A LINGUISTIC FUZZY METHOD TO STUDY ELECTRICITY

MARKET AGENTS

Santiago Garcia-Talegon

Universidad de Castilla-La Mancha

Escuela Superior de Inform

atica de Ciudad Real

Juan Moreno-Garcia

Universidad de Castilla-La Mancha

Escuela Universitaria de Ingenier

ıa T

ecnica Industrial de Toledo

Keywords:

Energy market, energy market agent, linguistic modelling, fuzzy logic.

Abstract:

The aim of this paper is to study the behavior of the agents that participate in the Spanish electricity market, for

this purpose, the data that the Market Operator provides us after the period of conﬁdentiality are analyzed. The

objective is to know the operation to simulate the offerings of blocks the some of them. Market participants

are companies authorized to participate in the electricity production market as electricity buyers and sellers.

The economic management of the electricity market is entrusted to Iberico Market Operator of Energy (MO)

(OMEL, ). A fuzzy (Zadeh, 1965) method has been created. It is based on the hour and in the matches obtained

of the previous day at this hour, and it is capable of model the behavior that is going to have an agent of the

electric market in each hour. We try with this method to deal as the agents realize the offer of production,

for it we take the information of three of them in June, 2004, the result of this work is understands better the

standard that they are still and the logic of the offers of blocks that fulﬁl the pool.

1 INTRODUCTION

The electricity market is the set of transactions arising

from the participation of the market agents in the ses-

sions of the daily and intraday markets and from the

application of the System Technical Operation Proce-

dures. Physical bilateral contracts concluded by buy-

ers and sellers are incorporated in the production mar-

ket once the daily market has closed. We will analyze

the daily market in this ﬁrst work.

The purpose of the daily market, as an integral part

of electricity power production market, is to handle

electricity transactions for the following day through

the presentation of electricity sale and purchase bids

by market participants.

For the purposes of the presentation of electricity

sale bids, a production unit is deemed to refer to any

thermal generating set, pumping station, management

unit of a hydro-electric power station or management

unit of a group of wind generators of a wind park that

unload their electricity for the same node of the net-

work.

Buyers on the electrical power market are dis-

tributors, resellers, qualiﬁed consumers and external

agents who are authorised to participate in the market

by the Ministry of Industry and Energy. Buyers may

present bids to purchase electricity on the daily mar-

ket. However, in order to do so, they must be regis-

tered with the Administrative Register of Distributors,

Resellers and Consumers and they must abide by the

Electricity Market Activity Rules. A purchasing unit

is deemed to refer to a group of network connection

nodes through which the buyer presents bids to pur-

chase electricity.

Sale and purchase bids can be made considering

between 1 and 25 energy blocks in each hour, with

power and prices offered in each block. In the case of

sales, the bid price increases with the block number;

in the case of purchases, the bid price decreases with

the block number.

Electricity sale bids presented by sellers to the mar-

ket operator may be simple or incorporate complex

conditions in terms of their content. Sellers for each

hour and production unit present simple bids, indicat-

ing a price and an amount of power. Complex bids are

those that incorporate complex sale terms and condi-

tions and those which, in compliance with the simple

bid requirements, also include technical or economic

conditions.

We will take as the agent a producer that carries

out simple offerings without restrictions, the study of

complex offerings with technical restrictions we post-

pone it for future studies.

The market operator matches electricity power pur-

394

Garcia-Talegon S. and Moreno-Garcia J. (2005).

A LINGUISTIC FUZZY METHOD TO STUDY ELECTRICITY MARKET AGENTS.

In Proceedings of the Seventh International Conference on Enterprise Information Systems, pages 394-399

DOI: 10.5220/0002532303940399

 SciTePress

chase and sale bids by means of the simple matching

method (Decree, 2000).

Figure 1: Procedure of Simple Matching.

The simple matching method 1 is the one that ob-

tains in an independent way the price in each hourly

period of programming, marginal price, as well as the

volume of electric power that is accepted for each unit

of production and acquisition for each hourly period

of programming.

