In-line chance-constrained large-scale wind farm station parallel distributed voltage optimization method

Abstract

The application discloses a large-scale wind power station in-parallel distributed voltage optimization method embedded with opportunity constraints. In view of node voltage fluctuation caused by wind power uncertainty, firstly, a station in-deterministic optimization model with the minimum node voltage deviation and network loss as targets is constructed; then, based on the correlation of wind turbine prediction error, the node voltage random disturbance relationship caused by the wind turbine prediction error is derived, and the node voltage opportunity constraint is equivalently converted into a deterministic tightening boundary constraint; then, taking a common connection point (PCC) bus as a coupling boundary, the model is decoupled into a grid-side and a plurality of power collection-side subsystems, and uniformity constraints of boundary active power, reactive power and voltage square are constructed; finally, a quadratic auxiliary coordination term limiting the change of adjacent iteration variables is introduced into the target functions of the subsystems, and parallel alternating solution and uniformity constraint iteration are performed until convergence. The application can effectively coordinate the station operation state, and significantly improve the convergence performance of parallel distributed solution.

Description

Technical Field

[0001] This invention belongs to the field of new energy power generation and power system operation control technology, specifically relating to a parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints. Background Technology

[0002] With the continuous growth of new energy installed capacity, wind power has become an important support for the low-carbon transformation of the power system. Large-scale wind farms typically contain a large number of wind turbines and long in-station collection lines. The output of the turbines needs to be collected by the collection system before being sent to the external power grid. Affected by factors such as wind power output fluctuations, line impedance voltage drop, and reactive power distribution, the node voltage within the wind farm is prone to exceeding the limit risk. Especially in the context of large-capacity wind power grid connection, the voltage safety within the station is not only related to the operating status of the wind turbines themselves, but also affects the overall power transmission capacity of the wind farm. In addition, existing optimization studies mostly determine the operating status based on the predicted wind power output. The optimization results obtained mainly ensure that the predicted operating point meets the voltage constraints, which is difficult to reflect the range of node voltage changes and the risk of exceeding limits after the actual output deviates from the predicted value.

[0003] In terms of voltage regulation within wind farms, existing research mainly employs centralized optimization methods to uniformly configure the reactive power output of all wind turbines. However, as the number of wind turbines and collector lines increases, the number of power flow variables, reactive power regulation variables, and operational constraints in the model also increases accordingly. Simultaneously, the central controller needs to continuously collect and process operational information from across the entire farm, placing higher demands on communication systems and computing power.

[0004] To address this, existing research has gradually adopted distributed optimization methods, reducing the solution scale of individual subproblems through system partitioning and boundary coordination. Based on the solution order of subproblems, distributed computing can be divided into serial and parallel approaches. In the serial approach, subsequent subsystems can use the boundary information updated in the current iteration, but there is a strict sequential dependency between subproblems. In the parallel approach, subsystems can be solved simultaneously, but they typically use historical boundary information from the previous iteration, resulting in a certain lag in variable updates. When the coupling terms in the local objective function do not adequately utilize historical iteration information, distributed parallel solutions are prone to residual fluctuations, slow convergence speeds, and even convergence failures. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is: how to provide a...

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints includes the following steps: S1. Construct a deterministic voltage optimization mathematical model for the system within a large wind farm. The deterministic voltage optimization mathematical model constructs an overall objective function with the optimization objectives of minimizing the node voltage deviation and network loss within the system within the large wind farm as the optimization objectives, and uses wind farm power flow constraints, wind turbine capacity constraints, collector line capacity constraints, and wind farm node voltage constraints as constraints. S2. Based on the correlation between the active power output prediction errors of each wind turbine, the voltage opportunity constraints of the nodes in the wind farm are equivalently transformed into deterministic tightening boundary constraints to replace the wind farm node voltage constraints in the deterministic voltage optimization mathematical model. S3. Using the common connection point PCC bus as the coupling boundary, the deterministic voltage optimization mathematical model containing the deterministic tightening boundary constraints is decoupled and divided into a grid-connected subsystem and several collector-side subsystems, and a consistent coupling constraint of boundary active power, boundary reactive power and boundary voltage amplitude square between the grid-connected subsystem and each collector-side subsystem is established. S4. In the local objective functions of the grid-connected subsystem and each of the collector-side subsystems, a quadratic auxiliary coordination term is introduced to limit the change amplitude of boundary variables between two adjacent iterations. In the parallel update mode, the grid-connected subsystem and each of the collector-side subsystems are solved independently and in parallel based on the boundary history information of the previous iteration, and are alternately coordinated and updated through the consistency coupling constraint until the algorithm meets the convergence condition and outputs the optimal reactive power output value of each wind turbine.

[0007] As an optimization, the process of constructing the deterministic voltage optimization mathematical model in step S1 includes: The overall objective function is constructed as follows: in, and These are the weighting coefficients for the node voltage deviation target and the in-station network loss target, respectively; the node voltage deviation objective function is: In the formula, Describes the 2-norm of a vector. It is a voltage vector composed of the voltages of each node in the wind farm. The reference voltage vector, composed of the voltage references of each node in the wind farm, is expressed as: The objective function for network loss within the site is: in, Let be the resistance of branch ij. and Let represent the active power and reactive power transmitted from the first node i to the last node j on branch ij, respectively. This is a collection of branch roads for the entire wind farm. It is the set of nodes of the entire wind farm; A linear approximation of the circular boundary of the apparent power capacity constraint of the collector line is made using an circumscribed regular polygon, and the linear approximation constraint is expressed as follows: in, The maximum apparent power allowed to be transmitted by branch ij. The number of sides of the selected regular polygon.

[0008] As an optimization, in step S2, a covariance matrix of the wind turbine power output prediction error is constructed based on the correlation between the active power output prediction errors of each wind turbine. Specifically, it includes: The power model that treats the actual active power output of a wind farm as a combination of predicted values ​​and prediction errors, including the vectors of actual, predicted, and prediction error values ​​of the active power output of each wind turbine in the wind farm, is as follows: in, , and These represent the actual value vector, predicted value vector, and prediction error vector of the active power output of each wind turbine, respectively, with elements in the vectors... , and These represent the actual value, predicted value, and prediction error value of the active power output of wind turbine unit k, respectively. It follows a normal distribution with a mean of 0 and a covariance matrix of . ; This represents the total number of nodes in the wind farm. Based on the correlation coefficient matrix between the prediction errors of each wind turbine and standard deviation diagonal matrix Construct the covariance matrix : in, and Expanded representation: in, For wind turbines Standard deviation of active power output prediction error; Elements contained Indicates wind turbine With wind turbine The correlation coefficient between the active power output prediction error and the actual power output prediction error.

[0009] Furthermore, in step S2, deriving the relationship between the active power output prediction error and the random disturbance of node voltage based on the power flow model specifically includes: Construct a compact matrix-form power flow model based on LinDistFlow: in, It is a column vector of all 1s with dimensions of . ; , These are the node injection power vectors, which consist of the active and reactive power injected by each node that is not the root node. , These are the branch power vectors composed of the active and reactive power flows of each branch; The voltage vector is composed of the squared values ​​of the voltages at each non-equilibrium node. The square of the root node voltage; defined , This is the reduced-order branch-node incidence matrix for non-root nodes; , Let be the matrix representing the influence of active power and reactive power injected into the node on the square of the node voltage, respectively, and satisfy the following: In the formula, , These are diagonal matrices composed of the resistances and reactances of each branch; Substituting the power model into the power flow model yields: in, The square vector of node voltage amplitude after taking into account the wind turbine output prediction error; This is the square vector of node voltage amplitudes based on the predicted wind turbine output. This is the squared fluctuation vector of the node voltage amplitude based on the wind turbine output error; Covariance matrix of collector line node voltage disturbance satisfy: Collection line node The standard deviation of voltage disturbance is ,in Covariance matrix The One diagonal element.

