A power grid maintenance plan optimization method and system based on Benders decomposition
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NARI INFORMATION & COMM TECH
- Filing Date
- 2026-05-22
- Publication Date
- 2026-06-19
Smart Images
Figure CN122243476A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power grid maintenance technology, and in particular to a method and system for optimizing power grid maintenance plans based on Benders decomposition. Background Technology
[0002] In power system operation and management, the formulation of annual maintenance plans is a crucial and extremely complex periodic task. This work requires the overall planning and coordination of maintenance tasks for hundreds or even thousands of transmission and transformation equipment in the power grid throughout the year. Any maintenance activity essentially involves temporarily taking some power equipment out of operation, which directly alters the topology and power flow distribution of the power grid, potentially introducing new risks to the safe and stable operation of the system.
[0003] In the power industry, the traditional method for developing power grid maintenance plans combines manual experience with offline simulation verification. First, experienced dispatching or planning engineers manually draft an annual maintenance plan based on relevant regulations and their personal judgment. This draft is then submitted to a specialized analysis department, where analysts use professional power system simulation software to perform power flow calculations and N-1 safety checks on the daily operation modes outlined in the draft. If any potential risks are discovered during the verification process (such as power flow exceeding limits or voltage non-compliance), the analysis report is returned to the planning engineer for modification and adjustment, and the plan is resubmitted for another round of verification. This process is repeated until the plan passes all checks. In this approach, the planning stage, responsible for combinatorial optimization (primarily relying on manual experience), is disconnected from the simulation analysis stage, responsible for physical safety verification. This creates a time-consuming and inefficient trial-and-error feedback loop, where a complete annual plan development cycle can take weeks or even months, resulting in extremely low planning efficiency. At the same time, due to time and energy constraints, the number of solutions that can be fully verified is very limited, and the quality of the final solution is highly dependent on the engineer's personal experience and knowledge level, far from guaranteeing its global optimality.
[0004] Current power grid maintenance planning also employs heuristic or metaheuristic algorithms, mixed-integer linear programming (MILP), and other intelligent algorithms to improve planning efficiency. Heuristic algorithms abstract the maintenance planning problem into a combinatorial optimization problem, searching for optimal solutions by simulating processes such as biological evolution or physical annealing. During the iterative search process, a series of candidate maintenance plans are generated, and the merits of each plan are evaluated using a pre-defined "fitness function." This fitness function is typically a weighted sum of penalty terms for violating various constraints and planned cost terms. However, this method is essentially a probabilistic randomized search, exploring the solution space and failing to guarantee a systematic coverage and evaluation of the entire solution space, resulting in the power grid's economic efficiency and reliability not reaching the theoretically optimal level. The MILP method unifies the entire maintenance planning problem into a large-scale MILP model. This method requires linearizing the nonlinear power flow equations describing the power grid's physical characteristics. Among these, the most widely used approximation method is the DC power flow model. This model simplifies the complex power flow equations into a set of linear equations by idealizing the assumptions that reactive power and network losses are ignored and that the voltage amplitude at all nodes is constant at 1.0 per unit. However, if DC power flow is used throughout the formal solution phase of safety verification, the inherent limitations of the DC power flow model (ignoring voltage and reactive power) prevent it from reflecting the actual grid voltage distribution and reactive power flow. Therefore, safety assessments based on this model cannot predict or detect critical safety issues such as voltage exceeding limits and insufficient reactive power support caused by maintenance, leading to model distortion. A plan deemed safe under the simplified DC power flow model may, in actual physical power grid operation, cause serious voltage stability problems or even voltage collapse. Summary of the Invention
[0005] Purpose of the invention: The purpose of this invention is to provide a method and system for optimizing power grid maintenance plans based on Benders decomposition, so as to achieve global optimization of the maintenance plan among all feasible solutions, while satisfying the safety of physical operation and the efficiency of the calculation process.
[0006] Technical solution: The present invention provides a method for optimizing power grid maintenance plans based on Benders decomposition, comprising the following steps:
[0007] Obtain the original maintenance plan for power grid equipment, and establish the objective function of the main problem and the objective functions of the sub-problems. The objective function of the main problem is to minimize the operational risk, lost load, and plan offset cost, and the objective function of the sub-problems is to minimize the operational risk and lost load.
[0008] The objective functions of the main problem and sub-problems are solved using the Benders decomposition algorithm to obtain an optimized power grid maintenance plan. During the solution process, the sub-problems solve for the optimal cuts of operational risk and loss load corresponding to the candidate maintenance schemes given by the main problem, and add them to the constraints of the main problem.
[0009] Furthermore, during the solution process, candidate maintenance schemes are obtained by solving the objective function of the main problem. For each time unit in the candidate maintenance scheme, a sub-problem objective function is constructed. All sub-problem objective functions are solved in parallel to obtain the operating risk value and the loss load. Based on the solution results of all sub-problem objective functions, the optimal cut for operating risk and the optimal cut for loss load are generated.
