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Cluster ComputingThe Journal of Networks, Software Toolsand Applications ISSN 1386-7857 Cluster ComputDOI 10.1007/s10586-018-2045-y

Assessment of ramping cost for independentpower producers using firefly algorithm andgray wolf optimization

K. Kathiravan & N. Rathina Prabha

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Assessment of ramping cost for independent power producers usingfirefly algorithm and gray wolf optimization

K. Kathiravan1 • N. Rathina Prabha2

Received: 1 January 2018 / Revised: 1 February 2018 / Accepted: 7 February 2018� Springer Science+Business Media, LLC, part of Springer Nature 2018

AbstractIn Deregulated Environment, all the independent power producers (IPP) are clustered in nature and they were operated in

unison condition to meet out the cluster load demand of various levels of consumers in continuous 24 hours horizon. These

IPP were respond and reschedule their clustered operating units with time confine among the reliant conditions like

incremental in overall consumer demand, credible contingency and wheeling trades. Amid this process, the ramping cost is

acquired during the incidence of any infringement in the secured elastic limit or Ramp rate limits. In this paper, optimal

operating cost of the independent power producer is incurred with ramping cost considering stepwise and piecewise slope

ramp rate utilizing firefly algorithm and Gray wolf optimization algorithm. Optimal power flow is carried out for the three

standard test systems: five, six and ten power producers are having secured elastic limits are taken for computation in

Matlab environment.

Keywords Firefly algorithm � Gray wolf optimization � Piecewise linear ramp rate � Independent power producer �Optimal power flow � Ramp rate limits

1 Introduction

Optimal power flow (OPF) issue must be comprehended to

get the optimal cost of the power business by fulfilling the

framework working condition. Because of equality and in

equity limitations the issue is everywhere in level, very non

straight constrained enhancement issue. Keeping in mind

the end goal to upgrade, a novel strategy is expected to

make do with these inconvenience and those with high

pace pursuit to the ideal and not being intrigued in neigh-

borhood minima. The operational cost of energy frame-

work is subjected to the framework working imperatives.

Such non-linear constraint issues had been investigated by

computational artificial insight by numerous scientists to

improve the ideal arrangement. Optimization techniques

[1] are meta-heuristics and these are very straightforward

and roused by basic ideas commonly related with the

human wonders of developmental idea and conduct of

creature such meta-heuristics have the adaptability,

neighborhood optima shirking. Meta-heuristics are two

classes, they are single arrangement based and another is

populace based. Simulated Annealing [2] is the pursuit

procedure begins with the single hopeful and enhance over

emphasis procedure, Genetic Algorithm [3] is the populace

based. Here the advancement is done by set of arrange-

ments. Inquiry process begins with irregular introductory

arrangement and afterward enhanced over the emphasis

procedure.

Artificial Bee Colony [4] is an idea of swarm intelli-

gence which deals populace based meta-heuristics. Swarm

Intelligence was proposed by Bonabeau et al. [5]. It clari-

fies the aggregate canny gathering of basic specialists.

Probably the most mainstream swarm intelligence proce-

dures are Ant colony optimization [6], Particle Swarm

Optimization [7]. Inquiry procedures of the meta-heuristics

have two stages which are exploration and exploitation

[8–10]. Adjusting these two stages is testing assignment as

& K. Kathiravan

rndkathiravan@gmail.com

1 Department of Electrical and Electronics Engineering, Theni

Kammavar Sangam College of Technology, Theni,

Tamil Nadu 625534, India

2 Department of Electrical and Electronics Engineering, Mepco

Schlenk Engineering College, Sivakasi, Tamil Nadu 626005,

India

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a result in stochastic nature is obtained. Optimal Load

dispatch for piecewise slope ramp rate was explained using

Autonomous group of particle swarm optimization

(AGPSO) [11]. Optimal power stream answer for the

power framework is portrayed with three Hybrid Particle

Swarm Optimization calculations with choking factor [12].

Another variant of PSO is coordinated with nearby arbi-

trary search to take care of non-arched monetary dispatch

issues [13].

The firefly algorithm [14, 15] proposed by Yang was

utilized to understand non domed arrangement spaces.

GWO has a place with meta-heuristics advancement which

was proposed by Mirjalili [16]. The adequacy of the pro-

posed approaches was shown with 10 bus system with 5

IPP [17], 26 bus systems with six IPP [18] and 39 bus

system with 10 IPP [19] in non raised arrangement spaces.

