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Prototyping and cells modeling of the infrastructure interdependencies simulator I2Sim Liu, Lu 2007

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Prototyping and Cells Modeling of the Infrastructure Interdependencies Simulator 12 Sim by Lu Liu B . S . , Nanjing University o f Aeronautics and Astronautics (China), 1994  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF APPLIED SCIENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES (ELECTRICAL A N D COMPUTER ENGINEERING)  THE UNIVERSITY OF BRITISH C O L U M B I A August, 2007  © Lu Liu, 2007  ii  Abstract The functioning of modern societies is strongly dependent upon an array of complex national infrastructure networks such as power utilities, information technology, health care, water supply and transportation; these networks provide material support for the delivery of basic services to all segments of the society. However, these critical infrastructures are becoming increasingly complex and fragile because of their tightly coupled structures which can rapidly propagate failures. Thus, there is a need to investigate the highly complex physical, information, geographic, and logic interdependencies among critical infrastructures. One needs to fully understand the dynamic behaviors of these interdependent networks in order to analyze and evaluate their robustness and resilience to natural disasters. This also helps operators to take actions in order to optimize the coordination among infrastructures during emergencies. Models based on a novel approach have been implemented. In this thesis, a reduced scale test case model of the University of British Columbia's critical infrastructures has been developed and implemented in software. Critical entities are defined as cells. The cell models are built based on input-output relationships discussed with and validated by the personnel involved with the concerned infrastructures; the interconnections between the cells are modeled as a variety of channels that defines quantities exchanged by different infrastructures, like electric power. The aggregated cells and channels are simulated with an interactive graphical user interface for the study of infrastructure interactions. The simulation indicates that the redundant systems increase the robustness of the cells such as the backup generators in the Hospital; the critical connections, such as the steam pipe linking the Steam Station with the Hospital are identified. These give the decision makers a better understanding of the emergent system behavior under different operational scenarios. One scenario is studied by using a distributor, which allows an operator to find the optimum allocation of the limited resource in order to ensure the best possible operation of the other critical infrastructures during the event. The simulation itself was parallelized, and distributed in PC-cluster at the UBC Power Systems Lab.  iii  List of Contents Abstract List o f Contents List o f Tables List o f Figures Acknowledgement Dedication Chapter 1 Introduction 1.1. Background 1.2. Related Research 1.3. Research Obj ective Chapter 2 I2Sim System Description 2.1. I2Sim Overview 2.2. Characteristics o f Cells and Channels 2.3. The Input-Output M o d e l 2.4. Discrete Event Simulation Chapter 3 The Generic Cell-Channel M o d e l 3.1. General Description 3.2. The Substation M o d e l 3.2.1. Inputs and Outputs o f the Substation C e l l 3.2.2. The Generic M o d e l o f the Substation C e l l 3.3. The Power House M o d e l 3.3.1. Inputs and Outputs for the Power House C e l l 3.3.2. Generic M o d e l o f the Power House C e l l 3.4. The Water Station M o d e l 3.4.1. Inputs and Outputs for the Water Station C e l l 3.4.2. Generic M o d e l o f the Water Station C e l l 3.5. Steam Station M o d e l 3.5.1. Inputs and Outputs for the Steam Station C e l l 3.5.2. Generic M o d e l o f the Steam Station C e l l 3.6. Hospital M o d e l 3.6.1. Inputs and Outputs for the Hospital C e l l 3.6.2. Interdependent Performance o f the Hospital C e l l 3.6.3. Generic M o d e l o f the Hospital C e l l 3.7. Channel M o d e l 3.8. Reduced Scale Test Case M o d e l Chapter 4 Simulation and Results Analysis 4.1. Simulation M o d e l for the U B C Test Case 4.2. Simulation Results 4.2.1. Scenario 1 and Result Analysis 4.2.2. Scenario 2 and Results Analysis 4.2.3. Scenario 3 and Results Analysis 4.3. Distributed Simulation 4.4. Simulation Conclusion Chapter 5 Conclusions and Future Work 5.1. Conclusion  ii iii v vi viii x 1 1 2 6 9 9 12 17 20 24 24 28 28 30 32 32 34 36 36 37 39 39 41 43 43 46 48 51 52 54 54 61 61 67 73 77 80 81 81  iv  5.2. Future Work References Appendix  82 83 87  V  List of Tables Table 2.1: Cells and their Links to Critical Infrastructures 15 Table 2.2: Sample Data i n the Human Readable Table for a Hospital C e l l 18 Table 3.1: Status M a p p i n g for the Human Readable Table for the Substation Cell 31 Table 3.2: Status Mapping for the Human Readable Table for the Power House Cell ..35 Table 3.3: Status Mapping for the Human Readable Table for the Water Station 38 Table 3.4: Status Mapping for the Human Readable Table for the Steam Station 42 Table 3.5: Redundancy o f the Critical Infrastructures for the U B C Hospital 46 Table 3.6: Interdependency o f the Critical Infrastructures inside the U B C Hospital 47 Table 3.7: Interdependency between the Critical Infrastructures and the Backups inside the U B C Hospital 47 Table 3.8: Power Aggregator o f Hospital C e l l 48 Table 3.9: Water Aggregator o f Hospital C e l l 49 Table 3.10: Status M a p p i n g for the Human Readable Table o f the U B C Hospital 50 Table 4.1: Input-Output Table for the States o f Transformers, Tiebreakers and Feeders 57  vi  List of Figures Figure 2.1: Diagram o f Infrastructure Interdependencies Simulator [17] Figure 2.2: Infrastructure Interdependencies [7] Figure 2.3: C e l l Classification [17] Figure 2.4: Electrical and Gas Networks [20] Figure 2.5: Structure o f the Generic Cell-channel M o d e l Figure 2.6: The Input-Output M o d e l for Cells Figure 2.7: Piece-wise Linear Approximation for One Dimensional Function Figure 2.8: The Input-Output M o d e l for Cells with Critical Components Figure 2.9: Events i n the Cell-Channel M o d e l : Figure 3.1: GIS-Mapping of the U B C ' s Test Case [20] Figure 3.2: Data F l o w for the Cell-Channel M o d e l Figure 3.3: Diagram o f the Basic Functions of the U B C Substation Figure 3.4: Diagram o f the Substation C e l l M o d e l Figure 3.5: Diagram o f the Basic Functions of U B C ' s Power House Figure 3.6: Diagram o f the Power House C e l l M o d e l Figure 3.7: Function o f O i l i n the Power House C e l l Figure 3.8: Diagram o f the Basic Functions of U B C ' s Water Station Figure 3.9: Diagram o f the Water Station C e l l M o d e l Figure 3.10: Diagram o f the Basic Function of U B C ' s Steam Station Figure 3.11: Diagram of the Steam Station Cell M o d e l Figure 3.12: Diagram o f the Basic Functions of the U B C Hospital Figure 3.13: Diagram o f the Hospital C e l l M o d e l Figure 3.14: Reduced Scale U B C Test Case M o d e l Figure 4.1: Interconnection Structure i n the Reduced Scale U B C Test Case Figure 4.2: State o f O i l Usage i n the Power House Figure 4.3: Input-Output Table for Beds for Urgent Medical Service Figure 4.4 Simulation M o d e l of the Reduced Scale U B C Test Case Figure 4.5: Interface o f the Substation C e l l M o d e l Figure 4.6: Timeline o f Scenario 1 Figure 4.7: Scenariol - Simulation Results for the Substation C e l l Figure 4.8: Scenariol: Simulation Results for the Power House C e l l Figure 4.9: Scenariol - Simulation Results for the Water Station C e l l Figure 4.10: Scenariol - Simulation Results for the Steam Station C e l l Figure 4.11: Scenariol - Simulation Results for the Hospital C e l l (A) Figure 4.12: Scenariol - Simulation Results for the Hospital C e l l (B) Figure 4.13: Interrelationship o f Electrical Power between Cells Figure 4.14: Timeline o f Scenario 2 Figure 4.15: Scenario2 - Simulation Results for the Substation C e l l Figure 4.16: Scenario2 - Simulation Results for the Power House C e l l Figure 4.17: Scenario2 - Simulation Results for the Water Station C e l l Figure 4.18: Scenario2 - Simulation Results for the Steam Station C e l l Figure 4.19: Scenario2 - Simulation Results for the Hospital C e l l (A) Figure 4.20: Scenario2 - Simulation Results for the Hospital C e l l (B) Figure 4.21: Scenario 3 - Distributor Sent Power to the Hospital and Power House  10 12 13 14 16 18 19 19 21 25 27 28 29 32 33 34 36 37 39 40 44 49 53 55 56 58 59 60 62 63 64 64 65 65 66 67 69 69 70 70 71 72 72 75  vii  Figure Figure Figure Figure Figure Figure Figure  4.22: 4.23: 4.24: 4.25: 4.26: 4.27: 4.28:  Scenario3 - Simulation Results for the Water Station C e l l Scenario3- Simulation Results for the Steam Station C e l l Scenario 3 - Simulation Results for the Hospital (A) Scenario 3 - Simulation Results for the Hospital (B) Structure o f the P C Cluster Simulation P C Cluster Simulation A P C Cluster Simulation B  75 75 76 77 78 79 80  viii  Acknowledgement I am greatly indebted to D r . Jose R. Marti, one o f the best advisors and teachers I have ever met i n m y academic life.  H i s advice, supervision, and crucial contribution made h i m the  backbone o f this research and thesis. Without his support and guidance, I would never have had the chance to come to the University o f British Columbia and finished this research. H i s broad vision, profound knowledge, and creative thinking were a source o f inspiration to me when working on this research and thesis. He could not possibly realize how much I have learned from him.  I am also grateful to D r . Juri V . Jatskevich for his helpful suggestions in simulation and relevant research discussions with me. I want to thank Dr. Jorge Hollman for his leadship in procuring the contacts and coordinating the work o f the U B C test case team, and Dr. Mazana Armstrong for her insights i n building the cell models from the Human Readable Tables. A very special thanks to my close office mates: Quanhong Han, T o m D e Rybel, Hafiz Rahman, Marcelo Tomim, M i c h a e l Wrinch, Y a n L i , L i w e i Wang and Siva Singupuram for their help when I was working on m y research. I would like to thank m y peers i n the U B C Test Case Group and the Infrastructure Interdependencies Simulator (I2Sim) Group at the University o f British Columbia. During the one-and-a-half year o f this research, they gave me a great deal o f help and good advice. I would like to thank all the members i n the JIIRP project; the monthly regular meeting inspired me to complete the project. I would also like to thank all o f the members i n the Power Electronics and Power System Group. I cherish the experience o f working with members o f this group i n the last two years and w i l l always remember our valuable discussions. I also thank all o f them for their assistance and friendship.  M a n y thanks are due to: M r . R o n Ewart, Assistant Chief Engineer and M r . Phil Carriere, Shift Engineer i n the U B C Power House; M r . Stan Tekenaka, Head Electrician o f U B C Utility; M r . John Manougian, Manager o f U B C Hospital Facilities Development; and M r A l l a n Fairbairn o f the U B C Hospital. I am grateful for their support and for providing me with information and assistance throughout m y research.  ix  Finally, I would like to thank m y family for their love and support. Especially, I would like to thank  m y husband,  Kaifeng  Huang,  encouragement when it was most required.  for his understanding,  endless  patience  and  X  To My  Family  Chapter 1  Introduction  1.1. Background The advancement in science and technology has made the critical infrastructures o f a society tightly interconnected and mutually dependent. Some aspects o f this interdependency include physical factors, human behavior and information sharing; however, a l l these are vulnerable to disasters.  Natural or man-made disasters happen and can cause thousands o f severe  casualties. The A s i a n Tsunami on December 26, 2004 caused a total loss o f 229,866 human lives [1]. Another unfortunate incident, Hurricane Katrina, which struck on August 23, 2005, was responsible for a total damage o f $81.2 billion and a loss o f 1,464 human lives [2]. These disasters have made the protection and restoration o f critical infrastructures, such as health care, utilities, transportation and communication, a serious national concern. The joint infrastructure interdependencies research program (JIIRP) is part o f an ongoing national effort to secure and protect Canada's critical infrastructures [3]. The objective o f the JIIRP research at the University o f British Columbia is to study decision making for critical linkages i n infrastructure networks. A well developed model is essential for facilitating coordinated decision making.  Rinaldi [4] has defined four primary classes o f interdependencies: the physical, cyber, geographical and logical. T w o infrastructures are physically interdependent i f the state o f each is dependent on the material output(s) o f the other. A n infrastructure has cyber interdependency i f its state depends on data transmitted through the information system. Infrastructures are geographically interdependent i f a local environmental event can create state changes i n all o f them. T w o infrastructures are logically interdependent i f the state o f each depends on the state o f the other v i a a mechanism that is not a physical, cyber, or geographical connection. The emphasis in this thesis is on the physical layer. Modeling interdependent infrastructures is a complex, multifaceted, multidisciplinary problem, where it  2  is necessary to choose a specific approach to encompass the infrastructures and their interdependencies.  1.2. Related Research The modeling o f individual entities i n the system as w e l l as the combined whole system is fundamental  and  essential for the  analysis o f infrastructure  interdependencies,  the  optimization o f the restoration process, and for support make the best decisions. Various modeling approaches are reviewed i n this section. Disaster situations such as natural disasters, deliberate attacks or accidental system failures within infrastructures may result i n cascading effects; these effects between infrastructures are dynamic and may not be apparent or immediately understood. Therefore, the  literature on interdependency modeling and  simulation has to be reviewed.  Some research has been done on certain types o f disasters. In the case o f earthquakes, floods and  hurricanes, a tool based on GIS has been developed b y the Federal Emergency  Management A g e n c y called H A Z U S ; this agency analyzes potential losses from disasters such as earthquakes according to geographic locations; it also analyzes the severity o f an earthquake b y estimating the physical damage, economic loss and social impact [5].  A  similar research has been developed b y M C E E R at the State University o f N e w Y o r k at Buffalo, which is a national center o f excellence dedicated to establishing disaster-resilient communities through the application o f multidisciplinary, multi-hazard research. M C E E R mainly focuses on restoration modeling o f lifeline systems and has conducted relevant research on multiple infrastructures [6].  A survey [7] o f U . S and International work on critical infrastructure interdependency modeling has been compiled; this survey identifies and catalogs many o f the state-of-the-art research being conducted i n the area o f infrastructure interdependency modeling and analysis. The  thirty types o f simulations listed i n the survey are based on different modeling  approaches such as agent-based models, effect-based operation models ( E B O ) , input-output models, system dynamics models, mathematical models, models based on game theory,  3  models based on risk, etc. In recent years, modeling approaches such as the system dynamics model, input-output model, Petri-Nets model and agent-based model have been implemented in various works on critical infrastructure interdependency modeling. One o f the modeling approaches is the cell-channel model for the Infrastructure Interdependencies Simulator (I2Sim) developed at the University o f British Columbia.  System Dynamics System dynamics, founded i n the late 1950s by Jay W . Forrester o f the M I T Sloan School o f Management, is an approach for understanding the behavior o f complex systems over time. It deals with internal feedback loops and time delays that affect the behavior o f the entire system. The system components o f this approach are the use o f feedback loops, stock and flows. A stock is the term for any entity that accumulates or depletes over time. A flow is the rate o f change i n a stock. Stocks and flows help describe how a system is connected by feedback loops. In the terminology o f system dynamics, a system is defined as a collection o f elements that continually interact over time to form a unified whole. Dynamics refers to change over time. System dynamics is, therefore, a methodology used to understand how systems change over time [8]. The system dynamics model uses differential equations to describe the behavior o f systems, so it is well suited to modeling continuous systems and less well suited to providing a detailed representation o f a system where there are discrete changes i n state variables.  