Flexibility in Power Systems - Requirements, Modeling, and Evaluation - PHD Thesis - 2016
Flexibility in Power Systems - Requirements, Modeling, and Evaluation - PHD Thesis - 2016
Flexibility in Power Systems - Requirements, Modeling, and Evaluation - PHD Thesis - 2016
Vollständiger Abdruck der von der Fakultät für Elektrotechnik und Informationstechnik
der Technischen Universität München zur Erlangung des akademischen Grades eines
genehmigten Dissertation.
Abstract
Many of the world’s power systems are currently transforming towards systems with
high shares of renewable energy sources like wind and solar power. As these technologies
generate electricity depending on weather conditions, the residual system constituted by
thermal generation, storage, and transmission must be able to cope with the occurring
fluctuations. Its timely reaction to changes in output from renewable sources, whether
foreseen or unforeseen, requires the residual system to be flexible. In this thesis, the
quantitative flexibility requirements for power systems with different degrees of variable
generation are assessed in a first part. Results highlight the importance of the mix of wind
and solar power independent of the country being considered: systems with high shares of
solar power impose especially high flexibility compensation by other sources. Results also
indicate a significant reduction of flexibility requirements by increasing system sizes, which
can be realized by powerful transmission grids. Mathematically, the operational behavior of
a power system can be modeled as the unit commitment and economic dispatch problem. It
aims at optimizing production costs while considering technical and economical constraints.
In the second part of this thesis, an innovative and superior model for describing start-up
costs in the unit commitment model is developed based on the current state-of-the-art
formulations. This new approach includes the power plant temperature as an additional
variable, which leads to improved computational efficiency and accuracy. As this new
approach resembles real physical behavior closer, other technological features like limited
heat-up speed or start-up speed dependent wear-and-tear costs can be introduced with
only little additional computational burden. The overall model implementation includes
a linear load flow modeling, which allows including flexible transmission elements such
as phase shift transformers and direct current lines. In the third part of this thesis, the
developed model is employed to evaluate different options for increasing the flexibility
of a power system: flexible thermal generation, transmission extension, transmission
flexibility, and storage. A dataset is developed containing information on all thermal
power plants, renewable generation, storage, and transmission lines for a European power
system reduced to 268 regions. All options are evaluated regarding their operational costs,
their requirement to curtail renewable generation, and their effect on CO2 emissions. Two
different systems are considered: a model of Germany alone where all technical details are
included and a model of the entire European power system with reduced model complexity.
Results indicate the importance of enhanced thermal power plants as well as storage for
the German system. For the entire European case, transmission is the most important
measure for efficient integration of variable renewable energy sources.
2
Zusammenfassung
Acknowledgments
The work of this thesis was carried out between 2011 and 2016 at the Technical University
of Munich, the TUM CREATE Centre for Electromobility in Singapore, and the University
of Texas at Austin. I want to use this opportunity to express my gratitude to several
people who strongly supported me throughout the course of this thesis.
First of all, I want to thank my supervisor Professor Thomas Hamacher who gave me the
chance to work at his chair(s) and to conduct this PhD thesis. The fruitful discussions,
ranging from technical parts of the research to their political and philosophical dimension,
inspired many of my ideas. His incredible ability to motivate people definitely helped to
bring some of these ideas to results and to overcome doubts and hesitations. I am very
grateful to him for granting me the necessary freedom, giving me the chances to work
interdisciplinarily, and for encouraging me to go abroad, which significantly broadened
my scientific horizon.
Also, I am indebted to Professor Ross Baldick for giving me the chance to spend several
months with his research group at UT Austin and for his ongoing support (among other
things, his willingness to examine this thesis). I very much enjoyed the intensive and in-
depth discussions and group meetings with him. Working with him also greatly improved
my knowledge about optimization procedures in power system planning.
Next, I would like to thank Professor Rolf Witzmann who graciously and on short notice
agreed to be part of the examination board and to fill in for the oral examination.
An important part of this thesis was conducted in cooperative work with the Research
Unit Applied Geometry and Discrete Mathematics of Professor Peter Gritzmann, namely
together with my co-authors Matthias Silbernagl and René Brandenberg, to all of whom
I would like to extend my deepest gratitude. Only with their outstanding expertise in
discrete optimization, their ingenious ideas, and their drive for perfection through many
sleepless nights was it possible to obtain major results of this thesis.
With regard to the joy of working across institutes, I am also grateful to Professor Wolfgang
Utschick for his support and his contagious passion for exciting research questions.
Without naming individuals, many thanks also go to all of my colleagues at each of the
institutions I spent time in the last years. My research greatly profited from the shared
project work and the countless brainstorming sessions. I cherish the memorable times we
spent far from academics and the friendly atmosphere that made the many hours we did
spend in the office so enjoyable.
I extend my heartfelt thanks to my mother, Gertraud, for her love and support throughout
the years, my father, Richard, for bringing my attention to energy problems and renewable
technology, and my sister, Christina, for always helping me out when I found life getting
complicated.
I want to express my sincere and deep gratitude to my wife, Sina, for her incredible
patience support during all the ups and downs throughout the course of this thesis. Her
undying optimism always brought me back on track and, at least in some moments,
spread over improving my own mood and motivation. Finally, I want to thank my son,
Johann, for reminding me of more important things and for the sleepless nights that
finally motivated me to bring the thesis to an end.
Contents
Abstract 2
Acknowledgements 4
1 Introduction 8
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.1 Supply and Demand Balancing in the Beginning of Electrification 10
1.1.2 The Current Situation - A System in Transition . . . . . . . . . 10
1.1.3 Look Ahead - Old Challenges with New Complexity . . . . . . . 11
1.2 Objectives and Contributions . . . . . . . . . . . . . . . . . . . . . . . 13
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4
CONTENTS 5
3 Flexibility Requirements 35
3.1 Literature Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Database and Scenario Generation . . . . . . . . . . . . . . . . . . . . 37
3.2.1 Database Description . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.2 Scenarios for Wind and PV Generation and Resulting Net Load 38
3.2.3 Limitations of Net Load Modeling . . . . . . . . . . . . . . . . . 41
3.3 The Wind/PV Mix as Determining Factor . . . . . . . . . . . . . . . . 41
3.3.1 Ramp Properties of Wind and PV Generation in Europe . . . . 41
3.3.2 One-hour Net Load Gradients . . . . . . . . . . . . . . . . . . . 42
3.3.3 Multihour Net Load Gradients . . . . . . . . . . . . . . . . . . . 45
3.4 Why are Countries Different? . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.1 System Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.2 Wind and PV Full Load Hours . . . . . . . . . . . . . . . . . . 50
3.5 Benefits from Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.6 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 53
II Modeling 54
4 Unit Commitment and Load Flow Modeling 55
4.1 Modeling Operation with Perfect Market Assumption . . . . . . . . . . 55
4.2 Mixed-Integer Programming as Basic Approach . . . . . . . . . . . . . 56
4.2.1 Quality of MIP Formulation and Solution Algorithms . . . . . . 57
4.2.2 Literature Review on Modeling Approaches . . . . . . . . . . . 60
4.3 State-of-the-Art UC Models . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3.1 Base Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3.2 Modeling Part Load Efficiencies . . . . . . . . . . . . . . . . . . 62
4.3.3 Start-up Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.4 Improving the 1-Bin and 3-Bin Formulations . . . . . . . . . . . 65
4.4 The Temperature Model . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4.1 Start-up Costs of Thermal Units . . . . . . . . . . . . . . . . . 66
4.4.2 Temperature as a New Variable in the Modeling Framework . . 67
4.5 Advantages of the Temperature Model . . . . . . . . . . . . . . . . . . 69
4.5.1 Scenarios and Data Description . . . . . . . . . . . . . . . . . . 69
4.5.2 Compared Model Formulations . . . . . . . . . . . . . . . . . . 70
4.5.3 Problem Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.5.4 Computational Effort for Solving the LP . . . . . . . . . . . . . 71
4.5.5 Integrality Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.5.6 Performance With Scaling to a Larger Number of Periods . . . . 74
4.6 Modeling Start-up Times . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.6.1 Limited Heating Speed . . . . . . . . . . . . . . . . . . . . . . . 76
4.6.2 Maximum Temperature Increase . . . . . . . . . . . . . . . . . . 77
4.6.3 Objective Function . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.6.4 Comparison of Approaches . . . . . . . . . . . . . . . . . . . . . 79
6 CONTENTS
Nomenclature 190
Acronyms 194
Bibliography 195
Chapter 1
Introduction
Genesis 1:3
Modern society has long adapted to the notion of constant energy availability. Both,
the industry and residential sectors run on the precontext of having electrical power
available whenever needed. In the hydro-thermal power systems of the 20th century,
this varying demand could be met by planning power generation accordingly. When
there was said to be light, there was light.
However, this light came at a cost. The dependability of traditional power sources
such as coal, oil, and gas was found to have drawbacks regarding world climate as well
as finiteness and distribution of these resources. Hence, the 21st century has brought
one of the largest changes in power systems planning and operation. Many countries
increasingly started integrating alternative energy sources such as wind and solar power
into their grids. This poses a fundamental challenge to the constant availability of
power. With varying supply from wind and sun, power systems of the present and
future will need to be profoundly more flexible in meeting the needs of modern societies.
This thesis is concerned with exploring this flexibility and investigates how planning in
a modern power system can be improved to ensure that there will always be light when
it is needed.
This first chapter of the thesis presents the motivation and goals of this dissertation.
Section 1.1 gives a short introduction and motivation to the topic in a historic context.
Section 1.2 provides an overview of the objectives and lists the major contributions
of this thesis. Afterwards, Section 1.3 shortly outlines the thesis. Finally, Section 1.4
provides a list of all articles that were published within the course of this dissertation.
1.1 Motivation
Today, the power systems of many countries are in a phase of transition. New technolo-
gies that generate electricity from wind and solar energy are introduced into former
8
1.1. MOTIVATION 9
hydro-thermal power systems. This yields great chances for many countries and global
society as a whole since renewable energy sources promise sustainability and indepen-
dence. At the same time, as the generation from those variable renewable energy (VRE)
forms are highly fluctuating and uncertain in their production, new challenges for power
system operation arise. The system balance has to be kept in every moment although
the electricity output from this new sources changes very fast and can only be predicted
with uncertainty. Fluctuations have to be balanced by the residual power system of
remaining controllable generators and storage. The ability to perform this balancing
act by adapting to changing and unexpected situations can be called power system
flexibility.
Europe, especially Germany, is on the forefront of this new trend. Considerable amounts
of renewable energy generation have already been introduced to the power system.
Fig. 1.1 depicts the development of photovoltaic (PV) and wind generation capacity
installations for Germany and worldwide. In both cases, growth is tremendous and
clearly indicates the paradigm shift towards those sources. This yields the requirement
to analyze and prepare for the challenges ahead.
This thesis is concerned with the challenges that power systems will face from those
installations in their operation and the necessary flexibility that must provided. It
includes a statistical analysis of the variability from the new sources, an extensive
discussion and further development of modeling techniques, and finally, an application
of the developed model methodology in numerical simulations evaluating different
measures to enhance system flexibility. Both the statistical analysis and the numerical
model computations are conducted in the German and European context.
This first section puts the current challenge with the integration of VREs into a historic
perspective of power system development. An overview is given of how balancing was
handled and which flexibility measures where used in the early years of electrification,
in the present situation, and in a prospective future power system.
Installed Capacity (GW)
Wind PV Wind PV
100 600
80
60 400
40 200
20
1995 2000 2005 2010 2015 1995 2000 2005 2010 2015
Year Year
Figure 1.1: Development of wind and PV capacities in Germany (left) [32] and globally
(right) [23, 70]. The overall installed electricity generating capacities are at around
200 GW in Germany [33] and at roughly 6800 GW globally [41]
10 CHAPTER 1. INTRODUCTION
Interestingly, those measures are still seen as the key factors in the current transition
towards the integration of high shares of renewable energies.
• The controllable part of the power system has to be able to balance the upcoming
fluctuations and the resulting ramps on different timescales.
• The variation in load and the variable generation will show deviations from their
predictions. This leads to an uncertainty in the operational planning that has to
be handled.
12 CHAPTER 1. INTRODUCTION
80 Net Load
Wind
PV
60
Power (GW)
40
20
0
12 24 36 48 60 72 84 96 108 120 132 144 156 168
Time (h)
Figure 1.2: Illustration of net load ramps in a power system with high shares of wind
and solar power
Regarding the temporal challenge, power systems planning will have to face situations
of extreme steep ramping events. As an example, one of the most critical times of day
has been shown to be the early evening: sun and consequently electricity generation
from PV is declining while demand is rising at the same time. Californian System
Operators called this effect the “duck curve” [35]. Fig. 1.3 illustrates the situation for
Germany and Italy and demonstrates the challenge system operators will face. The
figure illustrates load, net load (NL), and PV generation for a Sunday and a subsequent
Monday. While in Germany, demand is only rising on weekend evenings, the effect
is pronounced strongly for both days in Italy: Net load rises from around 10 GW to
45 GW within hours in the scenario with highest PV installations of 45 GW. This steep
increase is an example of a load ramp that has to be provided by an output increase of
on-line generators and the start-up of additional generators.
Another major challenge in the integration of renewable energy sources is a new spatial
divergence of generation and load. A system of nuclear and fossil power plants leads to
spatial convergence of generation and demand since power plants could be built close
to load centers. As wind and solar generation are heavily dependent on the location,
the introduction of VREs requires long distance transportation of electricity. A similar
situation was experienced at the beginning of electrification with the installation of
hydro power plants. Some countries still rely on large shares of distant hydro power
plants (e.g. Brazil) and their experience in transmission planning might be helpful for
planning systems with high shares of wind and solar generation.
All in all, the challenges that have to be faced in future power system operation are
similar to the challenge in the beginning of the electrification: balancing enormous
uncertain fluctuations in the system across time and space. However, the system of
the 21st century has grown considerably more complex and reliability standards have
substantially increased.
Remarkably, the measures discussed to overcome the challenge are still similar to the
1.2. OBJECTIVES AND CONTRIBUTIONS 13
80 PV 75 PV 50 PV 25 50 PV 45 PV 30 PV 15
NL 75 NL 50 NL 25 NL 45 NL 30 NL 15
Load Load
40
60
Power (GW)
Power (GW)
30
40
20
20
10
0 0
12 24 12 24 12 24 12 24
Hour of the Day Hour of the Day
Figure 1.3: Duck curves (dark gray, NL=net load) for Germany (left) and Italy (right)
for different installed PV capacities (orange, PV in GW)
ones suggested more than a century ago: transmission grids need to be further extended
in order to balance generation of VREs at different sites. Furthermore, discussions
revolve around storage plants to store power from renewable sources and demand side
management (DSM) including changing demand to other hours of the days. Finally,
the important questions of the flexibility of fossil power plants arise anew: How fast
can on-line plants react? How long does start-up take and how much does it cost?
The statistical analysis, model development, and model evaluation within this thesis
ought to shed a light on the challenges of future complex and high-stakes power systems
and to examine which of the measures are best suited to tackle these challenges.
the future European power system, which is modeled based on publicly available data.
Scenarios investigate the effects of increased power plant flexibility, grid extensions, grid
flexibility, and storage. Finally, the different options to better deal with the fluctuating
sources are evaluated and compared.
The main contributions can be summarized to the following bullet points:
• The state-of-the-art modeling for the unit commitment (UC) problem is improved
by the introduction of power plant temperatures as a new variable. This new
approach improves both the computational efficiency of the UC modeling and the
accuracy of power plant representation (joint work with Matthias Silbernagl and
René Brandenberg).
• Based on the temperature model, new ideas for evaluating the flexibility of fossil
power plants are presented and partly implemented and tested (joint work with
Matthias Silbernagl).
• Different modeling approaches for regarding power flows in UC models are pre-
sented, compared, and evaluated. The implemented model allows to model flexible
components in the grid like high voltage direct current (HVDC) lines or phase
shift transformers (PSTs).
• A dataset is developed that represents the European power system with 268 nodes.
The model serves as structural test case in this thesis and is a basis for future
power system studies at Technical University of Munich (TUM).
• The computational burden of different levels of details for the large-scale power
system with 268 nodes, 510 lines, and 2860 power plants (of which 1252 are
controllable) is investigated.
• Different concepts for enhancing the flexibility in the system are evaluated in
extensive numerical studies for the German and European power system.
• Conclusions for future planning and operation of power systems with high shares
of variable renewable energies are derived and presented.
1.3. OUTLINE 15
1.3 Outline
The thesis can be split into three main parts:
1.4 Publications
Parts of the thesis have already been published as papers or are rewritings of published
papers. Part I and Part II are based on articles already published by the author as
prepublication, while the results in the numerical simulations of Part III are introduced
within this thesis for the first time. Minor differences in the datasets of the three parts
are due to further development of the main dataset over the course of this dissertation.
Yet, comparisons and conclusions across parts are still possible. The main dataset that
is a result of this thesis is described and used in Part III. The publications that are
relevant and (partially) included in the different chapters are provided below.
Other publications that where conducted within the course of this disserta-
tion:
18
Chapter 2
This chapter briefly describes the basics of current power system operation from a
technical and control perspective. Further, an overview of the current electricity markets
is provided and the methods to approximate market operation within this thesis are
introduced.
• Voltage Stability: Voltage at each node in the network is another critical system
variable. Whenever electricity is transported over long lines or whilst appliances
are consuming power, voltage drops at those nodes according to Ohm’s law.
Voltage stability requires the voltage differences between all nodes of a network to
be within a certain limit in the steady state and after disturbances. In alternate
19
20 CHAPTER 2. POWER SYSTEM OPERATION AND PLANNING
current (AC) systems, voltage stability is a complex issue that requires control of
both active and reactive flows. For detailed information on this matter, the reader
is referred to standard literature, e.g. the textbook of Prabha Kundur [129].
While this thesis is mainly concerned with the provision and balancing of active power
achieving frequency stability, planners of the large-scale integration of renewable energy
sources must remember that system requirements go beyond active power balances.
Investment Planning
Maintenance Planning
Unit Commitment
Spatial Scale
Economic Dispatch
Ancillary Services
Speed Control AGC
Kinetic Energy
Exciter, Stabilizer
Protective Systems
Time Scale
Figure 2.1: Temporal and spatial scales of key tasks in the planning and operation
process of power systems. This thesis focuses on blue tasks in the operational time
range. Illustration adapted and adjusted from Jokić [117]
.
With a longer time horizon of month to years, the maintenance and investment planning
takes place. Maintenance planning includes revision of power plants or parts of the grid,
which are not available during those times. Maintenance planning can be seen as an
optimization problem as, for instance, electricity prices are expected to be lower during
some month of the year due to seasonal effects of load and renewable generation. Power
plants should be maintained during times with lower prices and where opportunity
costs for the utility are lowest. For a system operator or integrated utility, maintenance
should be scheduled in a cost optimal way while enough capacity has to be available
throughout the year.
In the longest time horizon considered, investment planning is executed. Utilities
or governments have to adequately plan their infrastructure, i.e. power plants and
transmission grids, for the upcoming years and decades. Investment decisions are crucial
and underinvestment can have severe consequences as (partial) blackouts might occur.
The actual actors responsible for different parts of the infrastructure vary from country
to country. In the case of Germany, power plants are owned by private utilities that
also decide on their investment plans individually. The grid is operated by Transmission
System Operators (TSO), a highly regulated company. This company must operate the
power grid in order to fulfill transmission and stability according to market outcomes.
For most tasks, a valid correlation between temporal and spatial scales can be observed:
the smaller the timescale, the smaller the spatial scale. Control actions that are
executed within milliseconds are mostly performed directly at components of power
plants while planning for transmission investments is done on the spatial scale of the
entire system. Still, the categorization of tasks in the temporal scale of Fig. 2.1 is a
simplified approximation and interpretation.
The scope of this thesis is the development and application of models that are applied
to study balancing processes in the operational timescale including unit commitment,
economic dispatch, and scheduling of ancillary services. By evaluating different options
for improving the operational behavior of the system, the model results at those
operational scales can give insights on investment planning.
Price Price
Demand Demand
Oil Oil
Gas-GT Gas-GT
Price w/o Renewables
Gas-CCGT Gas-CCGT
Coal Price w Renewables Coal
Lignite Lignite
Nuclear Renewable Nuclear
Quantitiy Quantitiy
Figure 2.2: Reduction of market prices by the introduction of renewable energies with
zero marginal costs
The liberalization and the introduction of VREs are the major aspects of current power
system transformation. Modeling power system operation requires understanding the
underlying markets as driving force for decision-making. Different aspects of electricity
markets and their consequences for model development are discussed in the following.
Types of bids Two basic regimes can be distinguished: systems with complex bidding
functions and systems with simple price quantity bids [45]. In the first type of systems,
there typically is an independent system operator (ISO) that conducts all operational
steps from a security-constrained unit commitment to all types of transmission operation.
This type of market is referred to as a centralized market by Baldick et al. [9] and an
integrated system by Wilson [210]. A suggestion for naming such markets types could
24 CHAPTER 2. POWER SYSTEM OPERATION AND PLANNING
Time schedules and products Markets have to secure the matching of supply and
demand in each point of time ranging from milliseconds to hours as shown in Fig 2.1.
The different timescales result in various market products. In most systems, there is a
separate market for energy and for different types of reserves. The concrete products
are manifold and especially energy products are traded with varying time ranges.
In the case of Germany, markets for primary, secondary, and tertiary reserves exist
in addition to a market for energy. Markets for capacities are discussed but have not
yet been implemented. Other regions, e.g. New England, implemented such capacity
markets, where generators are paid for being installed and being able to provide
electricity in times of scarcity [46].
Energy is traded with different products and at different places. Bilateral trading is
possible in most markets on the over-the-counter (OTC) market, and different auctions
take place at exchanges like the European Power Exchange (EPEX) spot market which
includes a day-ahead market and an intraday market. While the day-ahead market is
cleared one day before actual dispatch, the intraday market allows for corrective actions
up to an hour before dispatch [141].
Depending on the specific power systems, different definitions and specifications of
reserves exist [176]. In the following, the definitions are considered as they are used
in Germany, where three different reserve types are traded: primary reserve, which is
activated automatically as soon as frequency deviates by more than 10 mHz, secondary
reserve, which is activated whenever frequency deviations last for more than 30 seconds,
and tertiary (minute) reserve, which can replace secondary reserves if required [155].
Currently, reserve is procurred in auctions with a pay-as-bid format but discussions
about changing to a uniform pricing are ongoing [155].
problems can include the operation of storage with additional constraints or constraints
concerning the transmission system. Solving the UC problem is difficult since the on/off
decision has to be made for all power plants in the system and for each step in the
planning period. The number of possible combinations is exponentially growing by
the number of time steps and the number of power plants considered. Currently, the
commonly employed approach to solve UC problems is mixed-integer programming
(MIP) which allows to find solutions with a criterion for the degree of optimality.
A detailed description of the MIP modeling can be found in Chapter 4 which also
includes the improvements to current state-of-the-art formulations introduced with this
dissertation.
