A distributed self-stabilizing method and system for power systems independent of equilibrium points

Abstract

The present application relates to the technical field of power system stability analysis, and in particular to a distributed self-stabilization method and system for a power system that is independent of the balance point. The distributed self-stabilization method for the power system includes: determining a first set of grid-connected devices corresponding to the power system, and a target power system model set corresponding to the first set of grid-connected devices; based on the target power system model set, obtaining at least one grid-connected device in the first set of grid-connected devices that does not meet the distributed self-stabilization protocol, and obtaining a second set of grid-connected devices; adjusting the device parameters of at least one grid-connected device in the second set of grid-connected devices, so that all grid-connected devices in the second set of grid-connected devices meet the distributed self-stabilization protocol. The present application adopting the above scheme can ensure the overall stability of the power system in a self-stabilizing manner.

Description

Technical Field

[0001] The present application relates to the technical field of power system stability analysis, and in particular to a distributed self-stabilization method and system for a power system that is independent of the equilibrium point. Background Art

[0002] Maintaining power system stability is a top priority for system operation. Power system instability can lead to large-scale power outages and significant economic losses. Traditional power systems are primarily composed of synchronous generators, whose dynamic characteristics are dominated by a small number of large ones. However, with the rapid development of renewable energy and the electrification of loads, an increasing number of small and medium-sized power sources and devices are connected to the grid. These devices are numerous, geographically distributed, and exhibit significant variations in dynamic characteristics, potentially negatively impacting power system stability. Ensuring the safe and stable operation of power systems composed of a large number of heterogeneous distributed devices is an urgent challenge. Summary of the Invention

[0003] The present application aims to solve one of the technical problems in the related art at least to a certain extent.

[0004] To this end, the first purpose of this application is to propose a distributed self-stabilization method for power systems that is independent of the equilibrium point, the main purpose of which is to ensure the overall stability of the power system in a self-stabilizing manner.

[0005] The second objective of this application is to propose a distributed self-stabilizing system for power systems that is independent of the equilibrium point.

[0006] To achieve the above objectives, the first embodiment of the present application proposes a distributed self-stabilization method for a power system that is independent of the equilibrium point, including:

[0007] Determining a first grid-connected device set corresponding to the power system and a target power system model set corresponding to the first grid-connected device set;

[0008] Based on the target power system model set, obtaining at least one grid-connected device in the first grid-connected device set that does not satisfy the distributed self-stabilizing protocol to obtain a second grid-connected device set;

[0009] The device parameters of at least one grid-connected device in the second set of grid-connected devices are adjusted so that all grid-connected devices in the second set of grid-connected devices meet the distributed self-stabilizing protocol.

[0010] Optionally, in one embodiment of the present application, the first grid-connected device set includes dynamic devices and static devices, and determining the first grid-connected device set corresponding to the power system and the target power system model set corresponding to the first grid-connected device set includes:

[0011] Acquire at least one dynamic device in the first grid-connected device set to obtain a dynamic device set; determine a set of input state output nonlinear equations corresponding to the dynamic device set;

[0012] Acquire at least one static device in the first grid-connected device set to obtain a static device set; determine a set of input and output nonlinear equations corresponding to the static device set;

[0013] The target power system model set is determined according to the input-state-output nonlinear equation set and the input-output nonlinear equation set.

[0014] Optionally, in one embodiment of the present application, determining a first grid-connected device set corresponding to the power system and a target power system model set corresponding to the first grid-connected device set includes:

[0015] Acquire an initial power system model corresponding to at least one grid-connected device in the set of grid-connected devices to obtain an initial power system model set;

[0016] An equivalent transformation is performed on at least one initial power system model in the initial power system model set that does not satisfy the target model form, thereby obtaining a target power system model set.

[0017] Optionally, in one embodiment of the present application, the first grid-connected device set includes dynamic devices and static devices, and the step of obtaining, based on the target power system model set, at least one grid-connected device in the first grid-connected device set that does not satisfy the distributed self-stabilizing protocol to obtain the second grid-connected device set includes:

[0018] Acquire any grid-connected device in the first set of grid-connected devices;

[0019] If any of the grid-connected devices is a dynamic device, determining whether the dynamic device satisfies the dynamic distributed self-stabilizing protocol based on the target power system model corresponding to the dynamic device;

[0020] If any of the grid-connected devices is a static device, determining whether the static device satisfies a static distributed self-stabilizing protocol based on a target power system model corresponding to the static device;

[0021] The first set of grid-connected devices is traversed to obtain at least one grid-connected device in the first set of grid-connected devices that does not satisfy the distributed self-stabilizing protocol, thereby obtaining a second set of grid-connected devices.

[0022] Optionally, in one embodiment of the present application, adjusting the device parameters of at least one grid-connected device in the second set of grid-connected devices so that all grid-connected devices in the second set of grid-connected devices meet the distributed self-stabilizing protocol includes:

[0023] Obtaining initial device parameters and target device parameters corresponding to any grid-connected device in the second set of grid-connected devices;

[0024] Calculating the transformation matrix according to the initial device parameters and the target device parameters to obtain a target matrix;

[0025] The device parameters of any of the grid-connected devices are adjusted according to the target matrix.

[0026] Optionally, in one embodiment of the present application, after adjusting the device parameters of at least one grid-connected device in the second set of grid-connected devices so that all grid-connected devices in the second set of grid-connected devices meet the distributed self-stabilizing protocol, the method further includes:

[0027] Acquire a third grid-connected device set corresponding to the power system, where all grid-connected devices in the third grid-connected device set satisfy a distributed self-stabilizing protocol;

[0028] Determining power system parameters corresponding to the third set of grid-connected devices based on the distributed self-stabilizing protocol;

[0029] Based on the power system parameters, determining whether the power system has a balance point;

[0030] If the power system has a balance point, a stability analysis is performed on the power system.

