Wind farm distributed physical-data joint driving voltage optimization control method and system based on ADMM

Abstract

The application discloses a wind farm distributed physical-data joint driving voltage optimization control method and system based on ADMM, which decomposes a global optimization problem of a wind farm based on deep learning, and realizes distributed iterative solution through an ADMM algorithm framework, thereby reducing the calculation burden of a large-scale wind farm optimization problem based on deep learning. Secondly, a local input convex neural network is adopted to fit a dynamic prediction model of the wind farm, and a complex nonlinear MPC optimization problem is converted into a convex optimization problem with convex constraints, so that the global optimality of the solution is ensured. Then, the optimal solution of the optimization problem is directly predicted by using the PINN network, the KKT condition of the optimization problem is embedded into the loss function of the PINN, the PINN model can effectively learn the implicit physical law according to specific configuration point data, and the solution generated by the model can meet the physical feasibility and optimality.

Description

Technical Field

[0001] This invention relates to the field of voltage optimization control technology for large-scale wind farms, and in particular to a distributed physical-data joint drive voltage optimization control method and system for wind farms based on ADMM. Background Technology

[0002] Wind energy, as a clean and renewable energy source, has become a key force driving the global green energy transition. Wind farms (WFs), as the primary form of centralized wind power development and grid connection, require safe and stable operation as a crucial link in promoting efficient wind energy utilization and improving power system reliability. However, the randomness and intermittency of wind energy can easily lead to instability in the terminal voltage of wind turbines (WTs), especially in large-scale wind farms. Fluctuations in wind power output can cause significant voltage fluctuations at the grid connection point, potentially leading to wind turbine disconnection. Therefore, voltage control in wind farms has become fundamental to their safe and stable operation.

[0003] As wind farms expand in scale and system complexity increases, traditional centralized control methods face challenges in scalability and information security. Centralized control relies on a central controller, leading to increased computational burden as the system expands and posing a single point of failure risk. To address these challenges, distributed control has gradually become a research hotspot. By decomposing control tasks into various subsystems, distributed control methods can not only improve system reliability and information security but also respond more flexibly and in real-time to rapidly changing operating conditions. Compared to traditional centralized optimization control, ADMM-based distributed solutions eliminate the need for a central unit, reduce computational burden, and improve the scalability of wind farms.

[0004] Traditional wind farm voltage optimization control methods rely on complex physical models, resulting in high computational costs and difficulties in model maintenance. Furthermore, the dependence on system parameters and key coefficient tuning limits optimization effectiveness when facing dynamic changes and uncertainties in the wind farm's internal and external systems. These problems restrict the application of traditional physics-driven control methods. Data-driven techniques based on deep learning (DL) reduce the reliance on accurate physical models while exhibiting stronger adaptability and computational efficiency, improving the flexibility and response speed of the control system. Deep learning-based modeling methods provide a new research direction for distributed MPC control in wind farms. However, deep learning-based wind farm optimization problems typically involve high-dimensional nonlinear constraint functions. This not only increases computational complexity but also places higher demands on optimization algorithms. Although quadratic MPC problems can be generated using linear submodels, the approximate accuracy of linear models is often insufficient in systems with significant nonlinear characteristics, thus affecting control performance. Therefore, ensuring the optimality and computational efficiency of solutions to deep learning-based wind farm optimization problems is a crucial issue that urgently needs to be addressed. Furthermore, purely data-driven methods often fail to ensure strict satisfaction of physical constraints, which may lead to infeasible solutions in practical operations and compromise the safety and stability of the system. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a distributed physical-data joint drive voltage optimization control method and system for wind farms based on ADMM, which reduces the computational burden of large-scale wind farm optimization problems based on deep learning models while ensuring that the performance of distributed optimization control is close to the global optimum.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a distributed physical-data joint drive voltage optimization control method for wind farms based on ADMM, comprising the following steps:

[0007] S1. Transform the optimization objective function based on the deep learning prediction model of the wind farm into a function of the output variables and control variables of the wind farm, thus obtaining the optimization objective function of the wind farm.

[0008] S2. The optimization problem of the objective function is transformed into a global optimization problem by adopting a two-layer distributed solution algorithm based on ADMM.

[0009] S3. Design a PINN network to solve the global optimization problem, and directly predict the optimal solution of the wind farm optimization problem using the given input.

