Power distribution network voltage coordination control method based on event trigger mechanism

Abstract

The invention discloses a power distribution network voltage coordination control method based on an event trigger mechanism, and belongs to the technical field of power distribution control. Dividing the power distribution network into a plurality of sub-regions, establishing a coupling constraint of each region, and decomposing a global optimization problem into optimization problems of each region; a pre-designed ETM-DAL-ADMM algorithm is adopted, a Lagrange function of an optimization problem of each region of a penalty coefficient is linearly processed and dynamically adjusted, local decision variables including boundary variables of each region are updated, inter-region information exchange is carried out according to a preset event triggering mechanism, and a final local decision variable is iteratively solved; and according to the final local decision variable, adjusting the reactive power output of the distributed generator in each region, so that the voltage of the power distribution network conforms to the constraint and the branch loss is minimized. The problem that the stability of the power distribution system cannot be ensured when the communication capability is insufficient in the existing control method can be solved.

Description

Technical Field

[0001] This invention belongs to the field of power distribution control technology, specifically relating to a power distribution network voltage coordination control method based on an event-triggered mechanism. Background Technology

[0002] With the large-scale integration of distributed energy resources (DERs) such as photovoltaics (PV), wind power, and energy storage into distribution networks (DNs), traditional centralized scheduling methods often struggle to meet the high-frequency, low-latency real-time VCC requirements due to the highly concentrated computational and communication loads. Distributed optimization based on the Augmented Lagrange Multiplier Method (ADMM) provides a feasible path for voltage control in active distribution networks (ADNs): This method divides the entire network into multiple autonomous sub-regions through network community discovery or modularity maximization. Each region independently solves its local subproblem, and then only exchanges the "boundary variables" at the boundaries between adjacent regions. These boundary variables refer to node voltage and power flow information, thereby ensuring coordinated convergence among regions and ultimately achieving network-wide consistency.

[0003] Despite this, existing distributed ADMM methods still have significant shortcomings in engineering applications. First, because each iteration requires the transmission of boundary information for all sub-regions, the communication frequency increases in tandem with the number of iterations, which can easily lead to congestion in scenarios with limited network bandwidth or large scale, and significantly increase the energy consumption of the system. Second, the penalty factor ρ used in ADMM to balance the degree of constraint violation and convergence speed is often chosen empirically. This approach makes it difficult to quickly reduce the original and dual residuals in the early stages of iteration, and also makes it impossible to finely adjust them in the later stages to ensure high-precision convergence. The original residual represents the degree of violation of the constraints of the original problem, and the dual residual represents the change in the Lagrange multiplier update. Third, existing timed or conditionally triggered communication strategies often lack rigorous threshold design and minimum trigger interval analysis, and cannot theoretically eliminate the "Zeno phenomenon." The "Zeno phenomenon" refers to the runaway behavior that may produce an infinite number of triggers in a finite time. Therefore, existing timed or conditionally triggered communication strategies are difficult to maintain the global convergence of the algorithm and the stability of the system under conditions of significantly sparse communication. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a distribution network voltage coordination control method based on an event-triggered mechanism, which solves the problem that the existing methods cannot guarantee the stability of the power distribution system when communication capabilities are insufficient.

[0005] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution: This invention provides a distribution network voltage coordination control method based on an event-triggered mechanism, comprising: Based on distribution network operation data and equipment parameters, a global optimization model is constructed with the goal of minimizing branch losses, including distributed power flow equation constraints and security constraints. Based on the distribution network topology and load distribution characteristics, the distribution network is divided into multiple sub-regions. By replicating the boundary variables of each region, coupling constraints are established for each region. Based on the coupling constraints, the global optimization problem is decomposed into optimization problems for each region. The ETM-DAL-ADMM algorithm, based on a global optimization model and pre-designed coupling constraints, is adopted. The Lagrangian function of each region optimization problem is linearized and the penalty coefficient is dynamically adjusted according to the original residual and dual residual. The local decision variables of each region, including boundary variables, are updated. According to the pre-set event triggering mechanism, information exchange between regions is only performed when the change of boundary variables exceeds the preset threshold. The final local decision variables are solved iteratively. The reactive power output of distributed generators in each region is adjusted based on the final local decision variables to ensure that the distribution network voltage meets the constraints and branch losses are minimized.

[0006] The aforementioned event-triggered distribution network voltage coordination control method constructs distributed power flow equation constraints for a global optimization model, including: The secondary loss term was removed from the DistFlow model and then respectively... and Using the voltage magnitudes of node j and node i as values, the final distributed power flow equations are obtained: , In the formula, nodes For upstream nodes, node For downstream nodes; and They are branch roads Active power and reactive power; and These are nodes Active power and reactive power; It is a side road The resistance; branch road The reactance; The security constraints of the global optimization model include: security constraints in the power distribution network and power constraints of distributed generators; Safety constraints in power distribution networks: , In the formula, and They are nodes The lower and upper limits of voltage amplitude; A set of nodes; branch road Current, branch road The upper limit of the current; and Branch roads It has a lower limit and an upper limit for active power; and Branch roads The lower and upper limits of reactive power. For branch set; Distributed generator power constraints: , In the formula, , and Distributed generators at nodes Active power, reactive power, and apparent power; and These are nodes The lower and upper limits of the active power of distributed generators; and These are nodes The lower and upper limits of reactive power of distributed generators.

[0007] The aforementioned distribution network voltage coordination control method based on an event-triggered mechanism includes the following coupling constraints for each region: No. The coupling constraints for each region are: , In the formula, For the upstream area, For the downstream region; For the first Boundary variables for each region, including the first region. Boundary variables when the first region is an upstream region and the second region Boundary variables when a region is used as a downstream region; For the corresponding number The boundary variables of the adjacent regions of the nth region, when the nth region... When a region is an upstream region of an adjacent region For the boundary variable when the adjacent region is the downstream region, when the first... When a region is a downstream region of an adjacent region This is the boundary variable when the adjacent region is used as the upstream region; For the first Global variables for each region; , and The first The voltage magnitude, active power, and reactive power at the boundaries of each region, including the first... The boundary voltage magnitude, active power, and reactive power when the first region is considered as the upstream region, and the first... The boundary voltage magnitude, active power, and reactive power when each region is considered as a downstream region; , and Corresponding to the first The voltage magnitude, active power, and reactive power of the adjacent region boundaries of each region, when the first region... When a region is an upstream region of an adjacent region , and These represent the boundary voltage magnitude, active power, and reactive power when the adjacent region is considered as the downstream region. When a region is a downstream region of an adjacent region , and These represent the boundary voltage magnitude, active power, and reactive power when the adjacent region is considered as the upstream region.

