Accelerated SADMM-based voltage distribution control method for high penetration photovoltaic distribution network

Abstract

The application discloses a high-permeability photovoltaic power distribution network voltage distributed control method based on an accelerated SADMM, belongs to the field of power system operation and control, solves the problem of over-limit of distribution network voltage and large network loss caused by high-permeability photovoltaic access, and overcomes the defects of large communication pressure of traditional centralized control computing power, fixed conventional ADMM parameters, slow convergence and easy oscillation. A multi-objective optimization model of node voltage deviation and minimum network loss is constructed, a second-order cone relaxation is adopted to convert a non-convex power flow model into a convex optimization problem, a virtual boundary node is introduced to complete regional decoupling, an ADMM distributed collaborative framework is built, an accelerated SADMM algorithm based on a residual balance principle is adopted, a penalty parameter is adaptively adjusted according to a residual ratio for iterative solution, and optimal voltage control instructions are output. The application can protect the privacy of partition data, reduce the communication burden, guarantee the global optimality of the solution, suppress the iteration oscillation, accelerate the convergence speed, give consideration to safety and economy, and meet the real-time voltage regulation demand of the high-permeability photovoltaic distribution network.

Description

Technical Field

[0001] This invention relates to the field of power system operation and control technology, and in particular to a voltage distributed control method for high-penetration photovoltaic distribution networks based on accelerated SADMM. Background Technology

[0002] In recent years, distributed photovoltaic (PV) power has been widely adopted in distribution networks, with the grid-connected PV penetration rate continuously increasing, fundamentally changing the operating characteristics of traditional distribution networks. Distributed PV output is significantly affected by natural sunlight, exhibiting strong intermittency, randomness, and volatility. With a large number of distributed PV units connected to the distribution network, the network has transformed from a traditional unidirectional, passive, radial network into an active distribution network with bidirectional power flow. During periods of high PV power generation, reverse power flow is easily generated, causing abnormal voltage rises at the feeder ends and voltage exceeding limits. Simultaneously, disordered power interaction significantly increases network losses, severely impacting power quality and the safe and stable operation of the grid, thus placing higher demands on the optimization and control of distribution network voltage.

[0003] Currently, voltage optimization and control in distribution networks are mainly divided into two modes: centralized control and distributed control. Centralized voltage optimization and control requires the dispatching master station to collect all operational data from the entire network topology, loads, and distributed power sources to uniformly complete the optimization solution. For actual distribution networks with a large number of nodes, the centralized mode brings massive data transmission pressure, placing extremely high demands on communication bandwidth and the computing power of the central controller, and is prone to the curse of dimensionality. Centralized uploading of the entire data domain also poses a risk of privacy leaks for data from partitioned operations, and it is highly dependent on the central equipment; once the central controller fails, the entire voltage control system will fail, resulting in insufficient system reliability.

[0004] To overcome the inherent defects of centralized control modes, distributed control architecture, with its characteristics of decentralized computation and low communication requirements, has become a key technology for solving the aforementioned problems. Among them, algorithms based on the Alternating Direction Multiplier Method (ADMM) have been widely studied and applied. This type of method decomposes the whole-network optimization problem into multiple sub-regional sub-problems, with each sub-region interacting only with a small amount of boundary information, and solving the sub-problems locally. This can reduce communication and computing power pressure and protect data privacy within the region. However, standard ADMM algorithms mostly use fixed penalty parameters, which often result in slow convergence speed, excessive iterations, and numerical oscillations near the optimal solution when dealing with the complex non-convex power flow constraints of distribution networks. Although some existing improved algorithms propose variable step size strategies, they often lack adaptive adjustment mechanisms that fit the actual physical operating characteristics of distribution networks, making it difficult to meet the real-time voltage control requirements of high-penetration photovoltaic distribution networks while ensuring solution accuracy. Several publicly available technical solutions are currently being researched in this direction: CN117477575B discloses a voltage control method and system for power distribution networks. This method divides the system into clusters based on electrical distance and uses a sparrow search algorithm for staged power optimization, which reduces model complexity and improves control efficiency to some extent. However, the swarm intelligence optimization algorithm used in this method is prone to getting trapped in local optima when dealing with large-scale systems, and the staged independent adjustment strategy for reactive and active power severs the strong coupling relationship between variables, making it difficult to guarantee the theoretical optimality of global control. At the same time, this method has not established a collaborative control mechanism based on a distributed architecture, and cannot utilize the parallel computing capabilities of the cluster to solve the single-point computing bottleneck problem.

[0005] CN116545030A discloses a distributed energy storage operation optimization control method and device based on ADMM. This method uses the ADMM algorithm to decouple and solve the overall model of energy storage operation benefits and voltage quality. Through distributed coordination among sub-regions, it effectively alleviates the communication pressure of centralized scheduling and improves the system's scalability. However, this method mainly focuses on the optimal scheduling of a single type of resource, distributed energy storage, and does not fully explore the voltage support potential of key reactive resources such as high-penetration distributed photovoltaic inverters, resulting in relatively limited regulation methods. In addition, during the distributed iterative solution process, this method usually uses fixed penalty parameters and lacks dynamic optimization of network partitions. As a result, under conditions of large fluctuations in distribution network source and load or time-varying network parameters, the convergence performance and robustness of the algorithm are difficult to guarantee, and it cannot meet the requirement of rapid voltage recovery under complex operating conditions.

