Tái cấu hình hệ thống phân phối có xem xét phát sinh phân phối cho việc giảm thất thoát bằng sử dụng thuật toán tìm kiếm hấp dẫn

Distribution System Reconfiguration Considering Distributed Generation for Loss Reduction Using Gravitational Search Algorithm Nguyen Thanh Thuan', Truong VietAnh^* 'Dong An Polytechni

Distribution System Reconfiguration Considering Distributed Generation for Loss Reduction Using Gravitational Search Algorithm

Nguyen Thanh Thuan', Truong VietAnh^*

'Dong An Polytechnic

^University of Technical Education Ho Chi Minh City, No.}, Vo Van Ngan Thu Due District, Ho Chi Minh City

Received- March 04, 2014; accepted: April 22, 2014

Abstract

This paper presents a method for determining radial configuration of distribution network which is used in reconfiguration problem and an effective method based on Gravitational Search Algorithm(GSA) to identify real power losses in the system while satisfying all the distribution constraints To demonstrate the validity

of the proposed algorithm, computer simulations are earned out on 8 buses, 16 buses, 33 buses, 69 buses Algonthm.The simulation results have showed that the method of determining the radial configuration enables the optimization algorithms do not lose results and GSA algorithms are powerful optimization algorithm with a fast convergence and can be applied in reconfiguration distribution netvt/ork problems having large searching space

Keywords: Reconfiguration Gravitational Search Algorithm, Loss Reduction

1 Introduction

The distribution network transfers the electric

energy directly from the intermediate transformer

substations to consumers The transmistion networks

distribution networks are always operated radially By

operating radial configuration, it significantly reduces

the short-circuit current The restoration of the

closing/cutting manipulations of electrical switch pairs

located on the loops, consequently, hence, there are

many switches on the distribution network Network

reconfiguration is the process of altering the

topological structures of distribution feeders by

changing the open/close status of the sectionalizers

to satisfy the operator's objectives This is a non-linear

interrupted so it is difficult to solve the problem by the

traditional mathematical techniques In recent years

several optimizafion methods have been proposed for

solving the reconfiguration problem such as GA, PSO,

ACS, ABC [1-4], which is contributed to improve the

convergence and calculation speed and the newest

technique which is developed based on Newton's laws

is the Gravitational Search Algonthm (GSA), This

algorithm has showed many advantages in solving

optimization problems [5-7]

This paper uses GSA to reconfigure the elecfric distribution network with DG connection to reduce power loss The major contribution of this research is

to present a method of determming the optimal method of determining the radial structure to achieve the minium power loss

2 Mathematical model

The distribution network often uses loop structure but operates radially through open switches

in the electrical systems.The power loss on the system

IS equal to the total loss on the branches [ 1,3,4]

P-,Q

1.1'

Pf + 0?

(1)

• active power loss on the i* branch : total number of branches : active power and reactive power on the i"' branch

: connection bus voltage of the branch and current on the i"" branch

active power loss of system slate of switches, if k, = 0, the i"" switch opens and vice versa

* Conesponding Author' Tel (+84) 953117659

To reduce power loss of the electric distribution

network, the objective function is:

F(x) = mm (Pi„„) (2)

And the network constramts must be satisfied

are voltage and current that maintained within theu:

permissible ranges to maintain power quality

Vi.min^\K\^V,„^ (3)

l ' i l < / , , , ^ (4)

To solve the problem, power fiow problem

should be solved many times for network

reconfiguration and the Radial network structure must

be retained in all cases

3 Gravitational search algorithm

GSA IS one of the optimal algorithms which are

recently developed by Rashedi in 2009 [5, 6, 7] The

algonthm is based on Newton's rules on gravity load

and mass In GSA, each element is considered as one

object (Fig.l) and its characteristics are measured by

their masses Each object represents one solution or

solutions (objects) attracted each other by gravity

force and this force of attraction is produced due to the

having heavier mass Due to heavier objects having

better objective fiinction value, they describe better the

than lighter ones representing worse solutions GSA is

described in details as

follows-At the beginning of the algorithm the position of a

system are described with N (dimension of the

search space) masses

X, ={Xl Xf XI') withi-l,2, ,N (5)

where J , presents the position of ith agent in the d*

dimension

Initially, the agents of the solution are defined

randomly and according to Newton gravitation

theory, a gravitational force from mass j acts mass

i at the time t is specified as follows:

Ffj(t) = G(t)- -(x;(t)-x,Ht)) (6)

where M^, is the active gravitational mass related to

agent j , Mp, is the passive gravitational mass related

is a small constant, and Rpjn) is the Euclidian

distance between two agents i and j :