One o f the implementations o f the system dynamics modeling approach is i n the research o f a health care system, for example, modeling the consequences o f major incidents i n a health care system [9]. Natural disasters or terrorist acts can have severe impact on a health care system by overloading it with casualties. The model represents the interrelation between the population, the health care infrastructure and other infrastructures. The population is set as different types o f patients and based on the relationship between them, the population changes at different rates i n different disaster scenarios. The interactions between types o f patient flows are described in detail; the interactions between health care infrastructure and other infrastructures are not mentioned comprehensively. Another research group using system dynamics as the modeling approach is the Sandia National Laboratories [10]. They  4  have built a modeling framework based on system dynamics and J T J E F 0 (a method designed to model the decisions, actions, and activities o f an organization or system). Using the system dynamics, a model o f infrastructure interdependencies can be built using the causal-loop diagram to capture the structure o f the systems. It can provide a high-level view o f relationships, interactions, and feedback processes; however, it is hard to see the physical buildup and flows o f information and products through the system. A t the same time, the model also needs to use I D E F 0 for functional modeling to define data requirements and describe the exchange o f information between the individual models. The system dynamics approach can be used i n modeling interdependencies o f the infrastructures i n a high-level view.  Generalized Leontief Input-Output Model Inoperability Input-Output M o d e l (IIM) i n [7] is the model based on Leontief s linear inputoutput relationship. It characterizes interdependencies among sectors i n the economy and analyzes initial disruptions to a set o f sectors and the resulting ripple effects. Wassily Leontief received the 1973 Nobel Price i n Economics for developing what has come to be known as the L e o n t i e f s input-output model o f the economy[18]. H i s model gives an understanding o f the interconnectedness among the various sectors o f an economy and forecasting the effect on one segment o f a change i n another. W i t h his research group at the University o f Virginia, Professor Y a c o v Y . Haimes [11] [12] [13] developed the technology to model critical infrastructures using the inoperability input-output model. Based on the technology, a Leontief-based input-output model (IIM) is developed for modeling the impacts o f willful attacks on interdependent sectors. The I I M is a model for assessing sector vulnerabilities using the inoperability and economic loss impact metrics. For example, the model has been used to research a high-altitude electromagnetic pulse ( H E M P ) attack scenario. It is mainly used i n the economic and risk management o f complex interconnected systems. Leontief s model assumes linear relationships between inputs and outputs, also it does not consider the problem o f goods transportation.  5  ^  Petri-Net Model  A Petri Net is one o f several mathematical representations o f discretely distributed systems. It is a graph-based tool for depicting the structure o f a distributed system as a directed graph, which is composed o f place nodes, transition nodes, and directed arcs connecting places with transitions. Input arcs connect places with transitions, while output arcs start at a transition and end at a place. Places can contain tokens; the current state o f the system component is given by the number o f tokens i n each place. Transitions are active components; when they are triggered, the triggering removes tokens from its input places and adds them to some o f its output places.  A test case using Petri Net to model infrastructure interdependencies is  represented [14].  The model has been designed in high-level abstractions based upon a  general  interdependent  infrastructure  system,  which  includes  electric  power, o i l ,  transportation, natural gas, telecommunications and water. The static states o f the critical infrastructure are "on : 1" and "off: 0." Based on this model, the interdependencies o f the system are identified. However, it is not well suited for describing the model in quantitative and scalabilities analysis under different damage states.  Agent-Based Model Nowadays, the agent-based paradigm has become one o f the most popular approaches i n general software development. Nearly half o f the simulations i n [7] use the agent-based model. One o f them is the next-generation agent-based economic laboratory " N - A B L E " developed b y researchers at Sandia National Laboratories [15]. These agent-based systems try to tackle a variety o f complex problems using a fully distributed, bottom-up approach. The tool has been mainly used for studies involving the economic impact resulting from disruptions on infrastructures and supply chain.  Cell-Channel Model The cell-channel model used i n the I2Sim simulator under development at U B C [16] considers the nonlinear relationships among all interdependent entities i n the system. The model is based on the idea o f service token delivery to different infrastructure entities. The system components include cells, channels, and tokens. Tokens are goods and services that  6  are provided b y one entity to another entity that uses them. A cell is an entity that performs a function. Channels are the means through which tokens flow from one generator node to a load node. The interrelationship between the input(s) and output(s) o f the cells determines the cells' functionality. The channel is described using functions with capacity limitations and time delay. The combined cells and channels model makes up the multiple networks system. It has been used on physical layer modeling o f interdependent infrastructures and run in the I2Sim  simulator. The I2Sim  simulator aims at  simulating the  conditions o f each  infrastructure component (cells, channels, input and output tokens) for large disaster scenarios to support decision making to mitigate the disaster effects.  In conclusion, many modeling approaches have been implemented i n the research on interdependent infrastructures. Each o f them has its strengths i n specific study fields. Actually, the system o f the interdependent infrastructures is a mixed system, consisting o f both continuous and discrete subsystems. Considering the emergent scenarios after a disaster, the interdependent infrastructures are very complex and many discrete events are at work on the system, changing the state o f the variables in the model. Moreover, the model has to provide the quantity and scalability o f the nature for the system. A s a result, to study decision making for critical linkage i n infrastructure networks, especially for the physical layer o f the system, the best-suited approach for modeling the system is the cell-channel model. In this thesis, the cell-channel model has been chosen as the approach to model and simulate critical interdependent infrastructures.  1.3. Research Objective  The work presented i n this thesis has been part o f a team effort to develop U B C ' s I2Sim simulator. Specific contributions have been the development o f cell models for the U B C test case, including the complex hospital model. Another contribution has been the development of a test bench based on the M A T L A B / S i m u l i n k software to serve as a prototype o f the OVNI-based I2Sim software. In conjunction with the work b y Siva Singupuram, this prototype has been implemented i n a PC-cluster hardware architecture. The M A T L A B I2Sim  7  prototype has been used as a proof-of-concept for full working demonstrations o f the I2Sim capabilities to represent complex interdependencies scenarios.  Detailed nonlinear input-output models i n the form o f "Human Readable Table" ( H R T ) are developed in this thesis for five types o f cells i n the U B C campus: the electrical substation, the power house, the water station, the steam station, and the U B C hospital. The I2Sim concept was then implemented i n a M A T L A B / S I M U L I N K prototype using the detailed H R T tables developed. The prototype demonstrated the validity o f I2Sim to replicate complex interdependency scenarios. The work also included the development o f a user-friendly interface to allow operators to have a better insight into interdependencies. A soft clock was implemented to show the developed "real-time" simulation at human-friendly speeds for interactive  simulation. In terms o f hardware  the  prototype  was  implemented  and  demonstrated on a PC-cluster simulator developed at U B C ' s Power Systems Lab.  The thesis is organized as follows:  Chapter 1 gives a brief introduction o f the current JIIRP research and research objectives.  In  Chapter 2, the general description o f the interdependent  infrastructure  system is  represented. The modeling approach, which is best suited to accomplish the research objective, is described based on the characteristics o f the critical system components.  Chapter 3 describes the modeling o f each individual component o f the reduced-scale test case model, and then the overall system is described.  Simulation o f a real world scenario is implemented and simulation results are analyzed i n Chapter  4. A  simulation related  to  the  University o f British  Columbia's critical  infrastructures is described. A n interactive, graphical user interface was designed to allow the decision makers to get a better understanding o f the emergent system behavior i n different operational scenarios. One such scenario is studied by using a distributor, which allows an operator to find an optimum allocation o f a limited resource i n order to ensure the best  8  possible operation o f the other critical sectors during the event. The simulation was parallelized and distributed on the U B C Power Systems Lab PC-cluster.  The conclusion is i n Chapter 5, which also includes suggestions for future research.  9  Chapter 2  I2Sim System Description  A system o f interdependent infrastructure sectors is highly nonlinear and complex in nature. While modeling and simulation tools can provide insight into the behavior o f individual infrastructure networks, a far less understood area is that o f the interrelationships between multiple infrastructures. Specially, how does an event i n one infrastructure directly or indirectly affect the operation o f the other infrastructures? In this chapter, the I2Sim interdependent infrastructure system, including its critical components, is explained. I2Sim's critical components, cells, channels, and tokens are described. Finally, the I2Sim method o f discrete event simulation for an interdependent infrastructure system is explained to represent the multiple infrastructure systems behavior i n the time domain.  2.1. I2Sim Overview The research objective o f the JIIRP project in U B C is to study decision making processes i n the context o f critical linkages i n multiple infrastructure networks and develop better strategies to mitigate disaster situations. The present volatile world situation and the rising trends o f natural hazards have raised concerns for the smooth operation o f these critical infrastructures. However, up to this date, only a few computational frameworks have been developed to assist researchers, decision makers and infrastructure service providers to understand the operational characteristics o f these infrastructures during disaster scenarios. Based on this observation, the JIIRP group at U B C has been taken the initiative to develop simulation tools that can be useful for policy makers and infrastructure service providers. I 2 S I M is an effort which is a part o f that initiative.  A number o f modules are designed to support the functionality o f the I2Sim simulator, for example, the database and the visualization modules, to name a few. Integration o f the simulator with the database (I2DB), visualization (I2VIS), damage assessment (I2Dam), and other modules is shown i n the figure 2.1.  10  I2Sim (Infrastructures  Interdependencies Simulator) is a tool to achieve time-domain  simulation of disaster scenarios affecting large scale systems of infrastructures. In particular, it is concerned with the simulation of both the physical layer and the human layer of infrastructures consisting of a large number of functional units. The I2SIM simulator is based on the methodology developed for the simulation of large power systems and implemented in the OVNI (Object Virtual Network Integrator) simulator developed by U B C ' s Power System Laboratory. The components in the I2Sim are identified by their function and at the highest level they are divided into two categories: cells and channels. Mathematically each cell and channel has a unique mapping to a large infrastructure matrix. The solution of this infrastructure matrix is based on the Multi-Area Thevenin Equivalent (MATE) network [22] partitioning technique, which gives the ability to solve a very large infrastructure matrix in a very efficient manner. In order to get the infrastructure matrix, first we need to model the functions of these cells and channels using Human Readable Tables (HRT), and then using a linearization method to convert the HRT table to the matrix. The linearization coefficients are incorporated into the M A T E solution matrix.  scenarios dumps  !2dB  Update Cell/Channel  Node names; pt to Cell Model File;  HUMANA/IS  ! 2 D a m H "2See  C C Cell Model File Hospital  Linearized Cell Model 1 Linearized Cell Model 2 Flows; scripts  pick model  CC Cell Model  C C Channel Model File Roads  Roads Human Readable Table (HRT)  Linearized Chan Model 1  +  Linearized Chan Model 2  l2Thevenin  Linearized Cell Model 3  ~  Detailed Knowledge  CC Chan Model  Hospital Human Readable Table (HRT)  t  f l2Thevenin  -—  Detailed Knowledge  Figure 2.1: Diagram of Infrastructure Interdependencies Simulator [17]  11  The description o f a system o f infrastructures includes at least two layers: the physical layer and the human layer [16]. This thesis concentrates on modeling I2Sim aspects related to the physical layer. M a n y w e l l defined models exist for individual infrastructure's analysis, but they do not tie the infrastructures interdependencies  among  individual  together i n a form representative infrastructures  and  do  not  o f the actual  support  high-level  coordination. The I2Sim cell-channel model approach [16] allows to model the infrastructure interdependencies. Within this context, the critical components i n the cell-channel approach such as cells, channels and tokens have specific meaning and are defined as follows:  Definition 1: A cell is an entity that performs a function. Definition 2: Transportation channels are the means by which tokens flow from a generator node to a load node. Definition 3: Tokens are goods or services that are provided b y one entity to another entity that uses them.  The cell-channel model for interdependent infrastructures mainly represents two parts: one is the performance o f cells and channels themselves, and the other is the interconnecting relationship o f these individual entities.  Figure 2.2 shows how a collection o f infrastructure networks and their tight interconnection mechanisms compose a highly complex nonlinear system. The collection o f cells and channels represents a dynamic and complex structure. The links between the different infrastructures can be clearly described as channels; channels can link two cells i n two different infrastructures or i n the same infrastructure. Figure 2.2 illustrates how a channel links the electrical Substation cell i n a power system to the telephone service cell i n information and telecom system. A l l the critical points i n each infrastructure can be represented by cells and their interconnections by channels. Models o f cells and channels have to be identified and built. The U B C Campus test case w i l l be used i n this thesis [19] to build an I2Sim prototype.  12  Figure 2.2: Infrastructure Interdependencies [7]  2.2. Characteristics of Cells and Channels  In the U B C test case [19], cells are first classified into several types according to their functions. The following 19 general categories are the cells i n the U B C test case: Hospital ^  Fire H a l l Ambulance service  4-  RCMP Classroom and library Research lab and museum Residential Parking lots Recreation and society  ^  Substation Water station  13  Telecom generator Transportation Food A  Commercial  4* Administrator •b Services and utility Power House ^  Steam station.  