A privacy-considered distributed optimization method for active power distribution network with hydrogen coupling

Abstract

The application provides a distributed optimization method for an electric-hydrogen coupling active power distribution network considering privacy protection, a mathematical model based on a FedADMM algorithm is established, and a mathematical model of an improved FedADMM algorithm is obtained; an active power distribution network optimization model is constructed for partitioning, and each sub-region and a boundary coupling constraint are obtained, based on which, a sub-region optimization model is established for convex processing, and a convex processing sub-region optimization model is output; a three-layer distributed optimization framework is constructed based on the above-mentioned improved and convex processing models, each sub-region is solved by using a double-layer planning method, the optimization strategy is generated and uploaded to the constructed framework for iterative calculation, and a global optimal solution, namely, an optimal operation result of a distributed power supply, is obtained. Through flexible adjustment of hydrogen energy conversion and storage, the application effectively improves the regulation and control capability of a power distribution network and the new energy consumption level; through the improved FedADMM algorithm, the calculation complexity is reduced, the iteration convergence speed is accelerated, and the calculation efficiency is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of active power distribution network operation optimization, and particularly relates to a distributed optimization method for an electricity-hydrogen coupled active power distribution network considering privacy protection. BACKGROUND

[0002] With large-scale access of distributed energy, the structure and operation characteristics of the traditional power distribution network are becoming increasingly complex. In this context, the active power distribution network realizes the transformation from passive scheduling to active control through advanced information communication technology, providing strong support for building a new power system. However, distributed power sources have strong randomness and volatility, and the large-scale grid connection of distributed energy, while improving clean energy utilization, also poses challenges to the safe operation of the power distribution network, such as voltage out-of-limit and reverse power flow.

[0003] In addition, for the operation optimization solution problem of the active power distribution network, the traditional centralized optimization method has limitations such as low computational efficiency and insufficient data privacy protection in the large-scale, distributed energy environment, making it difficult to meet the current demand for efficient, real-time, and secure scheduling of new power systems. Distributed optimization algorithms have gradually become a research focus. However, although the distributed algorithm provides a practical solution to the complex operation optimization problem of the active power distribution network, the multiple iteration mechanism increases the computational burden to some extent. Moreover, the distributed optimization inevitably requires information exchange among sub-regions, and as the power grid scale continues to expand, data privacy becomes an unavoidable consideration.

[0004] In summary, as the penetration rate of distributed energy in the active power distribution network continues to rise and the operation requirements become increasingly diverse, the operation optimization problem of the active power distribution network becomes more complex. How to quickly solve complex optimization problems while ensuring real-time performance, high scalability, and strong data privacy protection is one of the current research challenges.

[0005] After searching, no identical or similar published patent documents were found. SUMMARY

[0006] In view of the deficiencies of the prior art, the application provides a distributed optimization method for an electricity-hydrogen coupled active power distribution network considering privacy protection, which aims to solve the problems in the background art.

[0007] To achieve the above-mentioned purpose, the application provides the following technical solution: a distributed optimization method for an electricity-hydrogen coupled active power distribution network considering privacy protection, comprising:

[0008] Step S1: a FedADMM algorithm mathematical model is established, a global augmented Lagrange equation based on the FedADMM algorithm mathematical model and an iterative updating equation of each variable are obtained, an auxiliary variable is introduced into the iterative updating equation of each variable, an approximate solution of the auxiliary variable is solved, when the approximate solution reaches a satisfaction condition of the approximate solution, an improved FedADMM algorithm mathematical model is obtained;

[0009] Step S2: an active power distribution network operation optimization mathematical model containing EHCS, PV and EES is established, and reasonable partition is carried out according to the characteristics of the power distribution network region, each sub-region of the power distribution network and the corresponding boundary coupling constraint condition are obtained;

[0010] Step S3: based on the boundary coupling constraint condition of step S2, a power distribution network sub-region optimization mathematical model is established, a convex processing is carried out on the power distribution network sub-region optimization mathematical model based on a second-order cone programming method, and the power distribution network sub-region optimization mathematical model after the convex processing is output;

[0011] Step S4: based on the improved FedADMM algorithm mathematical model and the power distribution network sub-region optimization mathematical model after the convex processing, a three-layer distributed optimization solving framework of the active power distribution network is constructed; each sub-region solves the power distribution network sub-region optimization mathematical model after the convex processing by using a double-layer programming method, generates an optimization strategy, uploads the optimization strategy to the three-layer distributed optimization solving framework of the active power distribution network for iterative calculation, and obtains a global optimal solution, that is, an optimal operation result of the distributed power supply of the power distribution network.

[0012] Further, the specific process of step S1 is as follows:

[0013] It is assumed that there are m clients locally, each client has a local data set, which is denoted as ; by introducing a local variable of the i-th client , it is indicated that

[0014] ;

[0015] In the formula, min is a minimum value; is a global variable; is a vector belonging to a d-dimensional real number space; m is the total number of clients; is a weight coefficient of the i-th client; is a loss function of the i-th client;

[0016] The introduced is rewritten as a global total loss function of the client, which is indicated as

[0017] ;

[0018] ;

[0019] wherein, is the global total loss function of the client; is the parameter value at which the global total loss function reaches the minimum value;

[0020] The mathematical model of the FedADMM algorithm is constructed, and the gradient of the global total loss function of all clients should satisfy the Lipschitz continuous condition; on the basis of satisfying the Lipschitz continuous condition, the corresponding global augmented Lagrangian equation is constructed and defined as:

[0021] ;

[0022] ;

[0023] wherein, is the corresponding global augmented Lagrangian equation; is the local variable; is the dual variable; is the global augmented Lagrangian equation of the i-th client; is the dual variable of the i-th client; is the penalty factor of the i-th client;

[0024] The t+1 rounds of iteration updating process of each variable in the corresponding global augmented Lagrangian equation are performed, and are represented as:

[0025] ;

[0026] ;

[0027] ;

[0028] wherein, is the global variable at the t+1th round of iteration; is the value of the global augmented Lagrangian equation that is minimized under the given and ; and are the local variable and the dual variable at the tth round of iteration, respectively; is the local variable of the i-th client at the t+1th round of iteration; is the value of the global augmented Lagrangian equation of the i-th client that is minimized under the given and ; is the dual variable of the i-th client at the tth round of iteration; is the dual variable of the i-th client at the t+1th round of iteration; ​​

[0029] wherein the introduction , let , denotes:

[0030] ;

[0031] in the formula, is the intermediate auxiliary variable of the i-th client at the t+1th round of iteration;

[0032] based on get the approximate solution satisfy the condition, denoted by:

[0033] ;

[0034] in the formula, is the gradient of the loss function of the i-th client; is the approximate value of the local variable of the i-th client at the t+1th round of iteration; is the solution accuracy of the approximate value of the i-th client at the t+1th round of iteration; wherein the approximate solution is solved, and the process is as follows:

[0035] Let the initial value ;

[0036] Let the initial value ; is the initial value of the solving auxiliary variable for solving the approximate solution of the i-th client; the k+1th iteration is performed on , and denotes:

