Empirical Analysis of Price-Curves at the EEX

Empirical Analysis of Price-Curves at the EEX

Nicolas Samyn

Matriculation Number 04 607 438

Etzelbüntstrasse 5a, 9011 St. Gallen, Switzerland

+41 (0) 78 603 05 92, [email protected]

Master Thesis

University of St. Gallen (HSG), Switzerland

Institute for Operations Research and Computational Finance (ior/cf-HSG)

Prof. Dr. Karl Frauendorfer

November 5th, 2010

[intentionally left blank]

I

Abstract

This paper provides an empirical analysis of price curves for the German electricity market at the

EEX with regard to the production margins, respectively the percentage of used capacity for each

generation type. The following fields of research are of particular interest: what is the impact of

changing generation capacities on price, on market volatility and on the shape of the demand and

supply curves.

The findings suggest that production margins respectively the percentage of used capacity per gen-

eration type in the German electricity market are a rather powerful indicator for prices, as well in the

day-ahead market as in the intraday market. On the other hand, their influence on market volatility

and on the shape of the demand and supply curve is rather marginal.

II

Acknowledgements

I would like to express my gratitude to everyone who motivated and supported me while I was writ-

ing on this master thesis. Special thanks go to Prof. Dr. Karl Frauendorfer, who sparked my interest

in the electricity market, for his helpful comments and precious suggestions. Furthermore, I owe

many thanks to all the people who assisted me in revising this thesis and to my family who supported

me during this special task.

III

Table of Contents

Abstract I

Acknowledgements II

Table of Contents III

Table of Figures V

Table of Tables VI

Abbreviations, Notions and German Words VII

Goal, Methodology and Build Up of the Thesis 1

1. Introduction 3

1.1 Electricity in General 3

1.2 The German Electricity Market 3

2. Data Set 7

2.1 Installed, Available and Actually Used Generation Capacities 7

2.1.1 General Information 7

2.1.2 Reporting Companies 8

2.1.3 Installed Capacities 9

2.1.4 Available and Forecasted Capacities 10

2.1.5 Actually Produced Electricity 12

2.2 Demand and Supply Curves 14

2.3 Price and Quantity 17

3. Preparing the Data Set 20

3.1 Analysing Production Capacities 20

3.1.1 Reserve Margin 20

3.1.2 Degree of Capacity Utilisation 23

3.1.2.1 Generation from Uranium 25

3.1.2.2 Generation from Lignite 25

3.1.2.3 Generation from Run-of-the-river 25

IV

3.1.2.4 Generation from Wind 25

3.1.2.5 Generation from Coal 26

3.1.2.6 Generation from Gas 26

3.1.2.7 Generation from Pumped Storage and Seasonal Storage 26

3.1.2.8 Generation from Oil 26

3.2 Elasticity 27

3.2.1 Point Elasticity 27

3.2.2 Arc Elasticity 34

3.2.3 Elasticity in the Literature 36

3.3 Volatility 38

3.3.1 Volatility of Day-ahead Prices 38

3.3.2 Volatility of Intraday Prices 43

4. Empirical Results 45

4.1 Dependent variables 45

4.2 Explanatory variables 45

4.3 Results 46

4.3.1 Regression Analysis: Day-ahead Prices 46

4.3.2 Regression Analysis: Intraday Prices 48

4.3.3 Regression Analysis: Price Elasticity of Demand 50

4.3.4 Regression Analysis: Price Elasticity of Supply 51

4.3.5 Regression Analysis: Day-ahead Price Volatility 53

4.3.6 Regression Analysis: Intraday Price Volatility 54

5. Concluding Remarks 56

References 58

Appendix 66

Declaration of Authorship 72

V

Table of Figures

Figure 1: Installed generation capacity by fuel type 4

Figure 2: Electricity production by fuel type 4

Figure 3: Grid of the transmission system operator 5

Figure 4: Generation capacities under 100 MW by generation type 9

Figure 5: Available capacity for each generation type on a daily basis 11

Figure 6: Expected electricity generation through wind turbines on an hourly basis 11

Figure 7: Actual production with respect to different generation types (in MW) 13

Figure 8: Price (in EUR per MW) – Quantity (in MW) bids for the demand 15

Figure 9: Price (in EUR per MW) – Quantity (in MW) bids for the supply 15

Figure 10: Intersection of the demand and supply curve on hour 1, June 6th 2010 16

Figure 11: Hourly intraday and day-ahead prices 17

Figure 12: Hourly intraday and day-ahead quantities 18

Figure 13: Hourly margin for the German electricity market 22

Figure 14: Margin distribution for the German electricity market 22

Figure 15: Used capacity over time with respect to generation type 24

Figure 16: Point elasticity of demand for the German electricity market 33

Figure 17: Point elasticity of supply for the German electricity market 33

Figure 18: Arc elasticity of demand for the German electricity market 35

Figure 19: Arc elasticity of supply for the German electricity market 35

Figure 20: ��,�� , average hourly volatility over a time window of 1 week 40

Figure 21: Hourly volatility using a rolling window 42

Figure 22: Relationship between intraday price (average, low, high) and day-ahead prices 43

Figure 23: Hourly intraday price fluctuation for the German market 44

Figure 24: Intraday volume to difference between expected and actual wind production 49

VI

Table of Tables

Table 1: Companies reporting to the transparency platform 8

Table 2: Installed capacity by generation type (Voluntary publication) 9

Table 3: Available production capacities with respect to different generation types (in MW) 10

Table 4: Actual production with respect to different generation types (in MW) 14

Table 5: Price and Quantity for intraday and day-ahead markets 18

Table 6: Margins in the German electricity market 23

Table 7: Used capacity with respect to generation type 23

Table 8: R2 for polynomials of different order fitting the demand and supply curves 30

Table 9: Point elasticity of demand and supply 32

Table 10: Arc elasticity of demand and supply 34

Table 11: Demand elasticity in the electricity market – a summary 36

Table 12: Daily volatility figures for intraday, trans-day and trans-week prices 39

Table 13: Hourly volatility over each day 40

Table 14: Hourly volatility for the German market 41

Table 15: Hourly volatility computation using a rolling window 42

Table 16: Relationship between intraday and day-ahead prices in the German market 43

Table 17: Hourly intraday price fluctuation: key figures 44

Table 18: Regression analysis: day-ahead prices 46

Table 19: Regression analysis: intraday prices 48

Table 20: Regression analysis: price elasticity of demand 50

Table 21: Regression analysis: price elasticity of supply 51

Table 22: Regression analysis(2): price elasticity of supply 53

Table 23: Regression analysis: day-ahead price volatility 53

Table 24: Regression analysis: intraday price volatility 54

VII

Abbreviations, Notions and German Words

Bundesministerium für Wirtschaft und Federal Ministry of Economics Technologie [BMWi] and Technology

Bundesnetzagentur Federal Network/Grid Agency

Bundesverband der Energie- und German Federal Association for Energy- Wasserwirtschaft and Watermanagement

Bundesverband WindEnergie German Federal Association for Wind Energy

EEX European Energy Exchange

EEG (Erneuerbare-Energien-Gesetz) Renewable Energies Source Act

EnWG (Energiewirtschaftsgesetzt) Energy Industry Act

EUR Euro

Hour 1 Hour from 00:00 – 01:00 am

kWH Kilowatt hour

MW Megawatt

MCP Market Clearing Price

MCQ Market Clearing Quantity

OTC Over The Counter

RTP Real Time Pricing

Statistisches Bundesamt German/Federal Statistical Office

TOU Time Of Use

TSO Transmission System Operator

TWh Terawatt hour


- 1 -

Goal, Methodology and Build Up of the Thesis

This paper’s purpose is to explore the effects of varying generation capacities in the German electric-

ity market. Installed generation capacity in Germany is constant in the short to mid- term, however

readily available generation capacities do vary over time as production units have to be taken off the

grid for maintenance, or for lack of natural resources (wind, water, etc.) to activate the generating

units. The focus of this study will lie on three main topics. Firstly: how are prices influenced by

changing generation capacities. Secondly: how is the shape of the demand and supply curve affected

by changes in the available generation capacities. Thirdly: how is the market volatility affected by

varying generation capacities in the German electricity market. The math, wherever needed, will be

mostly performed by using MATLAB 2009a.

In order to reach that goal, this paper will proceed as follows. Chapter 1 will give a brief introduction

on the characteristics of electricity as well as on the German electricity market in general. The focus

will clearly be on introducing the generation capacities of Germany as well as on presenting the

European Energy Exchange (EEX) in Leipzig which has advances to a neuralgic player in the Euro-

pean energy market in general, and in the German electricity market in particular.

Chapter 2 will present the data set used in this paper. First, the data for the generation capacities will

be explored. The focus will lie on answering the following questions: Who is providing the data?

How much of the market is covered? How much production capacity is installed? How much pro-

duction capacity is available? How much electricity has actually been produced on an hourly basis?

In a second part, the results of the day-ahead auctions for the German electricity market at the EEX

will be presented. The focus will here be to provide on the one hand some insights into the bidding

process which leads to the price-quantity bids for every hour of the following day as well as to pre-

sent on the other hand the demand and supply curve resulting from the bidding procedure and their

general shape. In a third section, Chapter 2 will briefly summarized two time series of prices and

quantities for the German electricity market. The first time series is the resulting price-quantity of the

day-ahead auction, while the second is the resulting time series of the intraday auction. Their respec-

tive role as well as their “raison d’être” will be introduced.

Chapter 3 will prepare the introduced data so that they can be used for further analysis in Chapter 4.

Production margins will be computed with respect to the generation capacities. These margins are

calculated for the German electricity market on an hourly bases, as well on a global generation level

as on an individual (generation unit type) level, for which case it has been decided to use the per-

centage of used capacity metric for convenience purposes. This section aims at quantifying the re-


- 2 -

sulting demand and supply curves from the day-ahead auction so that each curves is described by an

individual measure. Two possibilities will be introduced: on the one hand, point elasticity and on the

other hand, arc elasticity. Market volatility is another key aspect of the market, this is the reason why

the goal of the last section of Chapter 3 is to propose a volatility measure for each hour of either set

of hourly prices (day-ahead and intraday). The general methodology as well as the main problems

will be discussed along with the results obtained.

Chapter 4 will start discussing how varying generation capacities affect the electricity market by

running single and multiple regression analysis such as to describe their role in price changes, in

changes with regard to the shape of the demand and supply curve as well as their influence on market

volatility.

Chapter 5 will yield some concluding remark.


- 3 -

1. Introduction

1.1 Electricity in General

Electrical power is with respect to many aspects a peculiar commodity. Economic activity and daily

life in the western world in particular has become unimaginable without electricity. Be it for trans-

portation, production or recreation, the use and needs for electricity is omnipresent. The peculiar

characteristics of electricity have been major drivers for the electricity market and its design.

Thereby, especially physical and technical characteristics play an important role. From the technical

point of view, the need to service a grid for the distribution of electricity to end consumers is one

reason why the electricity business is very capital intensive. Furthermore, the physical supply from

generators and the physical demand from consumers must be equilibrated at all point in time and on

all points on the electrical grid, with essentially zero tolerance. Any disruption in this equilibrium

can have severe consequences for the power systems and equipment connected with the grid. An-

other trait of electricity is that it cannot be stored easily, so that you cannot produce your electricity

in advance and store it for whenever the demand will be higher (Purtscher, 2000). The only possibil-

ity to store electricity is to use water as a storage medium by pumping it up into a storage lake. Using

this methods however means to take into account (small) energy losses (Egger, 1997). For these rea-

sons, the production and distribution of electricity was for many years a monopolistic issue. As the

benefits of competitive markets have been proven by economic theory and empirical evidences in

many markets, especially in deregulated western industries, many countries started deregulating their

power sector. Nevertheless, the electric industry has been the last of the major industries to be de-

regulated due to its peculiar characteristics that make competition problematic (Kwoka & Madjarov,

2007). Furthermore, electricity prices exhibits unconventional characteristics. The price of electricity

is greatly inclined to change at each delivery period, exhibiting daily, weekly, monthly and even

yearly seasonality’s (Eyeland & Wolyniec, 2003).

1.2 The German Electricity Market

The liberalisation of the electricity market in Europe started back in the late 1980s with the deregula-

tion of the electricity industry in England and Wales after the election of Mrs. Thatcher, followed in

the next couple of years by the deregulation of the Nordic market (Norway, Sweden, Finnland). The

European Union started to prepare an EU-wide policy of electricity market liberalisation (Directive

96/92/EC) which came into force in February 1997. (Green, 2006)


- 4 -

lignite

23%

nuclear

22%coal

18%

gas

13%

renewable

16%

others

8%

lignite

15%nuclear

16%

coal

20%

gas

13%

renewable

24%

others

12%

To comply with the European Union’s regulation, Germany established the New German Energy

Law (Energiewirtschaftsgesetz, EnWG) in 1998 which induced the liberalisation of the energy mar-

ket in Germany. Since then, the German electricity market has undergone profound changes charac-

terized by mergers, cooperation, strategic partnership and the emergence of power exchanges of

which the European Energy Exchange (EEX) emerged in 2002 and remains as the unique electricity

exchange for Germany. According to official authorities in Germany, there are around 1’100 elec-

tricity producers, grid operators and traders which account for roughly 82% of the domestic electric-

ity production. Out of those 1’100 companies, four large utilities (RWE, E.ON, Vattenfall, and

EnBW) dominate the market, holding close to 84.7% of the production capacities of the German

electricity market (Krisp, 2008). To that, 360 companies owning own generators must be added

which account for another 8% of the German production. The remaining 10% are accounted for by

the EEG law (renewable energy sources act) and includes mostly electricity production from renew-

able energy sources; a sector whose importance is steadily increasing (Statistisches Bundesamt,

2009). The quantity of electricity produced in 2009 amounted to a total of 596.8 Billion kWh,

whereas the main energy sources where: lignite (24%), nuclear (23%), coal (18%), natural gas

(13%), renewable energies (16%) and others (8%) (Bundesverband der Energie- und Wasser-

wirtschaft, 2010). In order to produce this amount of electricity, generators with a production capac-

ity of around 132’700 MW are installed in 2009 (Bundesnetzagentur, 2009). Figure 1 and Figure 2

show that the installed generation capacities by fuel type differ largely with regard to the actually

produced electricity by fuel type. This can be explained by the fact that different production units

generate electricity during a different amount of hours throughout a year (Bundesministerium für

Wirtschaft und Technologie [BMWi], 2010).

