energy system risk assessmentenergy system risk assessment james d. mccalley, [email protected] iowa...
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Energy System Risk AssessmentEnergy System Risk Assessment
James D. McCalley, [email protected] State University
Workshop on Overarching Issues in Risk Analysis
October 28, 2005
Ames, Iowa
Five Infrastructure ProblemsFive Infrastructure Problems
1. Transmission control center economy/security system maneuvering
2. Responding to low probability, high consequence events with blackout potential
3. Maintenance: maximizing cumulative risk reduction with limited resources
4. Investing in capital-intensive infrastructure under uncertainty
5. Reliability/economy of national energy transportation system: electric, gas, coal.
Objective: Present five energy infrastructure problems involving risk, with some level of approach to each.
Energy control centers
Security assessmentSecurity assessment• Security: ability of the power system to withstand any of a defined set of next contingencies• Contingencies:
• faults followed by removal of faulted element(s)• “N-k”: k is # of removed elements. Prob ↓ as k ↑• Industry plans for, prepares for: N-1, some N-2.
• Consequences:• Circuit overload• Low voltage
• Voltage instability• Cascading
• Uncontrolled load interruption Blackouts
All control centers analyze these; they are precursors to next level consequences.
Reducing risk?Reducing risk?• Action must be taken if any one prescribed contingency violates performance criteria• Action: Redispatch generation (involves $$)
Prob 1: Optimal Power Flow (OPF)Minimize GenCosts
subject to1. Power flow equations2. Normal condition constraints
Prob 2: Security-constrained OPFMinimize GenCosts
subject to1. Power flow equations2. Normal condition constraints3. Security constraints
But risk is not quantified in these formulations:• Contingency probability varies• Probability of voltage instability/cascading varies
A Stressed SystemA Stressed System
•System is heavily stressed, but there are many companies making lots of $$ for their shareholders !
• August 12, 1999, Thursday, 2 pm• Ambient temperature is ~103 degrees F and still rising• Large city control center• Loading above that in 1999 summer peak planning case
• Bus1 500/230 kV bank has Bus1 500/230 kV bank has been over 100% since noonbeen over 100% since noon
•• It’s loss will result in collapseIt’s loss will result in collapse•• Now, at 2:10 pm, it is 110%Now, at 2:10 pm, it is 110%
Bus 1 500
Bus 1 230
Bus 1 115
Bus 2 500Bus 2 500
Bus2 230Bus2 230
Bus 2 115Bus 2 115
110%
Imports Operator’s view Operator’s view at 2:10 pm, at 2:10 pm, 8/12/998/12/99
200 MW flow
94%
93%
0.95 pu volts
Simulation Simulation Results of a Results of a Preventive ActionPreventive Action
Bus 1 500Bus 1 500
Bus 1 230Bus 1 230
Bus 1 115Bus 1 115
Bus 2 500Bus 2 500
Bus2 230Bus2 230
Bus 2 115Bus 2 115
103%
Imports
0 MW flow
101%
104%
0.91 pu volts
Risk Calculation
Evaluated using variants of power flow calculation (Newton-Raphson iterative solution to high dimensional nonlinear algebraic equations)
Forecasted operatingcondition
Low voltage
Cascading
Overload
Voltage instability::
p(1)
p(2)
p(3)
p(n)
∑∑=
jtype
problemj
kiescontingenc
kXSevkpXRisk )|()()(
Severity functions...• Risk:Expected severity in next hour. • Severity=1.0 atimposed limit.• Risk=1.0 isequivalent to one violation.
0.90
1
Sev
erity
Voltage magnitude (p.u.) 0.95
Fig 6.4: Low voltage severity function
90
1
Sev
erity
100 Percent loading
Fig 6.7: Overload severity function
0 5 Fig 6.9: Voltage instability severity function
1
%margin
Sev
erity
1E6
This value assigned to provide Risk=1.0 if lowest probability contingency (p=1E-6) results in voltage instability.
This amount of risk equates to what industry has indicated is unacceptable.