[0031] Optionally, in one embodiment of the present application, the third grid-connected device set includes dynamic devices and static devices, and determining the power system parameters corresponding to the third grid-connected device set based on the distributed self-stabilizing protocol includes:

[0032] Acquire at least one dynamic device in the third grid-connected device set to obtain a dynamic device set;

[0033] Determine a dynamic function set and a dynamic region set corresponding to the dynamic device set based on the distributed self-stabilizing protocol;

[0034] Determining a boundary parameter set according to the dynamic function set and the dynamic region set;

[0035] Determine a Cartesian product based on the dynamic region set; determine an objective function set based on the dynamic function set and the boundary parameter set;

[0036] The power system parameters are determined based on the Cartesian product and the set of objective functions.

[0037] Optionally, in one embodiment of the present application, the determining whether the power system has a balance point based on the power system parameter includes:

[0038] If the intersection of the objective function set and the Cartesian product is not an empty set and the intersection of the objective function set and the Cartesian product is bounded, then the power system has at least one equilibrium point in the dynamic region corresponding to the Cartesian product.

[0039] Optionally, in one embodiment of the present application, if the power system has a balance point, performing stability analysis on the power system includes:

[0040] analyzing the static stability of the power system based on the Cartesian product;

[0041] Obtaining an initial state value and an initial output value corresponding to the power system;

[0042] Determining disturbance parameters corresponding to the power system based on the initial state value, the initial output value, and the dynamic function set; determining target boundary parameters according to the boundary parameter set;

[0043] The transient stability of the power system is analyzed based on the objective function set, the Cartesian product, the target boundary parameter and the disturbance parameter.

[0044] To achieve the above objectives, a second embodiment of the present application proposes a distributed self-stabilizing system for a power system that is independent of the equilibrium point, including:

[0045] a set determining module, configured to determine a first grid-connected device set corresponding to the power system, and a target power system model set corresponding to the first grid-connected device set;

[0046] a device acquisition module, configured to acquire, based on a target power system model set, at least one grid-connected device in the first set of grid-connected devices that does not satisfy the distributed self-stabilizing protocol, to obtain a second set of grid-connected devices;

[0047] The parameter adjustment module is used to adjust the device parameters of at least one grid-connected device in the second grid-connected device set so that all grid-connected devices in the second grid-connected device set meet the distributed self-stabilizing protocol.

[0048] In summary, the technical solutions provided by the embodiments of the present application bring at least the following beneficial effects:

[0049] 1) This application adjusts the first grid-connected device set corresponding to the power system so that all grid-connected devices in the first grid-connected device set meet the distributed self-stabilizing protocol, thereby ensuring the overall stability of the power system in a self-stabilizing manner.

[0050] 2) The distributed self-stabilizing protocol of this application is independent of the equilibrium point. Therefore, this application does not rely on the control center of the power system, nor on the equilibrium point. It can perform stability analysis on the power system when the equilibrium point is unknown.

[0051] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0053] Figure 1 A flow chart of a distributed self-stabilization method for a power system independent of the equilibrium point provided in an embodiment of the present application;

[0054] Figure 2 A schematic diagram of the structure of an IEEE-9 node power system provided in an embodiment of the present application;

[0055] Figure 3 A method provided in the embodiment of this application Schematic diagram of the section on the (δ1-θ1)-V1 two-dimensional plane;

[0056] Figure 4 A method provided in the embodiment of this application Schematic diagram of a section on the θ2-V2 two-dimensional plane;

[0057] Figure 5 A method provided in the embodiment of this application Schematic diagram of a section on the θ3-V3 two-dimensional plane;

[0058] Figure 6 A schematic diagram of the waveform of the voltage at each node of an IEEE-9 node power system after a disturbance provided by an embodiment of the present application;

[0059] Figure 7 A schematic diagram of the waveform of the frequency of each node of an IEEE-9 node power system after a disturbance provided by an embodiment of the present application;

[0060] Figure 8 A schematic diagram of the structure of a distributed self-stabilizing device for a power system independent of the equilibrium point provided in an embodiment of the present application. DETAILED DESCRIPTION

[0061] The embodiments of the present application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present application and are not to be construed as limiting the present application. On the contrary, the embodiments of the present application include all variations, modifications, and equivalents that fall within the spirit and scope of the appended claims.

[0062] The present application is described in detail below with reference to specific embodiments.

[0063] Figure 1 This is a flow chart of a distributed self-stabilization method for a power system that is independent of the equilibrium point provided in an embodiment of the present application.

[0064] like Figure 1 As shown, an embodiment of the present application provides a distributed self-stabilization method for a power system that is independent of a balance point, comprising the following steps:

[0065] Step 110: determining a first grid-connected device set corresponding to the power system and a target power system model set corresponding to the first grid-connected device set;

[0066] Step 120: Based on the target power system model set, obtain at least one grid-connected device in the first grid-connected device set that does not satisfy the distributed self-stabilizing protocol to obtain a second grid-connected device set;

[0067] Step 130 : Adjust device parameters of at least one grid-connected device in the second set of grid-connected devices so that all grid-connected devices in the second set of grid-connected devices meet the distributed self-stabilizing protocol.

[0068] According to some embodiments, a power system refers to an electric energy production and consumption system consisting of power plants, transmission and transformation lines, power distribution stations, and power consumption. A power system converts natural primary energy into electrical energy through power generation devices, and then supplies electrical energy to various users through transmission, transformation, and distribution. This power system does not specifically refer to a fixed power system. For example, changes to power generation devices can change the power system. Changes to grid-connected equipment can also change the power system.

[0069] In some embodiments, a grid-connected device refers to a device that is electrically connected to the power system and performs power exchange. The grid-connected device does not specifically refer to a fixed device. The grid-connected device includes but is not limited to dynamic devices, static devices, etc.

[0070] In some embodiments, the first set of grid-connected devices refers to a collection of all grid-connected devices in the power system. The first set of grid-connected devices does not specifically refer to a fixed set. For example, when the power system changes, the first set of grid-connected devices may also change. When the grid-connected devices change, the first set of grid-connected devices may also change.

