A stabilizing distributed control method and system for a large-scale direct current microgrid

Abstract

The application discloses a kind of large-scale DC microgrid's stabilizing distributed control method and system, it is applied to the mesh DC microgrid system including distributed power supply and constant power load, steps include: establishing the system small signal model of mesh DC microgrid system and deducing high-order Jacobian matrix;High-order Jacobian matrix is reduced order, and the boundary layer subsystem for representing converter stability design and the reduced order subsystem for representing global relationship are obtained;The analytical stability condition of boundary layer subsystem and reduced order subsystem is obtained;Based on analytical stability condition, the stability of system is maintained, and the maximum load power corresponding to each constant power load in mesh DC microgrid system is determined.The method and system of the application determine the maximum power that each constant power load can accept under the condition of ensuring the stable operation of mesh DC microgrid system, and provide practical guidance for the design of stable converter controller in DC microgrid.

Description

Technical Field

[0001] This invention relates to the field of mesh microgrid control technology, and in particular to a stable distributed control method and system for a large-scale DC microgrid. Background Technology

[0002] To address the stability issues of microgrids under current-sharing control, research can be categorized into four types based on different topologies and control methods: star microgrids under droop control (multiple micro-sources, single load), distributed control star microgrids, mesh microgrids under droop control (multiple micro-sources, multiple loads), and mesh microgrids under distributed control. Currently, stability analyses of the first three types of systems have been reported, while the stability analysis of the fourth type is more complex and rarely reported.

[0003] In microgrids with a high proportion of renewable energy, voltage drop in the transmission network and the increase in constant power loads can easily lead to the absence of a balance point in the system, resulting in voltage collapse. Microgrids need to introduce distributed control strategies to achieve balanced output and voltage conditions among generating units. The stability of the balance point of a microgrid under distributed control, considering line losses, is a key focus in parameter design.

[0004] The stability problems of star-shaped DC power networks under droop control and distributed control have been widely addressed. Due to the high order of DC power networks, stability conditions are typically derived by neglecting the dynamics of the converters. Furthermore, the system can be reduced to a second-order model by ignoring line impedance and assuming consistent converter impedance ratios, allowing for the derivation of stability conditions. However, these studies neglect the coupling and interaction characteristics between converters, failing to accurately reflect the network characteristics. In the case of a star-shaped microgrid with a constant power load exhibiting negative impedance and multiple converter interactions, the equivalent impedance matrix has only one negative eigenvalue. The quadratic eigenvalue theory can be used to derive the stability conditions under droop control. Based on this, for the stability problem of star-shaped microgrids under distributed control, the negative impedance of the constant power load and the communication delay between micro-sources are the causes of system instability. Analysis of these factors allows for the determination of the conditions for maintaining system stability and the maximum permissible communication delay. However, micro-sources are usually treated as controlled voltage sources, ignoring the dynamics of DC / DC converters. Stabilization methods based on simplified models are difficult to apply to real-world models under complex conditions. In addition, the stability problem of mesh microgrids with multiple constant power loads has not yet been solved.

[0005] In summary, microgrids generally require converters to transform voltage levels. The coupling between converters and distributed intelligent algorithms (such as PI algorithms) can easily lead to system instability and further increase the system order, making stability analysis more difficult. In the existing technology, the stability control problem of mesh microgrids with multiple constant power loads has not been solved, and the maximum constant power load value under stability control of mesh microgrids with multiple constant power loads is difficult to determine.

[0006] Therefore, there is an urgent need to design a stable distributed control method and system for large-scale DC microgrids to solve or at least partially alleviate the above-mentioned technical problems. Summary of the Invention

[0007] The main objective of this invention is to provide a stable distributed control method and system for large-scale DC microgrids, aiming to solve the technical problem in the prior art where it is difficult to determine the maximum constant power load value of large-scale DC microgrids, resulting in poor grid system stability (easy to cause voltage collapse).

[0008] To achieve the above objectives, this invention provides a stable distributed control method for large-scale DC microgrids, applicable to mesh DC microgrid systems containing distributed power sources and constant power loads, comprising the following steps:

[0009] S10, Based on the control framework of a large-scale DC microgrid, a typical mesh DC microgrid system is pre-established. The mesh DC microgrid system includes distributed power sources, constant power loads, and DC-DC converters arranged one-to-one with the distributed power sources. The distributed power sources are regulated by a distributed control strategy, and the DC-DC converters are controlled by converter control parameters.

