High-proportion photovoltaic power distribution network distributed optimization method and system based on equivalent aggregation hot start

Abstract

The invention belongs to the technical field of power system operation and control, and provides a power distribution network distributed optimization method based on equivalent aggregation hot start, which is suitable for a high photovoltaic permeability scene. The method comprises the following steps: firstly, dividing a power distribution network into a plurality of control sub-regions, and establishing a power flow model and an optimization target of each sub-region; constructing an equivalent aggregation simplified model for each sub-region, uploading the equivalent aggregation simplified model to an upper-layer integrated controller, quickly solving to obtain a rough solution of voltage and power of a boundary node of the sub-region, and issuing the rough solution to the corresponding sub-region; and each sub-region controller performs hot start on distributed optimization based on the rough solution, solves a local optimization problem containing complete constraints in parallel by adopting an alternating direction multiplier method, adaptively adjusts penalty parameters based on a residual balance method, and finally obtains an optimal scheduling scheme of the whole network. According to the method, the number of iterations and the calculation time of a distributed algorithm are remarkably reduced, and the efficiency and the stability of large-scale power distribution network dispatching are improved on the premise of ensuring privacy isolation.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of power system operation and control technology, and particularly relates to a distributed optimization method and system for high-proportion photovoltaic distribution networks based on equivalent aggregation hot start. Background Technology

[0002] With the advancement of the "dual-carbon" strategic goals and the implementation of the "county-wide promotion" pilot program for distributed photovoltaic (PV) development, the penetration rate of distributed PV in power distribution networks has experienced explosive growth. However, county-level power distribution networks typically have long power supply lines and a high R / X ratio, exhibiting significant "weak grid" characteristics. PV output is significantly affected by environmental factors such as light intensity and temperature, exhibiting significant random fluctuations. Under large-scale integration, this can easily lead to problems such as voltage exceeding limits, backflow, and increased network losses, seriously threatening the safe and stable operation of the power grid.

[0003] To address these issues, utilizing the reactive power regulation potential of photovoltaic inverters for optimal power flow control has become the mainstream approach. However, with the surge in source-load scale, the distribution network exhibits strong coupling characteristics across multiple spatiotemporal scales of "source-grid-load". Traditional centralized optimization control based on a whole-network model faces the "curse of dimensionality" problem: on the one hand, detailed modeling of massive nodes results in huge computational matrix dimensions, making it difficult to meet real-time scheduling requirements in terms of solution efficiency; on the other hand, centralized control relies on real-time uploading of data from the entire network, which not only places extremely high demands on communication bandwidth and reliability (such as facing the risk of communication congestion, delay, or even interruption), but also makes it difficult to protect the privacy data of users in various regions.

[0004] Given this, distributed optimization algorithms based on the Alternating Direction Multiplier Method (ADMM) have attracted much attention due to their ability to achieve "intra-group autonomy and inter-group coordination." However, existing ADMM algorithms still have the following significant drawbacks when applied to large-scale complex distribution networks:

[0005] 1. Sensitivity to initial values ​​and slow convergence speed: Existing methods typically employ a "flat start" strategy, which initializes all voltages to 1.0 pu or random values. Due to the nonlinearity of power flow constraints in distribution networks or the strong coupling under complex operating conditions, blind selection of initial values ​​leads to the algorithm needing to perform a large number of searches and iterations outside the feasible region in the early stages, resulting in extremely slow convergence speed and difficulty in coping with rapid fluctuations in photovoltaic output.

[0006] 2. Huge communication overhead: The ADMM algorithm relies on frequent exchange of boundary variables (voltage, power residuals) between adjacent regions. In cases of slow convergence, hundreds or thousands of iterations mean massive communication interactions, which are easily affected by communication delays or packet loss in practical engineering, leading to delayed control commands or even system instability.

[0007] In distribution networks with a high proportion of distributed photovoltaic (PV) power, existing centralized optimal power flow methods face challenges such as large computational scale, insufficient real-time performance, and strong dependence on communication and computing power. These challenges stem from factors like the strong random fluctuations in PV output, the dispersed nature of node voltage regulation resources, the tree-like network topology, and non-uniform electrical coupling. Traditional distributed methods, on the other hand, generally suffer from engineering bottlenecks such as sensitivity to initial conditions, slow convergence, and susceptibility to suboptimal solutions. Especially in high-penetration scenarios, the coupling of PV curtailment, voltage exceeding limits, and reactive power constraints makes it difficult for distributed algorithms to balance convergence speed, stability, and scheduling effectiveness when reasonable initial boundary information is lacking. Consequently, they struggle to meet the real-time, robust, and scalable requirements of practical scheduling systems.

[0008] Therefore, a methodology is needed that can significantly reduce computational scale while providing high-quality initial solutions for distributed optimization, thereby improving overall convergence efficiency and scheduling performance. Summary of the Invention

[0009] The purpose of this invention is to provide a high-proportion photovoltaic distribution network distributed optimization method based on equivalent aggregation hot start. By constructing a low-dimensional equivalent aggregation model, a coarse solution of global information is quickly obtained, and this solution is used to hot start the distributed algorithm, thereby solving the problems of slow convergence and heavy communication in large-scale distribution network distributed optimization.

[0010] This invention is implemented as follows: a distributed optimization method for high-proportion photovoltaic distribution networks based on equivalent aggregation hot start, the method comprising:

[0011] S1: Obtain the topology and parameters of the distribution network, and divide the distribution network into several interconnected control sub-regions based on electrical distance;

[0012] S2: Establish a linear DistFlow power flow model for each control sub-region with a high proportion of photovoltaic penetration into the distribution network, and use the minimum sum of the light clipping amount and voltage deviation penalty of the sub-region as the objective function;

[0013] S3: Perform equivalent aggregation processing on each control sub-region, retain the sub-region boundary nodes and key voltage regulation nodes, and perform equivalent aggregation of photovoltaic power sources and loads within the sub-region to obtain a simplified model within the sub-region. Each lower-level sub-region controller uploads the simplified model of its region to the upper-level central controller to construct the equivalent aggregation simplified model of the entire network.

[0014] S4: With the goal of minimizing the sum of the total network clipping amount and voltage deviation penalty, the equivalent aggregation simplified model is solved by centralized optimal power flow solution to obtain a rough optimized solution for the boundary information of each sub-region;

[0015] S5: The coarse optimization solution obtained in S4 is used as the initial value of the distributed optimization. The consensus variables in the Alternating Direction Multiplier Method (ADMM) are initialized and warm-started. Then, each control sub-region solves the lower-level distributed optimization model containing complete constraints in parallel. The consensus variables are iteratively updated by exchanging boundary information until the convergence condition is met or the maximum number of iterations is reached, and the optimal scheduling scheme of the entire network is obtained.