Currently, there are four transmission system operators (TSO) in Germany which are responsible for

the transmission of electrical power from the generators to the end consumers. Those TSO have their

Figure 2: Electricity production by fuel type

Based on: Bundesnetzagentur (2009)

Figure 1: Installed generation capacity by fuel type

Based on: Bundesnetzagentur (2009)


- 5 -

origin with the big four (RWE, E.ON, EnBW and Vattenfall) in the German electricity market that

were forced over the course of the last 2 years to separate their grid from their other activities. Today

the 4 TSOs are: 50hertz, transpower, amprion and EnBW Transportnetze, whose control areas can be

seen on Figure 3 (Frontier Economics, 2009).

Beside the changes on the supply and distribution side, one major novelty brought about by the de-

regulation of the German electricity market is the introduction of power exchanges. Today, the Euro-

pean Energy Exchange (EEX) which emerged from the merger of the Leipzig and the Frankfurt ex-

changes in 2002 is the leading energy exchange in Continental Europe and offers trading possibilities

for power, natural gas, CO2 emission allowances and coal. Regarding the power market, the EEX is

offering the possibility for spot trading (day-ahead auctions, intraday auctions) as well as the possi-

bility for derivatives trading (futures and options trading), as well for Germany, France, Austria and

Switzerland (EEX, 2010a). The EEX is therefore offering a trading platform which co-exists with

the very large OTC market that is found in the electricity market. As of 2009, the power spot market

of the EEX observed a volume of 203 TWh, which represents roughly 34% of the total German elec-

tricity production (EEX, 2010a). Prices observed on both OTC and spot market are very similar,

since diverging prices would invite arbitrageurs to make riskless profits from the price differences,

Figure 3: Grid of the transmission system operator

Based on: Ice gixxe (2010)


- 6 -

therefore closing the gap. Even though roughly 66% of the electricity produced is sold OTC, traders

find it convenient to use to spot market of the EEX which allows trading on a day-ahead or even in-

traday time frame to balance their portfolios in the short term, since demand and supply of electricity

must always match.


- 7 -

2. Data Set

This chapter will provide a brief overview over the data sets that is used in writing this paper. First,

the data set regarding the generation capacities will be introduced before exploring the price quantity

bids the market participants place on the day-ahead auction at the EEX and closing with the market

clearing prices and quantities which do result from those auctions as well as the prices and quantities

that do result from the intraday trading for every hour. The time series of the data set account for 9

weeks, from the June 2nd

, 2010 to August 3rd

, 2010. These are 63 days, respectively 1512 hours. 1

2.1 Installed, Available and Actually Used Generation Capacities

2.1.1 General Information

On October 28th

2009, the EEX and the four German TSOs (Amprion GmbH, EnBW Transportnetze

AG, Transpower Stromübertragungs GmbH and Vattenfall Europe Transmission GmbH) announced

that “Transparency in Energy Markets” goes live. They have implemented a new central transpar-

ency platform for generation and consumption data. With this step, new publication requirements

under the “Congestion Management Guidelines”, which is an annex to the “EC Directive No.

1228/2003”, are implemented for the first time in this form in Continental Europe, integrating to the

platform the already existing practice of some market participants of voluntary publication. The aim

of this platform is to strengthen the confidence placed in the market by increasing the comprehensi-

bility of market pricing. The new platform can be found on www.transparency.eex.com and provides

all time series discussed in this part. (Amprion, EEX, EnBW, Transpower & Vattenfall, 2009)

The generation and consumption data that are published on the transparency platform can be divided

into two categories:

1. Statutory Publication Requirements of the Transmission System Operators: These publi-

cation are based on the “Congestion Management Guidelines” and on section 4.3 of the

“Report on Transparency”.2

2. Voluntary Commitment of the Market Participants: These data were already being pub-

lished before and the tried and tested structure of the EEX transparency platform were

perpetuated. (EEX-Transparency, 2010a)

1 The length of the time series was restricted to 9 weeks due to the fact that most data on generation capacities had to

be retrieved by hand. 2 The publication requirements are provided on the website of the Bundesnetzagentur:

http://bundesnetzagentur.de/cln_1931/DE/Sachgebiete/ElektrizitaetGas/AllgemeineInformationen/TransparenzStrom

markt/VeroeffentlichungErzeugungsdaten_Basepage.html


- 8 -

The actual degree of coverage reaches 79.26% and is established with regards to the Statutory Pub-

lication Requirements of the Transmission System Operators on the basis of the ratio of the installed

capacity reported on the platform and the entire installed generation capacity in Germany, which is

according to the Monitoring Report 2009 of the Federal Network Agency roughly equal to 132’700

MW. (EEX-Transparency, 2010b)

2.1.2 Reporting Companies

As of August 11th 2010, 12 companies are reporting to the transparency platform. Their name and

installed generation capacities can be taken out of Table 1.

Corporate Name Installed capacity in MW

E.ON 19’817

EnBW 9’606.1

EVN AG 1’120

Grosskraftwerk Mannheim AG 1’143

RheinEnergie AG 531

RWE Power AG 25’642.1

Stadtwerke Leipzig GmbH 167

SWM Services GmbH 1’009

TIWAG, Tiroler Wasserkraft AG 361.1

Trianel Gaskraftwerk Hamm GmbH & Co.KG 850

Vattenfall Europe AG 15’176

VSE AG 118

Total 75’540.3

Table 1: Companies reporting to the transparency platform

Based on: EEX-Transparency (2010c)

The figures presented in Table 1 involve the generation capacities from coal, gas, lignite, oil,

pumped storages, run-of-the-river, seasonal storage, uranium and others with production capacities

above 100MW. Next to those 75’540.3MW of installed capacities, Figure 4 on the next page shows

the installed facilities with generation capacities of less than 100MW which are not accounted for in

Table 1.

In total, 31’858.3MW of installed capacity belong to this later category and are distributed according

to Figure 4. (EEX-Transparency, 2010c)3

3 The total generation capacity installed for generators under 100MW has been updated since August 11

th and is now,

on 31th

October, equal to 49’649.6 MW.


- 9 -

Coal

1%

Garbage

2%

Gas

10%

Lignite

3%Oil

2%

Others

9%

Pumped storage

4%

Run-of-the-river

5%

Seasonal

storage

1%

Solar power

2%

Wind

61%

2.1.3 Installed Capacities

All further discussions will be based on the data published under the heading Voluntary commitments

by the market participants which cannot be directly compared with the installed capacity mentioned

above since the degree of coverage is smaller, as not all market participants do publish their data on a

voluntary basis. The reason for choosing this set of data is, that there is a clear fracturing between the

different generation types. The data are ex-ante information regarding the generation capacities and

include some generation units with less than 100MW of nominal output. Table 2 shows following

generation capacities that are installed according to the data published voluntarily by the market par-

ticipants.

Generation Type Installed capacity in MW

Uranium 20’279

Lignite 19’823

Coal 16’141.6

Gas 8’609

Pumped storage 5’993

Oil 1’135.9

Seasonal storage 594

Run-of-the-river 478.6

Total 73’054.1 Table 2: Installed capacity by generation type (Voluntary publication)

Based on: EEX-Transparency (2010d)

As electricity generated through wind energy plays an important role in the electricity generation in

Germany, the installed wind turbine capacities must be taken into account. According to the Bundes-

verband WindEnergie e.V. (2009), wind turbines with a generation capacity of 25’777MW were in-

Figure 4: Generation capacities under 100MW by generation type

Based on: EEX-Transparency (2010c)


- 10 -

stalled at the end of 2009. Data from the transparency platform show that wind generating units with

an installed production capacity of 19’494.5MW do report their expected output as well as their ac-

tual electricity production (EEX-Transparency, 2010e). Therefore, 92’548.6MW of installed capacity

are considered as our maximal possible output if all generating units are working under full load

which represents roughly 69.74% of the totally installed generation capacity in Germany and which

is, as already mentioned before, slightly lower than the total coverage provided by the transparency

platform of the EEX.

2.1.4 Available and Forecasted Capacities

Installed generation capacities are not always available for electricity production. On the one hand,

regular maintenance have to be realized while on the other hand, natural resources to power the tur-

bines might not be available, especially water (run-of-the-river, nuclear for cooling purposes) and

wind (not enough or too strong). For this reason, installed generation capacities are only interesting

from the point of view of the maximal generation capacity of a country. Much more insights into the

actual situation on the supply side is provided by the available power plant capacity, respectively by

the forecasted production when thinking of wind turbines. Wind turbines prove to be very peculiar

power plants since wind speed is very difficult to forecast accurately. Unlike all other generating

units (expect for solar generating plants which are not considered here since their importance for the

German electricity market is only marginal), wind turbines most important factor when deciding over

their availability to produce electricity is not only mankind but to a very large extend nature. This

explains the unpredictability of this energy source. The available power plant capacities for all gen-

eration types are provided on a daily basis. Expected wind turbine generation however is projected

on a quarter-hourly base for the following day.4 Figure 5 provides a graphical overview over the

availability of conventional generation capacities (lignite, nuclear, coal, gas, oil, run-of-the-river,

seasonal & pumped storage) for the German market from June 2nd

2010 to August 4th

2010, Figure 6

4 The quarter-hourly figures are compounded such as to have one hourly figure.

Average Median St. Deviation Maximum Mininum Difference St.Dev/Average

Uranium 14330.2 14277.9 1027.9 16586.7 12104.6 4482.1 7.17%

Lignite 15986.8 15993.3 721.1 17366.7 14291.2 3075.5 4.51%

Coal 13375.2 13536.2 718.1 14586.8 11580.1 3006.7 5.37%

Gas 6277.8 6353.5 552.2 7093.8 5002.3 2091.5 8.80%

Pumped storage 4445.3 4521.7 363 4868.7 3450.7 1418.7 8.17%

Oil 958.5 1033.2 167.5 1035.1 121.9 913.2 17.48%

Seasonal storage 456.3 477 70 522 288 234 15.35%

Run-of-the-river 419.9 421.2 8.4 435 400.8 34.2 2.00%

Wind 2182.1 1575.55 1869.8 12965 234.8 12730.3 85.69%

Table 3: Available production capacities with respect to different generation types (in MW)



- 11 -

provides furthermore the hourly expected wind production while Table 3 briefly summarizes the key

features of those available generation capacities.

0

2000

4000

6000

8000

10000

12000

14000

Exp

ect

ed

pro

du

ctio

n [

in M

W]

H [Hourly value for every day]

Figure 6: Expected electricity generation through wind turbines on an hourly basis

Based on: EEX-Transparency (2010f)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Av

ail

ab

ilit

y [

in M

W]

T [in days]

Uranium

Lignite

Coal

Gas

Pumped storage

Oil

Seasonal storage

Run-of-the-river

Figure 5: Available capacity for each generation type on a daily basis



- 12 -

The available generation capacities for production with uranium, lignite, coal and run-of-the-river

have a much lower volatility than the one with gas, pumped storage, oil and seasonal storage. Even

though electricity production (respectively consumption) is not looked at, weekly patterns are ob-

servable, especially in the availability of gas and to a lesser extend of coal fired power plants.

Regarding wind power generation, the most important aspect is wind forecast. Based on their wind

forecast, the transmission system operator publish daily at 6.00 pm the expected wind power genera-

tion for the next day on every specific quarter-hour (EEX-Transparency, 2010f). In order to reduce

the different time windows used, the quarter-hourly forecast is condensed to provide an hourly fore-

cast by taking the average over the 4 quarter-hourly quantities as is done by the EEX.

As could be anticipated, expected wind power generation does not follow any daily or weekly pattern

since it is only depended on available wind. Furthermore, as Table 3 on the page 10 shows, the vola-

tility in expected wind power generation is extremely large which requires an increased flexibility of

the electricity system in order to be able to handle those fluctuations.

2.1.5 Actually Produced Electricity

The next step is to explore actually produced electricity with regard to each individual generation

type. The time series for those data are on an hourly basis, since demand for electricity is very vola-

tile and production capacities therefore have to adjust on a regular basis. Table 4 summarizes the re-

sults from Figure 7 with respect to the actually produced electricity in the German market between

June 2nd

2010 and August 4th

2010.

Electricity produced through wind turbines has to be considered from a different point of view since

transmission system operators are committed by the Erneuerbare-Energien-Gesetz (EEG) to purchase

it prior to electricity from other sources (§21 and §8 Abs. 1 EEG). Practically speaking, electricity

produced by wind energy reduces the demand, which leads in theory to a lower market clearing price

(Fürsch, Nicolosi & Lindenberger, 2010).

Table 4 clearly shows that the actual production of the power plants generated by uranium, lignite as

well as run-of-the-river power plants have a fairly low volatility. This is the case because they are

used to cover the Baseload demand. The actual production for the remaining power plants (e.g. coal,

gas, pumped storage, oil and seasonal storage) exhibit on the other hand a much higher volatility.

Figure 7 displays clearly the daily and especially weekly pattern of those production facilities, with a

higher production on weekday rather than on Saturdays and Sundays coupled with an increasing pro-

duction during day time, in short during the on-peak hours.


- 13 -

0

2000

4000

6000

8000

10000

12000

Act

ua

l pro

du

ctio

n [

in M

W]


Coal

Oil

Gas

0

500

1000

1500

2000

2500

3000

Act

ua

l pro

du

ctio

n [

in M

W]


Pumped-storage

Run-of-the-river

Seasonal storage

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Act

ua

l pro

du

ctio

n [

in M

W]


Wind

Uranium

Lignite

Figure 7: Actual production with respect to different generation types (in MW)

Based on: EEX-Transparency (2010g and 2010h)


- 14 -

Table 4: Actual production with respect to different generation types (in MW)

Based on: EEX-Transparency (2010g and 2010h)

Coal and gas power plants always have a minimum production even though both are typical Peak-

load power plants: Fürsch et al. argues that this is due to some “must-run” facilities which have to

provide system services (2010), another reason could be the lead-up time that most thermal power

plants face.

