Power grid system out-of-age equipment state maintenance collaborative optimization method

Abstract

The invention discloses a power grid system out-of-age equipment state maintenance collaborative optimization method, which comprises the following steps of: 1, based on stock data of an existing operation management system of a power grid, establishing a service age rollback driven risk correction model, and outputting an instantaneous failure rate after equipment maintenance and a failure probability in an evaluation period; 2, calculating the partition overtime risk density to form a high-density partition list; 3, unifying the partition over-age risk density and the over-age equipment treatment plan into matrix data; 4, establishing a linearization model of the influence of the treatment plan of the age-out equipment on the partition age-out risk; 5, setting a multi-objective function and a constraint condition for the linearized model; and 6, solving the model to realize collaborative balance of risk cost and constraint. The method is simple in step, can give consideration to a multi-cycle maintenance strategy of equipment service age rollback characteristics, a state evolution law and resource constraint optimization, improves the risk voltage drop efficiency, guarantees the operation safety and operation and maintenance economy of a power grid system, is good in use effect, and is convenient to popularize and use.

Description

Technical Field

[0001] This invention belongs to the field of power grid equipment operation and maintenance technology, specifically relating to a collaborative optimization method for condition-based maintenance of aging equipment in a power grid system. Background Technology

[0002] As the scale of power grid system assets continues to expand and the service life of equipment continues to increase, traditional maintenance strategies based on fixed cycles and fixed service life are gradually revealing problems of resource waste and lagging risk identification. Especially in the transmission and transformation system, there are a large number of outdated but not retired boundary equipment. Because these devices have exceeded their design lifespan, their health status fluctuates greatly, becoming an important source of potential risks to the power grid.

[0003] Existing technologies often rely on static failure probabilities or historical maintenance records for single-year strategy formulation, lacking modeling and analysis of dynamic evolution of service life and state regression phenomena. This makes it difficult to accurately depict the regularity of equipment performance recovery after maintenance. Furthermore, the lack of maintenance resource allocation and risk peak-shaving control mechanisms under multi-year rolling budget constraints leads to overall scheme imbalance and unstable pressure reduction effects, hindering the further promotion and implementation of intelligent maintenance strategies.

[0004] Therefore, it is urgent to construct a multi-cycle maintenance strategy model that takes into account the characteristics of equipment service life rollback, the law of state evolution, and resource constraint optimization, so as to improve risk reduction efficiency and ensure the operational safety and maintenance economy of the power grid system. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a collaborative optimization method for condition-based maintenance of aging equipment in power grid systems, which addresses the shortcomings of the prior art. The method has simple steps, can take into account the characteristics of equipment service life rollback, the law of condition evolution and resource constraint optimization of multi-cycle maintenance strategies, improves risk reduction efficiency, ensures the operational safety and maintenance economy of power grid systems, has good performance and is easy to promote and use.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a collaborative optimization method for condition-based maintenance of aging equipment in a power grid system, comprising the following steps:

[0007] Step 1: Based on the existing data of the power grid's existing operation and management system, establish a risk correction model driven by service life rollback, and output the instantaneous failure rate after equipment maintenance and the probability of failure during the assessment period.

[0008] Step 2: Calculate the over-age risk density of each zone to create a list of high-density zones;

[0009] Step 3: Unify the aging risk density and aging equipment disposal plan of the aforementioned zones into matrix data;

[0010] Step 4: Establish a linearized model of the impact of the over-aged equipment disposal plan on the risk of over-aged equipment in different zones;

[0011] Step 5: Set multi-objective functions and constraints for the linearized model;

[0012] Step 6: Solve the model to achieve a synergistic balance between risk and cost constraints.

[0013] The aforementioned collaborative optimization method for condition-based maintenance of aging equipment in a power grid system, specifically the process of establishing a risk correction model driven by service life rollback based on existing data from the power grid's existing operation and management system, and outputting the instantaneous failure rate and the probability of failure during the assessment period after equipment maintenance, includes:

[0014] Step 101: Collect existing data from the power grid's existing operation and management system. The existing data includes actual service life of equipment, health index, life statistics of similar equipment, and maintenance data.

[0015] Step 102: Obtain the population baseline failure rate model by fitting a Weibull distribution to historical data of similar equipment;

[0016] Step 103: Using the log-linear mapping method, the individual health status of the equipment is converted into the observed failure rate at the time of exceeding the aging period;

[0017] Step 104: Using the inverse modeling method, the observed failure rate is substituted into the population baseline failure rate model, and the equivalent service life is obtained through mathematical inverse calculation.

[0018] Step 105: Combine maintenance methods to set service life regression factors and incorporate maintenance duration correction to construct a hybrid model;

[0019] Step 106: Calculate the instantaneous failure rate and the failure probability during the evaluation period after equipment maintenance.

[0020] The above-mentioned collaborative optimization method for condition-based maintenance of aging equipment in power grid systems, specifically the process of calculating the aging risk density of different zones and forming a high-density zone list in step two, includes:

[0021] Step 201: Divide the operation and maintenance management unit into partitions;

[0022] Step 202: Calculate the equipment importance coefficient;

[0023] Step 203: Discretize the risk signal of a single device in time;

[0024] Step 204: Set the risk density of the partition;

[0025] Step 205: Smooth the spatial adjacency;

[0026] Step 206: Normalize the data and set the grading thresholds;

[0027] Step 207: Sort the weighted urgency levels;

[0028] Step 208: Determine the list of high-density partitions.