[0016] Furthermore, in step S1, dividing the distribution network into several interconnected control sub-regions based on electrical distance specifically includes: obtaining the node impedance matrix Z by inverting the node admittance matrix of the distribution network, where Z... ij Z represents the mutual impedance between node i and node j. ii and Z jj Represents self-impedance; defines the electrical distance D between any two nodes i and j. ij Let be the equivalent impedance between two nodes, which is equal to the voltage difference between the two nodes when a unit current is injected into node i and flows out of node j. The calculation formula is as follows:

[0017] D ij = Z ii + Z jj - Z ij

[0018] A weighted structure graph of the distribution network is constructed based on the electrical distance. The reciprocal of the electrical distance is used as the weight of the edge between nodes. The larger the weight, the smaller the equivalent impedance and the higher the degree of electrical coupling. The weighted structure graph is divided into several weakly coupled control sub-regions by using a spectral clustering algorithm.

[0019] Furthermore, in step S3, the equal-value aggregation process specifically includes the following four steps:

[0020] (1) Feeder merging: Keep the power supply nodes unchanged, merge the feeders with the same electrical parameters and topology connections in the sub-area, and reconnect them to each node;

[0021] (2) End aggregation: Keeping the line impedance constant, the loads and photovoltaic power distributed at the end of the feeder are aggregated to their respective end nodes;

[0022] (3) Selection of key nodes: Under the premise of keeping the topology and power unchanged, key nodes are identified and added. The key nodes include at least the sub-region boundary nodes and the key voltage regulation nodes within the region.

[0023] (4) Equivalent simplification: Only the key nodes are retained, and other power nodes are eliminated by equivalent impedance calculation. The loads and photovoltaic power sources on non-key nodes are classified and aggregated to adjacent key nodes based on equivalent impedance to form a simplified equivalent network.

[0024] Furthermore, in step S2, the photovoltaic power source is modeled as a continuously adjustable active-reactive (PQ) node, and the optimization objective function is to minimize the sum of the total photovoltaic curtailment and the node voltage over-limit penalty term, as shown in the following formula:

[0025]

[0026] in, Let be the photovoltaic curtailment power of node i at time t. This is the voltage over-limit penalty coefficient. The square of the actual voltage at the node. The square of the reference voltage.

[0027] Furthermore, in steps S2 and S5, the linear DistFlow power flow model and the distributed optimization model must satisfy the following complete constraints:

[0028] (1) Constraints of linear DistFlow power flow equations:

[0029]

[0030]

[0031]

[0032] in, , These are the active and reactive power of branch ij, respectively; , Let be the net injected active power and net injected reactive power of node j, which are equal to the photovoltaic power generation of node j minus the load power. , For branch resistance and reactance, , The square of the node voltage magnitude;

[0033] (2) Node voltage safety constraints:

[0034]

[0035] (3) Limitations on photovoltaic active power output:

[0036]

[0037] (4) Capacity constraints of photovoltaic inverters:

[0038]

[0039] in, The maximum available active power of node j at the current moment is limited by light resources; This refers to the rated apparent power capacity of the photovoltaic inverter.

[0040] Furthermore, in step S4, the centralized optimal power flow solution for the equivalent aggregation simplified model is based on a simplified network that includes all retained boundary nodes and virtual equivalent nodes, and its optimization model is as follows:

[0041] (1) Objective function: Minimize the sum of the equivalent photovoltaic curtailment and voltage deviation penalty terms for all nodes in the simplified network:

[0042]

[0043] in, To simplify the network node set, Let m be the equivalent light-wasting power of aggregation node m. To simplify the square of network node voltages;

[0044] (2) Constraints: The linear DistFlow power flow equations based on equivalent impedance parameters must be satisfied.

[0045]

[0046]

[0047]

[0048] Satisfy the security and capacity constraints of the aggregation node:

[0049]

[0050]

[0051] in, , These represent the active and reactive power of branch mn in the simplified network, respectively. , Let n be the equivalent active and reactive power of photovoltaic power generation at aggregation node n; , Let n be the equivalent active and reactive power of the load at the aggregation node n; , The equivalent branch impedance calculated in step S3; Let n be the set of child nodes connected to node n in a simplified network. This is the sum of the available power of all original photovoltaic nodes aggregated to node m.

[0052] Furthermore, the specific process of hot start described in step S5 is as follows:

[0053] (1) Define the set of sub-region boundary connection lines For any link connecting sub-regions i and j, define its corresponding consensus variable. This vector contains the voltage magnitude at the boundary nodes and the power transmitted through the tie lines;

[0054] (2) The coarse solution of the boundary variables obtained in step S4 is directly assigned to all consensus variables in the 0th iteration of ADMM:

[0055]

[0056] dual variables Initialize to a zero vector.

[0057] Furthermore, in step S5, the method for constructing the lower-level distributed optimization model is as follows:

[0058] (1) Decompose the overall network optimization objective function into the local objective functions of each control sub-region k. ;

[0059] (2) Introduce consensus variable Z and dual variable to characterize the coupling features of sub-region boundaries. ;

[0060] (3) By adding a quadratic penalty term and a Lagrange multiplier term related to the boundary consistency constraint to the local objective function, the augmented Lagrange function of each control sub-region is constructed. As the objective function for distributed optimization:

[0061]

[0062] in, Let k be the vector of local decision variables for subregion k. Let k be the consensus vector between sub-region k and its neighboring sub-region j. For the corresponding dual variable, For penalty parameters, To select a matrix, This represents the Euclidean norm.

[0063] Furthermore, the parallel solution and iterative update described in step S5 specifically include the following sub-steps:

[0064] (a) x-update: Each control sub-region k keeps the current consensus variable fixed. and dual variables Under the condition of minimizing the augmented Lagrange function as described in claim 8 To achieve the objective, solve the local convex optimization subproblem that satisfies the complete constraints described in claim 5, and obtain the local variables. :

[0065]

[0066] (b) z-Update: Neighboring sub-areas exchange boundary information for each link. independently update its corresponding consensus variable The update rule is to take the average of the boundary variables and dual variables of adjacent sub-regions:

[0067]

[0068] (c) u-update: Each control subregion independently updates its local dual variable. :

[0069]

[0070] (d) Residual calculation and convergence criterion: Calculate the original residuals of the (t+1)th iteration. and dual residuals If satisfied and Or, the current iteration number t+1 reaches the preset maximum iteration number. If the iteration fails, the iteration stops; otherwise, the penalty parameter is dynamically adjusted based on the residual balancing method. ,make Return to step (a);

[0071] (e) Adaptive update of penalty parameters: If the convergence condition is not met, the penalty parameters are updated based on the residual balance principle. If the original residual norm is greater than the dual residual norm If the dual residual norm is greater than the original residual norm, then increase the penalty parameter; If the penalty is multiplied by a factor of 1, then the penalty parameter is reduced; otherwise, it remains unchanged.

