A system voltage optimization method and system for large-scale power collection lines of a wind farm

Abstract

The application discloses a kind of system voltage optimization method and system for wind farm scale collection line.It obtains wind farm operating state information;With grid-connected point PCC bus as boundary, wind farm is divided into grid-connected side system and several collection side systems, and main, sub-agent controller is respectively configured;Based on the difference of internal and external physical environment, each system is modeled respectively using differentiated power flow constraints, and a global optimal power flow model is constructed;Through main, sub-agent controller, the global optimal voltage control instruction is obtained by using the generalized Benders decomposition method with embedded asynchronous iteration mechanism to decouple and iteratively solve the model, and the corresponding regulation and control are executed respectively.The application takes into account the global calculation accuracy and solving efficiency, significantly reduces the communication pressure, and effectively overcomes the adverse effects of communication delay.

Description

Technical Field

[0001] This invention belongs to the field of power system automation control technology, specifically relating to a system voltage coordination optimization control method and system for large-scale power collection lines in wind farms. Background Technology

[0002] With the successive construction and commissioning of large-capacity, large-scale wind farms, the problem of system voltage fluctuations caused by power output fluctuations in wind farms has become particularly prominent. A large wind farm can be viewed as a large-scale power system with a large-scale topology, where multiple wind turbines are connected via medium-voltage collector lines and converge at the point of grid connection (PCC) bus. When large amounts of wind power are transmitted, a significant voltage drop occurs on the collector lines. Even if the PCC bus voltage is controlled within a reasonable safety range, the ends of the collector lines far from the substation are still highly susceptible to severe voltage deviations or even exceeding limits, potentially triggering large-scale cascading grid disconnection accidents.

[0003] To improve operational economy while ensuring voltage safety, existing technologies typically construct the system voltage control problem as an optimal power flow (OPF) mathematical model for centralized solution. Centralized control requires wind farms to be equipped with a central controller to uniformly schedule controllable equipment within the site. However, with the expansion of wind farm scale, the communication and computing pressure faced by the central controller increases significantly.

[0004] To alleviate communication pressure, existing technologies have introduced distributed voltage control methods (such as the alternating direction multiplier method based on augmented Lagrangian relaxation or the target cascade analysis method), which use distributed agent controllers to update and iterate local information. However, in practical engineering applications, existing distributed voltage control schemes have revealed the following prominent limitations: First, it is difficult to balance the accuracy and efficiency of the solution model. Existing technologies typically use a single power flow constraint: if a complex nonlinear power flow model is used for the entire network, the calculation of the OPF of a wind farm with hundreds of nodes will be extremely slow; if a coarse linearized model is used to pursue speed, the network loss and voltage deviation caused by the weak grid environment faced by the wind farm and the large Thevenin equivalent impedance are ignored, which significantly increases the global calculation error.

[0005] Secondly, existing distributed control schemes typically deploy an Agent controller at each wind turbine node in a wind farm. While this fully distributed architecture distributes the computational load, the excessive number of nodes makes the iterative convergence process of distributed optimization extremely lengthy, and any communication failure or interruption of any node can directly disrupt the global optimization process, resulting in low system reliability.

[0006] Finally, existing distributed voltage optimization control schemes do not consider the impact of computation and communication delays on the distributed voltage control execution process. In existing synchronous distributed computing architectures, the master controller must wait for all child nodes in the network to complete information transmission before executing the next iteration. In practical industrial applications, if there are differences in computation time among the physical control nodes or if communication network delays occur, this mechanism of waiting for all nodes will severely hinder the response speed of optimization control and greatly reduce the timeliness of distributed voltage optimization. Summary of the Invention

[0007] This invention aims to solve the technical problems in existing large-scale wind farm voltage optimization and control, such as the difficulty in balancing model accuracy and calculation speed, and the susceptibility of distributed control to physical communication delays leading to response lags. It provides a system voltage optimization method and system for large-scale wind farm power collection lines.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A method for optimizing system voltage in large-scale collector lines for wind farms includes the following steps: Obtain basic operating parameters and real-time status information of wind farms; Using the grid connection point PCC bus of the wind farm as the boundary, the wind farm is divided into one grid-connected system and several collector-side systems. A main agent controller is configured at the PCC bus, and a sub-agent controller is configured on each collector line inside the wind farm. Based on the differences in the physical environment of the power lines inside and outside the wind farm, differentiated power flow constraints are used to perform optimal power flow modeling on the grid-connected system and the collector system respectively, and a global optimal power flow model of the wind farm is constructed. The global optimal power flow model is decoupled and iteratively solved using the generalized Benders decomposition method with an embedded asynchronous iterative mechanism through the main agent controller and each of the sub-agent controllers to obtain the globally optimal voltage control command. The main agent controller solves the grid-connected main optimization problem containing discrete variables, while each of the sub-agent controllers solves the collector-side system slave optimization problem containing continuous variables. Each of the sub-Agent controllers performs reactive power regulation on the wind turbines on the corresponding collector lines according to the voltage control command, and the main Agent controller performs turns ratio regulation on the on-load tap-changing transformer on the grid-connected side according to the voltage control command.

[0009] As an optimization, the differentiated power flow constraints include nonlinear power flow constraints based on second-order cone scaling constructed for the grid-connected system, and linearized Distflow power flow constraints constructed for each of the collector-side systems.

