 Open Access
 Total Downloads : 224
 Authors : Atreya Chakraborty, Ashish Khatik
 Paper ID : IJERTV3IS042292
 Volume & Issue : Volume 03, Issue 04 (April 2014)
 Published (First Online): 03052014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Minimization of Losses Using Genetic Algorithm in Distributed Slack Bus Model
Atreya Chakraborty Department of Electrical Engineering
Indian Institute of Technology Roorkee, India
Ashish Khatik Department of Electrical Engineering
Indian Institute of Technology Roorkee, India
Abstract Powersystem environments are changingrapidly,e.g.,steady, rapidsignificant increasein distributedgeneration. Therefore, planning and strategy should be modified for effective Load Flow studies.Thispaper evaluates the multipleslackbus assumption which is typically employed in steadystateTransmissionpowerflows and illustrates the advantages and effectiveness of Distributed Slack Bus Model while distributing the system losses among all the generators as per present requirements of minimization of lossesusing Genetic Algorithm.Simulation results and tables are also given for better understanding.
Keywords Participation Factor (pf), Distributed Generators(DG), Distributed Slack Bus(DSB), NewtonRaphson Load Flow(NRLF), Genetic Algorithm (GA).

INTRODUCTION
Recent energy crisis in conventional energy sources has created the need to have nonconventional energy sources in the Power system network. As a result the implementation of nonconventional energy resources are increasing day by day.We have to change our conventional Load Flow procedure to accommodate all the energy sources effectively and fruitfully. The effective implementationcan be done using DSB model.
A reference bus or slack bus is defined as the V bus, which is used for balancing the active power P and reactive power Q in the network system when performing Load Flow Study in Power System.
Swing Bus is to provide whole system loss by absorbing or byinjecting active or reactive power from or to the system. Though thedescription ofpower flow study is true for a deterministic solution, it has a drawback while dealing with the uncertain variables, the swing bus shouldtake out all uncertainties arising in the network and thus, will possess wide nodal power probability distributions in the system.
In theoldfashionedload flow studies with single swing bus model, one bus is selected to take out all system losses, though practically there is no such swing bus in real power systems network. There it may considerablytwistprojected power flows. So to deliverfaithful power flow, power economic analysis (Kamh & Iravani, JUNE 2012)with distributed slack bus model (DSB) has been
adopted. Here slack bus is only for the reference of the bus voltage magnitude and angle.
In 2005,Tong proposed the distributed slack bus model (Tong & Miu, A NetworkBased Distributed Slack Bus Model for DGs in Unbalanced Power Flow Studies, MAY 2005). After a long period of 7 years,on 2012 another paper came by
M. Zakaria Kamh on sequence frame based model which demonstrated the use of energy management of active distribution network (Kamh & Iravani, JUNE 2012).
This paper demonstrates the applications of DSB model based on the participation factors (pf). This model is entrenched in aload flow solver and the pf quantify the real power output from the DGs as well as other generating buses including the slack bus, contributed to loss.Here in this paper, I have applied Genetic Algorithm to minimize losses of the system.Therefore not only loss is minimized but also we can minimize the cost as cost is proportional to loss.
.
The paper organized as follows. Section II describes a summary of the model of the system and power flow equations. Power Flow solving and Flowchart are illustrated in section III. The results and comparative studies are given in SectionIV. Chapter V is the conclusion. The paper ended with chapter VI.

CONCEPT OF DISTRIBUTED SLACK BUS
A Network based distributed slack bus model (Tong & Miu, A NetworkBased Distributed Slack Bus Model for DGs in Unbalanced Power Flow Studies, MAY 2005)is presented here for the slack bus as well as other generating buses including DGs whose real power injections can be adjusted.