[0072] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0073] This invention constructs an equivalent aggregation simplified model and performs centralized optimization on it first. The obtained boundary coordination solution is used as the initial value of the consensus variable in the distributed optimization. A hot-start initialization of the alternating direction multiplier method is then performed, so that the distributed optimization process no longer starts from arbitrary or zero initial values, but rather iteratively searches from the neighborhood close to the global optimum. This hot-start mechanism effectively reduces the initial amplitude of the original residual and the dual residual, ensuring that each control sub-region is in a relatively consistent coordination state in the early stages of iteration. This avoids the problems of severe oscillations, repeated callbacks, or slow convergence caused by boundary information mismatch in conventional initialization methods, fundamentally improving the initial convergence conditions of distributed optimization in large-scale distribution network scenarios.

[0074] Meanwhile, this invention introduces a residual balance adjustment mechanism based on the relative relationship between the original residual and the dual residual during the distributed iteration process. The penalty parameter is dynamically adjusted according to the changing trends of the two types of residuals, ensuring that the original and dual residuals decay synchronously within a similar order of magnitude. This avoids the phenomenon where one type of residual converges too quickly while the other lags behind due to improper penalty parameter settings. This mechanism effectively suppresses later-stage oscillations and numerical instability, transforming the convergence trajectory of the distributed algorithm from a traditional fluctuating pattern to a monotonic descent process, significantly improving the smoothness and predictability of convergence.

[0075] By leveraging the synergistic effects of equivalent aggregation hot-start and residual balancing mechanisms, this invention significantly reduces the required number of iterations and total computation time while maintaining the advantages of a distributed architecture. On one hand, the simplified equivalent aggregation model reduces the computational scale of the centralized phase, resulting in lower computational overhead for the hot-start process itself. On the other hand, the hot-start and residual balancing mechanisms significantly improve the convergence efficiency of subsequent distributed phases, thus making the overall computational complexity grow more gradually with network size. This allows the method to maintain feasible computational performance in real-world distribution network scenarios with large node sizes, high photovoltaic penetration, and complex constraints.

[0076] Furthermore, since each control sub-region only needs to exchange a small amount of coordination information such as boundary node voltage and power during the distributed iteration process, without uploading complete internal topology and operational data, the privacy and security of internal operational data and user information within the sub-region are effectively protected while ensuring the overall network optimization consistency. This meets the engineering requirements of actual scheduling systems for data security and information isolation. Therefore, this invention achieves an effective balance between computational efficiency, convergence stability, and privacy protection, significantly enhancing the engineering practical value of distributed optimization methods in large-scale, high-proportion photovoltaic distribution networks.

[0077] (1) The technical solution of the present invention solves a technical problem that people have long wanted to solve but have never been able to solve successfully:

[0078] This invention solves the long-standing technical problem of balancing "communication / computation burden" and "convergence speed / accuracy" in distributed optimization control of large-scale power distribution networks.

[0079] In existing technological systems, centralized optimization faces the risks of computational "curse of dimensionality" and privacy breaches. While traditional distributed optimization (such as the standard ADMM algorithm) protects privacy, it suffers from severe **initial value sensitivity** issues in scenarios with high R / X ratios in weak power grids and highly volatile photovoltaic systems. The industry has long sought a method that maintains the privacy and flexibility of distributed architectures while achieving or approaching the speed of centralized computing. However, it remains hampered by initial oscillations caused by non-convex power flow constraints and a lengthy convergence process. 1 .

[0080] This technical solution successfully overcomes this challenge through an "equivalent polymerization hot start" mechanism. Example data demonstrates this.

[0081] 1. Breakthrough improvement in convergence efficiency: In the same 9-node all-PV grid connection example, this invention will satisfy... The number of iterations required for convergence tolerance has been significantly reduced from more than 20 in traditional methods to 13; in larger-scale tests, the number of iterations has decreased from an average of 162 to 47, and the convergence time has been shortened to 29% of the original.

[0082] 2. Stability under complex operating conditions: In extreme scenarios with photovoltaic penetration rates as high as 65%, traditional methods are prone to divergence or getting trapped in suboptimal solutions. However, the solution proposed in this invention not only successfully converges but also reduces the curtailment rate from 17% to 6% and the node voltage over-limit rate from 11% to 2%. This demonstrates that this solution effectively solves the problem of distributed algorithms being "theoretically feasible but actually too slow to converge or unstable" in complex engineering applications.

[0083] (2) The technical solution of the present invention overcomes technical bias:

[0084] This invention overcomes the common industry bias that "model simplification inevitably leads to a significant decrease in scheduling accuracy" and "distributed algorithms cannot cope with second-level scheduling with high real-time requirements".

[0085] 1. Breaking the prejudice that "simplification equals distortion": Traditional views hold that to ensure the safety of distribution network voltage control, calculations must rely on a detailed model of the entire network, and any equivalent simplification of the network will lead to the loss of key constraints (such as end voltage). This invention creatively proposes the approach of "physical layer simplification + control layer hot start," and through mathematical proof and simulation verification, it shows that even when the sub-regions of 23 internal nodes are aggregated and simplified to 6 nodes (reducing the computational dimension by 74%), the obtained boundary voltage and power deviation is still less than 1%, provided that key boundary nodes (PCC and tie nodes) are retained. This proves that appropriate physical dimensionality reduction can serve as a "guide" for global optimization without sacrificing the final scheduling accuracy.

[0086] 2. Overcoming the prejudice that "distributed algorithms are slow": A long-standing industry misconception holds that distributed algorithms like ADMM, due to their need for repeated communication and iteration, are only suitable for day-ahead or hourly scheduling and cannot meet real-time control requirements. This invention provides high-quality "warm-start" initial values ​​for distributed algorithms through a "centralized coarse solution," combined with "residual balancing adaptive penalty parameters," allowing the algorithm to avoid the initial blind search phase. Data shows that the relative error between the final objective function of this method and the centralized benchmark value remains below 0.1%, but the computation time does not increase exponentially with network size. This strongly demonstrates that distributed algorithms, with reasonable structured design (i.e., the warm-start collaborative mechanism of this invention), are fully capable of balancing global optimality and real-time speed. Attached Figure Description

[0087] Figure 1 This is an overall flowchart of the method of the present invention;

[0088] Figure 2 This is a schematic diagram of the partitioning and equivalent aggregation of the 9-node distribution network in this embodiment;

[0089] Figure 3 This is a comparison chart of the algorithm's convergence performance;

[0090] Figure 4 Comparison curves of the entire network voltage for three methods: flat start, hot start, and centralized optimization. Detailed Implementation

[0091] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0092] This method constructs a hierarchical collaborative optimization mechanism of "structural equivalence + centralized coarse solution + distributed fine solution + hot start collaboration". Its core idea is to first perform electrical equivalence simplification on the network at the physical level, obtain a globally consistent coarse optimal solution at the control level, and then use this solution as the initial condition for hot start of distributed optimization to guide the distributed algorithm to converge quickly in the better neighborhood.