[0010] S20. Establish the system small-signal model corresponding to the mesh DC microgrid system. The system small-signal model is an equivalent linearized model of the system near the equilibrium point, which is derived from the dynamic characteristic equation of the DC-DC converter under the distributed control architecture. The high-order Jacobian matrix is ​​derived from the system small-signal model.

[0011] S30, based on the system small-signal model, reduces the order of the high-order Jacobian matrix according to the time scale differences reflected by different dynamic processes in the mesh DC microgrid system, to obtain the boundary layer subsystem for characterizing converter stability design and the reduced-order subsystem for characterizing global relationships;

[0012] S40, obtain the analytical stability conditions of the boundary layer subsystem and the descending layer subsystem respectively. The analytical stability conditions are used to determine the parameter constraints and distribution laws that the mesh DC microgrid system needs to satisfy for stable operation.

[0013] S50, based on analytical stability conditions, maintain the system stability of the mesh DC microgrid system and determine the maximum load power corresponding to each constant power load in the mesh DC microgrid system.

[0014] Furthermore, in step S10, the mesh DC microgrid system adopts a distributed control architecture. The mesh DC microgrid system includes n distributed power sources and m constant power loads, where n and m are positive integers greater than 1. The constant power loads and distributed power sources are electrically connected through transmission cables. The distributed power sources are regulated by a distributed control strategy, and the DC-DC converter is controlled by converter control parameters, specifically by a control method that integrates distributed control strategies.

[0015] Furthermore, in step S20, the mathematical expression of the system's small-signal model is: ,

[0016] The mathematical expression for a higher-order Jacobian matrix is: ,

[0017] in, R, L, C For the virtual impedance connected in series with the filter capacitor in the mesh DC microgrid system, and for the inductance and capacitance of the DC-DC converter, I represents the unit diagonal matrix. Let n be an n-dimensional vector in which all elements are 1. This is the Laplace matrix of the communication diagram corresponding to the mesh DC microgrid system. , A G It is an adjacency matrix. , For the number of nodes, For the first j The first distributed power source and the first k Communication weights between distributed power sources , , b This represents the gain coefficient for voltage regulation. , , t j For the first j Current distribution ratio coefficient of distributed power source , Y SS This is the self-admittance between power nodes. Y SL , Y LS The mutual admittance between the power node and the load node. Y LL The self-admittance between load nodes. , The load voltage in steady state.p It is a set vector of constant power loads.

[0018] Further, in step S30, when reducing the order of the higher-order Jacobian matrix, specifically based on the singular perturbation theorem, the 3n×3n higher-order Jacobian matrix is ​​reduced to two lower-dimensional matrices, 2n×2n and n×n, which are respectively used as the boundary layer subsystem and the reduced-order subsystem. The mathematical expression is:

[0019]

[0020] Descending Subsystem The mathematical expression is:

[0021]

[0022] in, , , It is a preset positive scalar. , , Let the filter inductor and capacitor be the j-th converter. Laplace matrix of the communication diagram corresponding to a mesh DC microgrid system The smallest non-zero eigenvalue.

[0023] Further, in step S40, the analytical stability conditions corresponding to the boundary layer subsystem are obtained based on the quadratic eigenvalue theorem; the analytical stability conditions corresponding to the reduced-order subsystem are obtained based on the inertia theorem and the rank-one perturbation theorem; when the system is stable, the boundary layer subsystem... The conditions to be met are

[0024]

[0025] When the system is stable, the descending subsystem The conditions to be met are

[0026]

[0027] in, Representing vectors p The infinite norm, CL represents the matrix -1 The first eigenvalue of R, v ref For input reference voltage, p Let the vector be the set of constant power loads in the entire system. Representation matrix The second eigenvalue.

[0028] Further, in step S50, when maintaining the system stability of the mesh DC microgrid system based on the analytical stability conditions and determining the maximum load power corresponding to each constant power load in the mesh DC microgrid system, specifically, the maximum load power corresponding to the constant power load is constrained based on the analytical stability conditions corresponding to the boundary layer subsystem, thereby determining the maximum load power corresponding to the constant power load that is acceptable under system stability conditions. At the same time, the analytical stability conditions corresponding to the step-down subsystem constrain the global relationship between network topology, current distribution weights and load power to maintain system stability.

[0029] The present invention also provides a stable distributed control system for a large-scale DC microgrid, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the stable distributed control method for the large-scale DC microgrid.

[0030] The present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the aforementioned large-scale DC microgrid stabilization distributed control method.

