Research on Mobile Energy Storage Configuration and Path Planning Strategy Under Dual Source-Load Uncertainty in Typhoon Disasters

Abstract

In recent years, frequent typhoon-induced disasters have significantly increased the risk of power grid outages, posing severe challenges to the secure and stable operation of distribution grids with high penetration of distributed photovoltaic (PV) systems. Furthermore, during post-disaster recovery, the dual uncertainties of distributed PV output and the charging/discharging behavior of flexible resources such as electric vehicles (EVs) complicate the configuration and scheduling of mobile energy storage systems (MESS). To address these challenges, this paper proposes a two-stage robust optimization framework for dynamic recovery of distribution grids: Firstly, a multi-stage decision framework is developed, incorporating MESS site selection, network reconfiguration, and resource scheduling. Secondly, a spatiotemporal coupling model is designed to integrate the dynamic dispatch behavior of MESS with the temporal and spatial evolution of disaster scenarios, enabling dynamic path planning. Finally, a nested column-and-constraint generation (NC&CG) algorithm is employed to address the uncertainties in PV output intervals and EV demand fluctuations. Simulations on the IEEE 33-node system demonstrate that the proposed method improves grid resilience and economic efficiency while reducing operational risks.

1. Introduction

Climate change is accelerating, resulting in increasingly frequent extreme weather events. According to the IPCC’s Sixth Assessment Report [1], the probability of catastrophic disasters continues to rise. Among them, typhoons represent a major threat to the reliability of power systems in coastal areas. Modern power systems, increasingly reliant on renewable energy sources and flexible distributed resources such as photovoltaic (PV) systems and electric vehicles (EVs), are more vulnerable to disruptions than traditional centralized grids. For example, Typhoon “Capricorn” in 2024 resulted in widespread outages across Hainan Province [2,3]. Typhoon often damages transmission infrastructure, such as lines and towers, potentially leading to partial or total system failure [4,5]. Therefore, comprehensive emergency strategies are essential throughout all phases of disaster management to improve grid resilience.

Existing research has explored various approaches to enhance power system resilience under typhoon disasters. These include physical reinforcement of transmission lines, though post-reinforcement restoration strategies for damaged systems have not been adequately investigated [6,7]; optimized layout design of distributed generation resources, without considering how mobile distributed resources could accelerate grid recovery [8,9]; and the pre-deployment of energy storage devices to maintain supply to critical loads, along with the development of planning and scheduling models for MESS to improve power supply reliability. While these studies utilize mobile energy storage as distributed resources to support restoration, they often overlook the impact of road disruptions and traffic congestion caused by disasters on power recovery efforts [10,11]. Some works have developed coordinated scheduling mechanisms between mobile energy storage and repair crews, yet most operate under deterministic constraints without accounting for uncertainties on both the supply and demand sides [12,13]. Others consider uncertainties related to renewable energy and load demand within a coupled transportation-power framework. Still, the treatment of load uncertainty tends to be oversimplified, neglecting the influence of user behavior uncertainty [14,15]. In summary, while existing studies address transmission line hardening under deterministic conditions, MESS scheduling for resilience enhancement, and restoration strategies accounting for supply–load uncertainties in a coupled transportation-power context, there remains a lack of integrated strategies that consider both resource allocation and mobile energy storage scheduling under source-load uncertainties to holistically improve power supply capability.

Under the “Dual Carbon” goals, the increasing proliferation of electric vehicles (EVs), along with the convenience, mobility, and maturation of vehicle-to-grid (V2G) technology, has established EVs as important distributed resources in distribution grid operation and scheduling [16]. In research on utilizing EVs to enhance power system resilience, Hasa M et al. proposed using battery swapping as a method to boost grid resilience, though without accounting for the randomness of user willingness to replace batteries [17]. Moore E A et al. suggested employing retired EV batteries as backup energy storage to ensure power supply, yet did not consider the mobility constraints of energy storage configuration [18]. Momen H et al. developed a mechanism for supporting critical loads using onboard EV energy storage, but did not incorporate the impact of source-side uncertainty in battery state on the power supply mechanism [19]. Li B et al. and Wang T et al. proposed strategies for using daily-operated electric buses and taxis as dispatchable resources to strengthen grid resilience, though without considering the source–load uncertainties related to the status of operational vehicles [20,21]. Gan W et al. established a novel resilience enhancement framework coupling transportation and power networks in a high-penetration EV environment, yet did not account for the impact of economic factors on user behavior in grid resilience strategies [22]. These studies, while exploring the use of EVs as distributed resources to improve grid resilience, generally lack systematic consideration of practical constraints such as battery health and uncertainties in user behavior, and fail to analyze the impact of dual source–load uncertainties of EVs on power system resilience.