Power
Power
0 1 2 3 4 5 6 0 1 2 3 4 5 6
Time(h) Time(h)
Figure 2.3: Deviations from load with hourly (left) and with 30 min (right) energy
scheduling. The blue lines are the power demand while the orange bars are the scheduled
energy blocks.
and might reduce reserve requirements. The major disadvantage of the ramp-based
approach is the pricing and exact definition of traded products. An alternative solution
to tackle the problem would be trading energy products in shorter periods, e.g. 5-minute
blocks. As computational possibilities increase, the latter solution might be favored by
operators. In unit commitment type markets, an option could be to compute day-ahead
commitment decisions in an hourly resolution followed by a real-time market with
marginal prices updated every 5 minutes.
taken. This is the case in many power systems, especially those being operated by an
ISO. In the second stage, the intraday market, an exact matching of load and demand
is organized by using multiple market products. Many power plants require a long time
horizon for planning their operation, e.g. a cold start of a coal power plant takes up to
12 hours [183]. During the whole planning procedure, forecasts on the net load must be
made and planning can be adjusted accordingly. When forecasts change several hours
ahead of the actual event, rescheduling in the intraday market might be an effective
measure. Whenever rescheduling is not possible anymore, the mismatch of generation
and demand has to be balanced by the control system.
The integration of VREs into the system increases the challenges for accurate forecasts.
While the forecast accuracy increases, absolute forecast errors might still increase
because of rising capacities. Lenzi et al. estimate an increase of secondary/tertiary
reserve requirements from currently around 4 GW up to 20 GW (roughly 20% of the
yearly peak load) with heavy VRE integration in Germany [136]. Alternative options,
such as adjusting the reserves with higher VRE capacities, and a further discussion on
whether requirements will actually increase are discussed in Chapter 5 of this thesis.
Frequency Frequency
f1
∆f
f0
p1 p0 Power p1 p0 Power
∆p ∆p
Figure 2.4: Droop control of two different power plants. At the same frequency deviation,
the power plant on the left is providing more primary reserves than power plant on the
right.
control being activated across the complete network while secondary reserve is activated
afterwards in the control area of fault to counter the imbalances locally.
In order to be able to provide reserves when required, power plants have to schedule
reserve bands. Returning to the example illustration in Fig. 2.4, the power plants have
to be operated above their minimum power output with enough buffer to ramp-down
according to the droop curve. For upward reserves, the power plant must be operated
below maximum power output. Assigning the reserve bands to the power plants is
a task that can be included in the UC problem formulation. For upward reserves, it
might be better to run more expensive power plants at lower levels, while for downward
reserves, cheaper plants operating at full power could be employed.
The flexibility of a System is the ability of the system to adapt to external changes, while
maintaining satisfactory system performance [152].
centralized fossil fuel-fired plants that will remain a major constituent of most power
systems for the next decades in Europe [69]. Three different types can be distinguished:
• Steam turbines: include coal, lignite, (old) oil and gas, and nuclear power plants.
The major characteristic of those plants is an external combustion process that
evaporates water and heats steam, which is then put through turbines.
• Gas turbines: are mostly natural gas and sometimes oil-fired power plants. The
fuel is burnt with compressed air and the expanding gas then drives the turbine.
• Combined cycles: are a combination of a gas turbine and a steam turbine. The
exhaust gas of the gas turbine is used to heat the steam for the steam turbine
leading to higher efficiencies.
Options to increase their flexibility are manifold and concern different parameters
and different parts of the power plant. The two different cycles have different major
limitations and challenges for improvement. While the operational range of gas turbines
requires a high minimum power output due to the internal combustion process and
resulting carbon monoxide emissions at lower power outputs, the ramping and start-up
capabilities are much better than those of steam cycles. The latter are quite slow
due to limitations of temperature increase/decrease in the steam cycle. Still, reducing
minimum power output to very low values seems to be possible because of external
combustion [92].
For gas turbines, the most important factor for further improvement lies in enlarging
the operating range. Ideas for reducing the minimum output can be a bypassing of
compressed air for increased fuel-to-air ratio or by preheating of air [213]. Operational
range can also be extended to values above the rated power by injection of water or
steam [189].
For steam turbines, increased ramp and start-up capabilities appear both essential and
challenging. Ideas to increase ramp rates include sliding pressure values in order to be
able to match steam and metal temperatures also during fast output changes [92]. An
effective measure to reduce start-up times of steam power plants is to employ steam
cooling of the outer casing, which allows reducing thickness of the casing and, in turn,
allows for faster temperature changes. This measure is reported to allow for a reduction
of start-up times to up to 50% [92]. Ideas to keep units warm, installing thermal storage,
or usage of improved material that withstands the thermal stress during heat-up are
also being discussed [92].
The aim of this thesis is to test different parameter variations and evaluate their effect
on the system. The technical details of how the parameter improvements are realized
are not considered. Yet, results indicate the importance of improvements in specific
areas.
Storage Another option to provide flexibility in the system is storage. Storage can
include pumped hydro in a form that already exists across Europe. Extension of those
2.6. THE CONCEPT OF POWER SYSTEM FLEXIBILITY 33
plants is possible to some extent but potentials are limited. Other options include
compressed air storage, hydrogen, or batteries. While hydrogen promises to be the
most interesting option for seasonal storage, batteries could be appropriate for solving
short and medium term balancing problems. Biggest challenges and weaknesses for
storage are insufficient efficiency in the case of hydrogen-based systems and high costs
in the case of battery systems. Especially for the latter, progress is observed and first
applications to power system balancing are tested on large-scale systems as well as on
small-scale smart homes [81]. The research of this thesis focuses on the effect of storage
on the operational timescale. However, storage might also be required for long-term
balancing to counter seasonal effects. As a further reading on effects of storage in this
context, the interested reader is referred to e.g. Kuhn [125] or Kühne [127].
Flexible demand Flexible demand is a further option that might help to integrate
VRE sources and has been discussed heavily in literature for some time. The basic idea
is to either shift electricity consumption to other points in time or to increase/decrease
consumption at certain times without any compensation at other times. Technological
options to perform such tasks are manifold. The simplest and oldest idea for such load
levelers are electric heaters [13]. Other ideas frequently discussed are electric vehicles
that can shift their charging according to availability of generation from VRE. The
same can be done with electricity consumption in households, e.g. washing machines,
or in commercial buildings, e.g. cooling devices or even elevators. In industry, there are
ideas to shift part of production to time with lower prices [193]. Within this thesis, an
idea of how to include flexible demand in a UC problem is described at the example of
controllable charging of electric vehicles.
Grid flexibility Power systems are coupled, networked systems. When regarding the
possibility to adapt for changes in the system state, a consideration of the network
structure and the resulting constraints is required (as mentioned and described e.g. by
Horn [102], see Section 3.1). There are technical options to influence the power flow.
These include direct current (DC) lines that are not determined by line reactances
but can be controlled directly. Depending on the situation in the grid, DC lines can
transport more or less energy and thereby enable increased efficiency in the remaining
AC grid. Another option to reach a similar effect can be achieved by phase shift
transformers (PSTs), that allow to change the angle between two nodes in a network.
Electricity flow can therewith be bypassed from overloaded lines and the overall grid
transport capacity is increased, see e.g. [18, 84, 203].
Flexibility Requirements
This chapter presents joint work with Desislava Dimkova and Thomas Hamacher [105].
We provide an extensive statistical analysis of occurring ramps in future power systems.
The geographical focus of this chapter is Germany and Europe and timescales considered
are 1-12 hours which is the most important time frame for operational planning.
35
36 CHAPTER 3. FLEXIBILITY REQUIREMENTS
described above are extended and a first move to a generalized characterization of future
flexibility requirements in power systems is undertaken.
The results provide a deeper understanding of the occurring ramp rates in many power
systems. They allow for designing the variable system in such a way as to minimize
problems in the controllable system or, if this is not possible, to foresee upcoming
requirements and adapt the controllable system in an adequate way.
where t = {h+1, ..., 8760}, P (t) is the wind or PV power production in a spatial
unit (country or region) at time t. In order to validate the simulated power output
profiles, the frequency distributions of hourly ramps of simulated wind and PV power
38 CHAPTER 3. FLEXIBILITY REQUIREMENTS
1200
800
400
0
AT BE BG CH CZ DE DK EE ES FI FR GB GR HU IE IT LT LU LV NL NO PL PT RO SE SI SK
Figure 3.1: Average onshore wind and solar PV full load hours per year over the period
2001–2011 as well as their range
are compared with respective data from the transmission system operators (TSO) in
Germany [79] and also with actual wind feed-in data for Ireland [58]. As Fig. 3.2 shows,
the model data reproduces very closely the actual ramp behavior both for wind and
solar power output.
a b c
2000 1500 500
Peak frequency:
Frequency per year
0 0 0
−0.1 −0.05 0 0.05 0.1 −0.1 −0.05 0 0.05 0.1 −0.2 −0.1 0 0.1 0.2
1−hour ramps [share of capacity] 1−hour ramps [share of capacity] 1−hour ramps [share of capacity]
Figure 3.2: Frequency distributions of hourly ramps of simulated and actual production:
(a) Wind 2011, Germany, (b) Wind 2010, Ireland, and (c) PV 2011, Germany. Wind
and PV power is normalized with respect to installed capacity.
are varied in scenarios. The VRE capacities are a function of the total contribution of
wind and PV to annual electricity consumption α and the share of PV in the wind/PV
energy mix β. The definitions for α and β are adopted from other studies focusing on
the capacity or storage requirements in power systems with high shares of PV and wind
power (e.g. [90, 182, 190] use similar methods) and are given by:
Pt=8760
PW (t) + t=8760
P
t=1 PPV (t)
α= Pt=8760 t=1 , (3.2)
t=1 D(t)
Pt=8760
t=1 PPV (t)
β = Pt=8760 Pt=8760 , (3.3)
t=1 PW (t) + t=1 PPV (t)
where PW and PPV are the hourly power outputs of wind and PV at time t and D(t) is
the electricity demand.
In each country, the net load NL(t) can be computed as load minus generation from
wind and PV by
For the computation of scenarios, the power generation from wind and PV should be
described in terms of the varied parameters α and β, the predefined hourly capacity
factors {CFW , CFPV } ∈ [0, 1], and the electricity demand D(t). The overall energy that
is produced throughout a year by either wind or PV can be defined to
t=8760
X t=8760
X t=8760
X t=8760
X
PW (t) = α(1 − β) · D(t) and PPV (t) = α · β · D(t), (3.6)
t=1 t=1 t=1 t=1
The occurring ramps are all computed relatively to the peak load in each country to
allow for comparisons across regions. Peak load is interpreted as an indicator of system
40 CHAPTER 3. FLEXIBILITY REQUIREMENTS
size because conventional power plant fleets are traditionally sized to meet the annual
demand peak with a reserve margin for accommodating outages and extreme load
events.
Thus, the system flexibility requirements posed by VREs are determined in the model
by the following factors:
• the VRE penetration level α and the wind/PV mix β as choice variables resulting
from policy and investment decisions;
• the ramp behavior of load and the inherent ramp properties of wind and PV power.
These properties are determined by geographical location, generator placement,
and system size, and will be described by means of frequency and temporal ramp
distributions in Section 3.3;
• the correlation between the load and the VRE gradients as well as between
wind and PV ramps. Load and VRE ramping up or down at the same time
counterbalance one another, whereas wind and PV power ramps in the same
direction add up to increase the system balancing requirements.
The combined energy penetration of wind and PV (α) that is considered is 10%, 30%,
50% and 70% of annual electricity demand. As there are other renewable energy
technologies such as hydropower, biomass and geothermal that can be deployed in
addition, a share of 70% of wind and PV can be interpreted as a fully renewable power
system. At each penetration level, the share of PV β is set to 20%, 40% and 60%.
After showing the effects of different levels of VRE penetration, a focus of the research
will be the 50% scenario. A 50% wind/PV share is discussed as an intermediate
target in 2030 on Europe’s way towards a fully renewable power system [95]. A further
argument for having a closer look at that scenario is that research showed that renewable
integration becomes especially challenging in terms of ramps at that share.
In the scenarios, excess energy is not cut off; the residual load can thus rise from
negative to the maximum load leading to ramps with a magnitude of more than one.
A ramp of one means that all controllable resources, except the capacity reserves, are
required to provide full load in the specific time frame.
An aggregated European net load is calculated from the country time series as follows:
a VRE penetration target α and a wind/PV mix β are selected for Europe as a whole
and this α/β combination is assigned to each country making up the European power
system. Unrestricted electricity transport is assumed between the countries.
It should be noted that the analysis focuses on flexibility requirements in certain
scenarios about future development of wind and PV power capacities. Changes in the
net load caused by DSM or storage are not modeled as they are already seen as a
countermeasure for the variability of renewables, i.e. as part of the flexibility of the
residual system.
3.3. THE WIND/PV MIX AS DETERMINING FACTOR 41
• Variability of wind may decrease as more turbines get installed but there may be
a saturation effect [101].
• Climate change might lead to more extreme weather events. Still, it is unclear if
this has any effects on ramping requirements [172].
• Improved wind turbines could be deployed. The effects are not predictable,
however, as the enormous ramping requirements challenge the system, wind
turbine producers might have incentives to develop turbines with “flatter” power
curves.
• Load might change as well: people’s work and leisure rhythm, a structural change
of the economies and upcoming flexible load and power autonomy of household
and industry can also have influence on flexibility requirements in the public
power system [74].
To summarize, there are several changes in the behavior of wind and solar generation on
the horizon, but most are likely to have low influence or their effects are not quantifiable
at present. Overall, the flexibility requirements will be lower than suggested in this
paper as new technologies and an optimized placement of generators could reduce
variability.
magnitude ramps concentrated around the center of the distribution. The largest ramps
occurring are in the range of 6–10% of installed capacity per hour in medium-sized
and large European countries, and 11–18% per hour in geographically small countries.
About half of all hourly solar power ramps are equal or close to zero because of zero
production at night but the distribution has long and heavy tails with ramps reaching
18–25% of capacity per hour in most analyzed countries and up to 12–14% in the Nordic
countries. The distribution of load gradients is skewed towards upward ramps, typically
reaching extremes of 10–15% of peak load per hour in the analyzed European countries.
On the basis of the frequency and temporal distributions of variable generation ramps,
the countries in Europe can be grouped into clusters which have similar wind and PV
flexibility requirements in terms of ramp magnitude and frequency: North, Center
and South. The load, wind and PV time series have a distinct ramp behavior whose
daily and seasonal pattern is shown in Fig. 3.3 for three different European countries
representing those clusters (North: Ireland, Center: Germany, South: Italy).
The first row depicts the hourly gradients of consumer load in each country. On a daily
basis, the largest load ramps are the morning rise with a duration of 2–3 hours and
a less prominent evening ramp up when lights and appliances are switched on at the
same time. While some differences exist, the same basic load ramp structure appears
in all European countries. Wind and solar power both follow a diurnal cycle. The
middle row of Fig. 3.3 shows that although wind power generation is very volatile, it
tends to decrease around sunrise and sunset, after which it tends to increase again.
This pattern is most prominent in Germany and also other countries in Europe’s
center whereas countries in Scandinavia and the Southern peninsulas rarely experience
large wind power ramps. In terms of frequency of large ramps, wind fluctuations pose
the highest flexibility requirements in small Northern countries such as Ireland and
Denmark. Regarding PV fluctuations, the frequency of large ramps clearly increases in
the North-South direction.
1−hour ramps [share of peak load] 1−hour ramps [share of peak load] 1−hour ramps [share of peak load]
0.14 0.14 0.14
2 2 2
Months in a year
Months in a year
Months in a year
4 0.07 4 0.07 4 0.07
Load
6 0 6 0 6 0
8 8 8
10 −0.07 10 −0.07 10 −0.07
1−hour ramps [share of capacity] 1−hour ramps [share of capacity] 1−hour ramps [share of capacity]
Onshore Wind
Months in a year
Months in a year
4 0.05 4 0.05 4 0.05
6 0 6 0 6 0
8 8 8
10 −0.05 10 −0.05 10 −0.05
1−hour ramps [share of capacity] 1−hour ramps [share of capacity] 1−hour ramps [share of capacity]
0.2 0.2 0.2
2 2 2
Months in a year
Months in a year
Months in a year
0.1 0.1 0.1
Solar PV
4 4 4
6 0 6 0 6 0
8 8 8
10 −0.1 10 −0.1 10 −0.1
Figure 3.3: Temporal distribution of 1-hour ramps of load, wind and PV power in
Ireland, Germany and Italy for the meteorological year 2011
and Italy, which differ considerably in terms of area as well as wind and PV FLH.
Fig. 3.4 shows the temporal distribution of the hourly net load ramps for those countries
in the scenarios with renewable penetration α = 0.5 and shares of PV in the VRE
mix of β ∈ {0, 0.2, 0.4}. The plot shows that PV has a far stronger influence on the
increase of hourly ramp rates than is the case for wind power. At the 100% wind mix,
the hourly net load ramps are distributed randomly but are still mostly dominated by
the load ramps. With an increase of PV to 20% (β = 0.2), the morning rise in load is
compensated by PV power generation, which reduces ramps. However, this reduction
in the frequency of large net load ramps in the morning is counteracted by an upward
ramp pattern in the late afternoon when PV power production slows down and load
increases at the same time. With 40% PV (β = 0.4), the ramps of PV power dominate
the net load variability. The frequency of high net load ramps increases dramatically,
with downward ramps in the morning and upward ramps in the evening. Ramps of
magnitude higher than the morning load rise are maintained over 3–4 consecutive hours
in each direction for a significant part of the year in all analyzed European countries.
As shown in Fig. 3.5 on the example of Germany, the frequency distributions of hourly
net load gradients at α = 0.5 are close for the mixes with high share of wind at
β = {0, 0.2} and this relationship holds for all analyzed countries. Compared to the
44 CHAPTER 3. FLEXIBILITY REQUIREMENTS
Net load 1−hour ramps Net load 1−hour ramps Net load 1−hour ramps
0.26 0.26 0.26
2 2 2
Months in a year
Months in a year
4 0.13 4 0.13 4 0.13
β=0
6 0 6 0 6 0
8 8 8
10 −0.13 10 −0.13 10 −0.13
Net load 1−hour ramps Net load 1−hour ramps Net load 1−hour ramps
0.26 0.26 0.26
2 2 2
Months in a year
Months in a year
4 0.13 4 0.13 4 0.13
β = 0.2
6 0 6 0 6 0
8 8 8
10 −0.13 10 −0.13 10 −0.13
Net load 1−hour ramps Net load 1−hour ramps Net load 1−hour ramps
0.26 0.26 0.26
2 2 2
Months in a year
Months in a year
4 0.13 4 0.13 4 0.13
β = 0.4
6 0 6 0 6 0
8 8 8
10 −0.13 10 −0.13 10 −0.13
Figure 3.4: Temporal distribution of 1-hour net load ramps for different shares of PV
in the wind/PV mix β at 50% penetration of variable renewables
4
10
Load
β=0
3
β=0.2
Frequency per year
10
β=0.4
β=0.6
2
10
1
10
0
10
−0.4 −0.2 0 0.2 0.4
1−hour net load ramps [share of peak load]
Figure 3.5: Frequency distribution of 1-hour net load ramps for different shares of PV
in the wind/PV mix β at 50% variable generation penetration in Germany, 2011
load gradient, the frequency of ramps close to zero is reduced nearly by half. Up to a
threshold share of 20% PV in the VRE mix (in some countries up to 30%) which is
equivalent to 10–15% of annual consumption, the frequency distribution of net load
ramps remains of similar shape as for a 100% wind mix. Adding more PV capacity
to the system above this threshold results in a large increase in the frequency of high
ramps. Depending on country area and full load hours, extreme net load ramps can
occur also with high shares of wind in the system, which is analyzed in Section 3.4.
3.3. THE WIND/PV MIX AS DETERMINING FACTOR 45
α = 0.1 α = 0.3
2 2
β=0.2 β=0.2
over time step [peak load units]
1st / 99th percentile of ramp
0.5 0.5
0 0
−0.5 −0.5
−1 −1
−1.5 −1.5
−2 −2
0 2 4 6 8 10 12 0 2 4 6 8 10 12
α = 0.5 α = 0.7
2 2
β=0.2 β=0.2
over time step [peak load units]
1st / 99th percentile of ramp
0.5 0.5
0 0
−0.5 −0.5
−1 −1
−1.5 −1.5
−2 −2
0 2 4 6 8 10 12 0 2 4 6 8 10 12
Time step [hours] Time step [hours]
Figure 3.6: Ramp envelopes for 27 European countries for different variable generation
penetrations α and shares of PV in the wind/PV mix β, 2011. Each plotted symbol
represents one country.
A method to display and analyze the ramp requirements over multiple hours are ramp
envelopes as introduced e.g. in [121]. Fig. 3.6 depicts ramp envelopes for the 27
European countries at levels of renewable penetration α ∈ {0.1, 0.3, 0.5, 0.7} and shares
of PV power in the VRE mix β ∈ {0.2, 0.4, 0.6}. Depicted are the 1st and the 99th
percentiles of gradients, which are crucial for future power system design: extreme
46 CHAPTER 3. FLEXIBILITY REQUIREMENTS
values will most probably not be predictable even shortly before occurrence and will
thus be balanced by spinning reserves. This, however, is not the scope this research, but
it seems reasonable that higher variability in net load will also lead to higher uncertainty
and thus higher requirements for spinning reserves.
Several interesting observations which have implications for power system planning can
be described from Fig. 3.6:
• At low penetrations of α = 0.1, the gradient envelopes of all countries and all β
are close; differences are rare. The major gradients might still come from variation
in load. 1-hour gradients are in the region of 10% of peak load. Even at a time
horizon of 6 hours, the ramps are all below 30% of peak load.
• Beginning with α = 0.3, the ramps become significantly larger and mixes differen-
tiate. Except for countries with very low wind FLHs, the ramp envelope is shifted
outwards with increasing β.
• An important trend that becomes evident with higher shares of VRE (α = 0.5
and α = 0.7) is a clustering according to the three values of β. The differences
arising from varying shares of PV power in the mix β tend to be larger than the
differences between countries. At α = 0.5, for each β-value, the differences in the
1-hour gradients between countries show a standard deviation of only 2–3% of
peak load, whereas the difference in the mean value of all countries, for example
between β = 0.4 and β = 0.6, is 18% to 26%.
Table 3.1 and Table 3.2 present the 1st and the 99th percentiles of the 1-hour and
6-hour net load gradients averaged across the 27 European countries for six different
scenarios. The range and the standard deviations show the dispersion of values that
the net load extremes can reach in different countries.
Table 3.1: 1-hour net load ramp rates – mean of all countries and their statistical
dispersion
Table 3.2: 6-hour net load ramp rates – mean of all countries and their statistical
dispersion
In a next step, two points on the envelope curves, the 1st and the 99th percentiles of
the 6-hour ramps, are considered and depicted on the net load gradient duration curves
in Fig. 3.7. On average, every second day a positive or a negative ramp occurs outside
the 1st–99th percentile range whereas 2.4 ramping events per day occur on average
outside the 5th–95th percentile range. Again, the differences between countries for one
mix are smaller than the divergence caused by different mixes.
1500
β=0.6
β=0.4
β=0.2
1000
Time [hours]
5th
perc. 95th
perc.
500
1st 99th
perc. perc.