Concept of Participation Factor:
We cannot supposed to have all generators in power systems to be allowed for adjusting their real power injections, as they may be small machines and thy may not have necessary control mechanisms. Therefore we consider two types of generators:

Nonparticipating generators ( simple PQ model)

Participating generators (P model)

Therefore, only the set of participating generators with controllable real power outcomeshave to be modelled using pf. Now, participation factor (pf) (Tong & Miu, Participation Factor Studies for Distributed Slack Bus Models in Three
Phase Distribution Power Flow Analysis, 2006) is defined as follows,
Now, the unknowns are, 1.
2. = 1, , ;
3. , = + 1, , = , , ;
Now, from normal NRLF procedure we can get the initial
=
= 1,2,3 (1)
value of
: = 1 (2)
Now, the equations are, For the substation buses:
=1
= +
= 0 (7)
Where:
n= number of buses;
m=number of generator buses(including slack buses);
Where,
=
=
(nm)=number of load buses;
is the load associated with the generator i.
= , + , + , (3)
=
is the local load associated to bus i.
And
For (nm) load buses:
= = 0 = + 1 , + 2 , , (8)
1 substation bus index
(m1) number of participating generators
Total power loss (real) in the system
Losses associated with generator i
, Losses associated with generator i, phase p
= = 0 = + 1 , + 2 , , (9)
Where,
= cos
=0
,


SIMPLE POWER FLOW SOLVER AND FLOWCHART
+ sin (10)
Now, it is crystal clear that,
,
= sin
+ = 1 (4)
=0
,
+ cos (11)
=1
= +1
,
As the participation factors for the load buses are zero, as they would not participate for supplying losses, therefore
, are real load &reactive load on bus i, in phase p.
= 0 (5)
= +1
Therefore,
Now, let us have the equations in matrix form which can clarify the whole thing in a better way.
F=J (12)
0
= 1 (6)
1
=1
+1
+1
=
1
2
1
2
2
2
1
1
2
1
1
2
1
2
1
+1
2
+1
1
2
1
1
1
1
1
1
2
1
+1
+1
2 1 +1
0
2
1
+1
0
+1
2
+1
1
+1
+1
+1
+1
+1
2
0
1
+1
( )
1
+1
(13)
+1
So, it is crystal clear that this is just like the Newton Raphson method. The Jacobian matrix is also like the normal NRLF method, only the difference is the 1st row and 1st
Flow chart:
Figure 1 GA Toolbox
column. So we can say it as a modified NRLF method.
Now, we will minimize the losses using GA. Practically, we will change the participation factor randomly, and thus we will change the generations also. We will optimize the loss using GA to find out the values of the participation factors for which the losses will be optimized.
Now here is the tool box for GA;

Initialize all the variables along with iterative counters.

Set the participation factors

Set initial generation set points.

Evaluate functional values from taylor series expansion.

Check the tolerance limit.

Evaluate Jacobian matrix for modified NRLF.

Solve for F=J. .

Update the values of the variables by x=x+

Check the generation limits of all the generators

Be sure that all are within limit.

All these limits will be checked through Genetic Algorithm

If any generator found to be out of the limit then make it generation fixed to its marginal value and set the participation factors again and follow this very path unless or until it converges.

Now in case of GA all these constraints will be taken care in the programme.
The flow chart is:
START
INITIALIZE VARIABES
INITIALIZE
Ploss FROM NORMAL NRLF
SET PARTICIPATI ON FACTOR
SET INITIAL LOADS AND GENERATION S
EVALUATE FUNCTIONAL VALUE
( F(x) )
END
PRINT OPTIMIZ ED VALUES
RUN GENETIC ALGORITHM
CALCULATE
Ploss
SOLVE FOR
F=J. x
EVALUATE JACOBIAN MATRIX
Table 3: FOR STANDARD 30 BUS SYSTEM
NO. OF GEN
NORMAL
NRLF(SINGLE SLACK BUS)
DISTRIBUTED
SLACK BUS SYSTEM
GA LOSS MINIMIZATION
GEN 1
238.675
224.428
232.779
GEN 2
57.560
60.409
57.784
GEN 3
24.560
27.409
24.887
GEN 4
35.000
37.849
35.827
GEN 5
17.930
20.779
21.722
GEN 6
16.910
19.759
16.979
LOSS
17.235
16.853
15.3482 (mean)
Table 4: PARTICIPATION FACTORS
No of GEN
Participation factor for
normal NRLF
Participation factor for distrb. slack bus
method
Participation factor for loss
min. With GA
GEN 1
1
0.1666
0.013
GEN 2
0
0.1666
0.002
GEN 3
0
0.1666
0.24
GEN 4
0
0.1666
0.244
GEN 5
0
0.1666
0.246
GEN 6
0
0.1666
0.255
V. CONCLUSIONS
Here in this paper it has been discussed that how to use distributed slack bus method along with loss minimization using Genetic Algorithm. This procedure provides us with a dependable solution of a load flow loss minimization problem.In case of normal load flow problem, slack bus provides the whole loss, hence that bus may get overloaded. But here, we distribute the losses among all the generators and also minimize the loss, so that we can overcome that overloading problem. Moreover, we are also reducing the losses, so we are reducing the energy wastages, which is cost effective also. Again for distribution system it is much more cost effective as we are reducing the generation of the slack bus to reduce loss, which is nothing but substation bus in distribution system. Therefore more cost effective in case of distribution system.


