eeh
power systems
laboratory
Matej Mesojedec
Marginal Price Forecast for Secondary
Control Power
Semester Thesis
PSL1231
Department:
EEH – Power Systems Laboratory, ETH Zürich
Examiner:
Prof. Dr. Göran Andersson, ETH Zürich
Supervisors:
Hubert Abgottspon, ETH Zürich
Dr. Britta Bohnenbuck, CKW
Thomas Reithofer, CKW
Zürich, February 2013
ii
Preface
The last two months have been challenging and informative time. A lot
of knowledge, insights and experiences were collected. It’s been a pleasure
doing semester thesis in cooperation between CKW – Central Schweizerische
Kraftwerke and PSL – Power Systems Laboratory of ETH Zürich.
Special thanks goes to my supervisors at CKW, Dr.Britta Bohnenbuck
and Thomas Reithofer. This work would not have been possible without
their support and fruitful inputs.
I would like to express my gratitude to my supervisor at ETH, Hubert
Abgottspon, for giving me a freedom to choose and work on the topic of my
own.
Thanks goes also to the head of Power Systems Laboratory of ETH,
Prof. Dr. Göran Andersson, for making cooperation between CKW and
PSL possible.
Last but not least, I would like to thank my family and friends for supporting me during the years of my studies.
Thesis was made possible by a grant from Slovene Human Resources
Development and Scholarship Fund.
Zürich, February 2013
Matej Mesojedec
iii
iv
Abstract
The model described in the scope of this thesis reveals one of the possibilities
for a marginal price forecast for Secondary Control power (SC). It is designed
to deliver forecast of the opportunity costs that power plants taking part in
the SC market face.
Electricity production of different power plants can be sold on various
markets. One of them is the market for ancillary services. Secondary Control
power is one of the products of the ancillary services for active power control
reserve. Once the power plant is granted the access to the SC market it is
eligible to place the bids.
Bids may consist of multiple volume and price combinations. Two remunerations exist – one for energy and the other one for capacity. The
remuneration of capacity is pay-as-bid. One gets paid according to the price
specified in the bid. Therefore it is of significant value for electricity producers taking part in the market for SC to know the price of the highest
bid accepted, in order to maximize their own revenue. This point was the
main motivation that led to set the model for marginal price forecast for
Secondary Control power for the Swiss control zone.
Main input data used to feed the model is:
• water statistics data (inflow and reservoir content data)
• historical capacity prices for Secondary Control power
• Hourly Priced Forward Curve values for Switzerland
It turned out that the model does not deliver reasonable forecast for the
time period around the reservoir bottom reverse point. In any other time
period the model delivers a good forecast of Opportunity Costs which could
be used for marginal price forecast for SC.
Additionally, many issues regarding the water statistics were brought up
shedding a light in direction of possible model improvements.
v
vi
Kurzfassung
Das im Rahmen dieser Arbeit beschriebene Modell zeigt eine der Möglichkeiten
für die Grenzpreis-Prognose für Sekundärregelleistung (SRL) auf. Modell ist
so aufgebaut, dass es Vorhersagen der Opportunitätskosten der Kraftwerke,
die am SRL-Markt teilnehmen, liefert.
Elektrischer Strom aus verschiedenen Kraftwerken kann auf mehrere
Arten vermarktet werden. Eine Möglichkeit ist der Systemdienstleistungsmarkt. Eines der Systemdienstleistungsprodukte ist die Sekundärregelleistungsreserve (SRL). Sobald der Zugang für diesen Markt gewährt wurde,
steht es dem Produzenten frei, Gebote auf dem Markt zu platzieren.
Gebote sind Kombinationen aus Volumen und Preis. Die Vergütung
erfolgt einerseits auf Basis der zur Verfügung gestellten Regelleistung, andererseits auf der abgerufenen Energie. Die zur Verfügung gestellte Leistung
wird pay as bid vergütet, das heisst, dass jeder Anbieter so viel erhält, wie
sein Angebot war. Für Produzenten ist deshalb zur Gewinnmaximierung
sehr interessant zu wissen, wie hoch das jeweils höchste noch zugeschlagene
Gebot war. Dies war die Hauptmotivation, ein entsprechendes Modell zur
Vorhersage des Marginalpreises für die Regelzone Schweiz zu erstellen.
Die benötigten Inputdaten sind:
• Wasser-Statistik-Daten (Zuflussdaten und Seeinhalte der Speicherseen)
• historische Leistungspreise der Sekundärregelreserve
• Hourly Price Forward Curve für die Schweiz
Das Modell kann für die Zeitperiode um den unteren Stauumkehrpunkt
keine plausiblen Vorhersagen machen. In den übrigen Perioden liefert das
Modell gute Vorhersagen der Opportunitätskosten, die für die marginale
Preisvorhersage der Sekundärregelleistungsreserve benutzt werden können.
Zusätzlich, wurden viele Probleme der Wasserstatistiken betreffend in
Anbetracht möglicher Modellverbesserungen näher beleuchtet.
vii
viii
Contents
1 Introduction
1
2 Model Background
2.1 Ancillary Services . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Secondary Control Reserve . . . . . . . . . . . . . . .
2.2 Mean Reverting Jump Diffusion Process . . . . . . . . . . . .
3
3
4
5
3 Modeling Approaches
3.1 Model Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Theoretical Basis – Energy Balance . . . . . . . . . .
3.1.3 Theoretical Basis – Financial Balance . . . . . . . . .
3.1.4 Model Inputs . . . . . . . . . . . . . . . . . . . . . . .
3.2 Model Configuration 1.0 . . . . . . . . . . . . . . . . . . . . .
3.2.1 Step 1: Computation of historical hours of production
3.2.2 Step 2: Computation of maximal power output . . . .
3.2.3 Step 3: Computation of forecast hours of production .
3.2.4 Step 4: Computation of Opportunity Costs forecast .
3.2.5 Potential Problems . . . . . . . . . . . . . . . . . . . .
3.3 Model Configuration 1.1 . . . . . . . . . . . . . . . . . . . . .
3.4 Model Configuration 1.2 . . . . . . . . . . . . . . . . . . . . .
3.5 Model Configuration 1.3 . . . . . . . . . . . . . . . . . . . . .
3.6 Water Statistics . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Data from two different sources . . . . . . . . . . . . .
3.6.2 Reservoir Content Data . . . . . . . . . . . . . . . . .
3.6.3 Inflow Data . . . . . . . . . . . . . . . . . . . . . . . .
7
7
7
8
10
12
13
13
19
24
29
32
34
37
41
41
42
43
44
4 Numeric Results
47
5 Conclusion and Outlook
49
Bibliography
53
ix
x
CONTENTS
Chapter 1
Introduction
Energy is a driver of today’s economy. Electrical energy plays an important
role among other energy forms. Electricity production of different power
plants can be sold on various markets. One of them is the market for ancillary services.
Since electrical energy cannot be stored in large quantities by conventional means, electricity produced must correspond precisely to the amount
being used at any point in time in order to assure its security of supply.
Such a balance can be maintained through provision of ancillary services by
the Transmission System Operator (TSO). Market for ancillary services is
therefore a place where electricity producers and a TSO meet.
One of the ancillary service products for active power control reserve
is Secondary Control power (SC). According to the specifications of this
product, electricity producers have to meet certain technical and operational
requirements in order to get access to the market. Once the TSO grants them
the access they are eligible to place their bids.
Bids may consist of multiple volume and price combinations. Two remunerations exist – one for energy and the other one for holding of capacity.
The remuneration of capacity is pay-as-bid. One gets paid according to the
price specified in the bid. Therefore it is of significant value for electricity
producers taking part in the market for SC to know the price of the last
bid accepted, in order to maximize their own revenue. This point was the
main motivation that led to set the model for marginal price forecast for
Secondary Control power for the Swiss control zone.
Thesis is structured in 5 chapters that lead you through the introduction,
background needed for set up and understanding the model, used modeling
approaches, acquired numeric results and finally to the conclusion and outlook.
1
2
CHAPTER 1. INTRODUCTION
Chapter 2
Model Background
In this chapter the background needed for set up and understanding the
model for marginal price forecast for Secondary Control power is introduced.
Section 2.1 consists of a short resume of [1] and [2]. In the section 2.2
application of Mean Reverting Jump Diffussion process implemented in the
model is introduced.
2.1
Ancillary Services
Transmission System Operator (TSO) of the Swiss control zone is Swissgrid. Its responsibility is to assure secure and reliable operation of the Swiss
transmission system and connections to the transmission systems of foreign operators. In order to meet this responsibility Swissgrid needs system
services. The quality of electricity supply is determined by the following
ancillary services:
• Primary control reserve
• Secondary control reserve
• Tertiary control reserve
• Voltage support
• Compensation of active power losses
• Black start and island operation capability
• System coordination
• Operational measurement
Provision of ancillary services is done through transparent, non-discriminatory
and market-based procedure.