[0006] CN116264399A discloses a voltage-distributed optimization control method for distributed photovoltaic (PV) grids. This scheme constructs a multi-objective model including node voltage deviation, PV reduction, and network losses. It utilizes second-order cone SOC relaxation to achieve model convexity processing, implements grid partitioning based on decomposition and coordination principles, and employs residual balance principles to achieve adaptive updating of penalty parameters. However, this scheme introduces a PV active power reduction term into its optimization objective, prioritizing voltage overshoot by reducing PV output, without fully exploiting the inverter's reactive power regulation capabilities. Furthermore, the iterative update process lacks an ultra-relaxation iteration stage, leading to iterative oscillation risks under strongly coupled grid conditions and limited adaptability to scenarios with severe source-load fluctuations.

[0007] CN115967078A discloses a distributed voltage optimization control method for rural distribution networks with distributed photovoltaic (PV) power. This scheme also employs second-order cone relaxation, residual balance adaptive penalty parameters, and over-relaxation techniques to accelerate the ADMM solution. However, the objective function of this scheme simultaneously considers voltage deviation, PV power reduction, and network losses, using PV active power reduction as a key control measure. In scenarios with high PV consumption requirements, this can lead to unnecessary renewable energy curtailment losses. Furthermore, the scheme uses a boundary replication method for partitioned decoupling, resulting in numerous boundary variable dimensions and a large amount of data exchanged between sub-regions, further increasing the communication burden.

[0008] CN104701849B discloses a fully distributed autonomous voltage control method for active distribution networks. This method is based on second-order cone programming to convexize the power flow model and uses ADMM to achieve multi-zone decoupling, thus realizing distributed voltage control of the distribution network. However, this patent uses fixed penalty parameters, which need to be pre-tuned based on human experience. Improper parameter selection will directly lead to slow iteration convergence and numerical oscillations, making it difficult to adapt to distribution network scenarios with different photovoltaic penetration rates and different network impedances. The algorithm lacks robustness and an adaptive adjustment mechanism for penalty parameters, and cannot dynamically adjust the penalty intensity based on the original residual and dual residual during the iteration process.

[0009] CN121689030A discloses an active distributed reactive power optimization control method for distribution networks. This method completes second-order cone power flow modeling and constructs a distributed solution framework based on ADMM, which can adaptively adjust the penalty parameters according to the original residuals and dual residuals. However, this scheme only takes minimizing network loss as the single optimization objective, and cannot take into account the suppression of node voltage deviations, nor can it simultaneously achieve multi-objective collaborative optimization of voltage quality improvement and network loss reduction. Furthermore, this scheme does not introduce an ultra-relaxed iterative strategy, resulting in insufficient stability of boundary variable and dual variable updates, and its convergence performance is limited in distribution network partitioning scenarios with high boundary coupling.

[0010] In summary, existing distribution network voltage control technologies still have significant shortcomings when dealing with large-scale distributed power generation integration. Traditional centralized optimization and heuristic algorithm-based control strategies are constrained by the curse of dimensionality and communication bottlenecks, making it difficult to simultaneously achieve global optimality and real-time performance. Among existing distributed ADMM-type schemes, some rely on the reduction of photovoltaic active power to achieve voltage regulation, sacrificing the benefits of renewable energy integration; some schemes only take minimizing network losses as the sole objective, failing to consider voltage control effects; some schemes use fixed penalty parameters, relying on manual adjustment, resulting in poor adaptability to operating conditions; a few schemes with adaptive penalty parameter capabilities lack ultra-relaxed iterative coordination, leading to prominent iterative oscillation problems when boundary coupling is strong; at the same time, some existing technologies ignore the impact of the rationality of cluster partitioning on algorithm performance, lack adaptive acceleration mechanisms adapted to the physical characteristics of the power grid, and are prone to convergence difficulties, numerous iterations, and control lag when dealing with large-scale non-convex power flow constraints, making it difficult to simultaneously meet the multiple requirements of voltage quality, network losses, photovoltaic integration, and algorithm convergence speed.

[0011] Therefore, there is an urgent need to study a distributed voltage optimization control method for distribution networks that takes into account both voltage quality and network loss optimization, makes full use of the reactive power resources of photovoltaic inverters, and combines the residual balance principle with the ultra-relaxation update strategy. Summary of the Invention

[0012] The technical problem to be solved by this invention is to provide a distributed voltage control method for high-penetration photovoltaic distribution networks based on accelerated SADMM, which aims to solve the problems of voltage exceeding the limit and increased network loss caused by high-penetration distributed photovoltaic access, while overcoming the shortcomings of traditional centralized control with high computational and communication pressure, fixed penalty parameters, slow convergence speed, and easy iterative oscillation of conventional distributed ADMM algorithms.

[0013] To achieve the above technical objectives, the present invention adopts the following technical solution: This invention adaptively iteratively updates the penalty parameter by considering the magnitude relationship between the original residual and the dual residual, balancing the original residual and the dual residual, accelerating the convergence speed of the distributed algorithm, and achieving the reduction of distribution network losses and the coordinated optimization control of node voltage while ensuring the privacy of local data in each partition, thus meeting the real-time operation requirements of online dispatching of the distribution network.

[0014] The high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM includes the following steps: Step 1: Divide the target distribution network into several independent zones according to electrical coupling relationships. Only boundary variables are exchanged between zones. Measurement and equipment operation data within each zone are stored locally and not transmitted externally. Construct a network-wide optimization objective function, which simultaneously considers network losses and node voltage deviation suppression. The objective function expression is: (1); In the formula, The objective function value; , They are nodes With nodes Active and reactive power between lines; , System nodes With nodes The voltage amplitude; For nodes Reference value for voltage. pu; , These are the weighting coefficients for the network loss term and the node voltage deviation term, respectively. And satisfy .

