a practical algorithm for optimal operation management of distribution network including fuel cell...

8/6/2019 A Practical Algorithm for Optimal Operation Management of Distribution Network Including Fuel Cell Power Plants

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A practical algorithm for optimal operation management of distribution

network including fuel cell power plants

Taher Niknam*, Hamed Zeinoddini Meymand, Majid Nayeripour

Electrical and Electronic Engineering Department, Shiraz University of Technology, Shiraz, Iran

a r t i c l e i n f o

Article history:

Received 16 July 2009

Accepted 31 December 2009

Available online 25 January 2010

Keywords:

Fuel cell power plant (FCPP)

Optimal operation management (OOM)

Fuzzy adaptive particle swarm optimization

(FAPSO)

a b s t r a c t

Fuel cell power plants (FCPPs) have been taken into a great deal of consideration in recent years. Thecontinuing growth of the power demand together with environmental constraints is increasing interest

to use FCPPs in power system. Since FCPPs are usually connected to distribution network, the effect of

FCPPs on distribution network is more than other sections of power system. One of the most important

issues in distribution networks is optimal operation management (OOM) which can be affected by FCPPs.

This paper proposes a new approach for optimal operation management of distribution networks

including FCCPs. In the article, we consider the total electrical energy losses, the total electrical energy

cost and the total emission as the objective functions which should be minimized. Whereas the optimal

operation in distribution networks has a nonlinear mixed integer optimization problem, the optimal

solution could be obtained through an evolutionary method. We use a new evolutionary algorithm based

on Fuzzy Adaptive Particle Swarm Optimization (FAPSO) to solve the optimal operation problem and

compare this method with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential

Evolution (DE), Ant Colony Optimization (ACO) and Tabu Search (TS) over two distribution test feeders.

2010 Elsevier Ltd. All rights reserved.

1. Introduction

Nowadays, the traditional centralized power generation is

slowly changing to a new paradigm, driven by environmental

considerations and flexibility of the topology. This new generation

model is known as distributed generation. It is characterized by

small generation size, proximity to the loads, its connection to

distribution networks, and renewability of the generating equip-

ment in most cases.The main task of the generating equipment is to

provide the active power required by the loads. It can also be

utilized for voltage regulation and power quality enhancement,

which improves the flexibility of the generating systems. The

proper distribution of different technologies in the network

reduces losses and increases the reliability and efficiency of theelectric system. In addition to traditional generating equipments

such as diesel or gas engines, new technologies such as micro

turbines or fuel cells have appeared [15]. These systems are highly

efficient for low power generation. FC power plants are one of the

most promising technologies for clean electricity generation, which

are very efficient even at partial load. They are also suitable for

domestic generation because of their lownoise and static operation

[15].

Fuel cells may work either apart from or connected to the

distribution network. Because of the voltage drop in distant points

of the network, there is a need to regenerate voltage profile and

improve the amount of voltage near the consuming centers.

Therefore, one of the purposes of using fuel cells is to improve the

voltage amount. Adjoining the FCPPs with consumers directly

reduces the transmission costs on one hand and the percentage of

the network losses on the other hand [15]. In situations that the

power required through the network is much and the network

cannot supply the power completely, it is possible to provide some

of the power from the fuel cells. It is also possible to supply

sensitive loads through this technology.Having low emission is a great advantage of FCPPs that forces

system operator to use them. So fuel cells are attractive because

they are environment friendly [15].

The most significant advantages of FCPPs are: high output, low

pollution, consistent with the place, high reliability and variety of

used fuels [15].

Studies performed by researching centers show that FCPPs

contribution in energy production will become more than 25% in

near future [6]. Therefore, it is necessary to study the effect of

FCPPs on the power systems, especially on the distribution

networks.* Corresponding author. Tel.: 98 711 7264121; fax: 98 711 7353502.

E-mail addresses: [email protected] , [email protected] (T. Niknam).

Contents lists available at ScienceDirect

Renewable Energy

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / r e n e n e

0960-1481/$ see front matter 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.renene.2009.12.019

Renewable Energy 35 (2010) 16961714
mailto:[email protected]:[email protected]:[email protected]://www.sciencedirect.com/science/journal/09601481http://www.elsevier.com/locate/renenehttp://www.elsevier.com/locate/renenehttp://www.sciencedirect.com/science/journal/09601481mailto:[email protected]:[email protected]


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Since the X/R ratio of distribution lines is small and the

configuration of distribution network is radial, OOM is one of the

most important schemes in the distribution networks, which can

be affected by FCPPs. X and R are reactance and resistance of

transmission line, respectively. In general view, optimal operation

management in power systems refers to the optimal use of all

equipments for generation and control of active and reactive

powers that have the lowest cost and meet the physical and tech-

nical constraints.