[0010] Furthermore, in step S2, the voltage machine is subject to the following constraints: Where CL is the given one-sided confidence level, and Pr(×) represents the probability of the random event within the parentheses occurring; Based on the voltage disturbance standard deviation and the inverse function of the cumulative distribution function of the standard normal distribution. The voltage opportunity constraint is equivalently transformed into a deterministic tightening boundary constraint: in, and They are nodes The upper and lower limits of the permissible square of voltage amplitude. CL represents the confidence level and is the one-sided quantile of the corresponding standard normal distribution.

[0011] As an optimization, in step S3, the consistency coupling constraint between the grid-connected subsystem and each of the collector-side subsystems is as follows: Among them, P PCC,G,k Q PCC,G,k and v PCC,G,k Let P be the PCC boundary variables associated with the k-th collector line on the grid-connected side; PCC,C,k Q PCC,C,k and v PCC,C,k These are the corresponding collector-side boundary variables; K C This represents the number of collector lines inside the wind farm.

[0012] Furthermore, in step S3, the PCC boundary variables of the grid-connected side and the k-th collector-side subsystem are respectively expressed as: D is the sign transformation matrix for boundary variables, expressed as: Among them, z G,k and z C,k These are the PCC boundary variables corresponding to the grid-connected side and the k-th collector-side subsystem, respectively; h k Let be the boundary consensus deviation of the k-th PCC.

[0013] Furthermore, in step S4, in the first... During the next iteration, the grid-connected side and the first Secondary auxiliary coordination items introduced on the collector side , for: in, This refers to the number of collector-side subsystems. , These are the boundary variable vector values ​​obtained from the previous iteration; The auxiliary parameter diagonal matrix is ​​represented as follows: in, , , These are the weighting coefficients for auxiliary parameters corresponding to active power, reactive power, and the square of voltage amplitude, respectively; αt G,k and αt C,k are the coordination coefficient vectors for the grid-connected side and the k-th collector side, respectively, expressed as: In the formula, For the first The Lagrange multiplier vectors corresponding to the PCC consensus constraints. This refers to the penalty parameters for the secondary penalty item.

[0014] Furthermore, in step S4, the steps of solving the distributed optimization subproblem, updating the consensus residual, multiplier iteration, and convergence determination are as follows: By incorporating the quadratic auxiliary coordination terms corresponding to the grid-connected side and the kth collector side into the regional objective functions of the grid-connected side and the collector side, a distributed optimization subproblem based on the auxiliary term expansion method is obtained: in, and They are respectively the grid-connected side and the first All optimization variables for the collector-side subsystem problem and These are the feasible regions for the corresponding areas. and The objective function is a function that does not contain a coordinating term; After the solution is completed, the first Group Boundary Consensus Bias Residual and Lagrange multipliers The update and iteration formula is: in, , These are the updated boundary variable vectors; after calculating and determining that the original residual and the dual residual both fall below the preset convergence threshold, the algorithm terminates and outputs the optimal reactive power output value of each wind turbine.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention introduces chance constraints, directly deriving the propagation relationship between the wind turbine output prediction error and the standard deviation and variance of the node voltage square fluctuation based on the power flow model. For the first time, it accurately models the spatial correlation between different wind turbines within the same wind farm using the prediction error correlation coefficient matrix and standard deviation matrix. By equivalently transforming the original probabilistic chance constraints into deterministic tightening boundary constraints, the voltage operating range can be safely tightened on both the high-voltage and low-voltage sides. This allows for a refined safety margin to account for random fluctuations in actual output within the original voltage safety range, effectively limiting the probability of node voltage exceeding limits caused by wind power uncertainties, and significantly improving the safety and disturbance resistance of the station's voltage operation.

[0016] 2. This invention uses the point of common coupling (PCC) bus as the natural physical boundary, finely dividing the model into one grid-connected subsystem and multiple collector-side subsystems. By constructing consistent coupling consensus constraints on active power, reactive power, and voltage amplitude squares at both boundaries, the distributed solution process only needs to exchange a small number of PCC boundary variables. Each subsystem does not need to centrally obtain all operational information of the entire system, greatly reducing the system's computational scale and network communication throughput overhead. Simultaneously, the distributed decoupled solution method, while ensuring safe operation at both boundaries, can faithfully and repeatedly reproduce the high-precision full-field reactive power distribution effect of centralized control without reducing control accuracy.

[0017] 3. This invention introduces a quadratic auxiliary coordination term in the local objective function of the grid-connected side and each collector-side subsystem to limit the amplitude of boundary variable changes between adjacent iterations. By adding a weighted quadratic proximity limiting term centered on the previous round's boundary result in the local region, a stable physical damping effect is injected into the iterative calculation process, effectively suppressing large oscillations in boundary variables caused by the lag in the previous round's boundary information. This invention, while excellently ensuring the convergence performance and iterative stability of parallel distributed solutions, fully unleashes the computational potential of multi-core processors for independent parallel solutions, possessing extremely high engineering application and promotion value. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of a typical large-scale wind farm system.

[0019] Figure 2 The diagram shows the node voltage distribution under the original operating state and under Scheme 1.

[0020] Figure 3 The diagram shows the node voltage distribution of Scheme 2 at different confidence levels.

[0021] Figure 4 Iterative curves of the objective function for different distributed optimization methods.

[0022] Figure 5The graph shows the residual iteration curves for different distributed optimization methods. Detailed Implementation

[0023] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0024] To elaborate on the specific implementation scheme of the present invention, the system structure and model setting of a large-scale wind farm are first described; on this basis, a deterministic voltage optimization mathematical model of the system is further constructed, which does not take into account the uncertainty of wind turbine output.

[0025] In specific system topology settings, a typical large-scale wind farm system structure is as follows: Figure 1 As shown, the system mainly consists of the in-station collector side, the PCC bus, and the external grid-connected side. The in-station collector side includes multiple collector lines, each connected to a wind turbine generator in sequence. The electricity generated by the wind turbine generator is stepped up by the turbine-end converter and box-type transformer before being connected to the collector lines and collected along the collector lines to the PCC bus. The external grid-connected side includes a step-up transformer, high-voltage transmission lines, and the receiving-end AC grid. The electricity collected at the PCC bus is stepped up by the substation and finally transmitted over a long distance to the receiving-end AC grid via a high-voltage transmission circuit. The PCC bus is located between the in-station collector side and the external grid-connected side, serving as the coupling link between the two sides.

[0026] In the aforementioned large-scale wind farm topology, the power-voltage relationship between the in-station collector side and the external grid-connected side can be described based on a power flow model. For the collector side: ① To avoid excessive line current causing conductor temperature rise during wind power collection and to ensure that the medium-voltage collector lines meet long-term thermal stability requirements, capacity constraints for each medium-voltage collector line are considered; ② Considering that the power losses of the converters and box-type transformers inside the wind turbines are typically smaller than the output power of the wind turbines and have a limited impact on the overall power distribution of the wind farm, their internal losses are ignored in the system-level modeling, and the coupling nodes between the wind turbines and the collector lines are equivalent to power injection nodes. For the grid-connected side: ① The step-up transformer is an ideal transformer; ② The relevant parameters of the transmission lines and the receiving-end AC grid are characterized by equivalent impedance and equivalent voltage; ③ When analyzing the voltage distribution within the wind farm, the external receiving-end AC grid is considered as a balancing node.

[0027] In this embodiment, the construction of the deterministic voltage optimization mathematical model mainly includes two parts: the objective function and the constraints. To improve the solvability of the model, the non-convex constraints in the power flow model of the collector system are made convex, and a corresponding convex optimization model is constructed. For ease of subsequent explanation, N and E are used to represent the set of nodes and branches, respectively. (×) W (×) C (×) GThese represent the optimization variables or system parameters related to the wind farm as a whole, the collector side, and the grid connection side, respectively. Specifically, the definition is indicated by ":=", to distinguish it conceptually from the "=" in equality constraints.

[0028] In constructing a deterministic voltage optimization mathematical model, the overall optimization objective mainly weighs and comprehensively considers the following two dimensions of the objective function.

