Exploring Complex Energy Networks

Florian Dorfler

@ETH for “Complex Systems Control”

compute

actuatethrottle

sensespeed

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@ETH for “Complex Systems Control”

system

control

“Simple” control systems are well understood.

“Complexity” can enter in many ways . . .

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A “complex” distributed decision making system

. . .

physical interaction

local subsystems and control

sensing & comm.

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local system

local control

local system

local control

Such distributed systems include large-scale physical systems, engineeredmulti-agent systems, & their interconnection in cyber-physical systems.

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Timely applications of distributed systems controloften the centralized perspective is simply not appropriate

Engineered multi-agent systems

Embedded robotic systems and sensor networks for

high-stress, rapid deployment — e.g., disaster recovery networks

distributed environmental monitoring — e.g., portable chemicaland biological sensor arrays detecting toxic pollutants

autonomous sampling for biological applications — e.g.,monitoring of species in risk, validation of climate andoceanographic models

science imaging — e.g., multispacecraft distributed interferometersflying in formation to enable imaging at microarcsecond resolution

Sandia National Labs MBARI AOSN NASA Terrestrial Planet Finder

J. Cortes MAE247 – Spring 2013

robotic networks decision making social networks

Engineered multi-agent systems

Embedded robotic systems and sensor networks for

high-stress, rapid deployment — e.g., disaster recovery networks

distributed environmental monitoring — e.g., portable chemicaland biological sensor arrays detecting toxic pollutants

autonomous sampling for biological applications — e.g.,monitoring of species in risk, validation of climate andoceanographic models

science imaging — e.g., multispacecraft distributed interferometersflying in formation to enable imaging at microarcsecond resolution

Sandia National Labs MBARI AOSN NASA Terrestrial Planet Finder

J. Cortes MAE247 – Spring 2013

sensor networks

self-organization

Further examples

Transportation networks: users that own part of the network makelocal decisions about the flow circulating over a portion of the network

Social networks: social agents and/or groups make decisions basedon local consensus or trends

Man-machine networks: humans make use of remote dynamicmachines while interacting over networks

Pervasive computing Ground traffic networks The Internet “Smart” power grids

J. Cortes MAE247 – Spring 2013

pervasive computing

Further examples

Transportation networks: users that own part of the network makelocal decisions about the flow circulating over a portion of the network

Social networks: social agents and/or groups make decisions basedon local consensus or trends

Man-machine networks: humans make use of remote dynamicmachines while interacting over networks

Pervasive computing Ground traffic networks The Internet “Smart” power grids

J. Cortes MAE247 – Spring 2013

traffic networks smart power grids

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My main application of interest – the power grid

NASA Goddard Space Flight Center

Electric energy is critical forour technological civilization

Energy supply via power grid

Complexities: multiple scales,nonlinear, & non-local

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Paradigm shifts in the operation of power networks

Traditional top to bottom operation:

I generate/transmit/distribute power

I hierarchical control & operation

Smart & green power to the people:

I distributed generation & deregulation

I demand response & load control

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Challenges & opportunities in tomorrow’s power grid

www.offthegridnews.com

1 increasing renewables & deregulation

2 growing demand & operation at capacity

⇒ increasing volatility & complexity,decreasing robustness margins

Rapid technological and scientific advances:

1 re-instrumentation: sensors & actuators

2 complex & cyber-physical systems

⇒ cyber-coordination layer for smarter grids

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Outline

Introduction

Complex network dynamicsSynchronizationVoltage collapse

Distributed decision makingMicrogridsWide-area control

Conclusions

Modeling: a power grid is a circuit

1 AC circuit with harmonicwaveforms Ei cos(θi + ωt)

2 active and reactive power flows

3 loads demanding constantactive and reactive power

4 synchronous generators& power electronic inverters

5 coupling via Kirchhoff & Ohm

Gij + i Biji j

Pi + i Qi

i

mech.torque

electr.torque

injection =∑

power flows

I active power: Pi =∑

j BijEiEj sin(θi − θj) + GijEiEj cos(θi − θj)I reactive power: Qi = −∑j BijEiEj cos(θi − θj) + GijEiEj sin(θi − θj)

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complex network dynamics:

synchronization

Synchronization in power networkssync is crucial for AC power grids – a coupled oscillator analogy

sync is a trade-off

i(t)

weak coupling & heterogeneous

i(t)

strong coupling & homogeneous8 / 22

Synchronization in power networkssync is crucial for AC power grids – a coupled oscillator analogy

sync is a trade-off

i(t)

weak coupling & heterogeneous Blackout India July 30/31 2012 8 / 22

Our research: quantitative sync tests in complex networks

Sync cond’: (ntwk coupling)∩ (transfer capacity)> (heterogeneity)

θ(t)

θ(t)

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+ 0.1% load

sync cond’violated . . .

