21, rue d'Artois, F-75008 Paris
http://www.cigre.org
C5-106
Session 2004
© CIGRÉ
IMPLEMENTATION ASPECTS OF POWER EXCHANGES
L. Meeus, K. Purchala, R. Belmans*
Katholieke Universiteit Leuven
(Belgium)
Abstract—Power exchanges organize auctions to which offers to buy and to sell electricity can be
submitted. Piecewise and stepwise clearing are two single market-clearing algorithms used by
European exchanges to implement auction trading. They are discussed and evaluated because given
the same inputs these algorithms can yield different cleared volumes, traded at different market prices.
An evaluation method is introduced and applied to four intersection cases that can be distinguished.
Index Terms— Power System Economics - Electricity Market Design - Power exchange
1. INTRODUCTION
In a liberalized electricity market, participants can trade on a variety of markets. Traditionally they can
trade energy bilaterally on the over-the-counter market (OTC). The bulk of transactions in Europe is
still being settled on OTC markets, where trading parties can specify the contract terms they desire.
Alternatively, in most countries organized markets (i.e. exchanges) have been established. As Stoft
(2002) pointed out, the flexibility of bilateral markets comes at a price [1]. Negotiating and writing
contracts is expensive and can take hours to weeks. Assessing the credit worthiness of one’s counter
party is also expensive and involves risk. Power exchanges facilitate a more standardized and
centralized way of trading providing benefits, such as a neutral marketplace, a neutral price reference,
easy access, low transaction costs, a safe counterpart, and clearing and settlement service. Because
trading on exchanges is standardized, they are much faster than bilateral markets and can operate
closer to real time.
Power exchanges organize auctions to which offers to buy and to sell energy can be submitted. At the
moment European exchanges clear single markets. Because network constraints are not taken into
account, they produce a single price for their national zones. Foreign traders can submit offers to
domestic day-ahead markets if they possess transfer rights. These transfer rights are allocated in
separate transmission capacity markets, sometimes also auctioned [2]. In other words, the current
system has zonal prices that are coupled by explicit arbitrage via transfer rights. It is generally
accepted that the European energy market could be organized more efficiently by jointly handling
energy in the different national markets and the border capacities between those markets. This has
been clearly brought forward for instance during the last ETSO conference in Brussels [3]. However,
*
[email protected]
the purpose of this paper is to discuss single market clearing. Multiple market clearing is outside the
scope of this paper.
The first part of the paper describes the European auction trading standards. In the second part single
market clearing is discussed in general. Finally, the third part evaluates piecewise and stepwise
clearing, two single market-clearing algorithms used by European exchanges to implement auction
trading.
2. TRADING STANDARDS
The first European power exchange to implement auction trading was Scandinavian Nord Pool in
1993. Nord Pool is also the only European exchange that clears more than one market with network
constraints between them. The Spanish exchange Omel and the Dutch Amsterdam Power Exchange
(APX) were the first exchanges in continental Europe respectively in 1998 and 1999. Currently, most
countries have an exchange organizing day-ahead energy auctions.
In Europe hourly day-ahead auction trading is the main activity of exchanges: the market is cleared
separately for every hour of the next day on the day ahead of the actual dispatch. These auctions are
uniformly priced and sealed auctions, meaning that the same price applies to every accepted offer and
offers are not disclosed to participants. They are also called double side auctions because both sellers
and buyers can submit offers.
With the exception of block bids, offers submitted are simple, only stating price and volume. A block
bid is a firm offer for a number of consecutive hours, meaning that either the block bid is cleared for
all the stated hours or none of them. After initial clearing, resulting in hourly prices, an average of the
market prices for the hours included in the block bid is calculated. This price has to be equal, or better,
than the price limit stated by the participant to satisfy the block bid. This means that a sales block bid
is accepted if the average market price of the hours included in the block bid is higher or equal than
the price of the block bid. A purchase block bid is accepted if the average market price of the hours
included in the block bid is lower than the price of the block bid. If not all conditions are satisfied the
initial solution is not valid. In this case one of the unfulfilled block bids is eliminated and the price
calculation is run again. This checking is iterated until all the remaining block bids can be fulfilled. In
this paper only the clearing of simple offers and single markets is discussed. For a more detailed
discussion of different types of bids that can be submitted to the different European power exchanges
see for instance [4].
3. SINGLE MARKET CLEARING
In this section market clearing is discussed in general. First, it is described how offers are submitted to
exchanges. Consequently, the concepts clearing, and clearing feasibility, efficiency and fairness are
introduced and illustrated.