[0029] The aforementioned collaborative optimization method for condition-based maintenance of aging equipment in power grid systems, specifically the process in step three of unifying the regional aging risk density and aging equipment disposal plans into matrix data, includes:

[0030] Step 301: Develop a plan for the disposal of outdated equipment;

[0031] Step 302: Addressing the evolving impact of risks;

[0032] Step 303: Determine the calculation index for constraint satisfaction judgment;

[0033] Step 304: Calculate the interface matrix.

[0034] The aforementioned collaborative optimization method for condition-based maintenance of aging equipment in power grid systems, specifically the process of addressing the evolving impact of risks in step 302, includes:

[0035] Step 30201: Determine the risk signal after handling a single device;

[0036] Step 30202: Determine the post-treatment risk density at the zoning level;

[0037] Step 30203: Cross-partition normalization and threshold segmentation.

[0038] The above-mentioned collaborative optimization method for condition-based maintenance of aging equipment in power grid systems, specifically the process of establishing a linearized model of the impact of the aging equipment disposal plan on the regional aging risk in step four, includes:

[0039] Step 401: Define decision variables;

[0040] Step 402: Express the processed zonal risk in a linear form.

[0041] The above-mentioned collaborative optimization method for condition-based maintenance of aging equipment in power grid systems, specifically the process of setting multi-objective functions and constraints for the linearized model in step five, includes:

[0042] Step 501: Construct an objective function that covers full-cycle risk control, total disposal cost optimization, and risk peak mitigation;

[0043] Step 502: Set constraints covering multiple dimensions, including operation logic, resource limits, and risk control.

[0044] The aforementioned collaborative optimization method for condition-based maintenance of aging equipment in power grid systems, specifically the process of solving the model in step six to achieve a collaborative balance between risk, cost, and constraints, includes:

[0045] Step 601: Preprocess the risk reduction and unit cost value;

[0046] Step 602: Establish an initial feasible solution;

[0047] Step 603: Based on the initial feasible solution, improve the quality of the solution through three types of incremental optimization operations;

[0048] Step 604: Column principal problem and pricing, add columns until there are no unbalanced cost columns;

[0049] Step 605: Relax the budget, resource, and window constraints into the Lagrange function;

[0050] Step 606: Align the plan with the latest budget, window, and health status dynamically;

[0051] Step 607: Output the disposal plan set, post-disposal zone risk and peak value.

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] 1. This invention is based on a weighted life index-based dynamic service life rollback method. It combines equipment maintenance history, health factors and operating environment to construct a service life function, which effectively simulates the incomplete update state of equipment life after maintenance. It is different from traditional cumulative service life or full life reset models and improves the simulation accuracy of equipment state evolution.

[0054] 2. This invention introduces a failure rate increasing factor and a service life decreasing factor, and constructs an equipment failure rate function under a health weight adjustment mechanism to form a causal chain of "state → failure rate → risk → handling priority", thereby enabling priority identification of high-risk equipment under resource-constrained conditions.

[0055] 3. This invention constructs a unit risk reduction cost index and, in conjunction with budget constraints and maintenance window resource limitations, designs a risk-peak-shaving-oriented multi-cycle rolling optimization model. Through a sorting initial solution + rolling adjustment mechanism, it collaboratively achieves overall risk reduction and local peak smoothing, supporting the scientific allocation of power grid operation and maintenance resources and improving the feasibility of maintenance plans.

[0056] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0057] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0058] like Figure 1 As shown, the collaborative optimization method for condition-based maintenance of aging equipment in a power grid system according to the present invention includes the following steps:

[0059] Step 1: Based on the existing data of the power grid's existing operation and management system, establish a risk correction model driven by service life rollback, and output the instantaneous failure rate after equipment maintenance and the probability of failure during the assessment period.

[0060] Step 2: Calculate the over-age risk density of each zone to create a list of high-density zones;

[0061] Step 3: Unify the aging risk density and aging equipment disposal plan of the aforementioned zones into matrix data;

[0062] Step 4: Establish a linearized model of the impact of the over-aged equipment disposal plan on the risk of over-aged equipment in different zones;

[0063] Step 5: Set multi-objective functions and constraints for the linearized model;

[0064] Step 6: Solve the model to achieve a synergistic balance between risk and cost constraints.

[0065] In this embodiment, the specific process of establishing a risk correction model driven by service life rollback based on existing data from the power grid's existing operation and management system, and outputting the instantaneous failure rate after equipment maintenance and the probability of failure during the assessment period, includes:

[0066] Step 101: Collect existing data from the power grid's existing operation and management system. The existing data includes actual service life of equipment, health index, life statistics of similar equipment, and maintenance data.

[0067] In practice, the actual service life of the equipment And becoming overage Sourced from PMS ledger;

[0068] Health Index H i ∈[0,1], source of test or inspection;

[0069] The Weibull parameters (β,η) of the population are derived from the statistical fitting of the lifespan of similar equipment;

[0070] The maintenance method m∈{minor repair, partial major repair, overall major repair, technical modification} is derived from the maintenance work order record;

[0071] Maintenance time Δτ i This is derived from the effective working time of the work order, excluding the transfer time.