0
−2 −1.5 −1 −0.5 0 0 0.5 1 1.5 2
Ramp magnitude [peak load units]
Figure 3.7: Top and bottom 1500 hours of the 6-hour net load ramp duration curves
for 27 European countries at 50% share of variable renewables and different shares of
PV in the wind/PV mix β
In a last analysis focusing on the influence of the wind/PV mix, Fig. 3.8 shows the 99th
percentiles for the 1-hour and 6-hour net load gradients, again for Ireland, Germany and
Italy. The first impression is that the images for the countries look similar supporting
the finding that the mix is more important than the country analyzed. The maximum
value is set to one for both time horizons. A net load ramp rate of one means that the
whole conventional power plant park (including storage plants) has to ramp up in 1
or 6 hours. The figure illustrates that 1-hour ramps are moderate (less than 25% of
48 CHAPTER 3. FLEXIBILITY REQUIREMENTS
peak load) as long as α is below 0.3. From there on, the ramp rates start to increase
dramatically, especially with β higher than 0.3. The behavior of Ireland and Germany
is very similar whereas Italy shows lower gradients. For 6-hour ramps, a net load ramp
of one is achieved with much lower α. Beginning with α = 0.3 and high β above 0.5,
the peak load has to be achieved within 6 hours. For PV shares β below 0.2, a much
higher share of renewables can be integrated with lower 6-hour ramps.
Net load 1−hour ramps Net load 1−hour ramps Net load 1−hour ramps
1−hour ramps
1 1 1 1 1 1
0 0 0 0 0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
Net load 6−hour ramps Net load 6−hour ramps Net load 6−hour ramps
6−hour ramps
1 1 1 1 1 1
0 0 0 0 0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
Share of renewables Share of renewables Share of renewables
Figure 3.8: 99th percentiles of 1-hour and 6-hour net load ramps as a function of the
variable Generation Penetration Level α and the Share of PV in the Wind/PV Mix β
The graphs in this section show the meteorological year 2011, however, the development
of the envelope curve is the same for the years 2001 to 2011. Even if the ramp rates
were surprisingly similar in the analyzed countries, differences remain. An attempt to
explain them is conducted in the next section.
are of particular interest for system operation and scenarios with higher hourly ramps
were also shown to feature higher ramps over multiple hour time horizons (see Fig. 3.6).
Fig. 3.9 plots three interpercentile ranges of the net load ramp distribution for each
country against the chosen region-specific factors: the minimum–maximum range, the
1st–99th and the 5th–95th percentile ranges. Scenarios are shown with shares of PV in
the mix β ∈ {0.2, 0.4, 0.6} at combined VRE penetration α = 0.5. To account for the
interannual variability of wind and solar power, net load time series are simulated using
wind and PV data for each of the meteorological years 2001–2011. The percentiles of
the net load ramp time series are then calculated for each year and finally averaged
over all years. Those percentiles are plotted in Fig. 3.9 against the average wind and
PV full load hours over the same period.
0 0 0
−0.6 −0.4 −0.2 0 0.2 0.4 0.6 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 −0.6 −0.4 −0.2 0 0.2 0.4 0.6
Figure 3.9: Three interpercentile ranges of 1-hour net load ramps for different shares of
PV in the Wind/PV Mix β at 50% penetration of variable renewables
50 CHAPTER 3. FLEXIBILITY REQUIREMENTS
0.3 Saxony
0.3 Germany
1−hour net load ramps
0.1
0.1 0
0 200 400
0
−0.1 0
−0.1
−0.2
−0.2
−0.3
−0.3 0 200 400
Figure 3.10: 1-hour net load ramp duration curves at the regional, country, and
European scale at 50% share of renewables and 20% PV in the wind/PV mix for the
meteorological year 2009
Having seen the benefits of cooperation in the 1-hour time horizon, multihour ramps are
analyzed next. Fig. 3.11 compares the ramp envelopes for Saxony, Germany and Europe
again in the scenario with α = 0.5 and β = 0.2. The 1st/99th percentile envelopes
contain 98% of all gradients in each time horizon. Scenarios are simulated with each of
the meteorological years 2001 to 2010, the percentile values are calculated for each of
those scenarios and then averaged (shown by the solid lines). The range over this period
is represented by the gray-shaded area. This plot shows clearly that gradients over all
time steps are much lower if power systems are operated cooperatively. Furthermore,
52 CHAPTER 3. FLEXIBILITY REQUIREMENTS
the variation between years (grey-shaded area) becomes smaller with larger systems.
This allows for less uncertainty in the system planning period. The effect is similar for
the maximum ramps of each duration.
Figure 3.11: 1st/99th percentile ramp envelope at the regional, country, and European
scale at 50% share of renewables and 20% PV in the Wind/PV mix; average values for
the period 2001–2010 and their range
Requirements for the conventional power plants will decrease dramatically. These
reductions in ramp rates will most probably lead to less start-ups and wearing of the
remaining thermal power plants, which can reduce costs and emissions [118].
Fig. 3.12 shows the reduction of extreme hourly net load ramp rates (the minimum/-
maximum and the 1st/99th percentiles) for the individual countries compared to the
interconnected European system at 50% VRE penetration. The values are again av-
eraged over scenarios for the years 2001–2010. As discussed before, small countries
have the highest ramp rates and will consequently benefit the most from a powerfully
interconnected European power system. The maximum hourly change of net load in
the European system is 11% of the peak load whereas small countries face hourly ramp
extremes of 30–50% of peak load, e.g. in Switzerland and Slovenia. Even large countries
like Germany can reduce the maximum ramp from 20% to 11%. Only very few countries
like the Nordic countries would not benefit substantially; the ramp rates in Norway and
Sweden are only slightly higher than in a European system.
The analysis provides additional arguments in support of large-scale transcontinental
power systems with strong transmission grids, besides the benefits of reducing backup
energy needs [14]. In Czisch [48] or Huber et al. [106], a power system spanning Europe
and North Africa is shown to be cost-effective, mainly because of wind power smoothing.
Several studies propose even a global super-grid to efficiently integrate renewable power
sources [2, 38]. Other authors focused on the very short term advantages of dispersing
PV power generation [145]. The results in this thesis show advantages of cooperation
in the timescale of 1–12 hours between the very long-term horizon, concerned with
capacity adequacy, and the short-term scales.
3.6. CONCLUSION AND OUTLOOK 53
0.5
Figure 3.12: Boxplot with 1-hour net load ramp extremes for individual countries (solid
lines/bars) and Europe (horizontal dashed lines) at 50% share of renewables and 20%
PV in the Wind/PV mix
Modeling
54
Chapter 4
Setting up a modeling framework is crucial for the evaluation of concepts for future power
systems. In this chapter, the applied methodology is described and new developments
that improve state-of-the-art modeling are highlighted. Before starting with the actual
modeling framework, some preliminaries on the basic market environment considered
and the main ideas of the mixed-integer (linear) programming (MIP) approach are
given. A major part of this Chapter presents joint work with Matthias Silbernagl and
René Brandenberg (i.e. Sections 4.3.4, 4.4, 4.5 [185], and Section 4.6 [111] ).
55
56 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
regions have a central planning of operations including power plant scheduling and
grid management [98]. The modeling approach in this thesis can be interpreted as
the complete European Power system being operated by one ISO with all rights on
infrastructure operation from unit commitment to reserve scheduling. Results will
reveal what is possible from a technical point of view after all regulatory and political
obstacles are overcome.
Mixed-Integer linear programming (MILP) can be seen as a special case of the more
general MIP. In the latter, also non-linear terms would be allowed while MILP is
constraint to linear equations. For the models described in this thesis, mostly MILP is
employed and, more specifically, the models are formulated as binary problem. Power
plants can be either on-line or switched off which is represented by x ∈ {0, 1} instead
of x ∈ Z. In the following, all integer approaches are referred to as the most general
MIP and specification are given when necessary. A special case being used for some
illustrations and explanations later on is pure IP (integer programming). These problems
only consist of integer variables without any linear variables, i.e. only the first part of
equation (4.1) is considered.
The main advantage of MIP over other approaches for solving integer problems is
its ability to provide guarantees on the optimality gap / degree of optimality that
accompanies the achieved solutions. A prevalent employed approach for solving MIPs
is branch and cut, constituting a combination of branch and bound and cutting plane
4.2. MIXED-INTEGER PROGRAMMING AS BASIC APPROACH 57
methods, whose basic ideas are described below in Section 4.2.1. The main drawbacks of
the approach are the restricted modeling flexibility and the high computational efforts
required. Both issues have been mitigated by new UC formulations, faster solvers, and
greater computational power; still, further progress is vital. The approach described in
this thesis contributes by further improving the formulation of an important part of
the UC model: the start-up costs.
An MIP formulation of the unit commitment problem that is currently widely used
in academic research was published in 2006 by Carrión and Arroyo [37]. Based on
this formulation, progress in several areas of development have been made in past
years, including amongst others: an application to the self scheduling problem with
a more accurate start-up process [186], attempts to tighten the quadratic production
costs function [76, 205, 212], a more efficient formulation for start-up and shut-down
ramping [149], and a formulation with three instead of one binary variable per unit
which showed to be more efficient in many cases [150]. Recently, new research is focusing
again on a more accurate and efficient formulation of start-up costs, e.g, see Tuffaha
and Gravdahl [199], showing the relevance of the topic.
5 x 5 x
2 c 2 c
Constrained Region Constrained Region
4 4
ZLP
ZLP
3 3
ZMIP ZMIP
2 2
1 1
Feasible Solutions Feasible Solutions
x1 x1
1 2 3 4 5 1 2 3 4 5
Figure 4.1: Illustration of the integrality gap. The formulation of constraints on the
right figure has a lower integrality gap then the formulation depicted on the left.
Solution Algorithms Two algorithms are predominant at present: the cutting plane
algorithm and the branch and bound algorithm. Those two approaches are combined
in the so-called branch and cut algorithm that is used for solving the MIPs within this
thesis. A very short and illustrative explanation is presented below which is based on
the illustration in Fig. 4.2 for the cutting plane and Fig. 4.3 for the branch and bound
algorithm. Both show the solution finding process for the MIP model which is displayed
in Fig. 4.1 on the left. The major idea of both approaches is to reduce the integrality
gap of the initial problem. The remaining gap during this process is called the (relative)
MIP gap which is in the case of CPLEX defined by [77]:
|bestbound − bestinteger|
MIPgap = , (4.3)
1e−10 + bestinteger
with “bestbound” being the best current solution of the linear relaxation and “bestinte-
ger” the best solution that has been found so far.
Cutting Plane Algorithm Starting with the cutting plane algorithm, the idea of
the algorithmic procedure lies in adding additional constraints to the original problem
(so-called “cuts”). These additional constraints will then reduce the feasible region of
the problem and bring the LP solution closer to the MIP solution. The MIP solutions
have to be found by heuristics and whenever the MIP gap is below a given limit
(MIP-tolerance), the solution is considered optimal. An illustration of the procedure of
adding cuts is given by the sequence in Fig. 4.2.
There are different strategies for finding cuts including both user specific cuts which
require problem specific knowledge and general purpose cuts. Gomory [83] was the first
to introduce a cutting plane algorithm for solving general integer problems; a short
summary of the idea is given in the following.
4.2. MIXED-INTEGER PROGRAMMING AS BASIC APPROACH 59
5 x 5 x 5 x
2 c 2 c 2 c
Constrained Region Constrained Region Constrained Region
4 4 ZLP1 4 ZLP1
ZLP0 ZLP0 ZLP0
3 3 3 ZLP3
ZMIP ZMIP ZMIP
2 2 2
1 1 1
Feasible Solutions Feasible Solutions Feasible Solutions
x1 x1 x1
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Figure 4.2: Illustration of cutting plane method. Own illustration inspired by a talk of
Morales-España [148].
The starting point for the algorithm is the final simplex tableau of the relaxed problem
which could in general form be described as [44]:
X
xi + āi,j sj = b̄i , (4.4)
j∈N
with xi being a basic variable, sj the nonbasic variables, and ai,j the fractional coefficients
(for details on simplex see e.g. Bazaraa et al. [12]). In order to depict the basic idea of
how Gomory cuts are constructed, a simple numerical example is taken here [24] with
i = 1, ā1 = 94 , ā2 = 14, and b̄1 = 49 :
9 1 9
x1 + s 1 − s 2 = . (4.5)
4 4 4
The steps for constructing a Gomory cut are the same for the general formulation,
however, this simple numerical example is more illustrative. In a first step, fractional
and integer values are separated, leading to
1 3 1
x1 + 2 + s1 − 1 − s2 = 2 + . (4.6)
4 4 4
1 3 1
x1 + 2s1 − 1s2 − 2 = − s1 − s2 + . (4.7)
4 4 4
1 3 1 1
− s1 − s2 + ≤ . (4.8)
4 4 4 4
As the the left hand side of equation (4.7) is integer, the additional constraint (the
Gomory cut) can be defined to
1 3 1
− s1 − s2 + ≤ 0. (4.9)
4 4 4
60 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
Branch and Bound Algorithm The branch and bound method is more complicated
to be described. The method is based on dividing the original problem in several steps
as depicted by the illustrative sequence in Fig. 4.3. The first LP solution of the original
problem lies in between 3 and 4 for both x1 and x2 . In a first step, the problem is
divided according to variable x2 and LP solutions are computed (LP “bounding”): in
one subproblem, x2 is set to be lower or equal than 3 (x2 ≤ 3) which leads to the
solution ZLP1 . In the other subproblem, x2 has to be larger or equal than 4 (x2 ≥ 4)
and the solution obtained is ZLP2 . The solutions are then compared and ZLP1 is found
to be the better one. In a next step, the subproblem with the better solution is further
divided (“branched”), this time according the x1 variable. Setting x1 ≤ 3 and setting
x1 ≥ 4 leads to the solutions ZLP1* and ZLP3 , where ZLP1* is proved to be an optimal
solution of the MIP problem. An illustrative example of the same style with given
numbers can be found in Conforti et al. [44].
5 x 5 x 5 x
2 c 2 c 2 c
Constrained Region
ZLP2 ZLP2
4 4 4
ZLP0 Constrained Region ZLP0 Constrained Region ZLP0
ZLP1 ZLP1* ZLP1
3 3 3
ZMIP ZMIP ZMIP
2 2 2 ZLP3
1 1 1
Feasible Solutions Feasible Solutions Feasible Solutions
x1 x1 x1
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Figure 4.3: Illustration of branch and bound method. Own illustration inspired by a
talk of Morales-España [148].
It has to be noted that those descriptions and illustrations are very simplified and
only provided to give a basic idea about solution procedures and a reason why some
formulations of the same MIP might be easier to solve than others. In the case of unit
commitment modeling as described in this thesis, the variables are binary, which is a
special case of an integer variable. They can only have the value 0 or 1. Branching
thus means setting the values to either 0 or 1. The UC problems for realistic test cases
have a tremendous amounts of variables which leads to high dimensional polytopes that
cannot be illustrated.
Tighter UC formulations have been of interest in general. Lee et al. [135] consider
minimal up- and down-time constraints and prove that the feasible operational schedules
can be described by O(2T |I|) inequalities. By using start-up and shut-down status
variables, Rajan and Takriti [175] characterize the same feasible set with O(|I|T )
inequalities—an example of how representations of polytopes may be simplified by
introducing additional variables.
The quadratic production costs have commonly been modeled by piecewise linear
approximations. Frangioni et al. [76] present tight valid inequalities for such costs,
enabling an iterative approximation scheme. A similar approximation scheme with
different valid inequalities is given in [205]. Finally, Ostrowski et al. [159] improves
solution times by using valid inequalities for the ramping process.
The start-up costs are discussed separately in Section 4.3.3. The production costs are
non-convex [93, 165] and approximated by a piecewise linear function of Carrión and
Arroyo [37]. In this thesis, simple linear production costs, as described by Morales-
España [150], are used. The costs depend linearly on the binary operational state vit
and the production pti with the parameter Ai for the fixed part and Bi for the linearly
increasing part:
The fixed part of the productions costs Ai is also referred to as no-load cost and leads
to lower efficiency in part-load operation (see next Section for details).
Generally used constraints of thermal power plants regard the minimal production Pimin ,
the maximal production Pimax , maximal up and down ramping speeds RUi and RDi as
62 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
well as maximal ramping at start-up SUi and shut-down SDi . The production limits
are formulated with the power plant state vit as
Pimin vit ≤ pti ≤ Pimax vit ∀ i ∈ I, t ∈ T . (4.13)
Ramping constraints can then be formulated according to Carrión and Arroyo [37] by:
pti ≤ pt−1
i + RUi vit−1 + SUi (vit − vit−1 ) + Pimax (1 − vit ) ∀ i ∈ I, t ∈ [2 .. T ], (4.14)
pti ≥ pt−1
i − RDi vit − SDi (vit−1 − vit ) − Pimax (1 − vit−1 ) ∀ i ∈ I, t ∈ [2 .. T ], (4.15)
with yit being the start-up indicator, zit the shut-down indicator, U Ti the minimum
uptime and DTi the minimum downtime.
In the large-scale numerical simulation of Chapter 7, however, minimum up and
downtimes are not considered. From a technical point of view, minimum downtimes
are only very short and mostly below one hour, representing the time that is required
to aerate the turbines. A technical report prepared by The Union of the Electricity
Industry (Eureletric) [68] reports the minimum downtime of all conventional power
plants to be non-existent supporting the approach of neglecting them. Minimum up-
times can also hardly be explained by technical constraints since power plants must be
able to shut down in emergency cases anytime. Kirschen and Strbac [122] argue for
minimum uptimes with a limitation of damage that is caused by frequent start-ups.
However, this is mainly an economic argument and gives reason to neglect the constraint
whenever start-up costs are modeled appropriately.
being a linear equation, the offset by the so called “no-load costs” represented with Ai
is proportionally lower with a higher power output and, in turn, fuel efficiency increases.
In Fig. 4.4 on the left, the costs or fuel inputs are illustrated as a function of electricity
output. When calculating the efficiency η as the ratio of output p to fuel input, the
result is a concave function as illustrated in Fig 4.4 on the right.
cost/fuel η
P max
η max
∆fuel
B= ∆p
η max
A∗ = P min η min
η min
p p
P min P max P min P max
Figure 4.4: Visualization of the cost function and reduced efficiency in part load. The
power plant considered here has a minimum production of 40%, a minimal efficiency of
50% and a maximal efficiency of 60%.
The two parameters Ai and Bi for each power plan i can be computed from the efficiency
at minimal load η min , the efficiency at maximal load η max , and the minimal power output
P min by
max
P P min
P min η max
− ηmin
cost/fuel = min + (p − P min ) · max . (4.19)
η (P − P min )
This equation can be reformulated to equation (4.12) by defining A and B as
max
P P min
P min
η max
− η min
A∗ = min , B = max
, → A = A∗ − P min B. (4.20)
η (P − P min )
where Fi are the fixed start-up costs and Vi are the maximum variable start-up costs,
such that the costs for a complete cold start are Vi + Fi . The fixed costs include labor
64 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
cost Kil
el
K i
approximation error
τ
hot warm cold
Formulation with one binary variable (“1-Bin”) The cost function is modeled
by an increasing step function, i.e. a piecewise constant, increasing function (see
Fig. 4.5). According to Carrión and Arroyo [37] or Nowak and Römisch [158], this can
be formulated with the power plant state vit at time t and preceding time steps l as
well as the offtime dependent start-up costs Kil as
l
X
cuti ≥ Kil vit − vit−n ∀ i ∈ I, t ∈ T , l ∈ [1 .. t−1] with Kil > Kil−1. (4.22)
n=1
Formulation with three binary variables (“3-Bin”) Simoglou et al. [186] and
Morales-España et al. [150] show that by using the start-up status yit , the shut-down
status zit , and the previous downtime P Di as described by Garver [78],
(
vi1 if PDi > 0,
yi1 − zi1 = ∀ i ∈ I, (4.23)
vi1 − 1 else,
yit − zit = vit − vit−1 ∀ i ∈ I, t ∈ [2 .. T ], (4.24)
the start-up costs may be modeled computationally more efficient than by using solely
vit as in 1-Bin. To this end, for each unit i, the off-times [1 .. T −1] are grouped by their
start-up costs into a minimal number Ei of intervals L1i ∪˙ . . . ∪˙ LEi = [1 .. T −1] with
i
0
Kil = Kil ∀ i ∈ I, e ∈ [1 .. Ei ], l, l0 ∈ Lei .
If unit i starts up in period t after l off-line periods with l ∈ Lei , then the start-up is of
type e, expressed by git (e) = 1. According to Simoglou et al. [186] this is modeled by
X
yit = git (e) ∀ i ∈ I, t ∈ T , (4.25)
e∈[1 .. Ei ]
X
git (e) ≤ zit−l ∀ i ∈ I, e ∈ [1 .. Ei −1], t ∈ T with t > max Lei . (4.26)
l∈Lei
4.3. STATE-OF-THE-ART UC MODELS 65
While git (e) may be used to model the start-up process and its power production [186],
the comparison in this thesis considers only the start-up costs by substituting the
variables cuti in the objective function (4.10) by
minLe
X
cuti := Ki i git (e) ∀ i ∈ I, t ∈ T . (4.27)
e∈[1 .. Ei ]
The minimum operator in equation (4.27) is required to select one element of the
interval Lei . Each other arbitrary element could be selected here as well.
Each of these inequalities is trivially fulfilled if unit i is off-line in period t, since then
its right-hand side is non-positive. If unit i is on-line in period t, consider all n ∈ [1 .. l]
with vit−n = 1. If no such n exists, then both the start-up costs cuti and the right-hand
side of the inequality equal Kil . Otherwise, choose a minimal n with this property.
Then, the start-up costs cuti equal Kin−1 and the right-hand side is at most Kin−1 . As
these inequalities dominate those in (4.22), i.e. as they provide a stronger bound on
cuti , they still properly model the start-up costs. The impact of the tightening on the
integrality gap is depicted in Fig. 4.8 in Section 4.6.5.
a←b+1
where l denotes the off-line time. The fixed costs are derived from the start-up status
yit as in constraints (4.23) and (4.24). The variable costs originate from the reheating
process at start-up, where fuel needs to be burned and where the unit experiences
thermal stress.
Here, the term (1 − e−λi l ) is proportional to the heat loss of the power plant incurred
while off-line, and models the exponential decay of the temperature,
where lit denotes the number of periods that unit i is off-line prior to period t.
1 [ ti
temp
h4i
tempi (t)
1
vi
t
1 2 3 4 5 6 7 8 9 10
cuti = Vi ht−1
i + Fi yit ∀ i ∈ I, t ∈ T , (4.40)
with Vi being the variable part of start-up costs and Fi the fix part as described in
equation (4.21).
Next, the exactness of the model is explained. It is easy to check that yit = 1 exactly
if there is a start-up in period t, and yit = 0 otherwise. Thus, the constant part of
the start-up costs is modeled correctly. The temperature losses increase proportionally
with tempti − vit . Thus, in a cost-minimal solution, heating is applied such that the
temperature is minimal while fulfilling tempti ≥ vit . This entails two consequences:
1. Heating is applied only in the period prior to each start-up. Earlier heating could
be postponed until this period, thus saving heating costs.
2. The amount of heating is exactly such that the temperature reaches 1. Excessive
heating could either be postponed until the period prior to the next start-up, or
be avoided if there is no such start-up.
Thus, the needed heating, considering the further cooling during period t − 1, matches
the expected temperature loss,
=0
z}|{
(4.39)
ht−1
i = tempti − e−λi tempt−1
i + (1 − e−λi ) vit−1 = 1 − e−λi l .
