Large-scale renewable energy power plant system voltage distribution non-convex optimization method

Abstract

The application discloses a large renewable energy power station system voltage distributed non-convex optimization method, and first constructs a system voltage optimization model based on nonlinear standard power flow constraints; the PCC bus is taken as a boundary, the constructed system voltage optimization model is split into distributed optimization models of a power collection side and a grid connection side; a voltage optimization consensus problem under ALADIN is constructed, and the ALADIN algorithm is adopted for distributed optimization solving. The application has the advantages of being capable of efficiently solving a non-convex voltage optimization model of a large renewable energy power station system, guaranteeing safe and stable operation of the renewable energy power station and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electric power, in particular to a large-scale renewable energy power station system voltage distributed non-convex optimization method. BACKGROUND

[0002] Under the background of "carbon peak and carbon neutral", the penetration rate of clean energy such as wind and light in the power system is increasing year by year, and the number of renewable energy power stations to be constructed and already in operation is increasing dramatically. However, the large-scale expansion and high proportion of renewable energy power stations connected to the grid have led to increasingly prominent voltage security problems in their own systems. The wind, light and other renewable energy resources in China are concentrated in the northwest, while the load center is in the coastal eastern region. The electric energy is sent out by long-distance transmission lines from west to east, so that large-scale renewable energy power stations are generally integrated into weak grid environments. Due to the small short-circuit capacity and large external equivalent impedance of the weak grid environment, the voltage at the point of common coupling point (PCC) of the renewable energy power station and the power system will change significantly with the fluctuation of the sent power. The large number of generator units of renewable energy (GURE) in the large-scale renewable energy power station are connected through long-distance collection lines. When the amount of renewable energy power sent through the collection line is large, it will cause a huge voltage drop at the beginning and end of the collection line. Thus, the overvoltage risk of the GURE access point at the end of the collection line is increased.

[0003] At present, the voltage optimization methods for ensuring the safe and stable operation of large-scale renewable energy power station systems mainly include model-driven and data-driven methods. 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 network operation scenarios with low system information perception. In addition, the model-driven method has the advantages of avoiding parameter overfitting and lack of generalization ability when obtaining the optimal solution of 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 the information of the whole system through the central controller and formulates the global optimal strategy. Although it has the characteristics of direct efficiency, with the expansion of the power station scale, its communication demand and calculation pressure increase significantly. The distributed voltage optimization method divides the original centralized voltage optimization problem into multiple independent sub-optimization problems and solves them respectively. The local optimization variables are updated and iterated by relying on the adjacent communication between the Agent controllers and the distributed optimization algorithm, so as to approach 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 is 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 finally converge to the global optimal solution, which is suitable for the scene with less communication burden.

[0005] The existing distributed voltage optimization methods, such as alternating direction multiplier method (ADMM), target cascade analysis method (ATC) and Benders decomposition, effectively control the voltage of the studied object system and achieve satisfactory regulation and control effect. However, the premise for the effectiveness of these distributed optimization algorithms is that the voltage optimization model of the system to be solved must be a convex optimization problem. Therefore, it is urgent to explore new distributed optimization methods to effectively solve the non-convex optimization problem corresponding to the voltage regulation and control of large-scale renewable energy power station system. SUMMARY

[0006] In view of the above problems of the prior art, the technical problem to be solved by the present application is how to provide a method capable of effectively solving the non-convex optimization problem corresponding to the voltage regulation and control of large-scale renewable energy power station system.

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

[0008] A large-scale renewable energy power station system voltage distributed non-convex optimization method, comprising the following steps:

[0009] S1, first construct a system voltage optimization model based on non-linear standard power flow constraints;

[0010] S2, divide the constructed system voltage optimization model into distributed optimization models of the collection side and the grid-connected side according to the PCC bus;

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

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

[0013] wherein, in which, is a set of collector-side nodes; is a column vector composed of node voltage magnitudes; V ref. is a column vector composed of node reference voltage magnitudes, each element in the vector is set to 1 p.u. nominal value; ||*||2 is the vector 2-norm; ":=" is the definition meaning, and is distinguished from "=" in the equality constraint formula; is a column vector composed of active power injected by each node on the collector side; P cg is the active power injected by the collector side through the PCC bus to the grid-connected side; ||*||1 is the vector 1-norm, ||P i ||1 is equal in value to the sum of the active power injected by each node on the collector side, and the difference between P cg is the network loss consumed on the internal collector line; ω V and ω P are weight coefficients;

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

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

[0016]

[0017] in which: P i , Q i are the active and reactive power injected by node i; V i , V j are the voltage magnitudes of nodes i and j; θ ij is the phase difference between nodes i and j; G ij , B ij are the real part and imaginary part of the element in the i-th row and j-th column of the node admittance matrix; is a set of grid-connected-side nodes;

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

[0019]

[0020] in which: P i,GURE , Q i,GURE are the active and reactive power output by GURE at node i; P i,MPPTS i,GURE is the maximum apparent power rating of GURE;

[0021] The voltage constraint of the collection side node is:

[0022]

[0023] wherein: V i is the voltage amplitude of node i; V i,min , V i,max respectively represent the minimum and maximum limit of the voltage amplitude when the system is safely running; θ i is the voltage phase of node i; θ i,min , θ i,max respectively represent the minimum and maximum limit of the voltage phase when the system is safely running.