3
4
CHAPTER 2. MODEL BACKGROUND
2.1.1
Secondary Control Reserve
Active Power Control Reserve Secondary Control reserve is one of the
ancillary services that belong to the active power control reserve. In order
to get a whole picture of all the ancillary services that belong to the active
power control reserve they are listed below:
• Primary Control reserve
• Secondary Control reserve
• Tertiary Control reserve
Since electrical energy cannot be stored in large quantities by conventional
means, electricity produced must correspond precisely to the amount being
used at any point in time in order to assure its security of supply. Such
a balance can be maintained through ancillary services for active power
control.
Balance has to be established at short notice by increasing or reducing the production of power plants supplying active power control reserve.
Technically this is achieved within the synchronous electricity grid of the
ENTSO-E1 by a three-stage regulation procedure consisting of primary, secondary and tertiary control.
Secondary Control Reserve Secondary Control reserve (SC) takes place at
a second stage of the active power regulation procedure. It is automatically
actuated through the control signal sent from the TSO to the bidder. It is
activated within a few seconds and typically completed after 15 minutes.
Requested amount for SC is proportional to bidder’s contracted capacity.
SC is a product with symmetrical control power bands that is contracted
for a whole week. Demanded volume for SC by the Swissgrid is ±400MW.
Supplier of SC has to constantly produce at a certain level in order to be
able to increase or reduce production within a contracted band.
Besides the remuneration of energy supplier of SC also receives remuneration for contracted capacity. Remuneration of capacity can be interpreted
as a compensation for the reduced flexibility of production.
Remuneration of energy is based on hourly spot price on SwissIX ±20%
including cap/floor weekly base.
The remuneration of capacity is pay-as-bid. One gets paid according to
the price specified in the bid.
1
ENTSO-E – The European Network of Transmission System Operators for Electricity
2.2. MEAN REVERTING JUMP DIFFUSION PROCESS
2.2
5
Mean Reverting Jump Diffusion Process
Mean Reverting Jump Diffusion process (MRJD) is an extension of the
mathematical concept of mean reversion. In our case MRJD was used to add
a stochastic term to the deterministic nature of HPFC (see figure 2.1). This
was done according to the procedure described in the unpublished paper [3].
As a background for [3] literature from [4] was used.
Comparison of HPFC
HPFC deterministic
HPFC deterministic + stochastic term
180
160
140
[ CHF / MWh ]
120
100
80
60
40
20
0
01/Jan
08/Jan
15/Jan
22/Jan
29/Jan
2012
Figure 2.1: Comparison of HPFC for Switzerland
Computation procedure from [3] is briefly described by the following
bullet points:
1. specify residuals
2. determine mean reverting rate
3. extract diffusion component from sample using the calculated value of
mean reverting rate
4. find jumps in the diffusion component
5. generate scenarios
6. add simulated residuals to the deterministic HPFC
6
CHAPTER 2. MODEL BACKGROUND
Chapter 3
Modeling Approaches
3.1
Model Basis
In this section theoretical basis and assumptions of the model built for
marginal price forecast for SC are explained.
3.1.1
Assumptions
The model for marginal price forecast for SC is based on the following assumptions:
1. Secondary Control power for Swiss control zone is delivered by only
one storage power plant. It is modeled as a simple storage power plant
with only one storage stage. No other stages such as must-run stages
exist.
2. The modeled storage power plant can produce within following turbine
regimes:
• full-power production (Pmax )
• half-power production if delivering SC ( Pmax
2 )
• no production (P = 0)
3. Marginal SC price ≥ Opportunity costs of delivering SC
(detailed explanation follows in section 3.1.3)
Power plants supplying SC to the Swiss control zone are mostly run-ofriver and storage power plants. Storage power plants are usually the ones
that determine the price of the highest bid accepted. Since the goal of this
thesis is to set up the model for the price of the highest bid accepted for SC,
assumption described in the first bullet point seems to be convenient and
reasonable.
7
8
CHAPTER 3. MODELING APPROACHES
Assumption described in the second bullet point was done for the sake
of simplicity.
According to the strategic bidding suppliers of SC never bid under their
opportunity costs of delivering SC. According to this the assumption described in the third bullet point was made. Marginal SC price refers to the
capacity price of the highest bid accepted.
3.1.2
Theoretical Basis – Energy Balance
When production of a storage power plant is observed from an energy balance point of view, it can be stated that it depends on the water available
for production.
P roduction planwithout
= Available W ater = P roduction planwith SC
(3.1)
P roduction planwithout SC relates to the production plan when no SC is
delivered. Respectively P roduction planwith SC relates to the production
plan when also SC is delivered.
SC
Defined Time Period Let’s define a time period as a period starting each
Monday in a year (later on marked as t0 ) and ending at the next following
reservoir reverse point (later on marked as tS ).
The term reservoir reverse point refers to the point in time when reservoir
content reaches its maximum or minimum level. When the reservoir content
reaches its maximum or minimum level depends on the water inflows filling
the reservoirs. Water inflows are subject to weather conditions. Reservoir
content of the water reservoirs in Switzerland usually reaches its minimum
level in April and its maximum in October.
This definition of the time period seems to be convenient for the production planning of a storage power plant and is going to be used in the
scope of this thesis. Its convenience is justified by the fact that it takes into
consideration available water from the storage reservoir that can be used for
production.
Available Water The amount of available water for production over a defined period of time is determined by the following two parameters:
• Inflows: inflows to the storage reservoirs over this period of time
• Delta Reservoir Content: difference between the reservoir content of
the last day and the reservoir content of the first day in the observed
time period
3.1. MODEL BASIS
9
Respecting defined time period and above mentioned parameters results
in the formulation of equation 3.2.
Available W ater = It0 ,tS − (RtS − Rt0 )
(3.2)
Rt0 represents the reservoir content of the first day in the defined time
period. Respectively, RtS represents the reservoir content of the last day in
the defined time period. According to the definition of the time period first
day is defined as each Monday in a year → t0 . Respectively, the last day is
defined as the next following reservoir reverse point→ tS .
It0 ,tS represents the inflows to the storage reservoirs over the defined
period of time from t0 to tS .
For the sake of better understanding of Delta Reservoir Content the
following examples are shown:
1. Accumulation of water in the reservoir
)
RtS = 0.5 R
RtS − Rt0 = + 0.1 R = + b · R
Rt0 = 0.4 R
2. Consumption of water from the reservoir
)
RtS = 0.3 R
RtS − Rt0 = − 0.1 R = − b · R
Rt0 = 0.4 R
(3.3)
(3.4)
R stands for the absolute value of the maximum storage capacity and b
stands for the percentage value of the maximum storage capacity. Variable b
was introduced in order to explain what kind of a sign denotes accumulation,
respectively consumption, of water from the reservoir.
Production Plan Respecting the assumptions specified in section 3.1.1
and the number of hours N that power plant is producing, results in the
formulation of equation 3.5 and 3.6. Each defined time period starting at
t0 and ending at tS has a specific N , which stands for the number of hours
that the modeled power plant is producing in this defined period of time.
P roduction planwithout
SC
= Pmax · Nwithout
SC
(3.5)
Pmax
· 168 + Pmax · Nwith SC
(3.6)
2
Nwithout SC relates to the number of hours that the power plant is producing
while not having delivered any SC in the defined time period from t0 to tS .
Respectively, Nwith SC relates to the number of hours that the power plant is
producing besides having delivered SC for a week in the defined time period
from t0 to tS .
P roduction planwith
SC
=
10
CHAPTER 3. MODELING APPROACHES
Putting together equation 3.1, 3.2, 3.5 and 3.6 results in formulation
of the equation 3.7, which represents an energy balance of a specific time
period starting at t0 and ending at tS .
Pmax ·Nwithout
SC
= It0 ,tS −(RtS −Rt0 ) =
Pmax
·168+Pmax ·Nwith
2
SC
(3.7)
It is important to mention that according to the equation 3.7 energy balance is set for each specific time period without considering what happened
in the time period before. Energy balance of each specific time period is
therefore based only on the water available for production in this specific
time period.
Out of the equation 3.7 relationships described in equation 3.8 and 3.9
are drawn.
Nwithout SC = 84 + Nwith SC
(3.8)
Ntotal
with SC
= 168 + Nwith
(3.9)
SC
Delivering SC for a week corresponds to the 168 hours of production.
Adding these hours up to the Nwith SC results in Ntotal with SC . Variable
Ntotal with SC represents the total number of hours that power plant is producing in defined period of time from t0 to tS where also SC is delivered for
a week.
3.1.3
Theoretical Basis – Financial Balance
When considering selling the production of a power plant on the market for
SC one usually compares the following two revenues:
1. the revenue from selling the production only on the spot market
2. the revenue of selling the production on the spot market and on the
market for SC
Opportunity Costs Term Opportunity Costs stands for the costs that
supplier of SC faces when delivering SC for a week. Value of the
Opportunity Costs is calculated according to equation 3.10, which basically
represents the difference between the two revenues mentioned before.
Opportunity Costs =
P roduction planwithout
SC
· HP F C − P roduction planwith
SC
· HP F C
(3.10)
By respecting equations 3.5 and 3.6, equation 3.10 can be reformulated
to equation 3.11.
3.1. MODEL BASIS
11
Pmax ·
P
HP F C(t)
t∈Nwithout
168 · Pmax
2
Opportunity Costs =
SC
!