On the other hand, the construction of distribution networks has evolved from traditional passive configurations to active management, with a progressively increasing share of distributed resources integrated on both the generation and load sides in actual operation, making uncertainties increasingly prominent. In research on grid resilience under such conditions, Yang X et al. proposed an optimization strategy for transmission lines under operational uncertainty but did not incorporate the potential correlated impacts of fluctuations in renewable energy outputs elsewhere in the system [23,24]. Wang Z et al. investigated uncertainty in the vulnerability and damage of distribution lines, considering only a single type of uncertainty while neglecting uncertainties on both source and load sides, such as PV output and electric vehicle status [25]. Zhang P et al. developed a resilience enhancement mechanism adapted to PV output uncertainty, yet the traditional algorithms used are inadequate for enhancing strategies under multiple overlapping uncertainties [26]. Liu L et al. proposed an optimal dispatch method accounting for uncertainty in offshore wind power output but did not achieve coordinated optimization to cope with complex scenarios where multiple types of uncertainties—such as PV fluctuation and load variation—occur simultaneously [27]. These studies are largely confined to analyzing individual types of uncertainty and lack a comprehensive integration of multiple potential uncertainties along with collaborative response mechanisms for their coupled impacts.

In summary, current research on power system resilience lacks integrated strategies that jointly consider multi-dimensional uncertainties from both supply and demand sides, as well as economic trade-offs in resource planning. To bridge this gap, this paper proposes a mobile energy storage system (MESS) configuration and routing strategy that addresses dual uncertainties in distributed PV output and EV charging/discharging behavior during typhoon-induced disruptions. The main contributions are as follows:

(1)

Considering the uncertainty of electric vehicle battery status, the randomness of charging and discharging caused by user economic driving behavior, and the uncertainty of distributed photovoltaic output, a more realistic dual uncertainty scenario is constructed to assess its impact on the power system. At the same time, electric vehicles are incorporated as key distributed resources into the post-disaster recovery process to enhance the system’s disaster resilience.

(2)

Develop a two-stage distributed robust optimization model framework for dual uncertainty that spans the entire disaster occurrence process. Utilize a mobile energy storage system as a resource allocation strategy for site selection and path planning, integrating spatiotemporal distributed resource output information with grid conditions to generate real-time dynamic path scheduling plans across the entire disaster process, thereby enhancing the power system’s supply capacity.

(3)

Propose an improved NC&CG algorithm to hierarchically decompose and iteratively solve complex two-stage models, thereby improving computational efficiency.

2. Two-Stage Distributed Robust Optimization Model Framework

Motivated by the increasing vulnerability of power systems under typhoon conditions, this study proposes a two-stage distributed robust optimization framework that accounts for dual uncertainties arising from both extreme weather events and distributed energy variability. The goal is to enhance system resilience and ensure power supply continuity under compound disaster scenarios. The structure of the proposed model is illustrated in Figure 1 and described in detail below.

(1)

Before a disaster, typhoon trajectory forecasts are used to estimate the likelihood of grid outages and traffic congestion. This information serves as the input to the two-stage model framework.

(2)

The first stage, which focuses on pre-disaster configuration, targets investment cost minimization through optimal siting and sizing of mobile energy storage systems (MESS). The configuration plan is then transferred to the second stage.

(3)

The second stage, which is the real-time scheduling layer, comprising three submodules:

(1)

EV uncertainty quantification;

(2)

operational dispatch planning;

(3)

worst-case PV output scenario generation.

The EV uncertainty module captures the stochastic features of user charging/discharging behavior and SoC fluctuations during disaster periods. The outputs of the EV scenario module and typhoon disaster forecasts are integrated into the operational planning module, which dynamically optimizes MESS dispatch routes. The optimization is bounded by worst-case PV output scenarios to minimize expected load loss. The resulting dispatch strategy is iteratively fed back to the first stage, forming a closed-loop solution process. The final outcome yields an optimal MESS configuration and path planning strategy that balances investment costs, enhances resilience, and ensures supply reliability.

3. MESS Configuration and Path Planning Model Under Double Uncertainty

3.1. Uncertainty Analysis Model

Typhoon disasters introduce significant uncertainty in both power supply and demand. To capture this, a dual uncertainty model is developed, incorporating the stochastic SoC and charging/discharging behavior of EVs, alongside the volatile output of distributed PV generation.

3.1.1. EV Uncertainty Model

Due to their high flexibility, EVs can act as both loads and distributed energy sources during typhoon scenarios. When unable to discharge, they behave as passive loads; when participating in V2G discharge, they contribute to the power supply. Accordingly, an SoC estimation model and a charging/discharging behavior model are developed to characterize EV behavior during disaster events.

(1)

EV SoC status estimation model

According to [28], SoC levels post energy usage and user charging/discharging patterns are analyzed. The SoC distribution at the disaster onset is modeled using uncertainty processing based on a probability density function. The uncertainty set of the SoC status of EVs is constructed based on the probability density function, and the uncertainty prediction set of EVs is shown in Equation (1):

$$U=\left\{E_{EV}|{\rm P}\left(E_{EV}^{nom}-\delta \le E_{EV}\le E_{EV}^{nom}+\delta \right)\ge 1-\alpha \right\}$$

(1)

In the Equation, $E_{EV}$ is the actual battery capacity at the time of the disaster; $E_{EV}^{nom}$ is the standard capacity upon arrival at the charging station; and $\delta$ is the capacity fluctuation deviation. $\alpha$ is the probability of capacity fluctuation exceeding permissible thresholds.