4.5. ADVANTAGES OF THE TEMPERATURE MODEL 69
This means, the variable part of the start-up costs is modeled correctly too, leading to
cuti = Kil .
While this model uses new additional variables, it reduces the number of constraints
significantly in comparison to 1-Bin, 1-Bin* (the tightened version of 1-Bin), and 3-Bin,
even with a start-up cost approximation tolerance of Ktol = 5% (see Section 4.5.3).
Fig. 4.8 suggests that the integrality gap of this model is on average smaller, while
the solution times of the linear relaxation remain comparable to 1-Bin and 3-Bin (see
Fig. 4.7). Both factors are crucial for the improved number of solved instances shown
in Fig. 4.9.
German power system The raising requirements for fossil-fuel power plants, which
stem from a more volatile residual load, include more start-ups and hence result in a
higher ratio of start-up to operational costs [118]. A higher percentage of start-up costs
will lead to higher solution times and increase the advantages of the temperature model
approach. To consider the impact of a more volatile residual load in the numerical
experiments, a forecast scenario for the year 2025 is employed.
Power plant data of the German power system of 2014 are published by the German
Federal Network Agency [33], comprising 228 individually controlled power plants.
The data is augmented by assumptions regarding minimal production, efficiency, and
start-up costs, which are partly based on [56, 66, 128]. As the year 2025 is modeled,
all nuclear power plants are phased out in favor of four additional combined cycle gas
turbines, reducing the number of plants to 223. Again, this assumption is different to
the dataset development described in Chapter 6, where thermal power plants are kept
at status quo for future scenarios as well.
70 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
The main benefits of this dataset compared to existing test datasets (e.g. as used by
Carrión and Arroyo [37]) are
In addition to power plant data, the model requires data of the residual load, i.e. of
the difference between load and electricity production from must-run renewable power
sources. The load data is taken from ENTSO-E [62] and scaled to a yearly electricity
consumption of 520 TWh. Wind and solar electricity generation profiles are computed
based on the NASA MERRA database [177] for the same base year. Afterwards, these
profiles are scaled according to the respective installed capacity (50 GW wind, 50 GW
solar). Biomass and hydro power plants are assumed to produce at full capacity (5.5 GW
biomass, 4.5 GW hydro).
Each experiment is performed using 14 time ranges of length T =72 (Sections 4.5.3 and
4.5.5), length T =240 (Section 4.5.4) or varying length (Section 4.5.6), starting in the
S-th hour of the year with S ∈ {624k + 433 : k ∈ [0 .. 13]}. This set is chosen such that
each time range starts at midnight, the time ranges are uniformly distributed over the
year 2025, and two time ranges start on any day of the week, respectively.
IEEE 118 bus system This scenario is based on the IEEE 118 bus test system
published in [146], and again augmented to include the relevant power plant data.
Apart from being well-studied, its major benefit is its realistic transmission network.
The test system provides load values for 24 hours and 20 wind scenarios which are
concatenated into a residual load of 480 periods. Since the low average wind production
of 5.4% of the load leads to a lower ratio of start-up to operational costs than in the
scenario of the German power system, the advantage of the new approach is expected to
be less pronounced. Analogous to the German power system, 14 uniformly distributed
starting points are given by S ∈ {24k + 1 : k ∈ [0 .. 13]}.
2. 1-Bin*: Same as 1-Bin, with the tightened start-up cost inequalities (4.28) instead
of the original inequalities (4.22).
3. 3-Bin: Same as 1-Bin, except that start-up cost inequalities (4.22) are replaced
by the inequalities (4.23)-(4.26), and the start-up costs are defined as in (4.27).
4.5. ADVANTAGES OF THE TEMPERATURE MODEL 71
4. Temp: New approach with explicit modeling of the power plant temperature, as
described in Section 4.4.2, including inequalities (4.35)-(4.39) and start-up costs
defined in (4.40).
These formulations are embedded into the two models described in Section 4.3.1,
• the extended formulation composed which further includes the tighter ramping
constraints according to Ostrowski et al. [159] as well as grid constraints with
power transfer distribution factors (PTDF) as described in Section 4.9.
The basic UC problem uses the German power system, while the extended UC problem
includes load flow constraints and thus requires the networked IEEE 118 bus system.
In 1-Bin, 1-Bin*, and 3-Bin, the start-up costs are approximated with tolerance Ktol ∈
{0%, 5%, 20%} (see Section 4.3.4). Using Ktol = 0%, the modeled start-up costs
are equal to Temp, resulting in equivalent problems and solutions, which is required
when comparing integrality gaps. With Ktol = 20%, the start-up cost functions are
approximated very roughly with 2.3 steps on average. Finally, as in the presented
scenarios, start-up costs amount to up to 10% of the total costs, Ktol = 5% is a sensible
choice leading to a maximal error of 10% · 5% = 0.5% of the objective value.
Fig. 4.7 compares solution times of the linear relaxations taken over 14 time ranges of
length T = 120 as described in Section 4.5.1 and using a start-up cost approximation
tolerance of Ktol = 5%. The results show that Temp significantly outperforms 3-Bin.
While 1-Bin and 1-Bin* are on average faster than Temp in the German power system,
this is reversed in the IEEE 118 bus system where Temp yields the fastest linear
relaxation by a considerable margin.
Computation time (relative to Temp)
200% 600%
500% 445%
153% 361%
150% 400% 379%
100% 300%
100%
85% 92% 200%
100%
50% 100%
1-Bin 1-Bin* 3-Bin Temp 1-Bin 1-Bin* 3-Bin Temp
Figure 4.7: Solution times of the linear relaxation for 14 test cases with T = 120 periods
and Ktol = 5% in the German power system (left chart) and the IEEE 118 bus system
(right chart). Temp outperforms 3-Bin consistently.
4.5. ADVANTAGES OF THE TEMPERATURE MODEL 73
280% 243%
233%
400%
270%
241%
200% 200%
109% 100%
100%
140%
113%
50%
100%
100%
1-Bin 1-Bin* 3-Bin Temp 1-Bin 1-Bin* 3-Bin Temp
Figure 4.8: Integrality gaps relative to 3-Bin, for 14 test cases with T = 72 periods in
the German power system (left chart) and the IEEE 118 bus system (right chart). In
both, 3-Bin dominates 1-Bin and 1-Bin*, but is on average inferior to Temp. Results in
the IEEE 118 bus system exhibit less variance.
Fig. 4.8 clearly illustrates the advantage of modeling the temperature as an explicit
variable. Since the inequalities (4.28) of 1-Bin* dominate the inequalities (4.22) of 1-Bin,
1-Bin* must have a lower integrality gap (11% and 4% decrease). 3-Bin consistently
provides a lower integrality gap than 1-Bin*, with an average reduction of 55% and
51%, corresponding in magnitude to the results in Morales-España et al. [150]. Temp
further decreases the average integrality gap of 3-Bin by 9 and 13 percentage points
and proves to be the tightest model analyzed.
74 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
1. As the residual load will become more volatile it will be beneficial to increase the
time resolution [50].
2. As renewable generation changes over several days and weeks, the storage man-
agement requires to consider longer time horizons than today where it is mainly
driven by day and night variation of load.
The scaling behavior is analyzed with 14 sets of test cases. The test cases have start
periods S as described in Section 4.5.1, a varying number of time steps considered
T ranging from T = 24 to T = 444, and start-up costs approximated to tolerances
Ktol ∈ {0%, 5%, 20%}. Fig. 4.9 shows the number of instances which have been solved
to an optimality gap of 1% within 30 minutes for the German power sytem (upper
chart) and the IEEE 118 bus system (lower chart).
In both cases, 3-Bin dominates 1-Bin and 1-Bin*, confirming the results of [150].
However, even if allowing the highest start-up cost approximation tolerance Ktol = 20%,
Temp consistently solves more instances than all other models.
Unsurprisingly, the superiority of the temperature model is more emphasized in the
basic formulation, since the higher complexity of the extended formulation and the
lower share of start-up costs in the IEEE 118 system lessen the impact of the start-up
cost model.
14
12
10
8
6
4
2
0
0 48 96 144 192 240 288 336
Number of instances solved
14
12
10
8
6
4
2
0
0 24 48 72 96 120 144
Figure 4.9: Scaling of computational effort with problem size for all formulations and
different start-up cost approximation tolerances Ktol . The upper chart shows the number
of instances solved to an optimality gap of 1% within 30 minutes of computation time
for the German power system, the lower chart shows the same for the IEEE 118 bus
system.
Start-up of power plants is mostly restricted by either thermal stress in the components,
which can be expressed as a temperature increase, or by limited heating capabilities,
which can be expressed by limiting the applied heating. This Section presents approaches
to integrate start-up times in the temperature formulation for either
• units with limited heating speed (c.f. Fig. 4.10 on the left), or
• units with limited temperature increase (c.f. Fig. 4.10 on the right).
76 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
1 1
∆tempmax
i
tempi (t) tempi (t)
cooling heating cooling
heating
1 hti 1 hti
Himax
1 vit 1 vit
Cooling time Heating time Cooling time Heating time
t t
Figure 4.10: Cooling and heating during the off-line time of a unit with limited heating
speed (left) and of a unit with limited temperature increase per period (right).
For both types of units, the resulting start-up time and costs are derived and compared
in Section 4.6.4. The start-up time, which is defined as the number of periods during
which the unit heats up, is denoted by SUTi (l). The sum of the variables hti during
start-up is denoted by TH i (l), such that Vi · TH i (l) equals the variable start-up costs in
4.40.
First, the development of the temperature of a unit in a continuous model is derived.
The off-line time can be split in two phases: the unit cools down and, subsequently, it
is reheated before the start-up takes place (c.f. Fig. 4.10 on the left).
During the entire off-line time, the unit continuously loses heat at a rate of λi tempti .
As shown above, the modeled temperature of unit i equals e−λi l after l offline periods.
During heating, the temperature is increased by supplying heat at a rate of hi (t).
Assuming the heating phase starts at t = 0, the continuous temperature tempi (t) may
be modeled as
While heating, the unit continues to lose further heat. Therefore, units heat as fast
as possible in a cost-minimal solution. So far, unbounded heating, which models the
typical start-up costs (4.30), was assumed. As noted, the following two sections consider
the effect of limiting the heating speed and the temperature increase.
can be computed to
Himax
tempi (t) = e−λi (l+t) + (1 − e−λi t ). (4.42)
λi
In the continuous model, the start-up heating finishes at time t∗ with tempi (t∗ ) = 1.
Equation (4.42) is the basis for
1 − e−λi l
∗ 1
t = ln 1 + H max ,
λi i /λi − 1
which results in dt∗ e periods of heating in the unit commitment formulation, and hence
in a start-up time of
1 − e−λi l
1
SUTi (l) = ln 1 + H max . (4.45)
λi i /λi − 1
If t∗ is integral, and therefore SUTi (l) = t∗ , the unit heats at maximal speed in the unit
commitment problem, and the total heating equates to
1 − e−λi max
TH i (l) = Hi SUTi (l). (4.46)
λi
If t∗ is not integral, and therefore SUTi (l) > t∗ , the unit needs to heat at sub-maximal
speed in the first heat-up period to reach a final temperature of exactly 1. As this is
equivalent to keeping the unit warm for the initial part of that period, it results in a
slightly higher total heating than TH i (l). However, the difference is generally small (c.f.
Fig. 4.11).
which is solved by
tempti ≤ tempt−1
i + ∆tempmax
i ∀ i ∈ I, t ∈ [2 .. T ] (4.50)
Assuming now that ∆tempmax i divides 1 − e−λi l evenly, i.e. that the unit heats at
maximal speed for the entire start-up time, the required heating in each period equals
hti = tempt+1
i − e−λi tempti = (1 − e−λi )tempti + ∆tempmax
i .
Noting that the temperature in the j-th period of heating equals e−λi l +(j −1)∆tempmax
i ,
the sum of the heating variables can be derived as
1 − e−λi 1 + e−λi l
−λi l
TH i (l) = (1 − e ) 1+ −1 . (4.52)
2 ∆tempmax
i
If ∆tempmax
i does not divide 1 − e−λi l evenly, then the effective total heating slightly
surpasses TH i (l); yet TH i (l) remains an excellent approximation (c.f. Fig. 4.11).
λi
hi (t) = ht ∀ i ∈ I, t ∈ T
1 − e−λi i
during period t. Introducing this factor in (4.40) as
λi
cuti := Vi ht−1 + Fi yit ∀ i ∈ I, t ∈ T , (4.53)
1 − e−λi i
results in start-up costs which remain approximately equal for equivalent operational
schedules, regardless of the period length f . Within this thesis, the period length is set
to 1 hour in all cases.
1.2
8
1
Start-up time
Total heating
6 0.8
0.6
4 Himax
Himax 0.4 TH i (l) for Himax
Himax cont. model ∆tempmaxi
2
∆tempmax
i 0.2 TH i (l) for ∆tempmax
i
∆tempmax
i cont. model Unbounded heating
0 0
0 20 40 60 80 100 0 20 40 60 80 100
Cooling time l Cooling time l
Figure 4.11: Start-up time (left) and total heating (right) when limiting heating/tem-
perature increase for a unit with parameters λi = 0.05 and Himax = ∆tempmax i = 3λi .
The total heating is compared to the respective approximations TH i (i) and the model
with unbounded heating.
increase significantly for larger models and strict limits (small M ). The model with
limited heating is more efficient and only increases computational times moderately
up to 200% compared to the model with unbounded heating. In contrast, the model
with limited temperature increase may increase computational times by up to 600% at
M = 40.
Effects on system costs As highlighted in Fig. 4.11, the required heating for a
start-up increases when modeling the start-up time. Fig. 4.12 on the right analyzes
the resulting increase in system costs, depending on Himax and ∆tempmax
i . The increase
amounts to less than 0.5% even for very strict limitations.
This observation applies only to a deterministic model; in a stochastic model the start-up
time may force a unit to stay at operational temperature during off-line time, possibly
increasing the system costs considerably.
0.4
1,500
0.3
1,000 0.2
500 0.1
0 0
0 5 10 15 20 25 30 35 40 3 6 9 12 15
Strictness of limits M Strictness of limits M
Figure 4.12: Increase in system costs and computational time with limited heat-
ing/temperature increase for test cases of two sizes and parameters Himax = M λi or
∆tempmax
i = M λi . The additional system costs amount to less than 0.5%.
start-up (so-called “indirect start-up costs”) to 40% of overall cycling costs. The share
of load following cycling is estimated to be only at around 5%. The authors also found
that the share of cycling costs in total operating costs will increase dramatically from
1.7% without any renewables to 14% with a 50% penetration of wind and solar. Denny
and O’Malley [51] simulated the additional cycling costs by introducing a carbon price.
They predict that the share of additional fuel costs represents 2-50% of cycling costs –
leaving at least 50% of costs coming from wear-and-tear, again pointing to the high
importance of this cost factor in future power system operation.
The wear-and-tear costs depend on the speed of the temperature increase and the
resulting thermal tensions. The temperature base modeling approach as presented in the
previous sections allows to account for this fact by introducing start-up speed dependent
costs. A piecewise linear function is employed which approximates quadratically
increasing costs by faster heating due to the higher thermal stress. Fig. 4.13 illustrates
this increasing characteristic of the start-up costs. The (additional) costs for wear-and-
tear can be included in the model with the following equation:
cwit ≥ ζic + φci · hti ∀t ∈ T , i ∈ I, c ∈ C, (4.54)
with ζic being the fix part and φci the variable part of each line c ∈ C.
In order to add those costs to the model, cwit can be added to the total costs in equation
(4.10). Start-up costs cuti are then split into one part representing additional fuel
requirements and one part for the wear-and-tear costs. The parameters of the start-up
costs Vi and Fi have to be adjusted and only represent additional fuel costs then.
Including heating-speed dependent wear-and-tear costs in UC can change operations:
while fast start-ups were the best option for keeping additional fuel consumption at
lowest level, when including the start-up type depending wear-and-tear costs, slower
82 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
Costs
c=3
c=2
c=1
Heating h
Figure 4.13: Exemplary illustration of wear-and-tear costs with number of lines |C| = 3
.
start-ups can be the better option. In stochastic optimization, the effects of including
variable wear-and-tear costs can be even more interesting: Postponing the start-up
process leads to higher costs when power plants need to be started unexpectedly.
Full AC modeling The basic formulation for the power flow on line m ∈ L between two
nodes a, b ∈ N can be described by equations (4.57), (4.58) (for a detailed description
and derivation see e.g. Andersson [5] or Kundur [129]):
L
fa,b = Va Vb (Gab · cos(δa − δb ) + Bab · sin(δa − δb )) , (4.57)
q,Lab = Va Vb (Gab · sin(δa − δb ) + Bab · cos(δa − δb )) . (4.58)
In those equations, V is the voltage at each node, G is the conductance, and B is the
susceptance of the lines. The difference in the phase angle is noted as δa − δb , the active
L L
flow as fa,b , and the reactive flow is noted as qa,b . These equations are nonlinear and
must be simplified in order to be used in large-scale UC modeling.
DC modeling with angles A very common approach for simplified load flow modeling
is the so-called DC modeling framework. Only active power is considered and voltage
differences are neglected (Va ≈ Vb ). As a further simplification, the reactive flow is
assumed to be compensated and thus not considered anymore. Furthermore, the angle
differences δa − δb are assumed to be very small, which leads to:
For a networked system, all flows can be described in matrix notation with the diagonal
matrix (index d) of the susceptances Bd , the incidence matrix A, and the angles at all
nodes δ as
f L = V02 · Bd · A · δ. (4.61)
84 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
When implementing this formulation, the angle at each node is a variable in the
optimization process. The usefulness of the DC model for techno-economic power
system simulations was, for instance, shown by Van Hertem et al. [94].
f N = V02 · AT · Bd · A · δ. (4.63)
By combining (4.61) and (4.63), the angles can be replaced leading to a formulation
where the flow on each line f L depends on the feed in on each node f N
The voltage level V02 is a scalar that can be cancelled out. This simplifies the line flow
to
The impact of nodal feed-in (nodal flow) on the line flow is represented by the matrix
of power transfer distribution factors PTDF which can be defined as
with dimension number of lines |L| times number of nodes |N |. The power flow
formulation with PTDF is then stated as
f L = PTDF · f N . (4.67)
The PTDF contains values that reflect the effect of a feed-in at each single node on the
entire resulting line flows. For each network, a slack node has to be defined (multiple
slack nodes are required to model Europe with its DC lines, see the paragraph on
modeling DC lines in Section 4.9.2 for further details). The slack node is required
as the system of equations would otherwise be linearly dependent, which results in a
determinant of (AT · BD · A) being zero and a singularity of its inverse. Slack nodes
are incorporated by deleting rows and columns in Bd · A and AT · BD · A as follows:
• Bd · A: This is a matrix of size |L|x|N |, the column of each slack node has to be
replaced by zeros.
4.9. MODELING OF POWER FLOW AND FLEXIBLE TRANSMISSION 85
• AT ·BD ·A: This is a matrix of size |N |x|N |, the column and the line corresponding
to each slack node has to be replaced by zeros.
P t
P t t
with i∈In pi + s∈Sn pss − Dn being the nodal net injection / nodal flow at node n
t
and fm,AC being the line flow over AC lines.
When applying the DC modeling framework with the PTDF, two constraints need to
be considered in addition to the power flows according to equation (4.68). The sum of
all net injections fat,N must equal zero in all periods by
X
fat,N = 0, ∀t ∈ T , (4.69)
a∈N
and the power flow over each line must stay within its limits:
L,max t L,max
−fm ≤ fm,AC ≤ fm ∀t ∈ T , m ∈ L. (4.70)
Modeling losses There are several approaches for modeling losses in power sytems.
Often, quadratic losses are assumed and modeled by a piecewise linear approach,
e.g. [53, 139]. The idea that loss minimization is a physical principle which is also
leading to the basic DC flow equations is described by Ahlhaus and Stursberg [4].
Therein, piecewise linear approximated losses are used to better approximate power
flows in a capacity extension model. For all models analyzed in this thesis, losses are
neglected since the focus of the analysis lies in the flexibility adequacy of the system.
High voltage DC lines HVDC lines connect two nodes by an AC-DC and a DC-AC
converter that are fully controllable. Electricity can be transported from one node to
another according to a predefined schedule.
The basic idea of modeling HVDC lines in the DC modeling approach is to subtract
the power that is fed to the AC-DC converter from the total nodal injection PN by
N
fAC = f N − fDC
N
. (4.71)
The nodal injections to the DC line and the line flow are related with the transposed
incidence matrix of all DC lines ATDC according to
N
fDC = ATDC · fDC
L
. (4.72)
Combining those two equations shows the effect of DC flows on nodal AC flows by
N
fAC = f N − ATDC · fDC
L
. (4.73)
N
Replacing fAC by the formula of equation (4.73) leads to
L
fAC L
= PTDF · f N − PTDF · ATDC · fDC , (4.75)
and to the definition of the so-called direct current distribution factor (DCDF) matrix
(an equivalent to PTDF matrix in functionality but applied for the DC lines) by
For a matrix-vector notation of an example grid, the reader is referred to Van den
Bergh et al. [18].
Phase shift transformers (PSTs) Another possibility for increasing the system
flexibility is the introduction of PSTs which allow for a partial routing of electricity in
the grid. PSTs can change the angle between two nodes by the phase shift angle which
is modeled by the variable psam . More details on the underlying technology can be
found e.g. in Verboomen et al. [204]. The equations describing the load flow including
the phase shift of psam can be formulated as [18]:
L
fa,b = V02 Bab (δa − δb + psaab ) (4.77)
Inserting the definition of the PTDF according to (4.66) and shortening the voltage
level where possible leads to
Finally, a matrix of phase shift distribution factors (PSDF), which indicates the changes
of flows that are induced by a phase shift on one line to all other lines in the network,
can be defined by
It is important to note that the PSDF matrix as defined must be multiplied by V02 to
transform the resulting power flows into Watts. Additionally, the values must be divided
by 57.3 when psa is given in degrees instead of radians (see equation (4.84)-(4.85)).
Van Hertem et al. [94] investigated the usefulness of analyzing the impact of PSTs
within the simplified DC modeling framework. The authors compared the load flows of
a test system with PSTs in the full AC case to the simplified DC version and found a
small increase of the error through introduction of PSTs. Their conclusion was that
the error is small enough that the simplified DC flow is suitable for testing PSTs as
done in this thesis.
Complete power flow equations Combining all definitions and elements of the
power flow equations that allow to include DC lines as well as PSTs and setting the
voltage to V0 = 380 kV leads to
L 3800002
fAC = PTDF · f N + L
PSDF · psa + DCDF · fDC . (4.84)
57.3
The equation can be written in index notation and by transforming the power unit
from [W] to [MW] by
" #
X
m
X X 3802 X
t
fm,AC = PTDFn t
pi + t t
pss − Dn + PSDFm
m0 · psam0 +
n∈N i∈In , s∈In
57.3 m0 ∈L
AC
X
m t
DCDFm0 · fm0 ,DC , ∀m ∈ LAC , t ∈ T , (4.85)
m0 ∈LDC
where the set of lines L is split into AC lines and DC lines, LAC ∪ LDC = L.
