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A double auction model for competitive generators and large consumers

considering power transmission cost

Debin Fang a,, Jingfang Wu a, Dawei Tang b

a Economics and Management School, Wuhan University, Wuhan, Hubei 430072, PR Chinab Manchester Business School, The University of Manchester, P.O. Box 88, Manchester M60 1QD, United Kingdom

a r t i c l e i n f o

Article history:

Received 28 January 2010

Received in revised form 5 March 2012

Accepted 24 May 2012

Available online 15 July 2012

Keywords:

Electricity market

Double auction

Power transmission constraint

Pricing mechanism

Large consumers

a b s t r a c t

The pricing mechanism in a deregulated electricity market is consistently a critical issue to improve mar-

ket operations. Along with the development of electricity market, large consumers may purchase electric

power from generators directly. In this paper, with an effort to introduce McAfees second-price sealed

auction mechanism into multi-unit electric power transaction between competitive generators and large

consumers, an auction model is developed to decide electric power price between competitive generators

and large consumers based on the inclusion of the transaction cost and power transmission cost in a

wholesale electricity market. After the description of pricing rules in the deregulated power market, auc-

tion rules and transaction rules arediscussed. In particular, auction rules can increase the probability that

generators providing a large number of supply and large consumers with high demand win the auction.

On the other hand, transaction rules can optimize the whole transmission cost andtransaction cost under

market equilibrium, and the whole system is dispatched to maximize social welfare. A numerical exam-

ple with eight suppliers and eight large consumers is provided to illustrate the essential features of this

method.

2012 Elsevier Ltd. All rights reserved.

1. Introduction

Since the 1980s, much effort has been made to restructure the

traditional monopoly power industry, with objectives to introduce

fair competition and promote economic efficiency. Nowadays,

many countries have carried out market-oriented reform in electric

power industry; and as a result, large consumers can purchase

electric power from generators directly in most of these countries.

More specifically, consumers whose demands reach a certain

quantity may sign a double-sided contract with generators or

power enterprises, which breaks monopoly market where power

grid companies traded the electric power exclusively. For genera-

tion side, competitions are introduced by separating plants from

power grids and accessing the power grid through competition,

while for electric demand side, competitions are introduced by

large consumers direct purchase behavior from generators di-

rectly. Therefore, an open bilateral electricity market should be

restructured, and it is definitely crucial that large consumers can

purchase electricity from generation companies directly [1].

In China, until 2002, the State Council authorized a comprehen-

sive set of electricity sector reforms under its Scheme of Reform for

Power Industry. According to the scheme, and with an aim to break

up monopoly as well as introduce competition, Chinese govern-

ment has split the State Power Corporation into five generating

companies and two grid companies in order to implement unbun-

dling strategy. Almost at the same time, Chinese government

formed and institutionalized a specialized central government

agency, the State Electricity Regulatory Commission (SERC), to sep-

arate the functions of government and business. All the above re-

forms were expected to reach the two objectives: (a) to improve

efficiency and lower the cost of the electric power industry; (b)

to form rational pricing mechanism and optimize resource alloca-

tion through the re-construction of the markets based on compet-

itive pricing mechanism and rational market models[2,3]. Chinese

government has already completed its first step of the electricity

reform, including separating power plants from transmission grids,

establishing transmission companies, and constructing a competi-

tive generation market. More details of the Chinese electricity mar-

ket, such as generation and transmission asset can be found in

[2,4]. After that, regional electricity market in Northeast started

to pre-operate based on this scheme, and the main contents in-

clude qualifications, rights and obligations of the market players,

transaction regulations of electricity market, schedule and opera-

tion management, and market regulation and intervention. At the

same time, regional electricity market of Northeast further intro-

duced the competition in the generating market, and simulated

competition before transmission. But this preoperation was failed,

0142-0615/$ - see front matter 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijepes.2012.05.041

Corresponding author. Tel.: +86 2768753104; fax: +86 27 68754150.

E-mail address:[email protected](D. Fang).