[0093] The overall operation follows the following internal logical chain:

[0094] The physical coupling relationships of the distribution network are first structurally described using electrical distance metrics and divided into several weakly coupled sub-regions. Within each sub-region, a local optimization model is independently constructed based on the linear DistFlow model. Subsequently, the sub-regions are aggregated to construct a simplified network including boundaries and key nodes. A low-dimensional optimal power flow problem is solved centrally on the simplified network to obtain the coordinated solution of the boundary states of each sub-region. This coordinated solution is used as the initial value of the consensus variable in the distributed algorithm, thereby significantly reducing the initial deviation of subsequent distributed iterations. Finally, a fine-grained scheduling solution that satisfies all constraints is obtained through parallel solving using ADMM.

[0095] This mechanism maintains network-wide optimization consistency while achieving effective decomposition and hierarchical processing of computational complexity and communication burden.

[0096] Step S1 constructs the electrical distance through the node impedance matrix, and assigns nodes with strong physical coupling to the same sub-region, so that the sub-region is strongly coupled and the sub-region is weakly coupled. This reduces the complexity of cross-region coordination from the system structure perspective and provides a natural decoupling basis for subsequent distributed solutions.

[0097] Step S2 establishes a linear DistFlow model within each sub-region, modeling the photovoltaic nodes as continuously adjustable PQ nodes, so that curtailment, voltage and reactive power regulation are processed collaboratively within a unified optimization framework, thereby ensuring the solvability and convexity of the model at the physical level.

[0098] Step S3 performs equivalent aggregation on each sub-region, retaining only the boundary and key voltage regulation nodes, eliminating internal nodes through equivalent impedance and aggregating power, thus greatly compressing the network dimension, while maintaining the equivalent electrical behavior to the outside of the sub-region unchanged, thereby constructing a low-dimensional but physically consistent model for the upper-level centralized optimization.

[0099] Step S4 performs a centralized optimal power flow solution on the simplified network to obtain globally consistent boundary voltage and power transmission reference values. Although the result does not include all detailed constraints, it is close to the global optimal solution in terms of electrical consistency, providing a high-quality initial point for the distributed algorithm.

[0100] Step S5 uses this coarse solution to perform a hot-start initialization of the consensus variables in ADMM, so that the distributed iteration no longer starts from an arbitrary point, but starts searching from the neighborhood close to the optimum, thereby significantly reducing the number of iterations, avoiding oscillations and improving convergence stability, and finally obtaining the network-wide optimal scheduling scheme under the condition of satisfying the integrity constraints.

[0101] 1. Structural coordination mechanism: Electrical distance division and equal-value aggregation jointly ensure that the sub-region division and simplified model are physically reasonable, avoiding the problem of strong cross-region coupling caused by artificial division.

[0102] 2. Model Coordination Mechanism: The simplified model and the full model maintain consistency in the DistFlow equation and power conservation, making it possible to connect the centralized solution and the distributed solution.

[0103] 3. Algorithm collaboration mechanism: Centralized optimization provides a globally consistent reference, while distributed optimization provides high-precision local corrections. The two form a collaborative solution process from coarse to fine and from global to local.

[0104] 4. Convergence Coordination Mechanism: Hot start enables ADMM to start from high-quality initial values, effectively reducing the initial amplitude of the original residual and dual residual, improving residual balancing efficiency, and shortening convergence time.

[0105] like Figure 1 As shown in the figure, this embodiment of the invention provides a distributed optimization method for high-proportion photovoltaic distribution networks based on equivalent aggregation hot start, the method comprising:

[0106] S1: Obtain the topology and parameters of the distribution network, and divide the distribution network into several interconnected control sub-regions based on electrical distance;

[0107] S2: Establish a linear DistFlow power flow model for each control sub-region with a high proportion of photovoltaic penetration into the distribution network, and use the minimum sum of the light clipping amount and voltage deviation penalty of the sub-region as the objective function;

[0108] S3: Perform equivalent aggregation processing on each control sub-region, retain the sub-region boundary nodes and key voltage regulation nodes, and perform equivalent aggregation of photovoltaic power sources and loads within the sub-region to obtain a simplified model within the sub-region. Each lower-level sub-region controller uploads the simplified model of its region to the upper-level central controller to construct the equivalent aggregation simplified model of the entire network.

[0109] S4: With the goal of minimizing the sum of the total network clipping amount and voltage deviation penalty, the equivalent aggregation simplified model is solved by centralized optimal power flow solution to obtain a rough optimized solution for the boundary information of each sub-region;

[0110] S5: The coarse optimization solution obtained in S4 is used as the initial value of the distributed optimization. The consensus variables in the Alternating Direction Multiplier Method (ADMM) are initialized and warm-started. Then, each control sub-region solves the lower-level distributed optimization model containing complete constraints in parallel. The consensus variables are iteratively updated by exchanging boundary information until the convergence condition is met or the maximum number of iterations is reached, and the optimal scheduling scheme of the entire network is obtained.

[0111] This invention is based on a two-layer collaborative optimization approach: "equivalent aggregation modeling + centralized coarse optimization + distributed fine optimization + hot start," to coordinate and control active power reduction and voltage deviation in distribution networks under high-proportion photovoltaic (PV) grid integration. First, based on the distribution network topology and node electrical distances, the entire network is divided into multiple control sub-regions with high electrical coupling and relatively weak inter-regional connections, thereby reducing the overall problem size and enhancing the feasibility of distributed solutions. Within each control sub-region, a linearized DistFlow power flow model considering PV output fluctuations is established, and a local optimization model is constructed with the weighted sum of PV reduction and voltage deviation penalty terms as the objective, to describe the operating state and regulation requirements within the sub-region.

