The influence of wind energy market share on market clearing prices, wind park
revenues and bid performance
Author: Sam Hartveld (321556)
Coach: Prof. Wolfgang Ketter
Co-reader: Dr. Jan van Dalen
MSc Business Information Management
Erasmus University Rotterdam, Rotterdam School of Management
August 14, 2014
Abstract
Wind energy presence has a strong influence on market clearing prices in day-ahead markets and imbalance prices.
Considering the growing market share of wind energy the importance of this influence is increasing. When the
influence on the Market Clearing Price (MCP) increases, this directly affects wind park revenues. This can be observed
in both short-term day-ahead bids and long-term income. We present a model for wind gencos that optimizes bids
in the day-ahead market by minimizing their imbalance costs. In this effort, the model takes into account the gencos
influence on the MCP. This way a new perspective on wind park revenue forecasting is provided. Wind speed forecast
data is used to calculate the influence of growing market shares of wind parks on their expected revenues. The expected
revenues of wind gencos are then assessed in multiple market configurations in order to determine the influence of
wind energy market share, wind speeds and imbalance prices on the expected revenue of wind gencos.
Keywords: Wind Energy, Bid Strategy, Wind Park Size, Market Share, Renewables, Revenue Forecasting, MCP
Forecasting
Preface
The copyright of the master thesis rests with the author. The author is responsible for its contents. RSM is
only responsible for the educational coaching and cannot be held liable for the content.
1. Introduction
Energy consumption and production patterns in todays environment are constantly in motion. New technologies are enabling consumers to become producers
and the influence of renewable energy sources (or renewables) is increasing. Especially the influence of
wind energy is growing because of its increasing market share in the US and many European markets. Wind
energy has unique elements, which do not apply to traditional energy sources. These elements result in a special
influence which wind energy have on energy prices and
the profit of generating companies (gencos). Many bid
strategies exist which aim to maximize profits of wind
Preprint submitted to Energy Economics
gencos assuming certain energy prices. At the same
time, research has been done on the influence of wind
energy on the market clearing price (MCP). This study
takes the first steps into combining these research objectives. A model is proposed which predicts energy prices
and determines optimal bids in the day-ahead market,
taking into account the influence of wind energy. This
information is used to assess how wind energy will influence the MCP and wind park profitability, when its
output quantity on the market increases.
1.1. Differences between Energy Sources
Before discussing the model, a general introduction
in wind energy is provided. This paragraph covers the
most essential differences between traditional, fossil fuels and wind energy. Four fundamental differences between the two sources exist. First, the earth contains
a limited reserve of fossil fuels, whereas wind energy
can be considered infinite. Also fossil fuels damage the
environment by emitting greenhouse gasses, while wind
energy uses the environment to generate energy in a susAugust 14, 2014
tainable manner. The third difference can be observed
in the adjustability of the energy production quantity.
Within a certain ramp-up rate, energy production plants
using fossil fuels can increase or decrease its energy output. The only limitation here is the maximum/minimum
capacity of the plant. Wind energy, however, is dependent on external factors, such as wind speed. This
means that fossil fuels have the advantage that they can
be used to adjust energy production according to demand, whereas wind energy cannot. A fourth difference
lies in the cost structures of the energy sources. Both
wind and fossil energy sources have high fixed costs.
However, the variable costs (VC) of the energy sources
differ fundamentally. The source of wind energy (wind)
is free, which results in relatively low VC. The VC of
fossil energy sources are higher, as they are dependent
on the price of coal and other fossil fuels.
the amount of energy which is traded on the spot market will increase. Also, the increase in variability of
production may result in more imbalances. Lastly, an
increase in market share of wind gencos enables them
to influence the MCP.
1.3. Increased Market Share of Wind Energy
In this paper we propose a model that calculates the
expected revenue of wind parks, while taking into account its influence on the MCP. Firstly, this provides us
with insights in a wind parks influence on the MCP. Second, expected revenues can are optimized and assessed
in multiple market configurations. Lastly, the performances of the bid strategies are compared. Initial expectations are that relative profit decreases, influence on
MCP increases and the added value of bid optimizing
strategies increases when wind energy market share increases.
1.2. Influence of Renewables
Renewable energy sources are dependent on external,
uncontrollable circumstances. For wind energy the primary source of influence is wind speed. Wind speeds
can change continuously and so does the energy output.
Most energy is traded in the day-ahead market, which
is between 12 and 36 hours before the actual energy delivery takes place. However, the problem is that wind
speeds can only be reasonably predicted within a 4 hour
forecast length. As a result, the connection of wind turbines to the electricity grid can potentially affect supply reliability and power quality (Chompoo-inwai et al.,
2005). Fluctuating energy output can influence prices,
because it results in peaks and shortages in supply. The
dependency on wind speed speeds also poses an issue
because of the required balance in the market. The imbalance prices, imposed by the TSO, have a major influence on wind park profitability; because errors in wind
speed forecasts result in a lack of energy production.
This in turn is penalized by the TSO.
In the United States and in many Western European
countries policies are made that stimulate the use of renewable energy sources. Hence, it can be expected that
the share of energy coming from renewable sources will
increase in the near future (Ketter et al., 2013). When
the overall market share of wind parks will increase, the
position of wind parks in the market is fundamentally
different.
Based on the influence of wind energy on the market,
four differences from the current situation can be expected when the market share of wind power increases.
The variability of the quantity of energy production on
the grid is expected to increase, as the amount produced
by more volatile energy sources increases. Secondly,
2. Theoretical Background
2.1. Energy Markets
There are three basic market structures in which energy can be sold: a pool-based market, contractual market and hybrid forms (Li et al., 2011). In a pool-based
market suppliers and demanders place their bids and
based on the supply and demand curves which result
from those bids an energy price is determined. Energy
on contractual basis is sold for a predetermined price
which the involved parties agreed upon. Hybrid forms
combine aspect of both markets. In this study a wind
park genco is considered in a pool-based market. In a
pool based market a TSO is responsible for balancing
supply and demand.
The energy pool market consists of three successive
short-term trading floors: day-ahead market, adjustment
market and the balancing market (Morales et al., 2010).
The primary source of income of wind park genco is
considered to be the energy traded on the day-ahead
market. The only costs incurred in this energy trading
are caused by imbalances in the grid. Gencos make real
time decisions in order to optimize their performance
and proper predictions help in this effort (Ketter et al.,
2012). According to Pina et al. (2012) the intermittence of most renewable resources can create problems
to electricity grids, when renewable energy provides a
significant share of the energy mix. This increases the
importance of role that the TSO has when the market
share of renewables increases.
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2.1.1. Market Clearing Price
The energy market works like any commodity market with supply and demand curves which are used to
determine a market price. However, the nature of the
energy and its market structure make the market a bit
more complicated. First, energy cannot be stored in
large quantities. Also, in the energy market, market participants offer and demand large quantities of energy.
Bids are placed in large blocks with a specific quantity
and price. This results in intermittent rather than continuous supply and demand curves. The MCP is the price
which lies between the ask price and the bid price which
are closest to each other, before the ask price exceeds
the bid price (Ott, 2003). More details about this can
be found in the PowerTAC Specifications (Ketter et al.,
2014).
For pool-based markets two pricing mechanisms exist: Uniform Pricing (UP) and Pay as Bid (PAB). In UP
every genco is paid the same amount, namely the Market Clearing Price (MCP) (Li et al., 2011). This implies
that the bids of each individual supplier and demander
influence the revenues of all other market participants.
For the purpose of this study a UP pricing mechanism is
assumed, hence MCP is considered the sell price for all
energy in the market.
