Coordinated Post-Disaster Recovery and Assessment Method for Integrated Electricity-Gas-Transportation System

Extreme disasters may cause damage to energy system’s components and transportation networks. How to achieve a rapid restoration of power supply is crucial. A coordinated post-disaster recovery and assessment method for the integrated electricity-gas-transportation system is proposed in this paper, and a repair sequence assessment model for the damaged road in transportation network based on topology and operational metrics is also established. Then, considering the dynamic changeability of the transportation network status, a rolling-updated model for dynamic road restoration and repair crew scheduling is proposed. Finally, we propose the coordinated post-disaster recovery and assessment model of electricity-gas-transportation system, in which the modified alternating direction multiplier of method is applied to solve. The impact of the transportation network repair process on system load recovery under different perspectives is verified by arithmetic examples.


I. INTRODUCTION
At present, with the tightened coupling, intensified complementarity and mutual aid of energy, the statue of integrated energy system (IES) in regional functional system is gradually prominent [1], [2]. However, due to the increasing extreme natural disasters caused by climate aggravation, the scale of IES failures may be further expanded through coupling factors. For example, in Taiwan's ''2017 blackout'', gas generators were disconnected from the grid, which eventually led to continuous power outages in 17 cities [3]. In February 2021, due to the shortage of natural gas caused by extreme cold weather, the natural gas generator was disconnected from the grid and the scale of power failure was further expanded in Texas [4]. It can be seen that the resilience of the IES is of great strategic significance for ensuring national and regional energy security [5]. As a key part to ensure the rapid The associate editor coordinating the review of this manuscript and approving it for publication was Ali Raza . recovery of energy supply, the research on coordinated post disaster enhancement strategies has also attracted extensive attention.
So far there has been some research literatures on coordinated recovery and enhancement strategy of IES. Generally speaking, the post disaster recovery strategy includes optimizing the load recovery sequence, flexibly dispatching emergency resources (mobile emergency power supply vehicle, energy storage vehicle, electric vehicle, etc.), switching the tie-lines for network reconfiguration, etc. The purpose is to give priority to ensuring the power supply for critical loads. Some research literatures have been explored in optimizing distributed generation [5], dispatching emergency power supply vehicles [6], dispatching emergency repair crew [7] and optimizing energy storage [8]. What's more, considering the AC power flow and gas hydraulic calculation, a coordinated operation strategy for the integrated gas-electricity distribution system is proposed in [9]. In [10], a two-stage optimization algorithm is used to solve the coordinated operation VOLUME 11, 2023 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ strategy problem of integrated gas electricity. Considering the effects of load, renewable energy, and demand response, [11] proposes an resilience enhancement framework for integrated electric-gas-heat systems. The above research did not include the impact of road traffic states in the recovery and enhancement strategy of the IES. However, extreme weather has a high probability of causing road damage or congestion, changing the travel time of repair crew and repair plan, and further affecting the formulation of optimal recovery strategy and repair path planning [12]. Therefore, precise evaluation of the emergency repair traffic status in each time period is the key basis for optimizing the repair strategy.
In recent years, there have been many studies on taking traffic effects into account in the optimal dispatching of multisystem integration [13], [14], [15]. The impact of dynamic transportation network is considered in emergency power supply vehicle dispatching [15]. Reference [16] applies riskaverting two-stage stochastic programming to solve the optimal trailer pre-allocation plan. In addition, research on the impact of transportation network on emergency repair and dispatching of IES has been gradually launched. In [7], considering the network reconfiguration and islanding influence, a coordinated repair dispatching model of electric power system (EPS) or natural gas system (NGS) is built under the consideration of transportation network, and a multistage dynamic recovery strategy is proposed.
Power lines and gas pipelines are not the only components that may be damaged. In EPS, the reason for power outages in many cases is due to the tower collapse and transmission line breakage. Fault factors may include humidity [17], vegetation [18], temperature [19] and earthquake [20]. The geometry and material properties of towers and lines under the extreme disaster occupy the main factor when judging the failure status. In NGS, the failure of pipelines occurs mainly due to earthquake, meteorological disasters and geological disasters. For damaged natural gas pipelines, the steps generally include depressuring, emptying the pipeline, excavating work pits, and repairing or replacing damaged pipelines. This is different from the principle of repairing power lines. The differences in repair process are reflected in the scale of damage, the length of repair time, and the number of repair crew personnel.
However, most of the existing post disaster recovery strategies are designed for a single system. In the IES that includes multiple energy operators, due to the differences in the interests' privacy, information barriers and technologies, the processing method of collecting all the information of the system in terms of operation and emergency repair does not meet the actual application situation. At present, the alternating direction method of multipliers (ADMM) is widely used to solve the problems of energy flow analysis [21], economic dispatch [22], operation optimization [23], stability control [24], resilience assessment [25], risk management [26], etc. The ADMM algorithm can effectively consider the impact of different stakeholders in the multi-energy system and meet the privacy protection requirements of the system's practical application. Considering the data privacy and technical barriers in the actual IES, this paper proposes a post disaster coordinated recovery strategy for IES considering the transportation network. The main contributions are as follows, 1) Considering the IES topology and operation metrics, a comprehensive decision-making model is proposed that weighs the repair sequence of damaged roads in the traffic network from the perspective of different energy sectors.
2) Considering the dynamic variability of the traffic network status, a dynamic scheduling framework for road repair crews is proposed, and the scheduling scheme for electric and natural gas repair crews is rolling-updated under real-time traffic status.
3) Under the demand for privacy protection of the command center and various departments, the multi-agent IES coordinated post disaster recovery model is established and solved by modified ADMM with limited information interaction. Based on the recovery strategy, the evaluation metrics of load recovery rapidity, load loss severity and traffic network impact degree are proposed.
The rest of the paper is organized as follows. Section II presents the multiagent IES coordinated post-disaster recovery and evaluation framework considering traffic network. Section III established the evaluation model of repair sequence of damage roads considering IES topology and operation indices. Section IV develops the dynamic road repair model and rolling updating model of repair crew dispatching. Based on the above Sections, Section V introduces recovery model and evaluation method. The effectiveness of the proposed method is demonstrated in Section VI through example analysis and Conclusions are drawn in Section VII.

