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Leonardo Electronic Journal of Practices and Technologies
ISSN 1583-1078
Issue 30, January-June 2017
p. 17-38
17
http://lejpt.academicdirect.org
Engineering, Environment
Generation scheduling of renewable energy resources under uncertainties
in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND*, Moein PARASTEGARI
Department of Electrical Engineering, University of Isfahan, Isfahan, Iran
E-mail(s): [email protected], [email protected],
[email protected] * Corresponding author, phone: +98 31 37934073, fax: +98 31 37933071
Received: January 30, 2017 / Accepted: June 14, 2017 / Published: June 30, 2017
Abstract
Over the past few years, utilization of renewable energy resources (RERs) has
become an active and interesting area of research in energy management of
power systems. In this paper, a new three-stage generation scheduling method
is proposed for thermal units and renewable energy resources. In the method,
all generation units are bidding in a competitive market along with the
external energy tie-line at the point of common coupling. The scheduling
problem is solved while considering uncertainties in both generation and
demand. At the first stage, Generation Companies (GenCos) use forecasted
information (such as market price and climate conditions) to determine their
optimal bidding strategy for maximum revenue. In the next stages,
independent system operator (ISO) manages available contracts to minimize
the operating cost of the power system. The proposed method is applied to a
10-unit network using GAMS software. Simulation results show that the
effectiveness of this method is to the benefit of generation companies and ISO
in the presence of traditional tie-line.
Keywords
Power Market; Renewable resources; Generation scheduling; Uncertainty
Generation scheduling of renewable energy resources under uncertainties in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND, Moein PARASTEGARI
18
Nomenclature
a j ,b j ,C j: Fuel cost coefficient of unit j
P sjk: Power generation of unit j at time k in scenario 5
P jMax , P j
Min: Maximum and Minimum generation limit of unit j
MU j‘ MD j: Minimum up and down time of unitj
RU j ‘ RD j: Ramp up and down limit of unit j
FC j(P sjk) : Generation cost of unit j at time k in scenario 5
SC jk: Startup cost of unit j at time k
HSC j , CSC j: Hot and Cold start-up cost of unit j
T jkcold
: Continuous off time of unit j at time k
T on , T o f f : Continuous on and off time of unit j
P skin,P s k
o u t : Power imported or exported with tie line at time k in scenario 5
C s j kp e n
: Penalty for each MWh of unit j at time k in scenario 5
P jkbest: Generation bid of unit j at time k
P skr: Available reserve at time k in scenario 5
RP k i MP k: Reserve and Market price at time k
RC s k: Spinning reserve cost at time k in scenario 5
P s krenew: Generation of renewable units at time k in scenario 5
P skl: Demand at time k in scenario 5
R skMin
: Minimum required reserve
P l i n eM a x
: Line flow limit
α , β : Reserve factors
Introduction
Nowadays, renewable energy resources are increasingly used in restructured power
systems. One of the main disadvantages of these resources is their uncertain generation.
Scheduling problem of generation units without considering renewable resources is a complex
problem, yet by considering these resources, scheduling problem becomes more complex. In
most studies, the generation scheduling problem is examined from the ISO’s point of view.
Hence, the ISO manages the generation units to minimize the total operating cost. In reality,
generation scheduling problem is considered from the favorable view of both ISO and
GenCos. In this condition, generation scheduling problem could be solved by two general
Leonardo Electronic Journal of Practices and Technologies
ISSN 1583-1078
Issue 30, January-June 2017
p. 17-38
19
objective functions: cost minimization [5,7,22] or profit maximization [24,25,28] and by Cost
Based Unit Commitment (CBUC) or Profit Based Unit Commitment (PBUC) solutions.
In [12-14], scheduling is performed in a cooperative environment. In this case, the
hourly load should be lower than the total generation capacity and the system should work in
a normal mode [18]. In a normal mode, no power is transferred from or to the system. In [18],
two more modes are additionally considered excess demand and excess renewable generation.
In these modes, unbalances between generation and consumption are controlled by
exchanging power through the tie-line. In [15], a hybrid method is developed through
adaptive search which is inspired from artificial immune system and genetic algorithm to
carry out profit maximization of generation companies. In a power market, GenCos sell their
energy and their reserve to energy and ancillary markets [24]. Changes in energy and reserve
prices along with payment methods have a direct effect on the amount of power and reserve
bids. There are several methods such as payment for the power delivered and payment for the
reserve allocated for reserve market clearing [24]. In a competitive environment, it is not
necessary for the power plants to supply the hourly demand. Accordingly, in [24, 29], it is
considered that the generated power has to be equal or lower than the hourly demand, so that
there is no excess generation in the system. Moreover, [23] tries to determine the optimal or
near optimal scheduling to find Influence of improvement of generation scheduling on
wheeling cost.