The hourly marginal price is the price that obtains

as a result itself of the process of matches, and is

equal to the price of the last offering of sale that has

been necessary to assign to cover the demand. This

price is the one that charge all the producers that have

been matched and that pay all it consumers that have

been matched. This price has hourly character (Low,

1997).

The necessary information for the participation of

a session of the daily market is facilitated for the op-

erator of the market and this is the following:

• The last forecast of demand.

• Information on available units.

• Maximum capacity in the interconnections.

The estimation of the demand is a daily evolution

forecast of the periods hourly national consumption.

This it is make public for all the agents of the market.

Several times of the day, the MO puts available in-

formation on the unavailable agents. This information

is prominent since available every unit of output is

obliged to present offering of daily market. An agent

is unavailable when for some cause is incapable to

generate energy by damages or another thing.

The capacity of interconnection in the borders with

the different bordering countries is limited. There-

fore it is necessary the knowledge of the so much,

hourly maximum capacities of importing as of export,

to avoid a net ﬂow that exceed some of these limita-

tions.

The variables that in a ﬁrst study can be considered

and besides they can inﬂuence in it takes of decisions

of the agents at the moment of to carry out their of-

fering of blocks of energy and price marginal they are

the following:

• Marginal price of previous day hours.

• Minimum costs of agent production.

• Weather prediction.

• Demand prediction system.

In our method we will use the two ﬁrsts to see as

the agents behavior are.

In principle since, an economic point of view the

producer interests him to produce a minimum quan-

tity to cover cost and it will offer to a price that gen-

erate him these incomes. It will offer other blocks of

energy to an upper price so that the tendency of the

sale curve rise and obtaining high marginal prices.

The next section explain the method that we use to

model the sellers. In section 3 we apply our method

to some sellers and we interpret the obtained results.

Finally, the conclusions and futures works are shown

in section. 4. This work begins to study the variables

that can inﬂuence that an agent who takes part on the

pool obtains a few major beneﬁts being capable of

interpreting the behavior of the market. For it, it’s

necessary to model an agent’s sample to see if we ﬁnd

pattern in his behaviors.

2 OUR METHOD

To study the behavior of the sellers we propose

a method based in fuzzy logic (Zadeh, 1965) and

linguistic variables (Zadeh, 1975a; Zadeh, 1975b;

Zadeh, 1975c). We obtain a linguistic fuzzy model of

a seller agent to study its behavior. Our method needs

the hour (h variable) and the hourly margined price at

this time in the previous day (c

t−1

variable). So, we

use the hour to the one that bid block is offered and

the hourly margined price of the previous day as input

variables, and the output variable is a list formed by

pairs like the following: [amount of energy, price of

energy]. We use s and p variables to represent amount

of energy and price of energy in this pair.

A set of examples with the values of the vari-

ables and a set of sort linguistic labels (Zadeh, 1975a;

Zadeh, 1975b; Zadeh, 1975c) for some variables are

needed to obtain the fuzzy model.

The set of examples, named E, is formed by ele-

ments with the following structure:

= (h

, c

t−1,i

, s

, p

)

where h

is an integer number that has values

between 1 and 24 (the hours of the day), c

t−1,i

a real number that is the hourly margined price

at this time the previous day, s

is the amount of

offered power in this block, and ﬁnally, p

is the

sold price of this block of energy (s variable).

A LINGUISTIC FUZZY METHOD TO STUDY ELECTRICITY MARKET AGENTS

395

To simply the algorithm of our method we suppose

that for each hour and day the examples of E are con-

secutive. We use three type of variables: linguistic,

integer and real variables. The variable c

t−1

takes in-

teger values, p variable takes real values, and the vari-

ables h and c are linguistic variables. The linguistic

labels of the linguistic variables are deﬁned a priori, i.

e., before our method is applied.