[0024] Further, in the step S2, by copying the PCC bus, the constructed system voltage optimization model is decomposed into a grid-connected side subsystem and a plurality of collection side systems, and the constraint conditions of the system voltage optimization model further include the following coupling constraints:

[0025]

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

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

[0028]

[0029] and satisfies the collection side and grid-connected side power flow constraints;

[0030] The kth collection line side subsystem is:

[0031]

[0032] It also satisfies the power flow constraints on the collector side and the grid-connected side, the power balance constraints of the collector side nodes, and the voltage constraints of the collector side nodes;

[0033] In the formula, F G and F k,C These are the decomposed optimization objective functions, F G Empty; For the augmented Lagrangian function associated with their respective optimization problems; This is an augmentation item.

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

[0035]

[0036] The optimization problems for the grid-connected side and collector side under ALADIN are as follows:

[0037]

[0038] Where: X G and X k,C These are the original centralized model variables contained in the grid-connected subsystem and the collector line subsystem, respectively; These are the auxiliary variables generated in the grid-connected subsystem and the collector line subsystem after replicating the boundary nodes, respectively; λ is the dual multiplication term; ρ is the penalty function term; (*)′ represents the replication variable of the boundary coupling variable in the consensus problem; This represents the result after optimizing the variables, and it is a constant value. The symbol for vector transpose;

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

[0040]

[0041] J G and J k,C Respectively with constraints The associated Jacobian matrix, G G and G k,C They are respectively with the objective function Associated gradients, The approximate calculation result for the Hessian matrix is ​​defined as follows:

[0042]

[0043] ALADIN solves the voltage optimization consensus problem and constraints by alternately solving the constraint. and G Gand G k,C The distributed optimization solution is realized.

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

[0045]

[0046] wherein: is a related parameter in the linear search method, and is set as

[0047] Further, in the step S3, for the non-positive definite The negative eigenvalues in the non-positive definite are turned into opposite numbers, and the zero eigenvalues are replaced by positive numbers.

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

[0049]

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

[0051]

[0052] wherein: Blkdiag is a symbol operator of matrix block diagonalization.

[0053] In summary, the application has the following advantages:

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

[0055] 2) The application proposes to solve the non-convex voltage distributed optimization model by using a novel ALADIN distributed optimization algorithm. The ALADIN algorithm can complete convergence after a few iterations, and obtain almost the same voltage optimization result as the centralized optimization.

[0056] 3) The GURE reactive power output obtained by solving the non-convex voltage optimization model by the ALADIN can effectively optimize the voltages of each node of the large-scale renewable energy power station system to a relatively safe range. And the implementation of the ALADIN algorithm only needs adjacent communication of each distributed Agent controller, which is smaller than the communication burden of the conventional centralized voltage optimization method. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 Figure for large-scale renewable power plant system grid-connection analysis model.

[0058] Figure 2 Distributed communication system architecture for supporting large-scale renewable power plant system distributed voltage optimization.

[0059] Figure 3 Decomposition figure for large-scale renewable power plant system.

[0060] Figure 4 Flow chart for ALADIN algorithm implementation.

[0061] Figure 5 Intra-station power flow calculation error under LinDistFlow constraint.

[0062] Figure 6 Out-of-station power flow calculation error under LinDistFlow constraint.

[0063] Figure 7 Method A convergence situation under different p values.

[0064] Figure 8 Method A and method B convergence situation comparison.

[0065] Figure 9 Method A residual situation under different collection line numbers.

[0066] Figure 10 Method A residual situation under different GURE unit numbers.

[0067] Figure 11 Voltage distribution optimization result comparison figure. DETAILED DESCRIPTION

[0068] The application will be further described below in conjunction with the embodiments.

