Optimal band provision by wind generation in the
Spanish secondary regulation market
E.Sáiz-Marín, E. Lobato, P.Linares
Institute of Research and Tecnology (IIT)
Comillas University, Madrid, Spain
elena.saiz@iit.upcomillas.es
Abstract— Participation of wind generation in the secondary
regulation has both technical and economic interest. From the
technical point of view, a higher wind penetration can be
facilitated. From the economic standpoint, wind generators can
make a profit by providing regulation that surpasses the loss by
not selling the maximum possible amount of energy. The aim of
this paper is determining the optimal quantity of the bid
presented by the potential participation of wind generation at the
secondary regulation market. The methodology proposed is
illustrated using real data of forecasted and real wind power
production of a portfolio of 730.58 MW for year 2008 in Spain.
Keywords-component; Wind power;
frequency control; monitoring system.
ancillary
services;
I. NOMENCLATURE
PBand
Price of the secondary regulation band (€/MW)
Prodforecasted Wind forecasted production (MW)
Prodmax
Maximum power of the wind portfolio (MW)
BTotal
Total band offered by the wind producer (MW)
Qfailure
Failure of the band volume (MW) of requested
secondary regulation band.
In accordance with the Spanish market rules all variables
are hourly based.
II. INTRODUCTION
Controlling frequency has always been an essential role in
order to guarantee the secure and reliable operation of a power
system. Active power control is designed to reestablish the
necessary equilibrium between generation and demand in order
to keep the frequency of the power system within admissible
bands, and is mainly provided by generators. Active power
control includes primary, secondary (AGC) and tertiary
regulation operating within different time scopes. Generators
incur in an extra cost for providing frequency control that
should be recovered through regulated or market–based tariffs.
Within the Spanish system, primary regulation is considered a
mandatory non-remunerated service, while secondary and
tertiary regulations are driven by market-based mechanisms.
Secondary regulation in Spain is provisioned by band and
energy markets. The band market defines the power resources
for the AGC and the secondary energy used by the AGC is paid
in accordance with a price defined by the so-called tertiary
reserve market.
Wind power has experienced a wide development
throughout the world due to technological advances in wind
turbines and favorable policy incentives. Spain is the fourth
largest country in wind power installed capacity, 20676 MW of
installed capacity at the end of year 2010 [1]. The Spanish
Ministry of Industry, Tourism and Commerce considers as a
probable scenario 29000 MW of installed wind power capacity
for the year 2016 [2]. The wind production has reached 16000
MW and during some hours it represents a 50% of the total
generation [3].Within this worldwide and national framework,
wind power poses increasing challenges to the planning and
operation of power systems. Transmission System Operators
(TSO) have often been cautious regarding massive penetration
of wind energy into the grid arguing that wind power does not
provide frequency and voltage control. However, nowadays
technology developments enable the design of operation and
control strategies of wind turbines to provide such grid services
[4, 5].
Most of the literature on wind power integration into
electricity markets have looked into ways to hedge uncertain
wind energy bids into energy markets [6, 7, 8], forecast wind
production [9], value capacity credits [10], forecast reserve
requirements [11] and [12], or proposing ways of joint
operation with other technologies, among other issues.
Nevertheless, these studies did not consider the possibility of
participating on the secondary regulation market.
The participation of wind power in the secondary regulation
has both technical and economic interest. From the technical
point of view, a higher wind penetration can be facilitated.
From the economic standpoint, wind generators can make a
profit by providing regulation that surpasses the losses by not
selling the maximum possible amount of energy. In [13] an
economic assessment of the potential participation of wind
power in the Spanish secondary regulation market is
performed. It is considered that the forecasted wind production
for each hour is going to be offered to the daily market. Next a
bid is presented to the secondary regulation market. In case that
the offered band is accepted the generation schedule must be
reduced in the first intra-daily market to allow for the cleared
up power band. It should be noted that with that strategy the
wind power only reduces its program in case that exists a
possible profit of participating in secondary regulation. In the
secondary regulation market each bid has a price [€/MW] and a
volume of offer [MW]. The offer price was determined in [13].
Nevertheless, in [13] the volume of the bid was considered
deterministic, fixed at a constant percentage of the forecasted
production. This paper expands the research evaluating which
is the optimal volume of the forecasted production that should
be offered as secondary band. For this propose a methodology
using decision methods is proposed. The analysis is done for
the Spanish system. For this purpose, historic data of forecasted
and real production of a wind portfolio have been used.
Although the Spanish system has some peculiarities the
reached results are of a much wider interest.
