Power line day-ahead maintenance plan optimization method considering voltage safety and stability

Abstract

The invention belongs to the technical field of electric power system maintenance optimization, and particularly relates to an electric power circuit day-ahead maintenance plan optimization method considering voltage safety and stability, which comprises the following steps of: constructing an electric power circuit day-ahead maintenance optimization mathematical model by taking minimum unit operation cost and electric power circuit maintenance cost as targets; comprising the steps of setting an objective function and constraint conditions thereof; determining a power transmission line model and an admittance matrix, and then modifying the admittance matrix by adopting a branch addition method to obtain a line switching model based on the branch addition method; and performing staged solution on the line switching model, including three stages of generation and reduction of an uncertain scene, a mixed integer linear main problem and a nonlinear sub-problem, outputting a final solution result, and taking the final solution result as an optimal day-ahead maintenance plan of the power line. According to the method, a maintenance scheme with higher feasibility and robustness is formulated through a reasonable solving strategy, and the overall safety and reliability of a power system are improved.

Description

Technical Field

[0001] This invention belongs to the field of power system maintenance optimization technology, specifically involving a method for optimizing day-ahead maintenance plans for power lines that takes into account voltage safety and stability. Background Technology

[0002] The increasing proportion of new energy power generation in the power system brings significant economic benefits to the grid operation, but also poses serious challenges. New energy power generation is greatly affected by weather changes, resulting in significant fluctuations in output. Coupled with load uncertainty, this leads to frequent voltage fluctuations in the grid. New energy units often operate at their maximum active power output, lacking reactive power regulation capabilities and struggling to effectively participate in voltage control, potentially causing voltage safety issues such as voltage exceeding limits. Furthermore, the large-scale integration of new energy units has significantly reduced the adjustable reactive power resources of the power system, leading to a continuous decline in the grid's voltage support capacity and increasingly prominent voltage stability problems. Therefore, maintenance plans that only consider line transmission congestion and economic efficiency are insufficient to meet the development needs of the new power system; it is urgent to incorporate grid voltage safety and stability into maintenance plans.

[0003] In terms of mathematical models for electrical equipment maintenance planning, existing research can be broadly categorized into two types: linear DC power flow models and nonlinear AC power flow models. The rapid development of power systems has placed higher demands on power system optimization and scheduling. Traditional linear power flow constraints are no longer sufficient to meet the voltage safety and solution accuracy requirements of power systems. Therefore, in recent years, scholars have established maintenance optimization models based on nonlinear AC power flow constraints. Among existing literature, the paper "Reliability Assured Generation Maintenance Scheduling under AC Transmission Constraints: Relaxation and Decomposition Approach" proposes a generator maintenance scheduling model that considers reliability and AC power flow constraints, capable of simultaneously considering the active and reactive power operation constraints of the system under normal and post-fault conditions. The paper "Cooperative Optimization of Transmission Line Switching and Unit Combination under AC Power Flow Constraints" establishes a cooperative optimization model for unit combination and transmission line switching considering AC power flow constraints and verifies that this model can effectively guarantee the voltage safety of power system nodes. However, the above studies only consider the impact of voltage safety constraints on maintenance plans, neglecting the importance of voltage stability constraints. Therefore, the proposed maintenance models are no longer applicable to the power line maintenance problem under the current high proportion of renewable energy connected to the grid.

[0004] The optimization model for electrical equipment maintenance plans is mathematically a mixed-integer nonlinear programming (MINLP) problem. Its main challenge lies in the presence of numerous discrete variables characterizing line maintenance status and continuous variables characterizing system operating status. This mixed-variable characteristic leads to strong nonlinear features in the model. The paper "A linear AC unitcommitment formulation: an application of data-driven linear power flow model" proposes a linearized AC power flow constrained unit commitment model, significantly reducing the complexity of the solution while maintaining high accuracy. The paper "A reliability-based approach for integrated generation and transmission maintenance coordination in restructured power systems" studies a reliability-based generation and transmission maintenance coordination mechanism that uses a hybrid genetic algorithm and quadratic programming to approximate the global optimum. Current literature often uses partial constraint approximation to solve such models, but this simplification method, which sacrifices model accuracy, may not be applicable to practical power grid maintenance decisions. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this invention is to provide an optimization method for day-ahead maintenance plans of power lines that takes into account voltage safety and stability. Under the background of uncertain renewable energy output, the method uses a voltage safety and stability constraint optimization model based on AC power flow and continuous power flow equations to formulate more feasible and robust maintenance plans through reasonable solution strategies, thereby improving the overall safety and reliability of the power system.

[0006] To achieve the above objectives, this invention provides a method for optimizing the day-ahead maintenance plan of power lines, taking into account voltage safety and stability, comprising the following steps: S1. Under the premise of meeting the voltage safety and stability requirements and operation requirements of the power system, and with the goal of minimizing the unit operating cost and power line maintenance cost, construct a mathematical model for optimizing the day-ahead maintenance of power lines, including setting the objective function and its constraints. S2. Determine the transmission line model and admittance matrix, and then modify the admittance matrix using the branch addition method to obtain the line switching model based on the branch addition method. S3. Perform a phased solution to the line switching model, which includes three stages: generation and reduction of uncertain scenarios, mixed integer linear main problem and nonlinear subproblems. Output the final solution results and use the final solution results as the optimal daytime maintenance plan for power lines.

