Optimal decision-making method for power grid maintenance scheduling during multiple power outage events based on large language models

Abstract

Introduction:

When several outage maintenance events take place at the same time, the topology and operating mode of the power system change considerably, and experience-based maintenance plans designed for single outage events can no longer capture the combined risk of these events.

Methods:

This paper proposes an optimal decision-making method for maintenance scheduling during multiple outage events based on a large language model. First, an adaptive load forecasting model is built, in which frequency-domain features extracted by the Fourier transform and convolutional networks are fed into a pre-trained large language model; the forecasts then support a weak-link evaluation based on electrical betweenness. Second, a risk overlapping degree model quantifies the cumulative risk of simultaneous outages. On this basis, a joint optimization model coordinates the monthly maintenance schedule and the day-ahead risk-prevention measures.

Results:

Case studies on a 35-node test system show that the method identifies weak links in each maintenance window and achieves a risk overlapping degree of 2.6. Compared with the baseline models, it reduces the level of risk. Tests on IEEE standard systems up to 118 buses confirm the applicability of the method to larger grids.

Discussion:

The proposed method provides a practical decision-making tool for maintenance scheduling under multiple power outage events and can be extended to integrated energy systems.

1 Introduction

The capacity and complexity of power systems have grown steadily in recent years. Renewable energy integration, electric vehicles, and high-load facilities such as data centers all contribute to this growth. Grid expansion has improved supply capability, but it has also made maintenance and repair harder to organize (Zhong et al., 2018; Niu et al., 2024; Jiang et al., 2026a; Zhou et al., 2025; Wu et al., 2026). Since maintenance planning is central to system stability and reliability, its workload has risen accordingly. Power companies face growing pressure on resource allocation and scheduling (Liu C. et al., 2019).

Traditional maintenance planning relies largely on engineering experience and rules of thumb (Wang et al., 2021; Dai et al., 2025a; Wang et al., 2016a). It works well for single outage events. In such cases the system generally meets the N-1 criterion, so one outage does not interrupt the load supply. However, grid companies concentrate maintenance in spring and autumn, when work zones submit large batches of requests. As the grid expands, these requests often number in the hundreds, and many of them have to be carried out at the same time. The topology and operating mode of the system then change considerably. Experience-based plans treat each outage in isolation and control risk only through time-window allocation and backup paths (Basciftci et al., 2018; Dai et al., 2025b; Wang et al., 2016b). They cannot capture the interaction between simultaneous outages. Uncoordinated outages may redistribute the power flow locally, push equipment beyond its ratings, and eventually cause forced load shedding.

Identifying weak links under multiple outage events is essential for preventing voltage violations and equipment overload (Dai et al., 2025c). Existing identification methods fall into three groups. Methods based on complex network theory reduce generators, transformers and substations to nodes, and lines to edges. They examine topological metrics such as betweenness centrality, degree centrality, connectivity and clustering. Methods based on the operating state build an index system from operational and equipment parameters and evaluate vulnerability within that framework. Comprehensive methods combine the topology and the operating state, mixing subjective judgment with objective factors (Yumbe et al., 2017; Ardabili et al., 2022; Jiang et al., 2026b; Behzadirafi and Salehfar, 2015). Few of these methods, however, are designed for multiple-outage maintenance scenarios, and the risks accumulating during such periods are rarely analyzed systematically.

Outage maintenance removes safety hazards in power equipment, improves supply reliability, and helps prevent large-scale accidents (Alvarado et al., 2023; Wang C. et al., 2015; Wang H. et al., 2015; Wang et al., 2016c). At the same time, it changes the operating state of the system and raises the risk of load loss and flow violations. Maintenance and system operation must be planned together. Existing optimization models pursue this goal by adjusting objective functions and constraints (Alizadeh et al., 2022). Maintenance of equipment in the same logical interval is scheduled at the same time. Mutually exclusive equipment is taken out of service at staggered times to avoid electrical islands, and work is placed in off-peak periods whenever possible to reduce load loss. These models, however, focus on coordinating generation- and transmission-side outage schedules. They neither identify risk-prevention measures for outage events nor reflect the risks that accumulate when several outages occur together.

