Large-scale photovoltaic power station system voltage distributed non-convex optimization method based on double-layer alternating direction multiplier method framework

Abstract

The invention discloses a large-scale photovoltaic power station system voltage distributed non-convex optimization method based on a double-layer alternating direction multiplier method framework. The method comprises the following steps: firstly, constructing a system voltage optimization mathematical model of a large-scale photovoltaic power station system; on the basis of a distributed communication architecture, a PCC bus is copied, and a system voltage optimization mathematical model is decomposed into distributed optimization models of a grid-connected side subsystem and a current collection side subsystem; constructing a grid-connected side sub-optimization problem and a current collection side sub-optimization problem under the TL-ADMM, solving the distributed optimization model by adopting a TL-ADMM algorithm, and in the solving process of the TL-ADMM algorithm, after inner layer iteration convergence, if an outer layer does not obtain a globally optimal solution, continuing to use a penalty term coefficient finally updated in the previous inner layer circulation as an initialization value of subsequent inner layer iteration. The method has the advantages that good convergence and optimality are achieved, and the obtained voltage optimization result can effectively guarantee the voltage safety of the photovoltaic power station system.

Description

Technical Field

[0001] The present invention relates to the field of power technology, and particularly to a method for non-convex optimization of voltage distribution in a large-scale photovoltaic power station system based on a two-layer alternating direction multiplier method framework. Background Art

[0002] With the advancement of the global energy transition, clean energies such as wind energy and photovoltaic power have become the core of the energy strategies of various countries. Among them, photovoltaic power generation has developed rapidly due to its advantages of cleanliness, renewability, and low cost. With the increase in the grid connection ratio of photovoltaic power stations, especially the centralized construction in remote areas, the voltage safety problems faced by the power grid are becoming increasingly serious. After a large number of large-scale photovoltaic power stations are connected to the grid, voltage problems are likely to occur, mainly due to the insufficient grid carrying capacity and the complexity of internal electrical coupling in the system. On the one hand, photovoltaic power stations are usually connected to weak links in the grid. Especially in the case of high-proportion renewable energy access, the traditional power grid is difficult to cope with the frequent fluctuations in the characteristics of photovoltaic power generation, resulting in increased voltage fluctuations at the Point of Common Coupling (PCC) between the photovoltaic power station and the grid. Especially when the light changes violently or during long-distance power transmission, overvoltage or undervoltage problems are likely to occur, endangering the stability of the power grid. On the other hand, the voltage fluctuations in the collector lines inside the photovoltaic power station are also aggravated due to the complexity of electrical coupling. The photovoltaic units far from the substation are more likely to experience voltage drops, resulting in voltage overlimits, affecting the normal operation of equipment and possibly triggering a chain reaction.

[0003] For the problem of voltage overlimits, two common technical means include: one is direct voltage regulation, mainly achieved by adjusting the on-load tap changer and implementing reactive power local compensation; the other is to optimize the power flow distribution and adjust the voltage level by controlling the output of the photovoltaic power station through the inverter. Voltage control methods can be divided into two forms: centralized and distributed. Centralized voltage optimization relies on a central controller that can obtain information about the entire system and formulate an optimal voltage optimization strategy within the entire system. The centralized voltage optimization method is simple and efficient to execute, but it relies on the point-to-point communication between the central controller and each controllable device. Under the trend of the gradual scale-up of photovoltaic power stations, the optimization decision of this method will face huge communication pressure.

[0004] In contrast, a distributed voltage optimization method with a smaller communication burden is more suitable for the system voltage optimization requirements of large-scale photovoltaic power stations. The core idea of distributed voltage optimization is to decompose the original centralized voltage optimization problem into multiple independent sub-optimization problems and solve them separately. Through neighborhood communication between Agent controllers and distributed optimization algorithms, the local optimization variables are gradually updated, and finally, the global optimal solution of the centralized optimization problem is approximated. In the distributed optimization mode, the global optimization problem is decomposed into multiple local sub-optimization problems and solved independently. The Karush-Kuhn-Tucker (KKT) conditions can be used to guide the optimization process of each local sub-optimization problem so that each local solution can finally converge to the global optimal solution.

[0005] Existing distributed voltage optimization methods, such as the Alternating Direction Method of Multipliers (ADMM), the Target Cascading Analysis (ATC), and Benders decomposition, etc., have effectively controlled the voltage of the system under study and achieved satisfactory regulation effects. However, the premise for the effectiveness of these distributed optimization algorithms is that the system voltage optimization model to be solved must be a convex optimization problem.

[0006] According to the foregoing analysis, the voltage problems faced by large-scale photovoltaic power stations mainly stem from the limited power grid carrying capacity and the complex internal electrical coupling of the system. Since the power grid connected to the photovoltaic power station is usually a weak link and the internal line impedance is large, the system is prone to being affected by both external power grid fluctuations and internal electrical coupling during operation, resulting in an exacerbation of the severity of voltage problems. Therefore, photovoltaic power stations often face the voltage regulation challenge of "internal troubles and external threats" during operation. In this case, using LinDistflow linearized power flow constraints may introduce certain system power flow calculation errors, which in turn affect the accuracy of voltage optimization decisions for large-scale photovoltaic power stations. Therefore, in order to accurately describe the overall power flow distribution state of photovoltaic power stations, it is particularly necessary to adopt non-linear standard Distflow power flow constraints. However, the standard Distflow power flow constraints make the voltage optimization model have non-convex mathematical characteristics. At this time, the "sufficient and necessary" relationship no longer holds between the KKT conditions and the global optimal solution, and the traditional distributed optimization algorithms (such as ADMM) cannot be strictly guaranteed in terms of convergence and optimality. Therefore, it has become an urgent task to explore new distributed optimization methods to effectively solve the non-convex optimization problems in the system voltage regulation of large-scale photovoltaic power stations.

[0007] Traditional ADMM lacks a strict guarantee of global convergence when solving non-convex optimization models, resulting in inaccurate final optimization results. Therefore, based on traditional ADMM, it is further developed into a two-level alternating direction method of multipliers (Two-Level ADMM, TL-ADMM) with inner and outer nested loops. For the solution of non-convex optimization problems, TL-ADMM has a unique two-level structure compared to ADMM, and can have better convergence guarantee in terms of global convergence performance. However, TL-ADMM still has certain limitations in terms of convergence and optimality, especially the optimality will directly affect the accuracy of the final control result. Summary of the Invention

[0008] Aiming at the deficiencies of the above-mentioned prior art, the technical problem to be solved by the present invention is: how to provide a large-scale photovoltaic power station system voltage distributed non-convex optimization method based on the two-level alternating direction method of multipliers framework, which has good convergence and optimality, and the obtained voltage optimization result can effectively guarantee the voltage safety of the photovoltaic power station system.

[0009] To solve the above technical problems, the present invention adopts the following technical solutions:

[0010] A large-scale photovoltaic power station system voltage distributed non-convex optimization method based on the two-level alternating direction method of multipliers framework, characterized by comprising the following steps:

[0011] S1. First, construct a system voltage optimization mathematical model for the large-scale photovoltaic power station system;

[0012] S2. Based on the structural characteristics of the large-scale photovoltaic power station, construct a distributed communication architecture: configure distributed Agent controllers on the PCC bus and each collector line. The distributed Agent controller on the collector line is used to uniformly control the PVGUs on the collector line, and boundary information is transmitted between the distributed Agent controllers on each collector line and the distributed Agent controller on the PCC bus;

[0013] S3. On the basis of the distributed communication architecture, decompose the system voltage optimization mathematical model into distributed optimization models of the grid-connected side subsystem and the collector side subsystem by replicating the PCC bus;

[0014] S4. Construct sub-optimization problems on the grid-connected side and the collector side under TL-ADMM, and use the TL-ADMM algorithm to solve the distributed optimization model. During the solution process of the TL-ADMM algorithm, after the inner iteration converges, if the outer layer has not obtained the global optimal solution, the penalty term coefficient finally updated in the previous inner loop is used as the initialization value for the subsequent inner iteration.