[0037] ;

[0038] in the formula, is the solving auxiliary variable for solving the approximate solution of the i-th client at the k+1th iteration; is the solving auxiliary variable for solving the approximate solution of the i-th client at the kth iteration; is the Lipschitz constant of the i-th client; ; is the maximum number of iterations preset in the process of updating ;

[0039] Let the gradient of the loss function of the i-th client satisfy the Lipschitz continuity condition and the Hessian matrix satisfy the condition; ​

[0040] satisfies the condition, which means that:

[0041] ;

[0042] wherein, is the constraint residual of the i-th client; is a constant greater than 1;

[0043] For the i-th client, by updating , an approximate solution satisfying the Lipschitz, Hessian matrix and conditions is obtained within at most iterations, that is, ; is the i-th iteration for solving the auxiliary variable in the i-th client to solve the approximate solution ; based on the satisfaction of the approximate solution satisfies the condition, the final is obtained, when the obtained satisfies the satisfaction condition of the approximate solution , it is the optimal solution, and the optimal solution is the improved FedADMM algorithm mathematical model, and when the obtained does not satisfy the satisfaction condition of the approximate solution , the k+1 iteration is performed again, and the optimal solution is obtained until the optimal solution is obtained. Further, an active distribution network operation optimization mathematical model containing EHCS, PV and EES is established, which is represented as:

[0044]

[0045] ;

[0046] wherein, is the objective function; is the line loss weight coefficient; is the set of all branches in the distribution network; is the current flowing through branch l at time t; is the resistance of branch l; is the voltage deviation weight coefficient; is the set of all nodes in the distribution network; is the voltage amplitude of node i exceeding the voltage optimization interval at time t; and are the maximum and minimum values of the voltage optimization interval, respectively; is the weight coefficient of the PV, EES and EHCS operation cost part; is the weight coefficient of the PV power item;​​ For the PV collection in the distribution network; Let be the active power reduction of the i-th PV at time t; The weighting coefficient for the EES operating cost item; For the EES set in the distribution network; and Let $t$ be the operating costs of the $i$-th EES and $i$-th EHCS at time $t$. The weighting coefficient for the EHCS operating cost item; For the EHCS set in the distribution network; Weighting factor for the revenue from the sale of excess hydrogen energy; The revenue obtained from selling excess hydrogen energy at time t; PV stands for photovoltaic system; EES stands for energy storage system; EHCS stands for hydrogen energy storage system;

[0047] Using the DisFlow line power flow model, the constraints on the DisFlow power flow equations are expressed as follows:

[0048] ;

[0049] ;

[0050] ;

[0051] In the formula, , Each node represents the set of the first and last nodes of a branch with node j as its end and first node, respectively. , Let be the active power and reactive power flowing from node i to node j in the branches of node i and node j; , and Let i represent the resistance, reactance, and current from node i to node j in the branch; , These represent the active and reactive power injected into node j, respectively. Let be the active power from node j to node k; Let be the reactive power from node j to node k; For node j exceeding the voltage optimization range The voltage amplitude; For node i exceeding the voltage optimization range The voltage amplitude; Let be the branch for all nodes i and j;

[0052] Safe operation constraints, representing:

[0053] ;

[0054] In the formula, , are the maximum and minimum values of the safe operation range of the node voltage of the distribution network, respectively; is the maximum value of the current allowed to pass through the branch node i to node j.

[0055] Further, the EHCS mainly consists of an alkaline electrolytic cell, a hydrogen fuel cell and a hydrogen storage tank; the alkaline electrolytic cell, the hydrogen fuel cell and the hydrogen storage tank are respectively constrained; and the PV and the EES are also respectively constrained.

[0056] Further, on the basis of the DisFlow power flow equation, the EHCS, the PV and the EES constraint conditions, the branch node i to node j is taken as a boundary coupling line, the branch node i to node j and the two end nodes i and j of the boundary coupling line are copied into each sub-region of the adjacent distribution network, and reasonable partitioning is performed according to the DisFlow power flow equation, the EHCS, the PV and the EES constraint conditions in the sub-region characteristics of the distribution network, so as to obtain each sub-region of the distribution network and the corresponding boundary coupling constraint condition.

[0057] Further, the specific process of step S3 is as follows:

[0058] An auxiliary variable of voltage square is introduced through a second-order cone programming method and The DisFlow power flow equation constraint condition is rewritten to obtain a rewritten active distribution network operation optimization mathematical model, and a distribution network sub-region optimization mathematical model is established based on the rewritten active distribution network operation optimization mathematical model; then, the non-convex problem of the distribution network sub-region optimization mathematical model is converted into a convex problem through a second-order cone programming method, and a convex processed distribution network sub-region optimization mathematical model is output; and are auxiliary variables of voltage square of the node i and the node j, respectively;

[0059] The distribution network sub-region optimization mathematical model is established and expressed as:

[0060] ;

[0061] ;

[0062] In the formula, N is the total number of sub-regions; is a global augmented Lagrange equation of the nth sub-region; is a local variable of the nth sub-region; is a dual variable of the nth sub-region; is a local variable objective function of the nth sub-region; is a penalty parameter of the nth sub-region; and Equation constraints and inequality constraints for the nth sub-region.

[0063] Further, based on the improved FedADMM algorithm mathematical model and the convex processed distribution network sub-region optimization mathematical model, a three-layer distributed optimization solving framework of active distribution network is constructed, which includes lower layer, middle layer and upper layer; the lower layer is the distribution network sub-region layer; the middle layer is the client layer; and the upper layer is the central server layer.

[0064] The is initialized, and the is iterated for l times to obtain . is the global variable at the lth iteration;

[0065] The original global variable and the original local variable are transmitted into the distribution network sub-region layer for processing to obtain . is the local variable of the nth sub-region at the lth iteration;

[0066] The is uploaded to the client layer for processing to obtain . is the sub-region auxiliary variable of the nth sub-region at the lth iteration;

[0067] The original global variable and the original local variable are transmitted into the distribution network sub-region layer for the l+1th iteration updating process, which is represented as:

[0068] .

[0069] .

[0070] .