[0010] Furthermore, if the candidate maintenance plan is not feasible, a feasibility cut of the candidate maintenance plan is generated, and the generation of the candidate maintenance plan is prohibited in the constraints of the main problem.
[0011] The candidate maintenance plan is infeasible if any one of the following exceeds its preset range: load shedding, power flow over-limit relaxation, power over-limit relaxation, or voltage over-limit relaxation.
[0012] Furthermore, the constraints of the main problem include the uniqueness constraint of the planned schedule, the correlation constraint of equipment maintenance status, the constraint of equipment shut down together, the constraint of mutually exclusive equipment, the joint carrying capacity constraint of the plant-work team, and the constraint of maintenance sequence.
[0013] Furthermore, the constraints of the sub-problems include power flow constraints and security constraints.
[0014] Furthermore, solving the objective function of the main problem and the objective functions of the subproblems using the Benders decomposition algorithm includes the following steps:
[0015] Step 1: Initialize the global upper bound and global lower bound of the objective function of the main problem to positive infinity and negative infinity, respectively;
[0016] Step 2: Solve the objective function of the main problem to obtain candidate maintenance schemes, and update the global lower bound based on the function value of the objective function of the main problem;
[0017] Step 3: Establish sub-problem objective functions for each time unit, solve the sub-problem objective functions in each time unit in parallel, and obtain the operational risk value and loss load of that time unit;
[0018] The total operational risk value and loss load for the planning period are obtained by summing the operational risk value and loss load for each time unit, and the global upper bound is updated based on the total operational risk value and loss load.
[0019] Step 4, perform a convergence check: If the algorithm converges, terminate the iteration and output the current optimal maintenance plan; otherwise, generate and add the optimal cut for running risk and the optimal cut for loss load or the feasible cut to the main problem, increment the iteration counter by 1, and return to step 2 to execute the next iteration; when the number of iterations exceeds the preset maximum value, the algorithm will be forcibly terminated regardless of whether it has converged, and the maintenance plan corresponding to the current upper bound will be output.
[0020] Furthermore, the planned offset cost is the absolute value of the time offset, which is the offset between the actual start time of the maintenance plan and the original time.
[0021] Furthermore, the operational risk is the sum of risks under normal operation and all N-1 scenarios, and the risks include load shedding costs, overload risk of grid branches, and voltage limit exceedance risk of grid bus.
[0022] The lost load is the sum of the load shedding amount under normal operation and all N-1 scenarios.
[0023] Furthermore, the optimal cut for operational risk is defined as follows:
[0024]
[0025] in, To mitigate operational risks, The minimum risk value obtained for the subproblem. These are candidate maintenance plans. The maintenance plan decision variables in the main problem. for The derivative of operational risk, where the subscript 'e' represents equipment and the subscript 't' represents time. It is a collection of equipment; , The device e is to be inspected on day t.
[0026] The optimal cut for the loss load is:
[0027]
[0028] in, To reduce load, The minimum loss load obtained for the subproblem. for The derivative with respect to the loss load.
[0029] The present invention discloses a power grid maintenance plan optimization system based on Benders decomposition, comprising:
[0030] The main problem module is used to obtain the original maintenance plan of the power grid equipment and establish the main problem objective function, which is to minimize the operating risk, lost load and plan offset cost.
[0031] The sub-problem module is used to obtain the original maintenance plan of the power grid equipment and establish the objective function of the sub-problem, which is to minimize the operating risk and lost load;
[0032] The solution module is used to solve the objective function of the main problem and the objective function of the subproblems using the Benders decomposition algorithm to obtain an optimized power grid maintenance plan. During the solution process, the subproblems solve for the optimal cut of operational risk and optimal cut of loss load corresponding to the candidate maintenance schemes given by the main problem, and add the constraints to the main problem.
[0033] The electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the power grid maintenance plan optimization method based on Benders decomposition.
[0034] The computer-readable storage medium of the present invention stores a computer program, which, when executed by a processor, implements the power grid maintenance plan optimization method based on Benders decomposition.
[0035] The computer program product of the present invention includes a computer program that, when executed by a processor, implements the power grid maintenance plan optimization method based on Benders decomposition.
[0036] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows:
[0037] (1) In the algorithm iteration process of this invention, the main problem provides an increasing global lower bound (LB), while the evaluation of the subproblems provides a decreasing global upper bound (UB). The algorithm theoretically guarantees that the upper and lower bounds will eventually converge to a point. Unlike heuristic algorithms, which can only obtain a "satisfactory solution" whose quality cannot be determined, this invention can mathematically guarantee that the final maintenance plan is the globally optimal solution among all feasible solutions, thereby reducing the overall cost and risk of power grid operation to the lowest theoretical level.