[0008] The aforementioned distribution network voltage coordination control method based on an event-triggered mechanism, wherein the decomposition of the global optimization problem into regional optimization problems according to coupling constraints includes: Based on the coupling constraints, the global optimization problem is decomposed into several regional optimization problems, and the objective function of the global optimization model is designed as follows: , In the formula, This represents the total number of areas into which the power distribution network is divided. For the first Local decision variables for each region Including the Boundary variables of each region ; For the first The objective function for each region; For the first The feasible region of local decision variables for each region that meets the constraints of distributed power flow equations and security constraints.

[0009] The aforementioned event-triggered voltage coordination control method for distribution networks, in the pre-designed ETM-DAL-ADMM algorithm, includes the design of the Lagrangian function for each region's optimization problem, which involves: linearizing the Lagrangian function of each region's optimization problem based on the global optimization model and coupling constraints to reduce computational complexity. Based on the objective function of the designed global optimization model, the Lagrangian function of the global optimization problem is constructed. The calculation formula is: , In the formula, For the Lagrange multipliers corresponding to the consistency constraints between boundary variables and global variables, T represents the transpose operation; This is the penalty coefficient; Square of the 2-norm operation; Based on the Lagrangian function of the global optimization problem and the domain partitioning, the Lagrangian functions of the optimization problems in each domain are obtained. The calculation formula is: , For the Lagrangian function of the optimization problem in each region, a first-order Taylor expansion is performed on the objective function of each region to obtain the linearized Lagrangian function of the optimization problem in each region. The calculation formula is: , In the formula, For the first The second iteration Objective function for each region In the Local decision variables for each region The linear term in the first-order Taylor expansion.

[0010] In the aforementioned event-triggered voltage coordination control method for distribution networks, specifically the ETM-DAL-ADMM algorithm, the first... Local decision variables for each region The formula for the (k+1)th iteration is: , In the formula, For the first The region in the first Local decision variables for the next iteration; For the first The region in the first Local decision variables for the next iteration; For the first The region in the first Global variables for this iteration; For the first The region in the first The Lagrange multipliers for the next iteration; the argmin function is used to output the input parameters that minimize the subsequent function. No. Global variables for each region The formula for the (k+1)th iteration is: , In the formula, For the first The region in the first Global variables for this iteration; For the first The region in the first Boundary variables for the next iteration; For the corresponding number The adjacent regions of the first region are in the second region. Boundary variables of the nth iteration; The region in the first Local decision variables in the next iteration Including the The region in the first Boundary variables of the next iteration ; No. Lagrange multipliers in each region The formula for the (k+1)th iteration is: , In the formula, For the first The region in the first Lagrange multipliers in the next iteration; For the first The region in the first Lagrange multipliers in the next iteration.

[0011] The aforementioned distribution network voltage coordination control method based on event-triggered mechanism, in the pre-designed ETM-DAL-ADMM algorithm, the design of the Lagrangian function for each region's optimization problem further includes: dynamically adjusting the penalty coefficient based on the original residual and dual residual to improve the convergence speed. No. Penalty coefficient for each region The formula for the (k+1)th iteration is: , , In the formula, and These are the minimum and maximum iteration indices that are allowed to be adjusted, respectively; For the first The region in the first The penalty coefficient for the next iteration; For the first The region in the first The penalty coefficient for the next iteration; For the first The initial values ​​of the penalty coefficient for each region; and These are the preset penalty coefficient adjustment parameters for increasing and decreasing; and These are the preset comparison parameters for the original residual and the dual residual, respectively; For 2-norm operations; and The first The region in the first The original residual and dual residual of the next iteration; No. The first region The original residual of the next iteration The calculation formula is: , No. The first region The dual residual of the next iteration The calculation formula is: .

[0012] The aforementioned distribution network voltage coordination control method based on an event-triggered mechanism, wherein the inter-regional information exchange is performed only when the boundary variable changes exceed a preset threshold according to a pre-set event-triggered mechanism, includes: No. The time point at which information is exchanged between regions The calculation formula is: , , , In the formula, For the first The next event trigger time for each region; For the first The time when the previous event was triggered in the region; The maximum allowed time; For the first Event triggering conditions for each region; For the first The region in the first The error of the next iteration; For the first The region in the first Boundary variables for the next iteration; For the first The region in the first Boundary variables for the next iteration; For the first Event triggering functions for each region; For the first The region in the first Error of the next iteration The weighted square, This is a preset weight matrix; To control the preset threshold parameters for event triggering, ; For the first The region in the first Boundary variables of the next iteration The weighted square; No. The event triggering conditions for each region are: .

[0013] The aforementioned event-triggered distribution network voltage coordination control method employs a pre-designed ETM-DAL-ADMM algorithm to iteratively solve for the final local decision variables, including: Lagrange multipliers for each region Initialize to 0, set global variables for each region. For the actual boundary variables of each region Set the iteration index ; The following process is executed repeatedly until the iteration termination condition is met, outputting the final local decision variables for each region, which are used for distribution network voltage coordination control: Each region according to the first Local decision variables for each region The iterative formula is used to solve the optimization problem in each region, and the boundary variables of each region are obtained. ; Based on the event-triggered mechanism (ETM), the error of each region is determined according to the event triggering conditions. If the event triggering conditions are met, the corresponding region exchanges information with its neighboring regions. Each region according to the first Global variables for each region The iterative formula updates the global variables for each region. ; Each region according to the first Lagrange multipliers in each region The iterative formula updates the Lagrange multipliers for each region. ; Each region according to the first Penalty coefficient for each region The iterative formula updates the penalty coefficient for each region. ; Each region according to the first Original residuals of each region and dual residual Calculation formula for calculating the original residuals of each region. and dual residual .

[0014] The aforementioned event-triggered distribution network voltage coordination control method includes the following iteration termination conditions: The iteration termination condition is determined based on the convergence condition formula. If the convergence condition formula is met, the ETM-DAL-ADMM algorithm converges and the iteration terminates. The convergence condition formula is as follows: , In the formula, Operations on infinity norms; As a preset tolerance level, It is the boundary residual; Alternatively, the iteration termination condition can be determined based on the number of iterations. If the number of iterations is greater than or equal to the preset upper limit of the iteration index, the iteration will be terminated.