Wind parks will always want to sell their energy,
because their energy source (wind) cannot be stored.
As a result wind parks are incentivized to always sell
the maximum amount of energy that they can produce.
This, combined with the low VC of wind parks, result in
the fact that wind parks are incentivized to sell a maximum amount of energy against any price. The MCP is
paid to all gencos, so the wind park will always get this
price as well.
park gencos use bidding strategies. This maximizes the
revenue generation on the day-ahead market and minimizes the costs for imbalances. In this effort gencos
constantly need to make a tradeoff between cost maximization and risk minimization (Ma et al., 2005). Optimization methods differ regarding auction methods and
assumptions. Most methods consider a UP market (Ma
et al., 2005; Matevosyan and Söder, 2006), others a PAB
market (Rahimiyan and Mashhadi, 2007). Regarding
prices most methods assume the genco has no influence
on the market price and is price-taker (Ma et al., 2005;
Matevosyan and Söder, 2006; Rahimiyan and Mashhadi, 2007). Others aim to use the influence of a genco
on the MCP in order to optimize its income (de la Torre
et al., 2002). However, de la Torre et al. (2002) did not
do this considering a wind genco.
Elements of the model by Matevosyan and Söder
(2006) are used for the purpose of this study. Their
method aims to minimize imbalance costs of wind
gencos by using error scenarios. The errors between
weather forecasts and actual wind speeds are used to
predict potential future forecast errors. These errors influence imbalance costs of the genco. The most basic
manner to bid for future energy production is by basing future energy production directly on weather forecasts. Henceforth, this is referred to as Direct Bids Matevosyan and Söder (2006) have shown that bids of their
methodology are more profitable than direct bids. In
this model power output scenarios are forecasted based
on potential wind speed scenarios. The MCP and imbalance prices are then given and used to optimize the
bid quantity.
2.2.2. Other Optimization Methods
In game-theory models, equilibria are determined by
combining the bid strategies of multiple gencos. This
way gencos cannot influence their profit merely by influencing their own strategy. In agent based methods, market participants are modeled as adaptive agents.
They are developed with bid preferences and strategies,
they can use past experience to improve their future performance (Li et al., 2011). This paper proposes a single
genco optimization method, so neither game-theory nor
agent based methods are considered in this study.
2.2. Bid Strategies
This paragraph contains a discussion of bid strategies which are used by wind parks to maximize their
expected revenue. Li et al. (2011) identified three different models which are used to achieve this goal: single
genco optimization, game theory and agent-based.
2.2.1. Single Genco Optimization
For wind gencos multiple sources of uncertainty can
be identified that affect wind park profitability, among
them are: the day-ahead market price, wind power generation and the imbalance price (Morales et al., 2010).
The day-ahead price is the energy price for the dayahead market, wind power generation depends on wind
speeds and the imbalance price is paid for energy shortages or surpluses. In order to maximize profits wind
2.3. Wind Park Influence on MCP
Valenzuela and Wang (2011) have developed a probabilistic model to determine long-term probability distribution of MCPs. In their model Valenzuela and Wang
(2011) state that one genco can have multiple bids on
different price levels and quantities. This is directly related to the stepwise cost increase of traditional gencos.
3
In their model block bids are based on the Marginal
Costs (MC) of the output of the respective block. Besides that they assume that wind gencos always bid the
lowest price, as wind parks have the lowest MC (Valenzuela and Wang, 2011). This methodology is used to
determine expected MCPs and related imbalance prices.
Research Question 1. What effect does the market
share of wind energy have on Market Clearing Prices?
In some countries (e.g. Germany and Denmark) wind
market shares are growing (Blanco, 2009), resulting in
a considerable effect on MCP. The increasing amount
of wind parks stresses the importance of a better understanding of prices patterns arising from wind energy
influence, because these patterns are becoming more apparent. This objective is achieved by assessing the MCP
for multiple wind speeds considering a certain wind
park size. The wind speed is manipulated by adjusting
the wind forecast. We then compare the MCP curves of
multiple wind park sizes to determine the influence of
wind park sizes. The wind park size is manipulated by
adjusting the amount of turbines.
3. Research Objectives
Many studies have been performed on wind park
profitability optimization bid strategies (Li et al., 2011;
Ma et al., 2005; de la Torre et al., 2002); most of them
focus on their dependency on wind forecasts and their
position in the market. Studies exist on the influence
on wind energy on MCP (Valenzuela and Wang, 2011;
Sensfuß et al., 2008). However, we found no studies that
combine these aspects in order to determine expected
wind park revenues when they are able to influence the
MCP. In this paper we present a model which predicts
wind park revenues based on wind forecast, taking into
account the wind parks influence on the MCP. First, the
influence of wind park size on the MCP is assessed, then
the expected revenues are calculated. This way the influence of the size of a wind park on its own profitability
can be assessed. Lastly, accuracy of bidding strategies
are evaluated by comparing expected revenues with actual optimal revenues.
Figure 1 provides an overview of the relation between
the variables in the model which we propose. In this
chapter we elaborate how our research objectives relate
to the variables and indicated relations. In chapter 4 we
provide a detailed explanation of the model and the content of the relations. Paragraph 4.5 contains the details
of the values of the independent variables that apply to
our analysis.
3.2. Expected Wind Park Revenue
In this study a model is proposed which calculates
optimal bids, while taking into account the wind parks
influence on MCP. These optimal bids are determined
by maximizing the expected revenues following from a
bid. The expected revenue is influenced by the bid quantity (which is being maximized), the MCP, the imbalance price and the surplus/shortage which follows from
the expected energy quantity and the bid. The second
goal is to assess the influence of wind speeds on expected revenue. This provides us insight in what the
expected revenue is for a specific wind speed forecast.
The outcomes are highly relevant for short term revenue
expectations in, for example, the day-ahead market. The
influence of wind speeds is assessed by calculating the
expected revenue for different wind speeds, keeping all
other variables constant. Subsequently, the amount of
turbines is adjusted in order to analyze the influence of
the wind energy market share.
Research Question 2. How is the expected revenue of
wind parks influenced by the market share of wind energy in the energy market?
3.1. MCP Influence
An increase in wind energy will result in a fundamental shift in the structure of the energy market and the
behavior of energy prices. Today, the key role of fossil fuel gencos in the energy market gives them strong
influence on energy prices. However, with the growing
availability of renewable energy it can be expected that
the influence of renewable energy gencos will increase.
This shift in the market power balance can be expected
to have an impact on the MCP. Prior studies have had the
relation between wind energy and the MCP as their primary focus (Valenzuela and Wang, 2011). This relation
is part of our study as well; it is represented in the relation between Forecasted Quantity and Market Clearing
Price.
The next topic of interest is the long term implication
of the differences in expected revenues of the assessed
wind park sizes. This provides us with an insight in the
relation between the revenues and sizes of wind parks
and enables us to assess profitability of wind parks in future energy markets. It impacts currently existing wind
parks, but also has implications for future investments in
wind energy. This objective is achieved by calculating
the expected revenue of the different wind park sizes.
Then, past wind speed data is used as an expectation for
future wind behavior. The expected revenue is divided
by the amount of turbines in the wind park in order to
4
Figure 1: Variable Overview
provide a clear view on the profitability of turbines for
given wind park sizes.
Research Question 4. What is the bid performance of
our bid method compared to direct bids and bids with
perfect information?
Research Question 3. How are long term revenues of
wind parks influenced by the market share of wind energy in the energy market?
4. Model
3.3. Bid Performance
Fundamental aspects of the bid method are derived
from the methodology of Matevosyan and Söder (2006).
