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Model: Dynamic nonlinear
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Input: Forecast
Model: Discretelinearized
optimization model
Schedule Actual operation𝑡𝑡𝑡𝑡𝑡𝑡 𝑡𝑡
51
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Predictive Demand Side Management Strategies for Residential Building Energy Systems
Hassan Harb
This thesis presents a generalized methodology, supported by a software framework, for modeling and assessing mathematical programming based predictive demand side management (DSM) strategies that exploit thermal and electrical flexibilities of residential building energy systems (BES) to enhance the integration of renewable energy sources. The modeling and simulation platform is formulated in Python and includes a set of forecasting methods as well as a discrete mixed inte-ger linear programming (MILP) modeling library based on the Gurobi optimizer API. The platform further integrates a nonlinear BES simulation model in Dymola/Modelica as a functional mock-up unit (FMU). The investigated scheduling models for individual buildings consist of a deterministic MILP strategy and a multi-stage stochastic programming approach that extends the MILP model while incorporating the uncertainties of the electrical and domestic hot water demands. The city district DSM strategies comprise a centralized approach, which serves as a benchmark, as well as distributed formulations based on decomposition techniques. The distributed DSM approaches considered are Dantzig-Wolfe decomposition based column generation algorithm as well as an integrated Lagrangian decomposition column generation approach.
ISBN 978-3-942789-50-9
Predictive Demand Side Management
Strategies for Residential Building Energy
Systems
Vorausschauende Demand Side Management
Strategien für Wohngebäudeenergiesysteme
Von der Fakultät für Maschinenwesen der Rheinisch-Westfälischen Technischen Hochschule
Aachen zur Erlangung des akademischen Grades eines Doktors der
Ingenieurwissenschaften genehmigte Dissertation
vorgelegt von
Hassan Harb
Berichter: Univ.-Prof. Dr.-Ing. Dirk Müller
Univ.-Prof. Antonello Monti, Ph.D.
Tag der mündlichen Prüfung: 09. November 2017
Diese Dissertation ist auf den Internetseiten der Universitätsbibliothek online verfügbar.
Bibliographische Information der Deutschen NationalbibliothekDie Deutsche Nationalbibliothek verzeichnet diese Publikation in der DeutschenNationalbibliografie; detaillierte bibliografische Daten sind im Internet überhttp://dnb-nb.de abrufbar.
D 82 (Diss. RWTH Aachen University, 2017)
Herausgeber:Univ.-Prof. Dr.ir. Dr.h.c. Rik W. De DonckerDirektor E.ON Energy Research Center
Institute for Energy Efficient Buildings and Indoor Climate (EBC)E.ON Energy Research CenterMathieustr. 1052074 Aachen
E.ON Energy Research Center | 51. Ausgabe der SerieEBC | Energy Efficient Buildings and Indoor Climate
Copyright Hassan HarbAlle Rechte, auch das des auszugsweisen Nachdrucks, der auszugsweisen odervollständigen Wiedergabe, der Speicherung in Datenverarbeitungsanlagen und derÜbersetzung, vorbehalten.
Printed in Germany
ISBN: 978-3-942789-50-91. Auflage 2017
Verlag:E.ON Energy Research Center, RWTH Aachen UniversityMathieustr. 1052074 AachenInternet: www.eonerc.rwth-aachen.deE-Mail: [email protected]
Hassan Harb
"Predictive Demand Side Management Strategies for Residential Building Energy
Systems"
Dedicated to my parents, Ali & Fattouma
and to my wife, Tanja.
Acknowledgments
First and foremost, I would like to thank my supervisor Univ.-Prof. Dr.-Ing. Dirk Müller
for giving me the possibility and freedom to work on this thesis and for his confidence
and excellent guidance. I would also like to thank Univ.-Prof. Antonello Monti, P.h.D for
his support and for reviewing this thesis as well as being the co-examiner on my doctoral
examination.
Further, I would like to thank my colleagues at the Institute for Energy Efficient Buildings
and Indoor Climate for the unbounded cooperation, great working atmosphere and the
beautiful memories. Especially, I would like to thank Peter Matthes for being a pleasant
office mate and a great friend, for the interesting discussions and valuable advice. I
also want to thank Ana Constantin and Thomas Schütz for the cheerful and successful
cooperation in the projects we worked on together and for their support in the preparation
for the doctoral examination. Henryk Wolisz, Roozbeh Sangi and Moritz Lauster, thank
you for the memorable moments within and outside of the institute and unforgettable,
adventurous and enjoyable conference trips.
In addition, I would like to thank all the students, Jan-Niklas Paprott, Alexander Hoffmann,
Joel Kröpelin, Hossam Houta, Jöran Hahn, Katja Rieß, Marc Baranski, Christian Schwager,
Jan Reinhardt, Neven Boyanov, Thomas Rosen, Markus van Hünsel, Lukas Körnich, Lennart
Weitz and Lennart Böse, whom I had the chance to supervise, for the amazing collaboration
and their valuable contribution to this thesis.
Finally, I would like to express my deepest and sincerest gratitude to my family especially
my parents Ali and Fattouma, thank you for your sacrifices, you are by far the two best,
kindest, generous, supportive and cheerful people I know, my reliable brothers Rabih,
Hussein, Abbas and Hassanein, my dear and selfless sister Abir and her husband Tarek
Ghaddar thank you for always supporting me, my kind and beautiful wife Dr. Rer. Nat.
Tanja Vajen and my best friends, μαλάκας Kostas Saxonis, "yellowjacket" Ali Zaraket and
"Bekh" Bahaa Berjewei, thank you for being part of my life and always there for me.
Aachen, November 2017
Hassan Harb
ix
Abstract
This thesis presents a generalized methodology, supported by a software framework,
for modeling and assessing mathematical programming based predictive demand side
management (DSM) strategies that exploit thermal and electrical flexibilities of residential
building energy systems (BES) to enhance the integration of renewable energy sources.
The modeling and simulation platform is formulated in Python and includes a set of
forecasting methods as well as a discrete mixed integer linear programming (MILP)
modeling library based on the Gurobi optimizer API. The platform further integrates a
non-linear BES simulation model in Dymola/Modelica as a functional mock-up unit (FMU).
The evaluation of the forecasting algorithms shows that the lowest forecast error for
predicting electrical and space heating demands is provided by SVR and for predicting
the weather variables, i.e. temperature and solar irradiation, by ARMA, respectively. The
persistence method is selected for predicting the strongly stochastic domestic hot water
demand.
The introduced scheduling HEMS models for individual buildings consist of a deterministic
MILP strategy and a multi-stage stochastic programming (SP) approach that extends the
MILP model while incorporating the uncertainties of the electrical and domestic hot
water demands. The city district DSM strategies comprise a centralized approach, which
serves as a benchmark, as well as distributed formulations based on decomposition
techniques. In this work, two distributed DSM approaches are formulated, Dantzig-
Wolfe decomposition based column generation (CG) algorithm as well as an integrated
Lagrangian decomposition column generation (LRCG). The performance of the scheduling
algorithms for individual buildings is evaluated for different BES configurations. The
results indicate that predictive HEMS with perfect information enhance the integration of
locally generated electrical power from PV units and enables a significant potential of load
shifting and cost reduction with respect to a reactive control strategy. Employing point
forecasts of weather and energy demand variables within the deterministic scheduling
model reduces this potential but further allows for a higher integration of PV power
as well as cost reduction compared with a reactive strategy. The multi-stage SP model
outperforms the deterministic approach but induces larger modeling and computation
effort. The analysis of the DSM strategies for city districts shows that the CG approach
provides comparable coordination performance as the centralized model while significantly
reducing the computation time. Further, the integrated LRCG approach enables a faster
convergence compared with the standard CG formulation.
xi
Zusammenfassung
Diese Arbeit stellt eine Methodik und ein Software-Framework vor, um prädiktive Demand-
Side-Management-Strategien (DSM) zu modellieren und zu evaluieren. Das Ziel dabei
ist es, die thermische und elektrische Flexibilität von Gebäudeenergiesystemen (GES)
auszuschöpfen, um die Integration von erneuerbaren Energiequellen zu fördern. Die
Modellierungs- und Simulationsplattform ist in Python formuliert und enthält verschiedene
Prognosemethoden sowie eine GES-Modellierungsbibliothek auf Basis der Gurobi-Optimizer-
API. Des Weiteren ist ein nicht-lineares GES-Dymola/Modelica-Modell als Functional
Mock-Up-Unit (FMU) in die Plattform integriert.
Die Evaluierung der Vorhersagemethoden zeigt, dass Support-Vector-Regression den ger-
ingsten Prognosefehler bei der Vorhersage des elektrischen und des Raumwärmebedarfs
erlaubt. ARMA liefert das beste Ergebnis für die Vorhersage der Wettervariablen, wie
Temperatur oder Sonnenstrahlung. Die Persistenz-Methode wird für die Vorhersage des
Warmwasserbedarfs verwendet.
Die vorgestellten Heimenergiemanagementsysteme (HEMS) für einzelne Gebäude beste-
hen aus einer deterministischen GGLP-Strategie sowie einem mehrstufigen stochastischen
Programmierungsansatz (SP), der das GGLP-Modell erweitert und dabei die Unsicherheit-
en der elektrischen und thermischen Anforderungen berücksichtigt. Die DSM-Strategien
für Stadtquartiere umfassen einen zentralisierten Ansatz, der als Benchmark dient, sowie
verteilte Formulierungen auf Basis von Dekompositionsverfahren. In dieser Arbeit werden
zwei verteilte DSM-Ansätze formuliert: Dantzig-Wolfe-Decomposition basierte Column-
Generation-Algorithmen (CG) sowie eine integrierte Lagrange-Decomposition-Column-
Generation (LRCG). Die Ergebnisse zeigen, dass prädiktive HEMS mit perfekter Informa-
tion die Einbindung von lokal erzeugtem PV-Strom erhöhen und ein großes Potenzial der
Lastverschiebung und Kostenreduzierung gegenüber einer reaktiven Steuerstrategie er-
möglichen. Der Einsatz von Prognosen der Wetter- und Energiebedarfsvariablen innerhalb
des deterministischen Scheduling-Modells reduziert dieses Potenzial, ermöglicht aber
dennoch eine höhere Einbindung von PV-Strom sowie eine Kostenreduzierung gegenüber
der reaktiven Strategie. Das SP-Modell übertrifft den deterministischen Ansatz, bewirkt
aber einen größeren Modellierungs- und Berechnungsaufwand. Die Analyse der DSM-
Strategien für Stadtquartiere zeigt, dass der CG-Ansatz eine vergleichbare Koordination
wie das zentrale Modell bietet und gleichzeitig den Rechenaufwand deutlich reduziert.
Darüber hinaus ermöglicht der integrierte LRCG-Ansatz eine schnellere Konvergenz
gegenüber der standard CG-Formulierung.
xiii
Contents
Nomenclature xviii
List of figures xxiii
List of tables xxviii
1 Introduction 1
1.1 Background: Trends and challenges . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 "Energiewende": Energy transition and consequences . . . . . . . . . . . . . . . 1
1.1.2 Building energy systems: Decentralization and flexibility . . . . . . . . . . . . . 2
1.2 Demand side management: Review . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Classification: Triggering criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Objectives for scheduling strategies . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Target devices in DSM concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.4 Approaches: Decision scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.5 Forecast models in predictive scheduling . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.6 Scheduling algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.7 Architecture of DSM strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Modeling of heating energy systems . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.2 Flexibility and extensibility of the modeling approach . . . . . . . . . . . . . . . 10
1.3.3 Uncertainty of underlying forecast models . . . . . . . . . . . . . . . . . . . . . . 11
1.3.4 Scalability of the DSM strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Thesis statement and contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Structure of this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Methodology: Framework 17
2.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Software configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 Framework programming language . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 MILP optimization solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 Dynamic simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
xv
3 Inputs: Synthesis and Forecast 25
3.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Forecasting methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Persistence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 ARMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.3 SVR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.4 Performance indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 Modeling of Building Energy Systems: Mathematical Programming
Formulation 35
4.1 Heat pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Micro combined heat and power unit . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 Electrical heating element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.4 Gas boiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.5 Photovoltaic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.6 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.7 Water tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.7.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.7.2 Definition of SoC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.7.3 Experimental evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.8 Building wall mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.8.1 Modeling: Grey-box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.8.2 Model identification approach: Parameterization . . . . . . . . . . . . . . . . . . 59
5 Scheduling Algorithms 61
5.1 Mathematical optimization: Fundamentals . . . . . . . . . . . . . . . . . . . . . . 61
5.2 Single building scheduling approaches . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2.1 Deterministic MILP model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2.2 Scheduling under uncertainty: Multi-stage stochastic programming . . . . . . 64
5.3 City district scheduling approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3.1 Centralized scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3.2 Distributed scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6 Analysis: Results and Discussion 79
6.1 Scheduling for single buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.1.1 Design and configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.1.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.2 Distributed scheduling for neighborhoods . . . . . . . . . . . . . . . . . . . . . . 90
6.2.1 Design and configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.2.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7 Conclusion and Outlook 99
7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
A Appendix 105A.1 Single building evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105A.1.1 PV-HP-EH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105A.1.2 PV-HP-EH-Bat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106A.1.3 PV-CHP-EH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108A.1.4 PV-CHP-EH-Bat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110A.1.5 PV-CHP-B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111A.1.6 PV-CHP-B-Bat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Bibliography 115
Nomenclature
Symbols and Units
Symbol Description Unit
af absorption coefficient (short-wave) of the exterior surface -
A area m2
cw specific heat capacity of water for constant pressure J/(kgK)
cgas specific gas price ct/kWh
cbuy specific price for bought electricity ct/kWh
csell specific price for sold electricity ct/kWh
C area specific thermal capacity in Grey-Box model Wh/(m2 K)
C pn cost of a proposal p by a subproblem n e
COP coefficient of performance -
DoD depth of discharge %
E energy J
I current A
L length m
Lmod modulation level %
m mass flow kg/s
p autoregression order -
q moving average order -
P power W
Q energy content Wh
Q heat flow W
R area specific thermal resistance in Grey-Box model (m2 K)/W
s scenario -
SoC state of charge %
t time index s
tH moving window horizon s
T temperature K, °C
u binary on/off status -
uc electricity consuming unit -
continued on next page
xix
Nomenclature Nomenclature
Symbols and Units
Symbol Description Unit
ug electricity generation unit -
U voltage V
V volume m3
V volume flow m3/s
m mass flow kg/s
xloss,∆t thermal loss coefficient %
y prediction value W
y measurement value W
zl layer height in water storage m
Greek Symbols
Symbol Description
α PV temperature coefficient %/K
αA heat transfer coefficient W/(m2 K)
εi forecasting error W
η efficiency %
∆t time step length or resolution s
γ quotient between the area of interior or exterior walls and
floor area
-
φ support vector regression kernel -
ksto storage thermal transmittance W/(m2 K)
λ thermal conductivity of water W/(m2 K)
π shadow price ct/kWh
πs probability %
σ CHP power to heat ratio -
ρ volumetric density kg/m3
v binary variable -
w binary variable -
Nomenclature
Indices and Abbreviations
Acronym Description
a ambient
AIC akaike information criterion
amb ambient
ANN artifical neural network
API application programming interface
AR auto regression
ARMA auto regression moving average
ARMAX auto regression moving average with exogenous input
BAT battery
BES building energy system
CHP combined heat and power
CG column generation
CS cross sectional
dem demand
DHW domestic hot water
DP dynamic programming
DR demand response
DSM demand side management
DWD Dantzig-Wolfe decomposition
E expected value
EA evolutionary algorithm
EH electrical heater
el electrical
env environment
eq equivalent
FMI functional mock-up interface
FMU functional mock-up unit
GA genetic algorithm
GHG greenhouse gas emissions
GUI graphical user interface
HEMS home energy management system
HP heat pump
HiL hardware in the loop
continued on next page
Nomenclature Nomenclature
Indices and Abbreviations
Acronym Description
in interior
ia indoor air
init inital
l storage water layer
LB lower bound
LD Lagrangian decomposition
LP linear program
LR Lagrangian relaxation
MAPE mean absolute percentage error
MAS multi-agent system
MILP mixed integer linear program
MINLP mixed integer non linear porgram
MPC model predictive control
noct nominal operation cellt temperature
NAC non-anticipativity constraint
NP non-deterministic ploynomial-time
NRMSE normalized toot mean squared error
PV photovoltaic
RBF Radial Basis Function
RE renewable energy
ret return
s scenario
SA simulated annealing
SARIMA seasonal auto regression integrated moving average
SH space heating
SLP standard load profile
SP stochastic programming
sto storage
SVR support vector regression
tap tapping
th thermal
TRY test reference year
TS thermal storage
UB upper bound
List of Figures
1.1 Development of renewable energy sources in Germany with regard to the share
in gross electricity generation based on the data from [Federal ministry for
economic affairs and energy, 2015b] . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Potential of buildings within the energy transition: Energy consumption by
the field of application in Germany in 2014; data from [Federal ministry for
economic affairs and energy, 2015a] . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Illustration of discrepancy between electrical demand and local PV generation
as well as load shifting strategies through demand modification and storage
management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Overview on the characterizing features of DSM concetps . . . . . . . . . . . . . 4
1.5 Descriptive illustration of the thesis outline . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Overview on the individual components and basic formulation of a predictive
HEMS. The inputs comprise weather, space heating, domestic hot water, electri-
cal demand, PV generation and occupancy. The building energy system includes
battery, CHP, electrical, building wall mass, HP and water storage tanks . . . . 17
2.2 Simplified illustration of the concept of the rolling horizon algorithm. The
rescheduling interval denotes the time between the scheduling steps or schedul-
ing re-initialization whereas the scheduling horizon defines the length of
scheduling step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 System testing and evaluation within the PyMPC framework. The left box rep-
resents the scheduling model which uses forecast and linearized BES models,
whereas the right box represents the realization platform which includes actual
weather and demands as well as non-linear BES dynamic simulation models
(integrated as a FMU) or HiL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 PyMPC framework structure and task diagram . . . . . . . . . . . . . . . . . . . . 20
2.5 Simplified overview on the space heating supply system within the dynamic
simulation models [Müller et al., 2015]. The main components are the thermal
zone which represents the thermal behavior of the building, the hydraulic
connection, the heat generation system e.g. HP and CHP and thermal storage
units as well as the rule-based control strategy . . . . . . . . . . . . . . . . . . . 22
2.6 Integration of the Modelica/Dymola dynamic BES simulation model within the
PyMPC framework as co-simulation Python FMU based on the FMI interface . 24
xxiii
List of Figures
3.1 Interconnection of weather, occupancy, demand and PV profiles. Occupancy
is only influenced by weather conditions and used to derive the electrical
and domestic hot water demands. PV generation is determined based on the
weather variables. Space heating is influence by the internal thermal gains
from active occupancy, electrical consumption and weather . . . . . . . . . . . 25
3.2 Stochastic occupancy based generation of demand profiles. The depicted
profiles, from top to bottom, are the electrical demand, occupancy and domestic
hot water demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Input data for the single building evaluation. The depicted profiles, from top
to bottom, are the domestic hot water, electrical demand, PV generation and
space heating demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4 Illustration of the transformation process from the input space to the high-
dimensional feature space, by applying the kernel function φ, within a SVR
model [Hong, 2013] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5 Electrical demand forecast results for the 5th of May using the daily persistence,
ARMA and SVR methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.6 Domestic hot water forecast results for two consecutive days, 5th and 6th of
May, using the daily persistence, ARMA and SVR methods . . . . . . . . . . . . 32
4.1 Illustrative overview of possible energy demand, generation and storage units
as well as their thermal and electrical interactions within a residential building
energy system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 COP and heat generation power development with respect to the ambient
temperature of an ASHP ’Dimplex A/W LA6TU’ for different application tem-
peratures [Dimplex, 2017] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 Characteristic voltage, current and electrical power trends during the charging
process of a Li-Ion battery storage system . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Illustration of the energy balance for a middle layer; the heat flows represent
the charging heat from the heat generation unit, the heat conduction between
neighboring layers, the drawn heat from the consumer cycle and losses to the
tank surrounding environment [Schütz et al., 2015a] . . . . . . . . . . . . . . . . 45
4.5 Generic representation of the different states for the SoC of the empirical
approach. The black solid line depicts the temperature profile [Harb et al., 2017] 47
4.6 Consideration of the usable and unusable amount of energy for the determina-
tion of the SoC [Harb et al., 2017] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.7 Experimental scehme depicting the supply unit for the storage during the
charging cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
List of Figures
4.8 SoC comparison of the storage modeling approaches with the respect to mea-
surement data for use case 1; The stratified storage model comprises 5 layers
while Cunusabl e is represented by the factor f and set to the value 0.5 . . . . . . 52
4.9 Comparison of the development of the temperature profile for the measured
data and the stratified storage model in use case 1 . . . . . . . . . . . . . . . . . 53
4.10 SoC comparison of the storage modeling approaches with the respect to mea-
surement data in use case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.11 SoC comparison of the storage modeling approaches with the respect to mea-
surement data in use case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.12 4R2C model structure [Harb et al., 2016a] . . . . . . . . . . . . . . . . . . . . . . 57
5.1 Derivation of the scenarios’ probabilities π(s) from the root to the leaf nodes
within the scenario tree of multi-stage stochastic programming . . . . . . . . . 65
5.2 Uncertainty characterization of DHW demand. In the left diagram, the expected
value is depicted as a black solid line and the scenarios in grey color. In the
right diagram, the reduced scenario set is depicted stage-wise. Three scenarios
(states) are chosen to represent every stage [Harb et al., 2016b] . . . . . . . . 66
5.3 Uncertainty characterization of electrical demand: scenario samples and re-
duced set [Harb et al., 2016b] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.4 Scenario tree structure for a four-stage problem with three states respectively
[Harb et al., 2016b] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.5 Structure of a Dantzig-Wolfe decomposition model as well as the interactions
between the master- and subproblems based on shadow prices and proposals
[Bradley et al., 1977] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.6 Procedural description of the column generation algorithm [Harb et al., 2015] 73
5.7 Relation between column generation and Lagrangian relaxation [Nishi et al.,
2009] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.8 Procedural description of the integrated Lagrangean relaxation - column gen-
eration algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.1 State-based representation of HP-EH-Bat reactive control strategy; The transi-
tions are defined in function of the thermal storage and battery status . . . . . 81
6.2 Dynamic performance of the thermal side for PV-HP-EH under the Ref strategy.
The depicted profiles, from top to bottom, are the space heating and domestic
hot water demands, the thermal power of the HP, the On/Off operation status of
the HP, the thermal generation of the auxiliary EH and the state of charge of
the water storage tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
List of Figures
6.3 Dynamic performance of the thermal side for PV-HP-EH under the DPI strategy.
The solid lines represent the operation status delivered by the MILP scheduling
algorithm whereas the dashed lines represent the operation within the dynamic
simulation model formulated in Dymola/Modelica . . . . . . . . . . . . . . . . . . 83
6.4 Dynamic performance of the electrical side for PV-HP-EH under the DPI strategy.
Pdemand denotes the elctrical demand, Pimport and Peyport the electrical import
and export from the public grid, PPV the local PV electricity generation, PHP
and PEH the electrical consumption of the HP and EH units . . . . . . . . . . . . 84
6.5 Dynamic performance of the thermal side for for PV-HP-EH under the DF strategy 86
6.6 Computation time comparison between DPI, DF and SP scheduling models; The
values denote the average time for computing one day-ahead schedule; The
arrow indicate the increase of computation time in percentage of SP models
compared to DF; The simulations were carried out on a work-station with 12
active cores Intel Xeon CPU [email protected] GHz and 32 GB of RAM . . . . . . . 89
6.7 Schedule profiles for a random day in February using the centralized and dis-
tributed approaches. ’D-R’ denotes the residual load, with ’D’ as the aggregated
electrical demand of lights and appliances for the participating buildings and
’R’ the renewable energy from wind and PV units; large negative value indicate
high availability of renewable energy. ’I-E’ represents the cluster’s interaction
with the public grid, with I and E as the electricity imported to and exported
from the cluster, respectively [Harb et al., 2015] . . . . . . . . . . . . . . . . . . . 91
6.8 Grid interaction (I-E) for the centralized and distributed scheduling approaches
over one year with respect to the residual load (D-R) [Harb et al., 2015] . . . . 92
6.9 Influence of including/excluding the production costs in the buildings’ proposals
on the grid interaction, over one year with respect to the hour of the day, within
the distributed approach. The green range indicates the desired self-sufficient
status, the blue range denotes electricity exports from the mircogrid whereas
the yellow to red range denotes electricity import [Harb et al., 2015] . . . . . . 93
6.10 Computation time analysis of the centralized and CG distributed scheduling
models for the coordination of two clusters comprising 34 and 102 buildings.
The arrow represents the computation time reduction achieved by the dis-
tributed approach compared with centralized. The other percentage ratios
denote the increase of the computation time when increasing the cluster size
within every approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.11 Convergence assessment of the CG (in black) and integrated LRCG (in red)
algorithms for a random day in March. The solid lines represent the develop-
ment of the linearly relaxed primal solution of the master problems whereas the
dashed lines depict the development of the lower bounds. The cross markers
denote the integer solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
List of Figures
6.12 Assessment of the primal zLRDW and integer zRDW solution, as well as the
computation time of the CG and integrated LRCG distributed scheduling ap-
proaches. Within the boxplot, the bottom and top of the box are the first and
third quartiles (25 % and 75 %), while the band inside is the median. The
whiskers represent a 1.5 multiple of the interquartile range. The ’+’ markers
denote the outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
A.1 Dynamic performance of the thermal side for PV-HP-EH under the SPdhw strategy105
A.2 Dynamic performance of the thermal side for PV-HP-EH under the SPel strategy106
A.3 Dynamic performance of the thermal side for PV-HP-EH-Bat under the Ref
strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
A.4 Dynamic performance of the thermal side for PV-HP-EH-Bat under the DPI
strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
A.5 Dynamic performance of the thermal side for PV-HP-EH-Bat under the DF strategy107
A.6 Dynamic performance of the electrical side for PV-HP-EH-Bat under the DF
strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A.7 Dynamic performance of the thermal side for PV-CHP-EH under the DPI strategy108
A.8 Dynamic performance of the electrical side for PV-CHP-EH under the DPI strategy109
A.9 Dynamic performance of the thermal side for PV-CHP-EH under the DF strategy109
A.10 Dynamic performance of the thermal side for PV-CHP-EH-Bat under the DPI
strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
A.11 Dynamic performance of the electrical side for PV-CHP-EH-Bat under the DPI
strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
A.12 Dynamic performance of the thermal side for PV-CHP-EH-Bat under the DF
strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A.13 Dynamic performance of the thermal side for PV-CHP-B under the DPI strategy 111
A.14 Dynamic performance of the electrical side for PV-CHP-B under the DPI strategy112
A.15 Dynamic performance of the thermal side for PV-CHP-B under the DF strategy 112
A.16 Dynamic performance of the thermal side for PV-CHP-B-Bat under the DPI
strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
A.17 Dynamic performance of the electrical side for PV-CHP-B-Bat under the DPI
strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
A.18 Dynamic performance of the thermal side for PV-CHP-B-Bat under the DF strategy114
List of Tables
3.1 Summary of the performance of the daily persistence, ARMA and SVR models
for forecasting the HEMS input profiles over an assessment period of 30 days
with a time resolution of 15 min and a forecast horizon of 24 h . . . . . . . . . . . 32
4.1 Parameters of ECOPower 3.0 [Vaillant, 2017] . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Parameters of a Schott PV module [Schott, 2017] . . . . . . . . . . . . . . . . . . . 41
4.3 Parameters of the battery model [Sundstrom O., 2010] . . . . . . . . . . . . . . . . 43
4.4 Configuration within the investigated use cases . . . . . . . . . . . . . . . . . . . . 51
4.5 Specific parameters boundaries [DIN - German Institute for Standardization,
2005, Recknagel et al., 2009, Association of Engineers, 2012a] . . . . . . . . . . 60
6.1 BES configurations: The characteristics of the primary heat generators, Dimplex
air-to-water LA9TU HP (QA2W35 = 7.5 kW) and Vaillant EcoPower 3.0 CHP (P =
3 kW, Q = 8 kW) are presented in Chapter 4 . . . . . . . . . . . . . . . . . . . . . . 80
6.2 Assessment results of the scheduling strategies for all BES configurations during
the months March, September and December. The optimization time resolution
is 15 min, the rolling horizon’s rescheduling interval and scheduling horizon are
24 and 48 h, respectively. The MIP gap is set to 1 % for DPI and DF and 1.5 %
for SPel and SPdhw. The costs are weekly averaged. Negative VS, VPI and VU
indicate a cost reduction whereas positive values denote an increase with respect
to the costs of the Ref , DPI and DF, respectively . . . . . . . . . . . . . . . . . . . . 87
xxix
1 Introduction
1.1 Background: Trends and challenges
1.1.1 "Energiewende": Energy transition and consequences
The impact of increased social awareness and concern about the potential consequences
of greenhouse gas (GHG) emissions is reflected in the energy and climate policy targets of
the German government, mainly, within the set of decisions taken in 2011 known as the
"Energiewende" or energy transition. This transition refers to a fundamental reformation
of the electricity sector to a decarbonized energy system mainly based on renewable
energy (RE) i.e. wind and solar, with emphasis on increased energy efficiency.
