Economic Model Predictive Control for Large-Scale and Distributed Energy Systems

201 Pages·2014·14.09 MB·English

Ph.D. Thesis
Economic Model Predictive Control
for Large-Scale and Distributed
Energy Systems
Laura Standardi
Department of Applied Mathematics and Computer Science
Technical University of Denmark
PHD-2014-356
Technical University of Denmark
Department of Applied Mathematics and Computer Science
Building 303B, Matematiktorvet, DK-2800 Kongens Lyngby, Denmark
Phone [phone]
[email protected]
www.compute.dtu.dk
PhD Thesis:
PHD-2014-356
ISSN: 0909-3192
Preface
This thesis was submitted at the Department of Applied Mathematics and
Computer Science (DTU Compute, formerly known as DTU Informatics) at
the Technical University of Denmark in partial fulfilment of the requirements
for acquiring the PhD degree in engineering. The project was funded by the
Southern Denmark Growth Forum and the European Regional Development
Fund in the project “Smart & Cool” (ERDFD-10-0083) started up in 2011.
Smart & Cool is a co-operation between DTU Informatics and public as well
asprivatecompanies: EuropeanUnion, RegionSyddanmark, AalborgUniver-
sity (AAU), Dong Energy, Danfoss and KVCA. The advisor of the thesis are
the associate professors John Bagterp Jørgensen and Niels Kjølstad Poulsen.
The thesis deals with control of the future power systems often referred to as
Smart Grids. We propose Economic Model Predictive Control (MPC) as a
control strategy. In addition, we tailored the control problem for the imple-
mentation of specific decomposition technique aimed to fasten the algorithm,
hence, to increase its applicability in industrial applications. Along the way,
we present numerical simulations alongside case studies as well as validated
models in realistic scenarios.
The thesis consists of a summary report and a collection of 11 research papers
and technical reports written during the period September 2011 to November
2014. Eight papers were published in international peer-reviewed scientific
conferences, one is published at peer-reviewed scientific journals and two are
technical reports.
”Fatti non foste a viver come bruti, ma per seguir virtute e canoscenza.”
(Ye were not made to live like unto brutes,
but for pursuit of virtue and of knowledge.)
Dante Alighieri, The Divine Comedy, 26.120
iii

Acknowledgements
IwouldliketothankmysupervisorJohnBagterpJørgensenandco-supervisor
NielsKjølstadPoulsen. Overthelastthreeyears,theyhavebeenmycontroller
that has handled uncertainties and disturbances, but it has always provided
optimal advices related to both work and life in general.
I thank also all the Smart & Cool sponsors for the interesting bi-annual meet-
ings that we had over the last 36 months.
In the same way, I would like to include in this acknowledgement the whole
DTU Compute (formerly known as DTU IMM) department and all PhDs and
PostDocs of the Scientific Computing Section.
Besides the official acknowledgements, I would like to thank other people that
have not been my colleagues but each of them has played a key role in this
PhD work.
ThankstotheguysinVedLinden11forwelcomingmeandmystuffintotheir
house.
I would like to thank my old friends in Italy because they have been always
there for me every time I go home and they have always supported me even
via chat and Skype.
I thank all members of the B.D.C. club for the great fun we have had together
and for their support. We are the proof that different nationalities don’t
matter in friendship.
I would like to thank Ferenzz for standing by my side, for his patience and for
have taken, with love, my punches whenever I needed a punching bag.
Last but not least, I thank Bonnie and my family in Italy. They have been
able to constantly support me over the last three years and they have been
the most important co-authors of all my works.
v