[0071] According to some embodiments, the distributed self-stabilization protocol refers to a condition that at least one grid-connected device in a set of grid-connected devices satisfies in accordance with the provisions of the distributed self-stabilization protocol. This condition is only relevant to the grid-connected device, not to other grid-connected devices in the set of grid-connected devices, and is independent of a control center. The distributed self-stabilization protocol does not specifically refer to a fixed protocol. The distributed self-stabilization protocol includes, but is not limited to, a dynamic distributed self-stabilization protocol, a static distributed self-stabilization protocol, and the like.

[0072] In an embodiment of the present application, the first grid-connected device set includes dynamic devices and static devices. Determining the first grid-connected device set corresponding to the power system and the target power system model set corresponding to the first grid-connected device set includes:

[0073] Acquire at least one dynamic device in the first grid-connected device set to obtain a dynamic device set; determine a set of input state output nonlinear equations corresponding to the dynamic device set;

[0074] Acquire at least one static device in the first grid-connected device set to obtain a static device set; determine a set of input and output nonlinear equations corresponding to the static device set;

[0075] The target power system model set is determined according to the input state output nonlinear equation set and the input output nonlinear equation set.

[0076] According to some embodiments, each grid-connected device corresponds to two basic electrical variables, namely, the node voltage of the grid-connected point and the injected current of the grid-connected point. In the synchronously rotating DQ coordinate system, the node voltage of the grid-connected point can be expressed as V Q +jV D , the injection current at the grid connection point can be expressed as I Q +jI D ; Among them, V Q is the Q-axis component of the node voltage; V D is the D-axis component of the node voltage; I Q is the Q-axis component of the injected current; I D is the D-axis component of the injected current; Is an imaginary unit.

[0077] In some embodiments, dynamic devices can cause node voltage and injected current to exhibit a dynamic relationship that must be described by a differential equation. Therefore, for each dynamic device, an input-state-output nonlinear equation can be constructed based on its corresponding device characteristics and parameters. Specifically, the input-state-output nonlinear equation can be expressed as follows:

[0078]

[0079] in, is the state variable of the dynamic device, is the input variable of the dynamic device, is the output variable of the dynamic device, f i and is a quadratically continuously differentiable function.

[0080] In some embodiments, the input and output corresponding to the dynamic device can have the following two combinations:

[0081] The first combination: u i =(V Qi ,V Di ) T and y i =-(I Qi ,I Di ) T , that is, the dynamic device takes the node voltage as input and the negative injection current as output;

[0082] The second combination: u i =-(I Qi ,I Di ) T and y i =(V Qi ,V Di ) T , that is, the dynamic device takes negative injection current as input and node voltage as output.

[0083] In some embodiments, static devices can make the node voltage and injection current present a static relationship described by an algebraic equation. Therefore, for each static device, an input-output nonlinear equation can be constructed based on its corresponding device characteristics and parameters. Specifically, the input-output nonlinear equation is expressed as follows:

[0084]

[0085] in, is the input variable of the dynamic device, is the output variable of the dynamic device, is a quadratically continuously differentiable function.

[0086] In some embodiments, the input and output corresponding to the static device can have the following two combinations:

[0087] The first combination: u i =(V Qi ,V Di ) T and y i =-(I Qi ,I Di ) T , that is, the static device takes the node voltage as input and the negative injection current as output;

[0088] The second combination: u i =-(I Qi ,I Di ) T and y i =(V Qi ,V Di ) T , that is, the static device takes negative injection current as input and node voltage as output.

[0089] In an embodiment of the present application, determining a first grid-connected device set corresponding to the power system and a target power system model set corresponding to the first grid-connected device set includes:

[0090] Obtaining an initial power system model corresponding to at least one grid-connected device in the grid-connected device set to obtain an initial power system model set;

[0091] An equivalent transformation is performed on at least one initial power system model in the initial power system model set that does not satisfy the target model form, thereby obtaining a target power system model set.

[0092] According to some embodiments, the target model form refers to the model form required to determine whether a grid-connected device satisfies the distributed self-stabilizing protocol. This target model form is not specifically defined as a fixed form. For example, when the grid-connected device is a dynamic device, the target model form may be an input-state-output nonlinear equation form; when the grid-connected device is a static device, the target model form may be an input-output nonlinear equation form.

[0093] It is easy to understand that the first set of grid-connected devices includes grid-connected devices with known initial power system models and grid-connected devices with unknown initial power system models. For grid-connected devices with unknown initial power system models, the corresponding target power system model can be directly constructed based on their corresponding device characteristics and parameters. For grid-connected devices with known initial power system models, it can be determined whether the known initial power system model meets the target model form. If not, the initial power system model is equivalently transformed to obtain the corresponding target power system model. Furthermore, the target power system model set corresponding to the first set of grid-connected devices can be obtained, which can improve the efficiency and accuracy of obtaining the target power system model set.

[0094] In an embodiment of the present application, the first grid-connected device set includes dynamic devices and static devices. Based on the target power system model set, at least one grid-connected device in the first grid-connected device set that does not satisfy the distributed self-stabilizing protocol is obtained to obtain a second grid-connected device set, including:

[0095] Obtain any grid-connected device in the first grid-connected device set;

[0096] If any grid-connected device is a dynamic device, then the target power system model corresponding to the dynamic device is used to determine whether the dynamic device satisfies the dynamic distributed self-stabilizing protocol;

[0097] If any grid-connected device is a static device, then the static device is judged based on the target power system model corresponding to the static device whether it satisfies the static distributed self-stabilizing protocol;

[0098] The first set of grid-connected devices is traversed to obtain at least one grid-connected device in the first set of grid-connected devices that does not satisfy the distributed self-stabilizing protocol, thereby obtaining a second set of grid-connected devices.

[0099] According to some embodiments, determining whether a dynamic device satisfies a dynamic distributed self-stabilizing protocol refers to determining whether there is a continuously differentiable function S i : A simply connected open set region as well as Class function α i , β i , γ i , and both of the following conditions are met:

[0100] The first condition: α i (||f i (x i ,u i )||)≤S i (x i ,u i )≤β i(||f i (x i ,u i )||);

[0101] The second condition: and in, is a 2-dimensional vector;

[0102] If it exists, it means that the dynamic device meets the dynamic distributed self-stabilizing protocol.