The paper is organized as follows. Firstly the suggested
methodology for determining the optimal quantity of the
secondary band bid is illustrated in section III. The results are
explained in section IV. Finally, conclusions are drawn in
section V.
III. METHODOLOGY
This paper determines the optimal volume of the band
offer. This decision must be taken under risk due to the high
variability of the wind forecast. Moreover, the decision must be
taken the previous day and in case of being accepted it cannot
be modified. If the generator fails to comply with commitments
acquired in the secondary regulation market, it will be
penalized. In the Spanish market, if the requested band is not
provided, the band remuneration has to be returned plus a
penalty factor. The actual penalty factor is established as 50%
of the band price for each hour. Thus, the total cost of an error
on the band estimation is:
–1.5PBandQfailure
(1)
In order to determine the quantity of the bid, this paper
presents the following methodology depicted in Figure 1.
Sorted values of the forecasted production
0
10%
20%
30%
40%
50%
-3
x 10
60%
70%
80%
8
Density
6
Level of utilization of the
wind portfolio
(Prodforecasted/Prodmax)
4
2
50
100
150
200
Wind production [MW]
250
The decision maker
is risk neutral
BTotalPBand – 1.5PBandQfailure
(2)
It must be taken into account that instead of maximizing the
additional profit explained in [13] only the band profit is
maximized. This fact is due to the bid price [€/MW] assessed
in [13] guarantees that each MW presented at that price
provides an additional profit. Nevertheless, increasing the
volume of the offer affects the probability failure of the band
requirements. Thus, it is important to determine the percentile
that should be offered evaluating just the band profit. From a
technical point of view, the maximum percentage that this
technology can provide as band reserve without incurring in
dynamic instability is 40% of its production. In addition, the
case study (Spain) considers the rule that in order to participate
in the market, the offered band must be greater than 5 MW
[14]. The total band is split in upward and downward band, in
accordance with the hourly TSO requirements.
Under the second hypothesis the strategy followed will
consist on choosing the percentile that maximizes the expected
value, using the utility function that represents the risk aversion
of the agent. In this paper the utility function is obtained by
50%-50% lotteries. These lotteries are performed asking the
decision maker what is his expected value between two
possibilities with 50% of probabilities. Consequently, the
question that should be asked to the decision maker is the
following one. What do you prefer, Z € with 100% of
probability, or a lottery between X € and Y € with 50% of
probabilities each case. It should be noted that Z should be a
value between X and Y. Moreover, in case that the decision
maker is risk neutral Z is computed as Z=0.5X+0.5Y.
IV. RESULTS
300
The decision maker
is risk averse
Maximizethe
themean
band band
profitprofit
[€] taking
into
Maximize
[€] taking
into
account
penalization
account
thethe
penalization
consist on choosing the percentile that maximizes the mean
band profit [€], computed as:
Maximize
the
mean expected
thefunction
utility
Maximize
the
expected
value value using
Utility
function
OPTIMAL PERCENTILE THAT SHOULD BE
OFFERED AS SECONDARY BAND
10 20 30 40 50 60 70 80 100
Percentile
Figure 1. Graphical representation of the methodology
Firstly, the forecasted production data are classified in eight
groups. Each group means a level of utilization of the wind
portfolio (Prodforecasted /Prodmax). The first group corresponds
with data of forecasted power between 0% and 10% of the
maximum wind portfolio power, the second group contains
data between 10% and 20% and so on. For each defined group
of forecasted production, a probability density function (PDF)
of the real production is assigned. For each level of power
forecasted, this paper will evaluate which percentile of the real
production density function to offer. This analysis will be
performed under two hypotheses. The first hypothesis
considers that the decision maker is risk neutral whereas the
second hypothesis considers that the decision maker is risk
averse. Under the first hypothesis, the strategy followed will
This section presents the results obtained applying the
methodology explained in section III. The section is organized
as follows. Firstly, the decision of the band that should be
offered is computed considering that the decision maker is risk
neutral. Secondly, the decision is taken assuming risk aversion.
The results have been obtained for a wind portfolio consisting
of an aggregation of several wind farms with the following
features:
 29 farms
 1125 wind mills
 730.58 MW of total installed power
In addition, in order to perform the study, the 2008 hourly
data of real production and forecasted production (the day
before) have been used. The characteristics of this production
are:


Annual production: 1.829 GWh
Equivalent hours: 2503 h
A. The decision maker is risk neutral
The first step consists of determining the real production
distribution for each forecasted level of utilization of the wind
portfolio. In order to simplify, Figure 2 shows these
distributions for levels of utilization of 10%-20%, 30%-40%
and 60% -70% of the maximum power of the wind portfolio
respectively. It can be appreciated how the normal distribution
suits best the data when the forecasted production is between
30% and 40%. On the contrary, when the level of utilization is
high or small the distribution that best suits the data is the
Weibull.