[0029] First, consider the optimization objective of the first dimension: the voltage deviation of system nodes within a large wind farm. A large wind farm system contains a large number of wind turbines, and changes in turbine output directly affect the voltage distribution at each node. To ensure that the voltage at each node within the farm has as much operational margin as possible, the deviation of the node voltage value from the reference value should be minimized to avoid voltage exceeding limits. The corresponding voltage deviation objective function is defined as follows: (1) (2) In equations (1) and (2): V is a voltage vector composed of the voltages of each node in the wind farm; V ref Let be the voltage vector reference composed of the voltage references of each node in the wind farm; ||×||2 represents the 2-norm of the vector; the above formula quantitatively describes the degree of deviation of the overall voltage of the wind farm system from the reference voltage.

[0030] Secondly, consider the second optimization objective: network losses within large wind farm sites. To improve the economic efficiency of power transmission from large wind farms, network losses generated during power transmission through the site's collection lines should be minimized. Therefore, the corresponding network loss objective function is established as follows: (3) In equation (3): r ij P is the resistance of branch ij; ij Q ij These represent the active power and reactive power transmitted from the first node i to the last node j on branch ij, respectively.

[0031] Equation (3) is a non-convex optimization objective. If it is directly adopted, the overall optimization problem will exhibit non-convex characteristics, thus significantly increasing the difficulty of solving the model. Considering that the voltage optimization model usually includes node voltage safety constraints, its allowable range is usually a small fluctuation around the per-unit value of 1pu, with V i ≈1pu holds true. Based on this characteristic, equation (3) can be approximated as: (4) Equation (4) is a standard convex quadratic expression, which guarantees that the optimization model is a convex optimization model.

[0032] In summary, the overall objective function of the deterministic voltage optimization model in this embodiment is: (5) In equation (5): ωV and ωP are the weighting coefficients of the node voltage deviation target and the network loss target within the station, respectively. Their specific values ​​can be flexibly set according to the voltage regulation requirements and network loss optimization requirements.

[0033] To ensure the safe and stable operation of systems within large wind farms, the deterministic voltage optimization mathematical model must satisfy various physical operational constraints within the site, in addition to the objective function mentioned above.

[0034] First, the power flow constraints of the wind farm must be satisfied. The power collection system within a large wind farm typically has a radial structure. Therefore, this embodiment uses the DistFlow model, suitable for radial networks, to describe the relationship between node injected power, branch power flow, and node voltage. Considering that the original DistFlow model contains nonlinear loss terms related to the square of the branch current, directly introducing these terms would increase the nonlinearity of the optimization model and the difficulty of solving it. To improve the solvability of the model and maintain the convexity of the subsequent voltage optimization model, this embodiment further uses the LinDistFlow model, which ignores higher-order line loss terms, to linearize the relationship between power balance and branch voltage drop: (6) In equation (6): p j q j These represent the injected active power and reactive power at node j, respectively; r ij x ij The resistance and reactance of branch ij are respectively; v i and v j Let be the squares of the voltage magnitudes at nodes i and j, respectively. ℂ(×) is a set mapping that, given a node in a radial network, returns the set of its child nodes.

[0035] Secondly, the wind turbine capacity constraint must be met. Since this embodiment ignores the power losses of the internal converter and box-type transformer of the wind turbine, the connection node between the wind turbine and the collector line can be considered as a power injection node. In the deterministic voltage optimization model, the active power output of the wind turbine is given by the predicted value, and the reactive power output participates in the station voltage regulation as an optimization variable. The power injection and reactive power regulation constraints of the wind turbine node are as follows: (7) In equation (7): PWT i and QWT i are nodes i respectively. The active and reactive power outputs of the wind turbine are given; SWT i is the rated apparent power of the wind turbine.

[0036] Third, the capacity constraints of the power collection lines must be met. In addition to the operating capacity limitations of the wind turbine itself, the active and reactive power transmitted by the power collection lines must also meet the apparent power capacity constraints of the lines, namely: (8) In equation (8): The maximum apparent power allowed to be transmitted by branch ij.

[0037] The apparent power capacity constraint of the line shown in Equation (8) has a circular boundary. If its nonlinear form is directly retained, the solution complexity of the optimization model will increase. In order to maintain the convexity of the overall optimization model and further improve the solution efficiency of the model, this embodiment uses an circumscribed regular polygon to linearly approximate the circular capacity boundary, and the corresponding constraint is expressed as: (9) In equation (9): N θ This indicates that in the process of approximating using a circumscribed regular polygon, the number of sides of the selected regular polygon is 2N. θ With N θ As the radius increases, the polygon boundary gradually approaches the original circular capacity boundary, thus improving the approximation accuracy. When a regular 32-sided polygon is used for approximation, the area of ​​the resulting polygon is only about 0.3225% larger than the area of ​​the original circle, achieving high-precision capacity boundary approximation.

[0038] Fourth, during the safe operation of a wind farm, the voltage amplitude at each node must also meet the node voltage constraints of the wind farm. The voltage amplitude at the wind farm nodes should meet the corresponding safe range as follows: (10) In equation (10): vmin i and vmax i are the minimum and maximum values ​​of the square of the voltage amplitude during safe operation of the system, respectively.

[0039] Given the stochastic nature of wind power output, with discrepancies between predicted and actual output, traditional deterministic voltage constraints struggle to accurately reflect the system's actual operational risks. Therefore, based on the wind farm voltage optimization model using the LinDistFlow power flow model, this paper constructs a wind power output uncertainty model and a feeder node voltage disturbance model. The node voltage opportunity constraints are then equivalently transformed into deterministic constraints, allowing them to be explicitly embedded into the voltage optimization model. This enables the effective solution of voltage optimization problems involving wind power output uncertainty.

[0040] In practical implementation, the first step is to construct an uncertainty model for wind turbine output. Due to variations in wind speed and meteorological conditions, the actual active power output of wind turbines typically deviates from the predicted value. Therefore, the actual output of the wind farm is considered a combination of the predicted value and the prediction error. Specifically, the vectors for the actual active power output, predicted active power output, and prediction error of each wind turbine within the wind farm are defined as follows: (11) In equation (11): , , These represent the actual output, predicted output, and predicted error vectors composed of each wind turbine, respectively, with elements in the vectors... , , Let represent the actual, predicted, and predicted error values ​​of the wind turbine k, respectively. In most cases, the wind turbine output prediction error can be considered to follow a normal distribution with a mean of 0 and a covariance matrix of . .

[0041] Because wind turbines within the same wind farm are affected by similar meteorological conditions, there may be a certain correlation between the prediction errors of different turbines. Therefore, the correlation coefficient matrix between the prediction errors of each wind turbine is defined as follows: (12) In equation (12): The correlation coefficient matrix for prediction errors contains the following elements. This represents the correlation coefficient between the prediction errors of wind turbine i and wind turbine j.

[0042] exist Based on this, a diagonal matrix of the standard deviation of wind power prediction error can be further defined. for: (13) In equation (13): is the standard deviation of the output prediction error of wind turbine i; diag(×) is the vector diagonalization operator.

[0043] At this point, the covariance matrix can be and The specific expression and elements within the matrix are as follows: (14) Therefore, based on equation (14) The matrix has a clear analytical expression. This matrix characterizes the statistical features of wind power output uncertainty and will serve as input to the subsequent node voltage stochastic disturbance model.

[0044] After constructing the wind turbine output uncertainty model, this embodiment further constructs a voltage disturbance model for the in-station collector line nodes to further analyze the error propagation process of wind power prediction errors in the in-station collector lines, thereby ultimately clarifying its impact on the wind power station system voltage. For ease of subsequent explanation, a compact matrix expression is established based on the aforementioned LinDistFlow power flow model, which facilitates the derivation and explanation of the relationship between the wind turbine output prediction errors and the voltage disturbances at each node of the collector lines.

