Transmission and distribution cooperative reactive power optimization method based on data-model driven acceleration

Abstract

The invention provides a transmission and distribution cooperative reactive power optimization method based on data-model driven acceleration. According to the method, flexible and adjustable resources of the power distribution network can be fully utilized, the power transmission network-power distribution network collaborative line loss optimization model meeting the safe operation condition is established, a power transmission network-power distribution network line loss optimization regulation and control strategy covering various adjustable resources is formed, important support can be provided for real-time regulation and control of a power transmission network-power distribution network two-stage power grid, and the method is suitable for large-scale popularization and application. And the convergence of the method at the boundary is obviously superior to that of the traditional generalized master-slave splitting method.

Description

Technical Field

[0001] This invention belongs to the field of transmission and distribution coordination optimization technology, and particularly relates to a data-model driven accelerated method for transmission and distribution coordination reactive power optimization. Background Technology

[0002] In recent years, the flexibility of power distribution systems has increased significantly, providing an objective basis for the shift from "passive operation" to "active control." As the power grid continues to expand, the dimensions of traditional centralized operation optimization have increased dramatically, placing a heavy management burden on transmission network control centers. To further activate the control potential of both transmission and distribution networks and meet the collaborative needs of scheduling functions, management, and data in their joint optimization, transmission and distribution collaborative optimization methods based on distributed computing frameworks show significant advantages over centralized methods.

[0003] The integration of large-scale distributed generation (DG) into the distribution system causes frequent voltage rises and power flow congestion, exacerbating the complexity of the distribution network's operating environment. Due to the close power flow coupling between the transmission and distribution networks, the integration of large-scale renewable energy sources often leads to risks such as voltage limit violations, posing new problems and challenges to the coordinated optimization of the distribution and transmission / distribution networks. However, existing distributed generation methods are insufficient in considering the impact of large-scale distributed energy sources on the convergence of the boundary system.

[0004] The following challenges regarding boundary convergence in distributed methods for coordinated transportation and distribution optimization still require further resolution:

[0005] (1) The large-scale distributed energy access to the grid leads to more complex power flow direction. The amount of information interaction at the boundary of traditional distributed algorithms increases and the computational burden intensifies, and the boundary convergence of the algorithms faces greater challenges.

[0006] (2) Discrete control variables such as transformer taps and capacitor switching introduce computational challenges such as non-convexity and discontinuity to the transmission and distribution coordinated optimization, which significantly reduces the solution efficiency of existing distributed methods.

[0007] (3) Sub-problem optimization involves interior point method, and its solution speed is affected by the initial value, so deep learning method is needed to optimize the initial value;

[0008] (4) Current acceleration methods only utilize one-way historical information and do not fully explore and utilize the characteristic that information can be communicated bidirectionally between the transmission network and the distribution network. Therefore, it is urgent to further design an Anderson acceleration transmission and distribution coordination optimization method based on bidirectional information communication. Summary of the Invention

[0009] The purpose of this invention is to solve the problem of convergence deterioration at the boundary in the coordinated optimization calculation of transmission and distribution, and to propose a data-model driven accelerated method for coordinated reactive power optimization of transmission and distribution.

[0010] This invention is achieved through the following technical solution: This invention proposes a data-model-driven accelerated method for coordinated reactive power optimization in power transmission and distribution, the method comprising the following steps:

[0011] Step 1: Establish an integrated optimization and control model for the transmission and distribution networks, and decouple the model based on the generalized master-slave splitting method;

[0012] Step 2: Construct the decoupled transmission network optimization control sub-model and each distribution network optimization control sub-model;

[0013] Step 3: Use a Long Short-Term Memory (LSTM) neural network to accelerate the initial value of the boundary iteration from the perspective of "data";

[0014] Step 4: Combining the bidirectional Anderson acceleration method, historical iteration information is introduced from the perspective of the "model" to update the boundary information and accelerate the boundary convergence speed;

[0015] Step 5: For solving the sub-problems of the transmission network and each distribution network, the primal dual interior point method and the branch and bound method are used. The boundary information after the solution is corrected by the Anderson acceleration method, and then the next iteration is carried out. Based on the optimization results obtained from the transmission network and each distribution network sub-model and the corrected boundary interaction information, a collaborative optimization scheduling strategy for the transmission network and distribution network covering multiple adjustable resources is formed.

[0016] Furthermore, in step one, considering the controllable variables such as transformer taps at the root node, capacitors, static var compensators, and controllable distributed power source regulation resources, the integrated optimal scheduling model for the transmission and distribution networks is as follows:

[0017]

[0018] In the formula, k = 1, 2, ..., N represents the number of distribution networks.

[0019] y T It is a vector of state variables within the transmission network excluding boundary nodes.

[0020] It is a vector of state variables inside the distribution network k, excluding boundary nodes.

[0021] y B,k It is the state variable vector of the boundary node between the transmission network and the distribution network k.

[0022] u T These are control variables used in power transmission networks.

[0023] It is the control variable used for k in the distribution network.

[0024] f, h, and g represent the objective function, equality constraint, and inequality constraint, respectively.

[0025] Subscripts T, B, and D k k represents the transmission network, the boundary network, and the distribution network, respectively.