[0007] As a preferred embodiment of the present invention, in S1, the objective function of the mathematical model for optimizing the day-ahead maintenance of power lines is expressed as: (1); In the formula, t is the time period index, T is the total number of time periods, and k is the power line index. This represents the total number of power lines. Let $t$ be the maintenance cost of power line $k$ during time period $t$. This represents the maintenance status of power line k during time period t. A value of 1 indicates no maintenance. A value of 0 indicates maintenance; g is the unit index. This represents the total number of generating units. Let g be the operating cost of unit g during time period t; The constraints of the mathematical model for optimizing daytime maintenance of power lines include maintenance status constraints, total maintenance time constraints, maintenance continuity constraints, maintenance start time constraints, maintenance resource constraints, power flow balance constraints, continuous power flow balance constraints, load margin constraints, safe operation constraints, unit output constraints, and unit ramping constraints.

[0008] As a preferred embodiment of the present invention, the maintenance state constraint is expressed as follows: (2); In the formula, , These represent the earliest and latest times when power line k can be repaired; A collection of power lines that require maintenance; The total maintenance time constraint is expressed as follows: (3); In the formula, Let K be the total maintenance time for power line k. Maintenance continuity constraints are expressed as follows: (4); In the formula, , These represent the time intervals t+1 and t+1 for power line k. The maintenance status. Represents the time offset, used to describe the time period after time t. Each time period; The start time constraint for maintenance is expressed as follows: (5); In the formula, Let be the state variable indicating when power line k begins maintenance. If power line k begins maintenance in time period t, then... It is 1 if it is true, otherwise it is 0; Maintenance resource constraints are represented as follows: (6); In the formula, This represents the maximum number of lines that can be inspected simultaneously within time period t. The load margin constraint is expressed as: (7); In the formula, This represents the load margin of the power system in time period t under scenario s; This refers to the load margin threshold requirement for the power system during time period t. Safe operation constraints are expressed as follows: (8); (9); (10); In the formula, Let be the voltage amplitude of node i at the power flow point in scenario s during time period t; , These are the upper and lower limits of the voltage amplitude at node i, respectively, at the power flow operation point; Let be the voltage phase angle difference between node i and node j at the power flow operation point in scenario s during time period t; , These are the upper and lower limits of the phase angle difference between nodes ij at the power flow operation point, respectively. , These represent the apparent power and its upper limit of line ij at the power flow operating point, respectively.

[0009] As a preferred embodiment of the present invention, in step S2, determining the transmission line model and admittance matrix includes the following steps: S2.1 Establishing a transmission line model: using The admittance of line ij in the equivalent circuit of type ij Half of the susceptance of the ground branch of line ij Connected in parallel with an ideal transformer, the tap ratio is Phase shift angle is The ideal transformer is located at the beginning of line ij; S2.2. Taking power line k as branch k, its corresponding branch admittance matrix. Represented as: (11); In the formula, , These are the self-admittances at the beginning and end of branch k, respectively; The mutual admittance between the beginning and end of branch k; The mutual admittance between the end and beginning of branch k; S2.3 Construct the admittance matrix of the power system based on the branch admittance. , represented as: (12); (13); (14); In the formula, , These are the branch admittance matrices at the beginning and end of the line, respectively; and for 3D sparse connectivity matrix This represents the total number of power grid nodes. Add a matrix to the ground susceptance; , These are the self-admittances at the beginning and end of the line, respectively; The mutual admittance between the beginning and end of the line; It is the mutual admittance between the end and the beginning of the line.

[0010] As a preferred embodiment of the present invention, the method for modifying the admittance matrix using the branch addition method in S2 is as follows: The essence of disconnecting branch k in time period t is to change the elements in the original admittance matrix of branch k in time period t. and , for The conductivity component, for The susceptance component, therefore, the admittance matrix of the power system after branch k is interrupted in time period t. The original admittance matrix branch admittance change matrix over time period t The sum is expressed as: (15); When branch k is interrupted during time period t Represented as: (16); In the formula, Let J be the node-branch incidence matrix, which has only two non-zero elements, 1 and -1, where 1 represents the position of the starting node i of branch k and -1 represents the position of the ending node k of branch k; J represents the imaginary unit. Let i be the position vector of the starting node i of branch k. Let be the position vector of the terminal node j of branch k; diag represents the diagonal matrix.

[0011] As a preferred embodiment of the present invention, in S3, the generation and reduction of uncertain scenarios specifically refers to the joint scenario set for time period t. It is a collection of renewable energy scenarios With load scenario set The Cartesian product, i.e.: (17); In the formula, for Elements in; for Elements in; A clustering method using the distance between operating points and load margins between scenarios as an indicator is used to reduce the generated renewable energy scenarios, resulting in representative typical uncertain scenarios.

[0012] As a preferred embodiment of the present invention, the mathematical model of the mixed-integer linear master problem in S3 is as follows: (18); In the formula, The estimated value for the subproblem; , These are equality constraints and inequality constraints concerning the variables, respectively. , , respectively, are the Jacobian matrices for equality constraints and inequality constraints; x is the system state variable; u is the system control variable; For load margin parameters; This refers to the system state variable corresponding to the point where the system voltage collapses. This refers to the load margin parameter corresponding to the system voltage collapse point. M represents the system control variable corresponding to the point where the system voltage collapses; M is the set of all maintenance lines and time periods under the current maintenance plan. Let M be the cardinality of set M; Y is the maintenance state vector of the current decision. The solution to the main problem is a certain line maintenance plan; for Operating costs below; for right The gradient; According to the route switching model construction strategy based on the branch addition method, the changes in control variables are encapsulated in the admittance matrix. Therefore, the changes in control variables are equivalently transformed into changes in the admittance matrix. After the transformation, the original mixed integer nonlinear programming problem becomes a convex optimization problem.