Pmax
2
· 168 · HP F Cbase
week SC
+ Pmax ·
P
HP F C(t)
t∈Nwith
−
168 ·
SC
(3.11)
Pmax
2
In order to acquire Opportunity Costs per unit of energy, the right hand
side of equation 3.11 is divided by the number of hours in a week, which is
actually a contract period for SC, and by the power at which power plant
needs to produce during the contract period in order to be able to deliver
SC whenever needed. Value of the Opportunity Costs per unit of energy is
needed for the sake of comparison with the capacity prices of SC that are
also expressed per unit of energy (see equation 3.13 and 3.14).
HP F Cbase week SC relates to the average value of HPFC for the week
when SC is delivered.
Equation 3.11 can be simplified by dividing the numerator and denominator by Pmax . Obtained result is shown in equation 3.12.
Opportunity Costs =
!
P
HP F C(t) −
t∈Nwithout
168
2
· HP F Cbase
week SC
+
P
HP F C(t)
t∈Nwith
SC
SC
(3.12)
168
2
Pay-off It pays off to deliver SC only when the remuneration is higher or at
least equal to the Opportunity Costs. Remuneration is marked as SC P rice
in equation 3.13. Keep in mind that only remuneration of capacity1 has
been considered.
SC P rice ≥ Opportunity Costs
(3.13)
Inserting equation 3.12 into 3.13 results in the formulation of equation 3.14.
SC P rice ≥
!
P
HP F C(t) −
t∈Nwithout
168
2
· HP F Cbase
week SC
+
P
HP F C(t)
t∈Nwith
SC
SC
168
2
1
For explanation of the term remuneration of capacity see section 2.1.1.
(3.14)
12
CHAPTER 3. MODELING APPROACHES
3.1.4
Model Inputs
Based on the assumptions from section 3.1.1 and theoretical basis from
section 3.1.2 and 3.1.3 following inputs are used to feed the model in
order to acquire the output → marginal price forecast for Secondary Control
power. Inputs listed according to the source are following:
1. CKW
• HPFC for Switzerland
• Historical SwissIX hourly spot prices
2. Swissgrid
• Capacity price of SC – the average price of the costliest awarded
20MW bids
3. BFE – Bundesamt für Energie
• Reservoir content data of storage reservoirs in Switzerland
• Electricity production data for Switzerland
4. Thomson Reuters Point Carbon2
• Inflow data for Switzerland
2
Thomson Reuters Point Carbon is a provider of independent news, analysis and consulting services for European and global power, gas and carbon markets.
3.2. MODEL CONFIGURATION 1.0
3.2
13
Model Configuration 1.0
In this section detailed model configuration for the marginal price forecast
for Secondary Control power is presented. The model consists of 4 different
computation steps.
3.2.1
Step 1: Computation of historical hours of production
In this section computation of historical values for Nwithout SC and Nwith SC
takes place. Nwithout SC relates to the number of hours that power plant
was producing while not having delivered any SC. Respectively, Nwith SC
relates to the number of hours that power plant was producing besides having
delivered SC for a week.
Computation is done based on the equation 3.14 with a slight modification – instead of SC P rice new variable M arginal SC P rice is inserted.
Marginal SC Price M arginal SC P rice relates to historical capacity
prices of SC published on Swissgrid homepage. The prices published
are the average prices of the costliest awarded 20 MW bids. Therefore
M arginal SC P rice.
Equation 3.15 serves as a basis for the computation of Step 1.
M arginal SC P rice ≥
!
P
HP F C(t) −
t∈Nwithout
168
2
· HP F Cbase
week SC
+
P
HP F C(t)
t∈Nwith
SC
SC
(3.15)
168
2
|
{z
Opportunity Costs
}
Input data required for the computation according to the equation 3.15
is the following:
• historical values of HPFC
• historical values of M arginal SC P rice
As an output of Step 1 historical values of Nwithout SC and Nwith
acquired respecting the assumptions mentioned in section 3.1.1.
SC
are
Computation Procedure
Opportunity Costs Computation procedure of the Opportunity Costs is
based on the assumptions and theoretical basis explained in section 3.1:
Out of HPFC a price duration curve is formed. Afterwards, cumulative sum
method is applied to the price duration curve. Opportunity Costs are calculated by taking each value of the cumulative sum curve for production
14
CHAPTER 3. MODELING APPROACHES
including one week of SC, corresponding value of the cumulative sum curve
for production without SC and HP F Cbase week SC . HP F Cbase week SC relates to the average value of HPFC for the week when SC is delivered. In
order to get a better picture of the computation procedure see figure 3.1 .
Price duration curve of HPFC without SC
120
[ CHF / MWh ]
60
40
20
0
Feb
Mär
2011
Apr
HPFC with SC
40
80
60
40
20
0
1000
2000
Hours
Mär
2011
Apr
Mai
1
0
1000
2000
Hours
3000
5
2.5
100
x 10 Cumsum HPFC with SC
2
80
60
40
0
1.5
0
3000
1.5
1
0.5
20
Feb
5
x 10 Cumsum HPFC without SC
0.5
Price duration curve of HPFC with SC
120
[ CHF / MWh ]
[ CHF / MWh ]
60
0
Mai
2.5
2
80
20
100
0
100
[ CHF ]
[ CHF / MWh ]
80
[ CHF ]
HPFC without SC
100
0
1000
2000
Hours
3000
0
0
1000
2000
Hours
3000
HPFC base week SC
[ CHF / MWh ]
100
80
60
40
03/Jan
05/Jan
07/Jan
2011
09/Jan
Figure 3.1: HPFC and its applications in the computation procedure of the
Opportunity Costs
M arginalSCP rice of a specific week is subtracted from each corresponding value of OpportunityCosts → Delta is acquired. Delta specifies the
margin, respectively profit, that suppliers of SC get according to the strategic bidding.
Delta = Opportunity Costs − M arginal SC P rice
(3.16)
All Delta values for each specific week of the sample are shown in the
figure 3.2.
Since M arginal SC P rice for a specific week is a constant value there
is just an offset between the value of Delta and Opportunity Costs. Shape
of Delta corresponds to the shape of Opportunity Costs (see figure 3.3).
3.2. MODEL CONFIGURATION 1.0
15
Delta = Opportunity Costs − Marginal SC Price
20
0
[ CHF / MWh ]
−20
−40
−60
−80
−100
0
500
1000
1500
2000
2500
N [ hours ]
3000
3500
4000
4500
5000
Figure 3.2: Delta values of all the weeks in the sample
Shape of Opportunity Costs and Delta
Opportunity Costs
Delta = Opportunity Costs − Marginal SC Price
50
40
30
[ CHF / MWh ]
20
10
0
−10
−20
−30
500
1000
1500
N with SC [ hours ]
2000
2500
Figure 3.3: Shape of Opportunity Costs and Delta
16
CHAPTER 3. MODELING APPROACHES
Explanation of the shape of Opportunity Costs See figure 3.4. Price
duration curve of HPFC is flatter till the point where minimal value of
Opportunity Costs lies than the price duration curve of HPFC after this
point. Reason for that can be found in the marginal difference between the
prices in price duration curve. At the beginning of HPFC price duration
curve prices lie closer to each other which results in a flatter curve. Consequently is the part of cumulative sum curve till the point where minimal
value of Opportunity Costs lies steeper than the other part of the curve →
marginal gains from producing more are higher till the point where minimal
value of Opportunity Costs lies than in the other part of the curve. This
point can be interpreted as an optimal point for taking part in SC market,
since profit gained by suppliers of SC is at this point the highest. Keep
in mind that such a shape of Opportunity Costs was acquired due to the
definition of the time period described in section 3.1.2.
Conclusion drawn for the application in real world is that production
of a storage power plant should be dispatched according to the number of
hours that corresponds to the point in time where value of Opportunity costs
reaches its minimum. This way profit from taking part in SC market would
be maximized by taking advantage of the prices from HPFC. Keep in mind
that this applies only to the case when dispatch of the power plant is optimized according to the definition of the time period from t0 to tS 3 used in
the scope of this thesis.
Price duration curve of HPFC with SC
[ CHF / MWh ]
100
80
60
40
20
500
5
x 10
1000
1500
2000
N with SC [ hours ]
Cumulative sum of price duration curve of HPFC with SC
2500
[ CHF ]
2
1.5
1
0.5
0
500
1000
1500
N with SC [ hours ]
Shape of Opportunity Costs
2000
2500
500
1000
1500
N with SC [ hours ]
2000
2500
[ CHF / MWh ]
50
40
30
20
10
Figure 3.4: Explanation of the shape of Opportunity Costs
3
See definition of the time period in section 3.1.2.
3.2. MODEL CONFIGURATION 1.0
17
N without SC Historical values of Nwithout SC for each time period are
determined by taking Nwithout SC that corresponds to the point in time
where the value of Delta for each specific week, respectively for each specific
time period, reaches its minimum. At this point in time supplier of SC gains
the highest profit from taking part in the SC market → optimal point for
taking part in the SC market (see the figure 3.5).
Acquired values for Nwithout SC are shown in the figure 3.6.