[0072] Historical paired samples are those from before and after the maintenance.

[0073] Step 102: Obtain the population baseline failure rate model by fitting a Weibull distribution to historical data of similar equipment;

[0074] In practical implementation, this model is used to calculate the baseline reliability and instantaneous failure rate of a family of similar devices:

[0075]

[0076] Where R(t) is the reliability at time t, λ(t) is the instantaneous failure rate at time t, β is the shape parameter, and η is the scale parameter.

[0077] Give independent lifetime samples The negative log-likelihood is:

[0078]

[0079] Through numerical iterative solutions get

[0080] Step 103: Using the log-linear mapping method, the individual health status of the equipment is converted into the observed failure rate at the time of exceeding the aging period;

[0081] In practice, the baseline failure rate of the population at the point when the equipment becomes aging is calculated using an instantaneous failure rate model. Then, a health amplification factor is constructed, and the health amplification factor is multiplied by the baseline failure rate of the population to obtain the observed failure rate of the individual equipment, thus achieving a quantitative conversion from health status to risk level.

[0082]

[0083] in, Let m(H) be the observed failure rate of device i at the point of becoming obsolete. i ) is the health amplification factor, θ0,θ1 are the historical sample calibration coefficients, and λ(·) is the population failure rate.

[0084] by For H i For linear regression, robust estimation can be achieved using Huber loss.

[0085] The logarithmic linear model is:

[0086]

[0087] OLS closed-form solution: y = [y1, ..., y n ] T ;

[0088] Huber robust regression, with the weight function as follows:

[0089]

[0090] The iterative solution is: θ (t+1) =(X T W (t) X) -1 X T W (t) y,

[0091] Step 104: Using the inverse modeling method, the observed failure rate is substituted into the population baseline failure rate model, and the equivalent service life is obtained through mathematical inverse calculation.

[0092] In practice, the Weibull distribution's scale parameter is multiplied by the product of the scale parameter and the observed failure rate, raised to the power of 1 / 2. This equivalent service life quantifies the true degree of equipment degradation, is not limited by the actual service life, and corresponds only to the actual risk level of the equipment.

[0093]

[0094] in, The equivalent service age is the age at which the ethnic group's baseline is equal to that of the population. The time position corresponding to the same risk level, if by As a lower bound, it avoids abnormal regression caused by health being superior to that of peers.

[0095] Step 105: Combine maintenance methods to set service life regression factors and incorporate maintenance duration correction to construct a hybrid model;

[0096] In practical implementation, to accurately balance the two core effects of accelerated deterioration of aging equipment and risk regression brought about by maintenance and repair, the construction logic of the hybrid risk model is further refined. This model is based on the baseline failure rate and uses a two-factor collaborative approach to characterize the dynamic changes in risk:

[0097]

[0098] Where, γ f ≥1 represents the failure rate increment factor during the f-th maintenance phase, ρ f ∈(0,1] is the service life reduction factor for the f-th maintenance stage, and λ(·) is the baseline failure rate.

[0099] To solve for the service life reduction factor and failure rate increase factor in the model, relevant variables and intermediate computational costs are first defined. Given the failure rate increase factor, the least squares analytical solution of the service life reduction factor is derived through closed-form derivation. This analytical solution can be directly calculated from sample data without complex iterations.

[0100] The sample set for stage f Each sample includes the equivalent service age after maintenance. Post-maintenance failure rate observation / estimation

[0101] remember

[0102] Given ρ, the least squares closed-form solution for γ is:

[0103] The sum of squared residuals is:

[0104] Use one-dimensional search or grid search to find Again

[0105] The search interval for ρ is set to (0,1], with a step size of 0.01 to 0.05. Monotonic priors and Tikhonov regular stable solutions can be added.

[0106] By setting a service life regression factor based on the maintenance method and then introducing a maintenance time reduction coefficient calibrated from historical data, the equivalent service life after maintenance is finally obtained, thus accurately quantifying the restorative effect of maintenance on the deterioration of equipment.

[0107]

[0108] in, For the equivalent service age after maintenance, φ m As a service life regression factor, maintenance method mapping, φ 小修 =0.3,φ 局部大修 =0.5,φ 整体大修 =0.8,φ 技改 =1.0 is the reference value, Δτ i To determine the effective maintenance time, δ is the time reduction factor, and max{·} ensures that the result is non-negative.

[0109] Step 106: Calculate the instantaneous failure rate and the failure probability during the evaluation period after equipment maintenance.

[0110] In practice, a model substitution method is used to re-substitute the obtained equivalent service life after maintenance into the population baseline failure rate model to calculate the instantaneous failure rate after maintenance and the failure probability during the assessment period.

[0111]

[0112] in, The instantaneous failure rate after maintenance. The evaluation window is ΔT, which represents the failure probability.

