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Meeting peak electricity demand through combinatorial reverseauctioning of renewable energy

Shubhashis Kumar SHIL1, Samira SADAOUI1

Abstract The option of organizing E-auctions to purchase

electricity required for anticipated peak load period is a

new one for utility companies. To meet the extra demand

load, we develop electricity combinatorial reverse auction

(CRA) for the purpose of procuring power from diverse

energy sources. In this new, smart electricity market,

suppliers of different scales can participate, and home-

owners may even take an active role. In our CRA, an item,

which is subject to several trading constraints, denotes a

time slot that has two conflicting attributes, electricity

quantity and price. To secure electricity, we design our

auction with two bidding rounds: round one is exclusively

for variable energy, and round two allows storage and non-

intermittent renewable energy to bid on the remaining

items. Our electricity auction leads to a complex winner

determination (WD) task that we represent as a resource

procurement optimization problem. We solve this problem

using multi-objective genetic algorithms in order to find the

trade-off solution that best lowers the price and increases

the quantity. This solution consists of multiple winning

suppliers, their prices, quantities and schedules. We vali-

date our WD approach based on large-scale simulated

datasets. We first assess the time-efficiency of our WD

method, and we then compare it to well-known heuristic

and exact WD techniques. In order to gain an exact idea

about the accuracy of WD, we implement two famous

exact algorithms for our constrained combinatorial pro-

curement problem.

Keywords Renewable energy auctions, Combinatorial

reverse auctions, Electricity auctions, Retail markets,

Winner determination, Genetic algorithms, Multi-objective

optimization

1 Introduction

1.1 Scope and problem

The electrical sectors in many countries are currently

undergoing reformations, particularly in the form of

deregulation of the markets and privatization of power

retailers [1, 2]. Furthermore, there has been a substantial

increase in the number of online electricity auctions over

the last decade due to their ability to improve allocative

efficiency and to foster competition among power suppliers

[1, 3, 4]. Auctions can be technology specific (one or more

renewable energy) or neutral (past and new technology)

[5]. Renewable energy, especially wind and solar, has

performed successfully in the markets, and its usage is

increasing rapidly due to the environmental concerns [6].

For instance, renewable energy grew by 66.4% in 2012 in

the Brazilian market [7], and by 60% in 2013 in the

Spanish market [3]. In some countries, such as Brazil and

Germany, a good portion of electricity is generated from

wind energy, which has almost no marginal costs [8].

Consequently, wind is preferred to other energy sources

[8]. It has also been shown that the entry of new energy

CrossCheck date: 17 September 2017

Received: 7 May 2017 / Accepted: 17 September 2017 / Published

online: 24 November 2017

� The Author(s) 2017. This article is an open access publication

& Samira SADAOUI

[email protected]

Shubhashis Kumar SHIL

[email protected]

1 Department of Computer Science, University of Regina,

Regina, SK, Canada

123

J. Mod. Power Syst. Clean Energy (2018) 6(1):73–84

https://doi.org/10.1007/s40565-017-0345-5

http://orcid.org/0000-0002-9887-1570

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sources into the markets is a catalyst for economic growth

[3]. Numerous governments have adopted renewable

energy auctions, and their number has increased from 9%

in 2009 to 44% by the beginning of 2013 [2]. A common

type of electricity auctions is for awarding contracts for the

construction of new renewable energy facilities [1]. The

target of all these auctions is to attract new investors (small

and large) [5]. Existing electricity auctions are mostly

oriented towards awarding long-term contracts, typically

with one or two suppliers over many months or years

[2, 5, 9], with very few focusing on short-term contracts

(few hours) [1, 10]. Nonetheless, most of the literature on

electricity markets does not disclose and describe the

auction design and features, bidding strategies and winner-

determination methods. The literature mainly reports on

the benefits and the economic impact of electricity auctions

that have been implemented in certain countries.

Electricity consumption is rapidly increasing due to the

growth of populations, infrastructures, and economies. This

growth in demand has created a very real challenge for

public utility companies, particularly with respect to

avoiding serious service problems, such as power outages

during high demand like in hot summer days and cold

nights. In order to meet the additional load during peak

periods, utility companies may need to procure electricity

from other sources. To this end, they can organize an

online auction to purchase electricity that has been gener-

ated from diverse sources of renewable energy. To the best

of our knowledge, organizing electricity auctions in order

to address peak load problems is a new strategy. Indeed, all

prior attempts to manage the demand load have been based

on recommendation systems for controlling electricity

consumption on the customer side [7]. The recommenda-

tions are generated based on the behavior, life style and

feedback of the consumer. In our point of view, this

approach is not only an invasion of the consumer’s privacy,

but it may also be untenable as consumers may not be able

to comply with the recommendations.

1.2 Contributions

For the sole purpose of offsetting anticipated extra

demand load, we introduce a new type of electricity auc-

tion tailored for Consumer-to-Business and Business-to-

Business contexts. Utility companies may procure the

needed power simultaneously from other available sources.

Our electricity auction differs substantially from those that

have been previously proposed and implemented for the

following reasons:

1) We devise an auction for the specific purpose of

avoiding power outages during peak load periods. Our

auction is defined by very short-term contracts with

terms that range from minutes to hours.

2) We contract electricity from diverse sources, such as

variable energy (solar and wind), active controllable

load (like battery storage, battery of electric vehicles,

and heat storage), and controllable renewable energy

(like hydroelectricity, biomass, and geothermal heat).

3) We encourage homeowners to be involved in our new

electricity market. Indeed, these small players will

have an active role. The authors in [11] claimed that

suppliers of varying sizes will be involved in the

electricity markets of the future.