II. MULTIAGENT IES COORDINATED POST-DISASTER RECOVERY AND EVALUATION FRAMEWORK CONSIDERING TRAFFIC NETWORK
There are multiple energy coupling modes and interaction relationships in the integrated electricity-gas energy system. Under the limited post disaster repair resources and dispatching capability, optimizing the repair sequence of fault components is an inevitable problem.
In addition, the states of connection of the post disaster transportation network will also affect the path and repair time of the repair crews. Therefore, it is of more practical significance to integrate the transportation network into the process of formulating multi-agent collaborative improvement strategies and resilience assessment after disasters. Coordinated post-disaster recovery framework is shown in Fig. 1.
This paper divides the problem into two stages. In the first stage, the repair sequence of damaged roads in the traffic network is determined based on IES topology and operation indices. Firstly, according to the specific damage information after the disaster, the IES topology and operation resilience indices are built and comprehensively evaluated. Then, according to the damage information of the transportation network and the deployment location of the repair center, the road repair sequences from different perspectives of power/natural gas are obtained, and the comprehensive weight of the emergency management center determines the repair priority weight. Then, dynamic repair of roads and rolling update of repair crew dispatching can be carried out until all faults are handled. The repair arrangement of repair crews obtained in the first stage will affect the states of connection of the traffic network in each period, and will indirectly affect the optimization results of the IES post disaster recovery in the second stage. In the second stage, taking the minimum load shedding loss of IES considering classification of load levels as the objective, considering that electricity and gas belong to different stakeholders and departments, the modified ADMM distributed algorithm is used to achieve distributed solution of each subproblem. The operation results of IES at each period, the repair crews dispatching strategy of each department can be obtained. Finally, we can calculate the evaluation indices for resilience assessment.

