GENCO Optimal Bidding Strategy and Proﬁt Based Unit Commitment using Evolutionary Particle Swarm Optimization Illustrating the Effect of GENCO Market Power

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 8, No. 4, August 2018, pp. 1997∼2013
ISSN: 2088-8708, DOI: 10.11591/ijece.v8i4.pp1997-2013 Ì 1997
GENCO Optimal Bidding Strategy and Profit Based Unit
Commitment using Evolutionary Particle Swarm
Optimization Illustrating the Effect of GENCO Market
Power
Adline K. Bikeri1
, Christopher M. Muriithi2
, Peter K. Kihato3
1,3
School of Electrical, Electronic, and Information Engineering, Jomo Kenyatta University of Agriculture & Technology,
Kenya
2
Department of Electrical and Power Engineering, Technical University of Kenya, Kenya
Article Info
Article history:
Received October 27, 2017
Revised April 10, 2018
Accepted May 3, 2018
Keywords:
Profit Based Unit
Commitment
EPSO
PSO
GENCO Market Power
Deregulated Electricity
Market
ABSTRACT
In deregulated electricity markets, generation companies (GENCOs) make unit com-
mitment (UC) decisions based on a profit maximization objective in what is termed
profit based unit commitment (PBUC). PBUC is done for the GENCO’s demand which
is a summation of its bilateral demand and allocations from the spot energy market.
While the bilateral demand is known, allocations from the spot energy market depend
on the GENCO’s bidding strategy. A GENCO thus requires an optimal bidding strat-
egy (OBS) which when combined with a PBUC approach would maximize operating
profits. In this paper, a solution of the combined OBS-PBUC problem is presented. An
evolutionary particle swarm optimization (EPSO) algorithm is implemented for solv-
ing the optimization problem. Simulation results carried out for a test power system
with GENCOs of differing market strengths show that the optimal bidding strategy
depends on the GENCO’s market power. Larger GENCOs with significant market
power would typically bid higher to raise market clearing prices while smaller GEN-
COs would typically bid lower to capture a larger portion of the spot market demand.
It is also illustrated that the proposed EPSO algorithm has a better performance in
terms of solution quality than the classical PSO algorithm.
Copyright c 2018 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Adline K. Bikeri,
School of Electrical, Electronic, and Information Engineering,
Jomo Kenyatta University of Agriculture & Technology,
P.O. Box 62000-00200, Nairobi, Kenya.
Email: adlinebikeri@gmail.com
1. INTRODUCTION
Traditionally, one of the most important aspects of power system operation is the prior scheduling
of generating units also referred to as unit commitment (UC) [1, 2, 3]. UC schedules are usually determined
on a week-ahead, day-ahead, or even just a few hours before operation. Prior scheduling of generating units
increases efficiency by ensuring a least-cost operating regime while keeping system reliability. In traditional,
regulated environments, UC is done from a “least-cost” point-of-view [4]. While in the very short-term rule-
of-thumb methods can be applied, power utilities usually invest in system optimization software as the extra
cost resulting from non-optimal operation could be significant.
UC in deregulated markets take a different approach. Unlike the regulated environment, the inde-
pendent system operator (ISO) who is in charge of ensuring that demand is met does not own or operate any
Journal homepage: http://iaescore.com/journals/index.php/IJECE

1998 Ì ISSN: 2088-8708
generating units [5, 6]. The ISO receives supply bids from the various generation companies (GENCOs) in the
system and then allocates the demand to these GENCOs based on a cheapest-first method. The GENCOs in the
system thus have to compete for a proportion of the demand so as to make money. In some systems, apart from
the allocations in the ISO operated energy market (spot market), GENCOs may independently negotiate bilat-
eral supply contracts with consumers though they may have to use the ISO’s transmission network to deliver
agreed power [6].
Each individual GENCO still has to draw up its own generations schedules especially because opera-
tional constraints on generating units such as minimum-up time or minimum-down times could significantly eat
into a GENCOs profit if not properly considered in the operational planning stage. A GENCO’s UC schedule
is based on expected own demand from both the spot and bilateral energy markets with the aim of maximiz-
ing profits [7]. Thus, in deregulated markets, UC is done from a profit maximization point of view hence the
term profit based unit commitment (PBUC) [8]. However, the allocation from the spot energy market depends
largely on a GENCO’s bidding strategy [9]. The GENCO may either lower its bids aiming to increase its al-
location or raise its bids so as to raise the electricity prices which means that the GENCO’s own demand and
hence its UC schedule depends significantly on its adopted bidding strategy.
An important determinant of a GENCO’s bidding strategy in the spot market is its market power i.e.
the GENCO’s ability to alter the market price and allocations in the market. A GENCO whose actions cannot
affect the market equilibrium is referred to a price taker and conversely, a GENCO whose actions significantly
affect the market is referred to as a price maker. Electricity markets usually assume an oligopolistic structure
characterized by several price takers and one or two price makers; usually large companies that are offshoots
of the previous regional or national utilities prior to deregulation [10]. Since the GENCO’s market power can
influence the market price, it is a significant consideration in the determination of an optimal bidding strategy
(OBS) and hence the solution of the PBUC problem.
Several approaches for the solution of the PBUC problem have been proposed in literature. Classical
mathematical methods such as Priority Listing (PL), Dynamic Programming (DP), Branch and Bound, Mixed
Integer Programming (MIP), and Lagrangian Relaxation have been proposed in [11, 12]. Newer, heuristic
based methods such as Genetic Algorithm (GA), Ant colony optimization (ACO), Particle swarm optimization
(PSO), and Artificial bee colony (ABC) have been proposed in [13, 14, 15]. Hybrid methods that combine two
or more solution approaches have also been proposed [16, 17].
Heuristic based methods provide the advantages of a more thorough search of the solution space and
being less prone to getting stuck at local optimum solutions. Also, there is a reduced mathematical computation
burden since these method don’t require the computation of gradients which may be quite difficult in certain
instances. The evolutionary particle swarm optimization (EPSO) algorithm [18, 19, 20], which combines the
classical PSO algorithm with evolutionary programming (EP) concepts, is one of the most promising algorithms
for the solution of various power system operation optimization problems. It has been shown that EPSO has
better convergence characteristics than the conventional PSO and usually gives better results. In this paper, an
EPSO algorithm based solution methodology is proposed to solve the combined optimal bidding strategy and
PBUC problem. The application of the proposed solution methodology is illustrated for several GENCOs of
differing sizes operating in a test power system.
The rest of the paper is organized as follows. Section 2. introduces the concept of GENCO bidding
strategies in electricity markets with an illustration of how a GENCO can set its bidding strategy to increase
its profits. Section 3. introduces the general EPSO algorithm. The problem formulation is given in section
4. and the proposed solution algorithm in section 5.. Numerical simulations are presented in section 6. while
conclusions are given in section 7..
2. GENCO BIDDING STRATEGIES IN ELECTRICITY MARKETS
In deregulated electricity markets, electric energy is sold either through bilateral agreements between
GENCOs and consumers or through an electricity pool operated by an independent system operator i.e. the
electricity spot market [21]. In the case of the bilateral market, the buyer and seller agree on a transaction
price from which the GENCO meets all costs for transmission, distribution, and other ancillary services. The
electricity pool is however operated by an independent system operator ISO who receives and aggregates hourly
energy supply bids from GENCOs and hourly demand bids from consumers after which a market clearing price
(MCP) is determined [6]. The GENCOs are allocated portions of the demand based on a cheapest-bid first while
Int J Elec & Comp Eng, Vol. 8, No. 4, August 2018 : 1997 – 2013