The remainder of this paper is organized as follows. Section 2 presents the weak-link evaluation method based on a large language model. Section 3 develops the multi-time-scale joint optimization model. Section 4 reports the case studies. Section 5 concludes the paper and outlines future work.

2 Weak link evaluation method for power systems based on large language models

When several outage maintenance events occur at the same time, the topology of the power system changes considerably, and the probability of flow violations and load loss during maintenance periods rises accordingly. Evaluating the weak links for each maintenance window reveals safety risks in advance. It also provides the basis for risk-prevention measures and for the optimized maintenance schedule.

2.1 Adaptive load forecasting method based on large language models

Maintenance tasks differ widely in duration, from several hours to several days, and the outage scope varies from task to task. The forecasting method must therefore remain accurate over different time scales. This paper proposes an adaptive load forecasting method based on a large language model.

Electricity load series contain periodic fluctuations at several time scales, such as daily and weekly periods. Extracting these features is important for predicting load variations during maintenance periods. To this end, the Fast Fourier Transform (FFT) is employed to extract low-, medium-, and high-frequency features from the load data. A large language model (LLM) is used to capture the temporal fluctuation characteristics, forming an adaptive load forecasting method. This paper employs FFT to transform time-series data into frequency-domain data. The normalized load window is first divided into overlapping patches and transformed into the frequency domain. In this paper the input window contains 168 hourly points. With a patch length of 24 and a stride of 12, the window yields 13 patches. The main equation is given in Equation 1.

Here, X_norm represents normalized time-series load data, X_f collects the complex Fourier coefficients. To build an adaptive load forecasting model (Chen et al., 2026), this paper converts the frequency spectrum into a power spectrum, as computed in Equation 2.

Here, L_p = 24 is the patch length and k indexes the 13 non-negative frequency bins of each patch. The frequency bins are then grouped into three bands. Each bin is represented by its power values across the 13 patches, and k-means clustering assigns every bin to the nearest centroid in Euclidean distance, as defined in Equation 3 (Chen et al., 2026).

Here, P_i represents the power spectrum vector for the ith frequency, C_j represents the jth cluster center. The number of clusters is set to three, reflecting the daily fundamental component, the sub-daily harmonics and the high-frequency stochastic fluctuations of load series. The cluster centers are initialized with the k-means++ strategy, and the clustering is restarted ten times to avoid poor local minima. The three clusters are ranked by the mean frequency of their members and labeled as the low-, medium- and high-frequency bands.

Convolutional neural networks are then employed to extract high-dimensional features from the three frequency bands (Chen et al., 2026). The main equations are given in Equation 4:

Here, F_i represents the frequency band feature map, A_i denotes the amplitude spectrum of band i. The convolution uses a kernel of size 3, 32 filters, unit stride and same padding, followed by a ReLU activation. Among the numerous frequency components, the low-frequency and mid-frequency bands represent the inherent periodic characteristics of load data. To capture these periodic features, this paper fuses the low-frequency and mid-frequency characteristics through a first-layer linear layer. The high-frequency band contains the random characteristics of load data; therefore, a second-layer linear layer is employed to fuse the random features with the periodic features. The main equations are given in Equation 5 (Chen et al., 2026).

Here, F_final represents the feature map resulting from the fusion of multiple features. This allows the feature map to capture both the long-term stable trends in power load data and the random short-term features.

A pre-trained LLM is adopted as the forecasting backbone for its generalization capability. Accordingly, inverse Fourier transforms are applied to convert high-dimensional feature vectors into time-series data (Chen et al., 2026). The fused features are converted back to the time domain and packed into token vectors before entering the large language model. This process consists of three successive steps. The main equation is given in Equation 6.

Here, E represents the input matrix for the LLM, E_pos represents the position encoding vector. The LLM backbone consists of stacked multi-head self-attention and feed-forward network (FFN) components, with the LLM backbone structure depicted in the figure below. The backbone of the forecasting model is a locally deployed GPT-2 model with 117 million parameters.