[0013] As a preferred embodiment of the present invention, the mathematical model of the nonlinear subproblem in S3 is as follows: (19); When a subproblem is infeasible under the current maintenance plan, a feasible cut constraint is constructed to exclude the maintenance plan, expressed as: (20).

[0014] As a preferred embodiment of the present invention, in S3, the following formula is used to approximately reflect the relationship between operating costs and the maintenance variables of the main problem during the solution process: (twenty one); The subproblem feeds the generated Benders cut back to the main problem, and the cut generated in each iteration needs to be added to the constraints of the main problem. When the maximum number of iterations is reached or the convergence condition is met, no new Benders cut is generated, and the computation ends. The convergence condition is expressed as: (twenty two); In the formula, for corresponding ; The value passed to the main problem; The optimality criterion is set.

[0015] The beneficial effects of this invention are: With the goal of minimizing costs, this invention establishes a voltage safety and stability optimization model based on AC power flow and continuous power flow equations under the background of uncertain new energy output. Under the premise of ensuring voltage safety and stability, it achieves effective optimization of maintenance plans. By using the distance between the operating point and the load margin between scenarios as an indicator, uncertain scenarios are generated and reduced, effectively constructing a set of typical scenarios that can reflect the voltage stability of the system.

[0016] This invention utilizes the Benders decomposition method to decompose a complex mixed-integer nonlinear model into a main problem of power line day-ahead maintenance planning considering voltage stability and an optimal power flow subproblem considering AC power flow constraints. It enables iterative solutions between the main and subproblems, prompting the main problem to approach the optimal solution of the original problem. Under the premise of ensuring voltage safety and stability, it guarantees computational speed and convergence accuracy.

[0017] This invention verifies the proposed optimization model and staged solution strategy in IEEE 39 and IEEE 118 node power systems through simulation. Compared with existing solution methods, the superiority of the proposed optimization model and solution strategy in terms of computation time and accuracy is verified, demonstrating the application potential of the proposed model and algorithm in practical power systems. Attached Figure Description

[0018] Figure 1This is a flowchart illustrating the principle of this invention; Figure 2 This is a schematic diagram of the transmission line model of the present invention; Figure 3 This is a flowchart of the solution strategy of this invention; Figure 4 This is a flowchart of the renewable energy scenario generation and reduction process of the present invention; Figure 5 This is the load prediction curve of the IEEE 39-node system in Verification Example 1 of this invention; Figure 6 This is the power output diagram of the IEEE 39-node system units at different time periods in Verification Example 1 of this invention; Figure 7 This is a graph showing the node voltage variation of the IEEE 39-node system in Verification Example 1 of this invention. Figure 8 This is a graph showing the load margin variation of the IEEE 39-node system under different maintenance schemes in Example 1 of this invention. Figure 9 This is the load prediction curve of the IEEE 118-node system in Verification Example 2 of this invention; Figure 10 This is the power output diagram of the IEEE 118 node system units at different time periods in Verification Example 2 of this invention; Figure 11 This is a graph showing the node voltage variation of the IEEE 118-node system in Verification Example 2 of this invention. Figure 12 This is a graph showing the changes in load margin of the IEEE 118 node system under different maintenance schemes in Example 2 of this invention. Detailed Implementation

[0019] The embodiments of the present invention will be further described below with reference to the accompanying drawings: Example 1: As Figure 1 As shown, the method for optimizing the daily maintenance plan for power lines, taking into account voltage safety and stability, includes the following steps: S1. Under the premise of meeting the voltage safety and stability requirements and operation requirements of the power system, and with the goal of minimizing the unit operating cost and power line maintenance cost, construct a mathematical model for optimizing the day-ahead maintenance of power lines, including setting the objective function and its constraints. S2. Determine the transmission line model and admittance matrix, and then modify the admittance matrix using the branch addition method to obtain the line switching model based on the branch addition method. S3. Perform a phased solution to the line switching model, which includes three stages: generation and reduction of uncertain scenarios, mixed integer linear main problem and nonlinear subproblems. Output the final solution results and use the final solution results as the optimal daytime maintenance plan for power lines.

[0020] In S1, the objective function of the mathematical model for optimizing the day-ahead maintenance of power lines is expressed as: (twenty three); In the formula, t is the time period index, T is the total number of time periods, and k is the power line index. This represents the total number of power lines. Let $t$ be the maintenance cost of power line $k$ during time period $t$. This represents the maintenance status of power line k during time period t. A value of 1 indicates no maintenance. A value of 0 indicates maintenance; g is the generator set index. This represents the total number of generating units. Let g be the operating cost of unit g during time period t; The constraints of the mathematical model for optimizing daytime maintenance of power lines include maintenance status constraints, total maintenance time constraints, maintenance continuity constraints, maintenance start time constraints, maintenance resource constraints, power flow balance constraints, continuous power flow balance constraints, load margin constraints, safe operation constraints, unit output constraints, and unit ramping constraints.