The generation scheduling problem has been studied from different aspects such as
considering renewable resources [14-17,21-22,24,26], energy storage systems [14-16,22,25],
generation uncertainty [14-18,21,27], reliability indices [27], Emission [1-4,14-15], and
demand response [14,28]. In [13-15, 18], it is shown that the penetration of renewable energy
resources brings about a decrease in the operating cost. Also, simultaneous scheduling of
storage systems and renewable resources improve the performance of renewable energy
resources [13]. In [26], the uncertainties of renewable energy resources are considered in
retail markets. In this case, the scheduling problem is defined as a Multi-Area Dynamic
Economic Dispatch (MA-DED) problem.
Scheduling problems can be solved by different methods. These methods can be
divided into two categories: mathematical and meta-heuristic. Mathematical methods which
can be used to solve different optimization problems are Lagrangian Relaxation (LR) [24],
Evolutionary Programming (EP) [10], and Dynamic Programming (DP) [8]. The Meta-
Generation scheduling of renewable energy resources under uncertainties in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND, Moein PARASTEGARI
20
heuristic methods which can be used to solve optimization problems are: Bee Colony [14];
Genetic Algorithm (GA) [8]; Unit Characteristic Classification by using Genetic Algorithm
(UCC-GA) [9]; Hybrid Particle Swarm Optimization (HPSO) [12]; and some hybrid methods
such as LRGA [11].
In this paper, a hybrid method is presented for the generation scheduling of thermal
and renewable units. In this method, a multi-objective problem tries to minimize the
generation cost and maximize the profit of GenCos simultaneously. For this purpose, at first
the optimal bidding strategy of generation units is determined without considering the power
system constraints. Then, based on historical data, all scenarios of renewable energy resources
and system loads are generated. Finally, by considering all scenarios, the main scheduling
problem is modeled by meeting the security constraints of the system and generation units.
Simulation results indicate that the proposed method can decreases the cost and increases the
profit of the coordinated thermal and renewable units by using the traditional tie-line.
Material and method
Problem Formulation
Generation units can be categorized into two main categories: Dispatch able units and
Non-Dispatch able units. In schedulable units, the scheduling program is determined based on
fuel cost and other ancillary costs. The goal of the operator of these units is to maximize the
profit. Operators of these units submit their bids to the market and if their bids are accepted,
the ISO should use the bids in the scheduling program. If there are any violations between
scheduling program and the actual state of the units, the ISO should pay the imbalance cost to
GenCos. On the other hand, there are uncertainties in the power generation of the non-
dispatch able units such as wind units; so, it is necessary to model these uncertainties to reach
the optimal scheduling program. First, the generation of non-schedulable units is forecasted
and then the uncertainties are modeled through the historical data by scenario method to
model these uncertainties. It should be noted that the ISO schedules units according to their
contracts, the scenarios of the generation of renewable resources, and the load scenarios. ISO
uses renewable resources first, then uses the schedulable units, and finally uses tie-line power
in its scheduling program.
Leonardo Electronic Journal of Practices and Technologies
ISSN 1583-1078
Issue 30, January-June 2017
p. 17-38
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Optimal bidding strategy of GenCos
In this section, optimal bidding strategy of generation units is determined. To
determine the optimal bidding strategy of the units, it is first necessary to determine the
pattern of the daily prices on the basis of the historical prices data and price fluctuations.
Then, optimal bidding strategy of the units is determined by solving optimization problem
consisting of an objective function and a set of constraints. The objective function of this
problem is as follows:
K
k
J
j
kjjkjkjkjkjkjk YYSCYPFCMPP
1 1
)1( )1.(.).(.:max (1)
The objective function consists of three parts. The first part represents the sales profit
in the market. The second part represents the cost of generated power and the last part
represents the startup cost. Yjk variable is a binary variable indicating the status of unit j in
period k. Generation and startup costs can be determined as follows:
2..)( jkjjkjjjkj PcPbaPFC (2)
jjoff
jk
jjoff
jkjjk
CSTMDTCSC
CSTMDTMDHSCSC
if
if (3)
In order to determine the optimal bidding strategy of the units, it is necessary that to
consider the constraints of the generation units. These constraints are as follows:
1. Generation limits: The output power must be within allowable limits:
jkjjkjkj YPPYP ..maxmin
(4)
2. Minimum up and down times:
jon
j MUT (5)
joff
j MDT
(6)
3. Ramp up and ramp down limits: The change in the output power of the units must
comply with the following limits:
jjkkj RUPP )1( (7)
jkjjk RDPP )1(
(8)
Generation scheduling of renewable energy resources under uncertainties in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND, Moein PARASTEGARI
22
Scheduling problem from the point of view of ISO
The scheduling problem used by ISO is introduced in this section. ISO executes the
scheduling problem and the inputs of the problem are the generation bids (determined in the
last subsection), the scenarios of the generation of the renewable energy resources, and the
load scenarios. The objective of this scheduling problem is to minimize the operation cost of
the system. This objective function is as follows.