[0015] Further, in step S1, the system voltage optimization mathematical model includes an objective function and constraint conditions, and its objective function is:

[0016]

[0017] Where: is the set of system nodes, including the grid-connected side nodes and the substation side nodes V i :=[V1,…,V n is a column vector composed of node voltage amplitudes; V ref is a column vector composed of node reference voltage amplitudes, ||*||2 is the vector 2-norm; ":=" means definition, to distinguish it from "=" in the equality constraint formula;

[0018] The constraint conditions include the power flow constraints on the substation side and the grid-connected side, the node power balance constraints on the substation side, and the node voltage constraints on the substation side;

[0019] The power flow constraints on the substation side and the grid-connected side are:

[0020]

[0021] In the formula, P i , Q i are the active power and reactive power injected by node i; V i , V j are the voltage amplitudes of nodes i and j; r ij , x ij are the real part and imaginary part of the line impedance between nodes i and j; k T is the transformer turns ratio on the branch. For a branch without a transformer, k T equals 1; P ij , Q ij are the active power and reactive power flowing from node i to node j; P fi , Q fi are the active power and reactive power flowing from node f to node i; is the set of system branches;

[0022] The node power balance constraints on the substation side are:

[0023]

[0024] In the formula, P i,PVGU , Q i,PVGU are the active and reactive powers output by the PVGU at node i; P i,MPPT is the maximum power point tracking power available at the PVGU at node i; S i,PVGU is the maximum rated apparent power of the PVGU;

[0025] The voltage constraint of the collector side node is as follows:

[0026]

[0027] In the formula, V i is the voltage amplitude of node i; V i,min , V i,max respectively represent the minimum and maximum limits of the voltage amplitude during the safe operation of the system.

[0028] Furthermore, in step S3, the constraint conditions further include a coupling constraint:

[0029]

[0030] In the formula, P PCC,G , Q PCC,G , V PCC,G are respectively the active power, reactive power, and voltage amplitude of the boundary node on the grid-connected side PCC bus; P k,PCC,C , Q k,PCC,C , V k,PCC,C are respectively the active power, reactive power, and voltage amplitude of the boundary node on the PCC bus of the kth collector line side; is the number of collector lines inside the renewable energy power station.

[0031] Furthermore, the boundary nodes P k,PCC,C , Q k,PCC,C , V k,PCC,C on the grid-connected side PCC bus are decomposed:

[0032]

[0033] In the formula, P k,PCC,G , Q k,PCC,G , V k,PCC,G are the active power, reactive power, and voltage amplitude of the boundary node on the virtual grid-connected side PCC bus for coupling with the kth collector side line.

[0034] Furthermore, in step S3, the distributed optimization model includes the distributed voltage optimization problems of the grid-connected side subsystem and the collector side subsystem. Among them, the distributed voltage optimization problem of the grid-connected side subsystem is:

[0035]

[0036] The distributed voltage optimization problem of the collector side subsystem is:

[0037]

[0038] and are the optimization objective functions of the grid-connected side subsystem and the collector side subsystem respectively, and are the augmented Lagrangian functions associated with the distributed voltage optimization problems of the grid-connected side subsystem and the collector side subsystem respectively, and each contains an augmented multiplier term and

[0039] Furthermore, under TL-ADMM, the augmented multiplier terms and are:

[0040]

[0041] In the formula, X k,G and X k,C are the original centralized model variables contained in the grid-connected side subsystem and the collector line side subsystem respectively; and are and under TL-ADMM; λ k,G and λ k,C are the dual multiplier vectors corresponding to the k-th virtual coupling node on the grid-connected side and the k-th collector side coupling node respectively; Diag is the vector diagonalization operator; ρ is the penalty term coefficient; is the global replication variable of the boundary coupling variables of the grid-connected side subsystem and the collector line side subsystem after copying the boundary nodes, β is the outer penalty term coefficient; η k,G and η k,C represent the outer dual multiplier vectors corresponding to solving the grid-connected side sub-optimization problem and the collector side sub-optimization problem respectively; Z k,G and Z k,C represent the local relaxation variable vectors corresponding to solving the grid-connected side sub-optimization problem and the collector side sub-optimization problem respectively.

[0042] Furthermore, during the TL-ADMM solution process, the global replication variable and the local relaxation variable are updated as follows:

[0043]

[0044] Among them, Proj is the projection operator to ensure that the obtained global replication variables are all within a convex set, ensuring that each step of calculation converges to the global optimal direction; (*) (t) represents the t-th iteration index of the inner layer of TL-ADMM; (*) {n} represents the n-th iteration index of the outer layer of TL-ADMM; represents the number of couplings of the k-th virtual node in the subsystem with the main system.

[0045] Furthermore, after each inner-layer convergence, each sub-Agent will store its respective local relaxation variables after the last iteration update of each inner layer, which are used to update the outer-layer dual multiplier term and the outer-layer penalty term coefficient of its own Agent:

[0046]

[0047] In the formula, c is a constant used to adjust the size of β.

[0048] Furthermore, the inner-layer convergence criterion of TL-ADMM is:

[0049]

[0050] The outer-layer convergence criterion of TL-ADMM is:

[0051]

[0052] In the formula, ω and ε are both constants used to adjust the corresponding convergence criterion thresholds; BlkDiag represents matrix block diagonalization; Er1, Er2, and Er3 are the thresholds corresponding to the convergence criteria respectively.

[0053] Furthermore, under TL-ADMM, the weight of the voltage deviation term in the objective function is increased, and the growth of the outer-layer penalty coefficient is controlled by the smoothing harmonic term. The adjusted objective function is:

[0054]

[0055] In the formula, a is a smoothing harmonic parameter used to adjust the smoothness of the growth process of the outer-layer penalty term coefficient; h is a harmonic factor, and P is a k,PCC,C matrix of all ones with the same number of rows and columns as V, and all elements in the matrix are 1.

[0056] In summary, the present invention has the advantages of good convergence and optimality, and the obtained voltage optimization results can effectively ensure the voltage safety of the photovoltaic power station system. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is an analysis model for the grid connection of a large-scale photovoltaic power station system.

[0058] Figure 2 is the distributed communication system architecture for distributed voltage optimization of a large-scale photovoltaic power station.

[0059] Figure 3 is a schematic diagram of the decomposition of a large-scale photovoltaic power station system.

[0060] Figure 4 is the implementation process of the TL-ADMM algorithm.

[0061] Figure 5 is the in-station power flow calculation error under LinDistflow constraints.

[0062] Figure 6 is the comparison chart of convergence speeds under different outer levels.

[0063] Figure 7 is the comparison chart of the convergence processes of TL-ADMM and E-TL-ADMM.

[0064] Figure 8 is the comparison chart of the convergence speeds of E-TL-ADMM and traditional ADMM under two scenarios.

[0065] Figure 9 is the comparison chart of the optimization results in Scenario 1.

[0066] Figure 10 is the comparison chart of the optimization results in Scenario 2. Specific implementation manners

[0067] The present invention will be further described in detail below in conjunction with embodiments.