[0071] In the formula, is the global variable at the l+1th iteration; and are the local variable and the dual variable at the lth iteration, respectively; is the local variable of the ith client at the l+1th iteration; is the dual variable of the ith client at the lth iteration; is the dual variable of the ith client at the l+1th iteration;

[0072] Combined with the output convex processed distribution network sub-region optimization mathematical model, the updating process of the local variable of the ith client is rewritten as the local variable of the nth sub-region, which is represented as:

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] wherein, is the local variable of the nth sub-region at the (l+1)th iteration; is the global augmented Lagrangian function of the nth sub-region at the lth iteration; is the value of the global augmented Lagrangian function of the nth sub-region at the lth iteration; is the dual variable of the nth sub-region at the lth iteration; is the dual variable of the nth sub-region at the (l+1)th iteration; is the sub-region auxiliary variable of the nth sub-region at the (l+1)th iteration. Further, based on the local variable of the nth sub-region, the value of is solved, and the original optimization problem becomes a mixed integer nonlinear programming problem, and the mixed integer nonlinear programming problem is solved by using a bi-level programming method, and the specific steps are as follows:

[0078] The outer iteration of the mixed integer nonlinear programming problem first determines the integer variable of the running state of the EES and the EHCS, and then the inner iteration of the mixed integer nonlinear programming problem is based on the integer variable to calculate the coupling variable ;

[0079] of the (e+1)th iteration. ; is the coupling variable of the nth sub-region obtained by the e rounds of outer iteration;

[0080] The value of is set as a known quantity, and the mixed integer nonlinear programming problem of the sub-region is converted into a mixed integer linear programming problem, and the mixed integer linear programming problem is solved to obtain the integer variable , which represents:

[0081] ;

[0082] ;

[0083] wherein, is the minimum value of the objective function of the nth sub-region; is the integer variable of the nth sub-region; is the integer variable of the nth sub-region at the (e+1)th iteration; is the mixed integer linear programming problem;

[0084] In the inner iteration process of the mixed-integer linear programming problem, the inner layer fixes integer variables. Transform the mixed-integer linear programming problem into a nonlinear programming problem and solve it quickly. ,express:

[0085] ;

[0086] ;

[0087] In the formula, This represents the minimum value of the globally augmented Lagrange equation for the nth subregion; This is a nonlinear programming problem. The coupling variables are obtained for the nth sub-region in the (e+1)th round of outer iteration;

[0088] when When the bi-level programming method for solving mixed-integer nonlinear programming problems converges, the optimization strategy obtained by the inner iteration is the optimal solution for sub-region n, i.e. ;Will Upload to the client layer for encrypted calculation to obtain ,based on Calculate the central server layer .

[0089] Furthermore, based on the central server layer The original residuals were calculated. and dual residual ;

[0090] When the original residual and dual residual The maximum values ​​in all cases are less than or equal to the residual threshold. The improved FedADMM algorithm mathematical model is determined to be globally converged. The optimization strategies for each sub-region are output, and the globally optimal solution is obtained, which is the optimal operating result of the distributed generation in the distribution network. When the original residual... and dual residual All are greater than the residual threshold The improved FedADMM algorithm mathematical model was determined not to have global convergence, and the output of the central server layer was determined. Continue with the (l+1)th iteration until the improved FedADMM algorithm mathematical model converges globally.

[0091] Compared with the prior art, the present application has the following beneficial effects: the present application is used to solve the technical problems of insufficient new energy consumption, high risk of data privacy leakage and low calculation efficiency of the active power distribution network containing a high proportion of distributed power supply; the present application fully considers the operation characteristics of the electric-hydrogen coupled system, and through the flexible adjustment of hydrogen energy conversion and storage, the self-regulation ability of the power distribution network and the new energy consumption level can be effectively improved; the present application can effectively reduce the calculation complexity by avoiding solving the closed-form solution, and greatly improve the solving efficiency of the distributed optimization strategy; the present application can realize the real data not leaving the area, ensure the privacy security of the key information, and effectively reduce the risk of data leakage in the distributed calculation process. BRIEF DESCRIPTION OF DRAWINGS

[0092] Figure 1 The flowchart of the present application.

[0093] Figure 2 The IEEE 33-node system topology diagram of the present application.

[0094] Figure 3 The power distribution network voltage distribution diagram under adverse scenarios of the present application.

[0095] Figure 4 The comparison diagram of calculation time of different algorithms of the present application. DETAILED DESCRIPTION

[0096] As shown in Figure 1 , the present application provides a technical solution: a privacy-protected electric-hydrogen coupled active power distribution network distributed optimization method, comprising:

[0097] Step S1: establishing a FedADMM algorithm mathematical model, obtaining a global augmented Lagrange equation based on the FedADMM algorithm mathematical model and an iterative update equation of each variable, introducing an auxiliary variable in the iterative update equation of each variable, and obtaining an improved FedADMM algorithm mathematical model when the approximate solution reaches the satisfaction condition of the approximate solution;

[0098] Step S2: establishing an active power distribution network operation optimization mathematical model containing an EHCS (electricity-hydrogen coupled system), a PV and an EES (electrochemical energy storage), and reasonably partitioning according to the characteristics of the power distribution network region, obtaining each sub-region of the power distribution network and the corresponding boundary coupling constraint condition;

[0099] Step S3: establishing a power distribution network sub-region optimization mathematical model based on the boundary coupling constraint condition of step S2, performing convex processing on the power distribution network sub-region optimization mathematical model based on the second-order cone programming method, and outputting the convex processed power distribution network sub-region optimization mathematical model;

[0100] Step S4: Based on the improved FedADMM algorithm mathematical model and the convex processed distribution network sub-area optimization mathematical model, a three-layer distributed optimization solving framework of the active distribution network is constructed; each sub-area solves the convex processed distribution network sub-area optimization mathematical model by using a double-layer planning method, generates an optimization strategy, uploads the optimization strategy to the three-layer distributed optimization solving framework of the active distribution network for iterative calculation, and obtains a global optimal solution, that is, an optimal operation result of the distributed power supply of the distribution network.

[0101] The improved FedADMM algorithm mathematical model includes a federated learning algorithm model, an ADMM algorithm model and a FedADMM algorithm mathematical model.

[0102] Suppose that there are m clients locally, and each client has a local data set, denoted as The loss function of the client is defined as:

[0103] (1);

[0104] In the formula, is the loss function of the i th client; is the total number of data in the data set of the i th client; is a single sample in the data set; is the data set owned by the i th client; is the continuous loss function of the i th client; is a global variable;

[0105] The global total loss function of all clients is represented as:

[0106] (2);

[0107] In the formula, is the weight coefficient of the i th client; is the global total loss function of all clients, and satisfies ;

[0108] The training target of the federated learning algorithm model is a global loss minimum value problem, represented as:

[0109] (3);

[0110] In the formula, is the parameter value when the global total loss function reaches the minimum value; is the minimum value; is a vector belonging to a d-dimensional real number space;

[0111] Let the original optimization problem be decomposed into several sub-problems, and the ADMM algorithm model solves the sub-problems by alternating iteration, as shown in the following formula (1):

[0112] (4);

[0113] In the formula, f(x) and g(z) are objective functions in the two sub-problems, respectively. x and z are original variables x and z, respectively. is a constraint matrix of x. is a constraint matrix of z. is a constant vector. The global augmented Lagrangian equation is introduced for solving, as shown in the following formula (5):

[0114]

[0115] (5);

[0116] In the formula, f(x) and g(z) are objective functions in the two sub-problems, respectively. is a constraint matrix of x. is a constraint matrix of z.