[0113] In this embodiment, the specific process of calculating the over-age risk density of the partitions and forming a high-density partition list in step two includes:

[0114] Step 201: Divide the operation and maintenance management unit into partitions;

[0115] In specific implementation, based on the existing operation and maintenance management units of the power grid, the entire network is divided into J independent zones. The set of all zones is denoted as a set of consecutive serial numbers from 1 to J. At the same time, a set of equipment that only includes outdated equipment is defined, and the mapping relationship between equipment and zones is defined, that is, each piece of equipment corresponds to a unique zone. This mapping is determined based on the equipment's primary wiring affiliation or main supply area. In addition, the number of key equipment in each zone is counted, specifically referring to the number of core equipment such as main transformers, key circuit breakers, and key line circuits in that zone. This can be counted according to the company's fixed management standards or updated dynamically every year.

[0116] Let the partition set be The equipment collection is (Includes only older devices), partition mapping is π: π(i) = j; indicating that device i belongs to partition j (based on primary wiring or main supply area), and the base number of critical devices in the partition is denoted as π(i) = j.

[0117] Step 202: Calculate the equipment importance coefficient;

[0118] In practice, to reflect the differences in the contribution of different devices to the risk of the partition, a weighted summation method is used to calculate the device importance coefficient. The device importance is equal to the sum of the topology criticality weighted value, the important user impact weighted value, the partition load normalization weighted value, and the N-1 constraint impact weighted value.

[0119] Define device importance I i ∈[0,+∞) is:

[0120]

[0121] Among them, T i For topological criticality, U i For important user influence, C is the normalized value of the load level of partition π(i). i Let ω be the degree of impact of the removal of this device on local connectivity or load transfer under N-1 constraints. T ,ω U ,ω L ,ω C The weights are non-negative.

[0122] To ensure calculation consistency, the topology criticality, important user impact, and N-1 constraint impact are truncated using quantiles before normalization. The normalized values ​​for zoned loads are normalized using the Min-Max normalization method to unify the quantization scale. iU i C i Perform quantile truncation and normalization, for Normalize the partitioned historical load using the Min-Max method.

[0123] Step 203: Discretize the risk signal of a single device in time;

[0124] In practice, a rolling evaluation window is first selected, and a time grid covering the planning period is constructed. For each device, three types of risk signals are defined for each time slice: probability signal, failure rate signal, and expected loss signal. The probability signal adopts the failure probability during the evaluation period, and the failure rate signal adopts the instantaneous failure rate.

[0125] Select the rolling evaluation window ΔT and construct the time grid. Coverage planning period, for each device i in each time slice t k Define risk signals.

[0126] The probability signal is:

[0127] The failure rate signal is:

[0128] The expected loss signal is:

[0129] in, This refers to the direct costs of repair and replacement after equipment failure. The economic equivalent of the expected power shortage induced by the failure of the device in partition π(i) is given.

[0130] Step 204: Set the risk density of the partition;

[0131] In practice, an aggregation method that weights equipment importance and normalizes the number of critical equipment is adopted to calculate the baseline risk density of each partition in each time slice. This density is calculated by weighting the risk density by equipment importance and normalizing the number of critical equipment in the partition, thus obtaining the risk density of partition j in time slice t. k The baseline risk density is:

[0132]

[0133] in, The denominator is the baseline risk density calculated in terms of X caliber. This ensures that zones of different sizes are comparable in density. If a zone currently has no critical equipment, it will... The quality inspection also indicated that the caliber was abnormal.

[0134] Step 205: Smooth the spatial adjacency;

[0135] In practical implementation, to accurately characterize the risk associations between partitions and capture the cluster risk effect, a partition adjacency graph is first established, and an adjacency weight matrix is ​​constructed. For each adjacent partition l of partition j, the adjacency strength between the two is calculated, and then this adjacency strength is divided by the sum of the adjacency strengths of all adjacent partitions of partition j to obtain the weight of partition j to adjacent partition l. Based on this weight matrix, a spatial smoothing is performed to establish the partition adjacency graph, and the weight matrix W = [w jl ],

[0136]

[0137] Spatial smoothing is:

[0138]

[0139] in, Let κ be the adjacency set of partition j. jl Let ξ be the adjacency strength, ξ∈[0,0.5], and let ξ be the spatial smoothness strength.

[0140] Step 206: Normalize the data and set the grading thresholds;

[0141] In practice, to achieve horizontal comparability across zones and time periods, the spatially smoothed risk density is normalized. Normalized to [0,1]:

[0142]

[0143] Among them, Q q％ (t k ) is at time t k Quantiles of the entire partition, | [0,1] This indicates that the line is truncated to [0,1].

[0144] Set the three-segment threshold as follows:

[0145]

[0146] A risk density of less than 0.4 is considered a low-risk density area, between 0.4 and 0.75 is considered a medium-risk density area, and greater than or equal to 0.75 is considered a high-risk density area.

[0147] Step 207: Sort the weighted urgency levels;

[0148] In practice, the maintenance window index W for each zone is used. j (t k )∈[0,1], forming a window-weighted urgency:

[0149]

[0150] Among them, window difference W j The small meeting increased the sense of urgency, U (X) Used to prioritize high-density partitions when the window is limited. κ controls the amplification effect of the window on urgency. The higher the urgency under the same risk density, the more it is used to prioritize scheduling resources to process high-urgency partitions when the maintenance window is limited.

[0151] Step 208: Determine the list of high-density partitions.

[0152] In practice, for a specific planning year, if the normalized risk density of a certain zone is greater than or equal to the high-risk threshold in that planning year, or if the average risk density of that zone over the past M years is greater than or equal to the improved medium-risk threshold, then that zone will be included in the list.

