A method for determining optimal power flow in main distribution coordination based on adaptive weighted Anderson acceleration

Abstract

The present invention discloses a method for determining the optimal power flow of main-distribution coordination based on adaptive weighted Anderson acceleration, the method comprising: first setting the initial value of the boundary condition of the distribution network sub-problem and various iteration parameters; then the distribution network control center solves the main network boundary condition according to the distribution network boundary condition, and the main network control center updates the distribution network boundary condition according to the main network boundary condition; then judging whether the algorithm converges and terminates; finally checking whether the upper limit of the number of iterations is reached, if the upper limit of the number of iterations is reached, the algorithm terminates, if not, checking whether the upper limit of the number of inner iterations is reached, determining whether to perform algorithm acceleration or continue iteration, for the iteration that needs algorithm acceleration, correcting and updating the outer layer iteration result of this time by weighted Anderson acceleration, as the initial value of the next outer layer iteration, accelerating the update of the distribution network boundary condition. The present invention improves the convergence efficiency and convergence performance of the heterogeneous decomposition method, improves the stability of the algorithm, and has good engineering application prospects.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-region collaborative distributed optimization scheduling, and in particular to a method for determining optimal power flow of main distribution collaboratively based on adaptive weighted Anderson acceleration. Background Art

[0002] As the proportion of new energy in the power grid continues to increase, the uncertainty of power grid operation has increased significantly, bringing huge challenges to voltage stability and power balance. Among them, the coordinated operation of the main grid and the distribution network is related to the overall safety and economy of the power system. Through the coordinated dispatching of multi-level power grids and the coordinated mutual assistance of source and load resources in various regions, the risk of voltage over-limit can be effectively reduced, the utilization rate of distributed power generation resources can be improved, and the power generation cost of the global system can be minimized. Therefore, the distributed optimal dispatching of the main-distribution coordination has important theoretical and practical significance.

[0003] At present, in the field of main-distribution coordinated optimization dispatch, the mainstream direction is to conduct research on economic dispatch, reactive power optimization, optimal power flow and other issues based on distributed architecture. In the process of determining the optimal power flow, dual decomposition method, isomorphic decomposition method and heterogeneous decomposition method are commonly used distributed algorithms. Among them, heterogeneous decomposition method, as an algorithm specially designed for main-distribution coordinated optimization problem, has the characteristics of strong engineering practicality and has therefore received widespread attention. However, for more complex network topologies, heterogeneous decomposition method still has problems in convergence efficiency and convergence performance. Summary of the invention

[0004] The purpose of the present invention is to provide a method for determining the optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration with high stability and good robustness, and to improve the convergence performance of the optimal power flow calculation of main distribution coordination based on heterogeneous decomposition method.

[0005] The technical solution to achieve the purpose of the present invention is: a method for determining the optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration, comprising the following steps:

[0006] Step 1: Set the initial values ​​of the boundary conditions and various iteration parameters of the distribution network sub-problem;

[0007] Step 2: The distribution network control center solves the optimal power flow of the distribution network according to the boundary conditions of the distribution network sub-problem, obtains the boundary conditions of the main grid sub-problem, and sends them to the main grid control center;

[0008] Step 3: The main grid control center solves the optimal power flow of the main grid according to the boundary conditions of the main grid sub-problem, and obtains the boundary conditions of the updated distribution network sub-problem;

[0009] Step 4: According to the residuals of the boundary conditions of the distribution network sub-problem before and after the update, determine whether the algorithm has converged and terminated: if it has converged, end the iteration and output the optimal power flow result; otherwise, go to step 5;

[0010] Step 5: Check whether the total number of iterations has reached the upper limit: if the total number of iterations has reached the upper limit, terminate the iteration and output the optimal power flow result; if the total number of iterations has not reached the upper limit, check whether the inner layer iterations have reached the upper limit. If the inner layer iterations have not reached the upper limit, return to step 2; if the inner layer iterations have reached the upper limit, proceed to step 6.

[0011] Step 6: Calculate the adaptive residual weight according to the historical iteration variables, and correct and update the outer iteration result through weighted Anderson acceleration, which is used as the initial value of the next outer iteration, and return to step 2 to accelerate the update of the boundary conditions of the distribution network sub-problem.