(2)

User charging and discharging behavior model

The advancement of V2G technology enables EVs to support grid optimization through bi-directional power flows. Given that V2G performance depends on battery degradation and user decisions, this model simplifies the behavior by omitting psychological factors and focuses solely on economic incentives. When the electric vehicle’s battery level falls below a specific threshold, battery degradation is high, and users exhibit weak discharge behavior. Discharge is disabled when the battery level is below a set threshold. Above this threshold, price-based incentives are introduced to stimulate discharge behavior. The discharge threshold represents the user’s willingness to participate in V2G activities. The formula for determining charging and discharging behavior is shown in Equation (2):

$$\left\{\begin{array}{ll}{E}_{EV(i,t+1)}=E_{EV(i,t)}-{\eta }_{dch}{P}_{dch}^{\max },\hfill & E_{EV(i,t)}\ge \gamma \hfill \\ E_{EV(i,t+1)}=E_{EV(i,t)}+{\eta }_{chg}{P}_{chg}^{\max },\hfill & E_{EV(i,t)}<\gamma \hfill \end{array}\right.$$

(2)

In the equation, $P_{dch}^{\max }$ is the discharge power of the electric vehicle; $P_{chg}^{\max }$ is the charging power of the electric vehicle; ${\eta }_{dch}$ is the discharge efficiency of the electric vehicle; ${\eta }_{chg}$ is the charging efficiency of the electric vehicle; $E_{EV(i,t)}$ is the electric vehicle power status of node i at time t; $E_{EV(i,t+1)}$ is the electric vehicle power status of node i at time t + 1; $\gamma$ is the discharge threshold.

3.1.2. PV Output Uncertainty Model

Distributed PV output is strongly influenced by environmental and meteorological conditions. During typhoons, this output becomes highly volatile and uncertain. To model this, a box-type uncertainty set is constructed based on pre-disaster PV output. The PV output is incorporated into a spatiotemporal-coupled uncertainty set indexed by time t, as shown in Equation (3):

$$V=\left\{P_{PV}\in {ℝ}^{N_{PV}\times T}\left|\begin{array}{c}\begin{array}{c}\exists q_{i,t}\in \{0,1\},\forall i=1,\dots ,N_{PV},t=1,\dots ,T\\ {\displaystyle \sum _{i=1}^{N_{PV}}{q}_{i,t}}\ge N_{PV}-e_t,\forall t=1,\dots ,T,\end{array}\\ P_{PV,i,t}=P_{PV,i,t}^{nom}\cdot \left(1-{\tau }_t+{\tau }_t{q}_{i,t}\right)\end{array}\right.\right\}$$

(3)

In the equation, $P_{PV}^{nom}$ is the initial photovoltaic output; $q_{i,t}=1$ is the nominal output maintained by node i during time period t; $q_{i,t}=0$ is the output degradation of node i during time period t; $N_{PV}$ is the total number of photovoltaic nodes; $e_t$ is the upper limit of the number of photovoltaic nodes experiencing output degradation during time period t; ${\tau }_t$ is the uncertainty during time period t; $P_{PV,i,t}$ is the actual photovoltaic output power of node i during time period t.

3.2. Mobile Energy Storage System Configuration Model

This section addresses the post-disaster recovery of distribution networks following typhoons by proposing a dynamic dispatch model. The model aims to optimize the pre-deployment and real-time dispatch of MESS under dual uncertainties from PV output and EV load variation, minimizing:

(1)

MESS configuration cost

(2)

EV power exchange cost under worst-case scenarios

(3)

load curtailment cost

3.2.1. Objective Function

The upper-level objective of the two-stage robust optimization model is to determine the optimal siting and economic efficiency of MESS under extreme uncertainty caused by typhoon-induced outages, thereby enhancing the resilience of the distribution network. The objective function is formulated as shown in Equation (4):

$$\underset{x_i,y_{ij}}{\min }\left[C_{MESS}{\displaystyle \sum _{i\in \chi }{x}_{i,0}}+Z\right]$$

(4)

In the equation, $x_{i,0}$ is 0–1, representing the connection status between the MESS and node i at time t = 0; $y_{ij}$ is 0–1, representing the circuit break status caused by the breakage of transmission line i to j; $C_{MESS}$ is the configuration cost per unit of MESS; $\chi$ is the set of all load nodes in the power grid; $Z$ is the objective function of the lower-level model.

3.2.2. Conditional Constraints

(1)

MESS quantity constraints

$${\displaystyle \sum _{i\in \chi }{x}_{i,0}}\le N_{MESS}^{\max }$$

(5)

In Equation (5), $N_{MESS}^{\max }$ denotes the maximum allowable number of mobile energy storage systems. Each node can connect to no more than one mobile energy storage device simultaneously, and the total number of MESS units deployed must not exceed the specified upper limit.

(2)

Benders’ cutting plane constraint

$$Z\ge C_{EV}{\displaystyle \sum _{k\in {\mathsf{\Omega }}_{EV}}{u}_{k,t}}+{\displaystyle \sum _{i\in \chi }{\beta }_i}{P}_{i,t}^L$$

(6)

In Equation (6), $C_{EV}$ represents the penalty cost associated with unmet EV charging and discharging demand, and ${\mathsf{\Omega }}_{EV}$ is the set of electric vehicles. $u_{k,t}$ denotes their respective charge/discharge power. ${\beta }_i$ refers to the penalty coefficient for load shedding at critical nodes, while $P_{i,t}^L$ is the corresponding load curtailment power. Equation (6) performs the linearization of economic losses under the worst-case uncertainty scenario in the lower-level problem.