[0031] Compared with existing technologies, the stabilization distributed control method for large-scale DC microgrids provided by this invention has the following beneficial effects:

[0032] This invention provides a stable distributed control method and system for large-scale DC microgrids. It models and analyzes typical mesh DC microgrid systems, fully considering the dynamic characteristics of the converter. A small-signal model of the system is established, and the corresponding high-order Jacobian matrix is ​​reduced in order, dividing it into a boundary layer subsystem and a reduced-order subsystem. Analyzing the low-order boundary layer and reduced-order subsystems significantly reduces the analysis complexity. Based on the boundary layer and reduced-order subsystems, a new theoretical perspective is provided for analyzing and understanding the overall dynamic behavior of mesh DC microgrid systems. By adjusting the converter's modulation strategy, the converter can receive the maximum amount of constant power load while ensuring system stability. Ultimately, the maximum acceptable power for each constant power load under stable operating conditions in a mesh DC microgrid system is determined, providing practical guidance for the design of stable converter controllers in DC microgrids. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0034] Figure 1 This is a schematic diagram of the topology of a mesh DC microgrid in a specific embodiment of the present invention, wherein a is the topology of the DC microgrid and b is the topology of the communication network;

[0035] Figure 2 This is a methodological framework diagram of the stabilization distributed control method for large-scale DC microgrids in this invention;

[0036] Figure 3 This is a flowchart of the stabilization distributed control method for large-scale DC microgrids in this invention;

[0037] Figure 4 This is a simulation structure diagram of a mesh DC microgrid in a specific embodiment of the present invention;

[0038] Figure 5 This is a block diagram of a distributed power supply control structure based on distributed control in a specific embodiment of the present invention;

[0039] Figure 6 The following are simulation waveforms for engineering cases in another specific embodiment of the present invention, wherein a is the output current waveform of the micro-source in engineering case 1, b is the weighted average output voltage waveform of the micro-source in engineering case 1, c is the output current waveform of the micro-source in engineering case 2, d is the weighted average output voltage waveform of the micro-source in engineering case 2, e is the output current waveform of the micro-source in engineering case 3, f is the weighted average output voltage waveform of the micro-source in engineering case 3, g is the output current waveform of the micro-source in engineering case 4, and h is the weighted average output voltage waveform of the micro-source in engineering case 4.

[0040] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0041] The present invention will be further described below with reference to the accompanying drawings and specific preferred embodiments, but this does not limit the scope of protection of the present invention.

[0042] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

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

[0044] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0045] Furthermore, the use of terms such as "first" and "second" in this invention is for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature. Additionally, the technical solutions of the various embodiments can be combined with each other, but only on the basis of being achievable by those skilled in the art. When the combination of technical solutions is contradictory or impossible to implement, such a combination of technical solutions should be considered non-existent and not within the scope of protection claimed by this invention.

[0046] like Figure 1 As shown, a typical gridded DC microgrid consists of n distributed generation sources (DGs) and m communication links (CPLs). The DGs employ distributed control, and the cables can be considered purely resistive. In the communication network, nodes represent converters, and edges represent communication links used for data exchange. Under the distributed control architecture, each node interacts only with its neighboring nodes. Both the physical and communication networks exhibit strong connectivity.

[0047] Based on the above characteristics, this invention provides a stable distributed control method for a large-scale DC microgrid, the methodological framework of which is shown in the figure below. Figure 2As shown, this paper models and analyzes a typical mesh DC microgrid system, fully considering the dynamic characteristics of the converter. A small-signal model of the system is established, and the high-order Jacobian matrix is ​​reduced to two parts: a boundary layer subsystem and a reduced-order subsystem. By analyzing the low-order boundary layer subsystem and the reduced-order subsystem, the analysis complexity is significantly reduced. Based on the boundary layer subsystem and the reduced-order subsystem, a new theoretical perspective is provided for analyzing and understanding the overall dynamic behavior of the mesh DC microgrid system. By adjusting the modulation strategy of the converter, the converter can receive the maximum constant power load while ensuring system stability. Finally, the maximum acceptable power of each constant power load under the condition of ensuring stable operation of the mesh DC microgrid system is determined, providing practical guidance for the design of stable converter controllers in DC microgrids.

[0048] Please refer to Figure 3 The present invention provides a method for stabilizing distributed control of a large-scale DC microgrid, applicable to a mesh DC microgrid containing distributed generation units and constant power loads, comprising the following steps:

[0049] S10, Based on the control framework of a large-scale DC microgrid, a typical mesh DC microgrid system is pre-established. The mesh DC microgrid system includes distributed power sources, constant power loads, and DC-DC converters arranged one-to-one with the distributed power sources. The distributed power sources are regulated by a distributed control strategy, and the DC-DC converters are controlled by converter control parameters.

