Introduction to Electricity Markets

8/9/2019 Introduction to Electricity Markets

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Pricing Electricity in Pools with Wind Producers 1

1. Introduction To Electricity Markets

In economic terms, electricity (both power and energy) is a commodity capable

of being bought, sold and traded. An electricity market is a system for effecting

purchases, through bids to buy; sales, through offers to sell; and short-term

trades, generally in the form of financial or obligation swaps. Bids and offers

use supply and demand principles to set the price. ong-term trades are

contracts similar to power purchase agreements and generally considered

pri!ate bi-lateral transactions between counterparties. "holesale transactions

(bids and offers) in electricity are typically cleared and settled by the marketoperator or a special-purpose independent entity charged e#clusi!ely with that

function. $arket operators do not clear trades but often re%uire knowledge of

the trade in order to maintain generation and load balance. &he commodities

within an electric market generally consist of two types' power and energy.

ower is the metered net electrical transfer rate at any gi!en moment and is

measured in megawatts ($"). nergy is electricity that flows through a

metered point for a gi!en period and is measured in megawatt hours ($"h) *+.

$arkets for energy-related commodities trade net generation output for a

number of inter!als usually in increments of , + and / minutes. $arkets for

power-related commodities re%uired and managed by (and paid for by) market

operators to ensure reliability, are considered ancillary ser!ices and include such

names as spinning reser!e, non-spinning reser!e, operating reser!es, responsi!e

reser!e, regulation up, regulation down, and installed capacity. In addition, for

most ma0or operators, there are markets for transmission congestion and

electricity deri!ati!es such as electricity futures and options, which are acti!ely

traded. &hese markets de!eloped as a result of the restructuring of electric

power systems around the world. &his process has often gone on in parallel with

the restructuring of natural gas markets.

lectricity is by its nature difficult to store and has to be a!ailable on demand.

1onse%uently, unlike other products, it is not possible, under normal operating

conditions, to keep it in stock, ration it or ha!e customers %ueue for it.

2urthermore, demand and supply !ary continuously. &here is therefore a

physical re%uirement for a controlling agency, the transmission system operator ,

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http://en.wikipedia.org/wiki/Electricity

http://en.wikipedia.org/wiki/Commodity

http://en.wikipedia.org/wiki/Short-term_trading


http://en.wikipedia.org/wiki/Power_(physics)

http://en.wikipedia.org/wiki/Energy_(physics)

http://en.wikipedia.org/wiki/Megawatt

http://en.wikipedia.org/wiki/Kilowatt_hour

http://en.wikipedia.org/wiki/Ancillary_services_(electric_power)

http://en.wikipedia.org/wiki/Operating_reserve

http://en.wikipedia.org/wiki/Nameplate_capacity

http://en.wikipedia.org/wiki/Derivative_(finance)

http://en.wikipedia.org/wiki/Futures_contract

http://en.wikipedia.org/wiki/Option_(finance)

http://en.wikipedia.org/wiki/Natural_gas


http://en.wikipedia.org/wiki/Transmission_system_operator

http://en.wikipedia.org/wiki/Commodity



http://en.wikipedia.org/wiki/Power_(physics)

http://en.wikipedia.org/wiki/Energy_(physics)

http://en.wikipedia.org/wiki/Megawatt

http://en.wikipedia.org/wiki/Kilowatt_hour

http://en.wikipedia.org/wiki/Ancillary_services_(electric_power)

http://en.wikipedia.org/wiki/Operating_reserve

http://en.wikipedia.org/wiki/Nameplate_capacity

http://en.wikipedia.org/wiki/Derivative_(finance)

http://en.wikipedia.org/wiki/Futures_contract

http://en.wikipedia.org/wiki/Option_(finance)

http://en.wikipedia.org/wiki/Natural_gas


http://en.wikipedia.org/wiki/Transmission_system_operator





to coordinate the dispatch of generating units to meet the e#pected demand of

the system across the transmission grid. If there are a mismatch between supply

and demand the generators speed up or slow down causing the system

fre%uency (either / or / hert3) to increase or decrease. If the fre%uency falls

outside a predetermined range the system operator will act to add or remo!e

either generation or load.

In addition, the laws of physics determine how electricity flows through an

electricity network . 4ence the e#tent of electricity lost in transmission and the

le!el of congestion on any particular branch of the network will influence the

economic dispatch of the generation units. &he scope of each electricity market

consists of the transmission grid or network that is a!ailable to the wholesalers,

retailers and the ultimate consumers in any geographic area. $arkets maye#tend beyond national boundaries.

1.1. Day-Ahead Electricity Market

5ay-Ahead-$arket (5A$) is a physical electricity trading market for deli!eries

for any6some6all + minute time blocks in 78 hours of ne#t day starting from

midnight. &he prices and %uantum of electricity to be traded are determined

through a double sided closed auction bidding process. &he operations are

carried out in accordance with the 9rocedure for scheduling of collecti!e

transactions: issued by the 1entral &ransmission tility (<1I), 91=1 (>pen

Access in Inter-?tate &ransmission) =egulations, 7//@, as amended from time to

time and the Bye-aws, =ules and Business =ules of the #change.*7

&rading rocess 2low

Bidding

+. articipants enter bids for sale or purchase of power for deli!ery on thefollowing day. (&+ day)