In the present study, we introduce an electricity com-

binatorial reverse auction (CRA). Designing an appropriate

auction format in the electricity sector is a challenging task

[4]; thus, in designing our particular CRA, we have

attempted to determine the most relevant features and

solving mechanisms that produce the best outcome in terms

of solution quality and time-efficiency. Our auction con-

sists of several items, each representing a time slot of

15 minutes. Each item possesses two negotiable attributes,

electricity price and quantity, and several trading con-

straints as well. However, the two attributes are in conflict,

as the buyer’s objective is to simultaneously realize lower

prices and increased quantities. Limited studies have been

conducted on electricity combinatorial auctions despite the

fact that they match demand and supply very efficiently

(price-wise) and maximize the buyer’s revenue [12]. Still,

these studies have several limitations. For example they

usually consider only the price attribute but not the other

attributes that are also important for trading. Moreover,

these studies take into account very few or no constraints of

the buyers and sellers.

The mechanism of electricity CRA leads to a complex

winner-determination (WD) problem. Searching for the

best solution (a set of winning sellers) in traditional CRAs

(i.e. multiple items and single attribute) is already difficult

due to computational complexity [12]. Past studies have

adopted exact algorithms to find the optimal solution in

CRAs, but these algorithms were accompanied by an

exponential time cost [13], which is unpractical in real-life

auctions. To address this time issue, researchers introduced

evolutionary optimization techniques, such as genetic

algorithms (GAs), which produce high-quality solutions

(sometimes the optimal solutions) with an excellent time

efficiency [14]. Furthermore, dealing with several con-

flicting attributes makes finding the best solution even

more difficult and time consuming. Consequently, evolu-

tionary multi-objective optimization (EMOO) methods

have been proposed as the best way of finding the best

trade-off solution that minimizes cost and time. In our

study, we customize our GA-based EMOO WD algorithm

74 Shubhashis Kumar SHIL, Samira SADAOUI

123

introduced to accommodate CRAs with multiple units,

multiple attributes, and conflicting objectives [15]. Our

WD technique returns a solution that consists of several

winning suppliers who are chosen to provide electricity for

multiple time slots. In theory, this solution should satisfy

all the buyer requirements as well as supplier constraints

and offers. In addition, this solution represents the best

combination of suppliers for lowering the price and

increasing the quantity. The way we produce the winning

solution ensures that the buyer gets power for each time

slot. With the help of our electricity CRA, grid companies

will be able to obtain the needed power at a good price due

to the highly competitive nature of auctions.

Moreover, we conduct a real case study to illustrate the

feasibility of our electricity procurement auction, WD

method, and generated solution. Afterwards, we validate

the WD approach using simulated data by generating large-

scale instances of our advanced electricity CRA problem.

The goal of the experiments is twofold: first, to assess the

time-efficiency of our WD method, and second, to compare

its performance to well-known heuristic and exact WD

techniques that have been proposed for much simpler

CRAs. The execution time is not the only critical auction

requirement; the quality of the winning solution is impor-

tant as well. Therefore, we fully implement two famous

exact algorithms to solve our complex combinatorial pro-

curement problem in order to evaluate the accuracy of our

WD method (how close the produced solution comes to

being optimal).

There are several significant benefits of our new elec-

tricity CRA. First, our auction represents a key solution to

the extra demand load problem. Second, designing an

auction with 15-minute intervals allows for greater equality

of opportunity between small players (such as residents)

and big players (plants). Third, our smart electricity market

will greatly benefit utilities and their consumers both

environmentally and economically. Fourth, this market will

encourage the expansion of renewable energy facilities

especially home-based technologies that are accessible to

customers, such as solar panels and plug-in electric

vehicles.

2 Related works

In most of the literature on electricity markets, auction

design and features, bidding strategies, and winner deter-

mination methods are not described. The literature mainly

reports on the benefits and the economic impacts of elec-

tricity auctions that have been implemented in certain

countries. There are few studies about the underlying

mechanisms of electricity auctions, and most of them have

several limitations. Researchers limit the auction features

and parameters to reduce the complexity of the WD

methods because the processing time is a real challenge for

these optimization procedures. In this section, we also

show that evolutionary algorithms are appropriate in the

context of combinatorial auctions.

2.1 Electricity auctions

Here we examine the few studies regarding the design of

electricity combinatorial auctions. There are limited elec-

tricity combinatorial auctions despite the fact they provide

a very efficient resource allocation and maximise the rev-

enue of the auctioneer. Even though the WD in these types

of auctions is a complex task, CRAs have been successfully

adopted in other domains for both governmental and pri-

vate sectors [16].

Reference [17] introduced a new double combinatorial

auction protocol called the probability bidding mechanism

(PBM) that takes into account several constraints to mini-

mize the price and to maximize the trading quantities. The

authors considered multiple attributes, such as the elec-

tricity price, transmission cost, network congestion and

technology constraints. They implemented an agent-based

system to develop and validate PBM and also to compare it

with the high-low matching bidding mechanism. They

claimed that PBM significantly optimizes electricity pro-

curement and promotes economic growth. However, PBM

is just an ideal model and has not been yet applied to real

electricity markets. In another study [8], the authors tackled

combinatorial reverse auctions with multiple units for both

single and multiple items in the context of electricity retail

market. They allowed partial bidding to maximize the

auctioneer profit. They exposed the optimal single-item and

multi-item clearing WD algorithms (based on brute-force

technique) with constrained bidding. Daily auctions are

held where the utility companies compete for 24 items

(each item is 1 hour long). The authors utilized Vickrey-

Clarke-Groves bidding format because in this protocol the

dominant strategy of bidders is to submit their true valua-

tion of the items. They validated the two WD methods by

comparing them with an existing optimal exact WD algo-

rithm. More recently, [16] developed a Web-based CRA

(single unit and single attribute) with user interfaces for the

electricity retail market to minimize consumer expendi-

tures. This auction allows consumers to open auctions,

define hourly consumption amounts and choose suppliers

with the cheapest power acquisition. The authors claimed

that this flexibility of consumers creates more competition

among suppliers, and ultimately increases the number of

suppliers and the profit of consumers. They employed the

well-known optimizer IBM CPLEX to determine the auc-

tion winners. They proved that their protocol produces

efficient allocation of electricity usage because consumers

Meeting peak electricity demand through combinatorial reverse auctioning of renewable energy 75

123

purchase electricity from several companies to minimize

their expenditures. Nevertheless, this auction system was

not tested yet with real markets.