Delta = Opportunity Costs − Marginal SC Price
15
10
5
[ CHF / MWh ]
0
−5
−10
Profit
−15
−20
−25
−30
0
500
1000
1500
N without SC [ hours ]
2000
2500
3000
Figure 3.5: Delta of a specific week
Term Hours F ROM − T O mentioned in figure 3.6 refers to the number
of hours according to the calender in the defined period of time4 .
Trend of acquired values for Nwithout SC displayed in figure 3.6 seems
plausible since it follows the trend of Hours F ROM − T O. Reasons for
such a spiky course of Nwithout SC are:
• Value of Nwithout SC were determined according to the procedure
described in this section. No other boundary conditions such as
Nnext ≤ Nprevious and Nnext −Nprevious ≥ −168 were introduced in the
computation since they would let the first value of Nwithout SC after
the reservoir reverse point influence greatly the other following values
of Nwithout SC .
4
For definition of the time period see section 3.1.2.
18
CHAPTER 3. MODELING APPROACHES
• Estimation of Nwithout SC might not be good enough due to the flatness of the HPFC price duration curve in the time period around
the reservoir bottom reverse point (for further explanation see section
3.2.5).
N without SC in comparison with Hours FROM−TO
Hours FROM−TO
N without SC
5000
4500
4000
3500
Hours
3000
2500
2000
1500
1000
500
0
2011
Figure 3.6: Nwithout
2012
SC
2013
in comparison with Hours F ROM − T O
3.2. MODEL CONFIGURATION 1.0
3.2.2
19
Step 2: Computation of maximal power output
In this section the maximal power output of the modeled storage power plant
is computed based on the equation 3.17 which was derived from equation
3.7. Modeled storage power plant supplies according to the assumptions in
section 3.1.1 all the SC needed for Swiss control zone.
Pmax =
It0 ,tS − (RtS − Rt0 )
Nwithout SC
(3.17)
Input data required for the computation according to the equation 3.17
is following:
• Nwithout
SC
computed in section 3.2.1
• historical reservoir content data of storage reservoirs in Switzerland
• historical production data of storage power plants in Switzerland
• historical SwissIX hourly spot prices
It is important to mention that computation of Pmax is very sensitive to
the input parameter Nwithout SC computed in section 3.2.1. Values of
Nwithout SC influence directly the values of Pmax .
As an output of Step 2 Pmax is acquired. It relates to the maximal
output power of the modeled storage power plant.
Computation Procedure
Historical Production of Storage Power Plants Historical production
data of storage power plants is available in monthly resolution from BFE.
Since daily resolution of the data was needed for the computation of historical inflows to the storage reservoirs, production data from BFE was distributed to corresponding dates according to the historical SwissIX hourly
spot prices (see first graph in figure 3.7). This distribution was done in order to acquire a bit more realistic production profile throughout the month.
Afterwards, production of storage power plants in the defined period5 of
time was calculated (see second graph in figure 3.7).
Winter Period and Summer Period Winter period refers to the time
period between October and April which is actually the period between the
two sequential reservoir reverse points. Respectively, summer period refers
to the time period between April and October.
Storage power plants are so called peak power plants – they produce
only when the prices are high, which is usually the case in peak6 time. Since
5
6
For definition of the time period see section 3.1.2.
Peak time refers to the time of the day between 8 am and 8 pm.
20
CHAPTER 3. MODELING APPROACHES
there is a higher probability that higher electricity prices occur in winter
period, power plant operators accumulate water in the storage reservoirs
during the summer period in order to be able to produce more in winter
period. Shape of the computed production of storage power plants in the
defined time period seems plausible since the production in winter period is
higher than in summer period (see figure 3.7).
Production of storage power plants
140
120
[ GWh ]
100
80
60
40
20
0
2011
2012
2013
Production of Storage Power Plants − BFE Data
Production of Storage Power Plants − distributed according to SwissIX
Production of storage power plants in the defined time period ( from t0 to tS )
12000
10000
[ GWh ]
8000
6000
4000
2000
0
Jan11
Apr11
Jul11
Okt11
Jan12
Apr12
Figure 3.7: Historical production of storage power plants
Historical Reservoir Content of Storage Reservoirs Historical reservoir
content data of storage reservoirs in Switzerland is available from BFE.
The difference between the reservoir content of the last day and the reservoir content of the first day in the defined time period is named as
Delta Reservoir Content.
As already mentioned, storage power plant operators accumulate water in their storage reservoirs during the summer period in order to be
able to produce more in winter period, where electricity prices are usually higher. This statement is well supported also by the computed values of Delta Reservoir Content shown in figure 3.8. In the summer
period values of Delta Reservoir Content are positive → accumulation
of water in the storage reservoirs takes place. Respectively, values of
3.2. MODEL CONFIGURATION 1.0
21
Delta Reservoir Content are negative in the winter period → consumption of water from the storage reservoirs takes place. Such a shape of
Delta Reservoir Content shown in the second graph of figure 3.8 is due to
the definition of the time period used in the scope of this thesis (see section
3.1.2).
Reservoir content ( BFE Data )
7000
6000
[ GWh ]
5000
4000
3000
2000
1000
0
Jan11
Apr11
Jul11
Okt11
Jan12
Apr12
Delta Reservoir Content in the defined time period ( from t0 to tS )
6000
4000
[ GWh ]
2000
0
−2000
−4000
−6000
Jan11
Apr11
Jul11
Okt11
Jan12
Apr12
Figure 3.8: Historical reservoir content of storage reservoirs
Calculated Historical Inflows to the Storage Reservoirs Historical inflows
to the storage reservoirs are calculated according to the equation 3.18 and
3.19 using following data:
• historical production data of storage power plants
• historical reservoir content data of storage reservoirs
Inf lows = P roduction + Delta Reservoir Content
It0 ,tS = P roduction + (RtS − Rt0 )
(3.18)
(3.19)
Calculation procedure from equation 3.18, respectively equation 3.19, is
graphically shown in the figure 3.9.
22
CHAPTER 3. MODELING APPROACHES
[ GWh ]
Production of storage power plants in the defined time period ( from t0 to tS )
10000
5000
0
Jan11
Apr11
Jul11
Okt11
Jan12
Apr12
Delta Reservoir Content in the defined time period ( from t0 to tS )
[ GWh ]
5000
0
−5000
Jan11
Apr11
Jul11
Okt11
Jan12
Apr12
[ GWh ]
Calculated Inflows in the defined time period ( from t0 to tS )
10000
5000
0
Jan11
Apr11
Jul11
Okt11
Jan12
Apr12
Jan12
Apr12
[ GWh ]
Calculated Inflows ( monthly resolution )
3000
2000
1000
0
Jan11
Apr11
Jul11
Okt11
Figure 3.9: Calculated historical inflows to the storage reservoirs
Maximal Power Output of the Modeled Storage Power Plant Having all
the input parameters needed, computation of Pmax is done according to to
the equation 3.17.
Brief explanation of the input parameters of equation 3.17:
• as It0 ,tS calculated historical inflows to the storage reservoirs in the
defined time period are inserted
• (RtS − Rt0 ) stands for difference in the reservoir content of storage
reservoirs in the defined time period
• Nwithout SC relates to the number of hours that power plant was producing while not having delivered any SC
Computation procedure described by equation 3.17 is graphically shown
in the figure 3.10. In the first graph of figure 3.10 the numerator of the
equation 3.17 is shown. Respectively, the denominator of equation 3.17 is
shown in the second graph of the figure 3.10. In the third graph of the figure
3.10 Pmax (an output of the equation 3.17) is displayed. It represents the
maximal power output of the modeled storage power plant that according to
the assumptions in section 3.1.1 supplies all the SC for Swiss control zone.
3.2. MODEL CONFIGURATION 1.0
23
The spike in the value of Pmax at the right hand side of the third graph
in figure 3.10 is due to the very low value of denominator Nwithout SC in the
equation 3.17. It is important to mention that computation of Pmax is very
sensitive to the input parameter Nwithout SC computed in section 3.2.1.
In the last graph of the figure 3.10 also the average value of Pmax is
shown. Keep in mind that this average value is going to be used in all
further calculations whenever variable Pmax is going to be mentioned. The
average value of Pmax was chosen in order to compensate the sensitivity of
the Pmax computation. As already mentioned computation of Pmax is very
sensitive to the input parameter Nwithout SC computed in section 3.2.1.
Average value of Pmax seems reasonable according to the estimation of
my supervisor at CKW, Mr.Thomas Reithofer. By going through the list
of all the power plants, the ones that are thought to participate in the SC
market were picked up. Afterwards, the sum of their installed power was
calculated. This sum was compared to the average value of Pmax . The difference was not big. Anyway, one have to keep in mind that this estimation
is purely subjective.
[ GWh ]
Production of storage power plants in the defined time period ( from t0 to tS )
10000
5000
0
Apr11
Jul11
Okt11
Jan12
Apr12
Okt11
Jan12
Apr12
Okt11
Jan12
Apr12
Jan12
Apr12
N without SC
Hours
4000
2000
0
Apr11
Jul11
[ GW ]
Pmax
30
20
10
0
Apr11
Jul11
Pmax ZOOM IN
[ GW ]
10
5
0
Apr11
Jul11
Okt11
Figure 3.10: Maximal power output of the modeled storage power plant
24
CHAPTER 3. MODELING APPROACHES
3.2.3
Step 3: Computation of forecast hours of production
In this section computation of forecast 7 values for Nwithout SC and Nwith SC
takes place. Nwithout SC relates to the number of hours that the power plant
is going to be able to produce while not having taken part in SC market.