[0010] As an optimization, the process of decoupling and iteratively solving the global optimal power flow model using the generalized Benders decomposition method with an embedded asynchronous iteration mechanism includes: In a single asynchronous iteration, the main agent controller sends boundary variables to each of the sub-agent controllers, and each of the sub-agent controllers solves the optimization problem of the collector-side system and uploads the solution status information. When the main agent controller receives the latest solution status information returned by a number of sub-agent controllers that have reached a preset threshold, it immediately stops waiting for sub-agent controllers that have not returned information. It then uses the latest solution status information that has been returned, as well as the historical temporary solution status information of the sub-agent controllers that have not returned, to generate Benders cut constraints and add them to the main optimization problem on the grid-connected side, directly triggering the next round of iterative calculation until the preset convergence condition is met.

[0011] As a further optimization, the process by which the main agent controller generates Benders cut constraints includes: When the corresponding sub-Agent controller finds a feasible solution to the collector-side system optimization problem, it generates a Benders optimal cut constraint based on the dual multiplier information of the optimization problem and adds the Benders optimal cut constraint to the grid-connected main optimization problem. When the corresponding sub-Agent controller finds no feasible solution to the collector-side system optimization problem, it introduces relaxation variables into the optimization problem to establish a relaxation model and solves it. Based on the solution result of the relaxation model, it generates Benders feasible cut constraints and adds the Benders feasible cut constraints to the grid-connected main optimization problem.

[0012] As a further optimization, the judgment logic of the preset convergence condition is as follows: the main agent controller obtains the optimization lower bound solved by the main optimization problem on the grid-connected side, and obtains the optimization upper bound solved by each sub-agent controller; when the aggregation degree difference between the optimization upper bound and the optimization lower bound is less than the set tolerance threshold, the distributed optimization iteration process is determined to have converged.

[0013] As an optimization, the overall optimization objective of the global optimal power flow model is set as minimizing the node voltage deviation of the wind farm collector side system and minimizing the active power loss of the wind farm system.

[0014] As an optimization, the discrete variable in the main optimization problem on the grid-connected side is the tap position of the on-load tap-changing transformer; the continuous variable in the optimization problem of the collector-side system is the reactive power injection of each wind turbine.

[0015] This invention also provides a system voltage optimization system for large-scale wind farm collector lines, comprising: The basic data acquisition module is configured to acquire basic operating parameters and real-time status information of the wind farm. The main agent controller is configured at the PCC bus at the grid connection point of the wind farm. It is used to solve the main optimization problem on the grid connection side that includes discrete variables and to control the turns ratio of the on-load tap-changing transformer on the grid connection side. Multiple sub-Agent controllers are configured on each collector line inside the wind farm. They are used to receive boundary variables transmitted by the main Agent controller to solve the optimization problem of the collector-side system containing continuous variables, and to perform reactive power regulation on the wind turbines on the corresponding collector lines according to the voltage control commands obtained from the solution. The main agent controller and the multiple sub-agent controllers interact in a distributed manner through a communication network. The main agent controller and the multiple sub-agent controllers are jointly configured to use a generalized Benders decomposition method with an embedded asynchronous iterative mechanism to decouple and iteratively solve the globally optimal power flow model with differentiated power flow constraints in order to obtain the globally optimal voltage control command. The differentiated power flow constraints include: a nonlinear power flow constraint based on second-order cone scaling constructed for the grid-connected system, and a linearized Distflow power flow constraint constructed for each collector-side system.

[0016] Compared with the prior art, the present invention has the following advantages: 1. This invention employs a differentiated power flow constraint model. Considering the characteristics of wind farms, which are typically located far from load centers, face weak grid environments, and have significant external Thevenin equivalent impedance and line losses, a nonlinear power flow constraint based on second-order cone scaling is adopted on the external grid-connected side. Simultaneously, considering the radial architecture of the internal collector lines and their relatively low network losses, a linearized Distflow power flow constraint is used on the internal collector line side. This differentiated design accurately matches the physical differences between the internal and external line environments of the wind farm.

[0017] 2. This invention employs a partitioned control architecture that combines centralized and distributed control. Using this control method, the collector line agent controller only needs to process a smaller scale of local data, effectively reducing computational and communication pressure compared to a central controller handling global data. Simultaneously, the collector line agent controller has the ability to centrally regulate each wind turbine, ensuring that distributed information transmission throughout the system exists only at the PCC bus boundary, rather than between nodes within the collector line. This avoids the problem of slow computational convergence caused by excessive agent configuration, achieving a complementary advantage of the two control technologies.

[0018] 3. This invention employs the generalized Benders decomposition method to solve the constructed mixed-integer convex programming (OPF) problem. Generalized Benders decomposition, as a distributed optimization algorithm specifically designed for solving large-scale mixed-integer convex programming problems, exhibits good convergence when solving this voltage optimization model. Using this method ensures that the numerical results of distributed optimization are essentially consistent with those of centralized optimization, thereby effectively improving the voltage limit violation situation within the wind farm system.

[0019] 4. This invention incorporates an asynchronous implementation within the distributed optimization algorithm. Considering the impact of actual communication and computation delays on the distributed control execution process, compared to the traditional synchronous implementation, the asynchronous implementation of this invention only needs to receive partial collector agent information in a single iteration to complete one round of iteration. This mechanism reduces the time consumed in each iteration compared to the traditional synchronous implementation. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the grid connection topology for a large wind farm.

[0021] Figure 2 This is a schematic diagram of the communication mechanism of a wind farm system.

[0022] Figure 3 This is a schematic diagram of the decomposition of a wind farm grid connection model.

[0023] Figure 4 A schematic diagram illustrating synchronous and asynchronous implementations optimized for distributed systems.

[0024] Figure 5 The voltage amplitude of the PCC bus under different power flow equation constraints.

[0025] Figure 6 This represents the residual of the distributed optimization result under ATC.

[0026] Figure 7 This represents the residual of the distributed optimization result under ADMM.

