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The Power System as a Complex Network. Jim Thorp June 2, 2011. C haos. The fact that a power system could, in principle, behave chaotically was established in 1982. 1

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The power system as a complex network

The Power System as a Complex Network

Jim Thorp

June 2, 2011


C haos

Chaos

  • The fact that a power system could, in principle, behave chaotically was established in 1982.1

  • It was generally believed that the protection and control systems keep the actual power system from steady state chaotic behavior.

  • 1Chaotic motions in the two-degree-of-freedom swing equations

  • Kopell, N.; Washburn, R., Jr.; Circuits and Systems, IEEE Transactions on Volume: 29 , Issue: 11


Outline

Outline:

I Chaos

The fact that the power system has the basic structure required for complicated dynamic behavior manifests itself in other ways.

  • Bifurcations in power systems.

    • Voltage Collapse - bifurcation

    • Hopf bifurcation

  • Fractal domains for load flow solutions,

  • Truncated fractal domains of attraction of equilibria,

  • Transient chaos

  • Power law behavior same system for 35 years

    II DOE Demonstration Projects


Voltage collapse

Voltage Collapse

  • Most major disturbances exhibit voltage instability in addition to real power imbalance. 1997 West Coast, 2003 North East

  • Associated with lack of reactive power

  • In 1980’s Tokyo experienced a pure voltage collapse.


Voltage collapse nose curves

Voltage collapse - Nose Curves

I1

Load increased at constant

power factor

V2 e jq2

V2

V1e jq1

V1

X

SD


Voltage collapse1

Voltage Collapse

  • As load increases

|V2|

Voltage control works correctly

Voltage control inverse

PD


Nose curves v 1 1 x 0 5

Nose Curves: V1=1, X=0.5

V2

PF=.94 leading

PF=.97.

PF=1

PF=.97

PF=.94 lagging

PD


Voltage instability

Voltage Instability

From the nose curve

there is a maximum amount

of power that a line can

transfer before voltage

stability becomes an

Issue.


Analysis and simulation of the rush island event

Analysis and Simulation of the Rush Island Event

32 minutes – operator could not stop the oscillation

  • HopfBifurcation

  • June 12, 1992 in Rush

  • Island Missouri

    Fault resulted in a

    sequence of events

    that ultimately led to

    the event

Angle

degrees

Speed (pu)

3 cycle Fault at Tyson Rush Island


Load flow fractals revisited

Load Flow Fractals Revisited*

Florida equivalent

Georgia equivalent

5

6

7

2

Gen 1 is the reference

2

1

1

fault

3

4

3

real machine

J.S. Thorp and S.A. Naqavi, “Load Flow Fractals” Proceedings of the 28th CDC, Tampa, Florida December 1989, pp 1822-1827


The power system as a complex network

750x750 or 562500 load flow solutions color coded by what equilibrium mod(2p) you converge to from each initial starting point

q3

q2


Self similar a fractal

Self Similara fractal

Spacing 0.48 o

Times 2p

Times 10

Spacing 0.01146 0


The power system as a complex network

PEBS potential energy boundary surface

bowl

mountain

saddle

saddle

Fault on trajectory

Type 1

Type 2

Type 1

stable


The power system as a complex network

Boundary of the domain of attraction of the stable equilibrium

4p

0

4p

0


Fractal forest with lakes tree heights number of iterations

Fractal Forest with Lakes(tree heights =Number of iterations)

The “lakes” are the solid colors areas < 5 iterations

Trees get taller if stopping criteria is stricter


Truncated fractal 562 500 simulations color coded by ultimate equilibrium

Truncated Fractal 562,500 simulations color coded by ultimate equilibrium

  • M. Varghese and J. S. Thorp, "Truncated-Fractal Basin Boundaries in Forced Pendulum Systems," Phys Rev Letters Vol. 60, No. 8, pp 665-668, February 1988


