Large-scale renewable energy power station system voltage distributed non-convex optimization method

Abstract

The invention discloses a large-scale renewable energy power station system voltage distributed non-convex optimization method. The method comprises the following steps: firstly, constructing a system voltage optimization model based on a nonlinear standard power flow constraint; dividing the constructed system voltage optimization model into distributed optimization models of a current collection side and a grid-connected side by taking a PCC bus as a boundary; and constructing a voltage optimization consensus problem under the ALADIN, and performing distributed optimization solution by adopting an ALADIN algorithm. The method has the advantages that the non-convex voltage optimization model of the large-scale renewable energy power station system can be efficiently solved, and safe and stable operation of the renewable energy power station is ensured.

Description

Technical Field

[0001] The present invention relates to the field of electric power technology, and in particular to a voltage distribution non-convex optimization method for a large-scale renewable energy power station system. Background Art

[0002] Under the background of "carbon peak and carbon neutrality", the penetration rate of clean energy such as wind and light in the power system has increased year by year, and the number of renewable energy power stations to be built and put into operation has increased dramatically around the world. However, the large-scale expansion and high-proportion grid connection of renewable energy power stations have led to increasingly prominent voltage safety issues faced by the system itself. The areas rich in renewable energy resources such as wind and light in my country are in the northwest, while the load center is in the eastern coastal areas. Electric energy is transmitted from west to east through long-distance transmission lines, making large-scale renewable energy power stations generally integrated into weak power grid environments. Due to the small short-circuit capacity and large external equivalent impedance of the weak power grid environment, the voltage between the renewable energy power station and the power system grid connection point (point of common coupling point, PCC) will change significantly with the fluctuation of the external power transmission. The large number of renewable energy generation units (GURE) in large renewable energy power stations are connected through collector lines at a long distance. When the amount of renewable energy power transmitted through the collector line is large, it will cause a huge voltage drop at the head and end of the collector line. This increases the risk of overvoltage limit at the GURE access point at the end of the collector line.

[0003] At present, the voltage optimization methods to ensure the safe and stable operation of large-scale renewable energy power station systems are mainly divided into model-driven and data-driven methods. Among them, the model-driven method is suitable for power system operation scenarios with complete topological parameter information, while the data-driven method is suitable for distribution networks and other operation scenarios with low system information perception. In addition, the model-driven method has the advantage of avoiding problems such as parameter overfitting and lack of generalization ability when obtaining the optimal solution for voltage control at the system level.

[0004] According to the degree of dependence on communication, the model-driven method is divided into centralized voltage optimization and distributed voltage optimization. The centralized optimization method collects system-wide information through a central controller and formulates a global optimal strategy. Although it is direct and efficient, its communication requirements and computing pressure increase significantly as the scale of the power station expands. The distributed voltage optimization method is to split the original centralized voltage optimization problem into multiple independent sub-optimization problems and solve them separately. It relies on adjacent communication between Agent controllers and distributed optimization algorithms to update and iterate local optimization variables, thereby approaching the global optimal solution of the original centralized voltage optimization problem. In the distributed voltage optimization mode, the global optimization problem is decomposed into multiple local sub-optimization problems and solved independently. The Karush-Kuhn-Tucker (KKT) condition can be used to guide the optimization process of each local sub-optimization problem so that each local solution can eventually converge to the global optimal solution, which is suitable for scenarios with less communication burden.

[0005] Existing distributed voltage optimization methods, such as the alternating direction multiplier method (ADMM), target cascade analysis (ATC) and Benders decomposition, effectively control the voltage of the system under study and achieve satisfactory regulation effects. However, the premise for these distributed optimization algorithms to be effective is that the system voltage optimization model to be solved must be a convex optimization problem. Therefore, it is urgent to explore new distributed optimization methods in order to effectively solve the non-convex optimization problem corresponding to the voltage regulation of large-scale renewable energy power station systems. Summary of the invention

[0006] In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is: how to provide a method that can effectively solve the non-convex optimization problem corresponding to the voltage regulation of a large-scale renewable energy power station system.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A non-convex optimization method for voltage distribution of a large-scale renewable energy power station system comprises the following steps:

[0009] S1. First, build a system voltage optimization model based on nonlinear standard power flow constraints;

[0010] S2, taking the PCC bus as the boundary, split the constructed system voltage optimization model into distributed optimization models on the collector side and the grid side;

[0011] S3, construct the voltage optimization consensus problem under ALADIN, and use the ALADIN algorithm for distributed optimization solution. Further, in step S1, the objective function of the system voltage optimization model is:

[0012] min ObjVP :=ω V ·Obj V +ω P ·Obj P

[0013] in, In the formula, is the node set on the collector side; is a column vector composed of node voltage amplitudes; V ref. is a column vector composed of node reference voltage amplitudes, and each element in the vector is set to a nominal value of 1 p.u.; ||*||2 is the vector 2 norm; “:=” is a definition, which is distinguished from the “=” in the equality constraint formula; P is the column vector composed of active power injected into each node on the collector side; cg is the active power injected from the collector side to the grid side through the PCC bus; ||*||1 is the vector 1 norm, ||P i ||1 is numerically equal to the sum of the active power injected into each node on the collector side, which is related to P cg The difference is the network loss consumed in the internal collector circuit; V and ω P is the weight coefficient;

[0014] The constraints of the system voltage optimization model include power flow constraints on the collector side and the grid-connected side, power balance constraints on the collector side nodes, and voltage constraints on the collector side nodes;

[0015] Among them, the power flow constraints on the collector side and the grid-connected side are:

[0016]

[0017] Where: P i , Q i Inject active and reactive power into node i; V i 、V j is the voltage amplitude of nodes i and j; θ ij is the phase difference between nodes i and j; G ij , B ij is the real part and imaginary part of the elements in the i-th row and j-th column of the node admittance matrix; is the grid-connected side node set;

[0018] The power balance constraint of the collector side node is:

[0019]

[0020] Where: P i,GURE , Q i,GURE is the active and reactive power output by GURE at node i; P i,MPPTis the maximum power point tracking power available to GURE on node i, which is considered as a constant; S i,GURE is the maximum apparent power rating of GURE;

[0021] The collector node voltage constraint is:

[0022]

[0023] Where: 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 when the system is in safe operation; θ i is the voltage phase of node i; θ i,min ,θ i,max They respectively represent the minimum and maximum limits of the voltage phase when the system is operating safely.