[0027] Figure 8 The aggregation degree of the distributed optimization results under the generalized Benders decomposition.

[0028] Figure 9 This is a diagram comparing the results of distributed optimization with those of centralized optimization.

[0029] Figure 10 The voltage of the collector line nodes before and after distributed optimization.

[0030] Figure 11 This represents the results of synchronous and asynchronous optimization iterations under ATC.

[0031] Figure 12 The results of synchronous and asynchronous optimization iterations under ADMM.

[0032] Figure 13 The results of synchronous and asynchronous optimization iterations under the generalized Benders decomposition. Detailed Implementation

[0033] The present invention will be further described in detail below with reference to the embodiments.

[0034] This embodiment takes a wind farm system as the research object and proposes a distributed optimization method for voltage regulation of its in-farm collector lines. The main components include: ① Minimizing system voltage deviation and network loss as the optimization objective, and establishing an OPF model for wind farm system voltage optimization based on differentiated power flow constraints according to the characteristics of the power environment inside and outside the wind farm. A linearization / convex relaxation method for key OPF constraints is also provided. ② Borrowing the concept of distribution network zoning voltage control, a wind farm system voltage control method based on in-farm collector line zoning is proposed. This control method can be seen as a combination of centralized and distributed control, integrating the technical advantages of both. ③ A collector line voltage optimization method based on three distributed optimization algorithms—generalized Benders decomposition, ADMM, and ATC—is proposed. Specifically, considering the impact of actual communication and computation delays on the distributed optimization algorithm, an asynchronous implementation method for the above distributed algorithms is further proposed. Through a typical wind farm system case, the effectiveness of the distributed optimization algorithm is verified. The optimal results of the OPF model under different power flow constraints and the distributed optimization algorithm are compared in terms of iterative convergence and result optimality. The characteristics of the algorithm are summarized, and analytical suggestions are given for the asynchronous implementation method of the distributed optimization algorithm.

[0035] Combination Figure 1 The schematic diagram of the grid connection topology of a large wind farm shown illustrates the system operation architecture and specific implementation of the present invention. The wind farm contains a large-scale power collection system, with several medium-voltage collection lines connected in parallel to the PCC bus. Wind turbine generators are sequentially connected from one end to the other to each collection line, and the power generated is ultimately collected on the PCC bus, stepped up by an on-load tap changer (OLTC), and connected to a high-voltage transmission line before being finally transmitted to the main power grid.

[0036] It is worth noting that this embodiment primarily focuses on the voltage exceeding limits of the collector lines within the wind farm, emphasizing how to optimize the system voltage from a system-level perspective. Stability issues related to the input / output control of controllable voltage regulating equipment within the wind farm are not within the scope of this embodiment. For the wind farm interior, a collector line impedance model needs to be constructed to support power flow analysis. For the wind turbines, assuming they all employ constant active / reactive power control, have well-designed controllers, and negligible line losses from the turbine outlet to the collector line connection point, each wind turbine connection node on the entire collector line can be equivalent to a PQ node, and the active / reactive power injected into the node is the optimized power output set for the wind turbine. For the external environment of the wind farm, the impact of the main power grid and high-voltage transmission lines on the wind farm voltage is represented by the Thevenin equivalent line impedance.

[0037] The wind farm communication method established in this embodiment can support zoned voltage control of the in-station collection lines, as follows: Figure 2 As shown, distributed agent controllers are configured on the PCC bus on the low-voltage side of the substation and on each collector line within the substation. The PCC bus agent controller establishes distributed communication with each collector line agent controller to mutually receive / transmit boundary electrical information located on the PCC bus; this process is distributed control. Each wind turbine is uniformly regulated by the collector line agent controller; this process is centralized control. Under this communication configuration, the technical advantages of centralized and distributed control are complementary. Compared to the centralized control method where the central controller processes massive amounts of global data, the control method proposed in this embodiment only requires the collector line agent controller to process a smaller amount of local data, thus reducing computational and communication pressure. Furthermore, the proposed control method allows the collector line agent controller to centrally regulate each wind turbine, ensuring that distributed information transmission exists only at the PCC bus boundary rather than between nodes within the collector lines, thereby avoiding the problem of slow computational convergence caused by excessive agent configuration.

[0038] Establish a voltage optimization model for a wind farm system: The mathematical description of the OPF problem corresponding to voltage optimization of a wind farm system is as follows: (1) (2) (3) (4) (5) (6) (7) (8) In the above formula: This represents the set of all nodes in the wind farm grid connection model; This represents the set of nodes in the station's power collection system; Represents the set of regular branches; Represents a set of branches containing transformers; Indicates the active power loss of the branch line; , , These represent the active power, reactive power, and voltage amplitude injected into the node, respectively. , These represent the active power and reactive power flowing through the branch, respectively. , These represent the branch resistance and reactance, respectively. , Let represent the real and imaginary parts of the nodal admittance matrix of the collector system, respectively; This indicates the phase difference between the voltages at the beginning and end of the branch. , , These represent the active power output, reactive power output, and rated capacity of the wind turbine units connected to the collector line, respectively. This indicates the adjustable ratio of OLTC, which typically ranges from ±1.25% to 8.

[0039] Taking into account the voltage safety and operational economy of the collection lines within the wind farm, Equation (1) aims to minimize the overall voltage deviation and active power loss of the collection lines. Equation (2) indicates that the power injected into the collection line nodes comes from the output power of the wind turbine generators. Equations (3) and (4) respectively represent the nonlinear power flow constraints with and without OLTC branches. Since the collection lines within the station are radial topologies, the system power flow can also adopt the Distflow power flow constraint. Equations (5) and (6) respectively represent the Distflow power flow constraints with and without OLTC branches. Equation (7) represents the wind turbine generator capacity constraint. Equation (8) represents the system node voltage amplitude constraint, with an allowable fluctuation range of ±5% of the nominal value. The system voltage control is mainly achieved by optimizing the OLTC transformer ratio and the reactive power output of the wind turbine generators.