[0026] Furthermore, a generalized master-slave splitting method is used to decouple the transmission network-distribution network collaborative model, and a boundary variable S is introduced. B,k Let represent the power value transferred from the transmission network to the k-th distribution network. The boundary equality constraints between the transmission network and the distribution network are decomposed into:

[0027]

[0028] In the formula, k = 1, 2, ..., N;

[0029] h T,B,k Boundary equality constraints for the decomposed transmission network;

[0030] This represents the boundary equality constraints for the k-th distribution network after decomposition.

[0031] Furthermore, in step two, through decoupling, the objective function of the power grid optimization scheduling sub-model is:

[0032]

[0033] The objective function consists of two parts, the first part The active power loss of a power distribution network is expressed as follows:

[0034]

[0035] In the formula, G l (i,j) represents the admittance value of the line between node i and node j in the distribution network.

[0036] U i This represents the voltage amplitude at node i in the distribution network.

[0037] θ ij This represents the phase angle difference of the voltage between node i and node j in a distribution network.

[0038] n l Indicates the total number of branches in the distribution network;

[0039] Part Two ξ auxT This is an auxiliary function that represents the impact of distribution network optimization results on the transmission network, ensuring the optimality condition of the global model. The specific expression of the auxiliary function is:

[0040] ξ auxT =(γ) BD ) T x B (5)

[0041]

[0042]

[0043] In the formula, Let k represent the objective function of the distribution network.

[0044] Vector γ BD The objective function and constraints of the distribution network are expressed with respect to the boundary variable x. B The sensitivity matrix;

[0045] and Let represent the Lagrange multiplier vectors of the equality constraints at k in the distribution network and the equality constraints at the boundary, respectively.

[0046] Let represent the Lagrange multiplier vector of the inequality constraint at the k boundary of the distribution network.

[0047] Furthermore, the constraints of the objective function of the power transmission network optimization scheduling sub-model consist of the following five parts:

[0048] Part 1: Power Balance Constraints

[0049]

[0050]

[0051] In the formula, i∈Ω T Ω T Represents the set of power transmission network nodes.

[0052] P gen,i and Q gen,i These represent the active and reactive power generated by the generator at node i in the power transmission network, respectively.

[0053] P load,i and Q load,i These represent the active and reactive power magnitudes of the load at the i-th node in the transmission network, respectively.

[0054] U i This represents the voltage magnitude at node i;

[0055] G ij and B ij Let represent the conductance and susceptance of the branch between node i and node j in the transmission network, respectively;

[0056] θ ij =θ i -θ j This represents the phase angle difference of the voltage between node i and node j;

[0057] Part Two: Constraints on Generator Active and Reactive Output

[0058]

[0059]

[0060] In the formula, P gen,i , and P gen,i Let represent the active power output of the generator at node i and its upper and lower limits, respectively.

[0061] Q gen,i , and Q gen,i Let i represent the reactive power output of the generator at node i and its upper and lower limits, respectively.

[0062] Part Three: Node Voltage Constraints

[0063]

[0064] In the formula, U i , and U i These represent the voltage amplitude at node i in the transmission network and its upper and lower limits, respectively.

[0065] Ω T Represents the set of nodes in a power transmission network;

[0066] Part 4: Branch Power Constraints

[0067]

[0068] In the formula, S ij and Ω represents the apparent power and the upper limit of apparent power of the branch between node i and node j, respectively. T,L It is the set of all branches in the power transmission network;

[0069] Part 5. Other Constraints

[0070]

[0071]

[0072] In the formula, K ij , and K ij Let represent the turns ratio and its upper and lower limits of the transformers on the branches between nodes i and j in the transmission network, respectively.

[0073] C i , and C i Let i represent the size of the capacitor connected at node i and its upper and lower limits, respectively.

[0074] Ω T This represents the set of nodes in the power transmission network.

[0075] N + It is a set of positive integers.

[0076] Furthermore, through decoupling, the objective function of the k-optimal scheduling sub-model of the distribution network is:

[0077]

[0078] The objective function consists of two parts, the first part The expression for active power loss in a distribution network is:

[0079]

[0080] In the formula, G l,k (i,j) represents the admittance value of the line between node i and node j in the distribution network k.

[0081] U i This represents the voltage amplitude at node i in the distribution network.

[0082] θ ij This represents the phase angle difference of the voltage between node i and node j in a distribution network.

[0083] n l,k This represents the total number of branches in distribution network k.

[0084] Part Two The influence of the transmission network optimization results on the distribution network k is expressed as follows: According to the generalized master-slave splitting method, the auxiliary function of the distribution network is:

[0085]

[0086] In the formula, λ TB The Lagrange multiplier vector represents the boundary equality constraints of the distribution network.

[0087] S B,k This represents the equivalent power of distribution network k at the boundary.

[0088] Furthermore, the objective function constraints of the k-optimal scheduling sub-model for the distribution network consist of the following five parts:

[0089] Part 1: Power Balance Constraints

[0090]

[0091]

[0092] In the formula, Represents the set of k nodes in a distribution network.

[0093] P gen,i and Q gen,i These represent the active and reactive power generated by the generator at node i, respectively.

[0094] P load,i and Q load,i These represent the active and reactive power magnitudes of the load on the i-th node, respectively.