[0010] The objective function for wind farm optimization is expressed as:

[0011] ;

[0012] st:

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] in, Deep learning prediction model for wind farms N P Step output variables, For k t The j-th step prediction vector of the wind farm node voltage at time n, where n represents the number of wind farm nodes. , , and V represents the real and imaginary parts of the voltage vector at the i-th node of the wind farm, respectively. i Let θ be the node voltage magnitude. i The node voltage phase angle, , and These represent the system output variable vector and control variable increment vector over the past T steps, respectively. For N P Step voltage vector transformation matrix, Represents the future N P Step node voltage magnitude square vector This represents the squared vector of the node voltage amplitudes in the wind farm. This is a reference value for the square vector of the nodal voltage amplitude of the wind farm. N represents P Step-by-step active power loss vector transformation matrix, , This is the transformation matrix for active power losses in a wind farm. Here is the conductance matrix. , and These represent the weight matrices of each sub-optimization function, and the control variable vector is... , Let k be the control variable vector of the wind farm at time k. Number of wind turbines; Let be the control variable for the i-th wind turbine at time k. and These represent the reference values ​​for active power and reactive power of a wind farm, respectively. Output the variable vector for the initial moment of the wind farm. , These represent the active power loss and reactive power loss of the wind farm at the initial moment, respectively. , This is the transformation matrix for reactive power losses in a wind farm. For susceptance matrix, N represents the i-th wind turbine. P Step active power reference value, N represents the i-th wind turbine. P Step active power reference value, , N P Step active power and reactive power vectors, , N P Step active power increment vector and reactive power increment vector, This is the constant coefficient matrix of the control variable equality constraints. This is the constant vector corresponding to the equality constraints of the control variables. For the constant matrix of inequality constraints on the control variables, To output the transformation matrix corresponding to the inequality constraints of the output variables, To output the constant matrix of the variable inequality constraints, Indicates about The number of inequality constraints Indicates about The number of inequality constraints.

[0019] In step S2, define , , , Combined with wind farm prediction models The equivalent form of the objective function optimization problem is obtained as follows:

[0020] ;

[0021] st:

[0022]

[0023]

[0024]

[0025]

[0026] in, The transformation matrix corresponding to the equality constraints of the control variables. , These are the initial measurements of the system, global variables. This is a consistency constraint.

[0027] The global problem is represented as:

[0028] ;

[0029] in, Let l and h be the Lagrange multipliers, where l and h represent the l-th and h-th elements of the Lagrange multipliers, respectively. ; As a penalty factor, ( ) represents the Lagrange function;

[0030] The update formula is:

[0031] ;

[0032] for The optimization function;

[0033] Local variables The update formula is:

[0034] ;

[0035] For local variables The augmented Lagrangian function;

[0036] ;

[0037] ;

[0038] , and The penalty factor iteration coefficient is defined as follows: when i=1, the original residual corresponding to the global constraint is defined as... The dual residual is defined as When i=2, the original residual corresponding to the consistency constraint is defined as Dual residual .

[0039] when At that time, the two-layer distributed solution algorithm based on ADMM converged; among them, and This is the tolerance threshold.

[0040] , Indicates about The number of inequality constraints.

[0041] In step S3, the PINN network includes three neural networks, and the inputs of the three neural networks are respectively... Three neural networks are used to calculate the optimal solution of the Lagrange function. ,in This represents the set of dual variables.

[0042] During the training of the PINN network, the deviation value φ of the Lagrange function KKT condition is added to the loss function of the corresponding neural network training, and the parameters of the PINN network are fixed by minimizing the deviation value during the training process.

[0043] The KKT conditions include:

[0044] For sub-variables :

[0045] The feasibility conditions include:

[0046] ;

[0047] The conditions for duality feasibility include:

[0048] ;

[0049] The necessary conditions for a first-order Lagrange multiplier include:

[0050] ;

[0051] Among them, the Lagrange function pairs The expression for the first-order partial derivative is:

[0052] ;

[0053] Complementary relaxation conditions:

[0054] ;

[0055] The feasibility conditions include:

[0056] ;

[0057] The conditions for duality feasibility include:

[0058] ;

[0059] The necessary conditions for a first-order Lagrange multiplier include:

[0060] ;

[0061] Among them, the Lagrange function pairs The expression for the first-order partial derivative is:

[0062] ;

[0063] In the formula, Indicates to The first-order derivative operator.

[0064] Complementary relaxation conditions:

[0065] .

[0066] The deviation values ​​of the KKT conditions include:

[0067] Define the deviation 𝜀 stat Used to measure the absolute deviation under static conditions: ;

[0068] in, , ;

[0069] The error of the complementary relaxation condition is defined as: ;

[0070] The dual feasibility error is defined as: ;

[0071] Feasibility error is defined as: ;

[0072] in, This represents the set of dual variables predicted by three neural networks.

[0073] Preferably,

[0074] The loss function of the PINN network is expressed as:

[0075] ;

[0076] The total static error is: The complementary relaxation condition error is The dual feasibility error is The feasibility error is , and These represent the number of training data points and the number of deployment points, respectively. , and They represent The mean absolute error between the predicted and actual values, This represents the average absolute value of violations of the KKT conditions. , , and These represent the weighting coefficients for each mean absolute error.

