Real-time Optimization for Power Distribution …...Real-time Optimization for Power Distribution...

Real-time Optimization for Power Distribution SystemsAdrian Hauswirth

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Laboratory Adrian Hauswirth 2017-05-23 1

Agenda

Introduction

Facts and terminology everyone should know about

Tutorial in control & optimization

Transmission system operations

Active distribution grids

Research: combining control and optimization in a novel way

Conclusion

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Electric Energy Supply

[BFE, Schweizerische Gesamtenergiestatistik 2015]

Swiss energy consumption by carrier (2015)

16,0%

34,7%25,0%

13,5%10,8%

Fossil fuels

Gasoline

Electricity

Natural Gas

Others

Power consumption

Electric energy consumption

Extra-HighVoltage

HighVoltage

Low Voltage

Transmission GridDistribution Grid

[Wikipedia, MBizon, 2010]

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Agenda

Introduction






Conclusion

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Fact 1:

Capacity 6= Flexibility

signs of inflexibility:• price volatility, negative market prices• significant renewable energy curtailment• balancing violations, frequency

excursions, etc.

increasing flexibility:• interconnected systems• fast generators, flexible loads, storage• market design, communication

infrastructure

Assumption 1

Enough capacity & flexibility such that demand can be met at all times.

[NREL, "Flexibility in 21st Century Power Systems," 2014]P L

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Fact 2:

supply 6= demand→ frequency deviation

50Hz 51Hz49Hz

Assumption 2

The power system is stabilized and operates in steady-state, i.e., at 50Hz.

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Terminology

congestion→ cascading line failures(overloaded transmission lines)

under-/overvoltage→ voltage collapse

undervoltage

power demand

overvoltage

generationP L

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Agenda

Introduction






Conclusion

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Primer in Control Engineering

Feedback actuate

observe

[Longchamp, 1995]

open-loop system (feedforward control):

Controller Systemr

u

y

closed-loop system (feedback control) :

Controller Systemr +

u

y

−

Feedback control can achieve:• no steady-state error, i.e., r(t) = y(t) for t→∞• stability: output y remains bounded (for bounded input r)• robustness: reduce influence of model uncertainties

r reference valueu control signaly output signal

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Example: Frequency Control in Power Systems

supply 6= demand→ freq deviation

50Hz 51Hz49Hz

FrequencyControl

PowerSystem

50Hz +u

y

frequency measurement

−

49.935 Hz

50 Hz

50.065 Hz

1200MW

Power plant output Balancing service

15min5min0.5min

[swissgrid, 2010]

0

5000

10000

15000

20000

25000

30000

35000

2011 2012 2013 2014 2015leng

th o

f fre

quen

cy d

evia

tions

[s]

Frequency deviation ≥ 75 mHz[Elcom/swissgrid, 2010]

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Steady-state AC power flow model

25

34

6

78

910

11

12 13

nodal voltagecurrent injectionpower injections

line impedanceline currentpower flow

Ohm’s Law Current Law

AC power

AC power flow equations

(all variables and parameters are -valued)P L

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Power system optimization

minimize φ(x)subject to x ∈ X

φ : Rn → R objective functionX ⊂ Rn constraint set

0

50

100

150

200

0 10 20 30 40 50 60 70 80 90 100

mar

gina

l cos

ts in

€/M

Wh

Capacity in GW

RenewablesNuclear energyLigniteHard coalNatural gasFuel oil

[Cludius et al., 2014]

(simple) Optimal Power Flow (OPF) problem

• minimize cost of generation

• respect generation capacity

• satisfy AC power flow laws

• no over-/under-voltage

• no congestion

minimize∑

k∈Ncostk(P G

k )

subject to P G + jQG = P L + jQL + diag(V )Y ∗V ∗

pk≤ P G

k ≤ pk, qk≤ QG

k ≤ qk ∀k ∈ N

vk ≤ Vk ≤ vk ∀k ∈ N|Pkl + jQkl| ≤ skl ∀{k, l} ∈ E

Y admittance matrix, P Gk , QG

k power generation,P Lk , QL

k load, {vk

, vk, . . .} nodal limits, skl line flow limit

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Agenda

Introduction






Conclusion

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Optimization and control in power system operations