[0068] 1. Grid connection analysis model of a large-scale photovoltaic power station system and non-convex voltage optimization mathematical model.

[0069] The grid connection analysis model of a large-scale photovoltaic power station system is as Figure 1 shown: The model is divided into a collector side and a grid connection side. The inside of the large-scale photovoltaic power station system is called the collector side. Multiple medium-voltage collector lines on the collector side are connected in parallel at the PCC bus. Further, multiple photovoltaic generation units (PVGUs) are connected in parallel on each medium-voltage collector line. The electric energy produced by all PVGUs inside the large-scale photovoltaic power station system is gathered at the PCC bus. The grid connection side includes a step-up substation, a high-voltage transmission line, and a receiving-end AC power grid. The electric energy gathered at the PCC bus is stepped up by the substation and finally transmitted over a long distance through the high-voltage transmission line to the receiving-end AC power grid. The PCC bus is the coupling link between the collector side and the grid connection side. It is worth mentioning that the tap position adjustment of the step-up substation is not included in the optimization problem in the grid connection analysis model of this embodiment. The reason is that the response speed of the tap adjustment of the step-up substation is much lower than the response speed of the output power adjustment of the PVGU, and considering the influence of service life factors, it should not act frequently. Therefore, in the grid connection analysis model of the system established in this embodiment, the tap position of the step-up substation is regarded as a fixed value.

[0070] In the above-mentioned large-scale photovoltaic power station system topology, the steady-state power-voltage relationship between the collector side and the grid-connection side can be analyzed using an impedance model. The following assumptions are made for the collector side: 1) Consider the impedance parameters of each medium-voltage collector line; 2) Without loss of generality and accuracy, ignore the converter losses inside the PVGU. Therefore, the coupling nodes between each PVGU and the collector line are regarded as PQ nodes, and the injected power at the corresponding nodes is the output power of the PVGU. The following assumptions are made for the grid-connection side: 1) The step-up substation is an ideal transformer; 2) The relevant parameters of the long-distance transmission line and the remote AC grid are characterized by the Thevenin equivalent impedance and voltage; 3) When analyzing the voltage inside the renewable energy power station system, regard the remote AC grid as a balanced node.

[0071] Considering the operation characteristics of the large-scale photovoltaic power station of "large-scale topology and weak grid connection": For the grid-connection side outside the system, since large-scale photovoltaic power stations are usually far from the load center, the long-distance transmission lines for power transmission outwards make the system generally connected to a weak grid environment, and the Thevenin equivalent impedance of the grid-connection side is large; for the collector side inside the system, the large-scale photovoltaic power station covers a large area, and the medium-voltage collector lines connecting between each PVGU are long, and the line impedance is also large. Therefore, when the large-scale photovoltaic power station conducts large-scale power transmission outwards, the power loss on the line impedance is large, and the impact on the system voltage distribution cannot be ignored.

[0072] System voltage optimization mathematical model: The system voltage optimization mathematical model of the large-scale photovoltaic power station system involves two parts: the objective function and the constraints.

[0073] The large-scale photovoltaic power station system should ensure that each node voltage has as much voltage amplitude safety margin as possible, so as to avoid overvoltage exceeding the limit in the case of system node voltage deviation caused by the output fluctuation of the PVGU. The corresponding objective function is as follows:

[0074]

[0075] Where: is the set of system nodes, which includes the grid-connection side nodes and the collector side nodes V i :=[V1,…,V n is the column vector composed of the node voltage amplitudes; V ref is the column vector composed of the node reference voltage amplitudes, usually set to 1 p.u.; each element in the vector is set to the per-unit value of 1 p.u.; ||*||2 is the vector 2-norm; ":=" means definition, to distinguish it from the "=" in the equality constraint formula.

[0076] The constraint conditions include the power flow constraints on the collector side and the grid connection side, the node power balance constraints on the collector side, and the node voltage constraints on the collector side. Specifically, in the large-scale photovoltaic power station system, there are problems such as large impedance and high power loss in both internal and external lines. In this case, the power flow calculation error brought by the linearized LinDistflow power flow constraint cannot be ignored, which will significantly reduce the effectiveness of voltage optimization decision-making. To ensure the decision-making accuracy, in this embodiment, the standard DistFlow power flow model will be adopted to construct the power flow constraints on the collector side and the grid connection side:

[0077]

[0078] where: P i , Q i are the active power and reactive power injected into node i; V i , V j are the voltage amplitudes of nodes i and j; r ij , x ij are the real part and imaginary part of the line impedance between nodes i and j; k T is the transformer turns ratio on the branch. For a branch without a transformer, k T equals 1; P ij , Q ij are the active power and reactive power flowing from node i to node j; P fi , Q fi are the active power and reactive power flowing from node f to node i; is the set of system branches.

[0079] The injection power of each node on the collector side of the large-scale photovoltaic power station system comes from PVGU. Among them, the active power output of PVGU is determined by the available maximum power point tracking power, and the reactive power output is determined by the solution result of the constructed voltage optimization model. The corresponding constraint conditions are shown in Equation (4):

[0080]

[0081] where: P i,PVGU , Q i,PVGU are the active and reactive powers output by PVGU on node i; P i,MPPT is the available maximum power point tracking power of PVGU on node i, which is regarded as a fixed value; S i,PVGU is the maximum rated apparent power of PVGU.

[0082] The amplitude of the collector side node voltage should meet the corresponding constraints, as follows:

[0083]

[0084] where: V iis the voltage amplitude of node i; V i,min and V i,max respectively represent the minimum and maximum limits of the voltage amplitude during the safe operation of the system.

[0085] II. Construction of the Distributed Communication Architecture and Distributed Voltage Optimization Problem of a Large-Scale Photovoltaic Power Station

[0086] As the conditional basis for the distributed voltage optimization of the system, first, according to the structural characteristics of the large-scale photovoltaic power station, a distributed communication architecture suitable for its characteristic requirements will be constructed. Then, combined with this communication architecture, the original centralized voltage optimization problem will be split to construct a distributed voltage optimization problem.

[0087] Distributed communication architecture: The traditional centralized communication is a "point-to-point" communication method. For renewable energy power stations, if the centralized communication method is adopted, it is necessary to rely on the central controller to establish communication connections with each PVGU unit. However, with the large-scale development of large-scale photovoltaic power stations, the installed capacity expands rapidly, and the number of PVGU units will increase significantly. As the central node, the central controller will face huge information processing pressure and it is difficult to handle a large number of PVGU unit control requests. Considering the disadvantages of centralized communication and the in-station cluster structure characteristics of large-scale photovoltaic power stations, splitting the original system into multiple subsystems and only performing adjacent distributed communication between the Agent controllers of each subsystem is more suitable for the scenario of this embodiment.

[0088] The distributed communication architecture adopted in this embodiment is as Figure 2 shown: Distributed Agent controllers are configured on the PCC busbar and each collector line in the station. Each PVGU on the collector line is uniformly regulated by the collector line Agent controller, and boundary information is mutually transmitted between each collector line Agent and the PCC busbar Agent. This distributed communication method performs zonal regulation on the in-station collector lines, rather than configuring a separate Agent for each PVGU for regulation, thus avoiding the problem of slow computational convergence caused by excessive Agent configuration.