7. Bids for a total of blocks of + minute each can be entered.

C. Bidding session' +/// hrs. - +7// hrs.

8. Bids can be single and6or block including linked bids'

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http://en.wikipedia.org/wiki/Electric_power_transmission

http://en.wikipedia.org/wiki/Frequency

http://en.wikipedia.org/wiki/Hertz

http://en.wikipedia.org/wiki/Physics

http://en.wikipedia.org/wiki/Electrical_network

http://en.wikipedia.org/wiki/Economic_dispatch

http://en.wikipedia.org/wiki/Electric_power_transmission

http://en.wikipedia.org/wiki/Frequency

http://en.wikipedia.org/wiki/Hertz

http://en.wikipedia.org/wiki/Physics

http://en.wikipedia.org/wiki/Electrical_network

http://en.wikipedia.org/wiki/Economic_dispatch




a. ?ingle bids' +-$inute bids for different price and %uantity pairscan be entered through this type of order. artial e#ecution of the

bids entered is possible.

b. Block bids' =elational Block Bid for any +-min block or series of +-min blocks during the same day can be entered. Although no partial e#ecution is possible i.e. either the entire order will beselected or re0ected.

. &he bids so entered are stored in the central order book. &he bids enteredduring this phase can be re!ised or cancelled till end of bid call period(i.e.+7// hrs. of trading day)

$atching

• At the end of the bidding session, bids for each + minute time block are

matched using the price calculation algorithm. (a!ailable in ID bye-laws)

• All purchase bids and sale offers are aggregated in the unconstrained

scenario. &he aggregate supply and demand cur!es are drawn on rice-Euantity a#es. &he intersection point of the two cur!es gi!es the marketclearing price ($1) and market clearing !olume ($1F) corresponding

to price and %uantity of the intersection point.

• $1 and $1F are determined for each block of + minutes as a function

of demand and supply which is common for the selected buyers andsellers.

• ?elected members are intimated about their partially or fully e#ecuted

bids and other trade related information.

•

By +C// hrs, transmission corridor re%uired to fulfill successfultransactions are sent to G51.

&he e#ample below illustrates price calculation. Assume the price tick as below'

2or the sake of simplicity we assume only C portfolios are entered. &he %uantityentered by each portfolio A, B and 1 for the specific price tick is as shown

below'

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&he algorithm will then add the entire purchase %uantum and sell %uantum after the bidding session and look for a solution where the net transaction is 3ero i.e.the buy %uantum is e%ual to the sell %uantum.

&he demand-supply graph in such scenario is shown below'

&ransmission corridor and funds a!ailability

• reliminary $1 and $1F are used to calculate the pro!isional

obligation of the selected participants and the pro!isional power flow.

• 2unds a!ailable in the settlement accounts of the participants are !erified

based on the pro!isional obligation.

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• In case of insufficient funds in the account, the bids entered by such a

participant are deleted.

• =e%uired corridor capacity and pro!isional power flow is sent to G51

for scrutiny and corridor allocation is re%uisitioned based on a!ailability.

• By +8// 4rs, G51 re!erts with actual transmission corridor a!ailability

during all + minute time blocks across congestion prone bid areas.

=esults

• Based on the reser!ed transmission capacity intimated by G51, ID

recalculates $1 and $1F as well as area clearing price (A1) and area

clearing !olume (A1F).

• A1 is used for the settlement of the contracts. >n receipt of final results,

obligations are sent to the 1learing Banks for ay In from buying$embers at +8.C/ hrs and the bank is asked to confirm the same.

1onfirmation

• 2inal results for confirmation and application for scheduling of collecti!e

transactions are sent to G51.

• G51 sends the details of the schedule to respecti!e ?51s.

?cheduling

• =51s 6?51s incorporate 1ollecti!e &ransactions in the 5aily

schedule.

• A scheduled transaction is considered deemed deli!ery.

• 5e!iations from schedules are dealt under I or 5e!iation ?ettlement or

Imbalance ?ettlement regulations. &he =egional ntities (those connectedat I?&? networks) are go!erned by 1=1 =egulations and mbeddedntities (those connected to state transmission or distribution network)are go!erned by respecti!e ?tate 1ommission:s regulations.

1.2. Balancing Market !eration

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&rading on the Balancing $arket is implemented through a platform for

collecting purchase and sale bids for electricity through which the ?ystem

>perator (?) buys and sells electricity intended for the settlement of

imbalances in the electricity system. &rading on the Balancing $arket is carried

out together with Intra-day trading, that is, one hour after the closure of the

latter and until actual supply of the product. All companies included in the

Balance ?cheme of the electricity market and which acceded to trading on the

Balancing $arket and Intra-day trading can participate in trading *C.

2. "o-!ti#i$ing Energy and %eser&e "a!acity

In order to ensure that enough balancing resources are a!ailable during the real-time operation of the power system, the system operator allocates reserve

capacity in ad!ance. In practice, the procurement and scheduling of reser!e

capacity implies operating the system at less than its full capacity, while its use

or deployment usually translates into the redispatch of units pre!iously

committed in the day-ahead market, the !oluntary curtailment of loads, and6or

the %uick start-up of e#tra power plants to co!er une#pected shortages of energy

supply in real time. &here e#ist two schools of thought on how reser!e should

be traded in electricity markets. >n the one hand, reser!e capacity may be sequentially procured in a series of auctions run once the day-ahead energy

dispatch has been determined. &hese auctions are organi3ed to procure reser!es

with different acti!ation times. &he rationale behind this approach is that the

free capacity that has not been successfully placed in one market can then be

offered in the following auctions where the re%uired acti!ation time for the

traded reser!e is not as demanding. 1onse%uently, reser!e capacity offers that

are successful in one market are not considered in the subse%uent ones *8.