[0069] I. Large-scale renewable power plant system grid-connection analysis model and non-convex voltage optimization mathematical model

[0070] The grid-connection analysis model of the large-scale renewable power plant system is as follows Figure 1As shown: the model is divided into the power collection side and the grid-connected side. The renewable energy power station system is internally referred to as the power collection side, and multiple medium-voltage power collection lines of the power collection side are connected in parallel at the PCC bus. Further, multiple GUREs composed of wind and light generating equipment are connected in parallel on each medium-voltage power collection line. The electric energy produced by all GUREs in the renewable energy power station system is collected at the PCC bus. 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 bus is boosted by the substation and finally transmitted to the receiving end AC power grid through the high-voltage transmission line. The PCC bus is the coupling link between the power collection side and the grid-connected side. It should be noted that the tap position adjustment of the booster station is not included in the optimization problem in the grid-connected analysis model of the embodiment, because the response speed of the tap position adjustment of the booster station is much smaller than that of the output power adjustment of the GURE, and the tap position adjustment should not be frequently adjusted due to the service life factor. Therefore, in the grid-connected analysis model of the system built in the embodiment, the tap position of the booster station is regarded as a constant value.

[0071] In the above large-scale renewable energy power station system topology, the power-voltage steady-state relationship between the power collection side and the grid-connected side can be analyzed by using an impedance model. For the power collection side: 1) the impedance parameters of each medium-voltage power collection line are considered; 2) without loss of generality and accuracy, the internal converter losses of the GURE are ignored, so the coupling nodes of each GURE and the power collection line are regarded as PQ nodes, and the corresponding node injection power is the output power of the GURE. For the grid-connected side: 1) the booster substation is treated as an ideal transformer; 2) the relevant parameters of the long-distance transmission line and the receiving end 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 end AC power grid is regarded as a balanced node.

[0072] Considering the operation characteristics of large-scale renewable energy power stations "large-scale topology and weak grid integration": for the grid-connected side outside the system, because the renewable energy power station is far away from the load center, the long-distance transmission line for power export makes the system generally integrated into a weak grid environment, and the Thevenin equivalent impedance of the grid-connected side is large; for the power collection side inside the system, the large-scale renewable energy power station occupies a large area, and the medium-voltage power collection line connecting each GURE is long, and the line impedance is also large. Therefore, when the renewable energy power station performs large-scale power export, the power loss on the line impedance is large, and the influence 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 the embodiment involves an objective function and constraint conditions. 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 plant systems: Large-scale renewable energy power plant systems should ensure that the voltage amplitude of each node has as much safety margin as possible, so as to avoid overvoltage exceeding the limit when the system node voltage shifts due to GURE output fluctuations. The corresponding objective function is shown below:

[0075]

[0076] in: For collector-side nodes; V is a column vector consisting of the magnitudes of the node voltages. ref. This is a column vector composed of the node reference voltage amplitudes, with each element set to the 1p.u. nominal value; ||*||2 is the vector 2-norm; ":=" is a defined meaning, distinguishing it from the "=" in the equality constraint formula.

[0077] Network losses in large-scale renewable energy power plant systems: To improve the economics of large-scale power transmission, it is necessary to minimize the internal network losses of large-scale renewable energy power plant systems. The corresponding objective function is shown below:

[0078]

[0079] in: Inject a column vector of active power into each node on the collector side; P cg This represents the active power injected into the grid-connected side from the collector side via the PCC bus; ||*||1 is the vector norm 1, ||P i ||1 is numerically equal to the sum of the active power injected into each node on the collector side, and it is related to P cg The difference is the network loss consumed on the collector lines inside the large renewable energy power plant 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: ω V and ω P This is a weighting 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 grid-connected side, power balance constraints at the collector side nodes, and voltage constraints at the collector side nodes.

[0084] Power flow constraints of collection side and grid-connected side: Large-scale renewable energy power station system has the problem of large internal and external line impedance and much power loss. In this case, the power flow calculation error brought by the linearization power flow constraint based on LinDistFlow cannot be ignored, which will significantly reduce the effectiveness of voltage optimization decision. Therefore, in order to ensure the accuracy of decision, the embodiment still constructs the power flow constraints of collection side and grid-connected side based on the nonlinear standard power flow model:

[0085]

[0086] Where: P i , Q i are the active and reactive power injected at node i; V i , V j are the voltage magnitudes at node i and j; θ ij is the phase difference between node i and j; G ij , B ij are the real and imaginary parts of the admittance matrix element in the i-th row and j-th column; is the set of grid-connected side nodes.

[0087] Power balance constraints of collection side nodes: The injected power of each node in the collection side of the large-scale renewable energy power station system comes from GURE. The active power output of GURE is determined by the maximum power point tracking power that can be utilized, and the reactive power output of GURE is determined by the solution result of the constructed voltage optimization model. The corresponding constraint conditions are as follows:

[0088]

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

[0090] Voltage constraints of collection side nodes: The amplitude and phase angle of the voltage of the collection side nodes should meet the corresponding constraints, as shown below:

[0091]

[0092] Where: V i is the voltage magnitude at node i; V i,min , V i,max represent the minimum and maximum limits of the voltage magnitude when the system is safely running; θ i is the voltage phase at node i; θ i,min , θ i,maxrespectively represent the minimum value, the maximum limit value of the voltage phase of the system when running safely.

