Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2016 / Article

Research Article | Open Access

Volume 2016 |Article ID 8262136 | 11 pages | https://doi.org/10.1155/2016/8262136

The Optimization Model for Electric System Emergency Facility Storage and Transportation Considering Information Credibility

Academic Editor: Francesco Franco
Received31 Dec 2015
Accepted29 May 2016
Published27 Jul 2016

Abstract

When dealing with power system emergency caused by natural disaster, information survey is the important foundation of emergency power supply and repair. The information credibility would directly inflect the credibility and timeliness of electric system emergency work. Therefore, this paper starts the study from the point of information credibility and sets minimizing total cost and loss as the objective function, taking time constraint, transportation road constraint, information credibility constraint, and the parameters of different facilities into consideration and building a location and storage optimization model for electric system emergency facility. And a corresponding facility transportation model was built considering the power loss in demand points. The simulation result shows that the models proposed by this paper could satisfy the requirement of information credibility, improve the adaptability to demand change, and cut down total cost and loss.

1. Introduction

Electric disaster means the electric power accident caused by natural disaster, which is the main risk that triggers power network large-scale blackout. As electric market develops, the vulnerability of power system and the bad nature of the electric power accident are important factors that threaten power system stable operation. Actively forecasting, preventing, and dealing with various types of electrical disasters to reduce the loss are the most important points that power companies should pay attention on. Based on the researches of major sudden disasters in power system characteristics, the literature [1] analyzed the problems and challenges that electric emergency management faced and introduced emergency management model, development stage, related theory, and related technology framework in detail. The literature [2] put forward a risk calculation equation and pointed out the major works of power system emergency management, namely, prevention, preparation, response, and recovery.

From the aspect of emergency prevention and preparation, risk evaluation, emergency scheme generation, and service site selection are the core points of power system emergency management. The literature [3] introduced an evaluation method based on time dimension and put forward a disaster loss preevaluation method. The literature [4] analyzed the vulnerability of power system emergency management evaluation and realized quantitative assessment with composite indicator and AHP method and pointed out the weak points in actual power system emergency management by calculating power grid vulnerabilities based on historical data. The literature [5] proposed the concept of electric emergency management, pointed out the emergency management platform and exchange system and content, and designed the integrated application system for electric emergency management. The literature [6] pointed out that power system emergency center is lacking clear decision basis, analyzed power system disaster accident based on real-time information provided by the Six Information System, and put forward power system accident situation grade evaluation index system. The literature [7] analyzed the content and structure of typical electric emergency preplan, put forward a preplan generation method based on the ontology, and built a digital electric emergency preplan storage based on the relational database model. The literature [8] put forward the method to determine power shortage risk in unit time considering shortage power, load type, and power shortage probability and built a power system emergency service site selection optimization model with the objective function of minimizing the total power shortage risk. The literature [9, 10] used neural network technology and built a multiagent systems two-level adaptive control scheme to prevent large-scale emergencies in electric power systems.

From the aspect of emergency response and recovery, the literatures mainly focus on power supply and logistics management. The literature [11] analyzed customers’ power shortage loss and set minimizing total loss and minimizing emergency power surplus capacity as the objective function and built a portable emergency power supply optimization scheduling model in urban districts as well as its corresponding solving algorithm. The literature [12] identified the fundamental characteristics required to appropriately model and solve electrical power districting problems. The literature [1316] researched on the classification of power emergency material and built a survey model and algorithms for emergency response logistics. The literature [17] proposed a mathematical model to handle emergency service requests in electric power distribution utilities. The literature [18] built a system based on processing operating modes of electric systems and geoinformation control of the operating modes. The literature [19] summarized the researches on power system restoration problems.

However, the above researches mainly lay emphasis on power system monitoring and related facility transportation optimization after power accident occurred. The importance of information reliability in the detecting stage has not gain enough attention. Therefore, this paper starts from the point of emergency facility demand prediction and builds storage volume calculation, warehouse location, and power system emergency facility scheduling models from the aspect of minimizing information loss, purchasing cost, and transportation cost, respectively.