A computational approach was performed through the

GWO and FFA were compared with Fitness Distance Ratio

Particle Swarm Optimization (FDRPSO), PSO, Evolu-

tionary programming (EP), Linear programming (LP) and

it confirms the efficacy of likely Meta-heuristics FFA and

GWO are upshot the excellence, reliability.

2 Problem formation

Mathematically optimal fuel cost of independent power

producers has been formulated with line flow constraints.

Over all power producer cost is expressed using the fol-

lowing form:

Minimize F Xð Þ ¼Xn

j¼1

ðfjðpjÞ þ RCjÞ $=h ð1Þ

where F(X) is the operating fuel cost of jth power producer

RCj is the ramping cost of power producer and n is the

number of power producers in the power system network.

fuel cost function of a jth power producer is written as:

fj pj� �

¼ aj þ bjPj þ cjP2j $=h ð2Þ

where pj is active power output of an jth power producer,

fj(pj) is the fuel cost of jth power producer and aj, bj, cj are

the fuel cost coefficients of the jth power producer.

The point at which the power producer work inside the

elastic limit as far as possible [20–23] the Ramping cost

isn’t considered in the evaluation process. However, strict

sloping breaking points put a roof on their operation. On

the off chance that power producer are allowed to broaden

their limits, the life of the rotor will get weariness.

Henceforth the operation outside the versatile slope is

charged as an inclining expense and it is collected with the

fuel cost which is named as the Ramping cost of the power

producer. Be that as it may, the sloping procedures of the

power producer are represented by secure elastic limits;

prompts change their working states as for time.

Variation of output power during the time period k.

Figure 1 shows Piecewise linear ramping period [0, RTk],

constant output period. [RTk, 1H]. The power delivery of

the power producer during the 1st interval of time between

ð0;RT1Þ is given by:

pj ¼ðpj2 � pj1Þ � ðRTÞ

RT1þ pj1 ð3Þ

where RT is the total ramping period of the power

producer.

The power delivery of the power producer during the

2nd interval of time between (RT1, RT2) is given by:

pj ¼ðpj3 � pj2Þ � ðRT � RT1Þ

RT2 � RT1þ pj2

Overall power delivery of the power producer in any

period of time among the k segments during the linear

ramping time interval (0, RTk) is given as follows:

pj ¼pjkþ1 � pjk� �

� RT � RT k�1ð Þ� �

RTk � RTk�1

þ pjk; 0\RT\RTk

ð4Þ

The power delivery of power producer during the con-

stant output period between the time intervals (RTk,1) is

given as follows:

pj ¼ pj þ RR � RT ;RTk\RT\1 ð5Þ

where RR is the Ramping Rate (up/down) and RT is the

ramping time of the jth power producer. In the kth linear

segment regions which is prior to the power producers to

get grip of its ramping limit in the specified period of time

is shown in Fig. 2. The mathematical formulation is used to

evaluate the ramping cost of the independent power pro-

ducers at their resultant operating point.

F Gð Þ ¼XRTk

t¼0

c1ðtÞ þX1

t¼RTk

c2 tð Þ ð6Þ

c1 tð Þ ¼ aj þ bjPj tð Þ þ cjPjðtÞ2; t 2 ð0;RTkÞ

pj tð Þ ¼pjkþ1 � pjk� �

� RT � RT k�1ð Þ� �

RTk � RTk�1

þ pjk

� �þ RR � t; t

2 0;RTkð Þð7Þ

c2 tð Þ ¼ aj þ bjPj tð Þ þ cjPjðtÞ2; t 2 ðRTk; 1Þ

pj tð Þ ¼ pj þ RR � RT ð8Þ

From above expressions, RR represents increment in

ramp rate (UR) or Decrement in ramp rate (DR).If inde-

pendent power producers operate beyond their safe elastic

permissible limits; the ramping cost is calculated using the

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above expression. Overall operating cost function of the

power producer is given by Eq. (1)

Subjected to the following constraints:

Xng

j¼1

pj � ploss � pdem ¼ 0 ð9Þ

where pdem is the total load of the system and ploss is the

transmission losses of the system. The inequality constraint

on real power generation pj of each power producer j is

given by:

pjmin � pj � pjmax ð10Þ

MVAfm;n �MVAf maxm;n ð11Þ

where MVAfmaxm;n is the maximum rating of transmission

line connecting m and n.