1990
1995
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Year
0
5
10
15
20
25
30
35
Share
of
RE e
lect
rici
ty g
enera
tion in %
3.65.4
7.0 7.18.3 8.0
9.8 10.611.6
14.214.816.116.8
20.4
22.923.9
25.8
30.0
Hydro + biomass
PV
Wind
Figure 1.1: Development of renewable energy sources in Germany with regard to theshare in gross electricity generation based on the data from [Federal ministryfor economic affairs and energy, 2015b]
This resulted in a significant increase of the share of renewable electricity generation
1
Introduction
which reached 30 % in 2015, corresponding to double the share of 2010. Figure 1.1 shows
the development of RE in Germany over the past 25 years. The intermediate goal of
reaching 35 % by 2020 is foreseen to be exceeded. The long-term goal is set to increase
the RE contribution to 80 % by 2050.
This rapid increase led to concerns with regard to the grid stability and supply security as
the accommodation of the rising share of volatile RE has proven to be a major challenge
[Stoyanova et al., 2013]. In contrast to conventional power plants, RE sources are
only partially dispatchable and characterized by distributed and uncertain generation.
Consequently, an adaptation of the energy system is required, mainly flexibility from other
parts of the system is required to achieve the balancing needs and ensure the network
reliability. These increased balancing needs may be addressed by a number of strategies
that include energy storage and increased flexibility of the demand side.
1.1.2 Building energy systems: Decentralization and flexibility
Buildings account for more than one third of the total primary energy consumption.
Mainly, the space heating share amounts to around to 30 % as shown in Figure 1.2. Hence,
buildings can play an important role in the energy transition.
2%3%
5%
22%
27%
2% 39%
ICT
Lighting
Domestic hot water
Other process heat
Spaceheating
Other process refrigeration
Mechanical energy
Figure 1.2: Potential of buildings within the energy transition: Energy consumption bythe field of application in Germany in 2014; data from [Federal ministry foreconomic affairs and energy, 2015a]
The promotion of RE and energy efficiency as part of the "Energiewende" strategy has
led to an increased installation of photovoltaics (PV) panels and modern heating systems
i.e. heat pumps (HPs) and micro combined heat and power (µCHP) units in residential
buildings. This resulted in the following trends:
2
1.2 Demand side management: Review
. electricity generation, through distributed PVs and (µCHPs), is switching from a
power plants based centralized structure towards a decentralized structure which
poses a challenge for the grid stability
. passive consumers are transforming into prosumers 1 that can participate directly in
the energy market
. flexibility in energy generation and consumption on the demand side is emerging.
This is achieved by coupling modern heating systems, HPs and CHPs with thermal
storage, PVs with electrical storage units i.e. batteries or through management of
electric vehicles or shiftable home appliances. Notably, the potential of the electrical
flexibility generated from heating systems is significant when considering the share
of space heating in the total energy consumption. The operational flexibility provided
by buildings can be exploited by intelligent control strategies to enable load shifting
which represents the "backbone" of the future concept of smart grid 2 and provide
the balancing needs for stabilizing the grid. These strategies are widely known as
demand side management.
1.2 Demand side management: Review
Demand side management (DSM) is generally defined as the modification of energy
demand of consumers through different methods such as financial incentives. The main
implementation mechanisms of DSM are short-term demand response (DR) and long-term
energy efficiency programs. According to [Albadi and El-Saadany, 2008], DR is defined
as “intentional electricity consumption pattern modifications by end-use customers that
are intended to alter the timing, level of instantaneous demand, or total electricity
consumption”. There are two general approaches to DR programs:
. direct load control which employs a load signal
. indirect load control respectively pricing-based approach which employs a price
signal e.g. time-of-use or real-time pricing
Recently, home energy management systems (HEMS) have emerged for local load man-
agement at the consumer side. According to [Beaudin and Zareipour, 2015], HEMS
are defined as residential DR tools that shift or curtail demand to improve the energy
consumption and production profile of a building on behalf of a consumer by providing
optimal operation schedules.
1This term denotes a new class of consumers that both consume and produce electrical energy throughlocally installed µCHPs or PVs
2The smart grid concept refers to an increased use of digital information and controls technology to integratecentralized and decentralize electricity generators, consumers and storage units and improve reliability,security, and efficiency of the electric grid.
3
Introduction
𝑡
Demand
PV generation
Storage management Demand modification
Figure 1.3: Illustration of discrepancy between electrical demand and local PV generationas well as load shifting strategies through demand modification and storagemanagement
Figure 1.3 exemplary depicts the discrepancy between a consumer’s electrical demand
and local PV generation. Further, it illustrates the strategies i.e. storage management and
demand modification, employed by a HEMS for adapting the consumption to enhance the
integration of PV. Storage management targets the surplus of PV generation while demand
modification adjusts the electrical demand according to the availability of PV generation.
DSMfeatures
Classification
Objectives
Targetdevices
Decisionscope
Forecastmodels
Schedulingalgorithms
Architecture
Figure 1.4: Overview on the characterizing features of DSM concetps
Numerous works in the literature provide in-depth reviews on HEMS or building energy
4
1.2 Demand side management: Review
management systems [Javaid et al., 2013, Khan et al., 2015, Vega et al., 2015, Beaudin
and Zareipour, 2015, Lee and Cheng, 2016], scheduling in buildings [Lazos et al., 2014,
Cardozo, 2014], and DR concepts [Albadi and El-Saadany, 2008, Barbato et al., 2013, Kosek
et al., 2013, Ansari, 2014, Adika and Wang, 2014, Siano, 2014, Müller et al., 2015, Vardakas
et al., 2015, Olatomiwa et al., 2016]. Accordingly, the main characteristic features of DSM
concepts are identified and illustrated in Figure 1.4.
1.2.1 Classification: Triggering criteria
DR programs can be categorized according to economic or reliability drivers [Siano, 2014].
Reliability programs target high-voltage connected customers e.g. large commercial and
industrial entities, and yield to technical objectives that are services to the grid, such
as frequency and voltage control, and power quality. The economic category addresses
customers available at low-voltage networks while providing economic incentives.
1.2.2 Objectives for scheduling strategies
The objectives for operation scheduling in HEMS vary depending on the consumer, the
application and DR framework. The list includes:
. energy costs reduction e.g. minimization of energy wastage
. increase consumer comfort and well-being
. environmental concerns e.g. GHG emissions’ reduction
. load profiling which evaluates the desirability of the load profile to some party such
as:
• reducing grid dependency for the consumer
• reducing peak demand for the utility
• adapting to the variations in power supply from renewable energy sources to
reduce the undesirable power imbalance (smart grid application).
1.2.3 Target devices in DSM concepts
According to the survey provided in [Beaudin and Zareipour, 2015], the majority of
HEMS and DR studies in the literature typically target electrical appliances or white
goods such as time-shiftable loads notably washing machines, dryers and dishwashers
as well electrical storage systems mainly stationary batteries and electric vehicles. The
underlying models of these electrical components are, to a certain extent, simple to
5
Introduction
formulate in the scope of mathematical optimization. In contrast, the scheduling of
heating systems, aside from electrical heater is scarcely addressed in the literature.
[Gunkel et al., 2012, Shaneb et al., 2012, Bakker, 2012, Di Zhang et al., 2013, Zapata
et al., 2014] formulated scheduling strategies for distributed µCHPs while [Adika and
Wang, 2014, Fink et al., 2015] incorporated a simplified HP model into a HEMS concept.
1.2.4 Approaches: Decision scope
HEMS can be classified into reactive and predictive approaches. Reactive HEMS are
typically heuristics, i.e. knowledge based techniques, that approximate solutions based
on certain prescribed rules for the actual system state, uniquely, with no consideration
of predictions. Hence, reactive HEMS are also referred to as online scheduling [Fohler,
2011]. An example of this approach for energy management in residential building is
provided in [Moshövel et al., 2015]. The development of heuristics require extensive
experience and knowledge about the considered system and are case-specific strategies
that cannot be generalized for other systems. The main advantage of a well-designed
heuristic is the low computational effort required for generating a good solution. Yet,
heuristics are difficult to derive for complex architectures including different components.
However, reactive HEMS have been recently formulated as multi-agent system (MAS)
concepts. MAS is a negotiation based framework which is characterized by a flexible and
extensible architecture. A notable example is provided by the ’PowerMatcher’ model in
[Kok et al., 2005].
Predictive HEMS incorporate forecasts for estimating states to provide an optimal sched-
ule under future conditions. Predictive HEMS are also known as proactive scheduling as
well as unit commitment. They are also referred to as preventive scheduling when infor-
mation about the behavior of uncertainties is considered in the formulation. Predictive
HEMS rely on a mathematical program or meta-heuristic for the scheduling model.
Typically, in the literature [Castro et al., 2010, Beaudin et al., 2012, Kopanos and Pis-
tikopoulos, 2014, Fang and Lahdelma, 2016] predictive scheduling is implemented in
a moving window framework, also referred to as sliding window, rolling or receding
horizon algorithms, which is similar to a model predictive control (MPC) methodology.
This framework is used to reduce the computational effort and increase the accuracy
of the scheduling by updating the forecasts in a cyclic manner which allows for react-
ing to disturbances, depending on the rescheduling rate, which is a feature of reactive
scheduling.
Through embedding forecasts, preventive HEMS and DR are expected to hold an advan-
tage over classical reactive approaches for the accommodation of volatile RE especially in
scenarios with a large share of renewable generation capacity.
6
1.2 Demand side management: Review
1.2.5 Forecast models in predictive scheduling
Proactive HEMS or scheduling incorporates several forecasts as inputs. These include
predictions of weather conditions e.g. solar irradiation and outdoor temperature, PV and
wind power generation, occupancy, as well as energy consumption behavior i.e. space
heating, domestic hot water and electrical demand.
Forecast models have been heavily investigated in the literature [Suganthi and Samuel,
2012, Veit et al., 2014] but still continue to evolve. Prediction methods are broadly
grouped in:
. black box models which are data driven formulated and require no knowledge about
the physical characteristics of the system. These comprise regression and machine
learning techniques as well as modified formulations i.e. adaptive and stochastic
models. These models are widely used in the literature [Hong, 2013, Suganthi
and Samuel, 2012]. The field of applications includes price, weather variables, PV
generation, electrical and thermal demand prediction among many others
• regression based methods include: (a) Statistical time series techniques which
use historical data as the basis of estimating future outcomes such as exponen-
tial smoothing, Holt-Winters method [Hoverstad et al., 2015], autoregressive
model i.e. ARMA, ARIMA, SARIMA (b) Causal methods which embed an ex-
ogenous input in the forecast model such as ARMAX and multiple regression
models [Bacher and Madsen, 2011]
• machine learning algorithms mainly artificial neural networks (ANN) [Frausto
and Pieters, 2004] and support vector regression (SVR) are the most known
black box models. These methods are widely applied to tackle complex defined
problems due to their strong non-linear learning ability and potential to be
made adaptive and self-learning
. white box models which are based on detailed physical representation of a specific
system [Li and Wen, 2014]. This approach is exhaustively applied for predicting the
building thermal behavior i.e. space heating demand or indoor air temperature
. grey-box models [Kristensen et al., 2004] that denote an intermediate stage between
white and black models and are typically applied to predict the thermal behavior as
well.
It is worthwhile to note that despite the advances in formulating complex forecast methods,
the naive prediction model remains a hard to beat approach for many applications [Veit
et al., 2014]. This is emphasized by the almost non-existing modeling and computational
burden. A naive prediction is a persistence routine based on cycle pattern i.e. prediction
for today is yesterday (daily persistence) or the corresponding day of past week (weekly
persistence).
7
Introduction
1.2.6 Scheduling algorithms
Several approaches have been proposed in the literature to schedule residential energy
systems. These can be categorized into:
. Mathematical optimization or programming:
• linear programming (LP) [Shaneb et al., 2012], quadratic programming (QP),
dynamic programming (DP) [Chang et al., 2012, Nguyen et al., 2012], mixed
integer linear programming (MILP), mixed integer non-linear programming
(MINLP) [Zhang et al., 2012]
• decomposition techniques such as Lagrangian Relaxation (LR) or Lagrangian de-
composition (LD) [Zelazo et al., 2012, Zhang et al., 2013, Diekerhof et al., 2014],
Benders decomposition and Dantzig-Wolfe decomposition (DWD) [Dantzig, 1965]
combined with the column generation algorithm [Gauthier et al., 2014]
• robust optimization [Ferreira et al., 2012] and stochastic programming.
. Meta-heuristic [Hutterer et al., 2010, Rahman et al., 2014, Huang et al., 2015,
Gamarra and Guerrero, 2015]: bio inspired evolutionary algorithms (EA), population
based genetic algorithm (GA) and particle swarm optimization (PSO), trajectory
based simulated annealing (SA) and tabu-search method (TSM).
. Heuristics: rule based or knowledge based techniques [Moshövel et al., 2015] and
priority listing [Delarue et al., 2013].
In LP, all decision variables are continuous, hence, on/off decisions, which are formulated
as binary variable, cannot be modeled. Hence, the suitability of LP for scheduling problems
is quite limited. MILP extends LP to allow for binary or integer variables modeling which
makes the problem then NP-hard 3. MILP based unit commitment is the most widely
used approach for formulating scheduling problems for HEMS and DR e.g. [Bozchalui
et al., 2012, Zhu and Chin, W.M Fan,Z., 2012, Gunkel et al., 2012, Beaudin et al., 2012, Di
Zhang et al., 2013, Wakui et al., 2014, Zapata et al., 2014, Tenfen and Finardi, 2015, Fink
et al., 2015]. MINLP and metaheuristic enable non-linear modeling, however, they tend
to face convergence problems or get stuck in local optima. MILP provides a higher
chance of achieving a globally optimal solution compared with MINLP and meta-heuristics
as well as direct measure of the optimality a solution, the MIP gap. More importantly,
several powerful solver packages have been established and optimized for tackling such
problems, such as IBM CPLEX [IBM, 2017] and Gurobi [Gurobi Optimization, 2017]
optmizers. Yet, MILP restricts the model to a linear formulation which depending on the
linearization scheme adopted can greatly affect the validity or reliability of the solution
3Non-deterministic polynomial-time hard which increases the computational effort to find an optimal solution
8
1.3 Challenges
despite achieving global optimality conditions. Therefore, robust formulation should be
adopted to allow for minimal loss of performance information.
1.2.7 Architecture of DSM strategies
[Scattolini, 2009, Law et al., 2012, Kosek et al., 2013] provide an overview of control
and DR system architectures. The arrangements comprise centralized, decentralized and
hybrid or distributed architectures.
In centralized architectures, the central component has access to all information. The-
oretically, a centralized approach allows for achieving the best solution. However, the
difficulty in this approach lies in application bottlenecks such as scalability, computation
tractability, data privacy concerns and communication infrastructure.
Decentralized architectures eliminate several disadvantages of a centralized approach
on the cost of stability and optimality. In a decentralized architecture, the centralized
problem is decomposed into sub-systems with no direct coupling between them.
Hybrid or distributed architectures are formulated based on a trade-off between stability
and information exchange. In non-hierarchical distributed architectures, subsystems with
similar or opposite goals, interact directly with each other in a cooperative or competitive
manner. An example for non-hierarchical distributed architecture is provided in [Barbato
et al., 2013], which apply a game theory based scheduling model for residential DSM.
Hierarchical distributed architectures employ a multi-layer structure with a coordinator or
aggregator entity which coordinates the negotiation across the subsystems. Hierarchical
distributed structures are typically applied to MAS [Harb et al., 2014]. Further, it is well
suited for mathematical optimization decomposition methods such as LR and DWD [Harb
et al., 2015].
1.3 Challenges
Despite the numerous research activities in the field of DR and HEMS shown in the prior
review, several challenges persist to exist for the development and implementation in
residential building and neighborhoods [Baharlouei and Hashemi, 2013, Beaudin and
Zareipour, 2015]. The main challenges include:
. Modeling of heating energy systems
. Flexibility and extensibility of the modeling approach
. Uncertainty of underlying forecast models
. Scalability of the DSM strategy
9
Introduction
1.3.1 Modeling of heating energy systems
The majority of HEMS papers consider batteries or white goods as flexibility source
[Beaudin and Zareipour, 2015, Olatomiwa et al., 2016]. In the context of predictive
scheduling, the underlying mathematical optimization model complexity, specifically MILP
based, of heating units within building energy systems (BES) mainly the operational
dynamics of air-to-water heat pumps (AW-HPs), µCHPs and water storage tanks remains
taxing and not fully explored.
The MILP models of AW-HPs in the literature are simplified with no consideration of
part load operation or dynamic development of the coefficient of performance (COP),
heat output and electical consumption with respect to the evaporator and condenser
temperatures. The widespread formulation represents the COP as a fix value, for example
[Molitor et al., 2013, Diekerhof et al., 2014] or simple linear dependency of the outdoor air
temperature. This approach doesn’t allow for a robust representation of the HP operation,
which directly impacts the scheduling reliability.
Another critical gap is found in the modeling of thermal water storage tanks. [Schütz et al.,
2015a, Schütz et al., 2015b] indicate that the most widespread MILP representation of
thermal water storage tank is based on a single capacity model for example in [Di Zhang
et al., 2013, Wakui et al., 2014, Zapata et al., 2014, Molitor et al., 2013, Diekerhof et al.,
2014]. Further, the investigations [Schütz et al., 2015a, Schütz et al., 2015b] show that
this modeling approach is unable to deliver an accurate representation of the state of
charge of the storage which leads to scheduling infeasibilities .
1.3.2 Flexibility and extensibility of the modeling approach
The installation of PVs, solar thermal panels, modern heating supply systems such as
HPs and µCHPs, thermal storages, stationary batteries and electric vehicles has led to
an unprecedented heterogeneity of units, that are subject to different unique charac-
teristics and dynamics, within residential building energy systems. As a result, future
configurations may include a combination of different flexibilities such as two electricity
generators i.e. PVs and CHPs as well as both thermal and electrical storage units. Further,
the modification of pre-existing setups by replacing or additionally installing units is quite
probable.
This heterogeneity and variability of thermal and electrical systems’ configurations is
challenging for the modeling of HEMS and DR. This requires a flexible and extensible
modeling framework which can easily integrate different as well as additional new systems.
10
1.3 Challenges
1.3.3 Uncertainty of underlying forecast models
The main advantage of predicitve sheduling is the incorporation of forecasts to anticipate
future states and provide an optimal operation under these conditions. However, these
forecasts represent a crucial source of uncertainty which can lead to scheduling infea-
sibilities. In a benchmark of state-of-the-art methods for household electricity demand
forecasting, [Veit et al., 2014] showed that the mean absolute percentage error for day-
ahead forecast ranges between 20 and 150 %. The forecast error increases with higher
time resolution considered i.e. small time steps. Yet, the majority of studies of HEMS
focus solely on scheduling and assume perfect forecasts. This approach is referred to as
deterministic unit commitment.
Scheduling under uncertainty, also referred to as preventive scheduling, is a framework
for modeling optimization problems that involves uncertainty. [Grossmann, 2012] and
[Cardozo, 2014] deliver a good overview on the integration of uncertainty in scheduling
models. Uncertainty can be characterized through a probability distribution description, or
in a bounded form if this distribution is not available and instead only error bounds can be
obtained. Accordingly, stochastic optimization also referred to as stochastic programming,
and robust optimization are applied for preventive scheduling.
Robust optimization incorporates the bounded range of the uncertainty, and focuses mainly
on minimizing the impact of the worst-case scenario. This approach is mostly suited for
risk-adverse consumers and may not be the most cost effective approach. [Conejo et al.,
2010] and [Chen et al., 2012] used the method proposed by [Bertsimas and Sim, 2001]
to tackle price uncertainty in real-time demand response strategies. [Wang et al., 2015]
used a robust optimization approach for day-ahead load scheduling in smart homes while
considering uncertainties from locally installed PV systems.
Stochastic programming (SP) is a systematic approach for dealing with uncertainty. In
SP, uncertainty is represented by a discretized scenario tree according to decision stages.
The basic idea is to make ’here and now’ decisions at the first stage and then take some
corrective ’wait and see’ actions in the future when the uncertainty is revealed [Grossmann,
2012]. The objective in SP is to optimize the cost of the ’here and now’ decisions and
the expected cost of the recourse action. [Chen et al., 2012] proposed a DR strategy
based on a two-stage stochastic MILP approach for residential appliances by considering
uncertainty in price forecast. The model is formulated as a rolling procedure in which the
two-stage, scenario based stochastic optimization is performed for every 5 minutes. The
appliances considered comprise white good as well as electric heaters. [Chen et al., 2012]
further compared the SP model with a robust counterpart and deduced that the SP model
achieves better performance. [Cau et al., 2014] integrated the probability distribution of
solar irradiation, wind speed and electrical and applied a 3-stage stochastic programming
approach for short-term scheduling in a microgrid. The focus lied on electricity generators
11
Introduction
i.e. PV and wind turbines as well as electrical batteries and hydrogen storage systems.
Similarly, [Huang et al., 2014] formulated a DR model based on a two-stage stochastic
MILP by considering the uncertainty of renewable wind and solar power generation.
In general, few studies have addressed scheduling under uncertainty in HEMS or DR
concepts. The focus lies on price and PV generation uncertainties with focus on electrical
appliances. Hence, the field remains not fully unexplored. Mainly, the integration of
thermal units and uncertainty in thermal demand remains untackled.
1.3.4 Scalability of the DSM strategy
The size of the scheduling model for a DR strategy inreases with increasing number
of participating buildings and their corresponding units to coordinate simultaneously.
Centralized MILP approaches for coordinating electro-thermal units yield theoretically
an optimal value for the coordination problem but display limitations with respect to
scalability. The traditional methods for solving generalized MILP, the branch-and-bound
and cutting planes algorithm as well their conjuction, the branch-and-cut algorithm, have
greatly enhanced solving the MILP, however the problem remains NP-hard. Another
drawback of centralized approaches is the assumption that the central controller has
access to all the information which rises the issue of information privacy.
The scalability restriction has been tackled in the literature by applying a special designed
hierachical architecture comprising a centralized controller as well as aggregators such as
the TRIANA [Bakker, 2012] concept. Another approach consists of applying traditional de-
composition techniques to reformulate the large scale MILP into a hierachical optimization
structure and facilitate the solution process. It should be noted that, branch-and-bound,
cutting planes and branch-and-cut can also be considered as decomposition algorithms as
they split a problem in its linear relaxation and integrality constraints.
For Problems with complicating constraints, Lagrangian relaxation (LR) and Lagrangian
decomposition (LD) are the most common decomposition techniques for MILP problems
[Grossmann, 2012]. The basic idea consists of relaxing the original problem and splitting
into a sequence of smaller subproblems which are then solved by employing an iterative
algorithm like the subgradient method [Fisher, 2004]. If the Lagrangian relaxation splits
the problem into independent subproblems, it is referred to as Lagrangian decomposition.
In the context of a DR strategy for the coordination of residential heating systems, [Diek-
erhof et al., 2014] applied the Lagrangian relaxation (LR) method for coordinating heat
pumps. The main limitations of [Diekerhof et al., 2014] is that the algorithm convergence
is not fully addressed especially when incorporating both consumption and generator
flexible units.
12
1.4 Thesis statement and contribution
Dantzig-Wolfe decomposition [Dantzig and Wolfe, 1961] is a well established method
for problems with complicating constraints, which exploits special structured problems
i.e. block-angular constraint matrix structure and decomposes the original problem into
dynamically decoupled subsproblems and a master problem with coupling and convexity
constraints. A column generation algorithm is then used to iteratively solve the problem.
This decomposition method is quite suitable for the formulation of DR coordination
startegies since the problem has a block-angular structure. [Mc Namara and McLoone,
2013] and [Altay and Delic, 2014] applied a DWD for designing a hierachical demand
response strategy. However, both models are strictly linearly formulated and don’t
consider heating systems as a source of flexibility.
1.4 Thesis statement and contribution
This thesis delivers a mathematical programming based generalized, flexible and extensi-
ble software framework which enables the implementation of robust predictive HEMS
and distributed DR strategies that exploit hybrid thermal and electrical flexibility for local
load optimization or the integration of RE in residential building energy systems.
The underlying formulation is an MILP scheduling problem, that is coupled with a rolling
horizon algorithm or model predictive control. Several forecasting methods e.g. ARMA
and SVR are implemented for predicting weather and demand profiles. Data-driven grey-
box modeling approaches are integrated for incorporating the building wall mass as a
thermal flexibility within the optimization problem.
The framework enables the extension of the deterministic MILP problem to a stochastic
programming approach for coping with demand forecasts’ uncertainties on a building
level. Further, the framework allows for reformulating the MILP problem for a city district
based on inner decomposition methods to tackle the scalability and information privacy
issues in coordinating multiple BESs within a cooperative DR strategy. Moreover, the
framework employs dynamic simulation models for the verification and evaluation of the
scheduling strategies on a building level.