(3)

Radial topology constraints

To account for islanding and reconnection phenomena during disasters, an enhanced single-commodity flow model is adopted to enforce distribution network radiality constraints [29]. These constraints are described in Equation (7):

$$\left\{\begin{array}{l}{\displaystyle \sum _{ij\in \phi }{y}_{ij}}=N_B-{\displaystyle \sum _{i\in \chi }{S}_i^{vs}}\\ {\displaystyle \sum _{j\in \mathsf{\Psi }(i)}{F}_{ij}}-{\displaystyle \sum _{k\in \varphi (i)}{F}_{ki}}=F_i^{vs}-1\\ -M_0{S}_i^{vs}⩽F_i^{vs}⩽M_0{S}_i^{vs}\\ -M_0{y}_{ij}⩽F_{ij}⩽M_0{y}_{ij}\end{array}\right.$$

(7)

In the Equation, $\phi$ denotes the set of all distribution lines, and $N_B$ is the total number of nodes. $S_i^{vs}$ is a binary variable indicating whether node i is virtually connected. $F_{ij}$ and $F_{ki}$ represent the virtual power flow between nodes i and j, and $F_i^{vs}$ is the virtual power at node i. ${\mathsf{\Psi }}_{(i)}$ and ${\varphi }_{(i)}$ indicate the sets of child and parent nodes for node i, respectively. $M_0$ denotes the maximum allowable virtual flow. Equation (7) ensures connectivity and physical operational feasibility among all nodes in the grid.

3.3. Air Conditioning Model for Mobile Energy Storage

3.3.1. Objective Function

$$\underset{u}{\max }\left[\underset{v}{\max }\underset{\begin{array}{l}y,P_{i,t}^{DG},Q_{i,t}^{DG},P_{i,t}^L,Q_{i,t}^L\\ P_{ij,t},Q_{ij,t},V_{i,t}^2,I_{ij,t}^2\end{array}}{\min }\left(C_{EV}{\displaystyle \sum _{k\in {\mathsf{\Omega }}_{EV}}{u}_{k,t}}+{\displaystyle \sum _{i\in \chi }{\beta }_i}{P}_{i,t}^L\right)\right]$$

(8)

In Equation (8), $u$ denotes the uncertainty set of EV state of charge, and ${\mathsf{\Omega }}_{EV}$ is the set of EV charging stations. $y$ refers to the MESS dispatching strategy. $P_{i,t}^{DG}$ and $Q_{i,t}^{DG}$ are the active and reactive power outputs of the internal combustion generator at time t, while $P_{i,t}^L$ and $Q_{i,t}^L$ represent the curtailed active and reactive loads, respectively. $P_{ij,t}$ and $Q_{ij,t}$ are the active and reactive power flows between nodes i and j. $V_{ij,t}^2$ and $I_{ij,t}^2$ denote the squared voltage and current magnitudes. $V_{i,t}$ is the photovoltaic power generation at time t.

3.3.2. Conditional Constraints

(1)

Mobility constraints for energy storage vehicle

$${\displaystyle \sum _{e\in \mathsf{\Omega }}{x}_{e,i,t_0}}=x_{i,0}$$

(9)

$$\left\{\begin{array}{l}{\displaystyle \sum _{e\in \mathsf{\Omega }}{x}_{e,i,t}}\le 1\\ {\displaystyle \sum _{i\in \chi }{x}_{e,i,t}}\le 1\end{array}\right.$$

(10)

$$\left\{\begin{array}{c}{\mathsf{\Omega }}_{i,t}=\left\{j|D_{j,i}\le V_0\cdot e^{\alpha (t)}\cdot (t_{ME}+\Delta t)\right\},t\in \tau \\ {\displaystyle \sum _{i\in {\mathsf{\Omega }}_{i,t}}{x}_{e,i,t}}=1\end{array}\right.$$

(11)

In Equations (9)–(11), $\mathsf{\Omega }$ denotes the set of MESS configurations. ${\mathsf{\Omega }}_{i,t}$ is the set of nodes reachable from node i at time t, while $D_{j,i}$ indicates the direct distance between nodes i and j. $V_0$ is the average driving speed of the MESS units, and $\alpha$ captures adjustments due to wind speed and road conditions. $t_{ME}$ is the residence time at node i, and $\Delta t$ is the required travel time to the next node. These constraints ensure spatial consistency with upper-level location planning, exclusive node-to-MESS connections at each step, and MESS units can only move directly to adjacent nodes. Among them, the constraints (2)–(5) related to MESS conditions are detailed in Appendix A.

4. Model Solution

Multi-layer nested models are difficult to solve directly, so this paper proposes a column constraint generation algorithm to solve the model.

