Micro-grid large signal stability analysis method for controlling heterogeneous inverter
By constructing equivalent oscillator models for GFM and GFL inverters, the stability analysis of hybrid islanded microgrids is simplified, solving the problems of computational complexity and insufficient applicability in existing technologies, and realizing efficient system stability assessment and engineering practicality.
Patent Information
- Application Number
- CN202610209823.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-02-13
- Publication Date
- 2026-05-26
AI Technical Summary
Existing technologies are insufficient to effectively solve the complex large-signal stability problem caused by the interaction and coupling of GFM and GFL inverters in hybrid islanded microgrids. Existing methods are inadequate in terms of computational complexity and applicability, and cannot meet the practical needs of engineering.
The dynamic characteristics of the GFM inverter are described using the Kuramoto oscillator, and the dynamic order reduction is performed by the singular perturbation method to establish the equivalent oscillator model of the GFM inverter. For the GFL inverter, the dynamics of the phase-locked loop and the inner current loop are ignored, and its equivalent oscillator model is determined by the external power loop. The equivalent oscillator models of multiple GFM and GFL inverters are combined to construct the oscillator model of the islanded hybrid microgrid network, the stability domain between each inverter is determined, and the frequency stability of the system is evaluated by traversing the stability domain.
It simplifies the dimensions and complexity of stability criteria, and provides a large-signal stability tool with high computational efficiency and strong topological universality. It can effectively evaluate the system stability of hybrid islanded microgrids and is suitable for practical engineering applications.
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Figure CN122092278A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of stability analysis technology, and in particular to a method for analyzing the large-signal stability of microgrids controlling heterogeneous inverters. Background Technology
[0002] Currently, the large-scale integration of new energy power generation equipment has made grid-connected inverters one of the core equipment of future new power systems. Based on their functions, they can be divided into two main categories: grid-forming inverters (GFM) and grid-following inverters (GFL). Given that power system electrification has become the mainstream trend, the mechanical inertia inherent in traditional generators is gradually being lost, and the stability of power systems is facing significant challenges. Stability analysis methods, as the main means of judging system operational stability, have attracted much attention. Previous grid stability analysis mainly relied on small-signal analysis. However, microgrids with a mix of GFM and GFM inverters (mixed islanded microgrids, or mix MG) exhibit highly nonlinear operating characteristics, making small-signal analysis inapplicable. It is necessary to shift to large-signal stability analysis to assess their behavior under larger disturbances.
[0003] In the prior art, there is a method for analyzing the transient synchronization stability of hybrid microgrids based on the Hamilton energy function. This method establishes a global Hamiltonian model of an islanded microgrid including GFM and GFL inverters, constructs the system Hamiltonian energy function Hg(δ, ω) and dissipation terms, and derives a synchronization stability criterion based on the passive principle.
[0004] However, the global Hamiltonian model for isolated microgrids requires a unified description of the heterogeneous nonlinear characteristics of GFM and GFL, resulting in the energy function containing high-dimensional cross-coupling terms. The final stability criterion involves multivariate operations, forming a set of explicit multi-constraint inequalities. This criterion is complex and difficult to apply on a large scale. Summary of the Invention
[0005] Therefore, it is necessary to provide a method for analyzing the large-signal stability of microgrids that controls heterogeneous inverters, in order to address the aforementioned technical problems.
[0006] This invention provides a method for analyzing the large-signal stability of microgrids controlling heterogeneous inverters. The microgrid controlling the heterogeneous inverters is specifically a hybrid islanded microgrid, which includes multiple GFM inverters and multiple GFL inverters connected in a hybrid configuration. The large-signal stability analysis method includes: For each GFM inverter, its dynamic characteristics are described using the Kuramoto oscillator, and the singular perturbation method is used to dynamically reduce the order of the original dynamic model of the GFM inverter to obtain the equivalent oscillator model of the GFM inverter; for each GFL inverter, the dynamic changes of the GFL inverter are determined by the dynamics of the external power loop to obtain the equivalent oscillator model of the GFL inverter. By combining multiple equivalent oscillator models of GFM inverters and multiple equivalent oscillator models of GFL inverters, an oscillator model of the islanded hybrid microgrid network is obtained. The islanded hybrid microgrid network oscillator model represents the overall dynamic behavior of the hybrid islanded microgrid. In the islanded hybrid microgrid network oscillator model, the first stability region between each GFM inverter and its connected paired GFM inverter, and the second stability region between each GFM inverter and its connected paired GFL inverter are determined respectively. By traversing and crossing the first and second stable domains of each GFM inverter, the overall frequency stability domain of the islanded hybrid microgrid is obtained. When the target phase difference of the hybrid islanded microgrid after being disturbed is within the overall frequency stability domain, the large-signal stability of the hybrid islanded microgrid is determined; otherwise, the large-signal instability of the hybrid islanded microgrid is determined.