The contribution of this thesis addresses the challenges introduced in Section 1.3 for the
development of HEMS and DR strategies and presents a methodology for:
. Integration of thermal and electrical flexibility of BES in energy management strate-
gies
. Advanced MILP models of heating supply systems
. Novel approach for modeling thermal water storage systems and validation through
measurement data
13
Introduction
. Stochastic programming scheduling approach to cope with forecast uncertainty
. Evaluation of the performance of the scheduling models based on non-linear dynamic
simulation models
. Scalable formulation of DR strategies for residential city districts based on hybrid
decomposition techniques
1.5 Structure of this work
The structure of this work is mapped in Figure 1.5. In Chapter 1, the motivation for
this work is reviewed and the novelty as well as the objectives of the thesis are defined.
The methodology comprising the concept, architecture and software configuration is
introduced in Chapter 2. The inputs i.e. user behavior, weather variables’ synthesis
and forecast are presented in Chapter 3. The MILP based modeling of the individual
components within a BES is formulated in Chapter 4. The algorithms used for self-
scheduling under uncertainty and distributed coordination of multiple buildings are
formulated in Chapter 5. In Chapter 6, the performance of the algorithms is evaluated for
building and city district use cases. The thesis is then concluded by a summary and an
outlook to future perspectives.
14
1.5 Structure of this work
Chap.2Methodologyframework
Chap. 3Inputs
Synthesis
Forecastmethods Chap. 4
MILPmodelsof BES
GeneratorsStorage
units
Chap. 5Schedulingalgorithms
Deterministic
Stochasticprogramming
Decompositionapproaches
Chap. 6Analysis
HEMS ina building
DSMin citydisticts
Figure 1.5: Descriptive illustration of the thesis outline
15
2 Methodology: Framework
This chapter defines the methodology, also referred to as PyMPC [Harb et al., 2017]
framework, developed in this work. This comprises the concept as well as the software
architecture and configuration.
2.1 Concept
An overview of the basic formulation of a predictive HEMS for an individual building is
illustrated in Figure 2.1. The scheduling problem is formulated as a discrete MILP opti-
mization model in which the operation costs, respectively expected costs, are minimized
subject to the constraints that describe the technical setup and operational behavior of
the individual units of the building energy system and their interaction. The forecasted
inputs comprise weather related variables such as the outdoor temperature and solar
irradiation, PV generation as well as resident related variables such as occupancy, electri-
cal, domestic hot water and space heating demands. The synthesis and forecast of the
inputs is introduced in Chapter 3. The optimization model of the building energy system
is presented in Chapter 4.
Operation and capacity
constraints
Energy import/export
from/to the grid
Storage dynamics
(charging/discharging)
s.t.
HP
+-Minimize costs
CHP
Inputs Building energy systemAlgorithm
Figure 2.1: Overview on the individual components and basic formulation of a predictiveHEMS. The inputs comprise weather, space heating, domestic hot water,electrical demand, PV generation and occupancy. The building energy systemincludes battery, CHP, electrical, building wall mass, HP and water storagetanks
The scheduling model is integrated within a rolling horizon algorithm that allows the re-
duction of the computational effort and the impact of prediction uncertainties by updating
17
Methodology: Framework
the forecasts in a cyclic manner. The rolling horizon approach is illustrated in Figure
2.2. It is characterized by a rescheduling interval which defines the time between two
scheduling processes and a horizon that represents the length of the scheduling interval.
The concept of the PyMPC framework is to enable a modular, flexible and extendable for-
mulation of the scheduling problems of residential buildings. This comprises the building
energy system, i.e. energy generation and storage units, and scheduling approach.
time steps 1 2 3 4 5 6
rescheduling interval scheduling horizon
run 2
run 3
run 1
Figure 2.2: Simplified illustration of the concept of the rolling horizon algorithm. Therescheduling interval denotes the time between the scheduling steps orscheduling re-initialization whereas the scheduling horizon defines the lengthof scheduling step
The basic formulation of the scheduling model for a single building is a deterministic
MILP model which can be inherited by robust optimization or stochastic programming
approaches for embedding uncertainties into the scheduling model. Moreover, the MILP
model of a single building can be integrated within a decomposition optimization approach
i.e. Dantzig-Wolfe decomposition method for the formulation of a city district DSM model.
The scheduling algorithms are described and formulated in Chapter 5.
The system evaluation is enabled by coupling the scheduling model with a dynamic simu-
lation model based or hardware-in-the-loop (HiL) setup in which hardware components
are embedded in a simulation environment. The assessment takes into consideration the
impact of the forecast, the linearized models of the units within the BES and finally the
scheduling algorithms. The evaluation approach is illustrated in Figure 2.3.
The first method makes use of dynamic simulation models which depict the non-linear
behavior of the units. In this approach, the dynamic simulation model is integrated as a
functional mock-up unit (FMU) based on the functional mock-up interface (FMI) standard
[Modelica Association, 2016]. The second approach allows a closer to reality assessment
but necessitates the availability of the investigated hardware and hence large investment
and installation effort.
18
2.2 Architecture
Input: Actual data
Model: Dynamic non-linear
simulation models – FMU
Real units - HiL
Input: Forecast
Model:
Discrete linearized
optimization model
Schedule Actual
operation
Initialization
Figure 2.3: System testing and evaluation within the PyMPC framework. The left boxrepresents the scheduling model which uses forecast and linearized BESmodels, whereas the right box represents the realization platform whichincludes actual weather and demands as well as non-linear BES dynamicsimulation models (integrated as a FMU) or HiL
2.2 Architecture
The task diagram in Figure 2.4 delivers a comprehensive overview of the architecture of
the PyMPC framework. The latter consists of three layers, source, library and run-time.
Source layer
The source layer includes:
. a database of the weather and demand profiles which are used for training the
forecasting algorithms, as well as the characteristics of energy conversion units
. a user interface for configuring and characterizing the desired use case. This
comprises:
• the building energy system considered i.e. which unit and its corresponding
MILP model
• the forecasting methods for every application i.e. which method and its parame-
ters as well as the source of training data
• the scheduling algorithm
• the rolling horizon parameters as well as the simulation/optimization general
setup e.g. time resolution, simulation start and end time
19
Methodology: Framework
Ru
n-t
ime
Sou
rce
Configuration:• Components’ identification• Algorithm selection• Execution parameters• Inputs’ configuration
Lib
rary
Constructor
BES components:• Heat Pump• µCHP• PV• Battery• Water storage• Building wall mass
Forecasting methods:• Persistence • ARMA• SVR
DesignBuilding
Main model
For each run
Update inputsInstantiate
main modelCompute schedule
PyFMIsimulation
Scheduling algorithms:• Deterministic• Robust• Decomposition
methods• Stochastic
Programming
Database:• Components’ datasheets• Measurement data• Results logging
Update intialsof next run
Inputs
Run time controller
Figure 2.4: PyMPC framework structure and task diagram
20
2.3 Software configuration
Library layer
The library includes the forecasting methods, the individual MILP models of the different
BES components i.e. energy generation and storage units and the scheduling algorithms
as well as different meta-classes that are employed by a constructor to build up the BES
optimization model. The constructor creates a design object based on the configuration
set by accessing the database content.
The design object is then used to instantiate the building model i.e. the available units and
the corresponding capacities and data sheets, and the inputs i.e. the forecasting method
employed and the corresponding parameters, based on the BES components and forecast
methods libraries, respectively.
The building model and the inputs’ object are aggregated along with the interconnecting
electricity energy balance constraint and an objective function e.g. cost minimization
into a main model which is forwarded to the Gurobi solver [Gurobi Optimization, 2017],
within the run-time layer, for computing and determining the optimal schedule within the
dynamic run-time layer.
Run-time layer
The run-time module involves the iterations of the moving window algorithm. In each
iteration, all inputs are updated mainly forecasts from the current time index up to the
predefined horizon are generated. The constructor is then called upon to generate the
main model. Thereafter, the main model is optimized by the Gurobi solver for determining
the schedule which is passed to a corresponding FMU that simulates the corresponding
time period. In the case of stochastic programming, the simulation results are reported
back into the controller which decides which strategy should be adopted according the
the uncertainty realization. The final values of the simulations are set as initial values for
the next iteration.
2.3 Software configuration
2.3.1 Framework programming language
Python is the programming language applied for formulating the framework. Python is an
interpreted, object-oriented, programming language. Python is developed and distributed
based on an open source license and provides a large portfolio of generic and domain
specific modules, packages and libraries. Several libraries are employed within the PyMPC
framework, mainly, GurobiPy [Gurobi Optimization, 2017], Matplotlib, NumPy, Pandas,
21
Methodology: Framework
Scikit-learn [Scikit-learn development team, 2016], SciPy [SciPy development team, 2014]
and Statsmodels [Statsmodels development team, 2016].
2.3.2 MILP optimization solver
The Python application programming interface (API) "Gurobipy" provided by the optimizer
Gurobi [Gurobi Optimization, 2017] is employed for formulating the MILP optimization
model.
2.3.3 Dynamic simulation model
The BES dynamic simulation models are formulated based on the in-house developed
library within the project dual demand side management (2DSM) [Müller et al., 2015] with
the programming language Modelica [Modelica Association, 2012] in the environment
Dymola [Dassault Systemes, 2016].
Pressure Loss(Pipes)
Controller
M
Heat Delivery(Radiator)
Supply System ThermalZone
Consumer System
T
Heat Generator
Pressure Loss(Pipes)
Pressure Loss(Pipes)
Buffer Storage
Tank
M
Figure 2.5: Simplified overview on the space heating supply system within the dynamicsimulation models [Müller et al., 2015]. The main components are the thermalzone which represents the thermal behavior of the building, the hydraulicconnection, the heat generation system e.g. HP and CHP and thermal storageunits as well as the rule-based control strategy
The models comprise the building envelope, its interaction with the ambient conditions
22
2.3 Software configuration
and user behavior as well as the heating supply and delivery system as exemplary depicted
in Figure 2.5. The building is modeled based on [Lauster et al., 2014] which extends the
German industry guideline VDI 6007 [Verein Deutscher Ingenieure, 2012] also known as
two capacitor (2-C) low order thermal network model. [Lauster et al., 2014] provides a
detailed description of the corresponding modeling approach.
The heating supply system comprises a heat generation unit and a buffer storage tank. The
space heating mass flow is drawn out of the storage unit into a radiator delivery system
with thermostatic valves. The domestic hot water is drawn out of the buffer storage tank
as well.
The heat generators are formulated as black box models with non-linear behavior. This
allows for reducing the computational effort while preserving the model behavior accuracy.
A detailed modeling approach is adopted to a level that hydraulic cycles with specific media
properties are computed. The HP model consists of two heat exchangers connected by the
HP circuit. Given a specific electrical power, the mean temperature of the evaporator and
condenser will adjust according to the attached hydronic systems and their power demand.
Tabulated values for electrical and thermal powers are taken from the manufacturer data
sheets. In all simulations, the HP is assumed as non-modulating and can only be switched
on or off.
The CHP is a table based black box model as well. An internal controller will set the
power level of the CHP to reach a target flow temperature. This corresponds to a mean
temperature of maximum device temperature and the current heating curve temperature
or domestic hot water tap temperature. In this manner, the system energy losses are
reduced and the efficiency of the CHP is increased at partial load conditions. According
to the power level of the CHP, controllable between 30 % and 100 %, the thermal and
electrical power output are calculated.
The storage tank model consists of a discrete number of layers that make up the total
water volume. The internal control of the heat generators will ensure that there is always
a sufficiently high flow temperature so that the user’s comfort will not be affected by the
demand side management strategy.
The models are exported as co-simulation FMU based on the FMI standard and imported
within the framework using the python library PyFMI [Modelica Association, 2016], as
illustrated in Figure 2.6. The FMI standard allows for tool independent exchange of
dynamic models on binary format. FMUs can be exported for both model exchange and
co-simulation applications. A co-simulation FMU extends the model exchange standard
to include a solver. This allows for solving the dynamic model independently within a
coupled heterogeneous system.
23
Methodology: Framework
Dymola
Figure 2.6: Integration of the Modelica/Dymola dynamic BES simulation model within thePyMPC framework as co-simulation Python FMU based on the FMI interface
24
3 Inputs: Synthesis and Forecast
This section introduces the synthesis of the input data and the forecasting methods
implemented in the PyMPC framework. Demand profiles are commonly formulated based
on representative standard load profiles (SLP) which deliver an average profile that is
devoided from significant individual demand characteristics. The assessment results of
an energy management strategy greatly depend on the input data used. Therefore, it is
critical to make use of high resolution measurement data or generate synthetic demand
profiles that provide a realistic pattern or approximation of the representing load. The goal
in this section is to present a method to generate realistic profiles as well as identifying
and formulating suitable forecasting method for the individual variables and evaluate the
resulting forecasting error or uncertainty.
3.1 Synthesis
The input data for a HEMS comprise weather variables, electrical demand, domestic hot
water, space heating demand, active occupancy, as well as PV generation. These profiles
are interdependent and impact each other as illustrated in Figure 3.1.
Domestic
hot water
Active
occupancy
PV
generationSpace
heating
Electricity
demand
Figure 3.1: Interconnection of weather, occupancy, demand and PV profiles. Occupancyis only influenced by weather conditions and used to derive the electricaland domestic hot water demands. PV generation is determined based on theweather variables. Space heating is influence by the internal thermal gainsfrom active occupancy, electrical consumption and weather
25
Inputs: Synthesis and Forecast
It can be seen that the basis is the active occupancy model, according to, an electrical
as well as a domestic hot water demand is derived. The occupancy profile as well as the
electrical and DHW consumption is influenced by weather variables. Further, based on the
weather conditions a PV generation profile can be approximated as well as a space heating
demand. The space heating demand mainly depends on the physical thermodynamic
characteristics of the building considered but is significantly influenced by the occupant
behaviour i.e. presence and electrical demand, that impacts the ventilation and internal
gains.
Based on this approach, a high resolution occupancy generation developed by [Richardson
et al., 2008] is adopted and implemented in the PyMPC framework. The occupancy profile
generator is coupled with an electricity demand profile as introduced in [Richardson et al.,
2010]. The occupancy is then used as input for the domestic hot water model which is
formulated based on the model developed by [Jordan and Vajen, 2003]. The resulting
synthetic profiles for, exemplary, 3rd of March are depicted in Figure 3.2.
0 .00 .51 .01 .52 .02 .53 .0
kW
Pdemand
0 .00 .51 .01 .52 .02 .53 .0
#reside
nts
Activ e occupancy
00 :0003 -Mar
03 :00 06 :00 09 :00 12 :00 15 :00 18 :00 21 :00
Date
0 .00 .51 .01 .52 .02 .53 .0
kW
Qdhw
Figure 3.2: Stochastic occupancy based generation of demand profiles. The depictedprofiles, from top to bottom, are the electrical demand, occupancy anddomestic hot water demand
This methodology is critical in evaluating DSM strategies for a city district energy system
26
3.2 Forecasting methods
with several buildings since measurement data for such a scale are hardly available. The
assessment of HEMS for a single building later introduced in Section 6.1 is carried based
on measurement data for domestic hot water and electricity demand provided from the
project [Osterhage et al., 2015]. The weather data is derived from the test reference year
(TRY) weather data for the respective geographical location of the dwellings considered in
the project [Osterhage et al., 2015]. The TRY data is used to generate a space heating
demand profile based on a design driven grey-box model [Lauster et al., 2014] implemented
in Dymola/Modelica as well as PV generation profile based on the model later introduced
in Chapter 4. An overview on the resulting raw input data is exemplary depicted in Figure
3.3 .
0 .00 .20 .40 .60 .81 .01 .2
kW
Qdhw
0 .00 .51 .01 .52 .02 .53 .0
kW
Pdemand
0 .0
0 .5
1 .0
1 .5
2 .0
kW
PPV
00 :0003 -Mar
03 :00 06 :00 09 :00 12 :00 15 :00 18 :00 21 :00
Date
1 .01 .52 .02 .53 .03 .54 .0
kW
Qspace heating
Figure 3.3: Input data for the single building evaluation. The depicted profiles, from topto bottom, are the domestic hot water, electrical demand, PV generation andspace heating demand
3.2 Forecasting methods
The forecasting models implemented in the PyMPC framework comprise persistence,
ARMA, and SVR models. Further, a time-series additive decomposition model is formulated
27
Inputs: Synthesis and Forecast
using the Statsmodels package [Statsmodels development team, 2016] to cope with non-
stationary time series. In an additive decomposition model, the time series consists of a
trend, a seasonality/periodicity and a remainder component. Accordingly, the trend and
the remainder are forecasted using an ARMA or a SVR model while the seasonality is
forecasted using a persistence model.
3.2.1 Persistence
A persistence or naive forecast model is a simple prediction method in which measured
values are assumed to reoccur in the future. A persistence model is characterized by
its cycle e.g. daily or weekly, re-occurrence of the measured value. Accordingly, a daily
persistence sets the prediction yi for the next day as the measured values yi−n of the
previous day and a weekly persistence prediction is the measured values a from the day
one week before.
yi = yi−n (3.1)
The corresponding amount of time steps n for a given cycle is determined depending on
the time resolution ∆t .
3.2.2 ARMA
ARMA is a widely used forecasting model that combines an autoregressive (AR) with
a moving average (MA) model. An AR process forecasts a random variable as a linear
function of its past values. A MA model is a weighted sum of the historic model errors.
Consequently, the ARMA process is a linear function predicting yi based on the past
measurements and the past forecasting errors:
yi =AR︷ ︸︸ ︷
ρ0 +ρ1 · yi−1 + . . .+ρp · yi−p +MA︷ ︸︸ ︷
α0 +α1 ·εi−1 + . . .+αq ·εi−q
with εi = yi − yi
(3.2)
ARMA is implemented based on the Statmodels package. An ARMA(p,q) model is deter-
mined by the choice of the orders p and q. This process is called model selection and
introduced in [Zucchini, 2000]. The parameters ρp and αq are determined by minimizing
the sum of squared errors. The latter step is referred to as model fitting. The order of the
ARMA(p,q) model is determined by fitting the model to the measurement data through
a grid search while minimizing the Akaike information criterion (AIC) [Akaike, 1974]
based on a "brute force" method using the SciPy brute optimizer [SciPy development
team, 2014]. The AIC couples the model error to the amount of model parameters so that
the quantity of model parameters and thereby the model complexity does not increase
28
3.2 Forecasting methods
infinitely. Big grids can lead to a decrease in the model error but also to an increase
in the computation time needed to determine the model order with the lowest AIC. The
ARMA model is configured within the PyMPC framework by setting the time resolution
∆t , the forecast horizon, the fitting window i.e. the time range of past observation to be
considered for the model fitting, the fitting cycle i.e. the cycle for re-determining the
orders p and q.
In the following investigations, the time resolution ∆t and the forecast horizon are re-
spectively set to 15 minutes and 24 hours analogously to the intra-day also referred to as
day-ahead energy market.
3.2.3 SVR
Support Vector Regression (SVR) is a machine learning or computational intelligence
model. The idea behind SVR is that input data generated by a non-linear function can be
mapped by a kernel φ into a high-dimensional feature space in which the relation between
input and output becomes linear as indicated in Figure 3.4.
set) fðxi; yiÞgNi¼1 into a so-called high-dimensional feature space (Fig. 2.3), which
may have infinite dimensions, <nh . Then, in the high-dimensional feature space,
there theoretically exists a linear function, f, to formulate the nonlinear relationship
between input data and output data (Fig. 2.4a, b). Such a linear function, namely,
SVR function, is as Eq. (2.47):
f ðxÞ ¼ wTφðxÞ þ b; (2.47)
where f(x) denotes the forecasting values and the coefficients w (w 2 <nh ) and
b (b 2 <) are adjustable. As mentioned above, using SVM method one aims at
minimizing the empirical risk as Eq. (2.48):
Rempðf Þ ¼ 1
N
XNi¼1
Θεðyi;wTφðxiÞ þ bÞ; (2.48)
whereΘεðy; f ðxÞÞ is the ε-insensitive loss function (as thick line in Fig. 2.4c) and isdefined as Eq. (2.49):
Θεðy; f ðxÞÞ ¼ f ðxÞ � yj j � ε; if f ðxÞ � yj j � ε0; otherwise
�: (2.49)
In addition, Θεðy; f ðxÞÞ is employed to find out an optimum hyperplane on the
high-dimensional feature space (Fig. 2.4b) to maximize the distance separating the
training data into two subsets. Thus, the SVR focuses on finding the optimum
hyperplane and minimizing the training error between the training data and the
ε-insensitive loss function.Then, the SVR minimizes the overall errors, shown as Eq. (2.50):
Minw;b;ξ�;ξ
Rεðw; ξ�; ξÞ ¼ 1
2wTwþ C
XNi¼1
ðξ�i þ ξiÞ; (2.50)
with the constraints
Input space
a
(x)ϕ
Feature space
b*iξ
iξ
0ε+
ε−
-insensitive loss functionε
ε+ε−
*iξc
Hyper plane
Fig. 2.4 Transformation process illustration of an SVR model
2.7 Support Vector Regression Model 33
Figure 3.4: Illustration of the transformation process from the input space to the high-dimensional feature space, by applying the kernel function φ, within a SVRmodel [Hong, 2013]
In the feature space the relation between input and output is described by a hyperplane.
This relation is determined by optimizing, respectively, minimizing the model error. Based
on the assumption that the input data is subject to noise, the optimization constraints are
relaxed by using soft margins whose width is given by the parameter ε [Cristianini and
Shawe-Taylor, 2000]. All data elements inside these margins are not considered while
calculating the model error. The errors above +ε are denoted as ξ∗i , whereas erros below
-ε are denoted as ξi . The influence of the model error on the optimization is determined
by the parameter C . The accuracy of the SVR model highly depends on how well the
non-linear relationship between input and output is captured by the kernel function φ.
Common kernels are the linear kernel, the polynomial kernel and the radial basis function
29
Inputs: Synthesis and Forecast
(RBF) kernel [Cristianini and Shawe-Taylor, 2000]. The choice of the kernel is decided
based on prior knowledge about the data or by trial and error. Depending on the kernel
different parameters have to be set. The linear and polynomial kernels includes the
aforementioned parameters C and ε, whereas the RBF kernel further includes a specifiv
parameter γ which defines how far the influence of a single training example reaches.
The SVR model is implemented in the PyMPC framework based on the scikit-learn library
[Scikit-learn development team, 2016]. The optimal model configuration is determined by
applying the "GridSearchCV" algorithm [Scikit-learn development team, 2016]. Since the
amount of parameters for a SVR model is fixed, the AIC is no a suitable for assessing the
goodness of fit. Instead the coefficient of determination (R2) [Nagelkerke, 1991] is used.
It is calculated by training the model with a subset of the training data and evaluating the
forecast against the remaining training data based on a cross-validation process.
3.2.4 Performance indicators
The quality of a forecast is typically determined by a posteriori evaluation i.e. comparison
of predicted yi and observed values yi . Several accuracy indicators are available for
evaluating the performance of time series forecasting methods e.g. mean absolute error
(MAE), mean absolute percentage error (MAPE), root mean squared error (RMSE) and
mean absolute scaled error (MASE). Every indicator has advantages and disadvantages.
Therefore, it is advisable to use several indicators to assess the prediction accuracy. The
error measures considered in this work are:
. Mean absolute percentage error (MAPE):1
N
∑Ni=1 |
yi − yi
yi| ·100%
. Normalized root mean squared error (NRMSE):
√1
N
∑Ni=1(yi − yi )2√
1
N
∑Ni=1(yi )2
·100%
The MAPE indicator is adopted since it does not depend on the series’ mmagnitude or unit
of measurement, thus allowing for a representative measure of the overall forecast quality.
However, MAPE has the disadvantage of being infinite or undefined if the measurement
values are equal to zero. Therefore, NRMSE is further employed as a forecast accuracy
measure.
3.2.5 Evaluation
The dynamic performance of the forecasting methods for predicting the electrical demand
is exemplary depicted in the Figure 3.5 for the 5th May. The measurement values are
derived from consumption data for a single family house [Osterhage et al., 2015]. The
30
3.2 Forecasting methods
results show the stochastic nature of the consumption profile. Mainly, the upper subplot of
the naive forecast indicates that the electrical consumption at the evening hours for this
specific day is significantly lower than the consumption at the same period the previous
day. The ARMA and SVR models outperform the persistence method and exhibit similar
NRMSE of 52.39 and 49.39 %, respectively. These values are comparable to the results
presented in the forecast assessment studies found in the literature [Veit et al., 2014].
However, the SVR forecast allows for a better estimation of the dynamic behavior of the
demand profile.
456
Meas urem entDda tapers is tentD-DNRMSE:D1 1 0 .1 9
0 .01 .0
0 .00 .51 .01 .52 .02 .53 .03 .5
Meas urem entDda taARMAD-DNRMSE:D5 2 .3 9
0 0 :0 00 5 -May
0 3 :0 0 0 6 :0 0 0 9 :0 0 1 2 :0 0 1 5 :0 0 1 8 :0 0 2 1 :0 0
Date
0 .00 .51 .01 .52 .02 .53 .03 .5
Meas urem entDda taSVRD-DNRMSE:D4 9 .3 9
2 .03 .0
.0.0.0
Ele
ctri
calDd
eman
dDin
DkW
Figure 3.5: Electrical demand forecast results for the 5th of May using the daily persis-tence, ARMA and SVR methods
Table 3.1 summarizes the performance results of the forecast model for the ambient
temperature Tamb, solar irradiation Isolar, electrical Pdemand, space heating Qspace heating
and domestic hot water Qdhw demands. The prediction period is 30 days whereas the
model fitting interval is set to the past 4 weeks. The rescheduling (model re-fitting)
interval is one week. The forecasting horizon is a day-ahead or 24 hours and the time
resolution is 15 minutes.
