point without interrupting the power supply, and simultaneously collects three key electrical signals.

[0035] This step enables active excitation of the system impedance response and closed-loop acquisition of multi-point responses, providing high signal-to-noise ratio, high synchronization, and full-band coverage raw data support for subsequent impedance modeling.

[0036] Step S104: Determine the source impedance on the grid side and the load impedance on the load side based on the common coupling point voltage signal, the grid side current signal and the load side current signal.

[0037] Among them, source impedance refers to the equivalent impedance seen from the common coupling point to the grid side. It reflects the dynamic impedance characteristics of the grid-side converters, transformers, lines, etc. It can quantify the strength and stiffness of the grid. For example, a weak grid exhibits high inductance and low amplitude source impedance, which is prone to oscillation.

[0038] Load impedance refers to the equivalent impedance seen from the common coupling point to the load side. It reflects the dynamic input characteristics of the inverter, motor, and power electronic equipment at the load end and can reveal the feedback effect of the load on system stability. For example, a high proportion of power electronic loads exhibits negative impedance characteristics, which can easily induce instability.

[0039] In this step, the three synchronization signals acquired by S102 are used to calculate the frequency domain complex expressions of the source impedance and the load impedance, respectively.

[0040] This step enables independent, synchronous, and high-precision identification of the impedances on both the power supply side and the load side. It breaks through the cognitive blind spot of traditional single-ended measurement methods, which can only obtain total impedance or single-sided impedance. This lays a physically interpretable and mathematically computable two-ended data foundation for building a source-network-load interaction model.

[0041] Step S106: Determine the hysteresis matrix based on the source impedance and load impedance, wherein the hysteresis matrix characterizes the impedance interaction strength and phase coupling relationship between the grid side and the load side.

[0042] The hysteresis matrix, a complex matrix composed of source impedance and load impedance, can quantitatively describe the bidirectional coupling strength of how grid disturbances are amplified by the load and how load fluctuations are fed back by the grid.

[0043] Among them, impedance interaction strength refers to the magnitude of each element in the hysteresis matrix, which reflects the degree of energy transmission and feedback between the source and load in the system. It can identify whether there is a risk of negative impedance oscillation. For example, when the load impedance is capacitive and the source impedance is inductive, the phase difference between the two is close to 180°, the amplitude of the hysteresis matrix increases sharply, and the system is prone to oscillation.

[0044] Among them, the phase coupling relationship refers to the phase angle difference of each element in the hysteresis matrix, which reflects the timing lag and lead characteristics of the impedance dynamic response. It can reveal the lag and lead mismatch mechanism of the system dynamic response. For example, if the load response lags the grid disturbance by 90°, the system exhibits a purely inductive unstable trend.

[0045] In this step, the source impedance and load impedance obtained in S104 are used to construct a hysteresis matrix through matrix operations.

[0046] This step transforms the two isolated sets of impedance data into a system-level interaction model that reflects the bidirectional dynamic game between the source and the load. It achieves a leap from single-point impedance to a system interaction matrix, solving the structural defect of traditional Bode plots that only analyze open-loop gain and ignore closed-loop feedback paths. It provides core parameters with clear physical meaning and complete mathematical structure for subsequent stability criteria.

[0047] Step S108: Based on the return rate matrix, determine the first eigenvalue and the second eigenvalue, wherein the first eigenvalue reflects the feedback response capability of the grid side to the fluctuations of the load side, and the second eigenvalue reflects the reverse coupling capability of the load side to the fluctuations of the grid side.

[0048] Among them, the first eigenvalue, λ1, is the principal eigenvalue of the reciprocity matrix L(s), which corresponds to the unidirectional dominant mode of the power grid and the load. It can quantify the power grid system's ability to suppress or amplify load disturbances. For example, if |λ1|>1 and the phase is close to 180°, it indicates that the power grid feedback is positive feedback and the system is prone to instability.

[0049] Among them, the second eigenvalue, λ2, refers to the secondary eigenvalue of the cyclicity matrix L(s), which corresponds to the load and the grid reverse dominant mode. It can reveal the load equipment's ability to reverse the disturbance of grid fluctuations. For example, in a multi-inverter parallel system, a large λ2 amplitude indicates that there is a group synchronous oscillation trend at the load end.

[0050] Eigenvalues ​​refer to the complex roots obtained after eigenvalue decomposition of the eigenvalue matrix. They can extract the intrinsic modes of the dynamic behavior of the system. For example, in MIMO systems, eigenvalues ​​replace traditional scalar gains and can accurately describe the stability boundary under multivariable coupling.

[0051] In this step, the eigenvalue decomposition of the return matrix L(s) is performed to obtain two complex eigenvalues, λ1 and λ2.

[0052] This step reduces the high-dimensional impedance interaction model to two key modal indices, enabling the separation of primary and secondary causes in complex multivariable systems. It solves the averaging distortion problem when traditional methods describe multimodal systems using a single phase margin, thus enabling stability assessment to move from fuzzy empirical judgment to modal-level precise diagnosis.

[0053] Step S110: Based on the first eigenvalue and the second eigenvalue, determine the first Nyquist curve corresponding to the first eigenvalue and the second Nyquist curve corresponding to the second eigenvalue, wherein the Nyquist curve represents the complex response trajectory of the hysteresis matrix at a specific frequency.

[0054] The first Nyquist curve refers to the trajectory formed by the change of the first eigenvalue λ1 with frequency. It can be used to specifically evaluate the power grid's ability to resist load disturbances. For example, if the curve is far away from the point (-1,j0), it indicates that the power grid has strong damping capability.

[0055] The second Nyquist curve, which is the trajectory formed by the change of the second eigenvalue λ2 with frequency, can be specifically used to assess the reverse impact of load on grid disturbances. For example, if the curve is close to the point (-1, j0), it indicates that there is a potential resonance risk at the load end.

[0056] Among them, the complex response trajectory refers to the path of the characteristic value that changes continuously with frequency in the complex plane. It can reflect the continuous evolution characteristics of the dynamic behavior of the system, such as identifying the segmented risks of low-frequency stability, mid-frequency criticality, and high-frequency oscillation.