Int J Elec & Comp Eng ISSN: 2088-8708 Ì 1999
ensuring system reliability and security. The MCP is defined as the cost of supplying the last MW of demand
and all GENCOs who receive load allocations for the given hour are paid at this price irrespective of their bids.
Each GENCO will combine the bilateral demand with the allocation from the spot market as its own
demand and from this data draw up a UC schedule based on a profit maximization objective. Since the spot
market allocation is based largely on the GENCO’s bid and those of its competitors, the GENCO bid decisions
significantly affect its allocation and hence its profits. Should a GENCO have enough influence, it could affect
the market clearing price and consequently its profits. The magnitude of this influence defines the GENCO’s
market power. Under perfect competition, so as to maximize its profits, a GENCO should bid at its marginal
cost (cost of supplying an extra MW of electricity) [9]. However, depending on the market environment, the
GENCO could increase its profits in one of two ways:
• The GENCO could lower its bid (bid low) thereby potentially increasing its allocation in the spot market
though this could reduce the MCP. Bidding low is justified if the reduced revenue due to the lower prices
is covered by the increased revenue due to a larger allocation.
• The could raise its bid (bid high) thereby potentially reducing its allocation in the spot market but in-
creasing the MCP. This is justified if the increased revenue due to the higher prices cover the revenue lost
due to a smaller allocation.
A minimal example to illustrate the spot market dynamics follows next.
The GENCO marginal cost curve forms the basis of its bidding strategy. The marginal cost curve is a
plot of the incremental cost of power generation against the total power output for a GENCO. Mathematically,
MCi – the marginal cost curve for GENCO i is given by:
MCi =
∂CT i
∂PT i
, (1)
where CT i is the total operating cost of GENCO i when supplying a total of PT i MW. Assuming a quadratic
cost curve for GENCO costs, CT i is given by:
CT i =
N
j=1
aij + bijPij + cijP2
ij , (2)
and
PT i =
N
j=1
Pij. (3)
In (2) and (3) aij, bij, and cij are the coefficients of the quadratic cost curves for unit j operated by GENCO i
while Pij is the output of unit j operated by GENCO i.
Consider two GENCOs each owning one generating unit with cost characteristics shown in Table
1. The marginal cost curves for the two GENCOs are plotted in Figure 1(a) showing that GENCO G1 has
the cheaper generating unit of the two GENCOs. If each GENCO submits its marginal cost curve as its sup-
ply curve, the combined system supply curve will be as shown in Figure 1(b). Assuming a nominal system
demand of 200 MW with a linear demand curve as shown in Figure 1(b), the market equilibrium will then
be the point at which the two curves intersect. When read from Figure 1(b) this point is (Pd = 200MW,
MCP = $30.78/MWh). When extrapolated to the supply curves of the two GENCOs, G1 and G2 will supply
144.4 MW and 55.6 MW respectively.
Table 1. Example GENCO cost characteristics
GENCO Pmin
i1 Pmax
i1 Cost Equation CT i(Pij)
G1 0 300 25P11 + 0.020P2
11
G2 0 150 28P21 + 0.025P2
21
Now, consider a case where GENCO G1 submits bids where the gradient of its marginal cost curve is
multiplied by a factor µ1. Its bid curve, BC1 is then given by:
BC1 = b11 + µ1 · 2c11P11 = 25 + 0.04µ1P11 (4)
OBS-PBUC using EPSO illustrating GENCO Market Power (Adline Bikeri et. al.)

2000 Ì ISSN: 2088-8708
0 50 100 150 200 250 300 350
20
22
24
26
28
30
32
34
36
38
40
$30.78/MWh
144.4 MW55.6 MW
GENCO Output [MW]
MarginalCost[$/MWh]
GENCO G1
GENCO G2
0 50 100 150 200 250 300 350 400 450
20
22
24
26
28
30
32
34
36
38
40
$30.78/MWh
200 MW
Power Supply / Demand [MW]
ElectricityPrice[$/MWh]
Supply Curve
Demand Curve
(a) (b)
Figure 1. (a) Marginal cost curves for two GENCOs and (b) market equilibrium obtained from the intersection
of the aggregated supply curve and the system demand curve
0 50 100 150 200 250 300 350
20
22
24
26
28
30
32
34
36
38
40
GENCO Output [MW]
MarginalCost[$/MWh]
GENCO G1
GENCO G2
µ1
= 0.8
µ1
= 1.0
µ1
= 1.2
0 50 100 150 200 250 300 350 400 450
20
22
24
26
28
30
32
34
36
38
40
Power Supply / Demand [MW]
ElectricityPrice[$/MWh]
Supply Curves
Demand Curve
µ
1
= 0.8
µ
1
= 1.0
µ
1
= 1.2
(a) (b)
Figure 2. Illustration of the effect of GENCO G1’s bid strategy on (a) the demand allocations and (b) the MCP
A value of µ1 > 1 raises the bid curve above the nominal meaning that the GENCO bids high while a
value of µ1 < 1 means that the GENCO bids low. The effect of µ1 on the MCP and the GENCO allocations is
illustrated in Figure 2 for values of µ1 = 0.8, and µ1 = 1.2. The results are summarized in Table 2 showing
that as µ1 increases, the MCP increases, GENCO G1’s allocation reduces (as does its revenue and costs) but its
profit increases.
Table 2. Effect of GENCO bidding strategy on spot market prices, allocations, revenues, costs, and profits
µ1 MCP P1 Revenue Cost Profit
[$/MWh] [MW] [$/h] [$/h] [$/h]
0.8 30.15 161.01 4, 854.98 4, 543.87 311.11
1.0 30.78 144.44 4, 445.68 4, 028.40 417.28
1.2 31.29 130.97 4, 097.48 3, 617.21 480.27
A plot of the GENCO profit against the value of µi for the two GENCOs acting individually is il-
lustrated in Figure 3 which shows that the two GENCOs achieve maximum profits at different values of µi
(µ1 = 1.9 and µ2 = 0.6). These results show that the larger GENCO G1 should bid high to increase its profits
while conversely, the smaller GENCO G2 should bid low to increase its profits.