K
k
k
out
sk
in
sksk
pen
sjk
S
s
K
k
J
j
kjjkjkjksjkjsMPPPRCCYYSCYPFC
11 1 1
)1()).()1.(.).(.(:min (9)
This objective function (Eq. (9)) consists of four parts. In (9), pensjkC represents the
violation penalty for any bid for unit j at period k in scenario s. skRC represents the cost of
the spinning reserve at period k in scenario s. Also, kout
skin
sk MPPP ).( presents the energy
cost of the tie-line. Meanwhile, s parameter indicates the probability of scenario s. Also,
imbalanced and the reserve cost can be calculated as follows:
kjkbest
jksjkpen
sjk MPYPPC .. (10)
kr
sksk RPPRC .
(11)
2..)( sjkjsjkjjsjkj PcPbaPFC
(12)
jjoff
jk
jjoff
jkjjk
CSTMDTCSC
CSTMDTMDHSCSC
if
if
(13)
Constraints of the scheduling problem from the point of view of ISO are as follows:
1. Generation Limits: This constraint is the same as that in (4);
2. Minimum up and down times: These constraints are the same as those presented in
(5) and (6);
3. Ramp up and ramp down limits: These constraints are the same as those presented
in (7) and (8);
4. System power balance: the following equation represents the load balance equality.
J
j
outsk
lsk
renewsk
insksjk PPPPP
1
(14)
Where: Pskin and Psk
out represent the input and output transmitted power by the tie-line at
period kin scenario s, respectively. Also, Pskrenew represents the power generated by the
Leonardo Electronic Journal of Practices and Technologies
ISSN 1583-1078
Issue 30, January-June 2017
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23
renewable resources at period k in scenario s, and Pskl represents the demand at period k in
scenario s.
1. System reserve: the reserve of the network must be provided under the following
conditions.
renewsk
lsksk
skin
skliner
sk
J
j
sjkjkjr
sk
PPR
RPPP
PYPP
..
)(
.
min
minmax
1
max
(15)
In Eq. (15), the spinning and non- spinning reserve value is specified. The total
available reserve must be at least equal to required amount (i.e. Percentage of hourly demand
or biggest generation unit capacity). Pskr represents the value of the spinning reserve provided
by schedulable units at period k in scenario s. Plinemax - Psk
in represents the non-spinning
reserve value provided by the tie-line at period k in scenario s. Also, Rskmin represents the
minimum reserve requirements at period k in scenario s. The coefficients α and β represent
the percentage of the demand and the generation of the renewable resources for the minimum
reserve requirements.
2. Tie-line flow limits: The value of the limits are as follows:
max0 line
insk PP (16)
max0 line
outsk PP (17)
A method proposed for the defined problem
The algorithm of the proposed method is shown in Figure 1.
Generation scheduling of renewable energy resources under uncertainties in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND, Moein PARASTEGARI
24
ISO
Start
Profit-Base Unit
Commitment
Generation Profile
For Thermal Units
Unit’s
Contract
Generate Scenarios & Computing PDF
Factors of Load And Generation of
Renewable Resources
Cost-Base Unit Commitment
Generation Scheduling
End
Forecasting of
Market Prices
Forecasting of Wind Speed,
Temperature, insolation And
Load With Uncertaintes
Load And Renewable
Generation Scenarios
Hour Ahead
Market
Stage I
Stage II
Stage III
Figure 1. The proposed algorithm
As shown in this figure, this algorithm consists of three stages. In the first stage, the
input data includes the market price forecasts, the predicted demand, and the forecast
determined for the generation of renewable resources. In the second stage, by solving the
PBUC problem, the optimal bidding strategies of GenCos are determined. The scenarios of
the renewable generation and demand should be determined at this stage as well. In the last
stage, based on previous results, the scheduling problem is modeled and solved by
considering the power system constraints from the point of view of ISO.
Generation scheduling problems can be examined with regard to two contexts:
Cooperative and Competitive. In the cooperative context, the generation units have to meet
the demand with minimum reserve requirements. In this case, the network has no dealings
with the outside network and the network must be self-sufficient to meet its demands. In the
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competitive context, the system operator can use the tie-line power to satisfy the demand. In
this case, the system generation can be lower or higher than that of the demand required.
