Power grid equipment life cycle decision optimization method based on asset wall dynamic evolution

Abstract

The invention discloses a power grid equipment full-life-cycle decision optimization method based on asset wall dynamic evolution, which comprises the following steps of: 1, constructing a data set for supporting asset wall calculation through multi-source data fusion and hierarchical modeling; 2, correcting life parameters through equipment individual characteristics, and outputting an equipment-level individualized life function and class-level accumulative scrap distribution in combination with KM survival curve initialization and Weibull distribution fitting methods; 3, constructing a quantity wall and a value wall according to the equipment commissioning year and category; 4, calculating a full life cycle cost present value of the power grid equipment in the evaluation period under the unified discount rate; and 5, determining the actual update execution amount of each type of equipment in each year through the multi-year optimization model, and reducing the investment peak value to obtain a smooth full-life-cycle optimization decision. According to the method, multi-source data are fused, the life precision is enhanced, collaborative optimization of economic and resource collaborative decision is supported, and the whole life cycle management level of power grid equipment is improved.

Description

Technical Field

[0001] This invention belongs to the field of power grid equipment operation and maintenance technology, specifically involving a power grid equipment lifecycle decision optimization method based on the dynamic evolution of asset walls. Background Technology

[0002] As the scale of power grid equipment put into operation expands year by year, the aging trend of the equipment group is becoming increasingly apparent. Some early-commissioned equipment is gradually entering its intensive scrapping period, posing a severe challenge to power grid operation safety, operation and maintenance cost control, and annual investment balance. Currently, the mainstream equipment replacement decision-making methods are mostly based on manual experience, single-dimensional index scoring, or fixed life cycle planning. They lack systematic integration of multi-source heterogeneous factors such as actual operating conditions, environmental stress, and historical operation and maintenance records. This results in inaccurate equipment scrapping assessments, drastic fluctuations in replacement demand, prominent annual investment peaks, and difficulty in matching with the actual budget capabilities of enterprises.

[0003] Traditional lifespan modeling methods primarily rely on univariate or categorical average models, neglecting the differences in health status among equipment and data quality fluctuations, thus failing to achieve individualized lifespan estimation at the equipment level. Simultaneously, most current equipment upgrade plans fail to explicitly consider multiple operational boundaries such as construction capacity, carryover constraints, and reliability floor limits, lacking a scientifically coordinated approach based on overall lifecycle economics. This disconnect between asset upgrade planning and operational economics and risk control leads to fragmented, rigid, and inflexible operation and maintenance strategies, making it difficult to support integrated investment strategy optimization.

[0004] Especially in widely distributed power grid systems with complex operating environments, equipment commissioning batches vary significantly, costs fluctuate frequently, and defect management records are inconsistent. Existing methods struggle to construct reusable quantity wall-value wall extrapolation links, and are unable to achieve dynamic evolution and optimization comparison of multiple types of equipment on a unified time scale. Therefore, there is an urgent need for an optimization method that integrates multi-source data, enhances lifecycle accuracy, and supports collaborative economic and resource decision-making to improve the level of full lifecycle management of power grid equipment. Summary of the Invention

[0005] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls. The method is simple and can be effectively applied to the overall management of equipment replacement and upgrading investments in power grid enterprises. By constructing a reusable quantity wall-value wall deduction link, it realizes the dynamic evolution and optimization comparison of multiple types of equipment at a unified time scale. It achieves collaborative optimization by integrating multi-source data, enhancing lifecycle accuracy, and supporting economic and resource collaborative decision-making, thereby improving the level of power grid equipment lifecycle management. It has good performance and is easy to promote and use.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by this invention is: a power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls, comprising the following steps:

[0007] Step 1: Through multi-source data fusion and hierarchical modeling, construct a dataset to support asset wall calculation, and obtain hierarchical asset index, equipment-level key attributes, and data quality assessment results;

[0008] Step 2: Correct the lifetime parameters based on individual equipment characteristics, and combine KM survival curve initialization and Weibull distribution fitting method to output the equipment-level individualized lifetime function and class-level cumulative scrap distribution;

[0009] Step 3: Construct quantity walls and value walls based on the year and category of equipment commissioning;

[0010] Step 4: Convert the equipment replacement quantity sequence and value sequence into annual cost streams, and calculate the present value of the total life cycle cost of the power grid equipment during the assessment period under a uniform discount rate;

[0011] Step 5: Determine the actual update volume of various types of equipment in each year through a multi-year optimization model, reduce the investment peak, and obtain a smooth full life cycle optimization decision.

[0012] The aforementioned power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls, in step one, involves constructing a dataset to support asset wall calculations through multi-source data fusion and hierarchical modeling, and obtaining hierarchical asset indexes, equipment-level key attributes, and data quality assessment results. The specific process includes:

[0013] Step 101: Perform multi-source data acquisition and fusion;

[0014] Step 102: Establish a hierarchical asset index and collection;

[0015] Step 103: Perform data timeline alignment and data cleaning, and determine the health index based on RPCA and robust Kalman spectroscopy.

[0016] Step 104: Construct the environmental intensity index;

[0017] Step 105: Set the operation and maintenance positive factor and data quality weight;

[0018] Step 106: Initial active duty scale and service age distribution.

[0019] The above-mentioned power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls, in step two, specifically involves correcting lifecycle parameters based on individual equipment characteristics, combining KM survival curve initialization and Weibull distribution fitting methods, and outputting the equipment-level individualized lifecycle function and the class-level cumulative scrap distribution.

[0020] Step 201: Construct a modeling dataset containing complete failure samples and censored samples;

[0021] Step 202: Construct nonparametric survival curves using the KM method;

[0022] Step 203: Based on the nonparametric baseline provided by the KM survival curve, construct a benchmark Weibull distribution model for shared parameters of devices within the class;

[0023] Step 204: Integrate three key covariates—health status, environmental conditions, and operational actions—into scale parameters to construct an individualized scale parameter model;

[0024] Step 205: Construct a Weibull distribution probability density function that includes the individual characteristics of the device;

[0025] Step 206: Construct the survival function, scrapping distribution function, and instantaneous hazard rate function for individualized equipment lifespan;

[0026] Step 207: Construct a mapping between annual interval scrapping probability and age;

[0027] Step 208: Check the goodness of fit and perform robustness verification;

[0028] Step 209: Calculate the approximate variance of the parameters through the observation information matrix to form a confidence band for the annual scrap probability.

[0029] The above-mentioned power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls, in step three, includes the specific process of constructing quantity walls and value walls according to the equipment commissioning year and category:

[0030] Step 301: Obtain the category-level average survival function through aggregation;

[0031] Step 302: Derive the original annual update quantity based on the batches put into operation;

[0032] Step 303: By introducing carryover unprocessed quantities, construct a quantity wall that fits the actual operation;

[0033] Step 304: Update the scale of active service annually and verify the asset inventory;

[0034] Step 305: Introduce a scenario-based price adjustment mechanism, and adjust the unit cost through a price amplification coefficient to obtain the value wall under different scenarios.

[0035] The above-mentioned power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls, specifically step four, involves converting the equipment replacement quantity sequence and value sequence into annual cost flows and calculating the present value of the power grid equipment's lifecycle cost during the evaluation period under a uniform discount rate.

[0036] Step 401: Determine the timeline and classification index for the economic assessment;

[0037] Step 402: Calculate the unit cost and the cost sequence for technological upgrading and renewal;

[0038] Step 403: Calculate operating costs and maintenance costs to obtain the expected annual cost of technological upgrading and renewal;

[0039] Step 404: Calculate the present value of the total life cycle cost.

[0040] The above-mentioned power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls, in step five, involves determining the actual update execution volume of various types of equipment in each year through a multi-year optimization model, reducing investment peaks, and obtaining a smooth lifecycle optimization decision. The specific process includes:

[0041] Step 501: Determine the composition of the original requirements;

[0042] Step 502: Set constraints; the constraints include minimum safe disposal ratio constraints, cumulative disposal and end-of-period carryover constraints, annual budget constraints, and construction capacity constraints.

[0043] Step 503: Construct a comprehensive objective function that combines economics and risk;

[0044] Step 504: Use a heuristic algorithm to solve the comprehensive objective function to obtain a smooth lifecycle optimization decision.