0 0.5 1 1.5 2 2.5 3
−200
−100
0
100
200
300
400
500
600
700
Bid Factor, µ
Profit[$/h]
GENCO G1
GENCO G2
Figure 3. Illustration of the effect of the bid factor µi on GENCO profits
3. EVOLUTIONARY PARTICLE SWARM OPTIMIZATION
Evolutionary particle swarm optimization (EPSO) is a heuristic optimization algorithm based on a
combination of the evolutionary programming (EP) and particle swarm optimization (PSO) concepts [18, 19,
22]. As with the classical PSO algorithm [23], candidate solutions (particles) are moved around the solution
space in search of the best possible solution. Each particle defines a position in the solution space and during
successive iterations, the particles are moved towards the best solutions discovered at the given point in the
solution process. The EPSO particle movement rule used in updating the particle position is similar to the PSO
particle update equation in that a particle moves towards its own personal best solution that it achieved so far
(pBest), as well as towards the global best (gBest) solution which is best among the best solutions achieved
so far by all particles present in the population. One important difference in the EPSO algorithm is that the
gBest position is “disturbed” hence the particles don’t just aim for the already found gBest position but rather
for the region around the gBest position which may actually be better than the already found gBest [18].
One of the main challenges of the classical PSO algorithm is parameter tuning i.e. the determination
of the best algorithm parameters to give the best solution. The EPSO algorithm addresses this challenge by
progressively “mutating” the weight parameters with successive iterations. Thus, as the algorithm progresses,
the weight parameters also evolve towards the best values. The basic structure of EPSO as originally explained
in [18] carries out the following processes at each iteration:
• REPLICATION - each particle is replicated a number of times.
• MUTATION - each particle has its weights mutated.
• REPRODUCTION - each particle (original and replicas) generates an offspring according to the particle
movement rule using the mutated weights.
• EVALUATION - each offspring has its fitness evaluated.
• SELECTION - the best particles between the original set and the mutated set survive based on a stochastic
tournament to form a new generation.
After a certain pre-set number of iterations (generations), the particle with the global best solution is stored
as the optimal solution. Incorporation of the Darwinistic characteristics of mutation and selection allows the
EPSO algorithm to take advantage of the faster convergence characteristics of Evolutionary Programming (EP)
strategies [19].
4. PROBLEM FORMULATION
Under the deregulated environment each individual GENCO seeks to capture a significant proportion
of the spot electricity market and then determine a generation schedule that maximizes its profit based on
expected prices at each scheduling period. If the GENCO can significantly affect the electricity price at a given

2002 Ì ISSN: 2088-8708
hour, then the GENCO can set up its bid to drive up profits at the specified hour. The GENCO’s decision is
then two-fold: (1) how to set up its bidding strategy either to capture a larger portion of the spot market or
to drive up the electricity price, and (2) how to schedule the generating units to maximize its profit given the
expected prices. This optimization problem is formulated here as an optimal bidding strategy - profit based
unit commitment (OBS-PBUC) problem. Revenues from both the day-ahead spot energy and reserve markets
and the GENCO’s bilateral contract commitments are considered. The objective function and the operational
constraints are explained in the following subsections.
4.1. Objective Function
Profit (PF) is defined as the difference between revenue (RV ) obtained from sale of energy and
reserve and the total operating cost (TC) of the GENCO. The objective function is thus given as:
Maximize PF = RV − TC. (5)
4.1.1. GENCO Revenue
In (5), RV is given by:
RV =
H
h=1
RV ph
+ RV rh
, (6)
where RV ph
and RV rh
are the revenues from the energy market and the reserve market at hour h respectively.
H is the number of hours in the scheduling horizon. RV ph
is calculated as:
RV ph
= αh
s Ph
s + αh
b Ph
b + κ αh
s − αh
b Ph
b , (7)
where αh
s and αh
b are the energy prices at the spot market and bilateral market respectively at hour h, Ph
s and
Ph
b are the power supplied to the spot market and bilateral market respectively at hour h, and κ is a contract
of differences factor [24]. The first term in (7) represents revenue from the energy sold at the spot market, the
second term represents revenue from bilateral contracts, while the third term represents revenue from contracts
of differences. Contracts of differences are usually included in bilateral contracts to compensate suppliers and
consumers for differences between the bilaterally agreed prices and the prevailing market price [24].
Revenue from reserve sales RV rh
is given as:
RV rh
= αh
r
N
j=1
Pmax
j − Ph
j , (8)
where αh
r is price of reserve capacity at hour h, Pmax
j is the maximum capacity of unit j, and Ph
j is the output
of unit j at hour h. N is the total number of generating units. In (8), the same price is assumed for both spinning
and non-spinning reserve. If the pricing is different, the equation could be split to have two terms accounting
for each type of reserve.
4.1.2. GENCO Costs
Total cost TC is a sum of generator fuel costs (FC) and start up costs (SUC) for all N units over the
entire scheduling period of H hours given as:
TC =
H
h=1
N
j=1
FCh
j + SUCh
j , (9)
where
FCh
j = aj + bjPh
j + cj Ph
j
2
, (10)
and
SUCh
j = γj 1 − Uh−1
j Uh
j , (11)
where
γj =
CSCj if
h
t=h−CShrj
Ut
j ≥ CShrj
HSCj if
h
t=h−CShrj
Ut
j < CShrj
. (12)
In (11) and (12), Uh
j is the status of unit j at hour h i.e. Uh
j = 0 if unit j is OFF at hour h and Uh
j = 1 if unit
j is ON at hour h. γj is the start up cost coefficient for unit j which is either the cold start cost CSCj if the
duration unit j has been ON is less than its cold start hour CShrj or the hot start cost HSCj otherwise.