[0153] For the planning year Given caliber X, the generated list is as follows:

[0154]

[0155] in, For high-density partitioned sets, To improve the historical average threshold, M represents the review period.

[0156] In this embodiment, the specific process of unifying the zoning over-aged risk density and the over-aged equipment disposal plan into matrix data in step three includes:

[0157] Step 301: Develop a plan for the disposal of outdated equipment;

[0158] In practice, the over-aged equipment disposal plan is transformed into discrete quantitative variables, basic constraints are set, and the planned quantities and corresponding funding and resource requirements at the partition level are aggregated to lay the variable foundation for subsequent calculations.

[0159] Define a binary plan variable and a partition aggregation quantity. If a single device executes a certain disposal method in a certain time slice, the variable takes the value of 1; otherwise, it takes the value of 0. This variable is used to achieve the discretization and quantification of the disposal plan.

[0160]

[0161] Where, q i,k,a ∈{0,1} indicates whether the plan is in t k For device i, method a is adopted. An index for the collection of outdated devices. Let E represent service extension, M represent minor repair, R represent bureau modification, and D represent decommissioning, where k = 1, ..., K are time slice indices within the planning period.

[0162] Single-device, single-period mutual exclusion is:

[0163]

[0164] The binary planning variables are summed and aggregated by partition, time slice, and disposal method to obtain the planned execution quantity of each partition for each disposal method in each time slice. This quantity is used for subsequent risk overlay and resource requirement calculation. The planned quantity for partition-period-disposal method is:

[0165] Q j,k,a =∑ i:π(i)＝j q i,k,a ;

[0166] in, For partition j in t k The number of devices using method a, π(i) = j is the mapping function from device to partition, and the summation range is all devices belonging to partition j.

[0167] Quantify the consumption of funds and resources during this period separately. The fund and resource requirements are as follows:

[0168] C(t k )=∑ j ∑ a ∑ i:π(i)＝j q i,k,a c i,a ;

[0169] R j,r (t k )=∑ a ∑ i:π(i)＝j q i,k,a ρ a,r

[0170] Wherein, C(t) k ) represents time slice t k Total funding requirements, c i,a For the funding requirements of equipment i using method a, R j,r (t k ) represents partition j in t k The amount of resource type r occupied, ρ a,r For method a, the unit usage of resource type r, It is a set of resource types.

[0171] Step 302: Addressing the evolving impact of risks; the specific process includes:

[0172] Step 30201: Determine the risk signal after handling a single device;

[0173] In practice, each treatment method needs to go through a corresponding effective lag period after the execution time slice before it can take effect. Therefore, before the effective lag period, the equipment risk signal uses the original risk signal. Starting from the time slice corresponding to the effective lag period, the equipment risk signal is updated to the post-treatment risk signal. At the same time, the risk reduction after the treatment takes effect is calculated, which is the difference between the original risk signal and the post-treatment risk signal.

[0174] Disposal method a in Effective immediately, assuming a post-processing signal has been given. but

[0175]

[0176] in, This indicates that if device i is in t k Using method a, the posterior risk signal at time t, This indicates the baseline risk signal before intervention. τ represents the risk signal after treatment method a takes effect. a ∈Z ≥0 The effective delay of representation method a, such as retirement τ D =0, local modification τ R >0.

[0177] The decrease for the period was:

[0178]

[0179] in, This represents the risk reduction of treatment method a at time t. Non-negativity ≥ 0 indicates that the risk after treatment is no higher than before treatment.

[0180] Step 30202: Determine the post-treatment risk density at the zoning level;

[0181] In practice, the risk impact of all planned and future actions on the current time slice is linearly superimposed. For each device, the risk reduction corresponding to all executed and effective actions is subtracted from its original risk signal. Then, the risk density after the actions are taken in each partition is obtained by summing the results by the importance of the device and dividing by the number of critical devices in that partition.

[0182] The historical plan has been planned / the planned disposal will be applied to the current period. k The effects are linearly superimposed as follows:

[0183]

[0184] in, This indicates that partition j in t considers both historical and current plans after the plan takes effect. k Post-treatment risk density I represents the cardinality of critical devices in partition j, used for size normalization. i This indicates the importance of device i. 1{·} represents the indicator function, taking 1 if the condition is true, and 0 otherwise, ensuring risk reduction only after the condition takes effect. The inner double summation represents the application of historical methods (h≤k) that have already taken effect to the current t. k The decline accumulates at the partition level.

[0185] Step 30203: Cross-partition normalization and threshold segmentation.

[0186] In practice, to achieve horizontal comparability of risk densities in different zones, the post-treatment risk densities of all zones are normalized across zones to obtain the normalized risk height. Then, two thresholds are set to divide the normalized risk height into three levels.

[0187]

[0188] Among them, H j (t k )∈[0,1] indicates that partition j in t k The normalization risk is high, Q q％ (t k ) represents time t k Full partition The q% quantile (e.g., 5% and 95%), | [0,1] This means truncating the result to [0,1] to prevent extreme values ​​from overflowing.

[0189] Low density is medium density is high density is:

[0190]

[0191] Where θ1,θ2∈(0,1) represents the segment threshold, which can be set according to historical distribution or strategy.