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>n the other hand, energy and reser!e may be simultaneously procured in the

same auction using a co-optimi3ation algorithm that captures the strong

coupling between the supply of energy and the pro!ision of reser!e capacity.

&he following illustrati!e e#ample ser!es to get a more intuiti!e understanding

of this coupling.

2.1. 'e(uential 'ettle#ent

1onsider an electricity market that solely includes two power producers, A and

B. ach of these producers runs a power plant with a capacity of +//$".

roducer A offers to sell energy at H+/ / $"h, while producer B does it at

HC/ / $"h. A demand of +C/ $"h is to be supplied. Additionally, with the aim

of dealing with unforeseen e!ents, the system operator estimates that 7/ $" of reser!e capacity are re%uired. roducer A is willing to pro!ide reser!e at no

cost, whereas producer B offers reser!e capacity at H7 / $".

&o start with, let us suppose that energy and reser!e capacity are sequentially

settled in this order. &hus, the energy-only dispatch is first determined as

follows

$in.10 P A+30 PB

s.t. P A+ PB=130,

0≤P A≤100,

0≤PB≤100,

where P A and

PB are the amounts of energy sold by producers A and B,

respecti!ely. >ptimi3ation problem is tri!ial, and its solution is gi!en by

P A

¿

=¿ +// $"h and PB

¿=¿

C/ $"h. &he clearing (marginal) price for

energy, which is defined as the dual !ariable of constraint, results in HC/ / $"h.

>nce the energy dispatch is determined, the reser!e capacity market is cleared

as follows

$in.0 R A+25 RB

s.t. R A+ R B=20,

0≤R A≤100− P A¿

,

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0≤RB≤100− PB,

¿

"here R A and

RB are the amounts of reser!e capacity sold by producers A

and B, respecti!ely. Gote that the reser!e scheduling takes the energy dispatch

{ P A

¿, PB

¿ } as input. &he solution to problem is also tri!ial and is gi!en by

R A

¿

/ and RB

¿

7/$". &hat is, since producer A has been dispatched at full

capacity in the energy market, reser!e needs are entirely co!ered by producer B.

&hus, the total system operation costs TC seq

, including both the procurement

costs of energy and reser!e capacity, are computed as

TC seq=10 P A

¿ +30 PB¿+0 R A

¿ +25 RB¿

H78//

&he clearing (marginal) price for reser!e capacity is H7 / $", which is the

!alue taken by the dual !ariable associated with the reser!e re%uirement

constraint. &herefore, the profits made by producers A and B, respecti!ely,

under the se%uential market organi3ation are calculated as follows

profit Aseq=(30−10 ) P A

¿ +(25−0 ) R A¿=$2000

profit Bseq=(30−30 ) PB

¿+(25−25 ) RB¿=0

2.2. 'i#ultaneous Trading

et us now consider that energy and reser!e capacity are simultaneously traded

in the same auction. &o this end, both commodities are 0ointly dispatched using

optimi3ation problem below, which minimi3es the total system operation costs.

$in.10 P A+30 PB+0 R A+25 RB

s.t. P A+ P B=130,

R A+ RB=20 ,

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must increase it by the same amount. &his action does not in!ol!e any

additional reser!e cost, but increases the cost of the energy dispatch by H7/.

2.). Pro*a*ilistic A!!roach

1onsider again the electricity market described in #ample. =ecall that this

market is a duopoly made up of producers A and B, in which reser!e

re%uirements are estimated by the system operator at 7/ $". &he reason for

this estimate is that the electricity demand may increase from +C/ $"h to +/

$"h without prior notice, and the system operator decides to protect the

electrical infrastructure against this une#pected growth of consumption by

scheduling 7/ $" of reser!e capacity in ad!ance. &he probability of this

happening is, though, relati!ely small, specifically /./. et us now rethink this

problem using a probabilistic approach. 2or this purpose, note that, in response

to a sudden increase of load, three different balancing actions may be taken,

namely

+. roducer A may increase its production from P A to

P A+r A . &he energy

increaser A is obtained from the reser!e capacity

R A scheduled beforehand

for this producer

7. ?imilarly, producer B may increase its production from PB to

PB+rB . &he

energy increaserB results from deploying the reser!e capacity

RB

dispatched beforehand for this producer.

C. A part of the load increase, Lshed

, may be simply not supplied. &his action,

howe!er, entails huge economic losses, which are estimated at H+/// / $"h.

Based on these three possible balancing measures, the energy-reser!e dispatch

problem can be reformulated as follows

M ∈.10 P A+30 PB+0 R A+25 RB+0.05 (10r A+30 rB+1000 Lshed )

s.t.

r A+rB+ Lshed=20,

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r A≤R A , rB≤RB ,

P A+ R A≤100,

PB+ RB≤100, Lshed

≤20,

P A , PB ,R A ,RB , r A , rB , Lshed

≥0,

&he solution to this problem is P A

¿

@/ $"h, R A

¿

7/ $", PB

¿

/

$"h, RB

¿

/ $",r A¿

7/ $"h, rB

¿

/, andshed∗¿

L¿ /. &herefore,

the energy and reser!e capacity dispatches, i.e., { P A

¿, PB

¿ }∧{ R A ,

¿ R B

¿ } , respecti!ely,

obtained from problem are the same as those resulting from problem in

pre!ious #ample &his is 0ust pure coincidence. Actually, these two models are

different inasmuch as the following

+. &his $arket-clearing problem takes into account e#plicitly both the

probability of occurrence of the 7/-$"h demand increase and its potential

impact on system operation costs through the utili3ation of balancing resources.