[0007] Optionally, for each GFM inverter, its dynamic characteristics are described using a Kuramoto oscillator, ignoring the rapid dynamics of its internal voltage and current loops. A singular perturbation method is then used to dynamically reduce the order of the original dynamic model of the GFM inverter, resulting in an equivalent oscillator model for the GFM inverter, specifically including: The first is determined based on the following formula. i Power loop of the GFM inverter: ; in, For the first i The angular frequency of a GFM inverter. For the first i The operating frequency of the GFM inverter. The system's rated frequency, For droop gain, To measure the active power, For reference active power; The first is determined based on the following formula. i Measured active power output of the GFM inverter: ; ; in, For local power consumption, For the firsti Terminal voltage of the GFM inverter. For the first i Taiwan GFM inverter and the first j The line inductance between the GFM inverters For the first i The operating phase of the GFM inverter. For the first j The operating phase of the GFM inverter. For the first i Taiwan GFM inverter and the first j The operating phase difference between the GFM inverters; Based on the following formula, the first i By combining the power loop and the measured active power output of the GFM inverter, we obtain the first... i Dynamic model of a GFM inverter: ; in, For the first i The rate of change of the angular frequency of the GFM inverter. This is the time constant corresponding to the cutoff frequency of the first-order power filter; Based on the following formula, the first i The dynamic model of the GFM inverter was processed to obtain the first... i The equivalent oscillator model of the GFM inverter is as follows: ; ; in, The inherent rotational frequency, This represents the coupling effect between the equivalent oscillator models of adjacent GFM inverters.
[0008] Optionally, for each GFL inverter, its dynamic changes are determined by the dynamics of the external power loop, while ignoring the dynamics of its phase-locked loop and the current inner loop, to obtain the equivalent oscillator model of the GFL inverter, specifically including: The first is determined based on the following formula. i Dynamics of the external power loop of a GFL inverter: ; in, For the first i The operating phase of the GFL inverter For the first i Terminal voltage of a GFL inverter For the first i The current component of a GFL inverter along the d-axis in a rotating coordinate system. and This refers to the PI control gain in the power loop; The first is determined based on the following formula. i Voltage-current relationship of a GFL inverter: ; in, For the first i The amplitude of the injected current of the GFL inverter. For the first i The phase of the injected current in the GFL inverter. The magnitude of the grid impedance. The phase of the grid impedance, The magnitude of the grid voltage. The phase of the grid voltage; Based on the following formula, the first i By combining the dynamics and voltage-current relationship of the external power loop of the GFL inverter, the first... i Equivalent oscillator model of a GFL inverter: ; ; in, For the first i The operating phase of the GFL inverter For the first j The operating phase of the GFL inverter For the first i Taiwan GFL inverter and the first j The operating phase difference between the GFL inverters This represents the coupling effect between the equivalent oscillator models of adjacent GFL inverters. and This represents the PI control gain in the power loop. For constant gain, is the natural rotational frequency of the equivalent oscillator model of the GFL inverter.
[0009] Optionally, based on the following equation, the equivalent oscillator models of multiple GFM inverters and multiple GFL inverters are combined to obtain the oscillator model of the islanded hybrid microgrid network: ; ; in, For the collection of inverters in an isolated, interconnected microgrid, For the collection of GFM inverters in an isolated, interconnected microgrid, For a collection of GFL inverters within an isolated, interconnected microgrid, For the first iTaiwan GFM inverter and the first j The operating phase difference between GFM inverters or the first i Taiwan GFL inverter and the first j The operating phase difference between the GFL inverters This refers to the coupling effect between the equivalent oscillator models of adjacent GFM inverters or the coupling effect between the equivalent oscillator models of adjacent GFL inverters.
