Research on Optimal Control Strategies on Distribution Network Power Transfer Under Extreme Weather Conditions

Abstract

Against the backdrop of global climate change, extreme weather events are increasingly challenging the safe and stable operation of power distribution networks. These events can cause sudden load fluctuations, equipment failures, and disruptions in power transfer. To address these, this paper proposes an optimal control strategy for distribution network power transfer, integrating Long Short-Term Memory (LSTM) networks and dynamic optimization models. By fusing meteorological data with grid characteristics, the LSTM model predicts load demand and fault probability, capturing complex system behaviors under extreme conditions. Combined with Mixed-Integer Linear Programming (MILP), a decision-making model is developed, and a deep-reinforcement-learning-based algorithm handles uncertainties in weather, load, and equipment faults, enabling accurate control. Validation on a 33-bus system shows the method enhances reliability under extreme weather, providing practical value. Furthermore, typhoons, as extreme weather events, can severely damage infrastructure, disrupt power lines, and affect grid stability. In the 33-bus system, typhoons can cause tower collapses and line failures, impacting power transfer. This paper explores the impact of typhoons on a bus model integrated with renewable energy, proposing optimal control strategies to ensure power supply to critical loads while minimizing equipment damage.

1. Introduction

With the intensification of global climate change, both the frequency and severity of extreme weather events—including typhoons, heavy rainfall, hail, heatwaves, cold spells, and snow or ice storms—have increased, posing substantial challenges to the secure and stable operation of distribution networks. Such events directly damage the physical topology of power systems. For example, typhoon winds may cause pole and tower failures, floods may result in line short circuits, lightning strikes can induce insulator flashovers, and icing during cold spells may break conductors, thereby forcing network reconfiguration [1]. In addition, equipment performance is often degraded. High or low temperatures, flooding, and dust accumulation may cause switch or mechanism malfunctions, while damage to communication infrastructure may disrupt remote-control signal transmission and significantly reduce the feasible region of power transfer decisions [2]. Moreover, sudden load fluctuations—for instance, increased air-conditioning demand during heatwaves or elevated drainage demand during storms—further complicate power supply management. Conventional scheduling strategies, which are inadequate for such rapidly changing conditions, frequently lead to large-scale outages and severe economic losses [3].

Among these extreme events, typhoons represent one of the most destructive hazards for distribution networks, with particularly significant impacts on the bus model, which functions as the key node for power transfer, load distribution, and the interconnection of distributed resources. When typhoons strike coastal or inland power infrastructures, strong winds may uproot poles, topple towers, or damage substations, directly leading to bus disconnections and cascading outages [4,5]. Torrential rainfall accompanying typhoons often induces flooding, which increases fault currents at bus nodes and accelerates insulation breakdown [6,7,8]. Moreover, sudden fluctuations in wind and solar generation caused by typhoon cloud cover or gust fronts propagate through bus systems, intensifying voltage instability and frequency oscillations [9]. In urban settings, storm-driven emergency loads, such as large-scale pumping systems for flood control or surge demand from hospitals and transportation hubs, typically concentrate on specific bus nodes, thereby pushing them beyond their safe operating margins [10,11,12]. Existing studies have shown that bus failure rates during typhoon conditions can be several times higher than under normal weather [13,14], and that restoring bus connectivity requires not only topological reconfiguration but also dynamic coordination of distributed energy and demand response [15,16,17]. Therefore, investigating typhoon-induced bus vulnerabilities is critical for improving distribution network resilience, as bus-level instability may propagate upward to feeders and eventually cause widespread system collapse [18,19].

Research on early warning, forecasting of extreme meteorological conditions, and corresponding control and decision-making strategies for distribution networks has attracted increasing attention worldwide. Several representative studies are summarized below. A physics-constrained Generative Adversarial Network (GAN) was introduced in [20] for short-term forecasting of extreme convective weather; however, its generalization capability is limited in small-sample scenarios and it cannot effectively address multi-disaster interactions. To enhance precipitation prediction, ref. [21] developed the CasCast cascading framework, which improves accuracy but significantly increases computational complexity, restricting real-time applications to high-performance platforms. A Deep Q-Network (DQN)-based topology reconfiguration method was proposed in [22], though it assumes stable communication conditions and neglects the risk of switchgear failures. An attention-based Deep Reinforcement Learning (DRL) framework for multi-UAV scheduling was presented in [23]; its reliance on expert-defined reward functions limits adaptability under dynamic disaster conditions. In [24], a hybrid method combining Genetic Algorithm (GA) and eXtreme Gradient Boosting (XGBoost) was applied to flood risk assessment, but the absence of compound-flood feedback mechanisms leads to underestimation of risks. Random Forest (RF) was employed in [25] to integrate social vulnerability indices, yet the approach depends heavily on historical data and exhibits limited ability to incorporate real-time satellite and IoT streams. A scenario-analysis framework for quantifying disaster-chain impacts was developed in [26]; however, the lack of inter-institutional coordination reduces its applicability to emergency planning. A multi-hazard coupling framework for landslide prediction was proposed in [27], but it fails to capture dynamic causal reasoning across multi-level disaster chains. The Bayesian Dynamic Linear Model (BDLM) was applied in [28] for typhoon prediction, though it adapts poorly to abrupt changes in extreme wind speeds. In [29], upper–lower optimization was combined to determine fault topology parameters and adjustment coefficients for phase-voltage scheduling; however, the method presupposes known disaster types, limiting its robustness to unforeseen events. A fault power-transfer strategy based on connection relationships was presented in [30], but the need to traverse every feeder undermines its suitability for rapid power transfer during extreme events. The orderly recovery of fault loads via temporal coordination of distributed resources and transportation-network status was examined in [31], yet the study does not consider control strategies when local compensation is insufficient. Finally, [32] proposed a DQN-based optimization method for distribution network power transfer, but under extreme conditions, DRL may fail to satisfy all hard constraints, often producing only suboptimal solutions. For clarity, the advantages and limitations of these representative methods are summarized in