Obviously, the profit of GenCos in competitive markets is more than that of cooperative
markets. It should be noted that in a competitive context, the GenCos offer bids in a way that
they make the maximum profit. But in a cooperative context, the GenCos should satisfy the
demand. In the following, the three stages of the proposed method are introduced.
First stage
At this stage, the information required for solving the scheduling problem is
determined as an input data to the generation scheduling problem.
These input data are as follows:
1. Forecasted day-ahead market prices.
2. Forecasted load and its scenarios.
3. Forecasted generation of renewable resources for the next 24 hours and its scenarios
Second stage
In this stage, by using the information determined in the previous stage, optimal
bidding strategies of the schedulable units are determined. For this purpose, the following
data should be determined.
1. Bids of the schedulable GenCos: the schedulable GenCos determine their optimal
bidding strategy based on market prices by solving the problem presented in section (2-
1).
2. Demand scenarios: ISO calculates the demand scenarios based on historical
information. The method used for scenario generation is described in the next sub-section.
Scenarios for the renewable generation of energy resources: based on the historical
data of the renewable energy resources, renewable generation scenarios can be determined.
The method used for the scenario generation is described as follows.
Scenario generation method: One of the main methods to generate the load and
renewable power scenarios is to discretize the probability distribution function (PDF) of the
forecasting error [18]. Demand and wind power generation errors can be modeled by using
this method based on normal PDFs. Each continuous PDF is discretized to create a set of
finite states such that a probability is assigned to each state according to its PDF. Forecasting
Generation scheduling of renewable energy resources under uncertainties in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND, Moein PARASTEGARI
26
errors are defined as per-unit and can be changed several times in one scenario. We assumed
that these values are provided by renewable resources. The discrete sets of the load D and
wind power W forecasting errors are described as follows:
n
i
m
i
iW
iD
mW
mWWWWWW
nD
nDDDDDD
eee
eee
1 1
2211
2211
1
,,,,,,
,,,,,,
(18)
mnS
s
n
i
m
j
jW
iDs
1 1 1
1. (19)
Where: n
De - the error of scenario n of the forecasted load, n
D - the corresponding
probability, and n - the total number of load scenarios. Also, mWe , and m
W - the error and
the probability of the wind generation forecast of the m-th scenario and m - the total number
of wind generation scenarios. S represents the total number of scenarios.
In this stage, the data which is determined in the previous stages are used to schedule
units. The optimal bidding strategy of the schedulable units determined in the previous stage
will be considered as contracts on the market. Also, all the pieces of information such as the
market price and the scenarios are collected for primary generation scheduling by solving the
objective function (9).
Results and discussion
In order to illustrate the advantages of the algorithm presented in Section 3, this
algorithm has been implemented on a 10-Units power system. At first, simulation results for
both the cooperative and competitive contexts are introduced and then the results are
compared with those of other studies. Finally, the results of the proposed algorithms are
evaluated. It should be noted that DICOPT (Discrete and continuous optimizer) solver of
GAMS software is used for solving the optimization problem. This solver is a program for
solving mixed-integer nonlinear programming (MINLP) problems that involve linear binary
or integer variables and linear and nonlinear continuous variables. While the modeling and
solution of MINLP optimization problems have not yet reached the stage of maturity and
reliability achieved by linear, integer, or non-linear programming modeling, these problems
Leonardo Electronic Journal of Practices and Technologies
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27
still have rich areas of application. The MINLP algorithm inside DICOPT solves a series of
NLP and MIP sub-problems. NLP and MIP solvers that used for this simulation are CONOPT
and CPLEX.
Initial data
The case under study consists of 10 thermal units with a total capacity of 1662 MW.
The details of the 10 power units are presented in appendix A. The demand profile and the
hourly market price are shown in Table 1 [24]. In this system, the required reserve is 10% of
the hourly demand (α=0.1).
Table 1. Forecasted demands and spot market price
Spot Price
($/MWh)
Demand
(MW)
Interval
(h)
Spot Price
($/MWh)
Demand
(MW) Interval
24.6 1400 13 22.15 700 1
24.5 1300 14 22 750 2
22.5 1200 15 23.1 850 3
22.3 1050 16 22.65 950 4
22.25 1000 17 23.25 1000 5
22.05 1100 18 22.95 1100 6
22.2 1200 19 22.5 1150 7
22.65 1400 20 22.15 1200 8
23.1 1300 21 22.8 1300 9
22.95 1100 22 29.35 1400 10
22.75 900 23 30.15 1450 11
22.55 800 24 31.65 1500 12
Comparing GAMS results with those of other solvers
By comparing the simulation result with [8-12, 24], scheduling problem is solved by
both CBUC and PBUC objective functions [24]. CBUC problem is considered in the
cooperative context and PBUC problem in the competitive context.