[0010] Optionally, a first stability region is determined between each GFM inverter and its paired GFM inverter, specifically including: The GFM inverter is determined based on the following formula. i and its paired GFM inverter j Network oscillator model: ; ; in, , ; The following formula will be used to pair GFM inverters. j Substituting the network oscillator model into the GFM inverter i The derivative of the network oscillator model is used to obtain the dynamics between the GFM inverter and its connected paired GFM inverter: ; in, , ; The dynamic equilibrium point between the GFM inverter and its paired GFM inverter is determined based on the following formula: or ; in, The steady-state operating frequency for isolated hybrid microgrids; Based on the following formula, shifting the equilibrium point to the origin, the dynamic change between the GFM inverter and its paired GFM inverter is as follows: ; in, , and ; Based on the dynamic changes between the GFM inverter and its paired GFM inverter, the Lyapunov function is constructed according to the following formula: ; Based on the following equation, the Lyapunov function is processed using the LaSalle invariance principle to obtain the first stability region: ; in, This is the first stable region.
[0011] Optionally, a second stability region is determined between each GFM inverter and its paired GFL inverter, specifically including: The GFM inverter is determined based on the following formula. i and its paired GFL inverter j Network oscillator model: ; ; The following formula will be used to pair GFL inverters. j Substituting the network oscillator model into the GFM inverter i The derivative of the network oscillator model is used to obtain the dynamic model between the GFM inverter and its paired GFL inverter: ; in, , ; The balance point between the GFM inverter and its paired GFL inverter is determined based on the following formula: or ; Based on the following formula, shifting the equilibrium point to the origin, the dynamic change between the GFM inverter and its paired GFL inverter is as follows: ; in, , , ; The Lyapunov function is constructed based on the dynamic changes between the GFM inverter and its paired GFL inverter: ; Based on the following equation, the Lyapunov function is processed using the LaSalle invariance principle to obtain the second stability region: ; in, This is the second stable region.
[0012] Optionally, the overall system frequency stability domain of the islanded hybrid microgrid can be obtained by traversing and crossing the first and second stability domains of each GFM inverter based on the following formula: ; ; in, For the overall frequency stability domain of isolated hybrid microgrids, For the first stable region, This is the second stable region.
[0013] The microgrid large-signal stability analysis method for controlling heterogeneous inverters provided in this invention has the following advantages compared with the prior art: This invention establishes two fundamentally different heterogeneous oscillator models for the dynamic characteristics of GFM and GFL inverters, respectively. Based on these two heterogeneous oscillator models, an equivalent network oscillator model capable of characterizing the overall dynamic behavior of a hybrid islanded microgrid is established. This process simplifies the dynamic description and stability domain analysis of heterogeneous inverters, reduces the dimensionality and complexity of stability criteria, and makes the criteria for large-signal stability of microgrids easier to analyze and calculate. It provides a large-signal stability tool for hybrid islanded microgrids that combines computational efficiency, topological universality, and engineering practicality.
[0014] Furthermore, this invention proposes a systematic evaluation scheme that, based on the established network oscillator model, effectively defines the frequency stability domain of the network oscillator through analysis and derivation, thereby providing a key criterion for the large-signal stability of the system. Attached Figure Description
[0015] Figure 1 This is a schematic diagram of the equivalent network oscillator model of a hybrid islanded microgrid, which is provided in one embodiment as a method for analyzing the large-signal stability of a microgrid controlling a heterogeneous inverter. Figure 2 This is a flowchart of a stability assessment scheme for a microgrid large-signal stability analysis method for controlling heterogeneous inverters, provided in one embodiment. Figure 3 This is an overview diagram of a controller hardware-in-the-loop experimental platform for a microgrid large-signal stability analysis method for controlling heterogeneous inverters, provided in one embodiment. Figure 4 This is a model verification diagram of a hybrid islanded microgrid under load variation, provided in one embodiment, for a large-signal stability analysis method for microgrids controlling heterogeneous inverters. Figure 4 (a) in the figure is a comparison of the response between the large-signal average model and the established equivalent oscillator model of the GFM inverter. Figure 4 (b) in the figure is a comparison of the response between the large-signal average model of the GFL inverter and the established equivalent oscillator model; Figure 5 This is a phase angle difference experimental result diagram of a microgrid large-signal stability analysis method for controlling heterogeneous inverters provided in one embodiment. Figure 5(a) in the figure shows the experimental results of the phase angle difference after the fault was cleared after 0.01s. Figure 5 (b) in the figure shows the experimental results of the phase angle difference after the fault was cleared after 0.2s; Figure 6 The following is a phase plane diagram of GFM1 and GFL2 inverters provided in one embodiment for a microgrid large-signal stability analysis method for controlling heterogeneous inverters. Figure 6 (a) in the diagram is the phase plane diagram after the fault is cleared after 0.01s. Figure 6 (b) in the diagram shows the phase plane after the fault was cleared after 0.2s. Detailed Implementation
[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0017] First, existing large-signal stability analysis work mainly focuses on microgrid systems dominated by GFM inverters, often oversimplifying or completely ignoring the complex dynamic characteristics of GFL inverters. However, recent studies have shown that in islanded hybrid microgrids, GFL inverters play an equally important role in determining the overall system stability as GFM inverters. Second, because hybrid islanded microgrids contain both GFL and GFM inverters, their system order and nonlinearity are significantly higher than those of GFM-dominated microgrids, greatly increasing the complexity and challenge of large-signal stability analysis. Existing large-signal analysis methods are insufficient in addressing this challenge: for example, while Hamiltonian model-based methods have established models of islanded hybrid systems and analyzed synchronization stability, the derived stability criteria are overly complex, lack practicality, and are difficult to apply to large-scale systems or real-world engineering projects; while proposed reduced-order model methods are only applicable to grid-connected systems and cannot effectively solve stability problems in islanded operation modes.