[0038] (2) In terms of time dimension, this invention decomposes a year-long, strongly coupled optimization problem into 365 independent daily safety verification sub-problems, enabling the computational tasks of the sub-problems to be distributed across multiple computing cores or server nodes for large-scale parallel computation. It is applicable to the annual planning of provincial and even higher-level power grids that include a large number of equipment and maintenance plans, and has extremely high engineering practical value.
[0039] (3) This invention mathematically decouples the main problem responsible for combinatorial optimization and logical decision-making from the sub-problems responsible for power grid physical simulation. When business requirements or constraints change, only the linear main problem model needs to be modified. When the power grid model is updated or safety standards are improved, only the sub-problems need to be adjusted, while the main problem remains unchanged. This clear modular architecture makes system maintenance, upgrades, and functional expansion extremely convenient, and has stronger engineering robustness and a longer technical life cycle.
[0040] (4) In the formal iterative solution stage of the sub-problem responsible for evaluating safety, this invention uses an AC power flow model that can accurately describe key physical characteristics such as grid voltage and reactive power as the core safety verification method; in the rapid pre-screening stage at the beginning of the algorithm, DC power flow can be flexibly selected to improve the overall computational efficiency. This phased strategy ensures the physical feasibility of the final solution while taking into account the computational speed requirements of engineering practice. Any candidate solution that may cause safety risks such as voltage exceeding limits and power flow overload in the real power grid will be accurately identified in the high-fidelity verification of the sub-problem. Its risk will be quantified and fed back to the main problem by generating corresponding Benders cuts (optimality cuts or feasibility cuts), thereby penalizing or directly eliminating the solution. Compared with the solution using simplified models such as DC power flow, this invention significantly bridges the gap between the optimization model and physical reality. Its output plan is not only mathematically optimal, but also physically feasible and highly safe, possessing the prerequisites for direct application in engineering practice. Attached Figure Description
[0041] Figure 1 This is an implementation architecture diagram of the power grid maintenance plan optimization method according to an embodiment of the present invention.
[0042] Figure 2 This is a flowchart of the power grid maintenance plan optimization method according to an embodiment of the present invention.
[0043] Figure 3 The parallel computing mode architecture diagram of this invention embodiment. Detailed Implementation
[0044] Optimizing the annual maintenance plan for a power grid is a complex multi-objective, multi-constraint combinatorial optimization problem. It requires rationally arranging the annual equipment maintenance plan while ensuring the safe operation of the power grid. The power grid maintenance plan optimization of this invention needs to balance the following objectives:
[0045] a) Minimize operational risks: Avoid equipment overload, voltage exceeding limits, and failure to meet N-1 safety requirements;
[0046] b) Minimize plan changes: Reduce adjustments to existing plans and lower coordination costs;
[0047] c) Minimize load loss: Reduce load loss;
[0048] d) Meet resource constraints: plant capacity, team manpower, power supply requirements, etc.
[0049] Solving this problem presents challenges such as an explosion in the number of decision variables, nonlinear power flow equations, and the need to assess a large number of fault scenarios for N-1 safety verification. Furthermore, the multi-level coupling between maintenance plans, equipment status, and power grid operation status further increases the difficulty of solving the problem.
[0050] like Figure 1 As shown, to overcome the challenges and achieve the above objectives, this invention adopts an overall architecture of mixed-integer nonlinear programming (MINLP) and Benders decomposition, decomposing the power grid maintenance plan optimization problem into a "scheduling master problem" and a "safety verification subproblem," and utilizing the iterative feedback mechanism between the two to achieve intelligent and efficient solution to the problem. The master problem uses mixed-integer linear programming (MILP) to determine the maintenance schedule, while the subproblems use nonlinear programming (NLP) or quadratic programming (QP) to assess power grid safety and operational risks. The modeling of the master problem and subproblems is described in detail below.
[0051] (I) Modeling the main problem
[0052] The basic sets used in the main problem include: the maintenance plan set. , In this embodiment Equipment collection , In this embodiment Time period set (sky), Factory and station collection , Team assembly , .
[0053] The derived set used in the main problem includes: maintenance plan. Included device set Maintenance Plan Allowed start time set Factory Station Included device set Assigned to factories and stations and work group Maintenance plan collection ; Same-stop equipment group collection , Mutual exclusion device set , ; Paired constraint set of connecting lines , Power supply guarantee period (Date set); Power supply equipment set Maintenance sequence constraint set ,in Indicates device Maintenance must be carried out on the equipment At least before maintenance begins Completed in one day.
[0054] The planning parameters used in the main problem include: planning The original start time ;plan Total duration (day); equipment In the plan Number of days offset from the relative start time ;equipment In the plan Maintenance duration (day); plan Is it fixed? 1 indicates that it cannot be changed.
[0055] The resource and constraint parameters used in the main problem include: plant and station work group Maximum number of maintenance plans that can be carried out simultaneously .