The power system as a complex network

  • The exact boundary of the stability boundary is composed of trajectories that are smooth in R4 but a slice in R2 for x3(0)=g and x4(0) =0 is the truncated fractal


The power system has a protection system like your house

The Power System Has a Protection System(like your house)

  • Circuit Breakers (interrupt 63,000 amps)

  • Relays (Inputs from local Current and Voltage Transformers and from communication channels - output trip signals to circuit breakers)

    Electromechanical (30’s)

    Solid State (60’s)

    Microprocessor-based (late 80’s and 90’s)

    Distributed Intelligence - Utility IntraNet LAN and Routers in substations, fiber on right-of-way

  • In the US system 5,000,000 relays 60% legacy analog


Fault clearing in 3 cycles 1 20 of a second high speed reclose in 20 cycles 1 3 of a second

Fault clearing in 3 cycles = 1/20 of a secondHigh speed reclose in 20 cycles = 1/3 of a second

The protection system was designed to protect equipment – why? – system was overbuilt. The system would work with a line out. Damaged equipment meant customers out of service - high cost. Multiple primary (3 on transmission lines) protection and layers of backup protection. Backup of a backup

A relay can do two things wrong – trip incorrectly or fail to trip. dependability is "the degree of certainty that a relay or relay system will operate correctly",. Security "relates to the degree of certainty that a relay or relay system will not operate incorrectly

The current system is dependable at the expense of security – trigger happy

NERC data: relays involved as contributing factor in 2/3 of major disturbances


Hidden failures

Hidden Failures

  • The “dark side of robustness”

  • Defect or error in relay that does not manifest itself immediately but which can causes a miss-operation when the system is stressed.

  • Largest single cause is maintenance (42% 1977 NYC blackout bent contact). The Internet also has hidden failures caused by maintenance.

  • Northeast Blackout 1965, NY City Blackout 1977, WECC summer of 1996, August 2003


The power system as a complex network

1 year

10 years

> .7 million customers

> 7 million customers

On average, once every

1

Note: 50 million every 35 years added Aug 2003

10

NERC data

0

10

-1

10

Aug 10, 1996

-2

10

104

105

106

107

there will be

an outage of

John Doyle Cal Tech


The power system as a complex network

1 year

10 years

> .7 million customers

> 7 million customers

On average, once every

35 years > 50 million customers

2003 – 1965 = 38 years

1

Note: 50 million every 35 years added Aug 2003

10

NERC data

0

10

Essentially the same power system in 1965 and 2003

-1

10

24 people NBA and Bill Gates

Aug 10, 1996

-2

10

104

105

106

107

there will be

an outage of


The power system as a complex network

MassoudAmin was at EPRI now University of Minnesota in Twin Cities


Power law tail of simulated power loss time series from hidden failure model

Power law “tail” of simulated power loss time series from hidden failure model

  • Fits NERC

  • data


2003 doe report

2003 DOE report

  • I was on the data adequacy subcommittee of the DOE-Canada team.

  • Following begins well into the event and is focused on power flow after things got close to the end


Initial conditions for aug 2003 1 30 pm

Initial conditions for Aug 2003 1:30 pm

Power Plants

> 3000 MW2,000-3,000 MW1,000-2,000 MW450-1,000 MW

< 450 MW

DC

.

Voltage

765kV

Beaver Valley


By 4 06 pm next 10 slides 5 minutes of kirchhoff and relays

By 4:06 pmNext 10 slides 5 minutes of Kirchhoff and relays

Increase

~100 MW

1,000 MW Reversal

500 MW

Loading shifts to remaining paths. Akron and surrounding areas go dark.

Alternate paths into Cleveland entail long 345kV paths or longer loops through PJM’s 500/230 system.

2,800 MW

1,900 MW

-500MW

Harding

Juniper

Chamberlain

Hanna

Star

CantonCentral

SouthCanton

Columbus

Muskingum

4:06 pm


Next event

Next Event:

About three minutes later, the shortest paths from the supply region to Cleveland begin to break up. Two segments are lost that isolate Cleveland from the rest of Ohio.