4.2. Operational Constraints
The GENCO operational constraints are given as:
(a) Power balance constraints
N
j=1
Ph
j = Ph
s + Ph
b ∀h (13)
(b) Generation limit constraints
Uh
j Pmin
j ≤ Uh
j Ph
j ≤ Uh
j Pmax
j ∀i, ∀h (14)
(c) Generator ramp up constraints
Ph
j − Ph−1
j ≤ RUj ∀i, ∀h (15)
(d) Generator ramp down constraints
Ph−1
j − Ph
j ≤ RDj ∀i, ∀h (16)
(e) Generator minimum up time constraints
Uh
j = 1 if Ut
j − Ut−1
j = 1, for h = t, ..., t + MUTj − 1 (17)
(f) Generator minimum down time constraints
Uh
j = 0 if Ut−1
j − Ut
j = 1, for h = t, ..., t + MDTj − 1 (18)
In (15) and (16), RUj and RDj are the hour-to-hour ramp-up and ramp-down limits on unit j respectively.
In (17) and (18), MUTj and MDTj are the minimum-up-time and minimum-down-time limits on unit j
respectively.
Constraints (14) to (18) define unit operation limits and are similar to the formulation of a traditional
utility’s cost minimization UC problem [25]. Constraint (13) – the power balance constraint – states that the
GENCO’s total output at any given hour must equal its own load which is the sum of its expected spot market
allocation Ph
s and its bilateral market commitment Ph
b . While the bilateral market load would typically be
agreed upon long in advance, the spot market allocation would depend on the GENCO’s bidding strategy. A
GENCO can predict the values of Ph
s and αh
s using its bidding strategy and the expected competitor bid curves.
Generally, Ph
b and αh
b can be treated as constants while Ph
s and αh
s are variables dependent on the market
dynamics. A GENCO would act in the day-ahead market to affect the values of Ph
s and αh
s so as to increase its
profits.
A second significant difference between the formulations of the OBS-PBUC problem and the tradi-
tional UC problem is the absence of a minimum spinning reserve constraint [25] in the new formulation. This
is because, supply of reserve, as well as other ancillary services, is not the responsibility of the GENCO. The
ISO ensures the supply of such ancillary services by engaging the GENCOs. A GENCO thus gets payments
for supply of both spinning and non-spinning reserve as given in the revenue equation (6). The adequacy of the
reserve is ensured by the ISO by aggregating reserves from all GENCOs participating in the electricity market.
5. OBS-PBUC SOLUTION METHODOLOGY
In this section, the procedure adopted in this paper to solve the OBS-PBUC problem is outlined.
Section 5.1. explains the procedure adopted to determine the profit corresponding to a given bidding strategy
while section 5.2. details the step-by-step procedure implemented to select an optimal bidding strategy using
the EPSO algorithm.

2004 Ì ISSN: 2088-8708
5.1. Profit Maximization Procedure
As illustrated in section 2., a GENCO can opt to bid high or bid low with respect to its marginal cost
curve aiming to maximize its profits. Assume a linear reference marginal cost curve given by1
:
MCref
= ρ + βPh
T , (19)
where ρ and β are the marginal cost curve coefficients for the GENCO and Ph
T is its total output at hour h.
Then, let µh
be the bid curve multiplying factor at hour h so that the GENCO bid curve at hour h is given by:
BCh
= ρ + µh
βPh
T . (20)
The value of µh
then defines the GENCO’s bidding strategy at hour h. For a scheduling period of H time
periods, the set of bid factors U = µ1
, µ2
, µ3
, . . . , µH
constitutes the GENCO’s bidding strategy.
Figure 4. Profit Maximization procedure for a given bidding strategy
For a given bidding strategy, the procedure used to determine a profit maximization schedule is shown
in Figure 4. Given a particular bidding strategy, the reference marginal cost curve, forecasted competitor bid
curves, and the hourly demand curves, the GENCO can forecast the market’s supply and demand curves and
hence the market equilibrium point as illustrated in section 2.. As seen from Figure 4, this gives the GENCO’s
spot market allocations and the MCPs (spot market prices). The spot market data is then combined with the
bilateral market data (demand and prices) which is fed to a profit maximization algorithm to determine the
optimal UC schedules and hence the profit associated with the bidding strategy U.
5.2. EPSO Algorithm
Different bidding strategies give different spot market allocations and hence different optimal UC
schedules. Thus, an algorithm that determines the optimal bidding strategy is implemented in this paper us-
ing the EPSO algorithm [18]. In the solution of the OBS-PBUC problem, a particle represents a candidate
solution to the problem which in this case is a set of bid factors with one bid factor for each time period
of the scheduling horizon. Given a scheduling period of H hours, the jth
particle after k iterations Uj,k =
{µ1
j,k, µ2
j,k, µ3
j,k, . . . , µH
j,k} represents a position in the H-dimension solution space. The particle also has an as-
sociated velocity Vj,k = {v1
j,k, v2
j,k, v3
j,k, . . . , vH
j,k} and an associated set of weights Wj,k = {w0
j,k, w1
j,k, w2
j,k}.
The velocity represents a direction in which the particle is moving in the solution space while the weights
govern the direction of particle movement. w0
j,k governs the particle’s inertia habit, w1
j,k governs its memory
habit, while w2
j,k governs its cooperation habit [18].
A step by step outline of the procedure used to solve the OBS-PBUC problem using the EPSO algo-
rithm follows.
Step 1: Initialization:
1the subscript i indicating the GENCO number is dropped to improve readability of the equations.

Randomly initialize J particles Uj,0 j = 1, 2, . . . , J. Each particle is a set of H bid factors defining a
particular bidding strategy. For each particle, an optimal unit commitment schedule is obtained using the profit
maximization procedure shown in Figure 4. The obtained profit PFj,0 is the particle’s initial fitness value.
Each initialized particle is stored as pBestj; the corresponding fitness values as the best fitness values; and the
fittest particle of all initialized particles as initial gBest.
Step 2: Set the algorithm generation counter k = 1.
Step 3: Set the particles counter j = 1.
Step 4: Replication
Each particle is replicated R times i.e. R new particles are created as:
Ur
j,k = Uj,k, r = 1, 2, . . . R. (21)
Step 5: Set the particles replica counter r = 0.
Step 6: Mutation
The weights for replica r of particle j are mutated as:
wl,r
j,k+1 = wl,0
j,k + τwl N(0, 1), l = 0, 1, 2; (22)
where τwl is the standard deviation of the random mutation of weight parameter wl
.
Step 7: Reproduction
A new offspring is generated according to the particle movement rule2
:
Ur
j,k+1 = Ur
j,k + V r
j,k+1, r = 0, 1, 2, . . . R, (23)
where
V r
j,k+1 = w0,r
j,k · V r
j,k + w1,r
j,k · pBestj,k − Ur
j,k + w2,r
j,k · gBest∗
k − Ur
j,k . (24)
In (24), the gBestk value is disturbed to give gBest∗
k using:
gBest∗
k = gBestk + τgN(0, 1) (25)
where τg is the standard deviation of the random disturbance of the gBest value.
Step 8: Fitness Evaluation
An optimal UC schedule is obtained using the procedure described by Figure 4. The profit obtained from the
optimal UC schedule is is the offspring’s fitness.
Step 9: Increase the replica counter by 1. If all replicas have been evaluated, go to Step 10, else go back to Step
6.
Step 10: Updating pBest
The fitness values of particle j’s offspring are used to update the pBestj,k.
Step 11: Selection
One offspring is chosen to survive to the next generation through a stochastic tournament. The stochastic
tournament is carried out as follows:
• The fittest between the particle’s offspring is determined.
• This particle survives to the next generation with a probability pluck while the other particles survive with
a probability (1 − pluck) /R.
• If pluck is set to 1 then the best particle will always be chosen (pure elitism selection) while if pluck is set
to 1/(R + 1), there will pure random selection.
Step 12: Increase the particle counter by 1. If all particles have been evaluated, go to Step 13, else go back to
Step 4.
2U0
j,k refers to the original particle while U1
j,k, U2
j,k, . . . refer to the replica particles.