The rest of this paper is organized as follows. In Section 2, this paper introduced the information detection stage in power disaster management and the importance of information credibility to power emergency management decision. Then take different information credibility in different scenario and facility into consideration, this paper defined the regional information credibility and put forward the corresponding calculation model. Section 3 put forward three models for reverse point location and reverse volume calculation before power disaster. The basic reverse scheme is determined by the predicted facility demand directly, and the centralized storage scheme selects some points to be the reverse points and provide facility for the other points according to their real-time facility demand. The decentralized storage and centralized storage combination scheme integrates the above two models and find the balance point among transportation cost, purchase cost, and storage cost to distinguish different facilities and store some of the facility with the basic reverse scheme and the others with the centralized storage scheme. Section 4 proposed the detecting facility scheduling model after power disaster occurred, which sets minimizing information error loss and information shortage loss as the objective function while taking information credibility requirement, transportation time limit, and facility demand-supply constraints into consideration. Section 5 did a case study to verify the models proposed and compared the effect of different storage schemes. Section 6 highlighted the main conclusions of this paper.

2. Information Credibility in the Detection Stage of Power Emergency Management

2.1. Detection Stage in Power Emergency Management

Power system emergency management could be divided into three stages according to their different key emphasis in work. The detection stage mainly detects disaster information and quickly returns the field information. Emergency power supply stage mainly provides instant power supply for important government apartments and institution or companies. Emergency urgent repair stage mainly repairs the impaired plant and power grid infrastructures and restores power supply.

Information of the demand points is the foundation of related emergency management apartment to make power supply and repair scheme. Therefore, the guarantee of information credibility in the detection stage is important for power system emergency management. However, for different kinds of detection facility and different detecting condition, the information credibility is not the same. For example, most areas could be detected by unmanned aerial vehicles and satellite communication facilities rapidly. However, some areas could not be detected by the above detection facilities, determined by their terrain characteristics, and these facilities should be detected by detection officers with corresponding individual facilities. Then the decision of the purchase quantities and allocation of each type of detection facilities are a main problem for power emergency management before the disasters occur. Therefore, this paper considers the information credibility of different kinds of facilities to define the information credibility of an area.

2.2. Regional Information Credibility

Limited by the characteristics of the detection facilitates, the feedback information is generally not entirely accurate, which could be described by information credibility degrees. The information credibility degree varies with the facility type and the application scenarios. To simplify the model, this paper only discusses the information credibility of a certain type detection facility in two scenarios, namely, applicable and not applicable. For a detection facility in an applicable scenario, the average information credibility could be calculated by the related historical statistics data. And this paper uses the average information credibility to represent the information credibility of this kind of detection facility in its applicable scenario. And in the not applicable scenario, the information credibility is 0, as inwhere is a 0-1 variable, when means the facility is applicable in region and when means the facility is applicable in region . is the number of times that the facility ’s feedback information is basically in line with the real disaster information or the error is acceptable. is the number of times that the facility participated in power emergency information detection.

A whole power emergency detection region could be divided into serval different subregions. And the information credibility of the whole region could be described by the information accuracies of its subregions, aswhere is the number of the subregions of region . is the information credibility of the subregion . and are the acreage of the subregion and the whole region, respectively.

Power emergency information detection should meet the requirement of full-area-coverage. The detection range of a certain detection facility could be described by its detecting radius in limited time. For subregion , the information credibility could be calculated by the applicate statues of the detection facilities.

Firstly, define the contribution of a detection facility to a subregion. If the detecting range of facility exceeds the acreage of subregion , namely, , then when is applied in subregion , only one device could complete the detection task. In this scenario, the information credibility of the subregion is

Else, facility ’s detection range is smaller than the acreage of subregion : namely, ; when is applied in subregion , more than one device are needed to complete the detection task. Then the information credibility of the subregion caused by facility could be described aswherein is the number of devices of facility applied in the subregion .

The actual detection scheme requires not only full-area-coverage, but also the whole information credibility not less than a certain degree. Therefore, in the same subregion, different types of detection facilities are applied to reduce the information error and improve the information credibility to the required level. Integrate the above two scenarios, assume the information credibility of different facilities are independent with each other, and the information credibility of subregion could be described by

3. Model for Reverse Point Location and Reverse Volume Determined before Power Disaster

Currently, in most provinces of China, power emergency information detection facilities are mainly stored in provincial power company and municipal electric power company according to the historical experience, which is lack of reasonable forecast and decision-making to some extent. For more suitable reverse decision, this paper builds reverse point location and reverse volume determined optimization model before power disaster to improve the preparations for power emergency information detection.