31
Inputs: Synthesis and Forecast
Table 3.1: Summary of the performance of the daily persistence, ARMA and SVR modelsfor forecasting the HEMS input profiles over an assessment period of 30 dayswith a time resolution of 15 min and a forecast horizon of 24 h
Persistence ARMA SVR
Tamb 26.06 13.68 14.97 MAPE [%]28.89 17.05 18.58 NRMSE [%]
Isolar 49.67 353.05 431.95 MAPE [%]53.58 45.53 47.08 NRMSE [%]
Pdemand 108.48 100.73 76.73 MAPE [%]83.14 65.12 61.7 NRMSE [%]
Qspace heating 5245.61 3980.67 3201.73 MAPE [%]68.33 69.86 57.41 NRMSE [%]
Qdhw 131.17 67.18 70.94 MAPE [%]130.1 94.82 94.88 NRMSE [%]
0 .0
0 .5
1 .0
1 .5
2 .0
2 .5Meas urem entVda tapers is tentV-VNRMSE:V1 4 9 .9 8
0 .0
0 .5
1 .0
1 .5
2 .0Meas urem entVda taARMAV-VNRMSE:V9 5 .0 4
0 0 :0 00 5 -May
0 0 :0 00 6 -May
0 6 :0 0 1 2 :0 0 1 8 :0 0 0 6 :0 0 1 2 :0 0 1 8 :0 0
Date
0 .0
0 .5
1 .0
1 .5
2 .0Meas urem entVda taSVRV-VNRMSE:V9 9 .3 9D
omes
ticVh
otVw
ater
Vdem
andV
inVk
W
Figure 3.6: Domestic hot water forecast results for two consecutive days, 5th and 6th ofMay, using the daily persistence, ARMA and SVR methods
32
3.2 Forecasting methods
It is important to note that the forecast models’ accuracy strongly depends on the con-
figuration assumed for the model fitting interval, rescheduling frequency, forecasting
horizon and time resolution. The model fitting interval describes the data window of past
observations included in the training phase. The value adopted depends on the available
data set. Typically, this parameter is more influential in machine learning algorithms
such as ANN and SVR than in statistical models such as ARMA. Furthermore, the impact
of this parameter depends on the specific time series or application. The value of 30
days was determined for the considered data sets through a sensitivity analysis within
the interval 7 to 60 days. The rescheduling interval denotes the frequency at which the
model is refitted to redetermine its parameters e.g. ρp and αq within ARMA. A higher
refitting frequency generally results in decreasing the forecast error but resuls with an
increasing computation effort. Moreover, the forecast typically improves with lower time
resolution e.g. increasing ∆t from 15 to 60 min as the dynamic behavior of the time series
becomes more smooth, due to the loss of high granularity information, which is then
more easily captured by the model characterization process and consequently results in
better predictions. The forecast performance is also expected to improves with shorter
forecasting horizon since the uncertainty development is reduced.
The values marked in green in Table 3.1 highlight the lowest forecasting error for every
application. It can be seen that SVR performs best for forecasting electrical and space
heating demands. ARMA provides the best prediction results for the strongly seasonal
weather variables, ambient temperature and solar irradiation as well as the domestic
hot water demand. However, the dynamic evaluation of Figure 3.6 shows that the do-
mestic hot water demand strong stochasticity could not be captured by SVR and ARMA.
Hence, the computational effort is not justified and accordingly the persistence method is
recommended for this application.
Based on these result, the forecast setup for the assessment of the scheduling algorithms
in Section 6.1 is determined. ARMA is employed for predicting the weather variables, SVR
for electrical and space heating demand and persistence for domestic hot water demand.
Furthermore, it can be noticed that the forecasting errors are the highest in the case of
domestic hot water and electrical demand that strongly depend on the resident’s behavior
which has a strong stochastic nature. Accordingly, the uncertainty of these two demands
is integrated in the formulation of the stochastic programming scheduling approach.
33
4 Modeling of Building Energy Systems: Mathematical
Programming Formulation
The setup of a building energy system determines its HEMS compatibility and load shifting
potential. In this chapter, the discrete mathematical optimization models of the individual
BES components are introduced in the framework of mixed inter linear programming
(MILP). These components can be mainly categorized into energy generation and storage
systems. Figure 4.1 delivers an overview on the possibly existing components and their
interaction on both the thermal and electrical side within a BES.
ECOS 16 | Hassan HarbFolie 3
Buidling Energy System: Generation and Flexibility
Folie 3
+-
HEMS
thermal side electrical side
PV
EH
EHHP
CHP
CHPHP
Boiler
Figure 4.1: Illustrative overview of possible energy demand, generation and storageunits as well as their thermal and electrical interactions within a residentialbuilding energy system
4.1 Heat pump
Residential heat pumps for HVAC, mainly space heating and domestic hot water applica-
tions are compression HP and can be categorized according to the operation, respectively,
evaporator heat source, into ambient or exhaust air source (AS), ground water or soil
source (GS), exhaust air (EA) and water source (WS) heatpumps. The most common type
is ASHP followed by GSHP.
The performance of a HP unit is determined by the source/evaporator temperature and
the condenser inlet temperature and is characterized by the coefficient of performance
(COP) which is the ratio of the heating energy provided to the work required. Figure
35
Modeling of Building Energy Systems: Mathematical Programming Formulation
4.2 depicts the performance of an ASHP i.e. the generated heat power and COP based
on the evaporator air temperature for three discrete application temperatures, 35, 45
and 55 °C. The condenser inlet temperature is a dynamic variable which depends on the
hydraulic connections as well as the storage type and status. The COP increases with
higher evaporator temperature as well as lower condenser temperature. The notable bend
in the curve corresponds to the typical defrost loss at air temperatures just above the
freezing point.
20 15 10 5 0 5 10 15 20Ambient temperature in ◦ C
1
2
3
4
5
6
7
8
9
Therm
al pow
er
in k
W
Q (Tset=35)
Q (Tset=45)
Q (Tset=55)
1
2
3
4
5
6
CO
P
COP (Tset=35)
COP (Tset=45)
COP (Tset=55)
Figure 4.2: COP and heat generation power development with respect to the ambienttemperature of an ASHP ’Dimplex A/W LA6TU’ for different applicationtemperatures [Dimplex, 2017]
The characteristic diagram in Figure 4.2 is extracted for the data sheets of a HP system
provided by the manufacturers e.g. [Dimplex, 2017]. Accordingly, the HP MILP model is
formulated as:
QHP(t ) = PHP(t ) /COP (t ) ∀ t (4.1)
COP (t ) = QUBHP (t ) / PUB
HP (t ) ∀ t (4.2)
PHP(t ) = uHP(t ) ·PUBHP (t ) ∀ t (4.3)
36
4.2 Micro combined heat and power unit
uHP(t ) is a binary variable which describes the operation status of the HP; 1 corresponds
to ’on’ and 0 to ’off’.
The values for QUBHP (t ) and PUB
HP (t ) are extracted from the data sheets based on interpolation,
using the ambient air temperature Tamb(t ) as source temperature and the flow set tem-
perature of the consumer cycle T flowset (t ). T flow
set (t ) is determined according to Equation 4.4.
The value of T flow, SHset (t ) is derived from the heating curve of the space heating distribution
system based on Tamb(t ) and the heat distribution system characteristics.
T flowset (t ) =
T flow, dhwset (t ), if Qdhw(t ) ≥ 0
T flow, SHset (t ), if Qdhw(t ) = 0
(4.4)
A modulation behavior can be realized by substituting the Equation 4.3 through:
PHP(t ) ≥ uHP(t ) ·Lmod ·PUBHP (t ) ∀ t (4.5)
PHP(t ) ≤ uHP(t ) ·PUBHP (t ) ∀ t (4.6)
with Lmod as the modulation level ranging between 0 and 1. In the investigations later
introduced in Chapter 6, the HP models considered are non-modulating or on-off systems.
Hence, the modulation level is set to one, Lmod = 1.
In order to reduce wear and tear of the device, a frequent change of operation status must
be avoided. This can be modeled through the following equations:
v(t )−w(t ) = uHP(t )−uHP(t −1) ∀ t ≥ 2 (4.7)
t∑i=t−t run
min
v(i ) ≤ uHP(t ) ∀ t ≥ t runmin (4.8)
t∑i=t−tdown
min
w(i ) ≤ 1−uHP(t ) ∀ t ≥ tdownmin (4.9)
v(t ) and w(t ) are binary variables, that account for startup and shutdown transitions,
respectively. The system has a startup at time step t if v(t ) equals one, and has a shutdown
at time t if w(t ) equals one. t runmin and tdown
min represent the minimum run and shut down
time, respectively. Both parameters are set to 30 min according to expert opinion from
manufacturing companies .
4.2 Micro combined heat and power unit
Micro combined heat and power (µCHP) units cogenerate heat and power using gas as
fuel thus enabling a high energy conversion efficiency. The performance of a CHP unit is
37
Modeling of Building Energy Systems: Mathematical Programming Formulation
characterized by a power-to-heat ratio σ, electric efficiency ηel, thermal efficiency ηth and
an overall efficiency ηtotal.
σ= PCHP /QCHP (4.10)
ηel = PCHP /QCHP, gas (4.11)
ηth = QCHP /QCHP, gas (4.12)
ηtotal = ηel+ηth (4.13)
The electric efficiency depends on the operation mode and decreases with the modulation
level. In contrast, the thermal efficiency increases at lower modulation level. Consequently,
the overall efficiency remains almost constant.
The MILP model of a CHP unit is formulated based on the following equations:
PCHP(t ) ≥ uCHP(t ) ·PminCHP ∀ t (4.14)
PCHP(t ) ≤ uCHP(t ) ·PmaxCHP ∀ t (4.15)
QCHP(t ) = c1 · (PCHP(t )−PminCHP ·uCHP(t ))+Qmin
CHP ·uCHP(t ) ∀ t (4.16)
QCHP, gas(t ) = c2 · (PCHP(t )−PminCHP ·uCHP(t ))+Qmin
CHP, gas ·uCHP(t ) ∀ t (4.17)
The parameters for the MILP equations can be extracted from the Table 4.1 and calculated
according to the stationary equations:
c1 =Qmax
CHP−QminCHP
PmaxCHP−Pmin
CHP
(4.18)
c2 =Qmax
CHP, gas−QminCHP, gas
PmaxCHP−Pmin
CHP
(4.19)
QmaxCHP, gas = Pmax
CHP/ηmax (4.20)
QminCHP, gas = Pmin
CHP/ηmin (4.21)
Frequent startup and shutdown can be limited by introducing Equations 4.7 - 4.9.
38
4.3 Electrical heating element
Table 4.1: Parameters of ECOPower 3.0 [Vaillant, 2017]
Parameter Value Unit
Pmax 3 kWPmin 1.5 kWQmax 8 kWQmin 4.7 kWηmax
el 25 %ηmin
el 17 %ηtot 90 %σ 0.375 -
4.3 Electrical heating element
Electrical heating elements are commonly used as instantaneous flow auxiliary heaters
within a mono-energetic HP system or as main heating systems such as night storage
heaters or integrated surface heaters.
The MILP model of an electrical heating element can be formulated as:
PEH(t ) ≥ uEH(t ) ·Lmod ·PmaxEH ∀ t (4.22)
PEH(t ) ≤ uEH(t ) ·PmaxEH ∀ t (4.23)
QEH = PEH(t ) ·ηEH ∀ t (4.24)
with Lmod as the modulation level ranging between 0 and 1, and ηEH as the energy
conversion efficiency. In this work, the efficiency is set equal to one (ηEH = 1) and the
operation is restricted to on-off. Hence, the modulation level is set to one (Lmod = 1).
Some EH can only operate at discrete modulation levels P iEH with i ∈ [1,n]. This behavior
can be formulated by introducing a set of binary variables uiEH for every modulation level
using the following equations:
PEH(t ) =n∑
i=1ui
EH(t ) ·P iEH ∀ t (4.25)
n∑i=1
uiEH(t ) ≤ uEH(t ) ∀ t (4.26)
39
Modeling of Building Energy Systems: Mathematical Programming Formulation
4.4 Gas boiler
Gas-fired boilers are the most widespread installed heat generator. Boilers are used as
primary heaters, instantaneous flow heater or auxiliary heater within a mono-energetic
µCHP system. The MILP model of a boiler is formulated as:
QBoiler(t ) ≥ uBoiler(t ) ·Lmod ·QmaxBoiler ∀ t (4.27)
QBoiler(t ) ≤ uBoiler(t ) ·QmaxBoiler ∀ t (4.28)
QBoiler(t ) = QBoiler, gas(t ) ·ηBoiler ∀ t (4.29)
4.5 Photovoltaic
The operation of a PV system is restricted as only power throttling is possible to avoid
network over-voltage but it is at the same not desirable since it means that energy is lost.
Consequently, a HEMS can only decides on the utilization of the generated electricity but
not the power output of the PV system itself.
A PV system is defined by the installed peak power Ppeak and the module specifications
provided by the manufacturer. Typically, the installed PV power ranges from 3 to 5 kWp for
a single-family house. A maximum power point tracker (MPPT) within the power inverter
ensures that the system is operated optimally.
The power output is formulated based on [Cau et al., 2014] as:
PPV(t ) = Isolar(t ) · APV ·ηPV(t ) ∀ t (4.30)
PPV(t ) ≤ Ppeak ∀ t (4.31)
where Isolar(t ) denotes the solar global irradiation.
The area of PV system APV and the temperature dependent module efficiency ηPV(t ) are
determined according to the following equations:
APV = Ppeak
P refmodule
· Amodule (4.32)
ηPV(t ) = ηref−α · (Tcell(t )−Tref) ·Pref (4.33)
Tcell(t ) = Tamb(t )+ (Tnoct−Tamb, noct) ·Isolar(t )
Inoct∀ t (4.34)
40
4.6 Battery
Table 4.2: Parameters of a Schott PV module [Schott, 2017]
Parameter Value Unit
Amodule 1.673 m2
P refmodule 240 Wp
ηrefPV 13.4 %α 0.4 %/K
Tamb, noct 20 °CTnoct 47 °CInoct 800 W/m2
ηref is the nominal module efficiency under reference conditions. α is the temperature
coefficient in [%/K] that defines the power decrement due to cell temperatures above
25 °C. The cell temperature Tcell can be derived by linear interpolation based on the
nominal operation cell temperature (NOCT) conditions. An overview of the parameters
employed for the PV module is presented in Table 4.2.
4.6 Battery
The battery model is based on Lithium-Ion (Li-Ion) type with a characteristic current curve
from [Sundstrom O., 2010]. Since the self-discharging rate of Li-Ion batteries usually
amounts to less than 2 %/month [Johnson and White, 1998], it is neglected in this model.
Furthermore, aging effects of the Li-Ion cells are not considered as well.
The MILP model is mainly based on an energy balance equation which represents the
development of the state of charge (SoC) with respect to the charging or discharging
power.
Ebat(t ) =Ebat(t −1)+(ηbat ·Pcharge(t )− 1
ηbat·Pdischarge(t )
)·∆t ∀ t (4.35)
Pcharge(t ) & Pdischarge(t ) ≥ 0 ∀ t (4.36)
SoCbat(t ) = Ebat(t )
Emax∀ t (4.37)
SoCbat(t ) ≤ 1 ∀ t (4.38)
SoCbat(t ) ≥ 1−DoD ∀ t (4.39)
Ebat(t ) represents the actual energy content of the battery storage. The parameter ηbat
is the charging/discharging efficiency which considers the cell and inverter losses of
the AC circuit connected battery system. A maximal depth of discharge (DoD) of 90 %
is allowed for discharging the battery to maintain the unit lifetime. Discharging below
41
Modeling of Building Energy Systems: Mathematical Programming Formulation
the specified DoD results in fast aging due to volume dilatation, respectively, internal
mechanical stress.
Pcharge(t ) ≤ Pmaxcharge ∀ t (4.40)
Pdischarge(t ) ≤ Pmaxdischarge ∀ t (4.41)
During the operation of battery storage systems, the rates of charging and discharging
rates have be limited due to the power limitation of the inverter and to prevent the battery
cells from overheating. Furthermore, with higher charging or discharging currents the
energy losses due to the internal resistance increase.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.5
1
1.5
2
2.5
3
3.5
4
0 0.2 0.4 0.6 0.8 1
Sp
ecif
ic r
ates
in
A/A
h o
r k
W/k
Wh
Vo
ltag
e in
V
SoC
U_oc
Datenreihen6
U_charge
I_discharge_max
Icharge,max
Linear fit
Uoc
Udischarge
Ucharge
Idischarge,max
Icharge,max
Linear fit
Figure 4.3: Characteristic voltage, current and electrical power trends during the charg-ing process of a Li-Ion battery storage system
Figure 4.3 shows the typical voltage trend of a Li-Ion battery at highest possible charging
rate. The charging voltage Ucharge lies above the open circuit voltage UOC, because of the
internal resistance of the battery cells. Consequently, the maximal charging current must
be further reduced by the end of the charging process to enable a full state of charge.
Hence, a second constraint for the charging rate must be considered.
Pcharge(t ) ≤ (α ·SoCbat(t )+β)
·Ebat(t ) ∀ t (4.42)
This effect is approximated by a linear fit of the descending part of the specific power trend
as a function of the battery state-of-charge, which results in a decreasing upper bound
42
4.7 Water tank
Table 4.3: Parameters of the battery model [Sundstrom O., 2010]
Parameter Value Unit
Emax 2 kWhPmax
charge 4.6 kW
Pmaxdischarge 4.6 kW
ηbat 97.47 %DoD 90 %α -5.8531 kW
kWhβ 5.8675 kW
kWh
of the charging rate towards the end of the charging process as indicated in Equation
4.42. The parameters α and β represent the linear fit coefficients. Table 4.3 provides an
overview of the parameters for the battery model.
4.7 Water tank
Up to now, the investment costs of batteries are relatively high, hindering a widespread
installation of electric storage systems on building level. Residential water storage tanks
are considerably less expensive and allow for desynchronizing a thermal unit’s generation
and building’s heating demand without affecting the residents’ comfort, consequently
providing a large potential for load shifting.
4.7.1 Modeling
It is evident that the modeling or representation of the storage capacity greatly impacts the
scheduling reliability since it is the core flexibility source. Different modeling approaches
for water thermal storage tanks have been proposed in the literature. The most common
MILP representation is based on a simplified single capacity model which assumes that
the storage is homogeneously (fully) mixed or ideally stratified 1, for example in [Di
Zhang et al., 2013, Wakui et al., 2014, Zapata et al., 2014, Zidan et al., 2015, Harb et al.,
2015, Renaldi et al., 2016]. [Schütz et al., 2015a, Schütz et al., 2015b] investigated
the impact of this representation of thermal storage systems and showed that it greatly
decreases the scheduling reliability. The main drawbacks of the single capacity model
are the missing representation of the thermal stratification [Shin et al., 2003, Fan and
Furbo, 2009, Arteconi et al., 2012] within the storage and a noncompliance with the
entropy balance. Mainly, the energy content, regardless of its corresponding temperature,
is always considered as a usable energy. However, the storage layers’ energy content
1The two different assumptions are only relevant for the calculation of the storage losses to the environment
43
Modeling of Building Energy Systems: Mathematical Programming Formulation
can only be considered usable when the corresponding layer’s temperature is equivalent
or above the required flow temperature on the sink side. When a layer’s temperature is
below the flow temperature energy content is considered unusable. Consequently, the
state of charge in single capacity models are expected to overestimate the real value.
Consequently, the thermal losses to the environment cannot be accurately estimated.
A less common approach for MILP applications is layered stratified storage model, which
represent the storage based on a discrete number of layers with corresponding capacities,
for example in [Schütz et al., 2015a, Schütz et al., 2015b]. This allows for a better estima-
tion of the usable energy content and thermal losses but results in high computational
effort due to the increased number of state variables.
In this section, both models for the single capacity and stratified storage are presented.
Furthermore, a novel empirical modeling approach that allows for considering both usable
and unusable energy contents based on the thermocline effect is introduced.
Single capacity
The simplified singe capacity model is formulated based on an energy balance around the
storage considering heat losses proportional to the storage energy content. A concrete
temperature distribution is not calculated, so there is no distinction between usable and
unusable energy based on the temperature level of the stored energy. The time-discrete
equation of this model is introduced Equation 4.43.
Q(t ) =Q(t −1) · (1−xloss,∆t )+ (Qcharge(t )−Qdrawn(t )
)·∆t ∀ t ≥ 1 (4.43)
Q represents the energy content of the storage. Qdrawn(t ) is the drawn heat at time t and
may comprise domestic hot water Qdhw(t ) and space heating Qspace heating(t ) demand.
Qdrawn(t ) = Qdhw(t )+Qspace heating(t ) ∀ t (4.44)
Qcharge(t ) is the charging thermal flow from a heat generation system e.g. HP, CHP, boiler
or auxiliary electrical heater.
Qcharge(t ) =QHP(t )+QEH(t ), for HP-EH systems
QCHP(t )+QBoiler(t ), for CHP-Boiler systems(4.45)
xloss,∆t is a thermal loss coefficient which is empirically determined for a certain time
period ∆t according to 4.46.
44
4.7 Water tank
xloss,∆t =κsto
ρ ·cω·
Asto
Vsto·∆t ∀ t (4.46)
with ρ and cw as the volumetric density and heat capacity of water, respectively. Asto is
the surface area, ksto the thermal transmittance and Vsto the volume of the storage tank.
Layer-based stratification
The stratified or layered storage model is based on a spatially discretized consideration
of the vertical temperature distribution of the storage medium. An energy balance is
formulated for each layer l . The total energy balance is presented in Equations 4.47 - 4.50
by taking into consideration the conduction between the layers, losses to the surroundings
and convective heat fluxes due to the cross section velocity. This formulation is derived
from [Schütz et al., 2015a, Schütz et al., 2015b].
ሶ𝑚charge(𝑡, 𝑙) · 𝑐w · 𝑇charge(t, 𝑙˗1)
ሶ𝑚charge(𝑡, 𝑙) · 𝑐w · 𝑇sto t, 𝑙
ሶ𝑚drawn(𝑡, 𝑙) · 𝑐w · 𝑇sto(𝑡, 𝑙)
ሶ𝑚drawn(𝑡, 𝑙) · 𝑐w · 𝑇ret(t, 𝑙˖1)
𝑇𝑠𝑡𝑜(𝑡, 𝑙) 𝑘sto · 𝐴sto 𝑙 · [𝑇sto 𝑡, 𝑙 − 𝑇env]
𝜆 · 𝐴cs · [𝑇sto 𝑡, 𝑙˗1 − 𝑇sto 𝑡, 𝑙
0.5 · [𝑧 𝑙 + 𝑧 𝑙˗1 ]]
𝜆 · 𝐴cs · [𝑇sto 𝑡, 𝑙˖1 − 𝑇sto 𝑡, 𝑙
0.5 · [𝑧 𝑙 + 𝑧 𝑙˖1 ]]
Figure 4.4: Illustration of the energy balance for a middle layer; the heat flows representthe charging heat from the heat generation unit, the heat conduction betweenneighboring layers, the drawn heat from the consumer cycle and losses tothe tank surrounding environment [Schütz et al., 2015a]
The equation for the top layer is formulated as:
msto(l ) ·cω ·Tsto(t , l )−Tsto(t −1, l )
∆t= mdrawn(t ) ·cω · [Tsto(t , l +1)−Tsto(t , l )]
+mcharge(t ) ·cω · [Tcharge(t )−Tsto(t , l )]−ksto · Asto(l ) · [Tsto(t , l )−Tenv]
+λ · Acs ·
[Tsto(t , l +1)−Tsto(t , l )
0.5 · [z(l )+ z(l +1)]
],∀ t
(4.47)
with mdrawn(t ) as the drawn mass flow rate through the heating distribution system which
45
Modeling of Building Energy Systems: Mathematical Programming Formulation
is determined according to Equation 4.48.
mdrawn(t ) =mnom
drawn, if Qdrawn(t ) > 0
0, if Qdrawn(t ) = 0(4.48)
Tsto is the vector for the vertical temperature distribution and Acs is the cross-sectional
area. The value for the heat generator temperature Tcharge depends on the installed unit.
mcharge(t ) is the mass flow rate through the heat supply system and has a nominal value in
case the unit is on or set equal to zero if it is off, similar to mdrawn(t ) in Equation 4.48. z
is the height of one storage layer. The term ksto · Asto(l ) represents the heat losses over
the surface and the term λ · Acs denotes the heat conductance between the layers. The
parameter λ is the thermal conductivity of water.
The equation for any middle layer is based on the energy balance depicted in Figure 4.4
and is formulated as:
msto(l ) ·cw ·Tsto(t , l )−Tsto(t −1, l )
∆t= mdrawn(t ) ·cw · [Tsto(t , l +1)−Tsto(t , l )]
+mcharge(t ) ·cw · [Tcharge(t , l +1)−Tsto(t , l )]−ksto · Asto(l ) · [Tsto(t , l )−Tenv]
+λ · Acs ·
[Tsto(t , l −1)−Tsto(t , l )
0.5 · [z(l )+ z(l −1)]+ Tsto(t , l +1)−Tsto(t , l )
0.5 · [z(l )+ z(l +1)]
],∀ t
(4.49)
The equation for the bottom layer is:
msto(l ) ·cw ·Tsto(t , l )−Tsto(t −1, l )
∆t= mdrawn(t ) ·cw · [Tret(t )−Tsto(t , l )]
+mcharge(t ) ·cw · [Tsto(t , l −1)−Tsto(t , l )]−ksto · Asto(l ) · [Tsto(t , l )−Tenv]
+λ · Acs ·
[Tsto(t , l −1)−Tsto(t , l )
0.5 · [z(l )+ z(l −1)]
],∀ t
(4.50)
Empirical thermocline
We propose a novel empirical approach for modeling water storage that extends the energy
balance of the capacity model by differentiating between usable and unusable energy
content. The formulation is presented in Equation 4.51 - 4.58. The usable energy amount
for the consumer cycle is determined by quantifying and subtracting an unusable amount
from the storage energy content. Under the assumption that the temperature profile of the
storage medium is linear at all times along the height of the tank, the storage is considered
to be empty when the tapping water temperature drops down to the flow temperature. At
this point, no further energy can be extracted from the tank. The temperature can only
decrease due to environmental losses. In this case, the drawn water temperature is below
46
4.7 Water tank
𝑇𝑟𝑒𝑡 𝑇𝑐ℎ𝑎𝑟𝑔𝑒𝑇𝑓𝑙𝑜𝑤 𝑇𝑟𝑒𝑡 𝑇𝑐ℎ𝑎𝑟𝑔𝑒𝑇𝑓𝑙𝑜𝑤 𝑇𝑟𝑒𝑡 𝑇𝑐ℎ𝑎𝑟𝑔𝑒𝑇𝑓𝑙𝑜𝑤 𝑇𝑟𝑒𝑡 𝑇𝑐ℎ𝑎𝑟𝑔𝑒𝑇𝑓𝑙𝑜𝑤
ℎ𝑒𝑖𝑔ℎ𝑡
𝑓𝑢𝑙𝑙𝑦 𝑐ℎ𝑎𝑟𝑔𝑒𝑑 ℎ𝑎𝑙𝑓 𝑐ℎ𝑎𝑟𝑔𝑒𝑑 𝑓𝑢𝑙𝑙𝑦 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒𝑑 𝑏𝑒𝑙𝑜𝑤 𝑓𝑢𝑙𝑙𝑦 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒𝑑
Figure 4.5: Generic representation of the different states for the SoC of the empiricalapproach. The black solid line depicts the temperature profile [Harb et al.,2017]
the consumer flow temperature and the storage must be charged to reach a usable SoC
of zero again. The behavior of the temperature distribution for the assumptions of this
model, and the corresponding states of charge, are exemplary shown in Figure 4.5.
Q(t ) =Q(t −1) · (1−xloss,∆t )+ (Qcharge(t )−Qdrawn(t )) ·∆t ∀ t ≥ 1 (4.51)
Qusable(t ) =Q(t −1) · (1−xloss,∆t )−Qunusable, bottom−Qunusable(t ) ∀ t ≥ 1 (4.52)
Qusable(t )/∆t +Qcharge(t ) ≥ Qdrawn(t ) ∀ t (4.53)
Qusable(t ),Qunusable(t ) ≥ 0 ∀ t (4.54)
The amount of unusable energy due to mixing effects in the storage Qunusable(t ) depends on
the consumer flow Tflow and return Tret temperature as well as the storage volume. Tflow
can be extracted from the heating curve of the corresponding heat distribution system
while Tret can be roughly approximated based on the heat exchanger characteristic while
assuming a constant mass flow rate. Both Tflow and Tret are assumed to be constant for
the considered time sequence, since the changes of the outside temperature are very slow
compared to the characteristic time scales in which the storage is (dis-)charged.