2.2 Demand and Supply Curves

The EEX offers a spot market that is used by the trading participants to optimise their procurement

and sale of electricity in the short term. As of August 12th

2010, there are 166 trading participants in

the spot auction market for Germany as well as 164 trading participants in the spot intraday market

for Germany (European Power Exchange [EPX], 2010). The day-ahead auctions for Germany have

the following characteristics (EEX, 2010a):

- Minimum volume is 0.1 MW

- Minimum price change is EUR 0.1 per MW

- Underlying is electricity traded on the following day

- Electricity has to be delivered within one of the TSO zones

- Daily auction at 12:00 noon, 7 days a week, 365 days a year including holidays

- Results of the daily auction are published between 12:35 and 12:45 am.

- Orders comprises up to 250 price/quantity combinations for every hour of the following

day

- Technical limits for the prices are between EUR -3000 per MW and EUR 3000 per MW.

The curves that result from this bidding process can be called demand respectively supply curve. On

the one hand, the demand side bids for each price the quantity it is willing to purchase and on the

other hand, the supply side bids for each price the quantity it would be ready to produce. This is ex-

actly the definition provided by Pindick and Rubinfeld: “The demand curve is the relationship be-

tween the quantity of a good that consumers are willing to buy and the price of the good”, and “The

Average Median St. Deviation Maximum Mininum Difference St.Dev/Average

Uranium 13527.4 13774.5 1561.3 16629.8 8145.8 8484.0 11.54%

Lignite 14879.8 14954.6 967.6 17050.4 11004.9 6045.5 6.50%

Coal 5784.7 5505.7 2905.9 11200.3 414.3 10786.0 50.23%

Gas 1297.9 1296.7 638.0 4890.8 382.4 4508.4 49.16%

Pumped storage 615.6 443.2 541.4 2570.2 6.6 2563.6 87.95%

Oil 90.9 0.0 187.6 768.0 0.0 768.0 206.36%

Seasonal storage 94.2 77.2 88.6 558.5 0.0 558.5 94.06%

Run-of-the-river 410.5 427.5 63.1 495.6 93.1 402.5 15.37%

Wind 2196.9 1555.8 2066.2 13597.9 120.7 13477.3 94.05%


- 15 -

supply curve is the relationship between the quantity of a good that producers are willing to sell and

the price of the good” (2005). Figure 8 and Figure 9 illustrate the general form of the demand curve

Figure 8: Price (in EUR per MW) – Quantity(in MW) bids for the demand

Based on: EEX (2010b)

Figure 9: Price (in EUR per MW) – Quantity (in MW) Bids for the Supply



- 16 -

respectively supply curve. These figures have been generated by using 302’400 price quantity bids

(200 price and quantity bids per hour, for 24 hours a day during 63 days) for both demand and sup-

ply.

The general form of the demand curve already reveals that the demand curve is almost flat for most

price bids, with the most interesting part of the demand curve, that is where the actual slope is, being

found in a range from -10 EUR per MW to +100 EUR per MW; in other words the range in which

prices normally fluctuates.

The general form of the supply curve also reveal a flat curve for most of the time, especially for

negative price bids. Again, the slope of the supply curve increases in a range from -10 EUR per MW

to +100 EUR per MW.

The auction procedure of the EEX basically combines the demand and supply curve of every hour

and determines in such a way the market clearing price and quantity. Figure 10 shows the result of

such an auction for June 6th

for hour 1, that is from 00:00 to 01:00 am. Please note that the scale of

the x-axis does not reflect reality but allows for a better overview of the behaviour of the demand and

supply curve for price bids between -10 EUR per MW and + 100 EUR per MW, since as already

described, the remainder of the curves is very uninteresting.

10000120001400016000180002000022000240002600028000

-30

00

-19

50

-90

0

-20

1.5

7

-11

6.7

3

-47

.45

-5.4

5

-0.0

9

2.0

5

12

.55

18

.55

24

.55

30

.55

34

.8

35

.6

36

.3

36

.9

37

.8

38

.6

42

.55

48

.93

57

.55

63

.55

68

.05

10

2.5

5

14

4.5

5

45

0

15

00

25

50

Qu

an

tity

[in

MW

]

Price in EUR per MW

Supply/Demand curve PHELIX-Spot Hour 1; MCP: €36.55,

MCQ: 19'132 MW

Demand

Supply

Figure 10: Intersection of the demand and supply curve on hour 1, June 6th

2010



- 17 -

2.3 Price and Quantity

This section introduces two time series for prices and quantities. On the one hand side, the prices and

quantities which result from the day-ahead auction will briefly be summarized while on the other

hand the prices and quantities which result from the intraday auction will be analysed. The idea be-

hind offering intraday trading is to give market participants the possibility to buy and sell power at a

very short notice in order to optimise their procurement and sale. Each hour can be traded until 75

minutes before the beginning of the delivery hour starting at 3:00 pm the day before (EEX, 2010a).

Due to the very volatile nature of electricity market, especially with regards to the production from

wind turbines which is very hard to forecast accurately on a day-ahead basis, intraday trading offers

a valuable opportunity to market participants.

Figure 11 shows the evolution of day-ahead prices and intraday prices during the observation period

from June 2nd

2010 to August 4th 2010, while Figure 12 displays the quantity traded in the respective

hours. Table 5 summarizes the key findings.

0

20

40

60

80

100

Act

ua

l Pri

ce in

EU

R p

er

MW


Day-ahead

Intraday

Figure 11: Hourly intraday and day-ahead prices

Based on: EEX (2010c) and EEX (2010d)


- 18 -

Day-ahead

Prices (in EUR)

Day-ahead Quan-

tity (in MW)

Intraday Prices (in

EUR)

Intraday Quantity

(in EUR)

Average 44.24 22'936.66 44.29 1'121.02

Median 45.30 21'690.20 44.95 927.00

Standard Deviation 12.54 4'584.17 14.26 839.37

Maximum 83.89 38'198.10 96.40 7'466.80

Minimum -0.08 15'185.40 2.04 68.00

St. Dev / Average 28.34% 19.99% 32.19% 74.87%

Table 5: Price and Quantity for intraday and day-ahead markets

Based on: EEX (2010c) and EEX (2010d)

Day-ahead and intraday prices exhibit very similar price paths and follow the expected daily and

weekly pattern. Furthermore, average prices for intraday and day-ahead markets are very close to

each other, even though the intraday market is somewhat more volatile, showing for the observation

period a higher maximum price. The day-ahead quantity also follows as expected a clear daily and

weekly pattern. On the other hand, intraday quantities follow a very random pattern in between 68

MW and 7’466.8 MW, which explains the very high volatility. The main reason for the lack of daily,

0

5000

10000

15000

20000

25000

30000

35000

40000

Act

ua

l Qu

an

tity

in M

W


Intraday

Day-ahead

Figure 12: Hourly intraday and day-ahead quantities

Based on: EEX (2010c) and EEX(2010d)


- 19 -

respectively weekly pattern is the fact that intraday auctions are used to balance procurement portfo-

lio in the very short term, for example in the case that the expected electricity production from wind

falls short of the forecast, or if a power plant has to be shut down on a short notice.


- 20 -

3. Preparing the Data Set

To be able to work with the data sets introduced during Chapter 2, the described generation capaci-

ties, the demand and supply curves and the day-ahead and intraday prices must be prepared. This

section will help to quantify reserve margins, demand and supply curve elasticity’s as well as volatil-

ity figures for the market prices.

3.1 Analysing Production Capacities

3.1.1 Reserve Margin

Reserve margins have been intensively discussed in late years in Europe, the US but also in other

countries, for example South Africa. In a study by Constable and Sharman (2008) which explores the

fundamental drivers and probable trends in the U.K. electricity market, the authors come to the con-

clusion that the actual reserve margin of 24% will be more rapidly eroded and eventually even be-

come negative in a future closer than expected. A bleak outlook is also drawn by RWE (2007) for

most of continental Europe, with the average reserve margin5 (as computed by the Cambridge En-

ergy Research Association) declining under 15% before 2010. Countries like Hungary and Poland

are even expected to exhibit negative reserve margins as soon as 2015. Just to name another exam-

ple, South Africa’s reserve margins has fallen in recent years to around 8%, a situation which has

placed considerable pressure on the industry since the reliability of the power grid was not ensured

anymore (Department of Minerals and Energy, 2008). The reliability of the generation capacities was

in such a poor shape in South Africa that the crucial mining companies even had to shut down their

activities since Eskom (South African electricity monopolist) was not able to ensure electricity deliv-

ery to run the elevators that move miners up and down into the mine (Timberg, 2008). Eskom argues

that relief is five to seven years away, since generation capacities cannot be build much faster. These

acute problems, especially in South Africa but more generally in many other countries, illustrate why

there might be good reasons to be nervous about reserve margins, especially very low ones.

The reserve margin is a key system characteristic which is used to describe the operational safety and

reliability as well as the price stability of an electricity system. The reserve margin describes the ex-

cess available generation capacity, if any is available, relative to the load and gives therefore a meas-

ure of how resistant the power system is to unforeseen generation capacity fall out. (Rochlin &

Huang, 2005)

5 Reserve margin in this case as the difference between dependable capacity and peak demand divided by peak de-

mand


- 21 -

� �� !�"#$ = �%&&'( − *��!$**��!$* +

Demand is in this case the actual quantity demanded at the prevailing electricity price while the sup-

ply refers to the amount of generating capacity available to serve the load at a specific point in time.

This is why Rochlin et al. describe the reserve margin as a stochastic variable which depends on the

distribution of the demand as well as on the distribution of the supply, both of which vary over time

(2005). The most common form of reserve margin found in the literature is the one looking at peak

demand. Among others, the U.S. Energy Information Administration (2010) defines reserve margin

“as the amount of unused available capability of an electric power system at peak load as a percent-

age of capacity resources”. For this paper, it is however more convenient to use the more general

definition of reserve margin which takes into account all hours of a day.

In practice, the proposed minimum value for reserve margin vary considerably from one regulator to

another. For example, the Federal Energy Regulatory Commission’s Notice of Proposed Rulemaking

(2003) proposes a minimum value of 12%, the California Public Utilities Commission (2003) sees a

reserve margin between 15-17% as adequate, the Electric Reliability Council of Texas (2005) be-

lieves that a 12.5% reserve margin is adequate while the New York Independent System Operator

(2006) prefers to keep a margin of at least 18%. Now that the reserve margin is defined and the re-

quired margin throughout the world have been discussed, it is time to take a closer look at the situa-

tion on the German market during the period from June 2nd

2010 to August 4th

2010. In a first step,

the overall reserve margin is computed while a second step will have a closer look at the used gen-

eration capacity with respect to each generation type separately. When considering wind energy, it

makes sense to assume the expected production to be treated like the available production capacity

for the non-wind generating units. This is not strictly a reserve margin since it estimates how well

electricity generation through wind was forecasted, nevertheless, it works in the same way as the re-

serve margins for conventional power plants.

Figure 13 shows the evolution of the margin over the two month period between June 2nd

2010 and

August 4th

2010. The daily pattern which is typical for the electricity consumption can also be ob-

served here. In order to grasp further information, Figure 14 provides insights into how those mar-

gins are distributed and Table 6 summarizes the key results. Interestingly enough, Germany only ex-

perienced a margin slightly below 20% during 5 hours (0.03% of the time), while the average margin

(as can be taken out of Table 6) is 51.43% with a standard deviation of 15.62%. Even though the

sample is not representative for the situation in Germany, it seems that the German electricity market

is not at stake to run out of electricity in the next couple of years.


- 22 -

Figure 13: Hourly margin for the German electricity market

Based on: own computation

0

10

20

30

40

50

60

17

.00

%

20

.00

%

23

.00

%

26

.00

%

29

.00

%

32

.00

%

35

.00

%

38

.00

%

41

.00

%

44

.00

%

47

.00

%

50

.00

%

53

.00

%

56

.00

%

59

.00

%

62

.00

%

65

.00

%

68

.00

%

71

.00

%

74

.00

%

77

.00

%

80

.00

%

83

.00

%

86

.00

%

89

.00

%

92

.00

%

95

.00

%

98

.00

%

10

1.0

0%

Occ

urr

en

ce

Distribution

Histogramm

Figure 14: Margin distribution for the German electricity market


0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

Ma

rgin


Margin


- 23 -

One might however want to consider that the electricity consumption in Germany somewhat dropped

due to the heavy financial and economic crisis of 2008-2009. Moreover, considering the German

wish to exit, at least in the long run, nuclear electricity production, there might be some very tight

margins ahead. Under current consumption, removing the nuclear power plants would lead to nega-

tive margins in 10.6% of the hours for the observed time window and replacing their generating

power through renewable energy might prove challenging when considering their extreme volatile

production (wind and solar).

3.1.2 Degree of Capacity Utilisation

Having showed that Germany did not face really tight production capacities during the observed two

month, it is certainly interesting to have a closer look at the individual generation types. Instead of

using the reserve margin computation, it is more intuitive to compute the actual percentage of gen-

eration capacity that has been used. For wind generation, this yields an estimate of how good the

production forecast was.

, %��* -!&!-#.(/012 3 = �%&&'(/012 3 − *��!$*/012 3�%&&'(/012 3 4

This measure gives us an idea which power plant were actually producing at what time respectively

how good the production forecast for wind was. The later is a relevant information since large differ-

ences between the actual wind production and its forecasted production must be compensated by

other power plants, either by producing more or by producing less. Figure 15 illustrated how used

capacity evolved between June 2nd

2010 and August 4th

2010, while Table 7 summarizes the key

findings.