Respectively, Nwith SC relates to the number of hours that power plant is
going to be able to produce besides having delivered SC for a week.
Computation is done based on equation 3.20 and 3.21 which was derived
from equation 3.7. For additional explanation see section 3.1.2.
Nwithout
Nwithout
SC
SC
It0 ,tS − (RtS − Rt0 )
Pmax
(3.20)
It0 ,tS − (btS − bt0 ) · R
Pmax
(3.21)
=
=
btS relates to the percentage value of the respective absolute reservoir
content value RtS . It tells us what percentage of the total storage capacity
is available in the reservoir. Same principle applies to bt0 .
R stands for absolute value of the total storage capacity of the reservoirs
in Switzerland. Keep in mind that this total storage capacity varies over
time, since some revisions on the storage reservoirs may take place, height
of the dams may be increased, new storage reservoirs may be built etc.
Input data required for the computation according to the equation 3.21
is following:
• average value of Pmax acquired in section 3.2.2
• normal value of the inflows to the storage reservoirs
• normal percentage value of the reservoir content
• total storage capacity of the reservoirs in Switzerland → R
Normal Term normal refers to the average value typical for a certain
time period of the year that was calculated based on the historical data of
the past years. Example: Typical value for the month of January therefore
represents an average value acquired by considering historical values for the
month of January over the past years.
As an output of Step 3 future values of Nwithout
acquired.
7
Historical values for Nwithout
SC
and Nwith
SC
SC
and Nwith
SC
were computed in section 3.2.1.
are
3.2. MODEL CONFIGURATION 1.0
25
Computation Procedure
Normal Value of the Inflows Normal value of the inflows to the system is
acquired from Thomson Reuters Point Carbon8 . These inflows represent all
the water that comes to the whole system – Switzerland – through precipitation etc.
As an input needed for the computation of equation 3.21 normal value of
the inflows (It0 ,tS ) that land in the storage reservoirs are needed. Therefore
one have to define what percentage of the normal value of the inflows to
the whole system, represents the normal value of the inflows to the storage
reservoirs. This was done by comparing normal value of the inflows to the
whole system with the calculated historical inflows to the storage reservoirs
from the section 3.2.2 (see equation 3.18 and 3.19). Ratio between the
two different types of the inflows mentioned above is shown in figure 3.11.
Interesting point is that the ratio in the summer period is higher than in
the winter period9 . This is due to the snow and glacier melting during
the summer period that contributes a great share of inflows to the storage
reservoirs.
Inflows
6000
[ GWh ]
Point Carbon NORMAL
Calculated
4000
2000
0
Jan11
Apr11
4
Jul11
Okt11
Jan12
Inflows in the defined time period ( from t0 to tS )
x 10
2
[ GWh ]
Apr12
Point Carbon NORMAL
Calculated
1.5
1
0.5
0
Jan11
Apr11
Jul11
Okt11
Jan12
Apr12
Ratio = Calculated Inflows ( t0 − tS ) / Inflows Point Carbon NORMAL ( t0 − tS )
80
[%]
60
40
20
0
Jan11
Apr11
Jul11
Okt11
Jan12
Apr12
Figure 3.11: Inflow ratio
8
Thomson Reuters Point Carbon is a provider of independent news, analysis and consulting services for European and global power, gas and carbon markets.
9
For explanation of the term summer and winter period see section 3.2.2.
26
CHAPTER 3. MODELING APPROACHES
The average value of the ratio for a specific period – summer or winter
– is used to scale down normal value of the inflows to the whole system
in order to acquire normal value of the inflows to the storage reservoirs →
It0 ,tS . It0 ,tS is an input parameter needed for computation of the equation
3.21. It is shown in the first graph of the figure 3.13.
Normal Percentage Value of the Reservoir Content Normal percentage
value of the reservoir content is displayed in figure 3.12. It was calculated
based on the historical data from 1997 to 2012 acquired from BFE. As an
input parameter to the equation 3.21 (btS − bt0 ) is needed. It corresponds to
difference between the percentage value of the reservoir content of the first
and last day in the defined time period. It is shown in the second graph of
the figure 3.13.
NORMAL percentage value of the reservoir content ( BFE 1997 − 2012 )
100
90
80
70
[%]
60
50
40
30
20
10
0
5
10
15
20
25
30
Weeks ( January to December )
35
40
45
50
Figure 3.12: Normal percentage value of the reservoir content
3.2. MODEL CONFIGURATION 1.0
27
Forecast Values of Nwithout SC Having all the input parameters needed,
computation of forecast values of Nwithout SC is done according to to the
equation 3.21. Two of the input parameters and the acquired output –
forecast values of Nwithout SC – are shown in the figure 3.13.
4
x 10
Inflows in the defined time period ( from t0 to ts ) − I ( t0 , tS )
PointCarbon NORMAL
I(t0,tS)
[ GWh ]
2
1.5
1
0.5
0
Mai
Jul
Sep
Nov
Jan
Difference in the percentage value of the reservoir content in the defined time period − ( btS − bt0 )
[%]
50
2012
0
−50
Mai
Jul
Sep
Nov
Jan
Nov
Jan
Future values of N without SC
Hours
2000
2012
1500
1000
500
0
Mai
Jul
Sep
Figure 3.13: Forecast values of Nwithout
SC
Forecast values of Nwithout SC were calculated for the time period from
the end of April 2012 to the beginning of January 2013. Reservoir top reverse
point was set to the beginning of October which can be seen in the figure
3.13. Reservoir bottom reverse point was set to the end of April.
28
CHAPTER 3. MODELING APPROACHES
In order to get a feeling about how good the forecast for Nwithout SC
is, see figure 3.14. Forecast values of Nwithout SC are smaller than
Hours F ROM −T O10 and follow also the trend of so called in-sample hours
Nwithout SC acquired in the section 3.2.1 .Therefore the following conclusion
can be drawn – forecast values of Nwithout SC are plausible. Anyway, keep
in mind that also in-sample hours Nwithout SC acquired in the section 3.2.1
might not be the actual (real) ones since there is a potential problem in their
estimation (see section 3.2.5). It is important to mention that forecast of
Opportunity Costs calculated in the computation step 4 (see section 3.2.4)
is sensitive to the forecast values of Nwithout SC .
Comparison
Hours FROM − TO
IN SAMPLE NwithoutSC
Forecast values of NwithoutSC
4500
4000
3500
Hours
3000
2500
2000
1500
1000
500
0
Mai
Jul
Sep
Nov
Jan
2012
Figure 3.14: Comparison of forecast values of Nwithout
SC
with other values
In the figure 3.14 one can notice that reservoir top reverse point was set
to the beginning of October.
10
Term Hours F ROM − T O refers to the number of hours according to the calender in
the defined period of time. Defined time period is a time period starting each Monday in
a year and ending at the next following reservoir reverse point. For detailed explanation
see section 3.1.2 .
3.2. MODEL CONFIGURATION 1.0
3.2.4
29
Step 4: Computation of Opportunity Costs forecast
In this section computation of forecast values of the Opportunity Costs
takes place.
Computation is done based on the equation 3.12 from section 3.1.3.
Input data required for the computation is following:
• forecast values of Nwithout
SC
computed in section 3.2.3
• HPFC
Forecast values of Nwith SC are calculated by inserting forecast values of
Nwithout SC to the equation 3.8 from section 3.1.2.
As an output of Step 4 forecast values of Opportunity Costs are acquired.
Computation Procedure
Forecast Values of Opportunity Costs Out of HPFC a price duration
curve is formed. Afterwards, cumulative sum method is applied to the price
duration curve. Forecast value of Opportunity Costs for each time period
from t0 to tS is computed according to the equation 3.12 by inserting following input parameters:
• value of the cumulative sum curve for production without SC that
corresponds to the forecast value of Nwithout SC
• value of the cumulative sum curve for production including one week
of SC that corresponds to the forecast value of Nwith SC
• the average value of HPFC for the week when SC is delivered →
HP F Cbase week SC
In order to get a better picture of the computation procedure see figure 3.1
from section 3.2.1 .
Marginal Price Forecast for SC According to the strategic bidding present
in the SC market, bidders bid above their opportunity costs. Marginal SC
price is defined by the highest accepted bid.
Comparison between the forecast value of Opportunity Costs and the
marginal SC price from Swissgrid homepage is shown in the figure 3.15,
where reservoir reverse points are marked with the black vertical line.
SC capacity price published on the Swissgrid homepage relates to the
average price of the costliest awarded 20MW bids and is therefore called
marginal price.
Forecast values of Opportunity Costs follow the trend of marginal SC
price pretty well with an exception in the time period around the reservoir
bottom reverse point. Reservoir bottom reverse point is defined to be at
30
CHAPTER 3. MODELING APPROACHES
the end of April. In the region around the reservoir top reverse point – the
beginning of October – forecast seems plausible.