2.2 Economic impact

Most of recent reports are about wholesale electricity

markets in South America (e.g. Brazil) and Europe (e.g.

Germany and UK). Over the years, many countries

embraced renewable energy, especially wind and solar.

Reference [3] showed that in Brazil, the largest producer of

electricity from renewable energy, auctions play a huge

role to recover the energy costs with profit. The authors

discussed the long-term incentive policies of renewable

energy markets and long-term auctions. Reference [18]

analyzed the markets of most of the European countries by

focusing on the day ahead, intra day and balance markets.

This paper compared these markets based on several bid-

ding mechanisms, price formation and timing. The target of

these auctions is to reduce the management cost. The

authors mentioned that a good knowledge of the electricity

markets is the key to gain profit from a single or a portfolio

of power plants. They also analyzed the projects conducted

by the European electricity agencies in order to harmonize

the wholesale markets in the continent. Moreover,

according to one of the agencies, integrating wholesale

balance electricity auction markets can save hundred mil-

lion dollars per year. In [2], the authors are interested in

auction design, information structure and bidding behavior

that influence the market outcome when bidders do not

fully know about their competitor costs. They examined the

market circumstances and addressed the market efficiency

that is enhanced when the number of steps of bid-schedules

is restricted. According to their research, market trans-

parency also plays an important role in the auction market

efficiency. The authors developed multi-unit procurement

auctions where suppliers have uncertain costs and pro-

duction units. Lastly [19] discussed the European transition

to green energy in the market. The authors concluded that

auctions are the best option in the electricity market

because they achieve considerable cost savings. As an

example, they mentioned the success of UK that droved

down the electricity price using renewable energy sources.

2.3 Evolutionary WD techniques

Reference [20] demonstrated that evolutionary algo-

rithms are suitable and perform well in the context of

combinatorial auctions. The authors exposed an Evolu-

tionary Iterative Random Search Algorithm defined for

auctions with multiple units and multiple rounds. They

showed that their protocol achieved Nash Equilibrium in

the following way: assume all the bidders offer the same

price at the begining; if any bidder bids higher, the utility

value of his bid will decrease; otherwise, the utility value

will be zero. The same case holds for sellers. This situation

indicates that the market is in Nash Equilibrium. Reference

[21] presented a GA-based optimal resource allocation

approach for combinatorial auctions with multiple units

and multiple rounds. This method, shown to be feasible and

effective through simulation, is able to maximize the total

trading amounts of sellers and to reduce the processing

time in the context of WD problem. Reference [21]

claimed that when the resource allocation problem has

feasible solutions, then Nash equilibrium is always guar-

anteed. Moreover, in [6], the authors proposed a Nash

Equilibrium Search Approach (NESA) that consists of a

local search procedure and an evolutionary algorithm. They

solved the WD problem in the context of standard com-

binatorial auctions, and validated the WD procedure by

measuring the performance of their Nash-Equilibrium

solution based on revenue performance, anytime perfor-

mance and optimal solution comparison. NESA is able to

produce near to optimal solutions. Moreover [6] showed

that NESA performs pretty well for large (2000 bidders and

200 items) and small (1000 bidders and 100 items) scale

settings. They also discussed the stability of Nash

Equilibrium to solve the WD problem in combinatorial

auctions. After a certain time, the equilibrium is established

and then remains in the equilibrium position.

3 Auctioning electricity from diverse sources

3.1 Auction features

We design the electricity CRA mechanism with relevant

features described below.

1) Reverse. The distribution company (buyer) purchases

electricity from multiple suppliers. This electricity is

needed for the under-supply period, which is usually

one or two hours. A supplier could be a resident or a

plant. We contract electricity from diverse energy

sources that fall into two main classes: renewable

energy and active controllable load (also called

storage). The former has two sub-classes: variable

energy (not controllable due to its unpredictable na-

ture) and non-intermittent renewable energy.

2) Combinatorial. The auction consists of multiple items,

each one representing a time slot of fifteen minutes

within the demand period. In this way, residents will

be able to sell energy to the grid company, as they will

be able to generate enough electricity to satisfy the

demand of a 15-minute window.


123

3) Two conflicting objectives. Suppliers compete on two

attributes, quantity and price of electricity. These

attributes are in conflict because the utility company’s

objective is to simultaneously reduce the price and

increase the quantity.

4) Trading constraints. The buyer must decide on certain

trading requirements, such as the demand period,

power quantity and set price. Providers must also

indicate their own requirements, such as the minimum

price and operational constraint, which depend on the

energy type and its production costs. Electricity price

may vary throughout the day in a free retail market.

5) Sealed bidding. Our auction is sealed-bid that is it does

not reveal any information about the competitors’

offers in order to protect their privacy. With a sealed-

bid protocol, truth telling is the dominant bidder

strategy [8]. Sealed auctions are simple, foster com-

petition among bidders and prevent their collusion

[17, 22]. It has been shown in the literature that sealed

auctions attract more participants than ascending open

auctions.