3 FDR PSO algorithm

The Fitness Distance Ratio PSO algorithm, in addition to

the social-cognitive learning procedure, individual particles

also be trained from the familiarity of neighboring particles

which have the enhanced fitness than itself [24]. This

FDRPSO performance is based on computing and maxi-

mizing the relative fitness distance ratio. This FDRPSO

algorithm does not initiate the complicated computation in

actual PSO algorithm. The FDRPSO results are originated

by shifting the pace updating equation and the position

update equation ruins same. Here, this algorithm selects

only one previous particle at a time when updating every

velocity measurement.

These particles are chosen to satisfy the following two

criteria.

1. It must be present nearer to the adjoining particle.

2. It should have stayed a point of enhanced fitness.

The above mentioned two criteria were satisfied by a

nearby particle to maximize the ratio of the fitness differ-

ence to the one-dimensional distance.

costðpjÞ � costðxiÞjpjd � xidj

ð12Þ

Three factors are influenced over the particle’s pace

update in FDRPSO algorithm, they are:

1. pbest ðpidÞ of the particle (earlier pbest)

2. gbest ðpgidÞ considering better pbest among other

particle in explore space.

3. nbest ðpnidÞ best adjacent neighbor.

Therefore, velocity update equation for FDRPSO is

written as:

vnþ1id ¼ w � vnid þ c1 � rand1 � pid � xidð Þ þ c2 � rand2

� pgid � xid� �

þ c3 � rand3 � pnid � xidð Þð13Þ

This ðpnidÞ has the most excellent fitness of the nearby

particle. FDRPSO algorithm has the middling and better

fitness sustained to be many more iteration than PSO

algorithm. This algorithm has less vulnerable to earlier

Fig. 1 Ramping process (power

delivery for 1 hour)

Fig. 2 Various ramping rates of

power producers

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convergence and less possible to get into confined mini-

mum of the function being optimized. In order to avoid the

prior convergence, this algorithm continue its searching for

overall best value in complicated optimization problems,

this FDRPSO gives the better solution than PSO.

4 Firefly algorithm (FFA)

Firefly algorithm was produced by Xin-She Yang which

depends on the emerging examples and behavior of fire-

flies. Basically, individual firefly will be pulled into the

brighter ones; while in the interim, it investigates and looks

for quarry arbitrarily. Likewise, the magnificence of a

firefly is dictated by the view of the target work. The

development of a firefly m is pulled into another more

appealing brighter firefly n is dictated by,

xtþ1m ¼ xtm þ b0e

�cr2mnðxtn � xtmÞ þ atetm ð14Þ

where in Eq. (14)

Second term is mainly due to attractions.

Third term is randomization. at represents the random-

ization parameter, etm is a vector of random number drawn

from a Gaussian distribution (or) uniform Distribution. b02 [0,1] is attrectiveness at r = 0 rmn ¼ j xtn � xtm

�� ��j is the

Cartesian distance.

For different issues, for example, booking, any measures

that can successfully portray the amounts of enthusiasm for

the improvement issue can be utilized as a separation r. For

most implementation we can take,

b0 ¼ 1; a ¼ O 1ð Þ and c ¼ O 1ð Þ ð15Þ

In a perfect world, the randomization parameter at oughtto be monotonically diminished bit by bit amid cycles.

A simple scheme is to use,

at ¼ a0dt; d 2 ð0; 1Þ ð16Þ

where a0 is the initial randomness d Randomness reduction

factor

It merits calling attention to that (16) is basically an

arbitrary walk one-sided towards the brighter fireflies. On

the off chance that b0 ¼ 0 and it was easy to random walk.

Moreover, the randomization term can without much of a

extend be reached out to dissimilar disseminations such as

Levy flights.

5 Gray wolf optimization

The GWO deals with the nature of social behavior of gray

wolves towards cluster hunting with leadership hierarchy

[16]. To design and implement the optimization, four types

of gray wolves are involved. They are alpha (a), Beta (b),

delta (d) and omega (x). The mathematical model of GWO

is working for simulating the leadership hierarchy besides

three main phases of GWO hunting are searching for

encircling the quarry and attacking quarry.