[0040] The power flow equations of the collector lines shown in equations (3) and (4) are nonlinear constraints. If no processing is performed on them, a feasible optimization method is to nest the power flow iterative calculation (such as the Newton-Laurel method, the forward-backward substitution method, etc.) into a "model-free" metaheuristic swarm evolution algorithm. However, this optimization method has two obvious problems: 1) The swarm evolution algorithm has the property of "brute force" solution. When the number of optimization variables is large, the calculation time is obviously long; 2) The optimization process of the swarm evolution algorithm has strong randomness. The algorithm is prone to getting trapped in local optima, and the quality of the optimal solution is difficult to guarantee.

[0041] In comparison, applying convex scaling / linearization to the power flow equation constraints before using mature convex programming methods for solution is a more efficient approach. This method sacrifices slightly higher accuracy in power flow calculations for significantly improved optimization and efficiency. Therefore, the aforementioned OPF-based voltage control model undergoes the following processing.

[0042] 1) For the nonlinear power flow constraint equation (3), if let , , Then, a second-order cone scaling can be constructed as follows: (9) At this point, the optimization objective (1) and the node voltage constraint (8) are also transformed accordingly as follows: (10) (11) 2) For Distflow power flow constraint equation (5), let , Then, a second-order cone scaling can be constructed as follows: (12) At this point, the optimization objective (1) and the node voltage constraint (8) are also transformed accordingly as follows: (13) (14) Furthermore, since the power loss on medium-voltage feeders is typically much smaller than the power flowing through the line, it can be ignored. Therefore, Distflow can be linearized, and the following equation holds: (15) At this point, the node voltage constraint equation (8) becomes equation (14). Since losses are neglected, the loss term formula in equation (13) is... No longer applicable, but has become .

[0043] 3) For power flow constraint equation (4) containing OLTC branches, a second-order cone scaling can be performed according to equation (9), but this process will introduce a bilinear term. , In response, let's assume... There are possible values. Then we have: (16) Substituting equation (16) into the equation... , In the middle, using the big M scaling method, the constraint equation is constructed as follows: (17) (18) In the above formula, M is defined as a very large positive integer.

[0044] Similarly, for power flow constraint equation (6) containing OLTC branches, it can be processed according to equations (16), (17), and (18). In this process, a bilinear term will also be introduced. Similarly, by using large M scaling, the constraint formula can be constructed as follows: (19) After constructing the aforementioned OPF model, to reduce global communication pressure, this embodiment further decomposes the wind farm system into physical topology and mathematical model based on collector line partitioning. Specifically, in conjunction with... Figure 2 and Figure 3 As shown, the wind farm grid-connected model is decomposed into a system model comprising a set of grid-connected side models and several sets of collector-side system models. The grid-connected side model represents the section from the PCC bus to the external power grid, while the collector-side system models represent the section from the PCC bus to the end of the internal collector lines. The PCC bus serves as a boundary node, and the associated boundary electrical quantities... (Including boundary voltage and boundary power) is copied as .

[0045] The decomposed grid-connected side model and collector-side system model have the following coupling relationship: (20) In the above formula, , These are vectors composed of boundary electrical quantities from the grid-connected side model and the collector-side system model, respectively, and must remain consistent. Next, distributed optimization solutions are performed on the grid-connected side model and the collector-side system model based on augmented Lagrangian relaxation and generalized Benders decomposition, respectively.

[0046] To achieve distributed solution for the decomposed system model, an augmented Lagrangian relaxation method can be used to relax the coupling constraint (21) and add it to the objective function of each side's optimization model. Simultaneously, a quadratic penalty function term is added to enhance model convergence. For the grid-connected and collector-side system sub-models, the augmented Lagrangian functions are constructed as follows: (twenty one) (twenty two) In the above formula, , These represent vectors composed of optimization variables that are only relevant to the grid-connected side model and the collector-side system model, respectively. , These represent the sets of lines on the grid-connected side and the collector line side, respectively. , ; , These represent inequality constraints and equality constraints that are only relevant to the grid-connected side model, respectively. , These represent inequality constraints and equality constraints that are only relevant to the collector-side system, respectively. It is a Lagrangian multiplier vector. This is the penalty factor corresponding to the quadratic penalty function term; It is the transpose symbol; This represents the optimization variables obtained from the grid-connected / collector-side system model, and these are constant values. tr represents the Hadamard product, tr represents the trace of a matrix, and diag represents the diagonalization of a vector.

[0047] For the system voltage optimization model based on augmented Lagrangian relaxation, composed of equations (21) and (22), ADMM and ATC can be further used for solving. The iterative forms of these two methods can be uniformly expressed as follows: (twenty three) (twenty four) In the above formula, This represents the k-th iteration. The main difference between the ADMM and ATC iterative forms lies in the iterative formulas for the Lagrangian multiplier and penalty function terms, which are expressed as follows: (25) (26) In the above formula, formula (26) is the Lagrangian update method corresponding to ADMM; formula (27) is the Lagrangian update method corresponding to ATC.

[0048] As another preferred solution architecture, for the mixed-integer OPF problem, this embodiment adopts the idea based on generalized Benders decomposition. It starts with a relaxed grid-connected main optimization problem with a few constraints, and iteratively adds optimal cut / feasible cut constraints to the grid-connected main optimization problem based on whether the collector-side system's secondary optimization problem has a feasible solution, for iterative solution. The collector-side system secondary optimization problem model is as follows: (27) If equation (27) has no feasible solution, then slack variables are introduced. , And establish the relaxation model as follows: (28) In the above equation, the optimization objective value obtained by solving equation (28) provides the upper bound ub in the generalized Benders decomposition.