[0056] The main decision variables in the main problem are and .in If the plan In the From the beginning of the heavens, then Otherwise, it is 0. If the equipment In the If the sky is under maintenance, then Otherwise, it is 0.
[0057] The main problem also includes auxiliary variables. , , , , and .in, Indicates plan The offset between the actual start time and the original time (can be positive or negative). ; yes The absolute value, ; It is the same group In the The daily maintenance status indicator variable. ; , It is equipment The start and end times of the maintenance. ; It is the first The estimated operational risk for each day (determined by Benders cut from the subproblems). ; It is the first Daily loss load estimate (determined by Benders cut from subproblems, unit: MW). .
[0058] The objective function of the main problem is:
[0059]
[0060] The first item is the total operational risk, which is assessed by sub-problems and approximated by cutting; the second item is the total planned offset cost, which aims to reduce changes to the original plan; and the third item is the total lost load, which aims to minimize the load loss caused by grid maintenance. This is the risk item weight (for example, it can be 1000); This is the weight of the planned offset item (for example, it can be set to 1); This is the weight of the loss load item (for example, it can be set to 100).
[0061] The constraints of the main problem include simultaneous shutdown, mutual exclusion, load-bearing capacity, power supply, maintenance sequence, and feasible cutting, which will be introduced below.
[0062] (1.1) Uniqueness constraint of the schedule (C1): Each maintenance schedule must have one and only one start time:
[0063]
[0064] Among them, if the plan There is a window period ,but If the plan fixed( ),but .
[0065] (1.2) Equipment maintenance status association constraint (C2), which associates the equipment maintenance status with the planned start time:
[0066]
[0067] Among them, when the plan exist At the start of time ,equipment The maintenance time window is Every day within this window , .
[0068] (1.3) Constraints on equipment shutting down simultaneously (C3): Equipment within the same shutdown group must be inspected or not inspected simultaneously:
[0069]
[0070]
[0071] (1.4) Mutual exclusion device constraint (C4): Within a mutual exclusion group, a maximum of one device can be repaired per day.
[0072]
[0073] (1.5) Joint bearing capacity constraint of plant and work team (C5):
[0074]
[0075] (1.6) Tie line constraint (C6): The 220kV bus / main transformer and each of its associated 110kV tie lines cannot be inspected on the same day:
[0076]
[0077] (1.7) Power supply protection constraint (C7): Power supply protection equipment cannot be repaired during the power supply protection period.
[0078]
[0079] (1.8) Maintenance sequence constraint (C8):
[0080]
[0081] The start / end times are derived from the initial variables of the plan:
[0082]
[0083]
[0084] (1.9) Calculation of time offset (C9):
[0085]
[0086] (1.10) Absolute value linearization (C10):
[0087]
[0088]
[0089] (1.11) Benders cut constraint, dynamically added during iteration:
[0090] When a subproblem detects that a candidate maintenance plan is infeasible, add a feasibility cut (C11):
[0091]
[0092] When a candidate maintenance plan is found to be feasible in a subproblem, add the operational risk optimality cut (C12) and the loss load optimality cut (C13).
[0093] Optimal cut for operational risk:
[0094]
[0095] Loss load optimality cut:
[0096]
[0097] Based on the above constraints, the complete form of the main problem is:
[0098]
[0099] (ii) Sub-problem modeling
[0100] Based on the candidate maintenance solutions given by the main problem For each time period within the planning period Construct a separate safety verification subproblem, the input of which is the maintenance plan given by the main problem. The output includes data for each day. Feasibility status Operational risk values Loss load (Unit: MW), Benders cut (feasibility cut, risk-optimal cut, and loss-load-optimal cut).
[0101] The set of power grid topologies used in the single-day problem includes: the set of buses (nodes). , In this embodiment Branch circuit (line / transformer) collection , ;No. Tianxian's branch collection Generator set , ; Load node set , .
[0102] The set of topological relationships used in the single-day problem includes: from nodes Outflowing branch set ; Inflow node branch set ;node generator set ;node load set .
[0103] The set of N-1 scenarios used in the single-day problem includes: The N-1 scenario set that needs to be verified each day , ,in It is the set of critical equipment (N-1 is usually not considered).
[0104] The parameters used in the single-day problem include grid topology parameters, operating constraint parameters, generation and load parameters, and risk weight parameters.
[0105] Power grid topology parameters include: branches electrical conductivity and susceptance (per unit value) busbar Earth-to-ground susceptance ;transformer The ratio of .
[0106] Operating limitation parameters include: branch upper limit of active power upper limit of reactive power (MW,MVar) branch road Apparent power limit (MVA); Busbar upper limit of voltage amplitude Lower limit (pu), branch road Maximum allowable phase angle difference .
[0107] Power generation and load parameters include: generator upper limit of active power output Lower limit (MW) ;dynamo upper limit of reactive power output Lower limit (MVar) ;load Predicted active power demand reactive power demand (MW,MVar) ;load load shedding cost (RMB / MWh); Rescheduling ramp limit for generators in the N-1 scenario (MW).