III. EVALUATION MODEL OF REPAIR SEQUENCE OF DAMAGED ROADS IN TRAFFIC NETWORK CONSIDERING IES TOPOLOGY AND OPERATION INDICES A. IES TOPOLOGY AND OPERATION RESILIENSE INDICES 1) DEGREE CENTRALITY
The greater the value of degree centrality is, the more important the line is when the system operates normally. In other words, it will play a more important role if the line with high degree centrality value is repaired first.
Here D G j,t r and D G p,t r represent the degree centrality of node j and the pipeline p between node j and node j ′ at time slot t r when there is no failures in the NGS. D E i,t r and D E l,t r represent the degree centrality of node i and the line l between node i and node i ′ at time slot t r when there is no failures in EPS. F GP p,max and P(j, t r ) refer to the maximum gas flow of gas pipeline p and the pipelines set connected to node j at time slot t r . F W j,t r , F P2G j,t r , F GG j,t r and F L j,t r refer to the gas flow from the gas source, the gas flow generated from the P2G equipment, the gas flow consumed by the gas-fired generator and the gas flow consumed by the load at node j at time slot t r when there is no failures, respectively. P max l and L(i, t r ) refer to the allowed maximum active power flow of power line l and the power lines set connected to node i at time slot t r . P grid i,t r , P P2G i,t r , P GG i,t r , P L i,t r refer to the power flow injected from the upper grid, the power flow consumed by the P2G equipment, the power flow injected from the gas-fired generator and the power flow consumed by the load at node i at time slot t r , respectively.

2) BRANCH/PIPELINE OUTAGE ENTROPY K
It is generally recognized that the more even distribution of power flow among multiple feeders is, the more reasonable it is. Similarly, the gas flow is also consistent. According to the improvement of branch outage entropy in [27], it is used to describe the transfer and balance ability of power flow or gas flow reaching a new state in IES after the fault lines/pipelines are repaired after the disaster. Here is the equation to determine the weighted indices S k of branch/pipeline k transmission capacity, where v k is the weight, and X k is the branch reactance in the power grid or the steady-state constant of the gas pipeline in the gas network. Design an equivalent transfer ratio λ t of energy flow transfer of the system, which refers to the energy flow transmission of all branches/pipelines at t. After the failure is repaired, the smaller the value is, the more even the energy flow load on the system branches/pipelines is, and the more reasonable the energy flow distribution is. Here's the expression, where n k refers to the number of branches/pipelines in normal operation in the current state of system, Refer t k and t 0 as the repair moment of branch/pipeline k and the initial moment, respectively. Then the branch/pipeline outage entropy K k is,

3) RATIO OF ENERGY SUPPLY RESTORATION R
The ratio of energy supply restoration measures the effect of load improvement after repairing a specific power line or VOLUME 11, 2023 gas pipeline compared with the initial state after the disaster. It can be expressed as, where R l and R p respectively represent the promotion ratios of repairing power line l and natural gas pipeline p to the restoration of load energy supply. t l and t p refer to the moment when the power line l and gas pipeline p resume energy supply respectively. The bigger the value, the more obvious the effect on the load energy supply restoration after the repair of this power line or pipeline.

B. MULTIPLE INDICES INTEGRATION AND COMPREHENSIVE IMPORTANCE INDICES
IES topology and operation indicators need to further realize multi-indicator fusion through weight allocation. Through the optimal comprehensive weights (OCWs) model (10), the optimal weight and the sum of squares of subjective and objective deviations are minimized, as shown in the following equation, where τ s,k , τ o,k refer to subjective and objective weight, which can be obtained using AHP and CRITIC respectively [28]. ρ s,k and ρ o,k denote the weighting coefficients of subjective and objective weight of index k. N m refers to the number of indices. w k refers to refer to the optimal comprehensive weight of k th index. According to the optimal comprehensive weight obtained, calculate the sum of comprehensive importance indices ψ α E and ψ α G of each fault power line or pipeline. For the specific process, please refer to [29].

C. ROAD PRIORITY
In the repair process, the road states are constantly changing, so the states of the traffic network at each time can be expressed by matrix TN t , which is calculated using initial state matrix TN 0 of traffic network and congestion coefficient matrix t . It can be expressed as, where t ij refers to the congestion coefficient of the road between node i and j at moment t. T ij refers to the travel time of road between node i and j under normal traffic condition.
According to the importance indices, the EPS department can formulate the repair sequence of damaged lines and the shortest traffic route for the repair crews. Similarly, the approach can be applied to the NGS department. Thereafter, the emergency management center and the road administration department need to balance the different repair sequences of damaged roads from the perspective of the EPS department and the NGS department, and formulate the repair route for the road repair crews, so as to achieve the goal of coordinated recovery among multiple departments.
In this paper, the sequence of road repair is measured by the shrunk time t E r and t G r of the total distance traveled by professional repair crews in the EPS or NGS department after road r restoration.
Here N E and N G refer to the number of fault power lines in EPS and gas pipelines in NGS. d E and d G refer to EPS and NGS's repair center. t r and t 0 refer to the traffic network congestion degree before and after road r is repaired to normal traffic state. Take T (k, α E , t r ) as an example, it refers to the total travel time from k to the damaged power line α E calculated by Dijkstra algorithm under the traffic network TN t r (TN t r = TN 0 * t r ).
Through weighting the shrunk time t E r and t G r , the shrunk time for the whole IES repair process can be obtained, and then the road repair priority can be obtained as below: where β E and β G refer to the impact coefficient of EPS and NGS to balance the impact of road restoration on IES.