Fig, 1 Objects interact with each other

The total force acting on the ith agent is calculated

as follows:

Fo'(t) - l%^_j^,randjF,'j(t) (8)

where rand, is a random number in the interval [0.1]

The acceleration (af(t)) and velocity (V,''(t-1-1)) of the ith agent at t time and t+1 fime in dth dimension are calculated through law of gravity and law of motion as follows'

af(t) = •, ( t )

(>>)

where M„ is the inerlial mass of ith agent

V,^(t-\-l) = rand,.Vf(t) + af(t) (10)

;i',''(t+ 1) = Xf(t) + ^ ^ ^ ( t + l ) (11)

where rand; is a random number in the interval [0,1 ]

The gravitational constant, G is a function of the initial value (Go) and time (t):

G(t) = G(Go.t) (12) Gravitadonal and mertia masses are calculated by

more efficient agent This means that better agents have higher attractions and move more slowly

Assuming the equality of the gravitational and inertia mass, the values of masses are calculated using the fitness fiinction The gravitational and inertia! masses are updated by the following equations

•• M„, : M„ - M,.i ^ 1 , 2 ,N,

m,(t) =

M,(t) =

(13)

(14)

(15)

ft here fit,(t) represent the fitness value of the agent

best(t) = m i n / i t , ( t ) ; ) 6 (1, W)

worst(t) ^ max/itj(t),y E(1, W) (17)

4 GSA application in distribution network

reconfiguration

4.1 Definition and controlled variables

In the reconfiguration problem of power

network, switches are considered as controlled

variables These switches have two states "0" for tie

power network is larger, the switch number is more

numerous, the searching space of every open switch is

radial topology is proposed However when

performing this algonthm, the problem becomes

complicated, the searching space is larger since the

feasible searching space is not limited Some

researches in [2,4] proposed the method of

determmmg the tie switches and the searching space

by independent loops However as each switch is

placed only in one unique independent loop at specific

times, the best solufions will be lost For instance,

considermg the power network in Fig, 2 there are two

has two tie switches being sw7 and sw9

However, If independent loops are defined as

follows

Loop_l includes switches* sw2, sw8, sw9, sw6

Loop_2 includes switches sw3, sw4, sw5

This definition will not give the best solution

smce the problem shall have two open switches and

the searching space of the first switch will be m

Loop_l, the second open switch will he in Loop_2

While the best solution is placed in space of Loop_l

To solve this matter, the paper recommends the

method for determining the number of open switch and

the radial configuration of power network as follows:

The number of open switch equals to the

number of mdependent loop and is determined by the

expression:

N,„itch - W,„„p = N^rancn - ^fcu + 1 (18)

The element number of each independent loop

IS defmed:

Loop, = [switchi]

Loop, - [switch,]

Loopij = [switch,,]

I<i,j<N,™p

Where, switch, and switch, are the collection of

switches belonged only to the independent i loop and the independent j loop respectivily; switch,, is the

loops 1 and j

o

i———<i—^^i;^—i

Fig 2 8-bus network

input data of network, Detemiine the search pace of every switches in independent loops

Evaluate fitness for each agent (Solving power flow for every network configuration) Evaluate the operating constrains (Vmin, Radial topology) Update G, minimum power loss (best) and maximum power loss (worst) of agents in population

Update !tie position of agents The configurations are clianged depent on the value of velocity and acceleration

Ketum best solution (network configuration has m

power loss)

Fig 3 DeltaP reduction flowchart for GSA algorithm

If the open switch i belong to independent Loop, then the searching space of secondary open switch J will he Loopj + Loopij and inverse if open switch i belong to Loop,, then the searching space of the secondary open switch j will be Loop,

4.2 The distribution network reconfiguration

GSA algorithm in the problem is descnbed as

Step 1: Determine the searching space include the

switch

Step 2: Create the randomly parameters ( position of

open switches via Eqs5) Each collection of tie

switches is considered as an agent and the tie switches

of collection are considered the posinon of the agent

Step 3: Calculate the value of objective function for

implemented by solving power flow problem

Step 4: Update the value of G(t), minimum power loss

best(l), maximum power loss worst(t) and Mi(t) with i

- I, 2, , N via Eqs,12, 15, 16 and Eqs.17 Mi(t)

presents relationship between power loss of current

configuration with configurations have minimum

power loss and maximum power loss and others in

current iteration

Step 5: Calculate the total force in different directions

via Eqs.8 Value of total force presents the interaction

between two network configurations (two agents)