6) Two bidding rounds. In the first round, suppliers of

variable energy are given a chance to compete on

items for which they can provide electricity according

to the weather forecast. Wind and solar sources have

greatly contributed to the Brazilian electricity market

during the winter and summer months, respectively

[3]. In long-term auctions, wind energy has proven its

market potential due its good performance [3]. To

secure any remaining power demand following the

first round, the other non-intermittent sources, like

controllable load and renewable energy, participate in

the second round. For instance, storage can accom-

modate the need of the power system at any time.

3.2 Auction process

Our electricity auction is conducted with six major

phases, which are described in the following sections.

Figure 1 presents an example of the electricity procure-

ment scenario.

3.2.1 Auction demand

The utility company specifies its needs with the fol-

lowing requirements:

1) Demand period. The time interval of the needed

electricity (peak period), which is split into slots of

fifteen minutes (called items).

2) Electricity quantity. The electricity that is required for

the demand period; the electricity quantity is defined

in terms of a minimum electricity amount (to avoid a

blackout) and a maximum electricity amount (to avoid

an excess).

3) Constraints on items. Each item is described in terms

of three hard constraints: minimum and maximum

electricity amount, and maximum allowable price.

3.2.2 Supplier registration

Potential power suppliers (those already connected to

the electric grid via smart meters) are then invited to the

auction, and buyer requirements are fully disclosed to

them. Smart metering enables a supplier to transfer elec-

tricity to the grid. Interested suppliers, including residents

and plants, can register to provide electricity according to

the auction demand.

3.2.3 Supplier constraints and bids

Suppliers differ in terms of electricity production costs

and also the constraints on how electricity can be generated

and transmitted. The price of electricity depends on pro-

duction costs, which may also increase as more electricity

is produced. Prior to bidding, participants submit two

constraints:

Round 1 Round 22. Supplier registration

Variable energy

Controllable loadand renewable energy

Plant 3

Resident 2

Hydro

Battery ofelectric vehicle

Supplier

3. Bidding

Buyer

Public utility

4. Winner determination

3. Bidding

1. Electricitydemand

5. Electricitysupply

Resident 1

Plant 1

Plant 2 Wind

Wind

Solar

Fig. 1 Electricity combinatorial reverse auction


123

1) The minimum price of each selected item. The

supplier is not willing to sell less than this price.

2) The operational constraint, or how long the supplier

will be able to stay active during the delivery period

after switching their status from OFF to ON.

Once the constraints have been established, suppliers

compete independently for one or more time slots (a bundle

of items). They bid on two attributes for each item:

quantity and price. Each bid should respect the buyer’s

requirements. If a seller commits for a certain item, he

should fully realize the contract if he is the winner of that

item. To help mitigate the uncertainties associated with

variable energy, we design our auction with two bidding

rounds (each one lasts 20 minutes).

Round 1: This round is for the suppliers of variable

energy. Only these providers are allowed to submit partial

bids because they might not be able to generate electricity

all the time. Besides, it has been shown that partial bidding

increases the buyers’ gains [8]. When these suppliers bid

for an item, we assume that they are able to allocate the

electricity according to the weather forecast.

Round 2: In the event that there is still unsatisfied

demand following round one, the remaining items are bid

upon by controllable energy providers (renewable energy

and storage). The items in round two are either: items that

do not have any placed bids, and/or items that did not

receive a winning offer during the first round.

3.2.4 Winner determination

Our WD algorithm searches efficiently for the best

trade-off solution, which is the solution that satisfies all the

buyer requirements as well as supplier constraints and valid

bids. The solution represents the best combination of sup-

pliers that results in the lowest price and greatest quantity

of electricity. More precisely, it consists of a set of winning

suppliers, their prices, quantities and schedules. There will

be several winners for the auction and one winner for each

item. Our WD is described in details in Sect. 4.

3.2.5 Trade settlement

The winning suppliers allocate the required electricity

with regard to the trading schedule and placed bids. To

conduct a successful delivery of power, we consider the

following assumptions:

1) All suppliers are in the OFF mode at the beginning of

the demand period.

2) Switching every fifteen minutes between suppliers will

not be an issue for the power grid.

3) We have full power output from the electricity

sources.

4 Auction winner determination

In [23], an efficient GA-based EMOO algorithm was

introduced to solve CRAs with multiple items, units,

attributes and objectives. We customize this algorithm [23]

specifically for our electricity auction: multiple items,

single unit, two attributes and two conflicting objectives.

For more details, refer to [23]. In Algorithm 1, we give an

overview of our WD approach for both rounds. All the

submitted bids (quantity and price values) should be first

validated using (1) and (2) to make sure they respect all the

stated constraints.

Demandmin;i �Quantitys;i �Demandmax;i ð1Þ

Pricemin;si �Pricesi �Pricemax;i ð2Þ

where Demandmin,i is the minimum demand of buyer for

item i; Quantitysi is the quantity supplied by seller s for

item i; Demandmax,i is the maximum demand of buyer for

item i; Pricemin,si is the minimum price of seller s for item

i; Pricesi is the bid price of seller s for item i; Pricemax,i is

the maximum price of buyer for item i.

Algorithm 1 WD algorithm for electricity CRA

1. Randomly generate initial population of solutions

based on uniform distribution

2. While (number of generations not reached) do

{ 2.1. Calculate fitness value of each solution based

on two utility functions for quantity

maximization and price minimization

2.2. Improve solutions with three GA operators

(selection, crossover and mutation) based on their

fitness values

2.3. Apply diversity (crowding distance) to the

solution population

2.4. Apply elitism (with an external population) to the

solution population

2.5. Choose the top ranked solutions from the

previous and current populations as the

participant solutions for the next generation

}

3. Return the top ranked solution


123

In our multi-objective optimization problem, the target

is to maximize the fitness function of the solutions by

respecting the buyer and sellers constraints in (1) and (2).