[0015] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: This invention presents a distribution network voltage coordination control method based on an event-triggered mechanism. It improves upon the traditional ADMM algorithm by linearizing the Lagrangian function of the optimization problem in each region to reduce computational complexity. Simultaneously, it dynamically adjusts the penalty coefficient based on the original residual and dual residual to improve convergence speed. Furthermore, it incorporates an event-triggered mechanism to trigger inter-regional information exchange only when necessary, reducing redundant data transmission and communication frequency. This addresses the problem that existing methods cannot guarantee the stability of the distribution system when communication capabilities are insufficient.

[0016] This invention aims to achieve completely independent optimization at the model level by dividing the distribution network into several autonomous sub-regions and virtually replicating boundary variables through regional decoupling based on network community discovery or modularity maximization. First-order Taylor linearization and dynamic penalty coefficient ρ adjustment based on primal / dual residuals are introduced into the ADMM framework to significantly accelerate iterative convergence. Simultaneously, an event-triggered communication strategy based on the quadratic threshold of the boundary variable increment is designed, and the Zeno phenomenon is completely eliminated through formal analysis of the minimum trigger interval. This ensures the global convergence of the algorithm and the stability of the distribution network operation while significantly reducing communication overhead and energy consumption.

[0017] This invention, through a complete mathematical model and constraint analysis, ensures the physical feasibility of the distributed power flow equations and the strict boundaries of node voltage and unit output, while also laying the foundation for high-precision optimization. On this basis, it adopts a flexible network region partitioning and coupling constraint design, enabling parallel computation in each region while maintaining global consistency. Furthermore, it introduces the DAL-ADMM algorithm to accelerate linearity, achieving rapid convergence of local updates and global coordination. Meanwhile, the event-triggered mechanism (ETM) only exchanges information when boundary variable changes exceed a threshold, significantly reducing redundant data transmission. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the ETM-DAL-ADMM algorithm construction process of a distribution network voltage coordination control method based on an event-triggered mechanism according to Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the ADN radiative topology features according to Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the process of establishing coupling constraints for each region by copying the boundary variables of each region in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the radial topology and regional division of the IEEE-33 distribution network according to Embodiment 1 of the present invention; Figure 5 This is a schematic diagram comparing the changes in boundary residuals with the number of iterations for five algorithms—ETM-DAL-ADMM, DAL-ADMM, L-ADMM, O-ADMM, and FALM—in Embodiment 1 of the present invention. Detailed Implementation

[0019] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0021] Example 1: This embodiment proposes a distribution network voltage coordination control method based on an event-triggered mechanism. Figure 1This is a flowchart illustrating the construction process of the ETM-DAL-ADMM algorithm in an event-triggered voltage coordination control method for distribution networks, as described in Embodiment 1 of the present invention. This flowchart merely illustrates the logical sequence of the methods described in this embodiment. Provided there are no conflicts, different sequences may be used in other possible embodiments of the present invention. Figure 1 The steps shown or described are performed in the indicated order. The method includes the following steps: S1: Based on distribution network operation data and equipment parameters, a global optimization model is constructed with the goal of minimizing branch losses, including distributed power flow equation constraints and security constraints. S2: Based on the distribution network topology and load distribution characteristics, the distribution network is divided into multiple sub-regions. By replicating the boundary variables of each region, coupling constraints are established for each region. Based on the coupling constraints, the global optimization problem is decomposed into optimization problems for each region. S3: The ETM-DAL-ADMM algorithm, which is pre-designed based on a global optimization model and coupling constraints, is adopted. The Lagrangian function of the optimization problem in each region is linearized and the penalty coefficient is dynamically adjusted according to the original residual and the dual residual. The local decision variables of each region, including the boundary variables, are updated. According to the pre-set event triggering mechanism, information exchange between regions is carried out only when the change of the boundary variable exceeds the preset threshold. The final local decision variables are solved iteratively. S4: Adjust the reactive power output of distributed generators in each region according to the final local decision variables so that the distribution network voltage meets the constraints and the branch losses are minimized.

[0022] Step S1 includes: Based on the system objective of distributed voltage coordination control (VCC), a global optimization model is constructed: on the one hand, the distributed power flow equation is derived to ensure the physical feasibility of the power flow, which means satisfying power conservation, voltage constraints, current constraints, etc.; on the other hand, combined with constraints such as the safe range of node voltage and the upper and lower limits of unit output, a complete mathematical program is formed to provide an accurate theoretical basis for subsequent algorithm design.

[0023] In step S1, the goal of the VCC problem is to reduce the losses caused by the current in each branch of the power grid. The constraints of the global optimization model include distributed power flow equation constraints and security constraints; the global optimization model aims to minimize branch losses, and the objective function is as follows: (1) In the formula, This is the branch loss function; It is a node To the node The resistance of the branch circuit; and They are branch roads The active and reactive power; It is a node The voltage amplitude; Represents the set of all branches; It is a set of nodes.

[0024] Distribution networks typically exhibit a radial topology and contain numerous distributed power sources and complex loads. Therefore, distributed power flow equations need to specifically reflect these characteristics. A commonly used classic model is the DistFlow model, which describes power flow characteristics through the recursive relationship between branch power and node voltage, including the following key equations: 1) DistFlow branch constraints: such as Figure 2 As shown, the Distflow branch equations are used to describe the radiative topology characteristics of the ADN.

[0025] Nodal power balance equation: For any node in a distribution network The active / reactive power flowing into the node is equal to the active / reactive power flowing out of the node; The equation relating branch power to voltage states that branch power loss is related to node voltage and branch impedance. Branch power loss equation: The active / reactive power loss of a branch can be directly calculated from the power and impedance; (2) (3) In the formula, nodes For upstream nodes, node For downstream nodes; and They are branch roads The active and reactive power; and Branch roads The active power loss and reactive power loss are secondary power loss terms. and These are nodes Active power and reactive power; It is a node The voltage amplitude; For nodes The voltage amplitude; It is a side road The resistance; branch road The reactance; This is a linear loss term, proportional to the branch power; This is the secondary loss term of the line impedance, which is proportional to the square of the branch power and reflects the nonlinear effect of the line impedance. and These are nodes The active and reactive power of the distributed generator; and They are nodes The active and reactive power of the load; It is a set of nodes with distributed generators; This is the set of nodes that do not have distributed generators.

[0026] The equations for DistFlow branch constraints contain quadratic terms, which include: , , This means that it contains non-convex terms, which makes the DistFlow model non-convex. Non-convex optimization problems have multiple local optima, making them difficult to solve and computationally inefficient, and thus difficult to apply directly to distributed optimization algorithms.