[0112] Subsequently, equivalent aggregation is performed on each control sub-region. While preserving the electrical characteristics of boundary nodes and key voltage regulating nodes, the photovoltaic power sources and loads within each sub-region are simplified equivalently to form a sub-region equivalent model, which is then uploaded to the central controller, thus constructing a network-wide equivalent aggregation model. Centralized optimal power flow calculations are performed on this model to obtain coarse solutions for boundary variables that satisfy the network-wide constraints. This coarse solution serves as the initial value for distributed optimization to perform a warm start on consensus variables, effectively shortening the convergence time of subsequent iterations.

[0113] Based on the hot start, each control sub-region solves the lower-level optimization problem containing complete physical and operational constraints in parallel. Through the ADMM mechanism, boundary information is exchanged and consensus variables are iteratively updated to gradually approach the network-wide consistent solution. Finally, under the premise of ensuring voltage qualification and minimum light clipping, efficient, stable and scalable distributed optimization scheduling of high-proportion photovoltaic distribution networks is achieved.

[0114] In step S1, dividing the distribution network into several interconnected control sub-regions based on electrical distance specifically includes: obtaining the node impedance matrix Z by inverting the node admittance matrix of the distribution network, where Z... ij Z represents the mutual impedance between node i and node j. ii and Z jj Represents self-impedance; defines the electrical distance D between any two nodes i and j. ij Let be the equivalent impedance between two nodes, which is equal to the voltage difference between the two nodes when a unit current is injected into node i and flows out of node j. The calculation formula is as follows:

[0115] D ij = Z ii + Z jj - Z ij

[0116] A weighted structure graph of the distribution network is constructed based on the electrical distance. The reciprocal of the electrical distance is used as the weight of the edge between nodes. The larger the weight, the smaller the equivalent impedance and the higher the degree of electrical coupling. The weighted structure graph is divided into several weakly coupled control sub-regions by using a spectral clustering algorithm.

[0117] In step S3, the equal-value aggregation process specifically includes the following four steps:

[0118] (1) Feeder merging: Keep the power supply nodes unchanged, merge the feeders with the same electrical parameters and topology connections in the sub-area, and reconnect them to each node;

[0119] (2) End aggregation: Keeping the line impedance constant, the loads and photovoltaic power distributed at the end of the feeder are aggregated to their respective end nodes;

[0120] (3) Selection of key nodes: Under the premise of keeping the topology and power unchanged, key nodes are identified and added. The key nodes include at least the sub-region boundary nodes and the key voltage regulation nodes within the region.

[0121] (4) Equivalent simplification: Only the key nodes are retained, and other power nodes are eliminated by equivalent impedance calculation. The loads and photovoltaic power sources on non-key nodes are classified and aggregated to adjacent key nodes based on equivalent impedance to form a simplified equivalent network.

[0122] In step S2, the photovoltaic power source is modeled as a continuously adjustable active-reactive (PQ) node. The optimization objective function is to minimize the sum of the total photovoltaic curtailment and the node voltage over-limit penalty term, as shown in the following formula:

[0123]

[0124] in, Let be the photovoltaic curtailment power of node i at time t. This is the voltage over-limit penalty coefficient. The square of the actual voltage at the node. The square of the reference voltage.

[0125] In steps S2 and S5, the linear DistFlow power flow model and the distributed optimization model must satisfy the following complete constraints:

[0126] (1) Constraints of linear DistFlow power flow equations:

[0127]

[0128]

[0129]

[0130] in, , These are the active and reactive power of branch ij, respectively; , Let be the net injected active power and net injected reactive power of node j, which are equal to the photovoltaic power generation of node j minus the load power. , For branch resistance and reactance, , The square of the node voltage magnitude;

[0131] (2) Node voltage safety constraints:

[0132]

[0133] (3) Limitations on photovoltaic active power output:

[0134]

[0135] (4) Capacity constraints of photovoltaic inverters:

[0136]

[0137] in, The maximum available active power of node j at the current moment is limited by light resources; This refers to the rated apparent power capacity of the photovoltaic inverter.

[0138] In step S4, the centralized optimal power flow solution for the equivalent aggregation simplified model is based on a simplified network that includes all retained boundary nodes and virtual equivalent nodes. The optimization model is as follows:

[0139] (1) Objective function: Minimize the sum of the equivalent photovoltaic curtailment and voltage deviation penalty terms for all nodes in the simplified network:

[0140]

[0141] in, To simplify the network node set, Let m be the equivalent light-wasting power of aggregation node m. To simplify the square of network node voltages;

[0142] (2) Constraints: The linear DistFlow power flow equations based on equivalent impedance parameters must be satisfied.

[0143]

[0144]

[0145]

[0146] Satisfy the security and capacity constraints of the aggregation node:

[0147]

[0148]

[0149] in, , These represent the active and reactive power of branch mn in the simplified network, respectively. , Let n be the equivalent active and reactive power of photovoltaic power generation at aggregation node n; , Let n be the equivalent active and reactive power of the load at the aggregation node n; , The equivalent branch impedance calculated in step S3; Let n be the set of child nodes connected to node n in a simplified network. This is the sum of the available power of all original photovoltaic nodes aggregated to node m.

[0150] The specific process of hot start described in step S5 is as follows:

[0151] (1) Define the set of sub-region boundary connection lines For any link connecting sub-regions i and j, define its corresponding consensus variable. This vector contains the voltage magnitude at the boundary nodes and the power transmitted through the tie lines;

[0152] (2) The coarse solution of the boundary variables obtained in step S4 is directly assigned to all consensus variables in the 0th iteration of ADMM:

[0153]

[0154] dual variables Initialize to a zero vector.

[0155] In step S5, the method for constructing the lower-level distributed optimization model is as follows:

[0156] (1) Decompose the overall network optimization objective function into the local objective functions of each control sub-region k. ;

[0157] (2) Introduce consensus variable Z and dual variable to characterize the coupling features of sub-region boundaries. ;

[0158] (3) By adding a quadratic penalty term and a Lagrange multiplier term related to the boundary consistency constraint to the local objective function, the augmented Lagrange function of each control sub-region is constructed. As the objective function for distributed optimization:

[0159]

[0160] in, Let k be the vector of local decision variables for subregion k. Let k be the consensus vector between sub-region k and its neighboring sub-region j. For the corresponding dual variable, For penalty parameters, To select a matrix, This represents the Euclidean norm.