[0108] Risk weight parameters include: branch Overload risk weight busbar Voltage over-limit risk weight Penalty coefficient for N-1 not satisfied Penalty coefficient for slack variables (For example, it can take the value of) ); DC line breaking Big-M constant , used for (S0b-DC)-(S0c-DC).
[0109] The decision variables in the single-day problem include grid state variables (continuous) and slack variables used for feasibility repair.
[0110] Power grid state variables include: busbars voltage amplitude (pu); busbar phase angle (rad); branch The meritorious trend and the trend of no effort (MW, MVar); Generator Contributing to the cause and doing nothing (MW,MVar).
[0111] Slack variables include: load load shearing (MW); branch road Positive slack quantity exceeding the limit of active current flow negative relaxation amount (MW); branch road Relaxation amount when power exceeds limit (MVA); Busbar Positive relaxation amount when voltage exceeds limit negative relaxation amount (pu).
[0112] The constraints of the single-day problem include basic power flow constraints and safety constraints with relaxation, which will be introduced separately below.
[0113] (2.1) Equipment availability and line interruption (DC model) (S0-DC)
[0114] make Indicates a branch Availability, of which To the side road The corresponding device. Big-M linearization is used to achieve... During maintenance shutdown, the angle-power flow coupling is released, and the power flow is forced to zero.
[0115] (S0a-DC)
[0116] (S0b-DC)
[0117] (S0c-DC)
[0118] when When the device is online, (S0b-DC)-(S0c-DC) forced ;when At that time, relax the above formula and (S0a-DC) make .
[0119] (2.2) Node power balance constraints
[0120] Active power balance:
[0121] (S1)
[0122] Reactive power balance:
[0123] (S2)
[0124] (2.3) Branch power flow equations (S3)
[0125] Option A: DC power flow approximation (linear model, suitable for initial implementation)
[0126] Assuming the voltage amplitude is close to 1 p.u. and the phase angle difference is very small, And ignore reactive power and network losses:
[0127] (S3-DC)
[0128] If (S0-DC) line availability gating is used, then (S3-DC) in The time is automatically implicit by (S0b-DC)-(S0c-DC), and it does not need to be applied again to avoid redundancy.
[0129] Option B: AC power flow (non-linear model, higher accuracy)
[0130] (S3-AC)
[0131] in, .
[0132] Option C: Second-order cone relaxation (convex approximation, balancing accuracy and solution speed)
[0133] Introduce auxiliary variables: , , .
[0134] The constraints are:
[0135] (S3-SOCP)
[0136] (2.4) Generator output constraints
[0137] (S4)
[0138] (S5)
[0139] (2.5) Branch flow restriction
[0140] Active power constraints:
[0141] (S6)
[0142] Apparent power constraint:
[0143] (S7)
[0144] Linearization approximation (applicable to MILP solvers):
[0145]
[0146] (2.6) Bus voltage limitation
[0147] (S8)
[0148] (2.7) Load shedding constraint
[0149] (S9)
[0150] In the single-day problem, for each of the N-1 scenarios that need to be verified (i.e., assuming a certain line) (Disconnection) requires solving a separate power flow optimization problem to assess the grid's safety after the fault. The decision variables in the N-1 safety verification model are indicated by superscripts. To distinguish between scenarios, such as And so on. The objective function for scenario N-1 is established based on minimizing control costs and default amounts:
[0151]
[0152] The constraints of the N-1 scenario include power flow equations and safety constraints ((S0-DC)-(S9)), but are applied to the scenario... Variables; also include zero power flow on the fault line: And generator rescheduling restrictions: This limits the speed at which the generator output adjusts after a fault.
[0153] For a given maintenance plan The objective of the sub-problem requires simultaneously assessing operational risk and calculating loss load. The methods for calculating operational risk and loss load are described below.
[0154] (a) Operational risk assessment
[0155] No. Daily operational risks It is defined as the sum of risks under normal operation (N-0) and all N-1 scenarios.
[0156]
[0157] The N-0 risk is:
[0158]
[0159] The N-1 risk is:
[0160]
[0161] In the main problem The estimation objects are related as follows: the subproblem forces the main problem to undergo risk optimality cuts. Gradually approaching reality That is, at the optimal solution .
[0162] (b) Loss load calculation
[0163] This embodiment provides two methods for calculating load loss: power loss (MW) and energy loss (MWh, also known as EENS, Expected Energy Not Served).
[0164] First, determine the intraday time resolution and define the intraday time index. (e.g., hourly) ), time step is (Hours); Perform time-based load forecasting. ,in For load nodes In the The load distribution factor for a given period (i.e., the proportion of the load during that period to the total daily load) satisfies the normalization condition. (in hours).
[0165] The load shedding variable is denoted by time period as follows: (N-0) and (Scene) ).