The bid strategy is proven to result in better results than
direct bids. In this study we assess the performance
of the method as well. We compare the actual revenue
which we receive with the optimal revenue which could
have been received; this is defined as the bid performance. The bid performance indicates the value of the
bid method in practice. If a bid closely represents actual optimal bids, it provides wind gencos with a better
tool to optimize their bids and predict their revenues.
Additionally, if the model performs well, it can be implemented in smart market simulations in order to improve their quality (Bichler et al., 2010). First, the actual
revenue following from our optimized bid, considering
actual wind speeds and market situations, is calculated.
The actual revenue of the genco is compared with the
best revenue which could have been achieved, having
perfect information about actual wind speeds, to determine the bid performance. Also, the bid performance
of the actual revenue which would have been received
with direct bids is calculated and used as a benchmark.
4.1. Bidding Strategy to Minimize Imbalance Costs
This paragraph contains a discussion of the model
which is simulated for the purpose of this study. It combines aspects of the models of Matevosyan and Söder
(2006) and Valenzuela and Wang (2011). The relevant
concepts of both models are explained in detail and their
relation to this study is elaborated on. The aim is to provide a knowledge base which is required in order to understand the following methodology. Matevosyan and
Söder (2006) developed a model that optimizes the energy bid amount based on given wind speed behavior,
forecasts and market clearing prices. It assumes that
wind parks have no variable costs and hence maximize
profits by minimizing the imbalance costs on the spot
market. Valenzuela and Wang (2011) also assume that
wind parks have no variable costs. They assumed a
given supply distribution in an effort to determine the
long term effect of wind energy on MCP. This model
contains a series of steps in which aspects of both models are combined. The model is depicted in figure 2.
Table 1 contains a concise explanation of each step. After that, they are discussed more in to detail. For each
5
phase it will be stated what data is required and which
methods are applied.
RMS E measured for given values of α, β and σz . The resulting α, β and σz provide a curve for RMS E ARMA ,
which matches the RMS Emeasured values as closely as
possible. Thereby it provides the best possible representation of the measured past error events. The
measured events in this model are represented by
the RMS Emeasured values. There is one value for
the RMS Emeasured for every forecast length (k). The
RMS Emeasured values can be found in AppendixA.
The RMS E ARMA follows a curve which is calculated
with formula (3), where (4) applies when k = 0, (5)
applies when k = 1, and (6) when k > 1:
V(0) =
p
V(k) (3)
V(1) =
σ2z (5)
V(k) =
i−1
σ2z (α2(k−1) + (1 + β2 + 2αβ)Σk.1
i−1 α ) (6)
σ(X(k)) =
0 (4)
Figure 2: Graphical representation of the model
Where: k = the forecast length and α, β and σz are
dependent variables, which are calculated in the effort
of minimizing Q as explained in formula (1). In this
formula σ(X(k)) represents the RMS E ARMA values.
4.1.1. Determination of statistical behavior of wind
speed forecast errors
The goal of this phase is to determine the statistical
behavior of wind speed forecast errors. It is a pattern
in which forecast errors are expected to occur in the future and is based on past wind speed forecasts and actual
wind speeds. The statistical behavior of forecast errors
is represented in parameters α, β, and σz . The manner in
which these parameters are used is discussed in section
4.1.2. The parameters are calculated in a Root Mean
Square Error (RMSE) calculation of an Auto Regressive Moving Average (ARMA) formula, this will be discussed later in this section. The RMSEs of errors in past
forecast data are used to determine RMS Emeasured values. Errors from past predictions follow from the data
set which is provided by the PowerTAC platform and
originates from the KNMI (KNMI, 2010). The RMSE
Auto Regressive Moving Average (ARMA) is used to
match the RMS Emeasured values, with formula (1):
minQ(α, β, σz )
4.1.2. Determination of wind speed error scenarios
With the parameters α, β and σz from the abovementioned RMS E ARMA curve the wind speeds error scenarios can be determined. Formula (7) is used to create the
scenarios.
Xi (t) =
X(0) =
0
Z(0) =
0
And, Xi (t) = wind speed forecast error in t hour forecast and Z(t) = a random Gaussian variable for hour t
(with standard deviation = σz and mean = 0).
It can be observed that α represents the degree to
which an error correlates with the preceding error value,
β represents the degree to which the error correlates with
the random value of the preceding timeslot and σz determines the standard deviation of the random variable.
The scenarios are created by generating values Z(t) until
the desired forecast time has been reached. Each value
X(t) represents a possible wind speed error at hour t.
For each X(t) only one Z(t + 1) is generated. This results in a probability tree, where t = 0 is the source of
where,
−RMS E ARMA (k)]
(7)
where,
(1)
K
Q(α, β, σz ) = Σk=1
[RMS E measured (k)
αXi (t − 1) + Z(t) + βZ(t − 1)
(2)
2
The goal here is to minimize the value of Q, where
Q represents the difference in between RMS E ARMA and
6
Phase no.
1
2
Title
Determination of statistical behavior
of wind speed forecast
Determination of wind speed error
scenarios
3
Calculation of wind speed scenarios
4
Calculate wind park power output
for the given wind speeds
Determination of MCP
5
6
Description
Based on wind speed forecast error data, parameters α, β and
σz are determined.
Wind speed error scenarios are determined, based on the α, β
and σz which represent the natural behavior of the wind
speed errors.
Wind speed scenarios are calculated based on the wind
speed error scenarios, with the same probabilities.
The wind speed is obtain from the aforementioned scenarios,
based on these, wind park power output is determined.
The MCP is required to determine the optimal bids and is
based on given market structure.
The final step is to minimize the imbalance costs and
consequently maximize the wind park’s expected profit.
Solving optimization problem to
determine the optimal bid
Table 1: Bidding strategy pase outline
every scenario. At higher values of t, there is only one
outcome possible for X(t + 1). A scenario is defined as a
series of consecutive nodes from X(0) to X(T ), where T
is the maximum value of t. For the purpose of this study
T = 24. This method of scenario creation is based on
the method by Söder (2004).
An infinite amount of scenarios can be created. For
the purpose of this study we created 1000 scenarios per
optimization. Each scenario is created randomly and
has the same likelihood of occurrence; hence they have
equal probability values.
Where Vi (t) = Wind speed at hour t for one scenario
(wind speed scenario), V f (t) = Wind speed forecast at
hour t and Xi (t) = Wind speed forecast error for one
scenario.
By adding the wind speed forecast to each error scenario, the error scenario is transformed to a wind speed
scenario. A forecast is given for a value t. So for every value t the same forecast value is used. As a result a wind forecast of value of t is transformed into a
series of potential wind speed values for a value of t.
The amount of wind speed equals the amount of error
scenarios. The error scenarios are repeatedly used for
multiple forecasts. This can be done because the values represent the natural behavior of the wind for the
specific region and hence apply in one location for all
points in time (assuming no major changes in the environment). Each wind speed scenario has a probability
which equals the probability of the corresponding error
scenario. Hence all wind speed scenarios have equal
probabilities.
4.1.4. Calculate wind park power output from given
wind speeds
This step involves the transformation from wind
speed into electrical energy. For each wind speed there
is a corresponding power output per turbine. The power
transformation values are provided in paragraph 4.5.4.
The size of the wind park is determined here; the output per turbine is multiplied time the amount of wind
turbines. The total power output is calculated per scenario. The potential scenarios of energy output are used
in twofold: first it is used to determine corresponding
MCP and second it is used as input variable in the calculation of the optimal bid value. Both are discussed in
the following steps.