The mathematical models of hunting optimization of

gray wolves are designed as follows: the foremost fittest

solution as alpha (a), second finest solution as Beta (b),third finest solution as delta (d) and the left over gray

wolves are omega (x) and this is the lowest among the

other respectively. Encircling the quarry is modeled as

follows:

S~¼ R~ � xi! kð Þ � x~ðkÞ

�� �� ð17Þ

x~ k þ 1ð Þ ¼ xi! kð Þ � P~ � S~ ð18Þ

where

k: indicates the present iterationP~and R~: coefficient

vector xi!: position vector of the quarry x~: position vector of

a gray wolf P~and R~ are calculated as follows:

P~ ¼ 2 � w~ � c1!� w! ð19Þ

R~¼ 2 � c2! ð20Þ

Here w~ decrease linearly from 2 to 0 during the iteration

process c1!andc2

! is random vector in [0, 1].

If the gray wolf is in random position and it can update

its position according to the availability of position of the

quarry. From the various positions of the agents (i.e.,

another gray wolf that involved in hunting the prey). Best

agent adjusts its current position and reached the quarry by

adjusting the co-efficient vectors. Random vectors permit

the wolves to reach any position inside the search space

around the quarry in any random position by the Eqs. (17)

and (18). The hunting is guided by alpha along with this

beta and delta is hunted together (participating). The alpha,

beta and delta have the better knowledge towards location

point of the quarry and other omega are updated its position

according to the alpha, beta and delta it is mathematically

expressed as follows:

Sa!¼ R1

�!� xa!� x~

������ ð21Þ

Sb!¼ R2

�!� xb!� x~

������ ð22Þ

Sd!¼ R3

�!� xd!� x~

������ ð23Þ

x1!¼ xa

!� P1�! � Sa

! ð24Þ

x2!¼ xb

!� P2�! � Sb

! ð25Þ

x3!¼ xd

!� P3�! � Sd

! ð26Þ

x~ k þ 1ð Þ ¼ x1!þ x2

!þ x3!

3ð27Þ

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Attacking quarry or exploitation by the gray wolves

finishes the quarry when it stop moving. Mathematically

this can be expressed as by decreasing the value of w~

likewise the P~ also decrease from 2 to 0 in the overall

iteration. When P~ are in [- 1, 1], the next location point of

the search agent can be in any location between its current

location point and the location point of the quarry if P~�� ��\1

the strength of the wolves assault in the direction of the

quarry. Therefore Gray wolf optimizer algorithm allows its

wolves to update the location point based on the alpha, beta

and delta wolves and hunting towards the quarry which is

the local best solution. It utilizes P~with unsystematic value

higher than 1 or lesser than - 1 to leaning the wolves to

diverge from the quarry and it emphasizes look for quarry

and let the gray wolf optimizer to search globally. Another

component R~ also in exploration. It contains unsystematic

values [0, 2] and it provides the unsystematic weight of the

quarry to R~[ 1 or R~\1 the effect of quarry in defining the

distance and it helps the GWO as more unsystematic

behavior during the optimization, it favors the searching

and the avoidance of local optimum solution. Here R~ is not

linearly reduced in contrast of P~. This component is very

useful in final iteration. Finally the GWO algorithm stops

by fulfillment of the end criterion.

6 Implementation of FFA/GWOfor calculation of ramping cost for IPP

The operation of each power producer in the power system

is limited by their real and reactive power limits. But in the

real 24 hours horizon operations all the power producer are

steady to the load beyond their ramping limits for the

scheduled hours, when subjected to probable contingency,

sudden augment in load conditions and wheeling

transactions.

These types of operations are making the rotor fatigue

(reduce the life of the rotor). In order to maintain the

reliable operations of power system, this operation is

inevitable and the power producers are realistically com-

pensated by the system optimiser. The change in their

condition of operations is mainly fixed by the slope of rate

limits. On the other hand, that the incline rate limits is

bigger than the possible communicated sloping cost, the

financial effect because of rotor weakness is communicated

up to the sloping expense of the power producer. Here, a

piecewise direct inclination rate is used to figure the time

cost of energy producers utilizing swarm insight and

additionally meta-heuristic streamlining calculations. This

processed calculation is shown for 10, 26 and 39 bus sys-

tem The computational method of operating cost with

(brought about or non-acquired) sloping expense for all

power producers in the test framework is given in Fig. 3.

