Mathematical Problems in Engineering
Volume 2019 (2019), Article ID 5489067, 15 pages
https://doi.org/10.1155/2019/5489067

Research Article

Optimization for Postearthquake Resilient Power System Capacity Restoration Based on the Degree of Discreteness Method

Lihua Wang,¹ Donghui Ma,² Xu Han,¹ and Wei Wang²

¹College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China
²Institute of Earthquake Resistance and Disaster Reduction, Beijing University of Technology, Beijing 100124, China

Correspondence should be addressed to Wei Wang; ieeww@bjut.edu.cn

Received 6 December 2018; Revised 3 March 2019; Accepted 27 March 2019; Published 10 April 2019

Academic Editor: Łukasz Jankowski

Copyright © 2019 Lihua 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.

Abstract.

The occurrence of a natural disaster such as a strong earthquake affects not only the capacity of a city’s power supply system but also the normal operation of other lifeline systems. An urban emergency power supply system is used to manage the power supply restoration with the consumers divided into three types based on their impact and importance during a power failure. In this study, a power supply system equipped to meet the requirements of different restoration level facilities and enable the restoration of power after the occurrence of an earthquake was developed. A three-stage power restoration curve was formulated based on the postearthquake recovery process. The relative importance factors of consumers can be calculated with a normalization model based on membership degree. These relative importance factors were then combined with the postearthquake recovery capabilities of each consumer to calculate the overall recovery capability and equilibrium degree of the urban power system. Using the two foregoing indicators, the power supply recovery level of the power system after an earthquake was quantitatively analyzed, and the power supply scheme of the consumers with different power supply guarantee types was rationally optimized.

1. Introduction

A lifeline system is composed of a series of engineering support facilities for urban and regional areas. It plays a key role in maintaining the normal operation of cities and the promotion of regional economic construction [1]. When the power system of an area loses its power supply capacity due to the occurrence of a natural hazard or an intentional disruption, not only is the normal operation of the lifeline system affected, but also postdisaster response and recovery activities are also impaired, resulting in substantial socioeconomic consequences [2–7]. An earthquake is an extreme natural disaster that poses a very serious threat to the operation of a power system, with the potential of causing widespread and prolonged blackouts. Such a scenario would negatively impact emergency relief work such as intelligence acquisition, emergency command, postearthquake relief, medical service delivery, and victim resettlement [8–12]. This has prompted intensive research on power system resilience in recent years.

In order to reduce the scope and loss of large-scale blackouts caused by natural disasters, it is necessary to improve the power system's ability to cope with extreme natural disasters [13]. After Hurricane Sandy caused great economic losses in 2012, industry and academia began to reexamine the impact of extreme natural disasters on power systems and proposed the initial idea of building a resilient power system. The resilience of a power system refers to its ability to reduce the economic losses caused by the failure process and return to the normal power supply state as quickly as possible when it suffers from major disasters (such as hurricanes and earthquakes). A resilient power system can not only gradually reduce the power supply capacity when external disasters intensify but also quickly restore output to the original state [14–16].

Current methods for assessing the resilience of a power system are divided into three main categories [17]: simulation-based methods [18–20], analytic methods [21], and statistical analysis methods [22]. Panteli et al. [23] unprecedentedly identified the resilience stages of a power system and presented the features that a resilient power system should possess at each stage. Espinoza et al. [24] put forward an assessment framework consisting of four phases, namely, threat characterization, vulnerability assessment of the system components, system reaction, and system restoration. As an important part of power systems research, resilience should be evaluated by stage to reduce the difficulties regarding the evolution of system states and disasters. However, researchers have previously not considered the importance of urban power supply consumers in the different recovery stages of a power system after an earthquake.

Urban power systems provide power to a variety of power supply service consumers. Because of the different importance of these consumers, the resilience construction schemes of different consumers are also different. When evaluating the resilience level of an urban power system, not only the power supply resilience of important consumers but also the resilience recovery ability of the whole urban power system should be analyzed for all the power supply service consumers. Among them, the evaluation indexes of the resilience recovery ability of the urban power system are the comprehensive value of the resilience recovery ability of all power supply service consumers and the discrete degree of resilience recovery ability of different power supply service consumers. As an important part of urban disaster prevention planning, the resilience of the urban power system needs to be evaluated. However, researchers never before considered the importance of the resilience construction level of different power supply service consumers to the postearthquake recovery capability of urban power systems.

In this paper, an urban power system is taken as the research object, focusing on evaluating the comprehensive value and discreteness of the resilience recovery ability of different power supply service consumers. Firstly, the type of consumer power supply security, the importance group of facilities, and power supply restoration scheme are solved. Secondly, the comprehensive value of the resilience recovery capability of the power system and the disparity between the resilience recovery capabilities of different consumers are evaluated. Finally, the main means of improving the resilience recovery capability of power systems are presented and verified via calculation examples.

2. Power Supply Restoration Level of Facilities

2.1. Types of Power Supply Protection Consumers

Although most facilities for daily life are inseparable from the power supply system, different types of consumers can play different roles in earthquake disaster relief. Referring to the factors considered in the standard classifying power systems (GB50137-2011) [25], this paper divides the power supply consumers into three types according to the importance of building facilities and the loss or influence degree that may be caused by power outage, as shown in Table 1 [26].

Table 1: Classification of power supply protection consumers.

Power supply protection type
Requirements for power supply protection

Primary power supply protection
Consumer’s power supply cannot be interrupted during a disaster, or emergency power protection should be commenced immediately.

Secondary power supply protection
Consumer requires prompt power protection after a disaster.