[0103] In some embodiments, A class function refers to a strictly monotonically increasing function with α(0)=0, that is, a continuous function α:[0,a)→[0,∞).

[0104] In some embodiments, the continuously differentiable function S i (x i ,u i ) can be in the form of S i (x i ,u i )=f i (x i ,u i ) T P i f i (x i ,u i ),in, is a symmetric positive definite matrix to be determined. In this case, whether the dynamic device satisfies the dynamic distributed self-stabilizing protocol can be determined by determining whether there is a symmetric positive definite matrix A simply connected open set region So that any For example, the following matrix inequality can be established:

[0105]

[0106] Where I is the 2-dimensional identity matrix.

[0107] If it exists, it means that the dynamic device meets the dynamic distributed self-stabilizing protocol.

[0108] According to some embodiments, determining whether a static device satisfies the static distributed self-stabilizing protocol refers to determining whether the following equation holds true based on a target power system model corresponding to the static device:

[0109]

[0110] If it is established, it means that the static device satisfies the static distributed self-stabilizing protocol.

[0111] It's easy to understand that the dynamic and static distributed self-stabilization protocols are distributed conditions that are specific to the grid-connected device itself and independent of other connected devices or the network. Each grid-connected device can be independently verified without the involvement of a control center. This eliminates central dependency and computational burden, improving the efficiency of distributed self-stabilization in power systems.

[0112] In an embodiment of the present application, adjusting the device parameters of at least one grid-connected device in the second set of grid-connected devices so that all grid-connected devices in the second set of grid-connected devices meet the distributed self-stabilizing protocol includes:

[0113] Obtaining initial device parameters and target device parameters corresponding to any grid-connected device in the second grid-connected device set;

[0114] Calculate the transformation matrix according to the initial device parameters and the target device parameters to obtain the target matrix;

[0115] Adjust the equipment parameters of any grid-connected device according to the target array.

[0116] According to some embodiments, adjusting a device parameter of at least one grid-connected device in the second set of grid-connected devices may specifically include the following steps:

[0117] Step 210: Obtain a target power system model, initial device parameters, and target device parameters corresponding to any grid-connected device;

[0118] Step 220: Determine the transformation matrix and the indeterminate equation group corresponding to the grid-connected device;

[0119] Step 230: converting the indeterminate equations into a deterministic equations system, and solving the deterministic equations system to obtain a set of solution matrices; selecting any reversible solution matrix from the set of solution matrices as a target matrix;

[0120] Step 240: Determine an input feedforward control equation and an output feedback control equation according to the target matrix; and adjust device parameters of the grid-connected device according to the input feedforward control equation and the output feedback control equation.

[0121] According to some embodiments, relevant power system stability analysis technologies and methods, such as time-domain simulation, eigenvalue analysis, and energy function methods, are centralized and rely on a control center. The dominant unstable point (BCU) method based on the stability boundary and the potential energy boundary (PEBS) method within eigenvalue analysis and energy function methods also require information about the equilibrium point. In distributed power system analysis methods, relevant theories also require information about the equilibrium point.

[0122] In some embodiments, the relevant power system stability analysis and control technologies are developed for traditional power systems. Faced with a large number of heterogeneous distributed devices, these methods will face two technical challenges. First, the challenge of computational burden. The relevant technologies require the control center to collect information from the entire system for centralized stability analysis. The integration of a large number of devices will cause the system dimension to explode, and the centralized methods will face a huge computational burden, making it difficult to continue to use. Second, the challenge of unknown balance point. The relevant power system stability analysis technologies are mostly based on a single balance point and require complete information about the balance point. However, with the integration of a large number of renewable energy sources, the uncertainty of wind and solar power output will cause rapid fluctuations in the system balance point. The system will also become increasingly complex, making it difficult to accurately determine the system balance point, and related balance point-dependent technologies will be difficult to use. In this context, how to analyze the stability of a power system composed of a large number of heterogeneous devices when the balance point is unknown is an important technical problem that needs to be solved urgently.

[0123] It's easy to understand that relevant power system stability analysis technologies primarily use centralized methods, target equilibrium points, and rely on complete information from the control center and the equilibrium point. Therefore, when a large number of new energy and distributed devices are connected, these technologies will face enormous computational burdens and the challenge of unknown equilibrium points, making them difficult to use. The synchronous state itself is independent of the equilibrium point. It describes a state in which the voltage phasors at all nodes in the entire network have constant amplitudes and rotate synchronously at the same frequency. This is the state that all AC power systems should maintain for stable operation.

[0124] In an embodiment of the present application, after adjusting the device parameters of at least one grid-connected device in the second set of grid-connected devices so that all grid-connected devices in the second set of grid-connected devices meet the distributed self-stabilizing protocol, the method further includes:

[0125] Obtaining a third grid-connected device set corresponding to the power system, where all grid-connected devices in the third grid-connected device set satisfy a distributed self-stabilizing protocol;

[0126] determining power system parameters corresponding to the third grid-connected device set based on a distributed self-stabilizing protocol;

[0127] Based on the power system parameters, determine whether there is a balance point in the power system;

[0128] If there is a balance point in the power system, the stability analysis of the power system is performed.

[0129] According to some embodiments, in the field of mathematics, the stability problem of the power system can be studied through the Lyapunov stability theory framework. Under the Lyapunov stability theory framework, the power system can be modeled as a set of ordinary differential equations (ODEs) or differential algebraic equations (DAEs). The equilibrium point of this set of equations corresponds to the equilibrium point of the power system after the fault. In addition, according to relevant mathematical conclusions, for an asymptotically stable equilibrium point, any solution starting from its stable domain will converge asymptotically to the equilibrium point. Therefore, if the post-fault equilibrium point is asymptotically stable and the initial value after the fault is within its stable domain, it can be judged that the system is transiently stable after the disturbance. This is the basic logic of the direct method. Therefore, the direct method can transform the transient stability problem into the Lyapunov asymptotic stability problem of the equilibrium point. In specific applications, since the true stable domain of the equilibrium point is often difficult to accurately characterize, a conservative temporary stability judgment can be obtained by finding an inner approximation of the stable domain. In related direct methods, a Lyapunov function or a level set of the energy function can be used as an approximation of the stability region.