2006 Ì ISSN: 2088-8708
Step 13: Updating gBest
The original gBestk−1 value and the highest proﬁt from the pBestj,k values are used to update the gBestk
value.
Step 14: Increase the algorithm generations counter by 1. If K generations have been exhausted, go to Step 15,
else go back to Step 3.
Step 15: Store gBestK and its corresponding UC schedule as the optimal solution and STOP.
6. RESULTS AND DISCUSSION
6.1. Test System
The IEEE 118-bus system data [26, 27] was used to simulate a deregulated electricity market environ-
ment with three GENCOs of different sizes in terms of installed capacity of generators. The three GENCOs
operate several of the 54 thermal units in the IEEE 118-bus test system and the generating units data are given
in Tables 3, 4, and 5 for GENCOs A, B, and C respectively. The generator cost coefﬁcients are scaled up from
the values given in [27] so as to give more realistic energy prices. Based on the installed capacity, GENCO A
controls 60% (4340 MW out of 7220 MW) of the system capacity; GENCO B controls 30% (2140 MW out of
7220 MW); while GENCO C controls 10% (740 MW out of 7220 MW) of the system capacity. The reference
linear marginal cost curves for each of the three GENCOs and the aggregated system marginal cost curve are
shown in Figure 5. The marginal cost curves show that GENCO A operates the cheaper units while GENCO C
operates the most expensive units. Nominal market clearing prices αh
s corresponding a spot market demand Ph
D
can be read off from the aggregated reference marginal cost curve of Figure 5(b). Additionally, linear demand
curves are assumed for various load levels with a per-unit gradient of −5 i.e.
∆αh
s /αh
s
∆Ph
T /Ph
T
= −5. (26)
Equation (26) implies that a 100% increase in the spot market price would result in a 20% reduction in the spot
market demand.
A 24-hour (day ahead) scheduling period is applied and the load level is shown in Figure 6. Apart from
the allocations in the spot market, GENCO A is assumed to have a bilateral load demand equivalent to 10% of
of the system spot market demand (Figure 6) at a constant price of $45/MWh. A contract of differences factor
(κ in equation (7)) is set at 0.1. GENCOs B and C are assumed to have no bilateral commitments. The price of
reserve power (both spinning and non-spinning) is set at a constant $4.50/MW.
Table 3. GENCO A’s Generator Data
Unit No. of P min
i P max
i Capacity a b c MUT MDT RU RD HSC CSC CShr
Code Units [MW] [MW] [MW] [$/h] [$/MWh] [$/MWh2
] [hrs] [hrs] [MW] [MW] [$/h] [$/h] [hrs]
A1 2 100 420 840 128.32 16.68 0.0212 10 10 210 210 250 500 20
A2 8 100 300 2400 13.56 25.78 0.0218 8 8 150 150 110 220 16
A3 2 50 250 500 56.00 24.66 0.0048 8 8 125 125 100 200 16
A4 1 50 200 200 13.56 25.78 0.0218 8 8 100 100 400 800 16
A5 3 25 100 300 20.30 35.64 0.0256 5 5 50 50 50 100 10
A6 2 25 50 100 117.62 45.88 0.0195 2 2 25 25 45 90 4
Total 18 4340
Table 4. GENCO B’s Generator Data
Unit No. of P min
i P max
B1 1 100 350 350 65.92 21.50 0.0060 8 8 175 175 100 200 16
B2 1 100 300 300 65.92 21.50 0.0060 8 8 150 150 440 880 16
B3 2 50 200 400 78.00 26.58 0.0088 8 8 100 100 100 200 16
B4 8 25 100 800 20.30 35.64 0.0256 5 5 50 50 50 100 10
B5 1 20 50 50 117.62 45.88 0.0195 2 2 25 25 45 90 4
B6 8 5 30 240 63.34 52.49 0.1393 1 1 15 15 40 80 2
Total 21 2140

Table 5. GENCO C’s Generator Data
Unit No. of P min
i P max
C1 4 25 100 400 20.30 35.64 0.0256 5 5 50 50 50 100 10
C2 1 30 80 80 48.66 30.94 0.0918 3 3 40 40 45 90 6
C3 6 5 30 180 63.34 52.49 0.1393 1 1 15 15 40 80 2
C4 4 5 20 80 35.90 75.39 0.0566 1 1 10 10 30 60 2
Total 15 740
0 500 1000 1500 2000 2500 3000 3500 4000 4500
10
20
30
40
50
60
70
80
90
GENCO output power [MW]
MarginalCost[$/MWh]
GENCO A
GENCO B
GENCO C
0 1000 2000 3000 4000 5000 6000 7000 8000
10
20
30
40
50
60
70
80
90
Aggregated GENCO output power [MW]
MarginalCost[$/MWh]
Aggregated for all GENCOs
(a) (b)
Figure 5. (a) Individual marginal cost curves for the three GENCOs and (b) aggregated system marginal cost
curve
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
1000
2000
3000
4000
5000
6000
7000
HOURS
SpotMarketDemand[MW]
Total spot market
energy demand
111,350 MWh
Figure 6. Spot market demand curve
First, in section 6.2. a discussion of the nominal system equilibrium is presented i.e. the market prices,
spot market load allocations, and expected GENCO proﬁts (results of the PBUC) if each GENCO were to bid
its nominal bid curve as shown in Figure 5(a). Then, the solution to the OBS-PBUC problem for each of the
three GENCOs using the proposed EPSO algorithm is presented in section 6.3.. Finally, in section 6.4., a
comparison of the simulations results using the proposed EPSO algorithm and the classical PSO algorithm is
presented.
6.2. Nominal System Equilibrium
The spot market demand curve plotted in Figure 6 shows the load varying from a low of 2900 MW at
midnight to a maximum of 6100 MW at 10 AM. If all three GENCOs bid their reference marginal cost curves,
the hourly market clearing prices (MCPs) will be as shown in Figure 7(a). As expected, the MCP curve follows
the spot market load with a minimum value of $34.17/MWh at midnight and a peak of $57.82/MWh 10 AM.
Also shown in Figure 7(b) is the hourly allocation of the spot market load to the three GENCOs. Figure 7(b)
shows that GENCO A gets most of the load and is actually limited during the peak hours of 8 AM to 4 PM