[0166] make Therefore, the power loss load (instantaneous, MW) is: , The energy loss load (EENS, MWh) is: , .
[0167] Power loss loads can be aggregated using expected, worst-case, or CVaR methods depending on the scenario.
[0168] Expected type (with probability weights): Given and , ;
[0169] Worst-case scenario: ;
[0170] CVaR (Robust): Define variables , , ; ;
[0171] Auxiliary variables , satisfy , ; The confidence level (e.g., 0.95).
[0172] In practical engineering, if we want to balance robustness and efficiency, we can use CVaR or expected type (when the mandatory N-1 is the main factor, the worst case is often used for verification).
[0173] In this embodiment, the main problem is... The unit is MW, therefore a power-type loss load is adopted. ,in Optional weights (e.g., take) Or all 1); at the optimal solution of the subproblem, the scalar value calculated by the above formula is denoted as (i.e., the main problem of loss load cut C13) This is fed back to the main problem, and the sensitivity is calculated accordingly. Generate the loss load optimality cut according to C13. That is, the estimated variables in the main problem. via C13 Approaching from below.
[0174] If the target metric is desired to be energy (MWh), an energy-type interface variable can be introduced. The corresponding weight in the main problem objective is adjusted to "cost per MWh" (this is an optional extension and does not affect other modeling steps). It is defined as follows: (i.e., the power loss load calculated using one of the three aggregation methods, in MWh), and the corresponding weights in the main problem objective. The unit of measurement is adjusted to cost per MWh (yuan / MWh).
[0175] Furthermore, if intraday resolution is not enabled for the time being, it can be made For example, the peak of the day. The above definition naturally degenerates into the original "single time period, MW" version to maintain backward compatibility.
[0176] When solving the objective function of a single-day problem, a "lexicographical" or "two-stage" calculation can be used: first minimize the load shedding (EENS or peak), then minimize the remaining relaxations; or first find the minimum risk solution, then fix / re-optimize EENS and peak values near that solution to generate the target function. Related cutting and sensitivity.
[0177] The results of solving the subproblems are used to generate the cutting planes that are fed back to the main problem. If the subproblems are feasible (i.e. all slack variables are 0 or within an acceptable range), then two types of optimal cuts are generated: the operational risk optimal cut and the loss load optimal cut.
[0178] Risk-optimal cut:
[0179]
[0180] in, It is the minimum risk value obtained from the subproblem. This is the current troubleshooting plan that was passed on from the main problem. It is under maintenance. The derivative with respect to risk (shadow price).
[0181] Loss load optimality cut:
[0182]
[0183] in, The minimum loss load amount is obtained by solving a subproblem. It is under maintenance. The derivative with respect to lost loads (shadow price).
[0184] These derivatives represent the device In the The maintenance status of the day from Become At that time, the marginal impact on the corresponding objective function. Because These are binary variables, and their derivatives are typically approximated by solving perturbation problems or using Lagrange duality.
[0185] If the subproblem is infeasible (even with the introduction of slack variables, the objective function value is still huge, exceeding a certain threshold). This indicates the current maintenance team. This is physically unacceptable. In this case, it is necessary to find the minimum set of conflicts that makes it infeasible. Then generate a feasible cut to prevent this combination from occurring again.
[0186] Feasibility of cutting:
[0187]
[0188] The meaning of this cut is that, in the set of devices that cause a conflict, at least one device must not be arranged in the first position. Daily maintenance. Finding the minimum conflict set is itself an NP-hard problem, and in practice, heuristics are often used, such as starting the set from the devices that cause the maximum default.
[0189] like Figure 2 As shown, the steps for solving the objective function of the main problem and the objective functions of the subproblems using the Benders decomposition algorithm are as follows:
[0190] Step S1, Initialize the upper bound The lower realm The global upper bound of the cost of the best solution found so far is set to positive infinity, indicating that no feasible solution has been found yet, while the global lower bound of the theoretically lowest possible cost is set to negative infinity, indicating that the exploration has not yet begun.
[0191] Set convergence tolerance (For example The main problem is initialized, without any Benders cuts. An iteration counter is used. .
[0192] Step S2: Solve the main problem to obtain a new maintenance plan. and a target value Update the Nether .
[0193] Step S3, feedback on the main issue At every time Construct independent sub-problem objective functions and perform safety checks for each sub-problem (daily). ):
[0194] Solve for N-0 power flow optimization, calculate and ;
[0195] For each N-1 scenario Parallel solution of power flow optimization, computation and ;
[0196] The total risk and loss load for the day is calculated as follows:
[0197]
[0198]
[0199] At the same time, calculate the total amount for the entire cycle:
[0200]
[0201]
[0202] Update Upper Realm .
[0203] Step S4, perform a convergence check, if If the algorithm converges, the current optimal solution is the one that leads to... If the maintenance plan is not met, the algorithm terminates. Otherwise, proceed to step S5.