An optimal operation management in distribution networkswith regard to FCPPs is the main purpose of this article. The

objective functions include the total electrical energy losses, the

total cost of electrical energy generated by FCPPs and substation

bus and the total emission of FCPPs and substation bus that use in

this problem for performing optimization.

Several researches have been worked on optimal operation of

the distribution network at the topic of Volt/Var control. For

instance, in [7] a supervisory Volt/Var control scheme, based on the

new measurements and computer resources which were available

at the substation bus was presented. They acquired the new

measurements based on this fact that the voltage drop on the

feeder varies linearly with the total feederload current measured at

the substation. In [8] a centralized Volt/Var control algorithm for

the distribution system management was presented. They

considered summation of power losses and power demands as the

objective function. The supervisory control systems for integrated

Volt/Var control at the substation and feeders were presented in

[9]. The supervisory controller, placed at substation, coordinates

the control of local regulating devices based on dynamically

changing system conditions. In [10] and [11] an approach for

modeling local controllers and coordinating the local and central-

ized controllers at the distribution system management was pre-

sented. A heuristic and algorithmic combined technique for

reactive power optimization with time varying load demand indistribution systems was presented in [12]. Volt/Var control in

distribution systems using a time-interval was described in [13].

The aim is to determine optimum dispatch schemes for on-load tap

changer (OLTC) settings at substations and all shunt capacitors

switching based on the day-ahead load forecast. A genetic algo-

rithm based procedure is used to determine both the load level

partitioning and the dispatch scheduling. In [14] an improved

evolutionary programming and its hybrid version combined with

the nonlinear interior point technique to solve the optimal reactive

power dispatch problems was proposed. T.Niknam et al. presented

methods for the Volt/Var control in radial distribution networks

considering Distributed Generations [1518]. They considered

electrical power losses as the objective function and used the

genetic algorithm and hybrid ACO evolutionary algorithm for

Nomenclature

X State variables vector including active power of FCPPs

Ng Number of FCPPs.

Nd Number of load variation steps

Nb Number of branches

Ri Resistance of ith branch

Ii Current of ith branch

PG Active power of all FCPPs during the day

Pgi Active power of the ith FCPP during the day

n Number of state variables

hj Electrical efficiency of jth FC

PLRtj Part load ratio of jth FC for the tth load level step

Psubt Power generated at substation bus of distribution

feeders for the tth load level step

CFCt Cost of electrical energy generated by FCPPs for the tth

load level step

Csubstationt Cost of power generated at substation bus for the tth

load level step

pricet Energy price for the tth load level step

EtFC Emission of FCPP for the tth load level step

EtGrid Emission of large scale sources (substation bus thatconnects to grid) for the tth load level step

NOxtFC Nitrogen oxide pollutants of FCPP for the tth load level

step

SO2tFC Sulphur oxide pollutants of FCPP for the tth load level

step

NOxtGrid Nitrogen oxide pollutants of grid for the tth load level

step

SO2tGrid Sulphur oxide pollutants of grid for the tth load level

step

Ptgi Active power of the ith FCPP for the tth load level step

Pmin,FC Minimum active power of the ith FCPP

Pmax,FC Maximum active power of the ith FCPP

jPLineij j Absolute power flowing over distribution lines

PLineij;max Maximum transmission power between the nodes iand j.

Tapmini Minimum tap positions of the ith transformer

Tapmaxi Maximum tap positions of the ith transformer

Tapti Current tap positions of the ith transformer during

time t

Pfmin Minimum power factor at substation bus

Pfmax Maximum power factor at substation bus

Pft Current power factor at substation bus during time t

Vit Voltage magnitude of the ith bus during time t

Vmax Maximum value of voltage magnitudes of the ith bus.

Vmin Minimum value of voltage magnitudes of the ith bus.

Vi Magnitude of voltage at ith bus

di Angle of voltage at ith bus

Pg Active power of FCPP

Qg Reactive power of FCPP

PLoad Active power for load

QLoad Reactive power for load

RjX Line impedance

t Current iteration number.

u Inertia weight

c1 and c2 Weighting factors of the stochastic acceleration terms,

which pull each particle towards thePbesti and

Gbestpositions.rand1($) Random function in the range of [0,1]

rand2($) Random function in the range of [0,1]

Pbesti Best previous experience of the ith particle that is

recorded

Gbest Best particle among the entire population

NSwarm Number of the swarms

fX Objective function values of OOM problem

Neq Number of equality constraints of the OOM problem

Nueq Number of inequality constraints of the OOM problem

hjX Equality constraints

gjX Inequality constraints

k1 Penalty factor

k2 Penalty factor

vi Velocity of the ith state variablexi Position of the ith state variable

T. Niknam et al. / Renewable Energy 35 (2010) 16961714 1697


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minimizing the objective function. Also they have not considered

the impact of active power of DGs on the Volt/Var control problem.