[0021] Maintenance status constraints are represented as follows: (twenty four); In the formula, , These represent the earliest and latest times when power line k can be repaired; A collection of power lines that require maintenance; The total maintenance time constraint is expressed as follows: (25); In the formula, Let K be the total maintenance time for power line k. Maintenance continuity constraints are expressed as follows: (26); In the formula, , These represent the time intervals t+1 and t+1 for power line k. The maintenance status. Represents the time offset, used to describe the time period after time t. Each time period; The start time constraint for maintenance is expressed as follows: (27); In the formula, Let be the state variable indicating when power line k begins maintenance. If power line k begins maintenance in time period t, then... It is 1 if it is true, otherwise it is 0; Maintenance resource constraints are represented as follows: (28); In the formula, This represents the maximum number of lines that can be inspected simultaneously within time period t. After the transmission line switching, any node i in the power system should satisfy the power flow balance constraint, that is: (29); In the formula, , These represent the active and reactive power outputs of the generator set at node i in scenario s during time period t. Let t be the active power output of the wind turbine at node i in scenario s during time period t. , These represent the active and reactive power demands of the load at node i in scenario s during time period t. , Let i and j be the voltage amplitudes at nodes i and j, respectively, at the power flow operation point in scenario s, during time period t; i and j are the first and last nodes of power line k, respectively. This represents the total number of power grid nodes. , These are the conductance and susceptance of power line k, respectively; Let be the voltage phase angle difference between node i and node j at the power flow operation point in scenario s during time period t; After a transmission line switchover, any node i in the power system should satisfy the continuous power flow balance constraint, i.e.: (30); In the formula, , These represent the directions of active and reactive power injection at node i in scenario s during time period t, determined by the growth of generators and load. This represents the load margin of the power system in time period t under scenario s; , These are the voltage amplitudes of nodes i and j at the extreme operating point in scenario s during time period t, respectively. Let be the voltage phase angle difference between node i and node j at the extreme operating point in scenario s during time period t; The load margin of the power system in each time period should meet the static voltage stability threshold requirement. The load margin constraint is expressed as follows: (31); In the formula, This refers to the load margin threshold requirement for the power system during time period t. Its value can be determined by the system operators according to the engineering requirements (i.e., based on different power system operating conditions and specific needs). After a power line is disconnected, the node voltages and branch power of the power system should meet the safety operation constraints, as expressed in: (32); (33); (34); In the formula, , These are the upper and lower limits of the voltage amplitude at node i, respectively, at the power flow operation point; , These are the upper and lower limits of the phase angle difference between nodes ij at the power flow operation point, respectively. , These represent the apparent power and its upper limit of line ij at the power flow operating point, respectively. The unit output constraint is expressed as: (35); In the formula, , These represent the upper and lower limits of the output of generator set g, respectively. The unit ramp-up constraint is expressed as: (36); In the formula, , These represent the rate of decrease and the rate of increase of generator set g per hour, respectively. Let be the active power output of the generator set at node i in scenario s during time period t+1.

[0022] A mathematical model for power line interruption is established using the branch addition method. This method allows modification of parameters in the line admittance matrix. Furthermore, since the impact of line interruption is directly reflected in the system admittance matrix, there is no need to introduce slack variables into the voltage at both ends of the line during the model solution process, thus avoiding the limitations of the traditional Big M method to a limited extent.

[0023] In S2, determining the transmission line model and admittance matrix includes the following steps: S2.1 Establishing a transmission line model: using The admittance of line ij in the equivalent circuit of type ij Half of the susceptance of the ground branch of line ij Connected in parallel with an ideal transformer, the tap ratio is Phase shift angle is The ideal transformer is located at the beginning of line ij; S2.2. Taking power line k as branch k (a line whose starting point is node i and whose ending point is node j), its corresponding branch admittance matrix. Represented as: (37); In the formula, , These are the self-admittances at the beginning and end of branch k, respectively; The mutual admittance between the beginning and end of branch k; The mutual admittance between the end and beginning of branch k; S2.3 Construct the admittance matrix of the power system based on the branch admittance. , represented as: (38); (39); (40); In the formula, , These are the branch admittance matrices at the beginning and end of the line, respectively; and for 3D sparse connectivity matrix; Add a matrix to the ground susceptance; , These are the self-admittances at the beginning and end of the line, respectively; The mutual admittance between the beginning and end of the line; This represents the mutual admittance between the end and beginning of the line, with the superscript T indicating transpose.

[0024] The method for modifying the admittance matrix using the branch addition method is as follows: The essence of disconnecting branch k in time period t is to change the elements in the original admittance matrix of branch k in time period t. and , for The conductivity component, for The susceptance component ( Therefore, the admittance matrix of the power system after branch k is interrupted in time period t is... The original admittance matrix branch admittance change matrix over time period t The sum is expressed as: (41); When branch k is interrupted during time period t Represented as: (42); In the formula, Let J be the node-branch incidence matrix, which has only two non-zero elements, 1 and -1, where 1 represents the position of the starting node i of branch k and -1 represents the position of the ending node k of branch k; J represents the imaginary unit. Let i be the position vector of the starting node i of branch k. Let be the position vector of the terminal node j of branch k; ... .

[0025] Since the optimization model is large in scale and is a typical mixed-integer nonlinear programming problem, it is difficult to solve directly. To improve the solution efficiency, a staged solution method is proposed.