88 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
The principle of all matrices, i.e. PTDF, DCDF, PSDF is similar. Their elements are
factors that indicate the effect of a change of a nodal feed-in (PTDF), a change in DC
flow in DC lines (DCDF), or a change in phase angle of all lines with phase shifters
(PSDF) on the considered line m. Concerning the change in phase angles, the elements
of the PSDF matrix must be multiplied by a scalar, in the case of this thesis given by
3802 /57.3. For general purposes, the entire system of equations can also be computed
in per-unit values. In this case, the PSDF must be multiplied by the power base [18].
Figure 4.14: The synchronous grids of Europe: map of the European network of
transmission system operators for electricity. Image: Wikimedia Commons [208]
divided into 268 zones according to the NUTS classification (see Section 6.1) and only
interzonal transmission is considered. Estimating an adequate PTDF matrix for this
reduced grid is a complicated task and methods for grid reductions are discussed for
example by Van den Bergh et al. [18] or Hasche [88].
dataset that is developed (see Chapter 6) is regarded as a stylized real power system.
Its realistic behavior and general system properties are more essential than the exact
representation of the European system - which is not fully possible in reduced models
anyway. Hence, the focus in the interpretation of results in this thesis is giving general
understandings on a networked power system with high shares of fluctuating generation
but not necessarily concrete policy recommendations for individual line upgrades.
In real world systems, operators must consider contingencies in their operational
planning. A commonly used method is computing so-called outage transfer distribution
factors (OTDF), which can be interpreted as PTDFs for a post contingency state [40,192].
Computation of such OTDFs for the reduced power system and considering thermal
contingency constraints seems to be a promising option for future research. So far, the
security constraints (N-1) are approximated by reducing the maximal line capacities to
70% of the computed transmission limit.
• The power output of the turbine (psts > 0) and the pump (psts < 0) has to be
within boundaries of a maximum pump capacity (−P Ssmax ) and maximal turbine
capacity (P Ssmax ), which are assumed to be identically at
ests = est−1
s − psts ∀ t ∈ T , s ∈ S. (4.88)
In the case that storage plays a part in providing reserve power, additional constraints
must be considered. They are explained in Section 5.3.
4.11. MODELING OF DEMAND SIDE MANAGEMENT 91
X
pti = Dt + clt ∀t ∈ T . (4.90)
i∈I
The flexible charging load can be shifted within boundaries that result from the parking
behavior of EVs. Fig. 4.15 exemplarily illustrates the parking times of several EVs
over the modeling horizon of 36 hours. After each parking process, EVs should be fully
charged. When considering all EVs within a larger power system, e.g. a whole country,
a large number of cars with different parking processes each must be considered. In
order to reduce complexity, all parking processes with the same start and end time
are summarized. For an illustration of this approach, the bars representing identical
behavior are highlighted with identical colors that deviate from the standard light blue
tone in Fig. 4.15. In addition, the maximal considered parking duration is limited to
24 hours. During this time, EVs must be charged even though their parking time might
be longer.
With this reduction of complexity, |T | possible arrival times remain, which can be
combined with 24 different options for the parking duration. A table of values CT (ta , tp )
for each pair of ta and tp is the major input to the flexible charging model. In order
to guarantee that EVs are charged according to this table, the sum of charging loads
cltaux (ta , tp ) over all modeled time steps tm from the arrival time ta to the end of parking
92 CHAPTER 4. UNIT COMMITMENT AND LOAD FLOW MODELING
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
...
EV 14
EV 12
EV 11
EV 10
EV 9
EV 8
EV 7
EV 6
EV 5
EV 4
EV 3
EV 2
EV 1
EVs parking in 5th hour of the day
Figure 4.15: EV parking durations. The different EVs are illustrated on the y-axis and
their parking behavior on the x-asis. The colored bars indicate that the EV is parking
during the respective time frame.
As an approximation for the maximal charging capability of the connected EVs, this
load over all EVs must be below a maximal charging load CLt,max , which is computed
by the number of EVs parking, their maximal charging power, and some factor for
security margin, leading to
• Load develops into a step function that reflect the optimal operating points of
thermal power plants.
• Flexibility allows for more efficient power plant operation and leads to a reduction
of costs and CO2 emissions.
The electricity demand for “Mean” and for “Dumb” are very similar which is in contrast
to other research (e.g. Kefayati [119]). Reasons for this lie in the constraints that require
EVs to be fully charged after each parking event and the possibly smaller mileage of
cars in Singapore compared to Texas or other states/countries. Other parameters and
different constraints for charging like charging only at home might alter the results
significantly and should analyzed in future research.
6,000 6,000
Power (MW)
Power (MW)
5,000 5,000
4,000 4,000
4 8 12 16 20 24 4 8 12 16 20 24
Hour of the day Hour of the day
Power systems had to handle uncertain events since the very beginning of electrification.
Power plant or line tripping incidents occurred and operators had to balance those
unexpected events [114]. Even though load predictions were never accurate, accuracy
increased over time reaching a forecast error of 1-2% in most modern power systems
today [34]. Forecast accuracy decreased slightly from a standard deviation of 1.7% of
peak load to more than 2% of peak load after liberalization in Germany. However, new
techniques that promise to reestablish formerly known forecast quality are developed [29].
While the quality of forecasts has increased over time, more uncertain production has
been integrated at the same time, bringing uncertainty management (again) high on
the agenda of power system operators [138].
Based on the modeling framework as described in Chapter 4, this chapter provides
some approaches of how to deal with the challenge of uncertainty. Uncertainty in
operational planning means future generation can only be predicted with a certain
error, e.g. in the form of multiple possible scenarios or a bandwidth of generation.
Fig. 5.1 schematically illustrates a forecasting approach with multiple scenarios. The
red line in the figure represents the actual wind power production (ex post) while the
0.4
0.2
0
2 4 6 8 10 12 14 16 18 20
hours
Figure 5.1: Exemplary illustration of uncertain VRE generation and possible forecasts
94
5.1. CLASSIFICATION OF APPROACHES TO MANAGE UNCERTAINTY 95
blue lines denote possible scenarios (ex ante). Research must not only provide point
forecasts (one single scenario), but it should also specify ranges and the likelihood
of those forecasts [166]. Depending on the quality and characteristic of the forecasts,
the computational capacities, and the operational schemes, different strategies for
incorporating uncertain information into daily planning can be considered.
In this chapter, several concepts are introduced that allow analyzing the additional
challenges arising from the uncertainty in the system. The most prominent of them are
applied within the numerical studies of Chapter 7. Considering the modeling concepts
introduced, this chapter also points out the advantages of the temperature model
developed in Chapter 4 that can be realized once uncertainty is considered in future
research and planning.
• Cost function approximation (CFA): The cost function or constraints are adjusted
in a way that the system is prepared for uncertain events. The introduction of
reserves in power systems is an example for these policies and is described below.
• Value function approximation (VFA): The value of different possible states after
the decision is considered in the optimization. In the example of storage operation
(given in [171]), the value assigned to having a specific state of charge in a point
of time t is defined a priori and considered in the optimization process.
• Lookahead policies: Decisions are based upon expectations about the future
development of several parameters/variables. The basic lookahead model assumes
a deterministic forecast and optimizes the system accordingly. In a receding
manner, actions are taken and forecasts are updated. Forecasts can also be of
stochastic nature, which is usually called stochastic optimization in power systems.
96 CHAPTER 5. UNCERTAINTY IN POWER SYSTEM OPERATION
For the topic of power system operation, the most common approaches belong to a
combination of lookahead policies with cost function approximations. A description of
these approaches is given in the next sections. Afterwards, the advantages of including
the temperature model to uncertainty modeling are explained.
t1 t2 t3 … t365
1. Day (36 h)
2. Day (36 h)
3. Day (36 h)
In real-world operations, limited and changing information about future events are
the major issues requiring lookahead policies, e.g. there is no sense in planning power
plant operations for an entire upcoming year on an hourly basis. Price information is
not available and operating constraints concern several subsequent hours or days but
not entire years, except for dam storage hydro generation or maintenance planning.
The latter requires planning of entire years but with lower temporal resolution. When
power systems are modeled for system evaluation (as conducted within this thesis), a
computational limitation requires dividing a year into smaller optimization problems
even though all relevant information for the entire year is available. However, a positive
effect of using such receding horizons in system studies is that real world operation is
resembled. The receding horizon can also be a first approach to model uncertainty by
introducing (partly) changing forecasts (compare Section 5.4).
and tertiary control, which must be scheduled in addition to energy. The first two are
spinning reserves which means that only power plants that are on-line are allowed to
provide them. Tertiary reserve can also be provided by fast-starting units like single
cycle gas turbines or units that are kept in a warm status. To give an example of the
magnitude of reserves required, Table 5.1 depicts the requirements for the reserve types
in Germany.
Table 5.1: Reserves types and their activation time in Germany according to Ziems et
al. [213]
In terms of the classification given in Section 5.1, the reserve scheduling approach for
preparing for uncertain events can be interpreted as a cost function approximation
[170, 171]. Additional constraints have to be added to the system that will result
in higher system costs while guaranteeing system security. This section describes
the required constraints as they are also employed in the numerical experiments of
Chapter 7.
Ancillary services have to be provided even in power systems without any VRE generation
since load is uncertain and outages can occur at anytime. As soon as variable renewable
generation is introduced to the system, the adjustment of those reserves is discussed.
One option that is often discussed and applied for scenario calculations, e.g. by Ziems
et al. [108, 213], is to increase reserve requirement in times with VRE feed-in. Several
studies suggest that reserve requirements will increase with more VRE [59] while the
question of calculating the optimal amount remains unanswered. Paradoxically, reserve
requirements in many European countries have not been increasing but decreasing
with more VRE generation so far [96]. While increased variability might lead to
higher requirements on the one hand, some drivers, like improved forecasts, improved
scheduling due to 15-minute trading, and transnational and TSO cooperation, amongst
others, might reduce requirements on the other hand [96].
For the simulations in this thesis, the AGC approach is considered in its most basic form:
primary and secondary reserves must be provided at current levels which are given in
Table 5.1. This considers the tradeoff between efforts for reduction and the increase
through higher percentages of VRE integration. Tertiary reserves are not considered as
they might mostly be provided by off-line plants. The provision of reserves from off-line
power plants with their “hot” state is also described below. However, computational
limits have led to the decision of neglecting this feature in the large-scale simulations of
Chapter 7.
98 CHAPTER 5. UNCERTAINTY IN POWER SYSTEM OPERATION
Power plant constraints Power plants are limited in supplying reserves by both ca-
pacity and ramp rates. During the full period of offering reserves, the upward/downward
ability to ramp and the required capacity needs to be guaranteed.
The scheduled power pti minus the sum of all negative reserves rvt,r −
i , r ∈ R has to
remain above a minimum power output. In the other direction, the sum of scheduled
power pti plus the sum of all positive reserves rvt,r +
i , r ∈ R has to remain below the
rated capacity. Furthermore, power plants cannot provide upward reserves in t when
they will be shut down in t + 1, which leads to the following capacity constraints:
X t,r
pti − rvi ≥ pmin
i · vit ∀t ∈ T , i ∈ I, (5.2)
r∈R−
X
pti + rvt,r
i ≤ Pi
max
· vit − (Pimax − SDi )zit+1 ∀t ∈ T , i ∈ I. (5.3)
r∈R+
The next set of constraints ensures that power plants are capable of providing the
required ramps. As stressed by Morales-España et al. [151], the required ramp rates
must be available on top of the ramping that is executed for the planned schedules.
Fig. 5.3 illustrates the additivity of different ramping tasks.
Power
rt,2+
1 t,3+
3
r
1
12
(pt+1 − pt )
Figure 5.3: Ramping requirements for a power plant with scheduled power increase and
provision of positive secondary and tertiary reserves.
5.3. DETERMINISTIC APPROACH - SCHEDULING OF RESERVES 99
The blue line shows the scheduled ramping for meeting the energy schedule in a linear
matter. On top, the orange and the green lines represent the ramps for the provision
of tertiary reserves and secondary reserves that have to be added. Morales-España et
al. [151] assume a power-based UC model and define all constraints for reserves within
that paradigm. The power-based approach reflects technical capabilities of the plants
more accurately. Energy-based scheduling, however, is still the common practice in
most electricity markets and is therefore employed for this thesis. In energy-based
scheduling, power plants often ramp even faster than in power-based scheduling in order
to fulfill their block bid as accurately as possible. At the same time, they may be able
to change the ramping behavior in situations where reserves are activated which makes
the definition of constraints a difficult task.
The exact ramping process for the energy ramps depends on the market rules: markets
might allow a smooth ramping, schedule 15-min blocks, or force power plants to follow
the average hourly power output as closely as possible. In discrete steps, an exact
following of the schedule is not possible and a common rule in many markets is to fulfill
only the energy requirement. Fig. 5.4 depicts possible generation pathways of a fast
unit (blue line) and a slow unit (red line) that both satisfy energy schedules (orange
bars) but deviate from the power schedules (hourly average of energy schedules). This
figure illustrates the difficulty of finding the exact constraints for the maximally allowed
ramping. In the scenarios considered in this thesis, power plants are assumed to ramp
up the average power output of the energy schedules from pti to pt+1 i within one hour,
which is an optimistic assumption. During this whole ramp-up process, the power plant
has to be capable to provide the scheduled reserves.
Power
0 1 2 3 4 5
Time (h)
Figure 5.4: Energy schedules and possible behavior of power plants (illustrative only).
The blue line shows a power plant that is capable of resembling the block bid reasonably
well while the red line symbolizes a power plant with slow ramping that only provides
energy over an hour but deviates from the block bid in terms of power. Author’s graph
based on [61].
100 CHAPTER 5. UNCERTAINTY IN POWER SYSTEM OPERATION
According to Fig. 5.3, the complete secondary reserves, one third of the tertiary as well
as one twelfth of the scheduled power increase have to be provided after 5 minutes.
Thus, the ramp-up capability for those five minutes is restricted by (5.4) and (5.5):
1 i + 1 +
(pt+1 − pit ) + rvt,sec
i + rvt,ter
i ≤ RUi · 5 ∀t ∈ T , i ∈ I, (5.4)
12 3
1 − 1 −
(−pit+1 + pit ) + rvt,sec
i + rvt,ter
i ≤ RDi · 5 ∀t ∈ T , i ∈ I, (5.5)
12 3
with RUi /RDi being the maximal possible up/down ramps per minute of a power plant.
For the simulations in this thesis, the constraints are assumed to dominate the ramp
requirements after 15 minute ramping. This simplification is valid as long as the
maximal ramping speed is the same for the first 15 minutes as for the first five minutes.
Due to the conservative parameter assumption used in the scenarios of Chapter 7, it
is assumed that power plants can ramp with RUi /RDi for the entire hour. If more
detailed parameters for power plant ramping are available, different values for 5 min,
15 min, and hourly ramping could be included.
Here, only primary reserves are considered separately, as ramp capabilities for primary
reserves RUiprim and RDiprim might be higher since plants have to ramp up/down for
30 seconds only. Further, primary reserves are only employed in the extremely short
term and are not required anymore after five minutes. The constraint for primary
reserves are modeled by
+
rvt,prim
i ≤ RUiprim · 0.5 ∀t ∈ T , i ∈ I, (5.6)
t,prim−
rvi ≤ RDiprim · 0.5 ∀t ∈ T , i ∈ I. (5.7)
Due to data unavailability, the ramp rates for primary reserves are set to the same
value as the overall ramp rates (RUiprim = RUi ) in the numerical studies. This can be
interpreted as a conservative assumption concerning power plant capabilities.
0.8
0.6
0.4
0.2
0
Base Flex1 Flex2 Flex3
Power Plant Type
Figure 5.5: Operational range of a power plant with different options for flexibility
enhancements. Own illustration based on Ziems et al. [213].
Power plants must be in the “hot” state (wti =1) in order to be able to provide tertiary
reserves. The reserves provided by “hot” but off-line power plants are indexed with
“stby” for stand-by reserve rvt,stby
i , leading to
rvt,stby
i ≤ wti · Pimax ∀t ∈ T , i ∈ I. (5.8)
Power plants can only be in the “hot” state whenever starting within the activation
time of the reserve of x-minutes is possible. Depending on the maximal temperature
increase ∆tempmax
i in 1/hour, this requirement can be formulated by
The maximal available reserves are limited by the power output that can be achieved
within the 15-minute activation time of tertiary reserves. A possible assumption is
that power plants are at minimum power output Pimin as soon as a temperature of 1 is
achieved. Afterwards, reserves above this minimum output can be provided by ramping
up with the maximal ramping speed RUi in the remaining time. The constraint can be
formulated by
1 − tempit
1
rvt,stby
i ≤ Pimin +RUi · 15 − max
· 60 +(1−wti )·RUi · ·60 ∀t ∈ T , i ∈ I.
∆tempi ∆tempmax
i
(5.10)
The maximal temperature increase ∆tempmax i can also have values above one which
does not change anything with respect to the hourly start-up process (see Section 4.6.2).
Yet, it allows ramping to higher values for reserve provision. The last part of equation
(5.10) has to be added to prevent the term being negative for long remaining start-up
times, i.e. for a lower current temperature tempit and/or low heat-up speed ∆tempmax i .
102 CHAPTER 5. UNCERTAINTY IN POWER SYSTEM OPERATION
As power plants operate above their minimum output whenever started, the reserves
offered by off-line units must be above this value:
rvt,stby
i ≥ wti · Pimin ∀t ∈ T , i ∈ I. (5.11)
Finally, equation (4.56) from Section 4.8 is required to guarantee that only off-line
plants can provide standby reserves (power plants can be either online or in hot state).
Concerning the real-world application of the approach, the exact requirements of the
power plants must be considered. Several power plants might not be allowed burning
fuel at these low levels and dumbing of heat would be required. Other power plants
might require technical reconfiguration before this status can be employed.
Storage constraints Reserve provision is not restricted to power plants but storage
can be employed as well. Storage is modeled linearly without any minimum power
output requirement. Thus, capacity constraints for reserve provision can be defined
by equations (5.12) and (5.13). The power output pts of storage can be negative when
pumping or positive when the turbine is activated. The maximal power capacity of the
turbine and the pump is assumed to be symmetric leading to the following constraints:
X
−pts + rvst,r max
s ≤ P Ss ∀t ∈ T , s ∈ S, (5.12)
r∈R−
X
pts + rvst,r max
s ≤ P Ss ∀t ∈ T , s ∈ S. (5.13)
r∈R+
Additionally, the energy content ests must be positive even after provision of scheduled
energy and reserves:
X
ests + psts − rvst,r
s ≥ 0 ∀t ∈ T , s ∈ S, (5.14)
r∈R−
Storage plants have to respect ramping constraints in the same way that power plants
do when providing reserves. The change of power output within 5 minutes is restricted
to
1 1
pst+1 − psts + rvst,sec+ · rvst,ter+
s s + s ≤ RUs · 5 ∀t ∈ T , s ∈ S, (5.16)
12 3
1 1
−pst+1 + psts + rvst,sec− · rvst,ter−
s s + s ≤ RUs · 5 ∀t ∈ T , s ∈ S. (5.17)
12 3
5.4. STOCHASTIC APPROACH BASED ON SCENARIOS 103
5.4.1 Method
Single-stage problems The most essential notion of a stochastic problem is to find
the minimum of the expected value over all possible realizations of the uncertain variable,
e.g. the load or production from renewable sources. For the base form of the UC
problem, this can be formulated with scenarios ω ∈ Ω for the uncertain demand Dt,ω
and the probability of occurrence πω by [52]
X X
min πω · Ai vit,ω + Bi pt,ω t,ω
i + cui , (5.18)
ω∈Ω i∈I,t∈T
X
s.t. pt,ω
i = D
t,ω
∀ t ∈ T , ω ∈ Ω, (5.19)
i∈I
the base form of the UC model, this two-stage model may be described by [36]
X X X
min Ai vit + cuti + πω Bi pt,ω
i , (5.20)
i∈I,t∈T ω∈Ω i∈I,t∈T
X
s.t. pt,ω
i =D t,ω
∀ t ∈ T , ω ∈ Ω. (5.21)
i∈I
The approach could be modified by assuming quick starting units that can also be
started during the intraday planning. Such a model was presented by Carøe and
Schultz [36] and integer variables are then required in both stages.
Another approach to distinguish the two stages is the temporal dimension. Meibom et
al. [144] employ a stochastic UC model where fixed UC (and dispatch) decisions are
made for the three succeeding hours of the “here and now”. Afterwards, the second
stage problem (or multiple additional stages) takes the first three hours for granted and
optimizes the system with respect to the different scenarios given. In order to give a
mathematical description, the set of considered periods T is split up into periods with
fixed demand T det and periods with uncertain demand T sto . Therewith, the problem
may be formulated as
X X X
min Ai vit + Bi pti + cuti + πω Ai vit,ω + Bi pt,ω t,ω
i + cui , (5.22)
i∈I,t∈T det ω∈Ω i∈I,t∈T sto
X X
s.t. pti = Dt ∀ t ∈ T det , and pt,ω
i = D
t,ω
∀ t ∈ T sto , ∀ω ∈ Ω. (5.23)
i∈I i∈I
The system operator can change the commitment/scheduling plan (first stage) whenever
new information on the forecasted generation is available. An increasing frequency of
forecast updates thereby significantly improves decision making [144, 200].
An example of an implemented stochastic optimization model can be found, for instance,
in Meibom et al. [144]. The paper studies Ireland’s power system with significant
amounts of wind production. The production schedules (including the UC decisions)
are updated in a rolling manner, i.e. every three hours, whenever improved information
on future wind production becomes available. The study found that the additional costs
rising from uncertain wind and demand realizations are, compared to overall operational
costs, very small. The study also found that power systems with higher shares of flexible
power plants, i.e. gas turbines, are less influenced by system uncertainties than systems
with high percentages of base load plants, i.e. coal fired plants. Abrell and Kunz [3]
compare a stochastic model to a deterministic model in order to evaluate impacts from
VRE integration and find a shift towards operation of more flexible power plants as
soon as stochastic planning is considered. Those two studies are examples that show
the relevance of uncertainty consideration when evaluating the value of power plant
portfolios and the value of enhancing their flexibility.
While the approach is intuitive and several studies show the benefits over deterministic
approaches [162], there are two major drawbacks of the idea:
• Generating scenarios requires detailed information about forecast errors and their
development over time. Furthermore, the probability of occurrence has to be
5.4. STOCHASTIC APPROACH BASED ON SCENARIOS 105
defined for each scenario, which is hardly possible. The latter question is tackled
for instance by Pinson [166, 167] or by Lee et al. [134].
0.4
0.2
0
0 6 12 18 24 30 36
1
0.8
0.6
CF
0.4
0.2
0
0 6 12 18 24 30 36 42
1
0.8
0.6
CF
0.4
0.2
0
0 6 12 18 24 30 36 42 48
Hour of the day
is depicted in the figure on the bottom with a deterministic part from hour 13 to 19.
Occurring deviations in the deterministic hours are assumed to be balanced by speed
control and AGC.
As the effects of uncertainty are only analyzed qualitatively in this thesis, a very simple
approach for generating this changing forecast for each renewable generation technology
is employed. The major assumptions of the forecasts are: a decreasing accuracy with
longer time horizons k, a forecast that deviates from deterministic generation with
a normally distributed random number, and a higher probability for deviations in
the same direction as in preceding periods by taking into account the deviation of
previous period ∆t−1 . The calculation of the forecasted generation pbt is described in
mathematical terms by:
√
pbt = N(µ, σ) with µ = pt + ∆t−1 and σ(k) = σ 0 k (5.24)
∆t−1 = pd
t−1 − pt−1 . (5.25)
The capacity factor has to remain within [0,1] so that all values above or below are
set to either 1 or 0, respectively.
