Improved ADMM-based distributed coordinated restoration method and system for power transmission network and power distribution network

Abstract

Disclosed in the present invention are an improved ADMM-based distributed coordinated restoration method and system for a power transmission network and a power distribution network. The method comprises: constructing an objective function to maximize the load restoration benefit of a power transmission network and a power distribution network and, in light of constraint conditions of the power transmission network and the power distribution network, establishing a coordinated restoration optimization model for the power transmission network and the power distribution network; on the basis of the coordinated restoration optimization model for the power transmission network and the power distribution network, introducing an augmented Lagrange function to construct an augmented objective function of the power transmission network and he power distribution network; using an improved alternating direction method of multipliers to solve the augmented objective function of the power transmission network and the power distribution network; using a dual update accelerated iteration policy to update a penalty coefficient and a Lagrange multiplier; and, on the basis of primal residual and dual residual convergence situations or the number of iterations, acquiring a coordinated restoration policy for the power transmission network and the power distribution network. The present invention efficiently solves distributed coordinated restoration of power transmission networks and power distribution networks, and not only increases restoration speed and reduces economic losses, but also reduces calculation complexity and communication burdens.

Description

A distributed collaborative restoration method and system for transmission and distribution networks based on improved ADMM Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a distributed collaborative restoration method and system for a transmission and distribution network based on an improved ADMM. Background Art

[0002] With the rapid development of the Energy Internet and smart grids, coordinated restoration technology for transmission and distribution networks is gaining increasing attention as a key means of improving grid resilience and reliability. Under the influence of unpredictable events such as extreme weather and natural disasters, power grid systems often face risks such as power outages and failures. The effective application of coordinated restoration technology for transmission and distribution networks can significantly enhance the grid's rapid recovery capabilities, reduce outage duration, and ensure the continuity and stability of power supply. However, in practice, transmission and distribution networks are governed by different dispatching entities and are constrained by factors such as data security and privacy protection, making it difficult to fully share data. This, to a certain extent, limits the practical application of coordinated restoration technology for transmission and distribution networks. Therefore, achieving distributed coordinated optimization of transmission and distribution networks while ensuring data security and privacy is a hot and challenging issue in current smart grid research.

[0003] Although existing research has made some progress in the coordinated restoration technology of transmission and distribution networks, there are still many challenges and problems that need to be solved. Among them, one of the most prominent problems is the selection and application of distributed solution algorithms. Although the traditional alternating direction multiplier method (ADMM) can achieve distributed optimization to a certain extent, its convergence is extremely sensitive to parameter settings. If the parameters are not selected properly, it may cause the algorithm solution process to be difficult to converge, or even obtain incorrect optimization results. In addition, with the expansion of power grid scale and the increase in complexity, the coordinated restoration problem of transmission and distribution networks has become highly nonlinear and complex, which further increases the difficulty of distributed solution. Therefore, how to improve the existing distributed solution algorithm and improve its convergence and stability to meet the needs of coordinated restoration of large-scale and complex power grids is a technical problem that needs to be solved urgently. At the same time, how to reduce the computational complexity and communication overhead of the algorithm while ensuring the accuracy of the solution is also the key to realizing the distributed coordinated restoration of the entire transmission and distribution network. Summary of the Invention

[0004] The purpose of this section is to summarize some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the abstract and title of this application to avoid obscuring the purpose of this section, the abstract and the title of the invention, and such simplifications or omissions should not be used to limit the scope of the present invention.

[0005] In light of the above-mentioned existing problems, the present invention proposes a distributed collaborative restoration method for transmission and distribution networks based on an improved ADMM. This method addresses the problem of how to accelerate the convergence of distributed solutions by improving the alternating direction multiplier method when transmission and distribution network information is not fully shared, thereby achieving rapid and efficient coordinated restoration of the transmission and distribution network and reducing economic losses after a major power outage.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0007] In a first aspect, the present invention provides a distributed collaborative restoration method for a transmission and distribution network based on an improved ADMM, comprising:

[0008] Acquire data related to the transmission and distribution network, construct an objective function to maximize the load restoration benefit of the transmission and distribution network, and establish a transmission and distribution network collaborative restoration optimization model based on the objective function and transmission and distribution network constraints;

[0009] Based on the transmission and distribution network coordinated restoration optimization model, an augmented Lagrangian function is introduced to construct augmented objective functions of the transmission network and the distribution network;

[0010] Setting a maximum number of iterations of the improved alternating direction multiplier method, a primal residual convergence threshold, and a dual residual convergence threshold, and using the improved alternating direction multiplier method to solve the augmented objective function of the transmission network and the distribution network;

[0011] A double-update accelerated iteration strategy is adopted. If the original residual is greater than the set threshold, the penalty coefficient and Lagrange multiplier are updated. If the original residual is less than or equal to the set threshold, the Lagrange multiplier is updated and the penalty coefficient remains unchanged.

[0012] According to the convergence of the original residual and the dual residual or the number of iterations, it is determined whether the improved alternating direction multiplier method should continue the next round of optimization or terminate the iteration to output the final transmission and distribution network coordinated restoration strategy.

