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Leonardo Electronic Journal of Practices and Technologies

ISSN 1583-1078

Issue 30, January-June 2017

p. 17-38

17

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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

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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


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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-



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.


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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)



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


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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.



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



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


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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.



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



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



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.


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)


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.


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.



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


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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



36

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