Due to Equipments existing in distribution systems, such as

Static Var Compensators (SVCs), FCPPs, Load Tap Changers (LTCs)and Voltage regulators (VRs), the OOM problem is modeled as

a mixed integer nonlinear programming problem. Evolutionary

methods because of independence on the type of objective function

and constraints can be used for solving this problem.

Recently researchers have presented new evolutionary methods

such as Particle Swarm Optimization (PSO) which is a new evolu-

tionary computation technique.

Studies confirm that the PSO should be taken into account as

a powerful technique, which is efficient enough to manage various

kinds of nonlinear optimization problems. Nevertheless, it is

strongly depends on the parameters (learning factors and inertia

weight) and the function being optimized. It is probably impossible

to find a unique set of parameters that work well in all situations.

In this paper, a new evolutionary optimization method, called

Fuzzy Adaptive Particle Swarm Optimization has been proposed to

solve the OOM problem.

The rest of this paper is organized as follows. In Section 2,

mathematical formulation of proposed Optimal Operation

Management problem is described. FCPP is modeled in section 3.

The effect of FCPPs on the voltage profile of distribution networks is

presented in section 4. In sections 5 and 6, Particle Swarm Opti-

mization and Fuzzy Adaptive PSO are described respectively. In

section 7 application of FAPSO in OOMproblem is presented. Finally

in section 8 the feasibility of the proposed approach is demon-

strated and compared with methods based on particle swarm

optimization, Tabu Search, differential evolution and genetic algo-

rithm for two examples distribution network.

2. Optimal operation management of distribution networks

with regard to FCPPs

The objective function of OOM problem comprises three

important parts, which are:

2.1. Electrical energy losses of distribution network in the

presence of FCPPs

min f1X PNd

t1PtLoss

PNdt1

PNbi1

Ri jIti j2

X

PG

1n

PG h

Pg1; Pg2;.; PgNg

iPgi

hP1gi; P

2gi;.; P

Ndgi

i; i 1;2; 3;.;Ng

n Nd Ng (1)

2.2. Summation of costs of electrical energy generate by FCCPs

and power of substation bus

min f2X PNd

t1

Costt PNd

t1CtFC C

tsubstation

CtFC 0:04$=KWh

PNgj1

Ptgj

hj

PLRtj Pt

gj

PmaxjFor PLRj < 0:050hj 0:2716

For PLRj ! 0:050hj 0:9033PLR5

j 2:9996PLR4

j

3:6503PLR3j 2:0704PLR2

j0:3747

Ctsubstation pricet Ptsub (2)

R+jX

V1 1

P+jQI

V2 2

Fig. 2. a 2-bus test system. Fig. 3. Concept of a searching by PSO.

Fig. 1. Models of FC power plants (a). PQ Model with simultaneous three-phase control. (b). PQ Model with independent three-phase control. (c). PV Model with simultaneous

three-phase control. (d). PV Model with independent three-phase control.

T. Niknam et al. / Renewable Energy 35 (2010) 169617141698


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In [19] the authors introduced a cost model for the FCPP oper-

ating strategy.

2.3. Summation of FCPPs and substation bus emissions

min f3X PNd

t1

Emissiont PNd

t1

EtFC E

tGrid

EtFC NOx

tFC SO2

tFC 0:03 0:006

lb=MWhPNg

j1

Ptgj

Et

Grid

NOxt

Grid

SO2t

Grid

5:06 7:9lb=MWhPt

sub

(3)

2.4. Constraints

Constraints are defined as follows:

Active power constraints of FCPPs:

Ptmin;FC Ptgi P

tmax;FC (4)

Distribution line limits:

jPLineij jt< PLineij;max (5)

jPLineij jt and PLineij;max are the absolute power flowing over distributionlines and maximum transmission power between the nodes i and j,

respectively.

Tap of transformers:

Tapmini < Tapti < Tap

maxi (6)

Tapmini , Tapmaxi and Tapi are the minimum, maximum and current

tap positions of the ith transformer, respectively.

Unbalanced three-phase power flow equations.