As shown in Figure 1, the LLM backbone contains a large number of parameters, which support its generalization capability. Adjusting all of these parameters during model construction would increase the training cost and compromise generalization. This paper adopts the Parameter Efficient Fine Tuning (PEFT) method. Accordingly, only specific LLM parameters are fine-tuned, primarily the Add & Norm and Embedding layers. This approach enhances the model’s accuracy in predicting electricity loads during maintenance periods. The output of layer l is computed as in Equations 7, 8 (Chen et al., 2026):

FIGURE 1

Here, Q, K and V are the query, key and value matrices of the self-attention block, LayerNorm represents normalization, O_l-1 is the output of the previous layer, H_l and O_l denote the outputs of the attention block and of the feed-forward block. The final load forecasting results are as shown in Equation 9:

2.2 Weak link evaluation system during multiple power outage maintenance periods

When multiple power outage maintenance events occur simultaneously, the power system topology undergoes significant changes. During these maintenance periods, different vulnerabilities emerge, which can reduce the power system’s supply reliability. Simulating these vulnerabilities in advance will facilitate the early implementation of risk mitigation measures. This paper establishes a Weak Link Evaluation System During Multiple Power Outage Maintenance Periods to assess the vulnerabilities of the power system during maintenance periods. Based on the prediction results from the aforementioned adaptive load forecasting method, it evaluates the vulnerability indicators of lines and nodes across the maintenance periods.

The power system is a complex network structure. This paper evaluates the weak links in lines and nodes within the power system, using the electrical betweenness of lines as the primary evaluation metric. The main equation is given in Equation 10.

Here, B(m,n) represents the electrical betweenness of line (m,n), S_G represents the set of all power generation nodes, S_L represents the set of all load nodes, W_i represents the weight of the ith power generation node, W_j represents the weight of the jth load node, which is primarily determined based on load forecast results, I_ij(m,n) represents the current value induced on line (m,n) when injecting a unit current element between generation node i and load node j. In this paper, the weight of a generation node is its share of the total available supply capacity, and the weight of a load node is its share of the total forecast demand produced by the adaptive forecasting module. The injection current is computed with the standard DC power-flow linearization, in which a unit current is injected at the generation node and withdrawn at the load node. The greater the electrical betweenness of lines, the larger the transmission load borne by that line during the maintenance period. If the line is disconnected due to a fault during the maintenance period, it will have a greater impact on the power grid, making it a weak link in the grid during that maintenance period. The electrical betweenness of nodes is used accordingly as the evaluation indicator for the nodes of the system. The main equation of electrical betweenness of nodes is as shown in Equation 11:

Here, S_G represents the set of all power generation nodes, S_L represents the set of all load nodes, W_i represents the weight of the ith power generation node, W_j represents the weight of the jth load node, which is primarily determined based on load forecast results. The larger the value of V(n), the greater the transmission role borne by the node during that period, indicating that the node is relatively vulnerable at that time.

3 Joint optimization model for multi-time-scale joint power outage maintenance scheduling and risk prevention measures

Power grid companies typically concentrate their maintenance schedules in spring and autumn. During these periods, work zones under their jurisdiction submit maintenance requests. Due to expanding grid scale, these outage maintenance requests often number in the hundreds. To mitigate operational risks during maintenance windows, this paper constructs a multi-time-scale joint optimization model for maintenance schedules and risk-prevention measures. At the monthly scale, the model coordinates multiple outage events. It measures the risk accumulation of simultaneous outages and arranges the monthly schedule to minimize it. On this monthly plan, a day-ahead model then optimizes the daily outage schedule together with the risk-prevention measures.