[0013] As a preferred solution of the distributed collaborative restoration method of the transmission and distribution network based on the improved ADMM described in the present invention, wherein: according to the objective function and the transmission and distribution network constraints, a transmission and distribution network collaborative restoration optimization model is established, including:

[0014] The objective function expression is:

[0015] in, and are the number of nodes in the transmission and distribution network, and are the unit restoration benefits of node n load in the transmission network and distribution network respectively, and are the load recovery powers of node n in the transmission network and distribution network at time step t, Δt is the time step interval, and T is the number of time steps in the recovery process;

[0016] The transmission and distribution network constraints include black start constraints, load recovery constraints and power balance constraints of non-black start units in the transmission network, as well as load recovery constraints and power balance constraints of the distribution network.

[0017] As a preferred solution of the distributed collaborative restoration method of the transmission and distribution network based on the improved ADMM described in the present invention, the augmented Lagrangian function is introduced to construct the augmented objective function of the transmission network and the distribution network, including:

[0018] The transmission network augmentation objective function is expressed as:

[0019] Among them, f TN Augment the objective function for the transmission network, and are the Lagrange multiplier and penalty factor of the transmission network, is the load recovery power of node n in the transmission network at time step t, is the number of coupling nodes in the transmission and distribution network, T Step is the number of time steps in the recovery process, is the transmission and distribution network interaction power that the transmission network expects the nth distribution network to receive, is the transmission and distribution network interaction power that the nth distribution network wants to transfer from the transmission network, f TN,B restoring revenue to the transmission grid;

[0020] The augmented objective function of the distribution network is expressed as:

[0021] Among them, f DN,n Augment the objective function for the distribution network, and are the Lagrange multiplier and penalty factor of the nth distribution network, is the load recovery power of node n in the distribution network at time step t, T Step is the number of time steps in the recovery process, is the transmission and distribution network interaction power that the transmission network expects the nth distribution network to receive, is the transmission and distribution network interaction power that the nth distribution network wants to transfer from the transmission network, f DN,n,B Recover revenue for the distribution network.

[0022] As a preferred solution of the distributed coordinated restoration method of the transmission and distribution network based on the improved ADMM of the present invention, wherein: the augmented objective function of the transmission network and the distribution network is solved by using the improved alternating direction multiplier method, including:

[0023] The transmission network collects the transmission and distribution interaction power strategy matrix expected by each distribution network, calculates the augmented objective function of the transmission network, and obtains the transmission and distribution interaction power strategy matrix expected by the transmission network;

[0024] After each distribution network receives the transmission and distribution interaction power strategy matrix expected by the transmission network from the transmission network, it calculates the distribution network augmented objective function and obtains the transmission and distribution interaction power strategy matrix expected by the distribution network.

[0025] As a preferred solution of the distributed collaborative restoration method of the transmission and distribution network based on the improved ADMM described in the present invention, a double-update accelerated iteration strategy is adopted. If the original residual is greater than a set threshold, the penalty coefficient and the Lagrange multiplier are updated, including:

[0026] The update penalty coefficient is expressed as:

[0027] in, is the original residual of the kth iteration of the transmission and distribution network, is the dual residual of the k-th iteration of the transmission and distribution network, is the penalty coefficient of the k+1th iteration of the transmission network, is the penalty coefficient of the k-th iteration of the transmission network, is the penalty coefficient of the k+1th iteration of the nth distribution network node, is the penalty coefficient of the kth iteration of the nth distribution network node, δ P is the original residual convergence threshold, δ D is the dual residual convergence threshold;

[0028] The updated Lagrange multiplier is expressed as:

[0029] in, is the expected transmission and distribution interaction power strategy matrix at the t-th time step of the transmission network at the k+1-th iteration, is the transmission and distribution interaction power strategy matrix at the t-th time step during the k+1-th iteration of the distribution network, is the Lagrange multiplier of the t-th time step at the k+1-th iteration of the transmission network, is the Lagrange multiplier of the t-th time step at the k-th iteration of the transmission network, is the Lagrange multiplier of the nth distribution network node at the k+1th iteration at the tth time step, is the Lagrange multiplier of the nth distribution network node at the kth iteration at the tth time step, is the penalty coefficient of the k+1th iteration of the transmission network, is the penalty coefficient of the k+1th iteration of the distribution network.

[0030] As a preferred solution of the distributed collaborative restoration method for transmission and distribution networks based on the improved ADMM described in the present invention, if the original residual is less than or equal to a set threshold, the Lagrangian multiplier is updated and the penalty coefficient remains unchanged, including:

[0031] The updated Lagrange multiplier is expressed as:

[0032] in, is the Lagrange multiplier of the t-th time step at the k+1-th iteration of the transmission network, is the Lagrange multiplier of the t-th time step at the k-th iteration of the transmission network, is the Lagrange multiplier of the nth distribution network node at the k+1th iteration at the tth time step, is the Lagrange multiplier of the nth distribution network node at the kth iteration at the tth time step, is the penalty coefficient of the k+1th iteration of the transmission network, is the penalty coefficient of the k+1th iteration of the distribution network, K D and K 1 are the integral and dual residual regulation parameters in classical control theory, is the expected transmission and distribution interaction power strategy matrix at the t-th time step of the transmission network at the k+1-th iteration, is the transmission and distribution interaction power strategy matrix at the tth time step during the k+1th iteration of the distribution network.