Substation power factor

Pfmin Pft Pfmax (7)

Pfmin, Pfmax and Pft are the minimum, maximum and current power

factor at the substation bus during time t.

Bus voltage magnitude

Vmin Vti Vmax (8)

3. Fuel cell power plant modeling

The demand for power generation systems of high efficiency

with low emission is increasing. Recently, the fuel cell has

attracted worldwide attention as a clean energy technology.

FCPPs are highly efficient electric energy systems because of

their ability of directly converting the chemical energy of the

fuel to electric energy. They are usually connected to the

distribution network close to the loads. Therefore, they can

increase the power quality and reliability from the customers

perspective. They can also help the utilities to face the load

growth while delaying the upgrade of distribution/transmission

lines [15].

Generally, FCPPs in distribution load flow can be modeled usingPV or PQ models. Since distribution networks are unbalanced

three-phase systems, FCPPs can be controlled and operated in two

forms:

Simultaneous three-phase control

Independent three-phase control or single-phase control

Regarding the control methods and FCPP models, four different

models can be used for simulation of these generators:

Fig. 4. First Membership functions of inputs and outputs.

Fig. 5. Second Membership functions of inputs and outputs.



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PQ model with simultaneous three-phase control (Fig. 1.a)

PV model with simultaneous three-phase control (Fig. 1.c)

PQ model with independent three-phase control (Fig. 1.b)

PV model with independent three-phase control (Fig. 1.d)

It must be taken into account that when FCPPs are considered as

the PV models, they should be able to generate reactive power to

maintain their voltage magnitudes. Many researchers have pre-

sented several procedures to model generators connected to

distribution networks as the PV buses [2022]. Fig.1 shows a model

of the FC power plants based on the type of their control. In this

paper, the FCPPs are modeled as the PQ model with simultaneous

three-phase control (Fig. 1.a).

4. The effect of FCPPs on voltage profile of distribution

network

Connecting a FCPP to the distribution network will affect the

flow of power and the voltage profiles. Since the X/R ratio of the

distribution lines is small, the FCPP has much impact on voltage

profiles. To explain this, consider a 2-bus test system (Fig. 2).

The voltage drop along the line from bus 1 to bus 2 is calculated

as follows:

DV V1:d1 V2:d2 R jXI

I PjQ

V*2P Pg PLoad

Q Qg QLoad

jDVj2 RPXQ2XP RQ2

V22z

RPXQ2

V22

(9)

As it was shown in the above equation, RPandXQare not negligible.

Also, since the X/R ratio is small and Q is less than P, the effect of

FCPPs active power has much more than their reactive power.

5. Particle swarm optimization (PSO) algorithm

PSO is a population-based stochastic search technique. It was

first introduced by Kennedy and Eberhart [23]. Since then, it has

been greatly used to solve a wide range of optimization problems

[2428]. The algorithm was presented as simulating animals social

activities, e.g. insects, birds, etc. It attempts to imitate the natural

process of group communication to share individual knowledge

when such swarms flock, migrate, or hunt. If one member sees

a desirable path to go, the rest of this swarm will follow it rapidly.In

PSO, this behavior of animals is imitated by particles with certain

positions and velocities in a searching space, wherein the pop-

ulation is called a swarm, and each member of the swarm is called

a particle. Starting with a randomly initialized population, each

particle in PSO flies through the searching space and remembers

the best position it has seen. Members of a swarm communicate

good positions to each other and dynamically adjust their own

position and velocity based on these good positions. The velocity

adjustment is based upon the historical behaviors of the particles

themselves as well as their neighbors. In thisway, the particles tend

to fly towards better and better searching areas over the searching

process. Mathematically the particles are operated according to the

following equation:

Vt1i

u$Vti

c1$rand1$$

Pbesti Xti

c2$rand2$$

Gbest X

ti

(10)

Xt1i X

ti V

t1i

(11)

The Eq. (10) is used to calculate the ith particles velocity by

consideration of three terms: the particles previous velocity, the

distance between the particles best previous and current positions,

and finally, the distance between the position of the best particle in

the swarm and the ith particles current position.

Fig. 3 represents a graphical depiction of the basic idea of the

particle swarm optimizer.

6. Fuzzy adaptive PSO (FAPSO)

There are three tuning parametersu, c1and c2as shown in Eq.

(10) that greatly affects the algorithm performance, often stated as

the exploration-exploitation tradeoff. Exploration is the ability to

test various regions in the problem space in order to locate a good

optimum, hopefully the global one. Exploitation is the ability to

concentrate the search on a promising candidate solution in order

to locate the optimum accurately.