[0192] Step 303: Determine the calculation index for constraint satisfaction judgment;

[0193] In practice, quantitative constraint judgment indicators are constructed to measure the satisfaction of budget, resources, and maintenance windows, respectively. The budget overrun indicator is as follows:

[0194]

[0195] Where, Φ bud (t k If C(t) ≥ 0, then k )≤B(t k If ), then it is 0; otherwise, it is the excess ratio, B(t) k ) represents time slice t k The budget ceiling.

[0196] The resource limit exceedance index for each partition is:

[0197]

[0198] in, Cap indicates that if resource usage does not exceed capacity, it is 0; otherwise, it represents the excess percentage. j,r (t k ) represents partition j in t k The maximum available capacity for resource r.

[0199] The window operability index is:

[0200]

[0201] in, W represents the excess amount of work done in the current period compared to the available operational window size. j (t k )∈[0,1] is the partition j in t k The maintainable window index is γ, which is the amplification factor from the window index to the "allowable rework volume", and ∈ is the zero-prevention constant to avoid numerical instability when the denominator is 0.

[0202] Step 304: Calculate the interface matrix.

[0203] In practice, the calculation results of risks, disposal plans, and constraint judgments are organized into a structured matrix form to ensure the convenience and standardization of data retrieval.

[0204] Construct a two-dimensional matrix as the risk height matrix, where the rows of the matrix correspond to each partition and the columns correspond to each time slice. The element in the j-th row and k-th column of the matrix represents the normalized risk height of the j-th partition in the k-th time slice.

[0205] H∈R J×K H[j,k]=H j (t k );

[0206] Construct a three-dimensional matrix as the disposal plan matrix. The rows of the matrix correspond to each partition, the columns correspond to each time slice, and the third dimension corresponds to each disposal method. The element in the j-th row, k-th column, and a-th dimension of the matrix represents the number of plans for the j-th partition in the k-th time slice using the a-th disposal method.

[0207]

[0208] Constraint decision matrix:

[0209]

[0210] Where H is the row dimension of the number of partitions J, the column dimension is the number of time slices K, the element is the normalized risk height, and the third dimension Q corresponds to the set of methods. The element represents the number of units in the partition-period-method. The third dimension, Φ, stores the three types of over-limit indicators in sequence: budget, various resources, and window. The element is non-negative.

[0211] In this embodiment, the specific process of establishing a linearized model of the impact of the over-aged equipment disposal plan on the zonal over-aged risk in step four includes:

[0212] Step 401: Define decision variables;

[0213] In practice, the first type of decision variables is a binary decision variable, which is specifically used to identify whether each device performs a certain treatment method in each time slice. The second type is the upper limit variable of the peak risk of the entire network partition, whose core function is to achieve risk peak control.

[0214]

[0215] Where, q i,k,a For equipment-phase-mode binary decision variables;

[0216] P≥0;

[0217] Where P is the upper bound variable of the peak value of the network-wide partition risk, used for "peak shaving".

[0218] Step 402: Express the processed zonal risk in a linear form.

[0219] In practice, in order to accurately quantify the impact of the handling actions on the risk of the zone, a linear calculation logic for the risk of the zone after handling is constructed. First, a risk reduction coefficient is defined. This coefficient is used to measure the extent to which the risk of the zone to which the device belongs will be reduced in future time slots if a specific handling method is adopted for a certain device in a certain time slot.

[0220]

[0221] Among them, G i,h,a→j,k If in period t h For device i, method a is used for partition j during period t. k The risk reduction coefficient, where 1{·} is the effective indication. Depend on Pushed.

[0222] In this embodiment, the specific process of setting multi-objective functions and constraints for the linearized model in step five includes:

[0223] Step 501: Construct an objective function that covers full-cycle risk control, total disposal cost optimization, and risk peak mitigation;

[0224] In practical implementation, the core of the objective function is to scalarize the three core objectives—overall risk control, total disposal cost optimization, and risk peak mitigation—into a single optimization objective through weighted settings, achieving a synergistic balance among multiple objectives. First, the overall risk integral, which is a weighted sum of the post-disposal risk densities across all time slices and all zones, with time weights used to measure the overall risk level of the entire network. Second, the total disposal cost, which is the sum of costs incurred by all equipment in all time slices for executing various disposal methods, reflecting constraints from the economic input dimension. Third, the risk peak mitigation term, centered on the upper bound variable of the risk peak, controls the maximum fluctuation range of network-wide risk by setting peak mitigation weights. By introducing cost and peak mitigation weights, the total disposal cost and the risk peak mitigation term are integrated, and then combined with the overall risk integral to form a single optimization objective function, ultimately achieving multi-objective synergistic optimization with minimum risk, optimal cost, and minimal risk fluctuation. The objective function is:

[0225]

[0226] in, For the entire period of risk score, For disposal costs, β,γ≥0 represent cost and peak load weights, w k This represents the time weighting / discount factor.

[0227] Step 502: Set constraints covering multiple dimensions, including operation logic, resource limits, and risk control.

[0228] In practice, seven types of strict constraints are constructed to ensure that the optimization results are executable in engineering practice, covering multiple dimensions such as operational logic, resource constraints, and risk control.