[0045] From the aforementioned LinDistFlow power flow model, the matrix form of the node power balance relationship and branch voltage drop relationship can be written as: (15) (16) In equations (15) and (16): , These are the node injection power vectors, which consist of the active and reactive power injected by each node that is not the root node. , These are the branch power vectors composed of the active and reactive power flows of each branch; The voltage vector is composed of the squared values ​​of the voltages at each non-equilibrium node. The square of the root node voltage; , These are diagonal matrices composed of the resistances and reactances of each branch.

[0046] Specifically, the above-mentioned This is a column vector consisting of the columns corresponding to the root node in the complete branch-node incidence matrix. For the reduced-order branch-node incidence matrix (i.e., excluding the root node), the l-th row corresponds to branch l, the i-th column corresponds to node i, and the corresponding elements are... Defined as: (17) For radial networks It is an invertible square matrix. (Definition) Furthermore, the influence matrices of resistance and reactance are defined as follows: (18) Therefore, the compact LinDistFlow power flow model of equation (15) can be further rewritten as: (19) In equation (19): , These are the influence matrices of node injected active power and reactive power on the square of node voltage, respectively; 1 represents a column vector of all ones with dimensions of . It can be seen that the branch power flow and the square of the node voltage amplitude can both be linearly expressed by the active and reactive power injected into the node.

[0047] Substituting the power model in equation (11) that includes the turbine output error into the compact power flow model equation (19), we get: (20) (twenty one) In equation (20): The square vector of node voltage amplitude after taking into account the wind turbine output prediction error; The vector of squared node voltage amplitudes based on the predicted wind turbine output values ​​can be obtained from deterministic parameters; Let be the vector of squared fluctuations in node voltage amplitude based on the wind turbine output error, and its sum to the uncertainty parameter. Related.

[0048] From equation (20), it can be seen that the random variation of the node voltage is caused by the wind turbine output prediction error. Since the wind turbine prediction error follows a multivariate normal distribution, and the node voltage disturbance is a linear function of the prediction error, the node voltage disturbance also follows a multivariate normal distribution. From the linear operation property of expectation and variance, we can obtain: (twenty two) In equation (22): Let be the covariance matrix of the voltage disturbance at the collector line nodes.

[0049] Specifically, the diagonal elements of the collector line node voltage disturbance covariance matrix represent the variance of the square of the voltage amplitude at each node. Therefore, the standard deviation of the voltage disturbance at collector line node i is: (twenty three) The standard deviation of node voltage disturbances calculated by equation (23) will be used for the equivalent deterministic transformation of the following chance constraints.

[0050] Building upon this, an equivalent deterministic transformation method for voltage opportunity constraints is established. When considering the uncertainty of wind power output, opportunity constraints can be used to limit the probability of node voltage exceeding limits, ensuring that the voltage meets the operating boundary at a given confidence level. This avoids the overly conservative approach of requiring the system to strictly meet voltage constraints under all possible random disturbances. However, opportunity constraints themselves contain random variables, making them difficult to directly embed into deterministic optimization models for solution. Therefore, it is necessary to combine the probability distribution characteristics of wind turbine output prediction errors and their impact on node voltage to transform the original voltage opportunity constraints into an equivalent deterministic form that can be explicitly embedded into the optimization model and supports direct solution.

[0051] For the node voltages of the collector lines, opportunity constraints are considered to ensure that the voltages of each node remain within a safe operating range at a given confidence level. Therefore, the original node voltage constraint equation (10) must be transformed into the following opportunity constraint expression: (twenty four) In Equation (24): CL is a given one-sided confidence level. The larger the CL, the higher the probability that the node voltage will meet the operating boundary. The safety requirements are higher, but the optimization results are also relatively more conservative. The smaller the CL, the higher the probability of voltage exceeding the limit is allowed. The model is less conservative, but the corresponding operating risk increases. Pr (×) represents the probability of the random event in parentheses occurring.

[0052] As mentioned above, the square of the collector line node voltage amplitude considering the wind turbine output prediction error. Following a normal distribution, let Let be the one-sided quantile of the standard normal distribution corresponding to the confidence level CL, then we have: (25) In equation (25): Φ −1 (×) is the inverse function of the cumulative distribution function of the standard normal distribution.

[0053] Based on the normal distribution quantile relationship shown in equation (25), equation (24) can be equivalently transformed into the following deterministic form: (26) Based on this, the original node voltage constraint equation (10) can be modified as follows: (27) Equation (27) shows that, considering the uncertainty of wind power output, the lower limit of the node voltage is tightened upwards, and the upper limit is tightened downwards, thus reserving a certain fluctuation margin within the original safe voltage range. The larger the standard deviation of the node voltage or the higher the confidence level, the more obvious the tightening of the voltage constraint. Through the above transformation, the original probability-based chance constraint is transformed into a deterministic linear constraint. In the optimization model, simply replacing the original deterministic voltage boundary with the tightened upper and lower voltage limits can limit the risk of node voltage exceeding the limit caused by random fluctuations in wind power output.

[0054] To achieve distributed coordination in voltage optimization, this embodiment proceeds to construct distributed sub-problems for the wind farm voltage optimization model. As a foundational condition for distributed voltage optimization in wind farms, this embodiment first constructs a distributed communication architecture suitable for coordinated optimization between the grid-connected and collector sides, taking into account the structural characteristics of the system within the wind farm. Then, based on this communication architecture, the original centralized chance-constrained voltage optimization model is decomposed to construct distributed sub-problems for the wind farm voltage optimization model.

[0055] In terms of specific communication flow settings, the distributed communication architecture of wind farms differs significantly from traditional centralized communication. Traditional centralized communication is a "point-to-point" communication method. For wind farm voltage optimization problems, if a centralized communication method is used, information such as wind turbine output, collector line parameters, node voltage, line power flow, and reactive power regulation variables need to be uniformly transmitted to the centralized controller, which then solves the voltage optimization problem for the entire system. This method is simple in structure, but as the wind farm capacity and the number of wind turbines increase, the amount of information and computation that the centralized controller needs to process will increase significantly, easily leading to increased communication and solution pressure. Considering that the wind farm system has a relatively obvious zoning structure, with the collector-side wind turbines collecting power through collector lines and connecting to the external power grid via the step-up substation and PCC node, the wind farm system can be divided into grid-connected and collector-side zones. Voltage optimization calculations can be completed within each subsystem, with only necessary boundary information exchange between subsystems. Compared with centralized communication, this method does not require centralized acquisition of all operational information of the entire system, making it more suitable for the distributed voltage optimization scenario of wind farms studied in this embodiment.

[0056] Further implementation of wind farm system decomposition and distributed sub-problem construction. This embodiment adopts a distributed communication system architecture supporting distributed voltage optimization within the wind farm system. The wind farm system is decomposed by replicating the PCC bus, resulting in a grid-connected subsystem and several collector-side systems. At this point, each subsystem retains its own network parameters, optimization variables, and operational constraints, coordinating only through electrical quantities at the PCC boundary. To ensure that the two decomposed subsystems can still equivalently describe the original wind farm system, the following coupling constraints need to be added. (28) In equation (28), P PCC,G,k Q PCC,G,k and v PCC,G,k Let P be the PCC boundary variables associated with the k-th collector line on the grid-connected side; PCC,C,k Q PCC,C,k and v PCC,C,k These are the corresponding collector-side boundary variables; K C This refers to the number of collector lines within the renewable energy power plant; (∗) G,k and (∗) C,k These are used to represent the parameters or variables associated with the k-th collector line on the grid-connected side and the collector system side after model decomposition.

[0057] Furthermore, the centralized optimization model corresponding to equations (5) to (9) can be extended to the following distributed optimization model. (29) (30) Equations (29) and (30) represent the distributed voltage optimization problems corresponding to the grid-connected subsystem and the k-th collector line subsystem, respectively. G and F C,k These are the optimization objective functions after decomposition; ɛ G andɛ C,k L represents the branch set of the grid-connected side and the k-th collector side subsystem, respectively; G and L C,k Let J be the objective function containing the PCC coordination term in each of the two types of subproblems, and let J be the augmented term J contained therein. G and J C,k This will be explained in detail later. (×) G and (×) k,C These represent the parameters, variables, and sets associated with the grid-connected subsystem and the k-th collector line subsystem, respectively.