Table 1. Summary of Switching and Resupply Optimization Approaches in Distribution Networks.

Method	Advantages	Disadvantages	Paper
DQN-Based Reconfiguration	High-dim states; Load adaptive	Weak hard constraints; Comm dependent; Reward bias	[6]
GA–XGBoost Assisted	Accurate risk; Global search	Ignores compound; Slow convergence; No RES link	[8]
Connectivity-Based Switching	Simple logic; Low precision	Complex calc; No dynamics	[14]
Multi-Flex Resource Coordination	DG integration; Cross-system synergy	No cross-area; DG failure risk	[15]
Traditional MILP	Hard constraints; Global optimum	Slow solving; Poor uncertainty	Section 3.4 (DRL module)

.

In response to these challenges, this paper proposes a joint optimization strategy that integrates a Long Short-Term Memory (LSTM) network with Mixed-Integer Linear Programming (MILP) to address the optimal control of distribution network power transfer under extreme meteorological conditions. A multi-source, meteorology-grid data-driven prediction model is constructed to enable dynamic perception of load demand and line fault probabilities. On this basis, a rigorous mathematical programming framework is employed to generate power transfer schemes that balance supply reliability with economic efficiency. The proposed approach provides both theoretical guidance and technical support for enhancing the resilience of distribution networks against extreme disaster scenarios.

2. Impact of Extreme Weather on Distribution Networks

Extreme weather events such as typhoons, heavy rainstorms, and extreme temperatures impose severe and wide-ranging impacts on the operation of distribution networks. These events not only damage physical infrastructure—including poles, transformers, and power lines—but also induce abrupt fluctuations in load demand, thereby complicating network operation and power distribution management [33,34].

Typhoons exemplify such threats, as strong winds and heavy rainfall can cause pole and tower collapses, line short circuits, and equipment failures [35,36]. In addition, flooding associated with typhoons may impair switchgear and communication systems, further complicating restoration and necessitating rapid reconfiguration of supply paths. Heavy rainstorms also frequently cause flooding, leading to line short circuits and reduced equipment operability. The resulting disruptions, combined with the loss of real-time monitoring data, hinder adaptive responses and prolong outage durations.

Extreme temperatures represent another critical hazard. Heatwaves accelerate the thermal stress and aging of transformers, conductors, and other components, increasing the likelihood of equipment failure. Conversely, extreme cold can lead to icing on lines and devices, causing mechanical breakages. Both conditions trigger sudden spikes in electricity demand, which aggravate load forecasting errors and further stress the distribution network.

To provide a clearer overview,

Table 2. Impacts of Extreme Weather Events on Distribution Networks.

Extreme Weather Event	Key Impacts on Distribution Network	Challenges for Distribution Network Operation
Typhoons	Strong winds can cause pole and tower collapses; heavy rainfall causes flooding and short circuits.	Power supply disruption due to infrastructure damage.
Heavy Rainstorms	Flooding leads to line short circuits and equipment malfunction.	Reduced equipment functionality and monitoring challenges.
Extreme Temperatures	High temperatures cause equipment overheating; cold temperatures cause icing on conductors and equipment.	Sudden demand spikes and stress on components due to temperature changes.

summarizes the impacts of various extreme weather events on distribution networks.

The increasing penetration of wind and solar power into distribution networks introduces additional challenges under typhoon and heavy rainfall conditions. For wind power, extreme wind speeds and intense precipitation during typhoons can cause blade fractures, tower collapses, and control system failures, often resulting in forced shutdowns or permanent equipment damage. Post-event recovery is typically prolonged due to extensive repair requirements, thereby reducing the continuity of wind power output and compromising grid reliability.