[0204] Step S5: Generate the cutting plane. For each time period... If the subproblem If it is not feasible, generate and add a feasible cut to the main problem; if the subproblem is not feasible, generate a feasible cut to the main problem. It is feasible to generate and add runtime risk optimality cut and loss load optimality cut to the main problem;
[0205] Increase the iteration counter .
[0206] Step S6: Return to step S2 and begin the next iteration until the termination condition is met. Or, it may reach the maximum number of iterations.
[0207] In the Benders decomposition algorithm described above, the sub-problems of each day are completely independent and can be distributed across different computing nodes or CPU cores for parallel processing. Within each day's sub-problem, the verification of the N-1 scenario is also independent and can be computed in parallel again. However, with iteration, the number of Benders cuts increases, slowing down the solution of the main problem. Therefore, this invention only retains "active" cuts (i.e., cuts that were effective in the most recent solution of the main problem) and periodically removes invalid or redundant cuts. Figure 3 The diagram shows the parallel computing architecture of this embodiment. The main problem solver sends the candidate maintenance plan for the kth round to the task dispatcher. Based on the candidate maintenance plan, the task dispatcher distributes the sub-problems of each day to the parallel computing nodes for security verification. The sub-problem result set is sent to the coordinator to generate and construct the Benders cut. Finally, a Benders cut set is added to the main problem solver as a constraint, and the next round of iteration is executed.
[0208] Furthermore, in the process of solving the Benders decomposition algorithm described above, the main problem is solved using commercial solvers such as Gurobi and CPLEX, while the subproblems are solved using IPOPT, KNITRO (for NLP) or Gurobi and CPLEX (for QP / SOCP).
[0209] Furthermore, this embodiment employs a phased power flow model strategy: in the initial iteration phase of the algorithm, DC power flow (linear) is used for rapid pre-screening to greatly accelerate the solution speed of subproblems and quickly identify critical N-1 scenarios; in the formal iteration solution phase, the algorithm switches to AC power flow (nonlinear, i.e., scheme B) or SOCP relaxation approximation (scheme C) for high-fidelity safety verification to ensure that the final output maintenance scheme is physically feasible. In addition, since not all N-1 faults will have serious consequences, "critical N-1 scenarios" that may cause problems can be identified in advance using a fast screening algorithm (such as PTDF - power transfer distribution factor), and only these scenarios are thoroughly verified.
[0210] Furthermore, in the process of solving the Benders decomposition algorithm described above, this embodiment adopts a warm-start approach. When solving the main problem, the solution of the previous iteration is used as the initial solution for the next iteration. For two consecutive days, the power grid state does not change much, and when solving the sub-problems, the solution of the previous day is used as the initial solution for the next day.
[0211] The present invention discloses a power grid maintenance plan optimization system based on Benders decomposition, comprising:
[0212] The main problem module is used to obtain the original maintenance plan of the power grid equipment and establish the main problem objective function, which is to minimize the operating risk, lost load and plan offset cost.
[0213] The sub-problem module is used to obtain the original maintenance plan of the power grid equipment and establish the objective function of the sub-problem, which is to minimize the operating risk and lost load;
[0214] The solution module is used to solve the objective function of the main problem and the objective function of the subproblems using the Benders decomposition algorithm to obtain an optimized power grid maintenance plan. During the solution process, the subproblems solve for the optimal cut of operational risk and optimal cut of loss load corresponding to the candidate maintenance schemes given by the main problem, and add the constraints to the main problem.
[0215] The electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the power grid maintenance plan optimization method based on Benders decomposition.
[0216] The computer-readable storage medium of the present invention stores a computer program, which, when executed by a processor, implements the power grid maintenance plan optimization method based on Benders decomposition.
[0217] The computer program product of the present invention includes a computer program that, when executed by a processor, implements the power grid maintenance plan optimization method based on Benders decomposition.
[0218] The computer-readable storage medium may include RAM, ROM, EEPROM, CD-ROM or other optical disc storage devices, magnetic disk storage devices or other magnetic storage devices, flash memory, or any other media that can be used to store program code in the form of instructions or data structures and is accessible by a computer.
[0219] The processor is used to execute a computer program stored in memory to implement the various steps in the methods described in the above embodiments.
Claims
1. A method for power grid maintenance scheduling optimization based on Benders decomposition, characterized in that, Includes the following steps: Obtain the original maintenance plan for power grid equipment, and establish the objective function of the main problem and the objective functions of the sub-problems. The objective function of the main problem is to minimize the operational risk, lost load, and plan offset cost, and the objective function of the sub-problems is to minimize the operational risk and lost load. The Benders decomposition algorithm is used to solve the objective function of the main problem and the objective functions of the sub-problems to obtain an optimized power grid maintenance plan. During the solution process, the subproblems solve for the optimal cuts of operational risk and loss load corresponding to the candidate maintenance schemes given by the main problem, and add constraints to the main problem.