Electrical Power and Energy Systems 43 (2012) 880888

Contents lists available at SciVerse ScienceDirect

Electrical Power and Energy Systems

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j e p e s
http://dx.doi.org/10.1016/j.ijepes.2012.05.041mailto:[email protected]://dx.doi.org/10.1016/j.ijepes.2012.05.041http://www.sciencedirect.com/science/journal/01420615http://www.elsevier.com/locate/ijepeshttp://www.elsevier.com/locate/ijepeshttp://www.sciencedirect.com/science/journal/01420615http://dx.doi.org/10.1016/j.ijepes.2012.05.041mailto:[email protected]://dx.doi.org/10.1016/j.ijepes.2012.05.041

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the main reasons lies in two aspects. First the reform was impeded

almost by severe electricity shortages that began in 2002 and con-

tinued through 2006. Second and more important, competition

was introduced just on generation side, and end-users cannot

choose the retailer or power supplier in this market. In this regard,

some scholars have demonstrated that large consumers should

participate in competition and it would be worthy to form a bilat-

eral electricity market[5].

Chinese government also experimented in some selected units,

such as Sichuan Province. The result displayed a good performance.

Today, there are several policies on large consumers directly elec-

tric power purchase fromcompetitive generators. Some of the most

important policies include: (a) the Scheme of Reform for Electric

power System, which was authorized by the State Council

(SC[2002] 5th), (b)the Scheme of Reform for Electricity Price, which

was authorized by the State Council General Office (SCGO 62th),

and (c) the Interim Procedure for Electricity Users Purchase Powerfrom

Generating Companies which was jointly issued by the State Elec-

tricity Regulatory Commission and the National Development and

Reform Commission ([2004] 17th). All these documents provided

the policy basis, presented the guiding ideology, purpose and prin-

ciple, and the specific regulations of the range and condition of the

pilot, main contents, organization and implementation[6,7].

Following this line of research, transaction mode betweengener-

ators andlarge consumers hasbeen developed fromelectricdemand

sidein electricity market. In Ref. [8], howlarge consumers purchase

electricity from suppliers were discussed, and a new scheme for

large consumers entering into electric power market to purchase

electricity directly was proposed. The large consumers who satisfy

some qualification candirectlyenterthe transactioncenter of the re-

gional electricity market (however they must take on certain cross-

subsidization, and this is also one of the market entry conditions),

become independent power purchase entity (namely market en-

tity),and pay the purchasefee basedon thepay as bidmode accord-

ing to the concrete market rules. In this sense, regional wholesale

power trade or regional retail power trade can be established(more

details have been further discussed in Section 2.1).However, one of the key problems in large consumers direct

electric power purchase from generators is the transaction mecha-

nism. At present, a significant amount of research has presented

the issue of bidding strategies for competitive generators and/or

investigating market power in electricity market using supply

function model [9,10], mathematical programming method [11],

and auction theory[12]. And auction-based mechanisms for elec-

tricity dispatch have been implemented in various countries, e.g.,

the United States, United Kingdom and Australia [13]. Compared

with one-sided auctions, double-sided auctions are better regard-

ing price formation, as they are more close to reality, and more

importantly, they can capture essential problems of trade better

than one-sided auctions [14]. The double auction problem for

power suppliers and demanders was addressed for the first timein Ref. [15], in which, market power and efficiency of electricity

market with discriminatory double-auction pricing was studied,

and an agent-based computational model of a wholesale electricity

market to use for economical experiments was constructed, based

on which how the relative market power of the buyers and sellers

varies in response to changes in market concentration and capacity

was discussed. Further, the distinction between traders market

power due to market structure and that due to buyer and seller

learning, as well as its market simulation results confirmed that ac-

tive bidding by buyers will limit the ability of sellers to exercise

market power. In Ref.[16], a method to build bidding strategies

for both power suppliers and large consumers in a poolco-type

electricity market was presented, in which each supplier/large con-

sumer bids a linear supply/demand function, and the system is dis-patched to maximize social welfare. In Ref.[17], the problem of

developing bidding strategies in oligopolistic dynamic electricity

double-sided auctions was studied, and it modeled electricity dou-

ble-sided auctions as dynamic systems and used Nash-Cournot

strategies for market participants.

In Ref.[18], a new method to analyze bidding price of each par-

ticipant (power suppliers and large consumers) in a pay-as-bid

market was presented. In the method, the bidding price is decom-

posed into a variety of components, andthe method is then numer-

ically verified through computer simulations with both generator

and large consumer bidding. In Ref. [19], double bilateral contract

auctions for electric energy purchase and sale in Brazil were ana-

lyzed, and the model proposed in[19]uses Bayes rule and Game

theory to aid the agent in its bid definition. Nash equilibrium

(NE) can be found through the expected payoff matrix of each

agent. In Ref.[20], a new pricing scheme was proposed to deter-

mine social welfare distribution in a centralized pool based on auc-

tion in the context of solving unit commitment problems under

competition. A significant contribution of Toczyowski and Zol-

towska[20]over previous publications on this subject is the inclu-

sion of the price-responsive demand side for multi-period auctions

with dynamic commitment characteristics. The model allows every

thermal unit and every consumer to obtain individual maximum

profits, and at the same time it gives the market coordinator an

adequate tool for solving the ensuing technologically constrained

unit commitment problem with fair market clearing. A detailed re-

search progress in electricity double auction was stated in Ref.[1].