CBUC Problem
The purpose of this scheduling is to minimize the operational cost resulting from
limitations in the generation and the network. The results of the GAMS software compared
with those of other methods are shown in Table 2.
Generation scheduling of renewable energy resources under uncertainties in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND, Moein PARASTEGARI
28
Table 2. Comparing simulation results of proposed method with others
Cost-Base Unit Commitment (Total Cost ($))
GA [8] UCC-GA [9] EP [10] DP [8] LR [24] LRGA [11] HPSO [12] DICOPT
Best 565,825 563,977 N/A 565,825 N/A 564,800 563,942.3 563,937.7
Average N/A N/A 565,825 N/A 565,825 N/A 564,772.3 -
Worst 570,032 565,606 N/A N/A N/A N/A 565,785.3 -
The responses obtained with respect to occurrence are divided into three categories:
the best, average and the worst. Also, because of the unavailability of all responses, the term
N/A is used in some methods. It is clear that the GA [8], DP [8], and LR [24] methods have
the same answer and UCC-GA [9] and LRGA [11] attain better results. The results obtained
by the GAMS software shows $563937.7 that is less than the amount obtained by the best
solution in [12]. Numerical generation result of the 10 thermal units for the day-ahead
scheduling is shown in Table 3. Compared to [24], better results are obtained due to changes
in the generation power of units 5 and 6 over a period of 23.
Table 3. Power setting and generation cost of 10-Units
Thermal Units Power Generation(MW) Start-Up Cost ($)
Total Generation
Cost ($) Unit
1 Unit
2 Unit
3 Unit
4 Unit
5 Unit
6 Unit
7 Unit
8 Unit
9 Unit 10
Tim
e In
terv
als
(h)
1 455 245 0 0 0 0 0 0 0 0 0 13683.13
2 455 295 0 0 0 0 0 0 0 0 0 14554.5
3 455 370 0 0 25 0 0 0 0 0 900 16809.45
4 455 455 0 0 40 0 0 0 0 0 0 18597.67
5 455 390 0 130 25 0 0 0 0 0 560 20020.02
6 455 360 130 130 25 0 0 0 0 0 1100 22387.04
7 455 410 130 130 25 0 0 0 0 0 0 23261.98
8 455 455 130 130 30 0 0 0 0 0 0 24150.34
9 455 455 130 130 85 20 25 0 0 0 860 27251.06
10 455 455 130 130 162 33 25 10 0 0 60 30057.55
11 455 455 130 130 162 73 25 10 10 0 60 31916.06
12 455 455 130 130 162 80 25 43 10 10 60 33890.16
13 455 455 130 130 162 33 25 10 0 0 0 30057.55
14 455 455 130 130 85 20 25 0 0 0 0 27251.06
15 455 455 130 130 30 0 0 0 0 0 0 24150.34
16 455 310 130 130 25 0 0 0 0 0 0 21513.66
17 455 260 130 130 25 0 0 0 0 0 0 20641.82
18 455 360 130 130 25 0 0 0 0 0 0 22387.04
19 455 455 130 130 30 0 0 0 0 0 0 24150.34
20 455 455 130 130 162 33 25 10 0 0 490 30057.55
21 455 455 130 130 85 20 25 0 0 0 0 27251.06
22 455 455 0 0 145 20 25 0 0 0 0 22735.52
23 455 425 0 0 0 20 0 0 0 0 0 17645.36
24 455 345 0 0 0 0 0 0 0 0 0 15427.42
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PBUC Problem
The purpose of this scheduling is to maximize the profit of generation companies due
to constraints and market price fluctuations. In a competitive context, reserve payment can be
made in different ways: payment for an allocated reserve and payment for a reserve that is
actually used. The second method is the method used in this section. The price of the ancillary
service market is fixed at five times the spot price. In Table 4, the results of the generation
and reserve scheduling for 10 units are shown. The results show that under these conditions
the maximum profit is $112642.1. This value can be calculated by subtracting the total cost
from the revenue in Table 4 which is $4767.1 more than [24]. This difference is due to
changes in the generation rates and reserve power in stations 2, 5, and 6.