Figure 3: Graphical representation of ten error scenarios, T=30
4.1.3. Calculation of wind speed scenarios
The wind speed scenarios are calculated by summing
the wind speed forecast and the forecast error scenario.
This is represented in formula (8):
Vi (t) =
V f (t) + Xi (t)
(8)
7
The wake effect is an attribute of wind farms related
to the decrease in downstream airflow in wind farms.
As the air passes through the wind turbine rotor disc,
downwards airflow streams are reduced. This results
in disturbed, reduced wind speeds for wind mills that
are positioned behind other turbines (Matevosyan and
Söder, 2006). However, this effect is not taken into account in this model as the shapes of the wind farms are
undetermined.
Ztt =
w
w
max[avg(Pisp Qwb + Pimb
i abs(Qi − Qb ))]
(9)
Where: Ztw = Revenue of wind park genco at hour t,
= Spot price for scenario i, Qwb = Quantity of power
bid to the market, Pimb
= Imbalance price, Qwi = Wind
i
park power output quantity prediction for scenario i.
sp
Pi
4.2. Notations
4.1.5. Determination of market clearing prices
For the purpose of this study the influence of the wind
park energy output on the MCP and consequently the
profitability of the wind park are assessed. In order to
achieve this goal the energy output of the wind park is
used as input value in the MCP calculation. This calculation is performed as explained in paragraph 4.3. The
imbalance price is determined by the TSO. Hence it is
dependent on the market in which the genco is operating. The imbalance price is difficult to predict, because
of its many dependencies on conditions in the market.
However, the price is influenced by factors which can
be modeled; this is further elaborated on in paragraph
4.4.
All notations are explained throughout the paper, table 2 is included to provide an overview of all used variables in the model.
Notation
t
T
k
K
l
Notation
α, β and σz
4.1.6. Optimize bid
In the final phase in this methodology the optimal bid
quantity is determined. The optimal bid is the bid which
is expected to result into the largest profit. This is calculated for every forecasted point in time. Given the fact
that the only costs taken into account are the imbalance
costs, this is done by minimizing the expected imbalance costs. The revenue is calculated as follows. First
the expected revenue, based on the bid is calculated, this
is the spot price (Pisp ) times bid quantity (Qwb ). Then
the expected imbalance costs added to this. The imbalance costs are the imbalance price (Pimb
i ) times the absolute difference between the scenario power output (Qwi )
and the bid quantity (Qwb ). The imbalance price changes
when the bid quantity exceeds the scenario power quantity. However the difference between the quantities must
remain absolute, because the imbalance price will determine whether the consequence will have a negative or
positive value. As the MCP is based on the scenario
quantity and the imbalance price on MCP, it follows
that for every scenario there is a different quantity, spot
price and imbalance price. Given the fact that each scenario has an equal probability, it follows that the revenue
is maximized by determining the optimal bid quantity
(Qwb ), which results in the highest average pay-off considering all scenarios. This results in equation (9):
Z(t)
Xi (t)
V f (t)
Vi (t)
Q(v)
Pwt
Qwt
Ztw
Pis p
Pimb
i
Qwi
Qbb
Pi, j
Qi, j
Indices and numbers
Definition
Hour of prediction
Maximum value of t
Forecast length
Maximum value of k
Position in merit order
Variables
Definition
Parameters used to illustrate error
behavior of wind
Random Gaussian variable with
standard deviation σz for hour t
Wind speed forecast error for
scenario i
Wind speed forecast at hour t
Wind speed at hour t for scenario i
Power generated for wind speed V
Bid price of genco W at hour t
Bid quantity of genco W at hour t
Revenue of genco W at hour t
Spot price for scenario i
Imbalance price for scenario i
Wind park quantity for scenario i
Wind park bid quantity
Bid price of genco i in block j
Bid quantity of genco i in block j
Table 2: Notations
4.3. MCP Calculation
As explained in section 2.1.1 the MCP is the price
at which supply and demand meet. In this method a
demand curve is taken as given. The supply at the other
hand is based on the cost structures of different energy
sources in the market.
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the total market size and decreases the MCP, assuming
the demand remains constant.
4.3.1. Establishing the supply curve
Valenzuela and Wang (2011) state that each energy
source has a different cost structure and that the prices
differ for each capacity level. In this model it is assumed that there are 10 energy sources. It is assumed
that each genco operates one energy source to produce
energy; hence the cost structure of a genco is based on
the energy source it uses. Gencos have given capacities which are divided into a set of blocks. Each genco
has a different cost structure, in which prices increase in
per capacity block. This is the result of decreasing efficiency of power plants when output increases. So for a
capacity block a genco i can bid a quantity Q (limited to
maximum capacity of the block) for price P at capacity
block j. Bids are ordered based on price (lowest prices
offered first). This results in a merit order in which multiple gencos offer multiple bids, resulting from the capacity blocks. Table 3 contains an example of the merit
order. Eventually the merit order determines the supply curve, with the lowest values being served first and
highest latest. Table 3: Block bids for Qi, j and Pi, j
Merit Order
6
5
4
3
2
1
4.4. Imbalance price determination
The imbalance price is an instrument which is used
by a TSO to incentivize gencos to provide accurate forecasts of the amount of energy which is going to be provided to the market (Ketter et al., 2014). It is used to
fine gencos which do not provide the amount energy
which has been bid in at the bidding phase (Morales
et al., 2010). The imbalance price always is related to
the MCP of the corresponding point in time. This is
the case, because in order to fine a genco a potential
revenue stream must be lower than the MCP or a fine
must exceed the MCP. The imbalance price changes depending on two aspects: the balance in the market and
the balance of the genco. The balance in the market is
explains whether the TSO has a surplus or shortage of
energy on the grid for a given hour t. When the balance
in the market is negative, the TSO has a shortage; the
suppliers deliver less energy than predicted or demand
is higher than expected. Vice versa, when the balance
is positive, the TSO faces a surplus; supply is higher
than predicted or demand is lower than expected. The
balance of the genco for an hour t depends on its actual
energy output and bid energy quantity. In the optimization the energy output of a scenario is taken as the actual
energy output, because it is assumed that this is a potential actual amount of energy that the genco can produce
for a given wind speed. The balance of the genco is negative in a situation in which a bid quantity exceeds the
actual quantity, because it cannot deliver the promised
amount of energy. Alternatively the balance is positive,
when the genco actual amount of energy exceeds the
bid the genco, because it can deliver more than initially
promised. This means that the genco balance changes
the moment that the bid energy quantity exceeds the
power quantity in the scenario. This results in four potential situations, which are explained in table 4.
The imbalance price is linked to the MCP. The downward regulating price mostly has a value between 0%
and 100% of the MCP and sometimes exceeds the MCP.
The upward regulation price can move up to high percentages of the MCP. This is the case because when
the TSO has a high negative balance it needs to provide strong financial incentives to punish or reward to
gencos that cause or solve that imbalance. In the dayahead bidding stage the gencos do not know whether the
market balance will be positive or negative. In case the
gencos would be aware of the balance in the market this
would result in unrealistic bidding behavior because of
the resulting imbalance prices. (e.g. when a negative
Quantity and Price
Q3,2 – P3,2
Q2,3 – P2,3
Q2,2 – P2,2
Q3,1 – P3,1
Q2,1 – P2,1
Q1,1 – P1,1
Table 3: Merit Order
4.3.2. MCP determination
The demand curve is determined in the same manner
as the supply curve, but the other way around: Block
asks in a merit order with the highest ask price coming
first and lowest coming last. The supply and demand
block bids move toward each other until they intersect.