[0024] Furthermore, in step S2, by replicating the PCC bus, the constructed system voltage optimization model is decomposed into a grid-connected side subsystem and several collector side systems. The constraint conditions of the system voltage optimization model also include the following coupling constraints:

[0025]

[0026] Where: P PCC,G , Q PCC,G 、V PCC,G and θ PCC,G is the active power, reactive power, voltage amplitude and phase of the boundary node on the PCC busbar on the grid side; P k,PCC,C , Q k,PCC,C 、V k,PCC,C and θ k,PCC,C is the active power, reactive power, voltage amplitude and phase of the boundary node on the PCC bus on the kth collector line side, K C It is the number of collector lines inside the renewable energy power station.

[0027] Furthermore, the distributed optimization model constructed based on the system voltage optimization model includes a grid-connected side subsystem and a kth collector line side subsystem, and the grid-connected side subsystem is:

[0028]

[0029] And meet the power flow constraints on the collector side and the grid side;

[0030] The kth collector line side subsystem is:

[0031]

[0032] And meet the collector side and grid side power flow constraints, collector side node power balance constraints and collector side node voltage constraints;

[0033] In the formula, F G and F k,C are the decomposed optimization objective functions, F G is empty; is the augmented Lagrangian function associated with the respective optimization problem; For expansion items.

[0034] Furthermore, in step S3, the voltage optimization consensus problem under ALADIN is constructed as follows:

[0035]

[0036] Among them, the sub-optimization problems on the grid-connected side and the collector side under ALADIN are:

[0037]

[0038] Where: X 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; are the auxiliary variables generated in the grid-connected subsystem and the collector line subsystem after copying the boundary nodes; λ is the dual multiplier term; ρ is the penalty function term; (*)′ represents the copy variable of the boundary coupling variable in the consensus problem; It represents the result after variable optimization, which is a constant value; Transpose the sign of a vector;

[0039] X G and X k,C The constraints are expressed as:

[0040]

[0041] J G and J k,C and constraints respectively The associated Jacobian matrix, G G and G k,C and the objective function respectively The gradient of the association, is the approximate calculation result of the Hessian array, which is specifically defined as follows:

[0042]

[0043] ALADIN solves the voltage optimization consensus problem by alternating between constraints and G Gand G k,C Realize distributed optimization solution.

[0044] Furthermore, in step S3, the auxiliary variables and dual multiplier terms solved by ALADIN are updated by a linear search method:

[0045]

[0046] in: is the relevant parameter in the linear search method, set to

[0047] Furthermore, in step S3, for non-positive definite will be non-positive The negative eigenvalues ​​in are flipped to their opposites and the zero eigenvalues ​​are replaced by positive ones.

[0048] Furthermore, in step S3, the Lagrangian function corresponding to the voltage optimization consensus problem is:

[0049]

[0050] In the formula, ΔX and S are original variables, λ QP , π are dual variables, and the corresponding KKT conditions are:

[0051]

[0052] Where: Blkdiag{*} is the symbolic operator for matrix block diagonalization.

[0053] In summary, the present invention has the following advantages:

[0054] 1) The non-convex voltage distributed optimization model based on nonlinear standard power flow constraints of this application can provide accurate system voltage calculation results, which is suitable for the operation scenarios of large-scale layout of renewable energy power station systems and long-distance power transmission.

[0055] 2) The present invention proposes to use a novel ALADIN distributed optimization algorithm to solve the non-convex voltage distributed optimization model. The ALADIN algorithm can complete convergence after very few iterations and obtain voltage optimization results that are almost the same as those of centralized optimization.

[0056] 3) The GURE reactive output obtained by solving the non-convex voltage optimization model through ALADIN can effectively optimize the voltage of each node of the large-scale renewable energy power station system to a fairly safe range. In addition, the implementation of the ALADIN algorithm only requires each distributed Agent controller to communicate with each other, which has a smaller communication burden on the power station than the conventional centralized voltage optimization method. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Model diagram for grid connection analysis of large-scale renewable energy power station system.

[0058] Figure 2 A distributed communication system architecture to support distributed voltage optimization in large-scale renewable energy power station systems.

[0059] Figure 3 This is an exploded diagram of a large renewable energy power station system.

[0060] Figure 4 Flowchart for the ALADIN algorithm implementation.

[0061] Figure 5 It is the error of power flow calculation within the station under the LinDistFlow constraint.

[0062] Figure 6 It is the error of off-station power flow calculation under LinDistFlow constraint.

[0063] Figure 7 The convergence of method A under different ρ values.

[0064] Figure 8 Convergence comparison between method A and method B.

[0065] Fig. 9 The residuals of method A under different numbers of collector lines.

[0066] Fig.10 The residuals of method A under different numbers of GURE units.

[0067] Fig.11 This is a comparison chart of voltage distribution optimization results. DETAILED DESCRIPTION

[0068] The present invention is further described in detail below in conjunction with embodiments.