Tertiary power supply protection
Consumer requires power supply restoration as soon as possible after a disaster.

According to the code for classification of urban land use and planning standards of development land (GB50137-2011) [25], urban land can be divided into eight major categories, 35 middle categories, and 42 subcategories. Because every category of urban land represents the function of the different consumers on such land, the classification standard in Table 1 can be used to classify the power supply consumers in the city.

As presented in Table 2, all consumers in the urban area can be divided into three types according to the postearthquake power supply recovery requirements in Table 1, namely, primary power supply protection consumers, secondary power supply protection consumers, and tertiary power supply protection consumers [26]. The first type of power supply protection consumers mainly includes important medical units, emergency command centers, dangerous goods warehouses, disaster relief trunk roads, convenient transportation facilities, and central shelters. The second type of power supply protection consumers includes general medical units, foreign affairs administrative units, large factories and mining areas, secondary trunk roads for disaster relief, facilities related to lifeline systems, and residential areas in shelters. The third type of power supply protection consumers includes buildings and facilities that play a relatively minor role in postearthquake rescue and disaster relief activities, such as residential buildings, administrative office buildings, recreational buildings, schools, stadiums, disaster relief sub-trunk roads, commercial service facilities, general warehouse logistics units, public facilities, and green spaces.

Table 2: Classification of power supply protection consumers.

Power supply protection type
Power supply protection consumers

Primary power supply protection
Medical units for rescuing the wounded in the disaster area.
Hygienic and epidemic prevention units for storing epidemic prevention drugs and virus specimens or for virus research.
Disaster prevention and emergency command center.
Airports and supporting facilities such as material transportation and casualty transfer systems.
Large computer data centers containing information for guidance in emergency relief.
Television and other communication facilities for reporting disaster situations and announcing disaster relief programs.
Fire control units for rescuing victims, controlling fire risks, and harnessing dangerous entities.

Secondary power supply protection
Medical units with significant ability to treat the wounded.
Embassies and foreign affairs agencies for contacting or transferring foreign personnel.
Transportation facilities such as evacuation secondary trunk roads and well-equipped urban roads for transportation of disaster relief materials and disaster victims.
Gas stations, gas storage facilities, and liquefied petroleum gas storage and distribution facilities that may have adverse effects or cause economic loss in the event of a power failure.
Facilities for coal mining, oil recovery, and other mining activities.
Facilities for the emergency monitoring and supply of domestic water, electricity, and gas, including to disaster victims.
Equipment for electric power supply for lighting and cooking in central shelters, fixed shelters, and short-term shelters.

Tertiary power supply protection
Public service facilities such as kindergarten centers, commercial facilities, health services stations, and post offices in residential areas.
Entertainment centers such as cinemas, theaters, auditoriums, lecture halls, and exhibition halls.
Business facilities such as farmer markets, restaurants, and hotels.
Finance and insurance offices including banks.
Wholesale buildings and facilities, single-story warehouses, and logistics and freight stations containing large amounts of commodities.
Urban secondary and minor roads.
Administrative office buildings not considered disaster relief command centers.
Schools, research institutes, exhibition centers, sports venues, sports training bases, parks, green spaces, city squares, and other construction facilities unrelated to refuge provision.

2.2. Facility Importance Grouping

The working ability of urban power supply consumers is accomplished by a series of facilities with different functions. Because these facilities determine the role that consumers can play in the process of emergency rescue after the earthquake, the importance of these facilities is to ensure that consumers have the ability to work after the earthquake varies [26]. For example, as an important consumer of power supply in urban postearthquake emergency rescue, hospitals usually include surgical treatment, inpatient observation, security services, and other facilities. Among them, surgical treatment facilities are far more important than inpatient observation and security services in facilitating critical capabilities to the postearthquake rescue capacity of hospitals.

In order to ensure that urban consumers can play a role corresponding with their type of power supply protection after the earthquake, these consumers need to be included in a series of facilities that can meet their needs. With the change of protection types of power supply consumers, the importance of facilities for consumers to play a role in disaster relief work has also changed. Based on this, this paper divides the facilities of different types of power supply protection consumers into groups according to their importance.

Since the first type of power supply protection consumers plays the most important role in postearthquake rescue work, this type of consumer includes the most critical functions and the most types of facilities. As shown in Table 3, the facilities included by the first type of power supply protection consumers are divided into three groups: the first group is important facilities, the second group is noncritical facilities, and the third group is unimportant facilities.

Table 3: Facility importance grouping for primary power supply protection consumers.

Consumer
Facilities
Group

(1) Departments for treating the wounded, such as surgical operation rooms, dressing and disposal rooms, nuclear magnetic examination rooms, and blood collection and supply department.
Group 1

Medical units
(2) Departments for internal medicine, neurology, and other professional medical services.
Group 2

(3) Transport corridors for the wounded and lighting systems and air conditioning for casualty resettlement wards.
Group 3

(1) Lighting, safety monitoring, and heat preservation equipment for high-risk substances such as virus samples and highly toxic and hazardous source samples in virus research laboratories.
Group 1

Health and epidemic prevention units
(2) Departments for epidemic prevention drugs and devices.
Group 2

(3) Import and export corridor lighting and monitoring systems.
Group 3

(1) Communication and computer analysis systems.
Group 1

Emergency command systems
(2) Lighting systems for conference rooms and command centers.
Group 2

(3) Lighting for command center lounges, exterior lighting, and building identification systems.
Group 3