[0026] S3 comprises three stages: handling uncertain scenarios, a mixed-integer linear MILP main problem, and nonlinear NLP subproblems. First, the uncertain scenario is generated and reduced. Then, the Benders decomposition method is used to decompose the original problem into a main problem and subproblems. Next, the Jacobian or Hessian matrix of the original problem is used to linearize the main problem, ultimately decomposing the original problem into a mixed-integer linear main problem and nonlinear subproblems. The main and subproblems iterate with each other, gradually converging to the optimal solution of the original problem through continuous feedback of the optimal and feasible cuts generated by the subproblems, thus achieving efficient joint optimization.

[0027] In S3, the generation and reduction of uncertain scenarios specifically involves the joint scenario set for time period t. It is a collection of renewable energy scenarios With load scenario set The Cartesian product, i.e.: (43); In the formula, for Elements in; for Elements in; Due to the large number of joint scenarios, it is necessary to reduce the number of generated scenarios to decrease computational complexity. To avoid erroneous reduction of extreme scenarios, a clustering method using the distance between the operating point and load margin of different scenarios as an indicator is adopted to reduce the generated renewable energy scenarios, resulting in representative typical uncertain scenarios.

[0028] The mathematical model for the main problem of mixed-integer linear MILP is: (44); In the formula, The estimated value for the subproblem; , These are equality constraints and inequality constraints concerning the variables, respectively. , , respectively, are the Jacobian matrices for equality constraints and inequality constraints; x is the system state variable (all systems are power systems); u is the system control variable; For load margin parameters; This refers to the system state variable corresponding to the point where the system voltage collapses. This refers to the load margin parameter corresponding to the system voltage collapse point. M represents the system control variable corresponding to the point where the system voltage collapses; M is the set of all maintenance lines and time periods under the current maintenance plan. Let M be the cardinality of set M; Y is the maintenance state vector of the current decision. The solution to the main problem (the main problem variable), i.e., a certain line maintenance plan; for Operating costs below; for right The gradient; According to the line switching model construction strategy based on the branch addition method, the changes in control variables are encapsulated in the admittance matrix. Therefore, the changes in control variables are equivalently transformed into changes in the admittance matrix. After the above transformation, the original mixed integer nonlinear programming problem becomes a convex optimization problem, which can be solved directly using the linear programming method.

[0029] The mathematical model for the nonlinear NLP subproblem is as follows: (45); When a subproblem is infeasible under the current maintenance plan, a feasible cut constraint is constructed to exclude the maintenance plan, expressed as: (46).

[0030] Since the subproblem is an AC power flow problem, which is nonlinear and nonconvex, it lacks strong duality and cannot be handled using slack variables or dual variables. Approximating the AC power flow would compromise the accuracy of the system's power flow. Therefore, this embodiment directly utilizes the original variables and objective function of the subproblem to approximate its sensitivity using the finite difference method. The sensitivity of the subproblem's objective function relative to the maintenance variable Y is approximated, and this sensitivity is then used to construct a first-order approximate cut as the optimal cut.

[0031] When solving the problem, the following formula is used to approximate the relationship between operating costs and the maintenance variables of the main problem: (47); The subproblem feeds the generated Benders cut back to the main problem, and the cut generated in each iteration needs to be added to the constraints of the main problem. When the maximum number of iterations is reached or the convergence condition is met, no new Benders cut is generated, and the computation ends. The convergence condition is expressed as: (48); In the formula, for corresponding ; The value passed to the main problem; The optimality criterion is set (which is a small positive number).

[0032] The method of this embodiment is verified through the following verification examples.

[0033] Verification Example 1: The method of the present invention is verified by simulation using the IEEE 39-bus power system as an example to verify the efficiency and effectiveness of the proposed optimization model and solution strategy.

[0034] Figure 2 This is a schematic diagram of the transmission line model for verifying Example 1. Figure 3 This is a flowchart of the solution strategy, which summarizes the staged solution strategy. When applied to nodal power systems, the solution process is as follows: The first step is to input the current power system network parameters, maintenance data, voltage stability margin requirements, and other system data, and then calculate the base-state system load margin.

[0035] The second step involves generating and reducing uncertain scenarios according to equation (43) to obtain representative typical uncertain scenarios. The flowchart for generating and reducing renewable energy scenarios is as follows: Figure 4 As shown.

[0036] The third step is to solve the main problem of day-ahead maintenance of transmission lines considering voltage stability, as shown in equation (44), and then pass the obtained maintenance plan to the NLP subproblem model.

[0037] The fourth step is to solve the optimal power flow subproblem under the AC power flow constraint shown in equation (45) to obtain the power flow solution under the maintenance scheme.

[0038] The fifth step is to determine whether the convergence condition has been met. If the subproblem is infeasible, it is fed back to the main problem through a feasible cut and then proceeds to the third step. If the subproblem is feasible but does not converge, it is fed back to the main problem through an optimal cut and then proceeds to the third step. If the subproblem is feasible and converges, that is, it satisfies the convergence condition (48), then the algorithm terminates the iteration and proceeds to the sixth step.

[0039] The sixth step is to output results such as the power system load margin and transmission line maintenance plan.

[0040] To verify the necessity of considering voltage stability during power line maintenance, a maintenance scheme (Scheme 2) that does not consider voltage stability was designed and compared with the scheme (Scheme 1) in this embodiment. The test platform was MATLAB 2018b, and the YALMIP language was used for modeling. The solvers Gurobi and IPOPT were used to solve the linear main problem and the nonlinear subproblems, respectively.