In Ref.[21], trade modes based on auction theory and incentive

compatibility principle of mechanism were designed under an

assumption that there areonly one supplierand oneconsumer. This

assumption seems unreasonable as multiple generators and large

consumers always participate in the power market to introduce

competition and improve economic efficiency. In Ref. [22], the

negotiation based bilateral transaction mode and matchmaking

based concentrated bidding transaction mode for generators and

large consumers were developed, transaction rule and algorithm

were designed, and cross-subsidization were studied emphatically.

However, the impact of power transmission cost was not taken intoconsideration.

Based on participants bidding strategies, auction is an impor-

tant market transaction mode to determine resource allocation

through a series of specific rules and clearing price. Its also an

effective method to distribute scarce goods with asymmetric infor-

mation, based on fair competition and effective utilization of the

scarce goods [23]. Auction has two kinds of essential function:

one is to reveal information; the other is to reduce agency cost

[24].Meanwhile, double auction is studied and applied widely, as

it can help to introduce competition, break relative advantage

and monopolization in monolateral auction, and prevent some par-

ticipators manipulating market. Ref. [25] applied game theory of

incomplete information to study double auction market, in which

there is only one demand, one supplier and one commodity. How-ever, both demander and supplier have motivation to hide real

information in simple double auction market. McAfee[26]studied

second-price sealed auction between multiple buyers and sellers,

and proved that the only dominant strategy of buyers and sellers

is to bid by real valuation and cost. Meanwhile, the mechanism

needs market organizers to balance the budget. All these are lim-

ited to trade one commodity, but there is always multi-unit of

commodities in the market. Ref. [27] modeled a double auction

transaction mechanism which allowed participants to bid with

multi-unit of goods, and it was achieved through the application

of four-dimensional data structure. Ref. [28] modified Vickreys

auction model [23] by introducing minimum order imbalance,

market pressure and reference price into matching algorithm to

form an auction mechanism, i.e., MinMax transaction mechanism.Ref.[29]introduced normalized price and developed an incentive

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compatible double auction mechanism, with the consideration of

transaction cost. There are much more research of double auction

developed in[30].

Most researchers in the area of electricity auctions have drawn

the conclusion that electricity double-sided auctions are more effi-

cient and competitive than supplier-only auctions. But most of the

research only focuses on design of auction mechanism itself and

was based on some assumptions, which are not always reasonable.

Furthermore, little research has considered the transaction cost

based on double-sided auctions, except Ref. [29]. However, in an

actual electric power market, because of large quantity and long

transmission distance, transmission cost takes up a great propor-

tion in total price, thus, it can affect equilibrium pricing strategy

considerably. Therefore, in auction mechanism, the key issue is

not only to prevent or reduce manipulation of market by some par-

ticipants and to inspirit participants to reveal their real informa-

tion, but also to achieve equilibrium strategies under the

consideration of electric power transmission cost.

Based on the research reviewed above, in this paper, a transac-

tion mode between generators and large consumers in bilateral

electricity market is designed, mainly considering impact of power

transmission cost. To be specific, this paper introduces McAfees

second-price sealed auction [26] into multi-unit electric power

transaction between generators and large consumers, designs a

double auction model considering the impact of transaction cost

and power transmission cost into a wholesale electricity market,

and analyses incentive compatibility of the pricing mechanism.

Besides, it also proves that the mechanism can ensure market

clearing and optimal allocation. The paper is organized in five

parts. In Section2, McAfees second-price sealed auction mecha-

nism is introduced into multi-unit electric power transaction

through development of double auction mechanism. Then, the is-

sue of transaction between competitive generators and large con-

sumers is proposed, and some basic assumptions are also stated.

Section 3 focuses on double auction mechanism and incentive

compatibility analysis, based on which, auction rules and transac-

tion rules are discussed. At the same time, considering the impactof transaction cost and power transmission cost, a model to form

electric power price mechanism between competitive generators

and large consumers under power transmission constraint in a

wholesale electricity market is developed. Section 4 examines a

numerical example; analyzing matched efficiency compared with

high and low matching way transaction rules, and other studies.