(1) Storage facilities for important cultural relics.
Group 1

Cultural relics protection units
(2) Lighting systems, security devices, and communication systems in cultural relics display areas.
Group 2

Primary power supply protection consumers

(3) Architectural signs and import/export corridor lighting in cultural relics display areas.
Group 3

(1) Constant-temperature, constant-humidity, and ventilation devices for auxiliary storage of dangerous goods.
Group 1

Dangerous goods warehouses
(2) Warehouse safety lighting, security devices, and communication systems.
Group 2

(3) Warehouse building signs and import/export corridor lightening.
Group 3

(1) Airport terminals, large hangars and buildings, and communication, water supply, and oil supply systems.
Group 1

Airports
(2) Airport security and lighting systems.
Group 2

(3) Airport monitoring systems.
Group 3

(1) Large computer systems and information storage and transmission systems.
Group 1

City data centers
(2) Office lighting and communication systems.
Group 2

(3) Security, air conditioning, ventilation, and lighting systems.
Group 3

Broadcasting, television, and communication facilities
(1) Communication systems, earthquake information broadcasting systems, and resettlement information dissemination systems.
Group 1

(2) Office lighting and air conditioning systems.
Group 2

(3) Exterior lighting, air conditioning, and indoor lounge lighting systems.
Group 3

(1) Communication equipment, computer dispatching systems, disaster analysis systems.
Group 1

Fire Department
(2) Garages, offices, and duty rooms for fire engines.
Group 2

(3) Monitoring systems.
Group 3

Although the second type of power supply protection consumers plays a relatively small role in postearthquake emergency rescue, it plays a significant role in large-scale disaster relief and temporary resettlement of victims [26]. As shown in Table 4, the facilities included in the second type of power supply protection consumers are divided into two groups: one is general facilities, and the other is unimportant facilities.

Table 4: Facility importance grouping for secondary power supply protection consumers.

Consumer
Facilities
Group

Medical units
(1) Departments for trauma treatment, blood collection.
Group 2

(2) Lighting systems of wounded delivery corridors, and lighting and air conditioning systems of casualty resettlement wards.
Group 3

Medical health units
(1) Indoor lighting and ventilation systems of wounded wards, and storage systems for trauma drugs.
Group 2

(2) Outpatient corridor lighting and monitoring system.
Group 3

Foreign affairs units
(1) Communication, computer, and lighting systems.
Group 2

(2) Building exterior lighting systems and general building monitoring systems.
Group 3

Gas and LPG stations
(1) Bottled filling stations, gas transmission corridors, and LPG reserve stations.
Group 2

(2) Lighting and monitoring systems of important nodes.
Group 3

Mining and manufacturing enterprises
(1) Mining fields, raw materials production plants, and manufacturing factories.
Group 2

(2) Lighting and monitoring systems.
Group 3

Secondary power supply protection
Water supply facilities
(1) Main structures of water purification plants, such as water intake facilities and pipelines, distribution wells, supply pump houses, central control rooms, and laboratories.
Group 2

(2) Lighting and monitoring systems.
Group 3

Powered facilities
(1) Power stations, hub substations, communication and dispatch buildings, and transmission lines and related equipment.
Group 2

(2) Lighting and monitoring systems.
Group 3

Gas supply facilities
(1) Main buildings of thermal power plants.
Group 2

(2) Dispatching buildings, relay pumping stations and other facilities.
Group 3

Heating facilities
(1) Rainwater pumping stations and inlet pump plants of main roads.
Group 2

(2) Sewage pipes, drainage pumping stations, and sewage treatment plants.
Group 3

Central shelter
(1) Lighting and cooking systems in residential areas.
Group 2

(2) Lighting systems and other equipment outside residential areas.
Group 3

Fixed refuge
(1) Lighting and cooking systems in residential areas.
Group 2

(2) Lighting systems and other equipment outside residential areas.
Group 3

Finally, the third type of power supply protection consumers is mainly responsible for restoring the daily lives of the victims, so it plays the smallest role in the postearthquake rescue process [26]. As shown in Table 5, this paper classifies all the facilities included in the third type of power supply protection consumers into one subgroup of unimportant facilities.

Table 5: Facility importance grouping for tertiary power supply protection consumers.

Consumer
Facilities
Group

Tertiary power supply protection consumers
General residences
(1) Living facilities within residences, such as lighting, cooking, and entertainment systems and devices.
Group 3

Urban branches
(1) Road lighting and vehicle access control systems.
Group 3

Public community facilities
(1) Lighting and fire protection systems.
Group 3

General administration buildings not considered as shelters
(1) Lighting, air conditioning, fire protection, and other building systems.
Group 3

Cultural facilities
(1) Lighting, air conditioning, fire prevention, and other related systems in cultural buildings.
Group 3

Educational and scientific research units not considered as shelters
(1) Lighting, air conditioning, fire prevention, and other building facilities.
Group 3

Sports facilities not used for refuge
(1) Lighting, air conditioning, fire prevention, and other systems.
Group 3

Retail business units
(1) Lighting, air conditioning, fire protection, and other systems.
Group 3

Financial insurance units
(1) Lighting, air conditioning, fire protection, and other systems.
Group 3

Exhibition buildings not considered as shelters
(1) Lighting, air conditioning, fire protection, and other facilities.
Group 3

Crowded business and shopping facilities
(1) Lighting, monitoring, and other related systems and facilities.
Group 3

General warehouses
(1) Powered ventilation, air conditioning, lighting, and other systems and facilities.
Group 3

Wholesale markets
(1) Lighting, monitoring, and other related facilities.
Group 3

Freight forwarders
(1) Dispatching, information, lighting, monitoring, and other systems.
Group 3

Postal facilities
(1) Office, lighting, and parcel distribution systems and other facilities.
Group 3

Large garbage stations
(1) Night lighting and other facilities.
Group 3

2.3. Facility Power Supply Restoration Levels

As indicated in Table 6, there are two criteria for classifying the power supply restoration level of a facility in postearthquake recovery operations. One is the type of power supply protection consumer, and the other is the importance group of the facility. By combining the influences of these two factors, all the facilities can be divided into three power supply restoration levels.