[0077] As an inventive concept, this invention provides a distributed physical-data joint drive voltage optimization control system for wind farms based on ADMM, including a memory, a processor, and a computer program stored in the memory; the processor executes the computer program to implement the steps of the above method.

[0078] This invention proposes a distributed physical-data joint optimization control method for wind farms based on Active Data Model (ADMM). The aim is to reduce the computational burden of solving large-scale wind farm optimization problems based on deep learning models while ensuring near-global optimal performance. First, the global optimization problem of the wind farm is decomposed and solved iteratively in a distributed manner using the ADMM method. A locally input convex neural network (PICNN) is used to fit the dynamic prediction model of the wind farm, transforming the originally complex nonlinear MPC optimization problem into a convex optimization problem with convex constraints. The optimal solution of the optimization problem is directly predicted using a PINN network. By embedding the KKT conditions of the optimization problem into the loss function of the PINN, the PINN model can effectively learn the implicit physical laws based on specific configuration point data, ensuring that the solution generated by the model satisfies physical feasibility and optimality.

[0079] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0080] 1. This invention reduces the computational burden of solving large-scale wind farm optimization problems based on deep learning models while ensuring that the proposed distributed optimization control method achieves near-global optimal performance. By decomposing the global optimization problem of wind farms based on deep learning and implementing distributed iterative solutions through the ADMM algorithm framework, the computational burden of large-scale wind farm optimization problems based on deep learning is reduced. Secondly, a Local Input Convex Neural Network (PICNN) is used to fit the dynamic prediction model of the wind farm, transforming the originally complex nonlinear MPC optimization problem into a convex optimization problem with convex constraints, ensuring the global optimality of the solution. Then, the PINN network is used to directly predict the optimal solution of the optimization problem. By embedding the KKT conditions of the optimization problem into the loss function of the PINN, the PINN model can effectively learn the implicit physical laws based on specific configuration point data, ensuring that the solution generated by the model satisfies physical feasibility and optimality.

[0081] 2. The ADMM distributed iterative computation method proposed in this invention for solving the global optimization problem of wind farms based on deep learning employs a two-layer distributed control framework. During the ADMM iteration process, local and auxiliary variables are alternately optimized to gradually approach the optimal solution of the original problem while ensuring that all constraints are met. This method can efficiently handle complex large-scale optimization problems based on deep learning models and ensure that both global and local constraints are satisfied. The proposed method uses a Local Input Convex Neural Network (PICNN) to fit the dynamic prediction model of the wind farm, transforming the optimization problem based on the nonlinear deep learning model into a convex optimization problem with respect to control variables, thereby guaranteeing the global optimality of the solution. The proposed PINN-based physical-data joint optimization network for solving wind farm optimization problems directly predicts the optimal solution of the wind farm optimization problem using given inputs. By embedding the KKT conditions of the optimization problem into the loss function of PINN, the PINN model can effectively learn the implicit physical laws based on specific configuration point data, ensuring that the solution generated by the model satisfies physical feasibility and optimality. Attached Figure Description

[0082] Figure 1 This is a block diagram of distributed optimization control for wind farms based on ADMM according to an embodiment of the present invention;

[0083] Figure 2 This is a PINN-based physical-data joint optimization network according to an embodiment of the present invention. Detailed Implementation

[0084] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0085] Example 1

[0086] like Figure 1 The diagram shown is a distributed optimization control block diagram of a wind farm based on ADMM. A two-layer ADMM optimization solution framework is designed, and the definition is... As global variables, all local information is collected in the upper-level controller to solve the problem. The upper-level controller uses all feedback measurements from the wind farm system to solve the global optimization problem, handles global constraints, updates global variables and penalty factors, and then sends the globally optimal solution to the lower-level controller. The upper-level controller achieves the global optimization objective of the entire wind farm system while ensuring that global variables such as voltage and power satisfy the corresponding equality constraints. The lower-level controllers are the controllers of each wind turbine, which receive global variables from the upper-level controller. and penalty factor It also uses local information to solve local sub-optimization problems, while handling local inequality constraints and updating local variables. and punishment factors To ensure that the output of each controller is within the constraints, calculate the optimal active power of each wind turbine. and reactive power reference value And it was distributed to each wind turbine.

[0087] This embodiment includes the following steps:

[0088] S1: Transform the optimization objective function based on the deep learning prediction model of wind farm into a function of the output variables and control variables of wind farm;

[0089] S2: Design an ADMM distributed solution framework for wind farm optimization objective function based on deep learning;

[0090] S3: Considering the optimality of solving the wind farm optimization objective function based on deep learning, establish a wind farm prediction model based on convex neural networks.