[0027] To address this issue, this embodiment employs a linear approximation of the DistFlow model, ignoring secondary loss terms and removing secondary loss terms related to power and line impedance, thus making the problem easier to solve. This embodiment uses... and The voltage magnitudes at nodes j and i are used to ensure that the constraints no longer contain non-convex terms. The final DistFlow branch equation is shown below: (4) Safety constraints include: safety constraints in the power distribution network and power constraints of distributed generators; 2) Safety constraints in power distribution networks: (5) In the formula, and They are nodes The lower and upper limits of voltage amplitude; A set of nodes; branch road Current, branch road The upper limit of the current; and Branch roads It has a lower limit and an upper limit for active power; and Branch roads The lower and upper limits of reactive power. For the set of branches.

[0028] 3) Distributed generator power constraints: (6) In the formula, , and Distributed generators at nodes Active power, reactive power, and apparent power; and These are nodes The lower and upper limits of the active power of distributed generators; and These are nodes The lower and upper limits of reactive power of distributed generators.

[0029] Step S2 includes: based on the existing model, dividing the distribution network into several regions according to the distribution network topology and load distribution characteristics; defining power and voltage boundary variables for each region boundary and establishing corresponding coupling constraints to ensure that the calculation results of each region after division are consistent with the global calculation results of the global optimization model.

[0030] In step S2, to address the inherent high communication pressure and slow computation speed in centralized optimization of the Active Distribution Network (ADN), the ADN is divided into multiple regions based on its topology and the load distribution characteristics of multiple distributed generators. Each region independently solves its distributed optimization problem. However, due to the inherent coupling between these regions, a decoupling method is required.

[0031] In this case, the following was adopted: Figure 3 The decoupling method is illustrated. Specifically, the boundary bus of the upstream region is "copied" to the downstream region as a virtual bus, and the voltage of this virtual bus is the same as the voltage of the boundary bus of the upstream region. Simultaneously, the power flowing through the boundary branches is "copied" to the upstream region as a virtual power source, and the power flow between regions is considered as power flowing through the boundary branches. To ensure that the solution of the distributed model after decoupling is consistent with the solution of the centralized model before decoupling, it is necessary to ensure that the constraints on the boundary variables of each region are consistent. Coupling constraints for each region are established by copying the boundary variables of each region. The coupling constraints for each region are: (7) In the formula, For the upstream area, For the downstream region; For the first Boundary variables for each region, including the first region. Boundary variables when the first region is an upstream region and the second region Boundary variables when a region is used as a downstream region; For the corresponding number The boundary variables of the adjacent regions of the nth region, when the nth region... When a region is an upstream region of an adjacent region For the boundary variable when the adjacent region is the downstream region, when the first... When a region is a downstream region of an adjacent region This is the boundary variable when the adjacent region is used as the upstream region; For the first The global variable for the nth region, when the nth region Boundary variables when a region is used as an upstream region It needs to be equal to the boundary variable of the downstream adjacent region. When the first Boundary variables when a region is a downstream region It needs to be equal to the boundary variable of the upstream adjacent region. Global variables for each region are used to ensure the consistency of boundary variables on both sides of the adjacent sides of two adjacent regions; , and The first The voltage magnitude, active power, and reactive power at the boundaries of each region, including the first... The boundary voltage magnitude, active power, and reactive power when the first region is considered as the upstream region, and the first... The boundary voltage magnitude, active power, and reactive power when each region is considered as a downstream region; , and Corresponding to the first The voltage magnitude, active power, and reactive power of the adjacent region boundaries of each region, when the first region... When a region is an upstream region of an adjacent region , and These represent the boundary voltage magnitude, active power, and reactive power when the adjacent region is considered as the downstream region. When a region is a downstream region of an adjacent region , and These represent the boundary voltage magnitude, active power, and reactive power when the adjacent region is considered as the upstream region. This coupling constraint allows each region to independently perform distributed optimization calculations, while maintaining consistency constraints on boundary voltage and power through global variables.

[0032] This embodiment uses a distributed approach to solve the optimization problem. Based on the regional division and decoupling of the power distribution network, the global optimization problem of the original global optimization model objective function (1) can be decomposed into several smaller regional optimization problems. By solving the regional optimization problems and coordinating between regions, the optimal solution of the global problem is finally obtained. According to the coupling constraints, the global optimization problem is decomposed into several regional optimization problems. The objective function (1) and its constraints are rewritten, and the objective function of the global optimization model is designed as follows: (8) In the formula, This represents the total number of areas into which the power distribution network is divided. For the first Local decision variables for each region Including the Boundary variables of each region ; For the first The objective function for each region; For the first The feasible region of local decision variables for each region that meets the constraints of distributed power flow equations and security constraints.

[0033] In step S3, the pre-design of the ETM-DAL-ADMM algorithm includes: based on the global optimization model in step S1 and the coupling constraints in step S2, a DAL-ADMM algorithm combining linearization processing and acceleration techniques is constructed, and an event-triggered mechanism (ETM) is added to the DAL-ADMM algorithm. This algorithm enables each sub-region to independently update its local variables, while achieving cross-region coordination through global variables, thereby ensuring consistency between distributed solution results and centralized optimization results.

[0034] Traditional distributed active-mode generator (ADMM) methods suffer from slow convergence speed and high computational cost. To address this shortcoming, this embodiment proposes a distribution network voltage coordination control method based on Distributed Accelerated Linear-ADMM (DAL-ADMM) for optimizing the active-mode network (ADN). This algorithm minimizes branch losses while ensuring that the voltage at each node remains within acceptable limits by coordinating the reactive power of each distributed generator.

[0035] Based on the objective function of the global optimization model designed according to formula (8), the Lagrangian function of the global optimization problem is constructed. The calculation formula is: (9) In the formula, the system is divided into The first region, the first Each region independently optimizes its objective function. ; The Lagrange multiplier corresponds to the consistency constraint between boundary variables and global variables, and is used to measure the difference between regions. T represents the transpose operation. The penalty coefficient ensures that the boundary variables of each region converge quickly to the same level as the global variables; Squared for the 2-norm operation.

[0036] In this embodiment, when the current region only has downstream adjacent regions, that is, when the current region only has boundary variables as an upstream region, the coupling constraint of the objective function of the current region only requires that the boundary variables of the current region as an upstream region be equal to the boundary variables of the downstream adjacent regions; when the current region only has upstream adjacent regions, that is, when the current region only has boundary variables as a downstream region, the coupling constraint of the objective function of the current region only requires that the boundary variables of the current region as a downstream region be equal to the boundary variables of the upstream adjacent regions; when the current region has upstream and downstream adjacent regions, that is, when the current region has upstream and downstream boundary variables, the coupling constraint of the objective function of the current region has two types of constraints: the boundary variables of the current region as an upstream region need to be equal to the boundary variables of the downstream adjacent regions, and the boundary variables of the current region as a downstream region need to be equal to the boundary variables of the upstream adjacent regions; when the current region has two types of constraints or has multiple adjacent regions, it is necessary to distinguish the adjacent regions and distinguish the types of constraints to calculate formula (9). Finally, perform the summation operation. .