[0049] The model for the relaxed grid-connected main optimization problem is as follows: (29) In the above equation, the optimization objective value obtained by solving equation (29) provides the lower bound lb for optimization in the generalized Benders decomposition.

[0050] For the case where the collector-side system voltage optimization control model has a feasible solution / no feasible solution, the following Benders optimal cut / feasible cut constraints are generated (in the k-th iteration process) and added to equation (29): (30) (31) (32) Equations (30) and (31) represent Benders' optimal cut and feasible cut, respectively.

[0051] 4. Asynchronous Implementation of Distributed Optimization Algorithms Considering Information Transmission Delay: As mentioned above, the distributed implementation of wind farm system voltage optimization relies on continuous information transmission between the PCC bus agent and the collector line agent. This process is affected by the agent's calculation time, leading to information transmission delays. Therefore, the execution process of distributed algorithms can be divided into synchronous and asynchronous methods. For example... Figure 4As shown, assuming the wind farm has 3 collector lines: In the synchronous implementation, the PCC bus agent must wait for all collector line agents to complete information transmission before executing the next iteration; while in the asynchronous implementation, the PCC bus agent only needs to wait for a few (shown as 2 in the figure) collector line agents to complete information transmission before executing the next iteration. Therefore, in the same time period, the asynchronous implementation can execute more iterations than the synchronous implementation. The augmented Lagrangian relaxation standard implementation shown in equations (21)-(26) and the generalized Benders decomposition standard implementation shown in equations (27)-(32) correspond to the synchronous implementation. Assuming that in each iteration, the set of collector line agent sequence numbers that have completed information transmission is The set of Agent serial numbers for power collection lines that have not completed information transmission is: ,but , The asynchronous implementations of augmented Lagrangian relaxation and generalized Benders decomposition are given in Tables 1 and 2.

[0052] Table 1. Distributed Voltage Optimization Asynchronous Implementation of Augmented Lagrangian Relaxation Table 2. Distributed Voltage Optimization Asynchronous Implementation of Augmented Lagrangian Relaxation It is important to note that: 1) As mentioned above, in the distributed voltage optimization model of this embodiment, differentiated power flow constraints are adopted for the grid-connected side and the collector lines, and there are multiple choices for the power flow model. Therefore, this embodiment will analyze and discuss the accuracy of voltage calculation under different power flow constraints. In particular, the voltage calculation error is mainly quantified by the following formula: (34) In the above formula, This represents the reference voltage amplitude calculated using the Newton-Raphson method based on the nonlinear power flow equation.

[0053] 2) For the generalized Benders decomposition, the convergence of its distributed optimization iterative process is determined by the degree of aggregation of the upper and lower bounds of the optimization. The degree of aggregation is defined as follows (in the k-th iteration): (35) 3) For ADMM and ATC, the convergence of their distributed optimization iterative process is determined by whether the boundary variables involved in the grid-connected side model and the collector-side model reach a stable consistency. The convergence of the distributed optimization iterative process (k-th iteration) is determined by the residuals defined below: (36) In the above formula, only when and The distributed optimization iterative process is considered to have converged only when all values ​​are less than the set threshold.

[0054] 4) The wind farm system voltage optimization model constructed in this embodiment is an OPF problem containing mixed integer variables. Generalized Benders decomposition is an effective method for solving large-scale mixed integer programming problems, and its optimality has been rigorously proven. However, there is still relatively little discussion on the application of ADMM and ATC in mixed integer OPF problems. This embodiment will analyze and discuss the iterative convergence and control optimality of ADMM and ATC.

[0055] Numerical Example Analysis: The numerical example analysis considers a large wind farm consisting of 3×10 2MW wind turbine units, with a system baseline capacity set at 100MVA. Specific line parameters are shown in Table 3. The numerical example analysis was completed using the Yalimp toolkit, and the convex optimization solutions involved in the programming process were implemented using the Gurobi solver.

[0056] Table 3. Line parameters in the example analysis Impact of Power Flow Equality Constraints on the Accuracy of Wind Farm System Voltage Calculation: This study analyzes the impact of different power flow equality constraints on the optimal calculation of voltage within the wind farm system. Specifically, three power flow equality constraints are defined as shown in Table 4.

[0057] Table 4. Three types of power flow equality constraints First, the influence of power flow equality constraints on the voltage calculation of the collector side system is analyzed. A single collector line is used as a case model for testing. The voltage of the first node of the collector line is fixed at 1p.u., and the active power injected by the other wind turbine nodes is randomly varied in the range of [0,2]MW. Then, reactive power optimization of the collector line is performed. This process is repeated 100 times. At this time, based on the three power flow equality constraints, the statistical data of the voltage calculation error of the collector line (the error quantification index is the formula defined by equation (34)) is shown in Table 5. In summary, the linearization method has the best performance in the voltage optimization calculation of the collector line. Although the statistical data under the second-order conical scaling B method has the smallest mean, its voltage calculation error fluctuates more. The performance of the second-order conical scaling A method is between that of the linearization method and the second-order conical scaling B method.

