Improvement of Economic Load Dispatch Using Fuzzified Particle Swarm Optimization Technique 

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ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)

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ISSN (PRINT) : 2320 – 8945, Volume -5, Issue -1-2, 2017 28

Improvement of Economic Load Dispatch Using Fuzzified Particle Swarm Optimization Technique

1Himanshu Shekhar Maharana, ²Saroja Kumar Dash

1 Department of Electrical and Electronics Engineering, GIET, Ghangapatna, Bhubaneswar, Odisha, India

2 Department of Electrical Engineering, GITA, Bhubaneswar, Odisha, India Abstract - With large interconnection of the electric networks,

the energy crisis in the world and continuous rise in prices, it is very essential to reduce the running charges of the electric energy i.e., reduce the fuel consumption for meeting a particular load demand. The main aim in the economic dispatch is to minimize the total cost of generating real power at various stations while satisfying the loads and the losses in transmission links Recently particle swarm optimization algorithms inspired by collective behaviour of swarm has been applied successfully to solve ELD problem. It is a population based stochastic optimization process driven by the simulation of a social psychological metaphor. In this dissertation we emphasize particle swarm optimization (PSO) for analysing various performance objectives namely cost of generation, cost of emission and a combine objective function involving both these objectives vide the experimental simulated results. A 6 unit 30 bus IEEE test case system has been utilized for simulating the results involving improved weight factor constraints for optimizing total cost of generation and emission. This method increases the tendency of particles to venture into the solution space to ameliorate their convergence rates .The results show that proposed improved PSO techniques gives the optimum operating cost with consistent results in terms of diversity of results. Hence to overcome the premature convergence and to speed up the process, a classical PSO technique is incorporated with fuzzy logic to get a faster convergence This improved technique is termed as Fuzzified Particle Swarm Optimization (FPSO). The proposed method can provide an accurate solution with fast convergence and has the potential to be applied to other power system optimization problems.

KEYWORDS: Economic load dispatch (ELD), Particle swarm optimization (PSO), Fuzzified particle swarm optimization (FPSO),

I. INTRODUCTION

Demand on energy is increasing day by day, whereas energy resources are decreasing on the other side. Thus optimization is necessary for power system operation and planning. Economic Dispatch provides the best optimization scheme for selecting the best generation schedule for supplying a preset load, with minimum cost and satisfying the constraints [1].. The computation of optimum generation schedules for the predicted loads over a period of time, with due considerations of generator ramping rate limits, non-smooth fuel cost function due to valve-point effect, spinning reserve contribution constraints and prohibitive operating zones leads to an advanced economic dispatch with multiple objectives and several adequate constraints, effectively termed as multi-constrained dynamic economic dispatch

[2]. For a 6 generating unit system vide 30 bus IEEE test case systems. The results obtained vide the proposed method were compared with various conventional methods like Lagrange multiplier method [6]-[7] , mixed integer linear programming method, evolutionary programming method [8]-[10] and quadratic programming method etc.[4]-[5].

II. METHODOLOGY

This section forecasts the objective function viz. Cost, emission and combined objective function satisfying equality and inequality constraints involving price penalty factor

F

_i.The basic ELD problem is formulated vide(1) and (2),

(

2

) sin( ( )) (1)

i i i i i i i i i i

Z  a PG  bPG C   K l P PG 

(

2

) (2)

i i i i i i

J  h PG  g PG  q

Where

Z

_iand

J

_i are cost and emission objective functions and

a

_i,

b

_i,

c

i,

K

i,

l

i and

h

_i,

g

_i,

q

_iare cost and emission objective function coefficients. In this dissertation the emission function involves global warming gases like NO2 and SO2 etc. The ultimate objective function involving combined objective formulation encompassing cost as well as emission objective function vide price penalty factor

F

_i is formulated as (3).

i i i i

(3)

S  Z  F  J

Where

max max

(4)

i i

i

F  Z J

(

2

) sin( ( )) (5)

i i i i i i i i i i

Z  a PG bPG C    K l P PG 

(

2

) (6)

i i i i i i

J  hPG  g PG q 

The constraints involved in this work are

(i) Equality constraint

1

(7)

n

D i

PGi P TL



 



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Where

P

_D= net power demand.