[0037] Based on the Lagrangian function of the global optimization problem and the region partitioning in formula (9), the Lagrangian function of the optimization problem in each region is obtained. The calculation formula is: (10) Considering that the traditional ADMM method is often time-consuming in optimization computation, this embodiment proposes an improved method that linearizes the Lagrangian function for each region. Specifically, it no longer aims to precisely minimize the objective function in each iteration. Instead of directly solving the problem, a faster approach is taken using an approximation. During iteration, the originally complex nonlinear objective function is replaced with its first-order Taylor expansion approximation at the current iteration point—a linearized objective function. The goal is to replace the complex nonlinear problem with a simpler linear form, thereby reducing the computational burden. Let the... The point of the next iteration is So in the next iteration, that is, the th In the next iteration Will be determined by it Perform a first-order Taylor expansion, retaining only the linear terms, which means reducing the nonlinear terms to the first-order Taylor expansion. The objective function of the next iteration Replaced by a linear approximation function: (11) In the formula, the first Local decision variables for each region Indicates the first The vector composed of the node variables in each region, that is, the vector composed of the first node variables in each region. Treating all variables within a region as a single vector, formula (11) refers to the vector obtained in the current iteration. The value of this set of vectors is used to find the first... The objective function for each region The partial derivatives of each component of this vector form the Jacobian matrix, and then a linear approximation is made using "constant term + derivative × (increment of variable relative to the current value)"; To ensure consistency of boundary variables between adjacent regions, this method introduces a linear dual term and a quadratic penalty term into the objective function of each region. The linear dual term dynamically characterizes the inconsistencies between regions using Lagrange multipliers and continuously drives the boundary solutions to converge during iteration. The quadratic penalty term penalizes the square of the boundary differences, making larger deviations more costly, thus effectively constraining the regions to gradually reduce differences and ultimately achieving boundary consistency. The modified Lagrange function for each region is shown below: (12) In the formula, the linear term Use the current iteration The first-order Taylor expansion replaces the original objective function, retaining only linear terms, transforming the nonlinear subproblem into a linear one, thus reducing the computational cost of each iteration; linear dual terms... Apply boundary consistency using Lagrange multipliers; For Lagrange multiplier vectors paired for consistency constraints; for Transpose; Secondary penalty item Further reduce boundary deviations to stabilize and accelerate uniform convergence; This is the penalty coefficient for the secondary penalty term.

[0038] The DAL-ADMM algorithm solves the problem in the following way: No. Local decision variables for each region The formula for the (k+1)th iteration is: (13) No. Global variables for each region The formula for the (k+1)th iteration is: (14) No. Lagrange multipliers in each region The formula for the (k+1)th iteration is: (15) In the formula, For the first The region in the first Local decision variables for the next iteration; For the first The region in the first Local decision variables for the next iteration; For the first The region in the first Global variables for this iteration; For the first The region in the first Global variables for this iteration; For the first The region in the first Lagrange multipliers in the next iteration; For the first The region in the first Lagrange multipliers in the next iteration; For the first The region in the first The boundary variable for the next iteration; the argmin function is used to output the input parameters that make the subsequent function reach its minimum value.

[0039] Due to the Global variables for each region Updates cannot be completed within a single region, therefore they require collection of the first... Boundary variables of each region and corresponding number Boundary variables of adjacent regions of each region To update the number Global variables for each region Therefore, by substituting formula (14), we obtain the final result. Global variables for each region The formula for the (k+1)th iteration is: (16) In the formula, For the first The region in the first Boundary variables for the next iteration; For the corresponding number The adjacent regions of the first region are in the second region. Boundary variables of the nth iteration; The region in the first Local decision variables in the next iteration Including the The region in the first Boundary variables of the next iteration ; This invention improves the convergence of the DAL-ADMM model by adaptively adjusting the penalty coefficient within each region. Based on the magnitudes of the original and dual residuals, the penalty coefficient is adaptively adjusted to dynamically balance convergence speed and constraint satisfaction; that is, a larger original residual results in a larger penalty to accelerate consistency, while a larger dual residual results in a smaller penalty to avoid oscillations caused by over-convergence. Penalty coefficient for each region The iterative formula is: (17) (18) In the formula, , These are the minimum and maximum iteration indices that are allowed to be adjusted, respectively; For the first The region in the first The penalty coefficient for the next iteration; For the first The region in the first The penalty coefficient for the next iteration; For the first The initial values ​​of the penalty coefficient for each region; , These are the preset penalty coefficient adjustment parameters, one for increasing and one for decreasing. , In this embodiment, the preset residual comparison parameters in the DAL-ADMM algorithm are: , ; For 2-norm operations; , The first The region in the first The primary residual and dual residual in the next iteration, the primary residual and dual residual The calculation formula is as follows: (19) (20) To reduce frequent iterative communication in step S3, an event-triggered mechanism (ETM) is introduced: inter-regional information exchange only occurs when the boundary variable changes exceed a preset threshold.

[0040] The DAL-ADMM algorithm requires a complete global data communication in each iteration. To reduce communication overhead, this embodiment introduces an event-triggered mechanism (ETM) based on the DAL-ADMM algorithm, designing the ETM-DAL-ADMM algorithm. Information exchange between regions is only triggered when the difference between the current boundary variable and the boundary variable transmitted in the previous communication exceeds a set threshold, thus avoiding unnecessary communication.

[0041] According to the ETM-DAL-ADMM algorithm, the first The time point at which information is exchanged between regions The calculation formula is: ,(twenty one) ,(twenty two) ,(twenty three) In the formula, For the first The next event trigger time for each region; For the first The time when the previous event was triggered in the region; The maximum allowed time; For the first Event triggering conditions for each region; For the first The region in the first The error of the next iteration; For the first The region in the first Boundary variables for the next iteration; For the first The region in the first Boundary variables for the next iteration; For the first Event triggering functions for each region; For the first The region in the first Error of the next iteration The weighted square, This is a preset weight matrix used to control the impact of errors; To control the preset threshold parameters for event triggering, ; For the first The region in the first Boundary variables of the next iteration The weighted square.