[0069] 1. Grid-connected analysis model of large-scale renewable energy power station system and mathematical model of non-convex voltage optimization

[0070] The grid-connected analysis model of large-scale renewable energy power station system is as follows: Figure 1As shown: the model is divided into the collector side and the grid-connected side. The inside of the renewable energy power station system is called the collector side. Multiple medium-voltage collector lines on the collector side are connected in parallel to the PCC busbar, and multiple GUREs consisting of wind and photovoltaic power generation equipment are further connected in parallel to each medium-voltage collector line. The electric energy produced by all GUREs in the renewable energy power station system is collected at the PCC busbar. The grid-connected side includes a booster substation, a high-voltage transmission line, and a receiving-end AC power grid. The electric energy collected at the PCC busbar is boosted by the substation and finally transmitted to the receiving-end AC power grid over a long distance through the high-voltage transmission line. The PCC busbar is the coupling link between the collector side and the grid-connected side. It should be noted that the grid-connected analysis model of this embodiment does not include the tap position adjustment of the booster station in the optimization problem. The reason is that the response speed of the booster station position adjustment is much slower than the response speed of the GURE output power adjustment, and considering the influence of the service life factor, it should not act frequently. Therefore, in the grid-connected analysis model of the system constructed in this embodiment, the tap position of the booster station is regarded as a constant.

[0071] In the above-mentioned large-scale renewable energy power station system topology, the power-voltage steady-state relationship between the collector side and the grid-connected side can be analyzed using an impedance model. For the collector side: 1) consider the impedance parameters of each medium-voltage collector line; 2) without losing generality and accuracy, ignore the GURE internal converter loss, so each GURE and collector line coupling node is regarded as a PQ node, and the corresponding node injection power is the GURE output power. For the grid-connected side: 1) the step-up substation is treated as an ideal transformer; 2) the relevant parameters of the long-distance transmission line and the receiving AC power grid are characterized by the Thevenin equivalent impedance and voltage; 3) when analyzing the voltage inside the renewable energy power station system, the remote receiving AC power grid is regarded as a balancing node.

[0072] Consider the operating characteristics of "scaled topology, weak grid connection" of large-scale renewable energy power stations: for the external grid-connected side of the system, since the renewable energy power station is far away from the load center, the long-distance transmission line for power transmission makes the system generally connected to the weak grid environment, and the Thevenin equivalent impedance on the grid-connected side is large; for the internal collector side of the system, large-scale renewable energy power stations occupy a large area, the medium-voltage collector lines connecting each GURE are long, and the line impedance is also large. Therefore, when the renewable energy power station performs large-scale power transmission, the power loss on the line impedance is large, and the impact on the system voltage distribution cannot be ignored.

[0073] The non-convex voltage optimization mathematical model of the large-scale renewable energy power station system of this embodiment involves an objective function and constraints, and the objective function comprehensively considers the overall voltage deviation and network loss of the large-scale renewable energy power station system.

[0074] Overall voltage deviation of large-scale renewable energy power station system: Large-scale renewable energy power station system should ensure that each node voltage has as much voltage amplitude safety margin as possible, so as to avoid overvoltage limit when the GURE output fluctuation causes the system node voltage deviation. The corresponding objective function is as follows:

[0075]

[0076] in: is the node set on the collector side; is a column vector composed of node voltage amplitudes; V ref. is a column vector composed of node reference voltage amplitudes, and each element in the vector is set to a nominal value of 1p.u.; ||*||2 is the vector 2 norm; “:=” is a definition, which is distinguished from the “=” in the equality constraint formula.

[0077] Grid loss of large-scale renewable energy power station system: In order to improve the economic efficiency of large-scale power transmission, it is necessary to ensure that the internal grid loss of large-scale renewable energy power station system is as small as possible. The corresponding objective function is as follows:

[0078]

[0079] in: P is the column vector composed of active power injected into each node on the collector side; cg is the active power injected from the collector side to the grid side through the PCC bus; ||*||1 is the vector 1 norm, ||P i ||1 is numerically equal to the sum of the active power injected into each node on the collector side, which is related to P cg The difference is the network loss consumed on the internal collection circuit of the large-scale renewable energy power station system.

[0080] Therefore, the overall objective function considered in this embodiment is as follows:

[0081] min Obj VP :=ω V ·Obj V +ω P ·Obj P (3)

[0082] Where: V and ω P It is the weight coefficient, and the specific value can be set according to the control requirements.

[0083] The constraints include power flow constraints on the collector side and the grid side, power balance constraints on the collector side nodes, and voltage constraints on the collector side nodes.

[0084] Flow constraints on the collector side and the grid side: Large renewable energy power station systems have problems with large impedance of internal and external lines and high power loss. In this case, the flow calculation error caused by the linearized flow constraint based on LinDistFlow is difficult to ignore, which will significantly reduce the effectiveness of voltage optimization decisions. Therefore, in order to ensure decision accuracy, this embodiment still constructs the flow constraints on the collector side and the grid side based on the nonlinear standard flow model:

[0085]

[0086] Where: P i , Q i Inject active and reactive power into node i; V i 、V j is the voltage amplitude of nodes i and j; θ ij is the phase difference between nodes i and j; G ij , B ij is the real part and imaginary part of the elements in the i-th row and j-th column of the node admittance matrix; It is the grid-connected node set.

[0087] Power balance constraints on the collector side nodes: The injected power of each node on the collector side of the large-scale renewable energy power station system comes from GURE. Among them, the active power output of GURE is determined by the available maximum power point tracking power, and the reactive power output is determined by the solution results of the constructed voltage optimization model. The corresponding constraints are as follows:

[0088]

[0089] Where: P i,GURE , Q i,GURE is the active and reactive power output by GURE at node i; P i,MPPT is the maximum power point tracking power available to GURE at node i, which is considered as a constant; S i,GURE is the maximum apparent power rating of GURE.