The test system line flows are computed by the Newton–

Raphson method with thermal power limits. The simulation

code was written in MATLAB 2016b environment on intel

core i3, 2 GHz, 4.00 GB RAM system. The effectiveness

of the proposed method has been demonstrated by con-

sidering 5 power producers, 6 power produces and 10

power producers.

6.1 Test system: 5 independent power producers

This 10 bus system consists of 5 power producers and 13

transmission lines. The fuel cost coefficient, unit limits of

the test system are taken from [17]. The meta-heuristic

algorithm was tested for this 10 bus system.

6.1.1 Case1: base load condition

The base load of the 10 bus system with 5 power producer

is 2.25 p.u. Under the base load condition, the following

parameter setting is used in GWO and FFA: For the

FDRPSO the dormancy weight (w) differs from 0.9 to 0.2,

which was utilized for the merging attributes of the swarm

knowledge calculation for FFA: Search agents = 4, k ¼0:2 during the iteration process random numbers generated

with uniform distribution in the interval of [0, 1]. The

optimal power flow solution has been obtained using FFA

and GWO algorithm. Table 1 shows the optimal setting of

the power producers and the obtained minimum fuel cost

values compared with other optimization methods. The real

and reactive power limits of the power producer for the

consequent optimal solution are within their secured elastic

limits. So, ramping cost are not incurred. Figure 4, shows

the Convergence characteristics of GWO and FFA. After

the significant number of generation, the production cost of

the power producer remains invariable and it is guarantee

the convergence of the proposed algorithm towards optimal

point. Convergence characteristics of meta- heuristic

(GWO and FFA) are measureless variation in five inde-

pendent power producer value settles down to the best

optimum value.

During the initial iteration FDRPSO, GWO and FFA are

finding the feasible solutions to the problem after that the

value settles down to the best optimum value. From Fig. 4,

shows clearly that GWO and FFA algorithms find the best

optimal value compared to the other optimization methods.

6.1.2 Production cost with ramping by increase in loadcondition

Power producers have to respond the load changes. The

operation of the generator setting depends upon their ramp

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rate limits. During the initial conditions of stepwise

ramping up/down (elastic limits) are considered. Based on

the changes made in load the power producers are

rescheduled to establish their most excellent setting point

with various stepwise ramping limits. From, Table 2 it is

inferred that production cost is maximum due to the power

producer operate their generator with stepwise ramp rate

limits and it is also inferred the obtained fuel cost of the

proposed method is improved, when compared with the

results of other optimization methods. Minimum

production cost is obtained when the ramp rate limit is

below 20%, but, additional strict ramp rate constraint will

limit them from vital search, and effect in more production

cost or in least cost saving.

6.1.3 Production cost with bilateral and multilateralwheeling transactions

In deregulated power market wheeling transaction is very

much important because maximum number of power

YES

NO

Start

Get the line data, bus data, load data and database of power producer

Carry out the load increment, plausible contingencies and wheeling transactions

Obtain best possible generation dispatch using FFA/GWO

Verify the output power of the power producer is inside the

boundary

Evaluate the Ramping Cost with Linear Model

Compute the Net Generation cost

Stop

Fig. 3 Flow chart of meta-

heuristic optimization

algorithms

Table 1 Comparison among

different methodsOptimization methods Generation power (p.u) Fuel cost ($/h)

P1 (MW) P2 (MW) P3 (MW) P4 (MW) P5 (MW)

LP [17] 0.414 0.05 1.224 0.05 0.059 164.177

EP [25] 0.285 0.052 1.183 0.058 0.727 164.019

PSO [26] 0.417 0.129 0.911 0.196 0.597 164.321

FDRPSO [26] 0.352 0.077 1.079 0.06 0.682 163.85

GWO 0.357 0.05 1.328 0.051 0.468 163.693

FFA 0.2388 0.05 1.4109 0.05 0.5051 163.6044

Bold values indicate the best values

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transfer have been carried out through wheeling transac-

tion. In this deregulated environment power producers have

to respond for the power transfer especially during the

wheeling transaction (Bilateral or Multilateral). The mag-

nitude of Power transfer and details of the bilateral and

multilateral wheeling transaction are given in Tables 3 and

4.