4.1. Model Objective Function

To facilitate tractable computation, the two-stage decision-making model is reformulated into a matrix-based structure [30,31]. The objective function is linearized and simplified as shown in Equations (12) and (13):

$$\underset{x}{\min }{c}_{set}^{T}x+\underset{u\in U}{\max }\underset{v\in V}{\max }\underset{y}{\min }{c}^{T}y$$

(12)

$$s.t\left\{\begin{array}{c}Ax\le a\\ Bx+Fv+My\le d\\ Px+Qu+Ny\le h\\ (1)\text{–}(3)\end{array}\right.$$

(13)

In the Equations, x denotes the configuration-layer decision variables, while u, y, and v represent the dispatch-layer decision variables. A, B, F, M, P, Q, and N are coefficient matrices, and d and h are the associated constant vectors.

4.2. Model Decomposition

According to the NC & CG algorithm framework, the two-stage robust optimization model is decomposed into main and sub-problems across inner and outer iterative layers. This paper proposes a reverse-nested NC&CG algorithm featuring a reverse-nested and inner-layer-driven iterative structure. Within a single inner-layer iteration, the joint worst-case scenarios of photovoltaic power and electric vehicles are solved in parallel. A bidirectional real-time feedback mechanism is established to simultaneously feed these joint worst-case scenarios back to both the inner-layer and outer-layer master problems, achieving real-time response to uncertainties. An active joint cut generation strategy is introduced to dynamically generate and add Benders cuts to the outer-layer master problem, thereby proactively hedging against risks and significantly reducing the number of outer-layer iterations. The solution proceeds progressively from the inner to the outer layer. Within the inner layer’s master-subproblem cycle, subproblems are incorporated to resolve the lower-level model.

4.2.1. Outer Main Problem

Based on the worst-case photovoltaic output scenarios under extreme weather conditions derived from the inner-layer loop, the outer main problem determines the optimal mobile energy storage configuration through iterative dispatch path planning and cutting plane updates, under the maximum EV cost. The configuration results are fed back to the inner loop, as shown in Equations (14) and (15):

$$\underset{x}{\min }{c}^{T}x+Z$$

(14)

$$\left\{\begin{array}{cc}s.t.& Ax\le a\\ \begin{array}{l}\\ \\ \end{array}& \begin{array}{c}Z\ge c^T{y}_o\\ Bx+F{v}_o+M{y}_o\le d\\ Px+Q{u}_o+N{y}_o\le h\end{array}\end{array}\right.\begin{array}{c}\\ \begin{array}{l}\forall o\le o_e\\ \forall o\le o_e\end{array}\\ \forall o\le o_e\end{array}$$

(15)

In the Equations, $y_o$ denotes the decision variable at the o-th outer-loop iteration. $v_o$ and $u_o$ are the probabilities of the photovoltaic and EV power scenarios under worst-case conditions obtained from the inner layer. Z is an auxiliary variable representing the upper-level objective.

4.2.2. Outer Subproblem

The max–min scheduling model—constructed using the worst-case PV output from the inner-layer problems and the EV power uncertainty—is transformed into a single-layer maximization model via dualization. This step identifies the EV scenario that leads to the highest dispatch cost. The result is returned to the outer main problem as the worst-case robust scheduling cost, as shown in Equations (16) and (17):

$$\underset{x,u}{\max }{Z}_1$$

(16)

$$\left\{\begin{array}{cc}s.t.& Px+Q{u}_o+N{y}_o\le h\\ & (1)\text{–}(2)\end{array}\right.$$

(17)

In the Equations, $Z_1$ is an auxiliary variable representing the cost contribution of the EV uncertainty scenario.

4.2.3. Inner Main Problem

The most adverse photovoltaic output scenario identified from the inner subproblem is used to construct a min–max optimization structure in the inner main problem. After dual transformation, it becomes a single-layer minimization problem to determine the minimum unserved load cost and derive the optimal dispatch path plan for the mobile energy storage system. The solution is returned to the outer subproblem, as shown in Equations (18) and (19):

$$\underset{y,Z_1^{*},Z_2^{*}}{\min }{\displaystyle \sum _{t\in T}{c}^T{y}_t}$$

(18)

$$\left\{\begin{array}{c}\begin{array}{cc}s.t.& Bx+F{v}_t+M{y}_t\le d\\ & Px+Q{u}_t+N{y}_t\le h\\ & (1)\text{–}(3)\end{array}\end{array}\right.\begin{array}{c}\forall t\in T\\ \forall t\in T\\ \end{array}$$

(19)

In the Equations, $Z_1^{*}$ and $Z_2^{*}$ are the solution values of the EV and photovoltaic auxiliary variables, respectively. $y_t$ denotes the current optimal dispatch plan.

4.2.4. Inner Subproblem

Using the MESS configuration from the outer-layer and inner-layer master problems, together with EV dispatch plans and path information, the inner subproblem solves a maximization model to identify the worst-case photovoltaic power output scenario. This scenario is returned to the inner-layer main problem for further iteration, as shown in Equations (20) and (21):

$$\underset{x,v}{\max }{Z}_2$$

(20)

$$\left\{\begin{array}{cc}s.t.& Bx+F{v}_o+M{y}_o\le d\\ & \left(3\right)\end{array}\right.$$

(21)

In the Equations, $Z_2$ is an auxiliary variable associated with the photovoltaic uncertainty scenario.