[0012] Compared with the prior art, the present invention has the following significant advantages: (1) Based on the adaptive weighted Anderson acceleration, a two-layer iteration method of main-distribution coordinated distributed optimal power flow is adopted, which effectively improves the convergence efficiency and convergence performance problems existing in the heterogeneous decomposition method; (2) An inner-layer iteration model of the main-distribution coordinated optimal power flow is constructed based on the heterogeneous decomposition method, and the interacting heterogeneous coupling variables cater to the existing industrial site implementation conditions and have good engineering application prospects; (3) The outer-layer Anderson acceleration method of the main-distribution coordinated optimal power flow is improved, and a calculation formula for the weighted Anderson acceleration is proposed, which realizes a high degree of customization of the algorithm convergence performance and robustness; (4) Based on the proposed weighted Anderson acceleration, an adaptive calculation method of the residual weight is proposed, which avoids the instability of artificial parameter adjustment and improves the practicability of the weighted Anderson acceleration in engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flow chart of the main distribution coordinated optimal power flow determination method based on adaptive weighted Anderson acceleration of the present invention. DETAILED DESCRIPTION

[0014] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0015] Combination Figure 1 The present invention provides a method for determining the optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration, comprising the following steps:

[0016] Step 1: Set the initial values ​​of the boundary conditions and various iteration parameters of the distribution network sub-problem;

[0017] Step 2: The distribution network control center solves the optimal power flow of the distribution network according to the boundary conditions of the distribution network sub-problem, obtains the boundary conditions of the main grid sub-problem, and sends them to the main grid control center;

[0018] Step 3: The main grid control center solves the optimal power flow of the main grid according to the boundary conditions of the main grid sub-problem, and obtains the boundary conditions of the updated distribution network sub-problem;

[0019] Step 4: According to the residuals of the boundary conditions of the distribution network sub-problem before and after the update, determine whether the algorithm has converged and terminated: if it has converged, end the iteration and output the optimal power flow result; otherwise, go to step 5;

[0020] Step 5: Check whether the total number of iterations has reached the upper limit: if the total number of iterations has reached the upper limit, terminate the iteration and output the optimal power flow result; if the total number of iterations has not reached the upper limit, check whether the inner layer iterations have reached the upper limit. If the inner layer iterations have not reached the upper limit, return to step 2; if the inner layer iterations have reached the upper limit, proceed to step 6.

[0021] Step 6: Calculate the adaptive residual weight according to the historical iteration variables, and correct and update the outer iteration result through weighted Anderson acceleration, which is used as the initial value of the next outer iteration, and return to step 2 to accelerate the update of the boundary conditions of the distribution network sub-problem.

[0022] As a specific example, the initial values ​​of the boundary conditions and various iteration parameters of the distribution network sub-problem described in step 1 are set as follows:

[0023] Step 1.1: Set the boundary conditions of the distribution network subproblem, that is, In the outer iteration The iteration variable of the next inner iteration for:

[0024] (1)

[0025] In the formula, For the In the outer iteration The iteration variables of the second inner iteration are the boundary conditions of the distribution network subproblem; For the In the outer iteration The voltage phase angle of the boundary nodes of the second inner iteration; For the In the outer iteration The voltage amplitude of the boundary nodes of the second inner iteration; For the In the outer iteration Lagrange multipliers for active power balance constraints at boundary nodes of the second inner iteration; For the In the outer iteration Lagrange multipliers for reactive power balance constraints at boundary nodes of the second inner iteration;

[0026] Step 1.2: Initialize iteration variables , the number of outer iterations , inner layer iterations , the upper limit of the number of inner iterations , convergence accuracy , maximum number of iterations .