[0050] S20. Establish the system small-signal model corresponding to the mesh DC microgrid system. The system small-signal model is an equivalent linearized model of the system near the equilibrium point, which is derived from the dynamic characteristic equation of the DC-DC converter under the distributed control architecture. The high-order Jacobian matrix is ​​derived from the system small-signal model.

[0051] S30, based on the system small-signal model, reduces the order of the high-order Jacobian matrix according to the time scale differences reflected by different dynamic processes in the mesh DC microgrid system, to obtain the boundary layer subsystem for characterizing converter stability design and the reduced-order subsystem for characterizing global relationships;

[0052] S40, obtain the analytical stability conditions of the boundary layer subsystem and the descending layer subsystem respectively. The analytical stability conditions are used to determine the parameter constraints and distribution laws that the mesh DC microgrid system needs to satisfy for stable operation.

[0053] S50, based on analytical stability conditions, maintain the system stability of the mesh DC microgrid system and determine the maximum load power corresponding to each constant power load in the mesh DC microgrid system.

[0054] Understandably, in this embodiment of the invention, the equilibrium point is the point where all differential equations are equal to 0, and the area near the equilibrium point is common knowledge to those skilled in the art; in step S30, the analytical stability conditions include the interaction relationship between variables between the boundary layer subsystem and the reduced-level subsystem, as well as the influence relationship of system parameter changes on the stability of the mesh DC microgrid system. The analytical stability conditions are used to determine the parameter constraints and distribution laws that the mesh DC microgrid system needs to satisfy for stable operation.

[0055] Understandably, order reduction involves dividing the system into two relatively independent dynamic subsystems based on the time scale differences reflected in different dynamic processes: the boundary layer subsystem and the order reduction subsystem.

[0056] Further, in step S40, the analytical stability condition corresponding to the boundary layer subsystem is obtained based on the quadratic eigenvalue theorem; the analytical stability condition corresponding to the reduced-level subsystem is obtained based on the inertia theorem and the rank-one perturbation theorem; in step S50, the maximum load power corresponding to the constant power load is constrained based on the analytical stability condition corresponding to the boundary layer subsystem, thereby determining the maximum load power corresponding to the constant power load that is acceptable under the system stability condition, and at the same time, the global relationship between the network topology, current distribution weight and load power is constrained based on the analytical stability condition corresponding to the reduced-level subsystem to maintain system stability.

[0057] Furthermore, the mesh DC microgrid system adopts a distributed control architecture, comprising n distributed power sources and m constant-power loads, where n and m are positive integers greater than 1. The constant-power loads and distributed power sources are electrically connected via transmission cables. The DC-DC converter employs a control method that integrates distributed control strategies. Understandably, in the embodiment of this invention, all distributed power sources employ distributed control strategies, transmission cables are considered purely resistive elements, and the converter employs a distributed control method that integrates stability strategies. Under the distributed control architecture, each agent only interacts with its neighboring nodes.

[0058] Furthermore, the mathematical expression for the system's small-signal model is: ,

[0059] The mathematical expression for a higher-order Jacobian matrix is: ,

[0060] in, , n The number of distributed power sources in the system. R, L, C For the virtual impedance connected in series with the filter capacitor, the inductance and capacitance of the converter, For the inductor current of the distributed power source, , For the input and output voltages of the distributed power source, , , for , , The corresponding small signal variable, , t j For the first j Current distribution ratio coefficient of distributed power source b This represents the gain coefficient for voltage regulation. , This is the Laplace matrix of the communication diagram corresponding to the mesh DC microgrid system. , A G It is an adjacency matrix. , For the first j The first distributed power source and the first k Communication weights between distributed power sources , , Y The admittance matrix of the power transmission network , Y SS This is the self-impedance between power supply nodes. Y SL , Y LS The mutual admittance between the power node and the load node. Y LL The self-admittance between load nodes. , , The load voltage in steady state. p The set vector of constant power loads in the entire system ( p (where I is a set of constant power loads in the entire system, and I is a unit diagonal matrix) Let O be an n-dimensional vector with all elements equal to 1, and let O be a matrix of all zeros.

[0061] Furthermore, the boundary layer subsystem The mathematical expression is:

[0062]

[0063] Descending Subsystem The mathematical expression is:

[0064]

[0065] in, , , It is a pre-defined positive scalar.

