Energy Systems Optimization Considering the Uncertainty of Future Developments E-Book

Wolf Gereon Wedel

• Herausgeber: BoD - Books on Demand
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2024

Seitenzahl: 304

Beschreibung

In light of anthropogenic climate change and the importance of energy to ensure high living standards, energy system optimization is used to explore different energy system layouts. A recent focus has been on determining cost-effective ways to mitigate greenhouse gas emissions. This work investigates how future uncertainties regarding technology costs influence optimization results. This is achieved through energy system optimization aimed at reducing system cost using stochastic optimization with probability distributions to capture expected future costs and uncertainties. Theoretical considerations and a minimal example energy system show that Jensen's inequality leads to an overestimation of necessary system costs when scenario optimization considers only the expected technology cost means. Stochastic optimization is applied to a model of the German energy system, including the electricity, heating, and transport sectors. Results from stochastic optimization are compared to scenario results based on mean cost distributions. The use of a factor effect-based meta-model and fewer optimizations in stochastic analysis are investigated to reduce computational effort. The results confirm the overestimation of necessary costs by scenario optimization, showing a 3.5% overestimation with an 80% emission reduction target and 0.4% for a completely renewable system. Stochastic optimization also provides the interquartile range to characterize uncertainty, with a 13.2 Euro MWh-1 interquartile range (27.3% of the mean) for a completely renewable system. Using 30 to 60 optimizations in the stochastic case yields results similar to 500 optimizations, the benchmark. The proposed meta-models offer limited advantages except for predicting extreme results, which are not evident with fewer optimizations. In some cases, especially for non-renewable systems, the expected values from stochastic optimization differ significantly from scenario optimization results. For instance, at a 20% emission limit of 1990 levels, scenario optimization yields 18% of the CO2 emissions compared to the mean of stochastic optimization. Similar differences are seen in other parameters, though most are well-represented by scenario results. Clustering helps manage the diverse results from stochastic optimization by identifying underlying system layouts. Stochastic optimization with probability distributions is robust, with small changes to distributions having minimal impact on outcomes.

Leseprobe

Preface

Die vorliegende Dissertation entstand im Rahmen meiner Tätigkeit als wissenschaftlicher Angestellter am Lehrstuhl für Energiesysteme der Technischen Universität München. Besonders bedanken möchte ich mich bei Herrn Prof. Spliethoff für die Möglichkeit und das Vertrauen an seinem Lehrstuhl zu forschen und diese Arbeit anzufertigen, sowie den Gestaltungsspielraum den ich genießen konnte. Außerdem möchte ich mich für seine beeindruckende Fähigkeit fachlich und menschlich hervorragende Mitarbeiterinnen und Mitarbeiter auszusuchen bedanken, ich schätze mich glücklich eine ganze Reihe von diesen zu meinen Freunden zählen zu dürfen. Während meiner Zeit am Lehrstuhl haben viele Mitarbeiter*innen dort angefangen und aufgehört. Jede und jeder von euch hat dazu beigetragen diese Zeit zu etwas ganz Besonderem zu machen. Dafür vielen vielen Dank!

Ganz besonders möchte ich mich bei Sebastian M. für die Unterstützung bezüglich der Optimierung, sowie die Automatisierung der Berechnung des COP bedanken. Bei Hans bedanke ich mich für seine Fachkenntnisse und Erläuterungen zur Jensen-Ungleichung. Andi H. möchte ich für seine Arbeit, erst als Student und nachher als Kollege danken. Dafür jeden Arbeitstag zu einem Tag unter Freunden gemacht zu haben möchte ich der 15 Uhr Kaffeerunde bestehend aus Moritz G., Felix, Julia, Michi A., Babsi, Jell und Manu., sowie dem Traderclub bestehend aus Vinni, Moritz, Philipp und Sebastian M. danken (Laura, wenn es dich damals schon gegeben hätte, würdest du hier bestimmt auch auftauchen). Felix außerdem vielen Dank für die vielen tollen Läufe und die Energie immer wieder alle zur Teilnahme an der Laufrunde zu motivieren. Lynn, Du warst die beste Bürokollegin, die ich mir vorstellen kann, danke für die vielen angenehmen und produktiven Stunden. Meinem Projektkollegen Benedikt möchte ich für die effektive Zusammenarbeit, den Versuch die Welt auch im Kleinen immer ein bisschen besser zu machen und das Korrekturlesen dieser Arbeit danken. He-Man, Sebastian E. und Claudia möchte ich für eine unvergessliche Konferenz sowie den technischen bis philosophischen Austausch danken. Dem He-Man soll außerdem hier für unvergleichliche Freude auf der Tanzfläche erwähnt werden, danke für die vielen schönen Zeiten! Moritz B., vielen Dank für deinen Humor, Blobby-Volley und die guten Unterhaltungen. Richi, PJ und Tobias G. vielen Dank dafür ein durchgehend positives Beispiel körperlicher Fitness gepaart mit einem scharfen Verstand und vielen guten Gesprächen gewesen zu sein. Michi H. danke ich für seine Ruhe und Gelassenheit, sowie ihm und jedem sowie jeder, der oder die Teilnehmer der LES-Band war, für die vielen glücklichen Stunden durch eure Musik. Flo und Peter vielen Dank für fußballerische und menschliche Meisterleistungen. Für glückliche Momente und gute Gespräche möchte ich mich außerdem bei Kristina, Gesa, Tobias N., Andi S., Roberto, Matthäus, Thorben, Clemens und Härzschel bedanken. Bestimmt habe ich jemanden vergessen, danke auch an Dich, falls Du dazu gehörst! Ein ganz besonderer Dank gilt auch den Kollegen*innen, die am Ende meiner Zeit und nach mir kamen und mich bei jedem Besuch am Lehrstuhl wärmstens willkommen heißen. Auch meinen Freunden außerhalb des Lehrstuhls möchte ich danken, dass sie während dieser ereignisreichen Zeit immer für Austausch und Unterstützung zur Verfügung standen.