Contingency Probability EstimationDistinguish between contingency probabilities based on
• Historical outage data
• Physical attributes: length, voltage level, geography
• Temporal attributes: weather
1. Separate outage data into 24 pools (8 zones x 3 kV levels)
2. For each pool,
• separate outage data into “weather blocks” and compute failure rate/mile for each block, resulting in about 30 values
• Use linear regression to determine dependence of failure rate on weather
3. On-line, evaluate failure rates/mile for each pool, multiply by line length for each circuit.
Contingency Probability Estimation
1 2 3 4 5 6 7 8 9 1011
1 2 3 4 5 6 7 8 9101112
0
2
4
6
8
Windspeed(miles/hour)/3Temperature(F)/10
Num
ber o
f out
ages
(200
1~20
04)
North central data
24
68
10
05101520
-14
-13
-12
-11
-10
-9
x2:Wind speed (miles/h)/3x1:Temperature (F)/10
y Lo
g(Fa
ilure
rate
)
0 5 10 15 20 253
3.5
4
4.5
5
5.5
6
6.5
7x 10-5
Time(one day)
failu
re ra
te
Visualization over time
…and operating conditions
and the ability to drill-down to identify nature & cause of high risk
Top 30 High-Risk Contingencies (from 714)Showing resulting OL+LV risk
…and space
Prob 3: Risk-Objective SCOPFMinimize GenCosts +β×Risk
subject to1. Power flow equations2. Normal condition constraints3. Security constraints
• This formulation requires sensitivity of risk to each generator injection. • Why is this formulation an improvement?
Deterministic security limits (normal and contingency) are enforced, on targeted basis
Overall risk is reduced.The balance between cost and risk reduction
may be observed (and controlled).
Risk reduction using “targeting” redispatchProb 2: Security-constrained OPFMinimize GenCosts
subject to1. Power flow equations2. Normal condition constraints3. Security constraints
Risk reduction using “targeting” redispatch
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
6.65 6.66 6.67 6.68 6.69 6.7 6.71 6.72 6.73
β=10000β=6000
β=5500
β=5200
β=5000
β=4800
Risk
Cost of redispatch
NN--k contingenciesk contingencies
What to say, operationally, about high-order (N-k, k>1) contingencies?
• If probability is high, put it in contingency list and treat it as any other N-1 contingency (e.g., take preventive actions as needed)
• If probability is low, monitor it, perhaps identify corrective actions for it should it occur, but do not spend money in preventive actions.
How to identify high-probability N-k contingencies?
Probability OrderProbability OrderDefinition: the probability order of a contingency is the number of independent events necessary for occurrence of that contingency.
Probability order is a rough way of comparing probabilities of different contingencies.
Assume the probability of any single event (faulted line, protection failure, etc) is 10-4.
Then, for independent events, occurrence of • two events is P(A)*P(B)=10-8 (order 2), • three events P(A)*P(B)*P(C)=10-12 (order 3), etc.
But probability of 2 dependent events is P(A)P(B|A), and P(B|A) can be 1.0, so the probability of the two dependent events is P(A).
Classification of NClassification of N--k contingenciesk contingenciesProtection system failures (NERC category C or D):Protection system failures (NERC category C or D):
Inadvertent operation, failure is exposed after a firstInadvertent operation, failure is exposed after a first--faultfaultFailure to operate when needed.Failure to operate when needed.
Both cases require Both cases require fault+existencefault+existence of protection failure: order=2.of protection failure: order=2.Are there single events that cause NAre there single events that cause N--k outages? Yes,…k outages? Yes,…
1.1. Common mode outage (NERC class D) such as hurricane, earthquake,Common mode outage (NERC class D) such as hurricane, earthquake, airplaneairplane2.2. Breaker fault (NERC class D)Breaker fault (NERC class D)3.3. Substation topology problem (maintenance or careless switching)Substation topology problem (maintenance or careless switching)4.4. Cascading following a firstCascading following a first--faultfault
But common mode and breaker faults have probabilities closer to But common mode and breaker faults have probabilities closer to order 2. This leaves #3 and#4.order 2. This leaves #3 and#4.Since #3 requires only a single fault, it has order 1.Since #3 requires only a single fault, it has order 1.Since #4 is dependent, it can have order close to 1.Since #4 is dependent, it can have order close to 1.