IV. DYNAMIC ROAD REPAIR MODEL AND ROLLINGUPDATED MODEL OF REPAIR CREW DISPATCHING
After the road repair priority w r is obtained, the optimal personnel allocation of the road repair crew can be achieved by minimizing the time for the road to resume normal traffic. The dynamic road repair process is shown in Fig. 2.
Here nc r is the number of personnel repairing road r, nc all is the total number of repair personnel, demand r is the workload of repairing road r, and d R refers to the road repair center. This part can get the traffic conditions of the traffic network at each moment, which is the dynamic dispatching basis of the following professional power line or pipeline repair crews of EPS and NGS. With the help of the importance indices in III-B, the optimal dispatching of professional repair crews of EPS and NGS can be achieved by minimizing the repair time of components.
In Eq. (17), ψ r denotes the comprehensive importance indice obtained from Section III-B. u r,t is a binary variable employed to indicate the time step at which the component r is repaired.
if the repair work is not started or already finished. r refers to the damaged power line α E or damaged gas pipeline α G . t 0 is the initial time.
The dispatching constraints of repair crew include dispatching constraints and travel time constraints. The following is an example of EPS. The fault element is power lines. Suppose that the number of repair centers is 1, the set of repair crews is R r , the number of repair crews is c r , and the set of all damaged lines is S r . The following constraints exist, r∈S r x c r d,r = 1, ∀c r ∈ R r (21) Here y c r r and x c r r,s respectively refer to 0/1 variable whether repair crew c r passes through damaged line r, and 0/1 variable whether repair crew c r heads to damaged line s from damaged line r. x c r d,r refers to 0/1 variable whether repair crew c r heads to damaged line r from road administration department repair center d. Eq. (19) constrains that each damaged line can only be repaired by one repair crew, Eq. (18) constrains that the repair crew will leave the node immediately after the repair task of the damaged line is completed. Eq. (21) constrains that the starting point of all repair crews is the repair center.
The following are the constraints on the repair of damaged lines including time state, Here t c r r , T c r r , t c r r,s refer to the moment repair crew c r reaches damaged line r, time for repairing the damaged line r, and time on the route for heading to damaged line s from damaged line r. M is a large enough number. τ r refers to the moment finishing repairing damaged line r. u r,t refers to 0/1 variable whether damaged line r is repaired at moment t. Eq. (22) and (23) respectively constrain the time for the repair crew to travel from the damaged line r to the damaged line s and the moment to arrive at the damaged line, and Eq. (24) constrains the time for the repair crew to repair the damaged line. Eq. (25) and (26) are constraints on repair states and its relationship with repair time.
The process of dynamic updating of route for repairing fault components is as follow: 1) Initialize t = 0 and initialize the repair scheme according to (17). 2) With reference to the traffic network states at each moment t, each repair crew updates the route decision scheme in the future fixed time period and records it. 3) Update moment t = t+1; Repeat b) until all repair crews complete the repair task. It is worth notice that at moment t when the repair crew is driving (not reaching the nodes at both ends of the road) or in the repair task, the initial state of the repair crew is set as the starting point of the road in the optimization problem solution, and the subsequent route decision records are retained. When the repair crew is at the end node of the driving road at moment t, the latest decision-making scheme shall be executed. The process above completes the determination of recovery priority and the optimal route planning for multiple repair crews, so the connection states of the traffic network and the operation states of each damaged component can be obtained in the post disaster recovery.