Vielen Dank an meine Eltern für Vertrauen und Freiheit. Außerdem danke ich meinen Schwestern, einfach dafür, dass ihr da seid, ihr seid die besten. Grazie anche a Tiziana e Bruno per l’aiuto e per permetterci di goderci al meglio la bella vita e la nostra famiglia. Eleonora und Olivia, ihr zeigt mir jeden Tag was wirklich wichtig ist im Leben, danke dafür.

Kurzfassung

In Anbetracht des fortschreitenden menschenverursachten Klimawandels und der Rolle von Energie bei der Sicherung eines hohen Lebensstandards für die Weltbevölkerung, wurde und wird die Energiesystemoptimierung genutzt um Erkenntnisse zu unterschiedlichen, möglichen Strukturen des Energiesystems zu gewinnen. Ein Hauptaspekt der aktuellen Forschung ist es kosteneffiziente Energiesysteme zu identifizieren, die eine Senkung der Treibhausgasemissionen erlauben. In diesem Kontext wird im Rahmen dieser Arbeit untersucht wie sich die Unsicherheit in Bezug auf zukünftige Technologiekosten auf die Ergebnisse von Energiesystemoptimierungen auswirkt. Erreicht wird dies mittels stochastischen Optimierungen mit dem Ziel der Kostenminimierung unter Berücksichtigung von Wahrscheinlichkeitsverteilungen. Diese repräsentieren erwartete, zukünftige Technologiekosten und deren zugrundeliegende Unsicherheit. Basierend auf theoretischen Überlegungen und einem vereinfachten Beispielenergiesystem wird gezeigt, dass die jensensche Ungleichung dazu führt, dass Szenariooptimierungen, die nur den Mittelwert der zukünftigen, erwarteten Kostenverteilung berücksichtigen, die notwendigen optimalen Systemkosten systematisch überschätzen.

Ein Energiesystemoptimierungsmodell für Deutschland, welches Wärme-, Elektrizitäts- und Verkehrssektor berücksichtigt, wird formuliert und stochastische Optimierung darauf angewendet. Die Ergebnisse werden mit den Szenarioergebnissen verglichen. Es wird untersucht in wie weit ein Metamodell basierend auf Faktoreffekten oder die Verwendung von weniger Optimierungen für die stochastische Optimierung eine Verringerung des Rechenaufwands ermöglichen. Die Ergebnisse bestätigen ein Überschätzen der notwendigen Systemkosten, wenn der Szenarioansatz basierend auf dem Mittelwert der erwarteten Kosten genutzt wird. Im Fall einer vorgegebenen minimalen Reduktion der CO2-Emissionen um 80 % gegenüber 1990 werden die notwendigen Kosten um ca. 3.5 % und im Falle eines vollständig erneuerbaren Systems um 0.4 % überschätzt. Die stochastische Optimierung liefert den Interquartilsabstand, der genutzt werden kann um die Unsicherheit des Ergebnisses zu charakterisieren. Dieser liegt für das komplett erneuerbare System zum Beispiel bei 13.2 € MWh-1 bzw. bei 27.3 % des Mittelwerts.