Indeed, the e#pression 0.05 (10r A+30r B+1000 Lshed

) represents the e#pected cost

incurred at the balancing stage. &his cost component is, in contrast, ignored in

pre!ious dispatch model

7. &he reser!e dispatch yielded by market-clearing model is directly determined

based on how !aluable this reser!e is to consumers by including the cost of the

e#pected load not ser!ed in ob0ecti!e function, where this cost appears as

0.05 (10 r A+30rB+1000 Lshed) . 2or the particular instance sol!ed abo!e, this cost

is e%ual to 3ero, meaning that consumers are willing to pay for 7/ $" of

reser!e capacity that can be deployed to satisfy a potential consumption

increase, if needed. In contrast, if the probability of occurrence of the 7/-$"h

demand growth is small enough, say /.//, or the !alue of lost load is

sufficiently low, e.g., H+//6$"h, no reser!e capacity is dispatched, i.e.,

{ R A ,

¿ RB

¿ }={0,0} and the whole demand increase is shed instead ( Lshed

7/

$"h), if it comes to it.

C. "hile the 7/-$" reser!e re%uirement enters pre!ious dispatch model as aninput in constraint, reser!e needs are an outcome of market-clearing in this

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model In fact, there is no reser!e re%uirement constraint in this problem.

Instead, we enforce constrain, in which all the !ariables in!ol!ed, namely,

r A , rB

and Lshed

, represent balancing energy %uantities. But if there is no such

reser!e re%uirement constraint, how do we determine the reser!e capacity priceJ

"e will get to the answer of this %uestion in due time.

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). Introduction to 'tochastic Progra##ing

nknown data abound in decision-making problems in the real world. &his lack

of perfect information is common in problems belonging to different knowledge

areas such as engineering, economics, finances, etc. 5ecision-making problems

in electricity markets are no e#ception. In fact, uncertainty is present in most

decision-making problems faced by electricity market agents. 2or e#ample,

electricity prices are unknown when agents ha!e to submit their offers or bids to

the pool. ?imilarly, at the time of procuring the energy needed to supply client

loads, retailers do not know precisely the electricity demands of these clients.

4owe!er, decisions need to be made e!en with lack of perfect information. &his

is what moti!ates the use of stochastic programming models for decision

making under uncertainty *.

$ost decision-making problems can be ade%uately formulated as optimi3ation

problems. If the input data of an optimi3ation problem are well-defined and

deterministic, its optimal solution (decision) is achie!ed by sol!ing the problem.

&he decision is then implemented to attain the best outcome. 4owe!er, more

often than not, the input data are uncertain but describable through probability

functions. In such a situation, it is not clear how the decision-making problem

should be formulated. >ne possibility is to substitute the uncertain input data

(describable through probability functions) by their corresponding e#pected

!alues, which results in a well defined and deterministic optimi3ation problem.

4owe!er, sol!ing such a problem may lead to a solution that once implemented

does not result in the best outcome. Alternati!ely, the probability distribution of

input data can be appro#imated by a collection of plausible sets of input data

with associated probabilities of occurrence. 2or instance, three sets of input data

with three !alues of probability of occurrence adding to +.

&hen a stochastic optimi3ation problem can be formulated implicitly weighting

(with the probabilities of occurrence) the indi!idual solutions associated with

each set of input data to achie!e a single solution that is the best in some sense

for all sets of input data. &hat is, we achie!e a solution that is ade%uately pre-

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positioned with respect to all the sets of input data, but not to any one of them

particularly. As a result of the uncertain input data being described by a

collection of different sets of data, the resulting ob0ecti!e function is uncertain

and needs to be characteri3ed as a random !ariable. ?ince such ob0ecti!e

function is not a real-!alued function but a random !ariable, the problem of

establishing a specific ob0ecti!e for the decision-making problem arises. >ne

alternati!e is to ma#imi3e the e#pected !alue of the ob0ecti!e function, other

one, to ma#imi3e the e#pected !alue of such function but limiting its !ariance,

etc. Implementing the solution obtained by sol!ing the stochastic problem

abo!e pre-positions the decision-maker in the best possible manner if

considering all possible input data sets duly weighted by their respecti!e

probabilities. &his solution is not the best for each indi!idual set of input data

but it is the best if all of them, weighted with their probabilities of occurrence,

are simultaneously considered. &he price to be paid for using a stochastic

programming approach is a dramatic increase in the si3e of the problem to be

sol!ed, which if handled without care may lead to intractability.

Illustrati!e e#ample from *'

An electricity consumer is facing both uncertain electricity demand and price

for ne#t week. 2or simplicity, we consider that both price and demand are

uncertain but constant throughout the week. ?cenario data pertaining to demand

and price are pro!ided in &able. Additionally, this consumer has the possibility

of buying up to / $" at H86$"h throughout ne#t week, by signing a

bilateral contract before ne#t week, i.e., before knowing the actual demand and

pool price it has to face. &he decision-making problem of this consumer can be

formulated as a two-stage stochastic programming problem. At the first stage,

the consumer has to decide how much to buy from the contract, and the second

stage reproduces pool purchases for each of the three considered demand6price

reali3ations (scenarios).