Section 5 concludes the paper and proposes the prospect of further

study.

2. Problem formulation

2.1. Transaction between large consumers and generators

As we discussed above, China had finished its first step of the

electricity market reform, separating power plants from transmis-

sion grids, establishing transmission companies, and constructing a

competitive generation market. Due to the failure of simulative

market in the Northeast, competition has been introduced to the

end-users, constructing competitive wholesale markets, and per-

mitting distribution companies and large consumers to either

buy electricity from competitive market or directly from power

producers[1]. At present time, regional electricity market of China

was just open to the large consumers and distributors, instead of

other consumers, in the way that large consumers can purchase

electricity from generation companies directly.

This competition model is to permit larger consumers and gen-

erating companies to participate in the competitive electricitymarket. However, there are two ways for competition,

(a) The generating companies and larger consumers declare the

amount and price of electric power they plan to buy and sell

only through the power transaction center, and then the

power transaction center can determine the amount and

price of transaction power according to the balance of supply

and demand. Therefore they cannot directly do the bilateral

transaction and it is a centralized competitive power market.

(b) The generating companies and larger consumers can directly

do deals. The amount of ongrid power is partly traded by the

power transaction center, and the power transaction center

also can determine the amount and price of transaction

power according to the balance of supply and demand. The

remaining ongrid power is traded by directly bilateral deal

between provider and demander, and the pair of quantity

and price is determined by the counterparty, just as exam-

ples in the electricity market of Northern European and

NETA in England. So, this is a moderately centralized com-

petitive market.

Under this competition model, electric power transmission net-

work is only open to large consumers, providing paid transmission

service, and charging the transmission fee from both sides or the

one. However the medium users and small users have to buy

electric power from distributors, that is to say, the transmission

network still owns the exclusive possession in the regional operat-

ing area. The competition model can be found in Fig. 1.

Compared with single-buyer model, the competition model has

the following several advantages. First, it is favorable for generat-

ing companies to make dispersive decisions, and the transmission

and distribution companies need not to take the whole price risk

which is caused by generating market. Second, the generating

companies can participate in the competitive market according

to their productive capacity and cost, and the larger consumers

can participate in the competitive market according to their de-

mands. In this way, the price of power can reflect the situation of

power production cost and the imbalance between supply and de-

mand. Third, it would be beneficial to improve the enthusiasm ofmembers to participate in the competitive market, and also im-

prove the efficiency and effectiveness. Especially the generating

companies and larger consumers can probably avoid the risk of

market price, when generating companies and large consumers di-

rectly sign long-term electricity deal contract, or build the electric

finance deal market. Fourth, it is favorable to protect electric power

investors, lead a long-terminvestment, and keep the relatively sta-

bility of power price. In conclusion, it is a more suitable model for

the stable operation for the development of electricity market.

To carry out trade betweenlargeconsumers andgenerators is an

important link in Chinas market-oriented reform of electric power

system, and it is also one of the important links in structuring a

many-to-many competitive market organization and liberalizing

demand side electricity market. On the premise of separatingplants from power grids and accessing the power grid through

Fig. 1. The competition model.

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competition in power market, large consumers can sign bilateral

contracts with independent generators or power enterprises, and

power is transmitted by power grid and electric distribution net-

works. Along withgradual perfection of Chinas electric power mar-

ket, power grid company will be only responsible for transmission

and distribution service, and withdraw from power transactions

gradually. Currently, a power grid company is just a network pro-

vider, to whom generators or large consumers shall pay wheeling

costand auxiliary service costfor transmission and distribution ser-

vice. The two kinds of cost make up a great proportion in the whole

power cost, so it is indispensable. In the paper, the cost of wheeling

and auxiliaryservice is viewed as power transmissioncost, whichis

shared by both generators and large consumers.

When generators are viewed as the supplyside, large consumers

are viewed as the demand side, the issues can be viewed as a bid

problem that they bid a pair of price and quantity information to

the market. Then, the electric power transaction center matches

generators and large consumers bidding quantity in accordance

with transaction rules of market, to reach the equilibriumof market

clearing. Thus, the problem of optimal pricing mechanism for large

consumers and generators is a double auction between suppliers

and consumers. Meanwhile, as for regional power market where

the market platform of the generation side has been well estab-

lished, especially for the South Regional Electricity Market in China,

transaction between large consumers and generation companies is

recommended to adopt concentrated auction transaction model

which needs specialized technical support system and a series of

supporting market mechanism. And then, participants need to

pay more to build the support systems for transaction, and so, they

have to pay higher transaction cost. Therefore, impact of transmis-

sion cost and transaction cost must be considered in analysis of the

issue of large consumers purchasing electric power directly, and

the double auction model of multi-unit considering power trans-

mission cost can be exactly applied in the following issue.