[0117] The iteration equation obtained from the above formula (5) is as follows:

[0118] (6);

[0119] (7);

[0120] (8);

[0121] In the formula, xk+1 is the original variable in the k+1 iteration. is the value of xk+1 that minimizes the global augmented Lagrangian equation given xk and yk. xk is the original variable in the k iteration. yk is the dual variable in the k iteration. xk+1 is the original variable in the k+1 iteration. is the value of z that minimizes the global augmented Lagrangian equation given xk+1 and yk+1. xk+1 is the original variable in the k+1 iteration. yk+1 is the dual variable in the k+1 iteration. is a constraint matrix of x. is a constraint matrix of z. ​​​​​​​​​​​

[0122] Wherein, the federated learning algorithm model and the ADMM algorithm model are integrated by the FedADMM algorithm mathematical model;

[0123] Taking the client i as an example, the local variable of the i-th client is introduced , which represents:

[0124] (9);

[0125] Rewrite the above formula (9) as:

[0126] (10);

[0127] (11);

[0128] The FedADMM algorithm mathematical model is constructed, and the gradient of the global total loss function of all clients needs to satisfy the Lipschitz continuity condition, that is:

[0129] (12);

[0130] In the formula, is the gradient of the global total loss function f of all clients at point; is the gradient of the global total loss function f of all clients at point; is the Lipschitz constant, which is the maximum change rate of ; ;

[0131] On the basis of satisfying the Lipschitz continuity condition, the corresponding global augmented Lagrange equation is defined as:

[0132] (13);

[0133] (14);

[0134] In the formula, is the corresponding global augmented Lagrange equation; is the local variable; is the global augmented Lagrange equation of the i-th client; is the dual variable of the i-th client; is the penalty factor of the i-th client;

[0135] Taking the t+1th round of iteration as an example, the update process of each variable in the corresponding global augmented Lagrange equation is as follows:

[0136] (15);

[0137] (16);

[0138] (17);

[0139] In the formula, This is a global variable during the (t+1)th iteration. In a given and In the case of finding the corresponding globally augmented Lagrange equation minimization value; and These are the local and dual variables at the t-th iteration, respectively; This is a local variable for the i-th client during the (t+1)-th iteration. In a given and In the case of finding the global augmented Lagrange equation minimized for the i-th client. value; Let be the dual variable for the i-th client in the t-th iteration; Let be the dual variable for the i-th client in the (t+1)-th iteration;

[0140] Among them, the introduction ,make , express:

[0141] (18);

[0142] In the formula, This is an intermediate auxiliary variable for the i-th client during the (t+1)-th iteration.

[0143] based on Obtain an approximate solution The condition for satisfying the condition is:

[0144] (19);

[0145] In the formula, For the first Loss function for each client The gradient; For the first Approximate values ​​of local variables for each client in the (t+1)th iteration; For the first The accuracy of the approximate value obtained by each client in the (t+1)th iteration;

[0146] Let equation (19) be in Defined as feasible, let equation optimal solution satisfy the following optimality conditions, denoted as:

[0147] (20);

[0148] wherein, is the optimal solution of the i-th client;

[0149] wherein, the approximate solution is solved based on the condition satisfying formula (19) , the process is as follows:

[0150] Let the initial value be ; is the initial value of the auxiliary variable for solving the approximate solution of the i-th client; taking the k+1th iteration as an example, the expression of

[0151] (21);

[0152] wherein, is the auxiliary variable for solving the approximate solution of the i-th client in the k+1th iteration; is the auxiliary variable for solving the approximate solution of the i-th client in the kth iteration; is the Lipschitz constant of the i-th client; ; is the maximum iteration number preset in the process of updating ;

[0153] Let the gradient of the loss function of the i-th client satisfy the Lipschitz continuous condition, and , the Hessian matrix of the loss function of the i-th client satisfies the following conditions, denoted as:

[0154] (22);

[0155] wherein, is the Hessian matrix of the loss function of the i-th client; is the semi-positive definite order relation of the Hessian matrix; is a positive constant corresponding to the loss function of the i-th client; is the Lipschitz constant, and I is the unit matrix;

[0156] The following conditions should be met:

[0157] (23);

[0158] wherein, is the constraint residual of the i-th client; is a constant greater than 1;

[0159] For the i-th client, by updating , an approximate solution satisfying the conditions of formula (22) and formula (23) is obtained within a maximum of iterations , that is ; is the i-th client in the approximate solution of the k+1 iteration to solve the auxiliary variable; based on the approximate solution satisfies the condition, the final is obtained is the optimal solution, and the optimal solution is the improved FedADMM algorithm mathematical model. When the obtained does not satisfy the condition of the approximate solution , the k+1 iteration is performed again , until the optimal solution is obtained. wherein, a maximum of iterations are calculated by the formula:

[0160]

[0161] (24);

[0162] wherein, is the logarithm operation with base σ.

[0163] Wherein, the specific process of step S2 is:

[0164] An active distribution network operation optimization mathematical model containing EHCS, PV and EES is established, which is represented as:

[0165] (25);

[0166] wherein, is the objective function; is the line loss weight coefficient; is the set of all branches in the distribution network; is the current flowing through branch l at t; is the resistance of branch l; is the voltage deviation weight coefficient; is the set of all nodes in the distribution network;​​ When t, node i exceeds the voltage optimization range. The voltage amplitude; and These represent the maximum and minimum values ​​within the voltage optimization range, respectively. Weighting coefficients for the operating costs of PV, EES, and EHCS; The weighting coefficient for the PV power term; For the PV collection in the distribution network; Let be the active power reduction of the i-th PV at time t; The weighting coefficient for the EES operating cost item; For the EES set in the distribution network; and Let $t$ be the operating costs of the $i$-th EES and $i$-th EHCS at time $t$. The weighting coefficient for the EHCS operating cost item; For the EHCS set in the distribution network; Weighting factor for the revenue from the sale of excess hydrogen energy; The revenue obtained from selling excess hydrogen energy at time t; PV stands for photovoltaic system; EES stands for energy storage system; EHCS stands for hydrogen energy storage system;

[0167] The established constraints are described as follows:

[0168] Using the DisFlow line power flow model, the constraints on the DisFlow power flow equations are as follows:

[0169] (26);

[0170] (27);

[0171] (28);

[0172] In the formula, , Each node represents the set of the first and last nodes of a branch with node j as its end and first node, respectively. , Let be the active power and reactive power flowing from node i to node j in the branches of node i and node j; , and These represent the resistance, reactance, and current from node i to node j in the branch; , These represent the active and reactive power injected into node j, respectively. Let be the active power from node j to node k; Let be the reactive power from node j to node k; the voltage amplitude of node i exceeding the voltage optimization interval ; the voltage amplitude of node j exceeding the voltage optimization interval ; the branch for all nodes i and node j

[0173] the safe operation constraint, indicating that

[0174] (29);

[0175] wherein, , are the maximum value and the minimum value of the safe operation range of the voltage of the node of the power distribution network respectively; is the maximum value of the current allowed to pass through the branch of node i to node j.