[0015] Step 2: Decouple the overall distribution network optimization model. Based on the SADMM algorithm, decompose the overall network optimization problem into independent sub-optimization problems for each region, and construct the first... Partitioned augmented Lagrange day optimization model: (5); In the formula, For cluster The Lagrange augmented function of the partition; For cluster The local objective function; For cluster The set of internal decision variables; For the first The penalty coefficient for the next iteration; For cluster Local boundary state variables; For cluster No. Globally consistent variables for each iteration; For cluster No. The dual variable of the next iteration; , Clusters Internal physical equality and inequality constraints.

[0016] Step 3: Each partition solves its own sub-optimization problem locally, updating boundary variables. Partitions only exchange boundary variables and dual multiplier information; they do not transmit internal partition running data. The original residuals for this iteration are then calculated. With dual residual The penalty parameter is adaptively updated based on the residual balance criterion. The penalty parameter update formula is as follows: (7); In the formula, , The first , The penalty coefficient for the next iteration; , These are the penalty parameter amplification factor and reduction factor, respectively; For the first The original residual of the next iteration; For the first The dual residual of the next iteration; This is the residual balance threshold coefficient; It is the vector norm.

[0017] When the original residual is greater than or equal to When the dual residual is doubled, the penalty parameter is amplified; when the dual residual is greater than or equal to When the original residual is doubled, the penalty parameter is reduced; the penalty parameter remains unchanged for other operating conditions.

[0018] Step 4: Update the dual multipliers and determine whether the original residual and the dual residual are both less than or equal to the preset convergence threshold. If the convergence condition is not met, return to step 3 and proceed to the next iteration. If the convergence condition is met, the iteration terminates, the optimized scheduling results of each partition are output, and the active and reactive power scheduling instructions for the distributed power supply in each partition are issued.

[0019] Furthermore, in step 1, the distribution network is divided into zones according to the location of the distribution network interconnection switch. Each zone contains complete nodes, branches, and distributed power supply equipment. The zones only exchange information through the interconnection boundary nodes.

[0020] Furthermore, the preset convergence threshold in step 4 includes the original residual convergence threshold and the dual residual convergence threshold. When the original residual L2 norm and the dual residual L2 norm are both less than or equal to their respective convergence thresholds, the algorithm is determined to be converged.

[0021] Furthermore, each partition solves its sub-optimization problem using only the device data within that partition. Partitions only exchange boundary variables and dual multiplier vectors. The original measurement data and device parameters within each partition are not shared externally, thus achieving data privacy protection.

[0022] The voltage distributed control method for high-penetration photovoltaic distribution networks based on accelerated SADMM provided by this invention has the following beneficial effects: 1. This invention constructs a multi-objective optimization model that takes into account both voltage quality and economy. It takes minimizing the voltage deviation of all network nodes and minimizing the network loss of the system as optimization objectives. It can simultaneously handle two types of operational problems caused by high-penetration distributed photovoltaic access: voltage exceeding limits and increased network loss, thus balancing the operational safety and economy of the distribution network.

[0023] 2. This invention effectively solves the non-convex problem of AC power flow constraints by utilizing second-order cone relaxation technology, transforming the complex non-convex nonlinear programming problem into a standard convex optimization problem, ensuring the global optimality and solution stability of the optimization problem, effectively eliminating the risk of voltage exceeding limits under high-penetration photovoltaic access, and overcoming the drawback of heuristic algorithms being prone to getting trapped in local optima.

[0024] 3. This invention adopts a distributed control architecture based on consistency constraints. By introducing virtual boundary nodes, it achieves regional decoupling, decomposes the large-scale network optimization problem into multiple regional sub-problems that can be solved in parallel, alleviates the computational pressure on the central controller under centralized control, and avoids the dimensionality curse brought about by large-scale distribution networks.

[0025] 4. In this invention, each region only needs to exchange information at the boundary with the adjacent region, without having to upload detailed internal topology, load and photovoltaic operation data. This significantly reduces communication pressure and bandwidth requirements while effectively protecting the data privacy of each region.

[0026] 5. The distributed control architecture of this invention eliminates the strong dependence on a single central controller, avoids the single point of failure risk of centralized control, improves the overall operational reliability of the voltage control system, and has good system scalability.

[0027] 6. This invention proposes an accelerated synchronous alternating direction multiplier method (accelerated SADMM) based on the residual balance principle. Unlike the traditional ADMM algorithm with fixed penalty parameters, it can calculate the original residual, which represents the degree of boundary coupling, and the dual residual, which represents the local optimization accuracy, in real time.

[0028] 7. This invention can intelligently and dynamically adjust the penalty parameters based on the iterative convergence state and by comparing the magnitude relationship between the original residual and the dual residual, thereby achieving a dynamic balance between the degree of boundary coupling and the accuracy of local optimization.

[0029] 8. The penalty parameter adaptive adjustment mechanism of the present invention effectively overcomes the iterative oscillation and convergence stagnation caused by fixed parameters, significantly reduces the number of algorithm iterations, and shortens the overall calculation time.

[0030] 9. This invention uses the original residual and dual residual as dual thresholds as convergence criteria, and simultaneously verifies the degree of consistency constraint satisfaction of boundary variables and the local optimization accuracy of subproblems, thereby improving the rigor of convergence judgment and ensuring the regulation accuracy of output voltage control commands.

[0031] 10. The sub-problems in each region of this invention support parallel computation, fully utilize distributed computing power, and maintain the same solution accuracy as the theoretical optimal solution of centralized optimization. It can meet the high real-time requirements of active distribution networks for voltage control and adapt to complex operating conditions with large fluctuations in source and load.