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&he node-!ariable formulation of this two-stage stochastic programming

problem is as follows

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Fariable PC

represents the power bought through the bilateral contract, while

!ariables P

1 , P

2 , and P

3 represent the power bought in the pool for

scenarios +, 7, and C, respecti!ely. &he ob0ecti!e function is the e#pected cost

faced by the consumer to supply its uncertain demand. owers are multiplied by

the number of hours in a week (+@) to obtain the energy consumed throughout

the week. &he first three constraints enforce energy supply for the three

scenarios, while the remaining constraints are the contract bounds and non-

negati!ity declarations for all the !ariables. Gote that the !ariables of this problem are associated with the nodes of the scenario tree and so the

denomination node-!ariable formulation. &he solution to this problem isC ∗¿ P

¿

@/, P

1

¿

C/, P

2

¿

7/, P

3

¿

/, which means that, before the week, the

consumer buys @/ $" using the bilateral contract, and during the week, C/, 7/

or / $" for demands (prices) ++/ (/), +// (8) or @/ (88) $" (H6$"h),

respecti!ely.

).1. ) + Bus 'yste# with and without %eser&e Bidding

&he proposed pricing scheme is illustrated ne#t using the three-node system

sketched in 2ig. +. ine reactances and capacities are all e%ual to /.+C p.u. and

+// $", respecti!ely. &he system includes three con!entional generators (<+,

<7, and <C) and one wind power plant ("). 5ata for the con!entional units

are pro!ided in &able I. Gote that, comparati!ely speaking, unit <+ is cheap, butinfle#ible; unit <7 is relati!ely cheap, but fle#ible; and unit <C is e#pensi!e, but

16




fle#ible. &he wind plant is located at node 7. Its uncertain power output is

modeled by means of three scenarios, which are referred to as medium (C

$"), high (/ $"), and low (+/ $"), with probabilities of occurrence e%ual

to /., /.7, and /.C, in that order. &he power block offered by the wind producer

is assumed to be e%ual to its forecasted power production (i.e., C/. $"). &he

three-bus system also includes an inelastic load (C) of 7// $" located at node

C, with a !alue of lost load e%ual to H+///6$"h *.

&he market is cleared based on this information. $arket outcomes related to

dispatched %uantities and deployed reser!e are collated in &able II. &he

scheduled wind power production W qs

7/ $". &he resulting energy and

balancing prices are shown in &able III. Gote that electricity prices are the sameat all nodes in the system, because the network does not become congested in

any of the three considered wind power scenarios. <i!en the energy and

balancing prices in &able III and the dispatched %uantities in &able II, the

payments to market participants per scenario can be computed. 2or instance, the

payment to generator <C in scenario low is gi!en by 30×29+10×30=$ 1170

2urthermore, considering that the energy production cost of unit <C is e%ual to

HC/6$"h, the profit that it makes in scenario low is

1170−30×40=−30$ / Mw h

. &able IF pro!ides the benefit obtained by market participants both per scenario

and in e#pectation. >bser!e that the profit made by generator <C is indeed a

random !ariable whose e#pected !alue −30×0.5+120×0.2−30×0.3=0 .

<enerator <C can be seen then as the marginal unit in a stochastic sense. &he

randomness of its profit is inherited from the uncertain character of the reser!e

deployment ser!ice, which in turn depends on the actual wind power

reali3ation. &he proposed market settlement guarantees cost reco!ery for

generating units in e#pectation, but this does not pre!ent generator <C from

incurring economic losses in scenarios medium and low (see &able IF).

17




18




&o reduce the risk of negati!e profits faced by market participants that are

willing to make real-time ad0ustments, reser!e capacity bids can be introduced

in the proposed market settlement as stated in ?ection II-A. 1onsider that

generator <7 offers both downward and upward reser!e capacity at a cost of

H+6$", while generator <C does it at a cost of H76$". &able F shows the day-

ahead schedule and the real-time redispatch in this case. &he wind power

production scheduled at the day-ahead stage is 7/ $" again. ikewise, &ables

FI and FII list, respecti!ely, the clearing prices and the profit made by market

participants per scenario and in e#pectation when the aforementioned reser!e

capacity bids are taken into account to clear the market. As an e#ample, obser!e

that the benefit of generator <C in scenario low is now gi!en by

40×30−40×30=$0 , where we ignore the KcostsL related to the reser!e

capacity bids inasmuch as the pro!ision of reser!e capacity does not entail

specific costs to generators. Gote, indeed, that generator <C does not incur economic losses in any of the three considered scenarios. 2urthermore, its

19




e#pected profit is e%ual to /, i.e., greater than /. &herefore, the possibility of

bidding reser!e capacity ser!es to competiti!ely reward the capability of and

the willingness to make real-time ad0ustments, thus promoting the fle#ibility of

market participants in an efficient manner.

20




21




,. "ase 'tudy + 1

&he pricing scheme described in ?ection II-B is further illustrated using a 78-

bus system based on the single-area !ersion of the I =eliability &est ?ystem

M+ *@. 2or simplicity, the generating units of this well-known system are

grouped by node and type. &he only purpose behind this grouping is to facilitate

the presentation and analysis of the simulation results. &hus, the simplified

system consists of C8 lines, +7 generating units, and +N loads. >n the

assumption of a perfectly competiti!e electricity market, the energy offers

submitted by generating units represent their marginal costs of energy

production, which are indicated in *@, &able FI. "e assume that nuclear and

hydro power producers offer their energy production at 3ero prices. &he amount

of reser!e capacity that each generating unit is willing to pro!ide, either

downward or upward, is listed in &able ID. "e assume that the nuclear and

hydro generators are not technically able to pro!ide reser!e. Go reser!e capacity

costs are considered.