[0045] Compared with the prior art, the present invention has the following advantages:

[0046] 1. This invention constructs an asset wall evolution mechanism that integrates quantity, value, and risk, breaking through the limitations of traditional life models that only output the remaining years of equipment. It realizes the annual linkage expression of the number of retired equipment and the amount of investment in replacement, and comprehensively reflects the rhythm and intensity of equipment replacement.

[0047] 2. This invention introduces an interpretable lifetime correction mechanism, which integrates multi-source factors such as health monitoring, environmental load and operation and maintenance records to perform lightweight scaling correction on the Weibull model. While maintaining the transparency of the model, it improves the ability to characterize individual differences in lifetime prediction and significantly enhances the model's adaptability to engineering heterogeneity.

[0048] 3. At the investment decision-making level, a multi-year updated optimization model based on conditional value-risk has been constructed. This model not only meets basic budget and capacity constraints, but also explicitly controls the annual investment peak, avoids resource shocks and financial pressure caused by centralized replacement, and achieves a flexible and smooth investment curve.

[0049] 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

[0050] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0051] like Figure 1 As shown, the power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls of the present invention includes the following steps:

[0052] Step 1: Through multi-source data fusion and hierarchical modeling, construct a dataset to support asset wall calculation, and obtain hierarchical asset index, equipment-level key attributes, and data quality assessment results;

[0053] Step 2: Correct the lifetime parameters based on individual equipment characteristics, and combine KM survival curve initialization and Weibull distribution fitting method to output the equipment-level individualized lifetime function and class-level cumulative scrap distribution;

[0054] Step 3: Construct quantity walls and value walls based on the year and category of equipment commissioning;

[0055] Step 4: Convert the equipment replacement quantity sequence and value sequence into annual cost streams, and calculate the present value of the total life cycle cost of the power grid equipment during the assessment period under a uniform discount rate;

[0056] Step 5: Determine the actual update volume of various types of equipment in each year through a multi-year optimization model, reduce the investment peak, and obtain a smooth full life cycle optimization decision.

[0057] In this embodiment, the specific process of constructing a dataset to support asset wall calculation through multi-source data fusion and hierarchical modeling in step one, and obtaining hierarchical asset indexes, equipment-level key attributes, and data quality assessment results, includes:

[0058] Step 101: Perform multi-source data acquisition and fusion;

[0059] In practice, the data source and specific parameters are set as follows:

[0060] The asset ledger in the ERP system includes a unique equipment code, model / manufacturer, and year of commissioning. i Original value v i Specialty / voltage level, site;

[0061] PMS maintenance includes work orders, defect closure, and power outage plans;

[0062] Online monitoring / status parameters include PD / PRPD, DGA gas (H2, C2H2…), temperature / load rate, SF6 alarms, etc.

[0063] Environmental data include humidity, extreme high-temperature days, salt spray / pollution levels, altitude, and wind and sand.

[0064] The temporary composite primary key is defined as: plant code interval bit equipment number UID i = Plant / Station Code - Interval Bit - Equipment Number - y i .

[0065] To address the issue of multiple IDs for a single item across ERP, PMS, and MON monitoring systems, a more stable UID-level mapping and matching confidence score is output, and this is included in the w... i .

[0066] For any two system record pairs, multi-dimensional features such as name similarity, location consistency, difference in commissioning year, and model consistency are selected as comparison criteria. For each feature, a probability distribution is established for record matching and record mismatch. The matching score of each record pair is calculated by log-likelihood ratio to quantify the association credibility. The EM algorithm is used to iteratively estimate the parameters of the two probability distributions and the prior matching rate.

[0067] For any pair of records between ERP and PMS, construct the following multidimensional comparison variables:

[0068] γ = (γ1, ..., γJ);

[0069] For each dimension j, a matching distribution m is established based on factors such as name similarity, location consistency, difference in years of operation, and model consistency. j (γ j ) and the unmatched distribution u j (γ j The overall log-likelihood ratio score is:

[0070]

[0071] Where, γ j Let m be the similarity of the j-th field. j (·),u j (·) represents the matching / non-matching conditional distribution, Λ(a,b) represents the log-likelihood ratio score of the pair (a,b), and m is estimated using EM. j ,u j The parameters and the prior matching rate π are:

[0072] P(M∣a,b)∝π∏ j mj (γ j ),P(U∣a,b)∝(1-π)∏ j u j (γ j );

[0073] M steps are used to update m using weighted samples. j ,u j The parameters are updated and the prior π is updated.

[0074] Construct a bipartite graph from the ERP and PMS records, with edge weights taking Λ(a,b) or their monotonic transformations. Use the Hungarian algorithm to find the maximum weight matching:

[0075]

[0076] Where Π is the pairing set (one-to-one); the constraint is that each a and b is paired at most once.

[0077] The matching is performed sequentially in the order of ERP–PMS-PMS-MON, and finally a unified device identifier mapping table is synthesized across the three major systems. If a matching conflict occurs, the pairing result with the highest score and confidence level is selected first.

[0078] Set hard threshold τ hard When Λ(a,b)<τ hard Edge connections are prohibited at this time;

[0079] Output matching confidence p ab =P(M|a,b) as the subsequent w i Part of;

[0080] After executing ERP–PMS and PMS–MON sequentially, a cross-database UID mapping is synthesized. In case of conflicts, Λ(a,b) and p are used. ab The largest one takes priority.

[0081] The matching confidence score is weighted and integrated with the consistency index of key fields across systems to form the link confidence component in the data quality weight. The matching confidence score accounts for 70% of the weight by default, and the consistency of key fields accounts for 30%. This approach highlights the core role of matching confidence while also taking into account the consistency verification of basic information. The final output is a UID mapping table containing the matching confidence score and a weighted link quality score.

[0082] The match confidence score will be incorporated into the link quality weight.

[0083]

[0084] Where, p ab Let s be the posterior probability of matching the corresponding UID mapping. iTo ensure consistency of key fields across systems, α is a trade-off coefficient, and the output is a UID mapping table that resolves cross-database ambiguities and a matching confidence score p. ab With link weighting

[0085] Step 102: Establish a hierarchical asset index and collection;

[0086] In practice, the core hierarchy is divided into three categories: professional, voltage level, and equipment category. Professionals cover three major categories: power transmission, substation, and power distribution. Voltage level and equipment category follow the company's existing management standards. At the same time, equipment batches are divided according to the year of commissioning or the batch of bidding, forming a two-dimensional asset set of hierarchy and batch. For each professional-voltage level-equipment category hierarchy, the number of in-service equipment in the base year is counted as the initial scale data for asset wall iteration.

[0087] Power transmission, transformation, and distribution:

[0088] p∈{power transmission, transformation, and distribution};

[0089] Voltage level v includes ±800kV, 500kV, 220kV, etc.; category c includes circuit breakers, main transformers, instrument transformers, cables, etc.; batch b refers to the year of commissioning or the batch tendered.

[0090] The hierarchical device set is a batch subset g = (p, v, c);

[0091] The base year's active-duty size is Q W (t0,l)=|I l |,l≡g.

[0092] Step 103: Perform data timeline alignment and data cleaning, and determine the health index based on RPCA and Robust Kalman Graph; the specific process includes:

[0093] Step 10301: Truncate and standardize the data;

[0094] In practice, the annual aggregation involves aggregating the monitoring sequence into annual averages, 95th percentiles, extreme value counts, etc. For various numerical data, the data is truncated and standardized according to the 5th and 95th percentiles of similar equipment, compressing the data to the [0,1] interval, which preserves effective information while suppressing the impact of extreme outliers. Missing data is marked with a missing identifier without interpolation to ensure data authenticity. Hard error data such as anomalies in the year of commissioning or negative original values ​​are marked with a verification failure identifier and will not be included in subsequent modeling calculations.

[0095] The basic cutoff and normalization are based on the same quantile P5–P 95 Clip standardization is as follows:

[0096]

[0097] Record relevant data to maintain traceability.

[0098] Step 10302: Construct a multivariate time series matrix;

[0099] In practice, for a single device, select 4-8 core monitoring indicators such as partial discharge, PRPD anomaly rate, oil chromatography gas, and temperature / load thermal stress, and sample monthly or weekly to form a time series matrix. The matrix rows correspond to the monitoring indicators, and the columns correspond to the time points to ensure a unified data structure and facilitate subsequent decomposition and processing.