[0095] U i This represents the voltage magnitude at node i;

[0096] G ij and B ij Let represent the conductance and susceptance of the branch between node i and node j, respectively;

[0097] θ ij =θ i -θ j This represents the phase angle difference of the voltage between node i and node j;

[0098] Part Two: Constraints on Generator Active and Reactive Output

[0099]

[0100]

[0101] In the formula, P gen,i , and P gen,i Q represents the active power output of the generator at node i and its upper and lower limits, respectively; gen,i , and Q gen,i Let i represent the reactive power output of the generator at node i and its upper and lower limits, respectively.

[0102] Part Three: Node Voltage Constraints

[0103]

[0104] In the formula, U i , and U i These represent the voltage amplitude at node i in the transmission network and its upper and lower limits, respectively.

[0105] Represents the set of nodes in distribution network k;

[0106] Part 4: Branch Power Constraints

[0107]

[0108] In the formula, S ij and This represents the apparent power and upper limit of the apparent power of the branch between node i and node j. It is the set of all branches in distribution network k;

[0109] Part 5. Other Constraints

[0110]

[0111]

[0112] In the formula, K ij , and K ij C represents the turns ratio and its upper and lower limits of the transformers on the branches between nodes i and j in the distribution network, respectively; i , and C i These represent the size and upper and lower limits of the capacitor connected at node i, respectively. N represents the set of nodes in distribution network k; + It is a set of positive integers.

[0113] Furthermore, in step three, in the Long Short-Term Memory network, C t G represents the stored information of the memory unit at time t. t and I t F represents the output of the update gate and the input gate at time t, respectively. t and O t These are the outputs of the forget gate and the output gate at time t, respectively. ⊙ represents the product operation. This represents an addition operation; all gating units receive the output data h from the short-term memory network unit at time t-1. t-1 And the input data x at time step t t ;

[0114] The forget gate, a key component of the Long Short-Term Memory (LSTM) network, uses the Sigmoid function to determine the information to be removed from memory. The forget gate operates as follows:

[0115] F t =sigm(θ) xf x t +θ hf h t-1 +b f (27)

[0116] The combined effect of the input gate and the update gate determines the data that needs to be recorded into the memory unit. The operating mechanism of the input gate and the update gate is as follows:

[0117] I t =sigm(θ) xi x t +θ hi h t-1 +b i (28)

[0118] G t =tanh(θ) xg x t +θ hg h t-1 +b g (29)

[0119] The information stored in a memory unit is updated recursively, that is:

[0120] C t =F t ⊙C t-1 +I t ⊙G t (30)

[0121] In addition, the output O of the output gate t and the output h of the entire Long Short-Term Memory network unit t for:

[0122] O t =sigm(θ) xo x t +θ ho h t-1 +b o (31)

[0123] h t =O t ⊙tanh(C t (32)

[0124] In the formula, θ xn and θ hnThese represent the output weight matrices, b and c, respectively. n Let n be a biased vector and {n|n=f,i,g,o}.

[0125] Furthermore, in step four, the boundary information is updated by incorporating historical iteration information using the bidirectional Anderson acceleration method. The Anderson acceleration method is described as follows:

[0126] First, we set the parameter m, which represents storing the boundary iteration information of the first m steps. After the current iteration value is solved, we correct the current value by combining the boundary iteration information of the previous m steps. Since we need to consider the case where the number of iterations is less than m, we define the correction information dimension m. n :

[0127] m n =min{m,n},n>0 (33)

[0128] In the formula, n represents the number of iterations; the new transmission network side boundary interaction variable From the previous m n The sum of the current boundary variables in each iteration Weighted average yields:

[0129]

[0130] Let g(x) = xf(x) be its iterative residual, then This can be transformed into an optimization problem that minimizes the residuals.

[0131]

[0132] To facilitate the solution, this optimization problem can be transformed into an unconstrained least squares model through a linear transformation:

[0133] Assuming coefficient vector satisfy:

[0134]

[0135] The original problem (35) can then be transformed into:

[0136] min||g n -H n β|| (37)

[0137] In the formula,

[0138]

[0139] If matrix H n If it is reversible, then the solution to (37) is:

[0140]

[0141] make in but The iterative expression can be expressed as:

[0142]

[0143] In summary, matrix E n , H n The latest iteration difference and residual difference are stored separately. Each time the transmission and distribution network performs a reactive power optimization calculation, E... n H n Then perform an update, and then calculate the new iteration value according to equation (40);

[0144] Based on equation (40), boundary variables are simultaneously adjusted on the distribution network side. The update and iteration, namely:

[0145]

[0146]

[0147]

[0148] In the formula, This represents the interactive information transmitted from the distribution network to the boundary in the (n+1)th iteration after correction, including power information. and variables Its iterative update form is the same as that of the transmission network side; the specific derivation process is as follows:

[0149] Boundary variables From the previous m n The sum of the current boundary power in each iteration Weighted average yields:

[0150]

[0151] Let g(x) = xf(x) be its iterative residual, then This can be obtained by solving an optimization problem that minimizes the residual:

[0152]

[0153] The least squares model is:

[0154]

[0155] The original problem can then be transformed into:

[0156] min||g n -L n b n|| (46)

[0157] In the formula,

[0158]

[0159] If matrix L n If it is reversible, then the solution to (46) is:

[0160]

[0161] make but The iterative expression can be expressed as:

[0162]

[0163] In summary, matrix F n L n The latest iteration difference and residual difference are stored separately. After each optimization of the distribution network, F n L n An update is performed, and then the new iteration value is calculated according to equation (49).

