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PE-13-119PSE-13-135

1／6Conference of Joint Technical Meeting of Power System Technology of IEEJ, Kyushu Institute of Technology, Kitakyushu, Japan, September 11-13, 2013

A New Approach Computation for Determining Committed Power

Outputs of Economic Power System Operation using HSABC

Considering Space Areas

A.N. Afandi, (Kumamoto University & State University of Malang)

Hajime Miyauchi, (Kumamoto University)

An economic power system operation (EPSO) can be expressed by a total operating cost. Technically, this

payment is presented by individual cost of generating units based on a schedule of committed power outputs

(CPOs) to meet a total load demand. Presently, a minimum operating cost is performed by considering an

economic dispatch and an emission dispatch, which are composed into a combined economic and emission

dispatch (CEED) problem. This paper introduces a newest artificial intelligent computation, harvest season

artificial bee colony (HSABC) algorithm, for determining CPOs based on a minimum total cost of CEED using

IEEE-62 bus system. Simulation results show that HSABC has short time computations and fast convergences.Space areas give different implications on HSABC’s performances.

Keywords: Artificial bee colony, economic dispatch, emission, combined economic and emission dispatch

1. Introduction

Recently, an economic power system operation (EPSO)

considers a global warming caused by pollutant

emissions in the air from thermal power plants. These

pollutants are released from combustions of fossil fuels

in various types like CO, CO2, SOx and NOx(1)-(4).Presently, the EPSO becomes complex with considering

pollutant discharges as an emission dispatch (EmD)

under operational limitations. Practically, an EPSO is

managed using economical cost strategies for providing

electric energy from generator sites to supply load

demand areas. These strategies are used to decide the

minimum total cost of EPSO to meet a total load demand

at a certain time. In particular, a minimum total cost is

obtained by minimizing a total fuel cost of generating

units troughout an economic dispatch (ED) problem and

reducing pollutant emissions in the EmD problem. By

involving an EmD, the ED problem is transformed into a

combined economic and emission dispatch (CEED)

problem for determining a committed power outputs

(CPOs) of generating units during operations(5).

Many methods have been introduced to solve CEED

problems using traditional and evolutionary methods(3),

(6)-(15). Evolutionary methods have been composed to

attempts the natural phenomenons for creating various

algorithms. These methods are frequent used to compute

CEED problems because of traditional methods sufferfor large systems and multidimension spaces. For a

couple of years, the most popular evolutionary method is

genetic algorithm and this algorithm is inspired by a

phenomenon of natural evolution(16). Recently, the

newest evolutionary method is artificial bee colony

(ABC) algorithm. This method was proposed in 2005,

based on foraging behavior of honeybees in nature (17).

The latest generation of ABC is harvest season artificialbee colony (HSABC) algorithm intoduced in this paper

for determining the CPOs of EPSO. The HSABC is

applied to a CEED problem for the power system model

of IEEE.

2. Harvest Season Artificial Bee Colony

The HSABC is inspired by a harvest season situation

in nature for providing flowers. In the HSABC, multiple

food sources (MFS) express many flowers located

randomly at certain positions in the harvest season

area(18), (19). This space area (SA) is explored by bees to

search food sources. To exploit a large number of food

sources, bees can fly randomly during foraging for foods

and move from a selected current food source to another

positions(16), (19), (20). In the HSABC, MFS are consisted of

the first food source (FFS) and other food sources (OFSs).

Each position of OFSs is directed by a harvest operator

(ho) from the FFS(18), (19). Mathematically, HSABC

algorithm is introduced as following expressions:

, ………………...(1)

, …………………………………..(2)




, ….....(3)

, ……………………………..(4)

. ……………………………………………….(5)

Here, xij is a current food, i is the ith solution of the food

source, j{1,2,3,…,D}, D is the number of variables of the

problem, xminj is a minimum limit of xij, xmaxj is a

maximum limit of xij, vij is the food position, xkj is a

random neighborof xij, k{1,2,3,…,SN}, SN is the

number of solutions, Øi,j is a random number within

[-1,1], Hiho is the harvest season food position,

ho{2,3,…,FT}, FT is the total number of flowers for

harvest season, xfj is a random harvest neighborof xkj, f

{1,2,3,…,SN}, R j is a randomly chosen real numberwithin [0,1], MR is the modified rate of probability food,

Fi is an objective function of the ith solution of the food,

fiti is the fitness value of the ith solution and pi is a

probability of the ith quality of food.