Figure 2.3: Cell Classification [17]  Gas Network gas_main gas_sec  Electrical Network elec main elec sec  n  135  270  540 Metare  JIIRP" U B C  I2C  campus  case  JIIRP U B C  I2C  campus  case  15  Eight types o f cells and two types o f channels i n the U B C test case are shown i n Figure 2.3 and Figure 2.4. Each o f them has its o w n functionality. It can be seen from Table 2.1 that different types o f cells have different tokens and various channels link the cells to critical infrastructures.  Type of C a l l s  Hospital Fire Hall Ambulance service RCMP Classrooat Research Residence Parking Recreetior. and society Substation Sater station Telecom generators and Hubs Transportation bus stop Food and shups Financial service and C c s s s r c i a l Acaini s i r a t ion Service and u t i l i t y Fewer bowse Steaasiaiien  C r i t i c a l Infrastructures  GO rater l_J>:*»i [2 rater D rater C W Q>sir»s D water (3 rater GDratsr Elsersr 13 rater D rater EI?josr Qrater 0;*»»r Orater Sss*«r 0rater JE3;>t»sr CJrater GDs**tr D rater 13 rater Q?e*er D rater *—% Drater Drater Q water E3 rater  O 5t«8X n  Q«ai  •Ute&x Qitess.  Osas Qs»J  f3.««ax Ostesx O:teex  0»5 • sa;  f""t LJstesx D s-eax Dstea* 0n«» LJ steaa Osseax Qstetx Qrtecu 0 t-.txx  OK:  Osas Oeas Os*s 0*K  Osas Ogas G3s»5  •oil •til Oca DciX Oeil • oil • eil Oosi OcU •cu Ocil Sell Oeil Oeil De-ii • til •oil Pl.il  (Zlcasitcaicatics f*} e«sBssieat«» EccatKaicatics O cssssaieat son CZJ cca3Ktwicat.ES £3 ccatcaicatics D ceasxsicat tea O esasciieatica O cemsnieatita LJccascsieatics (3 ecssuKisati^B O e«msssicaxi«a n uceanaaeattsn S3 c«sosi£«:«5 13 ecxncaicatiea LUesasnicatice OeaasaajicatJsn Seemcsitatiea  Table 2.1: Cells and their L i n k s to Critical Infrastructures  Cells have multiple inputs and outputs. Based on the relationship o f inputs and outputs, the functions can be represented. It can be seen from Figure 2.5 that the outputs o f cell #1 are the inputs o f channel 1 and channel 2, through which tokens flow to cells such as cell #2 and cell #3. Depending on the function o f a cell, the types o f input tokens and output tokens are not always the same. The inputs can be water, gas, or power, and the outputs can be the number of beds i n the hospital or steam flowing out o f the steam station.  16  Figure 2.5: Structure o f the Generic Cell-channel M o d e l A cell can have two other types o f inputs. One is external sources which come from cells outside the selected system, through a channel sending specific types o f tokens into the inside system o f the cell; this is shown as U n in the figure; the other is internal sources, which are the backup reservoirs inside the cell. Both o f them are the inputs to the cell model. Since they own the same type o f token, they are combined together as one input i n the cell model by a "aggregator", which is shown i n Figure 2.5. The variables in the figure follow the rules below: *Y* U : external sources "v* C : internal sources x : input variable o f each cell or output variable o f each channel y : output variable o f each cell or input variable o f each channel subside letters ij • i means i n cell #i • j means j  t h  input or output o f cell #i, the number o f j shows how many types  o f tokens the cell has According to the types o f tokens sent and received through the channel, the types o f channels defined i n the U B C test case are: "Y-  Electricity Water Gas Steam Oil  17  The generic channel model has one input and one output. Each channel has its characteristic function, capacity and time delay. For example, i n the water supply system, the water flowing through the water pipe from the sending end to the receiving end can be represented by using a function within three variables, which are the capacity, functionality and time delay o f the channel.  -Y*  The capacity constrains the maximum amount o f tokens transmitted through the channel.  *v-  The functionality o f the channel represents the state o f the channel, which ranges from values between zero to one according its damage state. •  1 : the channel can carry 100% o f its normal capacity.  •  0.5: the channel can carry 50% o f its normal capacity.  •  0 : the channel is fully damaged and can not carry any token.  The time delay depends on the type q f token and the functionality o f the channel. •  In the normal state, the time for a token to be transmitted from the sending end to the receiving end is the delay factor o f the channel. Usually the delay factor for the channel sending power can be zero, but the delay for transportation cannot be omitted. However, i n this thesis, the delay time is not taken into consideration because it w i l l not affect the performance o f the reduced-scale test case model.  •  After a disaster, the functionality o f a channel or cell drops because o f damage and the time needed for repairs; the repair time is added to the normal time delay o f the channel.  2.3. The Input-Output Model  The relationship between the inputs and the outputs o f the cell, which defines its functionality, is described using the equivalent input-output model developed i n I2Sim. Each cell has its own characteristic and is a non-linear system. The resolution represented b y the input-output model depends on the selection o f the critical components inside the cell.  18  -XJI—*  "Xi2  Cell #i [Input-Output Model]  Figure 2.6: The Input-Output M o d e l for Cells  The performance o f cell #i i n Figure 2.6 is illustrated as a black box. First, based on knowledge and industrial experiments, we can get information that certain amount o f outputs depends on certain amount o f combined inputs. For example, the hospital has seven input tokens—water, power, steam, heating, gas, medicines, doctors and nurses and three output tokens—numbers o f beds for long-term, short-term and urgent patients. The input-output relations indicate the performance o f the medical service capacity i n the hospital. The different amount o f each input token w i l l make a difference i n the outputs o f the hospital. When i n a normal state all o f these input tokens sent into the hospital, the generated tokens for outputs are the hospital's maximum capacity; when one o f these input tokens drops to zero, the outputs drop to zero. These two combined states can be described using the easily readable Table2.2 (defined as the "Human Readable Table" H R T i n I2Sim). Input s water  power x  steam x  i 2  heating x  i 3  Outputs doctors  nurses  medicines  Urgent  100% 100%  100% 100%  100% 100%  Vil 100% 0%  i 4  100%  100%  100%  100%  0%  100%  100%  100%  Table 2.2: Sample Data i n the Human Readable Table for a Hospital C e l l The H R T rows can be used to define  a multivariable piece-wise linear function.  Mathematically, the relationship o f the inputs and outputs o f the hospital represent a set o f nonlinear functions: >n  =  A( n> n>—> m). x  x  x  The rows i n the H R T correspond to particular  values o f these functions. In I2Sim simulator, the behavior o f the functions is assumed to be linear between these points. Figure2.6 illustrates the most basic case o f a single input single output cell.  19  Figure 2.7: Piece-wise Linear Approximation for One Dimensional Function  The critical components inside cells whose functionality can influence the interaction o f the input-output relationship are considered i n the Human Readable Table as internal variables.  -Xji—>  ,/Critical Component 1  -Xj2  Critical  -yn-  Component 3  Cell #i [Input-Output Model] Critical - X im  -yiin  Component 2  Figure 2.8: The Input-Output M o d e l for Cells with Critical Components  The input output model includes critical components as well as inputs tokens. The critical components inside cells have their own functionality which can influence the outputs, even i f the input tokens are maintained at fixed values. For example, i n the Water Station, pumps are critical components; their functionality is the pumping o f water. When the functionality o f the pump drops to zero under some conditions, even i f the input tokens o f power and water are at the maximum amount, the output w i l l be kept at zero. In the Water Station, many types o f equipment support the water supply system; they do not need to be modeled explicitly  20  because only the external interdependency are studied i n the model. In the input-output model o f the Water Station cell the functionality o f the pumps is one o f the internal variables. Small time constants i n the internal cell processes that are not relevant for the external scale o f events are not explicitly represented.  Since the cells are connected to different infrastructures, which mean they receive different types o f input tokens and produce some types o f output tokens, the H R T table w i l l describe the performance o f the cells b y combining quantities o f different physical nature. The inputs o f cells are multiple tokens such as water and power, and the physical amounts are different. For example, i n the hospital cell, the average amount o f power flow is about 1500kW and the average water consumption is about 14.5 m /hr; they are different both i n physical nature and 3  in level o f magnitude. In power system calculations a normalization o f variables called per unit normalization is almost always used [21]. It is especially convenient when transformers and different voltage levels are involved. The idea is to pick base values for quantities such as voltages, currents, impedances, power and so on, and to define quantities i n per unit as follows : quantity in per unit =  actual quantity base value of quantity  Using the per unit method o f power systems for the input-output model for interdependent infrastructures, the cell functions can be described on a percentage level; this is achieved b y using the maximum amount o f each token as the base value o f quantity; the actual quantity o f tokens under any situation is represented as per unit value ranging from 0 to 1. In table 2.2 the quantity o f input and output tokens has been calculated b y using the per unit method. In the case o f multiple cells with different physical units capacity, a common base needs to be chosen for the global system and the individual cell functions need to be scaled according to their rated capacity as compared to the global system base capacity.  2.4. Discrete Event Simulation  Based on the H R T input-output model for the cells, the interdependent infrastructures can be described as a discrete event-driven system. A discrete event system ( D E S ) is a dynamic  21  system with discrete time and event-driven characteristics, which are asynchronous and possibly nondeterministic. In physical systems, events correspond to the actions that can change the state o f the system, that is, they can trigger a transition between states. This form o f description is usually based on the internal observation o f the system dynamics. Alternatively, a discrete event system can be described by logical predicates over a set o f state variables. In this case, an event corresponds to the change i n one or more state variables and, consequently, results i n a transition from one state to another. A discrete event system can also be described externally through its observed behavior. This is represented formally by the set o f all event sequences that generate state transitions over time.  Event: Damage  ......  Event:  Decision_2 I  Figure 2.9: Events in the Cell-Channel M o d e l  Figure 2.8 shows three types o f events in the interdependent infrastructure system. These events are: •  Uncontrollable event: When a natural disaster or an operation failure occurs, the damage o f the system can be described as the event to each cell and channel which change the internal state variables such as functionality o f the cell or capacity o f the channel. When a nondeterministic uncontrollable event strikes the system, the damage to a critical component—to cells or channels w i l l depend on the type o f disasters and the time when the disaster takes place.  22  •  Time-dependent event: The event happens at a given cell at a certain time when a given cell is i n a specific state. The event w i l l  affect  both itself and through  the  interdependencies, the cells connected to it (Figure 2.9 cell #1). A s an example, the power house has o i l storage; when there is a power outage, the backup generator w i l l begin to work and the stored o i l w i l l be consumed b y the backup generator. H o w long the backup generator w i l l work depends on when the storage-oil w i l l be used up, and the oil run-out time is one o f the critical factors o f this event. After a certain time phrase, the event, "out o f backup o i l , " is triggered. It w i l l change the functionality o f the power house cell and the outcome w i l l affect cells linked to the power house. •  Decision-making event: This event is caused b y a human being and is a stochastic event; it happens when people make decisions. After a natural disaster, many restoration procedures are i n operation. Because o f limitation i n resources and repair crews, the restoration procedures follow a sequence o f priorities. According to the decisions and the sequence o f the procedures, events happening stochastically lead to different outcomes. For example, i n Figure 2.9, it can be seen that parts o f the cells and channels i n the model need to be repaired and the decision makers make the decisions i n a certain order. The action 'repair #1 channel first' is taken and the functionality o f #1 channel is restored to its fully operational state 1 after it has been fixed; this affects cell #2 which is connected with this channel and then other entities linked to cell #2. Next, the decision to "repair cell #3" is made and the repair crew is sent to fix it; then the decision is to fix the critical component i n cell #1. Each o f the decisions affects the performance o f the whole system.  The  interdependent infrastructure system is composed o f a set o f interaction cells and  channels. The interaction can be described by the change i n the quantity o f tokens sent or received by the cells or by the change i n the linkage state o f channels. The interaction schema o f the system components is usually specified i n one form or another and given as a part o f the system description. In general, the existence o f certain interactions between the cells means that the behavior o f each cell i n the system depends not only on its internal structure but also on the behavior o f the other cells or channels. For example, when the channel o f power, which is the transmission line sending power from the Substation cell to  23  the hospital cell, is damaged, the hospital cell w i l l change its functionality because o f this event (channel broken).  Furthermore, the interaction between the cells and channels also means that the set o f events at any time i n a given cell depends not only on the current state o f these cells and channels, but also on the current states o f the other components. For instance, i f the power house is out o f power; then the backup generator begins to work so that the power sent to the steam station w i l l have no change; consequently, the hospital cell w i l l receive steam from the steam station cell as usual. When the o i l for the backup generator runs out, the power w i l l drop to zero; at that moment, the event o f being out o f power w i l l be sent to the hospital cell and influence its functionality. The current state o f the hospital cell depends on the current state of the power house cell. This is a time-dependent event for it depends on how much o i l the backup generator w i l l use before it runs out and i n turn influences the hospital cell.  In general, the research o f infrastructure interdependencies is circumscribed to some degree because it cannot check the state o f the whole system and analyze the damage assessment and restoration process because the data records o f most real disasters are not complete. Although there are some damage analysis reports for natural disasters such as the disaster caused by Hurricane Katrina i n 2005 and the Asian Tsunami caused b y an earthquake in the Indian Ocean i n 2004, the information is not sufficient for the research. A s a tool, simulation has the capability to describe the different types o f disaster scenario and use the information in the damage reports for comparison. Simulation can also test different sets o f decisions for the same disaster scenario to find the optimal solution for restoration without wasting time and money; finally it can help to develop a strategy that can increase the resiliency o f the critical infrastructures.  24  Chapter 3  The Generic Cell-Channel Model  In this chapter, a reduced scale test case model is built, using the cell-channel model; the test case model represents an interdependent infrastructure system. The model includes the most critical infrastructures i n the U B C campus case and their interrelationship; it consists o f five cells—the Hospital, Power House, Water Station, Steam Station and Substation. These cells are built based on the input-output relationships discussed with and validated by the personnel o f the concerned infrastructures; the interconnections between these cells are modeled as channels. These cells are also modeled with the interaction to accommodate various sizes and capacities. Finally, the whole reduced scale test case model which includes cells and channels is summarized.  