[0032] 11. This invention fully incorporates node voltage safety constraints, branch current constraints, photovoltaic inverter capacity and power factor constraints, and the entire optimization solution process is limited to the grid safety feasible region. The output voltage control commands are engineering-executable and will not output control strategies that violate equipment safety limits.

[0033] 12. This invention fully taps the reactive power regulation potential of distributed photovoltaic inverters, relies on coordinating the reactive power output of photovoltaic inverters to complete voltage management, adapts to the intermittent and fluctuating operating characteristics of distributed photovoltaic power output, and quickly suppresses the problem of voltage rise exceeding the limit at the end of the feeder during periods of high photovoltaic power generation.

[0034] 13. The algorithm of this invention is robust. It can maintain good convergence performance in distribution network scenarios with different photovoltaic penetration rates and different network parameters by relying on the penalty parameter adaptive mechanism, which reduces the workload of manually debugging algorithm parameters and facilitates practical engineering applications.

[0035] 14. The multi-objective model of this invention can be configured with weighting coefficients, which can flexibly adjust the priority of voltage deviation optimization and network loss optimization. It can focus on improving voltage quality or reducing the loss of distribution network operation according to the needs of on-site dispatching, and the dispatching configuration is flexible. Attached Figure Description

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the overall voltage distributed control method proposed in this invention.

[0037] Figure 2 This is a schematic diagram of the distribution network cluster decoupling of the present invention; Figure 3 This is a voltage curve diagram illustrating the voltage distributed control method implemented in this invention. Figure 4 This is a comparison chart of the convergence curves of the voltage distributed control method implemented in this invention. Detailed Implementation

[0038] The technical solutions of the present invention will be further described below with reference to the embodiments and accompanying drawings: Example 1 like Figure 1 As shown in the figure, this embodiment provides a high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM, which specifically includes the following steps: Step 1: Obtain the line impedance parameters, network topology, and real-time operating status of the distribution network, and construct a distribution network voltage optimization control model with the objectives of minimizing the voltage deviation of all network nodes and minimizing network losses. (1); In the formula, The objective function value; , They are nodes With nodes Active and reactive power between lines; , System nodes With nodes The voltage amplitude; For nodes Reference value for voltage. pu; , These are the weighting coefficients for the network loss term and the node voltage deviation term, respectively. And satisfy .

[0039] Step 2: To address the nonlinear branch power flow constraints in the voltage optimization control model, a second-order cone programming relaxation technique is introduced. By introducing auxiliary variables, the non-convex equality constraints are relaxed into second-order cone inequality constraints, thereby transforming the original non-convex optimization problem into a convex optimization problem.

[0040] The specific second-order cone programming relaxation technique is achieved by defining the square of the voltage amplitude ( ) and the square of the current amplitude ( As a new decision variable, a convex optimization model is constructed as follows, which includes branch power flow constraints, second-order cone relaxation constraints, and safe operation constraints: (1) Branch flow constraints: (2); (2) Second-order cone relaxation constraint: The original non-convex equality constraint is relaxed. Relaxation is expressed as the following second-order cone inequality: (3); (3) Safety operation constraints: (4); In the formula, , They are nodes With nodes Active and reactive power between lines; , They are slave nodes Flow to Node Active power and reactive power; , They are nodes The active and reactive power injected by the distributed photovoltaic power source; , They are nodes The active and reactive power consumed by the load; For As an upstream node, Branches for downstream nodes ; For As an upstream node, Branches for downstream nodes ; , They are nodes With nodes Resistance and reactance between lines; , They are nodes With nodes The square of the voltage amplitude; For nodes With nodes The square of the current amplitude between the lines; , They are nodes The squares of the upper and lower limits of the voltage amplitude; , They are respectively The square of the upper limit of the branch current amplitude; For nodes The capacity of photovoltaic power generation; This is the power factor angle of the photovoltaic inverter.

[0041] Step 3: Based on consistency constraints, the convex optimization model of the entire network is decoupled into multiple parallel regional sub-problems. Lagrange augmented functions corresponding to the sub-objectives of each region are constructed to form a distributed cooperative control framework based on the alternating direction multiplier method.

[0042] The construction process of the distributed cooperative control framework is as follows: Virtual boundary nodes are set up on the connecting lines between adjacent regions, transforming the physical electrical connections between regions into mathematical boundary state variable consistency constraints. The Lagrange augmented function corresponding to each sub-objective of the partition is constructed as follows: (5); In the formula, For cluster The Lagrange augmented function of the partition; For cluster The local objective function; For cluster The set of internal decision variables; For the first The penalty coefficient for the next iteration; For cluster Local boundary state variables; For cluster No. Globally consistent variables for each iteration; For cluster No. The dual variable of the next iteration; , Clusters Internal physical equality and inequality constraints.

[0043] Step 4: The distributed control model is iteratively solved using the accelerated synchronous alternating direction multiplier method based on the residual balance principle. During the iteration process, the original residual representing the degree of boundary coupling and the dual residual representing the local optimization accuracy are calculated in real time. The penalty parameter is dynamically and adaptively adjusted according to the ratio of the two types of residuals until the model meets the convergence condition and the optimal voltage control command is output.

[0044] Specifically, the iterative steps include the following: Set the number of iterations when the algorithm starts. Initialize parameters. Initialize each cluster. a Globally consistent variables x 0 ref,a Dual variables λ 0 a and penalty coefficient ρ 0 .