[0093] Secondly, the distributed communication architecture and the distributed voltage optimization problem of large-scale renewable energy power station

[0094] As the condition basis of the system distributed voltage optimization, the embodiment will first construct a distributed communication architecture suitable for the characteristic requirements of the structure of large-scale renewable energy power station. Then, combined with the communication architecture, the original centralized voltage optimization problem is split to construct the distributed voltage optimization problem.

[0095] Distributed communication architecture: the traditional centralized communication is a "point-to-point" communication mode. For renewable energy power station, if the centralized communication mode is adopted, the communication connection between each GURE unit and the central controller needs to be established. However, with the large-scale of renewable energy power station system, the installed capacity expands rapidly, and the number of GURE units will increase significantly. The central controller as the center node will face huge information processing pressure and is difficult to cope with a large number of GURE unit regulation requests. Considering the disadvantages of centralized communication and the structure characteristics of the station cluster of large-scale renewable energy power station, the original system is split into multiple subsystems, and only adjacent distributed communication between the Agent controllers of each subsystem is more suitable for the scenario of the embodiment.

[0096] The distributed communication architecture adopted by the embodiment is shown in Figure 2 : the PCC bus and each collection line in the station are configured with distributed Agent controllers, each GURE on the collection line is regulated by the collection line Agent controller, and the boundary information is transmitted between each collection line Agent and the PCC bus Agent. This distributed communication mode regulates the collection lines in the station by partition, rather than configuring a separate Agent for each GURE to regulate, thereby avoiding the problem of slow convergence caused by excessive Agent configuration.

[0097] Distributed voltage optimization problem: according to the distributed communication architecture shown in Figure 2 , the large-scale renewable energy power station is split in the manner shown in Figure 3 . By copying the PCC bus, the original system is divided into a grid-connected side subsystem and several collection side systems. At this time, the following coupling constraints need to be added:

[0098]

[0099] Where: P PCC,G , Q PCC,G , V PCC,G and θ PCC,GP k,PCC,C , Q k,PCC,C , V k,PCC,C and θ k,PCC,C are the active power, reactive power, voltage magnitude and phase angle of the boundary node on the PCC bus of the kth feeder. K C is the number of feeders inside the renewable energy power plant.

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

[0101]

[0102] wherein equations (8) and (9) are the distributed voltage optimization problems corresponding to the grid-side subsystem and the kth feeder-side subsystem, respectively; F G and F k,C are the decomposed optimization objective functions, wherein F G is empty, and the main role of equation (8) is to provide boundary electrical quantity information for the optimization calculation of equation (9); is the augmented Lagrangian function associated with each optimization problem, wherein the augmented term will be described in detail later.

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

[0104] The embodiment compares the distributed optimization solution process of the novel ALADIN algorithm and the classic ADMM algorithm, in order to show the key points when applying the ALADIN algorithm to the distributed optimization of the non-convex voltage optimization model of the embodiment. In particular, the special steps in the ALADIN solution process will also be highlighted.

[0105] Comparison of distributed optimization solution of ALADIN and ADMM, ALADIN and ADMM have similar distributed iteration processes, that is, the Lagrange multiplier is iteratively updated by alternating direction, but the two methods differ in the construction of the augmented Lagrangian function and the consensus problem. In order to better illustrate the characteristics and advantages of ALADIN, first introduce the distributed optimization solution process of ADMM, and then further illustrate the distributed optimization solution process of ALADIN. Among them, the distributed optimization solution of ADMM is as follows:

[0106] The grid-side and feeder-side sub-optimization problems under ADMM are constructed according to equations (8) and (9). In particular, is written as follows:

[0107]

[0108] wherein: X G and X k,C are the original centralized model variables contained in the grid-side subsystem and the line-side subsystem, respectively; are the auxiliary variables generated in the grid-side subsystem and the line-side subsystem, respectively, after replicating the boundary nodes; denotes the expression under ADMM; λ G and λ k,C are the dual multiplier terms; ρ is the penalty function term; (*)' denotes the replicated variables of the boundary coupled variables in the consensus problem; denotes the result of the variable optimization solution, which is a constant value; is the vector transpose symbol.

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

[0110]

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

[0112]

[0113] wherein: (*) [ n ] denotes the optimization result after the nth iteration.