[0018] On the other hand, analysis methods based on coupled oscillator networks have been widely used in the study of system synchronization mechanisms due to their strong mathematical traceability, ability to derive explicit stability conditions, and applicability to general power grid topologies. They have also achieved success in GFM-dominated microgrids (e.g., equating droop-controlled GFM inverters with Kuramoto oscillators and analytically deriving their frequency stability and synchronization conditions). However, the main limitation of this advanced approach is that existing research almost entirely focuses on GFM-dominated scenarios. Although network-oscillator-based methods demonstrate strong analytical capabilities when dealing with GFM systems, they have not effectively incorporated and considered the dynamic behavior of GFL inverters and their potential impact on the oscillator network synchronization process. Therefore, existing network-oscillator-based methods cannot be directly applied to or suitable for islanded microgrids with mixed GFL and GFM inverters, and cannot solve the complex large-signal stability problems caused by the interaction and coupling of these two types of inverters.
[0019] This invention provides a method for analyzing the large-signal stability of microgrids controlling heterogeneous inverters. The microgrid controlling the heterogeneous inverters is specifically a hybrid islanded microgrid, which includes multiple GFM inverters and multiple GFL inverters connected in a hybrid configuration. The large-signal stability analysis method includes:
[0020] For each GFM inverter, its dynamic characteristics are described using a Kuramoto oscillator. The rapid dynamics of the internal voltage and current loops are ignored, and a singular perturbation method is used to dynamically reduce the order of the original dynamic model of the GFM inverter, resulting in an equivalent oscillator model. For each GFL inverter, the dynamic changes are determined by the dynamics of the external power loop. The dynamics of its phase-locked loop and inner current loop are ignored, resulting in an equivalent oscillator model.
[0021] By combining multiple equivalent oscillator models of GFM inverters and multiple equivalent oscillator models of GFL inverters, an oscillator model for the islanded hybrid microgrid network is obtained. This oscillator model characterizes the overall dynamic behavior of the hybrid islanded microgrid.
[0022] In the islanded hybrid microgrid network oscillator model, the first stability region between each GFM inverter and its paired GFM inverter and the second stability region between each GFM inverter and its paired GFL inverter are determined respectively.
[0023] By traversing and crossing the first and second stable domains of each GFM inverter, the overall frequency stability domain of the islanded hybrid microgrid is obtained. When the target phase difference of the hybrid islanded microgrid after being disturbed is within the overall frequency stability domain, the large-signal stability of the hybrid islanded microgrid is determined; otherwise, the large-signal instability of the hybrid islanded microgrid is determined.
[0024] The specific implementation is as follows: 1. Equivalent network oscillator modeling.
[0025] To analyze the frequency stability of the system, a lossless model of the transmission line was performed, with the bus voltage kept constant. Let... A collection of inverters within a microgrid (MG). For GFM inverter collection, This is a collection of GFL inverters.
[0026] 1.1 Equivalent oscillator model of GFM inverter.
[0027] The dynamic characteristics of a droop-controlled GFM inverter are described using a Kuramoto oscillator. The rapid dynamics of the internal voltage / current loop of the GFM inverter are ignored. i The power loop of a GFM inverter is represented as follows:
[0028] (1) In the formula, For the first i The angular frequency of the GFM inverter; For the first i The operating frequency of the GFM inverter; The system's rated frequency; It is droop gain; and These are the measured active power and the reference active power, respectively.