[0176] wherein, the EHCS mainly comprises an alkaline electrolyzer, a hydrogen fuel cell and a hydrogen storage tank; the alkaline electrolyzer, the hydrogen fuel cell and the hydrogen storage tank are respectively constrained; meanwhile, the PV and the EES are respectively constrained;

[0177] the constraint condition of the alkaline electrolyzer, indicating that

[0178] (30);

[0179] (31);

[0180] (32);

[0181] (33);

[0182] wherein, , , are the input power, the hydrogen production efficiency and the hydrogen production volume of the alkaline electrolyzer at the t period respectively; , , are the rated power, the maximum input power and the upper limit of the ramp rate of the alkaline electrolyzer respectively; , , are the quadratic term, the linear term and the constant term coefficient of ; is the input power of the alkaline electrolyzer at the t-1 period;

[0183] the constraint condition of the hydrogen fuel cell, indicating that

[0184] (34);

[0185] (35);

[0186] (36);

[0187] wherein, , are the output power and hydrogen consumption volume of the hydrogen fuel cell at t, respectively; is the Faraday constant; , are the stack voltage and power generation efficiency of the hydrogen fuel cell, respectively; and are the maximum input power and upper limit of the ramp rate of the hydrogen fuel cell, respectively; is the hydrogen consumption volume of the hydrogen fuel cell at t−1;

[0188] the constraint condition of the hydrogen storage tank, is expressed as:

[0189] (37);

[0190] (38);

[0191] (39);

[0192] (40);

[0193] (41);

[0194] wherein, is the hydrogen storage volume of the hydrogen storage tank at the end of t; is the hydrogen storage volume of the hydrogen storage tank at the end of t−1; and are the hydrogen charging amount and hydrogen discharging amount of the hydrogen storage tank at t, respectively; , , are the hydrogen storage self-consumption rate, hydrogen charging efficiency and hydrogen discharging efficiency of the hydrogen storage tank, respectively; and are the maximum value and minimum value of the hydrogen storage tank capacity, respectively; and are the hydrogen charging state and hydrogen discharging state of the hydrogen storage tank at t, respectively; is the maximum hydrogen charging amount of the hydrogen storage tank; is the maximum hydrogen discharging amount of the hydrogen storage tank;

[0195] the constraint condition of the PV, is expressed as:

[0196] (42);

[0197] wherein, and Pti and Qti are the active and reactive power of the ith PV at time t, respectively; Pti, nom is the nominal apparent power capacity of the ith PV; φi is the power factor angle of the PV; tan is the tangent function in trigonometry;

[0198] Constraints of the EES, denoted as:

[0199] (43);

[0200] (44);

[0201] (45);

[0202] (46);

[0203] (47);

[0204] (48);

[0205] wherein, Soct is the state of charge of the EES at the end of the time period t; Soct-1 is the state of charge of the EES at the end of the time period t-1; and Pct and Qct are the charging and discharging power of the EES at time t, respectively; , , Pct, dis and Qct, dis are the self-consumption rate, charging efficiency and discharging efficiency of the EES, respectively; and Pmax and Pmin are the maximum and minimum values of the EES capacity, respectively; and Soct and Soct-1 are integer variables, representing the charging and discharging state of the EES at time t, respectively; Pmax, ch is the maximum allowed charging power of the EES in the charging state; Pmax, dis is the maximum allowed discharging power of the EES in the discharging state.

[0206] wherein, on the basis of the DisFlow power flow equation constraint condition, the constraint condition of the EHCS, the constraint condition of the PV and the constraint condition of the EES, the branch node i to the node j is taken as a boundary coupling line, the branch node i to the node j of the boundary coupling line and the two end nodes i and j are copied into each sub-region of the adjacent distribution network, and on the basis of the DisFlow power flow equation constraint condition, the constraint condition of the EHCS, the constraint condition of the PV and the constraint condition of the EES selected in the distribution network sub-region characteristics, reasonable partition is carried out to obtain each sub-region of the distribution network and the corresponding boundary coupling constraint condition, which is specifically:

[0207] By region For example, the boundary coupling variable is { }; Let A be the set of boundary coupling variables for region A′; and For the region The active and reactive power from branch node i to node j in the boundary coupling variable set. and For the region The voltage magnitudes at nodes i and j at both ends of the boundary coupling variable set;

[0208] Similarly, we can obtain the region The boundary coupling variables are ={ }; Let B be the set of boundary coupling variables for region B′; and Let the active and reactive power of the branch node i to node j in the boundary coupling variable set of region B′ be . and Let be the voltage magnitudes of nodes i and j at both ends of the boundary coupling variable set of region B′; to ensure the consistency and accuracy of the distributed algorithm solution, region and region The constraints also need to satisfy the boundary coupling constraints, as shown in the following equation:

[0209] (49).

[0210] The specific process of step S3 is as follows:

[0211] An auxiliary variable, the square of the voltage, is introduced using a second-order cone programming method. and The constraints of the DisFlow power flow equations are rewritten to obtain a revised active distribution network operation optimization mathematical model. Based on this revised model, a sub-regional optimization mathematical model for the distribution network is established. Then, the non-convex problem of the sub-regional optimization mathematical model is transformed into a convex problem using a second-order cone programming method, outputting a convex-processed sub-regional optimization mathematical model for the distribution network. Specifically:

[0212] Introducing an auxiliary variable of voltage square and The constraints of the DisFlow power flow equations are rewritten as follows:

[0213] (50);

[0214] (51);

[0215] (52);

[0216] wherein, and are auxiliary variables of voltage square of node i and node j respectively; is the square of current amplitude on node i and node j;

[0217] The above formula (52) is relaxed as:

[0218] (53);

[0219] The power distribution network sub-area optimization mathematical model is established, and is represented as:

[0220] (54);

[0221] (55);

[0222] wherein, N is the total number of sub-areas; is the global augmented Lagrange equation of the nth sub-area; is the local variable of the nth sub-area; is the dual variable of the nth sub-area; is the local variable objective function of the nth sub-area; is the penalty parameter of the nth sub-area; and are the equality constraints and inequality constraints of the nth sub-area.

[0223] The specific process of step S4 is:

[0224] Based on the improved FedADMM algorithm mathematical model and the convex processed power distribution network sub-area optimization mathematical model, a three-layer distributed optimization solving framework of active power distribution network is constructed, and the three-layer distributed optimization solving framework of active power distribution network includes a lower layer, a middle layer and an upper layer; the lower layer is a power distribution network sub-area layer; the middle layer is a client layer; and the upper layer is a central server layer;

[0225] is initialized, and is iterated for times to obtain ; is the global variable at the lth iteration; ; is the global variable at the lth iteration;

[0226] The original global variable and the original local variable are transmitted into the power distribution network sub-area layer for processing to obtain ; is the local variable of the nth sub-area at the lth iteration;

[0227] will be uploaded to the client layer for processing, and the ; ; is the auxiliary variable of the nth sub-area at the lth iteration;

[0228] where the original global variable and the original local variable are passed into the power distribution sub-area layer for the (l+1)th iteration update process, which is represented as:

[0229] (56);

[0230] (57);

[0231] (58);

[0232] where, is the global variable at the (l+1)th iteration; and are the local variable and the dual variable at the lth iteration, respectively; is the local variable of the ith client at the (l+1)th iteration; is the dual variable of the ith client at the lth iteration; is the dual variable of the ith client at the (l+1)th iteration;

[0233] The update process of the local variable of the ith client is rewritten as the local variable of the nth sub-area in combination with the output convex processing of the power distribution sub-area optimization mathematical model, which is represented as:

[0234] (59);

[0235] (60);

[0236] (61);

[0237] (62);

[0238] where, is the local variable of the nth sub-area at the (l+1)th iteration; is the value of the global augmented Lagrange equation of the nth sub-area that is minimized; and is the dual variable of the nth sub-area at the lth iteration; is the dual variable of the nth sub-area at the (l+1)th iteration; ​​This is the auxiliary variable for the nth subregion during the (l+1)th iteration.