Some of the forecast values of Opportunity Costs are missing right before
the reservoir top reverse point in the figure 3.15. This is due to the fact that
forecast value of Nwith SC is at this point in time smaller than 168 hours
– no more SC can be offer due to the insufficient amount of water in the
storage reservoir. Consequently Opportunity Costs are not computed.
Comparison
Opportunity Costs − forecast
Marginal SC Price − Swissgrid
100
[ CHF / MWh ]
80
60
40
20
0
Mai
Jul
Sep
Nov
Jan
2012
Figure 3.15: Comparison of forecast values of Opportunity Costs with
marginal SC prices from Swissgrid homepage
Difference between the line of marginal SC price and the line of forecast
values of Opportunity Costs in the figure 3.15 and in figure 3.16 represents
margin, respectively profit, that suppliers of SC get due to their strategic
bidding. It is not reasonable that margin around the reservoir bottom reverse
point is so much higher than in other months. It would be reasonable that
margin would have more or less constant value over time with a slightly
decreasing trend since the market is getting mature and more liquid with
the course of time. In order to support this statement figure 3.16 is shown.
3.2. MODEL CONFIGURATION 1.0
31
Comparison
[ CHF / MWh ]
100
Opportunity Costs − forecast IN SAMPLE
Marginal SC Price − Swissgrid
80
60
40
20
0
2011
2012
Margin = Marginal SRL Price − Opportunity Costs
[ CHF / MWh ]
100
80
60
40
20
0
2011
2012
Figure 3.16: Decreasing trend of the margin value over the course of time
In the first graph of the figure 3.16 so called in-sample forecast values of Opportunity Costs are displayed. In-sample forecast values of
Opportunity Costs are computed by inserting values of Nwithout SC , acquired in section 3.2.1, to equation 3.12.
In the second graph of the figure 3.16 difference between the marginal
SC price and the forecast values of Opportunity Costs is displayed, where
reservoir reverse points are marked with the black vertical line. This difference may be interpreted as margin that represents a profit from suppliers’ point of view. Let’s focus just on the region where forecast values of
Opportunity Costs follow the trend of marginal SC price well. Only by
comparing margins from year 2011 and 2012, above mentioned decreasing
trend of the margin value can be confirmed.
32
CHAPTER 3. MODELING APPROACHES
3.2.5
Potential Problems
Potential problems that may hinder a reasonable forecast of
Opportunity Costs in the time period around the reservoir bottom
reverse point are:
1. Perhaps the point in time chosen for determination of historical values
of Nwithout SC was not the right one. Historical values of Nwithout SC
for each time period were determined by taking Nwithout SC that corresponded to the point in time where the value of Delta for each specific
week reached its minimal value (see section 3.2.1).
2. Estimation of Nwithout SC in section 3.2.1 might not be good enough
due to the flatness of the HPFC price duration curve in the time period
around the reservoir bottom reverse point. The reason for such a
flatness of the HPFC price duration curve in the time period around
the reservoir bottom reverse point lies in the shape of the HPFC in
this time period → prices from HPFC lie closer to each other than in
the other time periods.
Flatness of the HPFC in the time period around the reservoir bottom
reverse point results in a flatness of the Opportunity Costs in the
same time period (see figure 3.17 and the Explanation of the shape
of Opportunity Costs described in section 3.2.1). Therefore due to
the nature of the estimation procedure of Nwithout SC problems may
occur. Actual historical value of Nwithout SC lies perhaps somewhere
inside the range of the flatness of the HPFC price duration curve and
might be higher or lower than the one computed in section 3.2.1.
3. Assumption that the storage power plant produces only with half of
total power ( Pmax
2 ) if delivering SC might be too unrealistic since e.g.
the technical minimum of production is neglected (see section 3.1.1).
In reality also the amount in the bid placed for SC normally represents
a smaller value than Pmax
2 . One of the reasons for that is to keep a bit
of production flexibility of the power plant.
4. Used water statistics – inflow and reservoir content data – might not
represent appropriate input data needed to feed the model.
Each of potential problems listed is elaborated further in the scope of
section 3. See following sections:
• potential problem listed under the bullet point 1. → see section 3.3
• potential problem listed under the bullet point 2. → see section 3.4
• potential problem listed under the bullet point 3. → see section 3.5
• potential problem listed under the bullet point 4. → see section 3.6
3.2. MODEL CONFIGURATION 1.0
33
Price duration curve of HPFC with SC
[ CHF / MWh ]
100
80
60
40
500
5
1000
1500
N with SC [ hours ]
2000
2500
Cumulative sum of price duration curve of HPFC with SC
x 10
2
[ CHF ]
1.5
1
0.5
0
500
1000
1500
N with SC [ hours ]
2000
2500
2000
2500
Shape of Opportunity Costs and Delta
[ CHF / MWh ]
20
0
−20
−40
500
1000
1500
N with SC [ hours ]
Opportunity Costs
Delta = Opportunity Costs − Marginal SC Price
Figure 3.17: Explanation of the shape of Opportunity Costs in the time
period around the reservoir bottom reverse point
34
CHAPTER 3. MODELING APPROACHES
3.3
Model Configuration 1.1
In order to eliminate potential problem regarding the point in time chosen for
determination of historical values of Nwithout SC (see the first bullet point in
section 3.2.5), model configuration 1.0 explained in section 3.2 is modified.
The modification takes place in the computation step 1 explained in
section 3.2.1, where historical values of Nwithout SC for each time period
were initially determined by taking Nwithout SC that corresponded to the
point in time where the value of Delta for each specific week reached its
minimum (see also first graph in figure 3.18).
According to the modification, Nwithout SC are determined by the point
in time where the value of Delta is closest to zero value (see second graph in
figure 3.18). Such a modification was done in order to acquire the forecast
values of Opportunity Cost, computed according to the section 3.2.4, that
would fit the marginal SC price → no margin in contrast to the case of the
strategic bidding is added to the Opportunity Cost (pay attention to the
equality sign in equation 3.22).
Delta = Opportunity Costs − Marginal SC Price (Model Configuration 1.0)
20
[ CHF / MWh ]
10
0
−10
−20
−30
0
500
1000
1500
N without SC [ hours ]
2000
2500
3000
2500
3000
Delta = Opportunity Costs − Marginal SC Price (Model Configuration 1.1)
20
[ CHF / MWh ]
10
0
−10
−20
−30
0
500
1000
1500
N without SC [ hours ]
2000
Figure 3.18: Delta of a specific week (Model Configuration 1.0 vs. Model
Configuration 1.1)
3.3. MODEL CONFIGURATION 1.1
Keep
equation
equation
equation
35
in mind that the modification influences also the formulation of
3.15 from section 3.2.1. The new formulation is described by
3.22. When comparing the equation 3.15 from section 3.2.1 and
3.22 pay attention to the equality/inequality sign.
M arginal SC P rice =
!
P
HP F C(t) −
t∈Nwithout
168
2
· HP F Cbase
week SC
+
P
HP F C(t)
t∈Nwith
SC
SC
(3.22)
168
2
|
{z
Opportunity Costs
}
All the other computation steps of the model configuration 1.0 explained
in section 3.2 remain unchanged.
As a consequence of the modification the forecast values of
Opportunity Cost computed according to the section 3.2.4 should fit the
marginal SC price (pay attention to the equality sign in equation 3.22). This
is also the case that can be seen in the figure 3.19 where in-sample forecast values of Opportunity Costs are displayed. Reservoir reverse points are
marked with the black vertical line in figure 3.19.
Comparison
Marginal SC Price − Swissgrid
Opportunity Cost − forecast
100
[ CHF / MWh ]
80
60
40
20
0
2011
2012
Figure 3.19: Comparison of in-sample forecast values of Opportunity Costs
with marginal SC prices from Swissgrid.
36
CHAPTER 3. MODELING APPROACHES
In the figure 3.2011 forecast values of Opportunity Costs acquired by
the model configuration 1.1 described in this section are displayed.
Comparison
Marginal SC Price − Swissgrid
Opportunity Cost − forecast
100
[ CHF / MWh ]
80
60
40
20
0
Mai
Jul
Sep
Nov
Jan
2012
Figure 3.20: Forecast values of Opportunity Costs.
As it can be seen from figure 3.19 and 3.20 the potential problem mentioned under the first bullet point in section 3.2.5 was not eliminated. Forecast of Opportunity Costs in the time period around the reservoir bottom reverse point remains an issue. Since the forecast values of Opportunity Costs
were more reasonable – they followed the trend of marginal SC prices – in
model configuration 1.0 from section 3.2, we are going to stick to this procedure when trying to eliminate other potential problems mentioned in section
3.2.5.
Comparison of numeric results acquired in different model configurations
described in the scope of section 3 is done in section 4 .
11
Reservoir reverse points are marked with the black vertical line in figure 3.20. Some
of the forecast values of Opportunity Costs are missing right before the reservoir top
reverse point in the figure 3.20. This is due to the fact that forecast value of Nwith SC
is at this point in time smaller than 168 hours – no more SC can be offer due to the
insufficient amount of water in the storage reservoir. Consequently Opportunity Costs
are not computed.