[0029] Among them, the i The measured active power output of the GFM inverter is expressed as follows: (2) In the formula, For local power consumption, For the first i Terminal voltage of the GFM inverter. For the first i Taiwan GFM inverter and the first j The line inductance between the GFM inverters For the first i The operating phase of the GFM inverter. For the first j The operating phase of the GFM inverter. For the first i Taiwan GFM inverter and the first j The operating phase difference between the GFM inverters .
[0030] Most existing studies process the measured active power output of GFM inverters using first-order power filters. Combining equations (1) and (2), the dynamic model of the GFM inverter can be derived: (3) in, For the first i The rate of change of the angular frequency of the GFM inverter. Let be the time constant corresponding to the cutoff frequency of the first-order power filter. Assume... Small enough, and meets the requirements .
[0031] By applying the singular perturbation method to the first i The dynamic model of the GFM inverter was processed to obtain the first... i Equivalent oscillator model of a GFM inverter: (4) In the formula, The natural rotational frequency of the GFM equivalent oscillator; This represents the coupling effect between the equivalent oscillator models of adjacent GFM inverters.
[0032] 1.2 Equivalent oscillator model of GFL inverter.
[0033] Similar to GFM inverters, the dynamic changes of the inner current loop in GFL inverters are much faster than those of the power loop, and the dynamic effects of the inner current loop can be ignored during modeling. Traditional GFL inverters have two main control loops: a phase-locked loop (PLL) and an external power loop.
[0034] Synchronization between the GFL inverter and the grid is achieved through a phase-locked loop (PLL). The dynamics of the PLL are as follows: (5a) (5b) In the formula, The voltage component of the GFL inverter in the rotating coordinate system q-axis; Phase observation for phase-locked loop; and It controls the gain.
[0035] The external power loop of the GFL inverter uses a PI controller to regulate the injected current / power. (6) In the formula, For the first i The operating phase of the GFL inverter For the first i Terminal voltage of a GFL inverter For the first i The current component of a GFL inverter along the d-axis in a rotating coordinate system. and This represents the PI control gain in the power loop.
[0036] As is well known, the combination of (5) and (6) produces a detailed but highly nonlinear model. Although much work has focused on the dynamics of the phase-locked loop (PLL), it has been shown in the literature that by properly adjusting the PLL with a wider bandwidth, the dynamics of the GFL inverter will be dominated by the dynamics of the external power loop.
[0037] Voltage-current relationship of GFL inverter: (7) In the formula, For the first i The amplitude of the injected current of the GFL inverter. For the first i The phase of the injected current in the GFL inverter. The magnitude of the grid impedance. The phase of the grid impedance, The magnitude of the grid voltage. This represents the phase of the grid voltage.
[0038] Assumption Combining (6) and (7), the first i The equivalent oscillator model of the GFL inverter is as follows: (8) In the formula, The natural rotational frequency of the equivalent GFL oscillator. ,, For the first i The operating phase of the GFL inverter For the first j The operating phase of the GFL inverter For the first i Taiwan GFL inverter and the first j The operating phase difference between the GFL inverters This represents the coupling effect between the equivalent oscillator models of adjacent GFL inverters. and This represents the PI control gain in the power loop. It is a constant gain.
[0039] 1.3 Equivalent oscillator model of hybrid MG.
[0040] Comparing (4) and (8), it can be seen that due to the additional frequency coupling effect of the GFL oscillator (i.e. (Item), the oscillator model of the GFL inverter is heterogeneous with that of the GFM inverter. Combining equations (4) and (8), the equivalent network oscillator model of the islanded hybrid microgrid is:
[0041] (9a) (9b) in, For the collection of inverters in an isolated, interconnected microgrid, For the collection of GFM inverters in an isolated, interconnected microgrid, For a collection of GFL inverters within an isolated, interconnected microgrid, For the first i Taiwan GFM inverter and the first j The operating phase difference between GFM inverters or the first i Taiwan GFL inverter and the first j The operating phase difference between the GFL inverters This refers to the coupling effect between the equivalent oscillator models of adjacent GFM inverters or the coupling effect between the equivalent oscillator models of adjacent GFL inverters.
[0042] If the droop gain of each GFM oscillator is small enough, i.e. for If the network oscillator in equation (9) is locally stable, then the network oscillator is locally stable.
[0043] 2. Stability evaluation scheme based on network oscillator.