[0089] Distributed voltage optimization problem: According to the Figure 2 shown distributed communication architecture, the large-scale photovoltaic power station is split in the manner as Figure 3 shown. By replicating the PCC busbar, the original system is decomposed into a grid-connected side subsystem and several collector side systems. At this time, the coupling constraint of formula (5) needs to be added:

[0090]

[0091] Where: P PCC,G and Q PCC,G and V PCC,Gare the active power, reactive power, and voltage amplitude of the boundary node on the grid-connected side PCC bus; P k,PCC,C , Q k,PCC,C , V k,PCC,C are the active power, reactive power, and voltage amplitude of the boundary node on the PCC bus of the k-th collector line side. is the number of collector lines inside the renewable energy power station.

[0092] To better achieve the coupling constraint of Equation (5), the boundary node P on the grid-connected side PCC bus k,PCC,C , Q k,PCC,C , V k,PCC,C is decomposed again:

[0093]

[0094] where: P k,PCC,G , Q k,PCC,G , V k,PCC,G are the active power, reactive power, and voltage amplitude of the boundary node on the virtual grid-connected side PCC bus for coupling the k-th collector side line.

[0095] Through the two decompositions of Equation (5) and Equation (6), Equation (7) is finally obtained:

[0096]

[0097] Furthermore, the centralized optimization model corresponding to Equations (1)-(5) can be extended to the following distributed optimization model:

[0098]

[0099] where: Equation (8) and Equation (9) are the distributed voltage optimization problems corresponding to the grid-connected side subsystem and the k-th collector line side subsystem respectively; and are the decomposed optimization objective functions respectively. According to the original optimization objective shown in Equation (1), it can be known that is empty; and are the augmented Lagrangian functions associated with their respective optimization problems, which contain the augmented multiplier terms and III. Distributed solution of the non-convex voltage optimization problem of enhanced TL-ADMM.

[0100] Compare the distributed optimization solution processes of the novel TL-ADMM algorithm and the classical ADMM algorithm, and demonstrate the key points when applying the TL-ADMM algorithm to solve the non-convex voltage optimization model proposed in this embodiment. The TL-ADMM algorithm still faces some challenges in dealing with the standard Distflow power flow constraints, especially in terms of convergence and optimality. To address these issues, this embodiment proposes an improved algorithm, E-TL-ADMM. By deeply analyzing the deficiencies of TL-ADMM in dealing with Distflow power flow constraints and introducing optimization measures, E-TL-ADMM overcomes the limitations of TL-ADMM in convergence and optimality, thus significantly improving the convergence speed and stability.

[0101] TL-ADMM and ADMM have similar distributed iterative processes, that is, by means of alternating directions, the Lagrange multipliers are iteratively updated. However, there are differences in the construction of the augmented Lagrangian function between the two methods. In addition, TL-ADMM also introduces local relaxation variables to promote global convergence. More importantly, TL-ADMM adopts a structure of inner and outer nested loops, which enables it to effectively separate the calculations of the inner and outer levels when solving distributed non-convex optimization problems, thereby enhancing the stability and efficiency of the algorithm. Inside the inner loop, TL-ADMM adjusts local variables through local optimization, while the outer loop is responsible for coordinating the update of global information to gradually approach the global optimal solution. This two-layer structure not only enhances the ability of TL-ADMM to handle complex constraint problems but also optimizes the solution process of large-scale problems. To better elaborate on the characteristics and advantages of TL-ADMM, first introduce the distributed optimization solution process of ADMM, and then further elaborate on the distributed optimization solution process of TL-ADMM, especially the advantages of its inner and outer nested loop structure.

[0102] ADMM distributed optimization solution: The sub-optimization problems on the grid-connected side and the collector side under ADMM are constructed according to Equations (8) and (9). In particular, and are written in the following form:

[0103]

[0104] where: X k,G and X k,C are the original centralized model variables included in the grid-connected side subsystem and the collector line side subsystem, respectively; and are the auxiliary variables generated in the grid-connected side subsystem and the collector line side subsystem, respectively, after replicating the boundary nodes; and specifically refer to and Expression under ADMM; λ k,G and λ k,C are the dual multiplier vectors corresponding to the k-th virtual coupling node on the grid-connected side and the k-th collector-side coupling node respectively; ρ is the penalty coefficient; (*)' represents the replicated variable of the boundary coupling variable; represents the fixed values of the optimization variables, global replicated variables, and local relaxation variables under the current distributed optimization; is the vector transpose symbol.

[0105] ADMM realizes distributed optimization by alternately solving equations (10) and (11). The key dual multiplier terms are updated by the gradient ascent method, and the iterative formula is as follows:

[0106]

[0107] where: (*) [n] specifically refers to the optimization result after the n-th iteration.

[0108] The convergence of ADMM can be determined by the dual residual ε D and the primal residual ε P The definitions are as follows:

[0109]

[0110] TL-ADMM distributed optimization solution: The grid-connected side and collector-side sub-optimization problems under TL-ADMM are also constructed according to equations (10) and (11). However, different from equations (10) and (11), and The expressions are as follows:

[0111]

[0112] where: and specifically refer to and The expressions under TL-ADMM; Diag is the vector diagonalization operator; different from ADMM, in the grid-connected side and collector-side sub-optimization problems shown in (14) and (15), the auxiliary variables and obtained by replicating the boundary nodes in ADMM become the global replicated variables of the boundary coupling variables In addition, in TL-ADMM, an outer penalty coefficient β, an outer dual multiplier term vector, and local relaxation variables are added. η k,G and η k,C respectively represent the outer dual multiplier vectors corresponding to solving the grid-connected side sub-optimization problem equation (14) and the collector-side sub-optimization problem equation (15); Z k,Gand Z k,C respectively represent the corresponding local relaxation variable vectors when solving the grid-connected side sub-optimization problem in Equation (14) and the collector side sub-optimization problem in Equation (15).

[0113] TL-ADMM realizes distributed optimization by alternately solving (14) and (15). Among them, the key global replication variables and local relaxation variable updates are shown in Equation (16):

[0114]

[0115] where Proj is a projection operator, whose purpose is to ensure that the obtained global replication variables are all within a convex set, so as to ensure that each step of calculation converges in the direction of the global optimum; (*) (t) Specifically represented as the index of the t-th iteration in the inner layer of TL-ADMM; (*) {n} Specifically represented as the index of the n-th iteration in the outer layer of TL-ADMM; represents the number of couplings of the subsystem with the k-th virtual node of the main system.

[0116] Each Agent updates its respective inner-layer dual multiplier term by obtaining the above-mentioned updated global replication variables and local relaxation variables, as follows:

[0117]

[0118] After each inner-layer convergence, each sub-Agent will store the local relaxation variables updated at the last iteration of each inner layer for updating its own Agent's outer-layer dual multiplier term and outer-layer penalty term coefficient, as follows:

[0119]

[0120] where: c is a constant to adjust the size of β.

[0121] Since TL-ADMM has an inner and outer nested loop structure, different from the convergence condition shown in Equation (13) in traditional ADMM, TL-ADMM has specific convergence conditions. Its inner-layer convergence criterion is composed of the following Equation (19) and Equation (20), and the outer-layer convergence criterion is composed of the following Equation (21), as follows:

[0122]

[0123] where: ω and ε are both constants used to adjust the corresponding convergence criterion thresholds; BlkDiag represents matrix block diagonalization; Er1, Er2, and Er3 are the thresholds corresponding to the convergence criteria in Equation (19), (20), and (21), respectively.