[0045] In the k In the +1 iteration, each cluster solves the augmented Lagrange minimization problem in parallel, with adjacent clusters... a and cluster b For example, the solution for the local boundary state variables is expressed as follows: (8); In the formula, For cluster The Local boundary state variables for the next iteration; For cluster The local objective function; For cluster The set of internal decision variables; For the first The penalty coefficient for the next iteration; For clusterb Local boundary state variables; For cluster The Local boundary state variables for the next iteration; For cluster No. Globally consistent variables for each iteration; For cluster No. The dual variable of the next iteration.

[0046] Each neighboring cluster exchanges boundary information and calculates the average value to update the global consistency variable: (6); In the formula, , Clusters , No. Globally consistent variables for each iteration.

[0047] Each cluster updates its dual variable based on the residual between the local boundary variable and the global variable: (9); In the formula, For cluster No. The dual variable of the next iteration; For cluster No. The dual variable of the next iteration.

[0048] The convergence status of the algorithm is checked by calculating the original residual and the dual residual: (10); (11); In the formula, For the first The original residual of the next iteration; For the first The dual residual of the next iteration; The convergence threshold, .

[0049] like and If the result is positive, the algorithm converges; otherwise, it enters the adaptive step size update stage. Based on the residual balance principle, the penalty parameter is dynamically adjusted according to the residual ratio. (7); In the formula, , The first , The penalty coefficient for the next iteration; For the first The original residual of the next iteration; For the first The dual residual of the next iteration; It is the vector norm; This is the residual balance threshold coefficient, which is also the multiple of the difference between the original residual and the dual residual. ; , These are the amplification and reduction coefficients of the penalty parameter, respectively; they are also the proportional parameters for dynamically adjusting the penalty coefficient. .

[0050] After completing the parameter update, let And will update It is applied to the next round of iteration calculation, then returns to the loop iteration to continue execution until the convergence condition is met.

[0051] Example 2 In another preferred embodiment, based on Embodiment 1, this embodiment provides a voltage distributed control method for high-penetration photovoltaic distribution networks based on accelerated SADMM. This embodiment uses a modified IEEE-33 node distribution network for simulation verification, combined with... Figures 2 to 4 The cluster decoupling effect, voltage control effect, and algorithm convergence performance of the present invention are further explained.

[0052] Figure 2 This is a schematic diagram of the distribution network cluster decoupling according to the present invention. The upper diagram shows the original physical topology of the distribution network, and the lower diagram shows the decoupling model after introducing virtual boundary nodes. The diagram decouples the originally physically interconnected distribution network into relatively independent subsystems: the left side represents the cluster. The right side shows the cluster. To achieve distributed computing, the model introduces virtual boundary nodes at the connection points: clusters. Side introduces virtual nodes Cluster Side introduces virtual nodes To ensure the physical consistency of the two solutions, the ADMM (Alternating Direction Method of Multipliers) algorithm applies consistency constraints iteratively, strictly requiring that the local boundary state variables of all adjacent clusters eventually become equal.

[0053] Figure 2The circular arrow in the middle represents the algorithm's iterative process. This algorithm iterates through a cyclical mechanism of parallel solving of local subproblems, information exchange at boundaries, and updates of dual variables, gradually eliminating voltage and power deviations between virtual boundary nodes on both sides, forcing the electrical parameters at the virtual boundaries to converge. This process ensures effective distributed coordinated optimization of the entire network voltage without needing to share internal topology parameters or relying on a central controller.

[0054] In this embodiment, the IEEE-33 node distribution network is divided into clusters. (Nodes 1-17) and the cluster (Nodes 18-33) The aforementioned virtual boundary nodes are only set in two cluster interconnection branches. Clusters only exchange boundary voltage and power variables; load, photovoltaic output, and line parameters within each cluster are all stored locally and not transmitted externally, thus achieving data privacy protection. In the simulation example, the distribution network reference voltage is set to 12.66kV, multiple nodes are connected to distributed photovoltaic systems, and the photovoltaic penetration rate is set to 72%. Simulation tests are conducted at typical times of peak photovoltaic power generation. The model weighting coefficients are... , Prioritize voltage control effectiveness; Algorithm initialization parameters: Initial penalty coefficient Convergence threshold Residual balance threshold coefficient Penalty parameter adjustment ratio parameter .

[0055] Following steps 1 to 4 as described in Example 1, the model is constructed, second-order cone relaxation is performed, partition decoupling is implemented, and SADMM iterative solution is accelerated. Reactive power control commands for each node's photovoltaic inverter are output, yielding the node voltage distribution and algorithm convergence characteristics, as shown below. Figure 3 , Figure 4 As shown.

[0056] Figure 3The figure shows the voltage curves for implementing the distributed voltage control method of this invention. The horizontal axis represents the node number, and the vertical axis represents the per-unit voltage value of the nodes. As shown in the figure, the blue curve represents the system node voltage distribution without any control strategy (no control). It can be seen that during periods of high photovoltaic power generation, the voltage rise caused by the reverse power flow on the feeders leads to a significant voltage surge at some nodes, with the highest voltage reaching 1.072 pu, far exceeding the upper voltage threshold of 1.05 pu. This poses a significant threat to the safe operation of the distribution network. In contrast, the red curve marked with a triangle shows the voltage situation after applying the distributed control method proposed in this invention. After the method of this invention coordinates and optimizes the reactive power output of the photovoltaic inverters in each zone, the node voltage of the entire network is significantly suppressed and maintained within the safe operating range. As can be seen from the figure, the maximum node voltage of the controlled system is limited to 1.034 pu, fully meeting the voltage quality standards of the distribution network. Simulation results also show that compared with the uncontrolled condition, the network loss of the entire distribution network in this embodiment is reduced by 14.7%, balancing voltage safety and economical system operation. This fully verifies the effectiveness of the strategy proposed in this invention in solving the voltage over-limit problem caused by a high proportion of distributed power supply access, and can significantly improve the operational stability of the system.