[0130] In an embodiment of the present application, the third grid-connected device set includes dynamic devices and static devices, and determining the power system parameters corresponding to the third grid-connected device set based on the distributed self-stabilizing protocol includes:

[0131] Acquire at least one dynamic device in the third grid-connected device set to obtain a dynamic device set;

[0132] Determine the dynamic function set and dynamic region set corresponding to the dynamic device set based on a distributed self-stabilizing protocol;

[0133] Determine a boundary parameter set according to the dynamic function set and the dynamic region set;

[0134] Determine a Cartesian product based on a dynamic region set; determine an objective function set based on a dynamic function set and a boundary parameter set;

[0135] The power system parameters are determined based on the Cartesian product and the objective function set.

[0136] According to some embodiments, in the process of determining whether a dynamic device satisfies the dynamic distributed self-stabilizing protocol, the continuously differentiable function S corresponding to the dynamic device satisfying the dynamic distributed self-stabilizing protocol may be recorded. i (x i ,u i ) and simply connected open set regions And calculate S i (x i ,u i )exist The minimum value on the boundary can be expressed as follows:

[0137]

[0138] In some embodiments, for any dynamic device that satisfies the dynamic distributed self-stabilizing protocol, the corresponding continuously differentiable function S i (x i ,u i ) and simply connected open set regions There can be multiple, in order to reduce conservatism, you can choose r i The combinations with large values ​​are respectively used as the dynamic area and boundary parameters corresponding to the dynamic device.

[0139] In some embodiments, the Cartesian product refers to the product of all dynamic regions in the dynamic region set. Specifically, it can be expressed as follows:

[0140]

[0141] Where n is the number of grid-connected devices corresponding to the power system.

[0142] In some embodiments, the set of objective functions can be expressed according to the following formula:

[0143]

[0144] N=n1+n2+…+n n

[0145] in, is the set of objective functions, is the sum of all dynamic functions in the dynamic function set, r=min{r1,…,r n} is the boundary parameter with the smallest value in the boundary parameter set.

[0146] In some embodiments, it is possible to determine whether the power system has a balance point based on the Cartesian product and the objective function set. Specifically: and Bounded, the power system in the domain There is at least one equilibrium point in the memory. Among them, the conditions can also be judged by a decoupled distributed method. and Bounded", that is, if the dynamic area corresponding to each dynamic device in the power system Bounded, r i >0, and but and Bounded.

[0147] In an embodiment of the present application, determining whether a balance point exists in the power system based on power system parameters includes:

[0148] If the intersection of the objective function set and the Cartesian product is not an empty set, and the intersection of the objective function set and the Cartesian product is bounded, then the power system has at least one equilibrium point in the dynamic region corresponding to the Cartesian product.

[0149] In the embodiment of the present application, if there is a balance point in the power system, a stability analysis of the power system is performed, including:

[0150] Analyze the static stability of power systems based on Cartesian products;

[0151] Obtain the initial state value and output value corresponding to the power system;

[0152] Determine the disturbance parameters corresponding to the power system based on the initial state value, the initial output value and the dynamic function set; determine the target boundary parameters based on the boundary parameter set;

[0153] The transient stability of the power system is analyzed based on the objective function set, Cartesian product, target boundary parameters and disturbance parameters.

[0154] According to some embodiments, static stability is also known as small disturbance stability. When analyzing the static stability of a power system based on a Cartesian product, it can be determined based on the following two conditions:

[0155] The first condition: The set of all equilibrium points in is Lyapunov stable;

[0156] The second condition, All isolated equilibrium points in the system are asymptotically stable.

[0157] When the Cartesian product corresponding to the power system meets these two conditions, it can be determined that the power system is statically stable.

[0158] According to some embodiments, transient stability is also called large disturbance stability. Assume that the power system is subject to a large disturbance, causing the power system operating point to deviate from the original stable operating point. The initial state value and output value of each dynamic device after the disturbance is cleared are recorded as Transient stability is concerned with whether the power system can return to a stable operating point after the disturbance is cleared.

[0159] In some embodiments, when analyzing the transient stability of a power system, a disturbance parameter corresponding to the power system may be obtained. Specifically, the disturbance parameter corresponding to the power system may be expressed according to the following formula:

[0160] l=l1+l2+…l i +…+ln

[0161] Where l is the disturbance parameter corresponding to the power system; is the disturbance parameter corresponding to the dynamic device i in the power system, and n is the number of grid-connected devices corresponding to the power system.

[0162] like If r>l, it can be judged that the power system is transiently stable, that is, the power system can return to a stable operating state after being disturbed.

[0163] In some embodiments, when analyzing the transient stability of the power system, the target system model corresponding to the dynamic equipment in the power system is a model after the power system disturbance is cleared.

[0164] Take a scenario as an example, Figure 2 This is a schematic diagram of the structure of an IEEE-9 node power system provided in an embodiment of the present application. Figure 2 As shown, the grid-connected device corresponding to node 1 is a dynamic device synchronous generator SG; the grid-connected device corresponding to node 2 is a dynamic device power electronic power supply Inverter, which adopts virtual synchronous machine control; the grid-connected device corresponding to node 3 is a dynamic device power electronic power supply Inverter, which adopts droop control; the grid-connected devices corresponding to nodes 5, 7 and 9 are static devices constant impedance loads; nodes 4, 6 and 8 have no corresponding grid-connected devices, which are equivalent to static nodes with zero injection current and do not need to be considered in this application.