3.1. General Description Although there have been many research studies on interdependent infrastructure systems over the last few decades, no benchmark model has been developed for multiple infrastructure interdependencies. It is important to test, verify and evaluate these models before implementing them i n a disaster scenario. The U B C test case shown i n Figure 3.1 is the first test case to evaluate the proposed modeling approach discussed i n Chapter 2. The University o f British Columbia has been chosen as the test case because it has the attributes o f a small city and has infrastructures that represent an actual interdependent system containing enough interconnections for research on multiple infrastructure interdependencies. It can be the first step for investigating the interconnections between multiple networks.  The critical entities i n the campus test case include five cells—the hospital, power house, water station, steam station and Substation; three external sources, which are defined as ideal external cells which send tokens from outside the campus. In this test case, only selected infrastructures are considered; they are electricity, water, gas, o i l and steam. Five types o f  25  channels are defined i n the model. Each critical cell is located i n the U B C campus in one or several buildings as shown i n Figure 3.1.  The U B C electrical Substation is the connection link between the B C Hydro transmission network and the U B C campus power network. The electricity is transmitted from B C Hydro to U B C v i a two 6 0 k V A C high voltage overhead lines.  Figure 3.1: GIS-Mapping o f the U B C ' s Test Case [20]  The U B C Hospital is one o f two acute care facilities that are part o f the Vancouver General Hospital and the Health Sciences Centre. It is located in the U B C campus [23]. The U B C Hospital is composed o f three buildings—Detwiller Pavilion (Short-Term, Psychiatry), Koerner Pavilion (Acute Care, shown i n Figure 3.1) and Purdy Pavilion (Long-Term Care). In the Koerner Pavilion there is an urgent-care centre which offers specialized treatment for non-life threatening emergencies b y emergency-trained physicians and nurses [24].  In the case o f the U B C campus, water and heating are two critical infrastructures  for  supporting the normal functioning o f the campus' life. For the U B C water supply system, the water resource comes from the reservoir located outside the campus i n the Pacific Spirit Park. There is a water pumping station i n the water supply system which is located in the U B C Power House. O n the model, its functionality is defined as a " Water Station" cell.  26  The steam supply system provides heating to parts o f the campus where there are critical facilities such as the U B C hospital. The steam system contains one steam generator located in the U B C Power House. Although it is located in the same building as the water station, based on its functionality, it is defined as the "Steam Station" cell. The steam flows into buildings and then back to the Steam Station through a steam network i n a closed loop.  The external cells send electric power from B C hydro, water from Pacific Spirit Water Reservoir and gas from Terasen Gas to the U B C campus. The Pacific Spirit Water Reservoir supplies water to the Water Station, then the Water Station supplies water to the U B C Hospital. There are two transmission lines between B C Hydro and the Substation. The Substation supplies electricity to the Power House and the Hospital, and the Power House supplies electricity to the Water Station and Steam Station. The external resource Terasen Gas provides gas to the Hospital and Steam Station.  The interconnections between these cells are illustrated as follows: -Y*  ^  Electric power •  Power sent from B C Hydro to the Substation  •  Power sent from the Substation to the Hospital and Power House  •  Power sent from the Power House to the Water Station and the Steam Station  Water •  External water sent from outside to the Water Station  •  External water sent from the outside to the Steam Station  •  Water sent from the Water Station to the Hospital  Steam • 4-  Steam sent from the Steam Station to the Hospital  Gas •  External gas sent to the Steam Station  •  External gas sent to the Hospital  -> O i l •  O i l sent from the Power House to the Water Station  •  O i l sent from the Power House to the Steam Station  27  Data Collection Ken- Cells and Chanm-U  Damage \sscssinenl ( Larthquakc)  Cell & Channel Model  Figure 3.2: Data F l o w for the Cell-Channel M o d e l  A key to modeling is the availability o f credible and traceable data. Gathering information on a particular cell is a significant challenge when developing the model's structure. A l l the data used in this thesis comes from U B C Utilities and the U B C Hospital.  Actually only the owner o f the cell has the detailed knowledge o f the internal detailel structure and relationship for the entity. The model tries to capture the input-output relationship among the critical interdependencies with other sectors. The Human Readable table is exactly filled i n by the cell owner. In the case o f the reduced scale test case shown i n the thesis, we did it because it is the new approach for modeling the system and also we built it with the owners o f U B C facilities.  Another data source for the model is the functionality o f the system components.  The  functionality o f a building after an earthquake w i l l affect the performance o f the cells located in these buildings. The structural damage can be divided into four levels; each o f them has functionality data which are used for developing the model.  I f there is no damage to the  building, the functionality o f the cell is at 100% functionality; when the building gets slightly damage, the functionality is at about 80%, moderately damage at 50%, and severely damage at 0% [32]. These data can change depending on the type o f disaster.  28  In this thesis, the external sources are considered ideal sources; the external source is always in normal state without any damage. In this chapter, both the data collection and the models of the critical cells w i l l be described.  3.2. The Substation Model 3.2.1. Inputs and Outputs of the Substation Cell A s mentioned i n section 3.1, the U B C Substation gets power through two transmission lines from B C Hydro and it i n turn supplies power to the U B C campus. It primarily includes two matching transformers which have 4 7 . 6 M V A maximum capacity, two tiebreakers, buses and feeders. The basic functions o f the Substation are illustrated i n Figure 3.3.  Main Sub-station H-FH- —*• To Hospital  r  Linel From B C Hydro  S-H Transformer 1  Stand by for Hospital  ":rrr- O" Q) CD  T3 12-F22-  Line2 From B C Hydro  12-STransformer!;:  To Power House ^_ Stand by for Power House  Figure 3.3: Diagram o f the Basic Functions o f the U B C Substation  The consumption o f electricity at the campus sub-station is about 200 G W - h r over a period of one year; this means an average power flow o f 0.0228Gw for the whole campus. There are 16 high voltage "distribution" feeders i n two buses, which leave the main substation to other buildings. These bus feeders, known as the main substation common buses, are normally connected i n parallel with a normally closed tiebreaker, which is tiebreaker2 i n Figure 3.3. There is some redundancy built into the Substation. For example, tiebreaker2 is linked to busl and bus2; i f one o f the external transmission lines is broken or i f one o f the transformers does not work, the campus w i l l keep running. Each building on campus has two transmission  29  lines linking the building with the Substation. One o f the lines sends power to the building; the other is the standby line. When the working line is damaged, the standby line w i l l switch to " o n " state, and keeps sending power to the building. Figure 3.3 shows how power is sent through feeder 12-F11 to the hospital, and the other transmission line is linked with feeder SH , which is the standby line for the hospital.  If damage occurs i n the Substation, it has to be repaired or switched off manually. The length o f the operation time for repairs is the time delay represented i n the model.  Based on the data and information collected from experts working at U B C Utilities, a diagram o f the cell model for the Substation has been developed and shown i n Figure 3.4.  External Source B C Hydrol  T  External Source B C rlyc Hydro2 Up  •  t,-  * Substation Cell [Internal VariablesJ  ,  ->'ir  Channel 6 to Hospital Channel 1 to Powerhouse  Figure 3.4: Diagram o f the Substation C e l l M o d e l  It can be seen that there are two inputs and two outputs i n the model. The inputs come from the external power sources, which are set as external cells, and the outputs send power to the cells such as the hospital and the power house through channel 1 and channel 6. In reality, the Substation sends power to all the buildings on the U B C campus; i n this model, only two cells, the Hospital and the Power House, are considered.  30  3.2.2. The Generic Model of the Substation Cell The Substation cell uses one type o f input token, "electricity," to produce the output token, which is the same as the input token "electricity." The Human Readable Table ( H R T ) o f the Substation includes two inputs, two outputs, and internal variables such as the state o f the transformers T] and T2, the state o f tiebreakers B K i and BK2, and the state o f the feeders to the Hospital and the Power House. Figure 3.4 shows how the state o f the critical components w i l l affect the outcome o f the cell. The function between the inputs and outputs can be described as a nonlinear function,  [y^y ] n  = fPn^ J ,T BK BK K K ) n  x  2t  lt  2i  lt  2  (3-1)  Where: Ui 1 is the external source 1 from B C hydro U12 is the external source 2 from B C hydro "v*  Ti is the state o f transformer 1, T j = l normal state; Ti=0 damage state T2 is the state o f transformer 2, T2=l normal state; T2=0 damage state  -Y-  -v*  B K i is the state o f tiebreaker 1: •  BKi=0 normal state: Open  •  B K i = l other state  BK2 is the state o f tiebreaker 2: •  BK2=1 normal state: Closed  •  B K = 0 other state 2  K i is the state o f the feeder to the Hospital:  -Y*  •  K i = l normal state  •  Ki=0 damage state  K2 is the state o f the feeder to the Power House: •  K2=l normal state  •  K2=0 damage state  In equation (3-1), the Substation model is shown as a nonlinear function with eight variables; each o f them with its own characteristics. The external sources U n and U12 are ideal sources  31  from an outside system, the channels connecting them to the Substation can have their functionality influenced b y damage; the other internal variables such as the state o f the transformers are "on-off' state variables.  HRT Table for Substation 100% 100% 100% 100%  U,2 Tl 100% 1 100% 1 100% 0 100% 1  T2 BKI 0 1 1 0 1 0 0 0 - —  BK2 kl 1 1 0 1 1 1 1 1  Status k2 1 1 1 1 -  - - <"—  yu 100% 100% 100% 100%  yn 100% 100% 100% 100%  • Normal state - TieBreaker doesnot work - Transformerl does not work - Transformer! does not work  ••-»••»  Feeder2 does not work TieBreaker2 & Feeder2 doesnot work Transformerl & Feeder2 does not work Transformed & Feeder 2 does not work  ^100% 100% 100% 100%  100% 100% 100% 100%  1 1 0 1  1 1 1 0  0 0 0 0  1 0 1 1  1 1 1 i  0 0 0 0  100% 100% 100% 100%  0% 0% 0% 0%  :100% 100% 100% 100%  100% 1 100% 1 100% 0 100% 1  1 1 1 0  0 0 0 0  1 0 1 1  0 0 0 0  1 1 1 1  0% 0% 0% 0%  100% 100% 100% 100%  1 1 1 1  When functionality of channel linking with External Sources change., +• Normal state with changed sources 1 50% 100% *- TieBreaker doesnot work 1 50% 100% Transformer! does not work 1 50% 100% • Transformed does not work 1 50% 100%  : : : :  50% 50% 50% 50%  100% 100% 100% 1001  1 1 0 1  1 1 1 0  0 0 0 0  1 0 1 1  I * I * I * I * | * I o% I 0% h  -*- Feeder! does not work TieBreaker2 & Feeder! doesnot work Transformerl & Feeder! does not work Transformer! & Feeder 2 does not work  JFunctionality of channel linking with External Sources drops to zero  Table 3.1: Status Mapping for the Human Readable Table for the Substation Cell In Table 3.1, some statuses are listed according to the different states i n the Substation. If a natural hazard such as an intensity 9 earthquake strikes the U B C campus, the Substation w i l l be damaged. The damage is represented by the different status o f internal variables i n equation (3-1); b y checking the H R T table, the outputs o f the Substation can be calculated.  32  3.3. The Power House Model 3.3.1. Inputs and Outputs for the Power House Cell A s described i n section 3.1, the Power House gets power from the Substation and it i n turn supplies power to the Water Station and the Steam Station. It primarily includes one transformer, one diesel backup generator, and storage for o i l . The basic functions o f the Power House are illustrated i n Figure 3.5.  Power House —External powen  -External Oil-  -Power to WaterStation-  Transformer  External Oil Oil_restorage (3days)  -Power_to_SteamStation Backup Generator for Steam station  -Backup_Power_to_SteamStation-»-  -Oil to WaterStation-Oil to SteamStation-  Figure 3.5: Diagram o f the Basic Functions o f U B C ' s Power House A s indicated Figure 3.5 shows that the Power House gets power from the Substation and through its transformer sends power to the Water Station and the Steam Station. The daily electricity consumption is 3360 kW-hr. The average power flow into the Power House is 140kW. There is a backup generator, which works automatically when the external power drops to zero. The power generated by the backup generator only sends power to the Steam Station. Similarly, there is storage for o i l inside the Power House; it provides o i l not only to the Power House but also to the Water Station and to the Steam Station. The total amount o f oil can last three days, depending on the disaster scenario.  In reality, the cells o f the Power House, Water Station and Steam Station are i n the same building and any damage to a building w i l l affect all o f these three cells. For example, i n the Steam Station, the boilers use gas to generate steam; i f the gas pipe leaks or is damaged because o f some disaster, the whole building w i l l shut down immediately to prevent an  33  explosion. If an earthquake occurs and the building gets damaged, the effect o f the overall structural damage w i l l be the same for the three cells. This is because the performance o f the Power House cell is defined by its inputs and its critical components, and these are tightly connected with the states o f the other cells in the same location.  Based on the data and information collected from experienced engineers working in the U B C Power House [26] [27], a diagram o f the cell model for the Power House has been developed and shown in Figure 3.6.  Token: Electricity  i—•DUM!n>fti>\CTTOCTTtiTnM  >:i  M B — M rem substation  Token: Oil  -x r  latmcl to Water station  2  Token: Electricity  Power House Cell External Source  Oil  {Internal Varaibles]  Token: Oil  -Ur  4--  anntl to steam Station  Token: Oil  y-)7  —NraBBMfflKfflfflBBWMi  1  Token: Electricity  Figure 3.6: Diagram o f the Power House C e l l M o d e l  Figure 3.6 shows the Power House cell model and its relation with the linking channels. It has two inputs or two types o f tokens coming into the cell. One input comes from the Substation cell, and the other comes from an external o i l source. The external o i l source is oil sent to the U B C Power House through a transportation channel when the o i l i n the o i l tank in the Power House runs out. This model is set as an ideal source from an outside system. Two of the outputs send power to the Water Station and Steam Station cells through channel 2 and channel 3; the other two outputs send o i l to these same cells.  34  3.3.2. Generic Model of the Power House Cell The Power House cell includes two types o f tokens. Based on the number o f inputs and outputs and the relation between them, the input-output model for the Power House cell can be represented b y two parts: one represents the electricity token, the other represents the o i l token.  -fr Oil The o i l token comes from the external source U22 and the backup o i l C22. In this thesis, both U22 and C22 are time-dependent  variables [27]; the outputs are the states o f the o i l  consumption and y23 and y23 described as functions o f U22 and C22-  The function o f the o i l states is a time-dependent nonlinear function. [^23.^24] = / ( ^ 2 2 » C '  2 2  ,X  2 1  (3-2)  )  State of Using Oil  T  ».  