3.1. Basic Reverse Scheme

This scheme could also be called decentralized storage scheme. Firstly, predict the disasters probability and severity in each potential risk point and make the reverse scheme according to the demand, which means storing the facilities near to the risk points according to the predicted demand. Referring to related literature, assume the set of different levels of power disaster caused by natural disaster is and the given power disaster level number is ; then can be described as

Assume the probability of level power disaster is ; then different levels of power disaster probabilities distribution are

If a region is facing the risk of types natural disaster, this paper uses Poisson Distribution to simulate the probability of power disaster [20]. Assume in years that the number which nature disaster occurred and caused power disaster in level is ; then in the coming years, the probability caused by natural disaster and in level could be described by

Based on (8), the probability that natural disaster occurs and causes corresponding power disaster in the following years can be calculated by

Different type of natural disaster has different region; the corresponding subregion is also different. Assume when occurs in a region, and the acreage need detection is ; then the acreage in its subregion is . Then the expectations of detection acreage of the power disaster caused by natural disaster in subregion are

Choose the maximum detection acreage in all types of natural disaster as the expected detection demand of subregion , as

Based on the above equations, the basic reverse scheme model could be built with the objective of minimizing total purchase cost:wherein is the unit purchase cost of facility ; is the number of facilities : wherein is the demand of facility in the subregion .(1)Full-area-coverage constraint is(2)Information credibility constraint iswherein is the minimum information credibility requirement of the subregion .

The constraints also contain (1)–(5).

3.2. Centralized Storage Scheme

In Section 3.1 the scheme meets the maximum demand of each subregion and chooses the nearby-storage principle, which could provide reliable information detection and meet the credibility requirement when the disaster occurs. However, the actual situation is that this kind of scheme needs huge capital investment and the utilization of detection facility is quite low. To reduce the purchase cost and improve power emergency information detection facility utilization, the basic model could be optimized to be a centralized storage model. That is based on the original scheme, it eliminates some reverse point and centralized stored the detection facilities for a certain region in one point. The reverse point provides facility supply directly for the demand points nearby and also acts as a back-up point for the nearby reserve points.

Assume the number of the potential risk points is , and using the model in Section 3.1 we could calculate the demand of each type of detection facility in each point . Choose points from the points to be the central reverse points, which store the demanded facilities for itself and the risk points nearby. The objective is still minimizing the total purchase cost: wherein is the demand of facility in the subregion .(1)Transportation time limit constraint iswherein is the average transportation time from to . is the time limit of the detection facilities to arrival point . is 0-1 variable; when , the point is a reverse point of facility .(2)Facility supply constraint is as follows.The total storage in the reverse points that directly supply point should meet the demand from point , aswherein is the quantity of facility stored in the reverse point .(3)Back-up supply constraint is as follows.When a large-scale disaster occurred in a region, a reverse point may not be able to provide enough facilities for all its responsible risk points; then it needs the back-up supply points to provide the remaining demand. For a given time limit, the set of reverse points that are nearby the risk points could be gained, and assume the element number of the set is . Then the back-up supply constraint could be described aswherein is the storage volume of facility in the reverse point .

3.3. Decentralized Storage and Centralized Storage Combination Scheme

Based on the decentralized storage and centralized storage schemes in Sections 3.1 and 3.2, in further discussion it can be found that the centralized storage scheme could reduce the total purchase cost and improve facility utilization. But for some facilities with large frequency of use, the transportation cost, and small device price, the transportation cost may exceed the purchase cost. On the one hand, it may make the scheme not reasonable enough from the cost aspect; on the other hand, when centralized stored this type of facility would be not timely supplied when compared with the decentralized storage scheme, which would bring more information loss.

Therefore, based on Sections 3.1 and 3.2, this paper calculates the predicted purchase cost, storage cost, and transportation cost of the facilities in the two kinds of storage schemes and decentralized storage of the facilities whose purchase cost and transportation cost in the centralized scheme are more than the purchase cost and storage cost in the decentralized scheme. And other types of facilities are centralized stored. The selection basis is described as (20): the facilities that meet (20) are decentralized stored and other facilities are centralized stored:wherein is the average unit transportation cost of facility . is the transportation distance from point to point . is the planning year limit; is the discount rate. is the number transportation times (frequency) in which facility transported from point to point j. is the average annual storage cost of facility .