[0042] When the event is triggered function When the value is greater than or equal to zero, the event is triggered. At this time, inter-regional information exchange includes: [The following is a continuation of the previous sentence, likely related to the event itself.] When a region is used as an upstream region, its boundary variables are transferred to the downstream adjacent region, replacing the corresponding variables previously stored in the downstream adjacent region. Boundary variables of the region; the first The region receives boundary variables transmitted from the upstream adjacent region, replacing the first region. The boundary variables of the corresponding upstream adjacent regions previously stored in each region; If the event is not triggered, no information exchange occurs between regions, and each region retains the boundary variables from the last event trigger. Combining formula (21), the... The event triggering conditions for each region can be represented as follows: ,(twenty four) The following is the proof of formula (24): According to the event triggering condition, when the first Error in each region The event will be triggered when the threshold defined in formula (21) is reached. After the event is triggered, the variable... Will be updated, error Reset to zero. In the absence of an event, according to formula (23), the distribution network needs to satisfy the following inequality constraint: (25) In the formula, It is a pre-defined positive definite diagonal matrix. Using this formula, we can further obtain: (26) In the formula, yes The a-th eigenvalue, It is a vector The elements; s is a vector. These formulas ensure that the event-triggered mechanism operates effectively throughout the optimization process, and that errors are promptly constrained and effectively controlled after each trigger.

[0043] Substituting formulas (22) and (26) into formula (25) and further calculating, we get: (27) From formula (27), the condition for the event not to be triggered is expressed as: (28) According to formula (28), the event triggering condition is formula (24).

[0044] The Zeno phenomenon does not occur in the ETM-DAL-ADMM algorithm of this embodiment. The Zeno phenomenon refers to the triggering of an infinite number of events within a finite time frame. The reason why the Zeno phenomenon does not occur is that, as shown in formulas (21)-(23), the event triggering mechanism only detects the sampling points corresponding to the discrete time iteration step, and the optimization calculation and variable update of each iteration require time. Therefore, there must be a minimum interval between two adjacent triggers. Even if it is triggered in every iteration in the extreme case, the number of triggers only increases with the number of iteration steps and is always bounded within a finite time, thus avoiding the occurrence of the Zeno phenomenon.

[0045] The ETM-DAL-ADMM algorithm in this embodiment iteratively solves for the final local decision variables, and the process is as follows: 1. Initialization: Set the Lagrange multipliers for each region. Initialize to 0, set global variables for each region. For the actual boundary variables of each region Set the initial iteration index .

[0046] 2. Solving optimization problems: Each region, according to the... Local decision variables for each region The iterative formula (13) is used to solve the optimization problem in each region, and the reactive power of the distributed generators in each region is obtained. and boundary variables .

[0047] 3. Boundary variable transmission: Based on the event triggering mechanism ETM proposed by formulas (21)-(23), the error of each region is judged according to the event triggering condition formula (24). If the event triggering condition is met, each region receives data transmitted from the adjacent region. The adjacent region refers to the adjacent region with the distribution network connection relationship, rather than just the geographically adjacent region.

[0048] 4. Global variable update: Each region updates according to the first... Global variables for each region The iterative formula, formula (16), updates the global variables of each region. .

[0049] 5. Lagrange multiplier update: Each region is updated according to the first... Lagrange multipliers in each region The iterative formula, formula (15), updates the Lagrange multipliers of each region. .

[0050] 6. Penalty coefficient update: Each region updates its penalty coefficient based on the previous one. Penalty coefficient for each region The iterative formulas, formulas (17)-(18), update the penalty coefficients of each region. .

[0051] 7. Residual Calculation: Each region is calculated according to the... Original residuals of each region and dual residual The calculation formulas (19) and (20) are used to calculate the original residuals of each region. and dual residual .

[0052] 8. Termination Condition Judgment: If one of the following conditions is met, the iteration terminates, and the final local decision variables for each region are output for distribution network voltage coordination control. In this embodiment, the reactive power output of distributed generators in each region is subsequently adjusted based on the final local decision variables to ensure that the distribution network voltage meets the constraints and branch losses are minimized; otherwise, return to step 2: 1) Determine if the ETM-DAL-ADMM algorithm has converged. If the following convergence condition formula is satisfied, then the ETM-DAL-ADMM algorithm has converged: (29) In the formula, Operations on infinity norms; This is the preset tolerance level; It is the boundary residual.

[0053] 2) The number of iterations is greater than or equal to the preset upper limit of the iteration index.

[0054] The following is a simulation experiment demonstrating the implementation effect of the distributed voltage control method for distribution networks in this embodiment: like Figure 2 As shown, a radial distribution network topology with bus 0 as the root is depicted: nodes 1, ..., l are connected sequentially along the main trunk, and then branches are sent to... Nodes, each labeled with its voltage, active power, and reactive power injection, and branches. upper complex impedance and power flow The arrow indicates the direction from the upstream node. downstream nodes Transmission, and upstream nodes downstream nodes Transmission data, including the active and reactive power of each node, reflects the injection and absorption of distributed power sources and loads at each node.

[0055] Figure 3 The upper part is the original network: nodes in the upstream region. Nodes in the downstream region Active and reactive power flows are carried by branch circuits. ; Figure 3 The lower half of the diagram illustrates the "decoupling" process for this boundary: in the upstream region, the node... Its outflow power is equivalent to an injection source P represented by a ring in the diagram, with the voltage remaining constant. In the downstream region, the original upstream node will be... Copy as node Upstream node Voltage copy as voltage This parameter serves as an externally given parameter for the upstream region, replacing the coupling dependency on the upstream. In this way, the upstream and downstream sub-regions can independently complete power flow calculations and optimizations while ensuring the consistency of boundary injected power and voltage, achieving distributed decoupling and parallel solution.

[0056] Figure 4 The radial topology of the IEEE-33 distribution network is given and divided into three sub-regions according to function: Region 1 includes nodes 1–9 and two branches, one branch includes nodes 19–22 and the other branch includes nodes 23–25; Region 2 includes nodes 26–33; Region 3 includes nodes 10–18; nodes connected by a green box marked DG indicate that the node has a distributed generator.

[0057] Figure 5 Comparing the boundary residual changes of the ETM-DAL-ADMM algorithm (the algorithm of this invention) in this embodiment with those of five other algorithms—DAL-ADMM (distributed accelerated linear ADMM), L-ADMM (linear ADMM), O-ADMM (over-relaxed ADMM), and FALM (fast alternating linearization)—with the number of iterations, both ETM-DAL-ADMM and DAL-ADMM show that, with significantly fewer iterations than the other three algorithms, the boundary residual decreases rapidly to a level significantly lower than the other three methods. The iteration terminates when the boundary residual decreases to a preset tolerance level. Therefore, both ETM-DAL-ADMM and DAL-ADMM can obtain the final calculation results faster.