0 0  A  Power from Substation diops to 0  Power from Subst; tion restoration Or Oil Storage runs out  Time  Figure 3.7: Function o f O i l i n the Power House C e l l  O i l is supplied to the backup generator when power i n the Substation drops to zero. Figure 3.7 illustrates how the state o f o i l consumption depends on the event "power in Substation drops to zero"; the time o f the o i l consumption x depends on the event "power in Substation restored" and the amount o f o i l in the o i l storage.  35 -Y* Power Figure 3.6 shows that the cell function includes five factors: the input power, and internal variables such as the states o f the transformer, backup generator, o i l , and gas. The internal variables and the input power can change their states and performance because o f damage during or after a disaster, and these changes i n turn cause a change i n the output. Thus, the relationship o f the inputs and the outputs can be described by the nonlinear function,  [JW22] = A^T^BK^K^Kj  (3-3)  Where: x i : the input o f power from the Substation to the Power House cell 2  y 2 i : the output o f power sent to the Water Station y22: the output o f power sent to the Steam Station T i : the state o f the transformer B K the state o f the backup generator :  Koii: the state o f oil K  g a s  : the state o f gas  HRT Table for PowerHouse  Status  BK,  X21  1  0  *  1  1001  100%  Normal State  1  0  *  1  50%  50%  Input Power drops to 50%  ; 0%/*  */0  1  1  1  0%  100%  0%(*)  *(0)  0  1  1  0%  0%  0%(*>  *(0)  1  0  1  0%  0%  0  0%  0%  : 1008 50%  ;  •  —  *  *  Input power drops to 0, Backup generator works Input power drops to 0, Backup generator gets damaged Input power drops to 0, Oil storage runs out Gas leaking, PowerHouse shut down  Table 3.2: Status Mapping for the Human Readable Table for the Power House Cell Table 3.2 shows the changes o f the Power House cell under a normal state and after a disaster. The first row o f figures shows the outputs o f the cell i n a normal state. When the state o f the internal variables or the functionality o f channels change, the outputs change simultaneously. In the case o f the situation indicated i n the third row, the input power drops  36  to 0; this result can come about when the connected channel is damaged or the power sent from the Substation drops to zero. A t this point, the backup generator starts to work and sends power to the Steam Station. For a given state o f the disaster scenario, the outputs can be calculated using the Human Readable Table at Table 3.2.  3.4. The Water Station Model 3.4.1. Inputs and Outputs for the Water Station Cell The Water Station is a critical cell i n the U B C campus model; it provides water to the whole campus. It is set to provide water to the hospital cell i n the simplified model. The cell primarily includes three booster pumps, two o f them are working and one is the hot standby. The operating pumps are rotated once a month. The Water Station also has two backup diesel pumps, one o f them is working and the other is the standby, to be used i f there is no electricity from the Power House. A l l these pumps mainly add pressure from 60psi to 90psi into the water; the pressure allows the water reach to the top o f the high-rises on campus. The water comes through water pipes into the Water Station from the Sassamat water reservoir.  The basic functions o f the Water Station are illustrated i n Figure 3.8.  Water Station  -From Power House-H -From External Wateri -From Power House-H  Power  •  Booster Pumps 2work1 backup  -Water to Hospital-  Water  Fuel  Backup Pumps 1work1 backup  Figure 3.8: Diagram o f the Basic Functions o f U B C ' s Water Station  The daily electricity consumption is 960 kW-hr. The average power flow to the Water Station is about 40kW. The average daily water pumped by the booster pumps is about 9000  37  cubic meter per day, which is 375 cubic meters per hour. The backup pump can pump the same amount o f water [26] [27].  Based on the data and information collected from experienced engineers working in the U B C Power House, a diagram o f the cell model for the Water Station has been generated and shown in Figure 3.9.  Figure 3.9: Diagram o f the Water Station C e l l M o d e l  Figure 3.9 shows the input-output relationship o f the Water Station cell and its links with other cells through channels. Three types o f input tokens are sent into the Water Stationelectricity, water and o i l . O f the three inputs, two are from the Power House cell, and the third one is from an external source. O f these three inputs, the most critical input is water. In the Water Station, electricity and o i l are used to keep the pumps running; i f there is no power for the pumps, the backup o i l and diesel pumps w i l l be used to keep the Water Station working. However, i f there is no water, the whole water station w i l l shut down. The output token is water. In this model, the output is sent through one channel to the U B C hospital.  3.4.2.  Generic M o d e l of the W a t e r Station C e l l  The input-output model o f the Water Station cell can be represented by three inputs, one output and internal variables. Figure 3.8 and Figure 3.9 illustrate how the internal variables o f the Water Station are the state o f the three booster pumps and two diesel pumps. The function relating the inputs and output can be described as follows:  38  >31  _  f{ 31' X  ^32 > 33> kpump »  ' ^ga? )  X  0"4)  where: •  X31 : the input o f power from the Power House cell  •  U32 : the input o f water from the external source  •  X 3 3 : the input o f o i l from the Power House cell  •  kpump  •  •  : the state o f the booster pumps  •  1 : two booster pumps working  •  0.5 : one booster pump working  •  0 : idle or damage state  kbk : the state o f the backup diesel pumps •  1: working state  •  0 : idle or damage state  k  g a s  : the state o f gas  •  1 : normal state  •  0 : leaking  Status  H R T Table for Water Station  :  Output  Internal Variables  Input 100%  Us* 100%  *  1  *  1  100%  50%  100%  *  1  *  1  50%  Input Power drops to 5 0 %  100%  50%  *  i  0.5  *  25%  Input Water drops to One booster pump working  0%  100%  1  1  1  *  0%  50%  1  1  1  *  0%  *  |  *  1  *  1  1  1  i  1  1  1  1 100%  1  I  1  1 50%  *  1  0  1  0%  Normal state  Input Power drops to 0, Diesel pump works Input Power drops to 0, Input water drops to 5 0 % Diesel pump works Gas leaking, Water station shut down  Table 3.3: Status Mapping for the Human Readable Table for the Water Station It can be seen i n Table 3.3 that when the inputs o f the cell are i n a normal state (100%), and the internal variables are i n a working state, the output o f the cell is 100%. During or after a disaster, the damage causes the state to change. In the second row o f Table 3.3, the input  39  power drops to 50% because the connecting channel or cell providing power to the Water Station has lost its function. Although the two booster pumps are operational, the decrease i n power supply makes it impossible for them to work at the previous state; as a result, less water flows to the hospital. The last row i n Table 3.3 indicates that a leakage o f gas w i l l shut down the Water Station regardless o f the states o f the internal variables or the amount o f the inputs.  3.5. Steam Station Model 3.5.1. Inputs and Outputs for the Steam Station Cell The Steam Station is another critical cell i n the U B C campus model. It provides steam heating to the buildings i n the campus. In this model, the station only provides steam to the Hospital cell. This cell primarily includes boilers, water pumps, air fan, water conditioning equipment and deaerator.  The basic function o f the Steam Station is illustrated i n Figure 3.10.  r -Power from PowerHouse—•  Steam Station Water pump for steam  Power  s  —Water from External Source-H•  Water  oil  Oil from Power House— Gas from External Source-H *  -Returned Steam-  Returned"  Water Conditioning |—| Equipment Oil-  Boilers  -Steam-  -Gas iL Deaerator  Air Fan  Figure 3.10: Diagram o f the Basic Function o f U B C ' s Steam Station  The steam system is a closed loop circuit and the steam loss i n the loop is about 30% o f the total steam water when it flows back to the Steam Station. Both the returned steam water and the raw water combined are sent into the deaerator equipment to reduce its oxygen content and then sent into the boilers. The boilers generate steam by burning gas or oil.  40  The daily electricity consumption is 2400 kW-hr. The average power flow o f the Steam Station is about lOOkW. The average daily water pumped into to boilers is about 880 klbs, which is equal to 400,000 K g , or approximately 400 cubic meter per day and 16.7 cubic meters per hour. The returned steam, that is the condensed water, is about 70% o f the total water in the boiler. In this thesis, because only the hospital is considered as the building consuming the steam, the returned steam for the whole campus is set as the ideal source in the system. The external water sent into the Steam Station makes up for the 30% water loss through the steam supply system. The average daily total steam is about 2755.38 klbs per day, which is about 115 K l b s per hour. The average daily gas consumption is about 3834.36 G J , which is about 160 G J per hour.  Based on the data and information collected from U B C Utilities, a diagram o f the cell model for the Steam Station has been generated and is shown in Figure 3.11. •raDmnonmunmBi  x  4 ]  1  Figure 3.11: Diagram o f the Steam Station C e l l M o d e l  Figure 3.11 shows the input-output relationship o f the Steam Station cell and its links to channels connected to other cells. There are five types o f input tokens sent into the Steam Station—electricity, water, gas, returned steam and oil. O f the five inputs, electricity and o i l are from the Power House cell, water and gas are from external source cells, and the returned steam is from buildings in the U B C campus. O f these five inputs, the most critical input is water. Without water, no steam can be generated i n the Steam Station. The second critical input is gas, which is used to heat the boilers that generate the steam. If there is no gas, the  '41  boilers can use oil. The output token is steam only. In this model, the output is linked to one channel which sends it to the U B C hospital.  The diagram illustrates that the internal variables are also critical because they affect the output o f the Steam Station. For example, i f the deaerator is damaged, it can be very dangerous because it is on top o f the power house building and the water inside the deaerator has a high temperature and high pressure. If the deaerator is damaged, the whole power house building w i l l stop working. The same situation w i l l happen when the  water  conditioning equipment and air fan are damaged.  3.5.2. Generic Model of the Steam Station Cell The input-output model o f the Steam Station can be represented b y five inputs, one output and internal variables. Figure 3.10 and Figure 3.11 show that the internal variables o f the Steam Station are the states o f the pumps, air fan, deaerator, water conditioning equipment and boilers. The function relating the inputs and output can be described as follows:  ^41  =  f \ 4 \ ' ^42 ' 43 ' ^44' ^ pump »^boiler ' ^ gas »^ fan »^cond'j X  X  Where: -Y*  X41 : the input o f power from the Power House cell U42: the input o f water from the external source  *v-  X 4 3 : the input o f oil from the Power House cell U44 : the input o f gas from the external source kp  u m  p:  the state of pumps  •  1: working state  •  0: idle or damaged state  "v*  kboiier:  the state of the boilers  •  1: working state  •  0: idle or damaged state  "v*  k •  g a s  : the state o f gas  1: working state  (3"5)  42  •  0:leaking kf  a n  : the state of the air fan  •  1: working state  •  0: damaged state kcond: the state o f the water conditioning equipment  •  1: working state  •  0: damaged state ka : the state o f the deaerator  •  1: working state  •  0: damaged state  HRT Table for Steam Station Inputs  Status  Internal tfaraibles kb  100*  a* 100%  1  kp 1  100%  100%  10W  100%  100%  100%  0  lm  100%  100%  100%  1  100%  100%  100%  100%  100%  100%  100%  100%  100*  100%  100%  m  m  *  I *  Output Steam  l  k< 1  kr»i> 1  1  t  1  1  0%  Boilers damaged  0  l  1  1  0%  pumps damaged  1  0  1  1  0%  1  1  1  0  1  0%  100%  I  1  1  1  0  0%  100%  80%  1  1  1  1  1  60%  0 %  *  1  1  1  1  1  100%  [  0%  —»•  Normal State  Water_conditioning eqipment damaged -*•  Deaerator damaged  —»•  Air Fan Damaged Different state of water, power and returned steam  —»»  Gas Leaking  Table 3.4: Status Mapping for the Human Readable Table for the Steam Station It can be seen from Table 3.4 that when the inputs o f the cell and the internal variables are i n a normal state, the output o f the cell is at 100%. During or after a disaster, the damage can be broken pipes, power outage or breakdown o f critical components inside the building; these types o f damage states are also shown in the figure. When the water pump is damaged ( 3  rd  row in the table) or the power sent to the Steam Station drops to 80 % (7 row i n the table), th  the steam sent out w i l l decrease to a certain level, depending on the internal states. I f the air fan does not work ( 6 row i n the table), it w i l l affect the whole steam system because the th  boilers w i l l shut down and no steam can be generated. The amount o f generated steam from  43  the Steam Station depends on the variables and inputs and their relationship, as shown i n the table.  3.6.  Hospital Model  3.6.1. Inputs and Outputs for the Hospital Cell Hospitals are one o f the critical cells in the health care system, which is one o f the critical infrastructures described i n Chapter 1. It provides medical service to people living i n nearby communities and plays an important role i n people's health. The purpose o f building the hospital model is to estimate the hospital's capacity under different states and these are shown as follows: -Y*  While in a normal state, critical support infrastructures can get disturbed, for example, by a power outage for a short period. Both the critical support infrastructures and backup systems are struck during a disaster.  The U B C Hospital is a site o f the Vancouver Coastal Health and provides a variety o f medical and surgical services including short-stay surgery, sub-acute medical and diagnostic services, surgical and medical clinics, etc [30]. A n analysis o f the information and data from the U B C Hospital shows three main factors that allow the hospital to perform medical services to meet the needs o f patients. In the more realistic simulation, hospital need to consider the patients flow, i n this work this factor is neglected and only the capacity o f the hospital is considered. These factors are the critical support infrastructures, medical service staff and the capacity o f the medical service.  Critical support infrastructures: 1)  Electricity Power  2)  Water  3)  Steam  4)  Oil  5)  Gas  44  M e d i c a l service staff:  $  1)  Doctors  2)  Medicine  3)  Nurses  Capacity of the medical service 1)  Number of beds for long-term patients  2)  Number of beds for short-term patients  3)  Number of beds for urgent patients  Sn>2c 01 c5 >o Iii  Long term patients  -Long-term Beds-  Short term Patients  -Short-term Beds-  Emergency Patients  -Urgent Beds-  From Steamstatton Backup Heater  -Electrical—*\  Power From Substation Backup generator Fuel Reservoir  -Oil-  1-3days  Working Stuff (doctors & nurses)  —Medcines-  Storage 13days service Water Reservoir 1-3days  -Water  -Gas-  ExternalWater Water B a c k u p Boilers (3)  Steralization  E  UJ  Figure 3.12: Diagram o f the Basic Functions o f the U B C Hospital  It can be seen i n Figure 3.12 that the critical support infrastructures and medical service staff are the inputs o f the hospital model; any change in the quality and quantity of these factors  45  w i l l change the capacity o f the medical service i n the hospital, that is, the output o f the hospital model.  The hospital data from the U B C hospital is as follows [25][28]:  "Y*  The consumption of critical support infrastructures: •  Water: 4.5 M cubic feet o f water per year, that is 14.5 cubic meter per hour  •  Gas : 29,000 G J per year, which is about 3.3 G J per hour  •  Electricity : 12.4 G W - h r per year, that is 1416.7 k W  •  Steam : 1375 pounds per hour  Medical service staff and medicines •  •  Doctors: •  daytime: 25  •  after-hours: 10  •  after 10pm :1  Nurses •  daytime: 70  •  after-hours :25  •  Nearly 60% o f doctors and nurses live off campus  •  The medicines supply i n the hospital storage can last for 1-3 days  Numbers of beds •  Number o f beds for urgent patients = 20;  •  Number o f beds for short-term patients = 311;  •  Number o f beds for long-term patients = 300;  Compared with the data i n [29], which cites that the total monthly energy intensity is about 3301 Kw-hr/beds i n large hospitals i n Brazil, the total monthly energy intensity i n the U B C hospital is about 3238 Kw-hr/beds.  46  It can be seen from Figure 3.12 that the critical support infrastructures o f the hospital have backup systems. The backup for each o f the critical resources is listed i n Table 3.5. The backup resources are very critical and perform the functions o f the support infrastructures during an emergency or when the supply system is not working.  