The HSABC has three agents for exploring the SA,

those are employed bees, onlooker bees and scout bees.

Each agent has different taks and it is colaborated to

obtain the best food as the optimal solution. An

employed bee is defined to search a neighbor food source

in the SA. Each food source chosen represents a possible

solution to the problem. An onlooker bee is subjected to

select the best food for the optimal solution. This bee

chooses a food source based on the probability value each

nectar quality. A scout bee is used to explore food sources

for replacing abandoned values.

A set of MFS is prepared for providing candidate foods

in the SA for every foraging cycle. A foraging for the

foods of HSABC is preceded by searching the FSS and it

will be accompanied by OFSs located randomly at

different positions in the SA. A set initial population is

generated as candidate solutions and it is createdrandomly by considering objective constraints. For each

solution, it is corresponded to the number of parameter

to be optimized, which is populated using equation (1).

The nectar quality is evaluated using equation (4) and

the probability of each food source is determined using

equation (5). Each position of candidate food is searched

using equation (2) for the FSS and it is followed by OFSs

using equation (3).

3. Economic Power System Operation

Technically, the EPSO is presented by a minimum

total operating cost. This payment is optimized using a

CEED problem considered operational constraints for

determining the CPOs of generating units(7), (12), (15), (21),

(22). Basically, the CEED problem of the EPSO considers

a total cost of ED as shown in (7) with a fuel cost of each

generating unit is given in (6). Pollutant emissions are

also included in the CEED (15), (22), (23). Each pollutant

discharge of generating unit is formed in (8) and the

minimized function of EmD is given in (9) for a total

pollutan emission.

Currently, a minimizing total fuel cost and a reducing

total pollutant emission become an important thing in

the EPSO. An objective function of CEED is composed

using ED and EmD problems with including penalty and

compromised factors. Each penalty factor is performed

in (10) to shows the rate coefficient of each generating

unit at its maximum output for the given load(7), (12). A

compromised factor shows the contribution of ED andEmD in CEED’s computations(19). The CEED problem is

expressed in (11) and this single objective function is

constrained using equations (12) – (19). In general, the

dispatching problem is formulated by using

mathematical functions as follows:

Fi(Pi) =ci+biPi +aiPi2 , ………………………………….…(6)

ED minimize ………….(7)

, ………………………………(8)

EmD minimize ………..(9)

, ……………………………………….(10)

CEED minimize , ….……..(11)

, ………………………………………...(12)

…(13)

..(14)

, ……… (15)

, ……………………………………….(16)

, ……………………………………….(17)

………………………………………(18)

, ……………………………………………….(19)

where Fi is a fuel cost of the ith generating unit ($/h), Pi is

a output power of the ith generating unit, ai, bi, ci are fuel

cost coefficients of the ith generating unit, Ei is an

emission of the ith generating unit (kg/h), Ftc is a total

fuel cost, i, i, i are emission coefficients of the ith

generating unit, Et is a total emission of generating

units (kg/h), Etc is a total emission cost ($/h), hi is each

penalty factor of the ith generating unit, is the CEED

($/h), w is the compromised factor, h is the penalty factor

selected from ascending of hi, ng is the number of

generators, Pimin is a minimum output power of the i th




generating unit, Pimax is a maximum output power of the

ith generating unit, PD is the total demand, PL is the total

transmission loss, Pp and Pq are power injections at bus

p and q, PGp and QGp are active and reactice power

injections at bus p from generator, PDp and QDp are load

demands at bus p, Vp and Vq are voltages at bus p and q,

Qimax and Qimin are maximum and minimum reactive

powers of the ith generating unit, Vpmax and Vpmin are

maximum and minimum voltages at bus p, Spq is a total

power transfer between bus p and q, Spqmax is a limit of

power transfer between bus p and q.

4. Sample System and HSABC’s Procedures

In these works, IEEE-62 bus system is adopted as a

sample model of power system. This system is shown in

Figure 1 cosisted 62 buses, 89 lines and 32 load buses.