4.3. Model Solution Process

A reverse NC & CG algorithm is applied to solve the multi-layer robust optimization model. The corresponding flowchart is illustrated in Figure 2. The detailed steps are as follows:

(1)

Step 1: Import typhoon disaster data, initialize the outer loop, set the upper and lower bounds of the outer loop $UBA=Inf$, $LBA=-Inf$, outer loop convergence value ${\epsilon }_A$, iteration count $k=0$.

(2)

Step 2: Input line fault information, solve the outer-layer main problem, obtain the configuration of the mobile energy storage system $X_k$, and update the lower bound of the outer loop $LBA$.

(3)

Step 3: Initialize the inner loop, initialize the photovoltaic scenario and electric vehicle scenario $u_0$, set the inner loop upper and lower bounds $UBB=Inf$, $LBB=-Inf$, and the inner loop convergence value ${\epsilon }_B$ and iteration count $n=0$.

(4)

Step 4: Input fault information, mobile energy storage system configuration information $X_k$, photovoltaic output scenario $v_n$, and electric vehicle scenario $u_n$, solve the inner loop main problem to find the scheduling scheme $y_n$, and update the inner loop lower bound $LBB$.

(5)

Step 5: Determine whether the inner loop convergence meets the convergence conditions. If it does, exit the loop; if not, proceed to Step 6.

(6)

Step 6: Input the scheduling scheme $y_n$ and the uncertain electric vehicle scenario $u_n$, solve the inner loop subproblem 2 to find the worst-case photovoltaic output scenario $v_n$, and update the upper bound of the inner loop $UBB$

(7)

Step 7: Input the scheduling scheme $y_n$ and the worst-case photovoltaic power output scenario $u_n$, solve the inner loop subproblem 1 to find the electric vehicle uncertainty scenario $v_n$, and update the upper bound of the outer loop $UBB$.

(8)

Step 8: Determine whether the outer loop convergence meets the convergence conditions. If it does, exit the loop to obtain the optimal solution; if not, continue to Step 2.

5. Case Study and Analysis

5.1. Case Settings

This study employs a modified IEEE 33-node distribution network topology for simulation analysis. The original IEEE 33-node network structure is mapped to a road network structure, with an idealized correspondence between road distances and nodal distances. Each branch between nodes in the IEEE 33 system is assumed to represent an actual road segment with a uniform length of 2 km. The resulting electro-road coupled structure is illustrated in Figure 3. The distribution network is supplied by five gas turbines and five photovoltaic arrays. To enhance system resilience, distributed EVs and MESS are integrated into the topological network. Detailed parameters of the gas turbines, EVs, and MESS units are provided in

Table 1. Parameters of Gas Turbine.

Distributed Energy Resources	Min/Max Output (kW)	Quantities	Efficiency
Distribution Generation (GD)	100/120	3	0.98
	60/80	2	0.98

and

Table 2. Parameters of MESS and EV.

Distributed Energy Resources	Min/Max Output (kW)	Quantities	Rated Capacity	Round-Trip Efficiency
EV	30/40	3	120	0.98
MESS	170/200	2	400	0.98

.

As typhoon disaster evolution modeling is well-established, this paper does not simulate specific disaster progressions. Instead, fault and outage scenarios are derived from historical typhoon data as referenced in [32]. It is assumed that the typhoon disaster scenario begins at 6:00 and ends at 16:00, with a disaster duration of 10 h, and a scheduling prediction time scale of 1 h. The configuration cost of MESS is RMB 500 yuan/kW, and the reward and penalty cost for charging and discharging EVs is RMB 100 yuan/kW. Based on functional differences in load demand, nodes with essential services—such as hospitals, data centers, and municipal infrastructure—are designated as critical nodes, while residential load points are classified as ordinary nodes. To reflect their importance, the penalty cost for load reduction at critical nodes is set to be ten times higher than that at ordinary nodes. Predictions are made based on historical PV output during disaster periods, and road congestion conditions are randomly generated as shown in Figure 4 and Figure 5.

5.2. Results Analysis

This study improves power system reliability by integrating pre-disaster deployment and post-disaster dynamic scheduling of MESS, with economic efficiency serving as the core criterion for resource allocation. In the power supply support strategy, V2G technology enables EVs to participate in grid balancing. However, the uncertainty in user behavior is explicitly modeled: once an EV’s SoC exceeds a preset threshold (for example, 70%), the decision to discharge is made autonomously by the user. Consequently, EV power support displays intermittent characteristics. The power evolution patterns of EV charging and discharging, and SoC status during disaster periods are shown in Figure 6 and Figure 7.

When the battery of an electric vehicle is in good condition, discharging it can better protect battery health. Therefore, the discharge threshold for electric vehicles is set at 70% of the rated capacity. Once the battery level reaches this threshold, users can independently decide on discharge behavior and duration under the discharge incentive mechanism. As shown in Figure 6 and Figure 7, during the 6:00–7:00 time slot, EV1 and EV2 did not reach the discharge threshold and only performed charging, while EV3 users who met the discharge conditions did not choose to discharge; during the 8:00–9:00 time slot, EV3’s discharge power was significantly lower than that of EV1 and EV2. During the 13:00 to 15:00 time slot, EV1 and EV2 did not perform charging or discharging. This reflects realistic EV behavior and underscores how uncertainty in user actions directly affects the grid’s power support capacity.