√ The standard deviation is increasing by the forecast
horizon k with: σ(k) = σ k. Here, a value of σ 0 = 0.02 is assumed. As the same
0
parameters are assumed for all types of VREs in all locations, this is only a rough
estimation and more research is required for a sound analysis beyond the qualitative
statements achieved in this thesis. The standard deviation with this assumption ranges
from 2% for the upcoming hour to 12% for planning 36 hours ahead which is in the
5.5. ALTERNATIVE: ROBUST OPTIMIZATION APPROACH 107
same magnitude as the RMSE of actual predictions (see literature in Section 3.1 and
Lenzi et al. [136]).
This approach was developed as a simple intuitive solution but might be categorized as
ARMA (Autoregressive-Moving Average) model, where ∆(t − 1) can be seen as both
the moving average and as autoregressive term. However, the development of stochastic
scenarios is not the focus of this thesis and detailed discussions on that issue go beyond
the purpose of the chosen method. Further reading on generating adequate forecasts
can be found in Barth et al. [10], Pinson et al. [167], or von Roon [179], amongst others.
with Ω(x, d) being the solution space resulting from the first stage decisions and the
realization of d.
The approach showed promising results as scalability to multiple uncertain variables is
easier and distributions are not required. Still, there are problems with the solution
algorithm that require solving a bilinear problem and might not converge to feasible
solutions. The general solution idea is to build the dual of the second-stage scheduling
problem in order to obtain a single maximization problem. This, in turn, requires
solving a bilinear problem. All in all, the approach must be considered when thinking of
incorporating uncertainty in UC. However, solving the bilinear problem might require
new developments of algorithmic procedures that enable solving the problem with some
guarantees of optimality and feasibility.
108 CHAPTER 5. UNCERTAINTY IN POWER SYSTEM OPERATION
An illustration of the maximal possible up and down ramps is given with Fig. 5.7 on
the right and the maximal scheduled ramps can be defined to (vret,max
n − vret−1,min
n )
5.6. ALTERNATIVE: RAMP AND CAPACITY RESERVES 109
and (vret−1,max
n − vret,min ), respectively. The definitions of the maximal up and down
ramps as well as the illustration of those ramps highlight the purpose of scheduling
below forecasted values: the required maximal ramps can be reduced.
V REmax
vretmax
V REmin vret−1
Power (MW)
Power (MW)
max
vret
Max ramp-down Max ramp-up
vret−1 vretmin
vremax vret−1
min
vremin
6 12 18 24 t-1 t
Time (h) Time(h)
Figure 5.7: Determination of the maximal required ramps according to scheduled VRE
generation. The figure on the left shows the forecasted range (dotted lines, range from
V REtmin to V REtmax ) and the scheduled range (in blue, range from vremin
t to vremax
t ).
vret,R+
n = (vret,max
n − vretn ) + (vret−1 − vret−1,min
n ) ∀n ∈ N , t ∈ T , (5.30)
vret,R−
n = (vrent−1,max − vret−1
n ) + (vretn − vre t,min
) ∀n ∈ N , t ∈ T . (5.31)
After defining the required ramp reserves at each node, the system constraints can be
formulated. These include the provision of demand Dnt at each node n and period t by
thermal producers pti and by nominal production of renewable generation vretn at all
nodes:
X X X
pti = Dnt − vretn , ∀t ∈ T . (5.32)
i∈I n∈N n∈N
The capacity reserves guarantee the integration of every possible VRE generation
outcome within the scheduled range. This can include decreasing power output of
110 CHAPTER 5. UNCERTAINTY IN POWER SYSTEM OPERATION
t,R+ t,R−
with V[
RE n and V[ RE n being the maximal deviations from the nominal forecasted
ramp, which is a parameter that has to be defined by the system operator a priori.
The infimum functions guarantee that ramp requirements are neither higher than the
maximal deviation from the scheduled range nor higher than the maximal deviations from
the forecasted range. When implementing the approach including an MIP formulation
of the infimum function, the reader is referred to the original article [147].
Unit constraints When providing these reserves, each unit has to respect individual
constraints, which include the general minimum power output, the commitment logic,
and the ramp constraints as described in equations (4.13)-(4.18). Additional constraints
include the capacity reserve restrictions which are similar to those of (5.2) and (5.3) by
replacing the reserves with rvt,C+
i and rvt,C−
i .
Finally, all reserves have to be positive and several constraints have to hold that
interrelate the power and ramp capacity reserves which are described in detail in [147].
−rvt,R−
i ≤ rdpt,max
i − rdpt−1,max
i ≤ rvt,R+
i ∀t ∈ T , ∀i ∈ I, (5.37)
−rvit,R− ≤ rdpt,min
i − rdpt−1,min
i ≤ rvt,R+
i ∀t ∈ T , ∀i ∈ I. (5.38)
In order to guarantee the balances of demand and supply and the network constraints
in all cases, reserve deployments for minimal and maximal VRE generation are defined
by the maximal deviation of VRE generation from the nominal case:
X X
rdpt,max
i = (vretn − vret,max
n ) ∀t ∈ T , (5.39)
i n
X X
rdpt,min
i = (vretn − vret,min
n ) ∀t ∈ T . (5.40)
i n
5.7. CONCLUSIONS FROM UNCERTAINTY CONSIDERATIONS 111
For both the maximal and the minimal VRE generation and the respective reserve
deployments, network constraints have to be fulfilled. The constraints are the same as
in equation (4.85), but VRE generation and reserve deployments are added. Constraint
(5.41) guarantees line constraints for maximal generation and constraint (5.42) the same
for minimal generation:
!
X X
L,max
PTDFm pti + rdpt,max + vret,max − Dnt ≤ fm
L,max
−fm ≤ n i n
n∈N i∈In (5.41)
∀t ∈ T , ∀m ∈ L,
!
X X
L,max
−fm ≤ PTDFm
n pti + rdpt,min
i + vret,min
n − Dnt L,max
≤ fm
n∈N i∈In (5.42)
∀t ∈ T , ∀m ∈ L.
Including the grid constraints for the both extremes guarantees that reserves are not
only available within the system but can also be provided to the nodes where required.
Objective function The objective function considers the nominal case as well as the
extreme cases for VRE generation, thus leading to a two-stage stochastic model with
the objective function
X h i
Ai vit + cuti + Bi γ1 pti + γ2 pti + rdpt,max t t,min
min i + γ3 p i + rdp i , (5.43)
i∈I,t∈T
with γ1 + γ2 + γ3 = 1 being the weights for the three scenarios. The model framework
as proposed by [147] does not schedule energy but ramps. However, the approach is in
principal adjustable to energy scheduling as well.
This method is worth being considered for future system studies as major obstacles of
scenario-based stochastic modeling and robust modeling can be overcome: the model
can be formulated as MIP and knowledge about scenarios and probability distributions
is not required. The inclusion of the network constraints for the upper and lower bounds
of VRE generation can be seen as a further advantage.
• Deterministic reserves provision: The “hot” state can be introduced to consider the
reserve provision from off-line units as described above with equations (5.8)-(5.10).
112 CHAPTER 5. UNCERTAINTY IN POWER SYSTEM OPERATION
• Changing forecast (single scenario): Whenever forecasts are updated, the start-up
and commitment decisions for the next hours might be reconsidered reflecting the
costs for interrupted start-up processes without any extra variables. Additionally,
different costs for different start-up speeds as introduced in Section 4.7 could be
considered in such a context.
While there are alternative approaches which might allow VRE integration at lower
costs, reserves and reserve adjustments have been used in real-world applications until
now. As being the standard method at present, it will also be applied for the large-scale
system simulations in the evaluation chapter of this thesis (Chapter 7). Additionally,
the method of changing forecasts is considered in several scenarios in order to estimate
additional effects resulting from uncertainty. These scenarios give an outlook on the
size and quality of additional effects that can be further studied from thereon.
Part III
Evaluation
114
Chapter 6
In order to evaluate the different flexibility options, a model that reflects major char-
acteristics of a real-world power system is required. A system that is currently in
the transition to integrate large shares of VREs is the European power system. The
European Union its member countries have committed themselves to targets for a signif-
icant reduction of their CO2 emissions in the next decades. One important measure to
achieve this goal is the introduction of renewable energy sources in the power systems.
The European power system is therefore an ideal test case for the modeling framework
and allows to gain insights to the value of different flexibility options which might help
policy makers and system planners. This chapter presents an overview of the dataset
developed. The dataset represents major aspects of the real European power system
but remains an abstract test case for the course of this thesis. It lays the foundation
for further development and calibration of a power system model employed for policy
analysis and infrastructure planning at Technical University of Munich (TUM).
A country with especially high targets in renewable generation is Germany. Here, the
discussion on increasing flexibility in generation has been prevailing (see e.g. publications
on the topic by Brauner et al. [27] or Ziems et al. [213]). The country is connected to many
neighbors and electricity is exchanged continuously. Still, in some analyses, Germany
is considered as an island that must balance renewable generation independently.
Discussions in some Eastern European countries to block electricity imports from
Germany in order to prevent load flows [47, 174, 187] might make this assumption a
relevant policy scenario. For these “Germany-only” scenarios, relevant data is extracted
from the European dataset and all connections to neighboring countries are cut off.
The contributions of developing the described dataset based on publicly available data
can be summarized to the following:
• A test system is established that allows applying the theoretical modeling frame-
work of Chapter 4 in a realistic environment.
115
116 CHAPTER 6. DATASET DEVELOPMENT
• A model platform to analyze flexibility options at the German and European level
is set up. As the model data is deduced from a real-world power system, results
can be highly valuable for future system planning. This is especially true for the
general rules and system suggestions that are derived from the results.
• The models can be seen as the basis for future research and policy consulting (A
first consulting project for the Bavarian Ministry of Economic Affairs and Media,
Energy and Technology has already been conducted using the model and dataset
of this thesis [86])
The distribution of load to the regions is illustrated in Fig. 6.1 with colors indicating
the consumption relative to the respective area.
6.3. INTER-AREA TRANSMISSION 117
Demand (MWh/km^2)
0.05 - 0.19 0.66 - 0.91
0.19 - 0.27 0.91 - 1.30
0.27 - 0.43 1.30 - 2.06
0.43 - 0.54 2.06 - 3.00
0.54 - 0.66 >3
Figure 6.1: The 268 model regions and their electricity consumption relative to their
area
Electrical centers and line length For each region, the “electrical center” is defined
as a geographical center of all substations available from Platts PowerVision [168]
(commercial database). In some cases, the position of the electrical centers are moved
closer to actual load manually, e.g. closer to large cities. The electrical centers are the
endpoints of the connection lines and are depicted in Fig. 6.2.
118 CHAPTER 6. DATASET DEVELOPMENT
AC DC
Figure 6.2: Illustration of the reduced transmission grid model consisting of AC and
DC lines. The thickness of the lines gives a qualitative impression of the differences in
capacity.
Line capacities and reactances (AC lines) Information about the number and
voltages of lines from one region to another is obtained from Platts PowerVision [168]
and combined with the map of transmission lines from ENTSO-E [64]. The DC load
flow model requires calculating the matrix of susceptances B to subsequently compute
the PTDF matrix according to equation (4.66). The susceptances can be derived from
reactances X according to
X
B=− , (6.2)
R2 + X2
The base voltage system of the network is set to 380 kV and all reactances X have to
be transformed to this base voltage level accordingly. Reactances in the base voltage
system are then noted by X ∗ . The transformation is described by
∗ 380 kV
X =X . (6.5)
Vline
Maximal transferable power for each connection is computed by the surge impedance
loading (SIL) values as given in Table 6.1. SIL values present the (natural) power
loading at a set point, i.e. reactive power is neither produced nor absorbed.
Table 6.1: Reactances and SIL values for high voltage transmission based on Egerer et
al. [56] and Kundur [129] and internal discussions
For computing the maximal allowed power flow, the SIL values have to be multiplied
by a loadability factor LA(length) according to the St. Clair curve [42], representing
different limitations depending on the lengths of the transmission line. For short lines
of up to 80 km, thermal limits constrain the maximal flow. For longer lines in the
range of 80 km to 320 km, the voltage drop becomes the limiting factor and for even
longer lines, angle stability issues become dominant [129]. For the dataset developed,
the St.Clair curve and resulting loadability factors LA(length) are approximated by six
discrete steps according to Table 6.2.
When comparing reactances and line capacities to other reduced power system data, e.g.
Hasche [88] or Egerer et al. [56], reactances are similar. In terms of maximal capacity,
values differ significantly. The reason lies in the different methods for line limitations,
e.g. the use of a thermal transmission limit instead of the SIL approach.
Different cases must be distinguished for computing reduced line parameters. First,
reactances X for individual connections m ∈ L must be computed from voltage levels
and line length according to equations (6.2)-(6.5). Then, aggregated values are computed
according to the descriptions and formulas below. Lines with a voltage of 110 kV and
below are not considered and parameters of DC lines are computed separately.
120 CHAPTER 6. DATASET DEVELOPMENT
• One connecting line: In case of only one connecting line, the calculation of the
equivalent reactance is simple and defined by voltage and length of the line:
L,max
fm = SIL(voltagem ) · LA(lengthm ), (6.6)
Xm = X ∗ . (6.7)
• Multiple connecting lines with same voltage levels and same reactances Xi0 = X ∗ :
The maximal capacities of multiple lines add up. Concerning the reactances, the
lines are regarded as a parallel circuit:
L,max
fm = n · SIL(voltage) · LA(lengthm ), (6.8)
1 X∗
Xm = Pn 1 = . (6.9)
i=1 X 0 n
i
• Multiple connecting lines with different voltage levels: The principal idea of a
parallel circuit remains but reactances Xi0 between lines differ resulting in:
n
X
L,max
fm = SIL(voltagei ) · LA(lengthm ), (6.10)
i=1
1
Xm = Pn 1 . (6.11)
i=1 Xi0
In this case, the lower voltage lines might limit the overall transmission capacity [8],
and thus, the capacity is overestimated. Applying reactive compensation might
help in reducing the problem and make the approach a reasonable assumption.
HVDC Lines In contrast to AC lines, high-voltage direct current (HVDC) lines can
be controlled by the operators and line flows are not determined by the reactances.
Only a maximal capacity is required as data input and values are set individually for
each line according to the scenario considered.
Simplified N-1 In order to represent security constraints, the maximal line capacity is
L,max
reduced to 70% of the above computed fm . This is a simple approximation and does
e.g. not consider the different quantities and capacities of individual lines which are
aggregated in the reduced grid. More sophisticated approaches could consider outage
transfer distribution factors (OTDFs) for the inter-zonal line corridors [40,192], however,
this is not the focus of this thesis.
Wind and solar The installed capacity for renewable technology per region is defined
in a similar approach as the aggregation of grid points in the calculation of capacity
factors (CF) by Janker [116]: Regions with higher FLHs will install greater capacities.
An exponential approach is used to compute the share of of capacity ψn for a specific
region n in country k by
FLH2n
ψn = P 2 ∀n ∈ Nk . (6.12)
n∈Nk FLHn
The installed capacities of wind and solar for the three model years are depicted in
Fig. A.1 in the Appendix.
Hydro Concerning hydro power, open data sources (mainly Enipedia of Delft University
of Technology (TU Delft) [49] and Wikipedia [209]) are used to distribute the installed
capacity to the regions.
Biomass and geothermal Hardly any data is available on the geographical distribu-
tion of biomass or geothermal sources. Therefore, plants are distributed proportionally
to electricity consumption. Especially for geothermal generation, this might be an
erroneous assumption as geothermal fields are very local occurrences. However, since
the overall installed capacity is low, a small error of this estimation appears tolerable.
Figure 6.3: The FLH for PV (left) and wind (right) generation in the model regions
structure and is used directly. The different aggregations per region in the dataset
of [116] are employed depending on the technology:
• Wind Onshore: For each of the model regions, the time series for the best grid
point is used. Concerning the turbine height, 40 m or 80 m above ground are
employed in order to compensate for the over-/underestimation of wind speeds for
several regions. Mainly regions closer to the Alps and on the Iberian Peninsula
are underestimated. Thus, the 80 m turbine model is employed there.
• Wind Offshore: The linear interpolation of grid points per region is employed.
The turbine height is assumed to be at 60 m.
The resulting FLH for wind onshore and for PV are depicted in Fig. 6.3.
with a simple rule: In mountainous regions, 30% of the hydro capacity is availably as a
storage plant. An assumption that is reached by additionally installing pumped hydro
capacity of such size. The storage volume of those “proxy” pumped hydro plants is 6
hours of maximal capacity. Their losses are 5% for charging and 5% for releasing water.
In contrast to real pumped hydro storage, they are not allowed to participate in reserve
markets. With these proxy pumped hydro plants, the reservoir type hydro plants is
modeled and generation can be shifted within the 36 hours optimization time frame.
Tests showed that, especially in Norway, this assumption allowed to reduce curtailment
(negative slack) tremendously in the model for the year 2015; revealing the importance
of this assumption.
As the seasonality of real-world storage is represented by the monthly generation, the
addition of pumped hydro storage might be a valid approximation of the additional
system flexibility. In further work with the model, the ideal capacity of proxy pumped
storage should be evaluated by model calibrations.
Biomass Biomass is often seen as a further source of flexibility while currently most of
biomass production is used as a constant source of supply. Within this thesis, biomass
is also modeled as a constant source of supply with a utilization rate of 6000 FLHs per
year.
Geothermal Geothermal and all other power sources mentioned in EU Energy Trends
2013 [69] are summarized and run with a constant power output and a utilization rate
of 8000 FLHs per year.
in the Appendix show the installed capacities of coal, lignite, nuclear, gas, and oil power
plants.
In contrast to renewable generation, no scenarios on the capacity change over the next
decades are made. The thermal power plant fleet is kept at a status quo for 2025 and
2035. Decommissioning of plants would mainly influence capacity-relevant questions. It
would have less impact on the flexibility-concerned questions addressed in this thesis.
When applying the model to other concrete policy or investment decisions, data on
decommissioning and new installations must be compiled.
Parameters For modeling power plant behavior in UC models, several parameters are
required. The parameters for the base scenario are summarized in Table 6.3. Most of
them are own assumptions based on experience from industry projects and literature
(e.g. [27, 56, 128, 198, 213]). Parameters are assumed to be the same for power plants
of the same fuel type and year of construction. Individual plant characteristics are
neglected, which allows for future improvements to the database in this regard. As
these power plant parameters determine their flexibility, they are varied in scenarios
that analyze effects of increased power plant flexibility (see Table 7.1 in Section 7.2).
Two additional parameters are introduced with the temperature model: the heatloss
factor λ and the maximal heating speed H max . The latter is often described in literature,
even though seldomly used in UC models. The heatloss factor λ, however, is not directly
available from current sources but can be derived from the minimal off-time after which
a start-up is called “cold” start. Here, a cold start is defined whenever the temperature
of the power plant is below 10% of temperature during operation. This will be the case
after cooling times of around 50 h for coal, 60 h for lignite, 75 h for nuclear, 25 h for
combined cycle gas turbines (CCGT), and 7 h for open cycle gas turbines (OCGT) and
oil power plants. Given this assumption, λ can be calculated by
ln 0.1
λ= . (6.13)
cooling time
Afterwards, the maximally allowed heating is estimated from the time required for
an entire cold start; values are approximated from the start-up times given in [183].
Readers must keep in mind that all parameters are approximations and highly differing
values exist throughout the literature (see e.g. Hasche [88] for a comparison).
Parameters that are discussed intensively and which show a high variation are the start-
up costs. The costs for a power plant start-up result from additional fuel requirements
for heating as well as from wear-and-tear. Especially the wear-and-tear costs are highly
uncertain and companies do not publish the values they are assuming for internal
planning. In countries with increasing shares of renewable energy sources, several power
plants might be shut down in the next years. This dramatically reduces the current
value of the plants and hence the costs of damage. In other cases, newly built plants
might still be operated to minimize damage and extend lifetimes.
An extensive and often cited study on cycling and start-up costs was done by the
National Renewable Energy Laboratory (NREL) [128] based on a utility questionnaire.
6.5. THERMAL GENERATION 125
Herein, the costs show a very high variation, e.g. the capital and maintenance costs of
a small (< 300 MW) coal-fired sub-critical power plant range from around 50 $/MW to
more than 400 $/MW. Table 6.4 depicts the cost values that were identified by [128], i.e.
the median and the 25th/75th percentile of all power plants from the questionnaire. It
must be noted that those values are assumed to be lower bounds for start-up costs. For
this reason, values used within this thesis are oriented around the 75th percentile. In
the case of coal, an average of small and large power plants is assumed when calculating
the costs.
The sum of F and V is set to the 75th percentile value of a cold start as given in
Table 6.3. For CCGT and coal, hot start costs are assumed to be at around 50% of
a cold start. As hot starts can already include several hours of cooling, the variable
costs are set to a slightly higher value than the fixed costs. For gas turbines, on the
other hand, fixed costs have a higher share: costs for a hot start are more than 50% of
costs for a cold start. Lignite and nuclear power plants are assumed to be slightly more
expensive than coal power plants in terms of start-up costs [56, 213]. The exchange
rates between $ and A C are neglected as costs are lower bounds. In a study by Keatley
et al. [118], the non-fuel cold start costs (only damage and maintenance) of a 400 MW
are estimated at 73111 A C, which corresponds approximately to 180 A C/MW. In other
studies, however, values for start-ups are much lower.
The efficiency of power plants depends on the operating point and the year of power plant
construction. In the maximal power point, which is assumed to be the most efficient
point of operation, the efficiency is computed according to the year of construction by
In the scenario calculations, no minimum up- or downtimes are considered as they are
assumed to be non-existent [88]. In a report of the Eurelectric [68], minimum downtimes
are set to zero, which is a further indicator that this assumption is correct.
126 CHAPTER 6. DATASET DEVELOPMENT
6.7 Storage
The model considers short term pumped hydro storage (optimization horizon is only
36 hours). The storage data is based on publicly available data from Eurelectric [67]
which includes turbine power per country. The reservoirs are assumed to be able to
store 6 hours of full turbine power. The distribution to the regions is conducted by
individual research on storage and several open source data [49, 209]. The efficiency
of the pumped hydro storage is 90% for pumping and for turbining which results in a
cycle efficiency of 81%.
• Combined heat and power plants (CHP): CHPs might be restricted in their
operational range. In this thesis, the operation of CHPs is oriented on electricity
markets and neglects constraints from heat supply. This might overestimate
system flexibility and improved approaches could shed light on this question.
• Wind generation onshore and offshore: The database of Janker [116] is a global
database that includes all VRE generation. Underlying data are reanalysis data
from NASA [177]; a calculation of CFs was conducted whereby several parameters
like turbine height, turbine type, and many more have to be considered. Data
is calibrated for Germany and shows larger deviations for other countries and
regions across the globe. An individual calibration for all European countries
could improve the dataset further.
• Power plant database: The goal was to develop a model that can be made available
to the public. Details on power plants might still not be accurate for all regions
but a steady process of improvement will increase accuracy in the next years of
model employment.