[0058] After obtaining the distributed sub-models for the grid-connected side and the collector side, the wind farm voltage optimization model is solved in a distributed manner. The following will explain the distributed optimization solution process of the augmented Lagrange relaxation method and the augmented Lagrange auxiliary term extension method to demonstrate their application in the distributed solution of the wind farm voltage optimization model in this embodiment. In particular, the special steps in the distributed optimization process of the augmented Lagrange auxiliary term extension method will be explained in detail.

[0059] First, the distributed optimization solution process based on augmented Lagrange relaxation is established and explained. Previously, the voltage safety optimization model within a large wind farm was divided into a grid-connected subsystem and multiple collector-side subsystems. The objective functions and operational constraints within each subsystem are independent, maintained only by PCC boundary variables. Therefore, this embodiment employs the augmented Lagrange relaxation method, incorporating the PCC boundary variable deviations as augmented terms into the objective functions of each subsystem, thereby achieving alternating solutions for the grid-connected and collector-side subproblems.

[0060] The PCC boundary variables of the grid-connected side and the k-th collector-side subsystem are respectively expressed as: (31) in, (32) In equation (31), z G,k and z C,k These are the PCC boundary variables corresponding to the grid-connected side and the k-th collector-side subsystem, respectively; h kLet be the boundary consensus deviation of the k-th PCC; D is the boundary variable sign transformation matrix. Since the two sides use opposite power reference directions, the sum of the active and reactive power of the PCC should be 0, while the squares of the voltage amplitudes on both sides should be consistent.

[0061] The PCC boundary consensus constraints are embedded into the subproblems on the grid-connected side and the collector side, respectively, and Lagrange multipliers and quadratic penalties are introduced to construct coordination terms. In the t-th iteration, the grid-connected side is updated using the boundary variables from the previous round of each collector side, while the k-th collector side uses the boundary variables updated in the current round by the grid-connected side. Therefore, the augmented Lagrange coordination terms corresponding to the two subproblems are expressed as follows: (33) In the formula, JA,t G and JA,t C,k are the augmented coordination terms of the grid-connected side and the k-th collector-side subsystem in the t-th iteration, respectively; λt k is the Lagrange multiplier vector corresponding to the k-th PCC consensus constraint; and ρ is the penalty parameter. The first-order term in formula (33) is used to correct the iteration direction of the variable according to the boundary deviation, and the second-order penalty term is used to reduce the deviation between the PCC voltage and power on both sides.

[0062] Substituting equation (31) into the two subproblems established above, we can obtain the distributed voltage optimization problem under the augmented Lagrange relaxation method. (34) In equation (34), X G and X C,k Ω represents all optimization variables for the grid-connected side and the k-th collector side subproblem, respectively, including the corresponding PCC boundary variables; G and Ω C,k These are the feasible regions for the corresponding areas, including power flow constraints, equipment operation constraints, and voltage opportunity constraints after deterministic transformation within the region.

[0063] After solving the (t+1)th subproblem on the grid-connected side and collector side, the consensus residual is calculated based on the latest boundary variables on both sides of the PCC, and the corresponding Lagrange multipliers are updated using this residual. Therefore, the consensus residual and multiplier update method for the kth set of PCC boundary variables are expressed as follows: (35) In the formula, ht+1 k is the consensus residual vector of the k-th group of PCC boundary variables in the (t+1)-th iteration; zt+1 G,k and zt+1 C,k are the PCC boundary variables obtained by the grid-connected side and the k-th collector side after this round of solution, respectively.

[0064] Secondly, a distributed optimization solution process based on augmented Lagrange auxiliary terms is further presented. The auxiliary term expansion method follows the consensus relationship between the aforementioned regional subproblems and the PCC boundary. This method constructs a primary coordination term based on the consensus deviation of the current boundary variables, and adds a secondary auxiliary term centered on the boundary result of the previous round in each region's objective function to limit the changes in boundary variables between adjacent iterations.

[0065] To set auxiliary parameters corresponding to active power, reactive power, and the square of voltage amplitude respectively, the auxiliary parameter matrix is ​​defined as follows: (36) In the (t+1)th iteration, the subproblems on both the grid-connected side and each collector side independently construct coordination terms using the boundary variables from the previous iteration. There is no dependency on the order of solution among the subproblems, enabling synchronous parallel solving. The coordination terms on both sides can be expressed as: (37) In equation (37), αt G,k and αt C,k are the coordination coefficient vectors for the grid-connected side and the k-th collector side, respectively. The coordination coefficients for both the grid-connected side and the collector side are determined based on the boundary information from the previous iteration.

[0066] To limit the variation of the PCC boundary variables between adjacent iterations and improve the iterative stability of the APP algorithm, a quadratic auxiliary coordination term consisting of a linear auxiliary term and a weighted quadratic proximity term is further introduced. In the t-th iteration, the quadratic auxiliary coordination terms corresponding to the grid-connected side and the k-th collector side are respectively expressed as: (38) The primary coordination term adjusts the optimization direction of the current region's boundary variables based on the PCC boundary consensus deviation, while the secondary auxiliary term limits the magnitude of change of the boundary variables relative to the previous round's results for this region.

[0067] By incorporating equation (38) into the regional objective functions of the grid-connected side and the collector side, we can obtain the distributed optimization subproblem based on the auxiliary term expansion method. (39) In the formula, the regional objective function, optimization variables, and feasible region of the two types of subproblems remain consistent with Equation (34). The auxiliary term expansion method only changes the coordination method of the PCC boundary variables, without changing the power flow constraints, equipment operation constraints, and voltage opportunity constraints within the region.

[0068] After the subproblems of each region are solved, the PCC boundary consensus deviation and updated Lagrange multipliers are still calculated according to Equation (35). The auxiliary term expansion method and the augmented Lagrange relaxation method use the same boundary consensus relationship and multiplier update method, but due to the difference in the regional coordination terms, the boundary variables, consensus deviation and convergence process obtained in each iteration are also different.

[0069] To verify the effectiveness of the opportunity-constrained model and parallel distributed voltage optimization solution method proposed in this invention, a specific numerical example analysis process is given below. This embodiment uses a large-scale wind farm system with an installed capacity of 6×15×2.5MW for numerical example analysis to verify the effectiveness of the proposed opportunity-constrained distributed voltage optimization method. The key parameters of the numerical example are detailed in Table 1. This large-scale wind farm has a total of 92 nodes, and a total of 6 collector lines are set up within the wind farm. Each collector line connects to 15 wind turbine units in sequence. The wind turbine units are collected through the collector lines and connected to the grid at the grid connection point.

[0070] Table 1 Key parameters of the example The programs for the calculation examples were written in Matlab. Both the centralized chance-constrained voltage optimization model and the distributed optimization model were solved using the CPLEX solver. The centralized optimization model provides a unified model of the entire wind farm network, and the results are used as the benchmark for the distributed optimization results. The distributed optimization model divides the wind farm system into a grid-connected subsystem and a collector-side subsystem, and achieves coordinated solutions between different subsystems through the consistency conditions of boundary node voltage, active power, and reactive power. For ease of subsequent comparison, the following calculation example schemes are set up, as shown in Table 2. Table 2 Comparison of Calculation Examples Among them, Scheme 1 does not consider the impact of wind power prediction errors on the random fluctuations of node voltage and only uses ordinary deterministic voltage upper and lower limit constraints for optimization; Scheme 2 introduces voltage opportunity constraints in the centralized model and obtains the tightened voltage safety boundary through deterministic transformation; Schemes 3 and 4 are both solved in a distributed manner under opportunity constraints, the difference being that they respectively use a distributed optimization algorithm based on augmented Lagrange relaxation and a distributed optimization algorithm based on augmented Lagrange auxiliary terms to coordinate boundary variables.