This figure also shows locations of generating units andload positions in the power system. Load data, fuel cost

coefficients, power limits and emission coefficients are

listed in Table 2, Table 3 and Table 4, respectively. Bee’s

parameter are listed in Table 1.

Fig. 1. One-line diagram of IEEE-62 bus system

Table 1. Bee’s parameters for running test

No Parameters quantity

1 Colony size 100

2 Food source 50

3 Foraging cycle 100

Fig. 2. Flow chart of HSABC’s application

Table 2. Fuel cost and emission coefficients of generators

Bus Gen

a, x10-3 ($/MWh2)

b($/MWh) c

(kg/MWh2)

(kg/MWh)

1 G1 7.00 6.80 95 0.0180 -1.8100 24.300

2 G2 5.50 4.00 30 0.0330 -2.5000 27.023

5 G3 5.50 4.00 45 0.0330 -2.5000 27.023

9 G4 2.50 0.85 10 0.0136 -1.3000 22.070

14 G5 6.00 4.60 20 0.0180 -1.8100 24.300

17 G6 5.50 4.00 90 0.0330 -2.5000 27.023

23 G7 6.50 4.70 42 0.0126 -1.3600 23.040

25 G8 7.50 5.00 46 0.0360 -3.0000 29.030

32 G9 8.50 6.00 55 0.0400 -3.2000 27.050

33 G10 2.00 0.50 58 0.0136 -1.3000 22.070

34 G11 4.50 1.60 65 0.0139 -1.2500 23.010

37 G12 2.50 0.85 78 0.0121 -1.2700 21.090

49 G13 5.00 1.80 75 0.0180 -1.8100 24.300

50 G14 4.50 1.60 85 0.0140 -1.2000 23.060

51 G15 6.50 4.70 80 0.0360 -3.0000 29.000

52 G16 4.50 1.40 90 0.0139 -1.2500 23.010

54 G17 2.50 0.85 10 0.0136 -1.3000 22.070

57 G18 4.50 1.60 25 0.0180 -1.8100 24.300

58 G19 8.00 5.50 90 0.0400 -3.000 27.010

Table 3. Power limits of generators

Bus GenPmin

(MW)Pmax

(MW)Qmax

(MVar)Qmin

(MVar)