[0057] In this step, two independent Nyquist curves are plotted using λ1 and λ2 as inputs, respectively.

[0058] This step enables the first-ever visualization of dual-modal-hyperbolic stability diagnosis, overcoming the shortcomings of traditional single Bode curves that cannot distinguish between source / carrier dominant modes and misjudge risk sources.

[0059] Step S112: Determine the stability result of the power system at a predetermined disturbance frequency based on the first Nyquist curve and the second Nyquist curve.

[0060] Among them, the stability result refers to the binary determination (stable / unstable) of whether the system is closed-loop stable based on the generalized Nyquist criterion, and the stability margin can be quantified (such as the minimum distance to (-1,j0)). It can provide operators with quantifiable safety boundaries. For example, if neither curve encloses (-1,j0), the system is stable across the entire frequency band; if either curve encloses it, the control parameters need to be adjusted accordingly.

[0061] In this step, the geometric positions of the two Nyquist curves are combined, and a final stability decision is made based on the generalized Nyquist criterion.

[0062] This step constructs a complete closed-loop analysis chain from data acquisition, impedance modeling, interactive modeling, mode separation, trajectory visualization, and stability determination, enabling integrated intelligent assessment of broadband oscillation risks in power systems, including diagnosis, location, quantification, and decision-making.

[0063] Through steps S102-S112 above, in the power system, after injecting a disturbance current corresponding to a predetermined disturbance frequency into the point of common coupling (PCC), the PCC voltage signal, grid-side current signal, and load-side current signal are obtained. The PCC is the electrical coupling node between the grid side and the load side, and a predetermined disturbance frequency is set in the unified power quality conditioner. Based on the PCC voltage signal, grid-side current signal, and load-side current signal, the source impedance of the grid side and the load impedance of the load side are determined. Based on the source impedance and load impedance, a hysteresis matrix is ​​determined, where the hysteresis matrix represents the impedance between the grid side and the load side. The interaction strength and phase coupling relationship are determined. Based on the hysteresis matrix, a first eigenvalue and a second eigenvalue are determined, where the first eigenvalue reflects the feedback response capability of the grid side to load-side fluctuations, and the second eigenvalue reflects the reverse coupling capability of the load side to grid-side fluctuations. Based on the first and second eigenvalues, a first Nyquist curve corresponding to the first eigenvalue and a second Nyquist curve corresponding to the second eigenvalue are determined, where the Nyquist curve represents the complex response trajectory of the hysteresis matrix at a specific frequency. Based on the first and second Nyquist curves, the stability result of the power system at a predetermined disturbance frequency is determined. By employing an online dual-ended impedance detection method based on a unified power quality regulator (UPQC), a disturbance current is injected at the common coupling point, and electrical response signals from the grid side and the load side are acquired simultaneously. A hysteresis matrix is ​​constructed, and a dual Nyquist curve is plotted based on its eigenvalues. This achieves the goal of high-precision quantitative characterization and closed-loop stability discrimination of the impedance interaction characteristics between the grid side and the load side. Thus, it realizes the technical effect of wide-band system stability self-diagnosis without changing the original power quality regulation function of the UPQC. This solves the technical problem in related technologies that have strong limitations in determining whether a power system is stable and make it difficult to accurately assess the true degree of stability.

[0064] As an optional embodiment, determining the stability result of the power system at a predetermined disturbance frequency based on the first Nyquist curve and the second Nyquist curve includes: determining a target critical point corresponding to a target Nyquist curve, wherein the target Nyquist curve includes at least one of the following: a first Nyquist curve and a second Nyquist curve; determining whether the target Nyquist curve encloses the target critical point; and determining the stability result based on the enclosed result.

[0065] Among them, the target Nyquist curve refers to any curve selected for stability judgment in the dual Nyquist curve system (i.e., the first Nyquist curve or the second Nyquist curve), which can achieve independent stability assessment of a single dominant mode in the system and avoid the ambiguity of the criteria and the masking of risks caused by the merging analysis of the two curves. For example, when only the grid side’s ability to suppress load disturbances is considered, the first Nyquist curve can be selected alone for judgment to focus on the core risk source.

[0066] Among them, the target critical point, such as a fixed reference point (-1,j0) on the complex plane, can be used to establish a qualitative benchmark for determining whether the closed-loop system is stable. It can provide a unified, objective, and physically meaningful stability boundary for all eigenvalue trajectories. For example, regardless of whether the system is single-variable or multi-variable, as long as any eigenvalue trajectory surrounds the point counterclockwise, the system has an unstable mode.

[0067] Among them, the encirclement result refers to the binary output (encirclement / non-encirclement) of whether the target Nyquist curve completely surrounds the target critical point in a counterclockwise direction, which is determined by a geometric judgment algorithm (such as the amplitude-phase trajectory crossing method or the complex integral method). It can transform the complex dynamic system stability problem into a computable, automated, and standardized geometric criterion. For example, in embedded controllers, only the point sampling point of the curve needs to be judged to be inside the polygon to achieve millisecond-level stability diagnosis.

[0068] Among them, stability results refer to the final judgment on whether the system is closed-loop stable based on the encirclement results, and can further quantify the stability margin. This can provide operators with clear, operable and quantifiable decision-making basis. For example, if the first curve does not encircle the system but the second curve does, it is determined that the load-side oscillation risk is high, and the load-side control parameters should be adjusted first, rather than blindly enhancing the grid-side filtering.

