CNIP 060329JIIRP - UBC1 Design for Survival. Dynamic Infrastructures Coordination José R. Martí, Jorge A. Hollman, Carlos Ventura, Juri Jatskevich, The

CNIP 060329 JIIRP - UBC 1

Design for Survival. Dynamic Infrastructures Coordination

José R. Martí, Jorge A. Hollman, Carlos Ventura, Juri Jatskevich, The University of

British Columbia


NSERC/PSEPC/Industry

“Develop innovative solutions to mitigate large

disaster situations involving multiple

infrastructure systems”


JIIRP Canada ($3 M)

Jose Marti, University of British Columbia ($1.1 M), critical linkages in infrastructure networks

Vincent Tao, York University, emergency management using geographic decision support systems

Wenjun Zhang, University of Saskatchewan, models for critical infrastructure networks

Benoit Robert, École Polytechnique de Montréal, interdependencies and domino effects in life-supporting networks

Tamer El-Diraby, University of Toronto, interdependencies through an analysis of stakeholder needs, risks, and competencies

Edward McBean, University of Guelph, resilience of water infrastructure and health response systems against waterborne diseases


UBC Team

Electrical EngineeringPower SystemsCommunication Systems Data Security

Civil EngineeringEarthquakes Damage

Assessment Software Engineering

Human Decisions Metamodels

Computer ScienceSystems Visualization (SFU

Univ.)Disaster Room VirtualizationDatabases Integration

CommerceBusiness Recovery

GeographyGIS Systems

PsychologyPanic ControlPublic Education


UBC’s Partners British Columbia Transmission Corporation BC Hydro Telus Corporation Greater Vancouver Regional District Vancouver International Airport Authority


Design for Survival

Problem Identification Problem Modelling Solution Formulation Solution Implementation


Problem Identification


“First priority during disaster situations is, and should be,

human survival”


Infrastructures Recovery During normal life, each infrastructure

(power grid, telecom grid, etc.) knows how to recover from problems in its own system

Recovery times are adequate for normal life Normal recovery assumes the other

infrastructures are available During disasters multiple infrastructures are

damaged simultaneously Recovery times are those for survival


Disaster Timeline

Normal Alert Emergency Recovery

Months to years Days to weeks Hours to days Days to months

Mitigation

Preparedness

Response

Recovery

Physiological

Safety

Love/Belonging

Esteem

Being

Maslow’s Hierarchy of

Needs


System Formulation

Vital Survival Tokens Tokens Delivery Optimum Dispatch


Vital Survival Tokens1. Water (suitable for drinking)2. Food (adequate for emergency situations)3. Body Shelter (breathable air, clothing,

temperature, housing)4. Panic Control (hope, political and religious

leaders, psychologists, media)5. Personal Communication (whereabouts of

loved ones)6. Individual Preparedness (education)7. Sanitation (waste disposal, washing)8. Medical Care (medicines, physicians, nurses)9. Civil Order (fire fighters, police, army)


Tokens Delivery Survival tokens need to be delivered

from where they are available to where they are needed

Tokens availability and needs change as disaster evolves

Transportation channels capacity and delay changes as disaster evolves

System is time dependent


Optimum Dispatch In general there will be more than one

supply point and more than one destination point

Optimum dispatching will depend on tokens availability, needs, and transportation channels capacity and delays

Optimum dispatch needs readjustments as system conditions change (real-time)


System Modelling

Cells Nodes Channels


Components Cells: entity that performs a function Tokens: goods needed by cells to

perform function Nodes: contain cells in same

geographical location Channels: allow transportation of

tokens between separate geographical locations (from node to node)


System of SystemsElectric

Power PlantSubstation

Transmission

FoodDistribution center

Production centerLocal store

Water

PurificationPlant

Pump Station

Pipe

Oil & Gas

Refinery

Oil Field Compressor Station

Communications

PhoneInternet

Mobile

Transportation

Local roadBridge Regional Highway

Emergency Responders

FirefighterParamedic

Hospital

911 E-Comm

Critical EventLocal road


Example of Cells Hospital Fire Hall RCMP Station Electrical Substation Telecom Substation Water Station Residential Area Victims Refuge Area(we identified 17 cells in UBC test case)


Modelling & Simulation Challenge

Set up “System of Systems” … without knowing much

about any of them!