Even though we have a mixture of maximization and

minimization objectives, our WD approach converts it into

a maximization objective. At first the WD algorithm gen-

erates the initial population of solutions based on uniform

distribution. The solutions are chosen randomly from the

entire solution space. More precisely, WD selects ran-

domly a seller for each item, and then checks whether this

selection is feasible or not by verifying two equations: the

chosen seller has indeed bided for that item in (3), and the

supply of seller is possible because he is still active for that

time slot since he started transferring electricity to the

buyer in (4). In case of an infeasible selection for an item,

the algorithm tries another seller.

Bidsi ¼ true ð3ÞActiveDurations �CertainTime� StartingTimes ð4Þ

where Bidsi = true if seller s has placed a bid for item i,

false otherwise; ActiveDurationsis the operational con-

straint of seller s; CertainTime is the time slot being pro-

cessed within the delivery period; StartingTimes is the time

when seller s turned ON from OFF status.

In each iteration, the fitness value of a solution is cal-

culated based on two utility functions for quantity maxi-

mization and price minimization. The first function detects

the difference between the maximum demand of the buyer

and the quantity offered by the seller whereas the second

function calculates the difference between the bid price and

the minimum price set by the seller. Afterwards, based on

their quality measurement i.e. their fitness value, the

method improves the current population of solutions with

three GA operators: selection (Gambling-Wheel Disk [4]),

crossover (Modified Two-Point [14]) and mutation (Swap

Mutation [13]. To prevent the population from having

many similar solutions, the algorithm uses the diversity

mechanism based on the enhanced crowding distance

method given in [23]. In this variant, a relative fitness

function is derived to calculate the distance between two

candidate solutions. By doing so, we prevent our WD

algorithm from converging prematurely to local optimal.

Elite solutions are the top-ranked solutions found in each

generation. Thus, we utilize the elitism technique to store

these solutions in an external population. The target here is

to avoid losing good solutions and help our algorithm to

converge to the global optimal. Now, from the two popu-

lations of previous and current generation, the method

selects the top ranked solutions as the participants for the

next generation. After repeating this optimization process

for a certain number of times, it returns the first ranked

solution (sometimes optimal). The way we produce the

winning solution ensures that the buyer gets power for each

time slot by respecting all the trading constraints.

Our method is able to return a high quality solution in a

very efficient time as demonstrated in the experiment

section. The time complexity is a real challenge for opti-

mization problems. For instance, in our electricity CRA if

100 sellers compete for 8 items with two attributes, then

the solution space is 2� 10028

, which is very large. Exact

algorithms become infeasible because they deal with the

entire solution space, and even heuristic ones take a certain

amount of time. This is not practical in real-life applica-

tions like online auctions. Our method, which processes a

subset of the solution pool, is able to improve the fitness

quality in a very short time.

5 Case study

We have implemented the proposed WD algorithm in

Java using NetBeans IDE 8.0.2 and execute it on an Intel

(R) core (TM) i3-2330M CPU with 2.20 GHz processor

speed and 4 GB of RAM. Here we illustrate electricity

CRA with a small-scale market (8 items and 5 sellers). The

utility would like to secure electricity for the period of

11:00 to 13:00 with a minimum of 700 kW and a maxi-

mum of 850 kW. The buyer also specifies his needs for

each item shown in Table 1. Since we are dealing with two

conflicting attributes (quantity and price), the buyer needs

to rank them to be able to find a trade-off solution. He

might prefer one attribute over another. In our present

Table 1 Utility requirements

Item Minimum

quantity (kW)

Maximum

quantity (kW)

Maximum

price ($)

Item1

(11:00–11:15)

100 110 20

Item2

(11:15–11:30)

120 130 25

Item3

(11:30–11:45)

80 90 15

Item4

(11:45–12:00)

100 120 20

Item5

(12:00–12:15)

50 75 13

Item6

(12:15–12:30)

100 125 22

Item7

(12:30–12:45)

75 100 18

Item8

(12:45–13:00)

75 100 17

Total quantity 700 850


123

scenario, quantity has a higher importance than price for

the 8 items.

Let us assume we have in total five grid-connected

power sources (2 wind, 1 hydroelectricity, 1 battery storage

and 1 solar-resident) that registered to this auction in

Fig. 1. The variable energy suppliers compete in the first

round. First, they submit their minimal prices, and how

long they can stay active shown in Table 2. For example,

S1 might supply electricity for Item1 at the minimum price

of $18 and after getting ON, S1 remains active for 2 hours.

The symbol ‘–’ means that during that time interval, there

would be no power generation from the seller. Next the

three sellers submit qualified bids for the items of their

choice shown in Table 3. For instance, S1 bided only for

three items; for Item1, he can supply 105 kW for $20. We

can see that there are no bids for Item8.

Our WD algorithm solves the combinatorial problem

above for the first round. Table 4 shows the breakdown of

one of the candidate solutions. This solution is invalid

since it does not satisfy the two feasibility conditions ((3)

and (4)). Indeed, S3 has been selected for Item3 and again

for Item7, which means that source must be active for

75 minutes but the active duration of S3 is only 1 hour.

Also, S1 has been chosen for Item4 but did not bid for it.

The WD algorithm tries other sellers for Item4 and Item7.

After a certain number of generations (here 100), WD

returns the best solution of the first round, which is still not

complete because there is no feasible supplier found for

Item7 and no placed bids for Item8 shown in Table 4.