[0100] For device i, K monitoring indicators were selected and sampled monthly / weekly over a year, forming the following matrix:

[0101]

[0102] Where K is the number of indicators and T is the number of time points. For the DGA series, log(1+x) is taken first to compress the long tail and retain the zero value.

[0103] Step 10303: Decompose the monitoring data matrix into a low-rank matrix and a sparse matrix using the RPCA algorithm;

[0104] In practice, the monitoring data matrix is ​​decomposed into two parts, a low-rank matrix and a sparse matrix, using the RPCA algorithm. The low-rank matrix captures the common health trends of multiple indicators, while the sparse matrix captures sudden abnormal signals. The decomposition process is achieved by minimizing the weighted sum of the nuclear norm and the L1 norm, and the balance parameter is taken as the theoretical value by default.

[0105] Use RPCA to transfer X i Decomposed into low-rank trend L i With sparsity anomaly S i for:

[0106]

[0107] Among them, ∥·∥ * Let λ be the nuclear norm, ∥·∥1 be the L1 norm, and λ be the equilibrium parameter. i Capturing common health trends across multiple indicators, S i Capture sudden pulses / abnormal peaks.

[0108] Step 10304: Perform robust state space smoothing.

[0109] In practice, key features are further extracted from the low-rank matrix to construct a state-space model with the implicit health level as the state variable and the extracted features as the observation variable. The evolution of the health state is described by the state transition equation and the observation equation. To suppress the influence of residual outliers, the Huber loss function is used instead of the traditional squared loss. Small residuals are penalized by square and large residuals by linear penalty. The smoothed health trend curve is obtained by optimization, which improves the stability of the features.

[0110] For L i Key pathways in the process (such as temperature / load stress synthesis, or the first principal component z of RPCA) t The model is as follows:

[0111] State equation x t =Ax t-1 +ε t ,ε t ~N(0,Q);

[0112] Observation equation y t =Cx t +ν t ,ν t ~N(0,R);

[0113] Where, x t To imply the health level / thermal stress state, y t For L i The extracted observation sequence, A, C, Q, R are the state transition matrix, observation matrix, and noise covariance, respectively.

[0114] To suppress residual outliers, the observation residuals are added to the Huber loss, and the solution is as follows:

[0115]

[0116] Huber loss is defined as:

[0117]

[0118] Where δ is the Huber threshold, and the output is smoothed. With robust residuals.

[0119] Step 10305: Extract and standardize health features from the decomposed low-rank matrix, sparse matrix, and smoothed trend curve;

[0120] In practice, four core annual features are extracted from the decomposed low-rank matrix, sparse matrix, and smoothed trend curve: trend level, trend slope, anomaly intensity, and composite oil and gas indicators. For each feature, the direction is unified and the [0,1] interval is standardized according to the distribution of similar equipment to eliminate dimensional differences.

[0121] From L i ,S i , The four annual features were extracted as follows:

[0122] Trend Level

[0123] Trend slope

[0124] Abnormal intensity

[0125] Composite oil and gas index

[0126] By unifying the directions and standardizing the [0,1] values ​​according to the quantiles or ranges within the same class, we obtain...

[0127]

[0128] Step 10306: Synthesize the health index using a weighted summation method.

[0129] In practice, a weighted summation method is used to synthesize the health index:

[0130]

[0131] ω k The weights are calculated using the entropy weighting method, as follows:

[0132] d k =1-e k ,

[0133] in, Let be the standardized value of the k-th health sub-feature, and n be the number of samples.

[0134] Step 104: Construct the environmental intensity index;

[0135] In practice, four types of site-level indicators are selected: salt spray / pollution level S, annual average humidity RH, extreme high temperature days HD, and annual average load rate L. The humidity, extreme high temperature days, and load rate are annualized and smoothed using exponential moving averages to balance the timeliness and stability of annual data. All indicators are standardized in the [0,1] interval and then weighted and summed. The weights satisfy the constraint that they are non-negative and the sum is 1, and finally, the environmental intensity index is generated.

[0136] EWMA annualization of HD, RH, and L is as follows:

[0137]

[0138] After smoothing and standardizing S, RH, HD, and L, the environmental intensity is synthesized as follows:

[0139]

[0140] Step 105: Set the operation and maintenance positive factor and data quality weight;

[0141] In practical implementation, based on PMS operation and maintenance records, a binary indicator variable is constructed: if the equipment completes minor repairs, defect management, or preventative maintenance within the past 36 months and the work order is closed-loop, M... i The value is 1; if there are no relevant maintenance records or the work order is not closed, M i The value is 0; if the PMS record is missing and the device is in service, the default value is M. i The value is set to 0 and a record is marked as missing.

[0142] In the past month, minor repairs, defect elimination, and preventive maintenance have been carried out and the process has been completed in a closed loop.

[0143] M i =1 {There have been minor repairs / defect elimination / preventive maintenance in the past 36 months and the process has been completed in a closed loop}.

[0144] The data quality weights are calculated by combining three types of indicators: basic quality, link confidence, and anomaly penalty. The anomaly penalty is implemented through an exponential function, with higher anomaly intensity resulting in greater penalties. The weight values ​​are in the range of [0,1], with larger values ​​indicating better data quality. Low-quality data is marked and identified, and will only be used for scale statistics, not for modeling calculations.

[0145] Overall completeness c i Consistency i Matching confidence p ab And additional penalties are imposed for abnormalities:

[0146] w i =(ρc i +(1-ρ)s i )×(αp ab +(1-α))×exp(-γoutlier i );

[0147] Where ρ is the basic quality compromise coefficient, with a default value of 0.5; α is the link confidence compromise coefficient, with a default value of 0.7; γ is the outlier penalty coefficient, typically taken as 0.5–1. i This is an anomaly density threshold indicator based on RPCA.

[0148] Step 106: Initial active duty scale and service age distribution.

[0149] In practice, the number of in-service equipment in the base year is statistically analyzed according to the professional-voltage-equipment category hierarchy to form the initial in-service scale. The service life distribution histogram of each level is statistically analyzed according to the service life of the equipment to clarify the number of equipment in different service life segments. At the same time, the in-service scale of each level is statistically analyzed by batch to provide basic data for the batch iteration of the asset wall.

[0150] The tiered service capacity is as follows:

[0151] Q W (t0,l)=|I l |;

[0152] Histogram of service years N l (a) (by year):

[0153] N l (a) = #{equipment with service life of a under level l};

[0154] The batch of active-duty units is as follows:

[0155] Q W (t0,l,b)=|I l,b |

[0156] In this embodiment, the specific process of correcting the lifetime parameters based on individual equipment characteristics in step two, and combining KM survival curve initialization and Weibull distribution fitting methods to output the equipment-level individualized lifetime function and the class-level cumulative scrap distribution includes:

[0157] Step 201: Construct a modeling dataset containing complete failure samples and censored samples;

[0158] In practical implementation, to fully utilize the in-service, non-failed sample information of power grid equipment, it is necessary to clarify the observation lifetime and censoring status, construct a modeling dataset containing complete failure samples and censored samples, define the observation lifetime of equipment i as the smaller value between the actual failure or technical upgrade time and the observation cutoff time, and introduce a censoring indicator variable to distinguish whether a failure event has been observed. The specific formula is as follows:

[0159] t i =min(T) i C i ),δ i =1{T i ≤C i};

[0160] Among them, T i C represents the actual failure or technical upgrade time of device i. i t represents the observation or survey deadline. i δ represents the sample observation duration. i =1 indicates that a failure event was observed, δ i=0 indicates right deletion.

[0161] Step 202: Construct nonparametric survival curves using the KM method;

[0162] In practice, to obtain robust initial values ​​for the Weibull distribution parameters and examine the censoring structure of the dataset, the Kaplan-Meier (KM) method is used to construct nonparametric survival curves. The product limit is used to estimate the survival probability of the device at different times. The specific formula is as follows:

[0163] Based on the failure time sequence {τ j The Kaplan-Meier estimate for} is:

[0164]

[0165] Where, τ j For the j-th distinct failure time, d j For in τ j The number of failures that occurred, n j For τ j The number of samples previously in the risk set.