1 G1 50 300 0 450

2 G2 50 450 0 500

5 G3 50 450 -50 500

9 G4 0 100 0 150

14 G5 50 300 -50 30017 G6 50 450 -50 500

23 G7 50 200 -50 250

25 G8 50 500 -100 600

32 G9 0 600 -100 550

33 G10 0 100 0 150

34 G11 50 150 -50 200

37 G12 0 50 0 75

49 G13 50 300 -50 300

50 G14 0 150 -50 200

51 G15 0 500 -50 550

52 G16 50 150 -50 200

54 G17 0 100 0 150

57 G18 50 300 -50 400

58 G19 100 600-100 600




Table 4. Load demands of each bus

Bus no MW MVar Bus no MW MVar

1 0.0 0.0 32 0.0 0.0

2 0.0 0.0 33 46.0 25.0

3 40.0 10.0 34 100 70.0

4 0.0 0.0 35 107 33.0

5 0.0 0.0 36 20.0 5.0

6 0.0 0.0 37 0.0 0.07 0.0 0.0 38 166 22.0

8 109 78.0 39 30.0 5.0

9 66.0 23.0 40 25.0 5.0

10 40.0 10.0 41 92.0 910

11 161 93.0 42 30.0 25.0

12 155 79.0 43 25.0 5.0

13 132 46.0 44 109 17.0

14 0.0 0.0 45 20.0 4.0

15 155 63.0 46 0.0 0.0

16 0.0 0.0 47 0.0 0.0

17 0.0 0.0 48 0.0 0.0

18 121 46.0 49 0.0 0.0

19 130 70.0 50 0.0 0.0

20 80.0 70.0 51 0.0 0.021 0.0 0.0 52 0.0 0.0

22 64.0 50.0 53 248 78.0

23 0.0 0.0 54 0.0 0.0

24 28.0 34.0 55 94.0 29.0

25 0.0 0.0 56 0.0 0.0

26 116 52.0 57 0.0 0.0

27 85.0 35.0 58 0.0 0.0

28 63.0 8.0 59 0.0 0.0

29 0.0 0.0 60 0.0 0.0

30 77.0 41.0 61 0.0 0.0

31 51.0 25.0 62 93.0 23.0

Main procedures of the HSABC application for

determining the CPOs of EPSO are illustrated in Figure

2. This figure also describes sequencing computations for

searching the optimal solution based on a total minimum

cost of EPSO. HSABC’s procedures are consisted of three

steps. The first step is a formation of objective function

for the CEED problem, which is used to compute a

minimum total cost for every foraging cycle. The second

step is an algorithm composition using employed bees,

onlooker bees and scout bees to search the optimal

solution. The third step is programming developments

for three categories of subprograms in terms of datainput program, CEED program and algorithm program.

The data input program is consisted of a set data input

of parameters, such as generating units, transmission

lines, loads and constraints. The CEED program is

created to compute an objective function under

operational constraints and the number of CEED’s

variable is associated with exploring limits of food source.

The algorithm program is developed for searching the

optimal solution of the CEED problem based on HSABC’s

hierarchies. In these programs, three types of bee are

collaborated to explore food sources in the SA and the

programs are executed for choosing the best food as the

optimal solution of CPOs using bee’s parameters as listed

in Table 1. Specifically, the best food is selected by using

a greedy process in every cycle.

5. Simulation Results

In this section, these simulations are addressed to

determine the CPOs of EPSO considered operational

constratints given in Section 3. The HSABC is run out

using three food sources and the SA is demonstrated

using four scenarios for 100%, 75%, 50% and 45% areas.

A set population of these simulations are initialed in

Figure 3 for candidate foods considering power

constraints of generating units. The population is

created for 50 candidate solutions for G1 to G19 in every

foraging cycle. Convergence speeds of HSABC for

determining the optimal solutions are illustrated in

Figure 4. These characteristics are performed using 45%,50%, 75% and 100% of the SA. Obtained iterations and

time consumptions are listed in Table 5.

Fig. 3. Initial population

Fig. 4. Convergence speeds of HSABC

Table 5. Time consumptions of HSABC

-

100

200

300

400

500

600

700

0 10 20 30 40 50

F o o d c a n d i d a t e s ( M W )

Populations

G1 G2 G3 G4 G5 G6 G7 G8 G9 G10G11 G12 G13 G14 G15 G16 G17 G18 G19

26,000

27,000

28,000

29,000

30,000

31,000

32,000

33,000

34,000

1 6 1 1

1 6

2 1

2 6

3 1

3 6

4 1

4 6

5 1

5 6

6 1

6 6

7 1

7 6

8 1

8 6

9 1

9 6

O p t i m a l p o i n t

( $ / h r )

Iterations

HSABC 45% Area HSABC 50% Area





AlgorithmsMin.iter.

Time ofmin. iter.

(s)

Total time of100 cycles

(s)

HSABC 45% Area 25 3.31 12.91

HSABC 50% Area 32 4.43 13.02HSABC 75% Area 43 7.63 19.27

HSABC 100% Area 48 10.86 22.03

Fig. 5. Time consumptions of HSABC’s computations

Fig. 6. Statistical results of HSABC

StatisticResults

HSABC45% Area

HSABC50% Area

HSABC75% Area

HSABC100% Area

Max 30,299.16 29,601.37 31,625.36 32,773.61Min 27,005.93 27,005.93 27,005.93 27,005.93

Range 3,293.24 2,595.44 4,619.43 5,767.68Mean 27,319.18 27,361.65 27,625.08 27,767.72

Median 27,005.93 27,005.93 27,005.93 27,005.93

Mode 27,005.93 27,005.93 27,005.93 27,005.93Std.dev. 725.08 652.78 1,146.61 1,212.39

From Figure 4, it is known that the convergence speed

of HSABC using 45% of SA is faster than others. This

characteristic is demonstrated in 25 iterations for

searching a minimum solution of CEED after pointing at

30,299.16 $/h at the first iteration. HSABC used 50% of

SA is started at 29,601.37 $/h and it is converged to the

minimum value in 32 iterations. The HSABC used 75% of

SA needs 43 iterations to reach 27,005.93 $/h of a CEED’s

minimum result from 31,625.36 $/h at the first iteration.