[0033] As a preferred solution of the distributed coordinated restoration method of the transmission and distribution network based on the improved ADMM of the present invention, wherein: according to the convergence of the original residual and the dual residual or the number of iterations, it is determined whether the improved alternating direction multiplier method continues the next round of optimization or terminates the iteration to output the final transmission and distribution network coordinated restoration strategy, including:

[0034] To judge the convergence of the original residual and the dual residual, the expression is:

[0035] in, is the original residual of the kth iteration of the transmission and distribution network, is the dual residual of the kth iteration of the transmission and distribution network, δ P is the original residual convergence threshold, δ D is the dual residual convergence threshold;

[0036] If the improved alternating direction multiplier method satisfies the convergence expressions of the primal residual and the dual residual, or the maximum number of iterations is reached, the final transmission and distribution network coordinated restoration strategy is output.

[0037] In a second aspect, the present invention provides a system for distributed coordinated restoration of a transmission and distribution network based on an improved ADMM, comprising:

[0038] A data acquisition module is used to obtain data related to the transmission and distribution network and construct an objective function to maximize the load recovery benefits of the transmission and distribution network;

[0039] An optimization model establishment module is used to establish a transmission and distribution network collaborative restoration optimization model based on the objective function and transmission and distribution network constraints;

[0040] A distributed restoration optimization module is used to introduce an augmented Lagrangian function to construct an augmented objective function of the transmission network and the distribution network based on the transmission and distribution network collaborative restoration optimization model;

[0041] an iterative solution module, configured to set a maximum number of iterations of an improved alternating direction multiplier method, a primal residual convergence threshold, and a dual residual convergence threshold, and to use the improved alternating direction multiplier method to solve the augmented objective functions of the transmission network and the distribution network;

[0042] The accelerated iteration strategy module is used to adopt a double-update accelerated iteration strategy. If the original residual is greater than the set threshold, the penalty coefficient and Lagrange multiplier are updated. If the original residual is less than or equal to the set threshold, the Lagrange multiplier is updated and the penalty coefficient remains unchanged.

[0043] The optimization result output module is used to determine whether the improved alternating direction multiplier method should continue the next round of optimization or terminate the iteration to output the final transmission and distribution network coordinated restoration strategy based on the convergence status or number of iterations of the original residual and the dual residual.

[0044] In a third aspect, the present invention provides a computing device, comprising:

[0045] memory and processor;

[0046] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, the steps of the distributed collaborative restoration method for the transmission and distribution network based on the improved ADMM are implemented.

[0047] In a fourth aspect, the present invention provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the steps of the distributed collaborative restoration method for transmission and distribution networks based on the improved ADMM.

[0048] Compared with the existing technology, the beneficial effects of the present invention are as follows: the present invention realizes the efficient solution of distributed collaborative restoration of transmission and distribution networks by improving the alternating direction multiplier method, which not only improves the recovery speed and reduces economic losses, but also optimizes the solution process by adaptively adjusting the penalty factor, reduces the computational complexity and alleviates the communication burden, thereby significantly enhancing the practicality of the model and providing strong technical support for the stable operation of the power system and social and economic development. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive effort. Among them:

[0050] FIG1 is a schematic diagram of the overall process of a distributed coordinated restoration method for a transmission and distribution network based on an improved ADMM according to an embodiment of the present invention;

[0051] FIG2 is a schematic diagram of a 179-node power system topology of a distributed coordinated restoration method for a transmission and distribution network based on an improved ADMM according to an embodiment of the present invention;

[0052] FIG3 is a schematic diagram of power balance of a transmission network under three disaster scenarios of a distributed collaborative restoration method for a transmission and distribution network based on an improved ADMM according to an embodiment of the present invention;

[0053] FIG4 is a schematic diagram of the recovery of power generation and load power of a transmission system under three scenarios of a distributed coordinated restoration method for a transmission and distribution network based on an improved ADMM according to an embodiment of the present invention. DETAILED DESCRIPTION

[0054] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, the following detailed description of the specific embodiments of the present invention is given in conjunction with the accompanying drawings. It is obvious that the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in this field without creative work should fall within the scope of protection of the present invention.

[0055] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0056] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0057] The present invention is described in detail with reference to schematic diagrams. For ease of illustration, cross-sectional views of device structures may be partially enlarged and not to scale when describing embodiments of the present invention. Furthermore, the schematic diagrams are merely illustrative and should not limit the scope of the present invention. Furthermore, in actual production, the three-dimensional dimensions of length, width, and depth should be included.

[0058] Furthermore, in the description of the present invention, it should be noted that the terms "upper, lower, inner, and outer" and other references to orientations or positional relationships are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the systems or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first, second, or third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0059] In this disclosure, unless otherwise specified or limited, the terms "mounted," "connected," and "connected" should be interpreted broadly. For example, they may refer to fixed, removable, or integral connections. They may also refer to mechanical, electrical, or direct connections, indirect connections through an intermediary, or internal communication between two components. Those skilled in the art will understand the specific meanings of these terms in this disclosure.