Solar power systems are likewise vulnerable. Heavy rainfall may flood ground-mounted photovoltaic (PV) sites, submerging modules and inverters and causing short circuits or equipment failures. Strong winds can dislodge PV panels, damage support structures, and trigger large-scale outages. Furthermore, extended cloud cover and storm conditions significantly reduce solar irradiance, leading to sharp declines in PV output and exacerbating supply–demand imbalances in the distribution network during extreme weather events [37,38].

Extreme weather events not only cause infrastructure damage but also introduce unpredictable challenges for load forecasting and power transfer optimization, complicating the distribution network’s ability to maintain stable and efficient operation [39,40]. To capture these impacts more comprehensively, this paper investigates the operation of a bus model with integrated renewable energy under typhoon scenarios, providing a detailed characterization of how extreme weather affects system performance.

3. Decision-Making Model for Optimal Control of Distribution Network Power Transfer

3.1. Overall Framework

The overall framework of the proposed optimal control decision-making model for distribution network power transfer is illustrated in Figure 1. The model integrates power grid topology, historical load, real-time monitoring data (e.g., current and voltage), equipment status indicators (such as switch operation counts and line aging rates), meteorological information (e.g., extreme weather records, wind speed, and rainfall), and external factors such as holidays. The data is first subjected to cleaning and preprocessing: short-term missing values are filled using linear interpolation, long-term missing records are removed, and outliers are detected and corrected using the Z-score method. Subsequently, load and meteorological variables are normalized by the Min–Max method to eliminate dimensional inconsistencies. Feature engineering is then performed to extract temporal features (hour, weekday, holiday encoding), meteorological features (extreme weather markers and sliding-window statistics), and power grid state features (line load rates and switch operation histories), thereby constructing a multidimensional input dataset.

On this basis, an LSTM network is developed to construct both load forecasting and fault prediction models. The load forecasting model uses historical load, meteorological parameters, and temporal features as inputs, is trained with batch size 32 and early stopping (patience = 10), and outputs 24-h-ahead load predictions. The fault prediction model, which takes line status, meteorological data, and equipment aging indicators as inputs, employs the SMOTE algorithm to balance fault samples and outputs line fault probabilities. Lines with high risk (probability > 90%) are flagged for forced disconnection. The results are combined to generate a predicted system state matrix, including a line availability matrix and a node load matrix, which serve as inputs to the optimization stage.

The power transfer optimization model is formulated to minimize load loss and switch operation costs. Decision variables include switch states (0/1) and load curtailment. Constraints are imposed on power balance, line capacity, voltage limits, radial topology, and the number of switch operations. To address nonlinearities, absolute-value terms in the objective function are linearized. A preliminary transfer scheme is obtained via a deep reinforcement learning (DRL) algorithm, after which the solution is refined using mixed-integer linear programming (MILP). The final feasible scheme is derived by invoking the CPLEX solver with the branch-and-cut method.

In the proposed model, load curtailment and switch states are treated as random variables to capture operational uncertainties under extreme weather conditions. The randomness of load curtailment arises from abrupt variations in demand—for example, surges in heating or cooling loads during storms—as well as from renewable generation fluctuations caused by rapidly changing meteorological conditions. In addition, topology reconfiguration due to faults or switch operations alters load distribution, further increasing uncertainty. Similarly, the randomness of switch states is driven by fault probabilities, since extreme weather may trigger overloads, equipment aging, or sudden failures, necessitating frequent switching to maintain supply continuity. Although prediction models can estimate fault probabilities, actual fault occurrences remain influenced by complex environmental factors. By modeling both variables probabilistically, the proposed framework enables the generation of adaptive and robust power transfer schemes. Even under worst-case scenarios involving load forecast errors or unexpected faults, the model can ensure supply to critical loads while minimizing equipment stress from excessive switching.

3.2. Load Forecasting Model Based on LSTM

Long Short-Term Memory (LSTM) is a special type of Recurrent Neural Network (RNN) proposed by Hochreiter and Schmidhuber in 1997. Compared with traditional RNNs, LSTM effectively addresses the gradient vanishing problem in long-sequence training by introducing a gating mechanism, and performs excellently in time series forecasting tasks [41,42].

The core of an LSTM unit lies in its Cell State and three gating structures: the forget gate, input gate, and output gate. This design enables the network to selectively remember and forget information, thereby capturing long-term dependencies in time series [43].