[0058] Table 5. Calculation error of collector line voltage under different power flow equation constraints Next, the impact of the different power flow equation constraints on the voltage optimization calculation of the external grid-connected side of the wind farm is analyzed. The example model uses a two-node line with an OLTC (Optimal Power Controller), with the OLTC tap set to 0 and the PCC bus active and reactive power injected constant at 50MW and 20MVar, respectively. Considering that in real-world scenarios, wind farms are often located in remote areas far from load centers, long-distance power transmission may cause the wind farm to be connected to a weak grid environment, the influence of the external grid strength is considered. The Thevenin equivalent impedance is adjusted according to the short-circuit capacity ratio from large to small. Finally, the calculated PCC bus voltage under different power flow equation constraints is obtained as follows: Figure 5 As shown, nonlinear power flow refers to the power flow result calculated using Newton's method, which is considered a reference value. The figure shows that as the grid environment weakens, the PCC bus voltage amplitude obtained based on different power flow equation constraints gradually deviates significantly from the reference value. Only the PCC bus voltage amplitude obtained based on the second-order conical scaling B method remains essentially consistent with the reference value. Furthermore, although the linearization method is more accurate in calculating collector line voltages than other methods, when calculating grid-connected side voltages, if the grid-connected side short-circuit capacity is small and the corresponding Thevenin equivalent impedance is large, the accuracy of the linearization method decreases due to neglecting line losses.

[0059] Based on the above analysis results, from the perspective of voltage calculation accuracy, the collector line side model is suitable for using linearized power flow equation constraints, while the grid-connected side model is suitable for using second-order conical shrinkage B power flow equation constraints.

[0060] Iterative Convergence Analysis of Distributed Voltage Optimization: The choice of power flow model affects the established OPF model, thus influencing the iterative convergence of the optimization algorithm. Therefore, although from the perspective of voltage calculation accuracy, using second-order conical scaling (B) and linearization on the grid-connected side and collector line side respectively is ideal, this does not mean that it is still the ideal choice from the perspective of optimization iterative convergence. Therefore, in order to analyze the convergence of the distributed voltage optimization algorithm and compare the impact of different power flow constraint models, two distributed voltage control optimization models are specifically set up here, as shown in Table 6: The reason for choosing Model I is that this power flow constraint is beneficial to the accuracy of system voltage calculation, so it is necessary to continue to analyze the convergence of the algorithm under this model. Model II is widely used in other related studies. ,, It can be used as a comparison model.

[0061] First, convergence analysis is performed on ATC and ADMM based on augmented Lagrangian relaxation. The residual changes of Models I and II are as follows: Figure 6 , 7As shown: For ATC and ADMM, the Model II-based distributed optimization has a better convergence process. Taking the results of ATC distributed optimization as an example, if the residual convergence threshold is set to 1×10... -4 The distributed optimization results for Model II converged on the 16th iteration, while the distributed optimization results for Model I failed to converge within 30 iterations. Furthermore, ADMM showed better convergence iterations than ATC. For Model II, the number of convergence iterations was reduced to 11 under ADMM. For Model I, convergence was achieved within 30 iterations under ADMM. It is worth noting that although the convergence of the distributed optimization results for Model I was not as good as that for Model II, the convergence error was still acceptable. Regardless of whether based on ADMM or ATC, the maximum difference in the boundary voltage vector after 30 iterations for Model I did not exceed 1 × 10⁻⁶. -3 pu.

[0062] To further verify the technical advantages of Model I (differentiated power flow constraints) used in this invention in terms of voltage calculation accuracy, this embodiment introduces Model II, which uses linear constraints across the entire network, as a comparative verification.

[0063] Table 6 Distributed Voltage Optimization Control Model Next, the convergence of the generalized Benders decomposition is analyzed, and the changes in the degree of aggregation of the upper and lower bounds of optimization are obtained as follows: Figure 8 As shown: Model I and Model II have basically the same convergence effect. If the convergence threshold of aggregation is set to 1×10... -4 The distribution optimization results under both Model I and Model II converged on the 24th iteration.

[0064] The results from various distributed optimization algorithms show that the iterative convergence of the algorithm under Model I is not as good as that under Model II. Model I contains second-order cone constraints, which are more complex than the purely linear constraints in Model II, requiring more iterations. However, despite this, the iterative convergence of the algorithm under Model I is still acceptable. Specifically, according to... Figure 6 , Figure 7 The results show that although the standard application models of ADMM and ATC are pure convex programming problems, they can also be extended to solve the mixed integer OPF problem constructed in this embodiment, and still maintain good iterative convergence.

[0065] Optimality Analysis of Distributed Voltage Optimization Results: As mentioned earlier, Model I, as a system power flow constraint, exhibits the best performance in voltage calculation accuracy, but its distributed optimization iterative convergence is not as good as Model II. To select a suitable power flow constraint model for voltage optimization of large-scale wind farm systems and further analyze the optimality of the results obtained from various distributed optimization algorithms, ATC, ADMM, and generalized Benders decomposition were used to solve the distributed OPF problem based on Model I and Model II. The distributed optimization results are shown in Tables 7, 8, and 9.

[0066] Since the power flow equality constraints underlying the distributed OPF problem are convex-scaled / linearized versions of standard nonlinear power flow, the optimization decision quantities (including OLTC settings) should be considered when calculating active power loss and voltage deviation. Reactive power injection at the wind turbine connection node Substituting these values ​​into the nonlinear power flow equations, the results were calculated using the Newton-Laurel method. A review of the tables reveals that while Model II's distributed optimization results generally show slightly better convergence than Model I, its results are less ideal than Model I in terms of both collector line network losses and voltage deviation optimization. This is because the power flow equality constraints on the external grid side in Model II are based on linearization method A, which has lower accuracy in calculating the PCC bus voltage. This, in turn, affects the accuracy of the voltage calculation for the entire collector system, resulting in a decrease in the optimality of the distributed optimization results.