3.1 Optimization method for monthly maintenance schedules considering the cumulative risk effects of multiple power outage maintenance events

This paper establishes the Risk Overlapping Degree (ROD) metric to measure the cumulative effect of multiple power outage maintenance events, assess their impact on vulnerable sections of the power grid, and formulate an objective function for risk accumulation. The expression for ROD is given in Equations 12–15:

Here, denotes the Failure Index (FI) of the ith power supply G_i for object n during the execution of power outage maintenance event a, P_Gi,0 denotes the basic failure probability of the power supply under normal operating conditions, A denotes the set of components that assume additional load due to operational mode adjustments during the execution of power outage maintenance event a, P_Gi,m represents the fault probability transfer value indicating the impact of component m failure on power supply G_i, represents the dependency level of object n on power supply G_i during the execution of power outage maintenance event a, num_n,a indicates the number of available power sources for object n during the execution of maintenance request a. The coefficient t_ab is the ratio of overlapping days between events a and b within the monthly window, β_n is the coupling coefficient between the failure increments of two supply sources of object n, ω_n is the weight of object n proportional to its forecast demand, and P_n,L is its average load level. M denotes the set of maintenance events within the monthly window, and G denotes the set of supply sources of object n. The subscript 0 denotes the corresponding value under normal operating conditions. The set E contains all supply objects. In Equation 12, the first product term measures, for each pair of overlapping events, the simultaneous increase of the failure probability of one supply source and of the dependency on that source. The second product term captures the coupled failure increments of two supply sources, weighted by the coupling coefficient. The risk overlapping degree is large when two overlapping events reduce the supply redundancy of the same object. This is the main risk created by uncoordinated multiple outages.

To rationally schedule multiple power outage maintenance events, this paper constructs a multi-objective optimization model. It aims to minimize load losses caused by maintenance while evenly distributing maintenance tasks. This avoids concentrating maintenance on a few days, which would leave too little time for risk-prevention measures. The core expression is as shown in Equations 16–18.

Here, F_load represents the total load loss across the entire network due to maintenance during the entire monthly maintenance period, N represents the total number of days in the month, P_i represents the total load-loss energy caused by the maintenance scheduled on day i, F_amount represents the variance in workload distribution across the entire monthly maintenance plan, S_i represents the total maintenance workload on the ith day, S₀ is the average daily workload. In Equation 18, n_i is the number of maintenance tasks scheduled on day i, n_op,m represents the number of operational steps included in the mth maintenance task. λ_k is the weight of step k, T_op,k is its duration, and P_op,k is the load it affects. This paper transforms the multi-objective optimization function into a single-objective optimization function, with the final objective function expression shown in Equation 19.

Here, α represents the weight of each objective function. The three objectives have different units and magnitudes. Each objective is therefore divided by its value under the original schedule, so that all terms in Equation 19 are dimensionless. The weights α₁, α₂ and α₃ are determined through the analytic hierarchy process (AHP). Some dispatching engineers of the utility company scored the pairwise importance of the three objectives, giving α₁ = 0.5, α₂ = 0.3 and α₃ = 0.2, with a consistency ratio of 0.032, below the accepted threshold of 0.1. This ranking reflects the practical rule that operational risk is prioritized over economic loss in maintenance planning. A sensitivity analysis of the weights is reported in the case study.

Let x_a denote the start day of maintenance event a, and let t_a denote its duration in days, rounded up from the hourly duration. When scheduling power outage maintenance plans, maintenance tasks within the same power outage interval should be scheduled at the same time whenever possible to reduce the number of power outages. The monthly maintenance plan optimization model is therefore subject to the following constraints. The main constraint expressions are as shown in Equation 20.

Here, x_a and x_b denote the start days of two maintenance events in the same power outage interval. To ensure power supply reliability, certain electrical equipment cannot be de-energized simultaneously. To address this problem, mutual-exclusion maintenance constraints are formulated, with the primary expression shown in Equation 21.

Here, the constraint applies to each mutually exclusive pair (a, b) with event a scheduled before event b, and t_a is the duration of event a in days. To ensure power supply reliability, the power grid must not experience power flow or voltage limit violations during maintenance periods. This paper establishes safety verification constraints, with the primary expressions shown in Equations 22, 23.

Here, P_k represents the active power of the line, P_kmax represents the maximum value of active power in the line, U_k represents node voltage, U_kmax and U_kmin represent the upper and lower limits of the node voltage.