An ordered set of labels, named C, is deﬁned for

the c

t−1

variable. Its structure is given by the follow-

ing expression:

C = {very low, low, f ew low, medium, low high,

high, very high}

Figure 2 shows the trapezoidal labels used for the

t−1

variable, where V L is ’very low’, L is ’low’, F L

is ’few low’, M D is ’medium’, LH is ’low high’, H

is ’high’ and V H is ’very high’.

Figure 2: Ordered set of labels C for the c

t−1

variable.

This linguistic variable is used to represent the

hourly margined price at the previous day. We rep-

resent the price of sale of the energy with label by

means of variables linguistic that mean the following:

’Very low’ This label is used when the sale price is

very cheap. It takes values between 0 and 1, and,

normally, this label is not used in the daily market

because this price is never obtained.

’Low’ This label takes values between 0.75 and 2.

When the energy is sold to this price, it is cheap.

This sale price is frequently used from 3:00 or 4:00

until 5:00 or 6:00.

’Few low’ This label takes values between 1.75 and

3. It is a sale price a little cheap, and it is a price

frequently used during the day.

’Medium’ This label takes values between 2.75 and

4. This is the normal sale price, and it is a price

frequently used during the day.

’Low high’ This label takes values between 3.75 and

5. Normally, from 8:00 or 9:00 to 22:00 or 23:00

the energy price is this or the next label.

’High’ This label takes values between 4.75 and 6.

Normally, from 8:00 or 9:00 to 22:00 or 23:00 the

energy price is this or the previous label.

’Very high’ This label takes values between 5.75 and

10. In the daily market this price is never obtained.

An ordered set of labels, named P , is deﬁned for

the p variable. Its structure is given by the following

expression:

P = {not important, very cheap, cheap, little

cheap, norm, little expensive, expensive, more

than expensive, very expensive}

Figure 3 shows the trapezoidal labels used for the

variable, where N I is ’not important’, V C is ’very

cheap’, C is ’cheap’, LC is ’little cheap’, NR is

’norm’, LE is ’little expensive’, E is ’expensive’,

MT E is ’more than expensive’ and V E is ’very ex-

pensive’.

Figure 3: Ordered set of labels P for the p variable.

This linguistic variable is used to represent the of-

fered price in each energy block. Every deﬁnite label

means:

’Not important’ This label is used when the hourly

margined price is not important for the seller, that

is, the seller wants to sell the energy block be which

is the price. Normally, This label appears at least in

some block offered by the producers. This label

takes values from 0 to 1.

’Very cheap’ This label takes values from 0.75 to 2.

This label is used when the seller wants to sell the

energy to a minimum price. The energy blocks to

this price are frequently sold.

’Cheap’ This label is used when the seller wants to

sell the energy to a minimum price. The energy

blocks to this price are frequently sold when the

time is between 1:00 or 2:00 to 5:00 or 6:00. This

label takes values from 1.75 to 3.

’Low cheap’ This label takes values from 2.75 to 4.

The energy blocks to this price are frequently sold

when the time is between 20:00 or 21:00 to 24:00

or 1:00. This label is used to sell energy blocks at

these times.

’Norm’ or ’Few expensive’ These labels are used

when the energy market reaches the maximum

price, that is, the hourly margined price is rarely

more than 6. Normally, ’few expensive’ is the

biggest label obtained in the daily energy market.

When one productor seller sells energy to these

prices, he wants to obtain a great beneﬁt.

’Expensive’ to ’Very expensive’ These three labels

rarely are obtained in the daily energy market.

When a seller agent offers energy blocks to this

price, he doesn’t want these blocks, only if occurs

a ”special situation” like ’a powerful agent is dam-

aged’, ’there is necessary a lot of energy’, etc.

The order of the labels in C and P is based on the

defuzziﬁcation method named middle of maximum

ICEIS 2005 - ARTIFICIAL INTELLIGENCE AND DECISION SUPPORT SYSTEMS

396

(MOM ) (W. V. Leekwijck, 1999). Our method ob-

tains a system of fuzzy rules formed by rules with the

following structure:

IF (h is X) AND (c

t−1

is C

) THEN

[[s

is S, p

is P ],

is S, p

is P ],

. . .

is S, p

is P ]]

where X takes integer values, c

is the linguis-

tic variable that takes values from C, S is a real

variable and P is the linguistic variable that takes

values from P.