2. The Benders decomposition based power grid maintenance schedule optimization method of claim 1, wherein, In the solution process, candidate maintenance schemes are obtained by solving the objective function of the main problem. For each time unit in the candidate maintenance scheme, a sub-problem objective function is constructed. All sub-problem objective functions are solved in parallel to obtain the operating risk value and the loss load. Based on the solution results of all sub-problem objective functions, the optimal cut for operating risk and the optimal cut for loss load are generated.
3. The power grid maintenance plan optimization method based on Benders decomposition according to claim 2, characterized in that, If the candidate maintenance plan is not feasible, then generate a feasibility cut of the candidate maintenance plan and prohibit the generation of the candidate maintenance plan in the constraints of the main problem. The candidate maintenance plan is infeasible if any one of the following exceeds its preset range: load shedding, power flow over-limit relaxation, power over-limit relaxation, or voltage over-limit relaxation.
4. The Benders decomposition based power grid maintenance schedule optimization method of claim 1, wherein, The constraints of the main problem include the uniqueness constraint of the planned schedule, the correlation constraint of equipment maintenance status, the constraint of equipment that is shut down at the same time, the constraint of mutually exclusive equipment, the joint carrying capacity constraint of the plant-work team, and the constraint of maintenance sequence.
5. The Benders decomposition based power grid maintenance schedule optimization method of claim 1, wherein, The constraints of the subproblems include power flow constraints and security constraints.
6. The Benders' decomposition based power network maintenance schedule optimization method of claim 3, wherein, Solving the objective function of the main problem and the objective functions of the subproblems using the Benders decomposition algorithm includes the following steps: Step 1: Initialize the global upper bound and global lower bound of the objective function of the main problem to positive infinity and negative infinity, respectively; Step 2: Solve the objective function of the main problem to obtain candidate maintenance schemes, and update the global lower bound based on the function value of the objective function of the main problem; Step 3: Establish sub-problem objective functions for each time unit, solve the sub-problem objective functions in each time unit in parallel, and obtain the operational risk value and loss load of that time unit; The total operational risk value and loss load for the planning period are obtained by summing the operational risk value and loss load for each time unit, and the global upper bound is updated based on the total operational risk value and loss load. Step 4, perform a convergence check: If the algorithm converges, terminate the iteration and output the current optimal maintenance plan; otherwise, generate and add the optimal cut for running risk and the optimal cut for loss load or the feasible cut to the main problem, increment the iteration counter by 1, and return to step 2 to execute the next iteration; when the number of iterations exceeds the preset maximum value, the algorithm will be forcibly terminated regardless of whether it has converged, and the maintenance plan corresponding to the current upper bound will be output.
7. The Benders decomposition based power grid maintenance schedule optimization method of claim 1, wherein, The planned offset cost is the absolute value of the time offset, which is the offset between the actual start time of the maintenance plan and the original time.
8. The Benders decomposition based power grid maintenance schedule optimization method of claim 1, wherein, The operational risk is the sum of the risks under normal operation and all N-1 scenarios. The risks include load shedding costs, overload risk of grid branches, and voltage limit exceedance risk of grid bus. The lost load is the sum of the load shedding amount under normal operation and all N-1 scenarios.
9. The Benders decomposition based power grid maintenance schedule optimization method of claim 1, wherein, The optimal cut for operational risk is: ； wherein, is the operating risk, is the minimum risk value found for the sub-problem, is a candidate maintenance scheme, is a maintenance scheme decision variable in the main problem, is the operating risk, is the derivative of the operating risk with respect to the maintenance scheme, subscript e represents the equipment, and subscript t represents the time, is the set of equipment; , represents that equipment e is maintained on day t. The optimal cut for the loss load is: ； in, To reduce load, The minimum loss load obtained for the subproblem. for The derivative with respect to the loss load.
10. A power grid maintenance plan optimization system based on Benders decomposition, characterized in that, include: The main problem module is used to obtain the original maintenance plan of the power grid equipment and establish the main problem objective function, which is to minimize the operating risk, lost load and plan offset cost. The sub-problem module is used to obtain the original maintenance plan of the power grid equipment and establish the objective function of the sub-problem, which is to minimize the operating risk and lost load; The solution module is used to solve the objective function of the main problem and the objective function of the sub-problems using the Benders decomposition algorithm to obtain an optimized power grid maintenance plan; During the solution process, the subproblems solve for the optimal cuts of operational risk and loss load corresponding to the candidate maintenance schemes given by the main problem, and add constraints to the main problem.
11. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the power grid maintenance plan optimization method based on Benders decomposition according to any one of claims 1-9.
12. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the power grid maintenance plan optimization method based on Benders decomposition according to any one of claims 1-9.
13. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the power grid maintenance plan optimization method based on Benders decomposition according to any one of claims 1-9.