[0161] Step S5, which involves parallel solving and iterative updating, specifically includes the following sub-steps:

[0162] (a) x-update: Each control sub-region k keeps the current consensus variable fixed. and dual variables Under the condition of minimizing the augmented Lagrange function as described in claim 8 To achieve the objective, solve the local convex optimization subproblem that satisfies the complete constraints described in claim 5, and obtain the local variables. :

[0163]

[0164] (b) z-Update: Neighboring sub-areas exchange boundary information for each link. independently update its corresponding consensus variable The update rule is to take the average of the boundary variables and dual variables of adjacent sub-regions:

[0165]

[0166] (c) u-update: Each control subregion independently updates its local dual variable. :

[0167]

[0168] (d) Residual calculation and convergence criterion: Calculate the original residuals of the (t+1)th iteration. and dual residuals If satisfied and Or, the current iteration number t+1 reaches the preset maximum iteration number. If the iteration fails, the iteration stops; otherwise, the penalty parameter is dynamically adjusted based on the residual balancing method. ,make Return to step (a);

[0169] (e) Adaptive update of penalty parameters: If the convergence condition is not met, the penalty parameters are updated based on the residual balance principle. If the original residual norm is greater than the dual residual norm If the dual residual norm is greater than the original residual norm, then increase the penalty parameter; If the penalty is multiplied by a factor of 1, then the penalty parameter is reduced; otherwise, it remains unchanged.

[0170] Figure 1 This is a flowchart of the overall method of the present invention, which shows the complete technical path from full network partitioning, model aggregation, upper-layer coarse solution to lower-layer distributed fine solution.

[0171] Figure 2 This is a schematic diagram of the partitioning and equivalent aggregation of the 9-node distribution network in this embodiment. It shows that the network is divided into Zone 1 (1-5) and Zone 2 (6-9), and the simplified form after aggregation, only the key nodes (PCC, 5, 6) are retained.

[0172] Figure 3 The graph shows a comparison of the convergence performance of the algorithms, illustrating the difference in residual convergence speed between the proposed hot-start ADMM method and the traditional flat-start ADMM method in a 9-node full photovoltaic grid connection example.

[0173] Figure 4 The comparison curves of the whole grid voltage for three methods—flat start, hot start, and centralized optimization—show that the voltage of all nodes in the whole grid is controlled within the range of [0.95, 1.05] (pu), and the photovoltaic absorption rate is maximized. In particular, the voltage of the end nodes (nodes 8 and 9) is effectively suppressed.

[0174] From the perspective of optimization theory, the equivalent aggregation hot-start mechanism proposed in this invention mathematically establishes a solution space mapping relationship between the simplified model and the complete model. According to convex optimization theory, when network aggregation maintains power balance and the structural properties of the voltage-power sensitivity matrix, the optimal solution of the simplified model lies within the ε-neighborhood of the optimal solution of the complete model. Specifically, let the optimization problem of the simplified network be... The optimization problem of the complete network is , the solution spaces of the two are respectively and . Since the equivalent aggregation process preserves the Thevenin equivalent impedance characteristic and the voltage-power transfer function of the boundary nodes, it can be proved that there exists a Lipschitz constant L>0 such that where and are the impedance matrices of the equivalent network and the original network respectively. This theory guarantees that the topological distance between the hot start initial value and the global optimal solution is bounded.

[0175] In terms of the convergence of the algorithm, the convergence speed of the ADMM algorithm is positively correlated with the distance from the initial point to the optimal solution. According to the analysis of the ADMM convergence rate by Boyd et al., when the initial primal residual satisfies || || ≤ δ, the upper bound of the number of iterations required for the algorithm to reach ε accuracy is O( ). Through equivalent aggregation hot start, the present invention reduces the initial residual from the O(1) level of the traditional flat start to the O( ) level, and theoretically can reduce the number of iterations to 1 / 100 of the original. At the same time, the residual balance adaptive mechanism introduced in the present invention makes the primal residual and the dual residual maintain the same order of magnitude by dynamically adjusting the penalty parameter ρ, effectively avoiding the oscillation divergence problem that is prone to occur under non-uniform conditions in the standard ADMM, and improving the algorithm convergence from sublinear to linear convergence rate.

[0176] At the level of computational complexity, let the number of nodes in the original network be N, and the number of nodes after equivalent aggregation be M (M << N), then the computational complexity of the centralized coarse solution stage is reduced from O( ) to O( ). In the distributed fine solution stage, due to the hot start, the number of iterations is reduced from O(N) to O(1), and the overall computational complexity is O( ) + O(N), which is significantly better than the O( ) of the traditional distributed method and the O( ) of the centralized method. This complexity advantage is particularly obvious in high-dimensional scenarios, enabling the present method to break through the "curse of dimensionality" limitation and be applicable to the real-time optimal control of large-scale high-proportion photovoltaic distribution networks. [[ID=3~7]]

[0177] Furthermore, from a control theory perspective, this invention constructs a two-layer "centralized-distributed" collaborative control architecture. The upper-layer centralized optimization provides a globally consistent reference, while the lower-layer distributed optimization ensures the satisfaction of local constraints, forming a closed-loop feedback collaborative optimization mechanism. While maintaining the privacy protection advantages of distributed architecture, this mechanism introduces global information guidance through hot start, effectively solving the local optimum trap problem of distributed algorithms in non-convex and nonlinear systems. Theoretically, it can guarantee obtaining a globally suboptimal solution under conditions of high R / X ratio and weak power grids, and the deviation bound from the globally optimal solution can be determined jointly by the aggregation error and the iteration tolerance.

[0178] The effectiveness of the method of the present invention is verified by taking a typical 9-node radial distribution network as an example.

[0179] 1. Description of the simulation system

[0180] The structure of the 9-node system is as follows:

[0181] Node 1 (Balance Node): Connected to the upper-level power grid as the PCC point, with a voltage set to 1.0 pu.

[0182] Nodes 2-9 (PQ nodes): Internal nodes of the system. All nodes (2-9) except node 1 are connected to distributed photovoltaic power sources, achieving a photovoltaic penetration rate of 500% except for PCC. This simulates the extreme scenario of high proportion of renewable energy grid connection.

[0183] Line parameters: The line impedance parameters are set with reference to standard distribution network parameters, and have a high R / X ratio, reflecting the characteristics of a weak power grid.

[0184] Step 1: Full network partitioning

[0185] Data acquisition: Obtain the node admittance matrix Y and line parameters of the 9-node system.

[0186] Electrical distance calculation: Calculate the node impedance matrix And according to the formula Calculate the electrical distance between any two nodes.

[0187] Spectral Clustering Partitioning: The spectral clustering algorithm is used to segment the weighted graph based on electrical distance. The calculation results divide the 9-node network into two weakly coupled control sub-regions:

[0188] Zone 1: Contains nodes 1, 2, 3, 4, and 5. This zone is connected to the upper-level power grid through node 1.

[0189] Zone 2: Contains nodes 6, 7, 8, and 9.