&wo wind farms comprising 7.-$" wind turbines Gorde# G@/67// with a

hub height of +/ m are located at nodes N and @. &he power cur!e of this

turbine model is publicly a!ailable in *. "ind speeds at both wind sites are

described by means of the same "eibull distribution with scale and shape parameters e%ual to .N and +., respecti!ely. &his probability distribution for

wind speeds, in combination with the considered wind turbine model, results in

a capacity factor for both wind farms of appro#imately 8/O. &his capacity

factor has been estimated using the Wind Turbine Power Calculator pro!ided in

*. Besides, wind speeds at both wind sites are assumed to be correlated with a

correlation coefficient of /.. 1orrelated samples are then obtained by using the

sampling procedure described in *+/. An original set of +/ /// samples is first

generated and subse%uently reduced to +// by applying the scenario reductiontechni%ue proposed in *++ and *+7. ?electing the right number of scenarios

constitutes a tradeoff between model accuracy and tractability. "e belie!e that

current computational machinery allows considering a large enough number of

scenarios. Gote that the number of scenarios should be large enough so that

adding any additional scenario does not change the market outcomes

(preferably) or minimally changes them. "e assume that wind power producers

offer their forecast production at 3ero prices. Gote that nowadays this offering

22




strategy constitutes a common practice for wind producers participating in

electricity markets.

&he results reported below correspond to one single period characteri3ed by a

total system demand of 7@/ $". &his demand is geographically distributedamong nodes as specified in *@, &able F. oads are assumed to be inelastic

with a !alue of lost load e%ual to H7///6$"h. =esults for two different wind

penetrations le!els, +7.CO and 7.CO, are presented. &he wind penetration le!el

is gi!en as the ratio of the installed wind capacity to the total system demand.

&he number of wind turbines in the farms at nodes N and @ that are re%uired to

achie!e these penetration le!els are 8/ and +//, and +// and 7//, respecti!ely.

&he market-clearing problem has been sol!ed using 1D ./.7 under <A$?

on a "indows-based personal computer Intel(=) 1ore(&$) i with four processors clocking at 7.8 <43 and <B of =A$. &he re%uired computational

time is around fi!e seconds.

2or low wind penetration le!els, such as +7.CO, there is enough room in the

transmission network to accommodate the energy transactions settled at the

market stage plus the subse%uent energy redispatches in the form of deployed

reser!e without the occurrence of congestion e!ents. &herefore, the wind energy

in0ected at nodes N and @ is able to reach e!ery node in the system and as aresult, no differences in prices e#ist among nodes. In particular, for a wind

penetration le!el of +7.CO, the energy price ( λn) is e%ual to H+.6$"h at

e!ery node. ikewise, the probability-remo!ed balancing prices under the

highest and lowest wind production scenarios, which will be denoted,

respecti!ely, by λnw

π w and λnw /π w hereafter, are H+./6$"h and H7+.N6$"h

in that order, irrespecti!e of the node under consideration. &hese probability-

remo!ed balancing prices are obtained by di!iding each dual !ariable λnw by

its associated probability π w . &his way, the energy prices and the probability-

remo!ed balancing prices are of the same order of magnitude. 2urther, the

balancing prices so transformed are dual optimal for the real-time market model

that results from problem (+) once the wind power uncertainty is disclosed and

first-stage !ariables (scheduled %uantities) are fi#ed to their optimal !alues. >n

the contrary, for high enough wind penetration le!els, e.g., 7.CO, network

23




bottlenecks become probable and conse%uently, the nodal prices differ. As an

e#ample, &able D shows, for this wind penetration le!el, the !alues of the

energy price and the probability-remo!ed balancing prices under the highest and

lowest wind production reali3ations at some selected nodes. In light of these

prices, the following three obser!ations are in order

+. In the scenario of highest wind power production, the balancing

prices are 3ero at the nodes where the wind farms are connected,

namely, nodes N and @. &he reason for this is that any marginal

increment of load at these nodes is satisfied, in this scenario, by the

wind energy production that would be otherwise spilled due to the

network congestion.

7. &he balancing price in the scenario of lowest wind power production is node-independent. &his is so because, under this

scenario, the network does not become congested.C. !en though the scheduled productions do not cause network

congestion at the market stage, the energy price differs among

nodes. &his highlights the coupling between energy and balancing

prices induced by the two-stage stochastic programming approach.

Intuiti!ely speaking, the energy price anticipates probable network

bottlenecks during the real-time operation of the power system.

&he payments to market participants under the proposed pricing scheme are

indicated in &able DI for the two considered wind penetration le!els. "hile the

system operator makes payments to producers, it recei!es payments from

consumers. &his is why the payments to loads in this table are e#pressed in

negati!e numbers. >bser!e that if the wind penetration le!el grows, the

payments to con!entional producers diminish, whereas the payments to wind

producers increase. ogically, there is a transfer of re!enues from con!entionalgenerators to wind producers at the same time that the payments from loads are

reduced due to the free character of the wind energy. In either case, re!enue

ade%uacy in e#pectation is guaranteed. In fact, for a wind power penetration

le!el of 7.CO (condition such that network congestion e!ents are probable) the

system operator is e#pected to incur a financial surplus of HN7@.+.

astly, &ables DII and DIII pro!ide, respecti!ely, the e#pected profits achie!ed

by con!entional and wind producers under the proposed pricing scheme.