[0091] S4: Based on the wind farm optimization objective function and its physical constraints, a physical-data joint optimization method based on PINN network is established to solve the wind farm optimization objective function based on deep learning.

[0092] The specific steps of the distributed optimal control method for wind farms based on ADMM are as follows:

[0093] S1: The optimization objective function of the deep learning prediction model for wind farms can be transformed into a function of the wind farm's output and control variables. The wind farm prediction model is defined as a deep learning model. Then, the vector compact form of the centralized optimization problem of wind farms based on deep learning can be described as:

[0094] (1.1)

[0095] st:

[0096]

[0097]

[0098] in, For wind farm prediction model N P Step output variables, where Let be the j-th step prediction vector of the wind farm node voltage at time k, and n represent the number of wind farm nodes. , and These represent the system output variable vector and control variable increment vector over the past T steps, respectively. For N P Step voltage vector transformation matrix, Represents the future N P Step node voltage magnitude square vector, where Let be the square vector of the voltage magnitudes at the wind farm nodes. ,in This is the transformation matrix for active power losses in a wind farm. Here is the conductivity matrix. represent N P Step-by-step active power loss vector transformation matrix, , and These represent the weight matrices of each sub-optimization function. The control variable vector is... Define the control variable vector of the wind farm at time k as follows: Wherein, the control variable for the i-th wind turbine at time k is . and These represent the reference values ​​for active and reactive power of the wind farm, respectively, and are assumed to remain constant during the control period. , These represent the active power loss and reactive power loss of the wind farm at the initial moment, respectively, and can be measured. N represents the i-th wind turbine. P Step active power reference value, N represents the i-th wind turbine. P Step active power reference value. , N P Step active power and reactive power vectors, , N P Step active power and reactive power vectors. and These are the lower and upper limits of the square of the voltage amplitude at wind farm nodes, respectively.

[0099] definition ,make This represents the active and reactive power reference vector of the wind farm. Let the initial values ​​of active and reactive power losses represent the values. Then, the equality constraints for the active and reactive power of a wind farm can be expressed as:

[0100] (1.2)

[0101] In the formula, N represents all wind turbine units P Active power reference vector, N of wind turbine P The step reactive power reference vector is .definition Let represent the summation matrix, where This represents a vector whose elements are all 1s. It is an identity matrix.

[0102] The next step is to transform all the inequality constraints into conditions concerning... The expression, based on the conversion formulas for injected active power vector and reactive power vector at the PQ node of a wind farm, is further extended to N. P The compact expression for the step variable is:

[0103] (1.3)

[0104] (1.4)

[0105] In the formula, For N P The transformation matrix of the active power vector. For N P The transformation matrix of the reactive power vector. and Let N represent the transformation matrices between the active power vector and the reactive power vector at step k, respectively. P The step prediction matrix is ,in This is a diagonal matrix representing the active power vector at step k. The reactive power N... P The step prediction matrix is ​​represented as ,in Let be the diagonal matrix representing the reactive vector at step k.

[0106] definition ,in Then the inequality constraint between active and reactive power in the optimization problem can be expressed as:

[0107] (1.5)

[0108] In the formula, N represents all wind turbine unitsP Step active power upper limit matrix, N represents all wind turbine units P Step reactive power upper limit matrix, Let it be its lower bound matrix.

[0109] definition , , express The variable at step k, express The variable at step k. According to the active power conversion formula, we have... , The work done and the work not done constraint are as follows:

[0110] (1.6)

[0111] The active and reactive power increment constraints can be expressed as:

[0112] (1.7)

[0113] In the formula, This represents the upper limit of the increase in active and reactive power of a wind farm. This represents the lower limit of the increase in active and reactive power of a wind farm.

[0114] Through the above transformation, the objective function (1.1) can be simplified to:

[0115] (1.8)

[0116] st:

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] In the formula, The proposed deep learning prediction model for wind farms The transformation matrix corresponding to the equality constraints of the control variables. This is the constant coefficient matrix of the control variable equality constraints. This is the constant vector corresponding to the equality constraints of the control variables. For the constant matrix of inequality constraints on the control variables, To output the transformation matrix corresponding to the inequality constraints of the output variables, This is the constant matrix for the output variable inequality constraints. Indicates about The number of inequality constraints Indicates about The number of inequality constraints.