[0069] In this embodiment, the closed-loop stability of the system can be simplified: if the Nyquist curve of the L(s) characteristic function does not encircle the critical point counterclockwise, the system is stable. Furthermore, the greater the distance between the Nyquist curve and the critical point, the higher the system's stability margin and the stronger its ability to resist disturbances such as broadband oscillations, thus providing a more robust guarantee for the safe and reliable operation of the power system. This is significantly simpler than the requirement that the system maintains closed-loop stability only if the total number of counterclockwise rotations of the Nyquist curve of the L(s) characteristic function around the critical point is equal to the total number of poles in the right half-plane. The system stability determination no longer relies on complex counting of the number of rotations of the Nyquist curve of the characteristic value, nor does it require global spectral analysis of the system's pole distribution. Since the grid-side source impedance Zsdq and the load-side load impedance Zldq both naturally possess inherent stability under independent operating conditions, meaning neither has poles on the right half-axis of the complex plane, the closed-loop transfer function of the entire source-load interaction system also has no poles in the right half-plane. Therefore, the complex condition in the generalized Nyquist criterion that the number of counterclockwise encirclements equals the number of poles in the right half-plane can be simplified to: the system is closed-loop stable as long as the Nyquist curve of any characteristic function of the lapis latitude matrix L(s) does not encircle the critical point counterclockwise. This approach fundamentally simplifies the process from high-dimensional complex analysis to single-point geometric determination, transforming the mathematical derivations that previously required complex integrals, pole location, and multivariate trajectory tracking into a visual criterion that can be directly interpreted graphically in the engineering field. This simplification not only significantly reduces the computational burden on the controller and dramatically improves real-time diagnostic speed, but also allows maintenance personnel to intuitively judge the system status through a human-machine interface without needing to master complex control theory.

[0070] Furthermore, this simplified criterion naturally supports the quantitative assessment of stability margin. The minimum Euclidean distance between the curve and the critical point can be directly used as a stability margin index. The larger the distance, the stronger the system's resistance to disturbances, thus providing an accurate and traceable optimization basis for dynamically adjusting controller parameters (such as damping, bandwidth, and filter gain). Compared to the traditional Bode plot phase margin method, which is prone to misjudgment due to non-minimum phase and multi-mode coupling interference, the simplified criterion of this scheme has clear physical meaning, wide applicability, and strong anti-interference ability. It is especially suitable for broadband oscillation diagnosis in high-proportion power electronics grid-connected scenarios such as wind power, photovoltaics, and energy storage.

[0071] As an optional embodiment, determining the stability result based on the enclosure result includes: if the enclosure result is enclosure, determining the stability result as a stable result indicating that the power system is unstable at a predetermined disturbance frequency; and / or, if the enclosure result is not enclosure, determining the stability result as a stable result indicating that the power system is stable at a predetermined disturbance frequency, and determining the stability index based on the distance between the nearest point in the target Nyquist curve and the target critical point, wherein the nearest point is the point in the target Nyquist curve closest to the target critical point.

[0072] Among them, the stability index refers to the stability margin index quantified by the Euclidean distance from the nearest neighbor point to the target critical point on the target Nyquist curve. It can extend the binary judgment of stability / instability to a continuous, quantifiable, and sortable stability assessment. For example, when the stability index is 0.3, the system is on the edge of critical stability; when the stability index is 1.2, the system has sufficient disturbance resistance and can guide the gradient optimization of control parameters.

[0073] The nearest point refers to the point on the complex plane of the Nyquist curve that is closest to (-1,j0) among all the sampling points. It can accurately capture the coupling strength of the system at the most dangerous frequency point. For example, even if the curve is far away from the critical point, if the nearest point is close to (-1,j0), it indicates that the system has a potential oscillation risk in a certain frequency band, which needs to be taken seriously.

[0074] Among them, the encirclement result is called encirclement, which means that the target Nyquist curve completely surrounds the critical point in a counterclockwise direction. It can serve as a direct and deterministic criterion for system instability. For example, in broadband oscillation monitoring, once encirclement occurs, protection alarms or control interventions can be triggered immediately to avoid system collapse.

[0075] Among them, the encirclement result is not encircled, which means that the target Nyquist curve is not encircled counterclockwise throughout the entire frequency range. This can serve as a sufficient and necessary condition for the closed-loop stability of the system (based on the premise of inherent stability). For example, in new energy grid-connected power plants, this condition can serve as a hard indicator for grid access to ensure that the connected equipment does not cause oscillations.

[0076] In this embodiment, stability assessment no longer relies on complex counting of the number of times the Nyquist curve circles or theoretical assumptions about pole distribution. Instead, it directly outputs a binary conclusion based on the geometric criterion of whether the curve encircles the critical point counterclockwise: if the curve encircles the critical point at any disturbance frequency, the system is clearly unstable in that frequency band; if it does not encircle the critical point at all, the system is stable. Furthermore, the nearest neighbor point with the smallest distance to the critical point among all sampling points on the Nyquist curve is extracted, and the Euclidean distance from this point to the critical point is calculated as a stability index. This value is a real number and directly reflects the system's margin at the most dangerous frequency point.

[0077] This approach transforms stability assessment from a passive yes / no judgment into an active quantitative output of stability and margin values. For example, when the stability index is 0.25, the system is on the edge of critical stability, and the controller can automatically activate the damping enhancement strategy; when the index is 1.5, the system has sufficient safety margin and requires no intervention. This mechanism requires no additional simulation, no curve fitting, and no eigenvalue decomposition; it can be completed solely through real-time calculation of the coordinates of sampling points, resulting in extremely low computational load. It can be completed within 50ms using fixed-point arithmetic in the UPQC embedded controller. The stability index can also be directly used as an input parameter for the control strategy, such as for dynamically adjusting the proportional gain of the parallel-side current loop, adjusting the filter cutoff frequency, or triggering disturbance suppression commands. This truly realizes the closed-loop response of the criterion as the control command, solving the engineering gap problem of traditional methods where instability is known but the adjustment amount and timing are unknown. This transforms stability analysis from post-diagnosis to a core function of real-time self-healing.

[0078] As an optional embodiment, the source impedance on the grid side and the load impedance on the load side are determined based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal. This includes: acquiring the common coupling point voltage signal, the grid-side current signal, and the load-side current signal corresponding to multiple disturbance injections; determining the grid-side parameters and load-side parameters based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal corresponding to multiple disturbance injections, and the correspondence between voltage, current, and impedance. The grid-side parameters include the d-axis impedance characteristic parameters, the d-axis impedance coupling characteristic parameters, the q-axis impedance coupling characteristic parameters, and the q-axis impedance characteristic parameters. The load-side parameters include the d-axis impedance characteristic parameters, the d-axis impedance coupling characteristic parameters, and the q-axis impedance coupling characteristic parameters. The source impedance is determined based on the grid-side parameters, and the load impedance is determined based on the load-side parameters.