For the next round, hydro and battery storage compete

for the remaining two items. Table 5 exposes their con-

straints and valid bids. Supplier S5 and S4 are the winners

of Item7 and Item8 respectively. In Table 6, we expose the

details of the final winning solution consisting only of

eligible offers. The utility will obtain 617 kW from vari-

able energy with a price of $109, and 199 kW from the

non-intermittent renewable energy with $32.

6 Validation and comparison

We analyze the auction outcome in terms of two quality

metrics: solution optimality and time-complexity. We

perform several experiments with five artificial datasets.

Table 2 Constraints of wind and solar

Supplier Minimum price for 8 items ($) Active duration (h)

S1 (Wind) {18, 23, 14, –, –, –, –, –} 2

S2 (Solar) {–, –, –, –, 10, 20, –, –} 1

S3 (Wind) {17, 24, 13, 19, 12, 20, 17, –} 1

Table 3 Valid bids (quantity and price) of wind and solar

Item|Supplier S1 (Wind) S2 (Solar) S3 (Wind)

Item1 {105, 20} – {110, 18}

Item2 {125, 24} – {122, 25}

Item3 {85, 14} – {85, 13}

Item4 – – {110, 20}

Item5 – {72, 10} {50, 12}

Item6 – {110, 21} {120, 22}

Item7 – – {95, 18}

Item8 – – –

Table 4 Candidate and winning solutions for first round

Item Candidate solution (infeasible) Winning solution (partial)

Item1 S1 (Wind) S1 (Wind)




Item5 S2 (Solar) S2 (Solar)

Item6 S2 (Solar) S3 (Wind)

Item7 S3 (Wind) –

Item8 – –

Table 5 Constraints and valid bids of hydro and battery

Supplier Minimum price for

Item7 & Item8 ($)

Active

duration

(h)

Valid bid

(quantity and

price)

S4 (Hydro) {15, 15} 2 {98,16}, {100,

15}

S5

(Battery)

{17, 15} 2 {99, 17}

{95, 16}

Table 6 Supply analysis of final winning solution

Item Quantity (kW) Price ($)

Round 1 Item1 105 20

Item2 125 24

Item3 85 13

Item4 110 20

Item5 120 10

Item6 72 22

Round total 617 109

Round 2 Item7 99 17

Item8 100 15

Round total 199 32

Grand total 700 B 816 B 850 141


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6.1 Simulated datasets

We generate randomly five instances of the electricity

combinatorial procurement problem. In Table 7, we give

the details of the artificial datasets by varying the number

of sellers, items and generations.

The maximum value of each attribute is randomly

chosen from [100, 1000], and the minimum value from

[10% of maximum value, 50% of maximum value]. The

ranking of the two attributes is also done randomly.

Regarding the parameters of the GA algorithm (in total 5),

we perform several parameter tuning tests, and based on

the results, we use the following best configuration: the

number of solutions is 500, the crossover rate is 0.6,

mutation rate is 0.01, number of elite solutions = number of

participant solutions and elite solution rate = 0.2. All the

results returned by the WD method represent the average

value of 20 runs.

6.2 Statistical analysis

We examine statistically the WD algorithm based on

dataset 1. Figure 2 presents the average of the quality

measurement values for rounds 1 and 2 and by including

the maximum and minimum values of generations. Also

these figures depict the error bars with a confidence level of

95%. It is noticeable that after a certain number of

Table 7 Simulated datasets

Constant Value Variable Value

Dataset 1 Number of sellers 500 Number of generations 1–500

Number of items Round 1:15

Round 2: 5

Dataset 2 Number of sellers 500 Number of items 4, 8, 12, 16, 20

Round 1 3, 6, 9, 12, 15

Round 2 1, 2, 3, 4, 5

Number of generations 100

Dataset 3 Number of items Round 1: 15

Round 2: 5

Number of sellers 100, 200, 300, 400, 500, 600,

700, 800, 900, 1000


Dataset 4 Number of sellers Round 1: 60

Round 2: 40

N. A.

Number of items Round 1: 24

Round 2: 8


Dataset 5 Number of sellers Round 1: 600

Round 2: 400

N. A.

Number of items Round 1:15

Round 2: 5


Fig. 2 Statistical analysis of WD


123

generations, the maximum fitness value remains constant.

This means that the best solution found by WD might be

the optimal one. It is also obvious that WD is able to

control the solution variations and their differences after a

certain number of generations.

6.3 Computational time evaluation

The goal here is to assess the time-efficiency of our WD

algorithm. We utilize dataset 2 by varying the number of

items shown in Fig. 3, and dataset 3 the number of sellers

shown in Fig. 4. From the results, we may say that the

required computational time is not exponential but rather

polynomial. It is clear that the execution time increases

linearly with the increase of items and sellers.

6.4 Comparison with heuristic algorithms

We compare the computational time of WD with three

other well-know heuristic WD methods: improved ant

colony (IAC), enumeration algorithm with backtracking

(EAB), and genetic algorithms for multiple instances of

items in combinatorial reverse auctions (GAMICRA). All

these optimization methods return one best solution. The

comparison is based on dataset 4. Table 8 provides the

processing time of IAC, EAB and GAMICRA for much

simpler combinatorial reverse auctions. The first two were

taken directly from [24] and the last one from [15]. As we

can see WD is significantly superior to all of them.

6.5 Comparison with exact algorithms

In order to gain an exact idea about the accuracy of WD,

we have fully implemented in Java two exact procedures to

solve our constrained electricity CRA problem:

1) Brute Force that guarantees the solution optimality

since it checks the entire solution space.

2) Branch and Bound [25] that is the most time-

performing exact algorithm.