[0123] S2: Design a two-layer distributed solution algorithm based on ADMM. Introduce consistency constraints. Decompose the complex optimization problem into... Given the global problem (handled by the upper-level centralized controller) and the various local problems (handled by the lower-level local controllers), the equivalent form of the optimization problem is:

[0124] (1.11)

[0125] st:

[0126]

[0127]

[0128]

[0129]

[0130] Design a two-layer ADMM optimization solution framework, and define... As global variables, all local information is collected in the upper-level controller to solve the problem. And handle matters related to The global optimization problem and global equality constraints. Define a part of the objective function. And about All inequality constraints can be decomposed into local subfunctions. Including inequality constraints related to local variables, the optimal solution for the local controller can be obtained by solving the local subfunction at the lower level. During the ADMM iteration process, local and auxiliary variables are optimized alternately to gradually approach the optimal solution of the original problem while ensuring that all constraints are satisfied. This is achieved by introducing Lagrange multipliers. and penalty factor The augmented Lagrangian form of the above optimization problem is obtained as follows:

[0131] (1.12)

[0132] By solving for... Optimization function ,get The update formula is:

[0133] (1.13)

[0134] Will Decomposed into sub-functions that are independently optimized by each local controller. Only local variables need to be processed. The relevant inequality constraints also satisfy the global consistency constraint. During each iteration, according to... and Update Local variables The update formula is:

[0135] (1.14)

[0136] Regarding local variables augmented Lagrange function It is a small-scale quadratic sub-optimization problem with linear constraints, which is solved in parallel within the lower-level local controller, resulting in high computational efficiency and consistent constraints. This guarantees the global optimality of the solution to the subdivision problem.

[0137] Simultaneously, the dual variables are updated in the lower-level local controller to ensure... and It tends to be consistent in each iteration, and its update formula is:

[0138] (1.15)

[0139] The penalty factor is updated in real time based on the residual situation. Using a variable step size penalty factor can accelerate the convergence rate of ADMM and reduce the dependence on the initial penalty factor setting. The correction formula for the penalty factor is as follows:

[0140] (1.16)

[0141] The original residual corresponding to the global constraint is defined as follows: This indicates the degree to which the current solution violates the global constraint. The dual residual is defined as... This reflects the convergence of the dual variables. The original residuals corresponding to the consistency constraints are defined as follows: ,against and Global equality constraints between them are used to measure In Changes under consistency requirements, dual residuals measure The update changes under this equality constraint. , and The penalty factor iteration coefficient.

[0142] During the iterative process of the ADMM algorithm, these two residuals are used to determine whether the penalty parameter needs to be adjusted and whether the convergence condition is met. A common practice is to set a certain tolerance threshold; when both the original residual and the dual residual are less than this threshold, the algorithm is considered convergent.

[0143] (1.17)

[0144] In the formula, and This is the tolerance threshold.

[0145] like Figure 2 The physical-data joint optimization network based on PINN shown uses the PICNN model to fit the dynamic prediction model of the wind farm. This paper transforms the optimization problem based on a nonlinear deep learning model into a convex optimization problem with respect to control variables, ensuring the global optimality of the solution to the deep learning-based wind farm optimization problem. A PINN-based physical-data joint optimization network is used to solve the wind farm optimization problem, directly predicting the optimal solution using the given input. In this network, the deviation value *k* of the augmented Lagrangian KKT conditions of the wind farm sub-optimization problem is added to the loss function of the corresponding neural network training. By minimizing this deviation during training, the neural network gradually approximates the optimal solution of the wind farm sub-optimization problem, thus achieving an effective solution to the deep learning-based wind farm optimization problem. The specific implementation steps are as follows:

[0146] S1: The single-step prediction model for wind farm output variables is:

[0147] (1.18)

[0148] in, In this chapter, To fit the function .

[0149] According to the optimization function (1.8) of the wind farm, the problem is essentially a nonlinear MPC optimization problem. When solving for the optimal control variable vector in each prediction period, it is necessary to predict the output variables in future prediction periods based on the prediction model. The prediction model for the i-th step of the output variable is:

[0150] (1.19)

[0151] Specifically, the N of the output variableP The step prediction model is:

[0152] (1.20)

[0153] As can be seen from formula (1.19), Depends on That is, the decision variable vector of the optimization problem Secondly, It also depends on the measured values ​​of the control variables from the previous few time points. .at the same time It also depends on the measured values ​​of the output variables at the current and previous time points. Finally, you can also see The prediction formula is recursive, and it depends on the predicted values ​​from previous periods. However, training recursive models is more computationally demanding and time-consuming than training single-step prediction models. They are also susceptible to noise and improper selection of the order of the dynamic model, which can lead to the propagation of prediction errors, thereby reducing prediction accuracy and MPC control performance. Furthermore, it makes the MPC optimization problem multimodal and nonconvex.

[0154] To avoid recursive training and the use of recursive models in MPC, a multi-model approach can be used. The main advantage of multi-model approaches is that all sub-models are trained independently as single-step non-recursive models, eliminating the need for computationally demanding recursive training. A continuous sub-model is represented by the following function:

[0155] (1.21)

[0156] Here, the measurement vector at past time points is defined as:

[0157] (1.22)

[0158] Simultaneously, the control variable vector, i.e., the decision variable, calculated at future time points is defined as follows:

[0159] (1.23)

[0160] In particular, when hour, .