Table 6: Facility power supply restoration level.

Importance group
Power supply protection consumers

Primary power supply protection consumers
Secondary power supply protection consumers
Tertiary power supply protection consumers

Group 1
First level
- -
- -

Group 2
Second level
Second level
- -

Group 3
Third level
Third level
Third level

The postearthquake power restoration requirements corresponding to different power supply restoration levels of facilities are presented in Table 7 [26].

Table 7: Requirements of different power supply restoration levels of facilities.

Power supply restoration levels
Requirements

First level
Important facilities whose power supply should not be interrupted

Second level
Important facilities requiring prompt restoration of power supply

Third level
General facilities tolerating gradual restoration of power supply

To meet the postearthquake power supply recovery requirements of urban consumers, it is necessary to equip the power supply system to meet the demands of the consumers based on their types of facilities. The first power supply restoration level of facilities should be equipped with dual or multiple power sources, which means that their facilities should be equipped with not only conventional and standby power sources but also an emergency power supply that can be instantaneously activated. Emergency power supply is obtained from separate sources distinct from the conventional power supply or standby power supply, such as uninterrupted power supply (UPS) and entry-level power supply (EPS) [27]. To ensure that important facilities are quickly restored to their operation capacity, the emergency power supply should be started immediately after an earthquake.

The second power supply restoration level of facilities only needs to be equipped with a conventional power supply and standby power supply. The latter serves as a backup for the former and is activated when the conventional power supply fails after an earthquake. Standby power supply systems usually include on-site power generators and batteries.

The third power supply restoration level of facilities requires only conventional power supply through urban power transmission lines.

2.4. Restoration Stage for Different Power Supply Facilities

The Wenchuan earthquake disaster (2008 Great Sichuan earthquake) demonstrated that urban power systems are prone to functional damage under strong earthquakes, which results in the loss of working capacity of power consumers in disaster areas. The whole rescue process of an earthquake disaster can be divided into three stages, namely, the postearthquake emergency rescue stage, the large-scale disaster relief stage, and the disaster resettlement stage. Among them, during the postearthquake emergency rescue phase, the key point is to quickly start the use of relief personnel and materials for the treatment of the wounded, hazard assessment, and other works. During the large-scale disaster relief stage, the key point is to make full use of the national disaster relief resources and expert guidance and to complete the work of debris clearance and secondary disasters investigation. After the stage of resettlement, the focus of work gradually changes to rebuilding the disaster areas and restoring the daily life of the victims.

In order to meet the requirements of the above three disaster relief stages, this paper aims to organize the postearthquake restoration of urban power system optimally. Based on the power supply restoration levels of facilities, the power supply restoration can be divided into three stages, namely, the uninterrupted operation stage, the emergency recovery stage, and the conventional recovery stage. The restoration process is illustrated in Figure 1.

Figure 1: Power system postearthquake recovery curve.

(1) The uninterrupted working stage means that the recovery rate of power systems within the time range after an earthquake is always equal to . The uninterrupted operation stage is applicable to the first power supply restoration level of facilities, which are equipped not only with conventional power and standby power but also with emergency recovery power in key nodes. Among them, the proportion of the first power supply restoration level of facilities in the whole power system is equal to the probability of postearthquake recovery . Therefore, the first power supply restoration level facilities do not lose their work capability but deploy the emergency power supply equipment immediately after an earthquake, ensuring that the recovery rate of the power system can be instantly restored to when the postearthquake time is equal to 0. In addition, the power system recovery rate has not changed within the time range after an earthquake, because the maintenance personnel need to complete a series of preparations such as making maintenance plans, transportation arrangements, and deploying maintenance equipment for the urban power system.

(2) The emergency recovery stage refers to the gradual increase of the power system recovery rate from within the time range after an earthquake, during which the probability of postearthquake recovery equals the proportion of the second power supply restoration level of facilities in the whole power system. It is found that the second power supply restoration level of facilities is equipped with conventional power supplies and standby power supplies. Compared with emergency power supplies, the start-up mode of standby power supplies requires manual operation, so the start-up recovery time of emergency recovery phase is . In addition, the standby power supply has the characteristics of a relatively long start-up time, larger reserve power, and being able to meet the needs of multiple facilities at the same time, which results in the recovery curve of the second power supply restoration level of facilities in the emergency recovery stage roughly coinciding with a quadratic function. Thus, the recovery rate of the second power supply restoration level of facilities decreases gradually with the increase of postearthquake recovery rate and postearthquake recovery time. This is because maintenance personnel will give priority to restoring large standby power sources with greater reserve power, supplying more facilities and of which there are relatively few in the early stage of emergency recovery, while in the later stages of emergency recovery, smaller standby power sources, of which there may be many, are restored.