[0044] For ease of discussion, it is assumed that each bus of the microgrid under study is connected to a GFM or GFL inverter, and at least one GFM inverter should be provided. For microgrids with a general topology, Kron reduction can be used to satisfy this assumption. The topology of the equivalent network oscillator model of a hybrid islanded microgrid is as follows: Figure 1 As shown.
[0045] For ease of explanation, a hybrid islanded microgrid consisting of two GFM inverters and two GFL inverters is selected for demonstration. Figure 1 As shown in the left sub-diagram, the bus connected to the load connects two GFM inverters and two GFL inverters. Its topology can be equivalent to that shown in the right sub-diagram, where the two GFM inverters correspond to GFM1 and GFM3 oscillators, respectively... and Frequency rotation; the two GFL inverters correspond to GFL2 and GFL4 oscillators, respectively, with... and Frequency rotation; the GFM1 oscillator is connected to the GFL2 and GFM3 oscillators, and the GFM3 oscillator is also connected to the GFL4 oscillator, forming a 4-DG system. The line impedance between each inverter is equivalent to the coupling effect between the oscillator models. , and .
[0046] 2.1 Interconnection between GFM and GFM inverters.
[0047] Reference equation (9), GFM inverter i and its paired GFM inverter j The network oscillator model is represented as: (10a) (10b) In the formula, , .
[0048] Substituting (10b) into the derivative of (10a), the dynamics in (10) are: (11) in, , .
[0049] set up , The equilibrium point of (11) is calculated: or In the formula, For the steady-state operating frequency of the system, x The phase angle, y It is the angular frequency (i.e., the derivative with respect to the phase angle).
[0050] Moving the equilibrium point to the origin of the rotating coordinate system, then (11) becomes: (12) in, , and .
[0051] Referring to equation (12), construct the following Lyapunov function: (13) By referring to equation (13) and applying the LaSalle invariant principle, we can derive... and The domain is: (14) in, This is the first stable region.
[0052] From (14), we can know Independent of Therefore, GFM inverter i Local power switching Independent of .
[0053] 2.2 Interconnection of GFM and GFL inverters.
[0054] Reference equation (9), GFM inverter i and its paired GFL inverter j The network oscillator model is as follows: (15a) (15b) Similarly, combining the derivatives of (15b) and (15a), the dynamics in (15) are further expressed as: (16) In the formula, , .
[0055] The equilibrium point of the system is calculated as follows: or Moving the equilibrium point to the origin of the rotating coordinate system, the translated system is represented as: (17) In the formula, , , .
[0056] Referring to equation (17), construct the following Lyapunov function: (18) Similarly, the derivation of the stability region is as follows: (19) in, This is the second stable region.
[0057] Among them, item This can be further expressed as: think back This fact can be further approximated as follows: It can be seen from (19) GFM inverter i It is also independent of local power switching. .
[0058] 2.3 Frequency stability evaluation scheme.
[0059] For the initial version, it had a GFM inverter. i and a paired inverter j The system derived from (14) and (19) can first be extended to a system with one GFM inverter and multiple paired inverters; the system can then be derived for each pair of inverters. The stability region is determined by treating the remaining coupling effects on the inverter as local power exchange. This assumption makes the resulting stability conditions necessary, but not sufficient.
[0060] Then, for a hybrid islanded microgrid with multiple GFM inverters, its stability domain... It can be further estimated by traversing and crossing the stability region of each GFM inverter, i.e.: Finally, the flowchart of the stability evaluation scheme proposed in this invention is as follows: Figure 2 As shown.
[0061] 3. Verification process.
[0062] The effectiveness of the proposed method was verified on a hardware-in-the-loop experimental platform for controllers, such as... Figure 3 As shown, this experimental platform was developed for a 4-DG hybrid islanded microgrid with two GFM inverters (GFM1 and GFM3) and two GFL inverters (GFL2 and GFL4). Four hardware controllers are assigned to each inverter as local controllers. System parameters are set as follows: , , , , , , , , , Based on the proposed scheme, the following calculations are first performed: , , and Then, further... and Finally, estimate .
[0063] First, an additional 30kW local load was introduced into GFL2. The response comparison between the large-signal average model and the established equivalent oscillator model is as follows: Figure 4 As shown in the figure. Simulation results show that the response of the equivalent oscillator model is basically consistent with the response of the large-signal average model, verifying the reliability of the established equivalent oscillator models of GFM and GFL inverters.