Table 4. Power setting and generation cost of 10-Units
Thermal Units Power Generation/Reserve(MW) Start-Up
Cost ($)
Revenue
($)
Generation
Cost ($) Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit
7
Unit
8
Unit
9
Unit
10
Tim
e In
terv
als(
h)
1 455 /
0
245 /
70 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 15892.63 13744.15
2 455 /
0
295 /
75 0 / 0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0 16912.5 14620
3 455/0 395/60 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0 19981.5 16354.46
4 455/0 455/0 0/0 0/0 40/95 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 900 22055.44 18694.55
5 455 /
0 455 / 0 0 / 0 0 / 0
62 /
100 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 23180.25 19142.96
6 455 /
0 455 / 0 0 / 0
130 /
0
52 /
110 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 1120 25692.53 21812.16
7 455 /
0 455 / 0 0 / 0
130 /
0
47 /
115 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 25104.38 21716.71
8 455 /
0 455 / 0 0 / 0
130 /
0
42 /
120 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 24630.8 21621.45
9 455 /
0 455 / 0
130 /
0
130 /
0
32 /
130 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 1100 28146.6 24323.3
10 455 /
0 455 / 0
130 /
0
130 /
0 162 / 0
63.978
/
16.022
0 / 0 0 / 0 0 / 0 0 / 0 340 41089.52 28693.57
11 455 /
0 455 / 0
130 /
0
130 /
0 162 / 0 80 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 42571.8 29047.98
12 455 /
0 455 / 0
130 /
0
130 /
0 162 / 0 80 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 44689.8 29047.98
13 455 /
0 455 / 0
130 /
0
130 /
0
25 /
137 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 30184.2 24140.8
14 455 /
0 455 / 0
130 /
0
130 /
0
32 /
130 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 30245.25 24323.3
15 455 /
0 455 / 0
130 /
0
130 /
0
30 /
120 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 27675 24272.84
16 455 /
0 455 / 0 0 / 0
130 /
0
57 /
105 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 22149.48 19047.13
17 455 /
0 455 / 0 0 / 0
130 /
0
62 /
100 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 22183.25 19142.96
18 455 / 455 / 0 0 / 0 130 / 52 / 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 21818.48 18951.5
Generation scheduling of renewable energy resources under uncertainties in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND, Moein PARASTEGARI
30
0 0 110
19 455 /
0 455 / 0 0 / 0
130 /
0
42 /
120 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 21800.4 18760.79
20 455 /
0 455 / 0 0 / 0
130 /
0
25 /
137 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 21902.55 18388.34
21 455 /
0 455 / 0 0 / 0
130 /
0
32 /
130 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 22510.95 18570.84
22 455 /
0 455 / 0 0 / 0
130 /
0
52 /
110 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 22709.03 18951.5
23 455 /
0
445 /
10 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 20531.88 17186.68
24 455 /
0
345 /
80 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 / 0 0 18491 15497.41
To demonstrate the capabilities of the proposed algorithm in the network, the
influence of market price fluctuations, penetration of renewable resources, and uncertainty in
the scheduling problem have been tested. Four intended cases are shown in Table 5.
Case 1: Scheduling is offered without renewable resources, uncertainty, and volatility of the
market price.
Case 2: Scheduling is offered with the effects of fluctuations in the market price.
Table 5. Cases considerations
Uncertainty Renewable Unit Swinging Market Price
No No No Case1
No No Yes Case2
No Yes Yes Case3
Yes Yes Yes Case4
Case 3: Scheduling is offered with renewable resources and fluctuations in the market price.
Case 4: Scheduling is offered with renewable resources, uncertainty, and volatility of the
market price.
In the scheduling, communication line capacity is set to 700 MW and the coefficient
α= 0.1. Penalties for each megawatt hour are equal to the spot market. The reserve price is
equal to 25% of the market price. In this case, no penalties have been paid to the generation
companies. So, the generation companies are working at their optimum point for maximum
benefit. The results show that the cost is reduced from 565825 to 543034.9 because of the
exchanged power through the lie-line. Also, by the use of the proposed method the profit is
increased about $2531.9 in comparison with the generation pattern of thermal units in [8, 24].
Discussion of case 1:
The results of the proposed algorithm, in case 1, are presented in Table 6.
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31
Table 6. Simulation result of proposed method – Case 1
Thermal
Units
Generation Cost
($)
Start-Up Cost
($)
Profit
($)
Penalty
($)
Unit1 203179.728 0 55760.772 0
Unit2 212291.8202 0 45375.05481 0
Unit3 64897.05 550 3544.45 0
Unit4 67048.91175 560 4272.83825 0
Unit5 79927.84 900 1453.76 0
Unit6 0 0 0 0
Unit7 0 0 0 0
Unit8 0 0 0 0
Unit9 0 0 0 0
Unit10 0 0 0 0
Total Operation Cost ($)= 543,034.9 Total Profit ($)= 110,406.9
Using renewable energy resources and storage systems presented in [15] leads to,
operating cost about $554385.64. This cost is more than the cost of the proposed method. So,
by selling the surplus power to the market, ISO not only did not pay any penalties to
GENCOs but also reduced the operational cost. The details of the proposed scheduling are
shown in Table 7.