[0041] The IEEE 39-bus simulation system comprises 46 power lines and 10 conventional generators, with a total active and reactive load of 5702 MW and 1262 Mvar, respectively. The simulation assumes that 12 loads (nodes 15-16, 18, 20-21, and 23-29) will experience power increases, while the remaining loads will remain unchanged. Active power injection from two generators (nodes 30 and 31) is increased to balance the increased load demand. A load margin threshold of 1425 MW is set for each time period. The predicted active and reactive load values ​​for each time period are as follows: Figure 5 As shown. The system consists of three wind turbines, located at nodes 4, 8 and 20, each with a rated capacity of 200MW.

[0042] Under the current load and wind power forecast scenarios, the power line maintenance plan is obtained as shown in Table 1. The power output of each unit in the system at different times is as follows: Figure 6 As shown in the figure. The final optimized total operating cost of the system is 7,769,309 yuan.

[0043] Table 1 Power Line Maintenance Plan

[0044] According to Table 1 and Figure 6 The results show that generators G2, G5, G6, G7, G8, and G10, which have lower generation costs, operated at full capacity throughout the 24 time periods. During periods 3-6 and 9-11, the system load was relatively low, and generators G4 and G9 appropriately reduced their output to maintain power balance. During the maintenance of lines L18 and L30, the output of multiple generators changed significantly. The output of generator G3, which has lower generation costs, decreased sharply, while the output of generator G10, which has higher generation costs, increased significantly. This is because the maintenance and removal of lines L18 and L30 from the grid during period 16 altered the system's network topology, leading to a redistribution of power flow. At this time, multiple lines between nodes 4-14 and 16-19 reached their thermal limits, resulting in power flow congestion. To maintain system power balance, generator G10, located near the load, increased its generation to balance the load locally, reducing long-distance transmission and avoiding detour losses. Therefore, during the maintenance period, the output of generator G10 increased, while the output of generator G3 decreased.

[0045] Through simulation calculations, the voltage change curves of each node in the system at different time periods were obtained, such as... Figure 7 As shown in the figure, it can be seen that the voltage amplitude of all nodes in the system remains within the allowable range of 0.90pu~1.10pu in all time periods, which meets the set system node voltage requirements. Therefore, under this maintenance plan, the system meets the system safety constraints in all time periods, and the maintenance plan is feasible in terms of voltage safety.

[0046] Under the current load and wind power forecast scenarios, the power line maintenance plan, neglecting voltage stability, is shown in Table 2. The final optimized total system operating cost is 7,739,309 yuan.

[0047] Table 2. Power line maintenance schemes without considering voltage stability

[0048] Based on the optimized power line maintenance scheme 2, the system load margin of maintenance scheme 2 under each time period is calculated and compared with the system load margin under maintenance scheme 1. The results are as follows: Figure 8 As shown. For maintenance plan 1, the system load margin meets the set system load margin threshold in each time period, and the maintenance plan is feasible. For maintenance plan 2, during time period 1-2, the system load margin is lower than the set system load margin threshold, and the system has a certain voltage stability risk, which may lead to node voltage exceeding the limit or even voltage collapse, affecting the safety and stability of the power grid.

[0049] To verify the effectiveness of the proposed solution method, the method in this embodiment is compared with the branch and bound (B&B) method, and the results are shown in Table 3. It can be seen that due to the highly nonlinear nature of the model, the conventional MINLP solution method struggles to guarantee convergence. In contrast, both Scheme 1 and Scheme 2 in this embodiment achieve convergence. Although Scheme 2 has a lower cost, its corresponding maintenance scheme cannot guarantee voltage stability, posing a potential safety risk to the system. Therefore, Scheme 1 in this embodiment, while ensuring voltage stability, achieves convergence and achieves a lower cost, thus verifying the rationality and effectiveness of the proposed method.

[0050] Table 3 Comparison of solution results between the method in this embodiment and the B&B method

[0051] Verification Example 2: The method of this embodiment is verified by simulation using the IEEE 118-bus power system as an example to verify the efficiency and effectiveness of the proposed optimization model and solution strategy.

[0052] The IEEE 118-node simulation system comprises 186 power lines and 54 conventional generators, with a total active and reactive load of 4242 MW and 1438 Mvar, respectively. The simulation assumes that 39 loads (nodes 33-36, 39-60, 62, 66-67, 76-80, 97-99, and 118) will experience power increases, while the remaining loads will remain unchanged. Active power injection from three generators (nodes 10, 25, and 26) is increased to balance the increased load demand. A load margin threshold of 1850 MW is set for each time period. The predicted active and reactive load values ​​for each time period are as follows: Figure 9 As shown. The system consists of 5 wind turbines, located at nodes 39, 41, 43, 75 and 106, each with a rated capacity of 150MW.

[0053] In this example, based on the generation cost of each unit, the units with lower costs are selected to participate in the system power balance: G5, G11, G12, G21, G28, G29, G37, G40, and G45. The remaining units remain offline. Under the current load and wind power forecast scenario, the power line maintenance plan is obtained as shown in Table 4. The output of each unit in the system at different time periods is as follows: Figure 10 As shown in the figure. The final optimized total operating cost of the system is 3,116,965 yuan.

[0054] Table 4 Power Line Maintenance Plan

[0055] According to Table 4 and Figure 10 The results show that generators G5, G12, G21, G28, G29, G37, and G45 operated at full capacity throughout all 24 time periods, while G11 and G40 did not reach their maximum output. This is because the voltage at the nodes where these two generators are located is too high, approaching the set upper limit of voltage amplitude. Further increasing output would lead to voltage exceeding the limit, or even voltage collapse. Even though generator G40 has the lowest power generation cost, its output is significantly limited under system voltage safety constraints.