[0079] Among them, the impedance characteristic parameter of the grid side d-axis to d-axis refers to the self-impedance component of the grid side d-axis current change to d-axis voltage response in the dq rotating coordinate system. It can reflect the voltage support capability of the grid under active power fluctuations. For example, the larger the value of this parameter, the more rigid the grid is and the stronger its resistance to active power disturbances.

[0080] Among them, the impedance coupling characteristic parameter of the d-axis to the q-axis on the grid side refers to the cross-coupling response of the d-axis current disturbance on the grid side to the q-axis voltage. It can reveal the asymmetric and nonlinear dynamic behavior of the grid. For example, when this parameter is significantly non-zero, it indicates that there is asymmetric grounding or control loop coupling in the grid, which can easily induce oscillations.

[0081] Among them, the impedance coupling characteristic parameter of the q-axis to the d-axis on the grid side refers to the reverse coupling response of the q-axis current disturbance on the grid side to the d-axis voltage. It can characterize the dynamic interaction between reactive and active power in the grid. For example, in a weak grid, this parameter is often negative, reflecting the reverse disturbance of voltage regulation to reactive power injection, which is one of the causes of oscillation.

[0082] Among them, the grid-side q-axis impedance characteristic parameter refers to the self-impedance component of the grid-side q-axis voltage response to the change of q-axis current. It can quantify the relationship between the grid reactive power support characteristics and voltage stability. For example, when this parameter is capacitive, it is easy to form a resonant circuit with the inverter control delay.

[0083] Among them, the load-side parameters refer to the four independent components of the four-dimensional impedance matrix of the load end in the dq coordinate system. They can fully characterize the complex dynamic characteristics of power electronic loads, such as asymmetry, non-minimum phase, and negative impedance. For example, photovoltaic inverters often exhibit negative qq impedance under weak grid conditions, which is a typical cause of broadband oscillation.

[0084] In this embodiment, current disturbances are injected sequentially at multiple preset disturbance frequencies, and the instantaneous three-phase waveforms of the common coupling point voltage, grid-side current, and load-side current are collected for each disturbance. By utilizing the instantaneous correspondence between voltage and current, the eight-dimensional impedance parameter matrix of the grid side and the load side in the dq coordinate system is directly solved. That is, each side contains four independent complex parameters: dd self-impedance, dq coupling, qd coupling, and qq self-impedance, for a total of eight physical quantities. This method does not rely on any equivalent circuit model or simplification assumptions, but instead constructs multiple sets of linear equations to solve all parameters at once, thereby fully characterizing the bidirectional asymmetric dynamic coupling characteristics between the source end and the load end in the active and reactive power channels.

[0085] This approach elevates impedance identification from traditional single-axis average or scalar impedance to full-dimensional, multi-channel, physically interpretable matrix modeling. For example, when Zl_qq on the load side is negative and has a large amplitude, it can be clearly identified as a negative impedance oscillation source caused by the current loop delay in the photovoltaic inverter. When Zs_qd on the grid side is significantly non-zero, the reverse coupling interference of the reactive power compensation device at the grid connection point to the active voltage can be identified. These parameters are directly mapped to specific adjustment links in the UPQC control loop, which can guide the controller to specifically enhance d-axis damping, suppress qd coupling feedback, or adjust the reactive power reference. This truly achieves precise intervention by changing the control parameters wherever impedance is abnormal, completely eliminating the fuzzy diagnostic dilemma of traditional methods where the system is unstable but the cause is unknown and cannot be located. This significantly improves the UPQC's ability to trace the source of broadband oscillations and the accuracy of closed-loop control in complex weak grid scenarios.

[0086] As an optional embodiment, determining the source impedance on the grid side and the load impedance on the load side based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal includes: transforming the common coupling point voltage signal, the grid-side current signal, and the load-side current signal to a two-phase rotating coordinate system to obtain the common coupling point two-phase voltage signal, the grid-side two-phase current signal, and the load-side two-phase current signal; performing Fast Fourier Transform on the common coupling point two-phase voltage signal, the grid-side two-phase current signal, and the load-side two-phase current signal to obtain the common coupling point frequency domain voltage signal, the grid-side frequency domain current signal, and the load-side frequency domain current signal in the frequency domain; and determining the grid-side source impedance and the load-side load impedance based on the common coupling point frequency domain voltage signal, the grid-side frequency domain current signal, and the load-side frequency domain current signal.

[0087] Among them, the two-phase rotating coordinate system refers to the conversion of voltage and current signals in the three-phase stationary coordinate system to the dq coordinate system that rotates synchronously with the power grid through the abc / dq coordinate transformation. This can eliminate the influence of time-varying and asymmetrical components in the three-phase system and realize steady-state equivalent modeling of AC quantities. For example, in the dq coordinate system, the sinusoidal signal becomes a DC component, which is convenient for subsequent frequency domain analysis.

[0088] The Fast Fourier Transform (FFT) refers to the spectral decomposition of voltage and current signals in the dq coordinate system, extracting the amplitude and phase of each disturbance frequency component. It can separate the mixed response signal in the time domain into response spectra at independent frequency points. For example, when 10Hz, 80Hz, and 120Hz disturbances are injected, FFT can extract the voltage and current responses at the corresponding frequencies respectively, avoiding spectral aliasing.

[0089] Among them, the voltage and current signals in the frequency domain refer to the complex form of voltage and current amplitude-phase spectra obtained after FFT transformation, which can be directly used for frequency domain impedance calculation Z(f)=V(f) / I(f). For example, at 10Hz, if V_d=0.5∠15° and I_d=0.2∠-5°, then Z_d=2.5∠20° can be directly calculated to obtain the complex impedance at that frequency point.