Average Median St. Devia- Maximum Mininum

Margin 51.43% 50.14% 15.62% 101.21% 17.07%

Table 6: Margins in the German electricity market

Average Median St. Deviation Maximum Mininum

Uranium 95.30% 95.23% 2.98% 103.90% 76.97%

Lignite 93.04% 94.05% 5.02% 108.38% 71.13%

Coal 42.91% 40.96% 20.92% 83.40% 6.85%

Gas 20.35% 20.49% 9.17% 69.59% 6.87%

Pumped storage 13.85% 9.95% 11.93% 57.01% 0.14%

Oil 6.48% 0.00% 16.10% 80.06% 0.00%

Seasonal storage 16.51% 9.45% 18.86% 106.99% 0.00%

Run-of-the-river 100.02% 101.23% 7.06% 111.54% 63.21%

Wind 98.39% 95.36% 36.79% 268.94% 19.14%

Table 7: Used capacity with respect to generation type



- 24 -

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

Use

d C

ap

aci

ty


Oil

Pumped-storage

Gas

Seasonal storage

0.00%

50.00%

100.00%

150.00%

200.00%

250.00%

300.00%

Use

d C

ap

aci

ty


Wind

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%U

sed

Ca

pa

city


Uranium

Lignite

Run-of-the-river

Coal

Figure 15: Used capacity over time with respect to generation type



- 25 -

3.1.2.1 Generation from Uranium

On average, available generation capacities were used up to 95.30% with a lowest degree of capacity

utilisation at 76.97%. Hence, uranium fired power plants are the typical Baseload providers. In some

cases, figures above 100% can be observed. This might have several reasons: on the one hand, there

might be some errors in the data due to non-communicated stops of production, while on the other

hand, it might be due to changes in available capacities from one day to the other. From June 4th

23:00 to June 5th

00:00, available capacity dropped from 14’612.6 MW to 12’914 MW, while the

production of electricity only slowly retreated from 13’817.9 MW to 13’417.2 MW before dropping

further to 12’627 at 01:00. The registered 103.90% is here due to the fact that reducing actual nuclear

generation capacity takes some time into account, while the reported available capacities are daily

averages and might therefore show small differences with actually available capacities on boarder

hours to the previous or following day.

3.1.2.2 Generation from Lignite

On average, generation capacities were used up to 93.04%, with a minimum at 71.13% and a maxi-

mum at 108.38%. The argumentation for coal fired power plants is very similar to the one for the

uranium fired power plants since lignite fired power plants also belong to the typical Baseload pro-

viders. The volatility is somewhat higher for generators using lignite, which can be explained by

tighter regulations for uranium fired power plants (Fürsch et al., 2010).

3.1.2.3 Generation from Run-of-the-river

Run-of the-river power plants show an average use of their available capacity of 100.03%, with val-

ues ranging from 121.95% to 63.21%. Run-of-the-river also belongs to the typical Baseload provid-

ers. The volatility is somewhat higher than for nuclear and lignite power plant which is due to the

fact that the electricity production of run-of-the-river power plant can be changed very easily. There

is no ramp-up time per se.

3.1.2.4 Generation from Wind

Actual wind generation was on average 98.36% from the expected wind generation. However, the

lower bound is found at 19.14% while the upper bound reaches 268.94% which is among other a rea-

son why the volatility (36.79%) is very high. What these figures show is that forecasting wind inten-

sity is very difficult. However, on average, the wind forecast is pretty accurate. As already men-

tioned, electricity produced through renewable energy (among others: wind) is always induced into

the grid and is therefore considered as Baseload providing power plant with peculiar characteristics.


- 26 -

3.1.2.5 Generation from Coal

The average use of available coal generation capacity is 42.91% with the highest value reaching

83.40% and the lowest value being at 6.85%. Coal power plants are used to satisfy Peakload demand

and their electricity production is therefore very volatile (20.92%). The reason why their use doesn’t

drop to 0% is that there might be some generation units which offer system services and must there-

fore be kept running (Fürsch et al., 2010).

3.1.2.6 Generation from Gas

On average, 20.35% of available gas generation capacity are used with a peak at 69.59% and a low-

est value around 6.87%. Gas power plants are also used to satisfy Peakload demand and exhibit very

similar characteristics to coal power plants.

3.1.2.7 Generation from Pumped Storage and Seasonal Storage

Pumped storage and seasonal storage exhibit very similar numbers. The lower bound for used avail-

able generation capacities is at 0%. Both, pumped storage and seasonal storage are Peakload satisfy-

ing facilities which can concentrate their electricity production in period where prices are highest.

They do not face any run-up time and are therefore extremely flexible.

3.1.2.8 Generation from Oil

Available capacities of oil generation power plants are only used on average to an extend of 6.48%,

with a peak at 80.06% while the lower bound is, not surprisingly for a very flexible Peakload satisfy-

ing power plant at 0%. Interestingly, their median use is 0% which means that most of the time, oil

generation units are never used.


- 27 -

3.2 Elasticity

In order to analyse the relationship between the demand and supply curves formed through the bid-

ding procedure in the day-ahead auction market and other variables of the German electricity market,

both demand and supply curve must be characterised. Pricing policies were long considered as a

good instrument to improve energy efficiency; however, as Narayan, Smyth and Prasad note, pricing

policies to promote the efficient use of electricity do also depend on the price elasticity of demand

(and supply) for electricity (2007). Even so, demand and supply curves are often described using

elasticity as a measure, since it provides the percentage change in quantity demanded divided by the

percentage change in price, therefore providing a measure of the demand responsiveness that is uni-

versally used in economics. Eilon (1983) finds two definitions of elasticity that are commonly used

in the literature. On the one hand, point elasticity is defined for a given point on the demand (or sup-

ply) curve and therefore relies on the derivative of the curve, respectively function at that point

(which means that the eligible curve must be described by a function). On the other hand, arc elastic-

ity is defined for the midpoint of an arc connecting two points, irrespective of the shape of the de-

mand function since the construction assumes a straight line. The crucial point in this case is to de-

cided on how far apart the two points can be distant from each other. Eilon argues that point elastic-

ity is the most widely cited in the literature even though it is often difficult to determine and practi-

tioner therefore mostly prefer to use arc elasticity which does not require fitting a function to the de-

mand (or supply) curve (1983).

3.2.1 Point Elasticity

The first step in order to compute the point elasticity of the demand and supply curves that result

from the bidding process of the market participants in the day-ahead auction is to fit a function to

every single curve seen in Figure 8 and Figure 9. The method used here was already discussed by

Stone (1977) and Fan (1992, 1993) to name only two. They used a polynomial to fit a data sample.

The general equation of a polynomial regression has the following form:

[ 5(.) = &8 + &: ; + &< ;< + &> ;> + … … … … + &? ;? ] With &8 being an optional constant and &: through &? being coefficients of increasing power of ;.

The order of the polynomial is described by m and must be decided before searching for a polyno-

mial to fit the data. A polynomial of order one has the form of a linear equation, while a polynomial

of order two takes the form of a quadratic equation. Polynomials of higher order (4th or 5

th) are useful

to describe data points accurately, but the terms cannot generally be interpreted in any physical


- 28 -

sense. Furthermore, it is often not reasonable to choose polynomials of order beyond 12 since this

could lead to odd and unreasonable results. (Abdolkhalig, 2008)6

The polynomial that best fits the data is the one with the least squared error. Therefore, as-

suming a polynomial of the above described form is used to approximate the price quantity combina-

tions bid by the market participants.; the following set of data is given: (;� , ��), (!", �"), and so forth

to (!# , �#), where $ ≥ & + 1. The curve with the best fit ('(!))) is the one with the least squared

error that minimise the following equation:

- = .[�) − '(!))]"#)0� = .[�) − (23 + 2� !) + 2" !)" + 24 !)4 + … … … … + 25 !)5)]"#

)0�

The coefficients 23, 2� , … , 25 are unknown while all �) and !) are given. To minimise this equation,

the first derivatives of each coefficient must be equal to zero. Therefore:

6∏623 = 2 .[�) − (23 + 2� !) + 2" !)" + 24 !)4 + … … … … + 25 !)5)]#)0� = 0

6∏62� = 2 . !) [�) − (23 + 2� !) + 2" !)" + 24 !)4 + … … … … + 25 !)5)]#)0� = 0

and so forth...

6∏625 = 2 . !)5 [�) − (23 + 2� !) + 2" !)" + 24 !)4 + … … … … + 25 !)5)]#)0� = 0

These equations can be expanded so as to end up with a system of linear equations which can then be

solved to obtained the coefficients. The following expanded equations are obtained:

. �)#

)0� = 23 . 1#)0� + 2� . !)

#)0� + 2" . !)"#

)0� + … + 25 . !)5#)0�

6 Various types of curve fits do exist, with the main categories being least square curve fits, nonlinear curve fits and

smoothing curve fits. The decision to use polynomial to fit the data set is that is has the advantage of being relatively

simple in term of required computing power and it is well understood. Furthermore, there are no outliers in the data

set, therefore avoiding one of the main drawbacks for using this methodology.


- 29 -

. !)�)#

)0� = 23 . !)#

)0� + 2� . !)"#)0� + 2" . !)4#

)0� + … + 25 . !)5:�#)0�

. !)"�)#

)0� = 23 . !)"#)0� + 2� . !)4#

)0� + 2" . !);#)0� + … + 25 . !)5:"#

)0�

and so forth...

. !)5�)#

)0� = 23 . !)5#)0� + 2� . !)5:�#

)0� + 2" . !)5:"#)0� + … + 25 . !)"5#

)0�

The fundamental mathematical notions to compute the polynomial that best fits the data being intro-

duced, the next step can be taken.

The second step is to decide what kind of polynomial to take, that means to determine of

which order the polynomial ought to be. A straight forward possibility is to compute polynomial of

different order (from 1 to 12) and to assess their goodness of fit using R-Square. Based on that, the

polynomial which best suits the purposes of this paper can be chosen.

R-Square is the square of the correlation between the response values (that is the actual val-

ues) and the predicted response values (that is the values that would have been obtained using the

polynomial). R-Square is defined as the ratio of the Sum of Squares of the Regression (SSR) and the

Total Sum of Squares (SST), as illustrated hereafter. (Abdolkhalig, 2008)

<>>? = .(') − �@)"#)0� A

<>>B = .(�) − �@)"#)0� A

C? − >DEFGH = >>?>>BI

In order to enhance the results from the polynomial fit, one further restriction is added. As seen in

Chapter 2 the slope of the demand and supply curve does exhibit some steepness only in a fairly

short interval (from roughly -10 EUR per MW to roughly + 100 EUR per MW) being more or less

flat for all other price quantity combinations. To take this into account, the dataset for which poly-


- 30 -

nomials will be generated has been restrained to all price-quantity combinations found in between –

450 EUR per MW and + 450 EUR per MW. This restriction has been chosen after early computa-

tions had been performed without imposing it and the fit of the resulting function was, comparing to

later results, very poor7. Table 8 shows the mean R-Square for polynomials of different order fitted

to the demand and supply curve.

Polynomial R-Square (Demand) R-Square (Supply)

1 0.625829415 0.633393403

2 0.633093057 0.703197944

3 0.792929152 0.799777043

4 0.800402947 0.847787241

5 0.892619394 0.883441748

6 0.89836004 0.91421344

7 0.94149664 0.93605434

8 0.95167656 0.95335101

9 0.96587901 0.96139181

10 0.97334162 0.97014305

11 0.97897038 0.97706397

12 0.98262149 0.98171485 Table 8: R

2 for polynomials of different order fitting the demand and supply curves

Based on: own computation8

Without surprise, higher polynomial do fit the data in a better way, especially in the range (-10 EUR

per MW to + 100 EUR per MW) that is relevant. The R-Square found are fairly low for polynomials

of lower order, which is not astonishing since the demand and supply curve are far from being

straight lines. The size of the increase gets very small for polynomials of order higher than 10. Based

on those findings, the decision is taken to use a polynomial of order 12 to fit the data for further tasks

since the use of polynomials of higher order is not recommended.

Having decided how to describe each of the demand and supply curve, the point elasticity for each

hour, as well for the demand and supply curve, can be computed. Point elasticity of demand is de-

fined as:

C 2JK$L HMFNLKOKL� J' PH&F$P = 2Q(2) Q′(2)I with 2 being the market clearing price, Q(2) the demand function (the polynomial) and Q′(2) the

first derivative of the demand function. (Wilson, 2010)

7 A polynomial of order 12 used to fit the whole demand and supply curve exhibits an R-Square of 69.57% without re-

strictions, which is a very poor fit. 8 Please refer to Appendix 1 on page 66 for more details on the computation.


- 31 -

Computing the elasticity starting from the polynomial requires several steps:

1. Find the polynomial that fits the demand or supply curve for every hour

2. Compute the first derivate of it

3. Plug in the market clearing price of that hour, to get a numerical result.

A brief illustration for a random hour shall be provided in order to enhance the understanding of

what is being done. The demand curve for Hour 1 on June 6th

2010 is chosen.

1. Find the polynomial of order 12 that fits the demand curve for Hour 1, June 6th

2010

D(p) = 25′332 + (−143.3758)! + (1.5589)!"+ (0.0191)!4 + (2.1789Y;)!;+ (−1.3104YZ)!\+ (−1.2896Y_)!Z+ (4.0694Y��)!` + (3.5959Y�4)!_+ (−5.5850Y�Z)!a + (−4.6023Y�_)!�3 + (2.7087Y"�)!��+ (2.1370Y"4)!�"

2. Take the first derivative of it

D'(p) = − 143.3758 + (−3.1179)! + (0.0574)!"+ (8.7157Y;)!4 + (−6.5521YZ)!;+ (−7.7378Y_)!\+ (2.8486Y�3)!Z+ (2.8767Y�")!` + (−5.0265Y�\)!_+ (−4.6023Y�`)!a+ (2.9796Y"3)!�3+ (2.5644Y"")!��

3. Plug in the market clearing price of EUR 36.55 per MW

D(p) = 19'219.9466

D'(p) = -153.9604

2JK$L HMFNLKOKL� J' PH&F$P = 36.5519'219.9466 ∗ (−153.9604) = −0.2928

The point elasticity of supply can be computed in an analogous way, with >(2) being the supply

curve function and > ′(2) being the first derivative of the supply curve function.