[0057] Figure 4 This is a comparison of the convergence curves of the voltage distributed control method implemented in this invention. The horizontal axis represents the number of iterations, and the vertical axis represents the objective function value. The black dashed line represents the globally optimal objective function value under centralized control mode, serving as a theoretical benchmark for performance comparison; the blue dashed line represents the convergence trajectory of the traditional ADMM algorithm; and the red solid line represents the convergence trajectory of the accelerated SADMM (Synchronous Alternating Direction Method of Multipliers) algorithm proposed in this invention.

[0058] Depend on Figure 4 It is known that the traditional ADMM algorithm uses a fixed penalty coefficient, resulting in significant oscillations during convergence, and the objective function value decreases relatively slowly, requiring a long iterative process before gradually stabilizing (e.g., Figure 4 As shown, it requires 62 iterations to gradually stabilize, resulting in low convergence efficiency. In contrast, the accelerated SADMM algorithm proposed in this invention benefits from a parameter adaptive adjustment mechanism based on the residual balance principle. Its objective function value rapidly decreases in the early stages of iteration and smoothly approaches the theoretical optimal value of centralized optimization, reaching a stable convergence state within a very short iteration process (e.g., ...). Figure 4As shown, a stable convergence state is reached after only 10 iterations. Comparative results demonstrate that the method of this invention significantly improves the convergence speed and computational efficiency of the algorithm while maintaining the same solution accuracy as centralized optimization, thus better meeting the needs of real-time control.

[0059] The simulation results of this embodiment further verify that, under the partitioned distributed architecture, the present invention can both protect the data privacy within each partition and quickly address the voltage over-limit problem caused by photovoltaics; the accelerated SADMM algorithm with adaptive penalty parameters effectively suppresses iterative oscillations, significantly reduces the number of iterations, and has good engineering practical value.

[0060] In the preferred embodiment, step 1 involves constructing a distribution network voltage optimization control model with the objectives of minimizing the voltage deviation of all network nodes and minimizing network losses. This configuration comprehensively considers the safety and economic indicators of the distribution network, effectively mitigating voltage fluctuations caused by high-penetration photovoltaic access, improving power quality while reducing system operating costs, and providing a precise mathematical model that takes into account multiple objectives for subsequent optimization solutions.

[0061] In the preferred embodiment, the objective function of the voltage optimization control model in step 1 is the weighted sum of minimizing the voltage deviation of all network nodes and minimizing network loss. Weighting coefficients are set for the two objectives to complete the multi-objective optimization modeling. The above settings can flexibly adjust the weight allocation according to the operating priority of different distribution networks, ensuring voltage quality while taking into account the economic efficiency of system operation, so that the optimization results are more in line with the actual control needs on site.

[0062] In the preferred embodiment, step 2 introduces a second-order cone programming relaxation technique, which relaxes the non-convex equality constraint into a second-order cone inequality constraint by introducing auxiliary variables. This setting effectively solves the problem of the original AC power flow constraint being difficult to solve or getting trapped in local optima due to its nonlinearity and non-convexity. It transforms the complex non-convex optimization into a convex optimization problem solvable in polynomial time, and ensures the global optimality and computational efficiency of the model solution from a mathematical perspective.

[0063] In the preferred embodiment, the second-order cone programming relaxation technique described in step 2 defines the square of voltage amplitude and the square of current amplitude as new decision variables to construct a convex optimization model that includes branch power flow constraints, second-order cone relaxation constraints, and distribution network safety operation constraints. The above settings transform the originally non-convex and nonlinear AC power flow constraints into a standard convex feasible region, mathematically avoiding the local optimum trap and significantly improving the stability of optimization solutions in large-scale systems.

[0064] In the preferred embodiment, the safety operation constraints include upper and lower limits of node voltage, upper limit of branch current amplitude, and capacity and power factor constraints of distributed photovoltaic inverters. These settings fully incorporate various physical boundary conditions of the distribution network operation into the optimization model, ensuring that all control commands obtained from the solution will not exceed the equipment's carrying capacity limit, and guaranteeing the physical feasibility of system operation throughout the process.

[0065] In the preferred embodiment, step 3 involves constructing a distributed collaborative control framework based on the alternating direction multiplier method using consistency constraints, and constructing a Lagrange augmented function for decoupling. This setup breaks the dependence of traditional centralized control on the communication bandwidth and computing power of the central controller, enabling parallel computation and independent solution of sub-problems in various regions of the distribution network. While protecting the data privacy of each region, it achieves collaborative optimization at the network level through the interaction of boundary information.

[0066] In the preferred embodiment, when building the distributed collaborative optimization framework in step 3, virtual boundary nodes are set on the connecting lines between adjacent areas to transform the electrical connection relationship between areas into a consistency constraint of boundary state variables; a Lagrange augmented function corresponding to each sub-objective of the partition is constructed, and each area only interacts with the boundary variable information with the adjacent areas, without disclosing the internal topology and load data of the area to the outside world, thereby achieving data privacy protection; the above settings completely get rid of the strong dependence on the global central controller, and each area can independently complete local optimization calculations, which effectively avoids the risk of system paralysis caused by single point of failure while reducing the overall network communication bandwidth occupation.

[0067] In the preferred embodiment, step 4 employs an accelerated synchronous alternating direction multiplier method solution strategy based on the residual balance principle, dynamically and adaptively adjusting the penalty parameter according to the ratio of the original residual to the dual residual. This setting overcomes the problems of slow convergence speed and high parameter sensitivity caused by the fixed penalty parameter in the standard ADMM algorithm. By balancing the boundary coupling degree and local optimization accuracy in real time, the number of iterations is significantly reduced, meeting the strict real-time requirements of distribution network voltage control.