As a result price Pi, j , that corresponds with quantity Qi, j
which offers the final quantity before the supply price
exceeds the demand price, is the MCP.
4.3.3. Influence of wind energy
MC of fossil fuel gencos increase with quantity,
whereas the MC of renewable gencos do not (Soleymani
et al., 2007). A wind park places one bid offering all
its energy for a price lower than the lowest fossil fuel
genco, because it is assumed it has no variable costs;
wind parks always are first in the merit order. Hence,
its offer increases market supply and thereby moves the
supply curve to right. An increase in supply increases
9
No.
1
Market
Balance
Negative
Genco
Balance
Positive
2
Negative
Negative
3
Positive
Positive
4
Positive
Negative
Description
The market required more energy and the genco can offer this. Regular trading
takes place, so energy exceeding the bid is sold at MCP.
The market requires more energy, but the genco does not live up to its promise
of delivery. The genco receives a penalty over the size of the shortage for not
delivering when it is required. This penalty can be any percentage of the MCP.
This percentage is manipulated to study its influence. (Known as upward
regulation price)
The TSO has excess energy; the genco can deliver more than initially expected.
The genco will be able to sell its surplus against a tariff which is lower than the
MCP. (Known as downward regulation price)
The TSO has excess energy; the genco delivers less than expected. As a result
the shortage is the part of the initial bid, which cannot be met. This part of the
sale does not occur, but besides that the genco is not fined. The shortage is
deducted from the bid.
Imbalance
Price
MCP
< −100 of
MCP
0% of MCP
- MCP
Table 4: Imbalance price possibilities
balance is given then a genco would always bid 0, because it would always have a positive balance and sell
its energy for MCP.) Hence the market balance will be
randomly assigned to all scenarios in the simulation.
range between 100 and 2000, with respective markets
share of 2.5% and 25.1%.
4.5.4. Turbine efficiency
The power performance curve of a GE 1.5s wind turbine has been used. It assumes an air temperature of
−20◦C and an air density of 1.225kg/m3. Table 5 provides the turbine output in kW for the corresponding
wind speeds. The output values of wind speeds between
the wind speed values in the table are calculated as a
weighted average of the corresponding outputs.
4.5. Data
In this section contains a concise elaboration on the
variables which are used in the model and the sources
of the related data.
4.5.1. Wind speed forecast
We used wind speed forecasts of the city of Rotterdam, which originate from the Royal Dutch Meteorological Institute, KNMI (KNMI, 2010). The data set
contains forecasts with a forecast length of up to 24
hours. 24 forecasts are provided for every hour of every day in the year 2009.
Wind Speed
(m/s)
≤3
5
7
9
11
13
4.5.2. Forecast error behavior
Hourly wind forecasts and actual wind speeds of a
specific location are required in order to determine the
forecast error behavior. In addition to the forecasts, the
actual wind speeds in Rotterdam of every hour of every
day in the year 2009 have been provided by the KNMI
as well. As discussed in paragraph 4.1.1, the forecast error behavior is represented by parameters : α, β and σz .
The values resulting from the Rotterdam data set are as
follows: α = 1.0248, β = 1.3564 and σz = 0.0842.
Power
(kW)
0
104
344
774
1342
1494
Wind Speed
(m/s)
4
6
8
10
12
≥14
Power
(kW)
36
205
528
1079
1460
1500
Table 5: Power Performance Curve Data
4.5.5. Supply & demand bids
The market is assumed to be stable. This means
that bids are set and not changing over time. The only
changing bid is the one by the wind genco, which is
determined in this model. Characteristics of the supply bids are based on the IEEE reliability test system
(Grigg et al., 1999). Demand bids are set at random values, which are in line with the supply bids in terms of
quantities and price levels. Supply and demand bids are
provided in AppendixB.
4.5.3. Amount of turbines
This variable is manipulated based on the requirements of the research objectives. In this study its values
10
4.5.6. Imbalance price volatility
The imbalance price level is relevant for the upward
regulation market, when the genco has a shortage. The
volatility of the imbalance price is represented as a multiplier of the MCP. For the Dutch market we calculated
the difference between the average MCP between December 2013 and May 2014, provided by the APXGroup (2014), with the average upward regulating price,
provided by TenneT (2014).
This resulted in a multiplier of -1.8. The downward regulation price had been set to 0. We assumed that energy could not be sold when it was not bid on the dayahead market. This assumption has been made because
our data showed the downward regulation price is unpredictable and hence it did not fulfil our entry requirements.
less. In this situation the lowest priced buyer is willing to pay e74.00 and the total served market moves
from 1031MWh to 1181MWh. This increase can be
explained by the fact that there was more demand for
the price of e51.09/MWh, but a lack of supply. Subsequently, we assessed a 1000 turbine wind park; this park
has a market share of 15.9%.
The market share is not linearly related to the amount
of turbines, because of the difference in genco output,
the different market sizes and wind speeds in the given
region. A more detailed elaboration on the relation between the amount of turbines and the market share is
provided in AppendixC. Figure 4 illustrates the market
shares of wind parks for its corresponding amount of
turbines.
5. Results
This section contains a discussion of the findings related to our research objectives. First, this relation between wind energy market share and the MCP is discussed. Subsequently, an analysis is performed on the
effect of different wind speeds on the hourly wind park
revenues. This is done for multiple wind park sizes, in
order to illustrate how revenues differ when wind energy
market shares increase. The results provide an indication of the expected revenues for different wind speeds,
but it does not take into account the wind speeds that
actually occur within a specific region. In order to provide a realistic indication of wind park revenues over
different situations we assess the actual wind behavior for a specific region. These are then used in order
to determine the revenue per wind turbine for multiple
wind market shares. Another factor influencing the expected revenue is the imbalance prices in a market. An
overview of multiple imbalance price scenarios is provided to indicate its influence. Lastly, we assess how
accurate our revenue predictions are as compared to the
optimal revenues for multiple forecast lengths.
Figure 4: Wind park market share
The 1000 turbine park shows a fundamentally different pattern than the 100 turbine park. Due to its
1500MW capacity the wind park is able to offer energy
to energy to buyers which are willing to pay less. With
a wind speed of 0 m/s (and an output of 0MWh) the
MCP is e51.09/MWh. However, when wind speeds is
≥14m/s the MCP drops to e22.92/MWh. This is due to
the low priced wind energy, which serves buyers who
are willing to pay less. The MCP moves in a pattern
which is determined by the matching ask and bid prices
for different energy output levels. The market size
moves between 1031MWh and 2493MWh, with wind
speeds of 0m/s and 14m/s respectively. The market
size increases with 1462MWh, instead of the 1500MWh
which could initially be expected, because of the gencos
that are no longer willing to offer energy to the market
for this low MCP. Figure 5 provides a comparison of the
MCP development for the two wind park sizes.