3.4. MODEL CONFIGURATION 1.2
3.4
37
Model Configuration 1.2
In order to eliminate potential problem regarding the estimation of
Nwithout SC in section 3.2.1 due to the flatness of the HPFC price duration curve in the time period around the reservoir bottom reverse point (see
the second bullet point in section 3.2.5), model configuration 1.0 explained
in section 3.2 is modified.
The modification takes place in the computation step 1 explained in
section 3.2.1. Input parameter – historical HPFC – used in the computation
step 1 (see section 3.2.1) is modified using Mean Reverting Jump Diffusion
(MRJD) process (see section 2.2). Modification is done in order to reduce
the problematic flatness of the HPFC price duration curve.
Mean Reverting Jump Diffusion process Let’s first justify the use of
MRJD. In our case MRJD was used to add a stochastic term to the deterministic nature of HPFC (see figure 2.1 from section 2.2). This way the
steepness of the HPFC price duration curve is increased. Respectively, the
flatness is reduced. And exactly the flatness of HPFC price duration curve
is mentioned as a potential problem under the second bullet point is section
3.2.5. The reason for such a flatness of the HPFC price duration curve in the
time period around the reservoir bottom reverse point lies in the shape of
the HPFC in this time period → prices from HPFC lie closer to each other
than in the other time periods.
In order to get a better picture let’s have a look at figure 3.21, 3.22 and
3.23.
In figure 3.21 comparison of HPFC price duration curve from the model
configuration 1.0 described in section 3.2 is shown for two different time
periods of the same length. As we can see in the figure 3.21 steepness of
the HPFC price duration curve is a differentiating factor.
One of the two time periods is time period close to the reservoir
bottom reverse point. This is the time period where the forecast of
Opportunity Costs is problematic. This time period is marked as “PROBLEMATIC ” in figure 3.21 and 3.23.
The other period is time period where the forecast of Opportunity Costs
is reasonable. This time period is marked as “NON-PROBLEMATIC ” in
figure 3.21 and 3.22.
In figure 3.22 HPFC price duration curve for the same “NONPROBLEMATIC ” time period but for different model configurations is
shown. Same stands also for figure 3.23 where HPFC price duration curve
for the same “PROBLEMATIC ” time period but for different model configurations is shown.
38
CHAPTER 3. MODELING APPROACHES
In the figure 3.22 and 3.23 model configuration 1.0 described in section 3.2 is marked as “HPFC deterministic” and model configuration 1.2
described in this section is marked as “HPFC deterministic + stochastic
term”.
By comparing figures 3.22 and 3.23 one can see that the steepness has
been improved in a greater share in so called “PROBLEMATIC ” time period
than in ‘NON-PROBLEMATIC ” time period.
HPFC price duration curve
110
NON−PROBLEMATIC
PROBLEMATIC
100
90
80
[ CHF / MWh ]
70
60
50
40
30
20
10
0
0
500
1000
1500
2000
2500
3000
3500
Hours
Figure 3.21: Comparison of HPFC price duration curves of two different
time periods from the Model Configuration 1.0 described in section 3.2.
3.4. MODEL CONFIGURATION 1.2
39
HPFC price duration curve NON−PROBLEMATIC
HPFC deterministic
HPFC deterministic + stochastic term
140
120
[ CHF / MWh ]
100
80
60
40
20
0
0
500
1000
1500
2000
2500
3000
3500
Hours
Figure 3.22: HPFC price duration curve for “NON-PROBLEMATIC” time
period
HPFC price duration curve PROBLEMATIC
HPFC deterministic
HPFC deterministic + stochastic term
140
120
[ CHF / MWh ]
100
80
60
40
20
0
0
500
1000
1500
2000
2500
3000
3500
Hours
Figure 3.23: HPFC price duration curve for “PROBLEMATIC” time period
40
CHAPTER 3. MODELING APPROACHES
Forecast
values
of
Opportunity
Costs Forecast values of
Opportunity Costs computed according to the model configuration
1.2 described in this section are displayed in figure 3.24 12 , where reservoir
reverse points are marked with the black vertical line. Forecast values of
Opportunity Costs follow the trend of marginal SC price well. Anyway,
despite the increased steepness of HPFC price duration curve a reasonable
forecast of Opportunity Costs in the time period around the reservoir
bottom reverse point is not acquired.
Comparison
Opportunity Costs − forecast
Marginal SC Price − Swissgrid
100
[ CHF / MWh ]
80
60
40
20
0
Mai
Jul
Sep
Nov
Jan
2012
Figure 3.24: Forecast value of Opportunity Costs computed according to
the Model Configuration 1.2 described in section 3.4.
Comparison of numeric results acquired in different model configurations
described in the scope of section 3 is done in section 4 .
12
Some of the forecast values of Opportunity Costs are missing right before the reservoir
top reverse point in the figure 3.24. This is due to the fact that forecast value of Nwith SC
is at this point in time smaller than 168 hours – no more SC can be offer due to the
insufficient amount of water in the storage reservoir. Consequently Opportunity Costs
are not computed.
3.5. MODEL CONFIGURATION 1.3
3.5
41
Model Configuration 1.3
In order to eliminate potential problem regarding the unrealistic assumption that the storage power plant produces only with half of total power
( Pmax
2 ) if delivering SC (see the third bullet point in section 3.2.5), model
configuration 1.0 explained in section 3.2 is modified.
The modification affects the amount of power placed in a bid for SC. This
amount was initially defined as the half of the total output power ( Pmax
2 )
of the power plant. This parameter is defined already in the assumptions
described in section 3.1.1 and plays a big role in the computation of the
Opportunity Costs that takes place in the computation step 1 and 4 (see
section 3.2.1 and 3.2.4).
Assumption that storage power plant produces only with the half of the
total output power ( Pmax
2 ) when delivering SC might be too unrealistic since
e.g. the technical minimum of production is neglected (see section 3.1.1).
In reality also the amount in the bid placed for SC normally represents a
smaller value than Pmax
2 . One of the reasons for that is to keep a bit of
production flexibility of the power plant.
In order to make sure if the amount of power placed in a bid for SC is
really the problematic parameter that may hinder a reasonable forecast of
Opportunity Costs in the time period around the reservoir bottom reverse
point, model was run several times varying the denominator n in order to
influence the input parameter → Pmax
n . It turned out that model is pretty
robust considering this input parameter which led to conclusion that the
amount of power placed in a bid for SC ( Pmax
n ) does not belong to the group
of potential problems that hinder a reasonable forecast of Opportunity Costs
in the time period around the reservoir bottom reverse point.
3.6
Water Statistics
As one of the potential problems listed in section 3.2.5 also water statistics was mentioned. Data of water statistics is used to feed the model for
marginal price forecast for SC. There are few issues regarding this input
data that need to be elaborated.
In the section 3.6.1 difference between the data of water statistics from
two different data sources – Thomson Reuters Point Carbon and Bundesamt
für Energie (BFE) – is presented.
Issue regarding the reservoir content data from Bundesamt für Energie
(BFE) is described in section 3.6.2.
Issue regarding the inflows that land in the storage reservoirs is described
in section 3.6.3.
42
CHAPTER 3. MODELING APPROACHES
3.6.1
Data from two different sources
Data of water statistics used to feed the model was used from two different
data sources – Thomson Reuters Point Carbon and Bundesamt für Energie
(BFE).
Data taken from Thomson Reuters Point Carbon:
• Normal 13 value of the inflows to the system. These inflows represent
all the water that comes to the whole system – Switzerland – through
precipitation etc.
Data taken from BFE:
• reservoir content data of all the storage reservoirs in Switzerland
• electricity production data of storage power plants in Switzerland
which was needed for further computation (see section 3.2.2)
According to the energy balance described in equation 3.18 and 3.19
from section 3.2.2 normal value of the inflows that land in the system
were calculated using only the data from BFE – reservoir content data and
electricity production data of all hydro power plants in Switzerland. The
calculation was done based on historical data from 1991 to 2012. Calculated
normal value of the inflows to the system was compared with the normal
value of the inflows from Thomson Reuters Point Carbon in order to see if
data from two different data sources is consistent – unfortunately this was
not the case (see figure 3.25).
Due to the inconsistency of the data from different data sources decision was made to use only data from BFE to feed the model. It turned
out that this modification does not solve the issue with the forecast of
Opportunity Costs in the time period around the reservoir bottom reverse
point.
13
Term normal refers to the average value typical for a certain time period of the year
that was calculated based on the historical data of the past years.
3.6. WATER STATISTICS
43
Inflows
Thomson Reuters Point Carbon
BFE
5000
GWh per month
4000
3000
2000
1000
0
50
100
150
200
Days ( Jan − Dec )
250
300
350
Figure 3.25: Comparison of the normal value of the inflow data from two
different data sources.
3.6.2
Reservoir Content Data
Reservoir content data from BFE that is fed to the model may not be representative for the reservoir content of storage reservoirs of actual storage
power plants that take part on the SC market.
Normal 14 percentage value of the reservoir content calculated based on
the historical data from 1997 to 2012 is shown in figure 3.12. According to
the figure 3.12 storage reservoirs never seem to be completely full or empty,
since the percentage value of the reservoir content reaches its maximum at
88% and its minimum at 15%. This property might not represent realistic
level of the reservoir content of storage reservoirs of actual storage power
plants that take part on the SC market.
