Optimization Methods to Manage Uncertainty and Risk in Power Systems Operation

247 Pages·2016·3.98 MB·English

by  Imhof Markus

DISS. ETH NO. 23918
Optimization Methods to
Manage Uncertainty and Risk
in Power Systems Operation
A thesis submitted to attain the degree of
Doctor of Sciences of ETH Zurich
(Dr. sc. ETH Zurich)
presented by
Line Alnæs Roald
MSc ETH ME
born on 6 April 1987
citizen of
Norway
accepted on the recommendation of
Prof. Dr. G¨oran Andersson, examiner
Prof. Dr. Louis Wehenkel, co-examiner
Prof. Dr. Gabriela Hug, co-examiner
2016
ETH Zurich
EEH - Power Systems Laboratory
ETL G24.1
Physikstrasse 3
8092 Zurich, Switzerland
ISBN: 978-3-906327-65-5
(cid:13)c Line Alnæs Roald, 2016
[email protected]
For a copy visit: http://www.eeh.ee.ethz.ch
Cover illustration by Hannah Hewett
Based on Ansel Adams “Transmission lines in Mojave Desert, 1941”
(courtesy National Archives photo no. 79-AAB-3)
Printed in Switzerland by the ETH Druckzentrum
To my family.
Du kan hvis du vil.

Preface
This thesis summarizes work done over the course of four years at the
Power Systems Laboratory of ETH Zurich. It has been a wonderful
time, and I would like to extend my sincere gratitude to everyone I
have interacted with, both on a professional and a personal level.
First and foremost, I would like to thank my advisor Prof. G¨oran An-
derssonforprovidingmewiththeopportunitytopursuethisPhD.Iam
very grateful for the trust, freedom and generosity with which I have
beenallowedtoexploretheworldofresearch,bothinmyofficeatETH
and through various trips.
I am thankful to Prof. Louis Wehenkel from University of Liege for
accepting to be my co-examiner and taking the time to review this
thesis. From the very beginning of my PhD, Louis’ work as well as
our interactions at various conferences and workshops have been an
inspiration to me. I would also like to thank Prof. Gabriela Hug, both
for accepting to be my co-examiner and for having me around at PSL
after Go¨ran retired. It has been a pleasure to work with Gabriela and
her group, and I am looking forward to staying in touch.
My next thanks goes to Thilo Krause and Frauke Oldewurtel for their
importance both as mentors, office mates and partners on the UM-
BRELLA project. Thilo helped me set up my first optimal power flow
code. From him, I learnt that academic writing is about conveying a
storyandthatthereisnocontradictionbetweenbeingafirst-classpoet
and a researcher. Frauke deserves credit for introducing me to chance-
constraints(anyonereadingbeyondthisprefacewillquicklyunderstand
how important this has been), and for bothering to be a perfectionist,
including proof-reading my papers over and over.
v
vi Preface
When I first started the PhD, there were many people in our group
who were generous in sharing their experience with me. In particular, I
would like to thank Spyros Chatzivasileiadis for his help and our many
discussions, and for being an inspiration both personally and profes-
sionally.IamalsothankfultoMariaVrakopoulouforintroducingmeto
several important concepts, such as the scenario approach, and to Bart
Van Parys for showing me that distributionally robust optimization is
not necessarily hard.
I would like to extend my thanks to all members of the UMBRELLA
consortium, bothresearchand industry partners. In particular, I would
like to thank our close collaborators at TU Delft and TU Graz, as well
as all members of the project management team. I greatly appreciated
allfeedbackandalldiscussionswiththetransmissionsystemoperators,
which were pivotal in making our work practically relevant.
Someofmymostintenseandfuncollaborationswerecarriedoutduring
and after my stay at Center for Non-Linear Studies at Los Alamos
NationalLaboratory.IwouldliketothankScottBackhausandMichael
Chertkovforhostingme,andincludingmeinthemanydiscussionsand
projects that have both inspired and profoundly changed my way of
thinking about “grid science”. I would like to thank my Los Alamos
colleagues and friends for all good days and nights, including Marc,
Andrey, Theodor, Harsha, Kaarthik, Miles, Yury and Amanda. Special
thanks goes to Anatoly Zlotnik for our collaboration on gas-electric
systems-andforlettingmeexplorethemanytrailsaroundLosAlamos
on his mountain bike. I am deeply grateful to Sidhant Misra for his
inputs on optimization and coding, which contributed so significantly
to the completion of this thesis, and for spending time talking to me
about everything from boundary conditions to Belgian beers.
Throughout my PhD, I have been fortunate to supervise a number of
master and semester thesis projects. I would like to thank Jaka Strum-
belj, Bing Li, Georgios Chatzis, Haoyuan Qu, Eren Cam, Jeremias
Schmidli, Tobias Mohrhauer, Andrew Morrison and Aldo Tobler for
their contributions and for choosing to work with me. I would also like
to thank my collaborators who co-supervised some of these projects.
The experience of the PhD would have been completely different with-
out the enthusiasm of the crew at the Power Systems Laboratory, be
it in discussing improbable concepts for renewable generation or join-
ing for the monthly lønningspils. Thanks to Marina, Maria, Frauke,
Preface vii
Spyros, Matthias B., Olivier, Matthias G., Andreas, Johanna, Philipp,
Hubert, Roger, Monika, Osvaldo, Stephan, Markus, Vaggelis V., Thilo,
Emil, Marcus, Olli, Louis, Jo, Adrian, Dmitry, Conor, Uros, Vaggelis
K., Stavros, Andrew, Jack, Nadezdha, Tomas, Petros, Thierry, Chenye
and our visitors Martin and Sven Christian for many good discussions,
collaborations,skitrips,conferencesandexcursions.Aspecialthanksto
MarinaGonzalezVayaforbeingmyFrauen-Powerpartneroverallthese
years, and to Johanna Mathieu for her precious advice on all aspects of
(academic) life.
There is more to life than work, and my thanks also goes to all my
friends in Zurich, Oslo and beyond for their friendship and support.
In particular, I would like to thank my flat mates Hannah Hewett and
SimoneKubikforbeingsopatientandcaring,andforsharingourcom-
mon home. I would also like to thank Sara Kijewski for being my sister
in Zurich, and for opening her home to me when needed.
Last, but not the least, I would like to thank my family. My mother,
grandmas and aunts provide ample evidence that being a woman is no
excuse for not reaching far. The determination of my younger brother
Petter in pursuing his dreams is inspiring, and I am proud to share the
Alnæs Roald identity with him. Finally, I am endlessly grateful for the
love and support from my parents Helge and Monika, as well as their
respect for my freedom to choose my own ways in life. Without them, I
would never have been where I am today.
Thank you!
Line A. Roald
Zurich, December 2016