[0164] The beneficial effects of this invention are:

[0165] This invention fully utilizes the flexible and controllable resources of the distribution network to establish a transmission-distribution network collaborative line loss optimization model that meets safe operation conditions. It forms a transmission-distribution network line loss optimization and control strategy encompassing various adjustable resources, providing crucial support for real-time control of the two-level transmission-distribution network. Furthermore, the method employed in this invention significantly outperforms the traditional generalized master-slave splitting method in terms of convergence at the boundary. Specific advantages are as follows:

[0166] (1) A bidirectional Anderson acceleration strategy based on the interaction of multiple information such as power and voltage and the correction of historical information is proposed, which provides effective guidance for heterogeneous decomposition algorithms and significantly improves the convergence performance of such algorithms in large-scale distributed energy access scenarios.

[0167] (2) The latest generalized master-slave splitting method has been improved. For the first time, the bidirectional Anderson acceleration method has been applied to the power transmission and distribution coordinated reactive power optimization, which improves the generalized master-slave splitting method, greatly reduces the number of iterations, and improves the computational efficiency of the algorithm.

[0168] (3) Under the framework of the generalized master-slave splitting method with bidirectional Anderson acceleration, a subproblem solving method integrating the original dual interior point method, particle swarm algorithm and auxiliary function is proposed to optimize discrete variables such as transformer tapping and capacitor switching, and coordinate and operate more flexible resources of transmission and distribution networks.

[0169] (4) Use a long short-term memory neural network to optimize the initial values ​​of each subproblem to accelerate convergence. Attached Figure Description

[0170] Figure 1 This is a diagram of the internal structure of a Long Short-Term Memory (LSTM) neural network.

[0171] Figure 2 This is a flowchart of the method described in this invention. Detailed Implementation

[0172] 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, and 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.

[0173] This invention proposes a data-model-driven accelerated method for reactive power optimization in power transmission and distribution coordination, with the following steps:

[0174] Step 1: Establish an integrated optimization and control model for the transmission and distribution networks. Based on the generalized master-slave splitting method, the model is decoupled. Furthermore, considering controllable variables such as transformer taps at the root node, capacitors, static var compensators, and controllable distributed power sources, the integrated optimization and scheduling model for the transmission and distribution networks is as follows:

[0175]

[0176] In the formula, k = 1, 2, ..., N represents the number of distribution networks.

[0177] y T It is a vector of state variables within the transmission network excluding boundary nodes.

[0178] It is a vector of state variables inside the distribution network k, excluding boundary nodes.

[0179] y B,k It is the state variable vector of the boundary node between the transmission network and the distribution network k.

[0180] u T These are control variables used in power transmission networks.

[0181] It is the control variable used for k in the distribution network.

[0182] f, h, and g represent the objective function, equality constraint, and inequality constraint, respectively.

[0183] Subscripts T, B, and Dk k represents the transmission network, the boundary network, and the distribution network, respectively.

[0184] The transmission network-distribution network collaborative model is decoupled using a generalized master-slave splitting method, and a boundary variable S is introduced. B,k Let represent the power value transferred from the transmission network to the k-th distribution network. The boundary equality constraints between the transmission network and the distribution network are decomposed into:

[0185]

[0186] In the formula, k = 1, 2, ..., N;

[0187] h T,B,k Boundary equality constraints for the decomposed transmission network;

[0188] The boundary equality constraints for the k-th distribution network after decomposition;

[0189] Step 2: Construct the decoupled transmission network optimization control sub-model and each distribution network optimization control sub-model; further, through decoupling, the objective function of the transmission network optimization scheduling sub-model is:

[0190]

[0191] The objective function consists of two parts, the first part The active power loss of a power distribution network is expressed as follows:

[0192]

[0193] In the formula, G l (i,j) represents the admittance value of the line between node i and node j in the distribution network.

[0194] U i This represents the voltage amplitude at node i in the distribution network.

[0195] θ ij This represents the phase angle difference of the voltage between node i and node j in a distribution network.

[0196] n l Indicates the total number of branches in the distribution network;

[0197] Part Two ξ auxT This is an auxiliary function that represents the impact of distribution network optimization results on the transmission network, ensuring the optimality condition of the global model. The specific expression of the auxiliary function is:

[0198] ξ auxT =(γ) BD ) T x B (5)

[0199]

[0200]

[0201] In the formula, Let k represent the objective function of the distribution network.

[0202] Vector γ BD The objective function and constraints of the distribution network are expressed with respect to the boundary variable x. B The sensitivity matrix;

[0203] and Let represent the Lagrange multiplier vectors of the equality constraints at k in the distribution network and the equality constraints at the boundary, respectively. The Lagrange multiplier vector represents the inequality constraint at the k-boundary of the distribution network;

[0204] The constraints of the objective function of the power transmission network optimization scheduling sub-model consist of the following five parts:

[0205] Part 1: Power Balance Constraints

[0206]

[0207]

[0208] In the formula, i∈Ω T Ω T Represents the set of power transmission network nodes.