[0161] The general multi-model prediction equation for output variables is then:

[0162] (1.24)

[0163] At each sampling time, each prediction sub-model in the multi-model prediction uses model (1.24) to obtain the sub-model at future sampling times. The output predicted value.

[0164] S2: Based on subvariables The augmented Lagrangian function (1.12) of the wind farm optimization problem gives its KKT conditions as follows:

[0165] (1) The feasibility conditions include:

[0166] (1.25)

[0167] (2) The conditions for duality feasibility include:

[0168] (1.26)

[0169] (3) The necessary conditions for the first-order Lagrange multiplication include:

[0170] (1.27)

[0171] Among them, the Lagrange function pairs The expression for the first-order partial derivative is:

[0172] (1.28)

[0173] (4) Complementary relaxation condition:

[0174] (1.29)

[0175] In the formula, Indicates to The first-order derivative operator.

[0176] Similarly, based on subvariables augmented Lagrange function The KKT conditions can be obtained as follows:

[0177] (1) The feasibility conditions include:

[0178] (1.30)

[0179] (2) The conditions for duality feasibility include:

[0180] (1.31)

[0181] (3) The necessary conditions for the first-order Lagrange multiplication include:

[0182] (1.32)

[0183] Among them, the Lagrange function pairs The expression for the first-order partial derivative is:

[0184] (1.33)

[0185] In the formula, Indicates to The first-order derivative operator.

[0186] (4) Complementary relaxation condition:

[0187] (1.34)

[0188] S3: Design a PINN-based physical-data joint optimization network for solving wind farm optimization problems. This network directly predicts the optimal solution to the wind farm optimization problem using given inputs. The input to the proposed PINN network is set as... Three neural networks were designed respectively. To find the optimal solution of the augmented Lagrange daily function (1.13)-(1.16) for the wind farm. ,in This represents the set of dual variables.

[0189] A neural network is a set of interconnected nodes that are trained to connect the input and output layers. The nodes connecting the input and output layers are divided into K hidden layers, each hidden layer k having N nodes. K There are *n* neurons, each connected by a set of weights *w* and biases *b*, and each neuron is connected to a non-linear activation function *k*. The output of each layer of the neural network can be represented as:

[0190] (1.35)

[0191] In the formula, This is the output of the k-th layer. and These represent the weights and biases connecting the (k-1)th and kth layers, respectively. In this embodiment, the non-linear activation function is ReLU, which can accelerate the training process of the neural network. ReLU returns the input value when it is positive, and returns zero when it is negative or zero. The output of each layer after the ReLU activation function can be expressed as:

[0192] (1.36)

[0193] (1.37)

[0194] During the training of a neural network, the backpropagation algorithm is used to adjust the weights and biases to minimize the average prediction error in the training dataset. u For example:

[0195] (1.38)

[0196] In the formula, N t It represents the number of training data points.

[0197] In the designed PINN network, in addition to comparing the optimal solution obtained by the neural network fitting with the optimal solution in the training dataset, it is also necessary to verify whether the network output satisfies the physical constraint equations of the optimization problem during the training process. As the aforementioned analysis shows, the KKT conditions are necessary conditions for the optimal solution of the augmented Lagrangian function of the wind farm sub-optimization problem. Therefore, in this embodiment, the deviation value *k* of the KKT conditions is added to the corresponding loss function of the neural network training. During training, by minimizing this deviation, the neural network training ensures that it gradually approaches the optimal solution of the wind farm sub-optimization problem, thereby achieving an effective solution to the augmented Lagrangian function. The dual variables required to calculate the KKT condition deviation are predicted using a separate set of hidden layers.

[0198] The deviation value of the KKT conditions is used to describe the degree of violation of the KKT conditions, and its calculation formula is as follows:

[0199] (1) Define the deviation φ according to the first-order necessary condition of the Lagrange function. stat Used to measure the absolute deviation under static conditions:

[0200] (1.39)

[0201] in,

[0202] (1.40)

[0203] (1.41)

[0204] (2) The error of the complementary relaxation condition is defined as:

[0205] (1.42)

[0206] (3) The duality feasibility error is defined as:

[0207] (1.43)

[0208] (4) The original problem's feasibility error is defined as:

[0209] (1.44)

[0211] in, Indicated by respectively The variables predicted by the neural network. The activation function 𝜎 is used to represent the degree of violation of the inequality constraints in the dual feasibility and the feasibility of the original problem. If the neural network predicts the optimal solution to the optimization problem, then the values ​​of each error calculated by the deviation calculation formulas (1.39)-(1.44) are all 0.