C 2JK$L HMFNLKOKL� J' NE22M� = 2>(2) > ′(2) I


- 32 -

Figure 16 and Figure 17 (on page 33) provide an insight into how the point elasticity of supply and

demand evolves on an hourly basis during the observation period from June 2nd

2010 to August 4th

2010, while Table 9 gives more detailed numerical information. 9

Point Elasticity of

Demand [PEoD]

Point Elasticity of

Supply [PEoS]

Mean -0.343149 0.26452606

Median -0.34575799 0.26286074

St. Deviation 0.12078777 0.10255025

Max 0.00028229 0.57948729

Min -0.76419749 -0.00024799 Table 9: Point elasticity of demand and supply


The mean point elasticity of demand is -0.3431, which means that a price cut of 1% would lead to an

increase in quantity consumed of only 0.3431%. In such a case, economist would describe the price

elasticity of demand as being inelastic. The same hold for the mean point elasticity of supply which

is of 0.2645, meaning that an increase in prices of 1% would lead to an increase in production of

only 0.2645%. Regarding the shape of the price elasticity of demand and supply, a weak daily and

weekly pattern can be observed.

Before comparing the results obtained for the German electricity market during the observation pe-

riod with earlier empirical studies for other markets found in the literature, the arc elasticity of de-

mand and supply shall be computed.

9 Please refer to Appendix 2 on page 67 for more details on the computation.


- 33 -

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

Po

int

ela

stic

ity

of

De

ma

nd


PEoD

Figure 16: Point elasticity of demand for the German electricity market


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Po

int

ela

stic

ity

of

Su

pp

ly


PEoS

Figure 17: Point elasticity of supply for the German electricity market



- 34 -

3.2.2 Arc Elasticity

The arc elasticity of demand between two prices is defined as the proportional change in the quantity

divided by the proportional change in price (Wilson, 2010). Mathematically, this gives:

C FGO HMFNLKOKL� = % OℎF$fH K$ DEF$LKL�% OℎF$fH K$ 2GKOH = g" − g�(g� + g")/2 / i" − i�(i� + i")/2 I Arc elasticity basically assumes a linear relationship between price and quantity. Regarding the de-

mand and supply curves at hand, this might be true for small intervals. The following procedure was

used to compute arc elasticity:

1. Determine market clearing price and quantity for every hour

2. Set g� as the quantity bid directly smaller than the market clearing quantity

3. Set g" as the quantity bid directly larger than the market clearing quantity

4. Set i� as the price bid directly smaller than the market clearing price

5. Set i" as the price bid directly larger than the market clearing price

6. Compute the arc elasticity of demand and supply

Figure 18 and Figure 19 plot the results for the arc elasticity of supply and demand for every hour of

the data set. Table 10 gives a numerical overview over the results.10

Arc Elasticity of De-

mand [AEoD]

Arc Elasticity of

Supply[AEoS]

Mean -1.15321566 0.79224908

Median -0.37567054 0.19459266

St. Deviation 1.79926319 1.53742455

Max 0.02786809 19.3270189

Min -19.3594741 -0.00078644 Table 10: Arc elasticity of demand and supply


Using arc elasticity, we find a mean demand elasticity of -1.1532 which would mean that a increase

in the price by 1% would lead to a decrease in the demand by 1.1532%; in such a case, economists

speak of an elastic demand. The mean arc elasticity for the supply curve is found to be 0.7922. With

regard to the high volatility of the computed elasticity, it makes more sense to consider the median

results, which are much closer to the results found when computing the point elasticity of demand

and supply. For this reason, all further work will be accomplished using point elasticity rather than

arc elasticity. Arc elasticity figures were computed as a control variable to check whether the values

obtained by fitting polynomials to the demand and supply curve were realistic.

10

Please refer to Appendix 3 on page 68 for more details on the computation.


- 35 -

-20

-15

-10

-5

0

Arc

Ela

stic

ity

of

De

ma

nd


AEoD

Figure 18: Arc elasticity of demand for the German electricity market


0

2

4

6

8

10

12

14

16

18

20

Arc

Ela

stic

ity

of

Su

pp

ly


AEoS

Figure 19: Arc elasticity of supply for the German electricity market



- 36 -

3.2.3 Elasticity in the Literature

A large array of literature on demand responsiveness in electricity markets, that is to measure the

change in demand for electricity due to a change in price – in other words, elasticity – relies on rig-

orous econometric analysis that have high data requirements (especially with regards to information

on household-specific appliance holding and residence features) and therefore influence the outcome

of a study due to different characteristics of these durable goods (Fan & Hyndman, 2008). Two kinds

of studies have to be distinguished, there are the non- time of use (TOU) studies on price elasticity

and the time of use (TOU) studies on that subject (Lafferty, Hunger, Ballard, Mahrenholz, Mead,

Bandera, 2001).

Non-TOU Literature deals with flat electricity rates in the context of vertically integrated utilities and

are therefore in most cases somewhat older than TOU studies which deal with rates with different

unit prices for usage during different hours of a day, usually in block of time defined for a 24 hours

day. TOU rates therefore reflect the average cost of generating and delivering power during those

time periods. Some authors (for example Fan & Hyndman, 2008) distinguish between Real-time

pricing (RTP) and TOU, with RTP being a rate in which the price for electricity typically fluctuates

hourly, therefore reflecting changes in the wholesale price of electricity. One finding all studies have

in common is that the elasticity of electricity depends on the time frame (in that case, whether we

look at the short or at the long rate) and on the sector, this means whether they are looking at the

residential, industrial or an aggregation of both. Table 11 gives a summary on the price elasticity for

electricity demand in various studies performed in different markets.

Authors Year Region Sector Elasticity

Bohi & Zimmerman 1984 U.S. Residential Short-run: -0.2

Long-run: -0.7

Patrick & Wolak 1997 England and Wales Water supply Industry -0.142 to -0.27

Filippini 1995 Switzerland Residential -1.25 to -2.30

Filippini 1999 Switzerland Aggregation -0.3

Beenstock et al. 1999 Israel Residential and industrial Residential: -0.21 to -0.58

Industrials -0.002 to -0.44

Tishler 1991 Industrial -0.02 to -0.09

Tishler 1998 Israel Industrial -0.01 to -0.47

Earle 2000 California Aggregation Mean: -5.3

Median: -0.02

King & Chatterjee 2003 California Residential and commercial -0.1 to -0.4

Reiss 2005 California Residential -0.39

Faruqui & George 2005 California Aggregation 0.09

Taylor et al. 2005 U.K. Industrial -0.05 to -0.26


- 37 -

Fan & Hyndman 2008 Australia Aggregation -0.4165 Table 11: Demand elasticity in the electricity market – summary

Based on: Authors as mentioned here over, for further details, please find further details in the references on page 58-65

The results found for the point elasticity of demand in the present study are more or less in line with

findings in other studies, even though the range of variation is pretty large, with values between -

0.01 and -2.3. Most value however where found to be clustered between elasticity values of -0.1 and

-0.4 as compared to the -0.34 found in this study for the German electricity market.

There is no extensive literature on the elasticity of supply in electricity market, however most re-

search papers agree that the elasticity of supply is very inelastic (for example Borenstein, 2002), may

however vary with regard to the available generation capacities (in other words margins) in the mar-

ket (Boogert & Dupont, 2006).


- 38 -

3.3 Volatility

The aim of this section is to attribute a measure of fluctuation to each hour of our time series, as well

for the prices resulting from the day-ahead auction as for the prices resulting from intraday trading.

This however proves more difficult than expected.

3.3.1 Volatility of Day-ahead Prices

Volatility (j) is a measure of the uncertainty about the returns provided by an asset. Volatility is de-

fined as the standard deviation of the return provided by an asset over a time window B if the return

is expressed using continuous compounding. The usual estimate, s, of the standard deviation is given

by: (Hull, 2009)

N = k 1$ − 1 . (Gl,m − G̅m,o)"#l0� pℎHGH Gl,m = ln s >l>lYmt pKLℎ ℎ uHK$f NJ&H LK&H 2HGKJP

As already mentioned, electricity prices tend to follow the general trend of electricity demand and it

is therefore not surprising to face significant price fluctuation during one day, especially when mov-

ing from off-peak hours to on-peak hours. This is the reason why, unlike in most volatility studies

where the time period for returns is chosen to be ℎ = 1, the time period can be selected to be ℎ = 24

to study trans-day price fluctuations (Simonsen, 2005) or ℎ = 168 to study the trans-week price fluc-

tuations (Zareipour, Bhattacharya, Canizares, 2007). Generally speaking, the definition of historical

volatility is based on the assumption that the continuous return observation follow an i.i.d. random

variable. Those assumptions are correct for most stochastic returns in economic and finance, how-

ever, electricity market prices, as already mentioned, follow daily, weekly and seasonal patterns due

to the seasonal nature of electricity demand. As a result, continuous returns from electricity prices

are highly correlated and do not behave as an i.i.d. random variable. This is the reason why Zarei-

pour et al. (2007) proposes to use a time window B that is short enough in order to have negligible

return correlations and which furthermore allows analysing the original price time series without

considering separation of the periodic and random parts of the price data. This is for example the

case when choosing a time window B of 24 hours. Zareipour et al. furthermore suggests to use mar-

ket price data in two ways: in the first scenario, a price time series is treated as a whole signal for all

24 hours and volatility indices are computed such that the overall price behaviour can be analysed

while in a second scenario, a price time series is broken up into 24 time series corresponding to each

of the 24 hours such as to provide an insight into the risk associated with the price at each particular

hour of the day (2007).


- 39 -

The time window is in a first part selected to be one full day (24h), such that one figure is obtained

for every day. The following formula for the historical volatility where we have the possibility to

vary ℎ such as to have hourly (ℎ = 1), daily (ℎ = 24) and weekly (ℎ = 168) logarithmic returns as

the basis for the analysis is therefore faced.

v jm,";(B) = k 123 . (Gl,m − G̅m,o)" ";∗ol0�:";∗(oY�) w

In such a scenario, the averages of jm,";(P) is used as volatility indices. Table 12 summarizes the

results.

# of results Mean Median Max Min St. Dev � ,!" 63 0.1723 0.10851 1.5611 0.0415 0.2286

�!",!" 63 0.3008 0.1494 2.1185 0.0431 0.4264

� #$,!" 63 0.2309 0.1104 1.9990 0.0419 0.3573

Table 12: Daily volatility figures for intraday, trans-day and trans-week prices


Simonsen (2005), who did analyse the Nordic electricity market over a longer time period (12 years)

did find a volatility for %&',&' of 0.16 which is in comparison to most financial markets fairly high;

even though the Nordic power market is known for its actually “low” volatility. In fact, Zareipour et

al. finds volatility measures that are slightly higher for the Ontario market in his study ( %(,&' = 0.2469, %&',&' = 0.3203 and %(*+,&' = 0.3222) (2007). In the German electricity market %&',&'

= 0.3008 and is therefore found in between the results of both studies. However, unlike in Zareipour

et al.’s study for the Ontario market, the intraday price fluctuation %&',&' for the German electricity

market is higher than the trans-week price volatility %(*+,&', which means that price changes tend to

be higher going from one day to the next where they tend to be lower when going from one week to

the next. This can be explained by the fact that prices during Saturdays and Sundays are much lower

than during the rest of the week, therefore affecting the intraday price volatility very strongly.

Considering now the second scenario introduced by Zareipour et al. (2007), which uses a time win-

dow of 7 days (one full week), the following equation is considered:

- %&',(*+(/) = 1163 (45,7 − 4̅7,:)& ;∗:5>(?;∗(:@() A

11

Please refer to the Appendix 4 on page 69 for further details on the computation.


- 40 -

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Vo

lati

lity

H [Hour of the day]

Here ℎ = 24, this implies that market prices for two consecutive days are compared. The aim of this

calculation is to quantify the fluctuation of price at a particular hour in subsequent days over a 7-day

period. The sum in the equation is made over hour ℎ of each day during a 7-day period. The result

obtained is shown in Table 13. Note, for each week, 24 volatility figures (one for each hour) are

computed.

# of results Mean Median Max Min St. Dev �!", #$ 216 (24x9) 0.3777 0.2285 4.2427 0.0369 0.5530

Table 13: Hourly volatility over each day


Much more interesting is however the average volatility at each hour, that is %E&',(*+ and is presented on Figure 20.

The results obtained for %E&',(*+ show a similar volatility as the results obtained for the Ontario mar-

ket by Zareipour et al. (2007). However the volatility pattern over the day is completely different and

the differences between the individual hours are much more important for the German market. This

might be explained by the relatively short period observed in this paper.

The results obtained so far using the methods introduced in the literature do however not provide the

expected aim of this section, since an individual volatility measure for each of the 1512 hours of the

observation period has not been computed yet.

12

Please refer to Appendix 5 on page 70 for further details on the computation.

Figure 20: �F!", #$, average hourly volatility over a time window of 1 week



- 41 -

This is the reason why the electricity price volatility will be calculated by using a rolling window

where each hour of a week is treated as a separate asset. Hence, the volatility of 168 individual assets

(hours) is computed. The returns are computed by using ℎ = 168. The volatility is furthermore com-

puted as follows:

- %(*+,H∗(*+(/) = 1163 (45,7 − 4̅7,:)& ;∗:5>(?;∗(:@() A

The length of the rolling window is chosen to be 9 weeks, since the whole observation period is 9

weeks starting from June 2nd

2010 until August 4th 2010. For every time window, 168 volatilities are

obtained. Figure 21 illustrates the volatility obtained during the observation period. Table 14 summa-

rizes the key results13

. Table 15 gives an overview over the rolling windows used and computes as an

example the volatility for Hour 1 on Wednesday between June 2nd

2010 and August 4th

2010. The

star (*) in Table 15 refers to the starting day of the observation period.

The hourly volatility computed using a rolling window exhibits a weekly pattern. On average, vola-

tility peaks are found on weekends, especially Sunday between 12 a.m. and 14 a.m. with a slightly

lower peak on Sunday morning. The hourly volatility is relatively low during weekdays.