Optimization Controller Systemr +

u

y

−

short-termplanning

D-14 . . . D-2(SC-OPF)

day-aheadscheduling

D-1(SC-OPF)

manualredispatch

low-level,automaticcontrollersdroop, AGCAVR, PSS

Dynamic PowerSystem Modelx = f(x, u, δ)

δ

u

x

Steady-state modelh(x, δ) = 0 (AC power flow)Optimization stage

generationsetpoints

stateestimation

prediction (load, generation, downtimes)

schedule

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National & international redispatch

• in case of unforseen congestion orvoltage problems

• (manually) dispatched on a15-minute timescale

1 588

2010

5 030

2011

7 160

2012

7 965

2013

8 453

2014

15 811

2015

Redispatch actions in the German transmission gridin hours

[Bundesnetzagentur, Monitoringbericht 2016]

371.9267.1

352.9227.6

154.8

secondary frequencycontrol reserves

104.267.4

156.1106.0

50.2

tertiary frequencycontrol reserves

27.068.3

33.026.732.6

reactive power

41.6164.8

113.3185.4

411.9

national & internat.redispatch

111.882.385.2

103.4110.9

primary frequencycontrol reserves

Cost of ancillary services of German TSOsin mio. Euros

2011 2012 2013 2014 2015[Bundesnetzagentur, Monitoringbericht 2016]

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Agenda

Introduction






Conclusion

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Traditional distribution grids

short-termplanning

day-aheadscheduling

manualredispatch

low-levelcontrol

TransmissionSystem

DistributionSystems

Steady-state model

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Distribution grids with high renewable penetration

Challenges

• congestion (in urban grids)• under-/over-voltage (in rural grids)• hard to predict individual load/generation profiles

single PV plant

pow

er

time of day time of day

single residentialload profile

pow

er

Opportunities

• new degrees of freedom (flexibility!)• fast, inverter-based actuation• inexpensive, reliable communication

[IEEE 123 bus test feeder]P L

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The future of active distribution systems

short-termplanning

day-aheadscheduling

manualredispatch

low-levelcontrol

TransmissionSystem

optimization?smart charging,

load managementetc.

??local,

heuristiccontrol

DistributionSystems

Steady-state model

δprediction (load, distributed generation)

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Agenda

Introduction






Conclusion

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Research: “feedback optimization”

Optimization problem

minimize f(u, y)subject to h(u, y) = 0

u ∈ Uy ∈ Y

feedbackoptimizer

staticsystem

h(u, y) = 0

actuateu

ymeasure

• no need to solve optimization problem numerically• algebraic system constraint enforced automatically• relies static system (or asymptotically stability with fast settling time)

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The intuition behind feedback optimization

Update control variables

uk+1 = uk + ∆u ,

measurements adapt to

yk+1 ≈ yk + ∆y

where[∆u ∆y

]∈ kerDh(uk, yk).

Main Idea: Choose ∆u such that[∆u ∆y

]is a

descent direction that is feasible w.r.t. U and Y .

Optimization Problem

minimize f(u, y)subject to h(u, y) = 0

u ∈ Uy ∈ Y

feedbackoptimizer

staticsystem

h(u, y) = 0

actuateu

ymeasure

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Related work

Dynamical systems that solve optimization problems:

• Isospectral flows on matricesApplications: sorting lists, computing eigenvalues, solve LPs[Brockett 1988], [Bloch 1990], [Helmke and Moore 1994]

• Arrow-Hurwicz-Uzawa flows for “soft-constrained” strongly-convex optimization problemsApplications: distributed consensus-based optimization[Arrow et al. 1958], [Kose 1956], [Feijer and Paganini 2010], [Cherukuri et al. 2016], [Simpson 2016]