The mobility and flexible dispatch of MESS units play a pivotal role in post-disaster grid recovery. Therefore, this paper focuses on studying its pre-disaster configuration and post-disaster path planning strategies to enhance grid power supply reliability through optimized scheduling. Fixed mapping values are used for road and node distances, with a maximum vehicle speed of 60 km/h and an equipment switching time of 12 min. Two MESS units are pre-configured as dispatch units. Their charging/discharging profiles and SoC evolution are shown in Figure 8, with corresponding path planning details provided in

Table 3. Dynamic scheduling path planning for MESS.

Time	MESS1	Power/kW	MESS2	Power/kW
6:00	7	170	25	200
7:00	7	61.73	25	0
8:00	7	66.82	25	0
9:00	7	0	6	187.6
10:00	26	91.0	6	123.43
11:00	26	0	6	0
12:00	6	83.92	12	0
13:00	6	90.04	12	0
14:00	6	0	7	0
15:00	3	0	28	129.01
16:00	5	106.21	28	59.74

, and the routing diagram in Figure 9.

The routing of MESS is dynamically planned and scheduled based on real-time information, with decisions updated on an hourly basis. Constraints include real-time traffic congestion conditions and the number of nodes reachable per unit time. MESS units suspend discharging while en route to target nodes. As shown in Table 3, neither MESS1 nor MESS2 discharged during their movement from node 7 to 26 and from node 25 to 6, respectively—a strategy resulting from the algorithm’s trade-off between travel time and discharging benefits. If the target node cannot be reached within the scheduled time, the system automatically reroutes the MESS to the nearest node in urgent need of power to maximize supply capacity, as exemplified by MESS2’s return strategy during its movement from node 6 to 7. This adaptive retreat strategy in case of unreachable targets reflects the algorithm’s robustness against uncertainties. In scenarios where actual traffic congestion is more severe than predicted or the target node cannot be reached within the scheduled time, the algorithm triggers real-time emergency rescheduling. The immediate objective shifts to maximizing the support capability within the currently accessible range of the MESS, identifying the optimal node for assistance within its reach. During MESS routing and scheduling, power supply priority is given to critical nodes—such as hospitals, data centers, and communication base stations—and their adjacent nodes, followed by ordinary nodes. This prioritization is due to the higher importance of vital loads and their significantly higher penalty costs associated with power interruption. Therefore, both reliability and economic considerations justify prioritizing critical nodes. This decision is explicitly driven by the economic objective function of the model. The algorithm does not simply identify node types; it strictly follows an economic-driven principle. Thus, any scheduling action that reduces load shedding at critical nodes results in cost savings. During the solution process, the algorithm automatically prioritizes dispatching MESS to areas where the largest reduction in total system cost can be achieved. This not only enhances power supply reliability but also minimizes economic loss, directly mapping the optimization objective onto scheduling strategies.

The proposed two-stage robust optimization model achieves an average power supply rate of 99.1% for critical nodes and 92.05% for ordinary nodes throughout the disaster cycle. The power supply ratios for load nodes are shown in Figure 9.

5.3. Scenario Comparison Analysis

To verify the effectiveness of the proposed model and algorithm, four simulation scenarios were designed for comparative analysis. The scenarios are as follows:

(1)

Planning and scheduling without considering mobile energy storage configuration and uncertainty in EV scenarios.

(2)

Planning and scheduling without considering MESS configuration, but considering uncertainty in EV scenarios.

(3)

Planning and scheduling with MESS configuration but without considering uncertainty in EV scenarios.

(4)

Considering MESS configuration, planning, and scheduling under uncertain EV scenarios.

Different scenarios were simulated using the example parameters provided above and fault conditions caused by disasters as the background. The simulation analysis results are shown in Figure 10, which compares the grid load reduction power scenarios. The budget costs, consisting of pre-deployment costs and reduction costs, are shown in

Table 4. MESS configuration and budget costs in different scenarios.

Scene	Faulted Transmission Lines	Pre-Positioned Locations	Budgetary Constraints
Scene 1	1–2, 3–4, 12–22, 28–29, 32–33	1, 1	15,410
Scene 2	1–2, 3–4, 12–22, 28–29, 32–33	1, 1	16,321
Scene 3	1–2, 3–4, 12–22, 28–29, 32–33	7, 25	18,028
Scene 4	1–2, 3–4, 12–22, 28–29, 32–33	7, 25	13,299

. A comparison between the improved NC&CG algorithm and the standard NC&CG algorithm is presented in

Table 5. Efficiency Comparison Between the Improved and Standard NC&CG Algorithms.

Scene	Faulted Transmission Lines	Total Time (min)	Budgetary Constraints
NC&CG 1	1–2, 3–4, 12–22, 28–29, 32–33	13	13,299
NC&CG 2	1–2, 3–4, 12–22, 28–29, 32–33	30	13,299

.