3.1 Clearing
Clearing means determining the market price and the volume that can be traded at that price, starting
from a discreet amount of offers to buy and sell. A clearing algorithm is an algorithm that always
produces a feasible outcome. If the outcome would be non feasible, the market would not have been
cleared. However, the clearing price is not necessarily an efficient price.
It is common practice in Europe that participants submit flat bids to the exchange. In a flat bid system,
submitting offers to sell requires a trader to indicate the prices and the volume increments he want to
sell at these prices. Submitting offers to buy requires a trader to indicate the prices and the volume
increments he wants to buy at these prices.
2
Table I shows that trader A wants to sell 13 volumes in total, of which 3 at any price, starting from a
price of 5 he offers 4 more, and from a price of 11 on top of that 4 more, and finally if the price is the
maximum price 15, he offers 2 more or 15 in total. Trader D offers a volume of 2 starting from a price
of 13, which is called the price limit of the order. Based on this input table aggregated stepwise
demand and supply curves can be constructed (Figure 1).
Table I: Offers to sell and to buy volume (V) at different prices (P) with their feasibility and
fairness constraints
Supply
Trader A
Trader B
Demand
Trader C
Trader D
Ps
Vs
Ps
Vs
Pd
Vd
Pd
Vd
P
15
Input
0
5
3
4
11
2
Input
15 13
5
4
13
2
Area (S FAIR)
11
4
15
2
(5>) P00
(11>) P05
(15>) P011
(0<) V-3
(3<) V-7
(7<) V-13
P015
(13<) V-15
Area (D FAIR)
7
2
3
2
(13<) P-15
(7<) P-13
(3<) P-7
(0<) V-5
(5<) V-11
(11<) V-13
D
P-3
(13<) V-15
S
13
FAIR, FEASIBLE
11
D FAIR, FEASIBLE
9
7
S FAIR, FEASIBLE
5
NOT FAIR, FEASIBLE
3
1
1
3
5
7
9
11 13
15
V
Figure 1: Aggregated demand (D) and supply (S) curves based on Table I indicating the clearing
feasible area and the fairness areas (FAIR, D FAIR and S FAIR area).
3.2 Feasibility
The curves in Figure 1 cut the first quadrant of the graph in a feasible and a non-feasible area. Only
the first quadrant is considered because negative volumes offered to sell would simply mean demand
and vice versa. On the other hand, power exchanges do not allow negative prices to be offered even
though it could be argued that in some theoretical cases traders are willing to pay to be allowed to
supply. Power exchanges also use a maximum price at which offers can be submitted. These
constraints and the constraints in bold in Table I define the feasible demand and supply area; this is
respectively on or under the stepwise demand curve and on or above the stepwise supply curve, the
feasible area being the overlap between both.
The constraints in bold allow traders’ offers to be curtailed, meaning that they accept that sometimes
only a fraction of the volume increment they want to sell at a certain price is traded. Curtailing is a
consequence of flat bidding and occurs when demand does not equal supply at the clearing price.
3
3.3 Efficiency
Efficient trade maximizes total surplus, the sum of consumer surplus and producer surplus. An
efficient price is a price that maximizes trade; this is where demand and supply intersect. In Figure 1
the maximum wealth that can be created for participants is the area of the feasible area, a total surplus
of 89. Demand and supply intersect at volume 11. The maximal tradable volume, 11, can be traded at
prices between 11 and 13, being the efficient price interval. Note that choosing a price between 11 and
13 does not affect the market value but does affect how much of that market value is producer surplus
and how much consumer surplus. A higher price corresponds to more producer and less consumer
surplus.
Assuming that the clearing price is 11, supply has to be curtailed because supply is higher than
demand at price 11. Supply has to be reduced from 13 volumes to 11 to match demand. In order for
trade to be efficient, only the most expensive offers to sell with a price limit lower than or equal to the
market price should be curtailed. Equivalently, only the offers least willing to buy with a price limit
higher or equal to the market price should be curtailed. In other words curtailing means in this case
that only a fraction of the most expensive offers to sell can be cleared, being the offers with a price
limit 11 to sell 4 volumes (trader A) and 2 volumes (trader B). The volume of 6 has to be curtailed into
a volume of 4 to achieve the necessary reduction of requested supply by 2 volumes (13 – 11). One
approach can be to allocate both offers a fraction of the remaining volume 4, the fraction being
proportional to the offers’ requested volumes. The latter results in a total cleared volume of 9.67 (3 + 4
+ 4/6*4) for trader A and 1.33 for trader B (2/6*4). Alternatively, trader A could be given priority for
instance because his offer to sell a volume of 4 starting from a price 11 was submitted before the offer
of trader B, meaning that trader A has a total cleared volume of 11 and trader B 0.