# of results Mean Median Max Min St. Dev

Hourly volatility 1512 0.3639 0.1605 3.3704 0.0366 0.6011

13

Please refer to Appendix 6 on page 71 for further details on the computation.

Table 14: Hourly volatility for the German market



- 42 -

0

0.5

1

1.5

2

2.5

3

3.5

Vo

lati

lity

h [hour of the day]

volatility

Table 15: Hourly volatility computation using a rolling window


Return Period Rolling window(s) 45,7 Volatility of Hour 1

31/03/2010 – 07/04/2010 0.2317

0.1

46

0

07/04/2010 – 14/04/2010 0.0646

0.1

31

3

14/04/2010 – 21/04/2010 -0.2307

0.1

43

6

28/04/2010 – 05/05/2010 0.2323

0.1

13

2

05/05/2010 – 12/05/2010 -0.0196

0.0

85

9

12/05/2010 – 19/05/2010 0.1027

0.0

86

8

19/05/2010 – 26/05/2010 -0.0386

0.0

81

2

26/05/2010 – 02/06/2010* -0.0386

0.0

79

6

02/06/2010* – 09/06/2010 -0.0222

0.0

83

3

09/06/2010 – 16/06/2010 -0.1128

16/06/2010 – 23/06/2010 0.1762

23/06/2010 – 30/06/2010 0.0271

30/06/2010 – 07/07/2010 0.0390

07/07/2010 – 14/07/2010 -0.0352

14/07/2010 – 21/07/2010 0.0474

23/07/2010 – 28/07/2010 0.0076

28/07/2010 – 04/08/2010 -0.0756

Figure 21: Hourly volatility using a rolling window



- 43 -

3.3.2 Volatility of Intraday Prices

Since intraday prices are also considered; a second volatility index for every hour of the day has to

be constructed. Since volatility computation for hourly electricity prices turns out to be very com-

plex, another methodology is chosen for intraday prices. The intraday price volatility will be base on

the hourly price fluctuation, which can be computed due to the fact that, next to an average intraday

hourly price, a minimum as well as a maximum price during each hour are published.

Before computing an index for its volatility, it is first of interest to analyse how intraday prices are

related to the prices set through the day-ahead auctions. Figure 22 shows the relationship between

intraday (average, minimum and maximum price) and the price set through day ahead auction on

June 2nd

2010. Table 16 summarizes the findings for the overall period. The mean difference be-

tween intraday and day ahead prices is -8.32%, whereas the median difference is found to be -0.43%.

This means that intraday prices are on average slightly below the prices found in the day-ahead mar-

ket during the observation period with the highest difference found when day-ahead prices were

negative (here -179.5%). This means nothing else that market participants are willing to pay a pre-

mium to lock in prices early.


Price difference 1512 -8.3288% 0.4362% 6485.7% -17950% 553.5%

Table 16 : Relationship between intraday and day-ahead prices in the German market

0

10

20

30

40

50

60

70

Pri

ce in

EU

R p

er

MW

H [Hour of the day]

Intraday Low

Intraday High

Day-ahead

Intraday

Figure 22: Relationship between intraday price (average, low, high) and day-ahead prices



- 44 -

Having showed the very close relationship between day-ahead prices and intraday prices, an index

expressing the fluctuation during every hour regarding the intraday prices can be computed using

following formula:

I JKLMNLOMNPQR PRSTU = VWXYZ[\]@VWXYZ[^_ VWXYZ\`ab\ca d

The fluctuation index is a relative index whose value will be highest when the proportional price

movements during an hour are highest. Higher price uncertainty can therefore be recognized. Figure

24 gives an overview for the changes in intraday price fluctuation during the observation period

while Table 17 picks out the key numbers.


Price fluctuation 1512 52.2% 35.89% 1372.5% 5% 70.18%

Table 17: Hourly intraday price fluctuation: key figures


Intraday price fluctuation is not influence by any notable daily or weekly pattern.

0

2

4

6

8

10

12

Intr

a-d

ay

pri

ce f

luct

ua

tio

n


Fluctuation

Figure 23: Hourly intraday price fluctuation for the German market



- 45 -

4. Empirical results

The aim of this paper is to determine how generation capacities do affect the market price for elec-

tricity, the shape of the demand and supply curve as well as the market volatility. This chapter de-

fines the dependent and independent variables before performing simple and multiple regression

analysis in order to understand the effect of generation capacities on electricity prices as well as on

the shape of the demand and supply curve and on market volatility.

4.1 Dependent variables

The dependent variables which will be used in the following regression analysis are the price result-

ing from the day-ahead auction, the price resulting from the intraday trading activities, the price elas-

ticity of demand and supply which are used as proxis for the shape of the demand and supply curve

as well as the volatility figures computed for the day-ahead prices and intraday prices. Each variable

is described by a time series of 1512 data points corresponding to each hour during the observation

period.

4.2 Independent variables

As already seen the prices in the German electricity market are set through a bidding procedure,

where each market participants places his bids according to his costs of production (the merit order)

which leads to the demand and supply curves seen in Chapter 2.2. Therefore, market participant have

an influence on the outcome of the market as they decide how much to charge for their electricity

depending on their costs of production, which itself depends on their means of production, in other

words on their types of generators. The ten explanatory variables chosen are the one global margin

for the German electricity production as well as the nine individual capacity utilisation figures for

each generation type.

The ten explanatory variables are:

- Global margin (GM) - Capacity utilisation lignite (CL)

- Capacity utilisation uranium (CU) - Capacity utilisation coal (CC)

- Capacity utilisation gas (CG) - Capacity utilisation pumped-storage (CP)

- Capacity utilisation oil (CO) - Capacity utilisation seasonal-storage (CS)

- Capacity utilisation run-of-the-river (CR)- Capacity utilisation wind (CW)

All data is on an hourly basis, which therefore means that 1512 hours of data for each explanatory

variable is available. The data was tested for multicollinearity which was found to be not relevant,


- 46 -

expect between GM and CC. However, since GM is to some extend an aggregate of CU, CL, CG,

CC, CP, CO, CS, CR and CW, it makes no sense to use all 10 explanatory variables in a multiple re-

gression analysis. GM will only be used in a single regression analysis to avoid any multicollinearity

issues. In some cases, the day-ahead prices (DAP) and the day-ahead volumes (DAV) will be used as

explanatory variables. Both variables have been tested for multicollinearity.

4.3 Results

For each dependent variable, single and multiple OLS regression using the ten explanatory variables

were run using Newey-West standard errors. The decision to use Newey-West is motivated by the

fact that the residuals of the standard OLS regression show a high degree of autocorrelation. In such

a case, the OLS estimates are still unbiased and consistent but they are inefficient. Furthermore,

standard errors will tend to be underestimated, R2 overestimated and the confidence intervals too nar-

row (Greene, 2002). For this reason, Newey-West introduced a procedure to correct the variance of

the estimates to draw conclusion on their significance; this is done by using HAC (heteroskedasticity

and autocorrelation consistent) estimators for the covariance matrix. (Newey and West, 1994)14

4.3.1 Day-ahead Prices

Table 18 shows the regression on day-ahead prices of the global margin (GM) as well as the capacity

utilisation of uranium (CU), lignite (CL), gas (CG), coal (CC), oil (CO), pumped power plants (CP),

run-of-the-river (CR), seasonal power plants (CS) and wind energy (CW).

Reg.

No.

Con-

stant GM CU CL CG CC CO CP CR CS CW

Adj.

R2

(1) 79.30***

(1.35)

-68.15***

(2.72) 72.19%

(2) -3.34

(29.89)

50.04

(31.19) 1.34%

(3) -109.25***

(9.51)

164.99***

(10.22) 43.54%

(4) 24.80***

(1.64)

95.62***

(7.39) 49.24%

(5) 23.60***

(1.18)

47.97***

(2.25) 63.91%

(6) 42.29***

(0.72)

30.83***

(3.14) 15.80%

(7) 35.44***

(0.86)

63.95***

(3.90) 37.13%

14

The computation was done using regstats2 for MATLAB by Komarov (2010).


- 47 -

(8) 39.32***

(8.67)

5.00

(8.58) 0.01%

(9) 43.91***

(0.85)

2.42

(3.14) 0.06%

(10) 49.78***

(1.79)

-5.57***

(1.66) 2.61%

(11) -82.69***

(18.30)

47.39***

(14.54)

67.85***

(9.38)

22.88***

(2.43)

18.77***

(4.89)

28.89***

(2.31)

4.58***

(1.67)

-4.91***

(1.44)

0.89

(4.35)

0.62

(0.84) 77.90%

*** 1% significance level,

** 5% significance level,

* 10% significance level, numbers in brackets are the standard deviation of the coefficients

Table 18: Regression analysis: day-ahead prices

Regression (1) to (10) show the single regressions while regression (11) depicts the multivariate re-

gression where nine factors were combined.

The adjusted R2 for regression (1), which shows the influence of GM on the day-ahead price, is

72.19%. The negative sign for the coefficient, which is significant at the 1% level, signals that lower

margins tend to favour higher prices and vice versa. Without doubt, such a result could be expected,

since prices tend to increase during peak hour, and on the other side, capacity margins tend to be re-

duced during peak hours due to higher electricity consumption.

The adjusted R2 for regression (2), (8) and (9), which show the influence of capacity utilisation for

uranium, run-of-the-river and seasonal storage respectively, is very low, with 1.34%, 0.01% and

0.06% respectively. Furthermore, the obtained coefficient are not significant. According to these sin-

gle regression, the capacity utilisation for uranium, run-of-the-river and seasonal storage has almost

no impact on day-ahead electricity prices. A possible explanation for this finding is the fact that both

uranium fired power plants and run-of-the-river power plants produce Baseload electricity and there-

fore run and produce electricity no matter what the price is.

The adjusted R2 for regression (3), which shows the influence of CL, is 43.54%. The constant, which

is negative and the coefficient that is positive are significant at the 1% level. Even though, lignite

fired power plants are used to cover Baseload consumption and therefore exhibit similar characteris-

tics as uranium fired power plants, their influence on day-ahead prices seems to be much more im-

portant. As mentioned on page 25, lignite power plant exhibit a higher flexibility than nuclear power

plant, which might be the main reason for explaining their higher adjusted R2.

The adjusted R2 for regression (4), (5), (6) and (7), which show the influence of capacity utilisation

for gas (49.24%), coal (63.91%), oil (15.80%) and pumped power plants (37.13%) are fairly high.

Both the constant and the coefficients are positive and significant on the 1% level for all four regres-

sions. The role of oil-fired power plants is very limited, therefore it is not unexpected that their ex-

planatory power is smaller than the one of gas, coal and pumped power plants. All four power plant


- 48 -

type are used for Peakload generation and are therefore often the price setting power plants which

explains their importance with respect to day-ahead prices.

The adjusted R2 for regression (10), that shows the influence of capacity utilisation (the goodness of

the forecast) for wind electricity production, is very low with 2.61%. This result could be expected

since the goodness of forecast is not a known measure when day-ahead prices are computed. The

goodness of the forecast is an ex-post measure which can be approximated fairly closely on a short

time horizon (1-2 hours in advance) but by no mean on a day-ahead basis.

The adjusted R2 for the multivariate regression (11) is 77.90%. The results obtained do not contradict

per se the results of the single regressions. The main differences are the coefficient for the capacity

utilisation of uranium which has become significant at the 1% level and the one for run-of-the-river

which has also become significant at the 1% level. On the other hand, the coefficient for the good-

ness of the forecast for wind electricity generation is not significant anymore and has turned positive.

4.3.2 Intraday Prices

Table 19 shows the regression on intraday prices on the global margin (GM) as well as the capacity

utilisation of uranium (CU), lignite (CL), gas (CG), coal (CC), oil (CO), pumped power plants (CP),

run-of-the-river (CR), seasonal power plants (CS) and wind energy (CW).

Reg.

No.

Con-


Adj.

R2

(1) 80.15***

(2.16)

-69.54***

(3.74) 58.23%

(2) 14.50

(32.71)

31.43

(34.22) 0.37%

(3) -109.79***

(10.68)

165.71***

(11.53) 34.01%

(4) 21.64***

(1.97)

111.74***

(9.89) 52.10%

(5) 20.67***

(1.12)

55.06***

(2.45) 65.22%

(6) 42.09***

(0.79)

35.77***

(4.87) 16.47%

(7) 35.44***

(0.96)

64.88***

(4.82) 29.60%

(8) 41.48***

(8.57)

2.97

(8.52) 0.04%

(9) 43.37***

(1.01)

6.46*

(3.84) 0.06%

(10) 55.64***

(2.07)

-11.42***

(1.95) 8.65%


- 49 -

(11) -37.12*

(20.73)

34.38**

(16.64)

34.74**

(13.82)

32.90***

(3.15)

27.49***

(8.08)

20.15***

(3.02)

2.65

(3.08)

-1.87

(1.81)

-1.25

(4.87) -4.90

***

(1.18) 73.34%




Table 19: Regression analysis: intraday prices

The results obtained for the regressions (1) to (9) are very similar to the results obtained for the day-

ahead prices.

Regression (10), which shows the effect of the goodness of forecast of wind electricity generation on

intraday prices exhibits an adjusted R2 of 8.65% and a negative coefficient that is significant at the

1% level. Since intraday prices are generated on a very short time interval before the actual hour, the

electricity generation from wind turbines that is expected is much more precise which increases the

relevance of the goodness of forecast for wind generation. The negative coefficient means that elec-

tricity prices tend to be lower if more electricity is generated through wind turbines. A very interest-

ing figure with respect to the ability to better predict on a very short term the actual electricity gen-

eration from wind turbines is found when comparing the volumes of intraday trading and the actual

difference between expected generation from wind energy and actual generation from wind energy,

as shown on Figure 24.