Example of topological weakness
BR
EA
KE
R-1
BR
EA
KE
R-2
BR
EA
KE
R-3
SWIT
CH
-1
SWIT
CH
-2
SWIT
CH
-3 BUS-1
BUS-2
Line-1 Line-2 Line-3
SWIT
CH
-1
SWIT
CH
-2
SWIT
CH
-3
BUS-1
BUS-2
Line-1 Line-2 Line-3
There are thousands of such substations in a model.
We perform a topological graph search using the breaker/switch and connectivity data to identify these high-probability N-k contingencies.
Remove bus 1 from service, and a single fault on any line results in N-3 contingency.
CascadingCascading risk depends on:• Occurrence probability of a first contingency k (Level 0).• Probability of all possible Level 1 trips, computed as a function of
post-contingency loading on remaining circuits• Severity of cascading sequence following each Level 1 trip,
computed as a function of number of circuits lost, or if no convergence, as a function of voltage collapse severity.
Level: 0 1 2 3 4 5 6 7 8 9 10 11 12…
NL1=5NL2=8
NL4=Voltage instab severity
NL5=12
NL3=1
P1
P2
P3
P4
P5
∑=
=m
iLii NPkPkRisk
1*)()(
P(k)
Graphic comparison of different probability models for N-k contingencies
110 -10
10 -8
10 -6
10 -4
10 -2
10 0
2 3 4 5 6 7 8
Number of lines lost in each contingency (log scale)
Log-Probability
Poisson Model (Concave)
Cluster Model (Concave)
Power Law Model (Straight line) Observed Prob.
( ) ( )
1
1
3.1151 1
1 1
0.12657 1
3.115 2Pr( 3.115, 1.12657)
1
1.1266 1 3.115 for cluster model 1.1266 1 3.115 1.1266 1 3.115
Pr 0.12657 0.12657 1 ! for poisson
x
x
xX x
x
X x e x
α μ
λ
−
−
− −
− −
− −
⎛ ⎞+ −= = = = ⎜ ⎟
−⎝ ⎠
⎛ ⎞−⎛ ⎞× × ⎜ ⎟⎜ ⎟− + − +⎝ ⎠ ⎝ ⎠
= = = −
3.78
model
Pr(X 3.78 ) 0.9098 for pow er law model -x p x
⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪ = = =⎪⎩
Final result for maximum likelihood estimation of parameters for the three probability models
WHAT HAPPENED ON WHAT HAPPENED ON AUGUST 14, 2003???AUGUST 14, 2003???
1. 12:05 Conesville Unit 5 (rating 375 MW)2. 1:14 Greenwood Unit 1 (rating 785 MW)3. 1:31 Eastlake Unit 5 (rating: 597 MW)
INITIATING EVENT
4. 2:02 Stuart – Atlanta 345 kV5. 3:05 Harding-Chamberlain 345 kV6. 3:32 Hanna-Juniper 345 kV7. 3:41 Star-South Canton 345 kV8. 3:45 Canton Central-Tidd 345 kV9. 4:06 Sammis-Star 345 kV
SLOW PROGRESSION
10. 4:08:58 Galion-Ohio Central-Muskingum 345 kV11. 4:09:06 East Lima-Fostoria Central 345 kV12. 4:09:23-4:10:27 Kinder Morgan (rating: 500 MW; loaded to 200 MW)13. 4:10 Harding-Fox 345 kV14. 4:10:04 – 4:10:45 20 generators along Lake Erie in north Ohio, 2174 MW15. 4:10:37 West-East Michigan 345 kV16. 4:10:38 Midland Cogeneration Venture, 1265 MW17. 4:10:38 Transmission system separates northwest of Detroit18. 4:10:38 Perry-Ashtabula-Erie West 345 kV19. 4:10:40 – 4:10:44 4 lines disconnect between Pennsylvania & New York20. 4:10:41 2 lines disconnect and 2 gens trip in north Ohio,1868MW21. 4:10:42 – 4:10:45 3 lines disconnect in north Ontario, New Jersey, isolates NE part
of Eastern Interconnection, 1 unit trips, 820 mw22. 4:10:46 – 4:10:55 New York splits east-to-west. New England and Maritimes
separate from New York and remain intact.23. 4:10:50 – 4:11:57 Ontario separates from NY w. of Niagara Falls & w. of St. Law.