2008 Ì ISSN: 2088-8708
by its capacity less the bilateral market demand. GENCO B supplies mainly the intermediate load with the
allocation of 1978 MW at 10 AM almost equaling its capacity of 2140 MW. GENCO C primarily acts as a
peak load generator only supplying energy during the peak hours. During the low peak hours before 5 AM,
GENCO C receives no allocation thus only receiving payments from sale of reserve power.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10
20
30
40
50
60
70
HOURS
MarketClearingPrice[$/MWh]
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
0
1000
2000
3000
4000
5000
6000
HOURS
SpotMarketAllocation[MW]
GENCO A
GENCO B
GENCO C
GENCO Allocations
−−−−−−−−−−−−−−−−−−−−−−
GENCO A: 78,140 MWh (70.2%)
GENCO B: 29,660 MWh (26.6%)
GENCO C: 3,550 MWh ( 3.2%)
(a) (b)
Figure 7. (a) Hourly MCPs corresponding to the nominal marginal cost curves and (b) spot market allocations
for each individual GENCO
Also shown in Figure 7(b) is the total daily energy to be supplied by the three GENCOs in the spot
market. it is observed that GENCO A is allocated 70.2% of the spot market demand during the day while
GENCOs B and C are allocated only 26.6% and 3.2% respectively. While GENCO B’s allocation compares
relatively well to its installed capacity (30% relative to the system capacity) GENCO A’s allocation is signif-
icantly higher than its relative installed capacity while GENCO C’s allocation is significantly lower than its
relative installed capacity. Again, this is because GENCO A has cheaper units hence is usually allocated first
while GENCO C has more expensive units and is allocated last. A Profit Based Unit Commitment algorithm
was run for each of the three GENCOs with the base case spot market allocations shown in Figure 7(b) and the
the expected values of daily revenue, operating costs, and profits for each GENCO are shown in Table 6.
Table 6. Revenues, costs, and profits for nominal bidding strategies
GENCO A GENCO B GENCO C
REVENUES
Spot Market 3, 523, 184 1, 369, 344 177, 640
Reserve Sales 59, 434 86, 817 56, 838
Bilateral Market 501, 075 − −
CFDs 2, 922 − −
TOTAL REVENUE 4, 086, 615 1, 456, 161 234, 479
TOTAL COST 2, 620, 007 914, 826 148, 268
PROFIT 1, 466, 608 541, 335 86, 211
6.3. Optimal Bidding Strategy
The OBS-PBUC problem was solved using the EPSO algorithm described in section 5.2. for each of
the three GENCOs assuming that each is acting independently and using the competing GENCO’s nominal
marginal cost curves as the expected competitor bidding curves in each case. Values for the various parameters
used in the EPSO algorithm are given in Table 7. Simulation results including the optimal values of the hourly
bid factors, the expected MCPs, spot market allocations, revenues, costs, and profits are discussed next.

Table 7. Parameter values for EPSO algorithm
Parameter Value
no. of particles 20
no. of iterations 500
initial value of weight w0
0.4
1.0
2.0
standard deviation of weights, τwl 0.1
standard deviation of gBest, τg 0.01
no. of replica particles 1
probability of best particle surviving, pluck 0.8
The hourly values of the bid factors that give the maximum profits defines a GENCO’s optimal bidding
strategy. Figure 8 shows the obtained values of the optimal bid strategies for the three GENCOs. As seen from
Figure 8 , the optimal values of the hourly bidding factors are in the range of 2.0 to 4.3 for GENCO A, 0.9 to
1.8 for GENCO B, and 0.5 to 1.3 for GENCO C. The interpretation here is that GENCO A should generally
bid higher than its nominal bidding curve, GENCO B should bid just slightly higher than its nominal bidding
curve while GENCO C should bid lower than its nominal bidding curve in order to maximize their respective
profits.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
0
1
2
3
4
5
HOURS
OptimalBidfactor
GENCO A
GENCO B
GENCO C
Figure 8. Optimal hourly bid factors
Figures 9 (a), (b), and (c) show how the optimal bidding strategy for each GENCO would alter the
hourly spot market clearing prices. GENCO A’s high bidding factors significantly raise the MCPs; GENCO B’s
strategy would slightly raise the MCPs while GENCO C’s strategy has almost no effect on the MCPs. These
results confirm that GENCO C is in fact a price taker while GENCO A is a price maker with significant market
power to alter the MCPs. The effect of the optimal bidding strategies on the spot market allocations are shown
in Figures 9 (d), (e), and (f). GENCO A’s optimal bidding strategy would significantly reduce its allocation in
the spot market; GENCO B’s optimal bidding strategy would slightly reduce its allocation in the spot market;
while GENCO C’s optimal bidding strategy would significantly increase its allocation in the spot market during
peak hours.