[0166] Step 203: Based on the nonparametric baseline provided by the KM survival curve, construct a benchmark Weibull distribution model for shared parameters of devices within the class;

[0167] In practical implementation, based on the nonparametric baseline provided by the KM survival curve, a baseline Weibull distribution model of shared parameters among intra-class equipment is constructed. The survival function, distribution function, and hazard rate function comprehensively characterize the equipment lifespan characteristics. The baseline models for shared shape and scale parameters among intra-class equipment are as follows:

[0168] F0(t) = 1 - S0(t),

[0169] Where η0>0 is the baseline scale parameter, β>0 is the shape parameter, β>1 indicates aging, β=1 indicates exponential memorylessness, and β<1 indicates premature death.

[0170] The weighted maximum likelihood considering right censoring and sample quality weights is:

[0171]

[0172] in,

[0173] w i For quality weights, f0(t) is the baseline density function, which is obtained by numerical maximization. Get initial value The Newton-Raphson or quasi-Newton algorithm can be used, with a convergence threshold of ||Δθ||2<10.-6 Finally, the estimated values ​​of the benchmark Weibull parameters are obtained.

[0174] Step 204: Integrate three key covariates—health status, environmental conditions, and operational actions—into scale parameters to construct an individualized scale parameter model;

[0175] In practical implementation, to characterize the impact of individual equipment differences on lifespan, without changing the engineering caliber of shape parameters, only the scale parameters are modified with an exponential correction based on individual equipment characteristics. Through interpretable linear combinations and exponential links, three key covariates—health status, environmental conditions, and operational actions—are incorporated into the scale parameters to construct an individualized scale parameter model.

[0176] η i =η0·exp(θ H H i +θ E E i +θ M M i );

[0177] Where, η i Let ηi be the individual scale parameter of device i, and η0 be the reference scale parameter. i ∈[0,1] represents the health index, E i ∈[0,1] represents the environmental intensity, M i ∈{0,1} represents the operation and maintenance action instructions for the past three years, θ H ,θ E ,θ M This represents the influence coefficient that needs to be estimated.

[0178] The equivalent logarithmic form is:

[0179] logη i =logη0+θ H H i +θ E E i +θ M M i ;

[0180] It facilitates numerical stability and collinearity diagnosis.

[0181] Step 205: Construct a Weibull distribution probability density function that includes the individual characteristics of the device;

[0182] In practical implementation, based on the individualized scale parameter model, the Weibull distribution probability density function containing individual device characteristics is constructed as follows:

[0183]

[0184] The weighted log-likelihood is then:

[0185]

[0186] Where, θ=(θ H ,θ E ,θ M ).

[0187] To suppress small sample jitter, L2 regularization is introduced as follows:

[0188]

[0189] λ is the L2 canonical strength, empirically taken as 10. -4 ~10 -2 This ensures a robust engineering boundary condition |θ.|≤0.8.

[0190] The parameter solution employs a two-step strategy: the first step is to fix... Maximization Solve The second step can be a joint refinement into... Perform 1–2 rounds of block coordinate or quasi-Newton joint updates for the initial values; the convergence criterion is that the change in the objective value is <10. -6 or gradient norm <10 -5 .

[0191] Step 206: Construct the survival function, scrapping distribution function, and instantaneous hazard rate function for individualized equipment lifespan;

[0192] In practice, after the parameter estimation is completed, based on the obtained... and Construct equipment-level individualized lifespan-related functions, specifically including survival functions, scrapping distribution functions, and instantaneous hazard rate functions.

[0193] Device-level functions are:

[0194] F i (t)=1-S i (t),

[0195] Among them, S i (t) represents the survival probability in active service, F i (t) represents the cumulative probability of scrapping, h i (t) represents the instantaneous danger rate.

[0196] Commonly used quantile lifetimes are:

[0197] t 50,i =η i (ln2) 1 / β ;

[0198] Among them, t 50,i This represents the median lifetime of device i, which can be used for engineering-interpretable comparative visualizations.

[0199] Step 207: Construct a mapping between annual interval scrapping probability and age;

[0200] In practice, the asset wall iteration proceeds on a calendar year basis. It is necessary to convert the continuous time dimension of lifespan probability into an annual conditional scrapping probability. Let the equivalent service life of equipment i at the beginning of the year be a. i,t The conditional scrapping probability for the one-year period is:

[0201]

[0202] Where, p i,t Let S be the conditional probability of failure or need for technical upgrade within year t, and S be the denominator. i (a i,t This guarantees that the probability is within a normal range.

[0203] The annual cumulative distribution by category is as follows:

[0204]

[0205] Among them, I l (t) represents the set of equipment still in service at the beginning of the year and belonging to category l, Q W (t,l)=|I l (t)| represents the current year's active duty scale for category l, CDF l (t) represents the average decommissioning intensity within the class in that year.

[0206] Step 208: Check the goodness of fit and perform robustness verification;

[0207] In practice, after the parameters are determined, three types of rapid verification are performed:

[0208] AIC / BIC Information Guidelines

[0209]

[0210] Where k is the parameter dimension and n is the number of samples. This is the unregularized log-likelihood.

[0211] Probability plots and residual tests

[0212] Construct the uncensored samples as

[0213] u i =F i (t i )(δ i =1);

[0214] Theoretically, it should approximately follow Uniform(0,1). The model fit can be checked using uniform QQ-plot. Censored samples can be plotted using local log-cumulative danger plot.

[0215] Robustness of Deleted Structures

[0216] A separate report for high-censorship categories. The confidence interval and sensitivity are such that when the censoring rate is too high, only η can be used. i The relative comparison is used for sorting, not for extrapolating absolute lifetimes.

[0217] Step 209: Calculate the approximate variance of the parameters through the observation information matrix to form a confidence band for the annual scrap probability.

[0218] In practice, to quantify the uncertainty of parameter estimation and provide a risk boundary for asset wall prediction in step three, the approximate variance of the parameters is calculated using the observation information matrix:

[0219]

[0220] in, Let be the parametric covariance matrix.

[0221] Based on this, parameter scenarios can be sampled and generated, and then passed to CDF. l (t) Form an interannual confidence band. If the sample size is small, it is recommended to use the guided method to obtain a more robust interval. Based on the parameter covariance matrix, multiple parameter scenarios are generated by sampling. The parameter uncertainty is transferred to the class-level cumulative scrapping distribution to form a confidence band of annual scrapping probability, which provides input for the asset wall risk analysis in step three.

[0222] In this embodiment, the specific process of constructing the quantity wall and value wall based on the equipment commissioning year and category in step three includes:

[0223] Step 301: Obtain the category-level average survival function through aggregation;

[0224] In practice, the survival probability of a single piece of equipment at a specific service life has been modified by health index, environmental intensity, and operation and maintenance actions, and has individual adaptability. However, asset planning needs to be calculated in batches by category, so it is necessary to obtain the category-level average survival function through aggregation.

[0225] Lifespan distribution of individual equipment:

[0226] S i (a)=exp[-(a / η i ) β ];

[0227] Among them, S i(a) represents the survival probability of device i when its service life is a, η i Let be the scale parameter of device i, obtained after correction for health index, environmental intensity, and operation and maintenance actions; β be the shape parameter shared by this type of device; and a be the service life of the device. The survival functions of all devices within the same category are aggregated to obtain the category-level average survival function.

[0228]

[0229] Among them, S l (a) represents the average survival probability of category l at service age a, N l Let i represent the number of devices included in the statistics for category l, where i∈l indicates that device i belongs to category l.

[0230] The corresponding category-level cumulative distribution function for obsolescence is:

[0231] CDF l (a)=1-S l (a);

[0232] Among them, CDF l (a) represents the cumulative scrapping probability of category l when its service life is not greater than a.

[0233] The annual scrapping probability is expressed as:

[0234] p l (a)=CDF l (a+1)-CDF l (a);

[0235] Where, p l (a) represents the probability of category l being scrapped within the year from service age a to a+1 years.

[0236] Step 302: Derive the original annual update quantity based on the batches put into operation;

[0237] In practice, by tracing historical commissioning data and combining it with category-level scrapping probabilities, the original annual replacement needs are accurately derived, providing core data support for the construction of the quantity wall. First, the commissioning quantity of each historical batch within a category is clearly defined. This data comes from equipment ledgers and historical construction records, ensuring the authenticity of the batch scale. Second, the actual service life of each batch of equipment in the planning year is calculated. This is determined by the difference between the commissioning year and the planning year, accurately locating the equipment's position in its life cycle and providing a basis for matching scrapping probabilities. Based on service life and category-level annual scrapping probabilities, the expected scrapping quantity of a single batch in the planning year can be calculated. This quantity directly reflects the replacement needs of that batch of equipment due to natural aging. By summing the scrapping quantities of all valid batches, the category-level annual original replacement quantity is obtained, ensuring coverage of the natural expiration needs of all historical batches without omissions or duplicate calculations.