Table 7. Power setting and reserve cost of 10-Units – Case 1
Thermal Units Power Generation(MW) Ptn
(MW)
Pout
(MW)
Reserve
Cost($) Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit9 Unit 10
Tim
e In
terv
als(
h)
1 455 397.5 0 55 0 0 0 0 0 0 0 207.5 733.7188
2 455 455 55 110 0 0 0 0 0 0 0 325 522.5
3 455 455 110 130 68 0 0 0 0 0 0 368 658.35
4 455 455 130 130 136 0 0 0 0 0 0 356 147.225
5 455 455 130 130 162 0 0 0 0 0 0 332 0
6 455 455 130 130 162 0 0 0 0 0 0 232 0
7 455 455 130 130 162 0 0 0 0 0 0 182 0
8 455 455 130 130 162 0 0 0 0 0 0 132 0
9 455 455 130 130 162 0 0 0 0 0 0 32 0
10 455 455 130 130 162 0 0 0 0 0 68 0 0
11 455 455 130 130 162 0 0 0 0 0 118 0 0
12 455 455 130 130 162 0 0 0 0 0 168 0 0
13 455 455 130 130 162 0 0 0 0 0 68 0 0
14 455 455 130 130 162 0 0 0 0 0 0 32 0
15 455 455 130 130 162 0 0 0 0 0 0 132 0
16 455 455 130 130 162 0 0 0 0 0 0 282 0
17 455 455 130 130 162 0 0 0 0 0 0 332 0
18 455 455 130 130 162 0 0 0 0 0 0 232 0
19 455 455 130 130 162 0 0 0 0 0 0 132 0
20 455 455 130 130 162 0 0 0 0 0 68 0 0
21 455 455 130 130 162 0 0 0 0 0 0 32 0
22 455 455 130 130 162 0 0 0 0 0 0 232 0
23 455 455 130 130 162 0 0 0 0 0 0 432 0
24 455 455 130 130 162 0 0 0 0 0 0 532 0
Generation scheduling of renewable energy resources under uncertainties in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND, Moein PARASTEGARI
32
According to this table, it is clear that due to the cheaper cost of the market price
compared to the marginal cost of thermal units at peak points, lack of power is supplied by the
tie-line. By canceling the contracts of the expensive units over these hours, the system
operator purchases the required power from the market and vice versa.
Discussion of case 2:
In the case, the hourly price pattern is taken from [25]. To maximize profits, the
generation pattern of thermal units is shown in Figure 2. According to this figure, units 7 to
10 did not offer any power because of the average market price is low.
0
100
200
300
400
500
0 2 4 6 8 10 12 14 16 18 20 22 24
Hour
MW
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
Figure 2. Profit-Base unit commitment of 10-Units – Case2
As we can see in Table 8, no penalties have been paid to the units. So, the plants are
working at their optimum point for maximum profit.
Table 8. Simulation result of proposed method – Case 2
Thermal Units Generation Cost
($)
Start-Up Cost
($)
Profit
($)
Penalty
($)
Unit1 183051.314 0 63587.161 0
Unit2 190991.3903 0 54398.75969 0
Unit3 50438.05 1100 9508.7 0
Unit4 49884.95775 1120 10041.79225 0
Unit5 61198.5844 1800 9426.8756 0
Unit6 25318.192 340 116.108 0
Unit7 0 0 0 0
Unit8 0 0 0 0
Unit9 0 0 0 0
Unit10 0 0 0 0
Total Operation Cost ($) = 529,663.9 Total Profit ($) = 147,079.4
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33
As it is shown in the table, the total cost of the system is reduced from $543034.9 to
$529663.9, because a part of the energy is provided from power market via the tie-line. On
the other hand, price uncertainty leads to an increase in the total profit of the system from
$110406.9 to $147079.4. The hourly rates of the purchased ( inP ) and sold ( outP ) power are
shown in Table 9.
Table 9. T-Line power setting – Case 2 Time Intervals (h)
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
0 0 0 0 0 0 0 0 0 0 0 0 108 88 68 0 2 130 495 700 650 550 145 0 Pin
(MW)
532 462 292 112 12 212 312 412 362 212 112 12 0 0 0 6 0 0 0 0 0 0 0 152.5 Pout
(MW)
Discussion of case 3:
In this case, besides considering the volatility of the market price, there is a wind farm
with a capacity of 150 MW in addition to thermal power units [14] with a coefficient of β =
0.13 [18]. In this new condition, operational cost is decreased from $529663.9 to $445948.4
compared to case 2. Also, the operating cost is $84412.4 which is less than [14]. So, with
same amount of wind power, the use of the proposed method leads to more profit by selling
the exceeded power. In both cases of 2 & 3, profit is equal to $147079.4. The details of the
scheduling in case 3 are shown in Table 10.