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

[0115] The grid-side and line-side subsystem optimization problems under ALADIN are also constructed according to equations (8) and (9). However, the expression of is as follows:

[0116]

[0117] wherein: denotes the expression under ALADIN; unlike ADMM, in the grid-side and line-side subsystem optimization problems shown in equations (14) and (15), λ is unified.

[0118] Similar to ADMM, there is also a voltage optimization consensus problem formed in ALADIN:

[0119]

[0120] In particular, the constraints of the sub-problems in (8) and (9) are expressed as

[0121]

[0122] J G and J k,C are the Jacobian matrices associated with the constraints G G and G k,C are the gradients associated with the objective functions H is the Hessian approximation, which is defined as

[0123]

[0124] ALADIN solves the distributed optimization problem by alternatively solving (16), (17) and (18). The key auxiliary variables and dual multiplier terms are updated by a linear search method:

[0125]

[0126] where are the related parameters in the linear search method, which can be set as

[0127] In summary, the splitting idea of the original centralized voltage optimization problem is consistent when applying ALADIN and ADMM for distributed optimization, and both methods use an augmented term to deal with the boundary coupling constraints at PCC buses in the original centralized voltage optimization problem. The difference is that ADMM needs to solve the convex sub-problems of the original problem in each iteration, while ALADIN uses an inexact Newton method to approximately solve the sub-problems, which makes the convergence of ALADIN strictly guaranteed when dealing with non-convex optimization problems. The overall implementation process of ALADIN is shown in Figure 4

[0128] ALADIN algorithm is particularly noted that:

[0129] 1) The Hessian approximation matrix needs to be positive definite to make the ALADIN algorithm converge. However, it cannot be strictly guaranteed to be positive definite in each iteration, so it needs to be regularized. Here, the negative eigenvalues in are flipped to the opposite number, and the zero eigenvalues are replaced by a very small positive number.

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

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

[0132]

[0133] In formula (21), ΔX, 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 symbol operator of matrix block diagonalization.

[0136] As can be seen from the above discussion, the optimization solution of the quadratic programming problem formula (16) can be equivalently converted into the solution of the linear equation formula (22). Since the symmetric coefficient matrix contained in formula (22) has a sparse characteristic, a high-performance linear solver can be used to obtain a high-quality solution.

[0137] Four, example analysis

[0138] This embodiment uses a large-scale renewable energy power station system with an installed capacity of 8x12x2MW for example analysis to verify the effectiveness of the method. The system parameters are shown in Table 1: There are 8 collection lines in parallel inside the large-scale renewable energy power station, and 12 groups of GUREs are connected in sequence at equal distances on each collection line. It is a large-scale collection system. The external transmission environment of the large-scale renewable energy power station uses a Thevenin model for equivalence. Under the set equivalent impedance, the system short-circuit capacity ratio is 5.27, which can be regarded as being connected to a weak power grid environment.

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

[0140]

[0141] The example-related programs are compiled in the MATLAB environment. The non-convex voltage optimization mathematical model of large-scale renewable energy power station based on the ALADIN algorithm is realized by means of the CasADi framework; the non-convex sub-optimization problems (14) and (15) of the grid-connected side and the power collection side are solved by using the IPOPT solver; the voltage optimization consensus problem (16) is converted into a linear equation set (22), and the MA57 sparse matrix solver is used to complete the solution. The power flow calculation involved in the example analysis is realized by using the MATPOWER tool package, and is 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 is regarded as the benchmark result of the voltage optimization. All the programs involved above are executed by using a computer configured as a 2.5-GHz CPU / 16GB RAM, and the algorithm solving time is measured by using the tic / toc command built in MATLAB.

[0142] In particular, for the convenience of subsequent comparative description, three distributed optimization schemes are defined as follows:

[0143] Method A: the ALADIN algorithm is used to solve the non-convex voltage optimization model based on the nonlinear standard power flow constraint in a distributed manner, which is the method proposed in this embodiment;

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

[0145] Method C: the ADMM algorithm is used to solve the convex voltage optimization model based on the linear LinDistFlow power flow constraint in a distributed manner.

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

[0147] Necessity analysis of non-convex voltage optimization model: To verify the necessity of using non-linear standard power flow constraints to establish non-convex voltage optimization model for large-scale renewable power station system, this subsection analyzes the system power flow calculation error based on linearized power flow constraints LinDistFlow. Since the non-convex voltage optimization model proposed in this embodiment uses non-linear standard power flow constraints, the power flow calculation result is consistent with the benchmark value, so there is no need to compare it in particular.