[0071] Based on the above example setup, the subsequent analysis will focus on three aspects. First, by comparing the node voltage distribution under ordinary deterministic voltage constraints and opportunity constraints, the improvement effect of opportunity constraints on voltage safety risks under the uncertainty of wind power output will be verified. Second, using the centralized opportunity constraint optimization results as a benchmark, the node voltage, wind turbine reactive power output, and boundary coupling variables obtained by distributed optimization will be compared to verify that distributed solutions do not significantly affect the optimization results of the original problem. Finally, by comparing the residual convergence process, number of iterations, and objective function changes of two distributed optimization algorithms—one based on augmented Lagrange relaxation and the other based on augmented Lagrange auxiliary terms—the differences in solution stability and computational efficiency between the two distributed algorithms will be analyzed.

[0072] The six collector lines in the example have the same topology, wind turbine configuration, and line parameters. The node voltages and reactive power outputs of the wind turbines on each collector line show similar variation patterns. Therefore, to avoid repetitive presentation, the subsequent calculation results will mainly focus on the first collector line and its upstream grid-connected nodes for analysis.

[0073] First, the results of the chance-constrained deterministic transformation are analyzed. To analyze the impact of wind power output uncertainty on the node voltage within the station and to verify the effectiveness of the proposed chance-constrained model, the node voltage distribution under different confidence levels of chance constraints is calculated for the original operating state, Scheme 1, and Scheme 2. The allowable range of node voltage is set to 0.95~1.05 pu. Scheme 1 represents the deterministic voltage constraint without considering wind power output uncertainty.

[0074] Figure 2 This illustrates the node voltage distribution under the original operating state and Scheme 1. Figure 2 It can be seen that without reactive power voltage optimization, the voltage at node 1 is 1.00 pu, while the voltage at node 2 rises rapidly and exceeds the upper voltage limit. As the node location extends towards the end of the collector line, the node voltage continues to rise, with the voltage at node 12 approaching 1.12 pu. This indicates that when wind turbines deliver concentrated active power, the voltage rise along the collector line is quite significant, and the voltage limitation problem becomes more severe the farther away from the grid connection point.

[0075] After adopting Scheme 1, the voltage of each node was controlled within the allowable range. The voltage of node 1 remained at 1.00 pu, the voltage of node 2 decreased to approximately 0.99 pu, and thereafter the node voltage gradually increased along the line, with the voltage of node 12 reaching approximately 1.04 pu. Compared with the original operating state, the overall node voltage under Scheme 1 was significantly reduced, and the original overvoltage problem was effectively improved. This demonstrates that the basic reactive power and voltage optimization model can control the node voltage within the specified range under the predicted operating state by adjusting the reactive power output of the wind turbines.

[0076] However, Scheme 1 only determines the feasible range of node voltage based on the predicted wind power output, without considering the deviation between the actual wind power output and the predicted value. Although no node voltage exceeded the limit under Scheme 1, the voltage of the later nodes in the collector line is still close to the upper limit of 1.05 pu. When the actual wind power output is higher than the predicted value, the node voltage may rise further, so there is still a certain risk of overvoltage.

[0077] Figure 3 The node voltage distributions obtained under different confidence levels for Scheme 2 are shown. Figure 3 It can be seen that the node voltages at all confidence levels are within the range of 0.95 to 1.05 pu, and the voltage curves all show a trend of first decreasing and then gradually increasing. When the confidence level is 0.5, the voltage distribution is basically consistent with the results under Scheme 1. This is because, under the one-sided normal distribution condition, the standard normal quantile corresponding to a confidence level of 0.5 is 0, and the chance constraint does not further tighten the original voltage boundary.

[0078] As the confidence level gradually increased from 0.5 to 0.6, 0.8, and 0.9, the overall node voltage in the later stages of the collector circuit decreased, and the margin between the node voltage and the upper limit gradually increased. At confidence levels of 0.6 and 0.8, the voltage at node 12 decreased to approximately 1.04 pu and 1.035 pu, respectively; when the confidence level increased to 0.9, the voltage at node 12 further decreased to approximately 1.03 pu. Meanwhile, the voltage at each node remained above the lower limit of 0.95 pu, and no low-voltage problem occurred due to the tightening of opportunity constraints.

[0079] The results above show that Scheme 2 can adjust the tightness of the node voltage constraint according to the confidence level, allowing the optimized node voltage to reserve more safety margin on the high-voltage side, thereby reducing the risk of node voltage exceeding limits caused by random fluctuations in wind power output. However, as the confidence level increases, the conservatism of the optimization results will also increase accordingly.

[0080] In summary: ① Under the original operating conditions, the node voltage continuously increases with the extension of the collector line, and there is a relatively obvious overvoltage problem in the later sections of the line; ② Ordinary deterministic voltage constraints can control the node voltage under the predicted operating conditions within the allowable range, but do not consider the random voltage fluctuations caused by wind power output deviations; ③ The chance constraint model can adjust the node voltage safety margin according to the confidence level. The higher the confidence level, the lower the risk of node voltage exceeding the limit, which verifies the effectiveness of the proposed chance constraint model in improving the voltage operation safety within the station.

[0081] Then, the results of centralized and distributed optimization are compared. To verify the accuracy of the distributed opportunity constraint model, the centralized optimization results of Scheme 2 are used as a benchmark and compared with the distributed optimization results of Scheme 3. Since the topology, line parameters, and wind turbine operating status of the six collection lines are the same, Table 3 only lists the node voltage results of some nodes on the grid-connected side and representative collection lines, and Table 4 further gives the error index of the objective function and the reactive power output of the wind turbine.

[0082] Table 3 Comparison of node voltage results between Scheme 2 and Scheme 3 Table 4 Comparison of optimization results between Scheme 2 and Scheme 3 Table 3 shows that the node voltage variation patterns obtained from Scheme 2 and Scheme 3 are basically consistent, with the node voltage gradually increasing from the grid-connected side towards the downstream section of the collector line. Node 1 remains at 1.0 pu under both schemes, and the calculated voltage results for nodes 2-12 are also basically consistent, with absolute errors all within 10 ohms. -7 The magnitude is [not specified]. The maximum absolute voltage error at the listed nodes is only 2.36 × 10⁻⁶. -7 The result of `pu` indicates that distributed optimization can accurately reproduce the node voltage distribution obtained by centralized optimization. Table 4 shows that the absolute errors of the objective functions of Scheme 2 and Scheme 3 are very small, indicating that the system operating losses obtained by the two schemes are basically consistent. Regarding the reactive power output of the wind turbines, the maximum absolute error and average absolute error of both schemes are at low levels, indicating that the reactive power regulation results obtained by distributed optimization are close to those of centralized optimization. Combining the results of Tables 3 and 4, it can be seen that Scheme 3 maintains a high degree of consistency with Scheme 2 in terms of objective function, node voltage, and reactive power output of the wind turbines. This demonstrates that after splitting the complete system into grid-connected and collector-side subsystems, optimization results close to the centralized benchmark scheme can be obtained through boundary variable coordination, verifying the accuracy of the established distributed chance-constraint model and its solution method.

[0083] Finally, the performance of the distributed optimization algorithm under different sub-problem update methods is analyzed. In the distributed optimization framework, the grid-connected side and the collector side need to coordinate through boundary coupling variables. Depending on the method of updating information during sub-problem solving, the iterative process can be divided into two forms: serial iteration and parallel iteration. In the serial iteration method, the grid-connected side and collector side sub-problems are solved sequentially in a fixed order. After the previous sub-problem is calculated, the boundary variables obtained in the current round are passed to the next sub-problem, and then the coupling variables and Lagrange multipliers are updated. In the parallel iteration method, both the grid-connected side and collector side sub-problems use the boundary variables from the previous round and are solved independently in the same iteration. After both sub-problems are calculated, the coupling variables and Lagrange multipliers are updated uniformly.