[0067] Table 7. Distributed optimization results based on ATC Table 8. Distributed optimization results based on ADMM Table 9. Distributed optimization results based on generalized Benders decomposition Based on the aforementioned system voltage accuracy analysis results, iterative convergence analysis results, and current distributed optimization results, it can be seen that Model I is the most suitable power flow constraint for voltage optimization of large-scale wind farm systems. Next, we will mainly compare the distributed optimization results based on ATC, ADMM, and generalized Benders decomposition with the centralized optimization results under the power flow constraint of Model I, and obtain the following results: Figure 9 Results shown: After several iterations, the distributed optimization results of ATC, ADMM, and generalized Benders are basically consistent with the centralized optimization results. However, the final convergence results of ATC and ADMM show slight deviations from the centralized optimization results, each by 3 × 10⁻⁶. -4 8×10 -5The deviation between the convergence result of the generalized Benders decomposition and the result of the centralized optimization is less than 1×10⁻⁶. -7 It can be considered to have the same optimality as the centralized optimization result.

[0068] Since the distributed optimization results under the generalized Benders decomposition are most consistent with the centralized optimization results compared to ADMM and ATC, this paper specifically takes the optimization results under the generalized Benders decomposition based on Model I power flow constraints as an example to analyze the system voltage amplitude before and after distributed optimization. Figure 10 As shown (#0 is the PCC bus number): Before optimization, the voltage amplitude at the end node of the collector line was close to the nominal value of 1.05, which posed a risk of exceeding the voltage safety limit. By optimizing the OLTC tap and the reactive power output of the wind turbine, the voltage amplitude at the end node of the collector line was reduced to below the nominal value of 1.01, and the overall system voltage within the wind farm was effectively regulated to a safe range.

[0069] Validation of the effectiveness of asynchronous implementation of distributed optimization algorithms: As mentioned earlier, considering factors such as the accuracy of voltage calculation, iterative convergence, and optimality of results, Model I is superior to Model II. Therefore, the asynchronous implementation of distributed optimization algorithms is mainly based on the power flow constraints of Model I. The asynchronous implementation schemes of ATC, ADMM, and generalized Benders decomposition are validated, with two cases set as follows.

[0070] Asynchronous Method I: Assume that in each iteration of the distributed optimization algorithm, the next iteration only needs to wait for at least two of the three collector agents to complete the information transmission. Specifically, let's assume that the time taken for Agents #1, #2, and #3 to complete computation and information transmission is 1 unit time, 1 unit time, and 2 unit time, respectively. This means that collectors #1 and #2 will complete an information update once in each iteration, and collector #3 will complete an information update once every two iterations.

[0071] Asynchronous Method II: Assume that in each iteration of the distributed optimization algorithm, the next iteration only needs to wait for at least two of the three collector agents to complete the information transmission. Specifically, let's assume that the time taken for Agents #1, #2, and #3 to complete computation and information transmission is 1, 2, and 3 times the unit time, respectively. This means that collector #1 will complete an information update once in every 1 iteration, collector #2 once every 2 iterations, and collector #3 once every 3 iterations.

[0072] Finally, the asynchronous implementation processes of the above distributed optimization algorithms are as follows: Figure 11 , Figure 12 ,as well as Figure 13 As shown in Asynchronous Method I, the optimization results under the asynchronous method still exhibit good convergence. However, due to the smaller amount of collector agent information collected in each iteration, the number of iterations required for convergence is greater than that under the traditional synchronous method. Furthermore, as shown in Asynchronous Method II, if too little collector agent information is collected in each iteration, the iteration process may fail to converge.

[0073] Overall, while asynchronous methods reduce the duration of a single iteration by eliminating the need for all agents to complete computations in each iteration compared to synchronous methods, this also increases the number of iterations required for convergence and may even lead to unstable convergence. Therefore, although asynchronous methods can effectively reduce the amount of information exchange between agents in a single iteration, the distributed optimization process under asynchronous methods is not necessarily less time-consuming than that under traditional synchronous methods.

[0074] In summary, through the system voltage optimization method and system disclosed in this embodiment, in the actual operation of optimizing system voltage and regulating the voltage distribution of large-scale collection line nodes in large wind farms, based on the above theoretical analysis and calculation results, the specific solution of this embodiment can achieve the following technical effects: 1) It achieves precise matching of the differentiated line environments outside and inside wind farms. Since wind farms are usually far from load centers and face weak grid environments, the external Thevenin equivalent impedance and line losses are relatively large. The grid-connected side adopts nonlinear power flow constraints based on second-order cone scaling. However, the internal collector lines of wind farms have a radial structure and the proportion of grid losses is relatively small. The internal collector side adopts linearized Distflow power flow constraints. This differentiated model effectively balances global calculation accuracy and solution efficiency.

[0075] 2) High-quality solutions to the mixed-integer optimization model were ensured. The voltage optimization model constructed in this embodiment is a mixed-integer convex programming (OPF) problem containing discrete and continuous variables. Generalized Benders decomposition was used as the distributed optimization algorithm to solve this problem, demonstrating good convergence. Furthermore, the augmented Lagrangian relaxation algorithm was extended to solve this mixed-integer convex programming problem, also exhibiting good convergence.

[0076] 3) Voltage regulation accuracy consistent with centralized control was achieved. The numerical results of distributed optimization based on generalized Benders decomposition and augmented Lagrangian relaxation are basically consistent with those of centralized optimization. After optimization, the voltage amplitude of the over-limit collector line terminal node can be smoothly reduced back to the safe range, and the over-limit situation of the system voltage is effectively improved.