Qunusable(t ) is determined based on the assumption that the temperature distribution of
the storage medium depends not only on the SoC but also on the dynamic development of
the mixing zone between the hot and cold section area in the tank as observed in [Nelson
et al., 1999]. The authors in [Chung and Shin, 2011] observe a proportionality between
the thermocline thickness and the square-root of time. Hence, a saturation behavior of
the development of the mixing zone can be assumed. Since mixing of hot and cold water
47
Modeling of Building Energy Systems: Mathematical Programming Formulation
causes a loss of exergy, a part of the unusable energy is assumed to have a saturation
behavior as well, which is approximated in Equation 4.55.
Qunusable(t ) = Qunusable(t −1)+(Qmax
unusable−Qunusable(t −1))·Cunusable, thermo ·∆t ,∀ t ≥ 1
(4.55)
The coefficient Cunusable, thermo is an empirical value that is approximated by means of the
measurement data. Qmaxunusable is the upper bound for Qunusable and is defined in Equation
4.56.
Qmaxunusable =
1
2· (Tflow−Tret) · Acs · Hsto ·ρcw ·Cunusable (4.56)
Qunusable, bottom = (Tret−Tenv) ·cw ·ρ ·Vsto (4.57)
Cunusable denotes an empirical scaling factor for the amount of unusable energy that is
depicted in Figure 4.5. It ranges between 0 (for no mixing at all) and 1 (for the assumption
of a linear temperature profile). Furthermore, an additional unusable amount of energy is
defined in Equation 4.57 by considering the energy under the level of Tret with reference
to the environmental temperature Tenv, based on the storage volume which corresponds
to the product of the storage height Hsto and cross-sectional area Acs, to approximate
the environmental losses correctly. The amount of unusable energy is reset to the initial
amount when the TS is completely charged or after a longer standstill. Furthermore, the
whole storage content is considered to be unusable after longer time periods without
charging phases. The temperature level of the hot water section Ttap is approximated by
Equation 4.58. Ctap is an empirical scaling factor.
Ttap(t ) = Ttap(t −1)− (Ttap(t )−Tenv
)·xloss,∆t ·Ctap ∀ t ≥ 1 (4.58)
When Ttap drops down under Tflow the storage is considered to be empty. The remaining
energy is unusable. The content can be made usable by charging the storage another
time.
4.7.2 Definition of SoC
The thermal energy content of the storage is defined using a dimensionless factor, state of
charge (SoC). In this work, the SoC for water tank is defined as in Equation 4.59.
SoC = Qusable
Qmax(4.59)
The maximal storable energy Qmax corresponds to the state at which the whole storage
medium has the heat generator temperature Tcharge. Qusable denotes the usable amount of
48
4.7 Water tank
energy and is defined as the thermal energy that is available at a temperature level equal
or above the consumer flow temperature Tflow, with reference to the consumer return
temperature. Figure 4.6 shows exemplary the consideration for Qusable. The stored energy
at a level of L > Lsto−Lcrit is considered usable. The usable amount of energy is spatially
𝑇𝑟𝑟𝑟 𝑇𝑐𝑐𝑐𝑟𝑐𝑟 𝑇𝑓𝑓𝑓𝑓
L
usable storage content
unusable storage content
𝐿𝑠𝑟𝑓 − 𝐿𝑐𝑟𝑐𝑟
Figure 4.6: Consideration of the usable and unusable amount of energy for the determi-nation of the SoC [Harb et al., 2017]
discretized and evaluated according to Equation 4.60. Nl denotes the total number of
layers discretization within the storage.
Qusable =
Vsto ·ρ ·cw ·∆L
L
Nl∑l=1
(Tl −Tret), for Tl ≥ Tflow
0, for Tl < Tflow
(4.60)
With this definition of the SoC, the usable energy content in the tank is estimated very
conservatively. Energy that is available on a temperature level slightly below consumer
flow temperature is considered to be completely unusable. This definition allows for
determining the point in time when an additional heat generation is required.
4.7.3 Experimental evaluation
In this section, the performance of the above formulated modeling approaches for thermal
water storage tanks is evaluated based on measurement data from an experimental setup.
49
Modeling of Building Energy Systems: Mathematical Programming Formulation
Setup
The experimental setup comprises a water tank Logalux PNR 500E [Buderus, 2017] which
has capacity of 500 l and a thermal transmittance, ksto = 1.01805W/(m2 K). 5 rods made
of stainless steel are vertically inserted into the tank for measuring the temperature
profile. In each rod, 10 thermocouples are equidistantly installed with a gap of 150 mm.
Consequently, each temperature value along the 10 levels (vertically) is measured over 5
points (radially).
The built-in heat exchanger inside of the water tank has been removed, so that it is directly
charged and discharged. A diffuser is installed to reduce the mixing of the water influx
during both the charging and the discharging cycle. The setup comprises two supply units
each connected to a heat exchanger which allow for heating and cooling the tank. The
cooling is achieved by circulating the tank’s medium from the upper layer through the
cooling exchanger and reintroducing it into the inlet at the bottom of the storage. The
heating is carried out by circulating the tank’s medium from the bottom layer over the
heating exchanger and reintroducing it at the upper inlet of the tank.
T
T
T
TES
Figure 4.7: Experimental scehme depicting the supply unit for the storage during thecharging cycle
Figure 4.7 illustrates the instrumental scheme of measurement and control for the charg-
ing cycle. The setup of the cooling cycle is analogous to the setup introduced in Figure
4.7. The control of the inlet temperatures and flow rates are decoupled in both cycles
by integrating 2 bypasses in each supply unit. Thus, the dead time between changes in
the valve position and the control temperature can be kept constant and reduced to a
minimum. The temperature in the supply unit is measured by PT100 elements. A magnetic
inductive flow meter is installed for measuring the flow rate.
50
4.7 Water tank
Results
In the following sections the results of the experimental assessment of the storage model-
ing approaches based on three use cases are presented.
Table 4.4: Configuration within the investigated use cases
Parameter Use case 1 Use case 2 Use case 3 Unit
Tcharge 65 60 50 °CTenv 22 22 22 °CTret 30 35-45 35 °CT init 32 32 36 °C
Across the use cases, the storage is charged and discharged with different temperature
levels for both consumer return and heat generator flow temperatures to represent typical
energy system configurations in residential buildings. Furthermore, several standstills of
the tank are realized between the operation phases (charging/discharging) to examine
and evaluate the heat losses to the surroundings. Table 4.4 gives an overview on the
configuration of the use cases.
Use case 1 The goal of this use case is to examine the mixing between the hot and
the cold water fronts and the time-dependent development of the temperature profile in
general for non-operating tanks. Furthermore, the heat loss transmission coefficient to
the environment can be investigated based on the data of the standstill periods. At the
beginning, the storage is entirely cooled down. The initial temperature of the storage
medium is quite homogeneous and equivalent to the return temperature. After an effective
partial charging, the storage is operated in a standstill mode for a time period of 6 days.
Thereafter, the tank is charged again then put in standstill for 4 days.
The SoC for the measured data (mSoC) and the three modeling approaches is depicted in
Figure 4.8. The mSoC falls continuously during the standstill after the charging phase.
The development is relatively linear. After a standstill of three days, the mSoC rapidly falls
towards 0. At this point, the temperature level of the hot section area drops under the
defined flow temperature, so the remaining energy is considered to be unusable.
The single capacity approach greatly overestimates the energy content of the storage
through the whole test. The mixing of hot and cold water is not considered in the model
and, therefore, the usable storage potential is overestimated from the very beginning of
the test. Due to the expansion of the mixing zone, the difference between the SoC of the
capacity model and the mSoC increases. The drop under the flow temperature cannot
be depicted. Furthermore, the approximation for the environmental losses is not well
51
Modeling of Building Energy Systems: Mathematical Programming Formulation
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
Time in min
0.0
0.2
0.4
0.6
0.8
1.0SoC
measured datacapacity approachstratified approach - 5empirical approach - f. 0.5
measured datacapacity approachstratified approach - 5empirical approach - f. 0.5
Figure 4.8: SoC comparison of the storage modeling approaches with the respect tomeasurement data for use case 1; The stratified storage model comprises 5layers while Cunusabl e is represented by the factor f and set to the value 0.5
represented. There is no proportionality between the energy content of the storage and
the losses unless the return temperature Tret is on the same level as the environmental
temperature Tenv which would be unrealistically low.
In the stratified storage model, the SoC is slightly underestimated after the first operational
phase. During charging or discharging, the energy balance of a discretized layer for direct-
loaded tanks contains a convective term on account of the cross section velocity. Water
that goes from one layer to another is considered to be totally mixed as it enters the new
layer. For this reason, mixing effects due to operational phases are overestimated in this
model. This miscalculation becomes more evident when the storage is being charged
and discharged in parallel since the flow rates of the heat source and consumer are
considered autonomously. Figure 4.9 depicts the deviation of the calculated and the
measured temperature profiles. The deviation gets lower with increasing operational
time, as depicted in Figure 4.9d. The temperature difference between measurements and
simulation in the top layer is caused the missing consideration of the natural convection
phenomenon in the modeling approach. Therefore, the calculated temperature distribution
52
4.7 Water tank
is not strictly decreasing and interpolating over temperatures may lead to discontinuities
for the SoC approximated by the stratified storage model during a standstill. The drop
under the flow temperature is well depicted.
2 0 3 0 4 0 5 0 6 0 7 0 8 0tem peraturecin ◦ C
1
2
3
4
5
6
7
8
9
1 0
mea
sure
men
tcpo
ints
s im ula tionm eas uredcdata
2 0 3 0 4 0 5 0 6 0 7 0 8 0tem perature inc ◦ C
1
2
3
4
5
6
7
8
9
1 0
2 0 3 0 4 0 5 0 6 0 7 0 8 0tem perature cin ◦ C
1
2
3
4
5
6
7
8
9
1 0
2 0 3 0 4 0 5 0 6 0 7 0 8 0tem perature cin ◦ C
1
2
3
4
5
6
7
8
9
1 0
tcc=c16cmin tcc=c23cmin tcc=c100cmin tcc=c4300cmincccccccccccc(a) cccccccccccc(b) cccccccccccc(c) cccccccccccc(d)
Figure 4.9: Comparison of the development of the temperature profile for the measureddata and the stratified storage model in use case 1
In the empirical approach, the SoC is approximated sufficiently. The deviation from the
mSoC is relatively low, both at the beginning after the charging and during the standstill.
The drop of the temperature of the hot water section under the flow temperature is only
roughly approximated.
Use case 2 The goal of use case 2 is to examine the development of the temperature
profile during operational phases in comparison to the development during standstills
investigated in use case 1. The storage is partially charged and subsequently set in
a standstill of 21.5 h. Thereafter, the storage is continuously charged and discharged
alternately over a period of 5.5 h. Finally, the storage is charged and discharged another
time over a period of 3 hours and then completely discharged. During this period,
charging and discharging are done in parallel. The SoC for the measured data and
the three modeling approaches for use case 2 are shown in Figure 4.10. The SoC for
the capacity approach shows an increasing deviation from the mSoC. Furthermore, the
SoC is overestimated from the very beginning where the inaccurate approximation of
environmental losses has only a low influence on the deviation. In the stratified approach,
the SoC is underestimated at the beginning of the test. After the second operational phase,
the stratified approach gives a better approximation for the SoC. The storage content
53
Modeling of Building Energy Systems: Mathematical Programming Formulation
0 1000 2000 3000 4000 5000 6000
Time in min
0.0
0.2
0.4
0.6
0.8
1.0SoC
measured datacapacity approachstratified approach - 5empirical approach - f. 0.5
measured datacapacity approachstratified approach - 5empirical approach - f. 0.5
Figure 4.10: SoC comparison of the storage modeling approaches with the respect tomeasurement data in use case 2
is more mixed due to the influx of water over the diffusers. This effect is not explicitly
described by the stratified approach. However, it is indirectly considered as the convective
flows between the discrete layers result in a certain mixing. For a higher degree of mixing
in the water tank, the solution of the stratified approach gets better. The temperature
drop of the storage medium under the consumer flow temperature is well depicted. In the
empirical approach, the SoC is well approximated, especially at the beginning of the test.
Time-dependent mixing effects are simulated. However, the effects due to inlet mixing
characteristics are not represented. For that reason, the deviation of the model predicted
SoC from the mSoC rapidly changes during the second operational phase (t ~1300 min).
However, mixing due to the influx of water can be statistically represented through time
by adapting Cunusable, thermo. The temperature drop under the consumer flow temperature
is roughly simulated.
Use case 3 The goal of this use case is to generate typical conditions for a storage oper-
ation in connection with a heat pump resulting in a relatively low charging temperature.
The initial temperature of the storage medium is set close to a typical consumer return
54
4.7 Water tank
temperature. The storage is simultaneously charged and discharged for a period of 10 h
then set in a standstill of 24 h.
0 500 1000 1500 2000
Time in min
0.0
0.2
0.4
0.6
0.8
1.0
SoC
measured datacapacity approachstratified approach - 5empirical approach - f. 0.5
measured datacapacity approachstratified approach - 5empirical approach - f. 0.5
Figure 4.11: SoC comparison of the storage modeling approaches with the respect tomeasurement data in use case 3
The results of use case 3 are depicted in Figure 4.11. Due to a low temperature differ-
ence between Tflow and Tret, the unusable energy, with regard to the stored energy, is
relatively low compared with the other use cases. Thus, the temporal development of
the unusable energy has a lower influence on the SoC. For this reason, the deviation of
the capacity model is at the beginning of the test lower than it is for the previous use
cases. Nevertheless, the inaccurate approximation for the environmental losses results
in an increasing difference. The stratified storage model underestimates the SoC at the
beginning. For a discretization of 5 and 10 layers the stratified approach shows similar
results. An increase of the layers’ number considered does not improve the results. The
initial development of the SoC in the empirical approach accurately matches the mSoC.
The temporal development of the amount of usable energy calculated by the model is
low compared to the other use cases indicating that Qmaxunusable is overestimated for this
configuration.
55
Modeling of Building Energy Systems: Mathematical Programming Formulation
Conclusion The results indicate that the widely adopted simplified capacity storage
model greatly overestimates the usable energy content especially for high temperature
differences in the storage. Further, the approximation of the environmental losses within
this approach is insufficient.
The stratified storage approach provides a solution with general applicability for different
temperature ranges. However, the mixing due to convection between the discrete layers
caused by charging and discharging of the tank is highly overestimated in this modeling
approach.
The introduced empirical approach allows for representing the dynamic development of
the unusable energy content and delivers the best approximation of the storage’s state of
charge. Furthermore, this representation comprises less decision variables compared with
the stratified formulation which represents a decisive advantage for the implementation
and computational effort in the scope of MILP models.
4.8 Building wall mass
Building thermal wall mass provides a flexible heat capacity which can be effectively used
for load shifting, thus enabling demand side management. The most crucial barrier for
a practical application of buildings as short term heat storage is the lack of knowledge
about the building physical properties. The challenge lies in accurately estimating the
building thermal dynamics and response to avoid affecting the residents comfort. The
modeling concepts of building thermal behavior can be categorized into data driven and
design driven [Li and Wen, 2014]. Design driven models require extensive information on
the physical characteristics of the buildings, that are typically not available for existing
building stock. Data-driven models are an inverse modeling approach that explore his-
torical measurement data to estimate the building thermal behavior. This approach has
gained a lot of interest with the recent roll out of smart meters which led to increased
availability of sensors’ data.
Data-driven models comprise black-box and grey-box models. Black box models don’t
require fundamental knowledge of the building physical properties and comprise autore-
gression models with exogenous inputs, multiple regression, exponential smoothing and
machine learning algorithms i.e. artificial neural networks and support vector machines.
Autoregression models are frequently used in the literature for simulating the thermal
building behaviour to enable HVAC predictive control [Loveday and Craggs, 1993, Love-
day and Craggs, 1992]. However, these models do not allow for capturing non-linear
effects and are therefore only valid for a limited range of values [Kristensen et al., 2004].
Machine learning algorithms allow for modeling non-linear relation and have been ex-
tensively applied in the literature [Lundin et al., 2004, Lundin et al., 2005, Mustafaraj
56
4.8 Building wall mass
et al., 2011, Frausto and Pieters, 2004, Ruano et al., 2006]. However, the performance
of these algorithms is limited to the extent and quality of the data used for the model
training so that long periods of data from different seasons of the year are needed to
generate a robust building model. Grey-box denotes an intermediate stage that combines
the data based system identification of black-box models and partially physical relations
of white-box models.
4.8.1 Modeling: Grey-box
The structure of grey-box-models is developed based on knowledge of the physical effects
of the system. This structure is represented as xR yC networks with lumped parameters
in analogy to an electrical circuit with x as the number of thermal resistances and y of
thermal capacities. The choice of a proper model structure is critical for the ability of the
model to reproduce the building thermal behavior in an accurate way without increasing
the model complexity.
Te
Ce
Re,a
Exterior Ambience
Ta,eq
Tin
Cin
Interior
Ria,a
Ta
Rin,ia Ria,e
Indoor Air
Tia
Φsol, in
Φh, in
Φh, ia
Φsol, ia
Φh, e
Figure 4.12: 4R2C model structure [Harb et al., 2016a]
In [Harb et al., 2016a], four grey-box model structures were compared in their ability to
forecast the indoor temperature behavior in occupied buildings based on single zone rep-
resentation. The analysis revealed that a two-capacity model structure with an additional
consideration of the indoor air as a mass-less node (4R2C) enables the most accurate
qualitative prediction of the indoor temperature.
Figure 4.12 illustrates the 4R2C model structure. This structure comprises two capacities
summarizing the interior Cin and exterior Ce building components respectively. The indoor
57
Modeling of Building Energy Systems: Mathematical Programming Formulation
air is considered as a separate temperature node with no thermal capacity. The heat
dynamics are expressed by the following differential equations:
dTin = 1
Rin, ia ·Cin(Tia−Tin)d t + 1
Cin(Φh,in+ (1− fconv) ·Φsol)d t +dωin (4.61)
dTe = 1
Ria, e ·Ce(Tia−Te)d t + 1
Re, a ·Ce(Ta, eq−Te)d t + 1
CeΦh, ed t +dωe (4.62)
As well as the algebraic equation around the indoor air Tia node.
0 = 1
Rin, ia(Tin−Tia)+ 1
Ria, e(Te−Tia)+ 1
Ria, a(Ta−Tia)
+ fconv ·Φsol+Φh, ia
(4.63)
The infiltration heat resistance Ria, e connects the indoor air node with the outdoor air.
Rin, ia and Ria, e represent the convective heat exchange between the walls and indoor air.
Radiation heat transfer between interior and exterior is neglected. The heat flux from
the heating system is partly transferred directly to the indoor air. According to a rule
of thumb, presented in DIN EN ISO 13790 [DIN - German Institute for Standardization,
2008b], the convective contribution of the solar heat gains through transparent surfaces
i.e. windows can be assumed at fconv = 9%. The allocation of the heat supply Φh to the
indoor air Φh, ia as well as the interior Φh, in and exterior Φh, e wall is carried out according
to Equations 4.64-4.66:
Φh, ia =Φh · (1− fheat, rad) (4.64)
Φh, in = (Φh−Φh, ia) · (1− fheat,rad,ext) (4.65)
Φh, e = (Φh−Φh, ia) · fheat, rad, ext (4.66)
with fheat, rad = 0.2 representing the radiation contribution of the heat flux from the heater
and fheat, rad, ext = γe, floor/γin, floor as the share of the radiation contribution to the exterior
walls. γin, floor is the quotient between the area of interior walls and floor area while
g ammae, floor is the quotient between the area of external walls and floor area. γin, floor
and γe, floor are assumed as 2.5 and 1.5 respectively.
Ta, eq = Ta+Qirradaf
αA(4.67)
Ta, eq is an equivalent outdoor temperature at the exterior surfaces by considering the
influence of short-wave radiation calculated based on the VDI 6007 [Association of Engi-
58
4.8 Building wall mass
neers, 2012b] to allow for a more precise representation of the heat exchange between
the building exterior and the environment. The impact of long-wave radiation is neglected
as a simplification. Ta, eq is calculated as indicated in Equation 4.67 with a short-wave ab-
sorption coefficient of the exterior surface af = 0.5 and an exterior heat transfer coefficient
αA = 25Wh/(m2 K). Ta is the outdoor air temperature and Qirrad denotes the global solar
radiation on a horizontal surface. Ta, eq applies only for the transmission heat exchange
between building envelope and ambiance. The infiltration heat losses over the thermal
resistance Rin, a use further Ta as reference outdoor air temperature.
Φsol represents the solar heat gains absorbed by the interior building components and is
determined according to:
Φsol = fsol ·Qirrad (4.68)
fsol is a factor ranging between 0 and 0.25, which is empirically defined based on [Bacher
and Madsen, 2011]. The value of fsol is determined during the fitting process.
4.8.2 Model identification approach: Parameterization
The goal of the model identification process is to determine the set of the parameters
which reproduces the building thermal behavior most accurately during the training
period ttrain.
f (x) =ttrain∑
t(T (t )−T (t ))2 (4.69)
This is achieved by formulating an non-linear optimization problem that minimizes the
objective function f (x) in Equation 4.69 subject to the grey-box model structure equations
4.61 - 4.63 as constraints. x is a vector of the model parameters, T (t ) the simulated indoor
air temperature at the time step t and T (t ) the measured indoor air temperature vector
over the training period. Interior point method [Waltz et al., 2006] is useful to handle
large non-linear optimization problems with inequality constraints and therefore employed
as solver. Alternative solvers are metaheuristics such evolutionary algorithms or mixed
integer non-linear program.
The boundaries of the model parameters are defined based on several norms and guide-
lines [DIN - German Institute for Standardization, 2003, DIN - German Institute for
Standardization, 2005, DIN - German Institute for Standardization, 2008a, Recknagel
et al., 2009, Association of Engineers, 2012c, Association of Engineers, 2012a]. The
boundaries are defined as specific values to the building floor area and are then multiplied
by it during the simulation. An overview is provided in Table 4.5.
59
Modeling of Building Energy Systems: Mathematical Programming Formulation
Table 4.5: Specific parameters boundaries [DIN - German Institute for Standardization,2005, Recknagel et al., 2009, Association of Engineers, 2012a]
Parameter LB Initial value UB Unit
1/Re, a 0.77 1 2.0 W/(m2 K)1/Rin, ia 0.5 2.5 25 W/(m2 K)1/Ria, a 0.15 0.5 1.5 W/(m2 K)1/Ria, e 0.5 2.5 25 W/(m2 K)
Ce 10 50 200 Wh/(m2 K)Cin 30 70 500 Wh/(m2 K)
60
5 Scheduling Algorithms
This section delivers an overview on the fundamentals of mathematical programming
discrete optimization. Thereafter, the formulation of a deterministic MILP scheduling
model for a single building is presented, followed by a scheduling under uncertainty model
based on stochastic programming. Finally, distributed scheduling algorithms for city
districts or microgrids are formulated based on decomposition methods.
5.1 Mathematical optimization: Fundamentals
Linear programming: Mathematical programming optimization problems are formu-
lated based on an objective function zP comprising the decision variables’ vector ~x that
is maximized or minimized subject to restrictions known as constraints [Bradley et al.,
1977, Bertsimas and Tsitsiklis, 1997, Castillo, 2002]. The simplest form of a mathematical
optimization problem is a linear program (LP) where the dependencies between decision
variables in both the objective function and the constraints are linear and the decision
variable are continuous as in Equation 5.1. LPs are solved using two main classes of
methods, simplex method which is a gradient descent method that moves along the edge
or vertices of the feasible region i.e. solution space and interior point methods (IPM)
that move through the interior of the feasible region. Dual simplex method is an evolved
version of the simplex algorithm that takes advantage of the duality theory.
min zP = cT ·~x
s.t.: A~x ≤ b
~x ≥ 0
(5.1)
Duality theory: Given any LP in the form of Equation 5.1, which is known as primal
problem, there exists another corresponding problem called dual problem which is for-
mulated according to Equation 5.2. The latter is referred to as the dual of problem 5.1
and vice versa. The variables ~y are called dual variables or dual multipliers. For every
constraint in the primal problem there is a variable in the dual problem and for every
variable in the primal problem there is a constraint in the dual problem.
61
Scheduling Algorithms
max zD = bT~y
s.t.: AT~y ≥ c
~y ≥ 0
(5.2)
Let z∗P be the optimal solution to the primal problem and z∗
D be the optimal solution to the
dual problem. The duality gap is defined as z∗P − z∗
D. A problem is said to hold weak duality,
if this gap is greater than zero and it holds strong duality, if the duality gap is equal to
zero [Bradley et al., 1977]. Hence, it is possible to solve the primal problem by solving its
dual counterpart which is exploited by the dual simplex algorithm [Bradley et al., 1977].
Furthermore, the solution of the dual problem gives several information about the primal
problem regarding sensitivity e.g. through shadow prices.
Shadow prices: The dual theory properties are significant for sensitivity analysis in
mathematical economic problems. Analyzing incremental changes in the primal LP
problem allows for an economical interpretation of the dual solution vector. It can be
shown that a small change d in the right-hand side vector of a primal equality constraint
i results in a change equal to πi ·d in the optimal primal cost, with πi being part of the
optimal solution to the dual problem [Bertsimas and Tsitsiklis, 1997]. Therefore, the
optimal dual solutions can be interpreted as the marginal cost per unit increase of a
requirement associated with a particular constraint. This vector is referred to as shadow
prices vector. Shadow prices are determined automatically when using a modern solver
like the Gurobi [Gurobi Optimization, 2017] or CPLEX [IBM, 2017] optimizers.
MILP: Most practical optimization problems, e.g. scheduling, require integer decision
variables. A program, where the decision variables x are integer and continuous variables,
is called mixed integer linear program (MILP). The general method to solve a MILP is
the branch-and-bound algorithm. The branch-and-bound algorithm solves a MILP by
linearly relaxing the integrality conditions (LP-relaxation). Thereafter, a decision tree is
spanned called branch-and-bound tree which comprises all possible states of the integer
variables. Every new integer variable that is introduced to the problem results in an
additional node in the branch-and-bound tree. The algorithm sets up lower and upper
bounds of the optimal solution. Every optimal solution to the LP relaxation provides a
lower bound and every feasible integer solution provides an upper bound. The branching
strategy sequentially refines these bounds. An improved version of this method is the
branch-and-cut algorithm which is a combination of the branch and bound algorithm and
cutting planes. Cutting planes are constraints that are added to the problem with the aim
to reduce the size of the solution space. Therefore, previous solutions are "cut" from the
62
5.2 Single building scheduling approaches
branch-and-bound tree in case they lay outside the current UB. Thereby, non promising
nodes in the branch-and-bound tree can be dropped thus reducing the size of the problem
and the computation time [Castillo, 2002].