[0239] The solution is based on the local variables of the nth sub-region. Let the original optimization problem be transformed into a mixed-integer nonlinear programming problem. The mixed-integer nonlinear programming problem is solved using the bi-level programming method. Taking the (e+1)th iteration as an example, the specific steps are as follows:

[0240] The outer iteration of the mixed-integer nonlinear programming problem first determines the integer variables of the running states of EES and EHCS. Then, the inner iteration of the mixed-integer nonlinear programming problem calculates the coupling variables in the (e+1)th iteration based on the integer variables. ; The coupling variables are obtained for the nth sub-region in the outer iteration of round e;

[0241] Will Given known quantities, the mixed-integer nonlinear programming problem for the subregion is transformed into a mixed-integer linear programming problem. Solving the mixed-integer linear programming problem yields integer variables. ,express:

[0242] (63);

[0243] (64);

[0244] In the formula, Let the objective function be the minimum value of the nth subregion; Let n be an integer variable representing the nth subregion. For the nth sub-region, in the (e+1)th iteration, there is an integer variable. This is a mixed-integer linear programming problem.

[0245] In the inner iteration process of the mixed-integer linear programming problem, the inner layer fixes integer variables. Transform the mixed-integer linear programming problem into a nonlinear programming problem and solve it quickly. ,express:

[0246] (65);

[0247] (66);

[0248] In the formula, This represents the minimum value of the globally augmented Lagrange equation for the nth subregion; This is a nonlinear programming problem. The coupling variables are obtained for the nth sub-region in the (e+1)th round of outer iteration;

[0249] when When the bi-level programming method for solving mixed-integer nonlinear programming problems converges, the optimization strategy obtained by the inner iteration is the optimal solution for sub-region n, i.e. ;Will Upload to the client layer for encrypted calculation to obtain ,based on The central server layer in formula (59) is calculated. .

[0250] Among them, based on the central server layer The calculation process for the original residual and the dual residual is shown below:

[0251] (67);

[0252] In the formula, This represents the original residual of the nth sub-region during the (l+1)th iteration. This is the dual residual at the (l+1)th iteration;

[0253] The determination condition is:

[0254] (68);

[0255] (69);

[0256] In the formula, For the first The original residual at +1 iteration; Infinitely large; The threshold value for the residual;

[0257] when and The maximum values ​​in all are less than or equal to The improved FedADMM algorithm mathematical model is determined to be globally converged. The optimization strategies for each sub-region are output, and the globally optimal solution is obtained, which represents the optimal operating result of distributed generation in the distribution network. and Both are greater than The improved FedADMM algorithm mathematical model was determined not to have global convergence, and the output of the central server layer was determined. Continue with the (l+1)th iteration until the improved FedADMM algorithm mathematical model converges globally.

[0258] Verification Example

[0259] The accuracy and effectiveness of this invention were verified using the IEEE 33-node system as a test case.

[0260] The example of this invention is an IEEE 33-bus AC power distribution system, the topology of which is shown below.Figure 2 as shown;

[0261] Bus 1 is the reference node, and the voltage reference value is set to 1.0 p.u.; the node voltage safety range of the distribution network is [0.95, 1.05] p.u., and the voltage optimization interval is [0.985, 1.015] p.u., and when the node voltage exceeds the voltage safety range, the IEEE 33-node system starts optimization control; the IEEE 33-node system is divided into two areas, and the node set in area is {1, 2, 3, …, 9, 19, 20, 21, …, 33}, and the node set in area is {10, 11, …, 18}; p.u. (per unit) represents relative unit or unit value;

[0262] Among them, in area and area , some nodes are installed with distributed photovoltaic systems (PV) to support voltage optimization, which specifically includes:

[0263] PV1 is installed at nodes 5, 7, 10, 12, 14, 20, 22 and 32, and the installed capacity is 0.6 MVA;

[0264] PV3 is installed at nodes 2, 24 and 28, and the installed capacity is 1.2 MVA;

[0265] Node 29 is installed with EES;

[0266] PV2 is installed at nodes 26 and 30, and the installed capacity is 0.8 MVA;

[0267] Node 30 is also installed with EHCS;

[0268] Node 18 is connected to a variable load;

[0269] The power factor of the inverter of the photovoltaic system in the IEEE 33-node system varies in the range of [-0.95, 0.95]; EES is installed at nodes 14 and 29, and the installation position of EHCS is node 30.

[0270] Table 1 Photovoltaic system installation position and capacity

[0271] .

[0272] Two scenarios are set to verify the optimization effect of the method, as follows:

[0273] Scenario 1: No control means is taken for the example;

[0274] Scenario 2: The optimization strategy of the distribution network considering multiple regulation means such as PV, EES and EHCS is considered.

[0275] In the harsh scene, scene 1 and scene 2 are respectively optimized and simulated, and the voltage distribution of the power distribution network obtained is as shown in Figure 3 It can be seen that before the optimization control, the voltage out-of-limit problem of the IEEE 33-node system is serious; after the control strategy of scene 2 is adopted, the voltage out-of-limit problem is effectively solved, and the voltage level of the IEEE 33-node system is obviously improved; wherein, Figure 3 (a) t=12:00: under scene 1, the voltage of node 14 reaches 1.0646 p.u., which obviously exceeds the upper limit of voltage safety 1.05 p.u.; and under scene 2, through the optimization control strategy, the voltage of node 14 is reduced to 1.0200 p.u., effectively alleviating the voltage out-of-limit problem;

[0276] In Figure 3 (b) t=20:00: under scene 1, the voltage of node 18 is reduced to 0.9354 p.u., which is lower than the lower limit of voltage safety 0.95 p.u. Under scene 2, after taking the optimization measures, the voltage of node 18 is increased to 0.9504 p.u., solving the voltage out-of-limit problem and improving the power supply quality.

[0277] The above results show that the application can effectively improve the voltage level and power supply quality of the power distribution network.