• Capacity retirement: Capacity retirement is not considered so far while there will
be several changes in Europe’s thermal power plant structure like the nuclear
phase out in Germany. Future research could develop a European retirement and
investment plan to consider dynamic changes in the conventional power plant
portfolios.
• Transmission network physics: The same is true for the transmission network
which is also not a perfect dataset but an approximation that should be improved
over time. The zonal reduction and the resulting PTDF should be calibrated, e.g.
by setting up a model of the entire high voltage transmission system.
• Transmission network politics: Other constraints that are not represented in the
model and dataset are legal issues concerning power exchange between countries.
The limits of cross-country trading are not the physical constraints but the ex-ante
defined maximal capacities. Those so-called net transfer capacities (NTC) are
derived from physical limitations which are valid for all power flow situations
independent of the actual situation in a specific point of time.
Chapter 7
In this chapter, the effects of adding flexibility sources to a power system are evaluated.
As mentioned in the dataset description (cf. Chapter 6), the employed scenarios should
be understood as general test cases and results will give insights into the effectiveness
of different flexibility measures in large-scale power systems in a general sense.
As the major focus of this thesis lies on the model development for representing thermal
power plants in UC, there is also a focus on the effects from increased power plant
flexibility in the numerical studies. Still, various other experiments on grid extensions
and grid flexibilizations are conducted in the German as well as European context to
illustrate the powerfulness of the developed model.
• Renewable integration: The major reason for power systems to become more
flexible is the integration of VREs. Generation that cannot be integrated has to be
curtailed, e.g. because of insufficient ramping or because of insufficient transport
capacities. The amount of curtailed production serves as the most important
indicator for effective measures.
128
7.1. MODELS AND MEASURES 129
• Costs: Operating costs that include fuel costs as well as start-up costs (including
wear-and-tear costs). The differences in costs that can be achieved by certain
measures have to be compared to the base scenario. Costs are highly related to
the curtailed generation but include other aspects like start-up costs or a shift
towards cheaper technology as well.
• Emissions: Overall CO2 emissions can be compared between scenarios with newly
introduced technologies and the base scenario. Again, the curtailed generation
is a first proxy for this variable but changes in technology can have additional
effects.
Measuring security of supply in all aspects is more complicated and requires a model
with more technical details. One aspect of security of supply, however, is the ability to
fulfill energy schedules and provide the demanded energy in every instance. The model
in this thesis uses a so called “slack” variable whenever only an insufficient amount of
energy can be provided and load is lost. The amount of “slack” required is interpreted
as indicator for security of supply. Analyzing the results showed that “slack” is only
required in the scenarios with changing forecasts; load can be provided throughout
the year in all other scenarios and, therefore, the measure is not discussed for these
scenarios.
• The basic unit commitment constraints are employed including equations (4.10)-
(4.16) for cost definitions and basic technical constraints. The logic constraints
according to (4.23) and (4.24) are employed for all power plants that are modeled
with binary decisions.
• DC load flow with the PTDF approach is modeled by equation (4.85) and equations
(4.69)-(4.70) guarantee that line constraints are respected.
• Whenever reserves are considered (models named with “-ctr”), the equations from
Section 5.3 are applied for the control areas. This includes reserve requirements
for the different types according to (5.1), the technical constraints of power plants
(5.2)-(5.7) and the additional constraints for storage plants providing reserves
(5.12)-(5.17).
130 CHAPTER 7. EVALUATION OF FLEXIBILITY SOURCES
Different options for modeling details are described and tested. This includes the
optional consideration of reserve constraints and the decision on whether all or only part
of the power plants are modeled with binary decisions. The purpose is to understand
the possibilities of current computing and the effects on results that arise from the
constraints. Based on testing a variety of different levels of detail, appropriate variants
are chosen for the large-scale simulations. The geographic region is either the entire
European continent or Germany as a focus region. The reason for concentrating on
Germany in part of the simulations stems from the high computational complexity of
the European system. Furthermore, current data provides more details for the German
system, especially the power plant database is more accurate than for the rest of Europe.
Finally, Germany can be seen as a leader in terms of VRE integration. Thus, it yields
a compelling test case for modeling this integration and its consequences.
The models that are distinguished and tested can be categorized and named as:
• EUMIP
ctr : All power plants are modeled with binary decisions and reserve require-
ments are assumed for all countries.
• EUMIP : All power plants are modeled with binary decisions. Reserves are not
considered.
• EUlin DEMIP
ctr : Only the German power plants are modeled with binary decisions;
all other European plants are modeled linearly. Reserves are considered for the
German system only.
• DEMIP
ctr : Germany is modeled as an island and all grid connections to neighboring
countries are cut. All power plants are modeled with binary decisions and reserves
are considered.
• EUMIP MIP
ctr -rel: All binary decisions are relaxed. The basis is the model EUctr .
• EUMIP -rel: All binary decisions are relaxed. The basis is the model EUMIP .
• DEMIP MIP
ctr -rel: All binary decisions are relaxed. The basis is the model DEctr .
• DEMIP -rel: All binary decisions are relaxed. The basis is the model DEMIP .
For all models, uncertainty in form of changing forecasts can be introduced (with one
scenario only, according to the method described in Section 5.4.2). For this thesis,
this option is used to estimate additional benefits of flexible power plants with the
Germany-only model DEMIP ctr .
7.1. MODELS AND MEASURES 131
In this section, the basic scenario is computed and differences between model variations
are depicted. Differences are analyzed with respect to the computational burden but
also with respect to the results themselves. These findings shed light on the possibilities
for modeling with current computational limits. The computer used has 128 GB of RAM
and 64 cores with Intel(R) Xeon(R) processors of 2.70 GHz. The solver settings allow
using up to 24 cores for the parts of the optimization process that can be parallelized.
As computational power and effectiveness of solvers will continue to rise, more accurate
modeling might be possible in the future. However, relative differences between model
formulations might remain.
Comparison of runtimes and gap The computational burden of each level of detail
that is modeled can be described by the runtime required to reach a certain MIP gap
(see Section 4.2.1 for a definition) and the remaining gap after a maximal time. For the
experiments, the target MIP gap is set to 0.0001 (0.01%) and the maximum runtime is
28800 seconds (8 hours). In those tests, the first 7 days of a year are modeled with a
rolling horizon as described in Section 5.2 (36 hours are optimized at once whereof the
first 24 hours are considered for the final results).
Fig. 7.1 on the left depicts the remaining MIP gap (average over 7 runs) after the
maximal runtime. The right side shows the average runtime until the target MIP gap
is reached. The remaining MIP gap indicates the ability of the models to be used for
the evaluation of flexibility measures. When modeling all power plants in the entire
European system with binary decisions (EUMIP ctr and EU
MIP
), the average remaining
MIP gap is above 0.6. Results with such high gaps cannot be interpreted reasonably
and power plant dispatch is far from optimal. Modeling only the German power plants
with binary decisions and all other power plants in Europe linearly, the solvability of
the model depends on whether reserves are considered or not. For the models with
reserve consideration (EUlin DEMIP
ctr ), the remaining MIP gap is still high with 0.11 on
average. Again, a sensible interpretation of results is difficult. Only when neglecting
the reserve constraints (EUlin DEMIP ), the model becomes solvable.
For the models considering Germany only, the remaining MIP gap is small for both
models, with or without reserves. The relaxed models do not have any MIP gap by
definition. Here, only the time that is required for solving must be regarded. Solving a
relaxed model means solving a linear problem without any integer constraints. Such
models can be solved much faster. For the Germany-only models, the solving time for
the relaxed problem is only 60 seconds with reserves and 44 seconds without. Including
binary constraints leads to an dramatic increase of computational times and adding
reserve requirements further doubles the time required to achieve the defined MIP gap.
For the European system, average runtimes are above 8 hours which means the limit
was always reached before a solution was found. Runtimes of slightly above 8 hours are
due to model building, which was not included in the runtime limitation.
132 CHAPTER 7. EVALUATION OF FLEXIBILITY SOURCES
EUMIP
ctr 0.63 EUMIP
ctr 28,941.17
EUMIP 0.62 EUMIP 28,924.06
EUMIP
ctr -rel
EUMIP
ctr -rel 1,858.32
EUMIP -rel EUMIP -rel 1,138.12
EUlin DEMIP
ctr 0.11 EUlin DEMIP
ctr 24,174.03
EUlin DEMIP 5.44 · 10−5 EUlin DEMIP 2,765.01
DEMIP
ctr 9.05 · 10−4 DEMIP
ctr 25,479.13
DEMIP 4.58 · 10−4 DEMIP 12,531.75
DEMIP
ctr -rel
DEMIP
ctr -rel 60.21
Figure 7.1: Remaining MIP gap (left) and runtimes (right) for different levels of
modeling details
Comparison of costs and fuel mix Comparing the costs of the different approaches
gives further insights into the model: what is the effect of mixed-integer constraints?
What is the cost share of Germany within Europe? What is the burden of providing
reserves? Fig. 7.2 illustrates the costs for the European system on the left and for the
German system on the right, both for seven consecutive days. The models with very
high MIP gaps show cost values that are far higher than for the models that were solved
accurately. A real comparison is only possible for the German system, where all models
were solved with a small remaining gap. The model with all binaries and reserves
included leads to the highest costs of A C 131 m of which fuel costs account for A
C 130 m.
When neglecting reserves, the fuel costs are reduced from A C 130 m to AC 110 m, while
start-up costs remain at the same level. Interestingly, costs are not reduced further
when binary constraints are relaxed; for both, the model with and the model without
reserves, costs remain the same. The tests only consider the first seven days and results
might deviate as soon as entire years are considered.
As a last aspect to compare the different approaches, Fig. 7.3 shows the change in
fuel mix as a percentage of overall thermal generation. In the European system, a
shift from gas-, oil-, and coal-fired plants to the cheaper nuclear and lignite sources is
observed. Both the constraint for a binary on/off state and the additional constraints
for reserve provision lead to the same shift. Nuclear and lignite fired plants show
lower costs but are less flexible at the same time. The shift is greater when neglecting
the reserve requirement than when relaxing the binary constraint. The generation
mix in EUlin DEMIP
ctr has to be considered carefully as the MIP gap was too high. Still,
tendencies might remain but be less pronounced when being solved with a smaller MIP
gap.
7.1. MODELS AND MEASURES 133
Figure 7.2: Comparison of operational costs for seven days depending on the level of
modeling details. The figure on the left depicts models of the entire European system
and the figure on the right shows models with Germany modeled as an island.
For the German system, this is exactly the case. A shift towards more lignite and
less (hard) coal and gas is observed but at lower amplitude. Constraints like binary
decisions or reserve requirements necessitate more expensive solutions with power plants
of higher flexibility. An additional slight shift towards less nuclear generation can be
observed, which is difficult to explain. However, as the latter effect is very small, it
might originate from a special situation in the analyzed week.
Figure 7.3: Comparison of the shift in generation mix with different levels of modeling
details. The figure on the left shows values for Europe, the figure on the right the same
values for Germany when modeled as an island. The figures illustrate the results of one
model week.
achieving reliable results in large-scale numerical studies is not possible. The model
becomes solvable when modeling binary decision only for German power plants and
when neglecting reserve constraints. Since the latter leads to an underestimation of
the value of flexible generation, the approach does not appear to be appropriate for
evaluating enhanced generation technologies. An idea to overcome computational
problems is to improve the relaxed solution by adding valid inequalities as e.g. discussed
by Hua and Baldick [104]. While the problem remains continuous, the resulting solution
might be in closer correspondence to the original integer problem. This might allow
modeling larger parts with relaxed equations while still being able to derive valid and
interesting insights. Another option that might allow computing the entire system is to
employ decomposition techniques, in which each zone is optimized on its own and the
subsystems are then coordinated in a master problem. Such multi-region UC might
also resemble the current power system of Europe with its separated market zones more
realistically.
Following this analysis, two models seem to be the most relevant: models DEMIP ctr and
lin MIP
EU DE . Concerning the evaluation of effects from increased power plant flexibility,
modeling of reserves and binary decisions is inevitable. Otherwise, ramping possibilities
will not be as relevant in the model as they are in reality. Thus, the model DEMIP ctr is
the method of choice when regarding effects of increased power plant flexibility. In
order to be able to compare the effects of power plant flexibility to other measures, the
same model is also applied for research on grid extension, grid flexibility, or storage
extension in Germany. Investigation on a European scale can only be modeled with
fewer details. Power plant flexibility enhancement is not investigated, but for all other
questions, EUlin DEMIP is employed.
In future research, a combined model might be a promising method. An initial approach
in that direction was suggested by Trepper et al. [197]. In a first iteration, a relaxed
problem with the entire European system is computed. Then, in a second step, results
on power flows from and to Germany are set as parameters and the Germany-only
model is re-optimized. In this case, results will present effects of increased flexibility for
Germany within an interconnected European power system.
Storage Another very important measure discussed in the context of VRE integration
is storage. In this thesis, the benefits of short-term storage (up to 36 hours) are
evaluated for both the German and the European system. In several scenarios, the
storage capacity of the system is doubled and their location is varied. Concerning
the effects of seasonal storage, other types of models are required. A comprehensive
overview over conducted studies can be found in the PhD thesis of Kühne [127].
7.1. MODELS AND MEASURES 135
Phase shift transformers (PSTs) PSTs could be another measure to prevent lines
from overloading. Such elements allow to change the angle differences on a line and
therefore shift load flow to neighboring lines. Currently, some Eastern European
countries are using PSTs to prevent loop flows through their countries. For the
evaluation within this thesis, PSTs are installed in order to eventually reduce congestion.
The angle difference that is allowed for PSTs is limited to 30°, which is a typical value
in industry [18], leading to
−30 ≤ P SAmax
m ≤ 30 ∀m ∈ L. (7.1)
136 CHAPTER 7. EVALUATION OF FLEXIBILITY SOURCES
Three scenarios (“Flex1”: focus on ramps, “Flex2”: focus on minimum power, “Flex3”:
focus on both) are defined where parameters are varied from the “Base” scenario as
given in Table 6.3. Flexibility increases are not considered for nuclear plants (no
new installations / replacements planned). The values for the flexibility measures are
displayed in Table 7.1.
Table 7.1: Parameters of thermal power plants in scenarios. The different parameter
sets concerning the plant flexibility are named “Base”|“Flex1”|“Flex2”|“Flex3”.
The major results are derived with the option DEUMIP ctr concerning modeling of details
and key findings are presented in Sections 7.2.1 and 7.2.2. In order to estimate the
influence of the chosen modeling framework and possible effects from uncertainty
considerations, Section 7.2.3 compares system costs, number of start-ups, and emissions
with two alternative approaches: an approach without reserve constraints and an
approach with changing forecasts.
load. Cost reductions are almost as high as in the scenarios where both ramps and
minimum downtimes are improved (“Flex3”). Increasing only ramp capability of the
power plants (“Flex1”) leads to higher start-up costs while fuel costs reductions are
almost the same as in “Flex2”. Here, generation is able to follow the variable load;
power plants can be shut down even for shorter periods when necessary. With this
“Flex1” scenario, cost reductions mainly result from reducing curtailment of excess
generation.
Flex1 0.26 9.49 9.75 Flex1 0.34 6.89 7.22 Flex1 0.35 5.86 6.21
Flex2 0.24 9.48 9.72 Flex2 0.26 6.84 7.09 Flex2 0.23 5.8 6.02
Flex3 0.23 9.44 9.66 Flex3 0.28 6.78 7.07 Flex3 0.3 5.7 6
0 5 10 0 5 10 0 5 10
Costs in billion AC Costs in billion AC Costs in billion AC
Figure 7.4: Operational costs for for different scenarios on power plant flexibility
Figure 7.5: Power curtailment for different scenarios on power plant flexibility
The amount of curtailment can be reduced by 42.6% from 9.67 TWh to 5.55 TWh in
2025 and by 25.8% from 35.26 TWh to 25.78 TWh in 2035. Interestingly, the reduction
is percentage-wise higher in the scenario for 2025. The reason is that only part of
the curtailment is due to short-term flexibility requirements. In 2035 requirements for
seasonal storage as well as grid constraints become more prominent.
138 CHAPTER 7. EVALUATION OF FLEXIBILITY SOURCES
Emissions When analyzing power systems and VRE integration, an important measure
that must always be considered is the amount of CO2 emissions. Fig. 7.6 displays the
changes arising from flexibilization of power plants. The figure shows several effects:
emissions are reduced drastically by increased VRE generation. While emissions sum
up to 256 Mio. tons in 2015, they can be reduced to 152 Mio. tons in 2035 (a reduction
of 41%). In contrast, increasing the flexibility of fossil power plants only yields a very
small effect and leads to slightly increased emissions in almost all instances.
Flexible generation allows integrating a higher share of VREs as illustrated by the
reduced curtailment. More generally, it permits integrating a larger amount of generation
from sources with low marginal costs. Besides VRE, lignite is a technology with very
low marginal costs but with high emissions. A shift towards lignite away from gas and
coal power plants leads to increased CO2 emissions that overcompensate the reduction
through prevention of curtailment.
Figure 7.6: CO2 emissions for different scenarios of power plant flexibility
Fuel mix The effect of a shift in the fuel mix is illustrated in Fig. 7.7. The upper
charts show the overall fuel mix while the lower charts highlight the differences of the
scenarios with increased flexibility compared to the “Base” scenario. The effects that
were supposed to explain the increasing CO2 emissions can be observed now: more
lignite (and also slightly more uranium) is used while coal and gas generation is reduced.
The figure also shows a reduction of overall utilization of thermal generation, reflecting
the reduced curtailments. An additional 16 TWh of electricity production from lignite
7.2. VALUE OF ENHANCING THERMAL POWER PLANTS IN GERMANY 139
is observed with “Flex3” in 2035. This causes higher emissions that overcompensate
the savings of 20 TWh electricity generated by gas and 5 TWh generated by coal.
Figure 7.7: Generation mix for different scenarios on power plant flexibility. The upper
charts illustrate the absolute values whereas the lower charts show the difference to the
“Base” scenario.
decreased for an individual CCGT power plant in Huber et al. [108]. A reason for an
increasing number of start-ups (“Flex1” and “Flex3”) is an increased maximal speed of
start-up and shut-down (SU and SD). Shutting down and starting up is possible in a
shorter time frame and thus becomes more attractive. Additionally, increased ramps
allow the provision of reserves with fewer power plants - allowing more power plants to
be shut down during hours with very high generation from VREs.
Figure 7.9: Provision of secondary control for different scenarios on power plant flexibility.
The upper chart depicts the distribution of positive secondary reserve provision, the
lower chart the same for negative secondary reserves.
Effects in hourly time resolution Fig. 7.10 shows the hourly generation profile for
a summer week in the year 2035. The upper chart shows the “Base” scenario while
the lower chart shows the generation with improved power plant flexibility (“Flex3”).
In the first two days, large amounts of wind generation are fed into the system. In
both scenarios (“Base” and “Flex3”), this leads to curtailment/excess generation (pink
colored area). However, in the scenario with increased flexibility, curtailment is less.
The conventional power plants that are still on-line during this long phase of high wind
generation might mainly be used for reserve provision. Higher ramps allow providing
the same amount of reserves with less capacity on-line.
Beginning with hour 40, wind calms down and additional generation from thermal
plants is required. For “Base”, a portfolio of sources including nuclear, lignite, coal,
and gas provides this additional electricity. In the flexible scenario, the variety is lower:
the increase is mostly provided by nuclear and lignite plants as their ability to increase
their output (or to be started) is higher.
On the last day of the week beginning with hour 155, a very sunny day, generation
from PV peaks at noon and then decreases in the afternoon. Thermal power plants are
required to increase their output rapidly to fill the so-called “duck curve” (see Fig. 1.3
in the introduction). While gas and coal power plants run throughout the day and
curtailment occurs in “Base”, no gas and almost no coal power plant is running in
“Flex3”. Faster shutting down and restarting of plants allows for this more efficient
behavior.
142 CHAPTER 7. EVALUATION OF FLEXIBILITY SOURCES
50
50
Figure 7.10: Generation profile for a typical summer week in 2035. The upper figures
shows the “Base” scenario whereas the lower figure illustrates the scenario with improved
flexibility (“Flex3”).
• DEMIP -stoch: As discussed in Section 5.4, power systems might have to react to
unexpected events by re-planning their schedules. The approach of Section 5.4
with a changing forecast is employed. This simplified stochastic approach gives
7.2. VALUE OF ENHANCING THERMAL POWER PLANTS IN GERMANY 143
All of those additional scenarios are considered for the year 2035 where effects from
increased flexibility are highest.
Flex2 0.23 5.8 6.02 Flex2 0.39 5.57 5.96 Flex2 0.23 5.95 8.34
Flex3 0.3 5.7 6 Flex3 0.37 5.54 5.91 Flex3 0.32 5.74 6.07
0 5 10 0 5 10 0 5 10
Costs in billion Euros Costs in billion Euros Costs in billion Euros
Discussion on the importance of flexible power plants Van den Bergh et al.
[16, 17] show that the current portfolio of conventional power plants in Germany is
capable of providing enough flexibility for the integration of up to 50% generation from
wind and solar. While results in this thesis show occurring curtailment for the years
2025 and 2035, they still undermine the findings of Van den Bergh et al. for a unit
commitment problem without considering reserve provision: curtailment cannot or can
only slightly be reduced by increasing power plant flexibility. The curtailment might be
a result of grid constraints or required mid-term/long-term flexibility. However, as soon
as reserves must be provided, results change: Curtailment of renewable generation can
be reduced significantly through increased flexibility of thermal power plants. Especially
the increase of ramp capabilities with “Flex1”/“Flex3” proves to be helpful for the
7.3. GRID ENHANCEMENTS AND STORAGE EXTENSION IN GERMANY 145
system as soon as reserves and/or stochastic forecasts are considered. Since the real
system requires reserves and as forecasts are always uncertain, results indicate that
increased flexibility of power plants is indeed an important measure for improved
renewable integration, but it is not sufficient for full VRE integration in 2035. The
remaining curtailment does not require the short-term flexibility provided by power
plants but might rather constitute excess generation in several hours that could be
resolved by storage or grid constraints. Those two additional technological measures
for improved integration of VRE are discussed in the next section.
The results of this section also point to the importance of uncertainty considerations.
While the approach employed in this thesis is a first step, future research can be
conducted to evaluate the benefits of improved power plants or entire power plant
portfolios with increased flexibility capabilities. The temperature model is an ideal base
for such modeling as constraints in start-up times are mostly a result of limited heating
capabilities of plants.
flows over all lines) can be quantified to be at 248.7 GVA. Extending the lines in “All”,
i.e. neglecting the N-1 criterion, increases this number by 106.6 GVA to a total capacity
of 355.4 GVA.
• Kassel - Detmold
• Kassel - Braunschweig
• Lüneburg - Mecklenburg-Vorpommern
• Münster - Weser-Ems
• Oberfranken - Thüringen
• Münster - Detmold
• Hannover - Lüneburg
A further indication for the selection of lines to be extended are the line utilization
rates which are displayed in Fig. 7.15, showing that the lines with highest shadow
prices mostly also have the highest utilization rates. This gives further reason for their
extension and validates the applied methodology of using the average shadow price as
extension indicator.