2.2. Problem description

There are lplayers participated in an auction game of large con-

sumers purchasing power from generators directly. m generators

are willing to supply Munits of electric power, and n (n= lm)

large consumers will purchase Nunits of electric power. Each large

consumerjhas his own private value vjfor a unit of electric power,

and each generation company ihas its private cost ci for one unit of

electric power he produces. The generation companys bidding

price strategy is si(ci), the large consumers bidding strategy is

bj(vj), and they report their biddings at the same time. ci and vjare their private information respectively and are not affected by

other participants directly. Everyone will make decisions under

incomplete information, so the problem is a double auction issue

under incomplete information. Especially, when transaction center

of the market conclude the equilibrium status and equilibriumprice, they should consider power transmission cost in this paper.

Therefore, the problem is also a double auction issue considering

power transmission cost.

2.3. Basic assumptions

The following seven assumptions in this paper are proposed as

follows:

(a) Electric power is homogeneous, i.e., there are no difference

in variety, quality, etc.

(b) Suppliers and consumers are risk-neutral, and participants

are rational. Participants select to withdraw themselves

from the game under the situation that they will get moreif they do not take part in the game.

(c) Suppliers production cost and demanders estimated evalu-

ation of electric power are private information, which is

unknown to other players.

(d) Sealed auction and periodic double auction are adopted. In

an auction cycle, generators and large consumers offer their

bidding information to the organizers by their own valua-

tion, independently and simultaneously. Then the organizers

determine transaction quantity and price by auction rules.

(e) Uniform clearing pricep in the transaction is adopted. There-

fore, the generation company iobtains utility: usi pcixi,

the large consumerjobtains utility ubj vj pyj, and social

total surplus is U= US + UB (including transmission cost and

transaction cost). Meanwhile,xiandyjdenote efficient trans-

action quantity of generators and large consumers

respectively.

(f) Power is divided into items, so the quantity of power is con-

sidered as a discrete multi-unit. The unit can be freely

chosen.

(g) Only power transmission cost and transaction cost are con-

sidered in the transaction, and both are shared by large con-

sumers and generators. Transaction cost is an additional

expense that generators and large consumers must pay for

in the transaction.

3. The double auction for competitive generators and large

consumers with the consideration of power transmission cost

3.1. The double auction mechanism for competitive generators and

large consumers

Auction is a market mechanism to form a series of explicit rules

(auction rules, transaction rules), which determine resource alloca-

tion as well as market clearing price on the basis of the participants

bidding strategies. Auction organizers are rational social planners,

and their aim is to maximize generators and large consumers ex-

pected utilities by designing a double auction mechanism.

3.1.1. Auction rules

Thereare generators andlarge consumers in the electricity mar-

ket. Firstly, they apply for transaction to organizers, i.e., each par-

ticipant will offer his bidding information (price, quantity) to

organizers. Then, organizers check legality of their bids, and orga-

nize auction deal according to some certain auction rules. If prices

are unreasonable, organizers inform both sides to re-bid. Other-

wise, auction rules could be developed to buy or sell electric

power. To be more specific, organizers rank the generators bids

in an increasing order by price, while the large consumers bid-

dings in a decreasing order by price, and the same bidding price

randomly. At the same time, every bid repeats to be sorted accord-

ing to its quantity. That is, as every bid is only corresponding to

1 kWh electric power, if the quantity of some bid is 20 kWh, thecorresponding participant equal to 20 virtual participants whose

bidding quantity are 1 kWh. Therefore, we view l actual partici-

pants as L= M+ Nvirtual participants and every participant can

only trade 1 kWh electric power.

As it is shown above, generators bidding set is WS =

{s1, . . ., si, . . ., sm}, and large consumers bidding set is WB =

{b1, . . ., bj, . . ., bn}. Let rank() denote position of every bid in the

set. In addition, sk is thekth low price inWS, andbl is thelth high

price in WB. The clearing rules, clearing price and transaction set

which matches generators and large consumers immediately on

detection of compatible bids are proposed as follows: If blP sk,

bl< sk+1, sk> bl+1, the large consumer bids will be in transaction

set when it is no less than bl, the generators bids will be in the

same set when it is no more than sk, and the set is{si> 0jsi 6 sk} [{bj> 0jbjP bl}. However, some participants bids


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When large consumer bids by his real valuation, i.e., bj= vj(b), com-

bined with these equations and large consumers pricing formula of

normalized price, we get Eq.(6)andh = 1.

b0j vjb1 bkj=kj

P vlbkj=kjb1 bkj=kj vlb1> b0l 6

Then the large consumer can obtain the maximal expected utility.