[0278] In addition, the traditional ADMM algorithm is compared with the method of the application to verify the effectiveness of the method. As shown in Figure 4 The comparison chart of the calculation time of different algorithms is shown in the figure, and the FedADMM algorithm of the application is significantly better than the traditional ADMM algorithm in calculation time; specifically, the single iteration calculation time of the FedADMM algorithm is obviously shorter than that of the ADMM algorithm, for example, in the first iteration, the calculation time of the ADMM algorithm is 32.1 seconds, and the calculation time of the FedADMM algorithm is only 14.2 seconds. With the increase of the number of iterations, the cumulative iteration time of the FedADMM algorithm grows slowly, and the cumulative calculation time is only 66.1 seconds in the 10th iteration, which is reduced by 112.86 seconds compared with the 172.9 seconds of the ADMM algorithm, and the calculation time is only 38.23% of the ADMM algorithm. This is because the FedADMM algorithm decomposes the optimization problem into multiple sub-problems for parallel calculation on different clients through distributed optimization and privacy protection mechanism, reduces the data transmission and processing time, and speeds up the iteration convergence speed through the introduction of auxiliary variables and improved iteration update equation.

[0279] Those skilled in the art can clearly understand the implementation of the various embodiments by means of software and necessary general hardware platforms through the above description of the embodiments, and of course, the embodiments can also be implemented by hardware. Based on such understanding, the above technical solutions can be embodied in the form of a software product, and the computer software product can be stored in a computer readable storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, and the like, and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of the various embodiments or some parts of the embodiments.

[0280] Although the embodiments of the present application have been shown and described, it should be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made thereto without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A privacy-preserving distributed optimization method for electric-hydrogen coupled active power distribution networks, characterized in that, Comprise: Step S1: establishing a FedADMM algorithm mathematical model, obtaining a global augmented Lagrange equation based on the FedADMM algorithm mathematical model and an iterative updating equation of each variable, introducing an auxiliary variable into the iterative updating equation of each variable, and obtaining an improved FedADMM algorithm mathematical model when the approximate solution reaches the satisfaction condition of the approximate solution; Step S2: establishing an active power distribution network operation optimization mathematical model containing EHCS, PV and EES, and reasonably partitioning according to the characteristics of the power distribution network region to obtain each sub-region of the power distribution network and the corresponding boundary coupling constraint condition; Step S3: based on the boundary coupling constraint condition of step S2, establishing a power distribution network sub-region optimization mathematical model, and performing convex processing on the power distribution network sub-region optimization mathematical model based on the second-order cone programming method, and outputting the convex processed power distribution network sub-region optimization mathematical model; Step S4: based on the improved FedADMM algorithm mathematical model and the convex processed power distribution network sub-region optimization mathematical model, constructing a three-layer distributed optimization solving framework of the active power distribution network; each sub-region solves the convex processed power distribution network sub-region optimization mathematical model by using a double-layer programming method, generates an optimization strategy, uploads the optimization strategy to the three-layer distributed optimization solving framework of the active power distribution network for iterative calculation, and obtains a global optimal solution, that is, an optimal operation result of the distributed power supply of the power distribution network. 2.The method of claim 1, wherein: The specific process of step S1 is: Let there be m clients, each with a local data set denoted by ; by introducing the local variable of the i-th client, it is denoted that ； wherein is a minimum value; is a global variable; is a vector belonging to the d-dimensional real space; m is the total number of clients; is the weight coefficient of the i-th client; is the loss function of the i-th client; will be introduced Rewrite the global total loss function for the client as follows: ； ； wherein is the global total loss function for the client; is the parameter value at which the global total loss function is minimized. The FedADMM algorithm mathematical model is constructed, and the gradient of the global total loss function of all clients should satisfy the Lipschitz continuity condition; on the basis of satisfying the Lipschitz continuity condition, the corresponding global augmented Lagrange equation is constructed and defined as: ； ； wherein are the corresponding global augmented Lagrangian equations; are local variables; are dual variables; are the global augmented Lagrangian equations for the i-th client; are the dual variables for the i-th client; are the penalty factors for the i-th client; The t+1 round iteration updating process of each variable in the corresponding global augmented Lagrange equation is represented as: ； ； ； where is the global variable at iteration t + 1; is the local variable at iteration t; and is the value of the global augmented Lagrangian function minimized with respect to at iteration t + 1; and are the local and dual variables at iteration t, respectively; is the local variable of the ith client at iteration t + 1; is the dual variable of the ith client at iteration t; and is the value of the global augmented Lagrangian function of the ith client minimized with respect to at iteration t + 1; is the dual variable of the ith client at iteration t; is the dual variable of the ith client at iteration t + 1; wherein the introduction of , let , denotes: ； wherein is the intermediate helper variable for the i-th client at the t+1 iteration. Based on obtaining an approximate solution satisfying the condition, is represented by ； In the formula, For the first Loss function for each client The gradient; For the first Approximate values ​​of local variables for each client in the (t+1)th iteration; For the first The accuracy of the approximate value obtained by each client in the (t+1)th iteration; where the approximate solution is found by solving the process is as follows: Set initial values ; Solve for the approximate solution in the i-th client Solve for the auxiliary variable initial value; for Perform the k+1 iteration to obtain Indicate: ； In the formula, Solve for an approximate solution in the i-th client. Solve for the auxiliary variables in the (k+1)th iteration; Solve for an approximate solution in the i-th client. Solve for the auxiliary variables during the k-th iteration; Let be the Lipschitz constant for the i-th client; ; For updates The maximum number of iterations preset during the process; The gradient of the loss function of the ith client satisfies the Lipschitz continuity condition and the Hessian matrix satisfies the condition satisfies the condition, denoted by: ； wherein is the constraint residual for the i-th client; is a constant greater than 1. For the i-th client, by updating At most Within each iteration, the Lipschitz and Hessian matrices are obtained. Approximate solution to the conditions ,Right now ; Solve for an approximate solution in the i-th client. The Solve for auxiliary variables in the +1st iteration; based on approximate solution. The conditions for obtaining the final result Make a judgment, when the result is... Satisfying approximate solution The condition that is met is the optimal solution, which is the improved mathematical model of the FedADMM algorithm. When the obtained... Not satisfying the approximate solution If the conditions are met, then re-apply... Perform the (k+1)th iteration until the optimal solution is obtained. 3.The privacy preserving electric-hydrogen coupled active distribution network distributed optimization method of claim 2, wherein: The active power distribution network operation optimization mathematical model containing EHCS, PV and EES is established and represented as: ； wherein, is the objective function; is the line loss weight coefficient; is the set of all branches in the distribution network; is the current flowing through branch l at time t; is the resistance of branch l; is the voltage deviation weight coefficient; is the set of all nodes in the distribution network; is the voltage magnitude of node i out of the voltage optimization interval at time t; and are the maximum and minimum values of the voltage optimization interval, respectively; is the weight coefficient of the PV, EES and EHCS operation cost part; is the weight coefficient of the PV power item; is the set of PVs in the distribution network; is the active power curtailment of the ith PV at time t; is the weight coefficient of the EES operation cost item; is the set of EESs in the distribution network; and are the operation costs of the ith EES and EHCS at time t, respectively; is the weight coefficient of the EHCS operation cost item; is the set of EHCSs in the distribution network; is the weight coefficient of the revenue item from selling surplus hydrogen energy; is the revenue obtained from selling surplus hydrogen energy at time t; PV is a photovoltaic system; EES is an energy storage system; EHCS is a hydrogen energy storage system. The DisFlow line flow model is used, and the DisFlow power flow equation constraint condition is represented as: ； ； ； wherein, , are the set of branch head and tail nodes with node j as the tail head and tail nodes, respectively; , are the active and reactive power flowing from node i to node j in the branch of node i and node j; , and are the resistance, reactance and current of the branch from node i to node j, respectively; , are the active and reactive power injected at node j; is the active power from node j to node k; is the reactive power from node j to node k; is the voltage magnitude of node j out of the voltage optimization interval ; is the voltage magnitude of node i out of the voltage optimization interval ; is the branch for all nodes i and node j; The safe operation constraint is represented as: ； In the formula, , are the maximum and minimum values of the safe operating range of the node voltage of the power distribution network, respectively; is the maximum value of the allowed current through the branch from node i to node j.