Convex-hull pricing model: The definition of shadow prices is based on assumptions
that hold only for LP problems. To attain the optimal shadow prices when solving MILP
problems, a linear relaxation of the MILP problem has to be introduced that allows the
integer variables to take every value from within the convex hull of the integer solution
space. Therefore the optimal dual solution to this problem is called convex hull price.
5.2 Single building scheduling approaches
5.2.1 Deterministic MILP model
The deterministic formulation of the scheduling problem for a single building employs
point forecasts for both the weather variables and consequently PV generation as well as
DHW, electrical and space heating demands. Hence, a single scenario (s) is investigated
which corresponds to the expected values from the corresponding forecasts.
The scheduling problem minimizes the objective function formulated in Equation 5.3
subject to a power balance constraint shown in Equation 5.5 as well as the corresponding
energy generation and storage units presented in Chapter 4. The objective function is a
balance of the costs of the electricity bought from the grid and profit from remuneration
for electricity feed-in Psellug
(t , s) from PV or CHP surplus fed into the grid.
C (s) =tH∑
t=t0
cbuy ·Pbuy(t , s) ·∆t +tH∑
t=t0
cgas ·Qgas(t , s) ·∆t −tH∑
t=t0
∑ug∈Ug
csellug
·Psellug
(t , s) ·∆t ∀ s (5.3)
tH is the horizon of the moving window algorithm. cgas, cbuy and csellug
are constant
coefficients that define the specific cost of gas and imported energy from the public grid
as well as the feed-in compensation from the corresponding unit. Pbuy(t , s) and Psellug
(t , s)
are optimization variables. The simultaneous import from and export into the public power
grid is not allowed. Qgas(t , s) is the combined gas cosumption from available CHPs or
boilers as indicated in Equation 5.4.
Qgas(t , s) = QgasCHP(t , s)+Qgas
Boiler(t , s) ∀ t , s (5.4)
The power balance links the electricity generation and consumption of the individual
generating Ug = {CHP,PV,Batdischarge
}and consuming Uc =
{HP,EH,Batcharge
}units to the
63
Scheduling Algorithms
interaction with the grid and local electricity demand Pdem(t , s) for lights and appliances.
The local electricity generated Pug (t , s) may flow into the internal circuit of the building,
denoted as self-consumption Pselfug
(t , s) or exported/sold to public grid Psellug
(t , s).
Pbuy(t , s)− ∑ug∈Ug
Psellug
(t , s)+ ∑ug∈Ug
Pselfug
(t , s) = ∑uc∈Uc
Puc (t , s)+Pdem(t , s) ∀ t , s (5.5)
Pug (t , s) = Psellug
(t , s)+Pselfug
(t , s) ∀ t , s (5.6)
Pbuy(t , s),Psell(t , s),Psellug
(t , s),Pselfug
(t , s),Puc (t , s) ≥ 0 ∀ t , s (5.7)
5.2.2 Scheduling under uncertainty: Multi-stage stochastic programming
As previously shown in Section 3.2.5, the forecasts of domestic hot water and electrical
demand, which are both significantly influenced by the stochastic behavior of the resi-
dents, exhibit large errors. Consequently, schedules generated based on such forecasts
are expected to be unreliable when the uncertainty is realized. Multi-stage stochastic
programming allows for coping with demand uncertainties by taking into account different
realizations of the uncertainty in terms of probability distribution functions in the predic-
itve scheduling phase. The basic idea behind stochastic programming problem is to make
some ’here and now’ decisions before the actual realization of the uncertainty during
the first stage, and to take some ’wait and see’ or corrective decisions, in the second
stage after revelation of the uncertainty [Grossmann, 2012]. In a stochastic problem, the
cost of the decisions and the expected cost of the recourse actions are optimized [Conejo
et al., 2010]. If there are only two stages then the problem corresponds to a two-stage
stochastic program, while in a multi-stage stochastic program the uncertainty is revealed
sequentially, i.e. in multiple stages or periods, and corrective actions are then decided
over a sequence of stages.
Objective function
The objective function of the stochastic program extends the objective function for the
deterministic MILP which correpsonds to a single scenario. Consequently, an SP can be
formulated as:
arg min E {C (s)} (5.8)
E {C (s)} =NS∑s=1
π(s) ·C (s) (5.9)
E {C (s)} denotes the expected value of the scenario s specific objective function C (s) . It
is calculated by the probability weighted sum of the respective cost functions of each
64
5.2 Single building scheduling approaches
s1 s2 s3 s4 s5 s6 s7 s8 s9
π1 π3
π11 π12 π13 π21 π22 π23
π2
π31 π32 π33
root
leaf
Figure 5.1: Derivation of the scenarios’ probabilities π(s) from the root to the leaf nodeswithin the scenario tree of multi-stage stochastic programming
scenario. The scenario probabilities π(s) are derived from the product of transition
probabilities from the root to the leaf node in the scenarios tree as illustrated in Figure
5.1
Scenario tree generation
The initial step for formulating an SP is to describe the uncertatinty. Electrical and
domestic hot water demand are set as a source of uncertainty as they result in the highest
forecasting error. On the basis that the uncertainty follows a discrete probability distri-
butions, a stochastic process can be represented with scenario trees. The probabilistic
information for the electrical and DHW demand can be extracted either from a stochastic
forecast model by Monte-Carlo sampling which generates a large set of equi-probable sce-
nario, or from historical observation respectively measurement data. The obtained sample
set denotes a discrete representation of the underlying stochastic model; process and its
distribution; of the corresponding uncertainty. The set is then reduced for decreasing
computational complexity in the targeted optimization problem. The scenario reduction is
carried out by the fast forward selection heuristic [Gröwe-Kuska et al., 2003] for solving
the Kantorovich distance problem. This algorithm aims to find the best approximation
of the original set by a predefined number of scenarios similar to supervised clustering
algorithms.
The left diagram in Figures 5.2 and 5.3 depicts the scenario samples for DHW and electrical
demands. The solid black line denotes the point forecast and the scenario samples are
65
Scheduling Algorithms
0 5 1 0 1 5 2 0 2 50
5 0 01 0 0 01 5 0 02 0 0 02 5 0 03 0 0 03 5 0 04 0 0 0
Mean: 3 8 6 0 .5 7SD: 1 2 6 2 .4 5
0 5 1 0 1 5 2 0 2 50
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 0
5 0 0 0
Mean: 1 7 0 4 4 .3SD: 3 1 4 0 .9 4
0 5 1 0 1 5 2 0 2 50
5 0 01 0 0 01 5 0 02 0 0 02 5 0 03 0 0 03 5 0 04 0 0 0
0 5 1 0 1 5 2 0 2 50
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 0
5 0 0 0
Time steps in h Time steps in h
Time steps in hTime steps in h
Pow
er in
WP
ower
in W
Pow
er in
WP
ower
in W
Figure 5.2: Uncertainty characterization of DHW demand. In the left diagram, theexpected value is depicted as a black solid line and the scenarios in greycolor. In the right diagram, the reduced scenario set is depicted stage-wise.Three scenarios (states) are chosen to represent every stage [Harb et al.,2016b]
illustrated in grey color. The right diagram depicts the reduced three representative
samples, respectively states, per demand period (Nstates = 3).
The demand periods are chosen based on the observed characteristics of the electrical
demand pattern [Harb et al., 2016b]: a very low demand during the night (0-5 h), followed
by a moderate demand in the morning (5-11 h). During 11-18 h, the active occupancy
in private households is usually low since inhabitants are at work. Yet, the distribution
still shows a small probability of a moderate demand during this period. Finally, a high
demand is observed in the evening between 18-24 h. Each demand period represents a
decision stage in the multi-stage framework. Hence, the number of stages Nstages is equal
to four. 0 5 1 0 1 5 2 0 2 50
5 0 01 0 0 01 5 0 02 0 0 02 5 0 03 0 0 03 5 0 04 0 0 0
Mean: 3 8 6 0 .5 7SD: 1 2 6 2 .4 5
0 5 1 0 1 5 2 0 2 50
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 0
5 0 0 0
Mean: 1 7 0 4 4 .3SD: 3 1 4 0 .9 4
0 5 1 0 1 5 2 0 2 50
5 0 01 0 0 01 5 0 02 0 0 02 5 0 03 0 0 03 5 0 04 0 0 0
0 5 1 0 1 5 2 0 2 50
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 0
5 0 0 0
Time steps in h Time steps in h
Time steps in hTime steps in h
Pow
er in
WP
ower
in W
Pow
er in
WP
ower
in W
Figure 5.3: Uncertainty characterization of electrical demand: scenario samples andreduced set [Harb et al., 2016b]
66
5.2 Single building scheduling approaches
The scenario tree construction algorithm [Harb et al., 2016b] transforms the reduced
set of stage-wise samples into a data matrix where each column represents a scenario.
Stage-wise stochastic independence requires the scenario set to contain every possible
combination of states, resulting in a scenario set with the cardinality (Nstates)Nstages = 81.
The scenario tree structure is illustrated in Figure 5.4.S
tage
1
Sta
ge 2
Sta
ge 3
Sta
ge 4
S1
S81
0 24 time5 11 18
Figure 5.4: Scenario tree structure for a four-stage problem with three states respectively[Harb et al., 2016b]
The scenario tree generation must be conform with the non-anticipative nature of the
decision framework, meaning that a decisions made in former stages does not depend
on the realisation of the uncertain process in later stages. This is assured by the non-
anticipativity constraint.
Non-anticipativity
The non-anticipativity constraint (NAC) states that all ’here-and-now’ decisions, corre-
sponding to the same branch of the scenario tree, are equal up to the node where the
branches fork out. The mathematical formulation is provided by Equation 5.10.
xa(t , s) = xa(t , s +1) if A ( s,k(t ) ) = 1,
∀s ∈ S, ∀ t ∈ tH ,∀ a ∈ AX = {HP, CHP}(5.10)
67
Scheduling Algorithms
A is the non-anticipativity matrix, in which the rows correspond to scenarios and the
columns correspond to time stages. It contains structural information about the scenario
tree. It has the property, A ( s,k(t ) ) = 1, for all pairs of decision variables x(t , s), x(t , s +1)
that correspond to the same branch, and is zero otherwise. The function k(t ) maps the
time steps to their corresponding time stages. NAC is required at all stages except for the
last one. The inter-scenario constraints are set with a so-called NAC-Matrix. It consists of
binary variables that induce constraint links between scenarios. Furthermore, the matrix
representation allows a straightforward conversion of the deterministic problem into the
SP counterpart and vice versa.
5.3 City district scheduling approaches
The increasing share of distributed energy as well as renewable volatile generation
is expected to lead to large discrepancies between generation and consumption and
consequently grid destabilization or curtailment of renewable energy. Such a situation
cannot be mitigated by individual independent local load optimization with no direct or
indirect interaction with other buildings or information about the grid status. Hence,
a coordination or DSM strategy which integrates the available energy generation and
storage flexibilities is required. Such coordination is ideally formulated as a centralized
architecture. However, the latter typically imposes a binding restriction as the computation
time increases exponentially with the number of involved systems. Therefore, hierarchical
distributed architecture which are based on reformulation techniques have gained a lot of
interest. The reformulation is based on decomposition methods which enable a scalable
optimization approach. The cost is a trade-off between solution computation time and
optimality.
In this section, the formulation of a centralized as well distributed architectures for city
disrict DSM strategies is introduced. The centralized model only serves as a reference to
assess the solution quality for the proposed reformulations.
5.3.1 Centralized scheduling
A centralized architecture mainly revolves around a coordinator which has access to all
information and generates the schedules of the electro-thermal heating systems. This
can be formulated as a MILP with the objective of minimizing the total costs of involved
buildings N as indicated in Equation 5.11.
min z =tH∑
t=t0
(P import(t ) ·∆t ·c import−Pexport(t ) ·∆t ·cexport+
N∑n=1
Qgasn ·∆t ·cgas
)(5.11)
68
5.3 City district scheduling approaches
P import(t ) and Pexport(t ) represent the imported into and exported electrical power from
the cluster which are penalized by c import and remunerated by cexport, respectively. Qgas
denotes the aggregated gas consumption from available CHP and boiler of all buildings as
indicated in Equation 5.12.
Qgas =N∑
n=1
(Qgas
CHP,n(t )+QgasBoiler,n(t )
)∀ t ,n (5.12)
The electricity balance for the cluster of buildings is formulated in Equation 5.13.
P import(t )+N∑n
Peln (t ) = Pexport(t ) ∀ t (5.13)
Peln (t ) is the electricity balance on a building n level as indicated in Equation 5.14.
Peln (t ) = Pdem,n(t )+ ∑
uc∈Uc
Puc ,n(t )− ∑ug∈Ug
Pug ,n(t ) ∀ t ,n (5.14)
Pug ,n(t ) and Puc ,n(t ) are bounded by the energy generation and storage units specific
restrictions introduced in Chapter 4. The thermal comfort requirements of the residents
are ensured by a further constraint which indicates that the space heating and DHW
demand must be covered at all times.
5.3.2 Distributed scheduling
The centralized scheduling approach, theoretically, provides the best coordination results
for a limited number of buildings, however, it leads to significant disadvantages, mainly,
the high computation time and accordingly limited extensibility, as well as data privacy
concerns.
Decomposition techniques allow for reformulating large scale optimization problems
which exhibit a special structure. The principle of a decomposition technique is to break a
problem down into a set of smaller problems. As a result, the reformulated optimization
model can be easily solved, thus, reducing the computational effort.
Two separate approaches are investigated in this work, the Dantzig-Wolfe decomposition
(DWD), as well as an integrated Langrangean relaxation columnn generation (LRCG)
approach.
Dantzig-Wolfe decomposition
DWD was proposed for LP problems in which the constraint matrix exhibits a primal block
angular structure. The main idea is to decompose the original problem into a master
69
Scheduling Algorithms
and several subproblems by substituting the variables in the original formulation with a
convex combination of the extreme points or feasible solutions of the subproblems. The
subproblems compute feasible solutions with respect only to the subproblem specific
constraints. The master problem strives to find the optimal weights for the subproblems
feasible solutions that minimize the objective function with respect to a coupling resource
constraint. Figure 5.5 illustrates the structure of the DWD model and the interactions
between the master- and subproblems.
Subproblem 1Generates proposals
based on reduced costs
Subproblem 2Generates proposals
based on reduced costs
Master problemIntegrates proposals and
determines shadow prices
Shadow prices π ProposalProposal
Figure 5.5: Structure of a Dantzig-Wolfe decomposition model as well as the interactionsbetween the master- and subproblems based on shadow prices and proposals[Bradley et al., 1977]
For large scale optimization problems, it is not practical to add every possible subproblem
extreme point to the master problem. Therefore, DWD is coupled with the column
generation (CG) algorithm. The latter restricts the master problem to a selection of
feasible solutions and includes, in an interative manner, additional feasible solutions or
columns only if they have potential to further improve the solution. This corresponds to
columns with negative reduced costs also known as opportunity costs.
Formulation Based on the DWD, the restricted master problem is formulated according
to Equations 5.15 - 5.19. The objective function and ressource constraint are reduced to
Equation 5.15 and 5.16, respectively.
min zLRDW =tH∑
t=t0
(P import(t ) ·c import−Pexport(t ) ·cexport
)∆t +
N∑n=1
(∑p
C pnλ
pn
)(5.15)
P import(t ) represents the electricity bought from public grid with c import = 27.94 ct/kWh
and Pexport(t ) is electrical energy exported into the public grid at cexport=12.00 ct/kWh.
70
5.3 City district scheduling approaches
N∑n
∑p
Pel,pn (t ) ·λp
n +P import(t )−Pexport(t ) = 0 ∀ t (5.16)
P import(t ), Pexport(t ) ≥ 0 ∀ t (5.17)
The master problem finds feasible solutions by linearly combining all known proposals by
the weighting factors λpn . One weighting factor exists for each subsystem and for each
proposal. The convexity of the linear combination of proposals is ensured by introducing
the constraints in Equation 5.19.
∑p∈P
λpn = 1 ∀ n (5.18)
0 ≤λpn ≤ 1 ∀ n, p (5.19)
Since the weights are defined as continuous variables λn ∈ [0,1], the restricted master
problem is considered as a linear relaxation (LRDW) of the original MILP problem.
In each iteration k, the restricted master problem is provided with a new proposal by each
subsystem. The generalized formulation of the objective within the subproblems or pricing
problems is presented in Equation 5.20 subject to device specific and comfort restrictions.
min νn =tH∑
t=t0
(Qg as
CHP,n +Qg asBoiler,n
)·cgas ·∆t︸ ︷︷ ︸
costs for production
+tH∑
t=t0
Peln (t ) ·π(t ) ·∆t︸ ︷︷ ︸
costs for grid interaction
−σn ∀ n (5.20)
A proposal p contains the consumed or produced electricity Pel,pn (t ) and the corresponding
production costs C pn of a subsystem n. C p
n reduce to zero for an electricity driven heating
generator i.e. HP and EH. A positive value for Pel,pn (t ) indicates electricity consumption
and a negative value indicates electricity production. Only proposals with, νn ≤ 0, provide
valid solutions and are therefore added to the base of the master problem. The shadow
prices (or marginal costs) π(t ), and σn are derived from the resource (Equation 5.16) and
convexity (Equation 5.19) constraints. The shadow price vector π(t ) can be interpreted as
the current price for exchanging electricity within the microgrid. The values of π(t ) are
bounded by the low price for exports cgrid and the high price for imports c import. Hence,
π(t ) serve as incentives for the subsystems to shift their operation to pursue the global
goal on a city district level. σn are scalar values that are individual for each subsystem n
and represent its marginal costs. Consequently, the total costs of each subsystem must be
lower or equal to the marginal costs σn to ensure optimality.
71
Scheduling Algorithms
Integering step The solution of the master problem is a linear relaxation that provides
a lower bound (LB) for an integer solution when considering a minimization problem. This
bound will slightly improve in every branching step until a termination criterion is reached.
Solving the master problem can result in fractional weighting factors λpn . However, to
provide each subproblem with an explicit index that indicates which proposal yielded the
optimal solution, the master problem needs to generate integer solutions for the weighting
factors λpn at least in the last iteration. One possible way to obtain integer solutions is to
branch-and-price [Desrosiers and Lübbecke, 2010]. Thereby, the same procedure as in
branch-and-bound algorithms is applied to systematically introduce further constraints in
a branching tree and solve the linear relaxation of the master problem in each node until
a solution satisfying the integrality constraints is found. This approach induces a high
computational effort. Therefore, the approach proposed by [Belov and Scheithauer, 2004]
is adopted. Thereby, the weighting factors λpn are declared in the last iteration as binary
variables in the final optimization step of the master problem using all the proposals
obtained in every iteration.
Algorithm description The restricted master problem is initialized by arbitrary propos-
als and computes an initial vector of shadow prices π(t ) that is sent to the subproblems.
Thereafter, the cycle depicted in Figure 5.6 is executed. Based on the current shadow
price vector π(t ), the subproblems or pricing problems are solved. The corresponding
schedules and production costs are provided to the coordinator and new proposals are
added to the restricted master problem. The coordinator computes new shadow prices
to optimize the overall costs of the city district. Based on the new shadow prices, the
individual buildings adjust their electricity generation/consumption, in order to enhance
the overall objective of the microgrid. This leads to increased costs on subproblem level,
while on microgrid level the solution is continuously improving, thus a convergence is
witnessed, where the sum of all the subproblem costs approaches the objective calculated
by the master problem. The base of the master problem increases with every iteration and
might become very large but it is still smaller and less complex than the original mixed
integer problem formulation. The algorithm is terminated when no significant change
in the value of the objective function of the master problem z occurs, when adding new
proposals. This condition is formulated as:
zk−1 − zk
zk−1≤ ε (5.21)
with k as an iteration index. The threshold ε is set to 0.001. Furthermore, additional
termination criteria are introduced by setting an iteration or time limit. Finally the index
of the optimal proposal is determined based on the integering step as indicated in Section
5.3.2.
72
5.3 City district scheduling approaches
Start
Solve master problem
Solve subproblem
Propose schedule
Update shadow prices
Send new shadow prices
to buildings
Termination criterion reached?
no
End
yes
Solve master problem with binary weighting
factors
Send index of optimal proposal to building
Building
Coordinator
Figure 5.6: Procedural description of the column generation algorithm [Harb et al., 2015]
Integrated decomposition model
In CG approaches, the Dantzig-Wolfe restricted master problem has to be solved in every
iteration to determine the optimal shadow prices. As the algorithm proceeds the master
problem gets bigger with each iteration which results in a increased computation time.
[Vanderbeck and Wolsey, 1996] and [Barnhart et al., 1998] anaylzed the convergence of
CG algorithms and identified a ’tailing-off’ effect. The analysis showed that after a few
initial iterations in which the objective value improves fast, the convergence tends to slow
73
Scheduling Algorithms
down in the final phase. As a result, a large number of iterations is required to achieve an
optimal solution for large scale problems.
[Barahona and Jensen, 1998] proposed a combined algorithm that exploits the strong
relation between column generation and Lagrangian relaxation illustrated in Figure
5.7. The relation states that the Langrangian dual (LD) problem, that derives from
the Lagrangian relaxation (LR) reformulation, is the dual of the linear relaxation of the
Dantzig-Wolfe (LDW) reformulation and vice versa.
EMS | Hassan HarbFolie 1
DLDWLD
LR
DWDLD
MILP
LDW
Dantzig-Wolfe
reformulation
Lagrangian
relaxation
Lagrangian
dual
dual dualdual
equivalent
equivalent
Original problem
linear
relaxation
Figure 5.7: Relation between column generation and Lagrangian relaxation [Nishi et al.,2009]
The approach introduced in [Barahona and Jensen, 1998] employs the Lagrangian relax-
ation formulation and subgradient optimization method [Fisher, 2004] to generate new
columns inexpensively without solving the DW master problem in each iteration. The
same approach has been also used by [Degraeve and Peeters, 2003] for the cutting stock
problem.
LR is a decomposition approach that exploits the structure of primal block-angular ma-
trices, similar to the DWD. In LR, complicating constraints linking the subproblems are
dualized into the objective function using a fixed vector of Lagrange multipliers π as
indicated in Equation 5.22. This leads to a formulation without any linking constraints.
min zLR(x,π) = cx +π(Ax −b) (5.22)
The Lagrangian problem zLR(π) will always provide a lower bound of the original minimiza-
tion formulation, since negative π are introduced into the objective function. The goal is to
maximize zLR(π) over π in order to achieve the original optimal solution. This is referred
74
5.3 City district scheduling approaches
to as the Langragean dual formulation zLD and corresponds to the master problem.
max zLD(π) = cx +π(Ax −b) (5.23)
The LD is solved to determine the optimal values of the Lagrangian multipliers using an
iterative procedure such as subgradient method. The latter iteratively generates dual
feasible points according to Equation 5.24.
πk+1 =πk + sk g k (5.24)
g k is the subgradient and sk is the step size which can be approximated as a constant
value. [Fisher, 2004] proposed a progressive method to update the step size based on
Equation 5.25
sk = αk(
f k − qk)
‖g k‖2, (5.25)
where 0 < αk < 2, f k is the best known upper bound of the optimal cost, qk is the best
known value of the dual cost and g k is the subgradient of the dual problem.
The integrated algorithm can be described as a nested double loop. In the outer loop,
the DW master problem is solved with a simplex algorithm to obtain the optimal dual
variables as known from the CG algorithm. In the inner loop, the subgradient optimization
method is applied on the LR formulation of the problem to iteratively update the shadow
prices. Since the LR subproblems are effectively the same as the pricing subproblems in
CG, the LR subproblem solutions are used as new columns for the DW master problem.
As a result, the speed of convergence for the dual solutions is enhanced. Furthermore,
the LR provides a lower bounds for the optimal value of the linear restricted master
problem, which can be used to estimate the quality of the solution and as termination
criterion. When applying the DWD to reformulate the original MILP problem, the two
problem formulations are actually equivalent problems and thus share the same optimal
solution zMILP and zDW. Relaxing the integer variables of the DW master problem leads
to an improved solution zLDW, because of the extended solution space. As previously
introduced, the Lagrangian dual problem is the dual of the linear relaxation of the DW
master problem. Hence, based on the strong duality theorem, the optimal objective value
zLD is equivalent to zLDW. On the other hand, the weak duality theorem indicates that this
optimal Lagrangian dual solution gives an upper bound for every other optimal solution of
the Lagrangian relaxation problem with non-optimal shadow prices.
zLR(π) ≤ zLD = zLDW ≤ zDW = zMILP (5.26)
The optimal solution of the restricted Dantzig-Wolfe master problem zLRDW can be inter-
preted as an upper bound on the optimal solution of the non-restricted master problem
75
Scheduling Algorithms
zLDW, because its solution space is only a subspace of the full master problem. With every
variable introduced in an iteration, the objective value of the restricted master problem is
improves or at least remaining constant due to the extension of the solution space until
the optimal solution is found.
zLDW ≤ zLRDW
zDW ≤ zRDW
(5.27)
Algorithm description Figure 5.8 depicts the procedural algorithm of the integrated
approach. The algorithm comprises three steps, initialization, pricing step and integering.
The restricted master problem is initialized with random proposals and solved for several
iterations based on the traditional DWD-CG algorithm. Thereby, the aim is to exploit the
good convergence properties of the DWD in the first few iterations. The initialization is
followed by the pricing step which involves an outer and inner loop. In the outer loop
level, the master problem is solved to generate the shadow prices π. Thereafter, the
inner loop runs for a defined number of iterations, during which new shadow prices are
calculated using the subgradient method. The number of inner loop iterations is increased
in a progressive manner. The algorithm is terminated when the difference between the
current upper and lower bound becomes smaller than a specified tolerance value ε or
when the maximum number of iteration or time limit is reached.
76
5.3 City district scheduling approaches
Start
Generate random shadow prices πCompute initial proposals
Solve relaxed, restrictedmaster zLRDW
zk−1LRDW−zk
LRDW
zk−1LRDW
≤ ε,Final outer iteration?Time limit reached?
Solve subproblems
False
Set lower bound zLR
Update shadow pricesusing subgradient method
πk (t )+ sk g k (t )
1− zLRzLRDW
≤ ε,Time limit reached?
Final inneriteration?
False
False
True
Set weights λi
as integers
True
True
Solve restrictedmaster zRDW
End
Figure 5.8: Procedural description of the integrated Lagrangean relaxation - columngeneration algorithm
77
6 Analysis: Results and Discussion
This section delivers an assessment of the formulated scheduling strategies for individual
buildings and city districts.
6.1 Scheduling for single buildings
The first evaluation of the scheduling algorithms considers a single building with no
regard to the grid interaction. The load shifting strategy is motivated by the residents’
goal to increase the local consumption of PV power and reduce the operation costs of their
building energy systems.
The aim of this evaluation is to assess the expected advantage of the predicitve scheduling
algorithms for individual buildings with respect to a reactive strategy as a benchmark.
The analysis is conceptualized by first determining the best possible solution of predic-
tive scheduling by employing perfect forecasts then evaluating the performance of the
deterministic approach based on point forecasts and finally assessing the impact of incor-
porating demand forecast uncertainty in the scheduling model based on the stochastic
programming approach.