(3) The conventional recovery stage refers to the gradual increase of power system recovery rate from to 100% within the time range after an earthquake. The probability of postearthquake recovery is equal to the proportion of the third power supply restoration level of facilities in the affected power system. As the facilities are equipped with only conventional power supply, maintenance personnel are required to evaluate the damage of each power subsystem one by one and to maintain it in accordance with the actual situation. Compared with the start-up mode of emergency power supply and standby power supply, the conventional power supply requires the greatest amount of time for the maintenance process, and the recovery rate is significantly lower than that of the emergency recovery stage. In addition, since the voltage parameters of each power subsystem strictly limit the number of facilities and services that can be provided, the postearthquake recovery curve in the time range of the conventional recovery stage is approximately linear, which shows that the efficiency of power facilities during the conventional recovery stage is stable.

3. Resilience Comprehensive Recovery Ability Evaluation Method

3.1. Importance Factor of Power Supply Consumers

The importance of the power supply restoration levels of facilities can be assessed by evaluating its importance factors. This enables an analysis of the importance of different power supply guarantee types of consumers in an urban power system.

Here, the indicator set represents the number of facilities with the first level of power supply restoration, the number of facilities with the second level of power supply restoration, and the number of facilities with the third level of power supply restoration, respectively. While the number of different guarantee types of consumers is represented by the set , among them, represents the total number of consumers of various types of power supply guarantee in urban power system.

The evaluation value of the power supply guarantee consumer set is determined based on the evaluation criteria of the importance factors of the different power supply restoration levels of the facilities, where is the consumer impact factor score of the power supply guarantees consumers based on the index included in the facility, and its value is determined by the index evaluation criteria. The numerical value indicates the score of relative influencing factors controlled by the factor index . The relative impact factor matrix of consumers under the influence of index is calculated by scoring the impact factor of power supply guarantee consumers.

where represents the relative influence factor of restoration facility of protection consumer in power system under factor index . When does not have practical significance, we should select a value that has no effect on the results; let . When , we can see that

The row vector elements in the relative importance factor matrix (1) of a consumer are superimposed to calculate the comprehensive evaluation matrix of the relative importance factors under the control of index . The matrix measures the relative influence of different power supply guarantee consumers under factor index .

The relative influence matrix of power supply guarantee consumers only describes the relative influence of power supply guarantee consumers under one factor evaluation index. In order to consider the relative influence of different indicators on consumers of power supply security, it is necessary to sum up the relative influence to obtain the comprehensive relative influence matrix .

To avoid the discreteness of the comprehensive evaluation results of the relative importance factors of different power supply protection consumers, a normalization method based on membership degree was used in this study to transform the comprehensive evaluation matrix of the relative importance factors and determine the importance factors of different power supply protection consumers [28]. The Gaussian membership function [29] used for the calculation is presented as follows:

where and are as given by (5) and (6), respectively, and can be used to determine the shape and position of the membership function curve.

where , , and is a normalization coefficient.

Substituting the parameters and into the calculation formula (4), the importance factor values of the power supply protection consumer can be obtained as

3.2. Evaluation of Power System Restoration Capability

Power system restoration capability is the comprehensive power supply recovery capability of a power supply when it loses its operation capacity due to power supply interruption such as after an earthquake disaster. As a tool for emergency power supply recovery after an earthquake, the effect of the power supply configuration scheme on the power supply recovery capability is equivalent to that of a given facility’s power supply recovery capability on the comprehensive recovery capability of the entire power system [30].

Considering the concept of facility power supply level, the facility allocation scheme, which affects the postearthquake recovery state of the power system, was used in this study as a measure of the influence degree of the power supply allocation on the postearthquake recovery ability of the power system. The normalization coefficients of the postearthquake recovery functions for the different power supply restoration levels of facilities were calculated using the power allocation schemes of the different power supply levels.

Here, are the power supply types of the consumer’s different power supply restoration levels of facilities, and are the postearthquake recovery capabilities of the different power sources. The postearthquake recovery capabilities of the different power sources can be divided into three levels based on the postearthquake recovery function (), standby power recovery function (), and emergency power recovery function ().

The normalization coefficients of the postearthquake recovery functions for power supply restoration level I of facilities, power supply restoration level II of facilities, and power supply restoration level III of facilities were calculated using (8) and determined to be 0.6, 0.3, and 0.1, respectively. It was also necessary to calculate the overall postearthquake recovery capacity of consumers that simultaneously operate multiple facilities with differing power supply levels.

It is assumed that a power supply protection consumer in the power system requires restoration of power to power supply restoration levels of facilities after an earthquake. If the total number of facilities is facilities, the overall power recovery capability of consumer is given by

The effects of the postearthquake recovery capabilities of different power supply protection types of consumers on the overall power supply restoration level of the power system entirely differ. The overall power supply restoration capability is calculated by weighting the effects of the factors of the different power supply consumers to obtain the index , which reflects the overall capacity of the power system, as follows:

The postearthquake capacity restoration equilibrium is an index for evaluating the distribution of the power supply restoration capability of each consumer in the power system. Considering that the coefficient of variation in statistics affords an intuitive indication of the centralized or discrete state of the units of a system [31], a coefficient of variation algorithm was used in this study to calculate the equilibrium index of the postearthquake recovery capability of the power supply system. The following equation was employed:

where is the postearthquake recovery capability of consumer and is the overall postearthquake recovery capability of the power system.

The equilibrium degree of the overall postearthquake restoration capability of the power system is a relative value. This indicates that the differing postearthquake restoration capabilities of the different power supply protection consumers create a discrete situation in the overall postearthquake restoration capability of the entire power system [32]. For example, the higher the calculated equilibrium degree, the more significant are the differences between the postearthquake recovery capabilities of the power supply protection consumers. Through an analysis of the overall postearthquake restoration capability of the power system, it was found that the closer the restoration capabilities of different consumers were, the more reasonable the postearthquake restoration scheme of the power system would be. This would reduce the possibility of economic losses and casualties resulting from the earthquake. It can thus be concluded that the equilibrium index of the restoration capability of a power system after an earthquake reflects the postearthquake emergency power supply restoration capability of the power system based on the degree of discreteness among the restoration capabilities of the individual consumers.