RESULTS AND COMPARATIVE STUDY
Simulation results are as follows;
NO. OF GEN 
NORMAL NRLF(SINGLE SLACK BUS) 
DISTRIBUTED SLACK BUS SYSTEM 
GA LOSS MINIMIZA TION 
GEN 1 
236.891 
226.648 
221.484 
GEN 2 
18.3 
23.421 
32.903 
GEN 3 
11.2 
16.321 
11.200 
LOSS 
15.502 
14.803 
14.2419(me an) 
Table 1: FOR STANDARD 14 BUS SYSTEM
Table 2: PARTICIPATION FACTORS
VI.REFERENCES

ExpÃ³sito, A. G., Ramos, J. L., & Santos, J. R. (MAY 2004). Slack Bus Selection to Minimize the System Power Imbalance in LoadFlow Studies. IEEE TRANSACTIONS ON POWER SYSTEMS , 19 (2), 987 995.

Kamh, M. Z., & Iravani, R. (JUNE 2012). A Sequence FrameBased Distributed Slack Bus Model for Energy Management of Active Distribution Networks. IEEE TRANSACTIONS ON SMART GRID , 3 (2), 828836.

Tong, S., & Miu, K. N. (MAY 2005). A NetworkBased Distributed Slack Bus Model for DGs in Unbalanced Power Flow Studies. IEEE TRANSACTIONS ON POWER SYSTEMS , 20 (2), 835842.

Tong, S., & Miu, K. N. (2006). Participation Factor Studies for Distributed Slack Bus Models in ThreePhase Distribution Power Flow Analysis. IEEE.
No of GEN
Participation
factor for normal NRLF
Participation
factor for distrb. slack bus method
Participation
factor for loss min. With GA
GEN 1
1
0.333
0.004
GEN 2
0
0.333
0.027
GEN 3
0
0.333
0.970

Tong, S., Kleinberg, M., & Miu, K. (2005). A Distributed Slack Bus Model and Its Impact on Distribution System Application Techniques. Center for Electric Power Engineering. Philadelphia, PA 19104, USA.

T. Werner and R. Remberg, "Technical, economical, and regulatory aspects of virtual power plants," in Proc. 3rd Int. Conf. Electr. Utility Deregulation Restructuring Power Technol. (DRPT), 2008.

R. Lasseter, "Microgrids and distributed generation," J. Energy Eng. , vol. 20, no. 3, pp. 144149, 2007.

F. Kateraei and M. Iravani, "Transients of a microgrid system with multiple distributed energy resources," in Proc. Int. Conf. Power Syst. Transients (IPST), 2005.

F. Gao and M. Iravani, "A control strategy for a distributed generation unit in gridconnected and autonomous modes of operation," IEEE Trans. Power Del. , vol. 23, no. 2, pp. 850859, 2008.

J. Meisel, "System incremental cost calculations using the participation factor loadflow formulation," IEEE Tran. Power Syst., vol. 8, no. 1, pp. 357363, 1993.

S. Tong and K. Miu, "A participation factor model for slack buses in distribution systems with DGs," in Proc. IEEE Power Eng. Soc. Transm. Distrib. Conf., Dallas, TX, 2003.

C. Schauder and H. Mehta, "Vector analysis and control of advanced static VAr compensators," IEE Proc. Gener., Transm., Distrib., vol. 140, no. 4, pp. 299306, 1993.