The mean profit is obtained integrating in the probability
density function the profit obtained when the decision maker
offers a certain percentile. Figure 4 presents the band profit
obtained depending on the band offered at the secondary band
for the three probability distributions depicted in Figure 2.
-3
x 10
60%-70%
Weibull 60%-70%
30%-40%
Normal 30%-40%
10%-20%
Weibull 10%-20%
9
8
7
5
4
3
Percentile
that should be
offered 70%
700
600
Mean Profit [€]
Density
6
800
500
forecasted production
10%-20%
400
forecasted production
60%-70%
300
200
forecasted production
30%-40%
2
100
1
0
100
200
300
Production [MW]
400
500
600
Figure 2. Probability distribution of the real production for a day before
forecast between 10%-20%, 30%-40%, 60%-70% of the maximum power
respectively.
In case of being risk neutral, the strategy followed will
consist on choosing the percentile that maximizes the mean
profit. For the particular case of probability distribution
calculated for forecasted production values between 10%-20%,
Figure 3 presents the band profit (2) depending on the
percentile of the real production distribution offered. It must be
taken into account, that the band offered [MW] is a percentage
of the percentile of the real production. In this paper the
percentage of the percentile offered as secondary band is fixed
to 10%. This percentage could change in order to adjust the
program in future markets. Nevertheless, this fact is a future
research that it is not presented in this paper.
It can be appreciated how in case of offering the 10% of the
percentile 10% the profit obtained is constant. In this case the
agent never fails to comply with the commitments acquired.
However the profit is low. In case of offering 10% of the
percentile 80%, if the real production is less than this value the
agent will pay the penalty. Nevertheless, if the production is
higher than the value offered, the profit is considerable. In
Figure 3, for the particular case of offering 10% of the
percentile 40%, the region in which the agent pay the penalty
and the region in which the agent complies with the band
offered is depicted.
BTotalPBand – 1.5PBandQfailure
BTotalPBand
90
300
250
Band Profit [€]
80
70
60
50
40
30
20
PENALIZATION
200
150
10
100
Percentile offered as secondary band
350
50
0
-50
440
6
60
8
80
10
100
12
120
Band [MW]
14
140
16
160
18
180
Real production [MW]
Figure 3. Band profit depending on the percentile of the real production
distribution offered
0
20
40
60
80
100
Percentile [%]
Figure 4. Band profit obtained depending on the band offered at the secondary
band market.
In all the cases, the maximum profit is obtained when the
bid corresponds to the 70% percentile of the real production
distribution. For the rest of levels of utilizations, also the
percentile that should be offered is 70%. This fact means that
economically it is profitable to pay the penalty.
Figure 4 presents the band that should be offered by the
agent in MW depending on the forecasted production. The
secondary band that corresponds to the three probability
distributions presented in Figure 2 are depicted with solid bars
whereas the other distributions are depicted with dotted bars.
Forecasted production [%]
0
70%-80%
60%-70%
50%-60%
40%-50%
30%-40%
20%-30%
10%-20%
0%-10%
0
10
20
30
40
50
60
Secondary band offered [MW]
Figure 5. Band offered [MW], depending on the forecasted production.
Following the same analysis, Figure 6 presents how if the
penalty factor becomes higher the percentile that should be
offered will be lower, if the penalty factor is – 2PBand, the
percentile offered should be the 50% and if the is penalty factor
–3PBand the percentile offered reduces to 30%. Although Figure
6 corresponds to forecasted production values between 10%20%, the results for the rest of probability distribution are quite
similar.
1
Y=350€
The decision maker is averse to risk
The decision maker is neutral to risk
The decision maker likes the risk
0.9
0.8
0.7
Utility value
0.6
0.5
0.4
Y=350€
50%
0.3
0
1
2
3
4
5
6
Penalty factor
Figure 6. Percentile that should be offered depending on the penalization
factor, considering a forecasted production of 10%-20%.
Nevertheless, it is not reasonable to pay the penalty the
majority of the hours. In case of following this strategy the
TSO (Transmission System Operator), may not allow the agent
to provide this service.
B. The decision maker is risk averse
The level of non-fulfillment obtained in the previous
section is not admissible for the TSO. Thus, the agent could be
excluded from participating in the secondary regulation market.