[0060] Example 1

[0061] 1 , which is an embodiment of the present invention, provides a distributed collaborative restoration method for a transmission and distribution network based on an improved ADMM, including:

[0062] S100: Acquire relevant data of the transmission and distribution network, construct an objective function to maximize the load restoration benefit of the transmission and distribution network, and establish a transmission and distribution network collaborative restoration optimization model based on the objective function and the transmission and distribution network constraints;

[0063] Furthermore, the objective function expression is:

[0064] in, and are the number of nodes in the transmission and distribution network, and are the unit restoration benefits of node n load in the transmission network and distribution network respectively, and are the load recovery powers of node n in the transmission network and distribution network at time step t, Δt is the time step interval, and T is the number of time steps in the recovery process;

[0065] The transmission and distribution network constraints include black start constraints, load recovery constraints, and power balance constraints for non-black start units in the transmission network, as well as load recovery constraints and power balance constraints for the distribution network;

[0066] Preferably, the transmission network usually has large thermal power units. Such units are difficult to black-start on their own after a major power outage and are called non-black-start units. The black-start constraints of these non-black-start units are expressed as:

[0067] in, and are the restored power generation power, plant power and rated power of NBS at transmission network node n at time step t, is the climbing power value of NBS, t1 and t2 are the time step of NBS recovery start and the time step of recovery to rated power respectively. It is a Boolean variable indicating the recovery status of the node where the NBS is located. and They are the upper and lower limits of the black start time for non-black start units respectively;

[0068] Preferably, the load constraint condition of the transmission network is expressed as:

[0069] in, and are the restored load power and load rated power of transmission network node n, and are the sets of load nodes in the transmission network that cannot participate in demand response and those that can participate in demand response, is the upper limit of the recoverable load at each time step, is the load recovery state variable of transmission network node n, and are the load recovery state variables of transmission network node n at time t and t-1 respectively;

[0070] It should be noted that the load constraints of the distribution network are expressed in the same way as those of the transmission network;

[0071] Preferably, the power balance constraints of the transmission network and the distribution network are respectively expressed as:

[0072] in, and are the node sets of the transmission network and its distribution network connected to node n, and are the power generation capacity of the black start unit, new energy unit and energy storage equipment at the transmission network node n, is the load power of transmission network node n, The transmission and distribution network interaction power provided by the transmission network to the distribution network connected to node n, and are the output of the new energy unit, the output of the energy storage device and the load demand power of the transmission network node x connected to the transmission network node n;

[0073] It should be noted that by constructing a collaborative restoration optimization model with the goal of maximizing the load restoration benefits of the transmission and distribution network, while taking into account multiple constraints, the optimal allocation of resources and the rapid and efficient restoration of the power grid are achieved, the decision-making efficiency and the intelligence level of the power grid are improved, and a solid guarantee is provided for the safe and stable operation of the power grid.

[0074] S102: Based on the transmission and distribution network coordinated restoration optimization model, an augmented Lagrangian function is introduced to construct augmented objective functions of the transmission network and the distribution network;

[0075] Furthermore, the transmission network augmentation objective function is expressed as:

[0076] Among them, f TN Augment the objective function for the transmission network, and are the Lagrange multiplier and penalty factor of the transmission network, is the load recovery power of node n in the transmission network at time step t, is the number of coupling nodes in the transmission and distribution network, T Step is the number of time steps in the recovery process, is the transmission and distribution network interaction power that the transmission network expects the nth distribution network to receive, is the transmission and distribution network interaction power that the nth distribution network wants to transfer from the transmission network, f TN,B restoring revenue to the transmission grid;

[0077] The augmented objective function of the distribution network is expressed as:

[0078] Among them, f DN,n Augment the objective function for the distribution network, and are the Lagrange multiplier and penalty factor of the nth distribution network, is the load recovery power of node n in the distribution network at time step t, T Step is the number of time steps in the recovery process, is the transmission and distribution network interaction power that the transmission network expects the nth distribution network to receive, is the transmission and distribution network interaction power that the nth distribution network wants to transfer from the transmission network, f DN,n,B Recover revenue for the distribution grid;

[0079] Preferably, the transmission network and distribution network restoration benefits are specifically expressed as:

[0080] Among them, f TN,B For transmission network recovery revenue, f DN,n,B Recover revenue for the distribution network, and are the unit restoration benefits of node n load in the transmission network and distribution network respectively, Δt is the time step interval, T is the number of time steps in the restoration process, and are the load recovery powers of node n in the transmission network and distribution network at time step t respectively;

[0081] It should be noted that this technical solution constructs the augmented objective function of the transmission network and distribution network by introducing the augmented Lagrangian function, and realizes the distributed optimization of the coordinated restoration of the transmission and distribution network. It not only takes into account the load recovery benefits of the transmission and distribution network, but also ensures the power balance and constraint conditions of the transmission and distribution network during the restoration process through the introduction of Lagrangian multipliers and penalty factors; through distributed optimization, the computational complexity is reduced, the optimization efficiency is improved, and the global optimality of the restoration strategy is ensured.

[0082] S104: Setting the maximum number of iterations of the improved alternating direction multiplier method, the original residual convergence threshold, and the dual residual convergence threshold, and using the improved alternating direction multiplier method to solve the augmented objective function of the transmission network and the distribution network;

[0083] Furthermore, the transmission network collects the transmission and distribution interaction power strategy matrix expected by each distribution network, calculates the augmented objective function of the transmission network, and obtains the transmission and distribution interaction power strategy matrix expected by the transmission network;

[0084] After receiving the transmission and distribution interaction power strategy matrix expected by the transmission network from the transmission network, each distribution network calculates the distribution network augmented objective function and obtains the transmission and distribution interaction power strategy matrix expected by the distribution network;

[0085] It should be noted that for the current nth distribution network node, it receives the expected interactive power strategy of the transmission network and calculates its own recovery strategy based on this information. After the calculation is completed, n is increased by 1 and the next distribution network node is processed. The operation is repeated until all distribution network nodes (i.e., n reaches the total number of distribution network nodes) have been processed.