4. Example Analysis

4.1. Facility Distribution in Central Urban Area

The central urban area shown in Figure 2 was used for an example evaluation of the postearthquake restoration capability of a power supply system. Investigations revealed that the area contained 19 power supply protection consumers who required power restoration to 10302 facilities after an earthquake.

Figure 2: Consumer profile of the case study central urban area.

As can be observed from Figure 2, there are nine types of power supply consumers in the considered urban area, namely, hospitals, fire service, government buildings, schools, residential buildings, business enterprises, office buildings, exhibition halls, and green space. To evaluate the postearthquake restoration capability of the power system in the area, it is necessary to classify the power supply protection types of consumers. The first type of power supply protection consumers includes hospitals (H1), fire service (F1), and government buildings (G1), which would play a key role in postearthquake emergency relief work. The second type of power supply protection consumers includes schools (S1 and S2) and green space (L1). The third types of power supply protection consumers are residential buildings (R1–R8), exhibition halls (U1), government buildings (G2), business enterprises (M1), office buildings (W1), and warehouses (T1), which are less critical to postearthquake emergency relief. Further, it is also necessary to quantitatively sort the different facilities within each consumer based on the facility importance. Table 8 presents the relevant results of the investigation.

Table 8: Quantitative sorting of consumer facilities.

Consumer
First type of power supply facilities
Second type of power supply facilities
Third type of power supply facilities

H1
71
62
551

F1
43
47
233

G1
62
49
331

S1

90
180

S2

95
190

L1

80
160

R1

1272

R2

396

R3

456

R4

1512

R5

324

R6

588

R7

312

R8

614

U1

450

M1

1300

O1

600

G2

460

T1

400

Total
176
423
9969

The set of power supply consumers in Table 8 are , .

The relative influence factor matrix corresponding to the evaluation indexes of primary power supply restoration facilities for power supply guarantee users is calculated, and the calculation result is shown in Table 9.

Table 9: Relative influence factor matrix of consumers under the scoring index of primary power supply restoration facilities.

H1
F1
G1
S1
S2
L1
R1
R2
R3
R4
R5
R6
R7
R8
U1
M1
O1
G2
T1

H1
0
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8

F1
0.2
0
0.2
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8

G1
0.2
0.8
0
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8

S1
0.2
0.2
0.2
0
0.4
0.4
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8

S2
0.2
0.2
0.2
0.4
0
0.4
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8

L1
0.2
0.2
0.2
0.4
0.4
0
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8

R1
0.2
0.2
0.2
0.2
0.2
0.2
0
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

R2
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

R3
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

R4
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

R5
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

R6
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0
0.4
0.4
0.4
0.4
0.4
0.4
0.4

R7
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0.4
0
0.4
0.4
0.4
0.4
0.4
0.4

R8
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0
0.4
0.4
0.4
0.4
0.4

U1
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0
0.4
0.4
0.4
0.4

M1
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0
0.4
0.4
0.4

O1
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0
0.4
0.4

G2
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0
0.4

T1
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0

As shown in Table 10, the relative influence factor matrix corresponding to the evaluation indexes of secondary power supply restoration facilities for power supply guarantee users is calculated.

Table 10: Relative influencing factor matrix of consumers under the scoring index of secondary power supply restoration facilities.

H1
F1
G1
S1
S2
L1
R1
R2
R3
R4
R5
R6
R7
R8
U1
M1
O1
G2
T1

H1
0
0.4
0.4
0.1
0.1
0.1
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

F1
0.1
0
0.1
0.1
0.1
0.1
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

G1
0.1
0.4
0
0.1
0.1
0.1
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

S1
0.4
0.4
0.4
0
0.1
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

S2
0.4
0.4
0.4
0.4
0
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

L1
0.4
0.4
0.4
0.1
0.1
0
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

R1
0.1
0.1
0.1
0.1
0.1
0.1
0
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2

R2
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2

R3
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2

R4
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2

R5
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2

R6
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0
0.2
0.2
0.2
0.2
0.2
0.2
0.2

R7
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0
0.2
0.2
0.2
0.2
0.2
0.2

R8
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0
0.2
0.2
0.2
0.2
0.2

U1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0
0.2
0.2
0.2
0.2

M1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0
0.2
0.2
0.2

O1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0
0.2
0.2

G2
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0
0.2

T1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0

As shown in Table 11, the relative influence factor matrix corresponding to the evaluation indexes of tertiary level power supply restoration facilities for power supply guarantee users is calculated.

Table 11: Relative influencing factor matrix of consumers under the scoring index of tertiary power supply restoration facilities.