[0090] In this embodiment, for example, the UPQC sampling system collects 128 points per cycle at a sampling rate of 6.4kHz. It performs synchronous dq transformation on each group of three-phase signals (phase-locked loop accuracy ±0.1°), and then performs 128-point FFT on the transformed Vd, Vq, Id, and Iq signals respectively. Only the spectral components of the specified disturbance frequency points (such as 10Hz, 50Hz, 80Hz, and 120Hz) are retained, and the other frequency components are discarded. Only the complex voltage and current of these four frequency points are used to calculate eight impedance parameters.

[0091] This method transforms the three-phase common coupling point voltage, grid-side current, and load-side current into a synchronously rotating dq coordinate system, eliminating time-varying coupling errors caused by phase shift, imbalance, and harmonic interference in the three-phase system. This converts the originally complex AC time-domain signal into a stable DC component and a controllable disturbance component. Then, precise Fast Fourier Transform (FFT) is performed on the dq-axis components, extracting only the complex amplitude and phase of the frequency domain at preset disturbance frequencies (e.g., 10Hz, 50Hz, 80Hz, 120Hz), directly avoiding noise and harmonic interference in non-target frequency bands, ensuring... Each voltage and current pair corresponds to a pure response at a single frequency. Based on this, the four-dimensional impedance parameters of the grid side and the load side in the d-axis and q-axis directions are calculated by directly dividing the complex voltage in the frequency domain by the complex current in the corresponding frequency domain. The entire process requires no filter design, no moving average, and no curve fitting. It is completed entirely based on the original sampling points and standard mathematical operations. This provides a real, reliable, reusable, and engineering-deployable underlying data foundation for subsequent hysteresis matrix construction and stability criteria. It completely solves the engineering pain points of existing methods, such as impedance distortion and misjudgment of oscillation caused by signal aliasing, phase distortion, and noise.

[0092] As an optional embodiment, determining the hysteresis matrix based on the source impedance and the load impedance includes: performing a ratio calculation between the source impedance and the load impedance to determine the hysteresis matrix.

[0093] Among them, ratio operation refers to the high-dimensional expansion of impedance ratio by multiplying the source impedance matrix by the inverse of the load impedance matrix at the matrix operation level. This can extend the scalar impedance ratio to a multivariable, multi-channel, coupled system-level interactive model.

[0094] In this embodiment, the hysteresis matrix is ​​not derived theoretically or constructed by a simplified model, but is directly generated by precise numerical comparison calculation of the measured impedance characteristics of the power supply side and the load side, thus fully preserving the mutual influence relationship between the active and reactive power channels.

[0095] This approach transforms the system from representing the overall impedance relationship with a single numerical value to comprehensively characterizing the interaction between the power supply and the load across four key dynamic dimensions: active power response to active power, active power interference to reactive power, reactive power feedback to active power, and reactive power support capability to reactive power. Each value in this matrix corresponds to a ratio of actual measured data, thus accurately reflecting which part of the system exhibits abnormal coupling. For example, when the load's reactive power feedback to the power supply is excessively strong, it will be directly reflected at a specific location in the matrix, enabling engineers to quickly pinpoint the root cause of the disturbance. The resulting hysteresis matrix is ​​no longer an abstract symbol but a physical dimensional result that can be directly used for stability assessment. This transforms subsequent stability analysis from experience-based judgment to data-driven analysis, improving the accuracy of diagnosis and the targeted nature of control adjustments, truly achieving a closed-loop engineering process of accurate measurement, clear calculation, and correct rectification.

[0096] Based on the above embodiments and optional embodiments, an optional implementation method is provided, which is described in detail below.

[0097] Based on the analysis of relevant technologies, it was found that the low accuracy was due to the inability to fully reflect the interaction between the grid-side and load-side impedances. To address the problem that traditional single-ended impedance measurement methods cannot fully reflect this interaction, an optional embodiment of this invention uses a Unified Power Quality Regulator (UPQC) as a two-ended impedance measurement tool. This allows the UPQC to perform its original functions while also analyzing the system's stability online, enabling timely adjustments to the grid impedance. The UPQC itself has the functional characteristics of real-time monitoring and compensation for voltage sags, swells, harmonics, and imbalances, as well as rapid detection and suppression of harmonic currents generated by the load, and dynamic adjustment of reactive power to improve the power factor. An optional embodiment of this invention utilizes its parallel-side current injection function to achieve two-ended measurement of both grid-side and load-side impedances, and based on this, plots a Nyquist curve to determine system stability. Figure 2 This is a schematic diagram of the UPQC main circuit topology provided by an optional embodiment of the present invention; Figure 3 This is a flowchart of a two-terminal impedance measurement process provided by an optional embodiment of the present invention; Figure 4 This is an equivalent diagram of parallel-side injection provided by an optional embodiment of the present invention; Figure 5 This is a block diagram of the UPQC series-side control provided by an optional embodiment of the present invention; Figure 6 This is a block diagram of the parallel-side control of UPQC provided by an optional embodiment of the present invention. It will be described below.

[0098] like Figure 2The UPQC (Unified Power Quality Controller) shown mainly consists of three parts: a series converter, a parallel converter, and a DC energy storage unit. The series converter is connected in series between the grid and the load via a transformer, while the parallel converter is connected in parallel to the grid side. The DC energy storage unit serves as a common DC bus for both the series and parallel converters, providing stable DC voltage support. The control and detection system monitors grid voltage, current, and other electrical quantities in real time. After signal processing and analysis, it provides precise control commands to the converters, coordinating the collaborative work of the series and parallel converters, thereby achieving comprehensive management of voltage and current quality and optimization of source-grid interaction stability. Addressing the problem that traditional single-ended impedance measurement methods cannot fully reflect the interaction between grid-side and load-side impedances, an optional implementation of this invention utilizes the current injection function of the UPQC parallel side to achieve dual-ended measurement of grid-side and load-side impedances. Based on this, a Nyquist curve is plotted to determine system stability. The flowchart is shown below. Figure 3 As shown, the specific operation steps are as follows:

[0099] 1) Set the UPQC system parameters and specify the disturbance frequency array;

[0100] 2) Inject disturbance current (same as the disturbance current corresponding to the predetermined disturbance frequency mentioned above) into the parallel side of UPQC, and detect and record the three-phase voltage at the common coupling point (PCC point). and the current after the disturbance is injected on the load side Source-side current (Same as the voltage signal at the common coupling point, the grid-side current signal, and the load-side current signal mentioned above).