[0086] It should also be noted that the distributed solution method reduces the computational complexity and amount of calculations, and improves the optimization efficiency; the improvement of the alternating direction multiplier method enhances the convergence and stability of the algorithm, making the solution results more accurate and reliable; and by setting a reasonable convergence threshold, it ensures that the solution process can quickly converge to the optimal solution while meeting the accuracy requirements.

[0087] S106: Using a double update accelerated iteration strategy, if the original residual is greater than a set threshold, the penalty coefficient and the Lagrange multiplier are updated; if the original residual is less than or equal to the set threshold, the Lagrange multiplier is updated, and the penalty coefficient remains unchanged;

[0088] Furthermore, if the original residual is greater than the set threshold, the penalty coefficient and Lagrange multiplier are updated, and the updated penalty coefficient is expressed as:

[0089] in, is the original residual of the kth iteration of the transmission and distribution network, is the dual residual of the k-th iteration of the transmission and distribution network, is the penalty coefficient of the k+1th iteration of the transmission network, is the penalty coefficient of the k-th iteration of the transmission network, is the penalty coefficient of the k+1th iteration of the nth distribution network node, is the penalty coefficient of the kth iteration of the nth distribution network node, δ P is the original residual convergence threshold, δ D is the dual residual convergence threshold;

[0090] The updated Lagrange multiplier is expressed as:

[0091] in, is the expected transmission and distribution interaction power strategy matrix at the t-th time step of the transmission network at the k+1-th iteration, is the transmission and distribution interaction power strategy matrix at the t-th time step during the k+1-th iteration of the distribution network, is the Lagrange multiplier of the t-th time step at the k+1-th iteration of the transmission network, is the Lagrange multiplier of the t-th time step at the k-th iteration of the transmission network, is the Lagrange multiplier of the nth distribution network node at the k+1th iteration at the tth time step, is the Lagrange multiplier of the nth distribution network node at the kth iteration at the tth time step, is the penalty coefficient of the k+1th iteration of the transmission network, is the penalty coefficient of the k+1th iteration of the distribution network;

[0092] Furthermore, if the original residual is less than or equal to the set threshold, the Lagrange multiplier is updated and the penalty coefficient remains unchanged. The updated Lagrange multiplier is expressed as:

[0093] in, is the Lagrange multiplier of the t-th time step at the k+1-th iteration of the transmission network, is the Lagrange multiplier of the t-th time step at the k-th iteration of the transmission network, is the Lagrange multiplier of the nth distribution network node at the k+1th iteration at the tth time step, is the Lagrange multiplier of the nth distribution network node at the kth iteration at the tth time step, is the penalty coefficient of the k+1th iteration of the transmission network, is the penalty coefficient of the k+1th iteration of the distribution network, K D and K 1 are the integral and dual residual regulation parameters in classical control theory, is the expected transmission and distribution interaction power strategy matrix at the t-th time step of the transmission network at the k+1-th iteration, is the transmission and distribution interaction power strategy matrix at the t-th time step during the k+1-th iteration of the distribution network;

[0094] Preferably, the original residual and dual residual of the kth iteration are expressed as:

[0095] in, is the original residual of the kth iteration of the transmission and distribution network, is the dual residual of the kth iteration of the transmission and distribution network, T Step is the number of time steps in the recovery process, is the expected transmission and distribution interaction power strategy matrix at the t-th time step of the transmission network at the k+1-th iteration, is the transmission and distribution interaction power strategy matrix at the t-th time step during the k+1-th iteration of the distribution network;

[0096] It should be noted that the original residual threshold is set to 10 -3 ~10 -5 ;

[0097] It should be noted that by adopting a dual-update accelerated iteration strategy, the update method of the penalty coefficient and the Lagrange multiplier can be dynamically adjusted according to the size of the original residual. When the original residual is greater than the set threshold, the penalty coefficient and the Lagrange multiplier are updated at the same time, which accelerates the convergence speed of the algorithm and enhances the stability of the algorithm. When the original residual is less than or equal to the set threshold, only the Lagrange multiplier is updated, and the penalty coefficient remains unchanged, avoiding oscillation or instability caused by over-adjustment of parameters, thereby ensuring smooth convergence of the algorithm.

[0098] It should also be noted that the strategy for updating the penalty coefficient combines the information of the original residual and the dual residual. By comparing their size relationship with the preset threshold, the value of the penalty coefficient is dynamically adjusted to better balance the convergence speed and stability of the algorithm and improve the solution accuracy. At the same time, the strategy for updating the Lagrange multiplier has also been optimized. By introducing the integral and dual residual adjustment parameters in classical control theory, the value of the Lagrange multiplier can be adjusted more accurately, thereby further improving the convergence speed and stability of the algorithm.

[0099] S108: Determine whether to continue the next round of optimization or terminate the iteration based on the convergence of the original residual and the dual residual or the number of iterations, and output the final transmission and distribution network coordinated restoration strategy.