[0058] like Figure 4 As shown, the IEEE-33 distribution network system used in this embodiment is configured with 6 distributed generators (DGs), located at node numbers {4, 8, 11, 16, 21, 30}. The initial active and reactive power outputs of each DG are shown in Table 1. The root bus reference voltage is assumed to be 1.0 pu. The upper and lower limits of reactive power for the DGs are set to 1 MVar and 0, respectively. Furthermore, the initial penalty coefficient of the algorithm... Set to 2.5, the preset tolerance. Preset threshold parameters for controlling event triggering Furthermore, the preset upper limit for iteration index is 150.

[0059] Table 1. Location and initial power of DG in IEEE-33 distribution network system

[0060] Figure 4 The IEEE-33 distribution network system is shown in its regional division, which is divided into three regions, namely Region 1 to Region 3. Region 1 and Region 2 are adjacent to each other, and Region 3 is adjacent to each other. Each region contains at least one distributed generator (DG).

[0061] The ETM-DAL-ADMM algorithm in this embodiment is compared with several distributed algorithms: Linear ADMM (L-ADMM), Fast Alternating Linearization (FALM), Over-relaxed ADMM (O-ADMM), and DAL-ADMM. In distributed methods, convergence is defined as the ability of the objective function to quickly reach the global optimum, which directly affects the performance of the overall solution. Figure 5 The boundary residuals of the proposed algorithm applied to the IEEE-33 distribution network system are shown and compared with the results of other algorithms.

[0062] Table 2 compares the total running time of various algorithms under VCC, highlighting that the proposed ETM-DAL-ADMM and DAL-ADMM algorithms have significantly shorter total running times than other methods. This advantage stems not only from the reduced number of iterations in both algorithms but also from their lower single-optimization running time. The improved efficiency is due to the DAL-ADMM framework, which significantly reduces the time required for each optimization by linearizing the objective function. Furthermore, the adaptive adjustment of the penalty coefficient in the DAL-ADMM framework effectively reduces the number of iterations required for convergence, thereby further improving the overall running efficiency of the distributed algorithm.

[0063] Table 2 Total running time of different algorithms

[0064] Table 3 shows the number of inter-regional communications for ETM-DAL-ADMM and DAL-ADMM under the same number of iterations. It can be seen that the ETM-DAL-ADMM algorithm, which incorporates the event-triggered ETM mechanism, has significantly fewer inter-regional communications than the DAL-ADMM algorithm. Compared to the DAL-ADMM algorithm, the ETM-DAL-ADMM algorithm, after integrating ETM, reduces the number of inter-regional communications in the IEEE-33 distribution network system from 600 to 204, a reduction of 66.00%. Therefore, the ETM-DAL-ADMM algorithm can effectively alleviate communication congestion during large-scale data transmission in distributed optimization processes, reduce energy consumption for data transmission, and improve the stability of the distribution system.

[0065] Table 3 Number of inter-regional communications for different algorithms

[0066] As can be seen from the above simulation experiments, the distribution network voltage coordination control method based on the event triggering mechanism in this embodiment significantly reduces the computation and communication overhead through partitioned parallel computing, model linearization and intelligent triggering mechanism, and is suitable for real-time optimization control of large-scale distribution networks.

[0067] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0068] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0069] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0070] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0071] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A distribution network voltage coordination control method based on an event-triggered mechanism, characterized in that, include: Based on distribution network operation data and equipment parameters, a global optimization model is constructed with the goal of minimizing branch losses, including distributed power flow equation constraints and security constraints. Based on the distribution network topology and load distribution characteristics, the distribution network is divided into multiple sub-regions. By replicating the boundary variables of each region, coupling constraints are established for each region. Based on the coupling constraints, the global optimization problem is decomposed into optimization problems for each region. The ETM-DAL-ADMM algorithm, based on a global optimization model and pre-designed coupling constraints, is adopted. The Lagrangian function of each region optimization problem is linearized and the penalty coefficient is dynamically adjusted according to the original residual and dual residual. The local decision variables of each region, including boundary variables, are updated. According to the pre-set event triggering mechanism, information exchange between regions is only performed when the change of boundary variables exceeds the preset threshold. The final local decision variables are solved iteratively. The reactive power output of distributed generators in each region is adjusted based on the final local decision variables to ensure that the distribution network voltage meets the constraints and branch losses are minimized.

2. The distribution network voltage coordination control method based on event triggering mechanism according to claim 1, characterized in that, The distributed power flow equation constraints for constructing the global optimization model include: The secondary loss term was removed from the DistFlow model and then... and Using the voltage magnitudes of node j and node i as values, the final distributed power flow equations are obtained: ， In the formula, nodes For upstream nodes, node For downstream nodes; and They are branch roads Active power and reactive power; and These are nodes Active power and reactive power; It is a side road The resistance; branch road The reactance; The security constraints of the global optimization model include: security constraints in the power distribution network and power constraints of distributed generators; Safety constraints in power distribution networks: ， In the formula, and They are nodes The lower and upper limits of voltage amplitude; A set of nodes; branch road Current, branch road The upper limit of the current; and Branch roads It has a lower limit and an upper limit for active power; and Branch roads The lower and upper limits of reactive power. For branch set; Distributed generator power constraints: ， In the formula, , and Distributed generators at nodes Active power, reactive power, and apparent power; and These are nodes The lower and upper limits of the active power of distributed generators; and These are nodes The lower and upper limits of reactive power of distributed generators.

3. The distribution network voltage coordination control method based on event triggering mechanism according to claim 1, characterized in that, The coupling constraints of each region include: No. The coupling constraints for each region are: ， In the formula, For the upstream area, For the downstream region; For the first Boundary variables for each region, including the first region. Boundary variables when the first region is an upstream region and the second region Boundary variables when a region is used as a downstream region; For the corresponding number The boundary variables of the adjacent regions of the nth region, when the nth region... When a region is an upstream region of an adjacent region For the boundary variable when the adjacent region is the downstream region, when the first... When a region is a downstream region of an adjacent region This is the boundary variable when the adjacent region is used as the upstream region; For the first Global variables for each region; , and The first The voltage magnitude, active power, and reactive power at the boundaries of each region, including the first... The boundary voltage magnitude, active power, and reactive power when the first region is considered as the upstream region, and the first... The boundary voltage magnitude, active power, and reactive power when each region is considered as a downstream region; , and Corresponding to the first The voltage magnitude, active power, and reactive power of the adjacent region boundaries of each region, when the first region... When a region is an upstream region of an adjacent region , and These represent the boundary voltage magnitude, active power, and reactive power when the adjacent region is considered as the downstream region. When a region is a downstream region of an adjacent region , and These represent the boundary voltage magnitude, active power, and reactive power when the adjacent region is considered as the upstream region.