The assessment is carried out based on a coupled simulation of the optimization program
with a BES dynamic simulation model. This allows to consider both the modeling and
input data uncertainty.
6.1.1 Design and configuration
BES configurations The impact of the scheduling strategy is mainly influenced by
the design of the BES. Therefore, six different configurations are considered for the
assessment. This allows to evaluate the impact of the different combinations of heat
generators as well as the thermal and electrical storage systems. Table 6.1 delivers an
overview on the design of the investigated BES.
The building considered is a single family house with three residents. The heated floor
area is 125 m2and the nominal heating load is 6.5 kW. The maximal domestic hot water
load amounts to 15 kW. The design power of the heat generators are determined based on
conventional design criteria to satisfy the nominal heating load and domestic hot water
79
Analysis: Results and Discussion
demand. Both the HP and EH are non-modulating. The characteristics of the HP unit are
presented in Section 4.1. The characteristics of the CHP unit are presented in Table 4.1.
The CHP as well as the auxiliary boiler can modulate down to 30 %. All BES configurations
comprise a PV system and a single thermal water storage (TS).
Table 6.1: BES configurations: The characteristics of the primary heat generators, Dim-plex air-to-water LA9TU HP (QA2W35 = 7.5 kW) and Vaillant EcoPower 3.0 CHP(P = 3 kW, Q = 8 kW) are presented in Chapter 4
Configuration PV HP CHP EH Boiler TS Battery
PV-HP-EH 4.8 kWp LA9TU - 11 kWel - 500 l -PV-HP-EH-Bat 4.8 kWp LA9TU - 11 kWel - 500 l 4.6 kWh
PV-CHP-B 4.8 kWp - EcoPower 3.0 - 12 kWth 500 l -PV-CHP-B-Bat 4.8 kWp - EcoPower 3.0 - 12 kWth 500 l 4.6 kWhPV-CHP-EH 4.8 kWp - EcoPower 3.0 11 kWel - 500 l -
PV-CHP-EH-Bat 4.8 kWp - EcoPower 3.0 11 kWel - 500 l 4.6 kWh
HEMS setups The anaylsis of the scheduling strategies’s performance is conceptualized
by defining and evaluating the following HEMS configuration:
. reactive (Ref) as a benchmark
. deterministic based on perfect information (DPI)
. deterministic based on forecasts (DF)
. multi-stage stochastic programing incorporating electrical demand uncertainty (SPel)
. multi-stage stochastic programing incorporation domestic hot water demand uncer-
tainty (SPdhw).
A reactive strategy is defined for every BES configuration to serve as reference for
evaluating the impact of employing a predicitve scheduling algorithm. Ref aims to
satisfy the space heating and DHW demand with no regard to the availability of local PV
generation. It consists of a conventional 2-point hysteresis control strategy which turns
on the primary heating unit i.e. HP or CHP, when the set temperature required by the
consumer heat cycle is not satisfied anymore. The primary heat generator is kept on
until the tapping temperature reaches the maximal heating system’s supply temperature.
The assumptions for the control strategies within the dynamic simulation model, which
emulates the reality, are crucial for the performance of the predictive energy management
strategies as well as the conventional operation of the BES. Figure 6.1 depicts the status
and transition conditions within the reactive control strategy for a HP-EH-Bat system.
80
6.1 Scheduling for single buildings
HP: OffEH: Off
HP: ONEH: Off
HP: ONEH: ON
Ttap ≤ Tmin orSOCBat > 98 % & Ttap < Tmax -5 K
Ttap ≥ Tmax orSOCBat ≤ 20 % & Ttap >= Tmin + 10 K
Ttap ≥ Tmin+ 5 K
Ttap < Tmin
Figure 6.1: State-based representation of HP-EH-Bat reactive control strategy; The tran-sitions are defined in function of the thermal storage and battery status
Ttap is the drawn temperature from the storage tank, Tmin is the minimum flow temperature
necessary for matching the heat demand determined according to the DHW supply
temperature requirements and the heating curve. Tmax is the maximum heat pump
condenser’s temperature. SoCbat denotes the battery’s state of charge. The transitions
are subject to further restrictions related to the operation time of the HP unit, namely, the
minimum shut down and run time which are set to 30 mins.
DPI assumes perfect forecast and allows for determining the best bound for cost op-
timization enabled by employing a predictive HEMS while considering the modeling
uncertainties of the linearized MILP BES model.
DF is based on a predefined configuration of forecasting models for the different input data
according to the evaluation results presented in Section 3.2.5. Namely, SVR is used for
electrical and space heating demands, naive for DHW demand and ARMA for forecasting
the solar irradiation and outdoor temperature. The DF setup allows for determining the
real potential for a deterministic scheduling model under consideration of both input data
forecast and BES MILP modeling uncertainties.
SPel and SPdhw allow for assessing the impact of incorporating the uncertainty from the
electrical and domestic hot water demand in the predictive scheduling model, respectively.
The forecast evaluation presented in Section 3.2.5 showed that the strong stochasticity
of the domestic hot water and electrical demand induce the highest perdiction error and
are therefore integrated as uncertainties within the stochastic programming scheduling
approach.
6.1.2 Evaluation
The dynamic performance of the Ref, DPI and DF strategies is depicted in Figures 6.2-
6.5 for the PV-HP-EH configuration during two consecutive days in March, that are
representative for the transition period. The dynamic performance of SPel and SPdhw are
included in Appendix A.1.1. The transition period is characterized by the availability of
space heating and DHW demand as well a significant solar irradiation and thereby PV
81
Analysis: Results and Discussion
generation. Whereas, the winter period is characterized by low solar irradiation and
high heating demand, which leads mostly to an uninterrupted, inflexible operation of the
heating systems. In summer, the non-existing space heating demand significantly reduces
the operation of the heating generators and thereby the flexibility potential for load
shifting. Therefore, the transition period is chosen to evaluate the dynamic performance
of the energy management strategies in matching or coordinating the operation of flexible
heating systems and PV electricity generation. The dynamic performance for the rest of
the BES configurations is found in Appendix A.1.
02468
kW
Dymola_Qspace Dymola_Qdhw
036912
kW
Dymola_QHP
0
1
OnO
ff
Dymola_uHP
036912
kW
Dymola_QEH
00 :0028 -Mar2008
00 :0029 -Mar
06 :00 12 :00 18 :00 06 :00 12 :00 18 :000
20406080100
%
Dymola_SoCST
Figure 6.2: Dynamic performance of the thermal side for PV-HP-EH under the Ref strategy.The depicted profiles, from top to bottom, are the space heating and domestichot water demands, the thermal power of the HP, the On/Off operation statusof the HP, the thermal generation of the auxiliary EH and the state of chargeof the water storage tank
Figure 6.2 shows the operation of the BES using the reference reactive strategy. This
strategy is implemented within the dynamic simulation model in Dymola as an internal
controller. The upper subplot displays the actual space heating Qspace and DHW Qdhw
demands. The second and third subplots depict the thermal generation QHP and on/off
82
6.1 Scheduling for single buildings
status uHP of the HP. The last two subplots show the heat generation of the auxiliary
electrical heater QEH and the state of charge of the thermal water storage tank SoCST.
The operation of the HP displays the expected hysteresis based On/Off operation in
function of the storage drawn temperature, respectively the resulting SoC. The HP is
turned on when the drawn temperature is below its set value and kept on until the storage
is almost full i.e. SoC of around 100 %. The auxiliary electrical heater is additionally
turned on when the set temperature cannot be achieved by the sole operation of the HP
and turned off when the storage drawn temperature exceed the set point by a predefined
offset.
02468
kW
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
036912
kW
QHP
Dymola_QHP
0
1
OnO
ff
uHP
Dymola_uHP
01234
kW
QEH
Dymola_QEH
00 :0028 -Mar
00 :0029 -Mar
06 :00 12 :00 18 :00 06 :00 12 :00 18 :000
20406080100
%
SoCST
Dymola_SoCST
Figure 6.3: Dynamic performance of the thermal side for PV-HP-EH under the DPI strat-egy. The solid lines represent the operation status delivered by the MILPscheduling algorithm whereas the dashed lines represent the operation withinthe dynamic simulation model formulated in Dymola/Modelica
Figures 6.3 and 6.4 depcit the thermal and electrical loads for the DPI predictive scheduling
strategy, respectively. The solid lines represent the operation status as foreseen in the
scheduling model. The dashed lines represent the realization of the schedule status within
the dynamic simulation model in Dymola. The dynamic simulation model comprises an
83
Analysis: Results and Discussion
internal controller which ensures that the schedule set points are overridden when the
thermal comfort standards, the heating generator or storage restrictions are violated,
analogously to the conditions declared within the reactive strategy illustrated in Figure
6.1. Such an intervention is seen in the 3rd subplot of Figure 6.3 on 28th of March at
around 13:00 o’clock. The internal controller detects that the thermal storage is full and
turns off the HP sooner than foressen by the scheduling algorithm which underestimates
the thermal storage state of charge. Another overriding action is also seen on the same
day at around 15:00 o’clock. The foreseen operation of the HP is ignored by the internal
controller since the thermal storage is full.
02468
kW
PdemandDymola_Pdemand
036912
kW
Pimpor tDymola_Pimpor t
Pexpor tDymola_Pexpor t
02468
kW
PPVDymola_PPV
01234
kW
PHPDymola_PHP
0
1
OnO
ff uHPDymola_uHP
00 :0028 -Mar
00 :0029 -Mar
06 :00 12 :00 18 :00 06 :00 12 :00 18 :0001234
kW
PEHDymola_PEH
Figure 6.4: Dynamic performance of the electrical side for PV-HP-EH under the DPI strat-egy. Pdemand denotes the elctrical demand, Pimport and Peyport the electricalimport and export from the public grid, PPV the local PV electricity generation,PHP and PEH the electrical consumption of the HP and EH units
Overall, the results show that the operation of the HP is more dynamic, displaying frequent
switching, compared with the operation seen in Figure 6.2 under the Ref strategy. This
frequent switching behavior is usually avoided to reduce the tear and wear of the unit.
The HEMS strives to shift the operation of the HP to the time slots characterized by PV
84
6.1 Scheduling for single buildings
generation availability as depicted in the 3rd and 4th subplots of Figure 6.4. Moreover, the
HEMS allows for avoiding the operation of the less efficient auxiliary heater compared
with reactive strategy as shown in the 4th subplots of Figures 6.2 and 6.3. Further, the
results show that the foreseen schedule from the predictive HEMS is well followed by the
dynamic simulation model. This indicates that the MILP model of the BES allow for a good
representation of the real dynamic performance of the corresponding BES.
DPI is formulated based on the assumption of perfect information or perfect forecasts.
Hence, the forecast values of the scheduling model and the real values in dynamic
simulation model for space heating and DHW demand forecast (1st subplot in Figure 6.3),
as well as the electrical demand and the PV generation (1st and 3rd subplots in Figure 6.4)
are mostly identical. The discrepancies between the perfect forecast and the real values
result from the modified dynamic operation of the BES simulation model as well as the
different discretization or time resolution considered. The scheduling optimization model
is computed with a 15 minutes resolution while the dynamic simulation model is solved
with variable time step at a much higher resolution.
Consequently, the results of the perfect forecast based DPI strategy represent an upper
bound for assessing the predictive HEMS that integrate weather and demand forecasts.
Figure 6.5 displays the scheduling performance of the DF strategy under real forecast
conditions. As a result, discrepancies are observed between the forecasts, for space
heating, DHW and electrical demand as well as PV generation, assumed by the scheduling
model and the actual values computed within the dynamic simulation model. The discrep-
ancies for the space heating and DHW demand are shown in the upper subplot of Figure
6.5. The space heating demand is greatly overestimated by the forecast model during
the afternoon period on the 28th of March. The DHW demand forecast delivers a bad
estimation of the real consumption. The impact of the forecasts’ inaccuracy is observed in
the operation of the HP when compared to the DPI based operation in Figure 6.3. Mainly,
the foreseen schedule is ignored several times. The state of charge of the thermal storage
is underestimated in the scheduling model at around 9:00 o’clock due the DHW demand
forecast. Consequently, the later, extended operation of the HP during the afternoon
starting from 13:00 o’clock which aims to take advantage of the availability of PV genera-
tion and satisfy the falsely predicted space heating demand is overridden by the internal
controller. Nevertheless, the operation of the HP is partially shifted towards the time slot
of PV generation and the EH operation is reduced, compared with the reactive reference
strategy. This implicitly indicates that, despite the forecast error, a cost reduction can
be achieved. The scheduling efficiency can be increased by increasing the rescheduling
rate e.g. reduce the rescheduling interval from 24 h to 6 h. This results in reducing the
forecast and consequently the deviations in the schedules’ realization.
85
Analysis: Results and Discussion
02468
kW
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
036912
kW
QHP
Dymola_QHP
0
1
OnO
ff
uHP
Dymola_uHP
01234
kW
QEH
Dymola_QEH
00 :0028 -Mar
00 :0029 -Mar
06 :00 12 :00 18 :00 06 :00 12 :00 18 :000
20406080100
%
SoCST
Dymola_SoCST
Figure 6.5: Dynamic performance of the thermal side for for PV-HP-EH under the DF
strategy
An overview of the performance of all HEMS setups for all introduced BES configurations
of Table 6.1, under all HEMS strategies, is presented in Table 6.2. The results are averaged
over the simulations for three months during the heating period in March, September
and December. The assessment is described by evaluating the resulting operating costs.
Furthermore, three indicators are defined to quantify the impact of employing predictive
scheduling, the influence of forecast error and the integration of uncertainty within the
scheduling model:
. Value of scheduling (VS)
. Value of perfect information (VPI)
. Value of uncertainty (VU)
The costs’ column represents the averaged weekly operation costs of the BES. VS defines
the costs increase or decrease in % of the resulting costs from employing a predictive
HEMS compared to the costs of the conventional reactive strategy. VPI defines the costs’
deviation of the predictive HEMS from the best bound possible when applying a HEMS
86
6.1 Scheduling for single buildings
with perfect forecasts. The value of uncertainty (VU) represents the impact of considering
uncertainty of either the electrical or DHW demand prediction in the scheduling algorithm
compared to the determinstic formulation with point forecasts.
Table 6.2: Assessment results of the scheduling strategies for all BES configurationsduring the months March, September and December. The optimization timeresolution is 15 min, the rolling horizon’s rescheduling interval and schedulinghorizon are 24 and 48 h, respectively. The MIP gap is set to 1 % for DPI andDF and 1.5 % for SPel and SPdhw. The costs are weekly averaged. NegativeVS, VPI and VU indicate a cost reduction whereas positive values denote anincrease with respect to the costs of the Ref , DPI and DF, respectively
BES Strategy Costs in e VS in % VPI in % VU in %
PV-HP-EH Ref 102.62DPI 90.85 -11.5DF 98.78 -3.7 8.7
SPel 95.99 -6.5 5.6 -2.8SPdhw 95.05 -7.4 4.6 -1.0
PV-HP-EH-Bat Ref 99.95DPI 92.33 -7.6DF 95.16 -4.8 3.1
SPel 92.64 -7.3 0.3 -2.8SPdhw 92.44 -7.5 0.1 -2.9
PV-CHP-B Ref 80.6DPI 75.77 -6.0DF 78.27 -2.9 3.3
SPel 77.64 -3.7 2.5 -0.8SPdhw 75.82 -5.9 0.1 -3.1
PV-CHP-B-Bat Ref 80.91DPI 77.03 -4.8DF 79.28 -2.0 2.9
SPel 77.71 -4.0 0.9 -2.0SPdhw 77.93 -3.7 1.2 -1.7
PV-CHP-EH Ref 86.10DPI 79.90 -7.2DF 84.22 -2.2 5.4
SPel 79.97 -7.1 0.1 -5.0SPdhw 80.39 -6.6 0.6 -4.5
PV-CHP-EH-Bat Ref 80.63DPI 76.57 -5.0DF 80.57 -0.1 5.2
SPel 76.84 -4.7 0.4 -4.6SPdhw 65.76 -4.8 1.3 -4.7
87
Analysis: Results and Discussion
The MIP gap for the Gurobi optimization solver is set, respectively, to 1 % and 1.5 % for
the deterministic (DPI and DF) and SP (SPel and SPdhw) models. The convergence from
1.5 % to 1 %, withing the SP approach1, showed an extremly slow pattern which often led
to exceeding the time limit of 10000 s.
The results show that employing a predictive scheduling algorithm under perfect infor-
mation condition enable a cost reduction in all considered BES configuration compared
with a rule-based reactive strategy. The value of scheduling amounts to -11.5 % and -7.6 %
for PV-HP-EH and PV-HP-EH-Bat, -6.0 % and -4.8 % for PV-CHP-B and PV-CHP-B-Bat, as
well as, -7.2 % and -5.0 % for PV-CHP-EH and PV-CHP-EH-Bat. The highest cost reduction
potential is provided in the HP based BES setup and the CHP-EH configuration. This can
be attributed to the more balanced capacities of electricity consuming units i.e. HP or EH
and generation units i.e. CHP or PV within these configurations. Moreover, the results
indicate that the cost reduction potential of the predictive scheduling algorithm under
perfect information condition is lower in the BES configurations employing a battery
storage. It is foreseen that increasing the rescheduling time resolution of the rolling
horizon algorithm results in reducing the uncertainty from the BES model and thereby
enhancing the performance of the scheduling realization and consequently the cost re-
duction achieved. The value of scheduling with the DF strategy is reduced from -11.5 %
to -7.6 % for the HP-EH BES system as well as from -6.0 % to -4.8 % and -7.2 % to -5.0 %
for the CHP-B and CHP-EH systems, respectively. The battery allows for balancing the
discrepancy between the electricity generation from PV or CHP and the electrical demand,
hence enabling load shifting or optimization without requiring demand forecasts. The bal-
ancing through the battery is further facilitated in the presence of electrically driven heat
generator i.e HP and EH. Furthermore, the results verify the hypothesized cost reduction
potential of predictive scheduling compared with the reactive operation strategy despite
the embedded forecasting errors. The value of scheduling with the DF strategy amounts
to -3.7 % and -4.8 % for PV-HP-EH and PV-HP-EH-Bat, -2.9 % and -2.0 % for PV-CHP-B and
PV-CHP-B-Bat, as well as, -2.2 % and -0.1 % for PV-CHP-EH and PV-CHP-EH-Bat. Hence, the
DF strategy allows in all configuration for a clear cost reduction compared to the reference
reactive strategy, except for PV-CHP-EH-Bat. Within the configuration PV-CHP-EH-Bat,
the forecast deviation results in non-optimal schedules which lead to similar costs with
the reactive strategy. The highest saving potential is achieved by the configuration based
on an HP unit. The integration of the electrical or DHW demand uncertainty in the SP
scheduling model enables an average cost reduction of 5.8 % ranging between 3.7 and
7.5 %, with respect to the reactive strategy, over all considered configurations. Within
PV-HP-EH-Bat, PV-CHP-B and PV-CHP-EH, a value of perfect information around zero is
achieved. Hence, the SP scheduling model achieves in these setups within the considered
investigation period, the best bound of cost reduction potential set by DPI. This can be
1The mutli-stage SP model is formulated based on three states and four stages resulting in 81 scenarios
88
6.1 Scheduling for single buildings
related to the effectiveness of incorporating the uncertainty in the scheduling model and
to the stage-wise schedule update within the dynamic simulation which compensates the
MILP BES modeling uncertainties that reduce the potential of the DPI strategy. The value
of uncertainty shows a negative value throughout all considered configurations indicating
that the SP HEMS outperforms the DF strategy. An average cost reduction of 3.0 % is
achieved ranging between 1.0 and 5.0 %.
However, the average computation time increases from around 200 s in the DF to over
2300 s in the SP approach. Figure 6.6 illustrates the computational effort across the
DPI, DF and SP approaches for the scheduling step only ; The simulation time within
the dynamic BES model is not included. The computational time for a single day-ahead
schedule within the DPI approach only amounts to one second; this corresponds to the pure
optimization solving time. The training of the forecasting algorithms employed by the DPI
increases the time required for the scheduling step to 200 s. It must be noted that this time
interval varies depending on the forecasting model and training configurations, mainly,
the model complexity, number of exogenous inputs and past measurements considered. It
is important to note that the computation time of the SP model depends on the number
of scenarios considered, which results from the number of states (branches) and stages
used to characterize the uncertainty. An increasing number of scenarios increases the
scheduling model ’s complexity and results in an exponentially higher computation effort.
DPI DF SP
0
0.5
1
1.5
2
2.5
1 s200 s
2.3 103 s
+1000 %
HEMS setup
Ave
rag
eco
mp
uta
tion
tim
ein
103s
Figure 6.6: Computation time comparison between DPI, DF and SP scheduling models;The values denote the average time for computing one day-ahead schedule;The arrow indicate the increase of computation time in percentage of SPmodels compared to DF; The simulations were carried out on a work-stationwith 12 active cores Intel Xeon CPU [email protected] GHz and 32 GB of RAM
89
Analysis: Results and Discussion
6.2 Distributed scheduling for neighborhoods
The second evaluation involves a residential neighborhood. The DSM strategies’ goal is to
increase the integration of renewable energy internally within the microgrid of the city
district and optimize the interactions of the flexible electricity consuming and generating
units within the individual buildings.
The aim of this assessment is to evaluate the distributed coordination approaches with
regard to the quality of the generated schedules and consequently the coordination fitness
as well as the scalability potential.
6.2.1 Design and configuration
The performance of the distributed scheduling algorithms is assessed by considering a
cluster of 34 residential buildings.
The heating units are designed as bivalent systems according to conventional standards.
The CHP units are designed to run at least 4000 h/a while a bivalence temperature of
-2 °C is set for the heat pump units. The CHP units are supported by an additional gas
boiler while heat pumps are provided with an integrated electrical heater to cover peak
loads. All BESs comprise a PV system as well as a 300 l thermal storage tank to enable a
flexible operation. The ratio between installed capacity of µCHP units and HPs is roughly
set to 140 % to ensure that the µCHPs are able to cover both the electrical demand for
appliances and the electricity consumption of the HPs.
The demand profiles are generated synthetically for every building using the approach
introduced in Section 3.1 with respect to the number of residents assumed. The distributed
DSM strategies considered are the Dantzig-Wolfe decomposition based column generation
algorithm (CG) as well as the integrated Lagrangian relaxation column generation (LRCG).
A centralized approach is formulated to serve as a benchmark.
6.2.2 Evaluation
Comparison of CG and centralized approach
The goal of the following assessment is to evaluate the coordination performance and
scalability potential of the distributed CG approach with respect to the centralized formu-
lation.
Coordination Figure 6.7a and 6.7b exemplary show the schedules of the centralized
and distributed approaches, respectively, for a single day in February.
90
6.2 Distributed scheduling for neighborhoods
The upper subfigures illustrate the cluster’s internal microgrid status with respect to the
residual load. The residual load is represented by the dashed line and it is defined as the
difference of the total electrical demand of lights and appliances (D) and the electricity
generated by local wind and PV renewable energy sources (R). The solid line represents the
difference of electricity import (I) and export (E), which denotes the microgrid interactions
with the public grid.
The lower figure illustrates the scheduling results of both, HP and CHP units operating
within the cluster. The electricity consumption and production of all HP and CHP units,
respectively, are aggregated at each time step.
40
20
0
20
40
60
80
Po
we
rHin
HkW
DH-HR IH-HE
5 10 15 20
Tim eHinHhours
2030405060708090
100
Po
we
rHin
HkW
CHP HP
(a) Centralized
40
20
0
20
40
60
80
Po
we
rHin
HkW
DH-HR IH-HE
5 10 15 20
Tim eHinHhours
2030405060708090
100
Po
we
rHin
HkW
CHP HP
(b) Distributed
Figure 6.7: Schedule profiles for a random day in February using the centralized anddistributed approaches. ’D-R’ denotes the residual load, with ’D’ as theaggregated electrical demand of lights and appliances for the participatingbuildings and ’R’ the renewable energy from wind and PV units; large negativevalue indicate high availability of renewable energy. ’I-E’ represents thecluster’s interaction with the public grid, with I and E as the electricityimported to and exported from the cluster, respectively [Harb et al., 2015]
As expected, the centralized coordination is able to balance the load completely. However,
the distributed scheme is also able to balance a large amount of the residual load. The
operation of the HPs and CHPs is shifted according to the residual load development. In
the early morning hours around 4 h the HPs are operated to accommodate the available
wind energy while the CHPs’ employment is reduced. During the evening, around 20 h,
the electricity consumption is at its peak value. Accordingly, the operation of electricity
driven HPs is reduced while the electricity generating CHPs are maximally activated.
91
Analysis: Results and Discussion
0 50 100 150 200 250 300 350
Time in days
60
40
20
0
20
40
60
80
Pow
er
in k
W
D - R I - E
(a) Centralized
0 50 100 150 200 250 300 350
Time in days
60
40
20
0
20
40
60
80
Pow
er
in k
W
D - R I - E
(b) Distributed
Figure 6.8: Grid interaction (I-E) for the centralized and distributed scheduling ap-proaches over one year with respect to the residual load (D-R) [Harb et al.,2015]
Figures 6.8a and 6.8b illustrate the microgrid interaction over one year for the centralized
and distributed scheduling models, respectively. The observations in Figure 6.7 are further
affirmed. Mainly, the centralized approach achieves a high coordination level. This allows
for integrating the surplus of renewable energy indicated by a negative residual load, and
reducing the amount of imported electricity from the public grid. The grid interaction
(I-E) exhibit an export pattern only when the renewable generation is quite high e.g.
during the day 60 and 2500. In summer, the imports are reduced but cannot be balanced
effectively since the missing space heating demand restricts the employment of the flexible
heating generators mainly µCHP units. The optimal coordination is achieved during the
transition periods e.g. around day 100 and 280. During this period, a self-sufficient status
is achieved as the grid interaction (I-E) often reaches the value zero. The distributed
approach achieves a comparable coordination performance. Similar as in the centralized
setup, the renewable energy surplus integration within the microgrid is enhanced and the
imported electricity is reduced. However, the self-sufficient status during the transition
period, is reached less often compared with the centralized approach. This result is
expected when taking into consideration the formulation of the centralized model which
has access to all information on the individual building energy systems.
The impact of the coordination through the predicitive DSM strategies on the total
operation costs of the city district can be assessed by evaluating the resulting total gas
and electricity costs compared with a heat-driven reference scenario. Within this reference,
the heating generators are operated based on the conventional heat-driven mode. This
operation mode aims to satisfy the heat demand with no consideration of renewable energy.
The evaluation shows that for the considered city district with 34 buildings, the centralized
approach results in reducing the total yearly operation costs by 9% while the CG algorithm
allows for 4% reduction compared with the heat-driven scenario. These values are strongly
dependent on the amount of renewable energy available within, the feed-in electricity
92
6.2 Distributed scheduling for neighborhoods
tariffs for PV and CHP systems as well as the available flexibility capacities i.e. thermal
storage and battery units. With increasing share of renewable energy systems or size of
the microgrid, the cost reduction potential of the DSM strategies is foreseen to increase.