The computation process of an LSTM unit at a time step includes the following units.

$$f_t=\sigma (W_f\cdot [h_{t-1},x_t]+b_f)$$

(1)

$$i_t=\sigma (W_i\cdot [h_{t-1},x_t]+b_i)$$

(2)

$$o_t=\sigma (W_o\cdot [h_{t-1},x_t]+b_o)$$

(3)

$${\tilde{C}}_t=\tanh (W_C\cdot [h_{t-1},x_t]+b_C)$$

(4)

$$C_t=f_t\odot C_{t-1}+i_t\odot {\tilde{C}}_t$$

(5)

$$h_t=o_t\odot \tanh (C_t)$$

(6)

Wherein, $x_t$ is the input vector at time $t$; $h_t$ is the hidden state at time $t$; $C_t$ is the cell state at time $t$; $f_t$ is the output of the forget gate; $i_t$ is the output of the input gate; $o_t$ is the output of the output gate; ${\tilde{C}}_t$ is the candidate cell state; $W_f$, $W_i$, $W_o$ are weight matrices; $b_f$, $b_i$, $b_o$, $b_C$ are bias vectors; and $\sigma$ is the Sigmoid activation function.

In this study, a deep LSTM network model is developed based on preliminary experimental optimization. The input layer consists of an 18-dimensional feature set over 24 time steps. Temporal dependencies are captured using two stacked LSTM layers, each with 64 neurons and a dropout rate of 0.2. Dimensionality reduction is then performed through fully connected layers with a neuron configuration of 64 → 32 → 1, yielding 24-h load forecasts as the final output.

For training, time-series cross-validation is employed with an 8:2 training–validation split. The model is optimized using the Adam algorithm (learning rate = 0.001) with the mean squared error (MSE) as the loss function. Training is performed for up to 100 epochs with a batch size of 32, while an early stopping mechanism is adopted to terminate training if the validation loss does not improve for 10 consecutive epochs. The overall forecasting workflow is illustrated in Figure 2.

3.3. Line Fault Probability Prediction Model

This study develops a line fault probability prediction model based on a feedforward neural network. The model takes six-dimensional meteorological features as input and consists of three hidden layers: the first two layers each contain 64 neurons with RELU activation and a dropout rate of 0.3, while the third layer has 32 neurons with RELU activation and a dropout rate of 0.2. The output layer employs a Sigmoid activation function to generate predicted fault probabilities.

This deep network effectively captures complex relationships between meteorological conditions and fault occurrence through multi-layer nonlinear transformations. The RELU activation function ensures efficient gradient propagation, while the layered dropout mechanism (0.3 → 0.3 → 0.2) mitigates overfitting without compromising feature representation. The Sigmoid output layer constrains predictions to the [0,1] probability range, providing a quantitative basis for power grid risk assessment. Historical fault records and meteorological conditions are then used to define fault probability labeling rules as follows:

$$P_{fault}=\left\{\begin{array}{ll}0.05\hfill & Normal weather, no historical faults\hfill \\ 0.15\hfill & Severe weather or with historical malfunctions\hfill \\ 0.5\times I_{typhoon}+0.25\hfill & Typhoon weather\hfill \end{array}\right.$$

(7)

The fault probability $P_{fault}$ is defined to quantify the likelihood of grid failures under varying meteorological conditions, with values constrained within [0,1], thereby providing a numerical basis for risk assessment. In typhoon scenarios, a normalized typhoon intensity indicator $I_{typhoon}$ (ranging from 0 to 1) is introduced to characterize the severity of the typhoon and incorporated into the calculation of fault probability.

3.4. Power Transfer Optimization Model Based on MILP

Mixed-Integer Linear Programming (MILP) is adopted as the core optimization method in this study due to its distinct advantages in addressing emergency control problems in distribution networks [44,45]. Under extreme meteorological conditions, MILP effectively coordinates discrete switch operations with continuous power allocation decisions, transforming LSTM-based load and fault predictions into executable optimization schemes. This approach ensures computational efficiency while supporting multi-objective optimization, allowing for simultaneous minimization of load losses and operational costs while satisfying hard constraints such as voltage limits and line capacities. Compared with heuristic algorithms, MILP guarantees global optimality and precise constraint handling. The integration of this deterministic optimization framework with deep learning prediction models provides a robust technical pathway for enhancing distribution network resilience under extreme weather events.

3.4.1. Objective Function

Under extreme weather conditions, the specific expression of emergency control for distribution networks is as follows:

$$\min {\displaystyle \sum _i{s}_i\cdot {\omega }_i}+{\displaystyle \sum _k\left|x_k-x_k^{prev}\right|}\cdot c_k$$

(8)

The definitions of each variable are as follows: $s_i$ represents the load curtailment of node $i$ (unit: kW or MW), indicating the amount of load to be shed due to insufficient power supply. ${\omega }_i$ denotes the load importance weight of node $i$ (dimensionless), which is used to distinguish critical loads (e.g., hospitals) from ordinary loads. $x_k$ is the current state of switch (0 or 1), where 1 indicates closed and 0 indicates open. $x_k^{prev}$ represents the state of switch $k$ at the previous moment (0 or 1). $c_k$ is the operation cost of switch $k$ (unit: yuan/operation), including physical switching losses and maintenance costs.