[0229] Single-phase mutual exclusion and number of reactivations:

[0230]

[0231] Budget and resource capacity:

[0232]

[0233] Window off-peak:

[0234]

[0235] Strong dependency synchronization:

[0236]

[0237] Retirement is irreversible:

[0238]

[0239] High-density voltage drop compliance and peak load constraints:

[0240]

[0241] in, For high-density, mandatory grids, Θ is the pressure drop target, Δk is the buffer period; P is used to control the peak value.

[0242] In this embodiment, the specific process of solving the model in step six to achieve a synergistic balance between risk, cost, and constraints includes:

[0243] Step 601: Preprocess the risk reduction and unit cost value;

[0244] In practical implementation, the risk reduction and unit cost value are expressed as follows:

[0245]

[0246] Where ΔRiskValue i,h,a The Ratio measures the total reduction in risk over the entire period by action (i,h,a). It is the risk reduction efficiency per unit cost and is used for ranking and pruning.

[0247] Step 602: Establish an initial feasible solution;

[0248] In practice, within the feasible domain that satisfies all constraints, actions are selected one by one in descending order of risk reduction efficiency per unit cost, and corresponding binary decision variables are set.

[0249] The initial solution is obtained by approximating the simplified choice problem as follows:

[0250]

[0251] Try setting q in descending order of Ratio. i,h,a =1, if a certain constraint is violated, then the set is in the nearest period.

[0252] (l is usually taken as 1 to 2) to find h′ so that (i,h′,a) is still feasible; if it is still not feasible, then abandon the action.

[0253] Step 603: Based on the initial feasible solution, improve the quality of the solution through three types of incremental optimization operations;

[0254] In specific implementation, the three types of increments are as follows: First, shift operation, which calculates the change in the objective function after shifting the disposal action of a certain device from the current time slice to another time slice. If the objective function is better after the shift and the constraints are satisfied, the shift adjustment is accepted. Second, change of method operation, which compares the difference in the objective function of the same device performing different disposal methods in the same time slice, and selects the better disposal method to replace the original scheme. Third, strong dependency synchronization correction, which calculates the change in the objective function of synchronizing the rework of the other device to the same time slice, or adjusting the rework of both devices to other common feasible time slices, for devices with strong dependencies. The optimal synchronization scheme is selected.

[0255] Given a feasible solution q, its objective value is:

[0256]

[0257] Approximate change of target for shift (i,h,a)→(i,h′,a) (considering only the linear difference of the risk term):

[0258] ΔObj move ≈-∑ k w k (G i,h′,a→π(i),k -G i,h,a→π(i),k )+γΔP;

[0259] Wherein, ΔP is the necessary increment of the upper bound of the peak (if the shift causes the peak risk of a certain grid to increase, then ΔP≥0, otherwise ΔP≤0);

[0260] The target change when changing from (i,h,a) to (i,h,a′) is as follows:

[0261] ΔObj swap =β(c i,a′ -c i,a )-∑ k w k (G i,h,a′→π(i),k -G i,h,a→π(i),k )+γΔP;

[0262] Strong dependency synchronous correction, for If only one party has a duplicate activity in period k, then an equal amount of duplicate activities needs to be added for the other party in the same period (or existing duplicate activities need to be moved to the same k′ synchronously). This correction is expressed as ΔObj=∑ ξ∈{u,v} [β∑ a Δq ξ,k′,a c ξ,a -∑ k w k ∑ a Δq ξ,k′,a G ξ,k′,a→π(ξ),kUsing ]+γΔP as the evaluation criterion, the synchronization period k′ that is ΔObj<0 and satisfies all constraints is selected;

[0263] Acceptance criteria: If ΔObj < -τ (τ is a very small positive number), then adopt the change; repeat until there is no improvement or the maximum number of steps is reached.

[0264] Step 604: Column principal problem and pricing, add columns until there are no unbalanced cost columns;

[0265] In practice, the phrase "selecting a certain method for a certain device in a certain period" is treated as a column, denoted as Ω, and a continuous variable x is introduced. i,h,a ∈[0,1], the restricted principal problem is:

[0266] minz=∑ (i,h,a)∈Ω α i,h,a x i,h,a +γP+ constant α i,h,a =βc i,a -∑ k w k G i,h,a→π(i),k ;

[0267] The dual multiplier of the principal problem LP, constrained by linear form x, is denoted as λ. k μ j,r,k ν j,k ψ j,k , χ j,k And for equipment-side mutual exclusion / synchronization duality, the reduced cost is defined for actions (i,h,a) that are not enqueued:

[0268]

[0269] Add column conditions if RC exists i,h,a If the value is less than 0, add the column to Ω; repeat the column principal problem and pricing until there is no negative reduction cost column, then find the integer solution on Ω to obtain q.

[0270] Step 605: Relax the budget, resource, and window constraints into the Lagrange function;

[0271] In practice, the dual multipliers are iteratively updated using the subgradient method to gradually tighten the constraints. Finally, an approximate optimal solution is obtained by judging convergence through upper and lower bounds. This approach ensures both solution efficiency and result quality by relaxing budget, resource, and window constraints into the Lagrangian function.