Kinder-Morgan-200MW

-500MW

Harding

Juniper

Chamberlain

Hanna

Star

CantonCentral

SouthCanton

Muskingum

4:08 – 4:10 pm


Reaction

Reaction:

Increase

500-600 MW

With all direct paths to Cleveland open, power flows up the 765kV network into western Michigan. Within 10 seconds of the two trips, flow thru Michigan goes up 2,000 MW.

Voltage in Michigan and Ohio declines.

4,800 MW

3,700 MW

2,200MW

-500MW

Harding

Juniper

Chamberlain

Hanna

Star

CantonCentral

SouthCanton

Muskingum

4:08 – 4:10 pm


The power system as a complex network

Snapshot:4:10:38 PM

Eastern Michigan is isolated with Cleveland.

Voltage collapsing in Detroit/Cleveland.

MCV

-1265MW

Kinder-Morgan-500MW

-500MW

-2174 MW

Harding

Juniper

Chamberlain

Hanna

Star

CantonCentral

SouthCanton

Muskingum

4:10:38 pm


Snapshot 4 10 38 pm

Snapshot:4:10:38 PM

DC

Voltage

765kV

Some load still remains in the isolated portion of the system, but the only way to flow from the supply region is through PJM & NY. Power surges into Ontario from NY.

Remains of Eastern Michigan and Northern Ohio hang from Ontario.

-2174 MW

-500MW

Beaver Valley

Harding

4:10:38 pm


Next event1

Next Event:

DC

Voltage

765kV

Interface along northern Pennsylvania line opens.

Remaining flow concentrates through New Jersey.

-2174 MW

-500MW

Beaver Valley

Harding

4:10:40 – 4:10:44 pm


Next event2

Next Event:

?

?

DC

Voltage

765kV

Cleveland separates.

Remaining paths through NJ open,walling off NY and NE.Flow from south through NY stops.

-2174 MW

-500MW

Beaver Valley

Harding

4:10:42 – 4:10:45 pm


Next event3

Next Event:

DC

Voltage

765kV

-2174 MW

-500MW

Beaver Valley

Harding

Eastern NY, including NY City,separates from west NY and NE.West NY, now in surplus, flows into Ontario.

New England rebalances as an island.

Ontario shedding load.

4:10:46 – 4:10:55 pm


Next event4

Next Event:

DC

Voltage

765kV

Surplus!

-2174 MW

-500MW

Beaver Valley

Harding

NY reportedly speeds up because of surplus generation, reaching a frequency of 63Hz.

West NY plants shut down from over-frequency.

4:10:50 – 4:11:57 pm


The power system as a complex network

Blackout - August 14, 2003

~$6 billion lost due to 8/14/03 blackout

Cost of Power Disturbances: $25 - $188 billion per year

4


Innovative synchrophasor research will provide better real time information

Innovative Synchrophasor Research Will Provide Better Real-Time Information

  • August 21, 2009* WASHINGTON, DC – The Department of Energy’s Office of Electricity and Energy Reliability today announced that it will provide $4.3 million for four projects that will use innovative synchrophasor research to improve the reliability and efficiency of our Nation’s electricity grid.   These awards are part of the Department’s efforts to modernize the electric grid and enhance the security and reliability of the energy infrastructure.

  • DOE announced it would commit $2.25M to this area.

  • It received 300+ proposals and elected to fund four.