3.4.2. Constraints

(1)

Power Balance Constraint

Power balance is a fundamental requirement for power grid operation, and its mathematical expression is as follows:

$${\displaystyle \sum _{j\in upstream(i)}{P}_{ji}}={\displaystyle \sum _{k\in downstream(i)}{P}_{ik}}+P_{load,i}^{pred}-s_i$$

(9)

Wherein, $P_{ji}$ is the active power flowing from upstream node $j$ to the current node $i$ (unit: kW or MW). $P_{ik}$ is the active power flowing from the current node $i$ to downstream node $k$ (unit: kW or MW). $P_{load,i}^{pred}$ is the predicted load demand of node $i$ (unit: kW or MW), output by the LSTM model. $s_i$, as defined above, is the load curtailment of node $i$.

This constraint ensures that the power inflow of each node equals the sum of the power outflow and local load, while allowing for adjustment of the supply–demand balance through load curtailment $(s_i)$.

(2)

Line Capacity Constraint

The line transmission power is limited by its physical capacity, with the expression as follows:

$$\left|P_{ij}\right|\le x_{ij}\cdot P_{ij}^{\max }(\forall lineij)$$

(10)

The components in the formula are defined as follows: $P_{ij}$ is the active power transmitted on line $ij$ (unit: kW or MW); $x_{ij}$ represents the availability status of line $ij$ (0 or 1), where 1 indicates the line is in normal operation and 0 indicates a fault (determined by the fault prediction model); $P_{ij}^{\max }$ is the maximum transmission capacity of line $ij$ (unit: kW or MW), which is determined by the physical parameters of the line.

If a line is in a fault state (determined by the fault prediction model), it is forced to disconnect ($x_{ij}$ = 0) with zero transmission power; the power of a normal line must be lower than its rated capacity to avoid overload.

(3)

Voltage Constraint

During the operation of the power grid, node voltage must be maintained within a safe range, and the expression is as follows:

$$V_{\min }\le V_i\le V_{\max }$$

(11)

$V_i$ is the voltage amplitude of node $i$ (unit: kV or pu). $V_{\min }$ and $V_{\max }$ denote, respectively, the allowable minimum and maximum values of voltage (typically ±5% of the nominal voltage).

The constraint prevents voltage over-limit from causing equipment damage or power quality issues on the user side.

(4)

Radial Topology Constraint

$${\displaystyle \sum _k{x}_k}=N-1-A$$

(12)

$x_k$, as defined above, is the state of switch $k$. $N$ is the total number of nodes in the distribution network (dimensionless). $A$ is the number of faulty lines witch refers to the quantity of lines that fail due to extreme weather (output by the fault prediction model).

The number of closed switches equals the total number of nodes minus 1 minus the number of faulty lines, ensuring the grid topology forms a tree structure to avoid circulating currents and maloperation of relay protection.

(5)

Switch Operation Limit Constraint

In a single optimization, the number of switch operations must be controlled, with the expression as follows:

$${\displaystyle \sum _k\left|x_k-x_k^{prev}\right|}\le K_{\max }$$

(13)

$K_{\max }$ is the maximum allowable number of switch operations in a single optimization (dimensionless), intended to prevent equipment damage caused by frequent operations. This restricts frequent switch operations, thereby reducing mechanical wear of equipment and maintenance costs. The overview of the specific variables is provided in Appendix A.

4. DRL-MILP-Based Algorithm for Model Solving

4.1. Analysis of Algorithm Applicability

Under extreme weather events, deep reinforcement learning (DRL) exhibits notable advantages over evolutionary algorithms such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) in handling uncertainties within distribution networks. The proposed DRL–MILP collaborative framework combines dynamic system characterization with intelligent decision-making, demonstrating superior adaptability and robustness under scenarios involving meteorological fluctuations, topological changes, and variations in load or power sources.

For instance, GA generates 100 typhoon scenarios via scenario sampling and retains high-reliability solutions through selection operators. However, its discrete search nature results in slow convergence and limited power supply reliability during abrupt wind-speed changes. PSO accelerates the search process through inter-particle information sharing, but it does not explicitly capture the coupling between meteorological conditions and load demand. Consequently, during periods of intense typhoon impact (10–18 h), PSO exhibits large load forecasting errors, leading to suboptimal feasibility and poor reliability in subsequent power transfer optimization.

While DRL is well suited for high-dimensional uncertainty and dynamic decision-making, its solutions may violate complex constraints. Conversely, MILP rigorously enforces hard constraints (e.g., line capacities, voltage limits), but its computational speed is insufficient for real-time dynamic scenarios.

Motivated by these observations, this study proposes an integrated DRL–MILP algorithm for solving the distribution network power transfer optimization problem. A closed-loop decision-making framework with a “state–action–reward” structure is established, leveraging the complementary strengths of DRL and MILP to achieve both adaptability and constraint compliance under extreme weather conditions.