This section analyzes the decision avoiding this risk. The most
common way of modeling the risk adversity is by the utility
function. Instead of determining the percentile offered by
maximizing the mean economic profit, this percentile is
obtaining by maximizing the expected utility value. In Figure 7
the utility functions for different cases are presented, (neutral to
risk, averse to risk, and when the decision maker likes the risk).
The process followed in order to obtain the utility function
independent of the behavior of the decision maker is next
explained. Firstly, the utility value 1 is assigned to the highest
profit that could be obtained (that corresponds to 350 € in
Figure 7) and the utility value 0 is assigned to the worst profit
(that corresponds to -80 € in Figure 7). Then, the utility values
that are between 0 and 1 are obtained asking the decision
maker what his expected value is. The first expected value that
is calculated is the one that corresponds to a utility value of 0.5.
This fact is due to the values that are already known and
needed to build the lotteries are the ones that corresponds to
utility values of 0 and 1. Then, the next values that are
calculated are the ones that correspond to a utility value of 0.25
and 0.75 and so on. The expected value for a utility of 0.5 is
outlined in Figure 7. The question that is asked to the decision
maker is the following one. What do you prefer, Z € with 100%
of probability, or a lottery between -80 € and 350 € with 50%
of probabilities each case. It can be appreciated that when the
decision maker is neutral to risk his expected value is
135€=0.5·(-80€)+0.5·350€. Thus, the utility function for a
decision neutral to risk is linear. When the decision maker is
risk averse, he prefers a lower certain profit. This fact is due to
the decision maker gives more value to the possible loss of
profit than to the possible gain 20€ ~ 0.768· (80€)+0.232·350€. On the contrary when the decision maker
likes the risk gives more value to the possible gain than to the
possible loss 220€~0.3·(-80€)+0.7·350€.
50%
0.2
Z=20€
0.1
0
-100
-50
0
50
X=-80€
Z=135€
100
150
Band profit [€]
Z=220€
200
X=-80€
100%
250
300
Z
350
Figure 7. Utility function of the band profit if the decision maker is neutral
adverse or likes the risk.
With these utilities functions, the percentile that should be
offered is calculated by maximizing the mean utility. In Figure
8 can be seen that in case that the decision maker is adverse to
risk (in accordance with the utility function depicted in Figure
7), it will offer as secondary band 10% of the 50% percentile.
On the contrary, if the decision maker likes the risk, he will
offer 10% of the 80% percentile. These results were obtained
for the particular case of probability distribution calculated for
forecasted production values between 10%-20%.
1
The decision maker is averse to risk
The decision maker is neutral to risk
The decision maker likes the risk
0.9
0.8
Utility value
Percentile that should be offered
80
70
60
50
40
30
20
10
0
0.7
0.6
0.5
0.4
0.3
0.2
10
20
30
40
50
60
Band profit [€]
70
80
90
Figure 8. Utility function of the band profit if the decision maker is neutral
adverse or likes the risk.
It is important to take into account that the utility function
will depend on the decision maker. This paper depicts two
examples of utilities functions that were obtained for two
different secondary regulation market expert decision makers.
Both decision makers are risk averse when the band profit is
higher than 100€. In addition, the first decision maker gives
utility value equal to cero when the band profit is negative. On
the contrary, the second decision maker gives utility value
different than zero when the band profit is negative. In
addition, both decision makers like the risk until achieving a
certain band profit (~100€).
The decision that each decision maker should make is as
follows. The decision maker 1 should offer the 30% percentile.
On the contrary the decision maker 2 will offer the percentile
40%. In both cases decision makers are risk averse and they
would offer a percentile lower than the identified in subsection
IV A.1 (percentile 70%).
1
1,2
1
1
0,8
0,8
Utility function
Utility function
[4]
2
1,2
0,6
0,4
Utility function
[6]
[7]
0
0
-0,2
Utility function
0,4
0,2
0
-100
Risk neutral
0,6
Risk neutral
0,2
-200
[5]
100
200
300
400
-200
-100
0
100
200
300
400
Band profit [€]
Band profit [€]
Figure 9. Utility functions of the band profit for two different decision
makers
[8]
V. CONCLUSIONS
[9]
This paper has proposed two methodologies for
determining the volume of the secondary band bid of wind
generation. The first methodology maximizes the band profit
whereas the second one maximizes the expected utility value.
In case of using the first methodology it has been proven that
the agent assumes a high risk due to the penalty is not well
calculated. On the other hand, in case of maximizing the
expected value the agent will assumes a risk in accordance with
his utility function.
[10]
[11]
[12]
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