[0124] Generally speaking, both TL-ADMM and ADMM handle the boundary coupling constraints of the PCC bus in the centralized voltage optimization problem through the augmented term in distributed optimization, and the splitting ideas are the same. The difference is that ADMM gradually approaches the optimal solution by artificially convexifying the non-convex sub-problem; while TL-ADMM introduces local relaxation variables and global replication variables, and directly solves the non-convex sub-problem by means of three-block splitting. In the inner iteration, the local and global variables are alternately updated to reach a consensus, efficiently solving the sub-problem and accelerating the outer-layer convergence; in the outer layer, the global optimum is gradually approached through the ADMM framework to ensure convergence and consistency. The collaborative optimization of the inner and outer layers enables TL-ADMM to exhibit higher efficiency and reliability in solving non-convex optimization problems. This ensures the global convergence of TL-ADMM when dealing with non-convex optimization problems. The implementation process of TL-ADMM is as Figure 4 shown.

[0125] The TL-ADMM algorithm has a unique two-layer architecture, which means that during the solution process, global convergence usually requires multiple repetitions of the inner convergence loop, thus significantly increasing the overall number of calculations and time costs. In addition, the characteristics of its outer-layer architecture make the weight parameter of the outer-layer penalty term play a key role. When the penalty term coefficient is large, it may lead to too strong dependence on the penalty parameter, which in turn has an adverse effect on the robustness and convergence performance of the algorithm. Therefore, in practical applications, reasonably adjusting the penalty term coefficient and weight parameter becomes the key to improving the algorithm efficiency and stability. Next, this embodiment will further improve TL-ADMM from two aspects: the convergence of the distributed optimization process and the optimality of the results, so as to form the E-TL-ADMM (Enhanced TL-ADMM, E-TL-ADMM) method.

[0126] Improvement of the convergence of distributed optimization solution: During the process of solving the TL-ADMM framework, after the inner iteration converges, if the global optimum has not been obtained in the outer layer, the penalty term coefficient finally updated in the previous inner loop will be used as the initialization value for subsequent inner iterations. This mechanism can significantly reduce the number of inner iterations, thus accelerating the quadratic convergence process of the inner layer.

[0127] Improvement of the optimality of distributed optimization results: The optimized result of the improved TL-ADMM algorithm still does not reach the optimal level of the centralized algorithm, and there is a possibility of voltage falling below the lower limit. Analysis shows that the problem mainly stems from the design of the TL-ADMM framework. Compared with the traditional ADMM, the two-layer structure of TL-ADMM makes the outer-layer penalty term coefficient larger, while the weight of the voltage deviation optimization term in the objective function is lower, resulting in too high dependence on the penalty term coefficient and causing voltage optimization deviation.

[0128] To this end, a harmonic factor is introduced in this embodiment for optimization and coordination: on the one hand, by increasing the weight of the voltage deviation term in the objective function, its optimization influence is enhanced; on the other hand, by smoothing the harmonic term to control the growth of the outer penalty coefficient, its dependence is reduced. The two complement each other, not only improving the accuracy of the optimization result but also balancing the convergence speed. The improved objective function can express equations (2), (11), and (12) as:

[0129]

[0130] where: a is the smoothing harmonic parameter, which can adjust the smoothing degree of the growth process of the outer penalty term according to system requirements; h is the harmonic factor, and its value needs to be selected according to the actual problem; P is a all-one matrix with the same number of rows and columns as V k,PCC,C (that is, all elements in the matrix are 1).

[0131] IV. Numerical Experiment Analysis

[0132] In this embodiment, a large-scale photovoltaic power station system with an installed capacity of 3×10×2 MW is used for example analysis to verify the effectiveness of the proposed method. The system parameters are shown in Table 1 in detail. The relevant programs of the example are compiled in the MATLAB 2019b version environment. The non-convex voltage optimization mathematical model of the large-scale photovoltaic power station based on the E-TL-ADMM algorithm is implemented with the help of the yalmip framework; all non-convex sub-optimization problems on the grid-connected side and the collector side are solved using the IPOPT solver. The Newton-Raphson power flow calculation involved in the example analysis is implemented using the MATPOWER toolbox and regarded as the benchmark result of the power flow calculation. The centralized optimization result is obtained by directly solving the non-convex voltage optimization model shown in equations (3)-(6) and regarded as the benchmark result of voltage optimization. All the above-mentioned programs are executed on a computer configured with a 1.8-GHz CPU / 8GB RAM.

[0133] Table 1 Relevant parameters of the large-scale photovoltaic power station system

[0134]

[0135] The structure of this section is as follows: First, by comparing the calculation results of the standard Distflow power flow model and the LinDistflow model, the necessity of establishing a non-convex voltage optimization model for voltage regulation of large-scale photovoltaic power stations is verified. Then, the significant improvement of E-TL-ADMM formed after the improvement of TL-ADMM in terms of convergence speed and optimality of the solution result is analyzed, demonstrating its faster convergence efficiency and better optimization effect. By comparing the distributed iteration times of ADMM and E-TL-ADMM, the convergence advantage of E-TL-ADMM in non-convex optimization problems is verified. Finally, by comparing the voltage optimization results under different methods, the optimality of the solution of E-TL-ADMM is verified.

[0136] Analysis of the necessity of the non-convex voltage optimization model: To verify the necessity of establishing a non-convex voltage optimization model by adopting non-convex Distflow power flow constraints in a large-scale photovoltaic power station system, this subsection specifically analyzes the power flow calculation error of the system based on the linearized power flow constraint LinDistflow. Since the non-convex voltage optimization model proposed in this embodiment adopts non-linear standard Distflow constraints and the power flow calculation results are consistent with the reference values, there is no need for special comparison.

[0137] When the linearized power flow constraint LinDistflow is used to replace the non-linear standard Distflow power flow constraint, it will affect the accuracy of the power flow calculation of the collector lines in the large-scale photovoltaic power station system. In the case study, the active power output of each PVGU is set to 1.6 MW and the reactive power is set to 0 MVar. To avoid unnecessary errors, centralized solution is adopted here.

[0138] As Figure 5 shown in the results, as the scale of the photovoltaic power station system continues to expand, the error of the LinDistflow power flow model in the power flow calculation of the collector lines accumulates gradually. When the number of PVGUs connected to each collector line reaches 14, its power error exceeds 10% at most, which indicates that the power flow model based on LinDistflow is no longer applicable at this time. This error not only affects the accuracy of the power flow calculation, but also causes the voltage optimization result to deviate from the true value, seriously threatening the operation reliability of the system.

[0139] In contrast, by retaining the non-linear terms in the power flow equation, the non-linear Distflow power flow model can capture the power loss and reactive power distribution characteristics in the line more accurately. In the scenario of high proportion of renewable energy access, the non-linear Distflow model shows better calculation accuracy. Especially in the case where the collector line is long or far from the load center, its prediction ability for power and voltage is significantly better than the linearized model. Therefore, introducing the non-linear Distflow model to optimize the voltage control of large-scale photovoltaic power stations can not only effectively reduce the voltage deviation caused by the power flow calculation error, but also better adapt to the complex power grid environment and improve the reliability and accuracy of the optimization results.

[0140] Verification of the improvement of distributed optimization performance based on E-TL-ADMM: To explore the improvement effect of E-TL-ADMM compared with TL-ADMM in distributed optimization solution, this experiment focuses on analyzing its performance in two aspects: solution convergence and optimality of the optimization result. The specific parameters of the experiment are shown in Table 1.