[0100] Furthermore, the convergence of the original residual and the dual residual is judged by the expression:

[0101] in, is the original residual of the kth iteration of the transmission and distribution network, is the dual residual of the kth iteration of the transmission and distribution network, δ P is the original residual convergence threshold, δ D is the dual residual convergence threshold;

[0102] If the improved alternating direction multiplication method satisfies the convergence expressions of the primal residual and the dual residual, or the maximum number of iterations is reached, the final transmission and distribution network coordinated restoration strategy is output;

[0103] It should be noted that by introducing the convergence judgment mechanism of the original residual and the dual residual and the limitation of the number of iterations, it is ensured that the iterative process of the improved alternating direction multiplier method can not only fully converge but also terminate within a reasonable time, thereby outputting the final coordinated restoration strategy for the transmission and distribution network; it effectively avoids the waste of computing resources and the reduction of solution efficiency due to excessive iterations, and at the same time ensures the accuracy and reliability of the solution results; in addition, this scheme also takes into account the actual situation and needs of the coordinated restoration strategy for the transmission and distribution network, and ensures the feasibility and effectiveness of the strategy in practical applications by setting a reasonable number of iterations.

[0104] The above is a schematic scheme of a distributed collaborative restoration method for a transmission and distribution network based on an improved ADMM in this embodiment. It should be noted that the technical scheme of the system for distributed collaborative restoration of a transmission and distribution network based on the improved ADMM and the technical scheme of the distributed collaborative restoration method for a transmission and distribution network based on the improved ADMM are of the same concept. For details not described in detail in the technical scheme of the distributed collaborative restoration system for a transmission and distribution network based on the improved ADMM in this embodiment, please refer to the description of the technical scheme of the distributed collaborative restoration method for a transmission and distribution network based on the improved ADMM.

[0105] The distributed coordinated restoration system for transmission and distribution networks based on the improved ADMM in this embodiment includes:

[0106] A data acquisition module is used to obtain data related to the transmission and distribution network and construct an objective function to maximize the load recovery benefits of the transmission and distribution network;

[0107] An optimization model building module is used to build a transmission and distribution network collaborative restoration optimization model based on the objective function and transmission and distribution network constraints;

[0108] Distributed restoration optimization module, which is used to construct the augmented objective functions of the transmission and distribution networks based on the transmission and distribution network collaborative restoration optimization model by introducing augmented Lagrangian functions;

[0109] An iterative solution module is used to set the maximum number of iterations, the primal residual convergence threshold, and the dual residual convergence threshold of the improved alternating direction multiplier method, and to solve the augmented objective functions of the transmission and distribution networks using the improved alternating direction multiplier method;

[0110] The accelerated iteration strategy module is used to adopt a double-update accelerated iteration strategy. If the original residual is greater than the set threshold, the penalty coefficient and Lagrange multiplier are updated. If the original residual is less than or equal to the set threshold, the Lagrange multiplier is updated and the penalty coefficient remains unchanged.

[0111] The optimization result output module is used to determine whether the improved alternating direction multiplier method should continue the next round of optimization or terminate the iteration to output the final transmission and distribution network coordinated restoration strategy based on the convergence status or number of iterations of the original residual and the dual residual.

[0112] This embodiment further provides a computing device applicable to distributed coordinated restoration of a transmission and distribution network based on an improved ADMM, including:

[0113] Memory and processor; the memory is used to store computer-executable instructions, and the processor is used to execute computer-executable instructions to implement the distributed collaborative restoration method of the transmission and distribution network based on the improved ADMM as proposed in the above embodiment.

[0114] This embodiment further provides a storage medium having a computer program stored thereon. When the program is executed by a processor, the method for distributed coordinated restoration of a transmission and distribution network based on the improved ADMM as proposed in the above embodiment is implemented.

[0115] The storage medium proposed in this embodiment and the distributed collaborative recovery method for the transmission and distribution network based on the improved ADMM proposed in the above embodiment belong to the same inventive concept. For technical details not described in detail in this embodiment, please refer to the above embodiment, and this embodiment has the same beneficial effects as the above embodiment.

[0116] Through the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented with the help of software and necessary general-purpose hardware, and of course it can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which can be stored in a computer-readable storage medium, such as a computer's floppy disk, read-only memory (ROM), random access memory (RAM), flash memory (FLASH), hard disk or optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute the methods of various embodiments of the present invention.

[0117] Example 2

[0118] Referring to Table 1 and Figures 2-4, an embodiment of the present invention provides a distributed collaborative restoration method for transmission and distribution networks based on an improved ADMM. In order to verify its beneficial effects, comparison results of two schemes are provided.

[0119] This embodiment uses the improved 179-node transmission network shown in Figure 2 as an example for analysis, where each node is connected to an IEEE-33-node distribution network.

[0120] Among them, nodes 14, 35 and 42 are connected to the black start units, nodes 26 and 81 are connected to the wind power station, and nodes 28 and 110 are connected to the photovoltaic power station.

[0121] Figure 3 shows the power balance of the transmission system under three different disaster scenarios (Scenario 1: a power outage occurs at 2 a.m., when only wind power is generated; Scenario 2: a power outage occurs at 10 a.m., when both wind and photovoltaic power are generated; Scenario 3: a power outage during a typhoon, when neither wind nor photovoltaic power is generated).

[0122] As shown in Figure 3, in the early recovery phase (i.e., the first five time steps), non-black start units have not yet fully recovered, so the output of renewable energy accounts for a large proportion of the total system output. At the same time, the system also restores some load to maintain system frequency stability.

[0123] In the middle and late stages of the recovery phase (i.e., time steps 6-25), as the non-blackstart units gradually recovered and the grid was gradually reconstructed, the load also recovered rapidly.