SW Connecticut separates from New York, blacks out.
FAST PROGRESSION
Location Date Scale in term of MW or Population
Collapse time
US-NE 10/9/65 20GW, 30M people 13 mins New York 7/13/77 6GW, 9M people 1 hour
France 1978 29GW 26 mins Japan 1987 8.2GW 20mins
US-West 1/17/94 7.5GW 1 min US-West 12/14/94 9.3GW US-West 7/2/96 11.7GW 36 secondsUS-West 7/3/96 1.2GW > 1 min US-West 8/10/96 30.5GW > 6 mins
Brazil 3/11/99 25GW 30 secs US-NE 8/14/03 62GW, 50M people > 1 hour London 8/28/03 724 MW, 476K people 8 secs
Denmark & Sweden 9/23/03 4.85M people 7mins Italy 9/28/03 27.7GW, 57M people 27mins
Larger Blackouts in Last 40 years
An Analogy to Air Traffic ControlAn Analogy to Air Traffic Control
Unfolding Cascading Event
Remedial action by the operator
Normal Stage
Emergency Stage
Catastrophic Outcome
Large area blackout avoided
Emergency Response System
Without action
time
Airplanes getting too close to each other Avoidance Action
by the TCAS
Normal Stage Emergency
Stage
Collision
Collision avoided
Traffic Alert and Collision Avoidance System
Without action
Rapid Response to Unfolding EventsRapid Response to Unfolding Events
Bus voltage
Contingency-1: Fau lt +N-3 outage from stuck breaker
Action-1: insert shunt cap
Behavior-2:Fast voltage co llapse due to lack of reactive power
Behavior-3:Slow voltage collapse due to LTC action
Action-2: block LTCs
10 sec 5 min
Behavior-1: System is normal. Everything is within lim it.
Time 0
1.0
B1 C1
S1 S2 S3
S4
S5 S7
S6
A1
B2
A2
B3
A Dynamic Decision Event TreeA Dynamic Decision Event Tree
Power System Maintenance (actually an interesting subject)
Deterioration level 4
(Failed)
Deterioration level 3
Deterioration level 2
Deterioration level 1 New
Haz
ard
Rat
e
Time
Δlambda
Δt
Before maintenance (Level 3)
After maintenance (Level 1)
When maintenance needs require resources that exceed When maintenance needs require resources that exceed available resources, how to strategically allocate available available resources, how to strategically allocate available resources to maximize benefit gained from them?resources to maximize benefit gained from them?
Fault from power line to trees Tree trimming
Examples of failure modes & maintenanceExamples of failure modes & maintenance
Transformer oil degradation and insulation failure
Oil Reconditioning
Cumulative risk calculation
Year long, hourly risk variation for each contingency
Contingencyprobabilities
Power system simulator
Mid-term load forecast
Benefit: Maintenance reduces contingency probabilities which reduces cumulative-over-time risk
Obtaining failure rate reduction
ajk
deterioration
function g(c(T+1))
Historical data c(t) t=1,…,T
Statistical
Processing
Most recent observation
c(T+1)
a23 a12 a34 Level 1 (new)
Level 2 (minor)
Level 3 (major)
Level 4 (failed)
⎭⎬⎫
⎩⎨⎧
=Δ
=Δ ∑8760
00
00
),(),()(
),,(),,(t
tkRtkCumRiskkp
tkmptkmCumRisk
Developed for each failure mode of each component
Optimization∑ ∑∑
component task time time) task,ent,ion(componRiskReduct
subject to:budget limits, crew constraints for different maintenance categories, timing constraints for maintenance tasks requiring outages
maximize
0
20
40
60
80
100
120
140
160
180
200
Quarterly allocated CRR and resource allocation for different maintenance categories -Case B
Tree Trimming
Trans Line
Xfmr Minor
Xfmr Major
CB Maint.