Under the same testing scenario, a performance comparison between the enhanced NC&CG algorithm (denoted as NC&CG 1) and the standard NC&CG algorithm (denoted as NC&CG 2) is summarized in Table 5. Although both algorithms produce identical results, NC&CG 1 achieves a reduction of 17 min in computation time compared to NC&CG 2, reflecting a 29.56% improvement in algorithmic efficiency. This outcome substantiates that the reverse-nested and inner-loop-driven iterative architecture of the proposed NC&CG 1 significantly enhances computational performance and decreases solution time.

From an economic perspective, Scenario 4 achieves the lowest total cost due to the cost-effective pre-deployment of MESS and the avoidance of excessive EV incentive costs under uncertainty. This is attributed to the fact that the incremental investment in MESS deployment is less costly than the compounded expenses associated with uncoordinated EV dispatch, especially under deterministic assumptions which drive over-incentivization. Compared to Scenario 3, Scenario 4 achieves a 26.23% reduction in total budget due to the elimination of over-incentivized EV discharging caused by deterministic modeling. Similarly, when compared with Scenario 2, Scenario 4 reduces load reduction costs by 18.52% by introducing pre-configured MESS units into the planning scheme. In Scenario 3, high costs result from EVs discharging continuously at full capacity due to deterministic assumptions, which drive up incentive expenditures. In contrast, Scenario 4 enables users to autonomously manage charging/discharging, reducing incentives during off-peak periods. This dynamic control yields more economical investment strategies while maintaining similar levels of power supply reliability.

From a grid resilience standpoint, all scenarios exhibit a similar resilience curve characterized by a sharp decline during disaster onset, followed by stepwise recovery toward stability. During disasters, grid supply capacity plunges to a minimum level, followed by a sustained and staged recovery until system stabilization is reached. The initial rate of decline serves as a key indicator of system resilience. As illustrated in Figure 10, Scenarios 3 and 4 experience a slower drop in supply capacity than Scenarios 1 and 2, confirming the effectiveness of pre-deployed MESS in enhancing disaster-time support. In the power supply maintenance phase, Scenario 4 exhibits slightly lower supply levels than Scenario 3 due to intermittent EV discharging caused by user behavior uncertainty. Scenario 2, lacking MESS and facing islanding from line faults as well as unpredictable EV performance, suffers the most severe supply drop. Scenario 1, although lacking MESS, benefits from consistent EV discharging, mitigating islanding effects, and providing partial support to the system. During post-disaster recovery, the presence of MESS in Scenarios 3 and 4 enables faster recovery in the early phase than in Scenarios 1 and 2. This is enabled by the rapid redeployment of MESS units toward high-priority nodes, enhancing system resilience during early-stage restoration. However, in the later recovery phase, Scenarios 2 and 4 experience oscillating recovery trends due to uncertainty in EV charging/discharging, which leads to fluctuations in system output.

In summary, considering economic efficiency, grid supply capacity, and the inherent uncertainty of disaster scenarios, Scenario 4—which incorporates the mobile energy storage configuration strategy proposed in this study—demonstrates superior overall performance. It not only achieves optimal cost-effectiveness, but also provides enhanced pre-disaster resilience and accelerated post-disaster recovery, thereby significantly improving the system’s comprehensive configuration strategy.

6. Conclusions

This paper is based on a background of recovering from typhoon disasters and power system failures caused by source-load uncertainty. It constructs a two-stage distributed robust optimization model framework and proposes a MESS configuration and path planning model under dual uncertainty. The pre-disaster configuration cost of mobile energy storage and the post-disaster load loss cost are used as economic objectives to complete the configuration and path planning of MESS. The improved NC & CG algorithm is used to achieve multi-layer iterative solutions, ultimately generating the economically optimal pre-disaster configuration and post-disaster path planning strategies. The main conclusions are as follows:

(1)

The proposed dual uncertainty-based mobile energy storage configuration and path planning model quantifies the impact of electric vehicle state uncertainty and user charging/discharging behavior randomness on the power system, significantly enhancing the robustness of grid power supply reliability;

(2)

The two-stage distributed robust optimization model framework integrates pre-disaster MESS site selection and configuration with post-disaster dynamic path planning, achieving long-term and short-term optimization scheduling. This ensures power supply reliability while maximizing pre-disaster investment benefits and guiding the post-disaster recovery process to minimize loss costs.

(3)

The improved NC & CG algorithm proposed efficiently solves the complex two-stage model under dual uncertainty through a hierarchical decomposition strategy.

(4)

The simulation results confirm that the proposed mobile energy storage configuration and path planning strategy substantially improve the distribution network’s resilience and economic performance. The average power supply rate for critical loads is 99.1%, economic losses are reduced by 26.23%, and system operation risks are significantly mitigated, thereby validating the effectiveness of the strategy.

This study solely characterizes electric vehicle user behavior from an economic perspective, neglecting critical psychological and behavioral factors in disaster contexts, such as range anxiety, risk aversion mentality, and dynamically changing travel demands. Subsequent research will focus on refining the user decision model and exploring cross-network coordination between transportation and power systems to enhance the practical guidance of the model.