[0090] Collector-side node voltage constraints: The magnitude and phase angle of the collector-side node voltage should satisfy the corresponding constraints as shown below:

[0091]

[0092] Where: 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 when the system is in safe operation; θ i is the voltage phase of node i; θ i,min ,θ i,maxThey respectively represent the minimum and maximum limits of the voltage phase when the system is operating safely.

[0093] 2. Distributed Communication Architecture and Distributed Voltage Optimization Issues for Large Renewable Energy Power Stations

[0094] As the prerequisite for system distributed voltage optimization, this embodiment will first build a distributed communication architecture suitable for the structural characteristics of large-scale renewable energy power stations. Then, combined with the communication architecture, the original centralized voltage optimization problem is split to build a distributed voltage optimization problem.

[0095] Distributed communication architecture: Traditional centralized communication is a "point-to-point" communication method. For renewable energy power stations, if a centralized communication method is adopted, it is necessary to rely on the central controller to establish a communication connection with each GURE unit. However, with the large-scale renewable energy power station system and the rapid expansion of installed capacity, the number of GURE units will increase significantly. The central controller, as the central node, will face tremendous information processing pressure and will find it difficult to cope with a large number of GURE unit control requests. Taking into account the disadvantages of centralized communication and the characteristics of the in-station cluster structure of large renewable energy power stations, the original system is divided into multiple subsystems, and only adjacent distributed communication is performed between the Agent controllers of each subsystem, which is more suitable for the scenario of this embodiment.

[0096] The distributed communication architecture adopted in this embodiment is as follows Figure 2 As shown in the figure: the PCC bus and each collector line in the station are equipped with distributed agent controllers. Each GURE on the collector line is uniformly controlled by the collector line agent controller, and boundary information is transmitted between each collector line agent and the PCC bus agent. This distributed communication method divides the collector line in the station into partitions for control, rather than configuring a separate agent for each GURE, thus avoiding the problem of slow computation convergence caused by too many agent configurations.

[0097] Distributed voltage optimization problem: According to Figure 2 The distributed communication architecture shown in the figure is used for large-scale renewable energy power plants. Figure 3 By duplicating the PCC busbar, the original system is decomposed into a grid-connected subsystem and several collector-side systems. At this time, the coupling constraints shown below need to be added:

[0098]

[0099] Where: P PCC,G , Q PCC,G 、V PCC,G and θ PCC,Gis the active power, reactive power, voltage amplitude and phase of the boundary node on the PCC busbar on the grid side; P k,PCC,C , Q k,PCC,C 、V k,PCC,C and θ k,PCC,C K is the active power, reactive power, voltage amplitude and phase of the boundary node on the PCC bus on the kth collector line side. C It is the number of collector lines inside the renewable energy power station.

[0100] Furthermore, the centralized optimization model corresponding to equations (3)-(6) can be expanded to the following distributed optimization model:

[0101]

[0102] Where: Equation (8) and Equation (9) are the distributed voltage optimization problems corresponding to the grid-connected subsystem and the kth collector line subsystem, respectively; F G and F k,C are the decomposed optimization objective functions, where F G is empty, the main function of formula (8) is to provide boundary electrical quantity information for the optimization calculation of formula (9); is the augmented Lagrangian function associated with each optimization problem, which contains the augmented terms This will be introduced in detail later.

[0103] 3. Distributed solution of non-convex voltage optimization problem based on ALADIN

[0104] This embodiment compares the distributed optimization solution process of the novel ALADIN algorithm and the classic ADMM algorithm to show the key points when the ALADIN algorithm is used to perform distributed optimization on the non-convex voltage optimization model of this embodiment. In particular, the special steps in the ALADIN solution process will also be emphasized.

[0105] Comparison of distributed optimization solutions of ALADIN and ADMM. ALADIN and ADMM have similar distributed iterative processes, that is, they iteratively update the Lagrange multiplier by alternating directions, but the two methods differ in the construction of augmented Lagrangian functions and consensus problems. In order to better explain the characteristics and advantages of ALADIN, the distributed optimization solution process of ADMM is first introduced, and then the distributed optimization solution process of ALADIN is further explained. Among them, the distributed optimization solution of ADMM is as follows:

[0106] 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, Write in the following format:

[0107]

[0108] Where: X 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; They are the auxiliary variables generated in the grid-connected subsystem and the collector line-side subsystem after copying the boundary nodes; Specifically Expression under ADMM;λ G and λ k,C is the dual multiplier term; ρ is the penalty function term; (*)′ represents the replica variable of the boundary coupling variable in the consensus problem; It represents the result after variable optimization, which is a constant value; Transpose the sign of a vector.

[0109] The voltage optimization consensus problem under ADMM is constructed as follows:

[0110]

[0111] ADMM achieves distributed optimization by alternately solving equations (10), (11) and (12). The key dual multiplier term is updated by the gradient ascent method. The iterative formula is as follows:

[0112]

[0113] in:(*) [ n ] Specifically refers to the optimization result after the nth iteration.

[0114] The ALADIN distributed optimization solution is as follows:

[0115] The sub-optimization problems on the grid-connected side and the collector side under ALADIN are also constructed according to equations (8) and (9). The expression is as follows:

[0116]

[0117] in: Specifically Expression under ALADIN; Different from ADMM, λ is unified in the sub-optimization problems on the grid side and the collector line side shown in (14) and (15).