A real example of a rule obtained by using our

method is the following:

IF (2) AND (’Medium’) THEN

[[180,

′

not important

′

[50,

′

very cheap

′

[50,

′

cheap

′

[50,

′

cheap

′

[20, very expensive]]

As you can see, the output of the rule is a list of

pairs [amount of energy, price of energy]. Each pairs

of the list understands it better because we use lin-

guistic labels for the P variable. This rule can be in-

terpreted as the following text:

”When the hourly margined price in the previ-

ous day is ’medium’ and it is the second hour

of the day, then the seller agent sells 180 energy

units be which is the hourly margined price in the

current day, 50 energy units when the energy is

’very cheap’, two blocks of 50 energy units when

the energy is ’cheap’ and 20 energy units when

the energy is ’very expensive’”

When we study the Spanish electric market, we ob-

serve that when the energy is ’very cheap’ or ’cheap’

it is very possible that the offered blocks at this price

are sold, and when the energy is ’very expensive’ the

offered blocks at this price are never sold. Thus, in

this case, we can conclude that the productores seller

wants to sell one block of 180 energy units and three

blocks of 50 energy units because the offered energy

has a null price in the ﬁrst case and a price that it is

very possible to sell in the second case; and it doesn’t

want to sell a block of 20 energy units because The

block has a price at which the energy never sells.

Algorithm 1, it shows the code used to obtain the

linguistic fuzzy model. As you can see, the algorithm

has three inputs: the set of examples E, the ordered

set of labels C and the ordered set of labels P . The

output is a linguistic fuzzy model named M.

The idea of this algorithm is to be crossing the ex-

amples in E. To obtain the items that compound the

antecedent (the hour and the hourly margined price);

and the items that compound the consequent (a list

of pairs like [amount of energy, price of energy]), for

this purpose, some consecutive iterations of the for

loop are used (so many iterations like energy blocks

are offered for the hour that the rule represents). Af-

ter that, the rule that represents this hour is calculated.

This process is repeated while there is some example

in E. As you can see, the algorithm obtains a rule for

each hour.

INPUTS

Set of examples E

Ordered set of labels C

Ordered set of labels P

OUTPUT:

A linguistic fuzzy model M

ALGORITHM 1:

1. M =< >

2. C

t−1

= ObtainLabel(c

t−1,1

, C)

3. p = O btainLabel(p

, P )

4. P airs = [ [s

, p] ]

5. for i = 2 to |E| do

6. if h

is equal to h

i−1

then

7. p = ObtainLabel(p

, P )

8. P airs = P airs + [s

, p]

9. else

10. R = CreateRule(h

i−1

, C

t−1

, P airs)

11. M = AddRule(R)

12. C

t−1

= ObtainLabel(c

t−1,i

, C)

13. p = ObtainLabel(p

, P )

14. [ [s

, p] ]

15. EndIf

16. EndFor

Now, we show the behavior of the algorithm line to

line. M is assigned to empty (

′

< >

′

) in the line 1.

Line 2, we calculates the label C

t−1

, for this purpose,

it is used the following equation:

t−1

= max

t−1,i

), ∀C

∈ C (1)

That is, the label of C that has the maximum mem-

bership grade to c

t−1,i

of e

Line 3 calculates the label p, for this purpose, it is

used the following equation:

p = max

(pi), ∀P

∈ P (2)

That is, the label of P that has the maximum mem-

bership grade to p

of e

In the algorithm, the list of pairs is denoted as Pairs.

In line 4, the ﬁrst pair [amount of energy, price of en-

ergy]), that represents the ﬁrst offered block, is ob-

tained and added to Pairs. Its ﬁrst component is as-

signed to s

, and the second one is the label p (calcu-

lated in line 3).