[0238] Let the number of units put into operation be N. τ,l The number of equipment put into operation in the year τ and category l is derived from equipment ledgers and historical construction data. Under the planning year t (t≥τ), the service life of the above batches of equipment is:

[0239] a = t - τ;

[0240] Where 'a' represents the service life of the equipment put into operation in year τ in the planned year t.

[0241] The expected number of this batch to be scrapped in year t is:

[0242] D raw (t,τ,l)=N τ,l ·p l (t-τ);

[0243] Among them, D raw (t,τ,l) represents the original replacement demand quantity generated in year t by category l equipment with commissioning year τ, p l (t-τ) represents the probability that the equipment in this batch will be scrapped within the year from t-τ to t-τ+1 years of its service life.

[0244] Summing over all historical commissioning years yields the total number of original updates for category l in year t:

[0245] D raw (t,l)=∑ τ≤t N τ,l ·p l (t-τ);

[0246] Among them, D raw (t,l) represents the original update quantity for year t and category l. The summation range τ≤t indicates that only batches that were put into operation before year t and are still within the service life range are considered.

[0247] Step 303: By introducing carryover unprocessed quantities, construct a quantity wall that fits the actual operation;

[0248] In practical implementation, actual project constraints are fully considered. By introducing carryover unprocessed quantities, a quantity wall is constructed that closely reflects the company's operational realities, addressing the mismatch between model recognition needs and actual processing capacity. Constrained by annual budgets, construction capacity, and power outage windows, the actual annual update volume U... t,l Often cannot fully cover the original update requirements D raw (t,l), therefore it is necessary to explicitly characterize the carryover and unprocessed amount to construct a quantity wall that better reflects the actual operation of the business.

[0249] Define category B(t,l) as the cumulative number of high-risk or nearing-the-end equipment that has not yet been dealt with as of the beginning of year t.

[0250] The dynamic update relationship of carryover amount is as follows:

[0251] B(t+1,l)=max{0,B(t,l)+D raw (t,l)-U t,l};

[0252] Where B(t+1,l) represents the carryover quantity at the beginning of period t+1 of year t, and B(t,l) represents the carryover quantity at the beginning of period t of year t. raw (t,l) represents the original update requirement quantity for year t, U t,l The number of updates actually performed in year t is given. max{·,0} is used to ensure that the carryover quantity is not negative. When the actual processing exceeds the sum of the current year's demand and the historical carryover, the carryover quantity is set to 0.

[0253] Given B(t,l) and D raw Based on (t,l), the baseline update requirement for year t is defined as:

[0254] D base (t,l)=D raw (t,l)+B(t,l);

[0255] Among them, D base (t,l) represents the baseline update demand quantity for year t and category l, D raw (t,l) represents the number of newly added naturally expiring equipment in the current year, B(t,l) represents the number of historically unprocessed equipment carried over from previous periods, with year t as the horizontal axis, and D... base With (t,l) as the vertical axis, the quantity wall of category l can be drawn. The height of the bars reflects the pressure of equipment replacement required each year, and can intuitively identify the peak year of future updates.

[0256] Step 304: Update the scale of active service annually and verify the asset inventory;

[0257] In practice, the annual rolling update of the in-service scale is used to achieve quantitative balance verification of the asset wall evolution, avoid asset scale imbalance caused by calculation deviation of update requirements, and ensure that the plan is consistent with the company's total asset target. In order to ensure the consistency between the asset wall simulation process and the total equipment evolution, the in-service scale needs to be updated annually to verify the quantitative balance between commissioning, scrapping and carry-over.

[0258] Let the in-service scale QW(t,l) be the total number of equipment of category l that are in operation at the beginning of year t.

[0259] Under the simplifying assumptions, the scale of active duty personnel will be represented as follows:

[0260]

[0261] Where QW(t+1,l) represents the in-service size at the beginning of year t+1. For the number of new equipment categories put into operation in the year, U t,l This refers to the number of devices that are retired from service due to reaching the end of their service life or being subject to risk management in a given year. This represents the number of equipment units reduced due to reasons other than lifespan (such as accidental scrapping, demolition, etc.). If missing, it can be approximated as 0.

[0262] Through the aforementioned rolling relationship of active-duty personnel, inspections can be conducted annually:

[0263] First, whether QW(t,l) remains within the asset scale range planned by the enterprise to prevent asset redundancy due to excessive updates or insufficient power supply capacity due to insufficient updates.

[0264] Secondly, whether the quantities of commissioning, scrapping, and carry-over are balanced, thereby verifying the rationality of the asset wall projection results.

[0265] Step 305: Introduce a scenario-based price adjustment mechanism, and adjust the unit cost through a price amplification coefficient to obtain the value wall under different scenarios.

[0266] In practical implementation, the core construction logic of the value wall is to multiply the quantity wall benchmark update demand by the corresponding annual unit cost, realizing the conversion from quantity units such as number of units / km to monetary units such as yuan / ten thousand yuan. This intuitively presents the annual investment scale pressure. Considering that equipment prices may be affected by uncertainties such as market fluctuations and raw material price increases, a scenario-based price adjustment mechanism is introduced. The unit cost is corrected through a price amplification coefficient to obtain the value wall under different scenarios, ensuring that the depiction of monetary demand can adapt to various uncertain scenarios. Since the annual investment amount needs to be used as input for economic analysis, the quantity wall must be converted into a value wall.

[0267] Define benchmark unit cost PR t (l) is the unit cost of category l in year t, which is obtained based on the winning bid price, cost index or project budget in recent years. It can be adjusted for different time points by combining the price index or price level.

[0268] The benchmark investment demand (value wall) for year t and category l is:

[0269] V base (t,l)=D base (t,l)·PR t (l);

[0270] Among them, V base(t,l) represents the benchmark investment size (amount) for year t and category l, D base (t,l) represents the baseline update quantity given by the quantity wall, PR t (l) represents the unit cost of this type of equipment in that year.

[0271] If price fluctuations under different scenarios need to be considered, then the following approach should be adopted in scenario s:

[0272]

[0273] in, For scenario s, the unit cost for year t and category l, Let be the price amplification factor of category l in year t under scenario s.

[0274] The corresponding scenario value wall is:

[0275]

[0276] in, This provides the benchmark investment scale for year t and category l under scenario s, and serves as input for multi-scenario cost assessment and investment optimization in steps four and five.

[0277] In this embodiment, the specific process of converting the equipment replacement quantity sequence and value sequence into an annual cost stream in step four, and calculating the present value of the total life cycle cost of the power grid equipment during the evaluation period under a uniform discount rate, includes:

[0278] Step 401: Determine the timeline and classification index for the economic assessment;

[0279] In practice, if the base year for the asset economic valuation is t0 and the valuation period is T years, then the valuation year is:

[0280] t = t0+1, t0+2, ..., t0+T;

[0281] Meanwhile, the aforementioned hierarchical index is used, denoted as l = (p, v, c), where p represents the profession including power transmission, substation, and distribution, v represents the voltage level, and c represents the equipment category.

[0282] The initial in-service scale Q for each type of equipment has been given in step three. W (t,l), the number of original updates identified in that year, D raw (t,l), unprocessed carryover amount B(t,l).

[0283] Step 402: Calculate the unit cost and the cost sequence for technological upgrading and renewal;

[0284] In practice, for each type of equipment, engineering samples matching the specifications and voltage levels of that type of equipment are selected from the enterprise cost information system or typical project settlement data from the past three to five years. After removing obvious outliers, the average value is taken to obtain the unit cost for the base year:

[0285]

[0286] in, This indicates the unit cost of equipment in category l of type t0 in the base year.

[0287] Equipment Price Index I eq (t,l) is obtained by comparing historical cost data with the annual average, reflecting the relative level of equipment prices in each year since the base year. Based on this, the unit cost of category l in year t is evaluated as follows:

[0288]

[0289] Among them, PR t (l) To assess the unit cost of equipment in category l for year t, I eq (t,l) represents the price index for category l in year t, where l is the evaluation index. eq (t0,l) represents the base year price index.