To conclude, mentioned issue regarding the reservoir content data
might be the potential problem that hinders a reasonable forecast of
Opportunity Costs in the time period around the reservoir bottom reverse
point.
14
Term normal refers to the average value typical for a certain time period of the year
that was calculated based on the historical data of the past years.
44
CHAPTER 3. MODELING APPROACHES
NORMAL percentage value of the reservoir content ( BFE 1997 − 2012 )
100
90
80
70
[%]
60
50
40
30
20
10
0
5
10
15
20
25
30
Weeks ( January to December )
35
40
45
50
Figure 3.26: N ormal percentage value of the reservoir content (BFE).
3.6.3
Inflow Data
Historical inflows to the storage reservoirs of storage power plants are calculated according to the equation 3.18 and 3.19 from section 3.2.2 using
following data:
• historical production data of storage power plants from BFE
• historical reservoir content data of storage reservoirs from BFE
Let’s consider the following two facts:
1. Historical production data of storage power plants from BFE represents the sum of production from storage stages and must-run stages
of all the storage power plants in Switzerland.
2. In the assumptions described in section 3.1.1 it is stated that the
modeled storage power plant supposed to deliver SC for Swiss control
zone consists of only one storage stage. No other stages such as mustrun stages exist.
3.6. WATER STATISTICS
45
According to the facts mentioned, conclusion can be drawn, that according to the equation 3.18 and 3.19 from section 3.2.2 calculated historical
inflows to the storage reservoirs of storage power plants are not plausible.
The calculated historical inflows are further on used in the computation step
3 (see section 3.2.3) which makes accuracy of the output of this computation
step questionable. This output has a direct impact on the forecast values
computed in step 4 (see section 3.2.4).
To conclude, mentioned issue regarding the inflow data might be the
potential problem that hinders a reasonable forecast of Opportunity Costs
in the time period around the reservoir bottom reverse point.
46
CHAPTER 3. MODELING APPROACHES
Chapter 4
Numeric Results
This section is dedicated to comparison of numeric results acquired in different model configurations described in the scope of section 3. Focus is
placed on the comparison of the main output of the model – forecast values
of Opportunity Costs.
Forecast values of Opportunity Costs from the following different model
configurations are shown in figure 4.1:
• Model configuration 1.0 described in section 3.2
• Model configuration 1.1 described in section 3.3
• Model configuration 1.2 described in section 3.4
Reservoir reverse points are marked with the black vertical line in figure
4.1. Some of the forecast values of Opportunity Costs are missing right
before the reservoir top reverse point in the figure 4.1. This is due to the
fact that forecast value of Nwith SC is at this point in time smaller than 168
hours – no more SC can be offer due to the insufficient amount of water in
the storage reservoir. Consequently Opportunity Costs are not computed.
Observations and Conclusions One of the conclusions drawn out of the
comparison done in figure 4.1 is that forecast values of Opportunity Costs
acquired in model configuration 1.1 (see section 3.3) are the worst and
completely useless. This tells us that the point in time initially chosen for
determination of historical values of Nwithout SC in the model configuration
1.0 (described in section 3.2) was certainly more appropriate than the point
in time from the model configuration 1.1 described in section 3.3. The more
appropriate point in time refers to the point in time where the value of
Opportunity Costs for each specific week reaches its minimal value (see
section 3.2.1). This is also the point in time where suppliers of SC gain
highest profit.
47
48
CHAPTER 4. NUMERIC RESULTS
Forecast values of Opportunity Costs from model configuration 1.0 (see
section 3.2) and model configuration 1.2 (see section 3.4) follow the trend
of marginal SC price well with an exception in the time period around the
reservoir bottom reverse point.
Forecast values of Opportunity Costs from model configuration 1.2 (see
section 3.4) are a bit higher than the ones from model configuration 1.0
(see section 3.2). Reason for this lies in the modification applied in the
computation step 1 (see section 3.2.1) of the model configuration 1.2 (see
section 3.4) – stochastic term is added to the deterministic nature of the
HPFC.
No other big difference exists between the forecast values of
Opportunity Costs from model configuration 1.0 (see section 3.2) and model
configuration 1.2 (see section 3.4).
Comparison
Opportunity Cost − forecast − Model configuration 1.0
Opportunity Cost − forecast − Model configuration 1.1
Opportunity Cost − forecast − Model configuration 1.2
Marginal SC Price − Swissgrid
100
[ CHF / MWh ]
80
60
40
20
0
Mai
Jul
Sep
Nov
Jan
2012
Figure 4.1: Forecast values of Opportunity Costs from different model configurations.
Chapter 5
Conclusion and Outlook
Conclusion A model for marginal price forecast for Secondary Control
power (SC) was set up. It turned out that model does not deliver reasonable
forecast for the time period around the reservoir bottom reverse point. In
any other time period model delivers a good forecast of Opportunity Costs
which could be used for marginal price forecast for SC by adding the margin
according to the strategic bidding on top of the Opportunity Costs.
M argin that suppliers of SC get for their service is changing with the
course of time (see figure 3.16). Reason for that lies in the fact that market
is getting mature and the number of market participants is increasing. Due
to the increased supply, marginal SC prices are dropping and margin is
getting smaller. Such a market behavior would need to be modeled in order
to define the value of margin for a certain time period. This was out of the
scope of this thesis.
Additionally, many issues regarding the water statistics were brought up
shedding a light in direction of possible model improvements. For detailed
description of these issues see section 3.6 and following paragraph where
outlook is described.
Outlook Issues regarding the water statistics that were brought up in section 3.6 shed a light in the following two directions of possible model improvement:
1. Due to the specifics of the available water statistics, quality of the
model output might be improved by incorporating a must-run stage
to the modeled storage power plant.
2. Find out a method that would filter the amount of inflows to the
storage reservoirs out of the available data for total inflows to the
whole system – Switzerland.
49
50
CHAPTER 5. CONCLUSION AND OUTLOOK
Another idea would be to build a completely new model that would
reflect the course of Pmax between the two sequential reservoir reverse points
shown in figure 5.1. Pmax represents a total installed power of all the power
plants that take part in the SC market. There is no doubt that number
of market participants – power plants – in the SC market varies over time.
Let’s focus just on the following three periods of time:
A time period right after the reservoir reverse point
B time period right before the reservoir reverse point
C time period somewhere in between the two sequential reservoir reverse
points
Pmax
8
7
6
C
5
B
Power [ GW ]
A
4
3
2
1
0
5
10
15
Weeks from one reservoir reverse point to another
20
25
Figure 5.1: Course of Pmax between the two sequential reservoir reverse
points.
51
Explanation of the proposed course of Pmax between the two sequential
reservoir reverse points displayed in figure 5.1 is following:
A Let’s assume that time period marked with a letter A in figure 5.1 is
time period right after the reservoir bottom reverse point. Production
from storage power plants is low due to the scarcity of the water in
storage reservoirs. Not many storage power plants are able to take part
in the SC market. Some of them could increase production in compensation for a good remuneration – positive SC could be delivered.
On the other side not many of them would be able to reduce production – negative SC could not be delivered – because they are already
producing at their technical minimum or don’t produce at all. Since
SC is a product with symmetrical control power bands, not many storage power plants are able to deliver it right after the reservoir bottom
reverse point. Consequently is the value of Pmax low.
B Let’s assume that time period marked with a letter B in figure 5.1
is time period right before the reservoir top reverse point. Production
from storage power plants is close to its maximum in order to prevent
a spill over from storage reservoirs. Not many storage power plants are
able to take part in the SC market. Some of them would be ready to
reduce production in compensation for a good remuneration – negative
SC could be delivered. On the other side not many of them would
be able to increase production – positive SC could not be delivered
– because they are already producing very close to their maximum.
Since SC is a product with symmetrical control power bands, not many
storage power plants are able to deliver it right before the reservoir top
reverse point. Consequently is the value of Pmax low.
C Let’s assume that time period marked with a letter C in figure 5.1 is
time period somewhere in between the two sequential reservoir reverse
points. Production from storage power plants is neither close to its
minimum nor its maximum. Storage reservoirs are half-full, respectively half-empty. Many storage power plants are both willing and
able to take part in SC market. Consequently is the value of Pmax
high.
Current model, set up in the scope of this thesis, is unable to reflect the
course of Pmax between the two sequential reservoir reverse points shown in
figure 5.1. Reason for that may be the issues regarding the data of water
statistics that is used to feed the model (see section 3.6).
Keep in mind that besides the course of Pmax between the two sequential
reservoir reverse points also finding out the absolute values of Pmax represents a challenge since one does not know who the market participants are
not.
52
CHAPTER 5. CONCLUSION AND OUTLOOK
Bibliography
[1] Swissgrid. Overview of ancillary services, 1.0 edition, 2010.
[2] Swissgrid. Basic principles of ancillary service products, 6.5 edition,
2013.
[3] T.Reithofer. Mean Reverting Jump Diffusion (MRJD) Prozess: Schätzen
der MRJD Parameter. HPFC Szenarios.
[4] L. Clewlow and C. Strickland. Energy Derivatives: Pricing and Risk
Management. Lacima Publications, 2000.
53