3.2 A joint optimization model for outage maintenance day-ahead scheduling and risk prevention and control measures

To ensure power supply reliability, either shifting electricity loads in advance or conducting maintenance during off-peak periods can effectively reduce outage-related load losses. On this basis, a joint optimization model is constructed. Based on the monthly maintenance schedule, the daily maintenance planning optimization problem is treated as the primary optimization problem, while the electricity load transfer path optimization serves as the sub-optimization problem. The objective function of the daily maintenance planning optimization model is as shown in Equation 24.

Here, F_loss represents the cost of electricity sales losses, p represents the average electricity price, P_it is the load curtailed at device i in period t, U_it indicates the operational status of the ith device during the tth time period, with values of 0 and 1 representing normal and maintenance status, respectively. The objective function of the sub-optimization model is as shown in Equations 25–27.

Here, F₁ indicates minimizing network losses caused by transfer loads, N_sw denotes the number of switching operations, P_i is the interrupted load at bus i, and T_i is the corresponding outage duration, ΔP_i is the additional loss, D_i represents the duration of load transfer during maintenance of the ith piece of equipment, F₂ indicates that the number of switching operations should be minimized as much as possible, F₃ indicates that power loss load should be minimized as much as possible. The relevant constraints for the joint optimization model are similar to those discussed in the previous section and will not be repeated here.

4 Case study

To validate the proposed method, 35-node test system is used as the primary analysis subject. The system is a 10 kV distribution network with 35 load nodes and one slack node, and its peak demand is about 60 MW. The slack node is treated as the single generation node in the electrical-betweenness calculation. The topology is adapted from the distribution systems in (CHEN et al., 2019) and (Liu Zhen et al., 2019) and is shown in Figure 2. Each line is equipped with sectionalizing switches, only part of which are drawn for clarity, and S1 to S4 are the interconnection switches between feeders, while S5 and S6 are sectionalizing switches.

FIGURE 2

The maintenance tasks are anonymized for confidentiality. Table 1 lists the ten representative tasks and their optimized start days.

Table 1 lists ten representative tasks with durations between 4 and 28 h. Tasks T1 and T2 belong to the same outage interval and are therefore scheduled on the same day, while tasks T3 and T9, whose simultaneous outage would endanger the supply of the same area, are separated by the mutual-exclusion constraint. The optimized start days spread the workload evenly over the month while avoiding risky overlaps.

The scheduling models are implemented in Python and solved by Particle Swarm Optimization (PSO) on a computer with an Intel Core i7 processor. The settings of the algorithm are listed in Table 2.

The proposed model is compared with four widely used baselines, namely, autoregressive integrated moving average (ARIMA), long short-term memory (LSTM), convolutional neural network (CNN) and a standard Transformer, and with two ablation settings in which the large language model backbone or the frequency-domain module is removed. The root mean square error (RMSE) and mean absolute percentage error (MAPE) are used as metrics. All models are trained and tested on the same three-year hourly records with the same chronological split. The results are summarized in Table 3.

The proposed method achieves a MAPE of 2.31%, outperforming all baselines. The best baseline, the standard Transformer, reaches 3.05%. Removing the LLM backbone raises the MAPE to 3.42%, and removing the frequency-domain module raises it to 3.96%, indicating that the two components complement each other.

Based on the forecast load of the maintenance period, the weak links of the system are then evaluated through the normalized electrical betweenness of the nodes. This evaluation determines which supply objects enter the risk accumulation and how they are weighted. The evaluation result is shown in Figure 3.

FIGURE 3

Five nodes, namely, nodes 8, 12, 19, 24 and 33, exceed the threshold of 0.7. These nodes sit on the main transfer paths of the feeders. Consequently, an outage in their neighborhood affects a large share of the load. The maintenance events involving these nodes are therefore prioritized in the risk overlapping degree model and receive the largest weights in the optimization.