H1
F1
G1
S1
S2
L1
R1
R2
R3
R4
R5
R6
R7
R8
U1
M1
O1
G2
T1

H1
0
0.2
0.2
0.2
0.2
0.2
0.05
0.2
0.2
0.05
0.2
0.05
0.2
0.05
0.2
0.05
0.05
0.2
0.2

F1
0.05
0
0.05
0.2
0.2
0.2
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05

G1
0.05
0.2
0
0.2
0.2
0.2
0.05
0.05
0.05
0.05
0.2
0.05
0.2
0.05
0.05
0.05
0.05
0.05
0.05

S1
0.05
0.05
0.05
0
0.05
0.2
0.05
0.05
0.05
0.2
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05

S2
0.05
0.05
0.05
0.2
0
0.2
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05

L1
0.05
0.05
0.05
0.05
0.05
0
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05

R1
0.2
0.2
0.2
0.2
0.2
0.2
0
0.2
0.2
0.05
0.2
0.2
0.2
0.2
0.2
0.05
0.2
0.2
0.2

R2
0.05
0.2
0.2
0.2
0.2
0.2
0.05
0
0.05
0.05
0.2
0.05
0.2
0.05
0.05
0.05
0.05
0.05
0.05

R3
0.05
0.2
0.2
0.2
0.2
0.2
0.05
0.2
0
0.05
0.2
0.05
0.2
0.05
0.2
0.05
0.05
0.05
0.2

R4
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2

R5
0.05
0.2
0.05
0.2
0.2
0.2
0.05
0.05
0.05
0.05
0
0.05
0.2
0.05
0.05
0.05
0.05
0.05
0.05

R6
0.2
0.2
0.2
0.2
0.2
0.2
0.05
0.2
0.2
0.05
0.2
0
0.2
0.05
0.2
0.05
0.05
0.2
0.2

R7
0.05
0.2
0.05
0.2
0.2
0.2
0.05
0.05
0.05
0.05
0.05
0.05
0
0.05
0.05
0.05
0.05
0.05
0.05

R8
0.2
0.2
0.2
0.2
0.2
0.2
0.05
0.2
0.2
0.05
0.2
0.2
0.2
0
0.2
0.05
0.2
0.2
0.2

U1
0.05
0.2
0.2
0.2
0.2
0.2
0.05
0.2
0.05
0.05
0.2
0.05
0.2
0.05
0
0.05
0.05
0.05
0.2

M1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.05
0.2
0.2
0.2
0.2
0.2
0
0.2
0.2
0.2

O1
0.2
0.2
0.2
0.2
0.2
0.2
0.05
0.2
0.2
0.05
0.2
0.2
0.2
0.05
0.2
0.05
0
0.2
0.2

G2
0.05
0.2
0.2
0.2
0.2
0.2
0.05
0.2
0.2
0.05
0.2
0.05
0.2
0.05
0.2
0.05
0.05
0
0.2

T1
0.05
0.2
0.2
0.2
0.2
0.2
0.05
0.2
0.05
0.05
0.2
0.05
0.2
0.05
0.05
0.05
0.05
0.05
0

4.2. Computing Facility Recovery Capability

The relative impacts of the powered facilities of the primary, secondary, and tertiary power supply restoration levels are shown in (2).

The normalization coefficient was assumed to be 0.5, and the parameters and were determined to be 35.1 and 17.85, respectively. Finally, (7) was used to calculate the influence factors of the different power supply consumers, as presented in Table 12.

Table 12: Calculated restoration capabilities of the different power supply consumers.

Consumer
Influence factor
Resilience
Power system resilience

H1
0.81
116.3
Power system restoration capability: 67.6
Resilience equilibrium degree: 49.2%

F1
0.71
63.2

G1
0.75
85

S1
0.52
45

S2
0.53
47.5

L1
0.50
40

R1
0.46
127.2

R2
0.42
39.6

R3
0.43
45.6

R4
0.47
151.2

R5
0.41
32.4

R6
0.45
58.8

R7
0.40
31.2

R8
0.46
61.4

U1
0.43
45

M1
0.47
130

O1
0.45
60

G2
0.44
46

T1
0.42
40

If it is assumed that all the facilities of a power supply protection consumer are damaged by the earthquake, the resilience of the consumer can be calculated based on the work capacity of the power that would have been supplied to those facilities, as presented in Table 9.

The influence factors and resilience of the different power supply consumers were substituted into (10) to determine the overall resilience of the power system of the considered central urban area. By substituting the above results into (11), the equilibrium degree of the postearthquake restoration capability of the power system can be obtained.

As can be observed from Table 12, the postearthquake recovery capacities of the H1, R1, R4, and M1 power supply consumers in the considered central urban area are all greater than 100, while those of the R5 and R7 power supply service consumers are lower than 40. This results in a postearthquake restoration equilibrium of the power system of 49.2%, indicating highly discrete postearthquake power restoration capacities of the different power supply consumers.

The main reasons for the above observations were found to be of two types. Firstly, the hospitals H1, fire station F1, government buildings G1, and the other power supply consumers with higher power supply restoration levels include three types of powered facilities, resulting in a stronger postearthquake recovery capacity than that of the third-level power supply protection consumers G2, which only contain the third type of powered facilities. Secondly, the power supply consumers with the lowest power supply restoration level, such as the residential buildings R1 and R2 and the business enterprises T1, include only the third type of powered facilities. However, because these power supply consumers contain a much higher number of such facilities than the other power supply consumers, their postearthquake power supply restoration capability is higher.

5. Resilience Recovery Optimization

As noted above, the determined equilibrium postearthquake restoration capacity of the entire power supply system was higher than 50%. It can be concluded from this result that there are significant differences between the postearthquake power supply restoration capabilities of the different power supply consumers. In the present work, the power allocation scheme of the entire power system was varied by adjusting the number of facilities or the number of more important facilities contained in the power supply consumers. This method enabled reduction of the degree of discreteness of the postearthquake restoration capabilities of the different power supply consumers, thus enhancing the overall restoration capability of the entire power system.