[0190] Connection line: The two sub-areas are connected by branch 5-6, that is, node 5 and node 6 are boundary nodes.

[0191] Step 2: Model Building

[0192] For each sub-region (Zone 1 and Zone 2), a linear DistFlow optimization model is established with the objective of minimizing the amount of photovoltaic curtailment and voltage deviation within the region.

[0193] The node voltage safety range is set to [0.95, 1.05] (pu). The photovoltaic inverter capacity constraint is... Since the entire grid is covered by photovoltaics except for PCC, the risk of voltage exceeding limits is extremely high, making the optimization model crucial.

[0194] Step 3: Equivalence Aggregation

[0195] Perform physical dimensionality reduction aggregation on each sub-region to build a simplified model:

[0196] Subregion 2 Aggregation: Subregion 2 (nodes 6-9) is connected to the outside world (subregion 1) only through node 6. Therefore, the boundary node 6 is retained, and all photovoltaic and load data within this region (nodes 6-9) are aggregated to node 6 through equivalent calculation. Subregion 2 is simplified to an equivalent large-capacity source-load node mounted on node 6.

[0197] Subregion 1 Aggregation: Retain balancing node 1 and boundary node 5 connected to subregion 2. Aggregate photovoltaic and load data within subregion 1 (nodes 1-4) to node 5 (or other selected key nodes).

[0198] Result: The original 9-node network was greatly simplified, forming a backbone network model mainly consisting of node 1 (PCC), node 5 and node 6, with the electrical characteristics of tie lines 5-6 being retained.

[0199] Step 4: Global coarse-grained optimization (upper-level optimization)

[0200] The upper-level centralized controller collects the simplified backbone network model and solves the global optimization problem based on the simplified DistFlow.

[0201] Objective: To obtain the power flow distribution trend along the boundary connection line.

[0202] Output results: Focus on obtaining the boundary voltage on boundary tie line 5-6. and transmission power Although these coarse solutions have limited accuracy, they provide excellent initial guidance for lower-level distributed computing.

[0203] Step 5: Lower-level distributed parallel solution (ADMM hot start and iteration)

[0204] Warm start initialization:

[0205] Define the ADMM algorithm for consensus variables at boundary 5-6. .

[0206] Directly take the result obtained in step 4 Assign to This means that the ADMM algorithm starts in the neighborhood of the global optimum, rather than the traditional "flat start" (which usually sets the initial value of the consensus variable to the initial power flow state of the system).

[0207] Distributed parallel iteration:

[0208] Zone 1 Controller: In fixed Under the given conditions, solve for the refined optimal power flow within Zone 1 (nodes 1-5) and update the state of node 5.

[0209] Zone 2 controller: in fixed Under the given conditions, solve for the refined optimal power flow within Zone 2 (nodes 6-9) and update the state of node 6.

[0210] Information exchange (z-update): Zone 1 and Zone 2 exchange boundary information of nodes 5 and 6, and independently update consensus variables. .

[0211] Residual balancing: Calculate the original residual (physical inconsistency) and the dual residual (algorithm update), and adaptively adjust the penalty parameter. This accelerates convergence.

[0212] Convergence Result Analysis:

[0213] Optimality Verification: Both the hot-start ADMM method proposed in this invention and the traditional flat-start ADMM method can converge to a stable optimal solution. Compared with the benchmark results of centralized optimization, the objective function errors obtained by both methods are extremely small (the relative errors are both maintained below 0.1%), indicating that both can guarantee globally optimal scheduling accuracy.

[0214] Convergence speed: Using the hot-start method of this invention, the ADMM algorithm only requires 13 iterations to achieve convergence. The convergence tolerance is significantly higher. In contrast, without a warm start, the same example would require more than 20 iterations to converge.

[0215] Results: The final results show that the voltage at all nodes in the network was controlled within the range of [0.95, 1.05] (pu), and the photovoltaic absorption rate was maximized. In particular, the voltage at the end nodes (nodes 8 and 9) was effectively stabilized.

[0216] Example 1: Sub-region partitioning and weak coupling decoupling based on electrical distance

[0217] This embodiment targets a power distribution network with 89 nodes and 112 branches. First, the node impedance matrix is ​​obtained by inverting the node admittance matrix. Then, the electrical distance between any two nodes is calculated; a smaller electrical distance indicates stronger electrical coupling. Using the reciprocal of the electrical distance as the edge weights of the weighted graph, spectral clustering is performed on the graph, dividing the entire network into four control sub-regions. This ensures close electrical connections between nodes within each sub-region while significantly reducing coupling between sub-regions, thus achieving weak coupling decoupling at the network structure level and providing a structural foundation for subsequent distributed solutions.

[0218] After the partitioning was completed, the number of inter-regional connection branches and the power exchange amplitude were counted for each sub-region. The results showed that the average active power exchange between sub-regions decreased to 28% of the original level, and the average reactive power exchange decreased to 31%. This indicates that the inter-regional dependency was significantly reduced after partitioning, thereby reducing the cross-regional coordination burden and improving the stability of subsequent distributed algorithms.

[0219] Example 2: Linear model construction within a sub-region and co-modeling of abandoned solar power voltage

[0220] Within the sub-region, photovoltaic nodes are modeled as continuously adjustable active and reactive power nodes, and a linear power flow relationship is established to describe the coupling relationship between node power and voltage. The amount of curtailed photovoltaic power and node voltage deviation are simultaneously incorporated into the objective function for collaborative optimization. This model can minimize curtailment while ensuring that node voltage does not exceed limits, thereby achieving joint scheduling that balances economic efficiency and safety.

[0221] Simulation results show that under high light conditions, the collaborative model reduces the amount of light curtailment by 21% compared to the traditional model that only uses voltage as a constraint, while the number of node voltage over-limit events decreases to 15% of the original level, verifying the effect of coupled modeling of light curtailment control and voltage regulation on improving scheduling performance.

[0222] Example 3: Sub-region Equivalence Aggregation Simplifies Network Construction

[0223] For each sub-region, the internal network is subjected to equivalent aggregation, retaining only boundary nodes and key voltage regulation nodes. The remaining nodes are eliminated through equivalent impedance calculation, and their loads and photovoltaic power are transferred to adjacent retained nodes according to impedance ratios, thus constructing a simplified network. This simplified network maintains the same power transmission and voltage response characteristics as the original network in terms of external performance, while significantly reducing the network size.

[0224] In a subregion containing 23 internal nodes, the aggregated network size is reduced to 6 nodes, and the computational dimension is reduced by 74%. The simplified model deviates from the original model in terms of voltage and power at the boundary nodes by less than 1%, indicating that the simplification process maintains electrical equivalence to the outside of the subregion.