TL=

6 6

1 1

m n mn

m n

PG PG B

 

 



^Where ^TL ^is

transmission loss.

(ii) Inequality constraint

i i j

(8)

P PG P  

Where PG_i represents the output power of

i

^th

generating unit,

P

_i and

P

_j are minimum and maximum output

Power of

i

^thgenerating unit respectively

III. NEED FOR FUZZIFIED PSO –

The fuzzy logic method is treated as robust method because it deals with fuzzy or crisp values and does not require precise inputs and it can be programmed even if a feedback sensor quits or is destroyed. Even though there is a wide variation in the inputs the output control is a smooth control function. The fuzzy logic controller processes user-defined rules hence it can be modified easily to improve or modify system performance. By the generation of appropriate governing rules the system can be incorporated with new sensors. Fuzzy logic is not limited one or two control outputs, and it is not necessary to compute rate-of-change of parameters in order for implementation. The sensor data is sufficient because that provides some indication of a system's actions and reactions. Hence the sensors will be inexpensive and less complex [3].

This method involves dispersed particles i.e. swarms in search space randomly updating their position using their velocity heuristically resembling their neighbours so as to obtain position and velocity vectors viz.

P

bestand

g

_best i.e.(

P

₁_best,

P

_2best…..

P

_ibest) and (

g

₁_best,

g

₂best…..

g

_ibest) respectively. The updated values of position and velocity are computed using equation (9) and (10).

( 1)

2^k

[

^k1 1 1

(

0 ^k

)

2 2

(

^k

)] (9)

n n i best i

Y

^

 WY CRand L S    C Rand g  S

1 1

1

(10)

k k k

n i i

S

^

 S  V

^

Where

C

₁

,C

₂ are acceleration coefficients W = Inertia weight

1 k

V

i = Updated velocity of the k+1 iteration L0 =

P

_bestfunction

k

S

i = Initial

i

^th particle after

k

^th iteration

C

1Rand1

( P

_best

 S

_i^k

)

= Particle’s Private thinking

C

2Rand2

( g

_best

 S

_i^k

)

= Collaboration amongst particles

max min

max

W W (11)

W W n

k

   

K = Maximum number of iterations n = Iteration number

W

max = Initial Weight in per unit = 0.85

W

min= Final Weight in per unit = 0.35

To optimize the valve point loading effect the ramp rate constraints are imposed upon the iteration inequality constraints as under.

min 0 max 1

(

_i

,

_i _i

)

_inew

(

_i

,

_i _i

) (12) Max PG P DR PG    Min PG P UR 

Subject to condition that

i i

gi

P UR

P 

₀



(Generation increases)

0 1

(13)

i i i

P  P  D R

(Generation decreases)

Where

P

_i₁ = Power generation of

i

^th unit in the current interval

0

P

i = Power generation of

i

^th unit just before the interval

Looking into the valve point loading a constriction factor finds use in advanced constriction factor

-based well defined ramp rate particle swarm optimization algorithm given by,

CF= 3 2

4 (14)

4          3 2.2

Where  lies between 2.1 and 3.1.

As rises, CF decreases giving rise to slower convergence because of diminished population velocity up-gradation

Using (14)

( 1)

2^k

[

^k1 1 1 0

(

^k

)

2 2

(

^k

)] (15)

n n i best i

Y

^

 CFWY CRand L S    CRand g  S IV. FUZZIFIED PARTICLE SWARMOPTIMIZATION BASED

ECONOMIC LOAD DISPATCH :

This presents an overview of some superior stochastic optimization techniques followed by the need and formulation of Fuzzified Particle Swarm Optimization

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(FPSO) algorithm for solving Multi-constrained Dynamic Economic Dispatch, Emission Constrained Economic Dispatch (ECED) and Multi-area ED problems. Subsequently the FPSO algorithm is applied on standard test systems for solving the above mentioned ED problems and the optimal results obtained are compared and analyzed with other stochastic optimization techniques[7][8].