[0212] PINN learns the patterns behind the data, enabling it to solve problems not only under specific configurations but also generate accurate optimal solutions under different input conditions, demonstrating strong generalization ability. Therefore, this embodiment adds configuration points to the training set. Like the neural network training data, these are a set of random input values ​​included in the input set. The difference is that the configuration points do not contain... The label value represents the optimal solution set of the optimization problem.

[0213] This embodiment designs a separate PINN network and uses the bias calculation formula of KKT conditions to evaluate the neural network model. The prediction accuracy is improved, and the parameters of the neural network are updated through backpropagation of the error. The following loss function is used to adjust the shared parameters of the three neural networks:

[0214] (1.45)

[0216] The total static error is: The complementary relaxation condition error is The dual feasibility error is The original problem's feasibility error is , and These represent the number of training data points and the number of deployment points, respectively. , and They represent The mean absolute error between the predicted and actual values, This represents the average absolute value of violations of the KKT conditions. , , and These represent the weighting coefficients for each mean absolute error.

[0217] In three independent neural network models In this process, training data is used to train models, and each model uses a corresponding loss function combined with... relevant parts To train the model parameters separately. As for the location point, since it doesn't have a label value set, its... , and All are set to 0, and only one is considered during training. Used as a loss function to train neural networks.

[0218] This invention proposes a distributed physical-data joint optimization control method for wind farms based on Active Data Model (ADMM). This method reduces the computational burden of solving large-scale wind farm optimization problems based on deep learning models while ensuring near-global optimal performance. First, it decomposes the global optimization problem of wind farms based on deep learning and implements distributed iterative solutions using the ADMM algorithm framework, thus reducing the computational burden. Second, it employs a Locally Input Convex Neural Network (PICNN) to fit the dynamic prediction model of the wind farm, transforming the originally complex nonlinear MPC optimization problem into a convex optimization problem with convex constraints, ensuring global optimality. Then, it directly predicts the optimal solution of the optimization problem using a PINN network. By embedding the KKT conditions of the optimization problem into the loss function of the PINN, the PINN model can effectively learn the implicit physical laws based on specific configuration point data, ensuring that the solution generated by the model satisfies both physical feasibility and optimality.

[0219] Example 2

[0220] Embodiment 2 of the present invention provides a terminal device corresponding to Embodiment 1 above. The terminal device can be a processing device for a client, such as a mobile phone, a laptop, a tablet computer, a desktop computer, etc., to execute the method of the above embodiments.

[0221] The terminal device in this embodiment includes a memory, a processor, and a computer program stored in the memory; the processor executes the computer program in the memory to implement the steps of the method in Embodiment 1 described above.

[0222] In some implementations, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.

[0223] In other implementations, the processor can be any type of general-purpose processor, such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation here.

[0224] Example 3

[0225] Embodiment 3 of the present invention provides a computer-readable storage medium corresponding to Embodiment 1 above, on which a computer program / instructions are stored. When the computer program / instructions are executed by a processor, they implement the steps of the method of Embodiment 1 above.

[0226] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.

[0227] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0228] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0229] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0230] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0231] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A distributed physical-data joint drive voltage optimization control method for wind farms based on ADMM, characterized in that, Includes the following steps: S1. Transform the optimization objective function based on the deep learning prediction model of the wind farm into a function of the output variables and control variables of the wind farm, thus obtaining the wind farm optimization objective function; S2. The optimization problem of the objective function is transformed into a global optimization problem by adopting a two-layer distributed solution algorithm based on ADMM. S3. Design a PINN network to solve the global optimization problem, and directly predict the optimal solution of the wind farm optimization problem using the given input.

2. The wind farm distributed physical-data joint drive voltage optimization control method based on ADMM according to claim 1, characterized in that, The objective function for wind farm optimization is expressed as: ； s.t.: in, Deep learning prediction model for wind farms N P Step output variables, For k t The j-th step prediction vector of the wind farm node voltage at time n, where n represents the number of wind farm nodes. , , and V represents the real and imaginary parts of the voltage vector at the i-th node of the wind farm, respectively. i Let θ be the node voltage magnitude. i The node voltage phase angle, , and These represent the system output variable vector and control variable increment vector over the past T steps, respectively. For N P Step voltage vector transformation matrix, Represents the future N P Step node voltage magnitude square vector This represents the squared vector of the node voltage amplitudes in the wind farm. This is the reference vector for the squared magnitude of the node voltage in the wind farm. N represents P Step-by-step active power loss vector transformation matrix, , This is the transformation matrix for active power losses in a wind farm. Here is the conductance matrix. , and These represent the weight matrices of each sub-optimization function, and the control variable vector is... , To control the increment vector of the variable, Let k be the control variable vector of the wind farm at time k. Let be the control variable for the i-th wind turbine at time k. and These represent the reference values ​​for active power and reactive power of a wind farm, respectively. , These represent the active power loss and reactive power loss of the wind farm at the initial moment, respectively. This provides the initial measurement vector for the output variables of the wind farm system. , This is the transformation matrix for reactive power losses in a wind farm. For susceptance matrix, N represents the i-th wind turbine. P Step active power reference value, N represents the i-th wind turbine. P Step active power reference value, , N P Step active power and reactive power vectors, This refers to the number of wind turbines in a wind farm. , N P Step active power increment vector and reactive power increment vector, This is the constant coefficient matrix of the control variable equality constraints. This is the constant vector corresponding to the equality constraints of the control variables. For the constant matrix of inequality constraints on the control variables, To output the transformation matrix corresponding to the inequality constraints of the output variables, To output the constant matrix of the inequality constraints for the variables, Indicates about The number of inequality constraints Indicates about The number of inequality constraints.