Von den untersuchten Möglichkeiten den Rechenaufwand zu verringern zeigt die Nutzung von 30 bis 60 Optimierungen anstatt der 500 Optimierungen, die als Benchmark genutzt werden, vergleichbare Ergebnisse. Die Nutzung der betrachteten Metamodelle hat, abgesehen von der Möglichkeit extreme Ergebnisse vorherzugsagen, im Vergleich dazu keine Vorteile.

Für einige Ergebnisgrößen, insbesondere in den untersuchten nicht erneuerbaren Fällen, weicht der Erwartungswert, der aus der stochastischen Optimierung resultiert, stark von dem Ergebnis der Szenariooptimierung ab. Ein Beispiel dafür sind die CO2-Emissionen, von denen in einem kostenoptimalen System nach der Szenariooptimierung nur ca. 18 % des Erwartungswerts der stochastischen Optimierung emittiert würden. Ähnliche Abweichungen können für andere Ergebnisgrößen identifiziert werden auch wenn die meisten Erwartungswerte durch den Szenarioansatz relativ genau approximiert werden.

Die Anwendung von Algorithmen zur Klassifizierung der Ergebnisse zeigt sich nützlich um die Vielzahl der unterschiedlichen aus der stochastischen Optimierung resultierenden Systeme auszuwerten und z. B. zugrundeliegende Systemstrukturen zu identifizieren. Die inhärente Robustheit der stochastischen Optimierung gegenüber kleinen Änderungen der Eingangsgrößen erhöht das Vertrauen in die Ergebnisse. Dies ist besonders relevant, da der Einfluss von geänderten Einflussgrößen bei Szenariooptimierungen, die die meisten veröffentlichten Studien darstellen, aufgrund der Komplexität der Optimierung nicht a-priori bestimmbar ist.

Abstract

In the light of anthropogenic climate change and the importance of energy to ensure high standards of living, energy system optimization has been and is used in order to gather knowledge regarding different possible energy system layouts. One main driver in recent years has been determining possibilities to cost efficiently mitigate greenhouse gas emissions. In this context this work investigates the influence future uncertainties regarding technology costs have on optimization results. This is achieved by performing energy system optimization with the optimization objective of reducing system cost using stochastic optimization with underlying probability distributions to capture expected future cost and its uncertainty. Based on theoretical considerations and a minimal example energy system, it is shown that Jensen’s inequality leads to an overestimation of necessary, optimal system cost when a scenario optimization taking into account only the expected technology cost means is used.

Stochastic optimization is used on a herein constructed model of the German energy system that comprises electricity, heating and transport sector. Stochastic optimization results are compared to the corresponding scenario results based on the cost distributions means. The derivation of a factor effect based meta model as well as the use of fewer optimizations in stochastic analysis is investigated as means to reduce the computational effort of the proposed methodology. The results confirm the overestimation of necessary cost achieved by scenario optimization, in the complex example by about 3.5 % at the boundary condition of at least 80 % emission reduction compared to 1990 and 0.4 % if the system is completely renewable. Stochastic optimization also yields the inter quartile range which can be used to characterize uncertainty. In the case of a completely renewable energy system the inter quartile range is 13.2 € MWh-1 respectively 27.3 % of the mean.

From the investigated possibilities to reduce computational demand the use of 30 to 60 optimizations in the stochastic case yields similar results compared to the use of 500 optimizations, which serve as benchmark. The use of the proposed meta models does not yield significant advantages apart from the possibility to predict extreme results, which do not show up in the reduced case with 30 to 60 underlying optimizations.

For some result parameters, especially in the not completely renewable cases, the expected value from stochastic optimization differs greatly from that achieved by scenario optimizations. One example are expected carbon emissions at an emission limit of 20 % of 1990 emissions. In this case the scenario optimization yields only about 18 % of the CO2 emissions that result as the the mean of stochastic optimization. For other parameters similar differences are revealed while most parameters are represented well by the scenario results.

Clustering is shown to be useful to manage the plethora of different results from stochastic optimization as it allows to identify underlying system layouts. Stochastic optimization with probability distributions are inherently robust as small changes to the distributions effect the outcome only little. This allows strengthening trust in results as usually readers of energy system studies do not agree with the authors on cost assumptions and the implications of input parameter changes are not predictable due to the complexity of the topic.