The largest size of SA produces 48 of iterations for the

convergence speed and 32,773.61 $/h of initial cost for the

HSABC. In detail, statistical results of each HSABC

using each size of SA are given in Table 6. This table

provides values of the HSABC for max and min points,

ranges, means, medians, modes and standard deviations.

Concerning in the number of time execution for the

designed programs during searching minimum solutions,

Table 5 provides time consumptions of HSABC using

each area. This table shows the time consumption forobtaining minimum total costs and completing the

running out programs in 100 foraging cycles. From Table

5, it is known that various sizes of SA affect to HSABC’s

performances. In details, by using 45% of SA, the

minimum of HSABC is searched in 3.31 minutes. This

computation is completed in 12.91 minutes for 100

foraging cycles with various running times of execution

as shown in Figure 5.

Fig. 6. Progressing powers of generating units

Table 6. Final results of simulations

UnitsPower(MW)

Emission(kg/h)

Fuel cost($/h)

EmissionCost ($/h)

G1 157.86 187.13 1,342.88 480.95G2 104.90 127.90 510.12 328.73G3 133.87 283.77 679.06 729.34G4 100.00 28.07 120.00 72.15G5 188.67 323.55 1,101.47 831.59G6 152.93 416.48 830.34 1,070.43G7 170.00 155.98 1,028.85 400.90G8 111.53 142.23 696.93 365.57G9 201.38 1,004.79 1,607.99 2,582.51

G10 100.00 28.07 128.00 72.15G11 150.00 148.26 406.25 381.06G12 16.01 3.86 92.25 9.91G13 183.35 297.54 573.11 764.73G14 150.00 158.06 426.25 406.25G15 102.05 97.75 627.32 251.25G16 150.00 148.26 401.25 381.06G17 100.00 28.07 120.00 72.15G18 230.91 566.11 634.40 1,455.01G19 546.37 10,328.57 5,483.15 26,546.49

Total 3,049.83 14,474.45 16,809.62 37,202.23

Progressing powers of HSABC’s computation are

presented in Figure 6. This figure is performed using

45% of SA for G1 to G19 to meet a total load demand.

This figure is also evaluated by load flow analysis and

power output constraints. The final results of CPOs

based on a total minimum cost are listed in Table 6.

These final results are performed using all size of SA in

terms of powers, emissions, fuel costs and emission costs.

Generating units produce 3,049.83 MW of a total power

for supplying 2,912 MW of a total load. The total

pollutant is emitted around 14,474.45 kg/h from

generating units. The total payment of power stations

-

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

1 6

1

1

1

6

2

1

2

6

3

1

3

6

4

1

4

6

5

1

5

6

6

1

6

6

7

1

7

6

8

1

8

6

9

1

9

6

T i m e c o n s u m p t i o n s ( s )

Iterations



-

100.00200.00

300.00

400.00

500.00

600.00

700.00

800.00

1 6 1 1

1 6

2 1

2 6

3 1

3 6

4 1

4 6

5 1

5 6

6 1

6 6

7 1

7 6

8 1

8 6

9 1

9 6

G e n e r a t e d p o w e r s ( M W )

Iterations

G1 G2 G3 G4

G5 G6 G7 G8

G9 G10 G11 G12

G13 G14 G15 G16

G17 G18 G19




for providing CPOs is 54,011.85 $/h contributed by

16,809.62 $/h of total fuel cost and 37,202.23 $/h of total

emission cost.

6. Conclusions

This paper introduces a harvest season artificial bee

colony (HSABC) algorithm to compute committed poweroutputs of generating units based on a minimum total

cost. By using various size of the space area (SA), the

small size of SA produces better results in terms of time

consumption and convergence speed. Refers to

applications of SA, a size of harvest season area is able to

use for controlling HSABC’s performances. From these

works, evaluations of limited abandoned solutions are

devoted to the future works.

Acknowledgments

The authors gratefully acknowledge the support to

Kumamoto University (Japan) and the BLN DIKTI

(Indonesia).

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