[0084] To analyze the impact of augmented term construction and subproblem update order on distributed optimization performance, four distributed solution methods were compared under the same chance constraint model and system operating conditions. The augmented term forms and subproblem update methods for each method are shown in Table 5. Methods A and C employ augmented Lagrangian relaxation forms, while methods B and D add auxiliary quadratic terms based on the linearization of the augmented Lagrangian function. Methods A and B use a serial update method, while methods C and D use a parallel update method. All methods use the same system parameters and initial conditions, and the convergence thresholds for both the original and dual residuals are set to 1 × 10⁻⁶. -4 The maximum number of iterations was set to 100. The solution results for different methods are shown in Table 6.

[0085] Table 5. Settings of different distribution optimization methods Table 6 Solution results of different distribution optimization methods Note: Method C did not converge within 100 iterations, therefore the data for Method C in Table 6 is the calculation result of the 100th iteration.

[0086] As shown in Table 6, Method A converged after 13 iterations, with an objective function of 25.2523MW and a total solution time of 28.4323s, exhibiting a relatively fast convergence speed. Method B converged after 88 iterations, with an objective function of 25.2502MW and a total solution time of 138.5812s. Although Method B achieves optimization results close to those of Method A, its number of iterations and solution time are significantly increased. For the parallel update method, Method C failed to meet the convergence condition within 100 iterations, with an objective function of 25.9661MW in the 100th iteration; Method D converged after 52 iterations, with an objective function of 25.2537MW and a total solution time of 82.8741s.

[0087] Further comparison reveals that the maximum difference in the objective functions of methods A, B, and D is only 0.0035MW, indicating that the optimization results obtained by the three convergence methods are basically consistent. Method D has a shorter computation time than method B, but a longer time than method A. This is because the current example is only divided into two subsystems: the grid-connected side and the collector side, and the time advantage of parallel computation of sub-problems has not yet been fully realized. Therefore, the computation times in Table 6 mainly reflect the actual solution situation under the current example, while the main characteristic of method D is that it can still guarantee algorithm convergence under parallel update conditions.

[0088] The iteration of the objective function for different methods is as follows: Figure 4 As shown. By Figure 4It can be seen that the objective functions of each method fluctuated to some extent in the early stages of iteration, and then exhibited different patterns of change. The objective function of method A decreased relatively quickly, stabilizing at around 25.25MW after a few iterations. Methods B and D showed relatively significant fluctuations in the early stages of iteration, but as the boundary coupling variables were continuously corrected, their objective functions gradually stabilized, eventually becoming basically consistent with the calculation results of method A. In contrast, the objective function of method C oscillated continuously during the iteration process, and did not stabilize to the level of the objective functions of the other three methods even in the later stages of iteration.

[0089] Figure 4 The local magnification results further show that the objective function curves of methods A, B, and D after convergence basically overlap, indicating that the construction method of augmented terms and the update method of subproblems do not significantly change the final optimization result, but they will affect the convergence speed and iterative stability of the algorithm. The objective function of method C still exhibits significant fluctuations in a local range, indicating that under parallel update conditions, the augmented Lagrangian relaxation form is insufficient to achieve stable coordination between the grid-connected side and the collector side subproblems.

[0090] The fact that the objective function has become stable does not alone indicate that the distributed algorithm has converged. It is also necessary to determine whether the boundary variables on the grid-connected side and the collector side meet the consistency requirements. Figure 4 The changes in the original and dual residuals for different methods are presented. The original residual reflects the deviation of the boundary coupling variables between the two subsystems, while the dual residual reflects the degree of change in the boundary variables between two adjacent iterations. Distributed iteration is considered to have converged only when both types of residuals are simultaneously below a set threshold.

[0091] Depend on Figure 5 As shown in the original residual plot, Method A exhibits the fastest decrease in original residuals, reaching convergence by the 13th iteration. The original residuals of Methods B and D fluctuate somewhat in the early stages of iteration, then gradually decrease overall, falling below the convergence threshold by the 88th and 52nd iterations, respectively. The original residuals of Method C decrease briefly in the early stages before increasing again, remaining at a high level in the later stages of iteration, indicating a significant discrepancy between the boundary variables obtained from the grid-connected side and the collector side.

[0092] Depend on Figure 5 As shown in the dual residual plot, the dual residual of method A can also be reduced to below the convergence threshold in a relatively small number of iterations. The dual residuals of methods B and D generally show a decreasing trend during the iteration process, and both eventually satisfy the convergence condition. Among them, method D can reduce both the original residual and the dual residual to 1×10-1 under parallel update conditions. -4The following explains how the augmented Lagrange auxiliary term can improve the coordination effect when the two subproblems are solved independently using the boundary information from the previous round. The dual residual of method C increases again after decreasing and never reaches the convergence requirement, a pattern consistent with the continuous oscillation of its objective function.

[0093] In summary: ① Under the serial update method, method A can utilize the latest boundary information obtained in the current iteration to sequentially correct the subproblems, thus exhibiting a faster convergence speed; ② Although method B can achieve convergence, the required number of iterations and solution time both increase, and the augmented Lagrange auxiliary term does not show a significant advantage under the serial update method; ③ Under the parallel update method, method C failed to converge within 100 iterations, while method D can maintain the objective function gradually stabilizing and ensure that both the original residual and the dual residual simultaneously satisfy the convergence condition. Therefore, combining the augmented Lagrange auxiliary term optimization method with the parallel update method can achieve independent solutions to the grid-connected and collector-side subproblems while ensuring the accuracy of the optimization results, providing a distributed solution method with parallel computing potential for voltage safety optimization in large wind farms.

[0094] In summary, this embodiment addresses the random fluctuations in node voltage caused by the uncertainty of wind power output, as well as the significant communication and computational burden on centralized voltage optimization in large wind farms. This embodiment constructs a chance-constrained distributed optimization model for voltage security within large wind farms and compares different augmentation term construction methods and sub-problem update methods. The main conclusions are as follows: (1) Considering the correlation between wind turbine prediction errors, a relationship between wind power output error and node voltage disturbance was established, and the node voltage opportunity constraint was transformed into a tightened deterministic voltage constraint. The results of the example show that the voltage at the end of the collector line is close to 1.12 pu under the original operating conditions. Ordinary deterministic optimization can reduce it to about 1.04 pu, but no space is reserved for voltage fluctuation caused by wind power output deviation. As the confidence level increases, the safety margin on the upper limit of the node voltage gradually increases. When the confidence level is 0.9, the voltage of node 12 is further reduced to about 1.03 pu, and the voltage of each node is still in the range of 0.95~1.05 pu, indicating that the established opportunity constraint model can adjust the node voltage safety margin according to the confidence level.

[0095] (2) Using the common connection point as the coupling boundary, the centralized optimization model is decomposed into grid-connected and collector-side sub-problems, and regional coordination is achieved through consistency constraints on boundary active power, reactive power, and voltage amplitude squares. Compared with the centralized opportunity-constrained optimization results, the maximum absolute error of the node voltage obtained by distributed optimization is 2.36 × 10⁻⁶. -7 The maximum absolute error and average absolute error of the reactive power output of the fan are 2.802 × 10⁻⁶.-3 MVar and 4.781×10 -4 MVar. The results show that the established distributed model can accurately reproduce the centralized optimization results after system decomposition.

[0096] (3) The construction method of augmented terms and the update method of subproblems significantly affect the convergence process of distributed algorithms. Under serial update conditions, the augmented Lagrange relaxation method and the auxiliary term expansion method converge after 13 and 88 iterations, respectively; under parallel update conditions, the augmented Lagrange relaxation method failed to converge within 100 iterations, while the auxiliary term expansion method reduced both the original residual and the dual residual to 1×10 after 52 iterations. -4 The maximum difference in the objective function obtained by the three convergence methods is only 0.0035MW, indicating that the expansion of auxiliary terms does not significantly change the final optimization result, but it can improve the boundary coordination effect under parallel update conditions, enabling the grid-connected side and collector side sub-problems to be solved independently and in parallel.