4. The method of claim 3, wherein the method further comprises: The EHCS mainly comprises an alkaline electrolytic cell, a hydrogen fuel cell and a hydrogen storage tank; the alkaline electrolytic cell, the hydrogen fuel cell and the hydrogen storage tank are respectively constrained; and the PV and the EES are also respectively constrained.

5. The method of claim 4, wherein the method further comprises: On the basis of the DisFlow power flow equation, the EHCS, the PV and the EES constraint condition, the branch node i to the node j is taken as a boundary coupling line, the branch node i to the node j of the boundary coupling line and the two end nodes i and j are copied into each sub-region of the adjacent power distribution network, and reasonable partitioning is performed according to the DisFlow power flow equation, the EHCS, the PV and the EES constraint condition in the characteristics of the power distribution network sub-region to obtain each sub-region of the power distribution network and the corresponding boundary coupling constraint condition.

6. The method of claim 5, wherein the method further comprises: The specific process of step S3 is: The auxiliary variable of the voltage square is introduced by a second-order cone programming method and The constraint condition of the DisFlow power flow equation is rewritten again, the rewritten active distribution network operation optimization mathematical model is obtained, and the distribution network sub-region optimization mathematical model is established based on the rewritten active distribution network operation optimization mathematical model; the non-convex problem of the distribution network sub-region optimization mathematical model is converted into a convex problem by a second-order cone programming method, and the convex processed distribution network sub-region optimization mathematical model is output; and The auxiliary variable of the voltage square of the node i and the node j respectively; The power distribution network sub-region optimization mathematical model is established and represented as: ； ； where N is the total number of sub-regions; is the global augmented Lagrangian equation of the nth sub-region; is the local variable of the nth sub-region; is the dual variable of the nth sub-region; is the local variable objective function of the nth sub-region; is the penalty parameter of the nth sub-region; and is the equality and inequality constraints of the nth sub-region.

7. The method of claim 6, wherein the method further comprises: The improved FedADMM algorithm mathematical model and the convex processed distribution network sub-area optimization mathematical model construct a three-layer distributed optimization solving framework of the active distribution network, and the three-layer distributed optimization solving framework of the active distribution network comprises a lower layer, a middle layer and an upper layer; the lower layer is a distribution network sub-area layer; the middle layer is a client layer; and the upper layer is a central server layer. Initialize the global variables Perform l iterations, obtaining ; ; is the global variable at the lth iteration The original global variable and the original local variable are transmitted into the power distribution network sub-area layer for processing to obtain ; the local variable of the nth sub-area at the lth iteration; Will Uploaded to the client layer for processing, resulting in ; This is an auxiliary variable for the nth subregion during the lth iteration. Wherein, the original global variable and the original local variable are transmitted into the distribution network sub-area layer to perform an (l+1)th iteration updating process, and the (l+1)th iteration updating process is represented by: ； ； ； wherein is the global variable at iteration l+1; and are the local and dual variables at iteration l, respectively; is the local variable of the i-th client at iteration l+1; is the dual variable of the i-th client at iteration l; is the dual variable of the i-th client at iteration l+1; In combination with the output convex processed distribution network sub-area optimization mathematical model, the updating process of the local variable of the i th client is rewritten as a local variable of the n th sub-area, and the updating process is represented by: ； ； ； ； In the formula, This is a local variable for the nth sub-region during the (l+1)th iteration; In a given and In the case of finding the minimized global augmented Lagrange equation for the nth subregion value; Let be the dual variable of the nth subregion during the lth iteration; Let be the dual variable of the nth subregion during the (l+1)th iteration; This is the auxiliary variable for the nth subregion during the (l+1)th iteration.

8. The distributed optimization method of the active distribution network considering privacy protection according to claim 7, characterized in that: Solve on the basis of local variables of the nth sub-region If the original optimization problem becomes a mixed integer nonlinear programming problem, the double-layer programming method is used to solve the mixed integer nonlinear programming problem, and the specific steps are as follows: The outer iteration of the mixed integer nonlinear programming problem first determines the integer variables of the operating states of the EES and the EHCS, and then the inner iteration of the mixed integer nonlinear programming problem performs the iteration calculation of the coupling variables based on the integer variables in the e+1th round ; is the coupling variable obtained in the e round of outer iteration for the nth sub-region Let be known quantities, the mixed integer nonlinear programming problem of the sub-region is converted into a mixed integer linear programming problem, and the mixed integer linear programming problem is solved to obtain integer variables , which represents: ； ； wherein is the minimum objective function for the nth sub-region; is an integer variable for the nth sub-region; is an integer variable for the nth sub-region at the e+1th iteration; is a mixed integer linear programming problem; In the inner iteration process of the mixed integer linear programming problem, the inner layer fixes the integer variable Convert the mixed integer linear programming problem into a nonlinear programming problem and solve it quickly , indicates: ； ； wherein is the minimum of the globally augmented Lagrangian equation for the nth subregion; is a nonlinear programming problem; is the coupling variable for the nth subregion obtained in the e+1 outer iteration When the bi-level programming method for solving mixed integer nonlinear programming problem converges, the optimization strategy obtained by inner iteration calculation is the optimal solution of the sub-region n, that is ; the upper client layer is calculated by encryption to obtain , based on the central server layer is calculated .

9. The distributed optimization method of the active distribution network considering privacy protection according to claim 8, characterized in that: Based on a central server layer Computing original residuals And dual residuals ; when the maximum value of the original residual error and the dual residual error is less than or equal to a threshold value of the residual error , it is determined that the improved FedADMM algorithm mathematical model is globally convergent, and an optimization strategy of each sub-region is outputted to obtain a globally optimal solution, i.e., an optimal operation result of the distributed power supply of the power distribution network; when the original residual error and the dual residual error are both greater than the threshold value of the residual error , it is determined that the improved FedADMM algorithm mathematical model is not globally convergent, and the of the central server layer is outputted to continue the (l+1)th iteration calculation until the improved FedADMM algorithm mathematical model is globally convergent.

Images