[0209] P gen,i and Q gen,i These represent the active and reactive power generated by the generator at node i in the power transmission network, respectively.

[0210] P load,i and Q load,i These represent the active and reactive power magnitudes of the load at the i-th node in the transmission network, respectively.

[0211] U i This represents the voltage magnitude at node i;

[0212] G ij and B ij Let represent the conductance and susceptance of the branch between node i and node j in the transmission network, respectively;

[0213] θ ij =θ i -θ j This represents the phase angle difference of the voltage between node i and node j;

[0214] Part Two: Constraints on Generator Active and Reactive Output

[0215]

[0216]

[0217] In the formula, P gen,i , and P gen,i Let represent the active power output of the generator at node i and its upper and lower limits, respectively.

[0218] Q gen,i , and Q gen,i Let i represent the reactive power output of the generator at node i and its upper and lower limits, respectively.

[0219] Part Three: Node Voltage Constraints

[0220]

[0221] In the formula, U i , and U i These represent the voltage amplitude at node i in the transmission network and its upper and lower limits, respectively.

[0222] Ω T Represents the set of nodes in a power transmission network;

[0223] Part 4: Branch Power Constraints

[0224]

[0225] In the formula, S ij and Ω represents the apparent power and the upper limit of apparent power of the branch between node i and node j, respectively. T,L It is the set of all branches in the power transmission network;

[0226] Part 5. Other Constraints

[0227]

[0228]

[0229] In the formula, K ij , and K ij Let represent the turns ratio and its upper and lower limits of the transformers on the branches between nodes i and j in the transmission network, respectively.

[0230] C i , and Ci Let i represent the size of the capacitor connected at node i and its upper and lower limits, respectively.

[0231] Ω T This represents the set of nodes in the power transmission network.

[0232] N + It is a set of positive integers;

[0233] By decoupling, the objective function of the k-optimal scheduling sub-model of the distribution network is:

[0234]

[0235] The objective function consists of two parts, the first part The expression for active power loss in a distribution network is:

[0236]

[0237] In the formula, G l,k (i,j) represents the admittance value of the line between node i and node j in the distribution network k.

[0238] U i This represents the voltage amplitude at node i in the distribution network.

[0239] θ ij This represents the phase angle difference of the voltage between node i and node j in a distribution network.

[0240] n l,k This represents the total number of branches in distribution network k.

[0241] Part Two The influence of the transmission network optimization results on the distribution network k is expressed as follows: According to the generalized master-slave splitting method, the auxiliary function of the distribution network is:

[0242]

[0243] In the formula, λ TB The Lagrange multiplier vector represents the boundary equality constraints of the distribution network.

[0244] S B,k This represents the equivalent power of distribution network k at the boundary;

[0245] The objective function constraints of the k-optimal scheduling sub-model for the distribution network consist of the following five parts:

[0246] Part 1: Power Balance Constraints

[0247]

[0248]

[0249] In the formula, Represents the set of k nodes in a distribution network.

[0250] P gen,i and Q gen,i These represent the active and reactive power generated by the generator at node i, respectively.

[0251] P load,i and Q load,i These represent the active and reactive power magnitudes of the load on the i-th node, respectively.

[0252] U i This represents the voltage magnitude at node i;

[0253] G ij and B ij Let represent the conductance and susceptance of the branch between node i and node j, respectively;

[0254] θ ij =θ i -θ j This represents the phase angle difference of the voltage between node i and node j;

[0255] Part Two: Constraints on Generator Active and Reactive Output

[0256]

[0257]

[0258] In the formula, P gen,i , and P gen,i Q represents the active power output of the generator at node i and its upper and lower limits, respectively; gen,i , and Q gen,i Let i represent the reactive power output of the generator at node i and its upper and lower limits, respectively.

[0259] Part Three: Node Voltage Constraints

[0260]

[0261] In the formula, U i , and U i These represent the voltage amplitude at node i in the transmission network and its upper and lower limits, respectively.

[0262] Represents the set of nodes in distribution network k;

[0263] Part 4: Branch Power Constraints

[0264]

[0265] In the formula, S ij and This represents the apparent power and upper limit of the apparent power of the branch between node i and node j. It is the set of all branches in distribution network k;

[0266] Part 5. Other Constraints

[0267]

[0268]

[0269] In the formula, K ij , and K ij C represents the turns ratio and its upper and lower limits of the transformers on the branches between nodes i and j in the distribution network, respectively; i , and C i These represent the size and upper and lower limits of the capacitor connected at node i, respectively. N represents the set of nodes in distribution network k; + It is a set of positive integers.

[0270] Step 3: A Long Short-Term Memory (LSTM) neural network is used to accelerate the initial value processing for boundary iterations from a "data" perspective. Furthermore, the LSTM network maintains an internal memory unit, which effectively solves the gradient vanishing and gradient exploding problems in traditional recurrent neural networks. The structure of a single LSTM network unit is shown in the attached figure. Figure 1 As shown, C t G represents the stored information of the memory unit at time t. t and I t F represents the output of the update gate and the input gate at time t, respectively. t and O t These are the outputs of the forget gate and the output gate at time t, respectively. ⊙ represents the product operation. This represents an addition operation. All gating units receive the output data h from the short-term memory network unit at time t-1. t-1 And the input data x at time step t t .