[0101] 3) Convert the two sets of three-phase currents and the voltage at point PCC to voltage in a rotating coordinate system using the abc / dq transformation. and current (As mentioned above, the voltage signal at the common coupling point, the grid-side current signal, and the load-side current signal will be transformed into a two-phase rotating coordinate system to obtain the two-phase voltage signal at the common coupling point, the two-phase current signal on the grid side, and the two-phase current signal on the load side.)

[0102] 4) Perform FFT analysis on the two sets of three-phase currents and the voltage signal at the PCC point after conversion, and convert the time domain signal into the frequency domain signal (similar to the above, perform fast Fourier transform on the two-phase voltage signal at the common coupling point, the two-phase current signal on the grid side and the two-phase current signal on the load side to obtain the frequency domain voltage signal at the common coupling point, the frequency domain current signal on the grid side and the frequency domain current signal on the load side).

[0103] 5) Calculate the source impedance and load impedance using the formula. (As mentioned above, the source impedance on the grid side and the load impedance on the load side are determined based on the frequency domain voltage signal at the common coupling point, the frequency domain current signal on the grid side, and the frequency domain current signal on the load side.)

[0104] 6) Calculate the hysteresis matrix, which is the ratio of source impedance to load impedance L(s) (similar to the above calculation of the ratio of source impedance to load impedance to determine the hysteresis matrix).

[0105] 7) Calculate the corresponding eigenvalues ​​based on the obtained return matrix. (As mentioned above, the first and second eigenvalues ​​are determined based on the return matrix.)

[0106] 8) Plot the Nyquist curve of the system based on the eigenvalues ​​and analyze the stability of the system (same as above, based on the first eigenvalue and the second eigenvalue, determine the first Nyquist curve corresponding to the first eigenvalue and the second Nyquist curve corresponding to the second eigenvalue; based on the first Nyquist curve and the second Nyquist curve, determine the stability result of the power system under the predetermined disturbance frequency).

[0107] In step 1), the system topology parameters and control algorithm parameters are reasonably set according to the actual power grid operating conditions and the characteristics of UPQC equipment. At the same time, based on the common frequency range of wideband oscillation, a disturbance frequency array including subsynchronous and supersynchronous frequency bands is preset to provide a benchmark for subsequent testing.

[0108] In step 2), after the disturbance current is injected on the parallel side of UPQC, the current will be split at the PCC point, with one part flowing to the grid side and the other part flowing to the load side, such as... Figure 4 As shown, the source impedance and load impedance are calculated by detecting the voltage at the common port and the current on the source and load sides. When the parallel-side converter injects a current disturbance, the series-side converter provides a stable voltage to the DC-side capacitor, i.e., as shown... Figure 5 , Figure 6 As shown in the series-parallel control strategy, the series-side DC voltage regulator switch S1 is closed, the series-side command voltage switch S2 is open, the parallel-side DC voltage regulator switch S3 is open, and the parallel-side disturbance injection switch S4 is closed.

[0109] In step 3), since the interface voltage and current in a three-phase AC system are time-varying and the system does not have a stable static operating point, and the switching characteristics and control strategies of the inverter itself are different, the equivalent source impedance and load impedance may also be time-varying. Therefore, in order to perform a more accurate system impedance stability analysis, it is necessary to transform the three-phase AC signal from the static abc coordinate system to the dq synchronous coordinate system.

[0110] In step 4), the Fast Fourier Transform (FFT) algorithm is used to perform spectral analysis on the voltage and current signals in the rotating coordinate system, extract the amplitude and phase information corresponding to each disturbance frequency, and realize the conversion from the time domain to the frequency domain.

[0111] In step 5), based on the two injected signals, and using circuit theory and the measured frequency domain voltage and current data, the impedance matrix on the grid side is calculated by substituting the pre-derived impedance calculation formula. (The same four parameters as the source impedance mentioned above) (Similar to the above-mentioned d-axis to d-axis impedance characteristics, d-axis to q-axis impedance coupling characteristics, q-axis to d-axis impedance coupling characteristics, and q-axis to q-axis impedance characteristics) and the load-side impedance matrix. (The same four parameters as the load impedance mentioned above) (The impedance characteristics of the load side d-axis to d-axis, the impedance coupling characteristics of the load side d-axis to q-axis, the impedance coupling characteristics of the load side q-axis to d-axis, and the impedance characteristics of the load side q-axis to q-axis) can be obtained according to Ohm's law, i.e., the relationship between voltage, current, and impedance:

[0112] (1)

[0113] In the formula, This represents the d-axis component of the voltage at point PCC. This represents the q-axis component of the voltage at point PCC. This represents the d-axis component of the source-side current. This represents the q-axis component of the source-side current. This represents the d-axis component of the load-side current after the injected disturbance. This represents the q-axis component of the load-side current after the injected disturbance.

[0114] Source impedance and load impedance From equations (2) and (3), it can be seen that:

[0115] (2)

[0116] (3)

[0117] Based on the two injected signals, the source impedance matrix parameters can be obtained by solving equations (4), (5), (6), and (7). Load impedance matrix parameters :

[0118] (4)

[0119] (5)

[0120] (6)

[0121] (7)

[0122] In the formula, U d1 U q1 This represents the dq-axis component of the grid-side voltage after the first set of disturbance current signals is injected into the load side. d2 U q2 This represents the component of the grid-side voltage on the dq axis after the second set of disturbance current signals is injected into the load side; The four parameters representing the source impedance matrix; I sd1 I sq1 This represents the dq-axis component of the grid-side current detected after the first set of disturbance current signals is injected into the load side. sd2 I sq2 This represents the component of the grid-side current on the dq axis detected after the second set of disturbance current signals is injected into the load side;

[0123] The four parameters representing the load impedance matrix; I ld1 I lq1 This represents the dq-axis component of the load-side current detected after the first set of disturbance current signals is injected onto the load side. ld2 I lq2 This represents the component of the load-side current on the dq axis detected after the second set of disturbance current signals is injected into the load side.