Type  :  Electricity  Supply s y s t e m ^ ^ Through  electric  channel  Backup from  the  Backup generators: l-3days  Substation Water  Through water channel from the  Water  Water reservoir: l-3days  Station Gas  Boilers using gas from gas channel  Boilers using o i l : l-3days  Steam  Through steam channel from steam station  Electric heaters  Table 3.5: Redundancy o f the Critical Infrastructures for the U B C Hospital  3.6.2. Interdependent Performance of the Hospital Cell Although each critical support infrastructure i n the hospital has its own backup system, the state o f the hospital's operation, which can range from normal operation to various levels o f disruption or restoration, must be considered i n interdependencies analysis. Furthermore, it is necessary to understand those changes i n the supply systems and i n the states o f the backup systems that cause changes i n the hospital interdependencies. For example, the power supply has no interconnection with other infrastructures in the hospital. When the power supply is disturbed, the backup generator starts to work with no delay by using oil. However, i f there is no o i l i n the hospital at that point i n time, the backup power supply system w i l l not perform any function for the hospital.  Table 3.6 shows that the supply systems inside the hospital are not directly interdependent; for example, the power supply cannot affect the water supply system. The steam system is the only system used for the sterilization o f surgical equipment, which is tightly dependent on water and gas.  47  Normal  Afftc t eil 1 II Iras t ru c 111 res  Type  power  power  V  Water  water  steam  V  V  Steam  heating  V  heating Gas  V  Oil Table 3.6: Interdependency o f the Critical Infrastructures inside the U B C Hospital Where V is the tight interdependent relationship between two infrastructures.  1 >am;ige  A f f e c t e d Infrastructures  Type  power  Power  V  BK  UK power  w.iler  Bk waiei  sicam  lx'jurm  BK heating  V V  power  B K "iienin  V  V  Water B K water Skvim BK  steam  1 Icaiing  V  B K heating Gas Oil  { ^  V  V  Table 3.7: Interdependency between the Critical Infrastructures and the Backups inside the U B C Hospital  The table illustrates that the most critical infrastructure is electric power. Without power, the backup system o f any other infrastructures cannot work. The steam system, which provides steam for the sterilization o f surgical equipment and other medical devices, is involved with almost all o f the infrastructures inside with the Hospital.  48  The interdependencies among the infrastructures are more complex during emergencies than under normal conditions. In Table 3.7, only direct effects to the infrastructures are listed. For example, when the backup water supply system is working, it needs power to run the pump; should there be a power outage at the same time, the backup generators that need o i l to run w i l l still work. However, i f there is no oil, the pump w i l l stop pumping and the water system w i l l not provide water anymore.  3.6.3. Generic Model of the Hospital Cell It can be seen that the output o f the U B C Hospital is divided into three types: the capacity for  serving long-term patients, short-term patients and urgent patients. Each o f these  capacities depends on the connected infrastructures i n the hospital, but the relationship between these resources and the patients is different for each type o f output. For example, the steam for heating is very important for long-term patients, but not that important for shortterm and urgent patients; the steam for sanitation is important for urgent patients, especially those who need surgery, but it is not nearly as important for long-term patients.  Separated tables are generated to represent the aggregators o f the inputs into the Hospital cell model. i m >ut powerl power2  100% 50% i  100% 50%  m  m  100% 0% 0%  100% 0% o%  oil  * 100% 100%  *  01  Varibles bkl  0% 0% 100% 100% 0% 100%  output ve2  bk2  yel  0% 0% 100% 100% 0% 100%  100% 501 100% 100% 0% 01  Table 3.8: Power Aggregator of Hospital Cell  100% 50% 100% 1001 0% 01  49  input ve2 water 100% *  *  m  OA 0% 01 0% 1  100% 100% 100% 50% 0% 0  Vari >les wbk pump 100% 0% 0% 100% 100% 100% 100% 50% 100% 0% 100% 100% 100% 100% 0 0  Output ywl 100% 50% 100% 100% 0% 0% 0% 1  Table 3.9: Water Aggregator of Hospital Cell  The tables describe one type o f input token aggregates in the hospital cell model. Since each o f the inputs has its backup, the aggregator is used to combine the external input and backup as one single input to the generic hospital input-output model. It can be seen from Figure 3.12 that there is a backup generator for power located inside the hospital. Under normal conditions, the functionality o f the power supply i n the hospital is 100%; however, i f disaster occurs and the power from outside the hospital drops to zero because o f failure in the supply or damage to cells or channels connected to the hospital, the hospital's backup system w i l l work immediately to supply power to the whole hospital, and the number o f beds does not change under this situation. Table 3.8 and 3.9 shows the interdependencies between the critical resources delivered to the Hospital and their corresponding backup system inside the Hospital.  Token: electricity  *-#Beds for Long-term Patients -*-#Beds for Short-term Patients ~H*#Beds for Urgent Patients  Transportation Channel  x J 56  Token: doctors, nurses, medicines  X57  Figure 3.13: Diagram o f the Hospital C e l l M o d e l  50  In order to describe the hospital performance and the complex interdependency between the infrastructures, a hospital model has been developed using H R T table to represent the interrelationship between the inputs and outputs. In this thesis, the transportation channel is set as an ideal channel and there are no detailed data and information for these channels.  The Human Readable Table that defines the simplified input-output model for the hospital to be used b y the Infrastructure Interdependencies Simulator I2Sim is shown i n the Table 3.10:  Status  HRT Table for Hospital  Outputs  Incuts jhl  xel  doctors  Urgent  nurses redi cities  short term Lonftterm  100*  100*  100*  100*  100*  100*  100*  100*  100*  100*  100*  100*  m  100*  100*  100*  100*  100*  100*  100*  100*  100*  100*  100* -  100*  I  100*  1 100* 1  100*  1  100*  80*  1  100*  100*  90*  100*  100*  100*  1 100*  I 100*  1 100* 1 100* 1 100* 1  ! 100%  1 100%  !  i  80*  1  80*  1  80*  \  0*  1  0*  1  0*  loo*  80*  1  1  100*  I  1  100*  1  90*  1  100*  1 100* 1  100*  !  80*  1  80*  1 £0* 1  80*  0*  1  0*  1  1  0*  100*  100*  1 o*  80*  100*  100*  100*  100*  100*  100*  100*  90*  100*  !  ts2  i  100*  1 100*  I 100*  I  1  80*  too*  100*  80*  95*  i  1 100* 1 100* 1 100* 1  100*  I  1 100* 1 100* 1  90*  i  95*  1  1  80*  1  80*  1  80*  1  SO*  i  0*  1  0*  1  0*  1  0*  100*  i  95*  1 1  100*  -  *• Normal State •Water drops to 90%  • Power sent to Urgent and short • term patients drops to 90% Power sent to longterm patients drops to 90% • Steam sent to Urgent and short  • term patients drops w 90% • Steam sent to long term patients 80* . drops to 90% Steam sent to long lerm patients 95* drops to 90% 50* 0*  Inputs in different states *"For example all in 80% Total Damge state  Data describing different states which are not listed on this table  Table 3.10: Status Mapping for the Human Readable Table o f the U B C Hospital The data i n Table 3.10 illustrates how the multiple inputs sent to the hospital affect the number o f beds i n the hospital. In the normal state, 100% inputs are sent into the hospital to allow it to give 100% outputs i n terms o f beds served. Each input or combined inputs can change the state o f the hospital's outputs; these interconnections and changes are calculated using the input-output H R T table.  For example, when the water sent to the hospital is reduced because o f a broken water pipe or a pump failure i n the Water Station, the operation in the hospital w i l l be affected. From the H R T table, it can be seen that when water drops to 90%, the hospital can still maintain its normal state because o f the hospital's emergency plan. One o f the plan's strategies is to cut  51  down the use o f water during the emergency by using one washroom i n each floor.  By  implementing this plan, the water needed for medical care operation w i l l only go down to about 85%.  The variables x i and x 2 indicate the steam heating for the patients i n the hospital. When s  S  both o f these variables are reduced to 80%, the results o f the output w i l l be remarkably different. A t this point, the hospital's output or its ability to provide medical service to longterm patients becomes about 80% o f its full capacity; and the output o f the short-term and urgent patients' care is 95%. This is because long-term patients totally depend on steam for heating, but short-term and urgent patients do not depend on steam as much as long-term patients do.  3.7. Channel Model In sections 3.2 to 3.6, each cell is linked to other cells by different types o f channels. A s mentioned in Chapter 2, i n this thesis, a delay associated with the delivery o f tokens i n normal state was not taken into account because o f the short distances o f facilities within the U B C campus. Delays associated with physical channels' damage are taken into account. The modeling for the channels can be represented as below:  y =f(y k>T>kf>C )  x  j  im  (3-6)  Where: -v" i j : the channel connecting cell i and cell j , and the token flowing from cell j to cell i . X y : amount o f token received by cell i . -v- Yjk: token sent from cell j , the k  th  input connected with the cell.  ^  x: time delay depending on repair procedure only.  ^  kf. functionality coefficient, ranging from 0 to 1 determined b y the type o f damage.  -V* C m : the total capacity o f the channel, the limit o f the total quantity o f token flowing ax  through it.  52  3.8. Reduced Scale Test Case Model A n overall cell-channel diagram for a simplified U B C test case model is shown i n Figure 3.19. It includes five cells, whose model has been developed i n the pervious sections. In addition, there are several external sources designated as external cells i n the model; these cells provide tokens such as electric power, water and gas from outside systems to the simplified U B C test case. The external sources are assumed to be i n an ideal state, which means there is no damage i n these cells.  The cell model is a generic model so that it can represent the same type o f cells with various sizes and capacities. The input-output model can be customized based on the limited information from the specific cell or the types o f input(s), which means the state o f its connection with the critical infrastructures needs to be considered. For example, the model o f the Hospital cell includes inputs such as power, water, gas and steam, and its internal sources are o i l and water from backup systems. If the model is applied to another hospital without water backup, the information related to the specific critical components for backup can simply be deleted. The table is flexible and data or information can easily be added or updated when more information is acquired from the industry or when there is an actual disaster scenario. The system model is designed to cover different situations ranging from normal state to various emergency states, depending on the types o f disasters.  The essential task o f the reduced scale test case model is to indicate the capacity o f the medical services i n the Hospital under different scenarios. The outputs o f the Hospital are the number o f beds for different types o f patients. These outputs depend on the quantities o f input tokens coming through the channels connected to the other cells. The Figure 3.14 shows that the Power House has no direct connection with the Hospital, but when the performance o f the Power House changes, the capacity o f the Hospital w i l l change because the Power House is connected with the Water and Steam Stations. In the next chapter, the interactions between these five cells and the performance o f the Hospital are shown in time domain using simulation.  External  External  Source BC_Hydroi  Source B C Hydro2  1  1  U.i  Token: water  #Beds for Long-term Patients  U.2  #Beds for Short-term Patients #Beds for Urgent Patients +  T o k e n : Electricity •nnnniiMnM\irit3KiRii  Power House Cell External Source  token: Oil  jlntemal Varublnj  Oil hi T o k e n : Electricity iiiRiiiiMBimwTOTkiir  ExtensalJSourc* Gas  Steam station [Internal Variables!  54  Chapter 4  Simulation and Results Analysis  In order to validate the infrastructures  interdependencies  model and the  theoretical  framework for the modeling o f I2Sim, it is important to test the model built i n Chapter 3 with a real-life known scenario with predictable results. In this chapter, the reduced-scale model o f the critical infrastructures o f the University o f British Columbia is set up using the MALAB/Simulink/Stateflow™ software [33]. A soft simulation clock and a graphic user interface with controllers and indicators have been developed to realize an interactive simulation that allows the decision makers to get a better understanding o f the emergent system behavior i n different operational situations. The simulation indicates that the redundant systems such as the backup generators in the Hospital increase the robustness o f the cells. Critical connections, such as the steam pipe linking the Steam Station with the Hospital are also identified. One such scenario is studied b y using a distributor, which allows an operator to find the optimum allocation o f a limited resource so that the operator can ensure the best possible operation o f the other critical infrastructures during an event. The simulation itself has been parallelized, and distributed on the University o f British Columbia Power Systems Lab PC-cluster [41].  4.1. Simulation Model for the UBC Test Case  In  the  previous  chapter,  a reduced-scale  model  o f the  critical  infrastructures  of  the University o f British Columbia has been developed. Based on this model, a prototype simulation has been built by using M A T L A B / S i m u l i n k / S t a t e F l o w ™ [33] [34] to validate the model and demonstrate the methodology o f the cell-channel modeling approach. A n analysis of the outcome demonstrates the interdependent relationship among the cell and channel components o f the system.  55  Figure 4.1: Interconnection Structure in the Reduced Scale U B C Test Case  The interconnection between the components o f the reduced-scale model is shown in Figure 4.1. These interconnections are represented by channels which send different types o f tokens from the sending-end cells to the receiving-end cells. The performance o f one cell affects the other cells to which it is connected by channels. The simulation model demonstrates the performance o f the interactive cells.  The simulation environment for this prototype is made for several types o f researches:  >  Off-line simulation •  Predefined input file o f the system, which includes variables such as the loss o f functionality o f a channel caused by a broken pipe, or the loss o f functionality o f a cell as a result o f damage due to an intensity VIII earthquake;  •  During simulation, the system variables change according to the input file;  56  •  Fast simulation speed.  On-line simulation •  A soft-clock for simulation has been adjusted to make the simulation run at a human friendly speed for an operator to observe;  •  A graphic user interface has been developed to illustrate the change o f system performance during simulation;  •  Discrete events corresponding to different states o f the system variables are updated during the simulation.  Support tool for decision making •  Combined with optimization techniques, the simulation can provide an analyst with estimations o f performance measures for various system alternatives;  •  Uses to test and verify the optimal solution o f limited sources re-allocation problems.  There are mainly three types o f blocks used i n the model. One o f them is the Stateflow Block, which represents the discrete events occurring i n the model. For example, the backup generator i n the Power House requires two conditions to start working: one is power from the Substation dropping to zero and the other is the quantity o f oil storage.  0 && ext_oil >=0 && koi! ==1 ] Jext^p^O && koil==1&&ext_oil>0] Swltch_on entry: oil s=oil s+1; oll=1; during: oil = 1:  Figure 4.2: State o f O i l Usage i n the Power House  57  The total o i l storage, the current state o f o i l and o i l usage are shown i n Figure 4.2. For example, the figure shows the state o f oil changes when the event "power from Substation drops to 0" or " o i l storage used up" occurs. The event is a time-based event; no matter what time the event happens, the function o f the o i l state runs to show the curve presented i n Figure 3.8.  