Contents

List of Figures

List of Tables

Nomenclature

1 Introduction and Motivation

1.1 Energy System Optimization

1.1.1 Uncertainty in Energy System Optimization

1.1.2 Opportunities and Challenges of Stochastic Optimization of Energy Systems

2 State of Knowledge

2.1 Energy System Optimization (ESO)

2.1.1 Aims of Energy System Optimization

2.1.2 Methods and Models

2.2 Uncertainty in Energy Systems

2.2.1 Origins of Uncertainty

2.2.2 Prediction of Technological Innovation and Development

2.2.3 Uncertainty and Probability in Energy System Models

2.2.4 Taking Uncertainty into Account

3 Research Objectives and Methods

3.1 Research Objectives

3.2 Methods

4 Systematic Errors if Uncertainty is Ignored

4.1 Theoretical Considerations

4.2 Model to Investigate the Effects

4.3 Quantification of Effects

4.3.1 Effect of Distribution Width and Number of Uncertain Parameters

4.4 Summary of Systematic Errors if Uncertainty is Ignored

5 Optimization Model of the German Energy System under Uncertainty

5.1 Energy Demand

5.1.1 Electricity

5.1.2 Transport

5.1.3 Heating demand

5.2 Generation and Transformation

5.2.1 Fluctuating Renewable Electricity Generation

5.2.2 Renewable Generation

5.2.3 Gas to Electricity Processes

5.2.4 Electricity to Gas

5.2.5 Gas to Heat

5.2.6 Electricity to Heat

5.2.7 Storage Applications

5.2.8 Fossil Energy Carriers

5.3 Probable Cost Reductions

5.4 Optimization Planning

6 Results

6.1 Results of the Scenario Approach

6.1.1 Renewable Generation and Fossil Consumption

6.1.2 Electricity Storage

6.1.3 Power to gas technologies

6.1.4 Gas Storage

6.1.5 Gas to Power Technologies

6.1.6 Power to Heat Technologies

6.1.7 Gas Heating Technologies

6.1.8 Heat Storage Technologies

6.1.9 Summary of the Scenario Results

6.2 Stochastic Optimization

6.2.1 Renewable Generation

6.2.2 Electricity Storage

6.2.3 Gas Storage

6.2.4 Gas to Power Technologies

6.2.5 Power to Heat Technologies

6.2.6 Gas Heating Technologies

6.2.7 Heat Storage Technologies

6.2.8 Summary of the Stochastic Optimization Results in the Renewable Case

6.3 Patterns within the Stochastic Optimization Results

6.3.1 Factor Effect Analysis Applied to the Stochastic Optimization Results

6.3.2 Clustering of the Stochastic Optimization Results

6.3.3 Summary of Patterns within the Stochastic Optimization Results

6.4 Stochastic Optimization with lower Computational Demand

6.4.1 Stochastic Optimization with less Optimization Runs

6.4.2 Factor Effect based Meta Model

6.4.3 Comparison of Benchmark Results With Reduced Computational Demand Approaches

6.4.4 Summary of the Comparison of Benchmark Results with Reduced Computational Demand Approaches

7 Discussion

7.1 Comparison of stochastic and scenario results

7.2 Stochastic optimization with reduced computational effort

8 Summary and Conclusion

8.1 Summary of the Influence of Uncertainty

8.2 Summary Energy System Optimization under Uncertainty

8.3 Conclusions, Research Demand and Significance for Decision-Making

9 Bibliography

A Investigation of Systematic Errors

A.1 Latin Hyper Cube and Transformation

B Energy System Opimization

B.1 Probable Cost Reductions

C Results

C.1 Stochastic Optimization Results at 95 % Emission Reduction

C.2 Stochastic Optimization Results at 80 % Emission Reduction

C.3 Patterns within the optimization results - 95% emission reduction

C.4 Patterns within the optimization results - 80 % emission reduction

C.5 Clustering comparison of benchmark and reduced demand stochastic analysis

List of Figures

2.1 Structure of ESO models

2.2 The Foresight Process

3.1 Structure of this work

4.1 Schematic representation of Jensen’s inequality for optimization problems

.

4.2 Influence of the distribution width on output parameters

4.3 Influence of distribution width and number of uncertain parameters

4.4 Influence of distribution width and number of uncertain parameters on installed capacities

5.1 Energy system model structure

.