3.4 Fairness
Figure 1 shows different gray areas within the feasible area. The D FAIR and S FAIR areas can be
obtained by adding the constraints in brackets in Table I to the demand and supply constraints in bold,
the FAIR area being the overlap of both. An outcome in the fair area is feasible and also satisfies the
added fairness constraints, being the constraints in brackets in Table I. To define fairness we illustrate
why traders do not consider clearing the market outside this area fair. Assume the market is cleared in
the feasible point (7,11). If the market price is 11, demand is 11 volumes and supply 13 volumes while
only 7 volumes can be traded. The outcome is not efficient because 4 more volume could have been
cleared, creating 8 extra surplus. The outcome will be even less efficient if the volume increments at
price 11 are curtailed together with the volume increments at lower prices. For every volume unit of
the offer to sell at price 11 of trader B that is cleared for instance at the cost of a volume unit of the
offer to sell at price 5 of trader A, 6 surplus is lost. In other words, to be efficient nothing of the offers
to supply at 11 should be cleared. Traders accept that only a fraction of their offer is cleared. However
a fraction of zero is not considered fair for supply that offered at a price below or equal to the clearing
price. Thus, if the market is cleared in point (7,11) outside the fair area, the exchange is confronted
with a trade-off between efficiency and fairness.
4. EVALUATION
Clearing a single market involves setting the price and consequently matching demand and supply at
that price. In this section pricing rules and matching rules of the stepwise and piecewise clearing
approach are evaluated on wealth distribution and wealth maximization.
4.1 Pricing rules
Because a simple aggregation of flat bids results in stepwise linear curves, as shown in Figure 1, there
may not be a well-defined price solution. Exchanges handle this problem in two different ways. Some
use linear interpolation instead of simple aggregation to get piecewise linear curves, being the
4
piecewise clearing approach. Others set up additional rules for price determination in case of multiple
price levels at the intersection of the two stepwise linear curves [4], being the stepwise clearing
approach.
Table II summarizes the 4 intersection cases of two stepwise linear curves. Figure 3 is an illustration
of the 4 cases of Table II. The figure shows the efficient clearing price interval per case.
Table II: Summary of the 4 intersection cases of two stepwise linear curves,
illustrated in Figure 3
Cases
Intersection
Demand
Supply
Case 1
Vertical
Vertical
Case 2
Horizontal
Horizontal
Case 3
Vertical
Horizontal
Case 4
Horizontal
Vertical
In the piecewise clearing approach linear interpolation of volumes between submitted price steps,
results in two curves that are piecewise linear like stepwise linear curves but without vertical and
horizontal pieces. Unlike stepwise linear curves, piecewise linear curves always intersect in a unique
point. Detailed information about pricing rules using linear interpolation is not publicly available. In
Figure 2 piecewise clearing is the authors’ interpretation of the pricing rules of Nord Pool, as
described by Nord Pool in [5].
In the stepwise clearing approach additional rules have to be set up for price determination in case of
multiple price levels at the intersection of the two stepwise linear curves. APX’s pricing rules can be
deducted from the market results because the clearing price is published daily with the aggregated
curves [6]. In Figure 2 stepwise clearing represents the pricing rules of the Dutch exchange.
1
EFFICIENT MARKET
CLEARING PRICES
2
3
4
STEPWISE CLEARING PRICE
PIECEWISE CLEARING PRICE
Figure 2: Illustrating the stepwise and piecewise clearing prices for the intersection cases of
Table II
Note that Figure 1 is another illustration of case 3 in Figure 2. The following conclusions can be made
about pricing rules of the piecewise and the stepwise approach:
Wealth distribution: if the clearing prices are different, the pricing rules of the piecewise and the
stepwise approach distribute wealth differently among sellers and buyers.
•
In Figure 2 both approaches yield equal clearing prices in case 2 but different prices in cases 1, 3
and 4.
•
In case 2 both approaches will always yield equal prices
•
In case 1, 3 and 4 approaches can yield equal prices depending on the steps with which the cases
are illustrated.
5
•
•
•
In case 3, the piecewise clearing price will always be higher or equal to the stepwise clearing
price. If offers are submitted as in case 3 and the piecewise clearing price is higher, trade resulting
from piecewise clearing distributes more wealth to sellers and less to buyers than stepwise
clearing.
In case 4, the piecewise clearing price will always be lower or equal to the stepwise clearing price.
If offers are submitted as in case 3 and the piecewise clearing price is lower, trade resulting from
piecewise clearing distributes more wealth to buyers and more to sellers than stepwise clearing
because the price is lower.
In case 1 everything is possible.
Wealth maximization: if the clearing price is not an efficient price, the pricing rules do not maximize
wealth for participants.