GWO and FFA methods are used to obtain the best

optimal production cost with the linear ramp model for the

test system and results are given in Table 5 in this case the

wheeling transaction was carried out by considering the

Fig. 4 Convergence

characteristics of 5 independent

power producers

Table 2 Production cost incurred with ramping cost (stepwise ramp rate limits)

%Ramp rate

limit

PSO [26] FDRPSO [26] GWO FFA

FC ($/

h)

RC ($/

h)

PC ($/

h)

FC ($/

h)

RC ($/

h)

PC ($/

h)

FC ($/

h)

RC ($/

h)

PC ($/

h)

FC ($/

h)

RC ($/

h)

PC ($/

h)

10 164.63 4.12 168.75 164.75 3.35 168.06 163.61 4.33 167.94 163.644 4.296 167.94

20 164.84 3.25 168.09 164.64 3.14 167.78 163.77 4.27 168.05 163.72 4.308 168.028

30 165.26 4.52 169.7 164.94 3.99 168.93 163.61 5.6 169.24 163.85 5.398 169.248

40 165.3 4.35 169.6 164.64 4.54 169.18 163.61 5.91 169.53 163.939 5.175 169.114

50 165.4 4.08 169.5 164.78 4.89 169.67 163.67 6.21 169.88 164.186 5.063 169.249

75 165.07 5.09 170.17 164.42 5.83 170.25 163.65 6.91 170.56 164.19 5.986 170.176

100 165.41 8.35 173.76 164.74 7.1 171.84 163.68 8.05 171.73 164.223 7.423 171.646

Bold values indicate the best values

FC fuel cost $/h

RC ramping cost $/h

PC production cost $/h

Table 3 Details of bilateral transactions

Transaction Bus no. Real power (p.u)

From To

BT1 10 4 0.2

BT2 8 5 0.1

Table 4 Details of multilateral transactions

Transaction Bus no. Real power (p.u)

From Real To

power (p.u)

MT1 9 0.2 6 0.1

7 0.15 3 0.15

2 0.1

Total 0.35 0.35

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transformer tap position in the network, voltage angle,

voltage limits of the buses and power flow limits in the

transmission lines(MVA limits). From Table 5 the

obtained results of GWO and FFA is very feasible as well

as better than the LP [17], EP [25], PSO [26] and FDRPSO

[26].

6.2 Test system: 6 independent power producers

The meta- heuristic algorithm like GWO and FFA were

used to obtain the best optimal production cost with strict

Table 5 Production cost incurred with ramping cost

Optimization methods FC ($/h) RC ($/h) PC ($/h)

PSO [26] 165.08 3.88 168.96

FDRPSO [26] 164.04 3.17 167.21

GWO 163.9269 0.1784 164.1

FFA 163.645 1.5554 165.2

Bold values indicate the best values

Table 6 Production cost of 6 independent power producer

Power producer FDRPSO [26] GWO FFA

Generator setting PC ($/h) Generator setting PC ($/h) Generator setting PC ($/h)

P1 (MW) 418.68 4397.868 440.3152 4679.349 444.0852 4729.078

P2 (MW) 183.46 2354.413 156.3398 1995.598 171.2505 2191.109

P3 (MW) 254.89 2971.412 282.2637 3336.297 260.704 3047.683

P4 (MW) 143.36 1961.999 125.3716 1720.55 130.2818 1785.859

P5 (MW) 200.98 2653.524 185.4772 2442.725 175.4692 2308.742

P6 (MW) 61.60 957.7187 73.2577 1109.343 81.2148 1214.046

Total 1263 15296.94 1263 15283.86 1263 15276.51

Bold values indicate the best values

Fig. 5 Convergence

characteristics of 6 independent

power producers

Table 7 Results for 26 bus

system with 6 power producers

after 100 trails

Evolution methods Standard deviation Max cost ($/h) Mean cost ($/h) Min cost ($/h)

FDRPSO 81.003 15530.97 15392.25 15296.94

GWO 14.0828 15334.36 15297.63 15283.86

FFA 4.6836 15289.1 15284.12 15276.08

Bold values indicate the best values

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elastic limit using linear ramp model for 26 bus systems

which consist of 6 power producers and 46 transmission

lines. Unit limits and fuel cost coefficients and bus loss

coefficients are taken from [18]. The obtained optimal

production cost of the power producer under the base load

condition (1263 MW). For this base load condition the

Table 8 OPF Solution with line contingency during three phase to ground fault condition

Power

producer

FDRPSO [26] GWO FFA

Gen

setting

FC ($/h) RC ($/

h)

PC ($/h) Gen

setting

FC ($/

h)