[0118] Similar to ADMM, ALADIN also has a voltage optimization consensus problem:

[0119]

[0120] In particular, the sub-optimization problem constraints in equations (8) and (9) are expressed as:

[0121]

[0122] J in formula (16) G and J k,C and constraints respectively The associated Jacobian matrix, G G and G k,C and the objective function respectively The gradient of the association, It is the approximate calculation result of the Hessian array, which has the following specific definition:

[0123]

[0124] ALADIN achieves distributed optimization by alternately solving (16), (17) and (18). The key auxiliary variables and dual multipliers are updated by linear search:

[0125]

[0126] in: is the relevant parameter in the linear search method, which can generally be set as

[0127] In summary, when ALADIN and ADMM are used for distributed optimization, the idea of ​​splitting the original centralized voltage optimization problem is consistent, and both methods use augmented terms to deal with the boundary coupling constraints at the PCC bus in the original centralized voltage optimization problem. The difference is that ADMM needs to solve the convex subproblem of the original problem in each iteration, while ALADIN uses the inexact Newton method to approximate the subproblem, which allows ALADIN to strictly guarantee convergence when dealing with non-convex optimization problems. The overall implementation process of ALADIN is as follows: Figure 4 shown.

[0128] Special instructions for the ALADIN algorithm:

[0129] 1) Hessian approximation matrix needs to remain positive definite in order for the ALADIN algorithm to converge. However, It cannot be strictly guaranteed to be positive definite in each iteration, so it needs to be positive definite. The negative eigenvalues ​​in are flipped to their opposites, replacing the zero eigenvalue with a very small positive number.

[0130] 2) The voltage optimization consensus problem shown in equation (16) actually scales the boundary coupling relationship on the PCC bus, that is, by introducing the slack variable S, a quadratic programming problem with equality constraints as shown in equation (14) is established, which is easier to solve than a quadratic programming problem with inequality constraints. However, even so, the solution of equation (16) is still relatively complex, and the optimization results obtained by convex programming solvers such as Cplex and Gurobi may not meet the required accuracy, thus affecting the overall iteration process of ALADIN. In this regard, the KKT conditions corresponding to equation (16) can be directly listed, and then the linear equations corresponding to the KKT conditions can be solved to obtain a high-quality analytical optimal solution.

[0131] For formula (16), the corresponding Lagrangian function is:

[0132]

[0133] In formula (21), ΔX and S are original variables, λ QP , π are dual variables, and the corresponding KKT conditions can be further written as follows:

[0134]

[0135] Where: Blkdiag{*} is the symbolic operator for matrix block diagonalization.

[0136] From the above discussion, it can be seen that the optimization solution of the quadratic programming problem (16) can be equivalently converted into the solution of the linear equation system (22). Given that the symmetric coefficient matrix contained in (22) has sparse characteristics, a high-performance linear solver can be used to obtain a high-quality solution.

[0137] 4. Example Analysis

[0138] This embodiment uses a large-scale renewable energy power station system with an installed capacity of 8×12×2MW for example analysis to verify the effectiveness of the proposed method. The system parameters are detailed in Table 1: There are 8 collector lines in parallel inside the large-scale renewable energy power station, and 12 groups of GUREs are connected to each collector line at equal distances in sequence. The station is a large-scale collection system; the transmission environment outside the large-scale renewable energy power station is equivalently calculated using the Thevenin model. Under the set equivalent impedance, the system short-circuit capacity ratio is 5.27, which can be regarded as being incorporated into a weak grid environment.

[0139] Table 1 Key parameters related to voltage control of large-scale renewable energy power station system

[0140]

[0141] The programs related to the example are compiled in the MATLAB environment. The mathematical model of non-convex voltage optimization of large-scale renewable energy power stations based on the ALADIN algorithm is implemented with the help of the CasADi framework; the non-convex sub-optimization problems (14) and (15) on the grid-connected side and the collector side are solved using the IPOPT solver; the voltage optimization consensus problem (16) is converted into a linear equation system (22) and solved using the MA57 sparse matrix solver. The Bull-Ray power flow calculation involved in the example analysis is implemented using the MATPOWER toolkit and is regarded as the benchmark result of the power flow calculation. The centralized optimization results are obtained by directly solving the non-convex voltage optimization model shown in equations (3)-(6) and are regarded as the benchmark results of voltage optimization. All the programs involved above are executed using a computer configured with a 2.5-GHz CPU / 16GBRAM, and the algorithm solution time is measured using the MATLAB built-in tic / toc command.

[0142] In particular, to facilitate subsequent comparative descriptions, three distributed optimization schemes are defined as follows:

[0143] Method A: using the ALADIN algorithm to distribute and solve the non-convex voltage optimization model based on nonlinear standard power flow constraints, which is the method proposed in this embodiment;

[0144] Method B: Using the ADMM algorithm to solve the non-convex voltage optimization model based on nonlinear standard power flow constraints in a distributed manner;

[0145] Method C: Use the ADMM algorithm to distribute the solution of the convex voltage optimization model based on the linear LinDistFlow power flow constraint.

[0146] First, by comparing the power flow calculation results based on the standard AC power flow model and the power flow model based on the LinDistFlow model, the necessity of establishing a non-convex voltage optimization model for large-scale renewable energy power station systems is verified. By comparing the number of distributed iterations of the ADMM algorithm and the ALADIN algorithm, the convergence advantage of ALADIN in solving non-convex optimization problems is verified. Finally, by comparing the voltage optimization results obtained by ALADIN and ADMM, the optimality of ALADIN in solving non-convex optimization problems is verified; by comparing ALADIN with the centralized optimization results, it is shown that the node reactive compensation decision results obtained by ALADIN are basically consistent with the results obtained by centralized optimization.