A single regression analysis using as independent variable the absolute difference in quantity be-

tween the forecasted wind generation in MW and the actually generated electricity through wind

generation in MW and using as dependent variable the volume for intraday trading exhibits an ad-

justed R2 of 37.67% with a coefficient of 0.5340 which is significant at the 1% level when using

Newey-West. This mean that market participants are able to assess with a fairly good accuracy the

actual production of electricity through wind turbines when intraday trading is still open (which

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1000 2000 3000 4000 5000 6000 7000 8000

Ab

s[fo

reca

st-a

ctu

al]

in M

W

Intraday Volume [in MW]

Volume

Figure 24: Intraday volume with respect to difference between expected and actual wind production



- 50 -

means until 75 minutes before the delivery hour starts) and are therefore able to react to large devia-

tions from forecasted production. One could expect the volumes traded during intraday trading to

increase as electricity generation through wind turbines is expected to increase in coming years.

The multivariate regression (11) does not contradict these findings. The adjusted R2 is found to be

73.34% with the main difference to the day-ahead prices being the fact that CW exhibits a negative

coefficient that is significance at the 1% level. The findings that electricity generation through wind

has a negative effect on prices coincides with practical experience. Fürsch et al. (2010) show that

since electricity produced through renewable sources must always be used; a shift to the left in the

demand curve by the produced amount occurs and, in such a case, a power plant with lower marginal

costs will be the price setting unit (merit-order effect). This does however not imply that end-

consumer prices will be lower, since electricity from renewable energy are subsidized and must

therefore be paid for15

.

4.3.3 Price Elasticity of Demand

Table 20 shows the regression of the price elasticity of demand on the global margin (GM) as well as

the capacity utilisation of uranium (CU), lignite (CL), gas (CG), coal (CC), oil (CO), pumped power

plants (CP), run-of-the-river (CR), seasonal power plants (CS) and wind energy (CW).

Reg.

No.

Con-


Adj.

R2

(1) -0.57***

(0.01)

0.44***

(0.03) 32.93%

(2) 0.12

(0.27)

-0.48*

(0.28) 0.01%

(3) 0.68***

(0.10)

-1.10***

(0.11) 21.01%

(4) -0.23***

(0.01)

-0.53***

(0.07) 16.38%

(5) -0.20***

(0.01)

-0.32***

(0.02) 31.27%

(6) -0.33***

(0.00)

-0.16***

(0.02) 4.7%%

(7) -0.31***

(0.01)

-0.18***

(0.03) 3.23%

(8) -0.08

(0.08)

-0.26***

(0.08) 2.29%

(9) -0.34***

(0.00)

-0.00

(0.03) 0.04%

15

Further discussion can be found in Sensfuss and Ragwitz (2007) as well as in Erdmann (2008).


- 51 -

(10) -0.35***

(0.01)

0.01

(0.01) 0.17%

(11) 0.75***

(0.26)

-0.32

(0.20) -0.49

***

(0.13)

-0.26***

(0.03)

-0.01

(0.07) 0.09

**

(0.03)

-0.00

(0.03) 0.04

*

(0.02)

-0.21**

(0.08)

-0.01

(0.01) 36.90%




Table 20: Regression analysis: price elasticity of demand

Regression (1), which investigates the effect of the global margin (GM) on the point elasticity of

demand exhibits an adjusted R2 of 32.93%. The coefficient is 0.44 and is significant at the 1% level.

This means that rising margins go hand in hand with higher point elasticity of demand. Since point

elasticity of demand is per definition negative, higher margins push the point elasticity towards ine-

lasticity, in other words to a point elasticity of demand of zero. High margins tend to be an indicator

for relative low consumption and therefore relative lower prices (as has been seen in section 4.3.1),

meaning that the price elasticity of demand is lower when prices are lower and vice versa. This

means that consumers are rather willing to forgo consumption of electricity when higher prices are

observed. This can be tested easily by regressing the price elasticity of demand with respect to the

day-ahead prices (DAP). The adjusted R2 obtained in this case is 37.23%, with a coefficient for DAP

of -0.005 that is significant at the 1% level (when corrected with Newey-West). This means that on

average higher prices lower the price elasticity of demand (the more negative it gets) and therefore

the higher the readiness of the consumers to forgo their electricity consumption. However, as well

the adjusted R2 for GM as the one for DAP points to the fact that other factors do play an important

role in influencing the price elasticity of demand.

Regression (2) to (10), as well as the multivariate regression (11) confirm the findings of regression

(1).

4.3.4 Prices Elasticity of Supply




Reg.

No.

Con-


Adj.

R2

(1) 0.29***

(0.02)

-0.06

(0.04) 0.9%

(2) -0.54***

(0.19)

0.84 ***

(0.20) 6.01%

(3) -0.18

(0.12)

0.48***

(0.13) 5.52%


- 52 -

(4) 0.29***

(0.01)

-0.13**

(0.05) 1.41%

(5) 0.24 ***

(0.01)

0.03

(0.02) 0.45%

(6) 0.26***

(0.00)

-0.07***

(0.02) 1.38%

(7) 0.28***

(0.00)

-0.14***

(0.03) 2.94%

(8) 0.17***

(0.06)

0.08

(0.06) 0.29%

(9) 0.27***

(0.00)

-0.06***

(0.02) 1.37%

(10) 0.24***

(0.01)

0.01

(0.01) 0.42%

(11) -1.09***

(0.21)

0.70***

(0.18)

0.77***

(0.14)

0.07**

(0.03)

-0.29***

(0.08)

-0.19***

(0.03)

-0.02

(0.02)

-0.03

(0.02)

0.01

(0.05)

0.01

(0.01) 23.30%




Table 21: Regression analysis: price elasticity of supply

The adjusted R2 obtained for the single regression analysis are very low, ranging between 0.42% and

6.01%. It seems that the influence of the individual capacity utilisation as well as the influence of the

global margin are marginal on the point elasticity of supply.

The multivariate regression (11) exhibits on the other hand an adjusted R2 of 23.30%. The coefficient

for nuclear and lignite fired power plants are clearly positive and are significant at the 1% level. This

means that the elasticity of supply tends to increase with rising use of those Baseload fired power

plants, or in other words, the variable cost of using those Baseload fired power plants is so low, that

the electricity generators are willing to increase their output even more for every Euro of price in-

crease. On the other hand, the coefficient for the typical Peakload power plants that are gas-, coal-

and oil-fired power plants are either close to zero (gas) or clearly negative and significant at the 1%

level. In other words, the variable costs of those power plants are so high that the producers willing-

ness to sell electricity for every price increase in Euro is decreasing. This means that their point elas-

ticity of supply tends to diminish with rising use of Peakload power plants. However, the low ad-

justed R2 obtained shows clearly that other factors also have an important role influencing the price

elasticity of supply.

A curious result is obtained if the price elasticity of supply is regressed with respect to day-ahead

prices. In this case, the adjusted R2 is of 2.97% with a coefficient of 0.001 which is significant at the

5% level. Electricity prices has therefore almost no affect on the elasticity of supply.

A further result that can be analysed is obtained when regressing the day-ahead volume with respect

to the elasticity of supply. Here, an adjusted R2 of 11.93% is found and the coefficient is slightly


- 53 -

negative (-0.000007) and significant at the 1% level. Therefore, day-ahead volume has a higher in-

fluence on the elasticity of supply as day-ahead prices, even though the influence of both is fairly

marginal.

Adding both DAV and DAP as independent variable to the multivariate regression (11) gives regres-

sion (12) as shown in Table 22 and increases the adjusted R2 to 50.30%. The coefficient obtained for

the variables already present in regression (11) do not vary much, and the coefficient for day-ahead

prices and day-ahead volume are almost identical with respect to the single regression coefficient

obtained and are both significant at the 1% level.

Reg.

No. DAV DAP CU CL CG CC CO CP CR CS CW

Adj.

R2

(12) -0.00***

(0.00)

0.05***

(0.00)

0.66***

(0.14)

0.18

(0.11) 0.06

*

(0.03)

-0.25***

(0.06)

-0.12***

(0.03)

-0.05**

(0.02)

-0.02

(0.01)

-0.09

(0.06) 0.01

*

(0.01) 50.53%




Table 22: Regression analysis(2): Price elasticity of supply

4.3.5 Day-ahead Price Volatility




Reg.

No.

Con-


Adj.

R2

(1) -0.08

(0.06) 0.69

***

(0.15) 14.71%

(2) 2.82***

(1.07)

-2.68 **

(1.11) 7.86%

(3) 1.85***

(0.44)

-1.69***

(0.47) 8.96%

(4) 0.38***

(0.04)

-0.55***

(0.18) 3.23%

(5) 0.44 ***

(0.04)

-0.40***

(0.08) 8.76%

(6) 0.26***

(0.01)

0.00

(0.08) 0.06%

(7) 032***

(0.02)

-0.37***

(0.09) 2.40%

(8) 0.51***

(013)

-0.24*

(0.12) 0.32%

(9) 0.23***

(0.01)

0.20**

(0.08) 1.76%


- 54 -

(10) 030***

(0.03)

-0.03

(0.02) 0.18%

(11) 3.92***

(1.35)

-2.28**

(1.10)

-1.32***

(0.48)

-0.22**

(0.10)

-0.10

(0.29)

-0.06

(0.07)

0.14

(0.11) 0.14

*

(0.08)

-0.07

(0.13) -0.08

***

(0.02) 21.29%




Table 23: Regression analysis: day-ahead price volatility

Regression (1) which looks at the influence of GM on the volatility of day-ahead prices exhibits an

adjusted R2 of 14.71%. The coefficient is positive (0.69) and significant at the 1% level, meaning

that rising margin tend to increase the hourly price volatility. Similar information is gained from re-

gressions (2) to (10) which however exhibit fairly low adjusted R2. The coefficients for regressions

(2) to (10) are negative and in most cases significant at the 1% level, meaning that rising capacity

utilisation reduces the day-ahead hourly price volatility.

The multivariate regression (11) confirm those findings, even though most coefficient founds are not

significant anymore. The results obtained show that generation margins respectively capacity utilisa-

tion are not a good indicator for day-ahead price volatility, neither the less, they demonstrate to some

extend that electricity producer might be facing a higher freedom for price setting as more produc-

tion capacities are left unused. In other words, the price spread tends to be higher when more produc-

tion capacities are available.

4.3.6 Intraday Price Volatility




Reg.

No.

Con-


Adj.

R2

(1) -0.23

(0.15) 1.47

***

(0.34) 10.70%

(2) 4.64*

(2.61)

-4.33

(2.73) 3.32%

(3) 6.40***

(1.39)

-6.32***

(1.47) 20.43%

(4) 0.90***

(0.10)

-1.85***

(0.38) 5.90%

(5) 0.99 ***

(0.12)

-1.10***

(0.21) 10.73%

(6) 0.55***

(0.04)

-0.44***

(0.09) 1.00%

(7) 0.68***

(0.06)

-1.19***

(0.23) 4.08%


- 55 -

(8) 0.58**

(0.26)

-0.06

(0.25) 0.06%

(9) 0.50***

(0.04)

0.08

(0.14) -0.02%

(10) 0.28***

(0.06)

0.24***

(0.06) 1.58%

(11) 10.23***

(3.24)

-4.63*

(2.53)

-6.12***

(1.73)

-0.05

(0.16)

-0.04

(0.31) -0.19

*

(0.11)

-0.04

(0.12)

0.17

(0.13)

0.31

(0.27) 0.13

*

(0.07) 25.47%




Table 24: Regression analysis: intraday price volatility

The results found for regressions (1) to (11) are very similar with the results found in the previous

section on day-ahead price volatility even though the respective volatility figures are completely dif-

ferent. The major difference is found in the adjusted R2 for CL which is found to be 20.43%. Rea-

sons for this high number cannot be provided readily, since expectation would have rather pointed to

a higher explanatory power of CW since electricity generation from wind turbine underlies heavy

fluctuation and must therefore be compensated for in the very short term, hence in the intraday mar-

ket.

The adjusted R2 for the multivariate regression (11) is 25.47% and therefore slightly higher than for

regression (11) of the previous section. However, most coefficients found are not significant. Again,

it seems that capacity margins are a rather bad indicator for price fluctuation at the intraday market.


- 56 -

5. Concluding Remarks

This thesis aims at analysing the relationship between the production capacities in the German elec-

tricity market and various other aspects of this market: on the one hand side, the influence of produc-

tion capacities on prices; on the other hand, its influence on the shape of the demand and supply

curve and finally its influence on the electricity markets volatility. In this context, this paper presents

an empirical analysis of the German electricity market for the period between June 2nd

2010 and Au-

gust 4th

2010 where the key issues are reviewed.

In a first phase, the German electricity market as a whole is introduced with its key characteristics.

The main producers as well as their means of production are briefly reviewed. Furthermore, a gen-

eral overview is provided with respect to the available information at the EEX and the EEX Trans-

parency portal. These included figures to the installed generation capacities, available generation ca-

pacities as well as actually produced electricity on an hourly bases. Furthermore, the EEX provides

the price/quantity bids placed by the market participants in the day-ahead market which represent the

demand and supply curves, and, finally, the prices and quantity resulting from these day-ahead mar-

kets as well as the prices and quantity resulting from the intraday market are also briefly introduced.

In a second step, the relevant variables for the empirical analysis are generated. In a first section, the

margin generation for the electricity market is computed and is found to be on average very comfort-

able with 51.43%. Instead of computing further margins for every individual type of power plants,

the decision was taken to use the figure “used capacity” since it is more intuitive. Therefore, the used

capacity for every type of generator was computed. Regarding wind generation, the same computa-

tional procedure was used even though it does not per se represent the used capacity. For wind gen-

eration, the computed figure refers to the goodness of forecast, since actually produced electricity

was compared to expected production since, unlike most other generation types where men decide

how much to produce, nature is here the technician. The second section deals with the demand and

supply curves and uses polynomial of 12th

order to describe each curve. Based on the curve fits, elas-

ticity measures, both for the demand and supply curve are computed. The result found for the point

elasticity of demand (-0.34) is within the expected scope as described by various studies in the last

years. The point elasticity of supply (0.26) cannot readily be compared to other researches, does

however seem to be consistent with what could be expected. The third section deals with the hourly

volatility in the German electricity market. On the one hand side, the hourly volatility of the day-

ahead market was computed using a rolling window and was found to be 0.3639 during the observa-

tion period. exhibiting a very high fluctuation. On the other hand, the volatility of the intraday prices

was computed using a different methodology, such as to show how much prices did fluctuate within


- 57 -

an hour. The results obtained show an average hourly volatility for intraday prices of 52.2% with a

very high fluctuation band with.