[0064] The estimated stability region was then verified. The effectiveness of MG. MG was initially in equilibrium, in Three-phase faults of 0.01s and 0.2s were introduced into GFL2, respectively, and the corresponding results are as follows. Figure 5 (a) and Figure 5 As shown in (b). When the fault is cleared after 0.01s, from Figure 5 As observed in (a), all target phase differences fall within the derived stability region. The system then returns to a stable state. When the fault is cleared after 0.2 seconds, from... Figure 5 As can be observed in (b), The system exceeds the derived stability region and loses synchronization even after the fault is cleared. Furthermore, the trajectory of the target phase difference is presented in the phase plane, as shown... Figure 6 As shown. From Figure 6 It can be seen that the system can overcome transient faults, but if the faults are not cleared in time, the system will diverge, and the result is consistent with the proposed stability assessment scheme.
[0065] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.
Claims
1. A method for analyzing the large-signal stability of a microgrid controlling a heterogeneous inverter, wherein the microgrid controlling the heterogeneous inverter is specifically a hybrid islanded microgrid, the hybrid islanded microgrid comprising: Multiple GFM inverters and multiple GFL inverters are connected in a mixed configuration; The large-signal stability analysis method is characterized by comprising: For each GFM inverter, the dynamic characteristics of the GFM inverter are described by the Kuramoto oscillator, and the singular perturbation method is used to dynamically reduce the order of the original dynamic model of the GFM inverter to obtain the equivalent oscillator model of the GFM inverter; for each GFL inverter, the dynamic changes of the GFL inverter are determined by the dynamics of the external power loop to obtain the equivalent oscillator model of the GFL inverter. By combining multiple equivalent oscillator models of GFM inverters and multiple equivalent oscillator models of GFL inverters, an oscillator model of the islanded hybrid microgrid network is obtained. The islanded hybrid microgrid network oscillator model characterizes the overall dynamic behavior of the hybrid islanded microgrid. In the islanded hybrid microgrid network oscillator model, the first stability region between each GFM inverter and its connected paired GFM inverter, and the second stability region between each GFM inverter and its connected paired GFL inverter are determined respectively. By traversing and crossing the first and second stable domains of each GFM inverter, the overall frequency stability domain of the islanded hybrid microgrid is obtained. When the target phase difference of the hybrid islanded microgrid after being disturbed is within the overall frequency stability domain, the large-signal stability of the hybrid islanded microgrid is determined; otherwise, the large-signal instability of the hybrid islanded microgrid is determined.
2. The method for analyzing the large-signal stability of microgrids controlling heterogeneous inverters as described in claim 1, characterized in that, The dynamic characteristics of each GFM inverter are described using a Kuramoto oscillator. The singular perturbation method was then used to dynamically reduce the order of the original dynamic model of the GFM inverter, resulting in an equivalent oscillator model of the GFM inverter, specifically including: The first is determined based on the following formula. i Power loop of the GFM inverter: ； in, For the first i The angular frequency of a GFM inverter. For the first i The operating frequency of the GFM inverter. The system's rated frequency, For droop gain, To measure the active power, For reference active power; The first is determined based on the following formula. i Measured active power output of the GFM inverter: ； ； in, For local power consumption, For the first i Terminal voltage of the GFM inverter. For the first i Taiwan GFM inverter and the first j The line inductance between the GFM inverters For the first i The operating phase of the GFM inverter. For the first j The operating phase of the GFM inverter. For the first i Taiwan GFM inverter and the first j The operating phase difference between the GFM inverters; Based on the following formula, the first i By combining the power loop and the measured active power output of the GFM inverter, we obtain the first... i Dynamic model of a GFM inverter: ； in, For the first i The rate of change of the angular frequency of the GFM inverter. This is the time constant corresponding to the cutoff frequency of the first-order power filter; Based on the following formula, the first i The dynamic model of the GFM inverter was processed to obtain the first... i The equivalent oscillator model of the GFM inverter is as follows: ； ； in, The inherent rotational frequency, This represents the coupling effect between the equivalent oscillator models of adjacent GFM inverters.