Step 6: Calculate acceleration and velocity via Eqs.9

and via Eqs.lO Velocity values present the change of

switches's position in each configuration

Step 7: Update the position of agents (position of tie

switchesviaEqs.il)

Step 8: Return to step 3 until slopping critena has

been achieved

Step 9: Result output, which retums the configuration

has the mmimum power loss

Fig 3 presents the proposed flowchart to

perform network reconfiguration for power loss

reduction using GSA algonthm

4.3 Numerical Results

The distribution network reconfiguraUon based

on GSA IS tested in Matiab software, its resuh is

compared to that performed in TOPO/ PSS/ADEPT

and PSO algorithm respectively

4.3.1 S-bus distribution network

Considering the simple distribution network

includes one generating unit of 12 6 kV connected to

bus I, 7 load buses and 9 switches The system

diagram is shown in Fig 2 The initial system has two

tie switches of s5 and s7 with the real power loss of

86.06 kW Using GSA algorithm with searching

dimension of d = 2, the number of agent N = 3 and

Iteration = 10, calculating the best configuration of

number; the resuh is compared to PSO and TOPO/PSS/Adept algorithms respectively

Loop_l-[s2, s4, s7, s8, s5] and Loop J = [s3, s6, s9]

The proposed algorithm gives the smallest power loss

g 140

«• no

"Z 120

i

a ^'"^

£ 100

" 90

Open switchs 8 9 ^ real

:r

-}-oss:718709kW GSA Algorilhiii 1

1 rf

-Iteration Fig 4 Convergence characteristics of S-bus network power loss in case 1

Open switchs; 8 7 ^ real loss 68.5296 kW

Iteration Fig 5 Convergence characteristics of 8-bus network power loss in case 2

Table I Comparison of two cases performing algorithm with performance result from PSS/Adept-Topo

Method Initial configuration TOPO/

PSS/ADEPT Case 1 (PSO) Case 1 (GSA) Case 2 (PSO)

Loss (kW)

86 06 68.50

71.87 71,87

68 53

Open switch s5,s7 s7, s8

s8,s9 s8, s9

Iterations

4

3

Case 2,

Loop_l=[s2, s5, s8], Loop_2 = [s3, s6, s9] and

Loop_12 = [s4, s7]

The proposed algonthm gives the smallest

power loss of 68 53 kW with two tie switches of s8,

s7

The two results collected m these 2 cases have

shown'

- GSA has fast convergence degree With the agent

1, GSA algonthm converges after 3 iterations while

PSO converges after 4 iterations In case 2, GSA

converges after 4 iterations and PSO takes 8 iterations

to find the best configuration of power network

- The proposed technique for determining

independent loops has found the solution which is

better than the method in case I smce the proposed

GSA and PSO algorithm have found the best

configuration At that time, with the defminon of

recommended independent loop, both the algorithms

have found the best performance configuration of the

power network with the smallest power loss

4.3.2 16-bus test system

16-bus test system have parameters slated in

[8], initial configuration having power loss of 511,4

kW conesponding to tie switches of s5, si 1, sl6 (Fig,

6) Assuming at bus 9, one DG having the output

power of 16 38 + J8.943 MVA is used [9]

In this problem, the searching dimension of

d = 3, the agent number of N = 10, Interaction = 25,

After performing GSA, it found the best operating

configuration with open switches of s9, s7, si 6 and

loss of 469 4 kW in case of without DG (Fig 7) While

in case of with DG is connected to the system, the

open switches are s2, si 4 and sl6 with the power loss

ofl36.37kW(Fig.8)

Ope

fl-I- TI

n switchs'9 7 l O r e a l l o s

J , 1:77:

• 4 - •

459.4 kW

PSOAlu^llIhll-!

Fig 7 Convergence characteristics of power loss of 16-bus lest system without DG at bus 9

Fig 8 Convergence characteristics of power loss of 16-bus test system with DG at bus 9

From the results shown in Table 2, the use of

DG in the distribution network will supply the local energy and contribute to reduce of transmission power loss on the network and the use of GSA algorithm has found the best network configuration after 2-3 iterations while PSO algonthm takes 3-5 iterations

searching space This result is similar to that executed firom TOPO and some recommended papers

4.3 3 IEEE 33-bus distribution network

IEEE 33-bus test system (Fig.9) have parameters shown in [8], using 4 DG [10, 11] with parameters are given in table 3

The initial configuration did not connect with DGs having power loss of 203,679 kW corresponding

to open branches: 25-29, 18-33, 9-15, 12-22 and 8-2

searching dimension of d = 5, the agent number of N

= 20, interaction = 50 The proposed algorithm found the new configuration with the open branches of 7-8, 25-29, 9-10, 14-15, 32-33 and loss of 138.876 kW But when applying GSA it takes only 5 iterations to find out the best configuration while PSO takes 23 Iterations with the same initial searching space as