Figure 4 compares the proposed method with two baseline approaches. The traditional method relies on manual scheduling based on engineering experience, and the single-event optimization method coordinates each maintenance task individually without considering cumulative risk effects. The proposed method achieves a risk overlapping degree of 2.6. These results demonstrate that the proposed method effectively mitigates the cumulative risk during concurrent maintenance events.

FIGURE 4

The proposed method is first applied to the monthly schedule, and the three objectives before and after optimization are compared in Table 4.

The risk overlapping degree falls from 38.1 to 2.6, the load loss decreases from 57.5 MWh to 49.2 MWh, and the workload variance drops from 23.9 to 16.3. To check that this result does not depend on the particular weight selection, the weights are perturbed around their nominal values, with their sum kept equal to one, and the model is solved again for every perturbed setting. The results are given in Table 5.

The risk overlapping degree varies between 2.4 and 2.9, and the workload variance between 15.1 and 17.2. The conclusion is therefore robust to the weight selection. Figure 5 shows the risk overlapping degree and the computation time as the number of maintenance tasks increases from 5 to 30. With 30 concurrent tasks, the proposed method keeps the risk overlapping degree at about 16, while the traditional method reaches 198.

FIGURE 5

Figure 6 shows the normalized objective of the base case over the iterations of a representative run.

FIGURE 6

The objective falls from about 1.0, its value under the original schedule, to the optimum of 0.427 within roughly 32 iterations. Over the 30 independent runs the final objective averages 0.427 with a standard deviation of 0.011, and all runs converge. The average solution time of the base case is 28.5 s, which is sufficient for offline planning.

Based on the monthly maintenance schedule, the day-ahead model refines the daily plan and generates the risk-prevention measures. Three measures are available, namely, load transfer through the interconnection switches S1 to S4, re-dispatch of the supply plan at the upstream substation, and feeder topology reconfiguration. Their effects, applied individually and in combination on top of the optimized monthly schedule, are compared in Table 6.

Each measure reduces the load loss on its own. The combination of all three measures lowers the load loss and removes all remaining voltage violations. The combined scheme is therefore adopted in the daily plan. Its intra-day effect is illustrated in Figure 7.

FIGURE 7

The left panel of Figure 7 gives the load profile of the maintenance day before and after load transfer. About 12% of the load is shifted to adjacent feeders during the maintenance window, which lowers the peak. The right panel gives the nodal voltages before and after optimization. Before optimization, ten nodes violate the lower limit of 0.95 p.u. After the coordinated measures are applied, all voltages stay within the range of 0.95–1.05 p.u.

Two further studies assess the robustness of the method. The first tests the load levels of 70% and 100% of the normal demand, and the results are listed in Table 7.

The risk overlapping degree stays low at all load levels. To verify the generalization performance of the proposed model, this paper applies the method to the IEEE 14-bus, 33-bus, 69-bus and 118-bus standard systems, with the number of maintenance tasks scaled from 6 to 25. The results are listed in Table 8.

The computation time grows from 5.2s to 245.3s as the system size increases. Monthly planning is an offline task, so a solution time of a few minutes on a standard workstation is acceptable in practice. The method thus scales to systems of realistic size.

5 Conclusion

Existing maintenance planning methods treat each outage in isolation and cannot capture the interaction between simultaneous outage events. As a result, the probability of flow violations and load losses rises during maintenance periods. This paper has proposed an optimal decision-making method for maintenance scheduling under multiple outage events based on a large language model. Future work will extend the method to integrated energy systems. The coupling between different energy carriers during concurrent maintenance events will be considered, and risk-prevention and optimal decision-making models for such systems will be established. A risk overlapping degree model then quantifies the cumulative risk of simultaneous outages, and a joint optimization model coordinates the monthly schedule and the day-ahead risk-prevention measures. On 35-node test system, the proposed method achieves a risk overlapping degree of 2.6. The forecasting module reaches a MAPE of 2.31%, and tests on IEEE standard systems up to 118 buses confirm that the method applies to larger grids.

Future work will extend the method to integrated energy systems. The coupling between different energy carriers during concurrent maintenance events will be considered, and risk-prevention and optimal decision-making models for such systems will be established.

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