Quarter 1Quarter 2 Quarter 3
Quarter 4Fiscal Year
ECRR (k$)
Labor (100Hrs)Cost (k$)
The National Electric Energy SystemThe National Electric Energy System
Fig. 1: Gas, Rail, and Electric Trans portation Systems
NEES:NEES: iintegrated infrastructure associated with ntegrated infrastructure associated with production, transportation, storage, endproduction, transportation, storage, end--use of four use of four energy forms: electricity, gas, coal, and water.energy forms: electricity, gas, coal, and water.NEES integrity depends on NEES integrity depends on
electric generation and transmission subsystems electric generation and transmission subsystems ability to produce and transport the fuelability to produce and transport the fuel
Vulnerability to disruptions is due to natural causes, Vulnerability to disruptions is due to natural causes, equipment failure, labor unavailability, equipment failure, labor unavailability, communication failures, terrorist attacks.communication failures, terrorist attacks.
The National Electric Energy SystemThe National Electric Energy System
The NEESRainfall & Snow
RunoffGas Wells Coal Mines
… … …
Raw Energy Supplies
WaterHydraulic System
GasPipelines
CoalRailroads, Barge
… ……
Gas StorageReservoirs Coal PilesStorage & Transport. Systems
… … …
… … …
Generation System
… … … … … … … … … … …Electric Energy Demand
ElectricityElectric Transmission System
Electric Transm. System :
Nuclear Plants
Other Plants
(wind, solar, etc)
Examples of DisruptionsExamples of Disruptions
Lightning strike
Labor strikesPekin, IL: 13 345kV transmission lines destroyed by a tornado in May 2003
El Paso, NM, 2000: Gas pipeline rupture
Ellet Valley, VA, 2003: Norfolk Southern coal train derailed
Examples of DisruptionsExamples of Disruptions
Black Thunder, WY, 2005: Coal train derailment
1993 Flood Stops Barge Traffic
Disruption to Gulf Coast Gas Production from Katrina/Rita
Examples of Disruptions Examples of Disruptions On August 22, 2000, a 30 inch pipeline ruptured in New On August 22, 2000, a 30 inch pipeline ruptured in New Mexico, and was forced out of service, taking with it two Mexico, and was forced out of service, taking with it two parallel lines that together form a major artery into Californiaparallel lines that together form a major artery into California. . This decreased availability of gas in California, significantly This decreased availability of gas in California, significantly driving up price as seen by owners of gasdriving up price as seen by owners of gas--fired electricity fired electricity suppliers as well as residential and commercial gas endsuppliers as well as residential and commercial gas end--users. users. At the same time, California was experiencing a decrease in At the same time, California was experiencing a decrease in precipitation, forced outage of several large coalprecipitation, forced outage of several large coal--fired units, fired units, and a weakened transmission system. These factors and a weakened transmission system. These factors contributed to what is now well known as the California contributed to what is now well known as the California energy crisis, characterized by electricity shortages and high energy crisis, characterized by electricity shortages and high prices. Yet, electricity endprices. Yet, electricity end--users were insulated from the users were insulated from the electricity price increases because of regulatory price caps. electricity price increases because of regulatory price caps. Therefore, as gas prices rose, and electricity prices did not, Therefore, as gas prices rose, and electricity prices did not, many consumers quite naturally switched from gas heat to many consumers quite naturally switched from gas heat to electric heat, further exacerbating the electricity shortage. electric heat, further exacerbating the electricity shortage.