5.2 Transport time series generation

5.3 Space heating and hot water demand time series generation

5.4 Heat and hot water demand series derivation

5.5 Historic renewable energy auction results

5.6 Impact of surface facility cost on hydrogen cavern storage

5.7 Optimization planning

6.1 Stochastic optimization result, cost of energy 100 % emission reduction

6.2 Stochastic optimization result, renewables 100 % emission reduction

6.3 Stochastic optimization result, electricity storage 100 % emission reduction

6.4 Stochastic optimization result, power to gas 100 % emission reduction

6.5 Stochastic optimization result, gas storage 100 % emission reduction

6.6 Stochastic optimization result, gas to power 100 % emission reduction

6.7 Stochastic optimization result, power to heat 100 % emission reduction

6.8 Stochastic optimization result, gas heating 100 % emission reduction

6.9 Stochastic optimization result, heat storage 100 % emission reduction

6.10 Factor effects for carbon emissions

6.11 Factor effects for PEM FC in centralized application

6.12 Clustering result - 100 % emission reduction

6.13 Clustering result - 100 % emission reduction

6.14 Clustering result - 100 % emission reduction

6.15 Box-plot comparison number of optimizations - cost of energy

6.16 Box-plot comparison number of optimizations - H

2

cavern

6.17 Box-plot comparison number of optimizations - PEM FC

central

6.18 Lathin hyper-cube rotation example

6.19 Quality grade of meta model depending on number of optimizaiton

6.20 Kriging fitting of factor effect PV cost with different approaches

6.21 Box-plot comparison meta model - cost of energy

6.22 Box-plot comparison meta model - H

2

cavern

6.23 Box-plot comparison meta model - PEM FC central

6.24 Histogram comparison reduced computational demand - 60 optimizations

A.1 Example energy system - normalized input parameter distributions

.

A.2 Latin Hyper Cube Transformation to Distribution

C.1 Stochastic optimization result renewables, 95 % emission reduction

C.2 Stochastic optimization result cost of energy, 95 % emission reduction

C.3 Stochastic optimization result electricity storage, 95 % emission reduction

C.4 Stochastic optimization result power to gas, 95 % emission reduction

C.5 Stochastic optimization result gas storage, 95 % emission reduction

C.6 Stochastic optimization result gas to power, 95 % emission reduction

C.7 Stochastic optimization result power to heat, 95 % emission reduction

C.8 Stochastic optimization result gas heating, 95 % emission reduction

C.9 Stochastic optimization result heat storgae, 95 % emission reduction

C.10 Stochastic optimization result renewables, 80 % emission reduction

C.11 Stochastic optimization result cost of energy, 80 % emission reduction

C.12 Stochastic optimization result electricity storage, 80 % emission reduction

C.13 Stochastic optimization result power to gas, 80 % emission reduction

C.14 Stochastic optimization result gas storage, 80 % emission reduction

C.15 Stochastic optimization result gas to power, 80 % emission reduction

C.16 Stochastic optimization result power to heat, 80 % emission reduction

C.17 Stochastic optimization result gas heating, 80 % emission reduction

C.18 Stochastic optimization result heat storgae, 80 % emission reduction

C.19 Clusters - 95 % emission reduction

C.20 Clusters - 95 % emission reduction

C.21 Clusters - 95 % emission reduction

C.22 Clusters - 95 % emission reduction

C.23 Clusters - 95 % emission reduction

C.24 Clustering result - 80 % emission reduction

C.25 Clustering result - 80 % emission reduction

C.26 Clustering result - 80 % emission reduction

C.27 Histogram comparison reduced computational demand - 30 optimizations

List of Tables

2.1 Top-down and bottom-up models

2.2 Examples of uncertainty

2.3 Uncertain quantities

5.1 Means of transport in Germany

5.2 Road transport and energy efficiency

5.3 Structure of heating Demand in Germany

5.4 Distribution of relative heating and hot water demand on building types

5.5 Distribution of relative heating demand on building types

5.6 Renewable generation cost

5.7 Photovoltaic potential in Germany

5.8 Technology data - gas turbines

5.9 Technology data - co-generation from gas

5.10 Technology data - alkaline electrolysis

5.11 Technology data - methanation

5.12 Technology data - heating with gas

5.13 Technology data - low temperature heat from electricity

5.14 Technology data - centralized heat from electricity

5.15 Technology data - battery storage

5.16 Technology data - redox flow batteries

5.17 Technology data - cavern storage

5.18 Technology data - heat storage

5.19 Technology data - future cost

5.20 Correlation between future costs

6.1 Renewable generation technologies in the scenarios

.

6.2 Power to gas technologies in the scenarios

.

6.3 Gas storage in the scenarios

.

6.4 Electricity generation from gaseous energy carriers in the scenarios

.

6.5 Power to heat technologies in the scenarios. Old and new building refer to decentralized, domestic heat production at 60°C and 40°C respectively. For centralized demand the resistance heater supplies heat at <100°C while the electrode boiler produces heat at 100-500°C. Direct electric heating is centralized as well and produces heat at over 500°C

.

6.6 Gas heating technologies in the scenarios

.

6.7 Scenario result - heat storage

6.8 Energy and technology cost means - 100 % emission reduction clusters

6.9 Prediction of cluster probabilities - reduced optimizations

6.10 meta model quality grades

6.11 Parameters meta model performance grade 1

6.12 Parameters meta model performance grade 2

6.13 Parameters meta model performance grade 3

6.14 Comparison scenario, stochastic and meta model mean part 1

6.15 Comparison scenario, stochastic and meta model mean part 2

6.16 Comparison stochastic and meta model IQR part 1

6.17 Comparison stochastic and meta model IQR part 2

7.1 Comparison - scenario and stochastic mean

7.2 Comparison - scenario and stochastic mean heating

A.1 Input parameters model energy system - economics

.