V. MULTIAGENT IES POST-DISASTER RECOVERY MODEL AND EVALUATION METHOD CONSIDERING THE IMPACT OF TRAFFIC NETWORK A. OBJETIVE FUNCTION
In order to reduce the economic loss caused by IES failure, this paper set the objective as minimizing the loss of IES load shedding which considers the importance level of loads.
Here C LS i,t and C LS j,t refer to the loss cost of unit electric load of node i and unit gas load of node j during period t. E is the conversion coefficient from gas flow unit to electric power unit. ω i and ω j refer to the importance level of electric load at node i and gas load at node j. P LS i,t and F LS j,t refer to the active power of electric load shedding at node i at moment t and the gas flow of gas load shedding at node j at moment t. t refers to time step.

B. OPERATION CONSTRAINTS OF ELECTRICITY-GAS INTEGRATED ENERGY SYSTEM 1) EPS CONSTRAINTS
The radial distribution network power flow model adopts the Distflow model with second-order cone relaxation, and the constraints are as follows, where ϖ i is 1 if node i is connected to the upper grid. refer to the active power and connection state of gas generator m at moment t. P P2G n,t , s P2G n,t refer to the active power and connection state of P2G equipment m at moment t.
refer to the active and reactive power of shed load and load of node i at moment t. U i,t refers to the square value of the voltage at node i at moment t. P ij,t , Q ij,t , s ij,t refer to the active and reactive power flow between node i and j and the states of transmission lines between node i and j.r ij , x ij refer to the resistance and reactance of transmission line between node i and j. I ij,t refers to the square value of the current on the transmission line between node i and j at moment t. M is a large enough number. Eq. (32) is the cone form of (31). What's more, upper grid power constraint, gas generator power constraint, P2G equipment power constraint, node load constraint and operational constraint of the grid are also included as follow: where P grid min , P grid max , Q grid min , Q grid max and s grid i,t refer to the lower and upper bounds of active power and reactive power and connection state of the upper grid connected to node i at moment t. P GG m,min , P GG m,max , s GG m,t refer to the lower and upper bound of active power of gas generator m at moment t and its connection state. P P2G n,min , P P2G n,max , s P2G n,t refer to the lower and upper bound of active power of P2G equipment n at moment t and its connection state. P LS i,t , Q LS i,t , P L i,t , Q L i,t refer to the active and reactive power of shed load and load of node i at moment t. U i,t , U min i , U max i refer to the square value of the voltage and its lower and upper bound at node i at moment t. I ij,t , I max ij refer to the square value of the current and its allowed maximum value on the transmission line between node i and j at moment t.

2) NGS CONSTRAINTS
Gas system constraints include gas source constraints, gas load constraints, node gas pressure constraints, pipeline gas flow constraints and node balance constraints, are shown as below, where F W w,t , F W w,min , F W w,max refer to the gas production of gas well w at moment t, its lower and upper bound respectively. F L j,t , F LS j,t refer to the required gas load and gas load shedding at node j at moment t. π j,t , π min j , π max j refer to the gas pressure, its lower and upper bound at node j at moment t respectively. B uv,t refers to the gas flow direction between node u and v at moment t, which is 1 when gas flows from u to v. k uv refers to the steady-state constant of the gas pipeline between node u and v. F GP uv,t and F GP uv,max refer to the gas flow and its upper bound in the pipeline between node u and v at time t. F P2G j,t and F GG j,t refer to the amount of gas generation from P2G equipment and the amount of gas consumption from gas turbine connected to node j at moment t. For the nonconvex and nonlinearity of pipeline gas flow constraint (46), variables are introduced for relaxation and linearization. For more details, please see [30].

3) COUPLING COMPONENT CONSTRAINTS
The relationships between the power and the gas flow for the gas generator and P2G equipment are as follows, P GG m,t = η GG m F GG m,t C gas , ∀t, ∀m ∈ GG (49) P P2G n,t = C gas · F P2G n,t η P2G n , ∀t, ∀n ∈ P2G where C gas refers to the high calorific value of natural gas. η P2G n refers to the conversion efficiency of P2G equipment n. η GG m refers to the conversion efficiency of gas generator m.