Abstract
Electricity from renewable energy sources is essential for a sustainable
energyfuture.Oneinherentpropertyofrenewablegenerationishowever
thatitispartiallyunpredictable,withuncertaintyarisingfromforecast
errors and real-time fluctuations. As the share of renewable generation
grows,thisuncertaintychallengesexistingpracticesforelectricgridop-
eration.
In the past, the operation of the electric grid was deemed secure if the
system could withstand any credible contingency, typically defined as
the failure of any single component. With increasing levels of forecast
uncertainty, the system experiences larger deviations from the planned
operating point. It therefore becomes more important to account for
possible adverse impacts of those deviations to ensure that the system
will remain secure in real time operation. This thesis is concerned with
the development of optimal power flow methods that help system op-
erators manage uncertainty and mitigate risk in day-to-day operational
planning.
In the first part of the thesis, we focus on chance-constrained optimal
powerflow,whichlimitstheprobabilityofconstraintviolation.Wepro-
posetoformulatetheproblemusingseparatechanceconstraints,which
are reformulated using an analytical reformulation based on either full
or partial knowledge about the uncertainty distribution. The approach
allowustomodelpolicy-basedcontrolactionsinreactiontouncertainty
realizations, which contribute to managing and mitigating possible ad-
verse impacts. The method is applied to selected cases in power system
operations, including investigations of different reserve activation poli-
cies and corrective control by HVDC connections and phase shifting
transformers. These studies show that a more flexible system decreases
ix
x Abstract
the cost of handling uncertainty. We also develop and demonstrate a
solution algorithm that allow us to solve the problem for large systems.
While the above mentioned applications are based on the linear DC
power flow equation, we also suggest an extension based on the non-
linear AC power flow equations. We model the system using the full
ACequationsforthenominaloperatingpoint,butapplyalinearization
aroundthispointtorepresenttheimpactofuncertainty.Duetothelin-
ear dependence on the uncertain variables, we can apply the analytical
chance constraint reformulation, which allows for a tractable optimiza-
tion problem. We further suggest different solution approaches, includ-
ing an iterative approach which leverages scalability of existing solvers
to tackle large problems, and compare the suggested analytical refor-
mulation method with two sample-based methods. We find that the
proposed method provides a good performance at low computational
cost.
In the second part of the thesis, we focus on risk-based optimal power
flow, where risk functions are used to model how the size of constraint
violations influence risk. First, we suggest a method to define risk func-
tions for post-contingency overloads based on system properties such
as cost and availability of remedial actions, and provide a comparison
with the N-1 criterion to argue for the choice of risk limits. We further
combine the proposed risk functions with a chance constrained optimal
power flow to limit the probability of high risk events.
Second, we introduce the weighted chance constraints, which measure
and limit the expected risk of constraint violations, as defined by the
probability distribution of the forecast errors and the chosen risk func-
tion.Itisshownthattheweightedchanceconstraintremainsconvexfor
convex risk functions and general control polices. We investigate how
thechoiceofariskfunctioninfluencesthenumberandsizeofconstraint
violations,andapplythemethodtoasituationwheretertiarycontrolis
activated during large wind deviations. Further, we investigate the op-
timal use of active power control from wind turbines, including reserve
provision and enforcement of output caps.