A.2 Input parameters model energy system - efficiencies

.

B.1 Component breakdown photovoltaic

B.2 Component breakdown onshore wind

B.3 Component breakdown offshore wind

B.4 Component breakdown battery capacity

B.5 Component breakdown battery power

B.6 Component breakdown PEM

B.7 Component breakdown AEL

B.8 Component breakdown redox flow battery power

C.1 Energy and technology cost means - 95 % emission reduction clusters

C.2 Energy, emission and technology cost means - 80 % emission reduction clusters

Nomenclature

Abbreviations

ATB

annual technology baseline

AEL

alkaline elektrolysis

BMWi

Bundesministerium für Wirtschaft und Energie

CAPEX

capital expenditure

CCGT

combined cycle gas turbine

CoE

cost of energy

COP

coefficient of performance

dom

.

domestic

ESO

energy system optimization

flh

full load hours

FOM

fixed operation and maintenance cost

futures

versions of the future

GMM

Global MARKAL Model

HP

heat pump

hs

heat storage

HT

high temperature, >1000°C

IQR

interquartile range

LCOE

levelized cost of electricity

lhc

latin hyper cube

lhv

lower heating value

LP

linear programming

LT

low temperature, <100°C

mid

medium temperature, 100-500°C

MIP

mixed integer programming

MM-x3

meta model based on three rotated data sets

MM-x6

meta model based on six rotated data sets

MSE

mean squared error

MT

medium temperature

NRES

not exclusively renewable energy system

OPEX

operational expenditure

PEM

proton exchange membrane

PEM EC

proton exchange membrane electrolysis cell

PEM FC

proton exchange membrane fuel cell

PV

photovoltaic

R

2

coefficient of determination

red

.

emission reduction

RES

renewable energy system

res

.

residential

RTE

round trip efficiency

SCGT

simple cycle gas turbine

SD

standard deviation

SR

scenario result

VOM

variable operation and maintenance cost

SR

scenario result

x1-x6

one time, resp. six times rotated latin hyper cube

Chapter 1

Introduction and Motivation

Energy is important. This is expressed in the use of energy related vocabulary and expressions in everyday life relating to our emotional and physical well being. The development and increase of energy use has historically been closely linked with the improvements in standard of living and economic development [1]. According to MacKay the use of 1 kWh d-1 is comparable to the availability of a human servant [2]. With a final energy consumption of about 2.5 PWh and a population of 82.9 million in 2018 [3] this equals about 85 servants for each person that lives in Germany, not including the energy expense of imported goods. Even though in the last decades a decoupling of energy consumption and the development of economic indicators as e.g. the gross domestic product has been observed [4], there is no doubt that availability of energy is crucial for achieving a high standard of living for the world’s population.

Research in energy systems in the past has been motivated mainly by the need to ensure security of supply. While this is still a relevant topic, in recent years the public consensus based on scientific evidence that anthropogenic climate change is taking place, has caused the mitigation of greenhouse gas emissions to become one of the most important motivations to investigate energy systems as well as to propose and plan possible futures of energy supply.

1.1 Energy System Optimization

Energy system optimization, i.e. a matching of energy supply and demand in an mathematical optimization model, is a useful tool for energy system planning and widely used in government and industry. Many different aspects spanning local to global energy supply, sometimes also including non energy sectors which interact with the energy sector, have been investigated using energy system optimization models.

1.1.1 Uncertainty in Energy System Optimization

Despite or because of the high value energy delivers, the goal of energy system optimization is usually to propose an energy system that supplies energy at the lowest cost, as a measure for efficiency. One of the great advantages of energy system optimization is the possibility to internalize currently externalized costs such as environmental damages from air pollution or the global damages caused by climate change. For these costs the German environmental agency recommends the the use of climate damage costs of 180 to 730 € tCO2-1 depending on the time of emission and how much of the cost inflicted on future generations is taken into account [5].

As the goal of energy system optimization is frequently to give design guidelines for a cost efficient future energy system, there is the necessity to assume values of future properties of the energy system. These are especially technology costs and conversion efficiencies. Any assumed value in this context is, without doubt, heavily uncertain, especially concerning costs. There are many methodologies to systematically derive future costs, and yet there is scientific evidence, that any estimate is always only a guess and for more than a couple of years in the future the prediction quality is basically that of chance [6].