3. The wind farm distributed physical-data joint drive voltage optimization control method based on ADMM according to claim 2, characterized in that, In step S2, define , , , Combined with wind farm prediction models The equivalent form of the objective function optimization problem is obtained as follows: ； s.t.: in, The transformation matrix corresponding to the equality constraints of the control variables. , These are the initial measurements of the system, global variables. This is a consistency constraint.

4. The wind farm distributed physical-data joint drive voltage optimization control method based on ADMM according to claim 3, characterized in that, The global problem is represented as: ； in, For Lagrange multipliers, the superscript 'l' indicates that the l-th multiplier is related to... Lagrange multipliers under inequality constraints The superscript h indicates that the h-th element is related to... Lagrange multipliers under inequality constraints , As a penalty factor, ( ) represents the Lagrange function; The update formula is: ； for The optimization function; Local variables The update formula is: ； For local variables The augmented Lagrangian function; ； ； , and The penalty factor is the iteration coefficient. When i=1, the original residual corresponding to the global constraint is defined as... The dual residual is defined as Reflecting the convergence of the dual variable; when i=2, the original residual corresponding to the consistency constraint is defined as Dual residual measure The update changes under this equality constraint.

5. The wind farm distributed physical-data joint drive voltage optimization control method based on ADMM according to claim 4, characterized in that, when At that time, the two-layer distributed solution algorithm based on ADMM converged; among them, and This is the tolerance threshold.

6. The wind farm distributed physical-data joint drive voltage optimization control method based on ADMM according to claim 4, characterized in that, , Indicates about The number of inequality constraints.

7. The wind farm distributed physical-data joint drive voltage optimization control method based on ADMM according to claim 4, characterized in that, In step S3, the PINN network includes three neural networks, and the inputs of the three neural networks are respectively... Three neural networks are used to calculate the optimal solution of the Lagrange function. ,in This represents the set of dual variables.

8. The wind farm distributed physical-data joint drive voltage optimization control method based on ADMM according to claim 7, characterized in that, During the training of the PINN network, the deviation value φ of the Lagrange function KKT condition is added to the loss function of the corresponding neural network training, and the parameters of the PINN network are fixed by minimizing the deviation value during the training process. The KKT conditions include: For sub-variables : The feasibility conditions include: ； The conditions for duality feasibility include: ； The necessary conditions for a first-order Lagrange multiplier include: ； Among them, the Lagrange function pairs The expression for the first-order partial derivative is: ； Complementary relaxation conditions: ； The feasibility conditions include: ； The conditions for duality feasibility include: ； The necessary conditions for a first-order Lagrange multiplier include: ； Among them, the Lagrange function pairs The expression for the first-order partial derivative is: ； In the formula, Indicates to The first-order derivative operator. Complementary relaxation conditions: 。 9. The distributed physical-data joint drive voltage optimization control method for wind farms based on ADMM as described in claim 8, characterized in that, The deviation values ​​of the KKT conditions include: Define the deviation 𝜀 stat Used to measure the absolute deviation under static conditions: ; in, , ; The error of the complementary relaxation condition is defined as: ; The dual feasibility error is defined as: ; Feasibility error is defined as: ; in, This represents the set of dual variables predicted by three neural networks. Preferably, The loss function of the PINN network is expressed as: ； The total static error is: The complementary relaxation condition error is The duality feasibility error is The feasibility error is , and These represent the number of training data points and the number of deployment points, respectively. , and They represent The mean absolute error between the predicted and actual values, This represents the average absolute value of violations of the KKT conditions. , , and These represent the weighting coefficients for each mean absolute error.

10. A distributed physical-data joint drive voltage optimization control system for wind farms based on ADMM, comprising a memory, a processor, and a computer program stored in the memory; characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 9.

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