[0141] First, to more deeply analyze the improvement effect of E-TL-ADMM on the convergence of distributed optimization solutions, the cases where the number of outer iterations is set from 1 to 5 are considered, and the parameters of the inner penalty term coefficient and the outer penalty term coefficient are fixed, which are ρ = 5 and β = 400 respectively, and the harmonic factor h = 20. The focus is on analyzing the acceleration effect of E-TL-ADMM compared with TL-ADMM during the convergence process. The comparison of the number of iterations after convergence of the algorithms before and after the improvement is as Figure 6 shown. The numerical experimental results show that when the number of outer iterations is greater than 2, the total number of inner iterations required by E-TL-ADMM is significantly less than that of TL-ADMM, and the convergence speed of the algorithm is greatly improved. For the solution of the optimization model in this embodiment, it is found through experiments that when the number of outer iterations reaches 3 times, the algorithm usually achieves global convergence, that is, a better optimization result is obtained, and the final result is output.

[0142] In addition, by analyzing the convergence process of the two convergence criterion judgment formulas in the inner iteration, the acceleration effect of E-TL-ADMM can be more intuitively understood. Here, in order to better describe the convergence process, the criterion formulas in Eqs. (19), (20), and (21) are represented by Err1, Err2, and Err3 respectively. Figure 7 shows the differences in the inner iteration processes of TL-ADMM and E-TL-ADMM when the number of outer iterations is 3 and the penalty coefficient ρ = 5. From Figure 7 the results, it can be seen that both algorithms complete the first outer update at the 11th iteration. However, TL-ADMM completes the second outer iteration at the 23rd iteration, while E-TL-ADMM only needs the 14th iteration to complete the second iteration. Finally, TL-ADMM completes the third outer iteration at the 35th iteration, while E-TL-ADMM only needs the 15th iteration to complete. This shows that the number of iterations and time required by E-TL-ADMM in each outer update gradually decrease, showing a significant acceleration effect.

[0143] During the inner iteration process, the convergence processes of TL-ADMM and E-TL-ADMM are the same in the first round of inner iteration updates, but in subsequent inner iteration updates, the two gradually show differences. TL-ADMM resets the penalty term coefficient after each outer update, and this initialization method leads to a sudden increase in the initial residual at the beginning of a new round of inner iteration, that is, the initial error is large and then gradually converges. While E-TL-ADMM adopts the strategy of using the penalty term coefficient after the previous round of update as the initialization value, which significantly reduces the sudden increase effect of the initial residual and makes the inner error curve smoother. This improvement effectively shortens the time required for the inner quadratic convergence, thus greatly improving the overall convergence efficiency.

[0144] In addition, in order to more comprehensively analyze the improvement effect of E-TL-ADMM on the optimality of optimization results, this study selected the optimization results with an outer iteration number of 3 for verification. In this experiment, h is set to 20, and the optimality of the E-TL-ADMM optimization results is verified by comparing the voltage results under distributed optimization and centralized optimization, as shown in Table 2.

[0145] Table 2 Comparison of voltage results between distributed optimization and centralized optimization

[0146]

[0147] As can be seen from Table 2, the relative error of TL-ADMM relative to the centralized optimization result is as high as 3.93%, while the maximum relative error of E-TL-ADMM relative to the centralized optimization result does not exceed 0.1%. This also shows that the E-TL-ADMM algorithm has been significantly improved in the problem of objective function conflict, which fully verifies the effectiveness of the improved strategy.

[0148] In summary, E-TL-ADMM not only shows faster convergence speed in both inner and outer layer iterations, but also further optimizes the coordination of the objective function by introducing the reconciliation factor, thereby achieving better distributed voltage control and significantly enhancing the efficiency and optimality of the algorithm.

[0149] In other words, compared with the TL-ADMM algorithm, E-TL-ADMM can more efficiently regulate the voltage of distributed large-scale photovoltaic power stations, helping distributed large-scale photovoltaic power stations to operate safely and stably.

[0150] Verification of the convergence advantage of E-TL-ADMM distributed voltage optimization: This section analyzes the convergence of the E-TL-ADMM proposed in this embodiment and the traditional ADMM when solving the non-convex voltage optimization model. In the distributed optimization process, the initialization value of the electrical boundary coupling information involved is uniformly set to 0, and the initial value of the Lagrange multiplier is 1. The traditional ADMM sets the convergence threshold through the original residual and the dual residual to determine whether it converges. However, due to the particularity of the E-TL-ADMM algorithm framework, the convergence judgment basis of its inner and outer layers are shown in (19), (20) and (21), respectively.

[0151] During the E-TL-ADMM solution process, Err1 and Err2 are used as the inner-layer convergence criteria. If one of the convergence conditions is met, it is determined to be convergent, and the latest electrical coupling information after inner-layer convergence is passed to the outer layer for subsequent calculations. Among them, Err2 reflects the error between the local sub-problem and global consistency, and also reflects the stability of the convergence process. The smaller its value, the more stable the convergence process, and the better the global convergence effect. Its role is similar to the dual residual in traditional ADMM. Err3 is used as the outer-layer convergence determination condition, indicating the coupling degree between the coupling variables and global variables in each independent subsystem. The smaller the value, the better the global coupling effect. Its role is similar to the primal residual in traditional ADMM. Since the calculation and storage frequency of Err3 is relatively low, it is not possible to directly compare and analyze it with the primal residual in ADMM. The convergence of the traditional ADMM algorithm mainly depends on the threshold accuracy settings of the dual residual and the primal residual. A lower threshold accuracy usually can accelerate the convergence process, but may lead to a poor coupling effect; on the contrary, a higher threshold accuracy will slow down the convergence speed, but can improve the quality of the coupling effect in the distributed system. Usually, the accuracy settings of the dual residual and the primal residual in the traditional ADMM algorithm are set to the conventional value of 1×10 -4 (assuming that the residual of the boundary voltage term should be less than 0.0001 p.u., and the residual of the boundary power term should be less than 0.01 MW. Considering the voltage deviation range of ±0.05 p.u. and the total installed capacity of the system at the gigawatt level, this convergence condition is reasonable). It should be noted that ADMM realizes strong coupling between variables through direct information interaction, while E-TL-ADMM realizes auxiliary coupling by introducing global replication variables. Therefore, there are significant differences in the performance of the residuals and the coupling characteristics during the convergence process between the two. Directly comparing the convergence processes of the two may not be entirely applicable.

[0152] Since the convergence processes of the two algorithms cannot be directly compared, in this embodiment, it is proposed to verify the convergence advantage by uniformly setting the accuracy and comparing the number of iterations required for the convergence of the traditional ADMM and E-TL-ADMM algorithms. In addition, due to the special nature of the E-TL-ADMM algorithm framework, after the output of the third iteration in the outer layer, the updated accuracy of Err3 is 1×10 -6 , and the setting of the corresponding Er3 threshold accuracy is meaningless. Therefore, in the numerical experiment of this embodiment, the threshold accuracies of Err2 and the dual residual are mainly unified. However, in order to better compare the convergence advantage of the E-TL-ADMM algorithm, in this embodiment, the convergence situation of the traditional ADMM under the conventional threshold accuracy and the equal threshold accuracy (the threshold accuracy settings of the dual residual and the primal residual are the same as those of Err2 and Err3, that is, the threshold accuracy of the dual residual is 1×10 -4 , and the threshold accuracy setting of the primal residual is the same as the accuracy after the third update of Err3, that is, 1×10 -6) The convergence of the traditional ADMM is compared with that of the E-TL-ADMM respectively. The following are two precision scenarios set for numerical experiment comparison:

[0153] Scenario 1: The role of Err2 is similar to the dual residual in the traditional ADMM algorithm. To maintain the principle of consistency in comparison, the threshold precision of both Err2 and the dual residual is set to 1×10 -4 ; The role of Err3 is similar to the primal residual in the traditional ADMM algorithm. As the outer convergence criterion, after the third iteration output of the outer layer, its precision reaches 1×10 -6 . This precision value cannot be adjusted because it is calculated based on the information passed from the inner layer to the outer layer. To make the comparison experiment more fair, the primal residual of the traditional ADMM algorithm is still set to the conventional threshold precision, which is 1×10 -4 , to compare the number of iterations of the E-TL-ADMM algorithm and the traditional ADMM algorithm with the conventional threshold precision for the calculation of the distributed large-scale photovoltaic power station voltage optimization control mathematical model.