1.1.2 Opportunities and Challenges of Stochastic Optimization of Energy Systems

The term stochastic optimization is not always used with the same meaning. Herein solving an optimization problem many times in order to achieve distributions of the output parameters is intended. This procedure allows for a discretization of the uncertainty regarding input parameters in the form of probability distributions. Therefore stochastic optimization enables both, to evaluate the effect of uncertainty on probable optimal future energy systems and to gain more information from an optimization model compared to a scenario analysis with a set of different scenarios.

Regarding the use of stochastic optimization there are some challenges which might be the cause for the not yet wide spread use of this methodology. These challenges include the communication and interpretation of results and assumptions. In the case of stochastic optimization all these are not single figures but distributions which makes their elaboration much more complex. Another drawback to stochastic optimization is the higher computational effort compared to a scenario analysis due to the necessity to run the optimization many times with different input parameter combinations. Generally models are becoming more complex and detailed, which leads, in the perception of the author, to little or no improvement regarding the computational time required to run an optimization as advances in computing are compensated.

In order to highlight the advantages and contribute to the possibility for wide spread use of stochastic optimization in energy systems some investigations are carried out. These include an investigation of systematic errors when not considering uncertainty as well as the effect and magnitude of the amount of uncertainty. This is expressed by the number of uncertain parameters and the probability distribution widths. Additional to these investigations on a simplified energy system model, a more complex and, in terms of comparability to state of the art energy models, more relevant model is constructed. It models the German energy system and is used for stochastic and scenario optimization. The results are compared and evaluated regarding the information gain. In order to address the before mentioned challenges of interpretability and communication regarding stochastic optimization, factor effect methodology and clustering algorithms are applied. These are used to investigate possible insights regarding the dependencies of optimal configurations from the uncertain parameters and to reduce complexity by introducing clusters with similar properties regarding the energy system structure. This allows for easier communication of energy system optimization results and additional insights, as the structure of the energy system itself, which for many decision makers is one of the important information from energy system optimization, is the criteria for clustering. To enable the use of stochastic optimization also for complex models which do now allow for many model runs, meta model derivation based on factor effect methodology is investigated alongside the use of distributions consisting of fewer optimizations. The comparison reveals comparable information gain for both approaches, with higher accuracy when stochastic optimization with smaller distributions is used compared to meta models based on the same number of optimizations. It is demonstrated that the use of less optimizations enables the computational effort to be reduced significantly while retaining many of the advantages of stochastic optimization.

Chapter 2

State of Knowledge

This chapter is intended to give insights into the development and current state of research regarding energy system optimization and the consideration of uncertainty. When using the term energy system optimization herein the focus is not on the technology scale as e.g. engines or gas turbines including thermodynamic modeling etc., but instead the energy system itself, providing energy in a spatial and temporal context to consumers when it is needed. In the first section of this chapter a definition of energy system planning is given. Furthermore the historic development of energy system optimization and the different aims with which research has been and is performed as well as the different model types and methods that are used are summarized. The research focused on uncertainties in energy systems, its origins, quantification and how it is accounted for in energy system optimization is part of the second section of this chapter.

2.1 Energy System Optimization (ESO)

Historically the development of ESO was catalyzed by two trends. On the one hand this was the growing complexity of energy systems including a mix of generation technologies such as hydro, pumped hydro and thermal power plants as well as more complex transmission grids [7]. The other important trend was the development of the necessary mathematical tools [7] which has ultimately led to ESO as we understand it today. Pumped hydro power plants e.g. introduce storage into the power system, the optimal operation of which is not trivial. An important milestone in the development of ESO was the definition of "System Planning" by a subcommittee of the Edison Electric Institute in 1953 that was disseminated by the Edison Electric Institute and the American Institute of Electrical Engineers [8].

“System planning is the preparation of a rational program for the development of an electric power system, so that it can evolve in an orderly and economic manner. It includes forecasting and analyzing loads, rationalizing standards of service, anticipating trends in equipment design and coordinating the various elements of the system into a well-designed whole; it is particularly concerned with plans for changes and additions to generation, transmission, substations and distribution facilities. It is not concerned with the problems of day to day operation or design except to the extent that these problems effect future system development. Briefly, electric system planning is the process of determining when, what facilities should be provided where in order to assure adequate electric service at minimum average annual cost to the community.” [8]

Contrary to the definition from the Edison Electric Institute, in the early stages the upcoming techniques have been used especially for power plant scheduling and plant operation. Kirchmayer [7] gives an overview over the scientific developments from 1942 to 1950. These include economic loading, reduction of transmission losses, the representation of incremental fuel costs and the necessary mathematical methods for optimized scheduling, automatic operation of networks and dispatching. All these advances have been made with the goal to lower the cost of providing electricity [7]. Kirchmayer himself contributed widely to the field of operation planning, the publications [9–11], co-authored by him, all regarding hydroelectric plants, their operation or interaction with other power plants, have each been cited over 20 times with the most recent citations in 2018 and 2019, showing the continued relevance of the approaches. The mathematical basis for ESO as we know them today, originating from the years 1949 to 1963, have been presented in 1963 by Dantzig [12]. This includes the introduction of the term linear programming for linear inequation theory with the goal of minimization. He states that what linear equation theory had been for the natural sciences, linear inequation theory, i.e. linear programming, has become for decision problems [12].