[0027] As a specific example, in step 2, the distribution network control center uses the iteration variable Solve the optimal power flow of the distribution network and get In the outer iteration The power injection amount of the boundary nodes of the second inner iteration , calculate the first In the outer iteration The shadow price of boundary node voltage in the second inner iteration , and and It is sent to the main grid control center as the boundary conditions of the main grid sub-problem, as follows:

[0028] Step 2.1: The distribution network control center calculates the iterative variables Solve the distribution network sub-problem and obtain the power injection amount of the boundary node , the formula is:

[0029] (2)

[0030] Calculate boundary node voltage shadow price , the formula is:

[0031] (3)

[0032] In the formula, the superscript It is the vector transpose operation; is the power cost function of the distribution network; is the control variable of the distribution network, is the state variable of the distribution network, is the feasible region of the distribution network, To solve the main power grid subproblem, we obtain the boundary state value. Lagrange multipliers for boundary equality constraints obtained for solving the main grid subproblem; is the boundary power injection value; is the shadow price of the boundary state; is the state variable of the boundary part, including the voltage amplitude and voltage phase angle of the boundary node; is the equality constraint for the distribution network part, is the inequality constraint of the distribution network, and are the Lagrange multipliers for partial equality and inequality constraints of the distribution network, is the Lagrange multiplier for the equality constraints of the boundary part; is the expression of the distribution network part after the boundary equality constraint split;

[0033] Step 2.2: The distribution network control center will and Sent to the main network control center.

[0034] As a specific example, in step 3, the main network control center and Solve the optimal power flow of the main power grid and obtain the next inner iteration, that is, In the outer iteration The iteration variable of the next inner iteration , as follows:

[0035] The main network control center and Solve the optimal power flow of the main power grid and get In the outer iteration The iteration variable of the next inner iteration , the formula is:

[0036] (4)

[0037] In the formula, The cost function of power generation for the main grid; is the control variable of the main power grid, is the control variable of the boundary part, is the state variable of the main power grid, is the state variable of the boundary part, The shadow prices of the boundary states obtained for solving the distribution network subproblem; is the feasible domain of the main power grid, The power injection amount at the boundary nodes obtained to solve the distribution network subproblem.

[0038] As a specific example, in step 4, whether the algorithm converges and terminates is determined based on the residuals of the boundary conditions of the distribution network sub-problem before and after the update, as follows:

[0039] Step 4.1, calculate the residual of the boundary conditions of the distribution network subproblem between this iteration and the last iteration boundary conditions. If , then the iteration ends and the optimal power flow result is output; represents the convergence accuracy parameter, Indicates the calculation of vector norm;

[0040] Step 4.2: If , then go to step 5.

[0041] As a specific example, step 5 is as follows:

[0042] Step 5.1: Determine whether the total number of iterations has reached the upper limit ,if , the algorithm does not converge and the iteration is terminated, and the optimal power flow result is output;

[0043] Step 5.2: If and , then the number of inner iterations is ,Will Send to the distribution network control center and return to step 2;

[0044] Step 5.3: If and , go to step 6.

[0045] As a specific example, step 6 is as follows:

[0046] Step 6.1, calculate the residual weight coefficient of each inner layer iteration in this outer layer iteration;

[0047] Step 6.2: Use the residual weight coefficients of each inner iteration in this outer iteration to correct and update the results of this outer iteration through weighted Anderson acceleration, and send them to the distribution network control center as the initial value of the next outer iteration, and return to step 2, so as to accelerate the update of the boundary conditions of the distribution network sub-problem.

[0048] As a specific example, the residual weight coefficients of each inner layer iteration in this outer layer iteration are calculated in step 6.1 as follows:

[0049] Step 6.1.1: For The outer iteration is to calculate The outer iteration and Each iteration point in the outer iteration , , the formula is:

[0050] (5)

[0051] (6)

[0052] Calculate the The outer iteration and The first-order residual matrix of the fixed point sequence in the second outer iteration , , the formula is:

[0053] (7)

[0054] (8)

[0055] (9)

[0056] In the formula, for dimensional difference calculation matrix, for The identity matrix of

[0057] Step 6.1.2: Perform a differential operation on the first-order residual matrix in two adjacent outer iterations to obtain the first-order adjacent point residual matrix , the formula is:

[0058] (10)

[0059] in The columns of indivual dimensional first-order neighboring point residual vector, specifically:

[0060] (11)

[0061] Step 6.1.3: Perform a first-order difference operation on the first-order adjacent point residual matrix to obtain the second-order adjacent point residual matrix , the formula is:

[0062] (12)

[0063] (13)

[0064] In the formula, for Dimensional difference calculation matrix;

[0065] Step 6.1.4: Calculate The residual weight coefficient of each inner iteration in the outer iteration , the formula is:

[0066] (14)

[0067] (15)

[0068] In the formula, is the residual weight transformation matrix.