The logic behavior o f the input-output model has been realized using truth table functions, which contain conditions, decisions and actions. For example, the state o f the transformers i n the Substation is at only 0 or 1, no other states i n between, and different combination o f transformers' state generates different outcomes. The logic behaviors are illustrated i n Table 4.1.  Description 5tate of Transformer 1  Condition'" Dl  ; I State of Transformer 2  D4  D5  D6  D7  istti  T  F  T  T  T  F  T  T  T  F  T  T  T  T  T  F  T  T  T  F  T  T  T  F  F  T  T  T  T  T  T  T  T  T  T  T  T  T  F  T  T  T  F  T  T  T  F  T  T  F  HE:  T  T  T  T  T  T  T  F  F  F  F  T  T  T  T  T  F  F  F  F  T  T  T  T  T  lllll  Al  Al  Al  A2  A2  A2  A2  A3  A3  A3  A3  A2|  sw2==l  4 State of feeder 1  kl == 1  5  State of feeder 2  DB . D9 D1Q D l l D12 D13  5Wl==0  3 State of TieBreaker 2  D3  t2==l  2 State of TieBreaker 1  D2  ti==i  k2 == 1  ; 6  Actions: Specify a row from  the  Table 4.1: Input-Output Table for the States o f Transformers, Tiebreakers and Feeders The Lookup Table (n-D) block evaluates a sample representation o f a function i n N variables by interpolating between samples to give an approximate value for y = F ( x i , X 2 , X 3 . . . x ) , even n  58  when the function F is known only empirically. The input-output model can be illustrated using the look-up table functions i n Figure 4.3.  ledicinefe # od beds for urgent medical service  Figure 4.3: Input-Output Table for Beds for Urgent M e d i c a l Service  The reduced scale U B C test case model is illustrated i n Figure 4.4.  Before running the off-line simulation, an m-file for the predefined scenario has to be compiled. During the simulation, the predefined parameters may be changed according to the scenario. Currently, based on the computation time o f the computer, the model runs about 900 time-steps (which indicates 900 minutes in the actual physical clock) i n less than five seconds.  60  In the simulations presented it is assumed that it is derived to use the full capacity o f each cell but that this full capacity may not be available due to structure damage or lack o f resources. A more realistic scenario would include the "people's flow" loop which would include the possibility that not all o f the resources are needed because nobody is using them.  The off-line simulation runs so fast that no action can be taken during simulation. In order to make the simulation run with interactive action by decision makers, a soft clock has been devised in the model (the time block in Figure 4.4) to slow the computation at speed. The soft clock makes the simulation time nearly the same as the actual physical clock, so that it can update events and make interaction possible between the operators and the simulation model. The operators have time to observe the outputs o f the simulation and change the system variables to adjust the outcome based on different objectives.  B y using M a t l a b / G a u g e s ™ and N I Labview™[35], an interactive interface was built and linked with the model. The output o f the model and the critical variables are listed in the interface so that it is easy for operators to update the parameters corresponding o f the events.  Figure 4.5: Interface o f the Substation C e l l M o d e l  61  4.2. Simulation Results  In order to check whether or not the model can reveal critical linkage among the infrastructures, it is vital to choose an actual disaster event with known outcomes as a scenario for the reduced scale test case model [36].  O n November 19, 2006, a Pacific storm brought 90 m m o f rain and strong winds to coastal B . C . Then a weather warning was issued on an Arctic ridge over the B C interior combined with a Pacific low-pressure system over southwest B . C . The result was that on November 26, 20-40 cm o f heavy snow fell across Greater Vancouver, Victoria, and the rest o f the South Coast. O n November 27 and 28, the Arctic front spread across the Lower Mainland and temperatures dropped as the skies cleared (-12° C i n Vancouver). The weight o f the heavy snow brought branches and trees down on power lines [37] [38] [39]. During this period, the impact o f the snowstorm and power outage caused by falling branches and trees affected the U B C campus. Because o f the snow and the resulting power outage at the U B C - P o i n t Grey campus, the whole campus was closed on November 27 following the N o . 68 university policy [40] [42]. The campus power outage lasted for about 12 hours.  This power outage at the U B C campus has been chosen as the disaster scenario. The timebased event happening during this scenario has been compiled [36] and set as the updated events during simulation and the known results o f the scenario is the criterion for measuring the simulation model. Three different scenarios as a result o f this power outage event are discussed i n the following sub-sections.  4.2.1. Scenario 1 and Result Analysis In this scenario, the snowstorm and resulting power outage make the related variables changes; for example, the transmission lines transporting external power from B C Hydro to  62  the U B C Substation were down and the water pipe sending water to the U B C hospital were broken because o f freezing temperatures. Scenario Description ^  A snowstorm with a power outage, the following events happened: •  Initial state : t = to, the whole system runs i n normal state until t = to+20(min) ;  •  t = t +21(min) 0  •  Event : A power outage occurs because o f fallen trees bring down the transmission lines sending power to the U B C Substation ;  •  A c t i o n : The functionality o f the channel linking the external source ( B C Hydro) and the Substation drops from 1 to 0;  •  t = to+40(min) •  Event: The water pipe linking the water station to the hospital burst;  •  A c t i o n : The functionality o f the channel linking the Water Station to the Hospital drops from 1 to 0;  •  •  t = t +781(min) 0  •  E v e n t : the water pipe is fixed after 12 hrs;  •  A c t i o n : The functionality o f the water channel is restored to 1;  t = t +861(min) 0  •  Event: After 14 hrs, the power is restored;  •  A c t i o n : The functionality o f the electric power channel is restored to 1;  1:20 AM Power Outage from BC_hydro  14:20 Power Restored  / 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00  i:00  12:00 13:00 |M:00  15:00  27/11/2006 4:00 PM  27/11/2006 1:00\M  Water Pipe Broken (Sending water to Hospital)  Water Pipe Fixed (Sending water to Hospital)  01:40  13:40  Figure 4.6: Timeline o f Scenario 1  63  Results Analysis During the simulation o f scenario 1, two events occur: a power outage and a broken water pipe. The consequences o f these events are shown i n Figures 4.7 to 4.13.  In Figure 4.7, the outputs o f the Substation change following the event settings o f scenario 1. The power outage happens at t = t0+20(min) and power is restored at t = t0+860(min); this influences the output o f the Substation and this i n turn influences the inputs o f the Hospital and the Power House. Power From BChydro to UBC-Substation  40  -BCHydro  20  1  .BCHydro  1500^ g. 1000 * 500 0  100  200  300  400  500  600  700  800  900  100  200  300  400  500  600  700  800  900  100  200  300  400  500  600  700  800  900  t(min) Power Sending to Hospital  t(min) Power Sending to PowerHouse  150^ g. 100 * 50  0  t(min)  Figure 4.7: Scenario 1 - Simulation Results for the Substation C e l l  Figure 4.8 shows the state o f the power in the Steam Station and Water Station. The power sent to the Water Station drops to zero when the input to the Power House drops to zero. The power sent to the Steam Station drops to zero and then is restored to the normal state because it receives power from the backup generator in the Power House. F r o m the figure, it can be seen that the power sent to the Steam Station has a spike (pointed by the arrow); this is caused by the switch time from using power from the external source to using power from the backup generator. A t the point t = t0+860(min), the power sent to the Substation is  64  restored, then the power sent from the Power House is restored and the power sent to the Steam Station and the Water Station is restored. The normal state returns.  When the backup generator starts working, the amount o f oil storage begins to drop. When the Substation restores power to the Power House, the backup generator stops working and then the o i l storage is kept at the state shown i n figure 4.8.  Power Sending to Water Station From PowerHouse 40 *  20 0 0 l  100  200  300  400  500  600  700  800  900  700  800  900  700  800  900  t(min)  Power Sending to Steam Station From PowerHouse 100  1  50 0 0  100  I  200  300  400  500  600  t(min)  Oil Storage In PowerHouse 4000 2000 0 0  100  200  300  400  500  600  t(min)  Figure 4.8: Scenariol: Simulation Results for the Power House C e l l Water Sending to U B C C a m p u s 400  I  l  I  I  I  I  I  1  I  Water pump  20D D D  Water „ n  L_  100  _  _  _  200  300  400  - - L. 500  .  1  BOD  Water i 700  BKpump  i 000  I  1 1 1 900  t(min)  Figure 4.9: Scenariol - Simulation Results for the Water Station C e l l Before the power outage, three booster pumps work i n the Water Station. The power sent to the Water Station drops to zero at t = t0+20(min), and the backup pumps start to work by  65  using o i l . When the Water Station switches from using external power to using o i l , the backup pumps begin to pump water to the Hospital. A t t = to+781(min), the power is restored and the booster pumps begin to work again. Although the state o f the internal critical variables o f the Water Station changes during the simulation, the amount o f water sent out to the Hospital is maintained at the level o f the normal state.  ^  S t e a m S e n d i n g to U B C C a m p u s F r o m S t e a m Station  120. 100 BO.  .  s gas c» Steam  S  ——  •  100  2DQ  300  i  500  AQO  BOD  70.0  i  BOD  900  t(min)  Figure 4.10: Scenariol - Simulation Results for the Steam Station Cell  The boilers in the Steam Station burn gas to generate steam i n the normal working state. Figure 4.10 shows how the Steam Station generates steam without disturbance during the power outage. # of beds for Urgent Patients |  0  100  200  i  300  400  t(min)  500  600  700  800  900  700  800  900  700  800  900  # of beds for Long-term Patients i  0  100  i  200  i  300  400  t(min)  500  600  # of beds for Short-term patients  0  100  200  i  300  400 500 t(min)  600  Figure 4.11: Scenariol - Simulation Results for the Hospital C e l l (A)  66  Oil Storage In U B C hospital  5000  400  500  900  t(min) Water Storage in U B C Hospital 5000 4000 3000 2000 1000 100  200  300  400  500  600  700  800  900  t(min)  Figure 4.12: Scenariol - Simulation Results for the Hospital C e l l (B)  Figure 4.11 and Figure 4.12 show how the performance o f the medical services i n the hospital is influenced by the power outage i n the Substation and water loss from the Water Station. When there is no power coming from the Substation, the backup generators start to work to provide power to the whole Hospital. The first spike i n Figure 4.11 shows the state of the power i n the hospital as a result o f switching from external power to power from the backup generator. A t t = t0+40(min), the water pipe sending water to the hospital is broken and it affects the hospital immediately; the performance o f the hospital, which is indicated by the number o f beds for long-term, short-term and urgent patients, drops to zero (the second arrow i n the figure). The hospital has its own water reservoir and it needs some time (30 minutes) to manually switch from the state o f using external water to using backup water; the switch is indicted by the third arrow i n Figure 4.11. After this switch, the performance o f the hospital is restored to its normal state. In Figure 4.12, it can be seen that the backup water is used until the pipe is fixed at t = to+780(min), and o i l from the o i l storage is used until power is restored at t = tn+860(min).  67  Figures 4.7 to 4.13 illustrate the performance o f each o f the cells and the interconnection between cells under scenario 1. The hospital was a full self-supporting system during the power outage.  Figure 4.13: Interrelationship o f Electrical Power between Cells  Figure 4.14 shows that the Power House and the Water Station also have backups for the critical components i n their systems; these backups enable the two stations to maintain their full capacity performance during the power outage. In general, the whole system, especially the Hospital, maintains its performance for a short period after a power outage and loss o f water by using its self-supporting backups. The length o f the short period depends on the backup sources. The results o f the simulation reflect the results o f the actual event that happened at the U B C campus during the late November storm. In other words, the results validate the correctness and usefulness o f the model and the cell-channel modeling approach ofI2Sim.  4.2.2. Scenario 2 a n d Results Analysis Based on the first scenario, the second scenario includes an extra event happening i n the Power House: the backup generator does not start working when the power outage occurs, affecting the performance o f the whole system. Another change i n the second scenario is the time-shift for the same event as i n the first scenario.  68  Scenario Description  A snowstorm with a power outage at the U B C campus; the following events occur: •  Initial state : t = to, the whole system runs i n the normal state until t = to+20(min)  •  t = to+21(min) •  Event 1: A power outage occurs because o f fallen trees bring down the transmission lines that send power to the U B C Substation.  •  A c t i o n 1: The functionality o f the channel linking the external source, B C Hydro, and the Substation drops from 1 to 0.  •  •  Event 2: The backup generator i n the Power House does not work immediately.  •  A c t i o n 2: The functionality o f the backup generator stays at "0".  t = t +40(min) 0  •  Event: The water pipe linking the water station to the hospital breaks down because o f the freezing weather.  •  Action: The functionality o f the channel linking the Water Station to the Hospital drops from 1 to 0.  •  •  •  t = t +50(min) 0  •  Event: The backup generator i n the Power House starts working.  •  Action: The functionality o f the backup generator stays at " 1 " .  t = t +860(min) 0  •  Event: After 14 hrs, B C Hydro's power is restored.  •  Action: The functionality o f the electric power channel is restored to 1.  t = to+1480(min) •  Event: The water pipe is fixed after 24 hrs.  •  Action: The functionality o f the water channel is restored to 1.  69  02:10  Backup Generator fixed! Power Outage from BC_hydro ^ Backup Generator delay!^,,-"'' 0 1 : 2 0  14:20  Power Restored  |  i  A-, ;  i  rn  rn rn n  r m  i  n r n rn n  i A  (2:00 03:00 04:00 05:0006:00 07:0008:00 09:0010:0011:0012:0013:0014:0015:0016:0017:00 18:0019:00 20:0021:00 22:0023:00 24:0001:00(12:00 27/11/2006 1:00,AM 28»11/2006 3:00 AM  \ \ Water Pipe Broken  Water Pipe Fixed (Sending water to Hospital) 01:40  (Sending water to Hospital) 01:40  Figure 4.14: Timeline o f Scenario 2  Results Analysis Using the data i n Figure 4.14, simulation results are generated and shown i n Figures 4.15 to 4.20. The simulation results for the Substation for Scenario 2 are the same as for Scenario 1. Power From BChydro to UBC-Substation  —  BCHydro  1  . _ BCHydro, 200  400  600  800  t(min)  1000  1200  1400  1600  1200  1400  1600  1200  1400  1600  Power Sending to Hospital  1500 1000 ~  500 200  400  200  400  150  600  800 1000 t(min) Power Sending to PowerHouse  g. 100 ^  50 600  800 t(min)  1000  Figure 4.15: Scenario2 - Simulation Results for the Substation C e l l  In Figure 4.16, Figure 4.17 and Figure 4.18, it can be seen that the backup generator has not kicked in immediately after the power outage. It takes about half an hour to fix the backup generator; this delays the switch time from using external power to using backup power.  70  The time delay influences the performance o f the Water Station and o f the Steam Station simultaneously. In Figure 4.17, it can be seen that the Water Station starts to pump water to the whole campus b y using the backup pump after the switch time (the time between the first and second arrow i n the figure). After t = t0+860(min), when power is restored, the booster pumps work again and the backup pump returns to its standby state and this is indicated b y the third arrow i n the figure. The water sent to the whole campus is now at full capacity. Power Sent to Water Station from PowerHouse  0  200  400  600  800 1000 1200 t(min) Power Sent to Steam Station from PowerHouse  1400  1600  0  200  400  600  1600  800 1000 t(min) Oil Storage in PowerHouse  1200  1400  I  I  I  I  i V  I  i  i  I  i  0  200  400  600  i  800 t(min)  i  1000  !  