4. Detecting Facility Scheduling Model after Power Disaster Occurred

Because of the uncertainty of natural disasters, the corresponding power disasters also have uncertainty. When power disaster occurred, the real-time detecting facility demand of each point could be calculated by model Section 3.1. If the real-time demand is not more than the predicted demand, the facilities could be provided by the corresponding reverse points. But when the facility storage in the points themselves and their direct supply points are not enough to meet the demand, the facilities need be deployed. This paper builds a deployed model for the scenario that the total demand in the whole region is not more than the total stored facilities in the reverse points, considering the constraints of power emergency information detection.

4.1. Information Loss

The information loss is used to describe the economic loss, social loss, and other losses related to power disaster. According to the literature [10], this paper uses information loss to evaluate the importance degree of each demand point, as wherein is the economic loss of demand point in a unit time. is the coefficient that social loss converts into economic loss: wherein is the population of point . is the number of special enterprises or institutions in point . and are the coefficients of the importance of life safety and special institution.

4.2. Power Emergency Detection Facility Deploying Model

The detection facility deploying scheme should minimize the total information loss of all demand points during the detection stage and minimize the loss caused by information shortage. Then for demand point , assume its demand of facility is , and then the loss would contain two aspects, namely, information error loss and information shortage loss, wherein the information error is the same as the information loss in Section 4.1, and the information shortage loss means the loss during transportation period of the corresponding facility.

Therefore, the objective is minimizing information error loss and information shortage loss, as (23):wherein is the transportation time from reverse point to demand point . is the coefficient of the importance of facility to demand point , which is determined by the average information credibility and detecting range of facility , as (26), wherein the average information credibility could be calculated by (1):(1)Demand-supply balance constraint is(2)Information credibility constraint is

5. Case Studies

5.1. Model Solving

The proposed models have many nonlinear functions, with make the problems mixed-integer nonlinear optimization problems. This paper chooses the Improved Particle Swarm Optimization [20] to solve the models. Introduce the solving steps of Section 3.1 as an example.

5.1.1. Generate Initial Particle Swarms

The optimization variables are the transportation volume of each type of facility from reverse points to demand points. Therefore, the solution of the model should be a matrix, and each element in the matrix is an integer whose range is . Assume a matrix describing the reverse point provides facility to the demand point , wherein and the position of each particle is described by the element of the this kind of matrix. To avoid premature convergence, when generating the initial particles, the particles should be as dispersed as possible, to expand the searching range of the feasible solution. The detailed method is introduced in the literature [20].

5.1.2. Update Particle Swarm

Based on the basic particle swarm algorithm the improved algorithm introduced the crossover, mutation, and selection steps in genetic algorithms to improve the global searching capability. Use row column th particle in th generation as an example to introduce the update progress. Assume is the local best position in th generation particle swarm, and is the global best position in th generation particle swarm. The detailed update steps are as follows:(1) cross with and generate new particles and . This step means new particles move toward the global best particle with different speed and direction and ensure that the distance between the global best position and the new particle is not too far.(2) cross with and generate new particles and . This step means new particles move toward the local best position with different speed and direction and ensure the distance between the local best position and the new particle is not too far.(3) and vary themselves to generate new particles and . This step is to avoid the particles from falling into the local best solution too early.(4)Calculate the fitness value of , , , , , and according to the objective function and get , , , , , and . Find the minimum valve from them, its corresponding position is , and compare with the local best value and the global best value. If then update the local best position ; if then update the global best position .(5)Calculate the related degree between , , , , , , and ; choose the particle that has the biggest related degree as the particle into the next iteration; that is, . This step is to make the solutions as dispersed as possible.

The detailed cross and varying operation is introduced in the literature [20]. Through the above operations, new , and could be gained. According to the steps, after multiple iterations the global searching in the space would gain particles with higher fitness value and finally gain a solution that has the optimal fitness value or approximate optimal fitness.

5.2. Basic Data

Assume the potential risk points are distributed as in Figure 1, which contains 21 risk points. Road connectivity is given and the minimum transportation time between each two points could be calculated by Dijkstra algorithm. Parameters of the common power emergency detection facilities are listed in Table 1. Assume the detection region mainly contains two types: A type could be detected by unmanned aerial vehicles and wireless communication detection facilities, which is the common detection region; in B type region, the unmanned aerial vehicles and wireless communication detection facilities could not arrive or work successfully, which makes this kind of region only be detected by staffs and individual facilities.