Fig. 3 Computational time of WD by varying number of items

Fig. 4 Computational time of WD by varying number of sellers

Table 8 Comparison with heuristic algorithms

Algorithm Time (s)

IAC 9

EAB 3

GAMICRA 0.83

WD 0.226 (Round 1)

0.019 (Round 2)

Table 9 Comparison with exact algorithms

Algorithm Round Accuracy (fitness value) Time

Brute Force Round 1 23.0126 (100%) [ 1 day

Round 2 7.9878 (100%) * 1 day

WD Round 1 20.0891 (87.3%) 0.182 s

Round 2 7.4526 (93.3%) 0.063 s

Branch & Bound Round 1 13.12 (100%) 39.687 min

Round 2 4.978 (100%) 33.375 s

WD Round 1 11.98 (91.32%) 10.271 s

Round 2 4.76 (95.62%) 0.231 s


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We compare WD with these two exact algorithms based

on two performance qualities: time-efficiency and accuracy

(how near is the solution to the optimal). Equation (5)

depicts how we measure the accuracy. We employ datasets

4 and 5 where the former dataset (relatively smaller) is for

Brute Force and the latter dataset is for Branch and

Bound.

WD

EXACT� 100% ð5Þ

Regarding dataset 4, 60 sellers compete for 24 items in

round 1, and 40 sellers for 8 items in round 2. After

applying Brute Force (BF) on the first dataset, we obtain

the following results. In round 1, the accuracy of WD is

87.3% and in round 2, 93.3%. The accuracy of BF is 100%

in both rounds. So we can conclude that our WD method is

able to return near to optimal solutions. On the other hand,

our method generates the solution in 0.182 s in round 1 and

0.063 s in round 2 whereas BF takes more than 1 day in

round 1 and almost 1 day in round 2. In summary, WD

takes only 0.245 s whereas BF approximately 2 days.

Now we discuss the second exact technique that we

apply to dataset 5. In round 1600 sellers bid for 15 items.

The accuracy of WD is 91.32% and WD produces the best

solution in 10.271 seconds. Branch and Bound (BB) takes

39.687 min. In round 2400 sellers compete for 5 items. The

accuracy of WD is 95.62% and a solution is returned in

0.231 s whereas BB takes 33.375 s. So, in total WD takes

only 10.502 s whereas BB 40.243 min.

All the results are summarized in Table 9. It is clear that

exact algorithms become unreasonable with the increased

values of the auction parameters (items and sellers). In

conclusion, we have demonstrated that our WD method not

only produces the solution in a very efficient processing

time but also generates near-to-optimal solutions.

7 Conclusion

To avoid power outages during anticipated peak load

periods, state utility companies can procure electricity from

other suppliers (in aggregate) with the help of online auc-

tions. The required electricity may be purchased from

diverse renewable energy sources. We have presented an

electricity combinatorial reverse auction that has been

specifically designed for very short-term resource pro-

curement. To be able to secure electricity, our auction

consists of two bidding rounds: in the first round, variable

energy suppliers bid on bundle of items; in the second

round, storage and controllable renewable energy suppliers

bid on any items still remaining. Our new, smart market

makes it possible for power suppliers of all sizes to

compete, including homeowners. We have solved our

constrained combinatorial procurement problem (multiple

items, two attributes and two conflicting objectives) by

using an evolutionary multi-objective optimization tech-

nique to be able to find the best trade-off solution. The

latter represents the best combination of sellers that results

in the lowest cost and highest quantity of electricity.

Designing an auction with 15-minute intervals allows for

greater equality of opportunity between small players (such

as residents) and big players (plants). We believe that the

proposed electricity auction will promote the expansion of

renewable energy plants as well as home-based generation

as new technologies become more and more accessible to

residents (electric vehicles and solar panels). In summary,

our electricity auction is a new concept in terms of: �the

problem being addressed (the anticipated peak demand

load); `features of our smart electricity market; ´auction

design (characteristics, bidding strategies and winner

determination).

Through several experiments, we have demonstrated

that our WD method can not only determine the winners

while maintaining a very efficient execution time, but it can

also generate near-to-optimal solutions. We view our

electricity allocation as a set of multiple optimal alloca-

tions, each corresponding to an item for which the con-

straints of the auction demand is met and for which a more

profitable allocation is not possible. Reference [21] pointed

out that combinatorial auctions that achieve the desired

resource allocation (because feasible solutions always

exist) ultimately fulfil the Nash Equilibrium (one type of

market equilibrium). Therefore, we can claim that our WD

algorithm also satisfies the market equilibrium.

In order to adopt our new electricity auction, public

utilities and their decision makers must establish policies

for contracting electricity with private companies and

individuals. Additionally, utilities should investigate in

practice the economic efficiency of the proposed market.

Open Access This article is distributed under the terms of the

Creative Commons Attribution 4.0 International License (http://

creativecommons.org/licenses/by/4.0/), which permits unrestricted

use, distribution, and reproduction in any medium, provided you give

appropriate credit to the original author(s) and the source, provide a

link to the Creative Commons license, and indicate if changes were

made.