1200  1400  1600  Figure 4.16: Scenario2 - Simulation Results for the Power House C e l l Water Sending to UBC Campus  ii : ii ir/ . . . . ::.  L._._.-.JL — . - J b  V  1  0  '  200  '  400  pump  if m n m  II l' -'  . . . . Water  V  : IL  800  1---  800  "  Wier  BKpump  Wiier I  1000  I  1200  I  1400  I  1603  t[min)  Figure 4.17: Scenario2 - Simulation Results for the Water Station C e l l  71  Steam Sending to UBC Campus From 3earn Station  i i  j-.-.l-^  Y\%.•r i ,  i• 1  1  _i  i  .i  j •  0!  i 200 i  •  o.. _ ""Steam S  J'. . •'  J  j  1000  1200  r  400  HE  800 t(min)  i i i i i ' 1400  1600  Figure 4.18: Scenario2 - Simulation Results for the Steam Station C e l l After the switching time, the backup generator still does not work; thus, this power outage affects the status o f critical components such as the air fan i n the Steam Station. The air fan in turn affects the operation o f the boilers. The boilers have to stop working until the air fan is restarted and the time for restarting boilers takes one to two hours, depending on the situation. Figure 4.18 shows that the boilers have stopped working for about one hour; this means that steam is not sent out to the campus during this period.  Figures 4.19 and 4.20 illustrate the performance o f the hospital when affected b y the different states o f the other cells. The medical service for long-term patients is affected differently from the medical service for short-term and urgent patients. A t t = t0+20(min), when the power outage occurs, the backup generators i n the Hospital begin to work. A t the same time, the steam from the Power House is delayed because the backup generator has dropped to 0. The performance o f the Hospital changes due to the loss o f steam. The number o f long-term patients taken care o f drops to zero because these patients depend on steam for heating; the number o f short-term and urgent patients experience little disturbance because o f the loss o f steam, which is shown i n Figure 4.19. A t t = t0+40(min), the water pipe breaks; the performance o f the hospital stays at zero. After the switching time o f 30 minutes and the restoration o f steam, the hospital reverts to its normal state gradually.  72  # of beds for Urgent Patients 20  1  1  1  200  400  600  I  I  I  400  600  1  1  1  1  1200  1400  I  I  1200  1400  - -/  10 0  300  800 1000 t(min) # of beds for Long-term Patients I  I  1600  200 100 0 0  i  200  800 1000 t(min) # of beds for Short-term patients  1600  -  300 200 100 0  200  400  600  800 t(min)  1000  1200  1400  1600  Figure 4.19: Scenario2 - Simulation Results for the Hospital C e l l ( A )  Oil Storage in UBC hospital  0  200  400  600  800 t(min)  1000  1200  1400  1600  Water Storage in UBC Hospital 5000 4000  —  3000  i  /  2000 1000 0  i  i  i  200  400  600  800 t(min)  1000  1200  1400  1600  Figure 4.20: Scenario2 - Simulation Results for the Hospital C e l l (B)  73  The difference between scenario 1 and scenario 2 is the state o f the critical component inside the Power House cell. The performance o f the system, especially the Hospital, has changed. Because o f the power outage, the loss o f water, and the delay time for the backup generator to take over, the performance o f the Power House drops immediately; this drop i n performance influences the Water and Steam Stations; finally the performance o f the hospital drops because o f the drop o f performance i n these cells, even though the backup system inside the Hospital works well. The results indicate that the backup inside the Power House is the critical component not only to its own cell but also to other cells linked to it. The performance o f the hospital, which is the end outcome i n the system, is the combination o f multiple events. B y using the I2Sim model, it is seen that the critical components should be set to a high-level priority o f repair after the disaster.  4.2.3. Scenario 3 and Results Analysis Scenario Description In this section, a new block, which represents a distributor controller i n the Substation cell, is added to the model. This block is used to re-direct power to the Hospital and Power House under different situations. The objective is to use a trial and error procedure to test optimal re-assignment solutions o f a limited resource to the system. In this model, the simple distributor controller is a ratio o f the amount o f power going to the Hospital and to the Power House. In the scenario, the ratio o f power sent to the Hospital changes from 0-1, so the performance o f the hospital changes accordingly. In order to have a better view o f the system without backup support, the time for the backup systems is reduced to a limited time (30 minutes). Power re-assignment with limited internal sources i n the Power House and Hospital. The following actions happen: •  Initial state : t = to, the whole system runs i n normal state until t = to+20(min).  •  t = to+21(min) •  Event: The water pipe linking the water station to the hospital is broken due to freezing cold weather.  74  •  Action: The functionality o f the channel linking the Water Station to the Hospital drops from 1 to 0.  •  t = to+51(min) •  •  t = to+81(min) •  •  Event: The backup water i n the Hospital begins to work.  Event: The backup water i n the Hospital runs out.  t = to+1 OO(min) ~ to+700(min) •  Event: The amount o f Power sent to the Hospital by the U B C Substation changes, using distributor control.  •  t = to+701 (min) ~ to+800(min) •  Event: The amount o f Power sent to the Power House from the U B C Substation changed, using distributor control.  • •  Event: The backup generator in the Power House is delayed to come to operate.  t = to+801 (min) ~ t +900(min) 0  •  Event: The steam pipe linking the Steam Station to the Hospital gets damaged.  •  Action: The functionality o f the steam channel changed from 1 to 0, and then back to 1.  Results Analysis The power is i n normal state. The water pipe breaks and then after 30 minutes' delay, the hospital manually switches to using its internal water source; the limited amount o f backup water is available for use for only 30 minutes. The performance o f the hospital drops to 0, goes back to full capacity and then drops to 0 again i n the first 100 minutes because o f changes i n the input water state. This is illustrated in Figure 4.28.  75  Power Sending to Hospital 1500  1  i  1  1  r  1000  s  500  Power Sending to PowerHouse 150  ~i  r  ~i  r  100  50  j  0  100  i  i  200  300  I 700  L  400 500 t(min)  600  I  800  900  Figure 4.21: Scenario 3 - Distributor Sent Power to the Hospital and Power House Water Sent to Hospital 300 200 100 100  200  303  400  SCO  000  700  BOO  t(min)  Figure 4.22: Scenario3 - Simulation Results for the Water Station C e l l Steam Sent to Hospital  I  0 0  43  100  200  300  4)0  SOD Umin)  Figure 4.23: Scenario3- Simulation Results for the Steam Station C e l l  000  76  It can be seen from Figures 4.24 and 4.28 that from 200 to 800 minutes, the power sent to the Hospital and the Power House is changed by adjusting the distributor's ratio i n order to affect the performance o f the Hospital. After using the backup generators for a limited time period, the Power House and Hospital's performance drops to 0 and is then restored when the external power returns. # of beds for Urgent Patients  t(min) # of beds for Short-term patients ]  1  ]ackl£iUq|errurvout  -  ...  ratios increase  i  0  100  200  300  400  <  1  1  500  ; r s :arr pipe got damaged  toil_J  i  600  700  800  900  t(min)  Figure 4.24: Scenario 3 - Simulation Results for the Hospital ( A )  Finally, the performance o f the Hospital changes following the functionality change o f the steam pipe i n the last 100 minutes. The figure illustrates that the hospital medical services for long-term patients changes rapidly when the amount o f input steam is decreased.  77  Oil Storage in UBC Hospital 1  II • ^-Using oill l  1  1 _  \ .Oil.riin.-out  1 i  200  300  1  400  500  600  700  800  900  t(min) Water Storage in UBC Hospital  30 20 10  j.  y  ]  Using water: i  ^ i \  ;  !  \\^\NaXet 0. 0  j  100  run-out 200  300  400  i  500  600  700  i~-  800  900  Figure 4.25: Scenario 3 - Simulation Results for the Hospital (B)  In scenario 3, the simulation results illustrate that the backups for cells increase the reliability of the cells' performance, depending on the amount o f storage. The results indicate how different distribution o f limited resources influences the system performance; the input token of steam is critical to long-term patients i n the Hospital. Based on the emergency plan o f the Hospital, when the loss o f steam lasts for more than 2 hours, the long-term patients have to be transferred to other hospitals such as the Vancouver General Hospital.  4.3. Distributed Simulation The simulation itself was parallelized, and distributed on the U B C Power Systems Lab P C cluster, so that the computational load, as well as the scalability o f the approach, can be studied. In this section, a distributed simulation for the simplified U B C test case is tested by using the S C I based P C cluster [41].  78  Figure 4.26: Structure o f the P C Cluster Simulation  Figure 4.26 illustrates how the simplified U B C test case model is separated into five P C s ; each o f them represents one o f the cells. For example, the cell Substation is installed in computer #1 and it is connected with the Hospital and the Power House cells by an S C I interface [36]; similarly, the other four cells are connected to the other P C ' s . The connection o f the different types o f channels to the P C cluster is also shown i n this figure. The computation speed is about five times faster when using the PC-Cluster [41] than using a single computer.  79  Figure 4.27: P C Cluster Simulation A  The distributed display o f each cell gives the decision makers a more practical view o f the actual situation than a single display. In reality any interdependent infrastructure system is composed o f a number o f cells and channels. The cells i n real-world are usually located in different geographical position and are linked with other cells b y physical channels. Because of the geographic separation, the models for cells are in different P C s . A t the same time, the P C cluster makes the system more understandable by using more indicators, controllers and time-dependent scopes for showing the simulation results i n multiple ways.  80  Figure 4.28: P C Cluster Simulation B  Figure 4.27 and 4.28 show how the simulation o f the simplified test case runs i n the P C cluster.  4.4. Simulation Conclusion In this chapter, the system model was validated and tested b y using known scenarios and the model demonstrated  its usefulness  and correctness for the research on  infrastructure  interdependencies. System's redundancy increases the robustness o f the cells, such as in the case o f the backup generators i n the Hospital; the critical connections, such as the steam pipes linking the Steam Station with the Hospital, influence the system performance in a very remarkable way. These critical connections have been analyzed and identified based on the simulation results. A distributor allows an operator to find the optimum allocation o f limited resources in order to ensure the best possible operation o f the other critical infrastructures during an event. The simulation itself can be parallelized and distributed on the U B C Power Systems Lab PC-cluster.  81  Chapter 5  Conclusions and Future Work  5.1. Conclusion  This thesis presented contributions made to the development o f U B C ' s  Infrastructure  Interdependencies Simulator I2Sim. In particular, this work has contributed a methodology to build the Human Readable Tables (HRT) which is an essential aspect o f the I2Sim modeling approach. A prototype o f I2Sim has been built and tested using M A T L A B / S D V I U L I N K / C V I . The prototype has been used to demonstrate the validity o f I2Sim to replicate complex interdependency scenarios. A user friendly interface was developed i n order to simulate various disturbances on-line to allow decision makers to have a better insight into interdependencies. A better understanding facilitates the formulation o f better strategies for each scenario. A reduced scale test model based on the U B C test case data o f the L2Sim project which includes the Hospital, Substation, Water Station, Power House and Steam Station was implemented.  To analyze the real case scenario o f the November 19  th  2006 snowstorm that affected the  U B C campus, the simulation's results were consistent with the outcome o f the actual event. The redundancy provided by the backup systems was vital i n increasing the robustness o f the critical U B C cells such as Hospital. Critical interconnections such as the channel between the hospital and the steam station were represented and identified through the simulation results. The capacity o f the Hospital's medical service was estimated under these conditions and the patients' sensitivity to the different input tokens was evaluated. The research shows that that a discrete event simulation with a distributor controller could provide a better distribution o f limited resources for the overall system's performance in the same scenario. These capacities give the decision makers a better understanding o f the emergent system behavior under different operational scenarios.  82  Other lessons were learned during the process o f setting up the system models for the U B C test case that point to important policy and operational issues i n the system. For example, i n the steam station, boilers can use gas or oil to burn the steam, the o i l is the backup o f the gas, but the boilers need gas to start-up. When there is no gas, or the gas pipe is broken, there is no start-up for boilers and it does not matter how much gas or o i l the powerhouse gets, the plant cannot generate steam any more. Another example is the following. When there is a power outage on Campus, the powerhouse can generate and send the steam out by using backup generator, but the problem is that i f other buildings have no power, fans and the equipment i n those buildings for sending the steam inside those building w i l l be shut down, therefore no steam w i l l be delivered.  5.2. Future Work In this thesis, no delay was assumed for the transportation o f tokens through channels i n their normal state. Future research is to include this delay which can have an important influence on the system's performance when it covers a large geographic area. The model takes into consideration the number o f available beds i n the hospital with urgent, short-term and longterm patients. Another extension to the research would be the estimation o f the capacity o f the hospital taking into account the physical presence o f types o f patients; the results would then depend on some factors such as the inflow and outflow o f patients after a disaster, priority i n treatment and so on. The results o f this thesis w i l l be used as a benchmark system for validating the full version o f the I2Sim Simulator, which is built around the full capabilities for large systems simulation o f the O V N I (Object Virtual Network Integrator) core [43] of U B C ' s power systems simulation group.  83  References [I] P. Athukorala and B . P. Resosudarmo, "The Indian Ocean Tsunami: Economic Impact, Disaster Management and Lessons" Division o f Economics, Research School o f Pacific and Asian Studies, Australian National University, 2005. [2] R. W . Kates, C . E . Colten, S. Laska and S. P. Leafherman, "Reconstruction o f N e w Orleans after Hurricane Katrina: a research perspective," Proc. Natl. A c a d . Sci. U . S. A . , vol. 103, pp. 14653-14660, Oct 3. 2006. [3] T. G . Lewis, Critical Infrastructure Protection i n Homeland Security: Defending a Networked Nation. Wiley-Interscience, 2006, [4] S. Rinaldi, "Modeling and simulating critical infrastructures and their interdependencies," System Sciences, 2004.Proceedings o f the 37th Annual Hawaii International Conference on, pp. 54-61,2004. [5] P. J. Schneider, B . A . Schauer and M . P E , " H A Z U S — I t s Development and Its Future," Nat. Hazards Rev., v o l . 7, pp. 40, 2006. [6] M . Shinozuka, "Resilience o f Integrated Power and Water System," Research Progress and Accomplishments, v o l . 4, 2003. [7] P. Pederson, D . Dudenhoeffer,S. Hartley, M . Permann, " Critical Infrastructure Interdependency Modeling: A Survey o f U . S . and International research," 2006. [8] G . P. Richardson and A . L . 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Moreira, " O V N I : Integrated Software/Hardware Solution for Real-Time Simulation o f Large Power Systems," Proceedings o f the 14th Power Systems Computer Conference ( P S C C ' 0 2 ) , 2002.  BC_hydro1 BC hydro 1 S  t1  S t2 a-  oo  S swl  S sw2  S_swf12  W  S_avf22  a  .2 •i  u  S_swh  w  S_swsh Switches of feeders  BC_hydro2 BC hydro 2  T X & Switches  power to ws  —•CD power to ss  oil to WS&SS Psub  Pbk  powerhouse  

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