[0124] In step 6), the source impedance obtained in step 5) is compared with the load impedance based on the known parameters, and the return matrix L(s) is constructed as shown in equation (8). This matrix reflects the impedance interaction relationship between the source and the load, and provides core parameters for system stability analysis.

[0125] (8)

[0126] In step 7), the eigenvalues ​​are calculated based on the return matrix. Formula (9) is shown below:

[0127] (9)

[0128] In the formula, These represent two eigenvalues ​​calculated from the return matrix. These are the four parameters of the return matrix.

[0129] In step 8), the Nyquist curve is plotted based on the eigenvalues. Based on the generalized Nyquist stability criterion, the closed-loop stability of the system is closely related to the characteristics of the Nyquist curve of the eigenfunction function of the lapis latitude matrix L(s). The stability is determined if and only if the sum of the number of counterclockwise rotations of the Nyquist curve of the L(s) eigenfunction around the critical point (-1, j0) is equal to the sum of the eigenvalues. The system can only maintain closed-loop stability when the total number of poles in the right half-plane is equal. In actual power systems, the grid and inverters both possess inherent stability under independent operating conditions, meaning that Zsdq and Zldq do not have poles in the right half-plane. Therefore, the closed-loop stability of the system can be simplified as follows: if the Nyquist curve of the L(s) characteristic function does not encircle the critical point (-1, j0) counterclockwise, then the system is stable. Furthermore, the greater the distance between the Nyquist curve and the critical point (-1, j0), the higher the stability margin of the system and the stronger its ability to resist disturbances such as broadband oscillations, thus providing a more solid guarantee for the safe and reliable operation of the power system.

[0130] The above optional implementation methods can achieve at least the following beneficial effects:

[0131] This invention, without altering the core functions of UPQC such as voltage compensation, harmonic suppression, and reactive power regulation, innovatively adds the function of dual-end measurement of grid-side impedance and load-side impedance. This provides a pathway for online impedance interaction analysis and stability assessment, upgrading UPQC from a single power quality management device into an intelligent device with system stability analysis capabilities. This significantly enhances the power system's ability to cope with the broadband oscillation risks of new energy grid integration, and substantially improves the safety and economy of grid operation. Compared to traditional single-end measurements, which only obtain information from a single node and cannot reflect the source-load impedance interaction, this invention, by constructing a systematic measurement and analysis process within the UPQC, can accurately capture the dynamic interaction characteristics of power source-side and load-side impedance, providing more comprehensive data support for system stability assessment. Simultaneously, the impedance ratio stability criterion solves the problem that the traditional Bode plot phase margin method cannot accurately assess the actual stability of complex power electronic systems. By combining the hysteresis matrix with the Nyquist criterion, high-precision quantitative analysis of system stability is achieved, effectively improving the accuracy and reliability of the assessment.

[0132] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0133] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods according to the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0134] Example 2

[0135] According to an embodiment of the present invention, a unified power quality conditioner is also provided, comprising:

[0136] The acquisition module is used to acquire the voltage signal of the common coupling point, the grid-side current signal, and the load-side current signal in the power system after injecting a disturbance current corresponding to a predetermined disturbance frequency into the common coupling point. The common coupling point is the electrical coupling node between the grid side and the load side, and a predetermined disturbance frequency is set in the unified power quality conditioner. The first determination module is used to determine the source impedance of the grid side and the load impedance of the load side based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal. The second determination module is used to determine the hysteresis matrix based on the source impedance and the load impedance, where the hysteresis matrix characterizes the impedance interaction strength and phase coupling relationship between the grid side and the load side. The system is divided into five modules: a third determining module, used to determine a first eigenvalue and a second eigenvalue based on the hysteresis matrix, wherein the first eigenvalue reflects the feedback response capability of the grid side to fluctuations on the load side, and the second eigenvalue reflects the reverse coupling capability of the load side to fluctuations on the grid side; a fourth determining module, used to determine a first Nyquist curve corresponding to the first eigenvalue and a second Nyquist curve corresponding to the second eigenvalue based on the first eigenvalue and the second eigenvalue, wherein the Nyquist curve represents the complex response trajectory of the hysteresis matrix at a specific frequency; and a fifth determining module, used to determine the stability result of the power system at a predetermined disturbance frequency based on the first Nyquist curve and the second Nyquist curve.

[0137] It should be noted that the above modules correspond to steps S102 to S112 in the method for determining the stability of a power system. The instances and application scenarios implemented by multiple modules and their corresponding steps are the same, but are not limited to the content disclosed in Embodiment 1 above.

[0138] Example 3

[0139] According to another aspect of the present invention, a power system is also provided, comprising: a unified power quality conditioner, a grid side, and a load side, wherein the unified power quality conditioner performs the above-described method, and the unified power quality conditioner is connected between the grid side and the load side.

[0140] Example 4

[0141] According to another aspect of the present invention, an electronic device is also provided, comprising: a processor; and a memory for storing processor-executable instructions, wherein the processor is configured to execute instructions to implement the power system stability determination method of any of the above embodiments.

[0142] Example 5

[0143] According to another aspect of the present invention, a computer-readable storage medium is also provided, which, when the instructions in the computer-readable storage medium are executed by a processor of an electronic device, enables the electronic device to perform the power system stability determination method described above.

[0144] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0145] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0146] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling, direct coupling, or communication connection may be through some interfaces; the indirect coupling or communication connection between units or modules may be electrical or other forms.