Ifvj b(kj)/kj< vl, utility ofjis negative. As the large consumer is ra-

tional, the large consumers optimal strategy is bj = vj.

Thus,vj< vl+ b(kj)/kj, h= 0, and the large consumers utility is 0.

Therefore, regardless of the large consumers valuation for electric-

ity, bidding according to their real valuation is always optimal.

(b) Whenp 2[ck,vl] utility ofj is defined by Eq. (7)as transaction

cost is considered.

uj vjbkj=kj ph 7

Ifvjb(kj)/kjPp, utility ofj is nonnegative, and as indicated pre-

viously, j always intends to maximize probability of winning auc-

tion in this situation. Because the large consumers bid satisfies

vjP bj, that is, the large consumer can obtain the maximum utilitywhen he bids by his real valuation,bj= vj. Ifvjb(kj)/kj

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sion cost are great disparity in numerical value (which is illus-

trated by calculation), transaction cost has little influence on

matched set, so it will not be considered. Therefore, multi-objec-

tive linear programming problem of Eq. (3) becomes a simple

transportation problem. Subsequently, by table operations method

of transportation problem, the final matched transaction result,

shown inTable 5, is given. According to matched transaction set,

the total transmission cost is 1,035,000 Yuan, the total transaction

cost is 19,630 Yuan, and the total cost is 1,054,630 Yuan.

4.2. Result analysis of matched efficiency

As social planners, auctioneer should focus on the matched effi-

ciency (market efficiency) in mechanism design besides the con-

sideration of cost. This paper introduces market efficiency

defined by Plott and Sunder [31], i.e., ratio of actual income w1and theoretical income w0. Theory income is calculated based on

two classic models of double auction: static competitive equilib-

rium model and dynamic Marshallian path [32]. The corresponding

formula is as follows:

w0

Xai1 pcixi

Xdj1

vjpyj

9

In Eq.(9),cidenotes the ith low cost,vjdenotes thejth high value,xiandyjdenote the participants transaction quantity. In the example,

the theory income in electricity market is 130,000 Yuan. When

transaction and transmission cost are not considered, actual income

is calculated in the same way. So

w1 X

us X

ub vg 2vb 2vc 2vf 3va 5cC cG

130; 000 Yuan 10

Therefore, market efficiency of the auction mechanism is 100%,

which illustrates that the auction mechanism is efficient. Addition-

ally, due to other factors, such as difference in commodities or par-

ticipants risk preference, the actual market efficiency is less than

100% in actual auction market.

4.3. Comparison analysis

4.3.1. Comparison with high and low matching way transaction

rules

In the example, if we adopt high and lowmatching way trans-

action rules, transaction set, transaction quantity and clearing

price remain the same. That is, sellers transaction set is {G, C}

and buyers transaction set is{g,f, c, a, b}. Meanwhile, b only trades

2 units of power. At the end of auction, 10 7 kWh power have been

traded and the price is 0.406 Yuan/kWh. Participants profit can be

calculated according to assumption (e) and the total social surplus

is 130,000 Yuan after transaction. However, according to high and

low matching way transaction rules, every bid repeats to besorted according to its quantity. Sellers transaction set is ranked

in an increasing order, i.e., {C, C, C, C, C, G, G, G, G, G,}, and buyers

transaction set is ranked in a decreasing order, i.e.,

{g,f,f, c, c, a, a, a, b, b}. Firstly, the buyer with the highest priority

trades with the seller with the highest priority; then the buyer

with the second highest priority trades with the seller with the sec-

ond highest priority; and so on. Finally, transaction set is matched,

as shown inTable 6, is given.

Table 1

Biddings information.

Seller Bidding (Yuan/kWh) Quantity (106 kWh) Buyer Bidding (Yuan/kWh) Quantity (106 kWh)

A 0.421 2 a 0.411 3

B 0.415 3 b 0.410 3

C 0.401 5 c 0.416 2

D 0.428 1 d 0.404 4

E 0.422 2 e 0.398 5

F 0.408 4 f 0.418 2

G 0.402 5 g 0.424 1

Table 3

The ranking of participants.