Table 10. T-Line & renewable resources power setting – Case 3 Time Intervals (h)
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
141.6 148.9 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 139.1 137 29.35 Pw
(MW)
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 345 550 500 410.9 8 0 Ptn
(MW)
673.6 610.9 442 262 162 362 462 562 512 362 262 162 42 62 82 156 148 20 0 0 0 0 0 181.85 Pout
(MW)
According to this table, it is clear that at any period the amount of the sale or purchase
increased or decreased based on generation amount of renewable resources, respectively. Of
course, it also depends on the capacity of the tie-line.
Discussion of case 4:
Results of case 4 are presented in Table 11. This table shows the effects of using
proposed multi-scenario stochastic model to solve the day-ahead UC problem.
Generation scheduling of renewable energy resources under uncertainties in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND, Moein PARASTEGARI
34
Table 11. Discrete probability distribution of wind and load
Wind Load
Expected Probability
Expected Probability
12-24 1-11 12-24 1-11
100% 100% 0.5 100% 100% 0.6
98% 99% 0.15 98% 98.5% 0.15
102% 101% 0.15 103% 102% 0.15
95% 97.5% 0.1 97% 98% 0.05
105% 102.5% 0.1 104% 103% 0.05
As shown in this table, five scenarios are considered for demand errors and wind
power generation [15]. So, there are 25 scenarios employed to calculate through the use of Eq.
(10). The scenario details include the PDFs and per unit errors as shown in Figure 3.
0.90.920.940.960.98
11.021.041.06
0.3
0.02
5
0.02
25
0.00
75
0.02
260.
06
0.00
5
0.01
51
0.00
52
Scenarios
pu
Load(1-11)
Wind(1-11)
Load(12-24)
Wind(12-24)
Figure 3. Scenario details
The operational cost of the system is increased from $445948.4 to $447112.4 and the
profit is equal to case 3. By checking the expected values, it is clear that the most frequent
scenario is no. 20. In this scenario, due to the decreased generation of renewable energy and
increased demand, costs have increased significantly. Scenario 3 is the most expected one. It
occurs when the demand is not changed and the renewable energy generation is reduced.
Conclusions
In this paper, a new method is presented for the generation scheduling in a competitive
environment. Simulation results show that power trade via tie-line makes the generation
scheduling problem more flexible. Therefore, ISO can prevent major penalties by exchanging
Leonardo Electronic Journal of Practices and Technologies
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Issue 30, January-June 2017
p. 17-38
35
power in the presence of high uncertainty. On the other hand, the proposed algorithm
increases the profit of GenCos by following their bidding strategies as much as possible. As a
result, the proposed algorithm improves the performance of energy management system by
increasing the profit of both participants in the market.
Appendix
Characteristic information for economic dispatch and unit commitment problems of units
for the 10-unit system are given in Tables 1 and 2, respectively.
Table a.1. Main characteristics of thermal units
Units Pmax
(MW)
Pmin
(MW)
a
($)
b
($/MWh)
c
($/MWh2)
1 455 150 1000 16.19 4.80E-04
2 455 150 970 17.26 3.10E-04
3 130 20 700 16.6 2.00E-03
4 130 20 680 16.5 2.11E-03
5 162 25 450 19.7 3.98E-03
6 80 20 370 22.26 7.12E-03
7 85 25 480 27.74 7.90E-04
8 55 10 660 25.92 4.13E-03
9 55 10 665 27.27 2.22E-03
10 55 10 670 27.79 1.73E-03
Table a.2. Additional characteristics of thermal units
Units MU
(h)
MD
(h)
RU
(MW)
RD
(MW)
HSC
($)
CSC
($)
CST
(h)
IS
(h)
1 8 8 152.5 152.5 4500 9000 5 8
2 8 8 152.5 152.5 5000 10000 5 8
3 5 5 55 55 550 1100 4 -5
4 5 5 55 55 560 1120 4 -5
5 6 6 68 68 900 1800 4 -6
6 3 3 30 30 170 340 2 -3
7 3 3 30 30 260 520 2 -3
8 1 1 22.5 22.5 30 60 0 -1
9 1 1 22.5 22.5 30 60 0 -1
10 1 1 22.5 22.5 30 60 0 -1
Generation scheduling of renewable energy resources under uncertainties in competitive environments
Emad NEMATBAKHSH, Rahmat-Allah HOOSHMAND, Moein PARASTEGARI
36
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