RC ($/

h)

PC ($/h) Gen

setting

FC ($/h) RC ($/

h)

PC ($/h)

P1 (MW) 478.83 5197.49 0 5197.49 480.32 5217.2 0 5217.2 476.23 5234.23 72.96 5161.27

P2 (MW) 198.94 2565.38 96.13 2661.51 193.31 2488.18 0 2488.18 196.03 2455.7 69.71 2525.41

P3 (MW) 271.81 3195.31 0 3195.31 263.97 3090.91 28.223 3119.13 263.13 3079.78 0 3079.78

P4 (MW) 124.49 1708.87 0 1708.87 142.2 1946.3 0 1946.3 147.51 2018.51 0 2018.51

P5 (MW) 199.18 2628.77 95.4 2724.17 190.9 2516 0 2516 193.44 2538.3 12.26 2550.56

P6 (MW) 116.01 1683.05 45.17 1728.22 118.57 1718.34 0 1718.34 112.93 1640.93 0 1640.93

Total 1389.26 16978.87 236.17 17215.04 1389.29 16977 28.223 17005.23 1389.26 16967.45 154.93 16976.48

Bold values indicate the best values

Table 9 Optimal solution for

base load for 10 independent

power producer

Power producers Lambda-iteration PSO [27] FDRPSO [27] FFA GWO

P1 (MW) 675 617.27 627.59 297.4915 244.219

P2 (MW) 1081.4 919.89 973.18 422.0756 480.7078

P3 (MW) 487.5 606.48 608.29 481.6187 600

P4 (MW) 465.3 514.35 469.07 550.4501 582.0006

P5 (MW) 406.2 584.99 481.59 483.1728 460.9328

P6 (MW) 629.3 649.73 652.66 656.7446 604.9276

P7 (MW) 528.9 630.46 611.79 619.9998 608.5333

P8 (MW) 651 508.05 612.67 643 639.4939

P9 (MW) 954.4 831.05 846.51 920 916.4605

P10 (MW) 298 262.19 241.25 1050 987.1095

Fuel cost ($/h) 206601.24 203170.5 201110.8 199507.5 200482.2

Ploss (MW) 52.42 53.42 51.84 53.1 53.85

Bold values indicate the best values

Fig. 6 Convergence

characteristics of 10

independent power producers

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GWO & FFA shows the better optimum production as well

as fuel cost which is given in Table 6. Figure 5 shows the

convergence characteristic of 6 independent power pro-

ducers, which exhibits the GWO and FFA has the best

convergence characteristics.

FFA and GWO methods reach the global optimum of

$15276.51 and $15283.86 respectively, which proven that

GWO and FFA performs better than the swarm intelli-

gence. Due to randomness of the GWO and FFA opti-

mization algorithm and their performance cannot be judged

by single run; if an algorithm is robust and it must gives

consistent result during all the trails. The comparison of the

result after 100 independent trials with the six power pro-

ducers are shown in Table 7.

6.2.1 Optimal production cost with credible contingencyin transmission lines

The optimal production cost for the 26 bus test system is

obtained through the GWO and FFA algorithm. In this

case, 10% increase in load condition is assumed and sub-

jected to three phase to ground fault condition that occurred

between the bus 1 and 18 in the transmission line. By

isolating the corresponding transmission line by 0.1 s the

fault was cleared. The rotor angle of the power producer

was found to be within the acceptable limit. The optimal

power flow results include the linear ramping cost incurred

by the power producer setting and optimal fuel cost is

presented in Table 8.

During credible contingency the rescheduling of power

producer operations was found due to violation in the

power limits of the power producers. Therefore ramping

cost is incurred. If the rescheduling of the power producer

does not violate the power limits of the power producer

operation, no ramping cost is levied.

6.3 Test system: 10 independent powerproducers

The meta- heuristic algorithm like GWO and FFA were

used to obtain the best optimal production cost with strict

elastic limit using linear ramp model for 39 bus systems

which consist of 10 power producers and 46 transmission

lines. Unit limits and fuel cost coefficients and bus loss

coefficients are taken from [19].

The obtained optimal production cost of the power

producer under the base load condition (6124.5 MW). For

this base load condition the GWO & FFA shows the better

optimum production as well as fuel cost which is given in

Table 9. Figure 6 shows the convergence characteristics of

the 10 independent power producers, which exhibits the

GWO and FFA has the best convergence characteristics.