[0271] The forget gate, a key component of the Long Short-Term Memory (LSTM) network, uses the Sigmoid function to determine the information that needs to be removed from memory. The forget gate operates as follows:

[0272] F t =sigm(θ)xf x t +θ hf h t-1 +b f (27)

[0273] The combined effect of the input gate and the update gate determines the data that needs to be recorded into the memory unit. The operating mechanism of the input gate and the update gate is as follows:

[0274] I t =sigm(θ) xi x t +θ hi h t-1 +b i (28)

[0275] G t =tanh(θ) xg x t +θ hg h t-1 +b g (29)

[0276] The information stored in a memory unit is updated recursively, that is:

[0277] C t =F t ⊙C t-1 +I t ⊙G t (30)

[0278] In addition, the output O of the output gate t and the output h of the entire Long Short-Term Memory network unit t for:

[0279] O t =sigm(θ) xo x t +θ ho h t-1 +b o (31)

[0280] h t =O t ⊙tanh(C t (32)

[0281] In the formula, θ xn and θ hn These represent the output weight matrices, b and c, respectively. n Let n be a biased vector and {n|n=f,i,g,o}.

[0282] Step 4: Combining the bidirectional Anderson acceleration method, historical iteration information is introduced from the perspective of the "model" to update the boundary information, thereby accelerating the boundary convergence speed; furthermore, combining the bidirectional Anderson acceleration method, historical iteration information is introduced to update the boundary information. The Anderson acceleration method is described as follows:

[0283] First, we set the parameter *m*, which represents storing the boundary iteration information from the previous *m* steps. After the current iteration value is solved, we correct the current value by combining the boundary iteration information from the previous *m* steps. Since we need to consider the case where the number of iterations is less than *m*, we define the correction information dimension *m*. n :

[0284] m n =min{m,n},n>0 (33)

[0285] In the formula, n represents the number of iterations. New transmission network side boundary interaction variables. From the previous m n The sum of the current boundary variables in each iteration Weighted average yields:

[0286]

[0287] Let g(x) = xf(x) be its iterative residual, then This can be transformed into an optimization problem that minimizes the residuals.

[0288]

[0289] To facilitate the solution, this optimization problem can be transformed into an unconstrained least squares model through a linear transformation:

[0290] Assuming coefficient vector satisfy:

[0291]

[0292] The original problem (35) can then be transformed into:

[0293] min||g n -H n β|| (37)

[0294] In the formula,

[0295]

[0296] If matrix H n If it is reversible, then the solution to (37) is:

[0297]

[0298] make in but The iterative expression can be expressed as:

[0299]

[0300] In summary, matrix E n , H n The latest iteration difference and residual difference are stored separately. Each time the transmission and distribution network performs a reactive power optimization calculation, E... n H n Then perform an update and calculate the new iteration value according to equation (40).

[0301] Based on equation (40), boundary variables are simultaneously adjusted on the distribution network side. The update and iteration, namely:

[0302]

[0303]

[0304]

[0305] In the formula, This represents the interactive information transmitted from the distribution network to the boundary in the (n+1)th iteration after correction, including power information. and variables Its iterative update form is the same as that of the transmission network side. The specific derivation process is as follows:

[0306] Boundary variables From the previous m n The sum of the current boundary power in each iteration Weighted average yields:

[0307]

[0308] Let g(x) = xf(x) be its iterative residual, then This can be obtained by solving an optimization problem that minimizes the residual:

[0309]

[0310] The least squares model is:

[0311]

[0312] The original problem can then be transformed into:

[0313] min||g n -L n b n || (46)

[0314] In the formula,

[0315]

[0316] If matrix L n If it is reversible, then the solution to (46) is:

[0317]

[0318] make but The iterative expression can be expressed as:

[0319]

[0320] In summary, matrix F n L n The latest iteration difference and residual difference are stored separately. After each optimization of the distribution network, F n L n An update is performed, and then the new iteration value is calculated according to equation (49).

[0321] Step 5: For solving the sub-problems of the transmission network and each distribution network, the primal dual interior point method and the branch and bound method are used. The boundary information after the solution is corrected by the Anderson acceleration method, and then the next iteration is carried out. Based on the optimization results obtained from the transmission network and each distribution network sub-model and the corrected boundary interaction information, a collaborative optimization scheduling strategy for the transmission network and distribution network covering multiple adjustable resources is formed.

[0322] The above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A data-model-driven accelerated method for coordinated reactive power optimization in power transmission and distribution, characterized in that, The method includes the following steps: Step 1: Establish an integrated optimization and control model for the transmission and distribution networks, and decouple the model based on the generalized master-slave splitting method; Step 2: Construct the decoupled transmission network optimization control sub-model and each distribution network optimization control sub-model; Step 3: Use a Long Short-Term Memory Neural Network to accelerate the initial value of the boundary iteration from the perspective of "data"; Step 4: Combining the bidirectional Anderson acceleration method, historical iteration information is introduced from the perspective of the "model" to update the boundary information and accelerate the boundary convergence speed; Step 5: For solving the sub-problems of the transmission network and each distribution network, the primal dual interior point method and the branch and bound method are used. The boundary information after the solution is corrected by the Anderson acceleration method, and then the next iteration is carried out. Based on the optimization results obtained from the transmission network and each distribution network sub-model and the corrected boundary interaction information, a collaborative optimization scheduling strategy for the transmission network and distribution network covering multiple adjustable resources is formed.