[0097] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints, characterized in that, Includes the following steps: S1. Construct a deterministic voltage optimization mathematical model for the system within a large wind farm. The deterministic voltage optimization mathematical model constructs an overall objective function with the optimization objectives of minimizing the node voltage deviation and network loss within the system within the large wind farm as the optimization objectives, and uses wind farm power flow constraints, wind turbine capacity constraints, collector line capacity constraints, and wind farm node voltage constraints as constraints. S2. Based on the correlation between the active power output prediction errors of each wind turbine, the voltage opportunity constraints of the nodes in the wind farm are equivalently transformed into deterministic tightening boundary constraints to replace the wind farm node voltage constraints in the deterministic voltage optimization mathematical model. S3. Using the common connection point PCC bus as the coupling boundary, the deterministic voltage optimization mathematical model containing the deterministic tightening boundary constraints is decoupled and divided into a grid-connected subsystem and several collector-side subsystems, and a consistent coupling constraint of boundary active power, boundary reactive power and boundary voltage amplitude square between the grid-connected subsystem and each collector-side subsystem is established. S4. In the local objective functions of the grid-connected subsystem and each of the collector-side subsystems, a quadratic auxiliary coordination term is introduced to limit the change amplitude of boundary variables between two adjacent iterations. In the parallel update mode, the grid-connected subsystem and each of the collector-side subsystems are solved independently and in parallel based on the boundary history information of the previous iteration, and are alternately coordinated and updated through the consistency coupling constraint until the algorithm meets the convergence condition and outputs the optimal reactive power output value of each wind turbine.

2. The parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints as described in claim 1, characterized in that, In step S1, the process of constructing the deterministic voltage optimization mathematical model includes: The overall objective function is constructed as follows: in, and These are the weighting coefficients for the node voltage deviation target and the in-station network loss target, respectively; the node voltage deviation objective function is: In the formula, Describes the 2-norm of a vector. It is a voltage vector composed of the voltages of each node in the wind farm. The reference voltage vector, composed of the voltage references of each node in the wind farm, is expressed as: The objective function for network loss within the site is: in, Let be the resistance of branch ij. and Let represent the active power and reactive power transmitted from the first node i to the last node j on branch ij, respectively. This is a collection of branch roads for the entire wind farm. It is the set of nodes of the entire wind farm; A linear approximation of the circular boundary of the apparent power capacity constraint of the collector line is made using an circumscribed regular polygon, and the linear approximation constraint is expressed as follows: in, The maximum apparent power allowed to be transmitted by branch ij. The number of sides of the selected regular polygon.

3. The parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints as described in claim 1, characterized in that, In step S2, based on the correlation between the active power output prediction errors of each wind turbine, a covariance matrix of the wind turbine output prediction error is constructed. Specifically, it includes: The power model that treats the actual active power output of a wind farm as a combination of predicted values ​​and prediction errors, including the vectors of actual, predicted, and prediction error values ​​of the active power output of each wind turbine in the wind farm, is as follows: in, , and These represent the actual value vector, predicted value vector, and prediction error vector of the active power output of each wind turbine, respectively, with elements in the vectors... , and These represent the actual value, predicted value, and prediction error value of the active power output of wind turbine unit k, respectively. It follows a normal distribution with a mean of 0 and a covariance matrix of . ; This represents the total number of nodes in the wind farm. Based on the correlation coefficient matrix between the prediction errors of each wind turbine and standard deviation diagonal matrix Construct the covariance matrix : in, and Expanded representation: in, For wind turbines Standard deviation of active power output prediction error; Elements contained Indicates wind turbine With wind turbine The correlation coefficient between the active power output prediction error and the actual power output prediction error.

4. The parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints as described in claim 3, characterized in that, In step S2, the relationship between the active power output prediction error and the random disturbance of node voltage is derived based on the power flow model, specifically including: Construct a compact matrix-form power flow model based on LinDistFlow: in, It is a column vector of all 1s with dimensions of . ; , These are the node injection power vectors, which consist of the active and reactive power injected by each node that is not the root node. , These are the branch power vectors composed of the active and reactive power flows of each branch; The voltage vector is composed of the squared values ​​of the voltages at each non-equilibrium node. The square of the root node voltage; defined , This is the reduced-order branch-node incidence matrix for non-root nodes; , Let be the matrix representing the influence of active power and reactive power injected into the node on the square of the node voltage, respectively, and satisfy the following: In the formula, , These are diagonal matrices composed of the resistances and reactances of each branch; Substituting the power model into the power flow model yields: in, The square vector of node voltage amplitude after taking into account the wind turbine output prediction error; This is the square vector of node voltage amplitudes based on the predicted wind turbine output. This is the squared fluctuation vector of the node voltage amplitude based on the wind turbine output error; Covariance matrix of collector line node voltage disturbance satisfy: Collection line node The standard deviation of voltage disturbance is ,in Covariance matrix The One diagonal element.

5. The parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints as described in claim 4, characterized in that, In step S2, the voltage machine constraint is: Where CL is the given one-sided confidence level, and Pr(×) represents the probability of the random event within the parentheses occurring; Based on the voltage disturbance standard deviation and the inverse function of the cumulative distribution function of the standard normal distribution. The voltage opportunity constraint is equivalently transformed into a deterministic tightening boundary constraint: in, and They are nodes The upper and lower limits of the permissible square of voltage amplitude. CL represents the confidence level and is the one-sided quantile of the corresponding standard normal distribution.

6. The parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints as described in claim 1, characterized in that, In step S3, the consistency coupling constraint between the grid-connected subsystem and each of the collector-side subsystems is as follows: Among them, P PCC,G,k Q PCC,G,k and v PCC,G,k Let P be the PCC boundary variables associated with the k-th collector line on the grid-connected side; PCC,C,k Q PCC,C,k and v PCC,C,k These are the corresponding collector-side boundary variables; K C This represents the number of collector lines inside the wind farm.

7. The parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints as described in claim 6, characterized in that, In step S3, the PCC boundary variables of the grid-connected side and the k-th collector side subsystem are respectively expressed as: D is the sign transformation matrix for boundary variables, expressed as: Among them, z G,k and z C,k These are the PCC boundary variables corresponding to the grid-connected side and the k-th collector-side subsystem, respectively; h k Let be the boundary consensus deviation of the k-th PCC.

8. The parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints as described in claim 7, characterized in that, In step S4, at the... During the next iteration, the grid-connected side and the first Secondary auxiliary coordination items introduced on the collector side , for: in, This refers to the number of collector-side subsystems. , These are the boundary variable vector values ​​obtained from the previous iteration; The auxiliary parameter diagonal matrix is ​​represented as follows: in, , , These are the weighting coefficients for auxiliary parameters corresponding to active power, reactive power, and the square of voltage amplitude, respectively; αt G,k and αt C,k are the coordination coefficient vectors for the grid-connected side and the k-th collector side, respectively, expressed as: In the formula, For the first The Lagrange multiplier vectors corresponding to the PCC consensus constraints. This refers to the penalty parameters for the secondary penalty item.

9. The parallel distributed voltage optimization method for large-scale wind farms with embedded opportunity constraints as described in claim 8, characterized in that, In step S4, the steps of solving the distributed optimization subproblem, updating the consensus residual, multiplier iteration, and convergence determination are as follows: By incorporating the quadratic auxiliary coordination terms corresponding to the grid-connected side and the kth collector side into the regional objective functions of the grid-connected side and the collector side, a distributed optimization subproblem based on the auxiliary term expansion method is obtained: in, and They are respectively the grid-connected side and the first All optimization variables for the collector-side subsystem problem and These are the feasible regions for the corresponding areas. and The objective function is a function that does not contain a coordinating term; After the solution is completed, the first Group Boundary Consensus Bias Residual and Lagrange multipliers The update and iteration formula is: in, , These are the updated boundary variable vectors; after calculating and determining that the original residual and the dual residual both fall below the preset convergence threshold, the algorithm terminates and outputs the optimal reactive power output value of each wind turbine.

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