[0066] Optionally, in specific implementation, It is a sufficiently small positive scalar. , , Let the filter inductor and capacitor be the j-th converter. Let be the smallest non-zero eigenvalue of the Laplace matrix of the communication graph corresponding to the mesh DC microgrid system. , For the first j The current allocation ratio coefficient corresponding to each distributed power source

[0067] Furthermore, the boundary layer subsystem when the system is stable The conditions to be met are

[0068] ,

[0069] in, p Let the vector be the set of constant power loads in the entire system. It is a vector p The infinite norm, It is a matrix CL -1 The first characteristic value of R. When the power of the constant power load in the system satisfies the above formula, it indicates that the system is stable.

[0070] Boundary layer subsystem This section explains the maximum acceptable constant power load corresponding to the specified load value. This condition directly transforms the converter's stability into a quantifiable parameter constraint. Based on this condition, the quantitative relationship between the converter parameters (filter inductance, capacitor, and virtual impedance) and the maximum constant power load the system can handle can be clearly defined. For example, to support a larger load power, the design can, based on this condition, increase the converter capacitor and virtual impedance or decrease the filter inductance. When determining whether the system is stable, it is only necessary to calculate whether the current load power falls within the range specified by v. ref Stability assessment can be completed quickly within the stability boundary determined by inherent parameters such as L, C, and R.

[0071] When the system is stable, the descending subsystem The conditions to be met are:

[0072]

[0073] in, For matrix The second eigenvalue.

[0074] Descending Subsystem The stability conditions reveal the relationship between the network topology, load, and current distribution ratio required for the system to remain stable: the network topology and load are determined by their impedance matrices. The eigenvalue spectrum distribution, its connectivity influences The magnitude of the current distribution weight matrix T determines the power distribution ratio among the units, and the system stability is essentially determined by the global relationship between these three factors.

[0075] The derivation process of the aforementioned formulas will be explained in detail below;

[0076] Please refer to Figure 4 The DC microgrid structure shown is a mesh DC microgrid system comprising n (n=10) distributed generation sources and m (m=20) constant power loads. The red and blue dots represent distributed generation sources and constant power loads, respectively. The black lines represent cable resistance values, the green numbers indicate the specific resistance values, and the black numbers are the node numbers. The constant power loads use a controlled current source model, and their current value is obtained by dividing the power by the voltage. The constant power loads satisfy the following equation:

[0077] In the formula, For the voltage, current and power of a constant power load ( p (This is the set vector of constant power loads in the entire system).

[0078] In step S20, the small-signal model of the mesh DC microgrid system is established, and the steps for deriving the high-order Jacobian matrix based on the small-signal model are as follows:

[0079] First, we calculate the dynamic characteristic equation of the DC-DC converter considering the distributed control architecture. For the j-th distributed power source, the dynamic characteristics of its converter can be described as follows:

[0080]

[0081] Then, by combining the distributed control strategy, the system state equation is obtained. Please refer to [reference needed]. Figure 5 The block diagram of the distributed power supply control structure shown is a buck converter model under a distributed control strategy, aiming to achieve current distribution and weighted average voltage regulation. For the first... j The control equation for a distributed power source is as follows:

[0082]

[0083] in, n The number of distributed power sources in the system. d j For the first j Duty cycle of a distributed power source For the first j The filter inductor, output capacitor, virtual resistance, and current distribution ratio coefficient corresponding to each distributed power source. For the k-th distributed power source, the current allocation ratio coefficient and the filter inductor current are respectively. The first j The input voltage, output voltage, output current, filter inductor current, and output capacitor current of a distributed power source. The control input generated for the j-th distributed controller, For the first j The first distributed power source and the first k Communication weights between distributed power sources This is the weighted average voltage. , , b This represents the gain coefficient for voltage regulation. v ref This is the input reference voltage.

[0084] Based on the above analysis and taking full account of the dynamic characteristics of the DC / DC converter under distributed control, the overall state equation of the system under distributed control can be obtained as follows:

[0085]

[0086] in, , n The number of distributed power sources in the system. R, L, C For the virtual impedance connected in series with the filter capacitor, the inductance and capacitance of the converter, , These are the inductor current and output current of the distributed power source, respectively. , Input voltage and output voltage for the distributed controller. for The corresponding small signal variable, , , t j , u Sj For the first j The current distribution ratio and output voltage of a distributed power source. b This represents the gain coefficient for voltage regulation. v ref For input reference voltage, , The Laplace matrix of the communication graph. , A G It is an adjacency matrix. , For the first j The first distributed power source and the first k Communication weights between distributed power sources , , Y Impedance matrix of the power transmission network , Y SS This is the self-impedance between power supply nodes. Y SL , Y LS The mutual impedance between the power supply node and the load node. Y LL The self-impedance between load nodes. , , The load voltage in steady state. For voltage, current and power of a constant power load, For all elements are 1 n Dimensional vector.