[0124] To better demonstrate the impact of different disaster scenarios on the full recovery of the transmission system, Figure 4 shows the recovery of the transmission system's power generation and load power under three scenarios.

[0125] As shown in Figure 4, scenario 2 occurs at 10 a.m., when both wind power and photovoltaic power are generating power and can serve as black start power sources. Therefore, the power generation and load power recovery speed of scenario 2 are the highest among the three scenarios.

[0126] Scenario 2 occurs at 2 a.m., when only wind power is output but no photovoltaic power is generated. Therefore, the black start speed is slower than that of Scenario 1, and its power generation and load power recovery speed is slightly slower than that of Scenario 1. Scenario 3 is a typhoon disaster. Due to rain, there is no photovoltaic output, and the typhoon wind speed is greater than the wind turbine shutdown power, so the wind turbine also has no output. At this time, the only black start power supply can be relied on the energy storage device. Therefore, the power generation recovery in Scenario 3 is 22.35% and 24.11% lower than that in S1 and S2, respectively, and the load recovery is 20.55% and 22.12% lower than that in S1 and S2, respectively.

[0127] In order to verify the effectiveness of the improved alternating direction multiplier method proposed in the present invention, the solution results of the present invention are compared with those of the traditional alternating direction multiplier method, as shown in Table 1;

[0128] Table 1 Comparison between the improved alternating direction multiplier method proposed in this invention and the traditional alternating direction multiplier method

[0129] As shown in Table 1, the deviation percentage of the total revenue of the transmission and distribution network solved by the algorithm of the present invention and the conventional alternating direction multiplier method is within 0.02%. The number of iterations of the algorithm of the present invention is reduced by more than 50% compared with the conventional alternating direction multiplier method, and the solution time is correspondingly reduced by 13174 seconds.

[0130] It can be seen that the improved alternating direction multiplier method used in the present invention can adaptively adjust the penalty factor according to the solution result of each iteration, thereby accelerating the convergence speed of the distributed solution and reducing the solution time of the distributed solution, making the recovery model proposed in the present invention more practical.

[0131] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A distributed collaborative restoration method for transmission and distribution networks based on improved ADMM, characterized in that: include: Acquire data related to the transmission and distribution network, construct an objective function to maximize the load restoration benefit of the transmission and distribution network, and establish a transmission and distribution network collaborative restoration optimization model based on the objective function and transmission and distribution network constraints; Based on the transmission and distribution network coordinated restoration optimization model, an augmented Lagrangian function is introduced to construct augmented objective functions of the transmission network and the distribution network; Setting a maximum number of iterations of the improved alternating direction multiplier method, a primal residual convergence threshold, and a dual residual convergence threshold, and using the improved alternating direction multiplier method to solve the augmented objective function of the transmission network and the distribution network; A double-update accelerated iteration strategy is adopted. If the original residual is greater than the set threshold, the penalty coefficient and Lagrange multiplier are updated. If the original residual is less than or equal to the set threshold, the Lagrange multiplier is updated and the penalty coefficient remains unchanged. According to the convergence of the original residual and the dual residual or the number of iterations, it is determined whether the improved alternating direction multiplier method should continue the next round of optimization or terminate the iteration to output the final transmission and distribution network coordinated restoration strategy.

2. The distributed collaborative restoration method for transmission and distribution networks based on improved ADMM according to claim 1, characterized in that: According to the objective function and the transmission and distribution network constraints, a transmission and distribution network collaborative restoration optimization model is established, including: The objective function expression is: in, and are the number of nodes in the transmission and distribution network, and are the unit restoration benefits of node n load in the transmission network and distribution network respectively, and are the load recovery powers of node n in the transmission network and distribution network at time step t, Δt is the time step interval, and T is the number of time steps in the recovery process; The transmission and distribution network constraints include black start constraints, load recovery constraints and power balance constraints of non-black start units in the transmission network, as well as load recovery constraints and power balance constraints of the distribution network.

3. The distributed collaborative restoration method for transmission and distribution networks based on improved ADMM according to claim 1 or 2, characterized in that: The augmented Lagrangian function is introduced to construct the augmented objective function of the transmission network and distribution network, including: The transmission network augmentation objective function is expressed as: Among them, f TN Augment the objective function for the transmission network, and are the Lagrange multiplier and penalty factor of the transmission network, is the load recovery power of node n in the transmission network at time step t, is the number of coupling nodes in the transmission and distribution network, T Step is the number of time steps in the recovery process, is the transmission and distribution network interaction power that the transmission network expects the nth distribution network to receive, is the transmission and distribution network interaction power that the nth distribution network wants to transfer from the transmission network, f TN,B restoring revenue to the transmission grid; The augmented objective function of the distribution network is expressed as: Among them, f DN,n Augment the objective function for the distribution network, and are the Lagrange multiplier and penalty factor of the nth distribution network, is the load recovery power of node n in the distribution network at time step t, T Step is the number of time steps in the recovery process, is the transmission and distribution network interaction power that the transmission network expects the nth distribution network to receive, is the transmission and distribution network interaction power that the nth distribution network wants to transfer from the transmission network, f DN,n,B Recover revenue for the distribution network.