  • Terms

    • Synchrophasor – a phasor measured with synchronous sampling - uses GPS

    • PMU phasor measuring unit

      *I stepped down as ECE Dept Head in Aug 2009-my second retirement


The power system as a complex network

  • Virginia Tech has a prominent role in two of the four totaling $2.6M and a minor role in a third

  • The North American SynchoPhasor Initiative (NASPI) an entity created by DOE, NERC, PNNL, and LBNL has identified more than $1B committed to SynchroPhasor demonstrations and installations


The power system as a complex network

US North American Synchrophasor Initiative NASPI

http://www.naspi.org/

A road map NASPINet

Obama announced 10/27/09

VT involved in two of these

850 PMUs


Why ny times june 8 2009

Why? NY Times June 8,2009

  • On Feb. 26, 2008, a short circuit in a Miami electric power substation and an operator's error gave managers of the nation's electrical grids a glimpse of an uneasy future. The events triggered a chain reaction of power plant and transmission line outages in the state, unleashing sharp swings in voltages and power frequency that blacked out power for nearly 1 million customers in southern and central Florida for up to four hours.

  • A video depicting the Florida incident's rippling spread has been created by Virginia Polytechnic Institute and State University's electrical and computer engineering department, which caught the disturbance on its first-generation grid frequency monitoring network. Some grid executives have downloaded the video on their laptops as a kind of horror flick for engineers of what could happen.


The power system as a complex network

q

Imaginary

q

Real

t=0

  • Introduction to phasors - Steinmetz

  • The starting time defines the phase angle of the phasor.

  • This is arbitrary.

  • However, differences between phase angles are

  • independent of the starting time.


The power system as a complex network

Substation A

Substation B

At different locations

  • Motivation for synchronization

By synchronizing the sampling processes for

different signals - which may be hundreds of miles

apart, it is possible to put their phasors on the same

phasor diagram.


Uses of pmus

Uses of PMUs

  • Monitoring – measure the state of the power system- it was estimated every few seconds

    • Can now be measured 60 times a second

  • Control

    • All control was based on local measurements and a mathematical model of the rest

  • Improved Protection

    • Keep relays from contribution to cascading outages


One of the two projects adaptive relaying

One of the two projectsAdaptive relaying

  • Use PMUs to sense if the system is under stress and guard against a trip due to a hidden failure

  • This will be done on a WECC line for the CIEE grant involving PG&E, SCE, SDG&E

  • We have shown that in 15000 cases ( all rare events) half of which would cause a major disturbance that the number can be reduced to less than 1%. Use data mining techniques


Pmu placement

PMUPlacement:

Reference


The power system as a complex network

Second Project: The first three phase, tracking State Estimator for the Dominion Virginia Power 500kV network

  • Monitoring –

    • Measure the state of the power system 30 times a second to track the dynamics of the system

    • To examine imbalance issues it will be the first three phase estimator. Under balanced conditions one equivalent phase is conventional


Some issues

Some Issues

.

  • All of these present opportunities for cyber security problems. The conventional CS cyber security techniques developed for conventional computer and communication systems can not be applied blindly. The threats are different.


The power system as a complex network

It is rumored that 60% of the one brand of digital relays installed still have the default factory password

It is accepted that access through a digital relay was the entry technique used by the Idaho National Laboratory in the Aurora Project in 2007 to gain remote access to a $1 Million diesel-electric generator and destroyed it. The Aurora tape is at

http://www.youtube.com/watch?v=fJyWngDco3g&feature=related

“Once you’re in, and you know something about synchronizing systems it's all too easy to destroy the engine/generator coupling or the entire engine”


The positive side

The positive side

Jim McIntosh Director of Grid Operations, CAISO

said in a JASONS Workshop in July 2010 in La Jolla that the stimulus PMUs being installed in California would save California from $200M to $300M a year.


Conclusion

Conclusion

  • These are delayed but welcome steps in modernizing the transmission system.

    • Deregulation provided incentives to build generation but not transmission

  • The success of the Smart Grid depends on the transmission system

    • Renewable resources are not near load centers

    • Permitting transmission takes too long (15 years)

    • Spinning Reserves vs. amount of penetration of renewable sources

    • Independent power producers do not want to supply reserves

    • We need affordable storage


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