2010 Ì ISSN: 2088-8708
0 3 6 9 12 15 18 21
20
30
40
50
60
70
80
90
100
HOURS
MCP[$/MWh]
Nominal
Optimal
0 3 6 9 12 15 18 21
20
30
40
50
60
70
80
90
100
HOURS
MCP[$/MWh]
Nominal
Optimal
0 3 6 9 12 15 18 21
20
30
40
50
60
70
80
90
100
HOURS
MCP[$/MWh]
Nominal
OptimalGENCO A GENCO B GENCO C
(a) (b) (c)
0 3 6 9 12 15 18 21
0
1000
2000
3000
4000
5000
HOURS
Spotmarketallocation[MW]
Nominal
Optimal
0 3 6 9 12 15 18 21
0
500
1000
1500
2000
2500
HOURS
Nominal
Optimal
0 3 6 9 12 15 18 21
0
100
200
300
400
500
600
HOURS
Nominal
OptimalGENCO A GENCO B GENCO C
(d) (e) (f)
Figure 9. Effect of individual GENCO optimal bidding strategies on the MCPs and the spot market allocations
Comparisons of the revenues, costs, and profits for each of the three GENCO’s are given in Tables 8,
9, and 10. Table 8 — corresponding to GENCO A — shows a reduction in the revenues from the spot market
resulting from the reduced allocations due to the optimal bidding strategy. However the reduction in operating
costs coupled with revenues from the increased reserve sales and CFDs gives an overall increase in profits.
These results show that it is more beneficial for GENCO A to bid high to increase the MCPs even though this
may reduce its spot market allocations and its spot market revenues as a result.
Table 8. GENCO A revenues, costs, and profits for optimal bidding strategy
Nominal Optimal Difference
REVENUES
Spot Market 3, 523, 184 2, 768, 844 −754, 340
Reserve Sales 59, 434 189, 213 +129, 779
Bilateral Market 501, 075 501, 075 0
CFDs 2, 922 85, 562 +82, 640
Total Revenues 4, 086, 615 3, 544, 694 −541, 921
Total Costs 2, 620, 007 1, 518, 954 −1, 101, 053
Profits [$/day] 1, 466, 608 2, 025, 739 +559, 131
(+38.1%)
Table 9 — corresponding to GENCO B — shows similar results to those of GENCO A though to a
lesser extent. The reduction in operating costs coupled with revenues from the increased reserve sales out-
weighs reduction in spot market revenues resulting from the reduced allocations due to the optimal bidding
strategy. However, GENCO B achieves only a 13.3% increase in profits compared to a 38.1% increase for
GENCO A. This is a consequence of the GENCO A’s market power enabling it to have a greater influence on

the MCPs a result that is also deduced from Figures 9 (a) and (b).
Table 9. GENCO B revenues, costs, and profits for optimal bidding strategy
REVENUES
Spot Market 1, 369, 344 1, 221, 779 −147, 565
Reserve Sales 86, 817 108, 219 +21, 402
Bilateral Market − − −
CFDs − − −
Total Revenues 1, 456, 161 1, 329, 998 −126, 163
Total Costs 914, 826 716, 916 −197, 910
Profits [$/day] 541, 335 613, 082 71, 747
(+13.3%)
Table 10 — corresponding to GENCO C — shows that for the smallest GENCO the optimal bidding
strategy is to bid low in order to capture slightly more of the spot market demand. As seen from Table 10,
the net increase in revenues (increase in spot market revenues less reductions in reserve sales) is greater than
the increase in operating costs for supplying more energy. However, the final increase in profits (+3.7%) is
relatively small when compared to the profit increases realized by GENCOs A and B. Again this is attributed
to GENCO C’s relative weakness in the electricity market.
Table 10. GENCO C revenues, costs, and profits for optimal bidding strategy
REVENUES
Spot Market 177, 640 228, 785 51, 145
Reserve Sales 56, 838 52, 467 −4, 371
Bilateral Market − − −
CFDs − − −
Total Revenues 234, 479 281, 252 46, 773
Total Costs 148, 268 191, 856 43, 588
Profits [$/day] 86, 211 89, 396 3, 185
(+3.7%)
The relationship between the GENCO market power (measured by the GENCO’s relative size in the
market) and the effect of their optimal bidding strategies on the market dynamics are summarized in Table 11.
Table 11. Effect of GENCO market power on market prices, allocations, and individual profits
% installed capacity
(market power)
60% 30% 10%
Average % change in spot energy
market prices
+31.4% +7.2% −0.8%
Average % change in spot energy
market allocations
−41.5% −18.1% +30.8%
% change in expected profits +38.1% +13.3% +3.7%

2012 Ì ISSN: 2088-8708
6.4. Comparison of EPSO and PSO algorithms
The performance of the EPSO algorithm implemented in this paper was compared to the performance
of a similar implementation using the classical PSO algorithm. The problem was solved for the three GENCOs
20 times using both algorithms starting from the same initial particles in each trial. The same parameter values
(i.e. number of particles, number of iterations, and weight values) given in Table 12 for the EPSO algorithm
were used for the implemented PSO algorithm. The performance of the two algorithms was measured in terms
of the objective function values from the 20 runs. Table 12 gives the best, average, and worst solutions obtained
for both algorithms for each of the three GENCOs. Also given in Table 12 is the standard deviation for the
solutions. The table shows that the proposed EPSO algorithm outperforms the classical PSO algorithm in all
cases. The superior performance of the EPSO algorithm is attributed to the mutation characteristics embedded
in the algorithm which tune the algorithm parameters in subsequent generations hence resulting in a better
search of the solution space.
Table 12. Comparison of solution quality using PSO and EPSO algorithms
PSO EPSO PSO EPSO PSO EPSO
Best solution [$/day] 1, 954, 488 2, 025, 739 610, 497 613, 082 88, 703 89, 396
Average solution [$/day] 1, 903, 261 1, 967, 363 598, 663 600, 745 87, 987 88, 982
Worst solution [$/day] 1, 850, 798 1, 931, 389 584, 485 585, 105 87, 293 88, 482
Standard deviation [$/day] 40, 644 31, 811 7, 348 6, 365 348 262
7. CONCLUSION
This paper presents a methodology for determining an optimal bidding strategy and unit commitment
for a GENCO operating in a competitive electricity market place. The proposed procedure seeks to determine
how a GENCO should structure its hourly bid curves so as to maximize profits where profit is calculated as
the difference between expected revenues and generation costs for expected GENCO own demand. GENCO
demand is determined as the sum of allocations from the spot market and bilateral market commitments. The
complex optimization problem is solved using an evolutionary particle swarm optimization (EPSO) technique.
Numerical results from simulations of a typical system with three GENCOs of different sizes confirms the
effectiveness of the proposed algorithm. Generally, it is shown that large GENCOs with significant market
power could raise their bids – thereby significantly raising electricity prices – and hence increasing their profits;
though the higher bids could reduce their allocations in the spot market. Smaller GENCOs with less market
power are generally price takers and have relatively less influence on the market equilibrium. The optimization
algorithm results in only slight increases in expected profits for these GENCOs. Finally, a comparison of
solution quality from the proposed EPSO algorithm with those obtained using the classic PSO algorithm shows
that the proposed methodology performs much better.
REFERENCES
[1] B. Saravanan, S. Das, S. Sikri, and D. P. Kothari, “A solution to the unit commitment problem — a
review,” Frontiers in Energy, vol. 7, no. 2, pp. 223–236, 2013.
[2] M. S. Javadi, “Security constraint unit commitment considering line and unit contingencies-particle
swarm optimization,” International Journal of Applied Power Engineering, vol. 1, no. 1, pp. 13–20, 2012.
[3] S. S. Sakthi, R. K. Santhi, N. M. Krishnan, S. Ganesan, and S. Subramanian, “Wind integrated thermal
unit commitment solution using grey wolf optimizer,” International Journal of Electrical and Computer
Engineering, vol. 7, no. 5, pp. 2309–2320, 2017.
[4] E. Delarue, D. Cattrysse, and W. D’haeseleer, “Enhanced priority list unit commitment method for power
systems with a high share of renewables,” Electric Power Systems Research, vol. 105, no. 0, pp. 115 –
123, 2013.
[5] K. Choudhary, R. Kumar, D. Upadhyay, and B. Singh, “Optimal power flow based economic generation
scheduling in day-ahead power market,” International Journal of Applied Power Engineering, vol. 6,