[0148] Firstly, the influence of the size of renewable power station system on the accuracy of the calculation of the power flow of the station's collection line when the linearized power flow constraints LinDistFlow are used to replace the non-linear standard power flow constraints is analyzed. In the example analysis, the active output of each GURE is set to 1.6 MW, and the reactive output is set to 0 MVar. Figure 5 The station's power flow calculation error based on linearized power flow constraints LinDistFlow is shown by Figure 5 (a) It can be seen that, with the increase of the number of parallel collection lines, the calculation error of the node voltage of the collection line and the active loss of the collection line increases; by Figure 5 (b) It can be seen that, with the increase of the number of GUREs on a single collection line, the calculation error of the node voltage of the collection line and the active loss of the collection line increases.

[0149] Then, the influence of the external grid-connected environment on the accuracy of the calculation of the power flow of the section from the PCC bus to the receiving end of the external grid when the linearized power flow constraints LinDistFlow are used to replace the non-linear standard power flow constraints is analyzed. In the example analysis, the grid-connected active power at the PCC bus is set to 50 MW, and the reactive power is set to 20 MVar. The short-circuit capacity ratio is changed to affect the size of the external grid's Thevenin equivalent impedance, thereby representing the change of the strength of the external grid-connected environment. Figure 6 The station's power flow calculation error based on linearized power flow constraints is shown by the figure, which shows that, with the decrease of the short-circuit capacity ratio, i.e. the change of the external grid-connected environment from strong to weak, the calculation error of the PCC bus voltage and the active loss of the external equivalent grid increases.

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

[0151] Convergence advantage verification of ALADIN distributed optimization: The convergence of method A and method B in solving non-convex voltage optimization model is analyzed. When distributed optimization is performed, the initial value of the boundary coupling variable involved is uniformly set to 0, the initial value of the Lagrange multiplier is set to 1, and the convergence condition is that the primal and dual residuals are both less than 1×10 -4 (As can be considered that the boundary voltage term residual should be less than 0.0001 p.u., and the boundary power term residual 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 of hundreds of megawatts, this convergence condition is reasonable).

[0152] Firstly, the convergence of method A under different penalty function coefficients ρ is analyzed, as shown in Figure 7 : 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 less than 1×10 -4 ) in about 8 iterations. When the number of iterations continues to increase to 12, the residual under different ρ values all drops to 1×10 -7 , reaching the ideal convergence.

[0153] Further, the convergence of method A and method B is compared to illustrate that the ALADIN algorithm has an advantage in convergence compared to the traditional ADMM algorithm in distributed solving of non-convex optimization problems. As previously described, since the value of ρ does not significantly affect the convergence of ALADIN, method A with ρ = 10 is selected for comparative analysis. However, the value of ρ significantly affects the convergence of ADMM. Therefore, for fair comparison, method B under multiple ρ values is listed for comparative analysis. The comparison results are shown in Figure 8 : The convergence of method B is very sensitive to the value of ρ, and both too large and too small ρ values will cause method B to converge slowly. Method B with ρ = 15 has relatively the best convergence, but it also needs about 70 iterations to meet the convergence condition. Method A has a significantly better convergence rate than method A, with the primal and dual residuals both dropping to 1×10 -7 after about 10 iterations.

[0154] Finally, the influence of the scale of renewable energy power stations on the convergence of the ALADIN algorithm is verified. By increasing the number of parallel lines and the number of GURE units connected to the collection line, the convergence of method A (based on ρ = 10) is analyzed, as shown in Figure 9 and Figure 10 : With the increase of the number of parallel lines or the number of GURE units connected to the collection line, ALADIN always maintains good convergence. After about 10 iterations, the primal and dual residuals under different system scales all drop to 1×10-7 The convergence is ideal.

[0155] In summary: ① The convergence of ALADIN (Method A) algorithm is robust to parameter variation, while the convergence of ADMM (Method B) algorithm is sensitive to parameter variation; ② Regardless of parameter value, ALADIN algorithm converges in a small number of iterations, while ADMM algorithm still needs a large number of iterations to converge under suitable parameter value; ③ With the expansion of the scale of renewable energy power station system, ALADIN algorithm still has good convergence.

[0156] Optimality advantage verification of ALADIN distributed optimization calculation: First, by comparing the distributed optimization results of Method A, Method B and Method C on the voltage of large-scale renewable energy power station system, it is shown that the proposed method ensures the accuracy and convergence in the distributed voltage optimization process of large-scale renewable energy system by establishing a reasonable optimization model and using an effective optimization algorithm. Figure 11 The voltage distribution optimization of the PCC bus to the end node of a certain collection line is shown based on the various methods compared in the embodiment (wherein #0 represents the PCC bus node, and #1-#12 represent the serial numbers of the nodes of the GUREs on the collection line). In particular, Table 2 gives the relevant numerical results of each distributed optimization method in the iterative calculation process.