[0147] Necessity analysis of non-convex voltage optimization model: In order to verify the necessity of adopting nonlinear standard power flow constraints in large-scale renewable energy power station systems and thus establishing non-convex voltage optimization models, this section specifically analyzes the system power flow calculation error based on the linearized power flow constraint LinDistFlow. Since the non-convex voltage optimization model proposed in this embodiment adopts nonlinear standard power flow constraints, the power flow calculation results are consistent with the reference values, so no special comparison is required.

[0148] Firstly, the influence of the scale of renewable energy power station system on the calculation accuracy of the power flow of the collector line in the station is analyzed when the linearized power flow constraint LinDistFlow is used to replace the nonlinear standard power flow constraint. In the case analysis, the active output of each GURE is set to 1.6MW and the reactive power is set to 0MVar. Figure 5 The error of the in-station flow calculation based on the linearized flow constraint LinDistFlow is shown: Figure 5 (a) It can be seen that as the number of parallel collector lines increases, the calculation errors of the collector line node voltage and the collector line active loss increase; Figure 5 (b) It can be seen that as the number of GUREs on a single collector line increases, the calculation errors of the collector line node voltage and the collector line active loss increase.

[0149] Then, the influence of the external grid-connected environment on the accuracy of the power flow calculation from the PCC bus to the receiving end is analyzed when the linearized power flow constraint LinDistFlow is used to replace the nonlinear standard power flow constraint. In the case analysis, the grid-connected active power at the PCC bus is set to 50MW and the reactive power is set to 20MVar. The short-circuit capacity ratio is affected by changing the size of the Thevenin equivalent impedance of the external grid, thereby characterizing the changes in the strength of the external grid-connected environment. Figure 6 The calculation error of the off-station power flow based on the linearized power flow constraint is demonstrated. It can be seen from the figure that as the short-circuit capacity ratio decreases, that is, the external grid-connected environment changes from strong to weak, the calculation error of the PCC bus voltage and the active power loss of the external equivalent power grid increases.

[0150] In summary: With the increase in the scale of renewable energy power station systems, the calculation error of the power flow of the collector line in the station caused by the linearized power flow constraint has become more and more obvious; since large-scale renewable energy power stations are usually far away from the load center, when they are connected to a weak power grid environment, the calculation error of the external equivalent power grid power flow caused by the linearized power flow constraint is also difficult to ignore. These factors will have a great impact on the accuracy of the system voltage optimization results. Therefore, in order to effectively optimize the system voltage of large renewable energy power stations, it is particularly necessary to establish a non-convex voltage optimization model based on nonlinear standard power flow constraints.

[0151] Verification of the convergence advantage of ALADIN distributed optimization calculation: The convergence of method A and method B in solving the non-convex voltage optimization model is analyzed. When performing distributed optimization, the initial values ​​of the boundary coupling variables involved are all unified to 0, the initial values ​​of the Lagrange multipliers are set to 1, and the convergence condition is that the primal and dual residuals are both less than 1×10 -4 (It can be considered that the boundary voltage term residual should be less than 0.0001pu, and the boundary power term residual should be less than 0.01MW. Considering the voltage deviation range of ±0.05pu and the total installed capacity of the system at the level of 100 megawatts, this convergence condition is reasonable).

[0152] First, the convergence of method A under different penalty function coefficient ρ values ​​is analyzed, such as Figure 7 As shown in the figure, the value of ρ does not significantly affect the convergence of the ALADIN algorithm. Under different ρ values, the ALADIN algorithm can reach the convergence condition (residual error less than 1×10 -4 ). When the number of iterations continues to increase to 12, the residuals under different ρ values ​​all drop to 1×10 -7 Below, the ideal convergence is achieved.

[0153] Furthermore, the convergence of method A and method B is compared to illustrate that the ALADIN algorithm has advantages over the traditional ADMM algorithm in terms of convergence when solving non-convex optimization problems in a distributed manner. As mentioned above, since the value of ρ does not significantly affect the convergence performance of ALADIN, method A when ρ=10 is selected for comparative analysis. However, the value of ρ will significantly affect the convergence of ADMM. Therefore, for a fair comparison, method B with multiple ρ values ​​is listed here for comparative analysis. The comparison results are shown in Figure 2. Figure 8 As shown in the figure, the convergence of method B is very sensitive to the value of ρ. Too large or too small a ρ value will cause method B to converge too slowly. When ρ = 15, method B has the best convergence, but it also needs about 70 iterations to meet the convergence condition. After about 10 iterations, the primal and dual residuals of method A have both dropped to 1×10 -7 The convergence rate is obviously better than that of method A.

[0154] Finally, the influence of the scale of renewable energy power plants on the convergence of the ALADIN algorithm is verified. By increasing the number of parallel collector lines and the number of GURE units connected to the collector lines, the convergence of method A is analyzed (based on the case of ρ = 10). Fig. 9 and Fig.10 As shown in Figure 2, ALADIN always maintains good convergence as the number of parallel collector lines or the number of GURE units connected to the collector lines increases. After about 10 iterations, the primal and dual residuals of different system sizes can drop to 1×10-7 Nearby, it shows ideal convergence.

[0155] In summary: ① The convergence of the ALADIN (method A) algorithm is robust to parameter changes, while the convergence of the ADMM (method B) algorithm is sensitive to parameter changes; ② Regardless of the parameter values, the ALADIN algorithm only requires a small number of iterations to converge, while the ADMM algorithm still requires a large number of iterations to converge under appropriate parameter values; ③ With the expansion of the scale of renewable energy power station systems, the ALADIN algorithm still has good convergence.