[0068] In the preferred scheme, the iterative solution of accelerating SADMM described in step 4 includes a loop process of parameter initialization, parallel solution of augmented Lagrange minimization problem in each cluster, exchange of boundary information between adjacent clusters to update global consistency variables, and updating dual variables. The above settings fully release the computing power advantage of multi-region parallel computing, decompose the originally centralized large-scale computing task into multiple light quantum tasks to be promoted simultaneously, and significantly reduce the overall time consumption of a single iteration.

[0069] In the preferred embodiment, the convergence criterion for accelerating SADMM is that the norm of the original residual is less than or equal to the convergence threshold, and the norm of the dual residual is less than or equal to the convergence threshold. The above settings simultaneously verify the iteration state from two dimensions: boundary variable consistency and local optimization accuracy. This avoids the false convergence problem caused by a single residual judgment and ensures that the final output control command has sufficient solution accuracy.

[0070] In the preferred embodiment, when the iterative convergence judgment condition is not met, according to the residual balance principle, the difference multiple between the original residual and the dual residual, the penalty coefficient adjustment ratio parameter is set, the penalty parameter is dynamically updated, and the next iteration is entered. The above settings can adaptively adjust the penalty intensity according to the actual convergence state of the current iteration, quickly eliminate the oscillation phenomenon in the iteration process, greatly reduce the number of redundant iterations, and allow the algorithm to approach the optimal solution faster.

[0071] In the preferred embodiment, the output optimal voltage control command in step 4 is used to adjust the reactive power output of the distributed photovoltaic inverters at each node, control the voltage of all nodes in the network within the allowable safe range, and reduce the network loss of the distribution network. The above settings fully tap the dynamic reactive power regulation potential of the distributed photovoltaic inverters, and can achieve fine control of the voltage of the entire network without the need for additional voltage regulation equipment, thereby improving the photovoltaic absorption capacity while reducing the operating loss of the system.

[0072] In summary, the distributed voltage control method for high-penetration photovoltaic distribution networks based on accelerated SADMM provided by this invention overcomes the problems of voltage exceeding limits and increased network losses caused by high-penetration photovoltaic access to the distribution network by relying on second-order cone programming convexity processing, virtual boundary node model decoupling, and residual balance-driven penalty parameter adaptive iteration mechanism. At the same time, it improves the engineering shortcomings of traditional centralized control, such as high communication pressure and single-point failure risk, and conventional distributed ADMM algorithm parameters with fixed parameters, iterative oscillations, and slow convergence speed, and realizes distributed voltage optimization and control of distribution network zones in a coordinated manner.

[0073] This invention addresses the nonlinear characteristics of power flow equations in distribution networks by employing second-order cone relaxation techniques to handle non-convex constraints. This significantly reduces computational complexity without sacrificing the physical accuracy of the model. By leveraging second-order cone relaxation, the non-convex constraints of AC power flow are transformed into second-order cone inequality constraints, converting the original non-convex nonlinear programming problem into a convex optimization problem that can be stably solved. This ensures that the global optimal solution can still be obtained quickly in large-scale node systems, overcoming the technical bottleneck of traditional algorithms that are prone to getting trapped in local extrema. It provides a reliable solution foundation for distribution network voltage management from the model level.

[0074] This invention successfully transforms a large-scale network optimization problem into multiple parallel regional sub-problems through an ADMM decomposition strategy based on consistency constraints. By setting virtual boundary nodes to decouple multiple clusters in the distribution network, and relying on boundary variable consistency constraints to build a distributed collaborative computing framework, this invention effectively alleviates communication bottlenecks and single-point computational pressure. Each cluster only interacts with boundary electrical information, while internal topology, load, and photovoltaic operation data are stored locally. This reduces communication bandwidth overhead while avoiding the system paralysis risk caused by single-point failures in centralized control architectures, greatly improving system scalability and data security, and making it suitable for engineering scenarios involving multi-regional distributed control of distribution networks.

[0075] This invention addresses the pain point of slow iteration in traditional distributed algorithms by proposing a parameter adaptive acceleration mechanism based on the residual balance principle. It introduces residual balance adjustment logic onto the framework of the synchronous alternating direction multiplier method. During the iteration process, the original residual and dual residual are calculated simultaneously. The penalty parameter is dynamically adjusted based on the quantization ratio of the two types of residuals, eliminating dependence on fixed penalty parameters, effectively reducing numerical oscillations during iteration, decreasing the number of iterations, and shortening the overall computation time. It can dynamically adjust the algorithm step size according to the actual residual during iteration, significantly improving the convergence speed while maintaining the convergence threshold. This provides a robust and efficient solution for real-time voltage control in highly volatile photovoltaic distribution networks.

[0076] This invention uses the original residual and dual residual as convergence criteria, and verifies the degree of consistency constraint satisfaction of boundary variables and the local optimization accuracy of subproblems. The convergence judgment conditions are more rigorous, and all output photovoltaic inverter reactive power control commands fall within the feasible domain of grid safe operation. It can adapt to the working conditions of large fluctuations in photovoltaic output and meet the actual operation requirements of real-time voltage control of active distribution network.

[0077] Simulation results of this invention show that the solution accuracy of this scheme can be consistent with that of centralized optimization. It can not only constrain the voltage of all network nodes within the allowable safe range and suppress voltage overruns caused by reverse power flow, but also reduce the network loss of the system simultaneously, taking into account both the safety and economy of power grid operation. The algorithm has good robustness, reduces the workload of manual parameter tuning, and is easy to implement and promote in engineering.