Reliability Test System 96 two loading conditions9 / 22

Our research: quantitative sync tests in complex networks

Sync cond’: (ntwk coupling)∩ (transfer capacity)> (heterogeneity)

θ(t)

θ(t)

220

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θ(t)

+ 0.1% load

Reliability Test System 96 two loading conditions

Ongoing work & next steps:

I analysis: sharper results for more detailed models

I analysis to design: hybrid control & remedial actions

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complex network dynamics:

voltage collapse

Voltage collapse in power networks

reactive power instability: loading > capacity ⇒ voltages drop

recent outages: Quebec ’96, Northeast ’03, Scandinavia ’03, Athens ’04

“Voltage collapse is still

the biggest single threat

to the transmission sys-

tem. It’s what keeps me

awake at night.”

– Phil Harris, CEO PJM.

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Voltage collapse on the back of an envelope

reactive power balance at load:

voltage

Esource

Eload

B

Qload

(fixed)

(variable)

EloadEsource0

Qload****

reactivepower

Q

load

= B E

load

(Eload

E

source

)

∃ high load voltage solution ⇔ (load) < (network)(source voltage)2/4

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Our research: extending this intuition to complex networks

IEEE 39 bus system (New England)

Ongoing work & next steps:

existence & collapse cond’: (load) < (network)(source voltage)2/4

analysis to design: reactive compensation & renewable integration12 / 22

distributed decision making:

plug’n’play control inmicrogrids

Microgrids

StructureI low-voltage distribution networks

I grid-connected or islanded

I autonomously managed

ApplicationsI hospitals, military, campuses, large

vehicles, & isolated communities

BenefitsI naturally distributed for renewables

I flexible, efficient, & reliable

Operational challengesI volatile dynamics & low inertia

I plug’n’play & no central authority13 / 22

Conventional control architecture from bulk power ntwks

3. Tertiary control (offline)

Goal: optimize operation

Strategy: centralized & forecast

2. Secondary control (slower)

Goal: maintain operating point

Strategy: centralized

1. Primary control (fast)

Goal: stabilization & load sharing

Strategy: decentralized

Microgrids: distributed, model-free,online & without time-scale separation

⇒ break vertical & horizontal hierarchy

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Plug’n’play architectureflat hierarchy, distributed, no time-scale separations, & model-free

Microgrid

…

…

……

…

…

source # 1 source # 2 source # n

Secondary

Primary

Tertiary

Secondary

Primary

Tertiary

Secondary

Primary

Tertiary

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Plug’n’play architectureflat hierarchy, distributed, no time-scale separations, & model-free

Microgrid:physics& power flow

Diθi =P ∗i − Pi − Ωi

kiΩi =Diθi−∑

j ⊆ inverters

aij ·(

Ωi

Di− Ωj

Dj

)Di ∝ 1/αi

τiEi =−CiEi(Ei − E∗i ) − Qi − ei

κiei =−∑

j ⊆ inverters

aij ·(

Qi

Qi

− Qj

Qj

)−εei

Primary control:mimic oscillators

Tertiary control:marginal costs ∝ gains

Secondary control:diffusive averagingof injections

Ωi/Di

Qi EiθiPi

Qi/Qi

Qi/Qi

. . .

. . .

Ωi/Di

. . .

. . .