5.1. Wind park size influence on MCP
In this section we discuss how the wind park size influences the MCP; in this analysis we take into account
how wind speeds affect this relation. First, we assessed
the MCP for a wind park with 100 turbines (market
share 2.5%). In this situation the MCP is e51.09/MWh
for all wind speeds. The market price is constant, because of the fact the small market share: even when
providing full output to the market (150MW) the genco
is unable to supply to buyers which are willing to pay
11
t=10
0.3%
e 0
e0
e1
e3
e 15
e 43
e 88
e 148
e 228
e 344
e 443
e 568
e 684
e 742
e 762
t=1100
17.1%
e 0
e7
e 59
e 357
e 1,672
e 4,722
e 9,188
e 15,218
e 21,868
e 30,023
e 30,534
e 30,878
e 34,538
e 35,620
e 35,503
t=100
2.5%
e 0
e1
e6
e 32
e 151
e 428
e 879
e 1,503
e 2,311
e 3,459
e 4,338
e 5,899
e 6,948
e 7,458
e 7,548
t=1200
18.2%
e 2
e 11
e 66
e 404
e 1,906
e 5,240
e 10,216
e 16,599
e 23,559
e 32,253
e 30,019
e 32,144
e 35,514
e 36,519
e 37,113
t=200
4.7%
e 0
e1
e 11
e 66
e 314
e 883
e 1,784
e 3,034
e 4,568
e 6,842
e 9,217
e 11,568
e 13,533
e 14,673
e 14,610
t=1300
19.3%
e 1
e8
e 67
e 421
e 1,890
e 5,196
e 10,022
e 16,174
e 22,327
e 29,764
e 26,096
e 29,448
e 32,937
e 35,019
e 35,058
t=300
6.6%
e 0
e2
e 16
e 96
e 457
e 1,313
e 2,685
e 4,514
e 6,523
e 10,155
e 12,547
e 16,383
e 18,401
e 20,027
e 20,407
t=1400
20.3%
e 1
e 11
e 75
e 449
e 2,112
e 5,912
e 11,831
e 18,802
e 25,275
e 34,234
e 27,871
e 34,020
e 38,570
e 41,266
e 40,229
t=400
8.4%
e 0
e2
e 21
e 131
e 614
e 1,746
e 3,555
e 6,015
e 8,848
e 13,252
e 16,464
e 21,376
e 24,679
e 26,078
e 25,769
t=1500
21.2%
e 1
e 12
e 83
e 462
e 2,200
e 6,221
e 12,190
e 19,238
e 25,793
e 34,068
e 30,601
e 31,891
e 31,781
e 25,302
e 23,819
t=500
9.9%
e 0
e3
e 26
e 152
e 749
e 2,141
e 4,379
e 7,317
e 11,005
e 16,110
e 20,077
e 25,279
e 28,607
e 31,792
e 31,656
t=1600
22.0%
e 1
e 12
e 83
e 532
e 2,485
e 6,794
e 13,392
e 21,152
e 26,931
e 33,765
e 29,700
e 29,256
e 25,344
e 24,437
e 25,071
t=600
11.3%
e 0
e4
e 30
e 191
e 939
e 2,665
e 5,383
e 8,962
e 13,463
e 18,956
e 23,306
e 29,541
e 34,563
e 36,906
e 37,643
t=1700
22.8%
e 1
e 11
e 92
e 561
e 2,595
e 7,168
e 14,079
e 21,749
e 29,543
e 32,888
e 30,438
e 26,063
e 24,203
e 23,072
e 23,130
Table 6: Expected revenue for multiple wind park sizes
t=700
12.6%
e 1
e5
e 39
e 223
e 1,101
e 3,170
e 6,171
e 10,381
e 14,849
e 21,811
e 25,922
e 33,958
e 40,412
e 43,130
e 41,690
t=1800
23.8%
e 0
e6
e 71
e 513
e 2,636
e 7,317
e 14,298
e 22,703
e 28,759
e 32,148
e 29,574
e 23,932
e 22,645
e 22,169
e 22,364
t=800
13.8%
e 1
e5
e 44
e 269
e 1,284
e 3,568
e 7,073
e 11,643
e 16,342
e 23,879
e 28,764
e 36,603
e 42,160
e 41,097
e 39,284
t=1900
24.6%
e 1
e 16
e 110
e 617
e 2,941
e 7,970
e 15,221
e 23,564
e 30,354
e 31,392
e 27,748
e 23,023
e 20,748
e 19,912
e 19,865
t=900
14.8%
e 0
e7
e 52
e 296
e 1,406
e 3,841
e 7,597
e 12,818
e 18,161
e 26,335
e 29,985
e 36,583
e 39,047
e 36,029
e 31,966
t=2000
25.1%
e 1
e 11
e 113
e 670
e 3,123
e 8,591
e 16,238
e 24,518
e 31,510
e 31,241
e 25,787
e 20,638
e 20,040
e 20,413
e 20,244
t=1000
15.9%
e 0
e5
e 44
e 311
e 1,499
e 4,342
e 8,640
e 14,169
e 20,356
e 28,867
e 32,705
e 32,840
e 32,547
e 33,612
e 33,857
12
Turbines
Market share
w=0
w=1
w=2
w=3
w=4
w=5
w=6
w=7
w=8
w=9
w = 10
w = 11
w = 12
w = 13
w = 14
Turbines
Market share
w=0
w=1
w=2
w=3
w=4
w=5
w=6
w=7
w=8
w=9
w = 10
w = 11
w = 12
w = 13
w = 14
Figure 5: Influence of wind speed on MCP
Figure 6: Revenue comparison of t = 10* 100 and t = 1000
5.2. Wind park size influence on expected revenues
Where other studies have taken the MCP as given
(Matevosyan and Söder, 2006), we are now able to assess the expected revenue given the wind parks influence on MCP. Again we use a 100 turbine and a 1000
turbine wind park to illustrate the relation between wind
park size and revenues.
5.2.2. Market share and expected revenue
Knowing the expected revenues of wind parks for different wind speeds and wind park sizes, we now analyzed them with actual wind forecasts. First, we analyzed the distribution of wind speed forecasts of one
month in 2009. The likelihood of occurrence for each
wind speed can be found in Appendix C. Taking this
wind speed distribution into account we analyzed the
expected revenue per turbine while manipulating the
market share of the wind park. As could be expected
from the previous paragraph, the revenue per turbine is
negatively related with the market share. With a market share of 2.5% and 15.9% the revenue per turbine is
e12.92 and e9.38 respectively. Figure 7 illustrates the
relation between market share and revenue per turbine.
In this graph the revenue per turbines of a 10 turbine
wind park is used as an index. Table 7 provides the revenue per turbines in absolute terms.
5.2.1. Wind speeds and expected revenue
Considering a 100 turbine wind park, we observe an
almost linear relation between the expected revenue and
the amount of energy produced. The reason for this is
that the MCP remains constant. The only deviation from
this is the anticipation for potential imbalance penalties.
Intuitively, one would expect that a wind park which has
10 times this size also has 10 times the revenue. However, this is not the case. The expected revenue of a 1000
turbine park is heavily influenced by its effect on the
MCP. With a wind speed of 5m/s the average expected
revenue of a 100 and 1000 turbine wind park is e439.29
and 4,361.78 respectively. This is where the downward trend starts. At wind speed 12m/s the average expected revenue of a 100 and 1000 turbine wind park is
e7,014.73 and e32,544.84 respectively. Here the 1000
turbine wind park only makes 464% of the 100 turbine
wind park, where 1000% would be expected. This trend
is comparable with the trend of the MCP. The relative
expected revenue decreases when wind park sizes increase because of the negative effect of wind park size
on the MCP and the increased imbalance risk to which
the wind park is exposed. Table 6 provides an overview
of the expected hourly revenues of wind parks with different sizes for wind speeds of 0 until 14 m/s. Figure 6
provides an overview of the revenue of a 1000 turbine
wind park as a percentage of a 100 turbine wind park,
it also includes the percentage of 10 times a 100 turbine
wind park as a benchmark.