In 1974 Finon describes a mathematical, linear programming model of the French energy sector [13]. The optimization model spans the years 1976 to 2020, divided in various sub periods. It includes energy conversion processes, distribution and storage, as well as different types of consumption including transport, residential and industry sector. The demand side is simplified via a representation of three demand configurations derived from time series analysis. The three load cases are peak load, i.e. the 120 hours with the highest load, base load and the “critical period”, which Finon identified as most influencing for the plant choice and which corresponds to a 800 to 1200 hour per year period with high load, inferior to that of peak load. With this representation in order to allow for an optimization of the installed capacity of energy infrastructure and conversion technology, Finon performs system planning according to the definition by the Edison Electric Institute [8]. The basis of the model is that energy supply and demand must be balanced during each period. Many current ESO models work similar to Finon’s model, their underlying structure is depicted in fig. 2.1. This structure is adapted to the different aims with which models have been developed. This combination of system planning with optimization is called ESO. As Finon’s model contains the simplification of only three load conditions, it is not suited to optimize volatile electricity production e.g. by photovoltaic or wind power plants. As these have become more important during the last decades, many models with a higher resolution in time have been developed.

A basis for the wide spread use of ESO is the ESO framework MARKAL, published by the International Energy Agency, founded in 1974. Even though other frameworks exist MARKAL is one of the most influential. The first efforts to develop an ESO model at the IEA began in 1976 with its Energy Technology Systems Analysis Program. The linear programming framework MARKAL was first presented at the Energy Systems Analysis International Conference in 1979 by Fishbone [14] and later published in the International Journal of Energy Research [15]. In MARKAL, optimization spans several decades and constraints are implemented, including that the demand of an energy form must be met by production or by supply from storage in each time step. Additional constraints can be introduced, the MARKAL framework e.g. contains constraints regarding the maximum capacity of district heating networks and there is the possibility to implement a constraint on growth of annual investment costs [14]. A typical constraint in more recent studies is the definition of maximal carbon dioxide emissions during the optimized period. In contrast to Finon, six typical electrical demands are identified by time series analysis that takes into account yearly and daily fluctuations. The availability of a technology during peak periods is considered with the use of availability factors. [15]

Figure 2.1: The underlying structure of ESO models

2.1.1 Aims of Energy System Optimization

ESO has been, and is used for different purposes ranging from the design of energy systems on the level of neighborhoods [16] to determining political pathways for energy system development on an international level [17]. MARKAL has been one of the first ESO model-frameworks with wide spread use. Extensions of it e.g. the Global Multi-regional MARKAL model [18] and TIMES [19] are still relevant today. Therefore it is suited for exemplary investigation of the evolution of ESO use, here with a focus on national or state level analysis. An analysis of an excerpt of the 355 publications listed in Scopus at the time of writing that cite the original MARKAL publication [15] enables us to determine a trend over time of the main aims with which ESO have been used. In the publication describing MARKAL [15], the goals with which the model has been created are named:

Comparing current and future energy technologies and recourses regarding how they satisfy expected future energy demands.

Evaluate future development of implementation and costs of technologies as well as resources and the change of current resource utilization (e.g. petroleum).

Gain knowledge about the sensitivity of an optimal future energy system regarding fuel costs and technology cost development.

Assessment of the effects efficiency improvements have on the energy system.

These objectives are in general the aims of the specific publications discussed hereinafter, as these are specifications of these goals. An additional objective that is frequently mentioned in the publications compared is the evaluation of political strategies or the definition of such, using the insights gained with the model. A more recent account of the various uses the MARKAL model has been put to is given in [20]. Additional to the above the following applications are reported:

5. The identification of investment strategies based on least-cost energy systems.

6. Finding solutions to comply with environmental restrictions in a cost efficient manner.

7. Gain insight into effective prioritization of research and development regarding emerging technologies.

8. Definition of greenhouse gas emission reduction goals and evaluation of emission trading considering the context of international cooperation.

Two relatively early publications that cite the original MARKAL publication [15], one by Cofala [21] in 1985 and one by Luthra and Fuller [22