4. The distributed collaborative restoration method for transmission and distribution networks based on improved ADMM according to claim 3, characterized in that: Solving the augmented objective function of the transmission network and the distribution network using the improved alternating direction multiplier method includes: The transmission network collects the transmission and distribution interaction power strategy matrix expected by each distribution network, calculates the augmented objective function of the transmission network, and obtains the transmission and distribution interaction power strategy matrix expected by the transmission network; After each distribution network receives the transmission and distribution interaction power strategy matrix expected by the transmission network from the transmission network, it calculates the distribution network augmented objective function and obtains the transmission and distribution interaction power strategy matrix expected by the distribution network.

5. The distributed collaborative restoration method for transmission and distribution networks based on improved ADMM according to claim 4, characterized in that: A double update accelerated iteration strategy is used. If the original residual is greater than the set threshold, the penalty coefficient and Lagrange multiplier are updated, including: The update penalty coefficient is expressed as: in, is the original residual of the kth iteration of the transmission and distribution network, is the dual residual of the k-th iteration of the transmission and distribution network, is the penalty coefficient of the k+1th iteration of the transmission network, is the penalty coefficient of the k-th iteration of the transmission network, is the penalty coefficient of the k+1th iteration of the nth distribution network node, is the penalty coefficient of the kth iteration of the nth distribution network node, δ P is the original residual convergence threshold, δ D is the dual residual convergence threshold; The updated Lagrange multiplier is expressed as: in, is the expected transmission and distribution interaction power strategy matrix at the t-th time step of the transmission network at the k+1-th iteration, is the transmission and distribution interaction power strategy matrix at the t-th time step during the k+1-th iteration of the distribution network, is the Lagrange multiplier of the t-th time step at the k+1-th iteration of the transmission network, is the Lagrange multiplier of the t-th time step at the k-th iteration of the transmission network, is the Lagrange multiplier of the nth distribution network node at the k+1th iteration at the tth time step, is the Lagrange multiplier of the nth distribution network node at the kth iteration at the tth time step, is the penalty coefficient of the k+1th iteration of the transmission network, is the penalty coefficient of the k+1th iteration of the distribution network.

6. The distributed collaborative restoration method for transmission and distribution networks based on improved ADMM according to claim 5, characterized in that: If the original residual is less than or equal to the set threshold, the Lagrange multiplier is updated and the penalty coefficient remains unchanged, including, The updated Lagrange multiplier is expressed as: in, is the Lagrange multiplier of the t-th time step at the k+1-th iteration of the transmission network, is the Lagrange multiplier of the t-th time step at the k-th iteration of the transmission network, is the Lagrange multiplier of the nth distribution network node at the k+1th iteration at the tth time step, is the Lagrange multiplier of the nth distribution network node at the kth iteration at the tth time step, is the penalty coefficient of the k+1th iteration of the transmission network, is the penalty coefficient of the k+1th iteration of the distribution network, K D and K 1 are the integral and dual residual regulation parameters in classical control theory, is the expected transmission and distribution interaction power strategy matrix at the t-th time step of the transmission network at the k+1-th iteration, is the transmission and distribution interaction power strategy matrix at the tth time step during the k+1th iteration of the distribution network.

7. The distributed collaborative restoration method for transmission and distribution networks based on improved ADMM according to claim 6, characterized in that: According to the convergence of the original residual and the dual residual or the number of iterations, it is determined whether the improved alternating direction multiplier method will continue the next round of optimization or terminate the iteration to output the final transmission and distribution network coordinated restoration strategy, including: To judge the convergence of the original residual and the dual residual, the expression is: in, is the original residual of the kth iteration of the transmission and distribution network, is the dual residual of the kth iteration of the transmission and distribution network, δ P is the original residual convergence threshold, δ D is the dual residual convergence threshold; If the improved alternating direction multiplier method satisfies the convergence expressions of the primal residual and the dual residual, or the maximum number of iterations is reached, the final transmission and distribution network coordinated restoration strategy is output.

8. A system for distributed coordinated restoration of transmission and distribution networks based on improved ADMM, characterized in that: include, A data acquisition module is used to obtain data related to the transmission and distribution network and construct an objective function to maximize the load recovery benefits of the transmission and distribution network; An optimization model establishment module is used to establish a transmission and distribution network collaborative restoration optimization model based on the objective function and transmission and distribution network constraints; A distributed restoration optimization module is used to introduce an augmented Lagrangian function to construct an augmented objective function of the transmission network and the distribution network based on the transmission and distribution network collaborative restoration optimization model; an iterative solution module, configured to set a maximum number of iterations of an improved alternating direction multiplier method, a primal residual convergence threshold, and a dual residual convergence threshold, and to use the improved alternating direction multiplier method to solve the augmented objective functions of the transmission network and the distribution network; The accelerated iteration strategy module is used to adopt a double-update accelerated iteration strategy. If the original residual is greater than the set threshold, the penalty coefficient and Lagrange multiplier are updated. If the original residual is less than or equal to the set threshold, the Lagrange multiplier is updated and the penalty coefficient remains unchanged. The optimization result output module is used to determine whether the improved alternating direction multiplier method should continue the next round of optimization or terminate the iteration to output the final transmission and distribution network coordinated restoration strategy based on the convergence status or number of iterations of the original residual and the dual residual.

9. An electronic device comprising: memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, the steps of the distributed collaborative restoration method of the transmission and distribution network based on the improved ADMM are implemented as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the steps of the distributed collaborative restoration method for transmission and distribution networks based on the improved ADMM according to any one of claims 1 to 7.

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