Figure 7: Revenue per turbine with average revenue per turbine of 10
turbine park as benchmark
13
t=10
e 12.38
t=100
e 12.49
t=1100
e 8.75
t=200
e 12.46
t=1200
e 8.55
t=300
e 11.87
t=1300
e 8.22
t=400
e 11.77
t=1400
e 7.90
t=500
e 11.40
t=1500
e 7.27
t=600
e 11.38
t=1600
e 6.96
t=700
e 11.15
t=1700
e 6.67
t=800
e 10.64
t=1800
e 6.24
t=900
e 9.87
t=1900
e 6.03
t=1000
e 9.23
t=2000
e 5.84
Table 7: Power Performance Curve Data
when wind speeds rise and hence the penalized quantity
increases. As a result a genco bids more moderately and
expected revenues decrease. This is illustrated in figure
8.
The negative relation between market share and
hourly revenue per turbine illustrate the decreasing profitability of wind parks when their market share increases. This is the result of strong influence of high
wind speeds on energy pricing. The low energy prices
resulting from high wind speeds can be mitigated by
spreading the wind parks over multiple locations. By
doing this the influence of high wind speeds at one location decreases and high wind speeds affecting energy
production are more likely to occur at more points in
time than would be the case for only one wind park. It
must be noted that in this data set in 69% of the observations the wind speed forecast is 6m/s or below. The remaining 31% is above 6m/s, with only 3% being 12m/s
or higher. This indicates that wind speeds were relatively low. When wind speeds would be higher it can be
expected that the negative relation between market share
and revenue per turbine increases. This is the case, because of the negative relation between relative revenue
and wind speeds.
Figure 8: Imbalance price influence
An important remark is that the optimal revenue decreases at a wind speed of 11m/s. This would indicate
that a wind genco should bid no more than the quantity that is produced at a wind speed of 10m/s. This is
discussed further in section 6.
5.3. Influence of imbalance prices on expected revenue
The imbalance price influences the expected revenue
by penalizing the genco when it is unable to supply the
bid quantity. In order to assess how exactly the expected revenue is influenced we manipulated the imbalance price considering a genco with 1000 turbines.
Three imbalance price levels have been used to assess
this relation (upward regulation = -2, -5 and -10 times
MCP). We found a negative relation between the imbalance price and the expected total revenue. Overall the
expected revenue decreases when the imbalance price
increases. When the imbalance price increases, potential penalties for overbids rise. As a response to this
optimal bids become more reserved. The difference between expected total revenue and the optimal revenue
increases when the optimal revenue increases. Here,
optimal revenue is defined as the bid income with no
imbalance penalty. This can be explained by the risk to
which a genco is exposed when the optimal revenue increases. In general, optimal revenues increase when the
wind speed increases. This model takes into account
potential errors in the forecast. The effect of an error
on the expected amount of produced energy increases
5.4. Bid performance
Direct bids and bids based on our methodology have
been applied on actual wind speeds in a market with
an upward regulating price multiplier of -1.8. We compared the revenues from directs and the simulated bids
with the actual optimal revenue which could have been
achieved for an actual wind speed. The performance
of both bid methods decreases when forecast length increases, because of the increasing error in the forecasts.
However, in this situation results show that overall actual revenues of the direct bids are 5.5% higher than the
bids resulting from the bid methodology. Figure 9 illustrates the performance of the two bid methodologies in
a situation in which the upward regulating multiplier is
-1.8.
14
increase.
Forecast
length
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Figure 9: Bid Comparison (upward reg price: -1.8)
However, the risk to which a wind park is exposed
can be increased by increasing the upward regulating
price. When the upward regulating multiplier is -8, the
risk is increases considerably. The performances of both
methods decrease. However, the simulated bids outperform the direct bids. Figure 10 shows both methods result in negative revenues, when the wind park is exposed
to this large risk.
Direct Bids
219.99
228.09
237.72
248.73
253.99
239.75
261.55
268.35
283.03
278.33
272.56
281.40
285.37
287.50
285.61
284.97
283.52
280.97
282.67
289.50
292.93
291.52
295.05
296.99
Sim. bids
imb = -1.8
252.96
263.88
273.01
296.52
300.59
291.80
310.84
323.30
332.75
329.10
318.13
336.39
341.42
337.78
329.03
331.07
330.63
333.49
329.14
333.48
338.93
346.58
339.72
344.58
Sim. bids
imb = -8
202.37
201.87
203.90
207.17
206.28
190.04
204.42
205.65
219.49
209.78
205.01
205.16
208.35
206.45
205.36
202.53
191.53
187.43
188.83
195.31
192.31
188.51
189.65
187.79
Table 8: Bid quantities (in MW)
6. Limitations
Our simulation model assumes a market in which
supply and demand bids, other than the wind park bids
remain constant. As a result, reactions of competing
gencos to the bids of the wind park are not taken into
account. Competing bids are placed at cost price of the
genco, so the factor most strongly influencing these bids
are fuel prices. The influence of fuel prices are represented in the bids of competing gencos, however as
they are constant fluctuations in fuel prices are not considered in this model. Bids in the demand side of the
market are considered to be stable as well. This means
that both production and consumption patterns resulting
from seasonality, week/weekend days and day/night remain unused. Also, the results of the model may vary
over different market compositions; we have only tested
in one market.
For price setting a uniform pricing market is assumed,
this means that the findings may not hold for markets in
which pay-as-bid regulation applies. In the optimization, the model assumes the upward regulating price to
Figure 10: Bid Comparison(upward reg price: -8)
This can be explained by the differences in bid quantities of the two bid methods. The bid quantities of the
simulated bids adjust the bid for an expected risk which
is the result of a combination of expected error and imbalance price, increasing or decreasing its quantity accordingly. However, the direct bids do not compensate
for any risk. Average simulated bids are higher than
direct bids when risks are low, but in this situation underestimate the risk. At the other hand simulated bids
decrease when risks are high, this increases the performance of the simulated bids. Table 8 shows the average
bids of the direct bids and simulated bids. The most
critical finding here is that the value of this simulation
method increases when the imbalance prices in a market
15
be stable at the average level in Dutch market. Where,
in fact the regulation prices fluctuate strongly over time.
All wind turbines in this simulation are considered to be
at the same location, no matter the market share of wind
energy in the market. This results in a strong influence
of wind speed on both wind energy market share and the
MCP. As a result of the risk pooling effect, the immediate influence of wind speed can be expected to decrease
when the same amount of turbines is distributed over
multiple wind parks.
The data set of wind speeds in Rotterdam contains a
set of relatively low wind speeds. As a result the average amount of energy delivered to the market is relatively low even though a large number of wind turbines
are used. As a result the amount of produced energy
per turbine and the market share rise only to a limited
extend. The negative effect of market share on wind turbine profitability would be stronger when average wind
speeds would be higher. This is the case, because of the
large difference in productivity between low and high
wind speeds. This simulation would provide even more
realistic results when a dataset with higher average wind
speeds would be used, as these better represent the locations where wind parks are built. Another note related
to the data set is that the market structure is now assumed to be such that the MCP becomes very low when
the total market size becomes larger than 2215MWh.
As a result of this decrease in MCP, it may be more
profitable for wind genco to bid below its maximum capacity. However, because of the fact that a strong price
decrease as a result of a small difference in market size
is not likely to occur in an actual market, we decided not
take this effect into account.
speeds where the upward or downward the delta of produced amount of energy is large the influence of the imbalance price is strongest. The greater the size of the
wind park, the stronger this influence is. This study
proved that when imbalance prices increase it is more
profitable to place lower bids on the day-ahead market.
Also, it confirmed the added value of this bid methodology when imbalance prices are high. The relative income of wind parks decreases when the market share of
wind energy increases. Our study showed that the relative income of a wind park can be 47.2% lower when
wind energy has a market share of 25.1% than in a situation in which the wind energy market share is 0.3%.