Table 2 Comparison of GSA algorithm with

performance result by PSS/Adept-Topo and PSO in

16-bus test system

Open s w i t c h s 7-8,26-29,9-10 14-15, 3 2 - 3 3 - > l o s s , 111 451B kW

Method I Loss (kW) | Open switch | Iterations

Initial

configuration

Topo/

PSS/Adept

[3,8]

System without D G

\q:-;|;;;;;H

•

-, ! : : : :

System connecting to DG atbus 9

configuration

Topo/

PSS/Adept

Fig 11 Convergence charactenstics of power loss of 33-bus network with DGs

Table 4 Comparison of GSA algorithm to result performed by PSS/Adepi-Topo and PSO in 33-bus network

Method I Loss (kW) | Open switch | Iterations

System witliout DGs

No

I

2

4

Bus

4

25

P(kW)

50

100

200

100

0 (kVar) 37,5

96 9

0

Fig.9 lEEE33-bus test system

O p e n s w i t c h s 7 - 8 2 5 - 2 9 9 - 1 0 14-15 3 2 - 3 3 - = I O B S 1 3 8 B 7 6 3 h W

1 , ; ; ; | | Gsa fliuoi.ti.iM 1

y:::':::;:;:

i

configuratioi Topo/

PSS/Adept

25-29, 18-33 9-15, 12-22.8-21

Topo/

PSS/Adept

System with DGs

[10,1

7-8,28-29,9-10 14-15,32-33 7-8,28-29,9-10 14-15, 32-33 When putting 4 DGs into operation, the algorithm convergence characteristics are shown in Fig.ll, with power loss of III 145 kW after 12 iterations, while PSO algorithm converges after 15 iterations The recommended algorithm resuh is fully similar to that performed by TOPO in PSS/Adept

4 3.4 IEEE 69-bus test system

IEEE 69-bus test system is proposed in [12] with initial configuration having power loss of

224 955 kW conesponding to open branches' 50-59, 27-65, 13-21, 11-43 and 15-46, In this case, die searching dimension of d = 5, the agent number of N

= 25, interaction = 50 are used

Fig, 10 Convergence characteristics of power loss of

33-bus network without DGs

Fig 12 69-bus test system

open switchs 11.43.14-15,13-21 57-58,61-62 ^ loss 987605 kV

Fig 13 Convergence characteristics of power loss of

69-bus network

Table 5 Comparison of GSA algorithm to result

69-bus network

Open

branch

AP

(kW)

Loops

Initial

conf

50-59

13-21

11-43

15-46

224,95

TOPO

11-43

14-15

56-57

98.59

GSA

11-43

13-21

57-58

98,57

12

PSO

I M 3 14-15 13-21 55-56

99.75

5

[13,14]

11-43

58-59

12-13

98 90

It can be seen fi-om the simulation results that

the algorithm has found a new configuration with open

branches of 11-43, 14-15,13-21, 56-57,61-62 and the

power loss of 98 57 kW While with the same initialed

conditions, PSO algonthm has converged after 5

iterations and did not only find the global optimal

configuration to the system but also dropping into the

local optimization with power loss of 99 75 kW

corresponding to open switches of 11-43 14-15 13-21,

55-56 and 62-63 (Fig 13)

4 Conclusion

In this paper, a simple method for determming

GSA algorithm optimize tiie best tie switches m the

objective fiinction of reducing the real power loss The algorithm is simulated by Matiab 2008 and 8, 16, 33,

assessment

The simulation results shown that the proposed method for determining the radial power network helps the optimal algorithms do not miss good solutions Aplication of GSA algorithm in the

found the best configuration of power network quickly, efficiently fi'om the power network of diffenrent power networks

Appendix 1: The data of 8-bus system

From

1

2

2

2

3

4

5

6

7

To

2

3

4

5

6

8

7

7

8

Line data R(p.u.)

1 091869255

1 091869255

1 091869255

2 18373851 1.091869255

1 091869255

2 18373851 2.18373851

1 091869255

X(p.u.) 1.902972131 1.902972131 1.902972131 3.805944261

1 902972131 1.902972131 3.805944261 3.805944261 1-902972131

Bus

1

2

3

4

5

6

7

8

Bus data Angle

0

0

0

0

0

0

0

0

MW

0

0 0.3 0.05 0.5 0.5 0.1

0 1

MYar

0

0 0.15 0.03 0.4 0.3

0 05 0.05

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