TypeTransportation speed
km/h
Detection area
km
Purchase price
104 Yuan
Number limitUnit transportation cost
Yuan/km
Information credibility

Broadband satellite communications facilities50620<10030.7
Satellite telephone15>1000.020.6
Unmanned aerial vehicles8050180≤3050.8
Individual equipment70410Unlimited100.9

Ensuring the emergency supplies speed and quantity, this paper uses the proposed models to gain reverse point location and reverse volume determined scheme. The scenarios are as follows.

Scenario 1. Basic reverse optimization scheme (the decentralized storage scheme) is deciding the scheme according to the model in Section 3.1.

Scenario 2. Centralized storage scheme is deciding the scheme according to the model in Section 3.2.

Scenario 3. Decentralized storage and centralized storage combination scheme is based on the schemes gained in Scenario 1 and Scenario 2, optimizing the schemes according to the model in Section 3.3.

For power emergency scenario, assume a natural disaster occurred in and around 2# risk point; the influenced points mainly contain 2#, 4#, 9#,10#, and 18#. The real-time demand of each point is listed in Table 2, wherein types A and B are mean different types of detection region, and type B could only be detected by individual facilities. Referring to the literature [10], this paper sets economic loss of unit electricity power to be 6.72 Yuan/kWh and the coefficient of life safety and special industrial to be 0.25 and 0.42, respectively. Assume the time which each risk point requires to transport the facilities from their direct supply point is all 2 hours, and the information credibility requirement is 0.8.


Demand pointType A
(km2)
Type B
(km2)
Important load
(104 kw)

2#15000150724
4#7800236132
9#16100115544
10#15700140650
18#15500221048

5.3. Result Analysis
5.3.1. Reverse Points Location and Reverse Volume Determined before Power Disaster Results

According to the model in Section 3.1 and the basic data, the facilities demand of each point could be calculated. In Scenario 1, the scheme is determined according to the demand directly, which means the facilities are distributed and stored. In Scenarios 2 and 3, some points are selected to be centralized stored points, as shown in Figure 2. In centralized stored mode, the direct demand-supply relationships are listed in Table 3. Under the objective of minimizing total purchasing cost, calculate facility store schemes in different scenarios and analyze and compare their transportation time, information loss, and transportation cost.


Supply point Demand point

1#1#, 5#, 6#, 17#, 18#
2#2#, 4#, 9#, 10#, 12# 18#
3#3#
7#7#
8#8#, 9#, 11#, 18#
13#11#, 13#
14#14#, 15#
16#10#, 16#, 17#
19#19#
20#20#
21#21#

5.3.2. Power Emergency Detection Facility Deployment Results

According to the model in Section 3.1, the real-time demand of each point is to meet their detection range requirement; the results are listed in Table 4, wherein symbols I, II, III, and IV are satellite communication facilities, satellite phones, unmanned aerial vehicles, and individual equipment, respectively.


Real-time demandIIIIIIIVInformation credibility
Type A Type B

2#222300.818 0.900
4#011470.802 0.900
9#522230.800 0.900
10#022280.800 0.900
18#022440.804 0.900

According to Table 4, the model in Section 3.1 could meet the full-area-coverage requirement and two types of detection regions’ information credibility requirement. When power disaster occurred the facilities scheduling relationship is shown in Figures 3, 4, and 5, respectively. Facility supply volume, transportation time, and information loss are listed in Tables 5, 6, and 7, respectively.


Demand-supply relationshipIIIIIIIVTransportation timeTransportation costInformation loss

16#-2#20001.09 0.15 175.80
1#-4#000292.41 4.88 73.66
8#-4#00023.35 0.27 7.07
13#-9#50003.98 1.11 1176.38


Demand-supply relationshipIIIIIIIVTransportation timeTransportation costInformation cost

8#-9#522231.943.94 573.62
16#-10#022281.613.27 540.96
1#-18#022441.384.33 445.13
2#-4#000141.361.33 20.10
1#-4#000112.411.85 27.99
8#-4#010213.354.92 351.35
13#-4#01014.550.32 381.12


Demand-supply relationshipIIIIIIIVTransportation timeTransportation costInformation cost

2#-4#000141.361.33 20.10
13#-4#001172.412.95 441.91
8#-9#500141.912.58 558.78
1#-18#00201.382.11496.70
16#-10#00201.611.79390.56

Combining Figure 1 and Table 5, when serval demand points’ real-time demand exceeds the expected demand, the facility demand is mainly meted by the points’ self-storage, and only 2#, 4# and 9# need other points to provide small amount of support. From the aspect of transportation cost and information loss, this scenario has related small loss. However, the facility purchase cost in this scenario is 135500 thousand Yuan. And the demand-supply relationships among the points are weak; if the disaster situation deteriorates, the corresponding transportation volume and transportation cost would increase obviously.

