meeting peak electricity demand through combinatorial reverse ... · meeting peak electricity...
TRANSCRIPT
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
Shubhashis Kumar SHIL
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
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.
76 Shubhashis Kumar SHIL, Samira SADAOUI
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
Meeting peak electricity demand through combinatorial reverse auctioning of renewable energy 77
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
78 Shubhashis Kumar SHIL, Samira SADAOUI
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
Meeting peak electricity demand through combinatorial reverse auctioning of renewable energy 79
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)
Item2 S1 (Wind) S1 (Wind)
Item3 S3 (Wind) S3 (Wind)
Item4 S1 (Wind) S3 (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
80 Shubhashis Kumar SHIL, Samira SADAOUI
123
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
Number of generations 100
Dataset 4 Number of sellers Round 1: 60
Round 2: 40
N. A.
Number of items Round 1: 24
Round 2: 8
Number of generations 100
Dataset 5 Number of sellers Round 1: 600
Round 2: 400
N. A.
Number of items Round 1:15
Round 2: 5
Number of generations 100
Fig. 2 Statistical analysis of WD
Meeting peak electricity demand through combinatorial reverse auctioning of renewable energy 81
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
82 Shubhashis Kumar SHIL, Samira SADAOUI
123
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
Meeting peak electricity demand through combinatorial reverse auctioning of renewable energy 83
123
[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.
84 Shubhashis Kumar SHIL, Samira SADAOUI
123