[0077] 4) Improved execution efficiency of distributed optimization in real-world communication environments. Compared to the traditional synchronous implementation that requires waiting for all network nodes to complete computation, the asynchronous implementation embedded in this embodiment only needs to receive partial collector line Agent information to complete one iteration, resulting in less synchronization waiting time during each iteration. In actual engineering deployments, the system can flexibly select between synchronous and asynchronous implementation methods based on detailed network communication parameters, effectively reducing the impact of communication latency on the distributed voltage control execution process.

[0078] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing system voltage in large-scale collector lines for wind farms, characterized in that, Includes the following steps: Obtain basic operating parameters and real-time status information of wind farms; Using the grid connection point PCC bus of the wind farm as the boundary, the wind farm is divided into one grid-connected system and several collector-side systems. A main agent controller is configured at the PCC bus, and a sub-agent controller is configured on each collector line inside the wind farm. Based on the differences in the physical environment of the power lines inside and outside the wind farm, differentiated power flow constraints are used to perform optimal power flow modeling on the grid-connected system and the collector system respectively, and a global optimal power flow model of the wind farm is constructed. The global optimal power flow model is decoupled and iteratively solved using the generalized Benders decomposition method with an embedded asynchronous iterative mechanism through the main agent controller and each of the sub-agent controllers to obtain the globally optimal voltage control command. The main agent controller solves the grid-connected main optimization problem containing discrete variables, while each of the sub-agent controllers solves the collector-side system slave optimization problem containing continuous variables. Each of the sub-Agent controllers performs reactive power regulation on the wind turbines on the corresponding collector lines according to the voltage control command, and the main Agent controller performs turns ratio regulation on the on-load tap-changing transformer on the grid-connected side according to the voltage control command.

2. The system voltage optimization method for large-scale wind farm collection lines according to claim 1, characterized in that, The differentiated power flow constraints include nonlinear power flow constraints based on second-order cone scaling constructed for the grid-connected system, and linearized Distflow power flow constraints constructed for each of the collector-side systems.

3. The system voltage optimization method for large-scale wind farm collector lines according to claim 1, characterized in that, The process of decoupling and iteratively solving the global optimal power flow model using the generalized Benders decomposition method with an embedded asynchronous iterative mechanism includes: In a single asynchronous iteration, the main agent controller sends boundary variables to each of the sub-agent controllers, and each of the sub-agent controllers solves the optimization problem of the collector-side system and uploads the solution status information. When the main agent controller receives the latest solution status information returned by a number of sub-agent controllers that have reached a preset threshold, it immediately stops waiting for sub-agent controllers that have not returned information. It then uses the latest solution status information that has been returned, as well as the historical temporary solution status information of the sub-agent controllers that have not returned information, to generate Benders cut constraints and add them to the main optimization problem on the grid-connected side, directly triggering the next round of iterative calculation until the preset convergence condition is met.

4. The system voltage optimization method for large-scale wind farm collector lines according to claim 3, characterized in that, The process by which the main agent controller generates Benders cut constraints includes: When the corresponding sub-Agent controller finds a feasible solution to the collector-side system optimization problem, it generates a Benders optimal cut constraint based on the dual multiplier information of the optimization problem and adds the Benders optimal cut constraint to the grid-connected main optimization problem. When the corresponding sub-Agent controller finds no feasible solution to the collector-side system optimization problem, it introduces relaxation variables into the optimization problem to establish a relaxation model and solves it. Based on the solution result of the relaxation model, it generates Benders feasible cut constraints and adds the Benders feasible cut constraints to the grid-connected main optimization problem.

5. The system voltage optimization method for large-scale wind farm collector lines according to claim 3, characterized in that, The logic for determining the preset convergence condition is as follows: the main agent controller obtains the lower bound of the optimization problem solved by the grid-connected side main optimization problem, and obtains the upper bound of the optimization solved by each sub-agent controller; When the difference in the degree of aggregation between the upper bound and the lower bound of optimization is less than the set tolerance threshold, the distributed optimization iteration process is determined to have converged.

6. The system voltage optimization method for large-scale wind farm collector lines according to claim 1, characterized in that, The overall optimization objective of the global optimal power flow model is set as minimizing the node voltage deviation of the wind farm collector side system and minimizing the active power loss of the wind farm system.

7. The system voltage optimization method for large-scale wind farm collector lines according to claim 1, characterized in that, The discrete variable in the main optimization problem on the grid-connected side is the tap position of the on-load tap-changing transformer; the continuous variable in the secondary optimization problem of the collector-side system is the reactive power injection of each wind turbine.

8. A system voltage optimization system for large-scale collector lines in wind farms, characterized in that, include: The basic data acquisition module is configured to acquire basic operating parameters and real-time status information of the wind farm. The main agent controller is configured at the PCC bus at the grid connection point of the wind farm. It is used to solve the main optimization problem on the grid connection side that includes discrete variables and to control the turns ratio of the on-load tap-changing transformer on the grid connection side. Multiple sub-Agent controllers are configured on each collector line inside the wind farm. They are used to receive boundary variables transmitted by the main Agent controller to solve the optimization problem of the collector-side system containing continuous variables, and to perform reactive power regulation on the wind turbines on the corresponding collector lines according to the voltage control commands obtained from the solution. The main agent controller and the multiple sub-agent controllers interact in a distributed manner through a communication network. The main agent controller and the multiple sub-agent controllers are jointly configured to use a generalized Benders decomposition method with an embedded asynchronous iterative mechanism to decouple and iteratively solve the globally optimal power flow model with differentiated power flow constraints in order to obtain the globally optimal voltage control command. The differentiated power flow constraints include: a nonlinear power flow constraint based on second-order cone scaling constructed for the grid-connected system, and a linearized Distflow power flow constraint constructed for each collector-side system.

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