[0147] 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 units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0148] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0149] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or 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, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0150] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for determining the stability of a power system, characterized in that, include: Applied to unified power quality conditioners, In a power system, after injecting a disturbance current corresponding to a predetermined disturbance frequency into a common coupling point, the voltage signal of the common coupling point, the grid-side current signal, and the load-side current signal are obtained. The common coupling point is the electrical coupling node between the grid side and the load side, and the predetermined disturbance frequency is set in the unified power quality regulator. Based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal, determine the source impedance on the grid side and the load impedance on the load side; Based on the source impedance and the load impedance, a hysteresis matrix is ​​determined, wherein the hysteresis matrix characterizes the impedance interaction strength and phase coupling relationship between the grid side and the load side; Based on the return rate matrix, a first eigenvalue and a second eigenvalue are determined, wherein the first eigenvalue reflects the feedback response capability of the power grid side to load-side fluctuations, and the second eigenvalue reflects the reverse coupling capability of the load side to power grid-side fluctuations. Based on the first eigenvalue and the second eigenvalue, a first Nyquist curve corresponding to the first eigenvalue and a second Nyquist curve corresponding to the second eigenvalue are determined, wherein the Nyquist curve represents the complex response trajectory of the retracement matrix at a specific frequency; Based on the first Nyquist curve and the second Nyquist curve, the stability result of the power system at the predetermined disturbance frequency is determined.

2. The method according to claim 1, characterized in that, Based on the first Nyquist curve and the second Nyquist curve, the stability result of the power system at the predetermined disturbance frequency is determined, including: Determine the target critical point corresponding to the target Nyquist curve, wherein the target Nyquist curve includes at least one of the following: a first Nyquist curve and a second Nyquist curve; Determine whether the target Nyquist curve encloses the target critical point; The stability result is determined based on the encirclement result.

3. The method according to claim 2, characterized in that, Based on the encirclement result, the stability result is determined, including: If the enclosure result is enclosed, the stability result is determined to be a stable result indicating that the power system is unstable at the predetermined disturbance frequency; and / or, If the encirclement result is not encircled, the stability is determined to be the stable result of the power system under the predetermined disturbance frequency, and the stability index is determined based on the distance between the nearest point in the target Nyquist curve and the target critical point, wherein the nearest point is the point in the target Nyquist curve that is closest to the target critical point.

4. The method according to claim 1, characterized in that, Based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal, the source impedance on the grid side and the load impedance on the load side are determined, including: Obtain the common coupling point voltage signal, the grid-side current signal, and the load-side current signal corresponding to multiple disturbance injections; Based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal corresponding to the multiple disturbance injections, and the correspondence between voltage, current, and impedance, the grid-side parameters and load-side parameters are determined. The grid-side parameters include the grid-side d-axis to d-axis impedance characteristic parameters, the grid-side d-axis to q-axis impedance coupling characteristic parameters, the grid-side q-axis to d-axis impedance coupling characteristic parameters, and the grid-side q-axis to q-axis impedance characteristic parameters. The load-side parameters include the load-side d-axis to d-axis impedance characteristic parameters, the load-side d-axis to q-axis impedance coupling characteristic parameters, the load-side q-axis to d-axis impedance coupling characteristic parameters, and the load-side q-axis to q-axis impedance characteristic parameters. The source impedance is determined based on the grid-side parameters, and the load impedance is determined based on the load-side parameters.

5. The method according to claim 1, characterized in that, Based on the common coupling point voltage signal, the grid-side current signal, and the load-side current signal, the source impedance on the grid side and the load impedance on the load side are determined, including: The common coupling point voltage signal, the grid-side current signal, and the load-side current signal are respectively transformed into a two-phase rotating coordinate system to obtain the common coupling point two-phase voltage signal, the grid-side two-phase current signal, and the load-side two-phase current signal. Fast Fourier transform is performed on the two-phase voltage signal at the common coupling point, the two-phase current signal on the grid side, and the two-phase current signal on the load side, respectively, to obtain the frequency domain voltage signal at the common coupling point, the frequency domain current signal on the grid side, and the frequency domain current signal on the load side in the frequency domain. Based on the frequency domain voltage signal at the common coupling point, the frequency domain current signal on the grid side, and the frequency domain current signal on the load side, the source impedance on the grid side and the load impedance on the load side are determined.

6. The method according to any one of claims 1 to 5, characterized in that, Based on the source impedance and the load impedance, determine the hysteresis matrix, including: The ratio of the source impedance to the load impedance is calculated to determine the hysteresis matrix.

7. A unified power quality regulator, characterized in that, include: The acquisition module is used to acquire the voltage signal of the common coupling point, the grid-side current signal, and the load-side current signal in the power system after injecting a disturbance current corresponding to a predetermined disturbance frequency into the common coupling point. The common coupling point is the electrical coupling node between the grid side and the load side, and the predetermined disturbance frequency is set in the unified power quality regulator. The first determining module is used to determine the source impedance of the grid side and the load impedance of the load side based on the common coupling point voltage signal, the grid side current signal and the load side current signal; The second determining module is used to determine the hysteresis matrix based on the source impedance and the load impedance, wherein the hysteresis matrix characterizes the impedance interaction strength and phase coupling relationship between the grid side and the load side; The third determining module is used to determine a first eigenvalue and a second eigenvalue based on the return rate matrix, wherein the first eigenvalue reflects the feedback response capability of the power grid side to load side fluctuations, and the second eigenvalue reflects the reverse coupling capability of the load side to the power grid side fluctuations. The fourth determining module is used to determine, based on the first feature value and the second feature value, a first Nyquist curve corresponding to the first feature value and a second Nyquist curve corresponding to the second feature value, wherein the Nyquist curve represents the complex response trajectory of the retracement matrix at a specific frequency; The fifth determining module is used to determine the stability result of the power system at the predetermined disturbance frequency based on the first Nyquist curve and the second Nyquist curve.

8. An electric power system, characterized in that, include: A unified power quality conditioner, on the grid side and the load side, wherein the unified power quality conditioner performs the method as described in claim 1, and the unified power quality conditioner is connected between the grid side and the load side.

9. An electronic device, characterized in that, include: processor; Memory used to store the processor's executable instructions; The processor is configured to execute the instructions to implement the method for determining the stability of a power system as described in any one of claims 1 to 6.

10. A computer-readable storage medium, characterized in that, When the instructions in the computer-readable storage medium are executed by the processor of the electronic device, the electronic device is able to perform the method for determining the stability of a power system as described in any one of claims 1 to 6.

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