• Projected dynamical systems for “hard-constrained” convex optimization problemsApplications: variational inequalities[Nagurney and Zhang 1996], [Heemels et al. 2000], [Cojocaru 2006]

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Projected dynamical systems for feedback optimization

Feedback optimization with saturation:minimize f(u, y)

subject to h(u, y) = 0u ∈ Uy ∈ Y

feedbackoptimizer

static systemh(u, y) = 0

u

y

U

Projected dynamical systems:

Initial value problem:

x = ΠK (x, F (x)) , x(0) = x0

where ΠK(x, v) ∈ arg minw∈TxK

||v − w||.

F : Rn → Rn vector field, K ⊂ Rn closed domain, TxK tangent cone at x

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Projected gradient descentTo find minimum on φ on a nonconvex K follow negative gradient vector field:

x = ΠK (x,−gradφ(x)) , x(0) = x0 .

• Does a solution trajectory exist? Is it unique? (yes, if K is convex, otherwise unknown)• Are solution trajectories (asymptotically) stable?• Do solution trajectories converge to a minimizer of φ?

Corollary [AH et al. 2016] (simplified)

Let x : [0,∞)→ K be a (Carathéodory-)solution of

x = ΠK (x,−gradφ(x)) x(0) = x0 .

Then, if φ has compact level sets on K sets x(t) will converge to a critical point x∗ of φ on K.Furthermore, if x∗ is asymptotically stable then it is a local minimizer of φ on K.A. Hauswirth, S. Bolognani, G. Hug, and F. Dörfler, “Projected gradient descent on Riemannian manifolds with applications to online power system optimization,” Allerton Conference, 2016

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Tracking OPF solution despite intermittency

G1

G2 C1

C3 C2

W

S

Generator

Synchronous Condensor

Solar

Wind

G

C

S

W

0 2 4 6 8 10 12 14 16 18 20 22 240

100200300400

Time [hrs]

Aggregate Load & Available Renewable Power [MW]Load Solar Wind

Controller: Penalty + SaturationA. Hauswirth, S. Bolognani, F. Dörfler and G. Hug, “Online Optimization in Closed Loop onthe Power Flow Manifold,” Powertech Conference, 2017, accepted

Time [hrs]

0.95

1

1.05

1.1Bus voltages [p.u.]

0

0.5

1

Branch current magnitudes [p.u.]0.9

0 2 4 6 8 10 12 14 16 18 20 22 240

50100150200

Active power injection [MW]

Gen1 Gen2 Solar WindP L

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Further topics

• Distributed control/optimization: reduce information exchange to neighbor-to-neighborcommunication[Bolognani et al. 2013], [Dall’Annese and Simmonetto 2016], [Li et al. 2014], [Gan and Low 2016], ...

Further desirable properties:

• plug-and-play: no tuning required, distributed performance certificates

• privacy-preserving: no need to share private information

• incentive-compatible: individual, rational choices lead to social optimum

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Agenda

Introduction






Conclusion

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Summary

• Energy transition opens up new challenges in the operation of power systems at all gridlevels.

• Optimization and control theory are essential for a safe and reliable power supply.

• New methods are required to robustly stabilize & optimize power grids under largeuncertainty and in real-time.

• Feedback optimization is a new paradigm that tries to combine the advantages of bothworlds.

• Simulations look promising, but the math behind is still active research.

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Thanks

Supervisors: Prof. Dr. Florian DörflerProf. Dr. Gabriela HugDr. Saverio Bolognani

Project students: Alessandro ZanardiJózsef Pázmány

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Questions

Adrian HauswirthPhD student

ETH ZurichAutomatic Control LaboratoryPower Systems Laboratory

Phone +41 44 632 [email protected]

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Real-time Optimization for Power Distribution …...Real-time Optimization for Power Distribution...

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