[0290] Based on the number of updates identified that year, D raw Given B(t,l) and the amount of undisposed carryover B(t,l), the total value required in the assessment year t can be obtained:

[0291] V(t)=∑ l (D raw (t,l)+B(t,l))·PR t (l);

[0292] Where V(t) represents the amount of renewal investment required in the assessment year t, and this amount is regarded as the expected value of technological upgrading in that year:

[0293] E[C tuc [(t)]=V(t);

[0294] Among them, E[C tuc [(t)] represents the expected cost of technological upgrading and renewal in year t.

[0295] Step 403: Calculate operating costs and maintenance costs to obtain the expected annual cost of technological upgrading and renewal;

[0296] In practice, the historical cost data of enterprises can be directly summarized, or the cost can be estimated based on the rate. The number of newly identified upgrade needs in each level in the current year is added to the number of carry-overs that have not been dealt with in the past to obtain the total number of equipment that needs to be dealt with in that level in the current year. Then, the total number of equipment is multiplied by the annual unit cost of equipment after conversion by the price index. Finally, the results of all levels are summarized to obtain the expected value of the annual technical upgrade and renewal cost.

[0297] For each assessment year t, extract relevant items such as energy consumption costs, operating personnel costs, operating material consumption costs, and environmental protection costs from the enterprise cost accounting system. After summarizing them by category index l, the energy consumption, personnel, material, and environmental protection costs are obtained as follows:

[0298] C oc (t)=∑ l (C 能耗 (t,l)+C 人员 (t,l)+C 材料 (t,l)+C 环保 (t,l));

[0299] Among them, energy consumption C 能耗 (t,l) represents the energy consumption cost of equipment of category l in year t, and personnel C... 人员 (t,l) represents the operating personnel wages and surcharges allocated by equipment type, and material C. 材料 (t,l) represents the cost of daily operating materials and spare parts consumption, and environmental protection C. 环保 (t,l) represents environmental protection treatment fees, sewage discharge fees, etc. The allocation rules for each item can be configured according to indicators such as capacity, electricity consumption, or number of equipment.

[0300] When stable records of individual expenses are lacking, the rate method can be used to estimate operating costs. N historical years τ are selected, and the historical operating costs are used to estimate these costs. With active service scale Q W (τ,l) and electricity consumption E load (τ,l) Estimate fixed rates and variable rates.

[0301] Defined as:

[0302]

[0303] in, The annual fixed operating expense rate is calculated based on the scale of service operations. Variable operating rate E calculated based on electricity consumption load (τ,l) represents the electricity consumption or loss converted to electricity for category l of τ in historical years.

[0304] During the assessment period, operating costs were estimated using the following formula:

[0305]

[0306] Among them, Q W (t,l) is obtained from the iterative results of the in-service scale, E load (t,l) can be obtained by extrapolation from load forecasting models or historical electricity consumption trends.

[0307] Maintenance costs include expenses for preventative maintenance, condition-based maintenance, and defect elimination. These can be directly summarized. Preventative condition-based maintenance costs are as follows:

[0308] C rc (t)=∑ l (C 预防 (t,l)+C 状态 (t,l)+C 缺陷 (t,l));

[0309] Among them, prevention of C 预防 (t,l) represents the cost of preventative routine maintenance for equipment of category l in year t, under state C. 状态 (t,l) represents the cost of condition-based maintenance implemented through condition monitoring, and defect C. 缺陷 (t,l) represents the cost of defect elimination and emergency repair.

[0310] When historical maintenance cost data is incomplete, the rate method can also be used for estimation. Select several historical years τ and use historical maintenance costs... and the scale of active service Q W (τ,l) calculates the annual maintenance cost rate:

[0311]

[0312] in, If the unit in-service scale maintenance rate is for category l, then the maintenance cost during the assessment period can be accrued based on the in-service scale as follows:

[0313]

[0314] Among them, Q W (t,l) is provided by the asset wall evolution results.

[0315] Step 404: Calculate the present value of the total life cycle cost.

[0316] In practice, after obtaining the annual sequence of operating costs, maintenance costs, and technological upgrading and renewal costs, a uniform discount rate is used to discount the expenses within the assessment period to obtain the present value of the life-cycle cost. Let the discount rate be r, which can be selected from the company's internal economic benchmark rate of return or the weighted average cost of capital.

[0317] If only operating costs, maintenance costs, and technological upgrade costs are considered, then the present value of the total life cycle cost is:

[0318]

[0319] Among them, C oc (t) is used to assess the operating cost in year t, C rc (t) is used to assess the maintenance cost in year t, E[C tuc [(t)] represents the expected cost of technological upgrading and renewal in year t. The discount factor is based on the base year.

[0320] When carbon costs need to be factored in, the present value of carbon costs (C) can be calculated separately. CO2 for:

[0321]

[0322] Where EF(t) is the grid operation emission factor for assessment year t, El(t) is the electricity consumption or loss-converted electricity during the operation period for assessment year t, and P CO2 (t) represents the carbon price or carbon emission penalty rate for the year t being assessed.

[0323] Residual value recovery present value C salv for:

[0324]

[0325] Among them, Ulv t To assess the unit recycling price of annually decommissioned equipment, Sty t To assess the annual scrapping quantity.

[0326] When considering optional economic factors such as carbon costs and residual value recovery, the total present value of the life-cycle cost is:

[0327]

[0328] Among them, z CO2 z salv This is a binary switch parameter. It is set to 1 when carbon cost or residual value recovery needs to be included, and 0 otherwise.

[0329] In this embodiment, the specific process of determining the actual update execution volume of various types of equipment in each year through a multi-year optimization model, reducing investment peaks, and obtaining a smooth full life cycle optimization decision in step five includes:

[0330] Step 501: Determine the composition of the original requirements;

[0331] In practical implementation, the original update requirement under the baseline scenario is as follows:

[0332] D base (t,l)=D raw(t,l)+B(t,l);

[0333] Among them, D base (t,l) represents the baseline update requirement for year t and category l, D raw (t,l) represents the number of updates identified in the current year, and B(t,l) represents the number of unprocessed items carried over to the planning period.

[0334] Under scenario s, the demand, adjusted for risk amplification factor, is:

[0335]

[0336] D (s) (t,l) represents the update requirements for year t and category l under scenario s. This is the risk amplification factor for scenario s based on category l and year t.

[0337] Step 502: Set constraints; the constraints include minimum safe disposal ratio constraints, cumulative disposal and end-of-period carryover constraints, annual budget constraints, and construction capacity constraints.

[0338] In practice, to ensure equipment reliability, a minimum annual disposal ratio ρ is set for each category. l The constraints are:

[0339]

[0340] ρ l ∈(0,1] represents the minimum annual disposal ratio for category l, derived from enterprise operation and maintenance and security management standards.

[0341] To prevent long-term carryover and backlog, a cumulative disposal constraint is introduced for each type of equipment:

[0342]

[0343] Among them, κ l The cumulative disposal ratio for category l reflects the proportion of risk stock that needs to be digested within the planning period. The left side represents the actual cumulative update volume within the planning period, and the right side represents the cumulative identification demand under scenario s within the planning period multiplied by the ratio coefficient.

[0344] The annual budget constraint is:

[0345]

[0346] Among them, BUD t Let t be the annual investment budget ceiling for year t. This constraint ensures that annual investment does not exceed the budget ceiling under any scenario.

[0347] The construction capacity constraints for the category – annual dimension are as follows:

[0348]

[0349] Among them, CAP t,l The annual construction capacity limit is defined as t, and category l. This constraint reflects the construction capacity of a single type of equipment and the power outage window limitation.

[0350] Step 503: Construct a comprehensive objective function that combines economics and risk;

[0351] In practice, different scenarios have different probabilities of occurrence, so the overall expected cost needs to be obtained through probability weighting. Using the scenario probability as the weight, the total discounted cost of each scenario is weighted and summed. The total discounted cost under scenario s is:

[0352]

[0353] Cost s Let C be the total discounted cost during the planning period under scenario s. oc (t) represents the operating cost in year t, C rc (t) represents the annual maintenance cost t, Inv t,s Let be the investment amount in year t under scenario s, and r be the discount rate. is the discount factor from year t to the starting year.

[0354] The expected cost across multiple scenarios is:

[0355] E[Cost]=∑ s∈S π s Cost s ;

[0356] Where E[Cost] is the expected total cost under multiple scenarios, and π s Let be the probability of scenario s occurring.