Claims

1. A high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM, characterized in that, Includes the following steps: Step 1: Obtain the impedance parameters of the distribution network lines, the network topology, and the real-time operating status of distributed photovoltaic systems, and construct a distribution network voltage optimization control model with the goal of minimizing the voltage deviation of all network nodes and minimizing the system network loss; Step 2: For the nonlinear branch power flow constraints in the voltage optimization control model, the second-order cone programming relaxation technique is adopted. Auxiliary variables are introduced to relax the non-convex equality constraints into second-order cone inequality constraints, thus transforming the original non-convex optimization problem into a convex optimization problem. Step 3: Based on consistency constraints, decouple the whole network convex optimization model into multiple parallel regional sub-problems, construct the Lagrange augmented function corresponding to the sub-objective of each region, and build a distributed collaborative optimization framework of alternating direction multiplier method; Step 4: The distributed control model is solved by the accelerated synchronous alternating direction multiplier method based on the residual balance principle, namely the accelerated SADMM. During the iteration process, the original residual and the dual residual are calculated. The penalty parameter is dynamically and adaptively adjusted according to the ratio of the two types of residuals. When the convergence condition is met, the optimal voltage control command is output.

2. The high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM according to claim 1, characterized in that: The objective function of the voltage optimization control model described in step 1 is a weighted sum of minimizing the voltage deviation of all network nodes and minimizing network loss. By setting the weighting coefficients for the two objectives, the multi-objective optimization modeling is completed.

3. The voltage distributed control method for a high-penetration distributed photovoltaic distribution network according to claim 2, characterized in that, The objective function of the voltage optimization control model is formulated as follows: （1）； In the formula, The objective function value; , They are nodes With nodes Active and reactive power between lines; , System nodes With nodes The voltage amplitude; For nodes Reference value for voltage; , These are the weighting coefficients for the network loss term and the node voltage deviation term, respectively.

4. The high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM according to claim 1, characterized in that: The second-order cone programming relaxation technique described in step 2 defines the square of voltage amplitude and the square of current amplitude as new decision variables to construct a convex optimization model that includes branch power flow constraints, second-order cone relaxation constraints, and distribution network safety operation constraints.

5. The high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM according to claim 4, characterized in that, The formula for the branch power flow constraint is: （2）； The formula for the second-order cone relaxation constraint is: （3）； In the formula, , They are nodes With nodes Active and reactive power between lines; , They are slave nodes Flow to Node Active power and reactive power; , They are nodes The active and reactive power injected by the distributed photovoltaic power source; , They are nodes The active and reactive power consumed by the load; For As an upstream node, Branches for downstream nodes ; For As an upstream node, Branches for downstream nodes ; , They are nodes With nodes Resistance and reactance between lines; , They are nodes With nodes The square of the voltage amplitude; For nodes With nodes The square of the current amplitude between the lines.

6. The high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM according to claim 4, characterized in that: The safety operation constraints include upper and lower limits for node voltage, upper limit for branch current amplitude, and capacity and power factor constraints for distributed photovoltaic inverters. The specific formulas are as follows: （4）； In the formula, , They are nodes The squares of the upper and lower limits of the voltage amplitude; , They are respectively The square of the upper limit of the branch current amplitude; For nodes The capacity of solar power; The power factor angle of the photovoltaic inverter.

7. The high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM according to claim 1, characterized in that: In step 3, when building the distributed collaborative optimization framework, virtual boundary nodes are set on the connecting lines between adjacent areas to transform the electrical connection relationship between areas into a consistency constraint of boundary state variables. A Lagrange augmented function corresponding to each sub-objective of the partition is constructed. Each area only interacts with the boundary variable information of the adjacent areas and does not disclose the internal topology and load data of the area to the outside world, so as to achieve data privacy protection.

8. The high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM according to claim 7, characterized in that, The expression for the Lagrange augmented function is: （5）； In the formula, For clusters The Lagrange augmented function of the partition; For clusters The local objective function; For clusters The set of internal decision variables; For the first The penalty coefficient for the next iteration; For clusters Local boundary state variables; For clusters No. Globally consistent variables for each iteration; For clusters No. The dual variable of the next iteration; , Clusters Internal physical equality and inequality constraints.

9. The high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM according to claim 1, characterized in that, Step 4, which accelerates the iterative solution of SADMM, includes a loop process of parameter initialization, parallel solving of the augmented Lagrange minimization problem in each cluster, exchanging boundary information between adjacent clusters to update the global consistency variable, and updating the dual variable. The iterative convergence criterion is that the norm of the original residual is less than or equal to the convergence threshold, and the norm of the dual residual is also less than or equal to the convergence threshold. The formula for calculating the updated global consistency variable is: （6）； In the formula, , Clusters , No. Globally consistent variables for each iteration; , For clusters , The The local boundary state variables of the next iteration.

10. The high-penetration photovoltaic distribution network voltage distributed control method based on accelerated SADMM according to claim 9, characterized in that: When the iterative convergence criterion is not met, according to the residual balance principle, the difference factor between the original residual and the dual residual, and the penalty coefficient adjustment ratio are set, and the penalty parameter is dynamically updated to enter the next iteration; wherein, the expression for dynamically updating the penalty parameter is: （7）； In the formula, , The first , The penalty coefficient for the next iteration; , These are the penalty parameter amplification factor and reduction factor, respectively; For the first The original residual of the next iteration; For the first The dual residual of the next iteration; This is the residual balance threshold coefficient; It is the vector norm.

Images