Granularity

“Zoom Level”, e.g. power system At transmission level large load centers

are represented as equivalent loads At distribution level transmission

system is represented as an equivalent Hierarchical structure

Solution in form of subsystem blocks Blocks inside blocks


Hierarchical Solution

S UP E RNO DE

IS L A N D II

IS L A N D III

IS L A N D I

CE LL

W A T E R

R O A D S

P O W E R

CE LL

W A T E R

R O A D S

P O W E R

CE LL

W A T E R

R O A D S

P O W E R

CE LL

CE LL

CE LL

CE LL

CE LL

CE LL


Token Networks

Cells, nodes and channels form token networks

Each token network has its generators, loads, and transportation channels

E.g., electric power, water, medicines Some channels are shared, e.g.,

roads, airports


Electric Power (token 1)

Power Utility Cell Emergency Diesel

Hospital Cell

(Load)

)()( 112112112112 tDzmtx k

1 2

3

Lights, equipment (Load)

D12

D13

)()( 113113113113 tDzmtx k

Residential Cell

(Gen) (Gen)

)(112 tx

)(113 tx


Medicines UsedBy Hospital (Load)

Medicines (token 3)

)()( 342342342342 tDzmtx k

MedicinesSupplier A(Gen)

2

3

4

1

D42

D43

)()( 343343343343 tDzmtx k

D12

R

R

Supply Room (Gen)

MedicinesSupplier B(Gen)

Medicines usedby Residential Cell (Load)

Hospital Cell)()( 312312312312 tDzmtx k


Dispatching Decisions Dispatching decisions determine how

much power is sent to the hospital and how much to the neighbourhood

Dispatching decisions determine how many medicines are sent to the hospital and how many medicines are sent to the residential neighbourhood

Optimum dispatch problem: Determine dispatching amounts Dik to “best” satisfy cells constraints


Doctors

hospital

Patients fromneighbourhood

ElectricPower

Water

Medicines

Food

Hospital Cell

Each token is delivered to the cell by corresponding token network

Nurses


Hospital Cell Input-Output Model

produced beds

used nurses

used doctors

used medicines

used water

usedy electricit

cellin

producedor used token

26

25

24

23

22

21

x

x

x

x

x

x

k

jxkj

Cell k=2

Token 1 Token 2

Token 3

waterelectricity

doctors


Hospital Cell Function

Node = 1st subscriptToken = 2nd subscriptx21 = electricity used

x22 = water used

x23 = medicines

x24 = doctors used

x25 = nurses used

x26 = beds produced

26

25

24

23

22

21

2

x

xx

x

x

x

X

Vector of Tokens


Hospital Cell Function

Beds generated x26 depends on availability of needed tokens. If the relationship were linear (which is not):

For the general nonlinear case:

26625524423322221126 xaxaxaxaxaxax

),,,,,(f 262524232221226 xxxxxxx

0)(f 22 X


Constraints

120 Beds 150 10 Doctors 15 15 Nurses 20500 Medicines needed in 15 minutesConstraints can be modified every 5

minutes (or whatever Δt is chosen) …


All System Cells One function for each cell

Subject to its internal constraints

0)(

0)(

0)(

33

22

11

Xf

Xf

Xf


Cell’s Wellness The cell’s wellness at a given moment can be

expressed as a function of the cell’s current operating capacity versus its needed capacity. In the hospital case

Cell wellness can be used to put weight in constraints

Other political, environmental, etc. constraints can also add weights to constraints

))(()( 222 tXtW g


Channel Model

Transportation channels have capacity limits and time delays

Some channels (e.g., roads, airports) may be shared by multiple token networks and only road/airport people can provide best routes and channel delays


Channel Model42

4242kzmg 4 2

)(42 tD )()( 42424242 ktDmtx

D 42

D(t) = dispatched token amount

x(t) = received token amount

g = conductance of channel

m = magnitude loss (usually = 1)

k = time delay, e.g., 2 hours

Channel capacity = constraint on D


Channel Saturation

ikx

(hours) k

k increases strongly with saturation


Channel Damage E.g., medicines truck route involves

broken road, to be repaired in 3 hours, plus 2 hours for travelling time

E.g., power line will be down for 4 hours

)5()()( 342342342342 hrstDtDgtx

)4()()( 112112112112 hrstDtDgtx


Continuity Condition (KCL)

)(342 tD )(343 tD )(345 tD

)(34 tx 4k

)(312 tx )(342 tx )(362 tx

)(32 tx 2k

Lo a d N o d e (to k e n 3 ) G e ne ra to r N o d e (to k e n 3 )