[0056] Through simulation calculations, the voltage change curves of each node in the system at different time periods were obtained, such as... Figure 11 As shown in the figure, it can be seen that the voltage amplitude of all nodes in the system remains within the allowable range of 0.90pu~1.10pu in all time periods, which meets the set system node voltage requirements. Therefore, under this maintenance plan, the system meets the system safety constraints in all time periods, and the maintenance plan is feasible in terms of voltage safety.

[0057] Under the current load and wind power forecast scenarios, the maintenance plan for power lines, neglecting voltage stability, is shown in Table 5. The final optimized total system operating cost is 3,095,715 yuan.

[0058] Table 5. Power line maintenance schemes without considering voltage stability

[0059] Based on the optimized power line maintenance scheme 2, the system load margin of maintenance scheme 2 under each time period is calculated and compared with the system load margin under maintenance scheme 1. The results are as follows: Figure 12 As shown.

[0060] Under maintenance plan 1, the system meets the system stability constraints in all time periods, and the maintenance plan is feasible. For maintenance plan 2, during time periods 5, 9, and 12-13, the system load margin is lower than the set system load margin threshold, and the system stability constraints are not met.

[0061] The method of this embodiment is compared with the B&B method, and the results are shown in Table 6.

[0062] Table 6 Comparison of solution results between the method in this embodiment and the B&B method

[0063] This embodiment proposes a power line maintenance optimization method considering voltage safety and stability constraints under uncertain scenarios. An optimization model for day-ahead power line maintenance plans, considering both AC and continuous power flow constraints, is established. The objective function is to minimize the operating cost of conventional generators and the maintenance cost of power lines, and the solution is obtained through an iterative solution strategy based on Benders decomposition. Simulation examples 1 and 2 lead to the following conclusions: This embodiment establishes an optimization model and method for power line maintenance plans that considers voltage safety and stability. The proposed model effectively improves the overall operational safety and stability of the power system during maintenance and significantly enhances the system's safe operation capability during maintenance.

[0064] This embodiment proposes a staged solution strategy for problem decomposition, which greatly reduces the difficulty of solving the original problem and improves the overall solution efficiency. Simulation results demonstrate that the solution results of this embodiment are consistent with those of the detailed calculation method in power systems of different scales. Furthermore, the proposed method exhibits good convergence and computational speed, verifying its effectiveness.

[0065] The research results of this embodiment provide new methodological support for subsequent adoption of other control measures and consideration of source-network collaborative optimization.

[0066] Example 2: A device for optimizing the day-ahead maintenance plan for power lines, taking into account voltage safety and stability, includes: One or more processors; Memory, used to store one or more computer programs; When one or more programs are executed by one or more processors, the one or more processors execute the method in Example 1.

[0067] Example 3: A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to perform the method in Example 1.

Claims

1. A method for optimizing the daily maintenance plan of power lines considering voltage safety and stability, characterized in that... Includes the following steps: S1. Under the premise of meeting the voltage safety and stability requirements and operation requirements of the power system, and with the goal of minimizing the unit operating cost and power line maintenance cost, construct a mathematical model for optimizing the day-ahead maintenance of power lines, including setting the objective function and its constraints. S2. Determine the transmission line model and admittance matrix, and then modify the admittance matrix using the branch addition method to obtain the line switching model based on the branch addition method. S3. Perform a phased solution to the line switching model, which includes three stages: generation and reduction of uncertain scenarios, mixed integer linear main problem and nonlinear subproblems. Output the final solution results and use the final solution results as the optimal daytime maintenance plan for power lines.

2. The method for optimizing the day-ahead maintenance plan of power lines considering voltage safety and stability according to claim 1, characterized in that: In S1, the objective function of the mathematical model for optimizing daytime maintenance of power lines is expressed as: （1）； In the formula, t is the time period index, T is the total number of time periods, and k is the power line index. This represents the total number of power lines. Let $t$ be the maintenance cost of power line $k$ during time period $t$. This represents the maintenance status of power line k during time period t. A value of 1 indicates no maintenance. A value of 0 indicates maintenance; g is the unit index. This represents the total number of generating units. Let g be the operating cost of unit g during time period t; The constraints of the mathematical model for optimizing daytime maintenance of power lines include maintenance status constraints, total maintenance time constraints, maintenance continuity constraints, maintenance start time constraints, maintenance resource constraints, power flow balance constraints, continuous power flow balance constraints, load margin constraints, safe operation constraints, unit output constraints, and unit ramping constraints.

3. The method for optimizing the day-ahead maintenance plan of power lines considering voltage safety and stability according to claim 2, characterized in that, Maintenance status constraints are represented as follows: （2）； In the formula, , These represent the earliest and latest times when power line k can be repaired; A collection of power lines that require maintenance; The total maintenance time constraint is expressed as follows: （3）； In the formula, Let K be the total maintenance time for power line k. Maintenance continuity constraints are expressed as follows: （4）； In the formula, , These represent the time intervals t+1 and t+1 for power line k. The maintenance status. Represents the time offset, used to describe the time period after time t. Each time period; The start time constraint for maintenance is expressed as follows: （5）； In the formula, Let be the state variable indicating when power line k begins maintenance. If power line k begins maintenance in time period t, then... It is 1 if it is true, otherwise it is 0; Maintenance resource constraints are represented as follows: （6）； In the formula, This represents the maximum number of lines that can be inspected simultaneously within time period t. The load margin constraint is expressed as: （7）； In the formula, This represents the load margin of the power system in time period t under scenario s; This refers to the load margin threshold requirement for the power system during time period t. Safe operation constraints are expressed as follows: （8）； （9）； （10）； In the formula, Let be the voltage amplitude of node i at the power flow point in scenario s during time period t; , These are the upper and lower limits of the voltage amplitude at node i, respectively, at the power flow operation point; Let be the voltage phase angle difference between node i and node j at the power flow operation point in scenario s during time period t; , These are the upper and lower limits of the phase angle difference between nodes ij at the power flow operation point, respectively. , These represent the apparent power and its upper limit of line ij at the power flow operating point, respectively.