Lastly, results show that the expected revenue decreases
when the forecast length increases, due to the increased
forecast error.
A factor which would be worth investigating is the
response of other gencos to growing wind energy market shares. The entrance of a low cost energy provider,
such as a wind park, will definitely influence the bid behavior of other gencos and would therefore increase the
quality of the outcomes. By including the behavior of
other gencos the influence of fossil fuel prices could be
included as well. Considering its strong influence on
the energy market this too would provide a valuable addition in this field of research. A second related point of
interest is the influence of large amount of wind energy
on consumer behavior. High wind speeds result in large
quantities of energy with low prices. It would be interesting to monitor and assess the change in consumption
which would result from these peaks. In the extension
of this, one could assess how these low energy prices
can be used to manipulate consumption. The adjusted
consumption patterns will likely positively influence the
expected revenue of wind parks.
Even though wind parks can be expected to be of high
value in energy markets, investors must take care in selecting their wind energy projects. In this selection it is
of great importance to take into account the level of the
imbalance prices in the market. Additionally, investors
should consider the spread of wind parks over multiple
locations, in order to mitigate the negative effect on the
MCP and optimize the value of the produced energy.
7. Conclusions and future work
Increasing market share of wind energy negatively
influences relative income of wind parks. This study
used a method to optimize the expected revenue of wind
parks to determine the influence of wind park sizes on
their income. Crucial factors in this relation are the
wind speeds and imbalance prices in the market. Wind
speeds are negatively related to the MCP and the expected revenue of wind parks. This study found that
the expected revenue of a wind park with 15.9% market share will be only 46% of the amount that would be
predicted based on the expected revenue of a wind park
with 2.5% market share. This confirms the negative relation between market share and relative income.
We found that the imbalance price negatively influences the expected revenue of wind parks. At wind
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Forecast length
t=1
t=2
t=3
t=4
t=5
t=6
t=7
t=8
t=9
t=10
t=11
t=12
t=13
t=14
t=15
t=16
t=17
t=18
t=19
t=20
t=21
t=22
t=23
t=24
RMS Emeasured
0.523089339
0.705629041
0.875926531
0.953981349
1.056341958
1.138682241
1.218881815
1.250618243
1.309439394
1.321466908
1.350401425
1.359090951
1.401155364
1.427541427
1.435217198
1.457247445
1.472541836
1.474839153
1.484460753
1.487388924
1.502779874
1.510013851
1.523917021
1.524351638
Table A.9: RMSEmeasured values used in simulation
17
AppendixB. Supply and demand bids
Supply: Generating unit loaded in economic order of the offers, which originates from Valenzuela and Wang (2011).
Demand: Random values, in line with supply quantities and prices.
Supplier
Wind Park
Hydro
Nuclear-1
Nuclear-2
Nuclear-3
Nuclear-4
Coal-155-1
Coal-350-1
Coal-155-2
Coal-350-2
Coal-155-3
Coal-350-3
Coal-155-4
Coal-76-1
Coal-350-4
Coal-76-2
Coal-76-3
Coal-76-4
Oil-100-1
Oil-197-1
Oil-100-2
Oil-197-2
Oil-197-3
Oil-100-3
Oil-197-4
Oil-100-4
Oil-12-1
Oil-12-2
Oil-12-3
Oil-20-1
Oil-12-4
Oil-20-2
Oil-20-3
Oil-20-4
Price-cap
Frequency
1
6
2
2
2
2
4
1
4
1
4
1
4
4
1
4
4
4
3
3
3
3
3
3
3
3
5
5
5
4
5
4
4
4
1
Price
1.10
5.61
5.68
5.83
5.96
18.98
19.18
19.59
20.27
20.38
21.04
21.44
21.91
22.19
22.83
26.73
30.18
101.91
105.05
109.65
111.11
116.01
118.55
120.95
124.26
128.14
130.03
146.75
165.70
166.14
170.27
237.63
240.16
999.99
Quantity
50
100
100
120
80
54.25
140
38.75
87.50
31
52.50
31
15.20
70
22.80
22.80
15.20
25
68.95
30
49.25
39.40
25
39.40
20
2.40
3.60
3.60
15.80
2.40
0.20
3.80
0.20
Inf.
Demand
Asker 1
Asker 2
Asker 3
Asker 4
Asker 5
Asker 6
Asker 7
Asker 8
Asker 9
Asker 10
Asker 11
Asker 12
Asker 13
Asker 14
Asker 15
Asker 16
Asker 17
Asker 18
Asker 19
Asker 20
Asker 21
Asker 22
Asker 23
Asker 24
Asker 25
Asker 26
Asker 27
Asker 28
Asker 29
Asker 30
Asker 31
Asker 32
Asker 33
Asker 34
Asker 35
Price
200
180
100
90
85
84
80
75
74
72
70
65
63
61
59
58
57
55
54
40
35
23
22
21
19
15
12.20
11
8
5
4
3
2
1.5
1
Quantity
100
80
50
100
30
160
150
300
200
200
20
150
55
60
30
80
20
400
30
100
200
24
16
10
300
130
150
20
60
100
50
30
20
100
200
Table B.10: Supply and demand bids
Total market
No. of suppliers
No. of demanders
Total supply quantity (MW)
Total demand quantity (MW)
34
35
1360
3725
Averages
Average supply price
Average demand price
Average supply quantity (MW)
Average demand quantity (MW)
Table B.11: Summary statistics
18
e78.22
e51.62
41.2
106.42
No wind energy situation
No. of serving suppliers
17
No. of served demanders
11
Served market size
e1031
MCP e
51.09
AppendixC. Market share calculation
Market share is determined in terms of quantity of energy delivered to the market. It is calculated as follows:
!
Qws
∗ ls
MS s =
Qtotal
s
Where, MS s = market share for wind speed s, Qws = quantity of wind park for wind speed s, Qtotal
= total quantity
s
of energy in the market for wind speed s and l s = the likelihood of wind speed s. l s is determined based on a one
month of forecasts of the used data set. The table below provides an overview of the market share calculation for a
wind park with 100 turbines (max capacity 150MW):
Wind speed
(m/s)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Total
Wind park
quantity (MW)
0
0
0
0
3.6
10.4
20.5
34.4
52.8
77.4
107.9
134.2
146
149.4
150
Total market
size
1031
1031
1031
1031
1034.6
1041.4
1051.5
1065.4
1083.8
1108.4
1138.9
1165.2
1177
1180.4
1181
Market share
0.00%
0.00%
0.00%
0.00%
0.35%
1.00%
1.95%
3.23%
4.87%
6.98%
9.47%
11.52%
12.40%
12.66%
12.70%
Likelihood of
wind speed
0.60%
3.03%
10.56%
14.12%
16.57%
14.19%
9.79%
8.56%
7.00%
5.12%
3.89%
3.12%
2.13%
0.83%
0.49%
100%
Actual market
share
0.00%
0.00%
0.00%
0.00%
0.06%
0.14%
0.19%
0.28%
0.34%
0.36%
0.37%
0.36%
0.26%
0.10%
0.06%
2.52%
Table C.12: Market share calculation
The wind speed is the speed of the wind at a certain point in time. Wind park quantity is the amount of energy
the wind park will produce at a given wind speed. The total market size is the total amount of energy traded on the
market considering the related wind park quantity. Market share is wind park quantity divided by total market size.
Likelihood of wind speed is the relative amount of observations of a given wind speed in the used data set. The actual
market share is the market share multiplied with the likelihood of wind speed.
19