2. The method according to claim 1, characterized in that: In step one, considering the controllable variables such as transformer taps at the root node, capacitors, static var compensators, and controllable distributed power source regulation resources, the integrated optimal scheduling model for the transmission and distribution networks is as follows: In the formula, k = 1, 2, ..., N represents the number of distribution networks. y T It is a vector of state variables within the transmission network excluding boundary nodes. It is a vector of state variables inside the distribution network k, excluding boundary nodes. y B,k It is the state variable vector of the boundary node between the transmission network and the distribution network k. u T These are control variables used in power transmission networks. It is the control variable used for k in the distribution network. f, h, and g represent the objective function, equality constraint, and inequality constraint, respectively. Subscripts T, B, and D k k represents the transmission network, the boundary network, and the distribution network, respectively.

3. The method according to claim 2, characterized in that: The transmission network-distribution network collaborative model is decoupled using a generalized master-slave splitting method, and a boundary variable S is introduced. B,k Let represent the power value transferred from the transmission network to the k-th distribution network. The boundary equality constraints between the transmission network and the distribution network are decomposed into: In the formula, k = 1, 2, ..., N; h T,B,k The boundary equality constraints of the decomposed transmission network; This represents the boundary equality constraints for the k-th distribution network after decomposition.

4. The method according to claim 3, characterized in that: In step two, through decoupling, the objective function of the power grid optimization scheduling sub-model is: The objective function consists of two parts, the first part The active power loss of a power distribution network is expressed as follows: In the formula, G l (i,j) represents the admittance value of the line between node i and node j in the distribution network. U i This represents the voltage amplitude at node i in the distribution network. θ ij This represents the phase angle difference of the voltage between node i and node j in a distribution network. n l Indicates the total number of branches in the distribution network; Part Two ξ auxT This is an auxiliary function that represents the impact of distribution network optimization results on the transmission network, ensuring the optimality condition of the global model. The specific expression of the auxiliary function is: x auxT =(γ BD ) T x B (5) In the formula, Let k represent the objective function of the distribution network. Vector γ BD The objective function and constraints of the distribution network are expressed with respect to the boundary variable x. B The sensitivity matrix; and Let represent the Lagrange multiplier vectors of the equality constraints at k in the distribution network and the equality constraints at the boundary, respectively. Let represent the Lagrange multiplier vector of the inequality constraint at the k boundary of the distribution network.

5. The method according to claim 4, characterized in that: The constraints of the objective function of the power transmission network optimization scheduling sub-model consist of the following five parts: Part 1: Power Balance Constraints In the formula, i∈Ω T Ω T Represents the set of power transmission network nodes. P gen,i and Q gen,i These represent the active and reactive power generated by the generator at node i in the power transmission network, respectively. P load,i and Q load,i These represent the active and reactive power magnitudes of the load at the i-th node in the transmission network, respectively. U i This represents the voltage magnitude at node i; G ij and B ij Let represent the conductance and susceptance of the branch between node i and node j in the transmission network, respectively; θ ij =θ i -θ j This represents the phase angle difference of the voltage between node i and node j; Part Two: Constraints on Generator Active and Reactive Output In the formula, P gen,i , and P gen,i Let represent the active power output of the generator at node i and its upper and lower limits, respectively. Q gen,i , and Q gen,i Let i represent the reactive power output of the generator at node i and its upper and lower limits, respectively. Part Three: Node Voltage Constraints In the formula, U i , and U i These represent the voltage amplitude at node i in the transmission network and its upper and lower limits, respectively. Ω T Represents the set of nodes in a power transmission network; Part 4: Branch Power Constraints In the formula, S ij and Ω represents the apparent power and the upper limit of apparent power of the branch between node i and node j, respectively. T,L It is the set of all branches in the power transmission network; Part 5. Other Constraints In the formula, K ij , and K ij Let represent the turns ratio and its upper and lower limits of the transformers on the branches between nodes i and j in the transmission network, respectively. C i , and C i Let i represent the size of the capacitor connected at node i and its upper and lower limits, respectively. Ω T This represents the set of nodes in the power transmission network. N + It is a set of positive integers.

6. The method according to claim 5, characterized in that: By decoupling, the objective function of the k-optimal scheduling sub-model of the distribution network is: The objective function consists of two parts, the first part The expression for active power loss in a distribution network is: In the formula, G l,k (i,j) represents the admittance value of the line between node i and node j in the distribution network k. U i This represents the voltage amplitude at node i in the distribution network. θ ij This represents the phase angle difference of the voltage between node i and node j in a distribution network. n l,k This represents the total number of branches in distribution network k. Part Two The influence of the transmission network optimization results on the distribution network k is expressed as follows: According to the generalized master-slave splitting method, the auxiliary function of the distribution network is: In the formula, λ TB The Lagrange multiplier vector represents the boundary equality constraints of the distribution network. S B,k This represents the equivalent power of distribution network k at the boundary.