4.2. Workflow of DRL-MILP Collaborative Optimization Algorithm

The DRL-MILP collaborative optimization framework employed in this paper adopts a two-stage optimization strategy: the first stage utilizes a deep Q-network (DQN) agent for global strategy learning to obtain the initial solution for scheduling decisions.

The inputs to the algorithm are: (1) fault probability prediction vector $F_t={\left[f_1(t) f_2(t) \dots \dots f_d(t)\right]}^T$; (2) load prediction vector $L_t={\left[l_1(t) l_2(t) \dots \dots l_d(t)\right]}^T$; (3) system state vector $X_t={\left[x_1(t) x_2(t) \dots \dots x_d(t)\right]}^T$. The state space is constructed as $S_t=[F_t,L_t,X_t]$, with a dimension of 66. The action space has a dimension of 37, of which 32 dimensions correspond to the active line switch action vector $a_i$, and the remaining correspond to action vectors for tie line activation. The DQN network is structured as a multi-layer perceptron, with its network architecture being

$$h_1=RELU(W_{1s}+b_1),W_1\in R^{256}$$

(14)

$$h_2=RELU(W_{2s}+b_2),W_2\in R^{256}$$

(15)

$$h_3=RELU(W_{3s}+b_3),W_3\in R^{128}$$

(16)

$$q=W_4{h}_3+b_4,q\in R^{37}$$

(17)

where $W_1, b_1, W_2, b_2, W_3, b_3, W_4, b_4$ denote network parameters. During the training process, the Adam optimizer is employed to minimize the loss function. The algorithm, through state space design and reward function construction,

$$R_t=0.5R_{rel}+0.3R_{\cos t}+0.2R_{stab}$$

(18)

where $R_{rel}$ represents the reliability reward, $R_{\cos t}$ denotes the economic reward, and $R_{stab}$ stands for the safety reward. Moreover, the specific algorithm flow chart in code implementation is illustrated in Figure 3.

In the second stage, the switch states generated by DRL are used as the initial solution and substituted into the MILP model. The CPLEX solver is then invoked to optimize load curtailment and detailed switch operations, ensuring that all constraints are satisfied.

To further enhance optimization accuracy, a dynamic superposition mechanism is incorporated at the final stage. When extreme weather conditions change abruptly—for example, wind speeds increasing from 35 m/s to 42 m/s—re-decision-making is triggered. In this process, DRL updates the initial solution based on the new system state, while MILP simultaneously adjusts constraint parameters, such as reducing line capacity by 10% due to elevated temperatures. The iteration cycle is set to 15 min, aligning with the update frequency of meteorological data.

This two-stage optimization strategy enables rapid response while ensuring constraint compliance under extreme weather conditions. By dynamically updating weather information, it also facilitates the formulation of more accurate and adaptive control strategies for distribution network power transfer. The functions and complementarities of each model are shown in

Table 3. Summary of model functions and complementarities.

Aspect	LSTM	DRL	MILP
Role in framework	Load/weather forecasting	Adaptive decision-making	Optimal scheduling/resource allocation
Input	Historical sequential data	Environment state, action space, reward function	Forecast results + system constraints
Output	Predicted load/weather profile	Near-optimal policy under uncertainty	Deterministic optimal transfer plan
Strengths	Captures temporal dependence	Handles stochasticity and learns adaptively	Guarantees mathematical optimality
Position in workflow	Data-driven prediction module	Decision-making module	Optimization solver module

.

5. Verification, Analysis of Results

5.1. Design of Simulation Case

The simulation is conducted on a 33-bus distribution system, as illustrated in Figure 4. The system comprises 33 nodes, 32 branch lines, and one slack node (substation) with a rated voltage of 12.66 kV and a total load of approximately 3.2 MW, representing a standard test model for distribution network optimization studies.

To reflect extreme weather scenarios, system parameters are adjusted accordingly. Line resistances and reactances are configured based on actual distribution line specifications (e.g., LGJ-120 conductors), with maximum transmission capacities ranging from 0.5 to 2.0 MW, depending on line lengths. Each line is equipped with smart switches capable of remote opening and closing. Nodes are categorized into three load types: critical loads (e.g., Nodes 5, 10, 20, corresponding to hospitals and emergency command centers; weight coefficient = 1.5; active curtailment prohibited), ordinary residential loads (e.g., Nodes 1–4, 11–25; weight coefficient = 1.0), and commercial loads (e.g., Nodes 26–33; weight coefficient = 0.8; moderate curtailment permitted).

Under normal operating conditions, the daily peak-to-valley load difference is 45%. During extreme heat, the proportion of air-conditioning load rises to 60%, while heavy rainfall increases the load of drainage pump stations (Nodes 8, 15) by 120%. The installed capacities of distributed photovoltaic (PV) and wind power (DWP) in the system are summarized in

Table 4. Renewable Energy Access Nodes and Power.