3. The method for analyzing the large-signal stability of microgrids controlling heterogeneous inverters as described in claim 1, characterized in that, For each GFL inverter, the dynamic changes of the external power loop are dynamically determined to obtain the equivalent oscillator model of the GFL inverter, specifically including: The first is determined based on the following formula. i Dynamics of the external power loop of a GFL inverter: ； in, For the first i The operating phase of the GFL inverter For the first i Terminal voltage of a GFL inverter For the first i The current component of a GFL inverter along the d-axis in a rotating coordinate system. and This refers to the PI control gain in the power loop; The first is determined based on the following formula. i Voltage-current relationship of a GFL inverter: ； in, For the first i The amplitude of the injected current of the GFL inverter. For the first i The phase of the injected current in the GFL inverter. The magnitude of the grid impedance. The phase of the grid impedance, The magnitude of the grid voltage. The phase of the grid voltage; Based on the following formula, the first i By combining the dynamics and voltage-current relationship of the external power loop of the GFL inverter, the first... i Equivalent oscillator model of a GFL inverter: ； ； in, For the first i The operating phase of the GFL inverter For the first j The operating phase of the GFL inverter For the first i Taiwan GFL inverter and the first j The operating phase difference between the GFL inverters This represents the coupling effect between the equivalent oscillator models of adjacent GFL inverters. and This represents the PI control gain in the power loop. For constant gain, is the natural rotational frequency of the equivalent oscillator model of the GFL inverter.
4. A method for analyzing the large-signal stability of a microgrid controlling a heterogeneous inverter as described in any one of claims 2-3, characterized in that, Based on the following equation, the equivalent oscillator models of multiple GFM inverters and multiple GFL inverters are combined to obtain the oscillator model of the islanded hybrid microgrid network: ； ； in, For a collection of inverters within an isolated, interconnected microgrid. For the collection of GFM inverters in an isolated, interconnected microgrid, For a collection of GFL inverters within an isolated, interconnected microgrid, For the first i Taiwan GFM inverter and the first j The operating phase difference between GFM inverters or the first i Taiwan GFL inverter and the first j The operating phase difference between the GFL inverters This refers to the coupling effect between the equivalent oscillator models of adjacent GFM inverters or the coupling effect between the equivalent oscillator models of adjacent GFL inverters.
5. A method for analyzing the large-signal stability of a microgrid controlling a heterogeneous inverter as described in any one of claims 2-3, characterized in that, The determination of the first stability region between each GFM inverter and its paired GFM inverter specifically includes: The GFM inverter is determined based on the following formula. i and its paired GFM inverter j Network oscillator model: ； ； in, , ; The following formula will be used to pair GFM inverters. j Substituting the network oscillator model into the GFM inverter i The derivative of the network oscillator model is used to obtain the dynamics between the GFM inverter and its connected paired GFM inverter: ； in, , ; The dynamic equilibrium point between the GFM inverter and its paired GFM inverter is determined based on the following formula: or ; in, The steady-state operating frequency for isolated hybrid microgrids; Based on the following formula, shifting the equilibrium point to the origin, the dynamic change between the GFM inverter and its paired GFM inverter is as follows: ； in, , and ; Based on the dynamic changes between the GFM inverter and its paired GFM inverter, the Lyapunov function is constructed according to the following formula: ； Based on the following equation, the Lyapunov function is processed using the LaSalle invariance principle to obtain the first stability region: ； in, This is the first stable region.
6. A method for analyzing the large-signal stability of a microgrid controlling a heterogeneous inverter as described in any one of claims 2-3, characterized in that, The determination of the second stability region between each GFM inverter and its paired GFL inverter specifically includes: The GFM inverter is determined based on the following formula. i and its paired GFL inverter j Network oscillator model: ； ； The following formula will be used to pair GFL inverters. j Substituting the network oscillator model into the GFM inverter i The derivative of the network oscillator model is used to obtain the dynamic model between the GFM inverter and its paired GFL inverter: ； in, , ; The balance point between the GFM inverter and its paired GFL inverter is determined based on the following formula: or ; Based on the following formula, shifting the equilibrium point to the origin, the dynamic change between the GFM inverter and its paired GFL inverter is as follows: ； in, , , ; The Lyapunov function is constructed based on the dynamic changes between the GFM inverter and its paired GFL inverter: ； Based on the following equation, the Lyapunov function is processed using the LaSalle invariance principle to obtain the second stability region: ； in, This is the second stable region.
7. The method for analyzing the large-signal stability of a microgrid controlling a heterogeneous inverter as described in claim 1, characterized in that, Based on the following formula, by traversing and crossing the first and second stability regions of each GFM inverter, the overall system frequency stability region of the islanded hybrid microgrid is obtained: ； ； in, For the overall frequency stability domain of isolated hybrid microgrids, For the first stable region, This is the second stable region.