no. 3, pp. 124–134, 2017.
[6] L. Philipson and H. L. Willis, Understanding Electric Utilities and De-Regulation, 2nd ed. Florida,
USA: Taylor & Francis Group, 2006.
[7] K. Asokan and R. Ashokkumar, “A simple approach for optimal generation scheduling to maximize gen-
cos profit using ppd table and abc algorithm under deregulated environment,” International Journal of
Electrical and Computer Engineering, vol. 2, no. 1, pp. 137–146, 2012.
[8] T. Li and M. Shahidehpour, “Price-based unit commitment: a case of Lagrangian relaxation versus mixed
integer programming,” Power Systems, IEEE Transactions on, vol. 20, no. 4, pp. 2015–2025, Nov 2005.
[9] R. H. Kwon and D. Frances, Handbook of Networks in Power Systems I. Springer Berlin Heidelberg,
2012, ch. Optimization-based bidding in day-ahead electricity auction markets: A review of models for
power producers, pp. 41–59.
[10] M. M. Belsnes, G. Warland, and O. Wolfgang, “Simulating equilibrium prices in oligopoly power mar-
kets,” in 2011 IEEE Trondheim PowerTech, June 2011, pp. 1–8.
[11] A. Rajan, C. Christober, P. Sundarajan, V. Jamuna, R. Madhusubash, and B. Udayakumar, “Multi-area
unit commitment in deregulated electricity market using DP approach,” Inter. Journal on Recent Trends
in Engineering and Technology, vol. 3, no. 3, pp. 210–213, May 2010.
[12] E. Delarue, P. V. D. Bosch, and W. D’haeseleer, “Effect of the accuracy of price forecasting on profit in a
price based unit commitment,” Electric Power Systems Research, vol. 80, no. 10, pp. 1306 – 1313, 2010.
[13] J. Raglend, C. Raghuveer, G. R. Avinash, N. Padhy, and D. Kothari, “Solution to profit based unit commit-
ment problem using particle swarm optimization,” Applied Soft Computing, vol. 10, no. 4, pp. 1247–1256,
Sept. 2010.
[14] H. S. Madraswala and A. S. Deshpande, “Genetic algorithm solution to unit commitment problem,” in
2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems
(ICPEICES), July 2016, pp. 1–6.
[15] T. Venkatesana and M. Sanavullahb, “SFLA approach to solve PBUC problem with emission limitation,”
International Journal of Electrical Power and Energy Systems, vol. 46, pp. 1–9, March 2013.
[16] A. Sudhakar, C. Karri, and A. J. Laxmi, “Profit based unit commitment for GENCOs using lagrange
relaxation - differential evolution,” Engineering Science and Technology, an International Journal, pp. –,
2016.
[17] S. Selvi, M. Moses, and C. Rajan, “LR-EP approach for solving profit based unit commitment problem
with losses in deregulated markets,” Przeglad Elektrotechniczny, vol. 11, pp. 210–213, 2013.
[18] V. Miranda and N. Fonseca, “EPSO-evolutionary particle swarm optimization, a new algorithm with
applications in power systems,” in IEEE/PES Transmission and Distribution Conference and Exhibition,
vol. 2, Oct 2002, pp. 745–750 vol.2.
[19] V. Miranda and N. W. Oo, “New experiments with epso – evolutionary particle swarm optimization,” in
IEEE Swarm Intelligence Symposium 2006, Indianapolis (IN), USA, 2006, pp. 1–8.
[20] J. Jamian, M. Mustafa, H. Mokhlis, and M. Baharudin, “Implementation of evolutionary particle swarm
optimization in distributed generation sizing,” International Journal of Applied Power Engineering, vol. 2,
no. 3, pp. 125–140, 2013.
[21] M. Shahidehpour and M. Alomoush, Restructured Electrical Power Systems, Operation, Trading, and
Volatility, 1st ed. New York: Marcel Decker, 2000.
[22] V. Miranda, H. Keko, and A. Jaramillo, Advances in Evolutionary Computing for System Design, Studies
in Computational Intelligence. Springer Berlin Heidelberg, 2007, vol. 66, ch. EPSO: Evolutionary
Particle Swarms, pp. 139–168.
[23] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Neural Networks, 1995. Proceedings.,
IEEE International Conference on, vol. 4, Nov 1995, pp. 1942–1948 vol.4.
[24] X. Ma, D. I. Sun, and K. W. Cheung, “Evolution toward standardized market design,” IEEE Transactions
on Power Systems, vol. 18, no. 2, pp. 460–469, May 2003.
[25] J. Lin and F. H. Magnago, Electricity Markets:Theories and Applications. Wiley-IEEE Press, 2017, ch.
Power System Unit Commitment, pp. 97–118.
[26] University of Washington. (2017, October) Power system test case archive. [Online]. Available:
http://www.ee.washington.edu/research/pstca/.
[27] Illinois Institute of Technology. (2017, October) PBUC Data. [Online]. Available:
http://motor.ece.iit.edu/data/PBUCData.pdf.

GENCO Optimal Bidding Strategy and Proﬁt Based Unit Commitment using Evolutionary Particle Swarm Optimization Illustrating the Effect of GENCO Market Power

More Related Content

What's hot (20)

Similar to GENCO Optimal Bidding Strategy and Proﬁt Based Unit Commitment using Evolutionary Particle Swarm Optimization Illustrating the Effect of GENCO Market Power (20)

More from IJECEIAES (20)

Recently uploaded (20)

GENCO Optimal Bidding Strategy and Proﬁt Based Unit Commitment using Evolutionary Particle Swarm Optimization Illustrating the Effect of GENCO Market Power