[0165] When the method proposed in the embodiment of the present application is used to perform stability analysis on the IEEE-9 node power system, the following steps are specifically included:

[0166] Step 310: Build a grid-connected device model;

[0167] Step 311: Construct a target system model corresponding to the synchronous generator corresponding to node 1. Since the synchronous generator is a dynamic device, it can be represented by the following third-order equation:

[0168]

[0169] Wherein, δ1 is the power angle of the synchronous generator; ω1 is the frequency of the synchronous generator; M1>0 is the inertia of the synchronous generator; is the damping of the synchronous generator; is a constant input mechanical power; E f >0 is a constant excitation voltage; is the active power output of the synchronous generator; T′ d0 >0 is the d-axis open-circuit transient time constant; E′ q1is the q-axis transient voltage; x d is the d-axis synchronous reactance of the synchronous generator; x′ d is the d-axis transient reactance of the synchronous generator; x q is the q-axis synchronous reactance of the synchronous generator; I d1 , I q1 is the component of the injected current of node 1 in the synchronous generator dq coordinate system; V d1 , V q1 is the component of the node voltage at node 1 in the dq coordinate system of the synchronous generator.

[0170] Among them, I d1 ,I q1 ,V d1 and C q1 The following stator circuit equation is satisfied (ignoring the stator winding resistance):

[0171]

[0172] The stator circuit equations form the input (V q1 ,V d1 ) T , the state is x1=(δ1,ω1,E′ q1 ), the input is -(I q1 ,I d1 ) T The input and output of the stator loop equation are transformed from the synchronous generator dq coordinate system to the common DQ coordinate system to meet the target model form. Specifically, the equivalent transformation is performed according to the following formula:

[0173]

[0174] By equivalent transformation, we obtain the input u1=(V Q1 ,V D1 ) T , the state is x1=(δ1,ω1,E′ q1 ), the input is y1=-(I Q1 ,I D1 ) T The target power system model that meets the target model form.

[0175] Step 312: Construct a target system model corresponding to the power electronic power supply controlled by the virtual synchronous machine corresponding to node 2. Since the power electronic power supply controlled by the virtual synchronous machine is a dynamic device, it can be represented by the following third-order equation:

[0176]

[0177] Wherein, M2>0 is virtual inertia; D2>0 is damping; θ2 is the phase angle of the node voltage of node 2 in the DQ coordinate system; V2 is the amplitude of the node voltage of node 2 in the DQ coordinate system; ω2 is the virtual frequency; is the preset reference output active power corresponding to node 2; is the preset reactive power corresponding to node 2; is the preset node voltage amplitude corresponding to node 2; T2>0 is the voltage control time constant; K I K is the frequency active power regulation control integral coefficient; Q is the reactive power regulation coefficient; P2 is the active power corresponding to node 2; Q2 is the reactive power corresponding to node 2.

[0178] Among them, P2 and Q2 satisfy the following equality constraints:

[0179] P2=I Q2 V Q2 +I D2 V D2 =I Q2 V2cosθ2+I D2 V2sinθ2

[0180] Q2=I Q2 V D2 -I D2 V Q2 =I Q2 V2sinθ2-I D2 V2cosθ2

[0181] Based on this, we can determine that the component of node 2 in the DQ coordinate system is V Q2 =V2cosθ2,V D2 =V2sinθ2.

[0182] Therefore, we can get the input u2=-(I Q2 ,I D2 ) T , the state is x2=(θ2,ω2,V2), the input is y2=(V Q2 ,V D2 ) T The target power system model that meets the target model form.

[0183] Step 313: Construct a target system model corresponding to the power electronic power supply using droop control corresponding to node 3. Since the power electronic power supply using droop control is a dynamic device, it can be represented by the following second-order equation:

[0184]

[0185] Wherein, τ1>0, τ2>0 are control time constants; θ3 is the phase angle of the node voltage of node 3 in the DQ coordinate system; V3 is the amplitude of the node voltage of node 3 in the DQ coordinate system; is the preset reference output active power corresponding to node 3; is the preset reactive power corresponding to node 3; is the preset node voltage amplitude corresponding to node 3; is the preset node voltage phase angle corresponding to node 3; d1 is the active power regulation coefficient; d2 is the reactive power regulation coefficient; P3 is the active power corresponding to node 3; Q3 is the reactive power corresponding to node 3.

[0186] Among them, P3 and Q3 satisfy the following equality constraints:

[0187] P3=I Q3 V Q3 +I D3 V D3 =I Q3 V3cosθ3+I D3 V3sinθ3

[0188] Q3=I Q3 V D3 -I D3 V Q3 =I Q3 V3sinθ3-I D3 V3cosθ3

[0189] Based on this, we can determine the component of node 3 in the DQ coordinate system: V Q3 =V3cosθ3,V D3 =V3sinθ3.

[0190] Therefore, we can get the input u3 = -(I Q3 ,I D3 ) T , the state is x3=(θ3,V3), the input is y3=(V Q3 ,V D3 ) T The target power system model that meets the target model form.

[0191] Step 314: Construct the target system model corresponding to the constant impedance load corresponding to nodes 5, 7 and 9. Since the constant impedance load is a static device, its admittance is y i =g i +jb i , where g i ≥0 indicates conductivity, b i Represents susceptance. The input-output nonlinear equations corresponding to the node voltage and injected current at this node are:

[0192]

[0193] The input-output nonlinear equation is the target power system model that satisfies the target model form.

[0194] Step 320: determine whether all grid-connected devices corresponding to the IEEE-9 node power system meet the distributed self-stabilizing protocol. i (x i ,u i )=f i (x i ,u i ) T P i f i (x i ,u i ); If the P corresponding to the dynamic device i If the dynamic distributed self-stabilizing protocol is not satisfied, the initial device parameters and target device parameters corresponding to the dynamic device can be obtained; according to the initial device parameters and target device parameters, the P i Calculation is performed to obtain a target matrix; and device parameters of the dynamic device are adjusted according to the target matrix.

[0195] Step 321, determine whether the synchronous generator corresponding to node 1 meets the dynamic distributed self-stabilizing protocol. Get r1=0.022 corresponding to node 1; the dynamic area corresponding to node 1 is a bounded region in five-dimensional Euclidean space, and its section on the (δ1-θ1)-V1 two-dimensional plane is as follows Figure 3 The shaded area is shown in the figure. Figure 3 It can be determined that the synchronous generator corresponding to node 1 satisfies the dynamic distributed self-stabilizing protocol.