24




>bser!e that all the participants reco!er their production costs in e#pectation,

thus making an e#pected profit greater than or e%ual to 3ero. In general, the

#pected profits of con!entional producers decrease as they are displaced from

the energy supply by an increasing wind power penetration. >nly generating

units C and 8 see their e#pected profit increased due to the fact that they get

more in!ol!ed in the deployment of reser!e with the increment in wind power

penetration.

25




,.1. "onclusions and uture Work

+. &he proposed pricing scheme * is adapted to the specificities of wind

producers, characteri3ed by their !ariability and unpredictability. &hisconstitutes no harm to con!entional producers.

26




7. &his pricing scheme is marginal and results in both cost reco!ery for

producers and re!enue reconciliation, both in e#pectation.C. &wo sets of marginal prices are deri!ed' pool prices that reflect energy

scheduling and balancing prices that reflect system operation.

8. &he proposed prices are deri!ed from the solution of an problem.&hus, they are obtained in an easy and robust manner.

. &he pricing scheme described in this paper does not embody non-

con!e#ities (e.g., start-up costs or minimum power output constraints).

2uture work is needed to incorporate such non-con!e#ities.

. "ase study + 2

=esults from a case study based on the single-area !ersion of the I

=eliability &est ?ystemM+ *@ are discussed in this section. 2or simplicity,generating units are grouped by type and node. &his way, 0ust one binary

!ariable is re%uired to determine the on6off status of each group of units.

2urther, the nuclear and hydro generators are considered must-run units. &hese

simplifications ha!e no purpose other than to alle!iate the computational burden

in!ol!ed in obtaining the results presented in this case study. By appealing to

the assumption that the electricity market is perfectly competiti!e, offers

submitted by generating units correspond to their marginal costs of energy

production, which are listed in *@, &able . &he generation mi# of the power system also includes two wind farms located at nodes N and @. &he same

"eibull distribution, with scale and shape parameters, and, e%ual to .N and +.,

respecti!ely, is used to model wind speed at both sites. &he two wind farms are

comprised of 7.-$" wind generators, model Gorde# G@/67// with a hub

height of +/ m. &he power cur!e of this turbine model can be found in *.

According to the Wind Turbine Power Calculator pro!ided in this reference, the

estimated capacity factor of both wind farms is appro#imately 8/O. "e

consider a system demand of 7@/ $", distributed among nodes as indicated in*C7, &able . oads are assumed to be inelastic. &herefore, the ma#imi3ation of

the social welfare in the market-clearing formulation *N boils down to the

minimi3ation of the operating costs.

Ge#t, we suppose a correlation coefficient between wind farms e%ual to /.@ and

we assess the impact of the wind power penetration le!el on $s in terms of

means and standard de!iations. 2or this purpose, we use +//// samples of the

wind farm power outputs in the simulation process. &his number of samples ishigh enough to pro!ide estimates for means and !ariances (the s%uare of

27




standard de!iations) with a degree of precision (coefficient of !ariation of

estimates e#pressed in percentage) below +.+/ and 7.8O, respecti!ely, for all

the simulations carried out in this case study. In a!erage !alues, these numbers

drop up to /.8 and +./+O in that order. 2ig. 7(a) and (b) shows the e!olution of

the mean and standard de!iation of $s at nodes N, @, and 7/ as the

penetration le!el of wind generation in the 78-node system increases. Gote that

the wind power penetration le!el is e#pressed as a percentage of the total

system demand (7@/ $") and is augmented by increasing e%ually the number

of wind turbines installed in the two wind farms. &he choice of the nodes for

analysis is not arbitrary. Godes N and @ are those where the two considered wind

farms are placed, while node 7/ can be seen as representati!e of those buses

electrically far from the nodes where the wind generation is in0ected into the

power network. 2irst, the wind power production is used to displace part of the

energy supplied by the groups of +N-$" and +//-$" units placed at nodes

+C and N, respecti!ely. &hen, for a wind penetration le!el around +N.O, the

power produced by the wind farms in some scenarios is high enough to keep the

units at node +C shut down, pro!ided that the group of +7-$" units at bus + is

started up. &hese units are the most e#pensi!e ones in the system and as a result,

their utili3ation pushes the $s up and causes the sudden increase that can be

obser!ed in 2ig. 7(a). If the wind penetration le!el is increased a little more, up

to 7+O, the percentage of scenarios in which the +7-$" units at node + need

to be used drastically decreases and the a!erage !alues of $s start to drop

again as a conse%uence. $oreo!er, the e#clusion of these small units from the

energy dispatch also 0ustifies the sudden fall in the standard de!iations of $s

that can be appreciated in 2ig. 7(b). In addition, for low wind penetration le!els

+O , the wind energy in0ected at nodes N and @ is able to reach e!ery bus in the

system and conse%uently, the means and standard de!iations of $s are all

!ery similar. &he e#isting differences stem from the loss component of $s.