[0069] As a specific example, in step 6.2, the residual weight coefficients of each inner iteration in this outer iteration are used to correct and update the results of this outer iteration through weighted Anderson acceleration, and sent to the distribution network control center as the initial value of the next outer iteration, and return to step 2, so as to accelerate the update of the boundary conditions of the distribution network sub-problem, as follows:

[0070] Step 6.2.1: For The outer layer iteration calculates the first-order residual matrix of the fixed point sequence of this layer , the formula is:

[0071] (16)

[0072] in The columns of indivual dimensional first-order residual vector, specifically:

[0073] (17)

[0074] Step 6.2.2: Take the first-order residual matrix Column, obtained from arrive of The first-order residual matrix of the iterative operation is:

[0075] (18)

[0076] (19)

[0077] In the formula, Extract the transformation matrix for the columns;

[0078] Step 6.2.3: According to The residual weight sequence of the inner iteration in the outer iteration , construct the residual weight diagonal matrix , the formula is:

[0079] (20)

[0080] Assign weights to each column in the first-order residual matrix to obtain a first-order weighted residual matrix , the formula is:

[0081] (twenty one)

[0082] Step 6.2.4: Perform a differential operation on the first-order weighted residual matrix to obtain arrive this The second-order weighted residual matrix of the iterative operation , the formula is:

[0083] (twenty two)

[0084] Step 6.2.5: According to the following formula The outer layer iteration result is corrected and updated as the Initial value of the outer iteration :

[0085] (twenty three)

[0086] Step 6.2.6: Send it to the distribution network control center and return to step 2, thereby accelerating the update of the boundary conditions of the distribution network sub-problem.

[0087] The present invention is further described in detail below with reference to specific embodiments.

[0088] Example

[0089] This embodiment constructs two main and distribution network examples, performs main and distribution coordinated optimal power flow calculations under the heterogeneous decomposition method, the Anderson acceleration method, and the method of the present invention, and compares the convergence times and calculation times.

[0090] Example data: Example A is composed of an IEEE 30-node main grid and an IEEE 69-node distribution network. The distribution network is connected to the 30th node of the main grid through an ideal transformer. The tie line resistance is 0.002pu and the reactance is 0.01pu. The 15th, 30th, 45th and 60th nodes of the distribution network are connected to distributed power sources respectively. The upper limit of active output is 2MW, the upper limit of reactive output is 1MW, the active secondary cost coefficient is 0.5, the active linear cost coefficient is 1, and the active fixed cost coefficient is 0. Example B is composed of an IEEE 118-node main grid and 4 IEEE 69-node distribution networks. The distribution network is connected to the 20th, 40th, 60th and 80th nodes of the main grid through an ideal transformer. The 15th, 30th, 45th and 60th nodes of the distribution network are connected to distributed power sources respectively. The parameters related to the transformer line and distributed power sources are the same as above.

[0091] Algorithm data: Convergence accuracy Set as , maximum number of iterations Set to 100 times, inner iteration parameter Set to 2, the initial value of the boundary node voltage amplitude Set to 1, the initial value of the boundary voltage phase angle Set to 0, the Lagrange multiplier of the active power balance constraint at the boundary node The initial value is 0, and the Lagrange multiplier of the reactive power balance constraint of the boundary node The initial value is 0.

[0092] Table 1 Comparison of the efficiency of three algorithms

[0093]

[0094] Table 1 shows the number of iterations and calculation time of the three methods. For example A, the heterogeneous decomposition method needs 13 iterations to converge, which takes 1.51 seconds; the Anderson acceleration method needs 11 iterations to converge, which takes 1.32 seconds, while the method of the present invention only needs 10 iterations to converge, which takes 1.18 seconds, indicating that the method of the present invention can improve the efficiency of the main-coordinated optimal power flow calculation. For example B, the heterogeneous decomposition method does not converge, the Anderson acceleration method needs 14 iterations to converge, which takes 3.36 seconds, while the method of the present invention needs 11 convergences, which takes 2.68 seconds, indicating that the method of the present invention can improve the convergence performance of the main-coordinated optimal power flow calculation and has better stability.