[0357] Traditional VaR only reflects risk quantiles and cannot characterize the extent of loss under extreme scenarios. CVaR, on the other hand, quantifies the average loss under extreme risks. By introducing quantile variables and excess variables, CVaR is defined as the weighted average of quantiles plus excess losses under extreme scenarios. Its core function is to accurately characterize the extreme risks of annual investment peaks. At the same time, through linearization, it transforms nonlinear risk indicators into a form that can be solved by the model, thus balancing the scientific nature of risk quantification with engineering feasibility.

[0358] The peak annual investment under scenario s is:

[0359]

[0360] Among them, P s This represents the maximum annual investment during the entire planning period under scenario s.

[0361] Given a confidence level α∈(0,1), CVaR is defined as:

[0362]

[0363] Among them, CVaR α (P s ξ represents the conditional value-at-risk of the annual investment peak at confidence level α, v represents the VaR (α quantile) of the peak distribution, and ξ represents the risk. s Let V be the excess variable exceeding VaR under scenario s.

[0364] The constraints are:

[0365]

[0366] First constraint guarantee ξ s At least equal to P s The excess portion relative to VaR; the second constraint ensures that the excess variable is non-negative.

[0367] Comprehensive objective function programming needs to simultaneously consider economic costs and peak risk. A single objective can easily lead to decision-making bias. Therefore, the expected cost and CVaR peak-shaving objective are weighted and integrated, with weight coefficients used to balance their priorities. Larger weights tend to suppress extreme peaks, while smaller weights prioritize economic optimization. Furthermore, risk penalty weights and scenario probabilities are introduced to quantify the cost of extreme risks, achieving a personalized balance between economic optimization and controllable risk.

[0368] The overall objective function is:

[0369] minZ=E[Cost]+μ·CVaR α (P s );

[0370] Where Z is the overall optimization objective of this step, μ>0 is the peak shaving weight coefficient, which is used to balance expected cost and peak risk. The larger the value of μ, the more it is biased towards smoothing the investment curve and suppressing peaks.

[0371] Step 504: Solve the comprehensive objective function using a heuristic algorithm to obtain a smooth, lifecycle-long optimization decision. The specific process includes:

[0372] Step 50401: Parameter preprocessing and baseline scheme construction;

[0373] In practice, the maximum demand for each year and category is calculated, i.e., the maximum demand under all scenarios. This is used as the calculation base for the minimum disposal limit, ensuring that even under extreme risk scenarios, the minimum disposal amount can still cover the core demand, providing rigorous parameter support for reliability constraints.

[0374] The biggest requirement in this scenario:

[0375]

[0376] Among them, D max (t,l) represents the maximum demand value for year t and category l under all scenarios, D (s) (t,l) represents the demand under scenario s.

[0377] Minimum annual disposal limit:

[0378]

[0379] in, ρ is the minimum update lower bound for year t and category l. l The minimum disposal rate for category l in a given year.

[0380] By introducing a flexibility coefficient, an initial update amount is constructed between the minimum disposal limit and the maximum demand of the scenario. Its core function is to balance the degree of demand fit and the flexibility of adjustment.

[0381] Initial baseline update:

[0382]

[0383] in, For baseline updates before budget scaling, γ l ∈[0,1] is the flexibility coefficient of category l, which reflects the proportion that can be flexibly adjusted above the rigid lower limit.

[0384] The annual total investment and total workload of the initial plan are calculated separately. The core function is to provide a basis for subsequent scaling and adjustment. The investment is calculated based on the benchmark unit cost, and the workload is the sum of the replacement of various types of equipment. By quantifying resource consumption, it is possible to quickly identify whether the initial plan exceeds resource constraints.

[0385] Annual benchmark investment and workload:

[0386]

[0387] in, Based on year t The amount of investment;

[0388]

[0389] in, The total workload for one year (t);

[0390] like or

[0391] This indicates that the baseline plan for that year exceeded the budget or the total capacity limit.

[0392] Then the year will be scaled uniformly:

[0393]

[0394] Where, θ t is a scaling factor for year t, used to compress the baseline update amount to within the budget and capacity limits.

[0395] The initial scheme after scaling is:

[0396]

[0397] in, The updated baseline plan, after budget and capacity adjustments, ensures that the minimum disposal threshold is not lowered.

[0398] The initial plan may have issues where the cumulative disposal volume does not meet long-term constraints, requiring supplementation. By comparing the set ratio of cumulative update volume to cumulative demand, cumulative constraint gaps can be identified. If not met, the update volume will be appropriately increased in later budgets and years with remaining capacity. Each category will be checked as follows:

[0399]

[0400] The left side shows the cumulative update volume of category l during the planning period, and the right side shows the cumulative volume of the maximum demand during the planning period proportionally to κ. l The required value. If not met, then moderately increased in years with budget and capacity surplus. This continues until the inequality is satisfied or the upper limit of the local constraint is reached.

[0401] Step 50402: Multi-scenario assessment and evaluation index calculation;

[0402] In practical implementation, based on the revised unit cost and decision variables, the annual investment amount under any given scenario can be obtained. t,l The evaluation indicators are calculated using the following steps:

[0403] Scenario unit cost and annual investment:

[0404]

[0405] For scenario s, the unit cost of category l in year t. Let be the price amplification factor for scenario s.

[0406]

[0407] Inv t,s Let t be the investment amount in year t under scenario s.

[0408] Scenario annual peak:

[0409]

[0410] P s This represents the peak annual investment during the entire planning period under scenario s.

[0411] Average annual investment and peak probability:

[0412] E[Inv t ]=∑ s π s Inv t,s ;

[0413] E[Inv t [ ] represents the expected investment amount in year t under multiple scenarios.

[0414]

[0415] This is the set of years in which investment peaks under a given scenario.

[0416]

[0417] The probability that year t will become the peak year.

[0418] For {P s Sort in ascending order:

[0419] P (1) ≤P (2) ≤…≤P (|S|) ;

[0420] P (k) It is the kth smallest peak value after sorting.

[0421] Corresponding scenario probabilities:

[0422] π (k) = and P (k) The corresponding scenario probability;

[0423] Cumulative probability:

[0424]

[0425] Π (k) This represents the cumulative probability of the first k scenarios after sorting.

[0426] Given α, VaR is:

[0427] Where k α =min{k∣Π (k) ≥α};VaRα The quantile of the annual peak at confidence level α.

[0428] CVaR is calculated as follows:

[0429]

[0430] CVaR α This is the weighted average peak value for tail scenarios with VaR and above.

[0431] Discount factor:

[0432]

[0433] c t,l,s Let $S$ be the discounted investment cost corresponding to the unit update quantity of category $t$ in year 2023 under scenario $s$. Scenario discounted investment cost:

[0434] C inv,s =∑ t,l c t,l,s U t,l ;

[0435] C inv,s Let be the discounted investment cost under scenario s.

[0436] Discounted expected value of operating and maintenance costs:

[0437]

[0438] C base This represents the total discounted costs of "operation + maintenance" that are unrelated to the decision made in this step. Expected total cost:

[0439] E[Cost]=C base +∑ s π s C inv,s ;

[0440] Overall evaluation value:

[0441] Z(U) = E[Cost] + μ·CVaR α ;

[0442] Z(U) is the comprehensive evaluation value of scheme U, used to compare the merits of different update schemes.

[0443] Step 50403: Peak Year Identification and Annual Weight Construction;

[0444] In practice, the annual reduction weight is defined as follows:

[0445]

[0446] Among them, w tThe reduction weights for year t are: λ1, λ2 ≥ 0, where a larger value indicates a larger investment scale in that year and that it frequently becomes a peak year. The numerator E[Inv] is the weighting parameter. t [ ] represents the expected investment amount for that year, with the denominator being the maximum expected investment amount within the planning period, used for normalization.

[0447] Initial acceptance weight:

[0448]

[0449] Among them, v t w is the initial acceptance weight for year t. t The smaller, v t The larger.

[0450] Remaining budget percentage:

[0451]

[0452] in, This represents the remaining percentage of the annual budget.

[0453] Remaining capacity ratio:

[0454]

[0455] in, This represents the percentage of total annual production capacity remaining.

[0456] Overall acceptance weight:

[0457]

[0458] in, To comprehensively assess the weighting of the projects undertaken, this reflects the overall undertaking capacity of the year, characterized by "low risk + sufficient budget + sufficient production capacity".