4owe!er, from a wind power penetration le!el higher than 7+O, the cur!es

represented in 2ig. 7 start to di!erge in a significant manner. &he different

beha!iors e#hibited by the means and standard de!iations of $s from this

point on are mainly due to the fact that situations in which the network becomes

congested begin to happen, or statistically speaking, begin to be probable. In

such situations, the network caps the amount of wind energy that can be

transferred from nodes N and @ to the rest of buses in the system and as a result,

the effect of wind generation on $s becomes locally accentuated. &his effect

is twofold' on the one hand, the probability of loads at nodes N and @ being

28




supplied by free wind energy increases, with the conse%uent sharp decrease in

the means of the corresponding $s; on the other hand, the energy supply

from wind sources is inherently uncertain and such an uncertainty is passed on

to the $s in the form of a considerable increase of their standard de!iations.

In general terms, the impact of a growing wind generation on $s translates

into a decrease of their means, but an increase of their standard de!iations. 2or

instance, the coefficients of !ariation of $s at nodes N, @, and 7/ (defined as

the ratio of the standard de!iation to the mean) go from / for a /O wind

penetration le!el to , NN, and 7+O, respecti!ely, for a /O wind penetration

le!el.

&his subsection is intended to illustrate that correlation among wind sites can

ha!e a significant impact on $s and therefore should not be ignored when

assessing the economic repercussions of wind integration. &o this end, we

consider that the number of 7.-$" turbines installed in the wind farms at

nodes N and @ is +8/ and 7//, respecti!ely. &herefore, the total wind capacity

connected to the power grid is @/ $", which represents a wind penetration

le!el of almost C/O. 2ig. C(a) and (b) represents, respecti!ely, the means and

the standard de!iations of $s at nodes N, @, and 7/ as a function of the

correlation coefficient between wind farms. &he dashed lines ha!e been

obtained by linear regression, and their only purpose is to stress the general

trends e#hibited by the simulation outcomes. In accordance with the results

pro!ided in the pre!ious subsection, a wind penetration le!el of C/O is high

enough to produce e!entual network bottlenecks and hence the remarkable

differences e#isting among means and standard de!iations of different $s.

Gote that the correlation between wind farms has a minor impact on the means

and standard de!iations of $s at nodes N and 7/, but a considerable effect onthe mean and standard de!iation of the $ at node @. In numbers, if the

correlation coefficient is augmented from / to /., the mean of such an $

e#periences a reduction of +/.CO, whereas its standard de!iation suffers an

increase of C/.NO. ogically, power output fluctuations from wind farms fed

with uncorrelated winds cancel out and as a result, the o!erall wind generation

!ariability diminishes.

$oreo!er, due to the occurrence of network congestion, which particularlyaffects the transmission line connecting buses N and @, the impact of the

29




correlation coefficient between wind farms on the $s should be locally

appraised. In this line, the a!erage !alue of the $ at node @ decreases as this

coefficient approaches +, because the percentage of scenarios in which the

power produced by the wind farm at this node is spilled increases considerably

from +/./NO ( ρ=0¿ to 7C.CO ( ρ=0.95¿ . &his remarkable growth of

wind spillage e!ents leads to a similar increase in the percentage of instances in

which the price at node @ is 3ero, specifically from +7.+O ( ρ=0¿ to 7N.+CO

( ρ=0.95¿ . In contrast, the mean of the $ at node N slightly increases with

the correlation coefficient between wind farms, because the a!erage power

generated by the thermal units at this bus also increases from .8 $" (

ρ=0¿ to @N.N $" (

ρ=0.95¿.

30




.1. "onclusion

&his paper *N pro!ides a simulation methodology to assess %uantitati!ely the

impact of an increasing integration of wind power on electricity $s. &he

impact on both a!erage !alues and !olatilities is analy3ed. An increasing

amount of wind power integration results in lower $s throughout the

network until bottlenecks appear, which makes local the $ reduction

inherent to increasing wind power integration. A high correlation among wind

plants has an important impact on $ !olatilities and a reduced impact on

$ a!erage !alues. &his is a conse%uence of the fact that no-correlation

originates the statistical cancelling out of wind fluctuations and thus stable

a!erage !alues. &he methodology proposed in this paper allows !isuali3ing the

abo!e phenomena and, which is more important, calculating their actual

numerical impacts. As future works, we intend to contrast the results pro!ided

by the proposed methodology with the empirical analysis of real measurements

from di!erse power markets, and to e#tend the simulation algorithm to account

for inter-hour comple#ities such as the temporal correlations of wind speed

series and the ramping capabilities of generating units.

31






* 5anish "ind Industry Association, "ind &urbine ower 1alculator.

*>nline. A!ailable' http'66guidedtour.windpower.org6en6tour6wres6pow.

*+/ 4. 4eitsch and ". =Umisch, K?cenario reduction algorithms in stochastic

programming,L Comput. !ptim. "ppl., !ol. 78, pp. +@NT7/,7//C.

*++ Q. 5upaVo!W, G. <rUwe-Suska, and ". =Umisch, K?cenario reduction in

stochastic programming' An approach using probability metrics,L #ath.

Program., !ol. , ?er. A, pp. 8CT++, 7//C.

*+7 . inson, 1. 1he!allier, and <. G. Sariniotakis, K&rading wind generation

from short-term probabilistic forecasts of wind power,L IEEE Trans. Power

yst., !ol. 77, no. C, pp. ++8@T++, Aug. 7//N.

http://guidedtour.windpower.org/en/tour/wres/pow

http://guidedtour.windpower.org/en/tour/wres/pow

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