According to Figure 4 and Table 6, when the disaster situation exceeded the expected scenario, the stored facilities in 2# of the centralized scheme cannot satisfy all the demand of the points around 2#. Other reverse points are called to provide facilities. Because of the long distance, the transportation time maybe longer than the expected transportation time, which would cause obvious increasing of information loss and transportation cost. Those are because the demands concentrated on outbreak in the neighboring regions, the supply ability of 2# could not meet all the requirements at the same time, and 2# calls for support from other reverse points. Further observation shows in this scenario taht the satellite phone and individual equipment have related large number of vacancies. The lack of satellite phone would make unmanned aerial vehicles not able to finish detection task alone and make the detection of type A region delayed. The lack of individual equipment would make the detection of type B region delayed, which furtherly lead to information loss increasing. The total facility purchasing in this scenario is 77600 thousand Yuan.

According to Figure 5 and Table 7, when the disaster situation exceeds the expected situation, the decentralized storage and centralized storage combination scheme could meet facility demands and gain support from other reverse points, which has good suitability. The facility purchase cost in this scenario is 107900 thousand Yuan.

5.3.3. Comparison and Analysis

The purchase cost, transportation cost, and information cost in the scenarios are shown in Figure 6.

According to Figure 6, scenario has related less transportation cost and information cost but has the most facility purchase cost. Scenario 2 has the least purchase cost but has the most information loss. Scenario 3 has moderate costs of transportation, facility purchase, and information loss. If only considering from the aspect of total cost, Scenario 2 has the least cost. But Scenario 2 has the most information loss. On the one hand, when disaster situation deteriorates, Scenario 2 has more information loss and the increasing speed of information loss would be much more than the transportation loss in other scenarios. On the other hand, the lack of credible information would influence the effect of power emergency management decisions, which may cause more risk in emergency scheme decision than that in other scenarios. Beside loss analysis, information credibility change in three scenarios should be considered to comprehensively compare the schemes.

For types A and B detection regions, the information credibility in the three scenarios is shown in Figures 7 and 8, respectively.

According to Figures 7 and 8, from the aspect of information credibility in different stages, all of the three scenarios could meet information credibility requirements within 5 hours. Scenario 1 has the best immediate information credibility when power disaster occurred, but the information credibility is hard to increase within 2 hours. Scenario 2 has the worst immediate information credibility when power disaster occurred, the information credibility of type B region could be increased quickly in 2 hours, but the information credibility of type A region is hard to be increased within 2 hours. Scenario 3 has the moderate immediate information credibility when power disaster occurred, and the information credibility of type B region could be increased quickly in 2 hours and the efficiency is better than Scenarios 1 and 2.

According to the above analysis, the decentralized storage scheme has a certain ability to adapt to centralized demand, but if the disaster expands and demand increase rapidly in a short period time, its advantage in controlling information loss would be weakened. The centralized storage scheme could reduce cost and improve facility utilization but hard to adapt to centralized demand. The decentralized storage and centralized storage combination scheme has the advantage of both decentralized storage scheme and centralized storage scheme, which could reduce total cost and control information credibility at the same time.

6. Calculations

From the aspect of information credibility in power emergency management information detection stage, this paper defined information credibility in a certain region and built facility storage reverse point location and reverse volume optimization model before power disaster occurs and corresponding detection facility scheduling model after power disaster occurs. Information credibility, transportation time, information loss in demand points, and other factors are considered in the decision model to improve the decision accuracy from both the ex-ante and ex-post sides of power disaster. The case study verified that the models proposed in this paper could meet the requirement of facility demand, time limit, and information credibility requirement and reduce total cost.

Competing Interests

The authors declare that they have no competing interests.

Acknowledgments

The work is partially supported by the National Science Foundation of China (Grant nos. 71273090 and 71573084) and the Fundamental Research Funds for the Central Universities (2016XS81).

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Copyright © 2016 Guan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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