References

[1] Ciarreta A, Espinosa MP, Pizarro-Irizar C (2017) Has renewable

energy induced competitive behavior in the Spanish electricity

market? Energy Policy 104:171–182

[2] Holmberg P, Wolak F (2015) Electricity markets: designing

auctions where suppliers have uncertain costs. Cambridge

Working Papers in Economics 1541. https://www.repository.

cam.ac.uk/handle/1810/255325


123

http://creativecommons.org/licenses/by/4.0/

http://creativecommons.org/licenses/by/4.0/

https://www.repository.cam.ac.uk/handle/1810/255325

https://www.repository.cam.ac.uk/handle/1810/255325

[3] Aquila G, Pamplona EDO, Queiroz ARD et al (2016) An

overview of incentive policies for the expansion of renewable

energy generation in electricity power systems and the Brazilian

experience. Renew Sustain Energy Rev 70:1090–1098

[4] Gong J et al (2007) A GA based combinatorial auction algorithm

for multi-robot cooperative hunting. In: Proceedings of inter-

national conference on computational intelligence and security,

Harbin, China, 15–19 Dec 2007, pp 137–141

[5] Lucas H, Ferroukhi R, Hawila D (2013) Renewable energy

auctions in developing countries. International Renewable

Energy Agency (IRENA), Abu Dhabi

[6] Tsung C, Ho H, Lee S (2011) An equilibrium-based approach

for determining winners in combinatorial auctions. In: Pro-

ceedings of the IEEE 9th international symposium on parallel

and distributed processing with applications (ISPA), Busan,

South Korea, 26–28 May 2011, pp 47–51

[7] Aritoni O, Negru V (2011) A multi-agent recommendation

system for energy efficiency improvement. e-Technol Netw Dev

171:156–170

[8] Penya YK, Jennings NR (2005) Combinatorial markets for

efficient energy management. In: Proceedings of IEEE/WIC/

ACM international conference on intelligent agent technology,

Compiegne, France, 19–22 Sept 2005, pp 626–632

[9] Marambio R, Rudnick H (2017) A novel inclusion of intermit-

tent generation resources in long term energy auctions. Energy

Policy 100:29–40

[10] Shil SK, Sadaoui S (2017) Combinatorial reverse electricity

auctions. In: Canadian conference on artificial intelligence,

Springer, pp 162–168

[11] Vale ZA, Morais H, Khodr H (2010) Intelligent multi-player

smart grid management considering distributed energy resources

and demand response. In: Proceedings of IEEE power and

energy society general meeting, Providence, RI, USA, 25–29

July 2010, pp 1–7

[12] Praktiknjo A, Erdmann G (2016) Renewable electricity and

backup capacities: an (un-) resolvable problem? Energy J 37

(Bollino-Madlener Special Issue)

[13] Eiben AE, James ES (2003) Introduction to evolutionary com-

puting. Springer, Heidelberg

[14] Shil SK, Mouhoub M, Sadaoui S (2013) Winner determination

in combinatorial reverse auctions. In: Ali M, Bosse T, Hindriks

KV, Hoogendoorn M, Jonker CM, Treur J (eds) Contemporary

challenges and solutions in applied artificial intelligence,

Springer, Heidelberg, pp 35–40

[15] Shil SK, Mouhoub M, Sadaoui S (2015) Winner determination

in multi-attribute combinatorial reverse auctions. In: Proceed-

ings of 22nd international conference on neural information

processing (ICONIP), Istanbul, Turkey, 9–12 Nov 2015,

pp 645–652

[16] Colak B, Gokmen MA, Kilic H (2015) A web-based auction

platform for electricity retail markets. In: Proceedings of IEEE

14th international conference on machine learning and

applications (ICMLA), Miami, FL, USA, 9–11 Dec 2015,

pp 1148–1152

[17] Han D, Sun M (2015) The design of a probability bidding

mechanism in electricity auctions by considering trading con-

straints. Simulation 91(10):916–924

[18] Mazzi N, Lorenzoni A, Rech S et al (2015) Electricity auctions:

a European view on markets and practices. In: Proceedings of

12th IEEE international conference on the European energy

market (EEM), Lisbon, Portugal, 19–22 May 2015, pp 1–5

[19] Newbery DM (2016) Towards a green energy economy? The EU

Energy Union’s transition to a low-carbon zero subsidy elec-

tricity system—lessons from the UK’s Electricity Market

Reform. Appl Energy 179:1321–1330

[20] Tabandeh S, Michalska H (2009) An evolutionary random

search algorithm for double auction markets. In: Proceedings of

the IEEE congress on evolutionary computation, Trondheim,

Norway, 18–21 May 2009, pp 2948–2955

[21] Wang XW, Wang XY, Huang M (2012) A resource allocation

method based on the limited english combinatorial auction under

cloud computing environment. In: Proceedings of the 9th

international conference on fuzzy systems and knowledge dis-

covery (FSKD), Sichuan, China, 29–31 May 2012, pp 905–909

[22] Maurer LTA, Barroso L (2011) Electricity auctions: an overview

of efficient practices. World Bank, Washington, DC

[23] Shil SK, Sadaoui S (2016) Winner determination in multi-ob-

jective combinatorial reverse auctions. In: Proceedings of 28th

international conference on tools with artificial intelligence

(ICTAI), San Jose, CA, USA, 6–8 Nov 2016, pp 714–721

[24] Qian X, Huang M, Gao T et al (2014) An improved ant colony

algorithm for winner determination in multi-attribute combina-

torial reverse auction. In: Proceedings of IEEE congress on

evolutionary computation (CEC), Beijing, China, 6–11 July

2014, pp 1917–1921

[25] Gonen R, Lehmann D (2000) Optimal solutions for multi-unit

combinatorial auctions: branch and bound heuristics. In: Pro-

ceedings of 2nd ACM conference on electronic commerce,

Minneapolis, MN, USA, 17–20 Oct 2000, pp 13–20

Shubhashis Kumar SHIL received both his M.Sc. and Ph.D degrees

from the Department of Computer Science, University of Regina,

Canada under the supervision of Dr. Samira SADAOUI. His current

research interests include artificial intelligence, data mining, and

software engineering.

Samira SADAOUI is a Professor in the Department of Computer

Science, University of Regina, Canada. Her current research interests

are in artificial intelligence, including fraud detection in E-commerce,

adaptive fraud detection, incremental learning, winner determination,

evolutionary algorithms, multi-objective optimization.


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