4. The method for optimizing the day-ahead maintenance plan of power lines considering voltage safety and stability according to claim 3, characterized in that, In S2, determining the transmission line model and admittance matrix includes the following steps: S2.1 Establishing a transmission line model: using The admittance of line ij in the equivalent circuit of type ij Half of the susceptance of the ground branch of line ij Connected in parallel with an ideal transformer, the tap ratio is Phase shift angle is The ideal transformer is located at the beginning of line ij; S2.

2. Taking power line k as branch k, its corresponding branch admittance matrix. Represented as: （11）； In the formula, , These are the self-admittances at the beginning and end of branch k, respectively; The mutual admittance between the beginning and end of branch k; The mutual admittance between the end and beginning of branch k; S2.3 Construct the admittance matrix of the power system based on the branch admittance. , represented as: （12）； （13）； （14）； In the formula, , These are the branch admittance matrices at the beginning and end of the line, respectively; and for 3D sparse connectivity matrix This represents the total number of power grid nodes. Add a matrix to the ground susceptance; , These are the self-admittances at the beginning and end of the line, respectively; The mutual admittance between the beginning and end of the line; It is the mutual admittance between the end and the beginning of the line.

5. The method for optimizing the day-ahead maintenance plan of power lines considering voltage safety and stability according to claim 4, characterized in that, In S2, the method of modifying the admittance matrix using the branch addition method is as follows: The essence of disconnecting branch k in time period t is to change the elements in the original admittance matrix of branch k in time period t. and , for The conductivity component, for The susceptance component, therefore, the admittance matrix of the power system after branch k is interrupted in time period t. The original admittance matrix branch admittance change matrix over time period t The sum is expressed as: （15）； When branch k is interrupted during time period t Represented as: （16）； In the formula, Let J be the node-branch incidence matrix, which has only two non-zero elements, 1 and -1, where 1 represents the position of the starting node i of branch k and -1 represents the position of the ending node k of branch k; J represents the imaginary unit. Let i be the position vector of the starting node i of branch k. Let be the position vector of the terminal node j of branch k; diag represents the diagonal matrix.

6. The method for optimizing the day-ahead maintenance plan of power lines considering voltage safety and stability according to claim 5, characterized in that, In S3, the generation and reduction of uncertain scenarios specifically refers to the joint scenario set for time period t. It is a collection of renewable energy scenarios With load scenario set The Cartesian product, i.e.: （17）； In the formula, for Elements in; for Elements in; A clustering method using the distance between operating points and load margins between scenarios as an indicator is used to reduce the generated renewable energy scenarios, resulting in representative typical uncertain scenarios.

7. The method for optimizing the day-ahead maintenance plan of power lines considering voltage safety and stability according to claim 6, characterized in that, In S3, the mathematical model for the mixed-integer linear master problem is as follows: （18）； In the formula, The estimated value for the subproblem; , These are equality constraints and inequality constraints concerning the variables, respectively. , , respectively, are the Jacobian matrices for equality constraints and inequality constraints; x is the system state variable; u is the system control variable; For load margin parameters; This refers to the system state variable corresponding to the point where the system voltage collapses. This refers to the load margin parameter corresponding to the system voltage collapse point. M represents the system control variable corresponding to the point where the system voltage collapses; M is the set of all maintenance lines and time periods under the current maintenance plan. Let M be the cardinality of set M; Y is the maintenance status vector of the current decision; The solution to the main problem is a certain line maintenance plan; for Operating costs below; for right The gradient; According to the route switching model construction strategy based on the branch addition method, the changes in control variables are encapsulated in the admittance matrix. Therefore, the changes in control variables are equivalently transformed into changes in the admittance matrix. After the transformation, the original mixed integer nonlinear programming problem becomes a convex optimization problem.

8. The method for optimizing the day-ahead maintenance plan of power lines considering voltage safety and stability according to claim 7, characterized in that, In S3, the mathematical model of the nonlinear subproblem is as follows: （19）； When a subproblem is infeasible under the current maintenance plan, a feasible cut constraint is constructed to exclude the maintenance plan, expressed as: （20）。 9. The method for optimizing the day-ahead maintenance plan of power lines considering voltage safety and stability according to claim 8, characterized in that, In S3, the following formula is used to approximate the relationship between operating costs and the maintenance variables of the main problem: （21）； The subproblem feeds the generated Benders cut back to the main problem, and the cut generated in each iteration needs to be added to the constraints of the main problem. When the maximum number of iterations is reached or the convergence condition is met, no new Benders cut is generated, and the computation ends. The convergence condition is expressed as: （22）； In the formula, for corresponding ; The value passed to the main problem; The optimality criterion is set.

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