C. SOLUTION ALGORITHM
The ADMM algorithm with simple form, good convergence and strong robustness does not require the sub-optimization objective function to be strictly convex. It is a distributed mathematical optimization method that has been widely used in recent years. The original ADMM only works for twoblock systems. According the introduction in [31], there are three fundamental types of multi-block ADMM which are: Variable Splitting ADMM(VS-ADMM), Gauss-Seidel ADMM(GS-ADMM), and Jacobian ADMM (J-ADMM). In addition, there are many modified ADMM algorithms based on traditional principles. The comparison of the different distributed optimization algorithms is shown in Table 1.
The subsystems in the IES belong to different interest agents, and there are differences in data privacy, operation and maintenance professionalism, which is not suitable for using centralized algorithms to solve in practice.
In order to realize distributed solution of each subsystem of multi-agent IES, coupling variables in EPS and NGS are selected as shared transfer variables, i.e. gas consumption of gas-fired generators and gas production of P2G equipment. In order to decouple the electricity-gas interconnected system, introduceF GG m,t andF P2G n,t into the power system and meets the following consistency relations, n,t C gas , ∀t, ∀n ∈ P2G (54) where C gas refers to the high calorific value of natural gas. η P2G n refers to the conversion efficiency of P2G equipment n. η GG m refers to the conversion efficiency of gas generator m. The modified ADMM algorithm with adaptive change of penalty coefficient has practical applicability, and the original objective function can be divided into two subproblems, namely, EPS and NGS subproblems. The objective functions of EPS and NGS subproblem are as follows, The distributed solution algorithm of integrated electricitygas energy system based on improved ADMM is detailed below.
Step 2: The operator of EPS and the operator of NGS share the information of coupling components, and calculate the average value of coupling variables according to (57) and (58) respectively.
Step 3: After the penalty coefficient of the k th iteration is obtained, each dispatching center can solve its own minimum load shedding loss problem in parallel: 1) The EPS operator solves the optimization problem (55) and updates the coupling variables. , and update them.
Step 4: Calculate the original and dual residuals to compare and determine whether they reach convergence. Based on theF If the maximum value of all original residuals is less thanε pri and the maximum value of all dual residuals is less thanε dual , the convergence condition is reached. The results can be output. Then go to step 5. Otherwise, the penalty coefficient is updated according to (63) Step 5: Record the iteration optimization results.

D. EVALUATION INDICES OF LOAD RECOVERY PROCESS
In order to better evaluate the coordinated post disaster recovery effect of the electricity-gas-transportation coupling system, on the basis of the above specific recovery strategies and the operation results of the post disaster recovery model, the load recovery process evaluation indices are built, and the evaluation results can be more intuitive and comprehensive. a) Load recovery rapidity index: It refers to the time taken for the load to recover from the initial state to x% after the disaster, reflecting the speed of load recovery.
b) Post disaster load shedding severity index: It refers to the load shedding during the whole process from time t 0 to t 1 after the disaster.
c) Traffic network influence index: It refers to the influence degree of considering the recovery of traffic network on the severity of load shedding.

VI. EXAMPLE ANALYSIS
A. BASIC DATA The example verification system selected in this paper is shown in Fig. 3. It is an electricity-gas coupling system which includes an improved IEEE 33-bus distribution system and a Belgian 20-node gas system. The traffic network is obtained by making appropriate improvements based on the topology of the 33-bus network. The initial energy system failure state and the traffic network congestion state have been marked in Fig. 3. It is assumed that the load importance levels of each bus in EPS or each node in NGS at every moment are the same and do not change dynamically with time in case analysis. The high and low importance loads are considered in this research. High importance level load is marked by a five-pointed star in Fig. 3 and each load is assigned with a coefficient. The importance coefficient equal to 1 for low-importance loads, while high-importance loads equal to 3 or more. The traffic network parameters and road repair workload are shown in Appendix A. The repair time needed for damage power lines and gas pipelines can be set to 3h and 2h in this paper, respectively. For more detailed EPS and NGS network parameters, please see [30] and [36]. The EPS repair station, NGS repair station, and road repair station are respectively located at nodes 4, 32, and 6 in the traffic network.