[0087] Linearizing the system's state equations near the equilibrium point (the point where all differential equations equal 0) yields the following small-signal model of the system:

[0088]

[0089] in, .

[0090] Finally, the higher-order Jacobian matrix is ​​obtained from the system's small-signal model. The process of deriving the higher-order Jacobian matrix from the system's equivalent linearization model is well-known in the field. The final higher-order Jacobian matrix of the system running near the equilibrium point is shown below.

[0091]

[0092] Because the order of a high-order Jacobian matrix is ​​relatively high (3n×3n; the Jacobian matrix of a distributed power source is 3×3, and the system has n distributed power sources), it is difficult to determine the stability of the system by directly analyzing the eigenvalues ​​of the high-order Jacobian matrix. In step S30 of this embodiment, a method for reducing the order of a high-order Jacobian matrix is ​​proposed based on the singular perturbation theorem, reducing a 3n×3n high-order Jacobian matrix to two lower-dimensional matrices, n×n and 2n×2n. The main conclusions are as follows.

[0093] Understandably, reasoning using the following received information leads to Reason 1, which defines... Let be a real matrix, where V1, V2, V3, and V4 are block matrices of the Jacobian matrix of the singular perturbation equation. If and Since they are all Herwitz matrices, then for any , It is Hurwitz's, meaning the system is stable. Where I is a unit diagonal matrix. , , , and These are equations and The solution.

[0094] Proof: Definition as follows

[0095]

[0096] Obviously and Similarity, that is and They have the same eigenvalues.

[0097] Assumption and If all are Herwitz matrices, then there exists a real symmetric positive definite matrix. and real symmetric positive definite matrix Satisfying the equations respectively and .

[0098] make Then we can get the following formula:

[0099]

[0100] because You can get and All are Herwitz matrices. According to Schul complement theorem... It is a negative definite matrix. Because It is a positive definite matrix. It is a negative definite matrix, from which we can obtain It is the Herwitz matrix. Therefore, it can be proven that the matrix... It is the Herwitz matrix.

[0101] Typically, to meet the practical application requirements of converters, the values ​​of inductor L and capacitor C are both sufficiently small. Therefore, it can be written as... , ,in It is a sufficiently small quantity. Therefore, the small-signal model of the system can be rewritten as the following singular perturbation system:

[0102] ,

[0103] in, , , , ;

[0104] The Jacobian matrix of the system can then be expressed as:

[0105]

[0106] Based on reasoning 1, the higher-order Jacobian matrix can be decomposed into a boundary layer subsystem. and reduced order subsystem ,when and Both are Herwitz matrices, for any , All of these are Herwitz matrices, meaning the system is stable. , The maximum value of the eigenvalues ​​of matrix F. , , , and These are equations and The solution.

[0107] Based on the above analysis, step S40 of this embodiment of the invention performs reasoning two and reasoning three respectively, and provides... and This is a sufficient condition for the Hurwitz matrix.

[0108] Understandably, further reasoning leads to Reasoning Two: When the following conditions are true, It is the Herwitz matrix.

[0109]

[0110] The specific proof process includes, in the matrix The characteristic equation can be expressed as:

[0111]

[0112] According to Schulbue's theorem, it can be equivalent to ,

[0113] Multiply both sides of the equation ,get ,

[0114] For a positive definite Helmet matrix, according to the quadratic eigenvalue theorem, if If it is a positive definite Helmet matrix, then The real parts of all eigenvalues ​​are negative, meaning Z1 is a Herwitz matrix.

[0115] definition ,in .because and Since they are all symmetric matrices, according to the inertia theorem, we can obtain:

[0116]

[0117] consider yes Shure supplement can be obtained .

[0118] because ,Right now You can get ,

[0119] when If this holds true, we can obtain the following inequality:

[0120]

[0121] Right now , It is a positive definite Hermite matrix.

[0122] Understandably, further reasoning leads to reasoning three, which states that when the following conditions are met, It is the Herwitz matrix

[0123]

[0124] The reasoning process of Reasoning 3 includes defining... .because It is easy to obtain the following based on the inertia theorem and the rank-one perturbation theorem. Based on the above reasoning, when the conditions are met... The Herwitz matrix, i.e. It is also the Herwitz matrix.