Rank Participants Bidding (Yuan/kWh) Rank Participants Bidding (Yuan/kWh)

15 C 0.4007 1 g 0.4240

610 G 0.4017 23 f 0.4181

1114 F 0.4077 45 c 0.4161

1517 B 0.4143 68 a 0.4112

1819 A 0.4209 911 b 0.4102

2021 E 0.4219 1215 d 0.4043

22 D 0.4280 1620 e 0.3983

Table 2

The participant s transcation cost (104 Yuan).

The number of transactions The quantity of a transaction/106 kWh

1 2 3 4 5

1 0.120 0.220 0.303 0.372 0.430

2 0.232 0.314 0.390 0.4543 0.320 0.406 0.476

4 0.420 0.497

5 0.512


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According to cost information inTable 2 and 4, the total trans-

mission cost and the total transaction cost are 1,130,000 Yuan and

19,430 Yuan respectively, combined with the matched transaction

set. Finally, the total cost is 1,149,430 Yuan, which is 94,800 Yuan

more than the auction mechanisms cost in this paper. Therefore,

considering power transmission cost, the auction mechanism in

this paper can optimize the total transmission cost and gain much

more social welfares.

4.3.2. Comparison with other studiesOur findings regarding market efficiency support the conclusion

reached by Nicolaisen et al.[15] that high and low matching way

transaction rules are efficient. However, since Nicolaisen et al. only

considered discriminatory pricing to differentiate between struc-

tural and strategic market power, they have not taken the maxi-

mum of social welfare into account. At the same time the

transaction cost and transmission cost also were not being consid-

ered, thus it cannot reach the optimal state.

In our context, the uniform auction protocol is used to maxi-

mize the social welfare. Auctioneer can attempt to increase the re-

mains of producers and consumers in the sense that liquidation

price is lower than the price the sellers ask and higher than the

price the buyers bid. On the other hand, auctioneer can attempt

to improve the social welfare by giving all buyers and all sellersless information rents, but the decrease of information rents is

not led to decline in incentive. In addition, our auction model con-

sider the minimum of transaction cost and transmission cost,

improving the efficiency of transaction further, and supply decision

support to realize the resource allocation. As discussed in part one

of Section4.3, only transaction cost and transmission cost are con-

sidered, and much more social welfares are got.

Our findings regarding the double auction are reminiscent of

the conclusion reached by Fang and Wang [21]and other previous

researchers regarding the double auction between one seller and

one buyer. A double auction between one seller and one buyer is

a double auction in which one large customer bids and one gener-

ation company asks, both of them carry out one-for-one transac-

tion and determine the price of electricity, at the same time,Fang and Wang [21] solved Bayesian Nash equilibrium, obtained

the equilibrium bidding strategies of the generation company

and large customer. As noted in [33], double auction between

one buyer and one seller for a single object have been observed

to induce very efficient outcomes under a wide range of treatment

conditions. For a wide class of problems, Myerson and Satterthwa-

ite [33]showed how to compute mechanisms that maximize ex-

pected total gains from trade, and mechanisms that can

maximize a brokers expected profit. However, since Fang and

Wang [21] only considered double auction between one seller

and one buyer for a single object, they are not led to consider the

competition among generators and among large consumers, and

also the transaction cost and transmission cost.

In our context, the double auction between competitive gener-

ators and large consumers for multiunit objects are developed,

auctioneer can attempt to use the set of allocation mechanisms

that are incentive compatible and individually rational to disclose

the cost of generators and the valuation of large consumers. At the

same time, transaction cost and power transmission cost are con-

sidered to optimize the allocation mechanisms.

Our model regarding game process is obviously different from

the model proposed by Azevedo and Correia[19]. In Brazilian elec-

tric power market, both in the purchase auctions and in the sales

auctions, there are two stages, the first stage is closed, and in it

the seller or buyer agents define their bids in levels. In the second

stage, the first level of the sellers or buyers agents bids is revealed

and the buyers or sellers negotiate in an English ascending auction.

They modeled the game in the double bilateral contract electric en-

ergy auctions in Brazil by only three agents. Therefore the issue of

the double auction is simplified.

In Chinese electricity market, Wholesale competition model is

adopted to permit larger consumers and generating companies to

participate in the competitive electricity market, in the competi-

tion model, all the sellers ask and all the buyers bid, they submit

sealed price and quantity to auctioneer simultaneously, then the

auctioneer discloses their submissions and organizes them to

transact according to auction model. At the same time, in China

the distance between generator and large consumer is perhapstoo long to omit the transmission cost, the quantity of power trans-

action is diverse, and transaction cost cannot be neglected. So in

this paper, a double auction model for competitive generators

and large consumers considering power transmission cost is

formed to capture Chinese electric power transaction.