6.3.1 Optimal production cost with increase in loadcondition

The optimal production cost for the 10 independent power

producers obtained through the GWO and FFA algorithm.

In case of 10% increase in load condition is assumed The

optimal power flow results include the linear ramping cost

incurred by the power producer setting and optimal fuel

cost is presented in Table 10.

Table 10 OPF Solution with increase in cluster load condition for 10 IPP

Power

producer

FDRPSO [27] GWO FFA

Gen

setting

FC ($/h) RC ($/

h)

PC ($/h) Gen

setting

FC ($/h) RC ($/h) PC ($/h) Gen

setting

FC ($/h) RC

($/h)

PC ($/h)

P1 (MW) 673.08 18832.1 1688.37 20520.47 330 14386.9 1430.43 12956.54 360 14519.81 0 14519.81

P2 (MW) 1062.54 33879.3 0 33879.3 524.5 20287.2 0 20287.2 529.6 18256.74 2313 20569.74

P3 (MW) 474.97 16214.8 0 16214.8 700 19639.9 4780.14 28615.62 593.8 20560.46 1811 22371.46

P4 (MW) 544.4 19465.1 0 19465.1 680 25552.3 0 25552.3 680 25552.3 0 25552.3

P5 (MW) 495.52 18714.2 0 18714.2 558 21703.9 1519.58 20184.35 592.5 17876.92 4187 22063.92

P6 (MW) 707.42 25953.5 0 25953.5 714.4 28066.4 1737.99 26328.44 748 28066.43 0 28066.43

P7 (MW) 614.53 22013.2 1930.09 22013.2 620 18712.5 0 18712.58 620 18712.58 0 18712.58

P8 (MW) 764.69 25452.3 2561.77 27382.39 640 17687.2 108.307 17578.94 643 17690.99 0 17690.99

P9 (MW) 1072.75 35567 0 38128.77 920 28372 0 28372.03 920 28372.03 0 28372.03

P10

(MW)

327.04 12816.2 6180.23 12816.2 1050 33279.6 0 33279.6 1050 33279.6 0 33279.6

Total 6736.9 228907 6180.23 235087.93 6736.9 227688.3 9576.46 231867.6 6736.9 222887.9 8311 231198.9

Bold values indicate the best values

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7 Conclusion

Gray wolf Optimization and firefly algorithm calculations

for IPP’s cluster issues with tenable possibilities with

piecewise linear sloping model are displayed in this paper.

The practical feasibility of the proposed strategy for taking

care of the optimal power stream issue was shown with

three standard test frameworks considering different pos-

sibilities and nonlinearities like piecewise linear sloping

model. The calculation of direct inclining expense of the

independent power producer represents ramping cost of the

power producer when subjected to line contingency,

wheeling exchanges and distinctive load request in dereg-

ulated conditions. From the correlation of re-enactment

comes about with Lambda-iteration, Linear programming,

Evolutionary programming, PSO and FDRPSO, it is

obvious that the meta-heuristics calculations of FFA and

GWO show the distributed artificial intelligence which

demonstrates the prevalence of the proposed technique are

taking care of the independent power producer issue in

deregulated conditions. These proposed techniques give

plausible financial solutions for control utilities when

subjected to the vulnerable circumstance in deregulated

control market and power ventures.

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K. Kathiravan received B.E.

degree in Electrical & Elec-

tronics Engineering from

Odaiyappa college of Engineer-

ing and Technology, Theni,

India in 2006, M.E. (Power

Systems Engg) from Anna uni-

versity Trichy in 2011. He is

currently pursuing his Ph.D.

degree in the faculty of Electri-

cal Engineering, Anna Univer-

sity Chennai, He is working as a

Senior Assistant Professor

Electrical & Electronics Engi-

neering at Theni kammavar

sangam college of Technology, Theni. since 2012. He has Teaching

Experience of 11 years and 5 months. His areas of interest include

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Power system optimization, Artificial intelligence, Circuit theory and

electrical machines.

N. Rathina Prabha received her

B.E. (EEE) and M.E. (Power

System Engg.) degrees from

Thiagarajar College of Engi-

neering, Madurai, India. She is

presently working as an Asso-

ciate Professor at Mepco Sch-

lenk Engineering College,

Sivakasi, India. Her areas of

interest include power quality,

power system control and elec-

trical machines.

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