[0196] Step 322: Determine whether the power electronic power supply controlled by the virtual synchronous machine corresponding to node 2 satisfies the dynamic distributed self-stabilizing protocol. Obtain r2 = 0.037 corresponding to node 2; the dynamic region D2 corresponding to node 2 is a bounded region in the five-dimensional Euclidean space, and a section thereof on the θ2-V2 two-dimensional plane is as follows: Figure 4 The shaded area is shown in the figure. Figure 4 It can be determined that the power electronic power supply controlled by the virtual synchronous machine corresponding to node 2 satisfies the dynamic distributed self-stabilizing protocol.

[0197] Step 323, determine whether the power electronic power supply using droop control corresponding to node 3 meets the dynamic distributed self-stabilizing protocol. Get r2 = 0.037 corresponding to node 3; the dynamic area corresponding to node 3 is a bounded region in a four-dimensional Euclidean space, and a section of it on the two-dimensional plane of θ3-V3 is as Figure 5 shown by the shaded area in. From Figure 5 it can be determined that the power electronic type power supply corresponding to node 3 adopting droop control satisfies the dynamic distributed self-stabilizing protocol.

[0198] Step 324: Determine whether the constant impedance loads corresponding to node 5, node 7, and node 9 satisfy the static distributed self-stabilizing protocol. From the input-output nonlinear equations corresponding to node 5, node 7, and node 9, it can be determined that:

[0199]

[0200] Therefore, it can be determined that the constant impedance loads corresponding to node 5, node 7, and node 9 satisfy the static distributed self-stabilizing protocol.

[0201] Step 330: From steps 321 - 324, it can be obtained that the grid-connected devices corresponding to this IEEE-9 node power system all satisfy the distributed self-stabilizing protocol, and the dynamic regions corresponding to each dynamic device are bounded and r i > 0. Further calculation gives Therefore, it can be determined that this IEEE-9 node power system has at least one equilibrium point in the domain .

[0202] Step 340: It can be determined that the set composed of all equilibrium points in is Lyapunov stable; and all isolated equilibrium points in are asymptotically stable. Therefore, this IEEE-9 node power system is statically stable.

[0203] Step 350: The target boundary parameter r corresponding to this IEEE-9 node power system is r = min{r1, r2, r3} = 0.022; assume that the initial state values and input initial values of each dynamic device after being perturbed are Each device independently calculates and communicates and sums to get l = l1 + l2 + l3. According to the method proposed in the embodiment of the present application, for any perturbation that makes l < r, this IEEE-9 node power system can recover to a stable allowable state, that is, transient stability.

[0204] [[ID=4l]]For example, in this IEEE-9 node power system, each grid-connected device originally operates in a stable working state, and each device knows that the current operating point is Assume that at the next moment, affected by the fluctuations of new energy, the active and reactive power outputs of Node 2 will decrease by 5%, while the active and reactive power outputs of Node 3 will increase by 5%. To ensure the transient stability of the IEEE-9 bus power system after the power fluctuation, it is necessary to determine whether the system can return to a stable state after the power fluctuation at the next moment. For this purpose, each device calculates respectively And by communicating the calculation results with each other, we can get l = l1 + l2 + l3 = 0.0198 < r = 0.022. Therefore, according to the method proposed in the embodiments of the present application, it can be directly determined that the IEEE-9 bus power system is transiently stable. Figure 6 FIG. is a waveform diagram of the voltages of each bus of an IEEE-9 bus power system after being disturbed provided by an embodiment of the present application; Figure 7 FIG. is a waveform diagram of the frequencies of each bus of an IEEE-9 bus power system after being disturbed provided by an embodiment of the present application. As Figure 6 、 Figure 7 shown, the IEEE-9 bus power system can return to the steady state after being disturbed, indicating that the IEEE-9 bus power system is transiently stable, and verifying the effectiveness of the method proposed in the embodiments of the present application.

[0205] In summary, the method proposed in the embodiments of the present application determines the first grid-connected device set corresponding to the power system and the target power system model set corresponding to the first grid-connected device set; based on the target power system model set, obtains at least one grid-connected device in the first grid-connected device set that does not satisfy the distributed self-stabilizing protocol, and gets the second grid-connected device set; adjusts the device parameters of at least one grid-connected device in the second grid-connected device set to make all grid-connected devices in the second grid-connected device set satisfy the distributed self-stabilizing protocol. The present application adjusts the first grid-connected device set corresponding to the power system to make all grid-connected devices in the first grid-connected device set satisfy the distributed self-stabilizing protocol, so the overall stability of the power system can be ensured in a self-stabilizing manner. The distributed self-stabilizing protocol of the present application is independent of the equilibrium point, so the present application does not depend on the control center of the power system, nor does it depend on the equilibrium point, and can perform stability analysis on the power system when the equilibrium point is unknown.

[0206] To implement the above embodiments, the present application also proposes a distributed self-stabilizing system for a power system independent of the equilibrium point.

[0207] Figure 8 FIG. is a schematic structural diagram of a distributed self-stabilizing system for a power system independent of the equilibrium point provided by an embodiment of the present application.

[0208] As Figure 8 shown, a distributed self-stabilizing system 800 for a power system independent of the equilibrium point includes:

[0209] A set determining module 810 is configured to determine a first grid-connected device set corresponding to the power system and a target power system model set corresponding to the first grid-connected device set;

[0210] The device acquisition module 820 is configured to acquire, based on the target power system model set, at least one grid-connected device in the first grid-connected device set that does not satisfy the distributed self-stabilizing protocol, to obtain a second grid-connected device set;

[0211] The parameter adjustment module 830 is configured to adjust device parameters of at least one grid-connected device in the second set of grid-connected devices so that all grid-connected devices in the second set of grid-connected devices meet the distributed self-stabilizing protocol.