5. Conclusions

A double auction model to structure optimal pricing mechanism

for both competitive generators and large consumers considering

power transmission cost in the wholesale electricity market is pre-

sented in this paper. After forming pricing issues in the deregulatedelectricity market, auction rules and transaction rules are pro-

posed. And analysis shows that the optimal pricing mechanism is

incentive compatible to participants with neutral attitude to risk.

An example with eight suppliers and eight large consumers has

been used to demonstrate the model. Compared with high and

low matching way trading rules, the auction model in this paper

can increase the probability that generators providing a large num-

ber of supply and large consumers with high demand win the auc-

tion. Further, the transaction rules in this paper can optimize the

whole transmission cost and transaction cost under market equi-

librium, and the system is dispatched to maximize social welfare

when transmission cost and transaction cost are considered. With

the application of the model in the paper, competition is intro-

duced into demand side electricity market and a fair, open, trans-parent and standardized electric power market is restructured.

Table 6

The results of matched transaction under high and low matching way transaction

rules.

Generatori Large consumerj

1(a) 2(b) 3(c) 4(f) 5(g) Supply/106 kWh

1(C) 0 0 2 2 1 5

2(G) 3 2 0 0 0 5

Demand/106 kWh 3 2 2 2 1 10

Table 4

Information of transmission cost (Yuan/kWh).


1(a) 2(b) 3(c) 4(f) 5(g)

1(C) 0.110 0.115 0.100 0.125 0.095

2(G) 0.135 0.090 0.120 0.105 0.130

Table 5

The results of matched transaction.


1(a) 2(b) 3(c) 4(f) 5(g) Supply/106 kWh

1(C) 3 0 1 0 1 5

2(G) 0 2 1 2 0 5

Demand/106 kWh 3 2 2 2 1 10


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Compared to other previous studies, our findings have impor-

tant implications for research. First, regarding the double auction,

transaction cost and transmission cost are considered simulta-

neously, the double auction in constraint of transaction cost and

transmission cost are constructed, which have been observedto in-

duce very efficient outcomes. Second, the pricing mechanism in

double auction is the uniform auction protocol, which inherently

improve the remains of producers and consumers. Thus, the social

welfare generated by the double auction will be improved greatly.

Last but not the least, our double auction between generators and

large consumers with the consideration of transmission cost model

the context of Chinese electricity market, it has more powerful to

simulate the reality.

Compared withthe on-goingrules of the Chinese electricity mar-

ket thatemphasized the one-for-onetransactionmode betweenone

large customer and one generation company, the auction rules in

this work are many-to-many transaction mode, and will improve

the operation efficiency (as discussed in Section4.3). In particular,

thistypeof efficiencyimprovementcanbe achievedthrough the fol-

lowing two ways. One is introducing competition both in supply

sideand in demandside, oncecompetition is introduced, generators

will be incentive to lower their cost, and large consumers will also

have theincentive to increase their valuation. The other is consider-

ing the transaction costand transmission cost, when the transaction

cost and transmission cost are considered, auctioneer will optimize

resource allocation by optimizing the matching process.

However, the double auction model for competitive generators

and large consumers only considers power transmissions cost and

transaction cost, while in a complete open bilateral electricity mar-

ket, to carry out transaction between large consumers and genera-

tors will cause adjustment of interests and cross-subsidization.

More research is needed on how to consider joint effect of power

transmission constraint and cross-subsidization at the same time.

In addition, the representation of the traders actions in the

current study is very simplistic: each trader submits a single price

offer anda singlequantity offer to theauction in each auctionround.

In each auction round, each generator submits a supply functionrather than a single pricequantity pair, each large consumer sub-

mits a valuation function rather than a single pricequantity pair.

So research is also needed on developing an optimal pricing mecha-

nismfor competitive generators and large consumers when bidding

strategy functions are the general continuous functions.

Acknowledgements

The authors thank Tharam S. Dillon and two anonymous refer-

ees for thoughtful constructive comments.

The work is supported by the National Natural Science Founda-

tion of China (NSFC71103135) and The Project-sponsored by SRF

for ROCS, SEM to Debin Fang and the Humanities and Social Sci-

ence Research Projects of the Ministry of Education of China

(11YJCZH221).

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