After that, a for loop is used to go through the ex-

amples in E pointed by the index i (line 5). The sen-

tences of the for loop are the sentences in the lines

from 6 to 16. If h

is equal to h

i−1

, it means that the

A LINGUISTIC FUZZY METHOD TO STUDY ELECTRICITY MARKET AGENTS

397

hour of the previous example is equal to the hour of

the current example, that is, the examples i and i − 1

represent energy blocks offered for the same time. In

this case, the algorithm adds the new pair to the list

of pairs Pairs. The sentences of the lines 7 and 8 are

used for this purpose. The sentence in the line 7 cal-

culate the label p to represent the offered price for the

current block by using the equation 2. The sentence

in the line 8 adds the pair to the list Pairs.

If h

is not equal to h

i−1

, it means that all consecu-

tive energy blocks offered for the same day and hour

has already been added to Pairs, thus, the rule that

represents the hour h

i−1

(R) is added to the model M

(lines 10 and 11), and it is begun to calculate the rule

that represent the hour h

(lines 12, 13 and 14). The

meaning of the lines from 10 to 14 are the following:

Line 10 The rule R is calculated by using the hour

i−1

and the label C

t−1

(the label to represent the

hourly margined price at h

i−1

in the previous day)

for the antecedent, and the list of pairs Pairs for the

consequent.

Line 11 R is added to the model M .

Line 12 The label C

t−1

is calculated by using the

equation 1.

Line 13 The label p is calculated by using the equa-

tion 2.

Line 14 Pairs is initialized at [ [s

, p] ]

Finally, the last sentences close the for loop and the

if sentence.

3 TESTING THE METHOD AND

THE INTERPRETATION OF

THE OBTAINED RESULTS

We apply the proposed method to the data of three

seller agents in the ﬁrst ﬁve days of the month of June

of 2003 to test our method. The producing agents are

named ABO1, ALL1 and V IES.

Our method obtains 24 rules for each day (one rule

for each hour of the day), so, the obtained models for

these 5 days are formed by 120 rules. For each hour,

our method obtains 5 rules, one rule for each day.

Now, we explain the interpretation of the obtain

model for each one of the producing agents:

ABO1 This agent maintains the sold energy at 350

energy units during all hour of the day, although it

changes some energy unit from a block to another

block hour at hour. It can be observed that the night

hours the energy offered is smaller than the day

hours. It carries out three types of offered blocks: a

ﬁrst block to prices qualiﬁed with the label Not Im-

portant is offered so that enter the matches; three

blocks to prices with labels qualiﬁed among ’’very

cheap’ or ’cheap’ are offered so that it wants a min-

imum value in the matches; and a last energy block,

labeled as ’’very expensive’, it is offered to a price

that the energy market has never obtained. Thus,

we can conclude that this agent offers three set of

blocks: a ﬁrst one that it will always be accepted;

a second one that it will be accepted when a mini-

mum price has been gotten; and a third one that it

will never be accepted.

ALL1 This agent maintains the sold energy at 364.9

energy units during all hour of the day, although

it changes some energy unit from a block to an-

other block. It can be observed that the night hours

the energy offered is smaller than the day hours.

It carries out three types of offered blocks: a ﬁrst

block to prices qualiﬁed with the label Not Impor-

tant; others blocks to prices with labels qualiﬁed

among ’very cheap’; and a last energy block, la-

beled as ’very expensive’. From 8:00 or 9:00 until

23:00 or 24:00, this agent only offers the following

two blocks: [335.0, ’not important’], [11.9, ’very

expensive’], that is, during these times, 335 energy

units will always be accepted and 11.9 energy units

will never be accepted. Thus, we can conclude that

this agent offers three set of blocks: a ﬁrst one that

will always be accepted; a second one that will be

accepted when a minimum price has been gotten;

and a third one that will never be accepted.