[0125] Figure 6 This is a simulation waveform for an engineering case in a specific embodiment of the present invention. Engineering case one demonstrates that the system is stable for any changing load when the load power always satisfies Inference Two. Figure 6 As shown in a and b; Engineering Case 2 shows that when the load power always satisfies Reasoning 3, the system is stable for any changing load, such as... Figure 6 As shown in c and d in the diagram. Engineering Case 3 demonstrates that when the load power satisfies robust stability conditions inferences two and three, the system is stable, as shown in... Figure 6 As shown in e and f, when the load power exceeds the maximum power allowed by the stability condition, the system becomes unstable and voltage collapses. When the load power decreases and the stability condition is satisfied again, the system returns to stability. Engineering Case 4 illustrates how the system becomes unstable when the load power exceeds the maximum power allowed by robust stability conditions in inferences two and three, as shown in... Figure 6 As shown in g and h, when the load power decreases, the robust stability condition is satisfied again, and the system is stable. When the load power increases, but does not exceed the maximum power allowed by the robust stability condition, the system is robustly stable.

[0126] Depend on Figure 6 The simulation results show that when the robust stability condition is met, the system is robustly stable under varying loads. When the robust stability condition is not met, the system may be unstable. The robust stability condition provides an upper bound on the load that ensures stable system operation, and the simulation results verify the correctness of the conclusions.

[0127] Furthermore, this invention also proposes a stable distributed control system for a large-scale DC microgrid, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the above method.

[0128] Furthermore, this invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the stabilization distributed control method for the large-scale DC microgrid.

[0129] In summary, this invention proposes a stable distributed control method and system for large-scale DC microgrids. Addressing the stability problem of high-order systems caused by the interaction between DC / DC converter dynamics and constant power loads under distributed control, a systematic solution based on singular perturbation theory is proposed. A high-order system model incorporating converter dynamics is established. The singular perturbation method is used to decouple the system into two low-dimensional subsystems: a boundary layer subsystem and a reduced-order subsystem, reducing analytical complexity. For the boundary layer subsystem, the converter stability condition is derived using quadratic eigenvalue theory, revealing the design relationship between converter parameters and network parameters. For the reduced-order subsystem, the stability condition of the distributed control system is derived using the inertia theorem and the rank-one perturbation theorem. Applying this condition to microgrids eliminates the need for real-time load information collection, ensuring system stability and providing guidance for constructing safe and stable microgrids, thus enabling large-scale grid integration of renewable energy.

[0130] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for stabilizing distributed control of a large-scale DC microgrid, applied to a mesh DC microgrid system containing distributed power sources and constant power loads, characterized in that, Including the following steps: A small-signal model of the mesh DC microgrid system is established, and the corresponding higher-order Jacobian matrix is ​​derived. The mathematical expression of the higher-order Jacobian matrix is ​​as follows: in, R, L, C For the virtual impedance connected in series with the filter capacitor in the mesh DC microgrid system, and for the inductance and capacitance of the DC-DC converter, I represents the unit diagonal matrix. Let n be an n-dimensional vector in which all elements are 1. This is the Laplace matrix of the communication diagram corresponding to the mesh DC microgrid system. b This represents the gain coefficient for voltage regulation. , , t j For the first j Current distribution ratio coefficient of distributed power source , Y SS This is the self-admittance between power nodes. Y SL , Y LS The mutual admittance between the power node and the load node. Y LL The self-admittance between load nodes. , The load voltage in steady state. p This is a set vector of constant power loads; The higher-order Jacobian matrix is ​​reduced in order to obtain a boundary layer subsystem for characterizing the stability design of the converter and a reduced-order subsystem for characterizing the global relationship. The analytical stability conditions of the boundary layer subsystem and the reduced-order subsystem are obtained respectively. The system stability of the mesh DC microgrid system is maintained based on the analytical stability conditions, and the maximum load power corresponding to each constant power load in the mesh DC microgrid system is determined. Specifically, the maximum load power corresponding to the constant power load is constrained based on the analytical stability conditions corresponding to the boundary layer subsystem, thereby determining the maximum load power corresponding to the constant power load that is acceptable under system stability conditions. At the same time, the global relationship between network topology, current distribution weight and load power is constrained based on the analytical stability conditions corresponding to the descending-level subsystem to maintain system stability.