Access Location	Type	Rated Capacity/kW
6	DWP	300
12	DWP	300
18	DWP	300
33	DWP	300
7	PV	300
13	PV	400
27	PV	500

.

The evaluation metrics focus on three aspects: power supply reliability, decision-making efficiency, and robustness (decision adjustment time under sudden wind speed changes), aiming to comprehensively verify the performance of the proposed DRL-MILP cooperative strategy.

5.2. Simulation Scenarios and Parameter Settings

This paper presents a code for generating extreme weather data with an hourly time granularity, constructing a comprehensive meteorological dataset for an entire year (365 days) that includes temperature, humidity, wind speed, and rainfall. The temperature is generated by a combination of an “inter-annual sinusoidal trend (20 ± 10 °C), daily cyclic fluctuations (±5 °C), and Gaussian noise (σ = 2).” Humidity is modeled based on “seasonal sinusoidal variations (70 ± 15%) and Gaussian noise (σ = 5),” constrained between 30% and 95%. Wind speed is generated from a “base value (8 ± 5 m/s), weekly cyclic fluctuations, and exponentially distributed disturbances,” with an upper limit set at 35 m/s. Rainfall is modeled using a “seasonally dependent probabilistic trigger (0.15 ± 0.1) and exponentially distributed intensity” (with a zero intensity during dry periods).

For the typhoon “ Koinu,” the impact period is set from 00:00 on 3 October 2023, to 00:00 on 6 October 2023, with the peak intensity occurring at 12:00 on October 4. A piecewise linear function is employed to simulate the intensity rise from 0 to 0.85 (normalized maximum value), followed by a decay back to 0. The base meteorological data is then adjusted by: “temperature decrease by 5 × typhoon intensity, humidity increase by 20 × typhoon intensity (bounded between 0% and 100%), wind speed increase by 40 × typhoon intensity, and rainfall increase by 100 × typhoon intensity.”

Finally, an integrated extreme weather index is calculated by weighted fusion of the temperature anomaly standardized value (20% weight), wind speed deviation standardized value (30% weight), rainfall normalized value (20% weight), and typhoon intensity (30% weight). This extreme weather index serves as input for subsequent analyses of the coastal 110kV substation system. A summary of the weather parameter design is provided in

Table 5. Summary of synthetic meteorological data generation methods.

Variable	Generation Method/Model	Parameters/Ranges	Constraints
Temperature	Inter-annual sinusoidal trend + daily cycle + Gaussian noise	20 ± 10 °C trend; ±5 °C daily cycle; σ = 2
Humidity	Seasonal sinusoidal variation + Gaussian noise	70 ± 15%; σ = 5	30–95%
Wind speed	Base value + weekly cycle + exponential disturbance	8 ± 5 m/s; upper limit 35 m/s	Max 35 m/s
Rainfall	Seasonally dependent probabilistic trigger + exponential intensity	Trigger 0.15 ± 0.1	Zero during dry periods
Typhoon (Koinu)	Piecewise linear intensity function; baseline adjustment of variables	Intensity peak 0.85 (October 4, 12:00)	Adjusts T, H, W, R as described

.

5.3. Performance Validation of Models and Algorithms

Typhoon Koinu directly struck the study area, causing multi-dimensional impacts on the power grid’s transfer links, and coupled with insufficient output from distributed renewable energy sources, this collectively exacerbated the power supply gap, highlighting the urgency of optimizing power transfer. The dense cloud cover brought by the typhoon caused surface irradiance to plummet from 1000 W/m² on a normal sunny day to only 30–50 W/m² (a reduction of 95–97%), and wind speeds exceeding the protective threshold (43.3 m/s) triggered inverter shutdowns, resulting in distributed photovoltaic output dropping from rated capacity to merely 3%. At the same time, Force 16 strong winds far exceeded wind turbine cut-out speeds (typically 25 m/s), causing all four 300 MW wind turbines in the region to trigger emergency shutdowns and fail to offset the power supply gap. Meanwhile, the power grid topology suffered severe damage, with 28% of feeders interrupted due to tower collapses or insulator flashovers, significantly reducing power transfer paths, and 35% of smart switches could not be remotely operated due to physical damage or communication disruptions (with 40% of base stations failing), further restricting power transfer execution. Under the superposition of these multiple factors, the power supply gap continued to expand, making it imperative to improve power transfer efficiency through dynamic optimization strategies to ensure reliability—as illustrated by the case of distributed photovoltaics, where the sharp irradiance drop led to a steep decline in output (Figure 5).