5.1. Adjustment of Facility Importance Level

As indicated in Table 12, there are significant differences between the postearthquake restoration capabilities of the different power supply protection consumers in the considered central urban area. To improve the integrity of the power system during the restoration process, it is necessary to adjust the importance of the facilities of the secondary power supply protection consumers such as schools S1 and S2 and green area L1, which play important roles during the earthquake relief process. For example, the medical facilities in the refugee centers should be upgraded from simple injury dressing functions to trauma operation functions, and the conference facilities should be upgraded from meeting functions to disaster relief command functions. Further, 30 second type powered facilities such as medical and conference facilities can be converted into the same number of first type powered facilities, as presented in Table 13.

Table 13: Facility allocation plan.

Status
Consumer
First type of powered facilities
Second type of powered facilities
Third type of powered facilities

Unadjusted
S1

90
180

S2

95
190

L1

80
160

Adjusted
S1
30
60
180

S2
30
65
190

L1
30
50
160

As can be observed from Table 13, the importance group of the 30 facilities included in the secondary power supply consumers in the central urban area, such as schools S1 and S2 and green area L1, have been upgraded from the second group to the first group. The power supply scheme of these facilities is thus upgraded from conventional power and standby power to conventional power, standby power, and emergency power. This power supply scheme upgrade results in a corresponding increase in the postearthquake power supply restoration capability of the consumers containing the facilities.

With the above adjustments, the postearthquake power supply restoration capability of the power system in the central urban area considered in this study was determined to be , while the power supply restoration equilibrium was again determined to be %. A comparison of these results with those for the unadjusted conditions shows that upgrading the importance of some of the facilities not only increases the restoration capability of the power supply system but also reduces the discreteness degree of the power restoration capabilities of the different power consumers.

5.2. Adjustment of Number of Facilities

Table 12 shows that although all eight residential building units R1–R8 of the considered urban area are tertiary power supply protection consumers, they have significantly varying resiliencies on the power system. For example, the resiliencies of residential buildings R1 and R4 are 127.2 and 151.2, while those of R5 and R7 are 32.4 and 31.2. From the calculation process, the differing resiliencies of the residential consumers may be mainly attributed to the differing numbers of facilities that they contain.

Urban emergency power supply planning generally considers a single power supply consumer as a unit of postearthquake rehabilitation work. Although residential consumers R5 and R7 contain a small number of facilities, they also require the same human and material resources as other consumers in the postearthquake rehabilitation work, and this increases the cost of the power supply restoration. Hence, in addition to adjusting the importance of facilities, the method for improving the postearthquake restoration capability of the power system also includes adjusting the facilities planning scheme of the power supply consumers.

Residential buildings R5 and R6 have relatively few facilities. Hence, to increase the postearthquake restoration capability of the power system, the facilities of residential buildings R6 were merged into residential buildings R5, as shown in Figure 3. This reduced the number of power supply consumers from 19 to 18, with the number of facilities in R5 increasing to 912 facilities. A reassessment of the power system produced power supply restoration capability and power supply equilibrium %, compared to and % prior to adjustment. The proposed method for adjusting the postearthquake power supply scheme of a central urban area thus effectively increases the restoration capacity of the power system, while reducing the discreteness of the restoration capacities of the individual power supply consumers.

Figure 3: Adjusted consumer plan of the central urban area, showing R5 and R6 merged into a new area R5.

6. Conclusion

In this study, a procedure for dividing all the facilities served by an urban power supply system into three power supply restoration levels based on their importance grouping and their possible adverse effects in the event of a power failure was developed. The postearthquake power restoration requirements correspond to different power supply restoration levels of facilities, namely, the first-level important facilities whose power supply should not be interrupted, second-level important facilities requiring prompt restoration of power supply, and third-level general facilities that can tolerate gradual restoration of power supply.

With reference to the emergency power supply restoration requirements of the different power supply restoration levels, a power supply restoration scheme was developed, and a curve reflecting the power restoration characteristics of the power supply system was drawn. Power supply restoration can be divided into three stages: the uninterrupted operation stage, emergency recovery stage, and conventional recovery stage. The uninterrupted operation stage is applied to the first-level important facilities, which are equipped not only with conventional power and standby power supplies but also with emergency recovery power in key nodes. It was found that the second-level facilities were equipped with conventional and standby power supplies. The third-level facilities were equipped with only a conventional power supply.

Finally, the postearthquake power supply restoration capability of the system was evaluated from a topological point of view. First, the normalization coefficients of the influence factors pertaining to power consumers of different types were calculated using the normalization method based on the membership degree. The power supply restoration capability of each consumer after an earthquake was then calculated. Finally, the overall power supply restoration capability and equilibrium degree of the entire power system after the earthquake were determined using a weighting algorithm and an improved algorithm with the variation coefficient. The power supply restoration capability is an indication of the ability of the overall power system to restore power supply after an interruption; the equilibrium degree of recovery capability describes the discrete degree of recovery capability of consumers with different types of power supply guarantee in the power system. The proposed procedure was applied to the power supply system of a central urban area as an example. It was found that the postearthquake power supply restoration capability of the area could be improved by adjusting the power supply importance levels of the different serviced facilities and the power supply schemes of the consumers.

Data Availability

All data included in this study are available upon request by contact with the corresponding author.

Conflicts of Interest

The authors declare that there are no conflicts of interest.

Acknowledgments

This research was supported by National Key R&D Program of China (Grant no. 2018YFD1100902-1), the National Natural Science Foundation of China (Grant no. 51678017), and Beijing Municipal Education Commission Science and Technology General Project (Grant no. KM201610005029).

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