[0154] Scenario 2: Usually, the threshold precision settings of the dual residual and the primal residual in the traditional ADMM algorithm directly affect the coupling degree of the boundary electrical information in the distributed large-scale photovoltaic power station voltage optimization control mathematical model. To more comprehensively compare the convergence performance of the E-TL-ADMM algorithm and the traditional ADMM algorithm under the same coupling degree, the threshold precision of the traditional ADMM dual residual and the primal residual is set to be consistent with the Er2 threshold precision and the Err3 precision of the E-TL-ADMM, that is, to compare the number of iterations of the E-TL-ADMM algorithm and the traditional ADMM algorithm with equal threshold precision for the calculation of the distributed large-scale photovoltaic power station voltage optimization control model.

[0155] In this experiment, the value range of ρ is selected as [5 - 30] with a step size of 5. The numerical experiment results in the above two scenarios are as Figure 8 shown, and the following conclusions are drawn:

[0156] 1) As can be seen from Figure 8 (a), in Scenario 1, the convergence speed of the traditional ADMM is better than that of the E-TL-ADMM. This shows that when solving the distributed non-convex voltage optimization model proposed in this embodiment, the traditional ADMM has a better speed advantage under the conventional threshold precision.

[0157] 2) From Figure 8As can be seen from (b), in Scenario 2, when ρ = 5, the convergence speeds of the two algorithms are similar. However, in the subsequent range of ρ values, the E-TL-ADMM has a faster convergence speed. This indicates that the E-TL-ADMM algorithm has a better speed advantage in solving the distributed non-convex voltage optimization model of this embodiment under the equal threshold accuracy.

[0158] However, the dual residual reflects the error between the local sub-problem and the global consistency. Although the traditional ADMM shows a faster convergence speed under the conventional threshold accuracy, due to its dual residual threshold accuracy being lower than that of Er3, this may lead to a poor accuracy of the final optimization result. Under the requirement of equal threshold accuracy, the E-TL-ADMM shows a faster convergence speed. This indicates that when solving the distributed non-convex voltage optimization control model, due to its unique inner and outer nested loop structure, the E-TL-ADMM can achieve convergence more efficiently and avoid the problems of premature convergence or insufficient accuracy that may exist in the traditional ADMM while maintaining high accuracy. Therefore, the application of the E-TL-ADMM in the voltage optimization control of large-scale photovoltaic power stations can significantly improve the convergence efficiency while ensuring a high computational accuracy, thus better meeting the dual requirements of optimization speed and accuracy in practical engineering.

[0159] Verification of the optimality advantage of E-TL-ADMM distributed voltage optimization: To fairly compare the optimality of E-TL-ADMM and the traditional ADMM in the distributed non-convex voltage optimization solution. In the numerical experiment, the value range of the parameter ρ is set to [5, 30] with a step size of 5. The optimization results of the two algorithms are solved respectively under the above two scenarios, and the optimization results of the two algorithms in the same scenario are compared with the centralized optimization result and the node voltage before optimization, so as to comprehensively evaluate the differences in the optimality of the voltage optimization results of the two algorithms.

[0160] From the above Figure 9 、 Figure 10 numerical experiment results, the following conclusions are drawn:

[0161] In Scenario 1, the optimization result of the E-TL-ADMM is significantly better than that of the traditional ADMM, which indicates that when solving the non-convex voltage optimization control model of the distributed large-scale photovoltaic power station in this embodiment, compared with the traditional ADMM algorithm under the conventional threshold accuracy, the former can obtain a better voltage optimization result.

[0162] In Scenario 2, the original residual threshold accuracy of the traditional ADMM is improved compared with Scenario 1, and the original residual threshold accuracy is 1×10 -6This adjustment leads to an improvement in the voltage optimization results of the traditional ADMM. This is because when the traditional ADMM solves non-convex optimization problems, the algorithm may fall into a local minimum. Improving the accuracy of the dual residual threshold of the traditional ADMM is conducive to the traditional ADMM to be more meticulous in the process of finding the optimal solution, avoiding prematurely jumping out of certain possible local minima, and thus finding a better solution. Despite this, the E-TL-ADMM still shows better optimality in this scenario, which is better than the traditional ADMM. This shows that when solving the distributed non-convex voltage optimization control model proposed in this embodiment, the E-TL-ADMM can provide more accurate voltage optimization results at the same degree of boundary information coupling. In other words, in the voltage optimization control model of distributed large-scale photovoltaic power stations, the E-TL-ADMM can achieve more reasonable voltage regulation behavior.

[0163] In summary, E-TL-ADMM has obvious advantages over the traditional ADMM algorithm when solving distributed non-convex voltage optimization control models. Specifically, E-TL-ADMM can better handle distributed non-convex optimization problems through its unique inner and outer nested loop structures and global convergence characteristics, thereby optimizing voltage regulation strategies and providing more effective guarantees for the safe and stable operation of large-scale photovoltaic power stations.

[0164] In order to solve the overvoltage risk faced by large-scale photovoltaic power stations during large-scale power transmission, this embodiment constructs a non-convex distributed optimization model for voltage control of large-scale photovoltaic power station systems, and realizes efficient distributed optimization solution of the model through the E-TL-ADMM algorithm. Combining theoretical analysis and example tests, the main conclusions are as follows:

[0165] 1) Linearized approximate power flow constraints such as LinDistFlow will cause certain errors in the voltage calculation of large-scale photovoltaic power station systems. The non-convex voltage distributed optimization model based on the standard Distflow power flow constraint established in this embodiment can provide accurate system voltage calculation results and is suitable for large-scale layout of large-scale photovoltaic power station systems and long-distance power transmission operation scenarios.

[0166] 2) Aiming at the limitations of the existing TL-ADMM algorithm in terms of convergence speed and optimization function conflict, an improvement was made and an E-TL-ADMM algorithm was proposed, which can more efficiently solve the non-convex voltage optimization model, thereby achieving the optimal decision of the reactive power output of the photovoltaic unit and optimizing the voltage distribution of the system.

[0167] 3) For the problem that the convergence and optimality are difficult to guarantee when traditional distributed optimization algorithms such as ADMM are used to solve the non-convex voltage distributed optimization model constructed in this embodiment, this embodiment proposes to use the E-TL-ADMM distributed optimization algorithm to solve the non-convex voltage distributed optimization model, and the E-TL-ADMM algorithm can obtain a better voltage regulation effect.

[0168] The reactive power output of the PVGU obtained by solving the non-convex voltage optimization model through E-TL-ADMM can effectively optimize the node voltages of the large-scale photovoltaic power station system to a quite safe range. Moreover, the implementation of the E-TL-ADMM algorithm only requires adjacent communication between each distributed Agent controller, which causes a smaller communication burden on the power station compared with the conventional centralized voltage optimization method.