5.3.1. Accuracy Analysis of Prediction Models

The LSTM model proposed in this study exhibits strong nonlinear adaptability in the emergency response to Typhoon Koinu. During the period of intense typhoon impact, it achieves a mean absolute percentage error (MAPE) of only 11.58%, reducing prediction error by approximately 40% compared with the traditional ARIMA method. This improvement is primarily attributed to the unique forget-gate mechanism of LSTM, which enables accurate modeling of non-stationary load curves under typhoon disturbances by dynamically learning the temporal characteristics of meteorological noise. Specifically, the forget gate effectively filters out abnormal fluctuations caused by abrupt wind-speed changes (e.g., gusts reaching 43.3 m/s), the input gate selectively retains key meteorological features (e.g., load patterns corresponding to a typhoon intensity index of 0.85), and the output gate produces probabilistic predictions that maintain errors below 1.2 MW during the passage of the typhoon eye (with maximum wind-speed fluctuations of ±15 m/s). These results verify the model’s capability to capture nonlinear relationships under extreme weather conditions. The prediction results and quantitative analysis are presented in Figure 6, Figure 7 and Figure 8 and

Table 6. Quantitative Indicators of Errors for Various Forecasting Methods.

Method	MAPE(%)	RMSE(MW)	RELATIVE ERRO
LSTM	11.8	14.2	1.1%
ARIMA	31.5	98.6	7.9%
SVM	14.7	28.8	2.3%

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5.3.2. Evaluation of the Optimization Effect of Power Transfer

During the emergency dispatch under Typhoon Koinu, the DRL–MILP–based optimization decision-making system demonstrated remarkable performance. Instead of disconnecting the high-risk line 3–23 (historical failure rate: 23%), the system imposed a flow limitation on this line while simultaneously activating three tie lines (8–21, 18–33, and 25–29) to establish a backup power supply network. This optimization strategy significantly enhanced system resilience, reducing the preventive power outage requirement to only one line. The results of the line transfer optimization are illustrated in Figure 9.

As shown in Figure 10, the system simulates a 72-h operational period, covering the stages before, during, and after Typhoon Koinu. Prior to wind speeds reaching the tripping threshold, the power system operates normally without intervention. At hour 20, the system forecasts the arrival of a strong typhoon within the next 24 h and issues an early warning for the high-risk line 3–23. Concurrently, an optimized power transfer scheme is deployed, completing the line transfer within 10 h to ensure uninterrupted system operation during the typhoon. By hour 50, the system detects that the typhoon has passed and performs systematic restoration of power to the previously transferred lines.

Figure 11 illustrates the load profiles of each node before and after power transfer. As shown, critical nodes near the generators exhibit no significant load reduction, thereby satisfying their power supply requirements. In contrast, nodes 26–33, located farther from the generators, experience noticeable load reductions due to the activation of two power transfer lines (18–33 and 25–29). These nodes are designated as commercial loads. During the typhoon, the system minimizes the load at commercial nodes to prioritize the power supply for critical nodes, ensuring system reliability under extreme weather conditions.

For the analysis of the DRL-MILP collaborative optimization algorithm in this paper, a single DQN network-based deep reinforcement learning algorithm is employed for comparative analysis. Both methods take power supply reliability as the reference index, and their comparative results are presented in

Table 7. Comparison of Power Transfer Results of Different Algorithms in the Scenario of Typhoon “Koinu”.

Algorithm	Number of Actions	Conformity Loss	Supply Rate
The algorithm in this paper	4	5.8%	94.2%
DQN algorithm	4	8.6%	91.4%

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The table compares the performance of the standalone deep reinforcement learning (DQN) algorithm with the DRL–MILP collaborative optimization method proposed in this study. The standalone DQN algorithm struggles to satisfy hard constraints, and its reward function cannot fully capture all constraint details, resulting in approximate optimal solutions. Consequently, the switching operations suggested by DQN may cause line overloads, leading to increased load loss and reduced power supply reliability. In contrast, in the proposed DRL–MILP framework, DQN serves to narrow the solution space, while the MILP model corrects and verifies the initial solution. Even if the preliminary DQN solution violates certain constraints, MILP optimizes the switch states mathematically to ensure full compliance with all hard constraints, thereby reducing load loss and enhancing the power supply rate of the distribution network.

6. Conclusions

To address the challenges of safe operation in distribution networks under extreme weather conditions, this study proposes an optimal control decision-making method for power transfer, integrating “accurate prediction–intelligent decision-making–dynamic optimization.” By combining LSTM-based load prediction, deep reinforcement learning (DRL), and mixed-integer linear programming (MILP), the proposed method enhances both the real-time performance and accuracy of optimal control decisions under uncertain extreme weather scenarios. Specifically, the LSTM model effectively captures complex nonlinear relationships between meteorological factors and load demand, while the DRL–MILP framework facilitates intelligent decision-making for network topology and power distribution. This integrated control strategy not only substantially improves operational reliability under disaster conditions but also ensures continuous power supply for critical loads.

Future work will focus on optimal control strategies for distribution networks under multi-hazard coupling scenarios, as well as rapid response mechanisms for multi-point distributed energy storage in emergency power supply, aiming to further enhance the resilience of power grids under extreme weather conditions.