)(302 tD

)5.0()1(9.0)3()()( 36234231230223 hrstDhrtDhrstDtDtx

( generated in the node – no channel delay))(302 tD


Solution Formulation

Transportation and cell equations Dispatch Optimization


0)(

0)(

0)(

33

22

11

Xf

Xf

Xf

System of Equations Cell Functions Transportation

Equations

)5.0()1(9.0)3()()( 36234231230223 hrstDhrtDhrstDtDtx

26

25

24

23

22

21

2

x

xx

x

x

x

X

)5.1(85.0)2()()( 45243240224 hrtDhrstDtDtx

e.g., cell 2 tokens 3 and 4


LTI Discrete Time System with Nonlinear Constraints Transportation equations are linear with

one to Nth-order delays Cell functions impose nonlinear

constraints Equations can be solved step by step at

∆t (delay-one) intervals using MATE/EMTP techniques

Dispatching values Dij-k can be optimized for a scenario interval length, e.g. 10 hrs, and updated at each solution step, e.g., every 10 minutes


Optimum Tokens Dispatch Diagonalize transportation equations

taking sparsity into consideration Solve the TPBV problem to meet the cell

requirements The shooting method (Perkins, Martí,

Dommel, 1995) or the waveform relaxation method (Wang, Martí, 1996) can be implemented with step by step solution of the difference equations


Optimum Power Flow Problem

Dommel & Tinney, 1968, solved OPF problem with Newton’s method and sparsity with very fast results

System 300x80 = 2,400 eqns was solved in 4 min on IBM 7040 (1.3 MHz 2 CPU)


Optimum Tokens Dispatch Real-time solutions are possible A case with 100 cells and 50 tokens:

100x50 = 5,000 eqns can take about 5 minutes for a 10-hour scenario updating every Δt=10 minutes using a dual-processor 3 GHz PC

PC-Cluster architecture (Hollman, DeRybel, Marti, 2003, 2005) can linearly escalate the computational power


MITS Real-Time Simulator

Multi-Infrastructures Tokens Simulator Fast Real-Time Solutions


MITS Simulator

Based on our MATE (Multi-Area Thevenin Equivalent) real-time simulator

Each token has its corresponding transportation system (matrix sub-block)

All tokens come together at cells subsystem and must satisfy the cell functions


Software-Hardware Mapping


Solution Lock-Up A large area system may well “lock-

up” and we may not be able to find feasible dispatching solutions for given disaster situation

What can be done at planning stage? Add resources Reallocate resources and loads Split system into ISLANDS


Conclusions Analytical tool to study disaster scenarios Useful for

Resilient system design Disaster mitigation plans Real time disaster room scenarios

Real-time solutions for what-if scenarios Based on proven tools for discrete-time

solutions and optimum dispatching solutions

Easy to interface with human layer


Dynamic Islanding for Survival


Breakup into Subsystems

S UP E RNO DE

IS L A N D II

IS L A N D III

IS L A N D I

ISL A ND 'SMA IN NO D E

Sub-Node

Sub-Node

Sub-NodeW A T E R

R O A D S

P O W E R


Sub-Node

Sub-Node

Sub-NodeW A T E R

R O A D S

P O W E R


Sub-Node

Sub-Node

Sub-NodeW A T E R

R O A D S

P O W E R


Islanding Strategy The network is segmented into “self-

sufficient islands” to prevent cascading effects.

An island is able to survive on its own for a limited time period. Beyond this period help needs to be coordinated and delivered from the external world

Panic control and prevention of cascading effects requires immediate response

Islanding can be less expensive than the redundancy approach


Advantages

Increases survivability of the network Minimizes restoration time Decreases impact of cascading events

by identifying high-load nodes Dynamic definition of islands for

different levels of quality service or catastrophe scenarios

Optimization of network upgrades


Implementation Partnerships among NCIs operators and

Government Identification of cells and islands Pre-established decision hierarchy

depending on emergency scenario Identification of NCIs for most critical

emergency scenarios Incentives (e.g. sleeping contracts) Long term mitigation oriented plans


Challenges

Identification of Interdependencies (Implies disclosure of sensitive information)

Cooperation among NCIs operators and Government

Management of sensitive information (central vs. distributed)

Panic control

Documents

CNIP 060329JIIRP - UBC1 Design for Survival. Dynamic Infrastructures Coordination José R. Martí, Jorge A. Hollman, Carlos Ventura, Juri Jatskevich, The