[0095] The above are only preferred embodiments of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for determining optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration, characterized in that: The following steps are involved: Step 1: Set the initial values ​​of the boundary conditions and various iteration parameters of the distribution network sub-problem; Step 2: The distribution network control center solves the optimal power flow of the distribution network according to the boundary conditions of the distribution network sub-problem, obtains the boundary conditions of the main grid sub-problem, and sends them to the main grid control center; Step 3: The main grid control center solves the optimal power flow of the main grid according to the boundary conditions of the main grid sub-problem, and obtains the boundary conditions of the updated distribution network sub-problem; Step 4: According to the residuals of the boundary conditions of the distribution network sub-problem before and after the update, determine whether the algorithm has converged and terminated: if it has converged, end the iteration and output the optimal power flow result; Otherwise go to step 5; Step 5: Check whether the total number of iterations has reached the upper limit: if the total number of iterations has reached the upper limit, terminate the iteration and output the optimal power flow result; if the total number of iterations has not reached the upper limit, check whether the inner layer iterations have reached the upper limit. If the inner layer iterations have not reached the upper limit, return to step 2; if the inner layer iterations have reached the upper limit, proceed to step 6. Step 6: Calculate the adaptive residual weight according to the historical iteration variables, and correct and update the outer iteration result through weighted Anderson acceleration, which is used as the initial value of the next outer iteration, and return to step 2 to accelerate the update of the boundary conditions of the distribution network sub-problem; In step 1, the initial values ​​of the boundary conditions and various iteration parameters of the distribution network subproblem are set as follows: Step 1.1: Set the boundary conditions of the distribution network subproblem, that is, In the outer iteration The iteration variable of the next inner iteration for: （1） In the formula, For the In the outer iteration The iteration variables of the second inner iteration are the boundary conditions of the distribution network subproblem; For the In the outer iteration The voltage phase angle of the boundary nodes of the second inner iteration; For the In the outer iteration The voltage amplitude of the boundary nodes of the second inner iteration; For the In the outer iteration Lagrange multipliers for active power balance constraints at boundary nodes of the second inner iteration; For the In the outer iteration Lagrange multipliers for reactive power balance constraints at boundary nodes of the second inner iteration; Step 1.2: Initialize iteration variables , the number of outer iterations , inner layer iterations , the upper limit of the number of inner iterations , convergence accuracy , maximum number of iterations ; In step 2, the distribution network control center uses the iteration variable Solve the optimal power flow of the distribution network and get In the outer iteration The power injection amount of the boundary nodes of the second inner iteration , calculate the first In the outer iteration The shadow price of boundary node voltage in the second inner iteration , and and It is sent to the main grid control center as the boundary condition of the main grid sub-problem; In step 3, the main network control center and Solve the optimal power flow of the main power grid and obtain the next inner iteration, that is, In the outer iteration The iteration variable of the next inner iteration .

2. The method for determining the optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration according to claim 1 is characterized in that: The step 2 is specifically as follows: Step 2.1: The distribution network control center calculates the iterative variables Solve the distribution network sub-problem and obtain the power injection amount of the boundary node , the formula is: （2） Calculate the voltage shadow price at the boundary node , the formula is: （3） In the formula, the superscript It is the vector transpose operation; is the power cost function of the distribution network; is the control variable of the distribution network, is the state variable of the distribution network, is the feasible region of the distribution network, To solve the main power grid subproblem, we obtain the boundary state value. Lagrange multipliers for boundary equality constraints obtained for solving the main grid subproblem; is the boundary power injection value; is the shadow price of the boundary state; is the state variable of the boundary part, including the voltage amplitude and voltage phase angle of the boundary node; is the equality constraint for the distribution network part, is the inequality constraint of the distribution network, and are the Lagrange multipliers for partial equality and inequality constraints of the distribution network, is the Lagrange multiplier for the equality constraints of the boundary part; is the expression of the distribution network part after the boundary equality constraint split; Step 2.2: The distribution network control center will and Sent to the main network control center.

3. The method for determining the optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration according to claim 2 is characterized in that: The step 3 is as follows: The main network control center and Solve the optimal power flow of the main power grid and get In the outer iteration The iteration variable of the next inner iteration , the formula is: （4） In the formula, The cost function of power generation for the main grid; is the control variable of the main power grid, is the control variable of the boundary part, is the state variable of the main power grid, is the state variable of the boundary part, The shadow prices of the boundary states obtained for solving the distribution network subproblem; is the feasible domain of the main power grid, The power injection amount at the boundary nodes obtained to solve the distribution network subproblem.