[0156] Verification of the optimality advantage of ALADIN distributed optimization calculation: First, by comparing the distributed optimization results of method A, method B, and method C on the system voltage of a large renewable energy power station, it is shown that the proposed method ensures the accuracy and convergence of the distributed voltage optimization process of a large renewable energy system by establishing a reasonable optimization model and adopting an effective optimization algorithm. Fig.11 The voltage distribution optimization from the PCC bus to the terminal node of a collector line based on various methods compared in this embodiment is shown (where #0 represents the PCC bus node, and #1 to #12 represent the access node number of the GURE on the collector line). In particular, Table 2 gives the relevant numerical results of each distributed optimization method in the iterative calculation process.

[0157] Combination Fig.11 Analyzing with Table 2, when no voltage optimization method is used (i.e. Q i,GURE Set to 0), the voltage of some nodes of the renewable energy power station exceeds its allowable upper limit, so it is necessary to perform voltage optimization control. When using method B to implement voltage optimization control, it takes 69 iterations to complete convergence, which takes 48.82 seconds; method C can complete convergence after 30 iterations, and because each iteration solves a convex optimization problem, the single solution time is also short. The combined effect of these two factors is that the total calculation time is only 3.77 seconds. However, the convex voltage optimization model solved by method C uses linearized power flow constraints, which leads to a large error between the expected voltage control result obtained by the optimization model and the actual voltage obtained based on the power flow calculation. The actual voltage deviation will be much higher than the expected voltage deviation, and the optimized system voltage has a low voltage limit. Compared with the above methods, method A completed convergence with a very small number of iterations (7 times), and the solution time is roughly equal to method C, which is only 5.22 seconds. And because the non-convex voltage optimization model solved by method A uses nonlinear standard power flow constraints, the expected voltage control result is consistent with the actual voltage. Fig.11As shown in the calculation results corresponding to method A, the voltage of each node is optimized to around 1 p.u., the overall system voltage is within a fairly safe range, and the risk of overvoltage limit is eliminated.

[0158] Table 2 Comparison of calculation results of various distributed optimization methods

[0159]

[0160] Then, considering that the voltage regulation effect of the renewable energy power station system depends on the reactive compensation decision of each GURE access node on the collector line, the node reactive compensation results of method A and centralized optimization are compared to show the accuracy of ALADIN optimization decision. The reactive compensation calculation results of a collector line node using method A and centralized optimization are shown in Table 3. It can be seen from the table that method A uses ALADIN to perform distributed optimization on the non-convex voltage optimization model, and the reactive compensation amount of each node of the collector line is basically consistent with the result under centralized optimization, and the maximum relative error is less than 0.3%.

[0161] Finally, the objective function value after compensation by method A is compared with the corresponding value before compensation to intuitively demonstrate the regulating effect of ALADIN on the voltage of large-scale renewable energy power station systems. Table 4 compares the objective functions before and after node reactive power compensation. It can be seen from the table that the objective function value is significantly reduced by optimizing the reactive output of GURE by method A for reactive power compensation of system nodes, among which the voltage deviation is particularly reduced. Due to the additional reactive power compensation, the current flowing through the collector line increases, and the overall active power loss of the optimized system increases compared to the system before optimization. However, thanks to the consideration of minimizing active power loss as one of the optimization goals, the active power loss result after optimization is only slightly increased.

[0162] Table 3 Comparison of reactive power compensation results of collector line nodes after optimization

[0163]

[0164] Table 4 Comparison of objective functions before and after reactive power compensation of the system

[0165]

[0166] In summary: when using ADMM to solve the non-convex voltage optimization model (method B), a large number of iterations are required to complete convergence, and the solution takes a long time; when using ADMM to solve the convex voltage optimization model (method C), although the number of iterations required is less than that of the non-convex voltage problem, the solution takes a short time, but due to the flow calculation error caused by the linearized flow constraint of LinDistFlow, the actual voltage distribution of the system is far from the expected voltage distribution, and the overall voltage deviation of the system is even greater than before optimization; in comparison, when using ALADIN to solve the non-convex voltage optimization model (method A), only a small number of iterations are required to complete convergence, the solution takes a short time, and the node reactive power compensation results obtained by distributed optimization are almost consistent with those obtained by centralized optimization. Under the action of ALADIN, the system voltage distribution is optimized to a fairly safe range.

[0167] In summary, in order to solve the overvoltage risk faced by large-scale renewable energy power stations during large-scale power transmission, this embodiment constructs a non-convex distributed optimization model for voltage control of large-scale renewable energy power stations, and realizes efficient distributed optimization solution of the model through the ALADIN algorithm. Combining theoretical analysis and example tests, the main conclusions are as follows:

[0168] 1) Linearized approximate power flow constraints such as LinDistFlow can lead to large errors in voltage calculation of large-scale renewable energy power station systems. The non-convex voltage distributed optimization model based on nonlinear standard power flow constraints established in this embodiment can provide accurate system voltage calculation results and is suitable for large-scale layout of renewable energy power station systems and long-distance power transmission operation scenarios.

[0169] 2) In view of the problem that the convergence and optimality of traditional distributed optimization algorithms such as ADMM are difficult to guarantee when solving the non-convex voltage distributed optimization model constructed in this embodiment, this embodiment proposes to use the novel ALADIN distributed optimization algorithm to solve the non-convex voltage distributed optimization model. The ALADIN algorithm can complete convergence after very few iterations and obtain voltage optimization results that are almost the same as those of centralized optimization.

[0170] 3) The GURE reactive output obtained by solving the non-convex voltage optimization model through ALADIN can effectively optimize the voltage of each node of the large-scale renewable energy power station system to a fairly safe range. In addition, the implementation of the ALADIN algorithm only requires each distributed Agent controller to communicate with each other, which has a smaller communication burden on the power station than the conventional centralized voltage optimization method.