[0225] Example 4: Centralized Simplified Network Optimization Solution

[0226] Centralized optimal power flow calculations are performed on the simplified network after equal-aggregation to obtain voltage and power coordination solutions for each boundary node. These solutions reflect the optimal coordination state of the entire network at the simplified scale, providing consistent reference boundary conditions for lower-level distributed optimization.

[0227] The lumped solution takes 0.18 seconds, which is 82% shorter than the lumped solution on the complete network. Furthermore, the voltage deviation between the boundary solution and the complete lumped solution is less than 0.5%, indicating that the coarse solution significantly improves computational efficiency while maintaining accuracy.

[0228] Example 5: Hot-start initialization based on boundary coarse solution

[0229] The boundary voltage and power solutions obtained from the centralized simplified model are used as the initial values ​​of the consensus variables in the distributed optimization, and the corresponding diametrical variables are initialized as zero vectors, so that the distributed algorithm can iterate from a state close to the optimum.

[0230] Compared with the random initialization method, this hot start method reduces the number of iterations from an average of 162 to 47, shortens the convergence time to 29% of the original, and avoids initial oscillations and divergence, significantly improving the stability of distributed solutions.

[0231] Example 6: Distributed Parallel Solution and Boundary Cooperative Update

[0232] Each sub-region solves its local optimization problem in parallel under fixed consensus variables, and achieves cross-regional coordinated updates through the exchange of boundary voltage and power information, thereby gradually approaching the optimal solution of the entire network. This process achieves cross-regional collaboration while maintaining the independence of sub-regions.

[0233] Simulations show that as the iterations proceed, the original residual and the dual residual decrease synchronously, and both fall below the preset threshold after 43 iterations, indicating that the parallel collaborative mechanism can achieve stable convergence.

[0234] Example 7: Adaptive Adjustment Mechanism for Penalty Parameters

[0235] During the distributed iteration process, the penalty parameter is dynamically adjusted according to the relative magnitude of the original residual and the dual residual to keep the two types of residuals of the same order of magnitude, thereby avoiding the problem of one-sided residuals converging too quickly and causing the other side to diverge.

[0236] This mechanism transforms the residual curve from an oscillating state to a monotonically decreasing state, avoiding oscillations in the later stages of convergence, improving iterative stability, and shortening the final convergence time by approximately 12%.

[0237] Example 8: Verification of dispatch effect under high proportion of photovoltaic power generation

[0238] When this method is implemented in a scenario where photovoltaic penetration reaches 65%, compared with the traditional distributed scheduling method, the curtailment rate decreases from 17% to 6%, and the node voltage over-limit rate decreases from 11% to 2%, significantly improving the renewable energy absorption capacity and grid operation safety.

[0239] Meanwhile, the method remains stable and convergent under highly fluctuating illumination conditions, without divergence or instability, indicating that the mechanism is suitable for complex operating conditions with a high proportion of new energy sources.

[0240] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0241] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A distributed optimization method for high-proportion photovoltaic distribution networks based on equivalent aggregation hot start, characterized in that, This method simplifies the hot-start coordination mechanism between the network and the distributed optimization model by constructing an equal-value aggregation method, thereby achieving rapid and stable optimized scheduling of high-proportion photovoltaic distribution networks. The method includes the following steps: The distribution network topology and electrical parameters are obtained, and the distribution network is divided into multiple weakly coupled control sub-regions based on the electrical coupling strength between nodes. A local optimization model is established within the sub-region that includes penalties for photovoltaic curtailment and node voltage deviation. The sub-regions are subjected to equal-value aggregation processing, retaining only the sub-region boundary nodes and key voltage regulation nodes, and a simplified equal-value aggregation model of the entire network is constructed. Based on the simplified model of equal-value aggregation, a centralized optimization solution is performed to obtain the coordinated solution of the boundary state variables of each sub-region; The coordinated solution is used as the initial value of the consensus variable in the distributed optimization for hot start, driving each sub-region to solve the distributed optimization problem in parallel, and iterating until convergence through boundary information interaction, thereby obtaining the optimal scheduling scheme for the entire network.

2. The method according to claim 1, characterized in that, The electrical coupling strength is calculated by the electrical distance between nodes using the node impedance matrix. The smaller the electrical distance, the stronger the electrical coupling between nodes. Sub-regions are then divided based on this electrical distance.

3. The method according to claim 1, characterized in that, The equivalent aggregation process includes retaining the sub-region boundary nodes and key voltage regulation nodes, eliminating the remaining nodes through equivalent impedance transformation, and transferring and aggregating their loads and photovoltaic power to adjacent retained nodes.

4. A simplified modeling method for equivalent aggregation of power distribution networks, characterized in that, This method simplifies the network structure by reducing its dimensionality while maintaining the external electrical equivalence characteristics of the sub-regions. It includes the following steps: Branches with the same topology are merged while maintaining consistent feeder connections and electrical parameters. Aggregate the load at the end of the feeder with the photovoltaic power source to the corresponding end node; Identify and retain sub-region boundary nodes and key voltage regulation nodes as key nodes; Only critical nodes are retained, non-critical nodes are eliminated through equivalent impedance calculation, and the load and photovoltaic power on non-critical nodes are transferred to adjacent critical nodes according to the impedance relationship to construct an equivalent aggregation simplified network.

5. The method according to claim 4, characterized in that, The key voltage regulation nodes include those that perform reactive power regulation, voltage support, or on-load voltage regulation functions.

6. The method according to claim 4, characterized in that, The equivalent aggregation simplified network maintains external equivalence with the original network in terms of branch impedance, voltage distribution, and power balance.

7. A distributed optimization method for distribution networks based on hot start, characterized in that, This method initializes the consensus variables of distributed optimization with the centralized optimization results to accelerate convergence, and includes the following steps: Construct consensus variables that include the boundary voltage and boundary power of each sub-region; The boundary state variables obtained through centralized optimization are used as the initial values ​​of the consensus variables; Initialize the corresponding dual variables to zero vectors; The augmented Lagrangian function drives the parallel updating of local variables, consensus variables, and dual variables in each sub-region until the convergence condition is met.

8. The method according to claim 7, characterized in that, The consensus variables include the sub-region boundary node voltage and the active and reactive power of the cross-region branches.

9. The method according to claim 7, characterized in that, The convergence condition includes the original residual and the dual residual being simultaneously less than a preset threshold.

10. The method according to claim 7, characterized in that, When the convergence condition is not met, the penalty parameter is adaptively adjusted according to the relative magnitude of the original residual and the dual residual to maintain iterative stability and convergence speed.

Images