Summary (in English)
In this thesis, we consider control strategies for large and distributed energy
systems that are important for the implementation of smart grid technologies.
Anelectricalgridhastoensurereliabilityandavoidlong-terminterruptionsin
the power supply. Moreover, the share of Renewable Energy Sources (RESs)
in the smart grids is increasing. These energy sources bring uncertainty to the
production due to their fluctuations. Hence, smart grids need suitable control
systemsthatareabletocontinuouslybalancepowerproductionandconsump-
tion. We apply the Economic Model Predictive Control (EMPC) strategy to
optimise the economic performances of the energy systems and to balance the
power production and consumption. In the case of large-scale energy systems,
the electrical grid connects a high number of power units. Because of this, the
related control problem involves a high number of variables and constraints
and its solution requires high computational times. Energy systems have a hi-
erarchicalcontrolframeworkandthecontrollershavetoworkinthetime-scale
requiredbytheirhierarchylevel. Dedicatedoptimisationtechniquesefficiently
solve the control problem and reduce computational time. We implement the
Dantzig-Wolfe decomposition technique to efficiently solve the EMPC prob-
lem.
The contributions of this thesis are primarily on:
Large-scale energy system
Smart-gridsconnectahighnumberofenergyunits. Insuchalarge-scale
scenario the energy units are independent and dynamically decoupled.
The mathematical model of the large-scale energy system embodies the
decoupled dynamics of each power units. Moreover, all units of the grid
contribute to the overall power production.
Economic Model Predictive Control (EMPC)
This control strategy is an extension of the Model Predictive Control
(MPC) strategy. Energy systems often involve stochastic variables due
totheshareoffluctuatingRenewableEnergySources(RESs). Moreover,
therelatedcontrolproblemsaremultivariablesandtheyarehard,orim-
possible, to split into single-input-single-output control systems. MPC
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strategy can handle multi variables control problems and it can embody
stochastic variables. The Economic MPC (EMPC) policy optimises the
economicperformancesoftheprocess. Inthiswork,weapplytheEMPC
to energy systems and it computes the control trajectory for each en-
ergy unit. This control policy minimises production costs and ensures
that the power production satisfies the customers’ demand. The EMPC
designs a linear control problem that has a block-angular constraints
matrix and it has two sets of constraints. The independent dynamics of
the energy units define the decoupling constraints sited on the diagonal.
The coupling constraints represent the common goal of all power units
in the energy system and this is to satisfy the customers’ demand. The
Dantzig-Wolfe optimisation technique applies to this structure of the
constraints matrix in the view of fastening the control algorithm and
increase its applicability.
Dantzig-Wolfe decomposition
The Dantzig-Wolfe decomposition solves the EMPC problem through a
distributed optimisation technique. The EMPC problem via Dantzig-
Wolfe decomposition algorithm computes the optimal input trajectory
foreachenergyunitandreducesthecomputationtimes. Moreover, such
acontrolalgorithmappliestolarge-scaleenergysystemsandthenumber
ofenergyunitsdoesnotaffecttheperformancesofthecontroller. Inthis
thesis, we also investigate suboptimal solutions of the EMPC problem
via modified versions of the Dantzig-Wolfe decomposition algorithms.
Thefeasibilityofthesuboptimalsolutionssufficesforstability. Thegoal
of these modified Dantzig-Wolfe decomposition algorithms is to reduce
computation time in the solution of the EMPC problem.
Resum´e
I denne afhandling, analyserer vi strategier for store og distribuerede ener-
gisystemer, der er vigtige for implementationen af smart grid-teknologier.
Elnettetskalsikrep˚alidelighedogundg˚alangvarigeafbrydelseristrømforsynin-
gen. Desuden er andelen af vedvarende energikilder i de intelligente elnet sti-
gende. Disse energikilder bringer usikkerhed for produktionen p˚a grund af
deres udsving. Derfor har de intelligente elnet brug for passende kontrolsys-
temer, der er i stand til at afbalancere løbende elproduktion og forbrug. Vi
anvender den økonomiske modelprædiktiv reguleringsstrategi (EMPC) for at
optimere de økonomiske resultater fra energisystemerne og for at skabe bal-
ance i elproduktion og -forbrug. I store energisystemer forbinder elnettet et
stort antal kraftenheder. P˚a grund af dette har det tilhørende kontrol prob-
lem et stort antal variabler og begrænsninger, og dets løsning kræver lange
beregningstider. Energisystemer har en hierarkisk kontrol struktur, og regu-
latorerne skal arbejde p˚a den tid skala, der kræves af deres hierarkiske niveau.
Dedikeredeoptimeringsteknikkerløsereffektivtkontrolproblemetogreducerer
beregningstiden. Vi implementerer Dantzig-Wolfe dekompositionstekniken til
effektivt at løse EMPC problemet.
Denne afhandling har primært bidraget inden for:
Storskala Energisystemer
Det intelligente elnet forbinder et stort antal energienheder. I et s˚a-
dant storskala scenario er de enkelte enheder uafhængige og dynamisk
afkoblede. Den matematiske model af et stort energisystem inkluderer
de enkelte enheders dynamik p˚a afkoblet vis. Desuden bidrager alle
enheder p˚a nettet til den samlede elproduktion.
Økonomisk Modelprædiktiv Regulering (EMPC)
Denne kontrolstrategi er en udvidelse af den modelprædiktive reguler-
ingsstrategi (MPC). Energisystemer involverer ofte stokastiske variable
p˚a grund af andelen af fluktuerende vedvarende energikilder. Yder-
mere er de tilhørende kontrolproblemer multivariable, og de er svære
eller umulige at opsplitte i single-input-single-output kontrolsystemer.
MPC-strategien kan h˚andtere multivariable kontrolproblemer, og den
kaninkluderestokastiskevariable. DenØkonomiskeMPCstrategi(EMPC)
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optimerer de økonomiske resultater i processen. I denne afhandling an-
vender vi EMPC til energisystemer, og beregner derved styringen for
hver energienhed. Denne kontrolstrategi minimerer produktionsomkost-
ningerne og sikrer, at elproduktion opfylder kundernes efterspørgsel.
Ved EMPC designes et lineært kontrolproblem, der har en blok-angulær
begrænsningsmatrix, og det har to sæt begrænsninger. De uafhængige
dynamikker af energienhederne definere afkoblingsbegrænsningerne er
placerede p˚a diagonalen. Sammenkoblingsbegrænsningerne repræsen-
terer det fælles m˚al for alle kraftenheder i energisystemet, hvilket er at
tilfredsstillekundernesefterspørgsel. Dantzig-Wolfeoptimeringsteknikken
kan anvendes p˚a denne struktur af begrænsningsmatricen med henblik
p˚a at gøre styringsalgoritmen hurtigere og øge dens anvendelighed.
Dantzig-Wolfe Dekomposition
Dantzig-Wolfe dekompositionen løser EMPC problemmet ved hjælp af
en distribueret optimeringsteknik. Via Danzig-Wolfe dekompositionsal-
goritmem beregner EMPC problemet det optimale regulatorinput for
hver energienhed og reducerer beregningstiden. Desuden kan en s˚a-
dan en kontrolalgoritme anvendes p˚a store energisystemer, og antallet
af energienheder p˚avirker ikke regulatorens effektivitet. I denne afhan-
dling undersøger vi ogs˚a suboptimale løsninger af EMPC problemet via
modificerede versioner af Danzig-Wolfe dekompositionsalgoritmen. Ek-
sistensen af suboptimale løsninger er tilstrækkeligt for at garantere sta-
bilitet. M˚aletmeddissemodificeredeDanzig-Wolfedekompositionsalgo-
ritmereratreducereberegningstidenvedløsningenafEMPCproblemet.