V IES This agent do not maintains the sold energy at

a constant number of energy units during all day. It

only offers the energy units that want sell to prices

qualiﬁed with the label Not Important. It can be

observed that the night hours the energy offered is

smaller than from the day hours. We can conclude

that this agent offers only the energy units that want

sell, for this purpose, it labels to ’not important’ the

only block that it offers.

As behavior common to all the studied agents, we

can say the following:

1. The hourly margined price is similar at the same

hour of the consecutive days.

2. All studied agents bids each days the same number

of blocks at the same hour. The amount of energy

is very similar for the same hour at different days.

3. The ﬁrst blocks to prices qualiﬁed with the label

not Important are offered so that enter the matches.

4. Blocks to prices with labels qualiﬁed among very

cheapor cheap are offered to obtain a minimum

price.

5. The tendency is that the last blocks have some

prices qualiﬁed with labels of expensive or very ex-

pensive.

ICEIS 2005 - ARTIFICIAL INTELLIGENCE AND DECISION SUPPORT SYSTEMS

398

6. Along the day, the agents change the amount of

energy from blocks labeled with labels not equal

to ’not important’ to the block labeled with labels

equal to ’not important’.

7. The agents doesn’t study the offered energy blocks

in detail. They present similar offers hour at hour.

A situation is described in which the agents always

offer a minimum to function in each hour to price

’not important’. From this point different tendencies

are seen, there are agents that directly offer blocks

to prices that in the historic one of marginal prices

never they have been reached, this signiﬁes that they

do not enter the matches, and other they offer to prices

that are going to enter. We interpret it since really the

agents have to maintain a most minimum operation

by technical restrictions of the head ofﬁces for that

reason be offered to ’not important’. The behavior is

different from here but is seen that there is not a ten-

dency to adjust the offering to the marginal price that

have greater possibilities to be. This due to that itself

not a study of forecast of the marginal price is done.

Also due to that the agents try with these high prices

in the last blocks to rise the tendency of the curve and

consequently to rise the point of cut of the curves of

sale and purchase.

4 CONCLUSIONS AND FUTURE

WORKS

For the ﬁrst time methods of fuzzy logic are in use

for interpreting the behavior of the producing agents

by means of a system of fuzzy rules that they allow

us to visualize better like it organizes his production

throughout the day, hereby the decisions will be able

to be analyzed better to taking. We can conclude of

the carried out studies that the agents maintains the

sold energy units during all hour of the day, although

it changes some energy unit from a block to another

block hour at hour. As we thought, the energy uses in

the night is cheaper than the energy in the day hours.

The agents offer set of energy blocks with different

purpose. The ﬁrst set is offered to produce a minimum

quantity to cover cost and it will offer to a price that

generate him these incomes. Other set of blocks are

offered to sell energy when the hourly margined price

has a minimum value. These blocks permit to the

seller agent to obtain beneﬁts. It offers other blocks

of energy to an upper price so that the tendency of the

sale curve rise and obtaining high marginal prices.

The agents doesn’t study the offered energy blocks

in detail. They present similar offers hour after hour

and day after day.

As future works, we can apply the presented

method but using another variables like the last fore-

cast of demand, information on available units, min-

imum costs of agent production, weather prediction

or demand prediction system. A seller agent can be

considered as a ”cyclical dynamic systems” (day af-

ter day). We can apply fuzzy technics that model

dynamic systems like (J. Moreno-Garcia, 2003a) and

(J. Moreno-Garcia, 2003b).

Seems clear that the model of agents is different

and differs depending on the volume of production or

sale of the agent. We should deepen in the analysis

of the market that permit us by means of temporary

systems of analysis to predict the marginal price of

the next day.

In this manner we would be able model the agent

so that we will use this value as entrance in his system

of offerings.

ACKNOWLEDGEMENTS

This work has been funded by the Spanish Ministry of

Science and Technology and Junta de Comunidades

de Castilla-La Mancha under Research Projects ”DI-

MOCLUST” TIC2003-08807-C02-02 and PREDA-

COM PBC-03-004.

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