0 50 100 150 200 250 300 350
Time in days
0
5
10
15
20
Hour
of
day
120
80
40
0
40
80
120
Power in kW
(a) Grid interactions based on subproblems’ proposals with produc-tion costs
0 50 100 150 200 250 300 350
Time in days
0
5
10
15
20
Hour
of
day
120
90
60
30
0
30
60
90
120
Power in kW
(b) Grid interactions based on subproblems’ proposals without pro-duction costs
Figure 6.9: Influence of including/excluding the production costs in the buildings’ pro-posals on the grid interaction, over one year with respect to the hour of theday, within the distributed approach. The green range indicates the desiredself-sufficient status, the blue range denotes electricity exports from themircogrid whereas the yellow to red range denotes electricity import [Harbet al., 2015]
Data privacy One of the main drawbacks of the centralized approach is the amount of
information needed which hinders a real-life application. The distributed approach allows
93
Analysis: Results and Discussion
for greatly reducing the amount of sensible information that needs to be communicated
between the buildings and the coordinator. To recap, the proposal of a building with an
electrical driven heat generator comprises only the electrical demand while the proposal
of a building with a gas driven heat generator further includes the production costs. This
inclusion may arise privacy concerns. Hence, the impact of removing the production costs
from the proposal provided by the building to the master problem is investigated. Figure
6.9a and 6.9b display the grid interactions in the distributed approach while including
and excluding the production costs in the proposal, respectively. In general, the results
restate that the coordination degree is best during the transition period (indicated by the
green color). Moreover, the impact of the daily electricity demand, which is characterized
by a morning and an evening peak, on the grid interaction is shown by the large imports
exhibited by the mircogrid (indicated by the yellow color) at the same peak periods. With
regard to the proposal formulation, it can be seen that the exclusion of the production
costs results in slight shift towards an energy positive cluster or a virtual power plant.
Mainly the electricity export (blue color) during the transition seasons is increased as
shown in Figure 6.9b. Excluding the production costs which reveal implicitly the efficiency
of the µCHPs results in reducing the weight of the coordinator while the local goal fo the
individual building becomes more dominating. As a result, the coordination of balancing
the residual load within the cluster decreases.
Centralized Distributed
0
2
4
6
-78 %
+140 %
+17 %
Scheduling architecture
Com
pu
tati
on
tim
ein
103s
34 buildings102 buildings
Figure 6.10: Computation time analysis of the centralized and CG distributed schedulingmodels for the coordination of two clusters comprising 34 and 102 buildings.The arrow represents the computation time reduction achieved by thedistributed approach compared with centralized. The other percentageratios denote the increase of the computation time when increasing thecluster size within every approach.
94
6.2 Distributed scheduling for neighborhoods
Scalability The scalability of the centralized and CG distributed approaches is investi-
gated by analyzing the development of the computation time required to generate the
daily schedules for one year in clusters comprising 34 and 102 buildings. Figure 6.10
shows the results of the average computation time for the considered clusters within
the centralized and distributed scheduling models. The computation time within the
centralized approach amounts to 2800 s for the cluster with 34 buildings. The increase in
the number of considered buildings results in a significant rise of the computation time to
over 6700 s, this corresponds to an increase of 140 %. In contrast, the computation time of
the distributed approach is around 600 s in the cluster with 34 buildings. This corresponds
to 22 % of the time needed by the centralized approach. The computation time increases
within the distributed scheduling approach to around 700 s when increasing the number
of considered buildings to 102. This corresponds to an increase of 17 %.
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0Tim e in s
2 0 0
2 5 0
3 0 0
3 5 0
4 0 0
4 5 0
5 0 0
Cos
t fu
ncti
on v
alue
in E
uro
CG: zLRDWCG: zLRCG: zRDWLRCG: zLRDWLRCG: zLRLRCG: zRDW
Figure 6.11: Convergence assessment of the CG (in black) and integrated LRCG (inred) algorithms for a random day in March. The solid lines represent thedevelopment of the linearly relaxed primal solution of the master problemswhereas the dashed lines depict the development of the lower bounds. Thecross markers denote the integer solutions
Comparison of CG and LRCG
The main challenge for implementing a DSM strategy on a city district level is the
scalability potential for including a large number of buildings. The goal of the following
assessment is to compare the performance of the integrated LRCG and standard CG
95
Analysis: Results and Discussion
algorithms. It is assumed that the integrated LRCG enables a faster convergence and
thereby a higher potential of scalability.
Figure 6.11 depicts the convergence development of the CG and LRCG algorithms for a
random day in February. zLRDW represents the linear relaxation primal solution of the
master problem, zLR the lower bound or dual solution and zRDW the integer solution of the
master problem. The primal problem is a minimization problem while the dual problem is
a maximization problem. Therefore, the primal solution should decrease in each iteration,
whereas the dual solutions increases. It can be seen that the integrated LRCG algorithm
allows for faster convergence compared with the traditional CG algorithm by updating the
dual solution or lower bound based on the subgradient method. The integer solution is
quite comparable in both approaches.
2 0 02 2 02 4 02 6 02 8 03 0 03 2 0
z LRDW
in E
uro
2 0 02 2 02 4 02 6 02 8 03 0 03 2 03 4 0
z RDW
in E
uro
CG LRCG2 0 02 5 03 0 03 5 04 0 04 5 05 0 05 5 06 0 0
Com
puta
tion
tim
e in
s
Figure 6.12: Assessment of the primal zLRDW and integer zRDW solution, as well as thecomputation time of the CG and integrated LRCG distributed schedulingapproaches. Within the boxplot, the bottom and top of the box are the firstand third quartiles (25 % and 75 %), while the band inside is the median.The whiskers represent a 1.5 multiple of the interquartile range. The ’+’markers denote the outliers
96
6.2 Distributed scheduling for neighborhoods
The boxplot in Figure 6.12 delivers an overview on the average performance of both CG
and LRCG approaches in the transition period in terms of primal and integer solution as
well the computation time. It can be seen that the observations in Figure 6.11 are affirmed.
The primal and integer solutions are similar. However, the average computation time is
significantly reduced from around 550 to 250 s. The outlier found in the bottom subplot of
Figure 6.12 is a result of a slower convergence at the subproblems level. Consequently,
the assumption that the integrated LRCG allows for faster convergence and a higher
scalability potential compared with the traditional CG algorithm is verified.
97
7 Conclusion and Outlook
7.1 Conclusion
This thesis presents a generalized methodology, supported by a software framework, for
modeling and assessing mathematical programming based predictive DSM strategies that
exploit thermal and electrical flexibilities of residential BES.
Chapter 1 delivers an overview on the motivation, classification and challenges of residen-
tial DSM strategies. The main challenges for formulating and developing DSM strategies
are identified as BES MILP modeling, extensibility and scalabiltiy of the architecture as
well as the uncertainty of the incorporated forecasts.
In Chapter 2, the methodology developed in this thesis is described. Mainly, the concept
as well as the software architecture and configuration are presented. The modeling and
simulation platform is formulated in Python and includes a set of forecasting methods as
well as a BES MILP modeling library based on the Gurobi optimizer API and integrates a
BES non-linear Dymola/Modelica simulation model. The main advantages of the methodol-
ogy are the modular structure of the forecasting and BES MILP libraries as well as the
defined interfaces for coupling the scheduling HEMS to dynamic simulation models based
on the FMI standard. The FMI standard allows for integrating the dynamic simulation
models independent of the modeling language as a black box. Consequently, the software
framework is solely written in the programming language Python. Thereby, the advantage
is eliminating the usage of multiple programming languages and simulation coupling
servers. Consequently, the methodology provides a software framework which enables a
flexible and extensible formulation of scheduling models as well as reliable evaluation of
the schedules’ realization.
In Chapter 3, the forecasting algorithms for predicting the weather and demand variables
are introduced and evaluated. The assessment showed that the machine learning algorithm
SVR results in the lowest forecasting error for electrical and space heating demand
prediction. ARMA delivered the best results for the strongly seasonal solar irradiation
and ambient temperature. The DHW demand strong stochasticity could not be captured
by SVR and ARMA. Hence, the persistence method is recommended for this application.
It must be noted that considering the negligible implementation effort and the plausible
prediction performance, the persistence method can be further used as a forecasting
model for the other variable as well.
99
Conclusion and Outlook
In Chapter 4, the discrete MILP optimization models of the individual building energy
systems components are formulated. The introduced modeling approach for the heat-
ing generators comprehensively integrate units’ specific dynamic characteristics from
manufacturer data sheets and enable a better representation compared to the tradition-
ally used simplified MILP models in the literature, that are formulated to averagely and
conservatively represent the units’ behavior. It is recommended to adopt this modeling ap-
proaches for short-term scheduling application since the modeling uncertainty is thereby
reduced. Furthermore, a novel empirical approach for modeling thermal storage systems
is introduced which allows for representing the dynamic development of the usable and
unusable energy content depending on time and operation, based on the thermocline
effect. This model was compared to the traditionally used capacity storage model and a
(layer-based) stratified model, based on measurement data from an experimental setup.
The results indicate that the capacity storage model greatly overestimates the usable
energy content especially for high temperature differences in the storage. This results in
decreasing the reliability of the scheduling model. The thermocline model delivered the
best representation of the storage thermal behavior and is the recommended modeling
approach especially when considering the lower computation effort compared with a
stratified storage model due to the lower number of state variables.
In Chapter 5, the concepts and formulation of the scheduling algorithms for individual
buildings HEMS and city districts DSM strategies are presented. The models for HEMS
consist of a deterministic MILP model and a multi-stage stochastic programming approach
that extends the MILP model while incorporating the uncertainties of the electrical and
domestic hot water demands. The city district DSM strategies comprise a centralized
approach, which serves as a benchmark, as well as distributed formulations based on
decomposition techniques. A decomposition approach separates a centralized problem
into a master and several smaller subproblems which allows for reducing the computation
effort. In this work, two distributed DSM approaches are formulated, Dantzig-Wolfe
decomposition based column generation algorithm as well as an integrated Lagrangian
decomposition column generation. The analysis results of the introduced scheduling
algorithms are presented in Chapter 6. On a single building level, the performance of the
predictive HEMS approaches was assessed based on coupling the scheduling models to
dynamic non-linear simulation models of the building energy system to enable a reliable
evaluation that integrates the uncertainties of the forecast input data as well as the
linearization error of the BES MILP model. The results show that predictive HEMS with
perfect information allowed for a significant potential of load shifting and cost reduction,
ranging between 4.8 and 11.5 %, with respect to the reactive control strategy. However,
the dynamic operation results in a frequent switching behavior which is usually avoided
to reduce the tear and wear of the unit. Further, the deterministic scheduling model,
employing point forecasts of the weather variables and space heating, DHW and electrical
100
7.1 Conclusion
demand, enabled a cost reduction with respect to the reactive strategy. The cost reduction
ranged between 2.8 and 4.8 %,for the considered BES configurations except for the PV-
CHP-EH-Bat system, in which similar costs where achieved as with the reactive strategy.
Based on the results of the perfect information HEMS, the improvement of the applied
forecasting methods is expected to enhance the performance of this scheduling model.
A further improvement is also foreseen when increasing the rescheduling rate within
the rolling horizon algorithm, which allows for reducing the uncertainty of the forecasts
as well as the BES modeling. The multi-stage SP model outperformed the deterministic
model and allowed for an average cost reduction of around 3.5 %. This comes on the
cost of an increased computationally effort due to the increased modeling complexity.
On the other hand, the usage of forecasting models becomes unnecessary if historical
measurement data based scenario generation is applied for characterizing the demand
uncertainties within the SP model. In general, it was shown that the cost reduction
potential of predictive scheduling algorithms, with respect to reactive control strategy is
higher in BES configurations wiht HP as in CHP based systems. The potential is enhanced
by including an electrical heater instead of a boiler as auxiliary unit within the CHP based
system. Furthermore, the relative cost reduction potential compared, with the reactive
setup, is reduced in the presence of a battery. Nevertheless, the hypothesized advantage
of predictive scheduling models compared with reactive control strategy is verified. Both
deterministic and SP scheduling enhance the local integration of PV generation and enable
cost reduction.
On a city district level, the comparison between the centralized and distributed CG
approaches showed that the former provides, as expected, better coordination results.
However, the computational time rises significantly by around 140 % while increasing
number of participants from 34 to 102 buildings. This indicates that a scheduling problem
for a large number of buildings is intractable for conventional solvers in a reasonable time.
On the other hand, the CG approach provides comparable coordination performance as
the centralized model while significantly reducing the computation time by almost 80 %.
The computational effort increases by 17 % when increasing the number of participating
buildings. This is attributed to the decomposed structure since the subproblems computa-
tional effort remains the same but only the master problem complexity slightly increases.
The distributed architecture further enables significant advantages with regard to the
model extensibitiy since the master problems requires no modifications when adjusting
the functions, constraints or the number of participating energy systems. Moreover, the
data privacy concerns that arise in a centralized approach are reduced through distributed
scheduling since the buildings’ specific subproblems can be solved by a local intelligence
thus limiting the amount of sensible information that needs to be shared with the master
problem. In the final assessment, the integrated LRCG approach enabled a faster con-
vergence compared with the standard CG formulation. Thereby, the computation time
101
Conclusion and Outlook
was reduced by almost 50 %. Consequently, the integrated approach based distributed
scheduling model is recommended for future investigation to develop predictive DSM
concepts for residential neighborhoods.
7.2 Outlook
The simulation based evaluation of scheduling algorithms, on a single building level, clearly
indicate the advantage of employing predictive HEMS. However, the implementation
within a hardware based environment is foreseen to impact the operation results. It is
expected that the schedules reliability is weakened due to the influence of BES modeling
uncertainty. Therefore, hardware-in-the-loop (HiL) based investigations are required to
assess the advantage of predictive HEMS and provide insights on its real potential. The
interface between the HEMS and hardware controller can either be established directly
or indirectly based on the smart grid (SG) interface. The challenge in integrating HEMS
within a HiL setup is expected to lie in the controller configuration of the heating systems.
Despite the fact that new HP and CHP systems are equipped with a SG-interface, the
internal system controller is not designed to integrate an external HEMS control signal.
The underlying concept is based on hystereses which restrict the desired flexible operation
of HEMS. Therefore, the system controller must be modified or extended to allow for an
HEMS compatible operation phase which enables an interruptible operation (as opposed
to a hysteresis based uninterruptible operation) bounded by the thermal storage state
according to the space heating and domestic hot water requirements. Furthermore, the
simulation time of a HiL setup is equivalent to real time e.g. a HiL coupled simulation
of one week requires one week in real time as well. This represents a limitation for a
HiL based assessment and hinders a long period evaluation. Consequently, a dynamic
assessment based on representative periods should be designed and employed. Similarly,
HiL based evaluation of the SP-model compared to the deterministic approach should be
carried out, with respect to the increased computational and implementation effort. The
analysis should consider the impact of increasing the rescheduling rate within the rolling
horizon on the performance of the deterministic model. Further investigations should also
focus on embedding HEMS on mini single-board computers, e.g. ’Rapsberry PI’, which
would pave the way for real life applications.
The concept of employing distributed small microgrids, to enable the integration of large
renewable energy capacity, provides a highly promising alternative to an infrastructure
development of the electric grid. Within this approach, the individual mircrogrids reduce
the imports and exports to the macrogrid and provide positive or negative load capacities
which can allow for compensating the fluctuations of renewables and ensuring grid stability.
The introduced simulation based results for distributed DSM strategies, in this work, can
102
7.2 Outlook
only be regarded as a proof of concept. However, it was shown that the predictive DSM
strategies for city districts provide a significant potential for BES coordination and residual
load balancing already in small microgrids comprising 34 buildings. Moreover, the DSM
strategies allowed for operation cost reduction of the whole microgrid. This can be used
to develop a business plan such as internal microgrid market regulations or contracting
based model which can promote the installation of the required flexible heat generators
i.e. HPs and CHPs and pave the way for the concept realization. Future research on
predictive DSM strategies for city districts should further address uncertainties with
regard to generation and demand profiles. Finally, future investigations should also be
focused on the implementation architecture to identify the bottlenecks, which are not
considered in simulation-based assessments. A cloud-based solution is recommended as a
testing platform.
103
Appendix
A Appendix
A.1 Single building evaluation
A.1.1 PV-HP-EH
0.00.51.01.52.02.53.03.54.0
kW
Thermal loads
Dymola_Qspace Dymola_Qdhw
0369
12
kW
Dymola_QHP
0
1
OnO
ff
Dymola_uHPDymola_uHP,PyMPC
02468
kW
Dymola_QEH
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
Dymola_SoCST
Figure A.1: Dynamic performance of the thermal side for PV-HP-EH under the SPdhw
strategy
105
Appendix
0.00.51.01.52.02.53.03.54.0
kW
Thermal loads
Dymola_Qspace Dymola_Qdhw
0369
12
kW
Dymola_QHP
0
1
OnO
ff
Dymola_uHPDymola_uHP,PyMPC
02468
kW
Dymola_QEH
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
Dymola_SoCST
Figure A.2: Dynamic performance of the thermal side for PV-HP-EH under the SPel
strategy
A.1.2 PV-HP-EH-Bat
0.00.51.01.52.02.53.03.54.0
kW
Thermal loads
Dymola_Qspace Dymola_Qdhw
0369
12
kW
Dymola_QHP
0
1
OnO
ff
Dymola_uHP
0369
12
kW
Dymola_QEH
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
Dymola_SoCST
Figure A.3: Dynamic performance of the thermal side for PV-HP-EH-Bat under the Refstrategy
106
A.1 Single building evaluation
02468
kW
Thermal loads
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
0369
12kW
QHP
Dymola_QHP
0
1
OnO
ff
uHPDymola_uHP
01234
kW
QEH
Dymola_QEH
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
SoCSTDymola_SoCST
Figure A.4: Dynamic performance of the thermal side for PV-HP-EH-Bat under the DPI
strategy
02468
kW
Thermal loads
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
0369
12
kW
QHP
Dymola_QHP
0
1
OnO
ff
uHPDymola_uHP
01234
kW
QEH
Dymola_QEH
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
SoCSTDymola_SoCST
Figure A.5: Dynamic performance of the thermal side for PV-HP-EH-Bat under the DF
strategy
107
Appendix
02468
kW
Electrical loadsPdemandDymola_Pdemand
0369
12kW
PimportDymola_Pimport
PexportDymola_Pexport
02468
kW
PPVDymola_PPV
01234
kW
PHPDymola_PHP
0
1
OnO
ff uHPDymola_uHP
01234
kW
PEHDymola_PEH
02468
kW
PBAT,chargeDymola_PBAT,charge
PBAT,dischargeDymola_PBAT,discharge
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
255075
100
%
SoCBATDymola_SoCBAT
Figure A.6: Dynamic performance of the electrical side for PV-HP-EH-Bat under the DF
strategy
A.1.3 PV-CHP-EH
02468
kW
Thermal loads
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
0369
12
kW
QCHP
Dymola_QCHP
0
1
OnO
ff
uCHPDymola_uCHP
0369
12
kW
QEH
Dymola_QEH
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
SoCSTDymola_SoCST
Figure A.7: Dynamic performance of the thermal side for PV-CHP-EH under the DPI
strategy
108
A.1 Single building evaluation
02468
kW
Electrical loadsPdemandDymola_Pdemand
0369
12kW
PimportDymola_Pimport
PexportDymola_Pexport
02468
kW
PPVDymola_PPV
01234
kW
PCHPDymola_PCHP
0
1
OnO
ff uCHPDymola_uCHP
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:00048
1216
kW
PEHDymola_PEH
Figure A.8: Dynamic performance of the electrical side for PV-CHP-EH under the DPI
strategy
02468
kW
Thermal loads
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
0369
12
kW
QCHP
Dymola_QCHP
0
1
OnO
ff
uCHPDymola_uCHP
0369
12
kW
QEH
Dymola_QEH
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
SoCSTDymola_SoCST
Figure A.9: Dynamic performance of the thermal side for PV-CHP-EH under the DF
strategy
109
Appendix
A.1.4 PV-CHP-EH-Bat
02468
kWThermal loads
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
0369
12
kW
QCHP
Dymola_QCHP
0
1
OnO
ff
uCHPDymola_uCHP
0369
12
kW
QEH
Dymola_QEH
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
SoCSTDymola_SoCST
Figure A.10: Dynamic performance of the thermal side for PV-CHP-EH-Bat under the DPI
strategy
02468
kW
Electrical loadsPdemandDymola_Pdemand
0369
12
kW
PimportDymola_Pimport
PexportDymola_Pexport
02468
kW
PPVDymola_PPV
02468
kW
PCHPDymola_PCHP
0
1
OnO
ff uCHPDymola_uCHP
048
1216
kW
PEHDymola_PEH
02468
kW
PBAT,chargeDymola_PBAT,charge
PBAT,dischargeDymola_PBAT,discharge
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
255075
100
%
SoCBATDymola_SoCBAT
Figure A.11: Dynamic performance of the electrical side for PV-CHP-EH-Bat under theDPI strategy
110
A.1 Single building evaluation
02468
kW
Thermal loads
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
0369
12kW
QCHP
Dymola_QCHP
0
1
OnO
ff
uCHPDymola_uCHP
0369
12
kW
QEH
Dymola_QEH
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
SoCSTDymola_SoCST
Figure A.12: Dynamic performance of the thermal side for PV-CHP-EH-Bat under the DF
strategy
A.1.5 PV-CHP-B
02468
kW
Thermal loads
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
0369
12
kW
QCHP
Dymola_QCHP
0
1
OnO
ff
uCHPDymola_uCHP
02468
kW
QBoiler
Dymola_QBoiler
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
SoCSTDymola_SoCST
Figure A.13: Dynamic performance of the thermal side for PV-CHP-B under the DPI
strategy
111
Appendix
02468
kW
Electrical loadsPdemandDymola_Pdemand
02468
kW
PimportDymola_Pimport
PexportDymola_Pexport
02468
kW
PPVDymola_PPV
01234
kW
PCHPDymola_PCHP
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
1
OnO
ff
uCHPDymola_uCHP
Figure A.14: Dynamic performance of the electrical side for PV-CHP-B under the DPI
strategy
02468
kW
Thermal loads
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
0369
12
kW
QCHP
Dymola_QCHP
0
1
OnO
ff
uCHPDymola_uCHP
048
1216
kW
QBoiler
Dymola_QBoiler
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
SoCSTDymola_SoCST
Figure A.15: Dynamic performance of the thermal side for PV-CHP-B under the DF strat-egy
112
A.1 Single building evaluation
A.1.6 PV-CHP-B-Bat
02468
kW
Thermal loads
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
0369
12
kW
QCHP
Dymola_QCHP
0
1
OnO
ff
uCHPDymola_uCHP
048
1216
kW
QBoiler
Dymola_QBoiler
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
SoCSTDymola_SoCST
Figure A.16: Dynamic performance of the thermal side for PV-CHP-B-Bat under the DPI
strategy
02468
kW
Electrical loadsPdemandDymola_Pdemand
02468
kW
PimportDymola_Pimport
PexportDymola_Pexport
02468
kW
PPVDymola_PPV
01234
kW
PCHPDymola_PCHP
0
1
OnO
ff uCHPDymola_uCHP
01234
kW
PBAT,chargeDymola_PBAT,charge
PBAT,dischargeDymola_PBAT,discharge
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
255075
100
%
SoCBATDymola_SoCBAT
Figure A.17: Dynamic performance of the electrical side for PV-CHP-B-Bat under the DPI
strategy
113
Appendix
02468
kW
Thermal loads
Qspace
Dymola_Qspace
Qdhw
Dymola_Qdhw
0369
12
kW
QCHP
Dymola_QCHP
0
1
OnO
ff
uCHPDymola_uCHP
048
1216
kW
QBoiler
Dymola_QBoiler
00:0028-Mar2008
00:0029-Mar
06:00 12:00 18:00 06:00 12:00 18:000
20406080
100
%
SoCSTDymola_SoCST
Figure A.18: Dynamic performance of the thermal side for PV-CHP-B-Bat under the DF
strategy
114
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126
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Thermal Sensation and
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Impact of Carbon Capture and
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Multi-Resonant Converters as
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A Contribution to the Design of
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Einsatz hybrider RANS-LES-
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The Internally Commutated
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Essays on Consumer Choices
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Panašková, J.
Olfaktorische Bewertung von
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Optimization of Geothermal
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Latency exploitation for
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Dual-ICT – A Clever Way to
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Li, W.
Fault Detection and
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Modeling Methodologies for
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Flieger, B.
Innenraummodellierung einer
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Measurement System and
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Experimentelle Untersuchung
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Thomas, S.
A Medium-Voltage Multi-
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Tang, J.
Probabilistic Analysis and
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The Diffusion of Selected
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Design considerations and
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Applications of Arbitrary
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The Energiewende in the
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Decision-Making under Multi-
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Design of Novel Control
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System-Level Multi-Physics
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Stochastics-based Methods
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Huchtemann, K.
Supply Temperature Control
Concepts in Heat Pump
Heating Systems
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Molitor, C.
Residential City Districts as
Flexibility Resource: Analysis,
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Spatial Perspectives on the
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Advanced Control Methods for
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Active Thermal Management
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Development of SiC GTO
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Distributed Energy Resources
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Occupants' Behavior and its
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A Multi-Agent-based
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New Approaches to Dynamic
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The Growing ESCO Market for
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Agentenbasierte
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High-Power Medium-Voltage
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Stieneker, M.
Analysis of Medium-Voltage
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Bader, A.
Entwicklung eines Verfahrens
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Chen, T.
Upscaling Permeability for
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Ferdowsi, M.
Data-Driven Approaches for
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Kopmann, N.
Betriebsverhalten freier
Heizflächen unter zeitlich
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Fütterer, J.
Tuning of PID Controllers
within Building Energy
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Adler, F.
A Digital Hardware Platform
for Distributed Real-Time
Simulation of Power Electronic
Systems 1. Auflage 2017
ISBN 978-3-942789-49-3
Input: Actual data
Model: Dynamic nonlinear
simulation model– FMU
Input: Forecast
Model: Discretelinearized
optimization model
Schedule Actual operation𝑡𝑡𝑡𝑡𝑡𝑡 𝑡𝑡
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Predictive Demand Side Management Strategies for Residential Building Energy Systems
Hassan Harb
This thesis presents a generalized methodology, supported by a software framework, for modeling and assessing mathematical programming based predictive demand side management (DSM) strategies that exploit thermal and electrical flexibilities of residential building energy systems (BES) to enhance the integration of renewable energy sources. The modeling and simulation platform is formulated in Python and includes a set of forecasting methods as well as a discrete mixed inte-ger linear programming (MILP) modeling library based on the Gurobi optimizer API. The platform further integrates a nonlinear BES simulation model in Dymola/Modelica as a functional mock-up unit (FMU). The investigated scheduling models for individual buildings consist of a deterministic MILP strategy and a multi-stage stochastic programming approach that extends the MILP model while incorporating the uncertainties of the electrical and domestic hot water demands. The city district DSM strategies comprise a centralized approach, which serves as a benchmark, as well as distributed formulations based on decomposition techniques. The distributed DSM approaches considered are Dantzig-Wolfe decomposition based column generation algorithm as well as an integrated Lagrangian decomposition column generation approach.
ISBN 978-3-942789-50-9