4. The method for determining the optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration according to claim 3 is characterized in that: In step 4, the residuals of the boundary conditions of the distribution network subproblem before and after the update are used to determine whether the algorithm has converged and terminated, as follows: Step 4.1, calculate the residual of the boundary conditions of the distribution network subproblem between this iteration and the last iteration boundary conditions. If , then the iteration ends and the optimal power flow result is output; represents the convergence accuracy parameter, Indicates the calculation of vector norm; Step 4.2: If , then go to step 5.

5. The method for determining the optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration according to claim 4 is characterized in that: The step 5 is specifically as follows: Step 5.1: Determine whether the total number of iterations has reached the upper limit ,if , the algorithm does not converge and the iteration is terminated, and the optimal power flow result is output; Step 5.2: If and , then the number of inner iterations is ,Will Send to the distribution network control center and return to step 2; Step 5.3: If and , go to step 6.

6. The method for determining the optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration according to claim 5 is characterized in that: The step 6 is specifically as follows: Step 6.1, calculate the residual weight coefficient of each inner layer iteration in this outer layer iteration; Step 6.2: Use the residual weight coefficients of each inner iteration in this outer iteration to correct and update the results of this outer iteration through weighted Anderson acceleration, and send them to the distribution network control center as the initial value of the next outer iteration, and return to step 2, so as to accelerate the update of the boundary conditions of the distribution network sub-problem.

7. The method for determining the optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration according to claim 6 is characterized in that: The calculation of the residual weight coefficients of each inner layer iteration in this outer layer iteration in step 6.1 is as follows: Step 6.1.1: For The outer iteration is to calculate The outer iteration and Each iteration point in the outer iteration , , the formula is: （5） （6） Calculate the The outer iteration and The first-order residual matrix of the fixed point sequence in the second outer iteration , , the formula is: （7） （8） （9） In the formula, for dimensional difference calculation matrix, for The identity matrix of Step 6.1.2: Perform a differential operation on the first-order residual matrix in two adjacent outer iterations to obtain the first-order adjacent point residual matrix , the formula is: （10） in The columns of indivual dimensional first-order neighboring point residual vector, specifically: （11） Step 6.1.3: Perform a first-order difference operation on the first-order adjacent point residual matrix to obtain the second-order adjacent point residual matrix , the formula is: （12） （13） In the formula, for Dimensional difference calculation matrix; Step 6.1.4: Calculate The residual weight coefficient of each inner iteration in the outer iteration , the formula is: （14） （15） In the formula, is the residual weight transformation matrix.

8. The method for determining the optimal power flow of main distribution coordination based on adaptive weighted Anderson acceleration according to claim 7 is characterized in that: In step 6.2, the residual weight coefficients of each inner iteration in this outer iteration are used to correct and update the results of this outer iteration through weighted Anderson acceleration, and sent to the distribution network control center as the initial value of the next outer iteration, and return to step 2, so as to accelerate the update of the boundary conditions of the distribution network sub-problem, as follows: Step 6.2.1: For The outer layer iteration calculates the first-order residual matrix of the fixed point sequence of this layer , the formula is: （16） in The columns of indivual dimensional first-order residual vector, specifically: （17） Step 6.2.2: Take the first-order residual matrix Column, obtained from arrive of The first-order residual matrix of the iterative operation is: （18） （19） In the formula, Extract the transformation matrix for the columns; Step 6.2.3: According to The residual weight sequence of the inner iteration in the outer iteration , construct the residual weight diagonal matrix , the formula is: （20） Assign weights to each column in the first-order residual matrix to obtain a first-order weighted residual matrix , the formula is: （21） Step 6.2.4: Perform a differential operation on the first-order weighted residual matrix to obtain arrive this The second-order weighted residual matrix of the iterative operation , the formula is: （22） Step 6.2.5: According to the following formula The outer layer iteration result is corrected and updated as the Initial value of the outer iteration : （23） Step 6.2.6: Send it to the distribution network control center and return to step 2, thereby accelerating the update of the boundary conditions of the distribution network sub-problem.

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