[0171] 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 in the protection scope of the present invention.

Claims

1. A non-convex optimization method for voltage distribution of a large-scale renewable energy power station system, characterized in that: The steps include: S1. First, build a system voltage optimization model based on nonlinear standard power flow constraints; S2, taking the PCC bus as the boundary, split the constructed system voltage optimization model into distributed optimization models on the collector side and the grid side; S3. Construct the voltage optimization consensus problem under ALADIN and use the ALADIN algorithm for distributed optimization solution.

2. The large-scale renewable energy power station system voltage distributed non-convex optimization method according to claim 1, characterized in that: In step S1, the objective function of the system voltage optimization model is: min Obj VP :=ω V ·Obj V +ω P ·Obj P in, In the formula, is the node set on the collector side; is a column vector composed of node voltage amplitudes; V ref . is a column vector composed of node reference voltage amplitudes, and each element in the vector is set to a nominal value of 1p.u.; ||*||2 is the vector 2 norm; ":=" is a definition, which is distinguished from the "=" in the equality constraint formula; P is the column vector composed of active power injected into each node on the collector side; cg is the active power injected from the collector side to the grid side through the PCC bus; ||*||1 is the vector 1 norm, ||P i ||1 is numerically equal to the sum of the active power injected into each node on the collector side, which is related to P cg The difference is the network loss consumed in the internal collector circuit; V and ω P is the weight coefficient; The constraints of the system voltage optimization model include power flow constraints on the collector side and the grid-connected side, power balance constraints on the collector side nodes, and voltage constraints on the collector side nodes; Among them, the power flow constraints on the collector side and the grid-connected side are: Where: P i , Q i Inject active and reactive power into node i; V i 、V j is the voltage amplitude of nodes i and j; θ ij is the phase difference between nodes i and j; G ij , B ij is the real part and imaginary part of the elements in the i-th row and j-th column of the node admittance matrix; is the grid-connected side node set; The power balance constraint of the collector side node is: Where: P i,GURE , Q i,GURE is the active and reactive power output by GURE at node i; P i,MPPT is the maximum power point tracking power available to GURE on node i, which is considered as a constant; S i,GURE is the maximum apparent power rating of GURE; The collector node voltage constraint is: Where: 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 when the system is in safe operation; θ i is the voltage phase of node i; θ i,min ,θ i,max They respectively represent the minimum and maximum limits of the voltage phase when the system is operating safely.

3. The large-scale renewable energy power station system voltage distributed non-convex optimization method according to claim 2, characterized in that: In step S2, by replicating the PCC bus, the constructed system voltage optimization model is decomposed into a grid-connected side subsystem and several collector side systems. The constraint conditions of the system voltage optimization model also include the following coupling constraints: Where: P PCC,G , Q PCC,G 、V PCC,G and θ PCC,G is the active power, reactive power, voltage amplitude and phase of the boundary node on the PCC busbar on the grid side; P k,PCC,C , Q k,PCC,C 、V k,PCC,C and θ k,PCC,C is the active power, reactive power, voltage amplitude and phase of the boundary node on the PCC bus on the kth collector line side, K C It is the number of collector lines inside the renewable energy power station.

4. The method for voltage distribution non-convex optimization of a large-scale renewable energy power station system according to claim 3, characterized in that: The distributed optimization model constructed based on the system voltage optimization model includes a grid-connected side subsystem and a kth collector line side subsystem. The grid-connected side subsystem is: And meet the power flow constraints on the collector side and the grid side; The kth collector line side subsystem is: And meet the collector side and grid side power flow constraints, collector side node power balance constraints and collector side node voltage constraints; In the formula, F G and F k,C are the decomposed optimization objective functions, F G is empty; and is the augmented Lagrangian function associated with the respective optimization problem; and For expansion items.

5. The large-scale renewable energy power station system voltage distribution non-convex optimization method according to claim 4, characterized in that: In step S3, the voltage optimization consensus problem under ALADIN is constructed as follows: Among them, the sub-optimization problems on the grid-connected side and the collector side under ALADIN are: Where: X 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 subsystem and the collector line subsystem after copying the boundary nodes; λ is the dual multiplier term; ρ is the penalty function term; (*)′ represents the copy variable of the boundary coupling variable in the consensus problem; It represents the result after variable optimization, which is a constant value; Transpose the sign of a vector; X G and X k,C The constraints are expressed as: J G and J k,C and constraints respectively and The associated Jacobian matrix, G G and G k,C and the objective function respectively and The gradient of the association, and is the approximate calculation result of the Hessian array, which is specifically defined as follows: ALADIN solves the voltage optimization consensus problem by alternating between constraints and and G G and G k,C Realize distributed optimization solution.

6. The large-scale renewable energy power station system voltage distribution non-convex optimization method according to claim 5, characterized in that: In step S3, the auxiliary variables and dual multiplier terms solved by ALADIN are updated by a linear search method: in: and is the relevant parameter in the linear search method, set to 7. The large-scale renewable energy power station system voltage distributed non-convex optimization method according to claim 6, characterized in that: In step S3, for non-positive definite and will be non-positive and The negative eigenvalues ​​in are flipped to their opposites and the zero eigenvalues ​​are replaced by positive ones.

8. The large-scale renewable energy power station system voltage distributed non-convex optimization method according to claim 6, characterized in that: In step S3, the Lagrangian function corresponding to the voltage optimization consensus problem is: In the formula, ΔX and S are original variables, λ QP , π are dual variables, and the corresponding KKT conditions are: Where: Blkdiag{*} is the symbolic operator for matrix block diagonalization.

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