Examples of Disruptions Examples of Disruptions
The 1993 Mississippi River flood caused major disruptions The 1993 Mississippi River flood caused major disruptions in the U.S. energy supply. The Mississippi River itself is a in the U.S. energy supply. The Mississippi River itself is a crucial part of the Midwest’s economic infrastructure. crucial part of the Midwest’s economic infrastructure. Barges carry 20% of the nation’s coal, a third of its Barges carry 20% of the nation’s coal, a third of its petroleum, and half of its exported grain. Barge traffic was petroleum, and half of its exported grain. Barge traffic was halted for two months; carriers lost an estimated $1 million halted for two months; carriers lost an estimated $1 million per day. Some power plants along the river saw their coal per day. Some power plants along the river saw their coal stocks dwindle from a twostocks dwindle from a two--month supply to enough to last month supply to enough to last just for a few days.just for a few days.
Examples of Disruptions Examples of Disruptions Ten giant coal mines in Wyoming 's Powder River Basin produce neTen giant coal mines in Wyoming 's Powder River Basin produce nearly arly 40% of the U.S. supply. And coal powers more than half of U.S. 40% of the U.S. supply. And coal powers more than half of U.S. electricity generation. A heavy snowstorm blanketed Wyoming on Melectricity generation. A heavy snowstorm blanketed Wyoming on May ay 11 2005, just as the ice in the surrounding mountains had begun 11 2005, just as the ice in the surrounding mountains had begun to thaw. to thaw. Icy water and coal dust merged into a thick, dirty slurry and ooIcy water and coal dust merged into a thick, dirty slurry and oozed across zed across a 100a 100--mile section of railroad freight track, causing two derailments mile section of railroad freight track, causing two derailments with with major track damage. Spotmajor track damage. Spot--market prices for the basin's coal are up nearly market prices for the basin's coal are up nearly 70% year to date. The hot summer weather left power plants with 70% year to date. The hot summer weather left power plants with especially low stockpiles exiting the summer, so utilities may nespecially low stockpiles exiting the summer, so utilities may not be able ot be able to rebuild stockpiles until after next year. As a result, electrto rebuild stockpiles until after next year. As a result, electric utilities ic utilities have been relying more on natural gashave been relying more on natural gas--fired plants to satisfy demand. fired plants to satisfy demand. Then the full effects of Katrina and Rita on coal (Mississippi bThen the full effects of Katrina and Rita on coal (Mississippi barge arge traffic) and on gas (Gulf wells) are not yet known. traffic) and on gas (Gulf wells) are not yet known.
How will prices and availability of electric energy evolve in thHow will prices and availability of electric energy evolve in the next year?e next year?
Reliability of the NEESReliability of the NEES
Identify conditions that significantly impact price Identify conditions that significantly impact price and availability of electrical energy.and availability of electrical energy.Assess the overall reliability of the energy system Assess the overall reliability of the energy system in order to elaborate preventive and corrective in order to elaborate preventive and corrective plans to avoid massive energy shortages.plans to avoid massive energy shortages.Present an network flow optimization model for Present an network flow optimization model for reliability assessment of the NEES, where the reliability assessment of the NEES, where the subsystems are analyzed together in a single subsystems are analyzed together in a single integrated mathematical framework for the energy integrated mathematical framework for the energy production, transportation, storage, generation, production, transportation, storage, generation, and transmission. and transmission.