Ωk/Dk

Qk/Qk

Qj/Qj

Ωj/Dj

Pi =∑

jBijEiEj sin(θi − θj) + GijEiEj cos(θi − θj)

Qi = −∑

jBijEiEjcos(θi − θj) + GijEiEj sin(θi − θj)

source # i15 / 22

Experimental validation of control & opt. algorithmsin collaboration with microgrid research program @ University of Aalborg

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4DG

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1DG

2DG 3DG

Load 1 Load 2

12Z

23Z

34Z

1Z 2Z

0 10 20 30 40 50300

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330Voltage Magni tudes

Time (s)

Voltage(V

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500Reactive Power Injections

Time (s)

Power(V

AR)

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50.1Voltage Frequency

Time (s)

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quency(H

z)

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800

1000

1200A ct ive Power Injection

Time (s)

Power(W

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t = 22s: load # 2

unplugged

t = 36s: load # 2

plugged back

t ∈ [0s, 7s]: primary

& tertiary control

t = 7s: secondary

control activated

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Experimental validation of control & opt. algorithmsin collaboration with microgrid research program @ University of Aalborg

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1DG

2DG 3DG

Load 1 Load 2

12Z

23Z

34Z

1Z 2Z

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Time (s)

Voltage(V

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0 10 20 30 40 50100

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Time (s)

Power(V

AR)

0 10 20 30 40 5049.5

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50.1Voltage Frequency

Time (s)

Fre

quency(H

z)

0 10 20 30 40 50200

400

600

800

1000

1200A ct ive Power Injection

Time (s)

Power(W

)

t = 22s: load # 2

unplugged

t = 36s: load # 2

plugged back

t ∈ [0s, 7s]: primary

& tertiary control

t = 7s: secondary

control activated

Ongoing work & next steps:

I time-domain modeling & control design

I integrate market/load dynamics & control

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distributed decision making:

wide-area control

Inter-area oscillations in power networks

Blackout of August 10, 1996, resulted from instability of the 0.25 Hz mode

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South ArizonaSoCal

NoCal

PacNW

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North

Montana

Utah

Source: http://certs.lbl.gov

0.25 Hz

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Remedies against inter-area oscillationsconventional control

Physical layer: interconnected generators

Fully decentralized control:

effective against local oscillations

ineffective against inter-area oscillations

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Remedies against inter-area oscillationswide-area control

Physical layer

Fully decentralized control

Distributed wide-area control

identification of architecture? sparse control design? optimality?18 / 22

Trade-off: control performance vs sparsity of architecture

K (γ) = arg minK

(J(K ) + γ · card(K )

)

optimal control = closed-loop performance + γ · sparse architectureper

form

ance

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Case Study: IEEE 39 New England Power Gridsingle wide-area control link =⇒ nearly centralized performance

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F

Fig. 9. The New England test system [10], [11]. The system includes10 synchronous generators and 39 buses. Most of the buses have constantactive and reactive power loads. Coupled swing dynamics of 10 generatorsare studied in the case that a line-to-ground fault occurs at point F near bus16.

test system can be represented by

!i = "i,Hi

#fs"i = !Di"i + Pmi ! GiiE

2i !

10!

j=1,j !=i

EiEj ·

· Gij cos(!i ! !j) + Bij sin(!i ! !j),

"##$##%

(11)

where i = 2, . . . , 10. !i is the rotor angle of generator i withrespect to bus 1, and "i the rotor speed deviation of generatori relative to system angular frequency (2#fs = 2# " 60Hz).!1 is constant for the above assumption. The parametersfs, Hi, Pmi, Di, Ei, Gii, Gij , and Bij are in per unitsystem except for Hi and Di in second, and for fs in Helz.The mechanical input power Pmi to generator i and themagnitude Ei of internal voltage in generator i are assumedto be constant for transient stability studies [1], [2]. Hi isthe inertia constant of generator i, Di its damping coefficient,and they are constant. Gii is the internal conductance, andGij + jBij the transfer impedance between generators iand j; They are the parameters which change with networktopology changes. Note that electrical loads in the test systemare modeled as passive impedance [11].

B. Numerical Experiment

Coupled swing dynamics of 10 generators in thetest system are simulated. Ei and the initial condition(!i(0),"i(0) = 0) for generator i are fixed through powerflow calculation. Hi is fixed at the original values in [11].Pmi and constant power loads are assumed to be 50% at theirratings [22]. The damping Di is 0.005 s for all generators.Gii, Gij , and Bij are also based on the original line datain [11] and the power flow calculation. It is assumed thatthe test system is in a steady operating condition at t = 0 s,that a line-to-ground fault occurs at point F near bus 16 att = 1 s!20/(60Hz), and that line 16–17 trips at t = 1 s. Thefault duration is 20 cycles of a 60-Hz sine wave. The faultis simulated by adding a small impedance (10"7j) betweenbus 16 and ground. Fig. 10 shows coupled swings of rotorangle !i in the test system. The figure indicates that all rotorangles start to grow coherently at about 8 s. The coherentgrowing is global instability.