[0212] In summary, the system proposed in the embodiment of the present application is used to determine the first grid-connected device set corresponding to the power system and the target power system model set corresponding to the first grid-connected device set through a set determination module; the device acquisition module is used to obtain at least one grid-connected device in the first grid-connected device set that does not satisfy the distributed self-stabilization protocol based on the target power system model set, and obtain a second grid-connected device set; the parameter adjustment module is used to adjust the device parameters of at least one grid-connected device in the second grid-connected device set so that all grid-connected devices in the second grid-connected device set satisfy the distributed self-stabilization protocol. The present application adjusts the first grid-connected device set corresponding to the power system so that all grid-connected devices in the first grid-connected device set satisfy the distributed self-stabilization protocol, thereby ensuring the overall stability of the power system in a self-stabilizing manner. The distributed self-stabilization protocol of the present application is independent of the balance point, so the present application does not rely on the control center of the power system, nor on the balance point, and can perform stability analysis on the power system when the balance point is unknown.

[0213] It should be noted that, in the description of this application, the terms "first", "second", etc. are used for descriptive purposes only and should not be understood as indicating or implying relative importance. In addition, in the description of this application, unless otherwise specified, the meaning of "plurality" is two or more.

[0214] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application belong.

[0215] It should be understood that various parts of the present application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used to implement: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0216] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0217] In addition, the functional units in the various embodiments of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into a module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0218] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc.

[0219] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0220] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A distributed self-stabilization method for power systems independent of equilibrium points, characterized in that: include: Determining a first grid-connected device set corresponding to the power system and a target power system model set corresponding to the first grid-connected device set; Based on the target power system model set, obtaining at least one grid-connected device in the first grid-connected device set that does not satisfy the distributed self-stabilizing protocol to obtain a second grid-connected device set; Adjusting device parameters of at least one grid-connected device in the second set of grid-connected devices so that all grid-connected devices in the second set of grid-connected devices satisfy the distributed self-stabilizing protocol; Acquire a third grid-connected device set corresponding to the power system, where all grid-connected devices in the third grid-connected device set satisfy a distributed self-stabilizing protocol; Acquire at least one dynamic device in the third grid-connected device set to obtain a dynamic device set; Determine a dynamic function set and a dynamic region set corresponding to the dynamic device set based on the distributed self-stabilizing protocol; Determining a boundary parameter set according to the dynamic function set and the dynamic region set; Determining a Cartesian product based on the dynamic region set; determining an objective function set based on the dynamic function set and the boundary parameter set; wherein the Cartesian product is the product of all dynamic regions in the dynamic region set; determining the power system parameters according to the Cartesian product and the set of objective functions; If the intersection of the objective function set in the power system parameters and the Cartesian product is not an empty set, and the intersection of the objective function set and the Cartesian product is bounded, then the power system has at least one equilibrium point in the dynamic region corresponding to the Cartesian product; If the power system has a balance point, performing stability analysis on the power system; If the power system has a balance point, performing stability analysis on the power system includes: analyzing the static stability of the power system based on the Cartesian product; Obtaining an initial state value and an initial output value corresponding to the power system; Determining disturbance parameters corresponding to the power system based on the initial state value, the initial output value, and the dynamic function set; determining target boundary parameters according to the boundary parameter set; The transient stability of the power system is analyzed based on the objective function set, the Cartesian product, the target boundary parameter and the disturbance parameter.

2. The method according to claim 1, wherein The first grid-connected device set includes dynamic devices and static devices. The first grid-connected device set corresponding to the determined power system and the target power system model set corresponding to the first grid-connected device set include: Acquire at least one dynamic device in the first grid-connected device set to obtain a dynamic device set; determine a set of input state output nonlinear equations corresponding to the dynamic device set; Acquire at least one static device in the first grid-connected device set to obtain a static device set; determine a set of input and output nonlinear equations corresponding to the static device set; The target power system model set is determined according to the input-state-output nonlinear equation set and the input-output nonlinear equation set.

3. The method according to claim 1, wherein The determining of a first grid-connected device set corresponding to the power system and a target power system model set corresponding to the first grid-connected device set includes: Acquire an initial power system model corresponding to at least one grid-connected device in the set of grid-connected devices to obtain an initial power system model set; An equivalent transformation is performed on at least one initial power system model in the initial power system model set that does not satisfy the target model form, thereby obtaining a target power system model set.

4. The method according to claim 1, wherein The first grid-connected device set includes dynamic devices and static devices. The method of obtaining, based on the target power system model set, at least one grid-connected device in the first grid-connected device set that does not satisfy the distributed self-stabilizing protocol to obtain the second grid-connected device set includes: Acquire any grid-connected device in the first set of grid-connected devices; If any of the grid-connected devices is a dynamic device, determining whether the dynamic device satisfies the dynamic distributed self-stabilizing protocol based on the target power system model corresponding to the dynamic device; If any of the grid-connected devices is a static device, determining whether the static device satisfies a static distributed self-stabilizing protocol based on a target power system model corresponding to the static device; The first set of grid-connected devices is traversed to obtain at least one grid-connected device in the first set of grid-connected devices that does not satisfy the distributed self-stabilizing protocol, thereby obtaining a second set of grid-connected devices.

5. The method according to claim 1, wherein The adjusting the device parameters of at least one grid-connected device in the second set of grid-connected devices so that all grid-connected devices in the second set of grid-connected devices satisfy the distributed self-stabilizing protocol includes: Obtaining initial device parameters and target device parameters corresponding to any grid-connected device in the second set of grid-connected devices; Calculating the transformation matrix according to the initial device parameters and the target device parameters to obtain a target matrix; The device parameters of any of the grid-connected devices are adjusted according to the target matrix.

6. A distributed self-stabilizing system for power systems independent of equilibrium points, characterized in that: The system implements the method according to claim 1, and the system includes: a set determining module, configured to determine a first grid-connected device set corresponding to the power system, and a target power system model set corresponding to the first grid-connected device set; a device acquisition module, configured to acquire, based on a target power system model set, at least one grid-connected device in the first set of grid-connected devices that does not satisfy the distributed self-stabilizing protocol, to obtain a second set of grid-connected devices; The parameter adjustment module is used to adjust the device parameters of at least one grid-connected device in the second grid-connected device set so that all grid-connected devices in the second grid-connected device set meet the distributed self-stabilizing protocol.

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