[0459] Step 50404: Local year-end adjustments and iterations;

[0460] In practice, the first step is to select the reduction year and the succession year.

[0461] The reduction year is selected as:

[0462]

[0463] t high The year with the highest priority is to be cut.

[0464] In the time window | tt high Select the year of succession within |≤ΔT:

[0465]

[0466] tlow To determine the year with the strongest capacity to handle the load within the allowed annual span, ΔT is the maximum allowed annual span (e.g., 1-2 years). If all candidate years... Therefore, year-end shifts are not possible in this round.

[0467] Then, calculate the adjustable update amount;

[0468] Reduce the amount that can be reduced year-on-year:

[0469]

[0470] To ensure that the minimum annual disposal requirement is met, it can be implemented starting from the year t high The number of items deleted.

[0471] Total available space for disposal:

[0472]

[0473] The remaining slashable space for category l under the cumulative disposal constraint.

[0474] Limit the magnitude of a single adjustment to no more than the proportion η:

[0475]

[0476] η∈(0,1) is the maximum scaling factor for a single adjustment (e.g., 0.1 to 0.2).

[0477] Annual increase:

[0478]

[0479] For the year t low The amount of updates that can be added to category l.

[0480] Migration amount in this round:

[0481]

[0482] δ l For category l in this round from t high To t low The amount of update during migration, if all δ l =0, then the current year cannot be adjusted.

[0483] Finally, the experimental design and acceptance criteria were constructed.

[0484] Test protocol update rules:

[0485]

[0486] U for other years and categories t,l It remains unchanged.

[0487] Recalculate like Then accept the adjustment, and Otherwise, refuse to adjust, retain the original plan, and try other years or end the current iteration.

[0488] Step 50405: Iteration Termination and Result Output.

[0489] In practice, let the maximum number of iterations be K. max The value is 100, and the iteration process is as follows: initialization; get U. cur ←U (0) ; Calculate Z(U) (0) ), and denoted as the current best value Z. best In each iteration: calculate E[Inv] t ]、 CVaR α With Z(U) cur ); construct w t and Choose (t) high ,t low ), calculate δ l Generate test plan like Then update Update Z as needed best .

[0490] The iteration will terminate when any of the following conditions are met: no adjustments are accepted for several consecutive iterations; the investment sequence for all years meets the preset smoothness metric (e.g., the difference between adjacent years is within a set threshold); or the number of iterations reaches K. max U at termination t,l This represents the final investment optimization result of this step, corresponding to the annual investment curve Inv. t,s Annual peak P s Furthermore, the CVaR index can be directly obtained through the calculation process. Under the premise of meeting reliability, budget, and construction capacity constraints, this invention achieves an explicit reduction in the annual investment peak through a limited number of regularized adjustments, forming a smooth and executable life-cycle investment arrangement.

[0491] 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 life-cycle decision optimization method for power grid equipment based on dynamic evolution of asset walls, characterized in that, Includes the following steps: Step 1: Through multi-source data fusion and hierarchical modeling, construct a dataset to support asset wall calculation, and obtain hierarchical asset index, equipment-level key attributes, and data quality assessment results; Step 2: Correct the lifetime parameters based on individual equipment characteristics, and combine KM survival curve initialization and Weibull distribution fitting method to output the equipment-level individualized lifetime function and class-level cumulative scrap distribution; Step 3: Construct quantity walls and value walls based on the year and category of equipment commissioning; Step 4: Transform the equipment replacement quantity sequence and value sequence into an annual cost stream, and calculate the present value of the total life cycle cost of the power grid equipment during the assessment period under a uniform discount rate; Step 5: Determine the actual update volume of various types of equipment in each year through a multi-year optimization model, reduce the investment peak, and obtain a smooth full life cycle optimization decision.

2. The power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls according to claim 1, characterized in that, The specific process described in step one, which involves constructing a dataset to support asset wall calculations through multi-source data fusion and hierarchical modeling, and obtaining hierarchical asset indexes, equipment-level key attributes, and data quality assessment results, includes: Step 101: Perform multi-source data acquisition and fusion; Step 102: Establish a hierarchical asset index and collection; Step 103: Perform data timeline alignment and data cleaning, and determine the health index based on RPCA and robust Kalman spectroscopy. Step 104: Construct the environmental intensity index; Step 105: Set the operation and maintenance positive factor and data quality weight; Step 106: Initial active duty scale and service age distribution.

3. The power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls according to claim 2, characterized in that, The specific process described in step 103, which involves aligning the data timeline and cleaning the data, and determining the health index based on RPCA and robust Kalman spectroscopy, includes: Step 10301: Truncate and standardize the data; Step 10302: Construct a multivariate time series matrix; Step 10303: Decompose the monitoring data matrix into a low-rank matrix and a sparse matrix using the RPCA algorithm; Step 10304: Perform robust state space smoothing. Step 10305: Extract and standardize health features from the decomposed low-rank matrix, sparse matrix, and smoothed trend curve; Step 10306: Synthesize the health index using a weighted summation method.

4. The power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls as described in claim 1, characterized in that, Step two describes the specific process of correcting lifetime parameters based on individual equipment characteristics, combining KM survival curve initialization and Weibull distribution fitting methods, and outputting the individualized lifetime function at the equipment level and the cumulative scrap distribution at the class level. Step 201: Construct a modeling dataset containing complete failure samples and censored samples; Step 202: Construct nonparametric survival curves using the KM method; Step 203: Based on the nonparametric baseline provided by the KM survival curve, construct a benchmark Weibull distribution model for shared parameters of devices within the class; Step 204: Integrate three key covariates—health status, environmental conditions, and operational actions—into scale parameters to construct an individualized scale parameter model; Step 205: Construct a Weibull distribution probability density function that includes the individual characteristics of the device; Step 206: Construct the survival function, scrapping distribution function, and instantaneous hazard rate function for individualized equipment lifespan; Step 207: Construct a mapping between annual interval scrapping probability and age; Step 208: Check the goodness of fit and perform robustness verification; Step 209: Calculate the approximate variance of the parameters through the observation information matrix to form a confidence band for the annual scrap probability.

5. The power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls according to claim 1, characterized in that, The specific process of constructing the quantity wall and value wall based on the equipment commissioning year and category, as described in step three, includes: Step 301: Obtain the category-level average survival function through aggregation; Step 302: Derive the original annual update quantity based on the batches put into operation; Step 303: By introducing carryover unprocessed quantities, construct a quantity wall that fits the actual operation; Step 304: Update the scale of active service annually and verify the asset inventory; Step 305: Introduce a scenario-based price adjustment mechanism, and adjust the unit cost through a price amplification coefficient to obtain the value wall under different scenarios.

6. The power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls according to claim 1, characterized in that, Step four describes the specific process of converting the equipment replacement quantity and value sequences into annual cost flows and calculating the present value of the total life-cycle cost of grid equipment during the assessment period under a uniform discount rate. Step 401: Determine the timeline and classification index for the economic assessment; Step 402: Calculate the unit cost and the cost sequence for technological upgrading and renewal; Step 403: Calculate operating costs and maintenance costs to obtain the expected annual cost of technological upgrading and renewal; Step 404: Calculate the present value of the total life cycle cost.

7. The power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls according to claim 1, characterized in that, Step five describes the specific process of determining the actual update volume of various types of equipment in each year through a multi-year optimization model, reducing investment peaks, and obtaining a smooth life-cycle optimization decision. This process includes: Step 501: Determine the composition of the original requirements; Step 502: Set constraints; the constraints include minimum safe disposal ratio constraints, cumulative disposal and end-of-period carryover constraints, annual budget constraints, and construction capacity constraints. Step 503: Construct a comprehensive objective function that combines economics and risk; Step 504: Use a heuristic algorithm to solve the comprehensive objective function to obtain a smooth lifecycle optimization decision.

8. The power grid equipment lifecycle decision optimization method based on dynamic evolution of asset walls according to claim 7, characterized in that, The specific process of solving the comprehensive objective function using a heuristic algorithm in step 504 includes: Step 50401: Parameter preprocessing and baseline scheme construction; Step 50402: Multi-scenario assessment and evaluation index calculation; Step 50403: Peak Year Identification and Annual Weight Construction; Step 50404: Local year-end adjustments and iterations; Step 50405: Iteration Termination and Result Output.

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