[0157] In combination Figure 11 In combination with Table 2, when there is no voltage optimization method (i.e., Q i,GURE is set to 0), the voltage of some nodes of the renewable energy power station exceeds the allowed upper limit, so it is necessary to perform voltage optimization control. When Method B is used to implement voltage optimization control, 69 iterations are needed to complete convergence, and the time consumption is 48.82 seconds; Method C can complete convergence after 30 iterations, and since the convex optimization problem is solved at each iteration, the time consumption of each solving is also short, and the total time consumption is only 3.77 seconds. However, the convex voltage optimization model solved by Method C uses linearized power flow constraints, resulting in a large error between the expected voltage regulation result obtained by the optimization model and the actual voltage based on power flow calculation, and the actual voltage deviation will be much higher than the expected voltage deviation, and the optimized system voltage even appears low voltage out-of-limit. Compared with the above methods, Method A completes convergence in a very small number of iterations (7 times), and the time consumption of solving is roughly equal to that of Method C, only 5.22 seconds. And since the non-convex voltage optimization model solved by Method A uses nonlinear standard power flow constraints, the expected voltage regulation result is consistent with the actual voltage. For example, Figure 11As shown, the voltage of each node in the calculation result of method A is optimized to about 1 p.u., and the overall system voltage is in a relatively safe range, eliminating the risk of overvoltage exceeding the limit.

[0158] Table 2 Comparison of calculation results of each distributed optimization method

[0159]

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

[0161] Finally, the objective function value after compensation and the corresponding value before compensation are compared to intuitively show the voltage regulation effect of ALADIN on the large-scale renewable power station system. Table 4 compares the objective function before and after node reactive power compensation. As can be seen from the table, through method A to optimize the GURE reactive power output for system node reactive power compensation, the objective function value is significantly reduced, and the voltage deviation is particularly obvious. Due to the additional reactive power compensation, the current flowing through the collection line increases, and the overall active power loss of the optimized system increases compared to that before optimization. However, thanks to considering minimizing the active power loss as one of the optimization objectives, the active power loss result after optimization only increases slightly.

[0162] Table 3 Comparison of optimized node reactive power compensation results of the collection line

[0163]

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

[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 the error caused by the LinDistFlow linearization power flow constraint affects the actual voltage distribution of the system and the expected voltage distribution, and the overall voltage deviation of the system is even larger than before optimization; compared with the above, when using ALADIN to solve the non-convex voltage optimization model (method A), only a small number of iterations are required to complete convergence, and the solution takes a short time, and the node reactive power compensation results obtained by distributed optimization are almost the same as those obtained by centralized optimization. Under the action of ALADIN, the voltage distribution of the system is optimized to a relatively safe range.

[0167] In summary, to solve the overvoltage risk faced by large-scale renewable power plant power transmission, the embodiment constructs a non-convex distributed optimization model for voltage regulation of large-scale renewable power plant system, and realizes efficient distributed optimization solution of the model through ALADIN algorithm. Combined with theoretical analysis and example test, the main conclusions are as follows:

[0168] 1) Linearized approximation power flow constraints such as LinDistFlow can cause large errors in the calculation of the voltage of large-scale renewable power plant system. The non-convex voltage distributed optimization model established based on the non-linear standard power flow constraint in the embodiment can provide accurate system voltage calculation results, and is suitable for the operation scenario of large-scale layout and long-distance power transmission of renewable power plant system.

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

[0170] 3) The GURE reactive power output obtained by solving the non-convex voltage optimization model by ALADIN can effectively optimize the voltage of each node of the large-scale renewable power plant system to a relatively safe range. And the implementation of ALADIN algorithm only requires adjacent communication of each distributed Agent controller, which causes less communication burden to the power plant than the conventional centralized voltage optimization method.

[0171] The above merely describes the preferred embodiments of the present application, and is not intended to limit the present application. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A distributed non-convex optimization method for voltage in a large-scale renewable energy power plant system, characterized in that, Includes the following steps: S1. First, construct a system voltage optimization model based on nonlinear standard power flow constraints; S2. Taking the PCC bus as the boundary, the constructed system voltage optimization model is divided into distributed optimization models for the collector side and the grid-connected side. S3. Construct a voltage optimization consensus problem under ALADIN and use the ALADIN algorithm for distributed optimization solution; In step S3, the voltage optimization consensus problem under ALADIN is constructed as follows: ； Among them, the optimization problems of the grid-connected side and collector side under ALADIN are: ； ； in: and These are the original centralized model variables contained in the grid-connected subsystem and the collector line subsystem, respectively; and These are the auxiliary variables generated in the grid-connected subsystem and the collector line subsystem after replicating the boundary nodes, respectively. For dual multiplication of subterms; For the penalty function term; This represents a copy variable of the boundary coupling variable in the consensus problem. This represents the result after optimizing the variables, and it is a constant value. This is the vector transpose symbol.