2. The stabilization distributed control method for a large-scale DC microgrid according to claim 1, characterized in that, The mesh DC microgrid system also includes DC-DC converters arranged one-to-one with distributed power sources. The distributed power sources are regulated using a distributed control strategy, and the DC-DC converters are controlled using converter control parameters. The mathematical expression of the system's small-signal model is: in, R, L, C This refers to the virtual impedance connected in series with the filter capacitor in a mesh DC microgrid system, as well as the inductance and capacitance of the DC-DC converter. , , For the inductor current of the distributed power source Distributed power supply input voltage Distributed power supply output voltage The corresponding small-signal variable, I, is an identity diagonal matrix. Let n be an n-dimensional vector in which all elements are 1. This is the Laplace matrix of the communication diagram corresponding to the mesh DC microgrid system. b This represents the gain coefficient for voltage regulation. , , t j For the first j Current distribution ratio coefficient of distributed power source , n This represents the number of distributed power sources in the mesh DC microgrid system. , Y SS This is the self-admittance between power nodes. Y SL , Y LS The mutual admittance between the power node and the load node. Y LL The self-admittance between load nodes. , The load voltage in steady state. p It is a set vector of constant power loads.

3. The method for stabilizing distributed control of a large-scale DC microgrid according to claim 2, characterized in that, The formula for calculating the Laplace matrix of the communication diagram corresponding to a mesh DC microgrid system is as follows: in, , For the number of nodes, For the first j The first distributed power source and the first k Communication weights between distributed power sources , n The number of distributed power sources in a mesh DC microgrid system. , .

4. The method for stabilizing distributed control of a large-scale DC microgrid according to claim 1, characterized in that, The reduction of the higher-order Jacobian matrix is ​​specifically based on the singular perturbation theorem, reducing the 3n×3n higher-order Jacobian matrix to two lower-dimensional matrices of 2n×2n and n×n, respectively, which serve as the boundary layer subsystem and the reduced-order subsystem. The mathematical expressions for the boundary layer subsystem and the reduced-order subsystem are as follows: in, It is a boundary layer subsystem. It is a descending subsystem. , , It is a preset positive scalar. , , Let the filter inductor and capacitor be the j-th converter. Laplace matrix of the communication diagram corresponding to a mesh DC microgrid system The smallest non-zero eigenvalue, R Let I be the virtual impedance connected in series with the filter capacitor in the mesh DC microgrid system, and let I be the unit diagonal matrix. Let n be an n-dimensional vector in which all elements are 1. This is the Laplace matrix of the communication diagram corresponding to the mesh DC microgrid system. , , t j For the first j Current distribution ratio coefficient of distributed power source , Y SS This is the self-admittance between power nodes. Y SL , Y LS The mutual admittance between the power node and the load node. Y LL The self-admittance between load nodes. , The load voltage in steady state. p It is a set vector of constant power loads.

5. The stabilization distributed control method for a large-scale DC microgrid according to claim 4, characterized in that, When obtaining the analytical stability conditions of the boundary layer subsystem and the reduced-order subsystem respectively, the step of obtaining the analytical stability condition of the boundary layer subsystem is included. Specifically, the analytical stability condition corresponding to the boundary layer subsystem is obtained based on the quadratic eigenvalue theorem. The mathematical expression of the analytical stability condition corresponding to the boundary layer subsystem is: in, Representing vectors p The infinite norm, CL represents the matrix -1 The first eigenvalue of R, v ref For input reference voltage, R, L, C This refers to the virtual impedance connected in series with the filter capacitor in a mesh DC microgrid system, as well as the inductance and capacitance of the DC-DC converter. p It is a set vector of constant power loads.

6. The stabilization distributed control method for a large-scale DC microgrid according to claim 4, characterized in that, When obtaining the analytical stability conditions of the boundary layer subsystem and the reduced-order subsystem respectively, the step of obtaining the analytical stability condition of the reduced-order subsystem is included. Specifically, the analytical stability condition corresponding to the reduced-order subsystem is obtained based on the inertia theorem and the rank-one perturbation theorem. The mathematical expression of the analytical stability condition corresponding to the reduced-order subsystem is: in, Representation matrix The second eigenvalue, , t j For the first j Current distribution ratio coefficient of distributed power source , Y SS This is the self-admittance between power nodes. Y SL , Y LS The mutual admittance between the power node and the load node. Y LL The self-admittance between load nodes. , The load voltage in steady state. p It is a set vector of constant power loads.

7. A stable distributed control system for a large-scale DC microgrid, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the stable distributed control method for a large-scale DC microgrid as described in any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the stable distributed control method for a large-scale DC microgrid as described in any one of claims 1 to 6.

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