B. RESULT ANALYSIS 1) IMPORTANCE INDEX AND ROAD REPAIR PRIORITY
The normalization results of the topology and operation resilience indices proposed according to the fault components are shown in Fig. 4. The values of various indices are different for each power line and pipeline. The degree centrality and outage entropy of T 2-3 L are lower than those of other power lines, but the energy supply restoration index is significantly higher than that of other power lines. Therefore, the comprehensive resilience index calculated according to the multiple indices integration model are the highest among all damaged power lines. The comprehensive resilience index of P 9-10 L is the largest among the damaged gas pipelines, that is, repairing it in priority is more significant for system recovery.
According to the multiple indices integration model, the subjective weight is obtained by analytic hierarchy process (AHP), and the objective weight is obtained by criteria importance though intercrieria correlation (CRITIC). Then the comprehensive weight can be solved by Eq. (10). The comprehensive indices calculated thereafter are shown in Table 2. All indices have been per-unit normalized. The evaluation results of metrics obtained through different methods (OCWs, AHP and CRITIC) have roughly the same numerical trend but the specific values are different. For example, for the CRITIC method, T 2-3 L is less important than T 21-22 L and the indices differ greatly. For the AHP method and the comprehensive weighting method, T 2-3 L is more important than T 21-22 L ; For the same line or pipeline, the value of the integrated resilience index obtained by AHP method and CRITIC method differs greatly. The optimal comprehensive weights method is a comprehensive consideration of the two methods, so the indices values obtained are more reasonable, avoiding the one-sided subjective or objective analysis.
According to the comprehensive resilience index of the fault component, the calculation results of road repair priority index from different perspectives are shown in Fig. 5. From the perspective of EPS department, the top four priorities of road needed to repair are Road 3-4, Road 4-5, Road 20-21, and Road 6-12. From the perspective of the NGS department, the top four priorities of road needed to repair are Road 3-4, Road 20-21, Road 4-5, and Road 25-29. It can be found that different departments propose the sequence of road repair from their own interests, which often conflicts with other departments. Therefore, we balance the EPS and NGS perspectives through the emergency management center. According to the obtained road repair priority index, the road repair crews' routes can be formulated.

2) THE CONVERGENCE ANALYSIS OF THE PROPOSED DISTRIBUTED POST-DISASTER RECOVERY SOLUTION ALGORITHM
The efficiency of the system under the proposed algorithm can be reflected in these two aspects: computation time and iteration times. The computation time mainly includes repair crew dispatching and post-disaster recovery process optimization. These two parts take 10.62 sec and 29.91 sec of computation time, respectively. At the initial penalty parameters ρ GG , ρ P2G of 5, the modified ADMM algorithm takes 25.32 sec after 19 iterations to reach the convergence condition. The evolution of max-residual in the iterative process is shown in Fig. 6. The factors influencing the computational efficiency contain the system size and the initial setting parameters in the algorithm, such as, Lagrange multiplier, penalty coefficient, convergence threshold, et al.
The proposed distributed post-disaster recovery solution algorithm is compared to the existing distributed optimization algorithms including the ADMM with constant penalty parameters (ADMM-c) in [37], Gauss-Seidel ADMM (GS-ADMM) in [33]. To compare the performance of algorithms, the initial values of coupling variables and penalty parameters are the same in these algorithms, and the maximum number of iterations is set to 200. The calculated results between the different algorithms are shown in Table 3.

3) ROAD REPAIR AND SYSTEM LOAD RECOVERY PROCESS FROM DIFFERENT PERSPECTIVES
The dynamically changing results of traffic network congestion degree are different under three different perspectives, as shown in Fig. 7. From the perspective of the emergency management center, the route schedule of road repair crews is shown in Fig. 8 after comprehensive consideration of the road repair sequence.
From the perspective of different departments, different road repair sequences have different impacts on the restoration process of EPS, NGS and the entire integrated energy system. In general, the restoration effect of EPS and NGS from comprehensive perspective is the best. In Fig. 9 (a), in the case of road repair from the perspective of NGS, the load recovery proportion of EPS is around 10∼13h higher than that from the perspective of EPS itself, but there is a significant slowdown in the later period. In Fig. 9 (b), when the road repair process is carried out from the perspective of NGS itself, the recovery effect is not optimal, which indicates that the perspective of a single department is one-sided and the road repair process from comprehensive perspective of the emergency management center is required to achieve the effect of optimal load recovery proportion for the whole system, as shown in Fig. 9 (c).