3.1 FPSO ALGORITHM :

Step 1 (Initialization): An initial swarm of particles Ii of size n is generated randomly within the feasible range and the distributions of initial trial parents are uniform.

The elements of each initial particle are the controllable real power outputs of committed ng generating units.

Step1.Initialize parameters like

6 5 4 3 2

1

, PG , PG , PG , PG , PG PG

Step 2 If

L

_iis better than

L

₀, then

L

_i

 L

₀_new

Else

L

_i

 L

₀_old

Step 3 Initialize

g

_best values for generating units

PG

1to

PG

₆

Step 4 Assign best of

L

_inewand

L

₀_old to

g

_best

Step 5 Current position

S

_i

 Z

_i

 F

_i

 J

_iand

current velocity

) ()(

_max _min

min

1 i i i

n

U Randi U U

Y   

Step 6 Update position for each particle

) 1 (

2 1

(  1 ) 

_i^k



_n^k^

n

k S Y

S

where

Y

_n^k₂^¹ is the update velocity for each particle

Step 7 If Particle position is greater than or equal to bounds in (12) then stop otherwise go to step 2.

IV RESULT ANALYSIS

The results obtained for the proposed FPSO method (Fig.1) for various objectives Viz. cost ,emission[16]

and combined objective for the IEEE 30 bus test case system vide Fig.1 suggest that beyond 500 MW cost as well as emission objective yield better performance over the classical methods like lambda iteration, mixed integer with linear programming method and quadratic method etc. Fig.2 represents Graph of Gbest value.

VARIOUS OBJECTIVE FUNCTIONS

(a) (b)

(c)

Fig.1.(a) Operating cost function vs Output Power (b) Emission level vs Output Power (c) Total objective function vs. Output power for 20

number of iterations

Fig - 2: Graph of Gbest value versus epoch

V. CONCLUSION

The primary objective of this paper is to develop efficient and fast Fuzzified Particle Swarm Optimization (FPSO) algorithm that can be applied to obtain the

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optimal solutions of multi-constrained dynamic ED, ECED, multi-area OPF, multi-area Security Constrained OPF (SCOPF) and OPF with multiple FACTS controllers.An enhanced ED problem is developed considering all the practical constraints leading to an advanced economic dispatch with multiple objectives and constraints.

A new improved stochastic technique namely Fuzzified Particle Swarm Optimization (FPSO) is applied to solve multi-constrained dynamic ED problem which is inferred to have superior features than the classical Particle Swarm Optimization (PSO) methods such as faster and stable convergence characteristics.

REFERENCES:

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[3] A. Laoufi, A Hazzab and M. Rahli, “Power

Dispatch Using Fuzzy-Genetic

Algorithm.”IJAER 2009.

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[5] Taher Niknam, Hasan Doagou Mojarrad and Majid Nayeripour. “A New Hybrid Fuzzy Adaptive Particle Swarm Optimization For Non- Convex Economic Dispatch.” IJICICI, Volume 7, January 2011.

[6] N.M Jothi Swaroopan., P. Somasundaram,

“Fuzzified PSO Algorithm For DC-OPF of Interconnected Power System” Journal of Theoretical and Applied Information Technology. 2010.

[7] A. Santos and G.R. da Costa, “Optimal power flow by Newton’s method applied to an augmented Lagrangian function” IEE poceedings generations, Transmission & distribution, Vol 142(1), pp.33-36, 1989.

[8] N Sinha, R. Chakrabarti and PK Chattopadhayay,

“Evolutionary programming techniques for Economic load Dispatch. IEEE transactions on Evolutionary Computations,” Vol 7(1), pp.83-94, 2003.

[9] K.P. Wong and J Yuryevich, “Evolutionary based algorithm for environmentally constraints economic dispatch”, IEEE transaction on power system. ” Vol 13(2), pp. 301-306, 1998.

[10] L Lai & Mata Prasad. Application of ANN to economic load dispatch. Proceeding of 4^th international conference on advance in power system control, operation and management, APSCOM-97, Hong-Kongpp.pp707-711, nov- 1997.

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