C. Remarks

It was confirmed that the system (11) in the New Eng-land test system shows global instability. A few comments

0 2 4 6 8 10-5

0

5

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!i /

ra

d

10

02

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04

05

0 2 4 6 8 10-5

0

5

10

15

!i /

ra

d

TIME / s

06

07

08

09

Fig. 10. Coupled swing of phase angle !i in New England test system.The fault duration is 20 cycles of a 60-Hz sine wave. The result is obtainedby numerical integration of eqs. (11).

are provided to discuss whether the instability in Fig. 10occurs in the corresponding real power system. First, theclassical model with constant voltage behind impedance isused for first swing criterion of transient stability [1]. This isbecause second and multi swings may be affected by voltagefluctuations, damping effects, controllers such as AVR, PSS,and governor. Second, the fault durations, which we fixed at20 cycles, are normally less than 10 cycles. Last, the loadcondition used above is different from the original one in[11]. We cannot hence argue that global instability occurs inthe real system. Analysis, however, does show a possibilityof global instability in real power systems.

IV. TOWARDS A CONTROL FOR GLOBAL SWING

INSTABILITY

Global instability is related to the undesirable phenomenonthat should be avoided by control. We introduce a keymechanism for the control problem and discuss controlstrategies for preventing or avoiding the instability.

A. Internal Resonance as Another Mechanism

Inspired by [12], we here describe the global instabilitywith dynamical systems theory close to internal resonance[23], [24]. Consider collective dynamics in the system (5).For the system (5) with small parameters pm and b, the set(!,") # S1 " R | " = 0 of states in the phase plane iscalled resonant surface [23], and its neighborhood resonantband. The phase plane is decomposed into the two parts:resonant band and high-energy zone outside of it. Here theinitial conditions of local and mode disturbances in Sec. IIindeed exist inside the resonant band. The collective motionbefore the onset of coherent growing is trapped near theresonant band. On the other hand, after the coherent growing,it escapes from the resonant band as shown in Figs. 3(b),4(b), 5, and 8(b) and (c). The trapped motion is almostintegrable and is regarded as a captured state in resonance[23]. At a moment, the integrable motion may be interruptedby small kicks that happen during the resonant band. That is,the so-called release from resonance [23] happens, and thecollective motion crosses the homoclinic orbit in Figs. 3(b),4(b), 5, and 8(b) and (c), and hence it goes away fromthe resonant band. It is therefore said that global instability

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Authorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on June 10, 2009 at 14:48 from IEEE Xplore. Restrictions apply.

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Ongoing work & next steps:

cyber-physical security: corruption of wide-area signals

data-driven & learning: what if we don’t have a model?20 / 22

wrapping up

Summary & conclusions

Complex systems control

distributed, networks, & cyber-physical

Apps in power networks

complex network dynamics

distributed decision making

Surprisingly related apps

coordination of multi-robot networks

learning & agreement in social networks

and many others . . .

. . .

physical interaction

local subsystems and control

sensing & comm.

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local system

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local system

local control

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Acknowledgements

SynchronizationJohn Simpson-PorcoMisha ChertkovFrancesco BulloEnrique MalladaChanghong ZhaoMatthias Rungger

Voltage dynamicsMarco TodescatoBasilio GentileSandro Zampieri

Wide-area controlDiego RomeresMihailo JovanovicXiaofan Wu

MicrogridsQuobad ShafieeJosep GuerreroSairaj DhopleAbdullah HamadehBrian JohnsonJinxin ZhaoHedi Boattour

Robotic coordinationBruce Francis

Cyber-physical securityFabio Pasqualetti

Port-HamiltonianFrank AllgowerJorgen Johnsen

Social networksMihaela van der SchaarYuanzhang Xiao

...

Group @ ETH

Bala Kameshwar Poolla

plus some students onother prof’s payrolls . . .

more people to join . . .

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thank you