HighHigh--level Representationlevel Representation
Period 1 for coal
Period 1for
electricity
Period 1 for gas
Period 2for
electricity
Period 3for
electricity
Period 4for
electricity
Period 2 for gas
… … … …
… … … …Period 2 for coal
Period 5for
electricity
Period 3 for gas
Period 6for
electricity
Period 7for
electricity
Period 8for
electricity
Period 4 for gas
… … … …
… … … …
……… …
Example of network representationExample of network representationS
CG1 CG2
CP2CP1
CS1
GG1 GG2
GP1
GS1
WG1
WS1
CA1,1 CA2,1
CG1,1 CG2,1 GG1,1 GG2,1 WG1,1
CA1,2 CA2,2
CG1,2 CG2,2 GG1,2 GG2,2 WG1,2
CA1,3 CA2,3
CG1,3 CG2,3 GG1,3 GG2,3 WG1,3
CG1 CG2
CP2CP1
CS1
GG1 GG2
GP1
GS1
WG1
WS1
CA1,1 CA2,1
CG1,1 CG2,1 GG1,1 GG2,1 WG1,1
CA1,2 CA2,2
CG1,2 CG2,2 GG1,2 GG2,2 WG1,2
CA1,3 CA2,3
CG1,3 CG2,3 GG1,3 GG2,3 WG1,3
Raw-Energy time step 1
Raw-Energy time step 2
Electric time step 1 Electric time step 2 Electric time step 3 Electric time step 1 Electric time step 2 Electric time step 3
b1(CA1,1) b1(CA2,1) b1(CA1,2) b1(CA2,2) b1(CA1,3) b1(CA2,3) b2(CA1,1) b2(CA2,1) b2(CA1,2) b2(CA2,2) b2(CA1,3) b2(CA2,3)
b2(WS1)b2(GS1)b1(WS1)
b1(CS1)
b1(GS1)
b2(CS1)
SS
CG1 CG2
CP2CP1
CS1
GG1 GG2
GP1
GS1
WG1
WS1
CA1,1 CA2,1
CG1,1 CG2,1 GG1,1 GG2,1 WG1,1
CA1,2 CA2,2
CG1,2 CG2,2 GG1,2 GG2,2 WG1,2
CA1,3 CA2,3
CG1,3 CG2,3 GG1,3 GG2,3 WG1,3
CG1 CG2
CP2CP1
CS1
CG1CG1 CG2CG2
CP2CP2CP1CP1
CS1CS1
GG1 GG2
GP1
GS1
GG1GG1 GG2GG2
GP1GP1
GS1GS1
WG1
WS1
WG1WG1
WS1WS1
CA1,1 CA2,1
CG1,1 CG2,1 GG1,1 GG2,1 WG1,1
CA1,2 CA2,2
CG1,2 CG2,2 GG1,2 GG2,2 WG1,2
CA1,3 CA2,3
CG1,3 CG2,3 GG1,3 GG2,3 WG1,3
CA1,1 CA2,1
CG1,1 CG2,1 GG1,1 GG2,1 WG1,1
CA1,1CA1,1 CA2,1CA2,1
CG1,1CG1,1 CG2,1CG2,1 GG1,1GG1,1 GG2,1GG2,1 WG1,1WG1,1
CA1,2 CA2,2
CG1,2 CG2,2 GG1,2 GG2,2 WG1,2
CA1,2CA1,2 CA2,2CA2,2
CG1,2CG1,2 CG2,2CG2,2 GG1,2GG1,2 GG2,2GG2,2 WG1,2WG1,2
CA1,3 CA2,3
CG1,3 CG2,3 GG1,3 GG2,3 WG1,3
CA1,3CA1,3 CA2,3CA2,3
CG1,3CG1,3 CG2,3CG2,3 GG1,3GG1,3 GG2,3GG2,3 WG1,3WG1,3
CG1 CG2
CP2CP1
CS1
GG1 GG2
GP1
GS1
WG1
WS1
CA1,1 CA2,1
CG1,1 CG2,1 GG1,1 GG2,1 WG1,1
CA1,2 CA2,2
CG1,2 CG2,2 GG1,2 GG2,2 WG1,2
CA1,3 CA2,3
CG1,3 CG2,3 GG1,3 GG2,3 WG1,3
CG1 CG2
CP2CP1
CS1
CG1CG1 CG2CG2
CP2CP2CP1CP1
CS1CS1
GG1 GG2
GP1
GS1
GG1GG1 GG2GG2
GP1GP1
GS1GS1
WG1
WS1
WG1WG1
WS1WS1
CA1,1 CA2,1
CG1,1 CG2,1 GG1,1 GG2,1 WG1,1
CA1,2 CA2,2
CG1,2 CG2,2 GG1,2 GG2,2 WG1,2
CA1,3 CA2,3
CG1,3 CG2,3 GG1,3 GG2,3 WG1,3
CA1,1 CA2,1
CG1,1 CG2,1 GG1,1 GG2,1 WG1,1
CA1,1CA1,1 CA2,1CA2,1
CG1,1CG1,1 CG2,1CG2,1 GG1,1GG1,1 GG2,1GG2,1 WG1,1WG1,1
CA1,2 CA2,2
CG1,2 CG2,2 GG1,2 GG2,2 WG1,2
CA1,2CA1,2 CA2,2CA2,2
CG1,2CG1,2 CG2,2CG2,2 GG1,2GG1,2 GG2,2GG2,2 WG1,2WG1,2
CA1,3 CA2,3
CG1,3 CG2,3 GG1,3 GG2,3 WG1,3
CA1,3CA1,3 CA2,3CA2,3
CG1,3CG1,3 CG2,3CG2,3 GG1,3GG1,3 GG2,3GG2,3 WG1,3WG1,3
Raw-Energy time step 1
Raw-Energy time step 2
Electric time step 1 Electric time step 2 Electric time step 3 Electric time step 1 Electric time step 2 Electric time step 3
b1(CA1,1) b1(CA2,1) b1(CA1,2) b1(CA2,2) b1(CA1,3) b1(CA2,3) b2(CA1,1) b2(CA2,1) b2(CA1,2) b2(CA2,2) b2(CA1,3) b2(CA2,3)
b2(WS1)b2(GS1)b1(WS1)
b1(CS1)
b1(GS1)
b2(CS1)
NodesNodes: actual facilities : actual facilities of the NEES of the NEES
ArcsArcs: transportation : transportation routes and modesroutes and modes