In a third phase, the empirical analysis per se is performed. Evidences are found that margins and

capacity utilisation in the German electricity market do indeed affect electricity prices, as well in the

day-ahead as in the intraday market. Rising margin have on average a lowering effect on prices,

while rising capacity utilisation tends to lead to higher prices. The one interesting aspect is the fact

that, when more electricity is generated through wind than expected, price tend to get lower. This has

been and is still a major discussion topic in Germany with regards to the subsidies for renewable

electricity. The findings of the present study, which are confirmed by various other studies suggest

that electricity through wind generation has a lowering effect on electricity prices and that therefore

the subsidies are to some extend covered by those lower prices.

The effect of generation margins and capacity utilisation in the German electricity market on the

elasticity of demand and supply has not provided surprising results. Even though the adjusted R2

were relatively moderate (36.90%), the results found are highly significant. Shrinking margins (re-

spectively increasing capacity utilisation) tend to increase the elasticity of demand indicating that

consumers are rather willing to change their consumption habits. The exact opposite effect is ob-

served for the supply elasticity which is increased as margin are reduced, therefore, producers of

electricity are rather willing to produce more electricity when margins are tighter. The adjusted R2

for the elasticity of supply is, with 23.30%, however rather small. Hence, other aspects than the ca-

pacity utilisation of the power plants must have an influence on the elasticity of demand and supply

and might be a question for further research.

With regards to the market volatility, most results of the empirical analysis where highly significant

even though the adjusted R2 are very low. The result show, as well for intraday as for day-ahead

markets that volatility tends to increase with shrinking capacity utilisation. In other words, the higher

the capacity utilisation is, the lower the latitude the electricity producers have to set the price. How-

ever, many other factors do affect price volatility, which might also be a question for further re-

search.


- 58 -

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Appendix

1. Computation of R-Square for the polynomial fitting of the demand and supply curve with

MATLAB

clear clc %we start from the data "Curvestudy" assets = xlsread('Curvestudy.xlsx'); for i = 1:3:192 price(:,(i-1)/3+1) = assets(4802:9601,i); demand(:,(i-1)/3+1) = assets(4802:9601,i+1); supply(:,(i-1)/3+1) = assets(4802:9601,i+2); end Price = 1; Demand = 1; Supply = 1; for i = 1:63 Price = [Price ; price(:,i)]; Demand = [Demand ; demand(:,i)]; Supply = [Supply ; supply(:,i)]; end Price = Price(2:end); Demand = Demand(2:end); Supply = Supply(2:end); %now i have a string for each deamdn, supply and price for z = 1:200:302400 for t=1:200 P(t,1)=[Price(z+t-1)]; D(t,1)=[Demand(z+t-1)]; S(t,1)=[Supply(z+t-1)]; bpos = P>-450; %lower value considered sumbpos = sum(bpos==0); bneg = P<450; %upper value considered sumbneg = sum(bneg==0); end %computation of the polynomial of order x (here 12) for the demand (polyfite) and supply (polyfitesupply) polyfite((z-1)/200+1,:) = polyfit(P(1+sumbpos:200-sumbneg),D(1+sumbpos:200-sumbneg),12); polyfitesupply((z-1)/200+1,:) = polyfit(P(1+sumbpos:200-sumbneg),S(1+sumbpos:200-sumbneg),12); %computation of Rsquare for demand (RSQUARED) and supply (RSQUAREDSUPPLY) Dsim = polyval(polyfite((z-1)/200+1,:),P(1+sumbpos:200-sumbneg)); RSS = sum((Dsim-mean(D(1+sumbpos:200-sumbneg))).^2); TSS = sum((D(1+sumbpos:200-sumbneg)-mean(D(1+sumbpos:200-sumbneg))).^2); RSQUARED((z-1)/200+1,:) = RSS/TSS; DsimSupply = polyval(polyfitesupply((z-1)/200+1,:),P(1+sumbpos:200-sumbneg)); RSSSupply = sum((DsimSupply-mean(S(1+sumbpos:200-sumbneg))).^2); TSSSupply = sum((S(1+sumbpos:200-sumbneg)-mean(S(1+sumbpos:200-sumbneg))).^2); RSQUAREDSUPPLY((z-1)/200+1,:) = RSSSupply/TSSSupply; end


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2. Point elasticity computation using MATLAB

clear clc %we start from the data "Curvestudy" and "Price_Quantity" assets = xlsread('Curvestudy.xlsx'); assets2 = xlsread('Price_Quantity.xlsx'); %Market Clearing Price (MCP) and Market Clearing Quantity (MCQ) MCP = assets2(2:1513,1); MCQ = assets2(2:1513,2); for i = 1:3:192 price(:,(i-1)/3+1) = assets(4802:9601,i); demand(:,(i-1)/3+1) = assets(4802:9601,i+1); supply(:,(i-1)/3+1) = assets(4802:9601,i+2); end Price = 1; Demand = 1; Supply = 1; for i = 1:63 Price = [Price ; price(:,i)]; Demand = [Demand ; demand(:,i)]; Supply = [Supply ; supply(:,i)]; end Price = Price(2:end); Demand = Demand(2:end); Supply = Supply(2:end); for z = 1:200:302400 for t=1:200 P(t,1)=[price(z+t-1)]; D(t,1)=[demand(z+t-1)]; S(t,1)=[supply(z+t-1)]; bpos = P>-450; %lower value considered sumbpos = sum(bpos==0); bneg = P<450; %upper value considered sumbneg = sum(bneg==0); end %computation of the polynomial of order x (here 12) for the demand (polyfite) and supply (polyfitesupply) polyfite((z-1)/200+1,:) = polyfit(P(1+sumbpos:200-sumbneg),D(1+sumbpos:200-sumbneg),12); polyfitesupply((z-1)/200+1,:) = polyfit(P(1+sumbpos:200-sumbneg),S(1+sumbpos:200-sumbneg),12); %First derivative of each function is taken diffequation((z-1)/200+1,:) = polyder(polyfite((z-1)/200+1,:)); diffequationsupply((z-1)/200+1,:) = polyder(polyfitesupply((z-1)/200+1,:)); end %Computation of the point elasticity of demand (ElasticityD) and of the %point elasticiy of supply (ElasticityS) for i =1:1512 Upperpart = MCP(i)*polyval(diffequation(i,:),MCP(i)); Lowerpart = polyval(polyfite(i,:),MCP(i)); ElasticityD(i,:) = Upperpart/Lowerpart; end for i =1:1512 Upperpart = MCP(i)*polyval(diffequationsupply(i,:),MCP(i)); Lowerpart = polyval(polyfitesupply(i,:),MCP(i)); ElasticityS(i,:) = Upperpart/Lowerpart; end


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3. Arc elasticity computation using MATLAB

clear clc %we start from the data "Curvestudy" and "Price_Quantity" assets = xlsread('Curvestudy.xlsx'); assets2 = xlsread('Price_Quantity.xlsx'); %Market Clearing Price (MCP) and Market Clearing Quantity (MCQ) MCP = assets2(2:1513,1); MCQ = assets2(2:1513,2); for i = 1:3:192 price(:,(i-1)/3+1) = assets(4802:9601,i); demand(:,(i-1)/3+1) = assets(4802:9601,i+1); supply(:,(i-1)/3+1) = assets(4802:9601,i+2); end Price = 1; Demand = 1; Supply = 1; for i = 1:63 Price = [Price ; price(:,i)]; Demand = [Demand ; demand(:,i)]; Supply = [Supply ; supply(:,i)]; end Price = Price(2:end); Demand = Demand(2:end); Supply = Supply(2:end); for z = 1:200:302400 for t=1:200 P(t,1)=[Price(z+t-1)]; D(t,1)=[Demand(z+t-1)]; S(t,1)=[Supply(z+t-1)]; bpos = P>MCP((z-1)/200+1); sumP = [sum(bpos==0)]; bneg = D<MCQ((z-1)/200+1); sumV = [sum(bneg==0)]; end %determination of the individual numbers needed Q1 = D(1+sumV); Q2 = D(sumV-1); P1 = P(1+sumP); P2 = P(sumP-1); QS1 = S(1+sumV); QS2 = S(sumV-1); %computation of the arc elasticity of demand (AEOD) and of the arc %elasticity of supply (AEOS) AEOD((z-1)/200+1,:) = ((Q1-Q2)/((Q1+Q2)/2)) / ((P1-P2)/((P1+P2)/2)); AEOS((z-1)/200+1,:) =((QS1-QS2)/((QS1+QS2)/2)) / ((P1-P2)/((P1+P2)/2)); end Output = [AEOD AEOS];


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4. Daily volatility computation using MATLAB

clear clc %we start from the data "Price_Quantity" assets = xlsread('Price_Quantity.xlsx'); prices = assets(2:end-24,1); quantity = assets(2:end-24,2); oldprices = assets(1:168,8); fullprice = [oldprices ; prices]; %computation for sigma(t = 1h, T = 24h), denote H1 for i = 169:1680 logreturnH1(i-168,1) = log(fullprice(i)/fullprice(i-1)); end %transform logreturns into real numbers logreturnH1 = real(logreturnH1); for i = 1:24:1512 meanlogreturnH1((i-1)/24+1,1) = mean(logreturnH1(i:i+23,1)); for H = 0:23 summ1H1(H+1,1) = (logreturnH1(i+H,1)-meanlogreturnH1((i-1)/24+1,1)).^2; end summ2H1((i-1)/24+1,1) = sum(summ1H1); volaH1((i-1)/24+1,1) = sqrt(summ2H1((i-1)/24+1,1)/23); end %computation for sigma(t = 24h, T = 24h), denote H2 for i = 169:1680 logreturnH2(i-168,1) = log(fullprice(i)/fullprice(i-24)); end %transform logreturns into real numbers logreturnH2 = real(logreturnH2); for i = 1:24:1512 meanlogreturnH2((i-1)/24+1,1) = mean(logreturnH2(i:i+23,1)); for H = 0:23 summ1H2(H+1,1) = (logreturnH2(i+H,1)-meanlogreturnH2((i-1)/24+1,1)).^2; end summ2H2((i-1)/24+1,1) = sum(summ1H2); volaH2((i-1)/24+1,1) = sqrt(summ2H2((i-1)/24+1,1)/23); end %computation for sigma(t = 168h, T = 24h), denote H3 for i = 169:1680 logreturnH3(i-168,1) = log(fullprice(i)/fullprice(i-168)); end %transform logreturns into real numbers logreturnH3 = real(logreturnH3); for i = 1:24:1512 meanlogreturnH3((i-1)/24+1,1) = mean(logreturnH3(i:i+23,1)); for H = 0:23 summ1H3(H+1,1) = (logreturnH3(i+H,1)-meanlogreturnH3((i-1)/24+1,1)).^2; end summ2H3((i-1)/24+1,1) = sum(summ1H3); volaH3((i-1)/24+1,1) = sqrt(summ2H3((i-1)/24+1,1)/23); end


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5. Hourly volatility computation using MATLAB

clear clc %we start from the data "Price-Quantity" assets = xlsread('Price_Quantity.xlsx'); prices = assets(2:end-24,1); quantity = assets(2:end-24,2); oldprices = assets(1:168,8); fullprice = [oldprices ; prices]; %computation for sigma(t = 24h, T = 168h), denote H4 for i = 169:1680 logreturnH4(i-168,1) = log(fullprice(i)/fullprice(i-24)); end %transform logreturns into real numbers logreturnH4 = real(logreturnH4); for i = 1:168:1512 for d = 1:7 for h = 1:24 hourperweek((i-1)/168*24+h,d) = logreturnH4((i-1)+(d*24)-24+h); end end end for i = 1:216 meanhourperweekH4(i,1) = mean(hourperweek(i,:)); end for i = 1:216 summ1H4(i,:) = (hourperweek(i,:)-meanhourperweekH4(i,1)).^2; summ2H4(i,1) = sum(summ1H4(i,:)); volaH4(i,1) = sqrt(summ2H4(i,1)/6); end


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6. Hourly volatility (rolling window) computation using MATLAB

clear clc %we start from the data "Prices_+" assets = xlsread('Prices_+.xlsx'); prices = assets(1:end,1); %computation for sigma(t = 168h, T = 1512h), denote H5 for i = 169:3048 logreturnH5(i-168,1) = log(prices(i)/prices(i-168)); end %transform logreturns into real numbers logreturnH5 = real(logreturnH5); for i = 1:17 for h = 1:168 hourperweek2(h,i) = logreturnH5(h+(i-1)*168); end end for d = 1:9 for i = 1:168 meanhourperweekH5(i+(d-1)*168,1) = mean(hourperweek2(i,(d-1)+1:(d-1)+9)); end end for d=1:9 for i = 1:168 summ1H5(i+(d-1)*168,:) = (hourperweek2(i,(d-1)+1:(d-1)+9)-meanhourperweekH5(i+(d-1)*168,1)).^2; summ2H5(i+(d-1)*168,1) = sum(summ1H5(i+(d-1)*168,:)); volaH5(i+(d-1)*168,1) = sqrt(summ2H5(i+(d-1)*168,1)/8); end end


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Declaration of Authorship

“I hereby declare

- that I have written this thesis without any help from others and without the use of docu-

ments and aids other than those stated above,

- that I have mentioned all used sources and that I have cited them correctly according to

established academic citation rules,

- that I shall not pass on any copies of this thesis to any third parties without the president’s

consent, with the exception of fellow students or persons who have provided me with es-

sential information for this thesis, to whom I max pass on copies of this thesis after the

procedure has been concluded.”

St. Gallen, 5th

November 2010

Nicolas Samyn

Empirical Analysis of Price-Curves at the EEX

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Transcript of Empirical Analysis of Price-Curves at the EEX