2. The voltage distributed non-convex optimization method for large-scale renewable energy power plant systems as described in claim 1, characterized in that, In step S1, the objective function of the system voltage optimization model is: ； in, , In the formula, For collector-side nodes; A column vector consisting of the node voltage magnitudes; This is a column vector consisting of the node reference voltage magnitudes, with each element in the vector set to a 1p.u. nominal value; It is the 2-norm of the vector; " is defined and has the same meaning as the " in the equation constraint formula" "To distinguish; Inject a column vector of active power into each node on the collector side; This refers to the active power injected into the grid-connected side from the collector side via the PCC bus; For vectors, the 1-norm, Numerically, it is equal to the sum of the active power injected into each node on the collector side, and it is equal to... The difference is the network loss consumed on the internal collector wires; and These are the weighting coefficients; The constraints of the system voltage optimization model include power flow constraints on the collector side and grid-connected side, power balance constraints on the collector side nodes, and voltage constraints on the collector side nodes. The power flow constraints on the collector side and the grid-connected side are as follows: ； In the formula: , Inject active and reactive power into node i; , The voltage amplitudes at nodes i and j; The phase difference between nodes i and j; , Let be the real and imaginary parts of the elements in the i-th row and j-th column of the node admittance matrix; For the set of nodes on the grid-connected side; The power balance constraint for the collector-side nodes is: ； In the formula: , The active and reactive power output by GURE at node i; The maximum power point tracking power available to GURE at node i is considered a constant. This represents the maximum apparent power rating of the GURE; GURE stands for Renewable Energy Generation Unit. The collector-side node voltage constraint is: ； In the formula: Let be the voltage amplitude at node i; , These represent the minimum and maximum limits of voltage amplitude during safe system operation, respectively. Let i be the voltage phase at node i; , These represent the minimum and maximum voltage phase values, respectively, during safe system operation.

3. The voltage distributed non-convex optimization method for large-scale renewable energy power plant systems as described in 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 subsystem and several collector-side systems. The constraints of the system voltage optimization model also include the following coupling constraints: ； in: , , as well as The active power, reactive power, voltage amplitude, and phase of the boundary nodes on the PCC bus on the grid-connected side; , , as well as Let represent the active power, reactive power, voltage amplitude, and phase of the boundary node on the PCC bus of the k-th collector line. This refers to the number of collector lines inside a renewable energy power plant.

4. The voltage distributed non-convex optimization method for large-scale renewable energy power plant systems as described in claim 3, characterized in that, The distributed optimization model constructed based on the system voltage optimization model includes a grid-connected subsystem and a subsystem for the k-th collector line. The grid-connected subsystem is as follows: ； And satisfy the power flow constraints on both the collector side and the grid-connected side; The subsystem on the k-th collector line side is: ； It also satisfies the power flow constraints on the collector side and the grid-connected side, the power balance constraints of the collector side nodes, and the voltage constraints of the collector side nodes; In the formula, and These are the optimization objective functions after decomposition. Empty; and For the augmented Lagrangian function associated with their respective optimization problems; and This is an augmentation item.

5. The voltage distributed non-convex optimization method for large-scale renewable energy power plant systems as described in claim 1, characterized in that, In step S3 and The constraints are expressed as follows: ； and Respectively, and constraints and The associated Jacobian matrix, and They are respectively with the objective function and Associated gradients, and The approximate calculation result for the Hessian matrix is ​​defined as follows: ； ； ALADIN solves the voltage optimization consensus problem and constraints by alternately solving the constraint. and ,as well as and Implement distributed optimization solutions.

6. The voltage distributed non-convex optimization method for large-scale renewable energy power plant systems as described in claim 5, characterized in that, In step S3, the auxiliary variables and dual multiplicative terms obtained by ALADIN are updated using a linear search method: ； in: , and For the relevant parameters in the linear search method, set as follows: .

7. The voltage distributed non-convex optimization method for large-scale renewable energy power plant systems as described in claim 6, characterized in that, In step S3, for non-positive definite... and , will be non-positive definite and The negative eigenvalues ​​are flipped to their opposites, and the zero eigenvalues ​​are replaced with positive numbers.

8. The voltage distributed non-convex optimization method for large-scale renewable energy power plant systems as described in claim 6, characterized in that, In step S3, the Lagrangian function corresponding to the voltage optimization consensus problem is: ； In the formula, , For original variables, , For the dual variable, the corresponding KKT conditions are: ； ； ； in: The symbolic operator for block diagonalization of a matrix.

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