[0272]

[0273] Given multipliers Each device can be decomposed into an independent 0-1 selection subproblem, and the multipliers are updated using subgradients:

[0274]

[0275] in,[·] + To truncate to non-negativity, η (t) Step size (e.g.) The lower bound is given above, and the upper bound is given by the feasible objective value of q. The convergence of the two bounds stops.

[0276] Step 606: Align the plan with the latest budget, window, and health status dynamically;

[0277] In practice, a fixed scrolling window is used to dynamically align the plan with the latest budget, window, and health status.

[0278] Step 607: Output the disposal plan set, post-disposal zone risk and peak value.

[0279] In practice, the disposal plan set is as follows:

[0280]

[0281] The post-treatment zone risk and peak value are:

[0282]

[0283] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A collaborative optimization method for condition-based maintenance of aging equipment in a power grid system, characterized in that, Includes the following steps: Step 1: Based on the existing data of the power grid's existing operation and management system, establish a risk correction model driven by service life rollback, and output the instantaneous failure rate after equipment maintenance and the probability of failure during the assessment period. Step 2: Calculate the over-age risk density of each zone to create a list of high-density zones; Step 3: Unify the aging risk density and aging equipment disposal plan of the aforementioned zones into matrix data; Step 4: Establish a linearized model of the impact of the over-aged equipment disposal plan on the risk of over-aged equipment in different zones; Step 5: Set multi-objective functions and constraints for the linearized model; Step 6: Solve the model to achieve a synergistic balance between risk and cost constraints.

2. The collaborative optimization method for condition-based maintenance of aging equipment in a power grid system according to claim 1, characterized in that, The specific process of establishing a risk correction model driven by service life rollback based on existing data from the power grid's existing operation and management system, and outputting the instantaneous failure rate after equipment maintenance and the probability of failure during the assessment period, includes: Step 101: Collect existing data from the power grid's existing operation and management system. The existing data includes actual service life of equipment, health index, life statistics of similar equipment, and maintenance data. Step 102: Obtain the population baseline failure rate model by fitting a Weibull distribution to historical data of similar equipment; Step 103: Using the log-linear mapping method, the individual health status of the equipment is converted into the observed failure rate at the time of exceeding the aging period; Step 104: Using the inverse modeling method, the observed failure rate is substituted into the population baseline failure rate model, and the equivalent service life is obtained through mathematical inverse calculation. Step 105: Combine maintenance methods to set service life regression factors and incorporate maintenance duration correction to construct a hybrid model; Step 106: Calculate the instantaneous failure rate and the failure probability during the evaluation period after equipment maintenance.

3. The collaborative optimization method for condition-based maintenance of aging equipment in a power grid system according to claim 1, characterized in that, The specific process for calculating the aging risk density of zones and forming a high-density zone list in step two includes: Step 201: Divide the operation and maintenance management unit into partitions; Step 202: Calculate the equipment importance coefficient; Step 203: Discretize the risk signal of a single device in time; Step 204: Set the risk density of the partition; Step 205: Smooth the spatial adjacency; Step 206: Normalize the data and set the grading thresholds; Step 207: Sort the weighted urgency levels; Step 208: Determine the list of high-density partitions.

4. The collaborative optimization method for condition-based maintenance of aging equipment in a power grid system according to claim 1, characterized in that, Step three describes the specific process of unifying the zoning over-age risk density and over-age equipment disposal plan into matrix data, which includes: Step 301: Develop a plan for the disposal of outdated equipment; Step 302: Addressing the evolving impact of risks; Step 303: Determine the calculation index for constraint satisfaction judgment; Step 304: Calculate the interface matrix.

5. The collaborative optimization method for condition-based maintenance of aging equipment in a power grid system according to claim 4, characterized in that, The specific process of how the treatment described in step 302 affects the evolution of risk includes: Step 30201: Determine the risk signal after handling a single device; Step 30202: Determine the post-treatment risk density at the zoning level; Step 30203: Cross-partition normalization and threshold segmentation.

6. The collaborative optimization method for condition-based maintenance of aging equipment in a power grid system according to claim 1, characterized in that, The specific process of establishing a linearized model of the impact of the over-aged equipment disposal plan on the risk of over-aged equipment in different zones, as described in step four, includes: Step 401: Define decision variables; Step 402: Express the processed zonal risk in a linear form.

7. The collaborative optimization method for condition-based maintenance of aging equipment in a power grid system according to claim 1, characterized in that, The specific process of setting multi-objective functions and constraints for the linearized model as described in step five includes: Step 501: Construct an objective function that covers full-cycle risk control, total disposal cost optimization, and risk peak mitigation; Step 502: Set constraints covering multiple dimensions, including operation logic, resource limits, and risk control.

8. The collaborative optimization method for condition-based maintenance of aging equipment in a power grid system according to claim 1, characterized in that, The specific process of solving the model as described in step six to achieve a synergistic balance between risk, cost, and constraints includes: Step 601: Preprocess the risk reduction and unit cost value; Step 602: Establish an initial feasible solution; Step 603: Based on the initial feasible solution, improve the quality of the solution through three types of incremental optimization operations; Step 604: Column principal problem and pricing, add columns until there are no unbalanced cost columns; Step 605: Relax the budget, resource, and window constraints into the Lagrange function; Step 606: Align the plan with the latest budget, window, and health status dynamically; Step 607: Output the disposal plan set, post-disposal zone risk and peak value.

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