7. The method according to claim 6, characterized in that: The objective function constraints of the k-optimal scheduling sub-model for the distribution network consist of the following five parts: Part 1: Power Balance Constraints In the formula, Represents the set of k nodes in a distribution network. P gen,i and Q gen,i These represent the active and reactive power generated by the generator at node i, respectively. P load,i and Q load,i These represent the active and reactive power magnitudes of the load on the i-th node, respectively. U i This represents the voltage magnitude at node i; G ij and B ij Let represent the conductance and susceptance of the branch between node i and node j, respectively; θ ij =θ i -θ j This represents the phase angle difference of the voltage between node i and node j; Part Two: Constraints on Generator Active and Reactive Output In the formula, P gen,i , and P gen,i Q represents the active power output of the generator at node i and its upper and lower limits, respectively; gen,i , and Q gen,i Let i represent the reactive power output of the generator at node i and its upper and lower limits, respectively. Part Three: Node Voltage Constraints In the formula, U i , and U i These represent the voltage amplitude at node i in the transmission network and its upper and lower limits, respectively. Represents the set of nodes in distribution network k; Part 4: Branch Power Constraints In the formula, S ij and This represents the apparent power and upper limit of the apparent power of the branch between node i and node j. It is the set of all branches in distribution network k; Part Five: Other Constraints In the formula, K ij , and K ij C represents the turns ratio and its upper and lower limits of the transformers on the branches between nodes i and j in the distribution network, respectively; i , and C i These represent the size and upper and lower limits of the capacitor connected at node i, respectively. N represents the set of nodes in distribution network k; + It is a set of positive integers.

8. The method according to claim 7, characterized in that: In step three, in the Long Short-Term Memory network, C t G represents the stored information of the memory unit at time t. t and I t F represents the output of the update gate and the input gate at time t, respectively. t and O t These are the outputs of the forget gate and the output gate at time t, respectively. ⊙ represents the product operation. This represents an addition operation; all gating units receive the output data h from the short-term memory network unit at time t-1. t-1 And the input data x at time step t t ; The forget gate, a key component of the Long Short-Term Memory (LSTM) network, uses the Sigmoid function to determine the information to be removed from memory. The forget gate operates as follows: F t =sigm(θ xf x t +θ hf h t-1 +b f ) (27) The combined effect of the input gate and the update gate determines the data that needs to be recorded into the memory unit. The operating mechanism of the input gate and the update gate is as follows: I t =sigm(θ xi x t +θ hi h t-1 +b i ) (28) G t =tanh(θ xg x t +θ hg h t-1 +b g ) (29) The information stored in a memory unit is updated recursively, that is: C t =F t ⊙C t-1 +I t ⊙G t (30) In addition, the output O of the output gate t and the output h of the entire Long Short-Term Memory network unit t for: The t =sigm(θ xo x t +θ ho h t-1 +b o ) (31) h t =O t ⊙tanh(C t ) (32) In the formula, θ xn and θ hn These represent the output weight matrices, b and c, respectively. n Let n be a biased vector and {n|n=f,i,g,o}.

9. The method according to claim 8, characterized in that: In step four, the boundary information is updated by incorporating historical iteration information using the bidirectional Anderson acceleration method. The Anderson acceleration method is described as follows: First, we set the parameter m, which represents storing the boundary iteration information of the first m steps. After the current iteration value is solved, we correct the current value by combining the boundary iteration information of the previous m steps. Since we need to consider the case where the number of iterations is less than m, we define the correction information dimension m. n : m n =min{m,n},n>0 (33) In the formula, n represents the number of iterations; the new transmission network side boundary interaction variable From the previous m n The sum of the current boundary variables in each iteration Weighted average yields: Let g(x) = xf(x) be its iterative residual, then This can be transformed into an optimization problem that minimizes the residuals. To facilitate the solution, this optimization problem can be transformed into an unconstrained least squares model through a linear transformation: Assuming coefficient vector satisfy: The original problem (35) can then be transformed into: min||g n -H n b|| (37) In the formula, If matrix H n If it is reversible, then the solution to (37) is: make in but The iterative expression can be expressed as: In summary, matrix E n , H n The latest iteration difference and residual difference are stored separately. Each time the transmission and distribution network performs a reactive power optimization calculation, E... n H n Then perform an update, and then calculate the new iteration value according to equation (40); Based on equation (40), boundary variables are simultaneously adjusted on the distribution network side. The update and iteration, namely: In the formula, This represents the interactive information transmitted from the distribution network to the boundary in the (n+1)th iteration after correction, including power information. and variables Its iterative update form is the same as that of the transmission network side; the specific derivation process is as follows: Boundary variables From the previous m n The sum of the current boundary power in each iteration Weighted average yields: Let g(x) = xf(x) be its iterative residual, then This can be obtained by solving an optimization problem that minimizes the residual: The least squares model is: The original problem can then be transformed into: min||g n -L n b n || (46) In the formula, If matrix L n If it is reversible, then the solution to (46) is: make but The iterative expression can be expressed as: In summary, matrix F n L n The latest iteration difference and residual difference are stored separately. After each optimization of the distribution network, F n L n An update is performed, and then the new iteration value is calculated according to equation (49).

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