•
In Figure 3 both approaches yield an efficient clearing price in the 4 cases.
•
In case 1 and 2 both approaches will always yield an efficient clearing price.
•
In case 3 and 4 the piecewise approach sometimes yields an inefficient clearing price, depending
on the steps with which the cases are illustrated.
STEPWISE CLEARING
PIECEWISE CLEARING
LOSS OF WEALTH
CLEARING PRICE
P
D
S
P
D
PRODUCER
SURPLUS
S
CONSUMER
SURPLUS
EFFICIENT CLEARING PRICES
V
V
Figure 3: Stepwise and piecewise clearing: different pricing rules with different total surplus
and different distribution of surplus.
In Figure 4 case 3 is illustrated with different steps. It is illustrated that in case 3 different pricing rules
can lead to a different distribution of wealth among sellers and buyers. The higher piecewise clearing
price yields more producer surplus but less consumer surplus than the lower stepwise clearing price. It
is also illustrated that the pricing rules of the piecewise approach can yield an inefficient clearing
price. The maximal tradable volume at the piecewise clearing price is lower than the maximal tradable
volume at the stepwise clearing price. The difference between total surplus in the two approaches,
being the sum of producer and consumer surplus, is a loss of wealth for participants. However, the
maximal tradable volume is not necessarily the cleared volume as a result of the matching rules.
Matching rules can imply a further loss of wealth for participants.
4.2 Matching rules
In auctions all offers to buy with a price limit higher than the clearing price and all offers to sell with a
price limit lower than the clearing price are executed. Just as for the case of price determination the
simple aggregation of the flat bids may not result in well-defined trade volume since supply and
demand curves are stepwise linear. Again different solutions to this problem are used, being the
matching rules [4].
6
The stepwise clearing approach is one category of matching rules. The market is cleared at the
intersection of the stepwise linear curves, for instance by APX, maximizing total cleared volume. In
the illustration in section 3 supply is curtailed to match demand. Two different curtailing options are
given, both leading to a maximal tradable volume. Note that the two curtailing rules that were given
distribute traded volume differently among traders.
Another category of matching rules involves linear interpolation [4]. However, information on how
linear interpolation, for instance by Nord Pool, is used to match supply and demand at the piecewise
clearing price is not publicly available. From the description in [5] it is not clear how total cleared
volume at the clearing price is determined in the piecewise approach. It is only stated that traded
volume is established by comparing the clearing price with the participants’ bid forms.
If the total cleared volume is determined like the clearing price, at intersection of the piecewise linear
curves, the matching rules of the piecewise approach can lead to a further loss of wealth for
participants. Clearing the flat bids of Table I at intersection of the piecewise linear curves, as
illustrated in Figure 5, means clearing the market in point (7,11). Even though the clearing price 11 is
an efficient price, as shown in section 3, the matching rules do not lead to the maximal tradable
volume 11. Because only 7 volumes are cleared, there is a loss of wealth for participants and the
exchange will be confronted with a trade-off between efficiency and fairness when implementing
curtailing as seen in section 3.
P
15
D
S
13
FAIR, FEASIBLE
11
D FAIR, FEASIBLE
9
7
S FAIR, FEASIBLE
5
NOT FAIR, FEASIBLE
3
1
1
3
5
7
9
11 13
15 V
Figure 4: Piecewise clearing of Table I at intersection of the piecewise linear curves, outside the
fair region.
4. CONCLUSION
At the moment European power exchanges clear single markets day-ahead. Mostly simple flat bids
can be submitted, stating the volume increments that are offered to sell or to buy at different prices.
Two algorithms used in practice to calculate the market price and the volume that can be traded at that
price yield different outcomes given the same inputs.
It has been shown in the four intersection cases that could be distinguished that the prices often differ
resulting in a different distribution of wealth among sellers and buyers. Only in one of the four
intersection cases piecewise and stepwise clearing always yield the same efficient price. Unlike
stepwise clearing, piecewise clearing does not always maximize wealth for participants.
7
5. BIBLIOGRAPHY
[1] S. Stoft. Power system economics, designing markets for electricity. IEEE Press, 2002, 496pp.
[2] K. Purchala, L. Meeus, R. Belmans, Implementation aspects of coordinated auctions for
congestion Management. Proceedings IEEE Bologna Power Tech Conference, 2003.
[3] ETSO. http://www.etso-net.org.
[4] R. Madlener, M. Kaufmann. Power exchanges spot market trading in Europe: theoretical
considerations and empirical evidence. http://www.oscogen.ethz.ch.
[5] Nord Pool. Bidding in the spot market. http://www.nordpool.com.
[6] Amsterdam power exchange (APX). Market results. http://www.apx.nl.
8