• Schleswig-Holstein - Unterfranken
• Schleswig-Holstein - Stuttgart
• Weser-Ems - Düsseldorf
• Düsseldorf - Karlsruhe
• Dessau - Schwaben
7.3. GRID ENHANCEMENTS AND STORAGE EXTENSION IN GERMANY 147
Effects of grid extension on costs in Germany Fig. 7.16 depicts the costs for the
three different extension scenarios and allows drawing several conclusions. In 2015, grid
extensions are not crucial as line limitations are still low and only very small effects can
be achieved. These are the same for all extension scenarios and signify a cost reduction
of only 0.2% from A C 9.84 b to AC 9.82 b. Cost reductions slightly increase in 2025 and
are significant in 2035 with a reduction of AC 230 m from A C 6.69 b to A
C 6.46 b (3.5%) in
the DC scenario. Results show that the most cost-effective measure for grid extension
is to install DC lines followed by increasing the capacity of selected AC lines (“Sel”).
Extending all lines similarly (“All”) is not as effective in terms of cost reductions.
Congestions will still exist in the same lines and extending non-congested lines does not
have positive effects (see below in paragraph on line utilization). Another observation
is that the amount of start-up costs is not influenced significantly by grid extensions
but will stay at a constant level.
148 CHAPTER 7. EVALUATION OF FLEXIBILITY SOURCES
All 0.19 9.63 9.82 All 0.26 7.25 7.51 All 0.25 6.28 6.54
Sel 0.19 9.63 9.82 Sel 0.25 7.23 7.49 Sel 0.26 6.22 6.48
Figure 7.16: System costs for different grid extension scenarios in Germany
Effects of grid extension on curtailment in Germany The main reason for the
cost reductions is the reduction of curtailment (see Fig. 7.17). Almost no curtailment
occurs in 2015, while significant curtailment of 35.3 TWh emerges in 2035. Depending
on the extension scenario, the value can be reduced to 26.2 TWh, which is a 25%
reduction of the curtailment. The ranking of different extension strategies is the same
as for the costs: setting up the DC lines is the most effective measure followed by the
extension of selected congested lines. The achieved reduction in curtailment lies in the
same order of magnitude as was achieved by power plant flexibilization.
Figure 7.17: Power curtailment for different grid extension scenarios in Germany
effect. CO2 emissions can at most be reduced from 152 Mio. tons to 144 Mio. tons
when installing the DC lines, which is a reduction of 5.3%.
Figure 7.18: CO2 emissions for different grid extension scenarios in Germany
Scenario setup Two different scenarios are investigated: one scenario where PSTs are
installed and one scenario where AC lines are replaced by controllable DC lines. For
both, the same lines that where extended with “Sel” are considered. The idea behind
choosing the most congested lines is that flexibilization might allow to “shift” electricity
transport to the neighboring and less congested lines.
Figure 7.21: Operational costs for different grid flexibilization scenarios in Germany
2015 2025 2035
Base 0.13 Base 9.67 Base 35.26
PST 0.13 PST 8.31 PST 31.7
FlexDC 0.13 FlexDC 8.37 FlexDC 31.69
0 20 40 0 20 40 0 20 40
Curtailment in TWh Curtailment in TWh Curtailment in TWh
scenarios. The leveling effect is visible with both approaches but less pronounced than
with grid extensions that were discussed in the previous section.
scenario, 129.15 MW (reservoir: 911 MWh) are installed in each region; the overall
capacities remain the same.
This section tries to combine the measures and give an idea which of them might
complement each other and, on the other hand, which of them address the same issues.
Additionally, an outlook on possible reductions of curtailment through international
cooperation is presented.
prices are high enough, the shift towards lignite might not be relevant anymore and
power plant flexibilities could also lead to reduced carbon emissions.
All connections (“All”) In the first transmission extension scenario, the N-1 criterion
is neglected, which means an increase of transmission line capacities from 70% to 100%.
In the European case, both AC and DC lines are extended and the overall capacity is
1670 GVA for AC lines and 14.4 GW for DC lines (instead of 1169 GVA and 10.1 GW
when considering the simplified N-1 criterion).
Selected connections but with DC (“DC”) In this scenario, line extensions are
the same as with “Sel2” but DC lines are employed for the extended connections; all
connections with prices above 10 A
C/MW are extended and modeled as DC lines.
7.5. GRID ENHANCEMENTS AND STORAGE EXTENSION IN EUROPE 159
Figure 7.28: Operational costs for different grid extension and flexibilization scenarios
in Europe
of 14.5 TWh or 81.6%. In 2035, the effect is a reduction of 43.3 TWh (60.0%) from
72.02 TWh to remaining 28.76 TWh. When only extending the lines with a shadow
price of above 10 A
C/MW, drastic reductions of curtailment can still be achieved with
“DC”, i.e. a reduction of 11.3 TWh (63%) in 2025 and of 33.7 TWh (47%) in 2035.
Installing PSTs or switching lines also has some effects on reduction although the effects
are less than for all extension scenarios. Further research could investigate the ideal
placement of such components and possibly find better solutions than to place them
directly at congested lines.
In comparison to the results for the German system, grid enhancements are more
effective and more important when considering the entire European system. A larger
part of the curtailment in Europe seems to be caused by transmission congestion. A
very significant effect is already observed for 2025 while for Germany alone this is only
the case for the scenarios of 2035.
Figure 7.29: Curtailment for different grid extension and flexibilization scenarios in
Europe
Figure 7.30: Emissions for different grid extension and flexibilization scenarios in Europe
Figure 7.31: Fuel mix for different grid extension and flexibilization scenarios in Europe.
The upper figures depict the absolute values while the lower figure depicts the change
compared to the “Base” scenario.
constraints as discussed above. Trading between the regions is not possible despite
existing comparative advantages. The figure shows that differences in zonal prices
already exist in 2015 and might even flatten with the integration of VREs in 2035. The
figure also shows that the regions constituting the political unit of a country face very
similar prices. Inner-country regions are much better connected to each other than
cross-country ones.
In 2015, France and Scandinavia show especially low prices (10-15 AC/MWh) which can
be explained by the high shares of nuclear generation in France and the high share
of hydro power in Scandinavia. Also, Eastern and Southeastern European regions
show lower prices of around 30-35 AC/MWh compared to the 40-45 A C/MWh in the UK,
Western Germany, Austria, Italy, and Spain. The reason can again be found in the
major sources for generation: while in Eastern Europe mostly coal or lignite are the
price-setting marginal power plants, gas power plants are employed more often in the
other countries. With the introduction of higher shares of VREs, the overall price
level drops due to the so-called merit order effect (compare Fig. 2.2 in Section 2.3).
Several of the former high-priced countries/regions converge with former cheaper areas.
7.5. GRID ENHANCEMENTS AND STORAGE EXTENSION IN EUROPE 163
This is true for the UK and the continental regions close to the coast (Netherlands,
Northern Germany, Denmark) where large-scale wind farms will be installed. Still,
already “cheap” countries like France will see a further drop in prices and some price
differences will remain. The country with highest prices in 2035 seems to be Italy where
average prices remain above 35 A C/MWh as gas-fired plants are still required in many
hours of the year.
The different scenarios for enhancing and extending the transmission capacities can
be evaluated with regard to their possible effect on flattening the prices. Fig. C.1 in
the Appendix displays the effects that are described here. Increasing system flexibility
by switching connections to DC (“FlexDC”) will only slightly change prices. However,
some flattening can be achieved in some German regions, Austria, the Czech Republic,
and Hungary. With the installation of additional lines, effects of flattening are higher.
Especially the scenarios “Sel1” and “DC” have strong effects. All Italian regions become
cheaper while prices in France increase at the same time. With all extension strategies,
a large area including Germany, Austria, Eastern European and Southeastern European
countries show all prices in the range of 20 A
C/MWh. These findings are in line with the
findings of Schaber et al. [181], where similar smoothening effects in the same directions
were found. Nevertheless, the absolute values differ as do the parameters of fuel prices
and the level of VRE integration.
Huber et al. [106], amongst many others). Still, with the results of this thesis, a more
detailed model is studied and, beyond demonstrating the model abilities, additional
findings can be retrieved. Even though the zonal DC load flow model is a simplification
and results might not be transferable exactly to the real-world European system, they
clearly show the importance of selecting the lines for extension. The physics of the
system does not allow to route electricity but congestion may occur in some connections
while unused capacity remains in the parallel lines. Flexible components like PSTs can
alleviate the problem and resolve grid constraints to some extent. System planners
should consider this measure whenever grid extension is too expensive or not possible
due to other circumstances.
Effects of storage extension in Europe Fig. 7.33 depicts the costs and Fig. 7.34
the curtailment for all scenarios. Compared with grid extensions, doubling storage
capacities (“Sto1” and “Sto2”) has only very little effect on costs and curtailment in
the European context. In 2015, costs are reduced by A C 20 m (0.05%) and curtailment
is reduced by 0.11 TWh (5.9% of curtailment in “Base”). The effects increase with
greater installations of VRE. Cost reduction increases to A C 230 m (0.7%) in 2025 and to
A
C 330 m (1.3%) in 2035. Still, compared to possible cost reductions by grid extensions,
those values are very low. The same is true for the reduction of curtailment which are
at 3.3 TWh (4.5%) in 2025 and at 8.1 TWh (11.2%) in 2035. A larger effect of storage
is achieved when the capacity is distributed across all regions; storage can then also be
used for a more efficient power flow by feed-in at specific nodes whenever this improves
the load flow in the system.
Discussion on storage extension in Europe The results show that storage has a
lower importance on the European than on the German level. For a better integration of
VREs in an European context, the extension of the transmission grid seems to be more
important and should be a major focus of European energy politics. As already found
by Kuhn [125] and Kühne [127], storage becomes most important at very high levels
of renewable generation beyond 50% of electricity production. Especially long-term
storage is predicted to be crucial in such cases. With the scenarios ranging only to
the year 2035 for the entire European system, VRE penetration is still below such
high penetrations and most of the renewable production can be integrated as long as
transmission is possible.
7.6. RÉSUMÉ OF NUMERICAL STUDIES 165
Figure 7.33: Operational costs for different storage extension scenarios in Europe
2015 2025 2035
So far, the model is only able to capture requirements for short-term or day-and-night
storage. Adding the ability to also investigate effects from seasonal storage yields more
applications and new insights: storage might be more effective. Ideas could be an
iterative model, where seasonal storage is optimized via a reduced model in a first step,
followed by the detailed UC model with fixed long-term storage operation.
• Results for the Germany-only case revealed the value of power plant enhancements
for the system. Both lowering the minimum power output and increasing the
ramping/heat-up speeds had significant effects on operational costs and the ability
to integrate variable generation from renewable sources.
• Some simplified tests with changing forecasts gave a hint that the enhancements
of ramping/heat-up speed might be even more important in a real-world power
system where uncertain events happen.
• Comparing the results with and without reserve consideration shows the reason for
the positive effect of power plant enhancements. Faster power plants are able to
provide more reserves, and in turn, less power plants must be occupied by reserve
provision. Furthermore, power plants can be shut down and restarted faster. This
allows reacting more efficiently to hours with very high renewable generation.
The lowering of minimum power output is also very helpful for efficient reserve
provision. During times with high VRE generation, curtailment can be prevented
by lowering the output while still being able to provide positive reserves.
• Grid extensions have significant effects in the German system and are of enormous
importance in the European context. Extending grids in Europe allows reducing
curtailment and emissions tremendously and should therefore be put high on the
agenda of European and German energy policies.
167
168 CHAPTER 8. CONCLUSIONS AND OUTLOOK
gradients. Additionally, the new approach allows modeling wear-and-tear costs arising
from start-ups that depend on the heating speed: the higher the heating speed, the
higher the temperature gradients and, therefore, the higher the costs. These additional
modeling abilities promise to be especially interesting in a stochastic modeling environ-
ment. Several approaches for considering uncertainty are presented. The chosen method
for most large-scale simulations consists of including reserve constraints. Furthermore,
the ability of including changing forecasts is implemented and employed. Regarding
transmission constraints, the developed model methodology and implementation in-
cludes a DC load flow model formulated with a PTDF matrix. The DC methodology is
superior to a simple transport model as loop flows or congestion on individual lines can
be represented and bottlenecks can be identified. The model with all its features allows
testing different options that enable more efficient renewable integration, i.e. enhanced
thermal power plants, storage, grid extensions, and grid flexibility measures like phase
shift transformers or DC links.
After analyzing possible requirements on ramps in the system in a first step and defining
and developing a model approach that allows evaluating different options for dealing with
the fluctuating nature of renewables in a second step, the consequent third step of this
thesis applies the methodology on a realistic test case. Therefore, data on the European
power system is gathered and a simplified model based on 268 regions is developed.
Most of the collected data stems from open sources, which allows the data set to be
published and to provide additional value to the scientific community. Computational
complexity permits modeling the entire European system with a simplified approach
only while Germany alone is modeled with all model features including binary decisions
for all thermal plants and reserve considerations. Results show that increasing the
ability of thermal power plants to ramp up and down, to lower their output, and to
heat up faster has significant effects on efficient integration of renewable energy sources.
Especially when reserves are considered, which is the case in real-world operations,
power plant enhancements are very beneficial. Storage also shows high effectiveness
as soon as reserves are considered for the German system. In the overall European
system, grid extensions are the most important actions policy makers should take when
aiming at building a future power system with high shares of wind and solar power.
Additionally, and in cases where extension is not possible, switching some lines to direct
current or installing phase shift transformers might allow for a more efficient power flow
and thereby reduce curtailment substantially.
Even though further validation of the proposed dataset and grid reduction is necessary,
this part of the thesis demonstrates the power of the model theory and the dataset
developed. In the process of writing this thesis, the model has already been applied in
a project for the Bavarian Ministry of Economics. In that study, different energy policy
options for the State of Bavaria were evaluated. This study already shows the relevance
of the outcomes of this thesis beyond the pure scientific achievements: developing and
establishing a ready-to-use model for policy research projects.
8.2. FURTHER RESEARCH QUESTIONS ARISING 169
171
172 APPENDIX A. ADDITIONAL VISUALIZATIONS OF THE DATASET
DC DC DC
0 200 400 600 0 200 400 600 0 200 400 600
Base Base Base
DC DC DC
−40−20 0 20 40 −40−20 0 20 40 −40−20 0 20 40
Energy (MWh) Energy (MWh) Energy (MWh)
174
175
181
182 APPENDIX C. ADDITIONAL RESULTS FOR THE EUROPEAN SYSTEM
Figure C.1: Nodal prices for different grid flexibility and grid extension scenarios in
Europe for the year 2035
183
Figure C.2: Shadow prices on transmission lines for grid flexibility and grid extension
scenarios in Europe for the year 2035
184 APPENDIX C. ADDITIONAL RESULTS FOR THE EUROPEAN SYSTEM
Figure C.3: Line utilization for grid flexibility and grid extension scenarios in Europe
for the year for the year 2035
List of Figures
2.1 Temporal and spatial scales of operational and planning schemes for power
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Reduction of market prices by the introduction of renewable energies with
zero marginal costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Deviations from load with hourly and with 30 min energy scheduling . . . 27
2.4 Droop control of two different power plants . . . . . . . . . . . . . . . . . . 29
3.1 Average onshore wind and solar PV full load hours per year over the period
2001–2011 as well as their range . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Frequency distributions of hourly ramps of simulated and actual production 38
3.3 Temporal distribution of 1-hour ramps of load, wind and PV power in
Ireland, Germany and Italy for the meteorological year 2011 . . . . . . . . 43
3.4 Temporal distribution of 1-hour net load ramps for different shares of PV in
the wind/PV mix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 Frequency distribution of 1-hour net load ramps for different shares of PV
in the wind/PV mix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6 Ramp envelopes for 27 European countries for different variable generation
penetrations α and shares of PV in the wind/PV mix β, 2011 . . . . . . . 45
3.7 Top and bottom 1500 hours of the 6-hour net load ramp duration curves for
27 European countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.8 99th percentiles of 1-hour and 6-hour net load ramps . . . . . . . . . . . . 48
3.9 Three interpercentile ranges of 1-hour net load ramps for different shares of
PV in the Wind/PV Mix β at 50% penetration of variable renewables . . . 49
3.10 1-hour net load ramp duration curves at the regional, country, and European
scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.11 1st/99th percentile ramp envelope at the regional, country, and European
scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.12 Boxplot with 1-hour net load ramp extremes for individual countries and
Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
185
186 List of Figures
6.1 The 268 model regions and their electricity consumption relative to their area117
6.2 Illustration of the reduced transmission grid model consisting of AC and DC
lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3 The FLH for PV and wind generation in the model regions . . . . . . . . . 122
7.1 Remaining MIP gap and runtimes for different levels of modeling details . 132
7.2 Comparison of operational costs for different levels of modeling details . . 133
7.3 Comparison of the shift in generation mix with different levels of modeling
details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.4 Operational costs for for different scenarios on power plant flexibility . . . 137
7.5 Power curtailment for different scenarios on power plant flexibility . . . . . 137
7.6 CO2 emissions for different scenarios of power plant flexibility . . . . . . . 138
7.7 Generation mix for different scenarios on power plant flexibility . . . . . . 139
List of Figures 187
C.1 Nodal prices for different grid flexibility and grid extension scenarios in
Europe for the year 2035 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
C.2 Shadow prices on transmission lines for grid flexibility and grid extension
scenarios in Europe for the year 2035 . . . . . . . . . . . . . . . . . . . . . 183
C.3 Line utilization for grid flexibility and grid extension scenarios in Europe
for the year for the year 2035 . . . . . . . . . . . . . . . . . . . . . . . . . 184
List of Tables
3.1 1-hour net load ramp rates – mean of all countries and their statistical
dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 6-hour net load ramp rates – mean of all countries and their statistical
dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1 Problem sizes for 72 periods and 223 units in basic formulation . . . . . . 72
6.1 Reactances and SIL values for high voltage transmission . . . . . . . . . . 119
6.2 Loadability factor according to St.Clair curve . . . . . . . . . . . . . . . . 119
6.3 Parameters of thermal power plants in the base case . . . . . . . . . . . . . 125
6.4 Estimation of start-up costs . . . . . . . . . . . . . . . . . . . . . . . . . . 126
189
Nomenclature
Sets
Symbol Description
C Segments of piecewise linear function, C = [1 .. C]
E Start-up types, E = [1 .. E]
I Generating units, I = [1 .. I]
Io Generating units in control area o, Io = [1 .. Io ]
L Lines in Graph/Network, L = [1 .. L]
N Nodes in Graph/Network, N = [1 .. N ]
Nk Nodes in a specific country k, Nk = [1 .. Nk ]
O Control areas, O = [1 .. O]
R Reserve types, R={Primary, Secondary, Tertiary}
R+ Positive reserves
R− Negative reserves
S Storage units, S = [1 .. S]
So Storage units in control area o, So = [1 .. So ]
T Time steps, periods, T = [1 .. T ]
Ω Set of scenarios in stochastic unit commitment
Indices
Symbol Description
c∈C Segment of piecewise linear function
e∈E Start-up type
i∈I Power plant / unit
m∈L Transmission line
a, b, n ∈ N Node/Buse
o∈O Control area
r∈R Reserve type
s∈S Storage plant
t∈T Time step, period
ω∈Ω Scenario
l∈N Look-back time, off-line time
190
List of Tables 191
Parameters
Symbol Description Unit
Ai Fix production costs in on-line state A
C
Bi Variable production costs A
C/MWh
CFi (t) Capacity factor of VRE technology i ∈ {W ind, P V } (-)
CLt,max Maximal possible charging in period t MW
CT (ta , tp ) Charging table for EVs arriving at ta and parking tp hours MWh
Dt Electricity demand MW
DTi Minimum downtime hour
ESsmax Maximal storage content MWh
L,max
fm Maximal power flow over line m ∈ L MW
Fi Fixed start-up costs A
C
Himax Maximum possible heating energy (-)
Kil Start-up costs after l off-line periods A
C
Ktol Start-up costs approximation tolerance (-)
NL(t) Net load in period t MW
PDi Previous downtime of power plant hour
Pi Power output of renewable technology i ∈ {W ind, P V } (-)
Pimax Maximum power output MW
Pimin Minimum power output MW
P Ssmax Maximim input/output of storage power plants (Pump/- MW
Turbine)
P SAmax
m Maximal phase shift angle on line m (°)
t
Ro,r Required reserve capacities in control area o MW
RUi Maximum ramp-up speed MW/min
RDi Maximum ramp-down speed MW/min
SUi Maximum ramp-up at start-up MW (/start)
SDi Maximum ramp-down at shut-down MW (/start)
SUTi (l) Required start-up time after cooling hour
TH i (l) Required heating after cooling (-)
U Ti Minimum uptime hour
Vi Variable start-up costs A
C
V REnt,min Minimal forecasted generation from VRE MW
V REnt,max Maximal forecasted generatoin from VRE MW
V REnt,nom Nominal forecasted generation from VRE MW
PTDF Power transfer distribution factors (-)
DCDF Direct current distribution factors (-)
PSDF Phase shift distribution factors (-)
α Share of VRE in electricity supply (-)
β Share of PV within the wind/PV mix (-)
γ Weight for scenario in stochastic optimization (-)
∆tempmax i Maximum temperature difference during heating (-)
ζi Fix part of wear-and-tear costs A
C
192 List of Tables
Variables
Symbol Description Unit
clt Charging load for EVs MW
vit State of power plant, vit ∈ {0, 1} (-)
wti Hot state of power plant, wti ∈ {0, 1} (-)
pti Power output MW
psts Power output of storage plant MW
ests Energy content of storage plant MWh
tempti Temperature, normalized to [0,1] (-)
hti Heating, normalized to [0,1] (-)
yit Start-up indicator, yit ∈ {0, 1} (-)
zit Shut-down indicator, zit ∈ {0, 1} (-)
git (s) Start-up type indicator (-)
cpti Production cost of power plant A
C
cuti Start-up cost of power plant A
C
cwit Wear-and-tear cost of power plant during start-up A
C
faN Active power flow at node a MW
fN Active power flow for nodal balances, matrix form MW
L
fa,b Active power flow from node a to b MW
fL Active power flow on lines in matrix form MW
L
qa,b Reactive power flow from node a to b var
psam Phase shift angle on line m (°)
psa Phase shift angle in vector form (°)
rvt,r
i Reserve provision from power plants MW
rvst,rs Reserve provision from power plants MW
vret,min
n Minimal scheduled generation from VRE MW
vret,max
n Maximal scheduled generation from VRE MW
vretn Nominal scheduled generation from VRE MW
rdpt,max
i Reserve deployment for maximal VRE generation MW
rdpt,min
i Reserve deployment for minimal VRE generation MW
List of Tables 193
Acronym Description
AGC Automatic generation control
AC Alternating current
DC Direct current
DSM Demand side management
ED Economic dispatch
EEX European Energy Exchange
ENTSO-E European Network of Transmission System Operators
EPEX European Power Exchange
Eureletric The Union of the Electricity Industry
FLHs Full load hours
GAMS General Algebraic Modeling System
GIS Geographic information system
HVDC High voltage direct current
IP Integer programming
LP Linear programming
MILP Mixed-integer linear programing
MIP Mixed-integer programming
NTC Net transfer capacities
OTC Over-the-counter
PST Phase shift transformer
RMSE Root-mean-square error
UC Unit commitment
USA United States of America
VRE Variable renewable energy
194
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