Energy system facilities can be represented Energy system facilities can be represented adequately by arcs and nodes. adequately by arcs and nodes. A network model allows representation of A network model allows representation of capacities, costs, and efficiencies.capacities, costs, and efficiencies.Bulk energy movements can be Bulk energy movements can be represented as flows.represented as flows.Take advantage of fast and existent Take advantage of fast and existent network optimization algorithms:network optimization algorithms:
Generalized minimum cost (GMC)Generalized minimum cost (GMC)Generalized maximum flow (GMF)Generalized maximum flow (GMF)
Capacities: uncertainty due to disruptionsCapacities: uncertainty due to disruptionsCosts/prices: market uncertaintyCosts/prices: market uncertaintyDemand: end user uncertaintyDemand: end user uncertainty
Where is the Where is the Randomness in the Randomness in the
Network Model?Network Model?
Why a Network Model?Why a Network Model?
Stochastic Network Model
Research OutlineResearch OutlineBuild an operational model, which should integrate and assess reBuild an operational model, which should integrate and assess reliability of liability of the NEES.the NEES.Gather & organize the necessary data of the different subsystem Gather & organize the necessary data of the different subsystem networks.networks.Predict and represent uncertainty associated with extreme continPredict and represent uncertainty associated with extreme contingencies: It is gencies: It is necessary to build a model to represent the uncertainty associatnecessary to build a model to represent the uncertainty associated to ed to catastrophic events and their effects in the energy grid.catastrophic events and their effects in the energy grid.Define plausible and credible multiple contingency scenarios, usDefine plausible and credible multiple contingency scenarios, using 2 different ing 2 different criteria: Cascading events and common mode events.criteria: Cascading events and common mode events.Evaluate the impact on the NEES of the contingency's scenariosEvaluate the impact on the NEES of the contingency's scenariosEvaluate how the effects of those contingencies propagate geograEvaluate how the effects of those contingencies propagate geographically and phically and in time.in time.
Conclusions
Transmission system risk assessment and related decision Transmission system risk assessment and related decision depends on:depends on:
Identification of contingencies and their probabilitiesIdentification of contingencies and their probabilitiesRigorous analysis of contingency consequencesRigorous analysis of contingency consequencesAppropriate operator decisionAppropriate operator decision--support tools for both preventive support tools for both preventive and corrective controland corrective controlLongLong--term implementation of strategic resource allocation for term implementation of strategic resource allocation for maintenancemaintenanceRiskRisk--informed decisions in facility investmentinformed decisions in facility investment
Delivering reliable and economic electric energy also Delivering reliable and economic electric energy also depends on understanding the entire, integrated energy depends on understanding the entire, integrated energy system from fuel source to electric distribution substation.system from fuel source to electric distribution substation.