4) INFLUENCE OF TRAFFIC NETWORK ON SYSTEM LOAD RESTORATION PROCESS
For further comparative analysis, we set up three scenarios from the comprehensive perspective of the emergency command center: 1) Scenario 1: only consider the initial post-disaster state of traffic network; 2) Scenario 2: The damage state of traffic network is not considered; 3) Scenario 3: Consider the dynamic real-time state of traffic network. In each scenario, the dynamic update of the route for EPS's or NGS's repair crews to repair the fault components is realized. Fig. 10 and Fig. 11 show the scheduling results for repair crews through relevant timetable.
The more intuitive change of load proportion in the recovery process is shown in Fig. 12. The evaluation indices of load recovery process proposed in section V-D are calculated, and the results are shown in Table 4. It can be seen that scenario 1 and Scenario 3 take the same time to recover the load from the initial state to 60%. The time taken to recover from the initial state to 90% of scenario 1 is more than 24h, and that of scenario 3 is 17.664 h. Only considering the initial damaged state of the traffic network after the disaster has little impact in the early recovery period. The recovery strategy that does not consider the dynamic update of the traffic network state has a low load recovery efficiency in the later period, and the evaluation effect is the most conservative.
It can also be seen from S r and T r that the load recovery process without considering the damage state of traffic network is more optimistic and has higher recovery efficiency, but this will also lead to a large gap with the actual situation. The reason is that the real-time state considering traffic dynamic changes is more practical. By analyzing the reasons, the difference between only considering the recovery process under the initial traffic network damage state and considering the dynamic updating traffic network is as follows. In the early period of recovery, the gap was not highlighted due to the time required for traffic driving and maintenance. However, in the later period, as more damaged roads returned to normal traffic state, and the rolling update method is adopted for repair routes of faulty components,    it made the consideration of a more efficient load recovery process in scenarios where traffic state dynamically change in real time.

C. FEASIBILITY ANALYSIS AND FUTURE PROSPECT
The method has both theoretical feasibility and practical feasibility. IES topology and operation resilience indices,  optimal comprehensive weights, dynamic repair crew dispatching model, multiagent IES post-disaster recovery model and solution algorithm are all theoretically applicable. For practical feasibility, whether the distinction of IES multi-agent perspectives or repair crew allocation meet the application background. The modified ADMM algorithm can be performed with limited information interaction and rolling-updated scheduling strategy can be adjusted at any time according to human decision-making, which has practical significance and strong operability.
The distribution network is designed in closed loop and operated in open loop. When we consider the network reconfiguration in the original framework, the IES topology and operation resilience indices will change accordingly due to the change of network connectivity. Considering distributed generation, relevant distributed resource constraints need to be added in Section V-B. Taking mobile energy storage system as an example, routing and scheduling constraints, energy storage constraints and charging or discharging constraints should be supplemented, which may affect the postdisaster recovery and optimization results at each moment to varying degrees. Therefore, network reconfiguration and distributed generation can be considered by supplying additional related mathematical models. Due to the different optimization results of post-disaster recovery, the dynamic rolling update result of repair crew dispatching may change at each moment, and then affect the scheduling of repair crews.
In the future, the interaction between transportation network and power distribution system will be further investigated. A more realistic transportation network will be studied for post-disaster dispatch of emergency resources. In addition, distributed generation and network reconfiguration will be taken into account in the model to make the restoration strategy more practical.

VII. CONCLUSION
This paper proposes a coordinated post-disaster recovery strategy for the multi-agent integrated energy system considering the transportation network. Firstly, the IES topology and operation indicators are calculated. Based on the comprehensive importance of IES's fault components obtained by the fusion of multiple indicators, an evaluation model for the repair sequence of damaged roads considering the traffic network is proposed from perspective of different energy sectors. Then, considering the dynamic variability of the repair status of the traffic network, a rolling update model of roads dynamic repairing and repair crews scheduling is established. Finally, under the premise of limited information interaction between the emergency management center and various departments, the multiagent integrated energy system post-disaster coordinated recovery and evaluation models are proposed. The modified ADMM algorithm is applied to effectively solve the problem, which meets the privacy protection requirements of the actual application of the system. At the same time, the calculation example shows that in the later period of restoration, as more damaged roads return to normal traffic state, the method of rolling update strategy makes the load restoration process more efficient considering the real-time dynamic changes of traffic conditions. WEI FU received the B.S. degree in electrical engineering from the South China University of Technology, Guangzhou, China, in 2020. He is currently pursuing the Ph.D. degree with the School of Electric Power Engineering, Xi'an Jiaotong University. His research interests include resilience of integrated energy system and energy internet, and quantum computing for power systems.
HAILAN ZENG received the B.S. degree in electrical engineering from Xi'an Jiaotong University, in 2022, where he is currently pursuing the M.S. degree with the School of Electric Power Engineering. His research interests include the uncertainty analysis and optimization of integrated energy systems. VOLUME 11, 2023