[0169] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for non-convex optimization of voltage distribution in a large-scale photovoltaic power station system based on a double-layer alternating direction multiplier method framework, characterized in that It includes the following steps: S1. First, construct a system voltage optimization mathematical model for a large-scale photovoltaic power station system; S2. Based on the structural characteristics of the large-scale photovoltaic power station, construct a distributed communication architecture: configure distributed Agent controllers on the PCC bus and each collector line. The distributed Agent controller on the collector line is used to uniformly regulate the PVGUs on that collector line, and boundary information is transmitted between the distributed Agent controllers on each collector line and the distributed Agent controller on the PCC bus; S3. On the basis of the distributed communication architecture, decompose the system voltage optimization mathematical model into a distributed optimization model for the grid-connected side subsystem and the collector side subsystem by replicating the PCC bus; S4. Construct the sub-optimization problems for the grid-connected side and the collector side under TL-ADMM, and use the TL-ADMM algorithm to solve the distributed optimization model. During the solution process of the TL-ADMM algorithm, after the inner iteration converges, if the outer layer has not obtained the global optimal solution, then continue to use the penalty term coefficient finally updated in the previous inner loop as the initialization value for subsequent inner iterations.

2. The voltage distributed non-convex optimization method for a large-scale photovoltaic power station system based on the double-layer alternating direction multiplier method framework according to claim 1, characterized in that In step S1, the system voltage optimization mathematical model includes an objective function and constraint conditions, and its objective function is: Wherein: is the set of system nodes, including the grid-connected side nodes and the collector side nodes V i :=[V1,…,V n is the column vector composed of the node voltage amplitudes; V ref is the column vector composed of the node reference voltage amplitudes, ||*||2 is the vector 2-norm; ":=” means definition, to distinguish it from "=” in the equality constraint formula; The constraint conditions include the collector side and grid-connected side power flow constraints, the collector side node power balance constraint, and the collector side node voltage constraint; The collector side and grid-connected side power flow constraints are: Where, P i and Q i are the active power and reactive power injected into node i; V i and V j are the voltage amplitudes of nodes i and j; r ij and x ij are the real part and imaginary part of the line impedance between nodes i and j; k T is the transformer turns ratio on the branch. For a branch without a transformer, k T equals 1; P ij and Q ij are the active power and reactive power flowing from node i to node j; P fi and Q fi are the active power and reactive power flowing from node f to node i; is the set of system branches; The collector side node power balance constraint is: where P i,PVGU , Q i,PVGU are the active and reactive powers output by the PVGU at node i; P i,MPPT is the maximum power point tracking power available to the PVGU at node i; S i,PVGU is the maximum rated value of the apparent power of the PVGU; The collector side node voltage constraint is: where, V i is the voltage magnitude of node i; V i,min , V i,max represent the minimum and maximum limits of the voltage magnitude during the safe operation of the system, respectively.

3. The voltage distributed non-convex optimization method for a large-scale photovoltaic power station system based on the double-layer alternating direction multiplier method framework according to claim 2, characterized in that In step S3, the constraint conditions also include coupling constraints: Wherein, P PCC,G , Q PCC,G , V PCC,G are respectively the active power, reactive power, and voltage amplitude of the boundary node on the PCC bus on the grid-connected side; P k,PCC,C , Q k,PCC,C , V k,PCC,C are respectively the active power, reactive power, and voltage amplitude of the boundary node on the PCC bus on the kth collector line side; is the number of collector lines inside the renewable energy power station.

4. The non-convex optimization method for voltage distribution of a large-scale photovoltaic power station system based on the double-layer alternating direction multiplier method framework according to claim 3, characterized in that, Decompose the boundary nodes P k,PCC,C , Q k,PCC,C , V k,PCC,C on the PCC bus on the grid-connected side: Wherein, P k,PCC,G , Q k,PCC,G , V k,PCC,G are the active power, reactive power, and voltage amplitude of the boundary node on the virtual grid-connected side PCC bus for coupling with the kth collector-side line.

5. The voltage distributed non-convex optimization method for a large-scale photovoltaic power station system based on the double-layer alternating direction multiplier method framework according to claim 3, characterized in that In step S3, the distributed optimization model includes the distributed voltage optimization problems for the grid-connected side subsystem and the collector side subsystem. Among them, the distributed voltage optimization problem for the grid-connected side subsystem is: The distributed voltage optimization problem for the collector side subsystem is: and are the optimization objective functions of the grid-connected side subsystem and the collector side subsystem respectively, and are the augmented Lagrangian functions associated with the distributed voltage optimization problems of the grid-connected side subsystem and the collector side subsystem respectively, and each contains an augmented multiplier term and 6. The voltage distributed non-convex optimization method for a large-scale photovoltaic power station system based on the double-layer alternating direction multiplier method framework according to claim 5, wherein Under TL-ADMM, the augmented multiplier terms and are as follows: where X k,G and X k,C are the original centralized model variables included in the grid-connected side subsystem and the collector line side subsystem, respectively; and are the expressions of and under TL-ADMM; λ k,G and λ k,C are the dual multiplier vectors corresponding to the k-th grid-connected side virtual coupling node and the k-th collector side coupling node, respectively; Diag is the vector diagonalization operator; ρ is the penalty term coefficient; is the global replication variable of the boundary coupling variables of the grid-connected side subsystem and the collector line side subsystem after replicating the boundary nodes, β is the outer penalty term coefficient; η k,G and η k,C represent the outer dual multiplier vectors corresponding to solving the grid-connected side sub-optimization problem and the collector side sub-optimization problem, respectively; Z k,G and Z k,C represent the local relaxation variable vectors corresponding to solving the grid-connected side sub-optimization problem and the collector side sub-optimization problem, respectively.

7. The voltage distributed non-convex optimization method for a large-scale photovoltaic power station system based on the double-layer alternating direction multiplier method framework according to claim 6, characterized in that, During the TL-ADMM solution process, the update of the global replication variable and the local relaxation variable is as follows: Among them, Proj is a projection operator to ensure that the obtained global replicated variables are all within a convex set, ensuring that each step of calculation converges towards the global optimal direction; (*) (t) It is denoted as the index of the t-th inner iteration of TL-ADMM; (*) {n} It is denoted as the index of the n-th outer iteration of TL-ADMM; It represents the number of couplings in the subsystem with the k-th virtual node of the main system.

8. The voltage distributed non-convex optimization method for a large-scale photovoltaic power station system based on the double-layer alternating direction multiplier method framework according to claim 7, characterized in that After each inner convergence, each sub-Agent will store the local relaxation variable updated in the last iteration of each inner layer for itself, which is used to update its own Agent outer dual multiplier term and outer penalty term coefficient: In the formula, c is a constant used to adjust the size of β.

9. The voltage distributed non-convex optimization method for a large-scale photovoltaic power station system based on the double-layer alternating direction multiplier method framework according to claim 8, characterized in that The inner convergence criterion of TL-ADMM is: The outer convergence criterion of TL-ADMM is: In the formula, ω and ε are both constants used to adjust the corresponding convergence criterion thresholds; BlkDiag represents matrix block diagonalization; Er1, Er2, and Er3 are the thresholds corresponding to the convergence criteria respectively.

10. The voltage distributed non-convex optimization method for a large-scale photovoltaic power station system based on the double-layer alternating direction multiplier method framework according to claim 6, characterized in that Under TL-ADMM, increase the weight of the voltage deviation term in the objective function, and control the growth of the outer penalty coefficient through the smoothing harmonic term. The adjusted objective function is: Wherein, a is a smoothing harmonic parameter for adjusting the smoothness of the growth process of the outer penalty term coefficient; h is a harmonic factor, and P is a all-one matrix consistent with the number of rows and columns of V k,PCC,C The number of rows and columns is the same all-one matrix, and all elements in the matrix are 1.

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