4. The distribution network voltage coordination control method based on event triggering mechanism according to claim 3, characterized in that, The process of decomposing the global optimization problem into regional optimization problems based on coupling constraints includes: Based on the coupling constraints, the global optimization problem is decomposed into several regional optimization problems, and the objective function of the global optimization model is designed as follows: ， In the formula, This represents the total number of areas into which the power distribution network is divided. For the first Local decision variables for each region Including the Boundary variables of each region ; For the first The objective function for each region; For the first The feasible region of local decision variables for each region that meets the constraints of distributed power flow equations and security constraints.

5. The distribution network voltage coordination control method based on event triggering mechanism according to claim 4, characterized in that, In the pre-designed ETM-DAL-ADMM algorithm, the design of the Lagrangian function for each region's optimization problem includes: linearizing the Lagrangian function for each region's optimization problem based on the global optimization model and coupling constraints to reduce computational complexity. Based on the objective function of the designed global optimization model, the Lagrangian function of the global optimization problem is constructed. The calculation formula is: ， In the formula, For the Lagrange multipliers corresponding to the consistency constraints between boundary variables and global variables, T represents the transpose operation; This is the penalty coefficient; Square of the 2-norm operation; Based on the Lagrangian function of the global optimization problem and the domain partitioning, the Lagrangian functions of the optimization problems in each domain are obtained. The calculation formula is: ， For the Lagrangian function of the optimization problem in each region, a first-order Taylor expansion is performed on the objective function of each region to obtain the linearized Lagrangian function of the optimization problem in each region. The calculation formula is: ， In the formula, For the first The second iteration Objective function for each region In the Local decision variables for each region The linear term in the first-order Taylor expansion.

6. The distribution network voltage coordination control method based on event triggering mechanism according to claim 5, characterized in that, In the ETM-DAL-ADMM algorithm No. Local decision variables for each region The formula for the (k+1)th iteration is: ， In the formula, For the first The region in the first Local decision variables for the next iteration; For the first The region in the first Local decision variables for the next iteration; For the first The region in the first Global variables for this iteration; For the first The region in the first The Lagrange multipliers for the next iteration; the argmin function is used to output the input parameters that minimize the subsequent function. No. Global variables for each region The formula for the (k+1)th iteration is: ， In the formula, For the first The region in the first Global variables for this iteration; For the first The region in the first Boundary variables for the next iteration; For the corresponding number The adjacent regions of the first region are in the second region. Boundary variables of the nth iteration; The region in the first Local decision variables in the next iteration Including the The region in the first Boundary variables of the next iteration ; No. Lagrange multipliers in each region The formula for the (k+1)th iteration is: ， In the formula, For the first The region in the first Lagrange multipliers in the next iteration; For the first The region in the first Lagrange multipliers in the next iteration.

7. The distribution network voltage coordination control method based on event triggering mechanism according to claim 6, characterized in that, In the pre-designed ETM-DAL-ADMM algorithm, the design of the Lagrangian function for each region's optimization problem also includes: dynamically adjusting the penalty coefficient based on the original residual and the dual residual to improve the convergence speed. No. Penalty coefficient for each region The formula for the (k+1)th iteration is: ， ， In the formula, and These are the minimum and maximum iteration indices that are allowed to be adjusted, respectively; For the first The region in the first The penalty coefficient for the next iteration; For the first The region in the first The penalty coefficient for the next iteration; For the first The initial values ​​of the penalty coefficient for each region; and These are the preset penalty coefficient adjustment parameters for increasing and decreasing; and These are the preset comparison parameters for the original residual and the dual residual, respectively; For 2-norm operations; and The first The region in the first The original residual and dual residual of the next iteration; No. The first region The original residual of the next iteration The calculation formula is: , No. The first region The dual residual of the next iteration The calculation formula is: .

8. The distribution network voltage coordination control method based on event triggering mechanism according to claim 7, characterized in that, The method of exchanging information between regions only when the boundary variable changes exceed a preset threshold, according to a pre-set event triggering mechanism, includes: No. The time point at which information is exchanged between regions The calculation formula is: ， ， ， In the formula, For the first The next event trigger time for each region; For the first The time when the previous event was triggered in the region; The maximum allowed time; For the first Event triggering conditions for each region; For the first The region in the first The error of the next iteration; For the first The region in the first Boundary variables for the next iteration; For the first The region in the first Boundary variables for the next iteration; For the first Event triggering functions for each region; For the first The region in the first Error of the next iteration The weighted square, This is a preset weight matrix; To control the preset threshold parameters for event triggering, ; For the first The region in the first Boundary variables of the next iteration The weighted square; No. The event triggering conditions for each region are: 。 9. The distribution network voltage coordination control method based on event triggering mechanism according to claim 8, characterized in that, The pre-designed ETM-DAL-ADMM algorithm is used to iteratively solve for the final local decision variables, including: Lagrange multipliers for each region Initialize to 0, set global variables for each region. For the actual boundary variables of each region Set the iteration index ; The following process is executed repeatedly until the iteration termination condition is met, outputting the final local decision variables for each region, which are used for distribution network voltage coordination control: Each region according to the first Local decision variables for each region The iterative formula is used to solve the optimization problem in each region, and the boundary variables of each region are obtained. ; Based on the event-triggered mechanism (ETM), the error of each region is determined according to the event triggering conditions. If the event triggering conditions are met, the corresponding region exchanges information with its neighboring regions. Each region according to the first Global variables for each region The iterative formula updates the global variables for each region. ; Each region according to the first Lagrange multipliers in each region The iterative formula updates the Lagrange multipliers for each region. ; Each region according to the first Penalty coefficient for each region The iterative formula updates the penalty coefficient for each region. ; Each region according to the first Original residuals of each region and dual residuals Calculation formula for calculating the original residuals of each region. and dual residuals .

10. The distribution network voltage coordination control method based on an event-triggered mechanism according to claim 9, characterized in that, The iteration termination conditions include: The iteration termination condition is determined based on the convergence condition formula. If the convergence condition formula is met, the ETM-DAL-ADMM algorithm converges and the iteration terminates. The convergence condition formula is as follows: ， In the formula, Operations on infinity norms; As a preset tolerance level, It is the boundary residual; Alternatively, the iteration termination condition can be determined based on the number of iterations. If the number of iterations is greater than or equal to the preset upper limit of the iteration index, the iteration will be terminated.

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