The inertia weight u is used to control the impactof the previous

history of velocities on the current velocity. A larger inertia weight

u facilitates global exploration while a smaller inertia weight leads

to facilitate local exploration to fine-tune the current search area.

Suitable selection of the inertia weight u can prepare a balance

between global and local exploration abilities, thus require less

iterations on average to find the optimum. The linearly decreasing

u-strategy [29] is a kind of setting for many problems. It allows the

swarm to explore the search-space in the beginning of the run, and

still manages to move towards a local search when fine-tuning is

needed.

The learning factors c1and c2determine the effect of personal

best Pbesti and global best Gbest, respectively as shown in Eq. (10).

Since c1 expresses how much the particle trusts its own pastexperience, it is called cognitive parameter. While c2expresses how

much it trusts the swarm, it is called social parameter. If c1 >> c2,

the particle will be much more drawn towards the best position

found by itself Pbesti , rather than the best position found by the

population (or the neighborhood) Gbest, and vice versa. Most

Table 1

Fuzzy rules for learning factor c1.

c1 NU

PS PM PB PR

NBF PS PR PB PB PM

PM PB PM PM PS

PB PB PM PS PS

PR PM PM PS PS

Table 2

Fuzzy rules for learning factor c2.

c2 NU

PS PM PB PR

NBF PS PR PB PM PM

PM PB PM PS PS

PB PM PM PS PS

PR PM PS PS PS

Table 3

Fuzzy rules for inertia weight correction Du.

Du u

S M L

NBF S ZE NE NE

M PE ZE NE

L PE ZE NE



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implementations use a setting withc1 c2 2, which meanseach particle will be attracted to the average of Pbesti and Gbest.

Recent work reports that it might be even better to choose a larger

cognitive parameter c1than a social parameterc2, but with

c1 c2 4.

In addition to the parameters discussed above, results of PSO are

influenced by the number of particles, the swarm size N, in the

swarm. Too few particles will cause the algorithm to become

trapped in a local minimum, while too many particles will slow

down the algorithm. The best tradeoff between exploration and

exploitation strongly depends on the parameters and the functions

being optimized. It is probably impossible to find a specific set of

parameters that work well in all cases but the following fuzzy

adaptive PSO (FAPSO) algorithm, based on a fuzzy system, has been

found to work in practice.

From experience, it is known that (i) when the best fitness is lowat the end of the run, e.g., in the optimization of a minimum

function, low inertia weight and high learning factors are often

preferred; (ii) when the best fitness is stuck at one value for a long

time, number of generations for unchangedbest fitness is large.The

system is often stuck at a local minimum, so the system should

concentrate on exploiting rather than exploring. That is, the inertia

weight should be increased and learning factors should be

decreased.

Based on this kind of knowledge, a fuzzy system is developed to

adjust the inertia weight and learning factors with inputs and

outputs.In this paper twokinds of membership functionsfor inputs

and outputs are used to implement the proposed algorithm.

In first membership function, best fitness (BF) and number of

generations for unchanged best fitness (NU) are as the input

Fig. 6. Flowchart of the FAPSO algorithm.



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Fig. 7. Daily energy price and load variations.

Fig. 8. Distribution system of Taiwan Power Company with original configuration.



8/19

variables, and learning factors (c1andc2) are as output variables. In

other membership function, best fitness (BF) and the inertia weight

(u) are as the input variables and the inertia weight correction (Du)

is as output value.

Table 4

Three-phase load and line data of test feeder.

Bus to bus Section

resistance (U)

Section

reactance (U)

End bus

real load (kW)

End bus reactive

load (kVAr)

A-1 0.1944 0.6624 0 0

12 0.2096 0.4304 100 50

23 0.2358 0.4842 300 200

34 0.0917 0.1883 350 250

45 0.2096 0.4304 220 10056 0.0393 0.0807 1100 800

67 0.0405 0.1380 400 320

78 0.1048 0.2152 300 200

79 0.2358 0.4842 300 230

710 0.1048 0.2152 300 260

B-11 0.0786 0.1614 0 0

1112 0.3406 0.6944 1200 800

1213 0.0262 0.0538 800 600

1214 0.0786 0.1614 700 500

C-15 0.1134 0.3864 0 0

1516 0.0524 0.1076 300 150

1617 0.0524 0.1076 500 350

1718 0.1572 0.3228 700 400

1819 0.0393 0.0807 1200 1000

1920 0.1703 0.3497 300 300

2021 0.2358 0.4842 400 350

2122 0.1572 0.3228 50 20

2123 0.1965 0.4035 50 20

2324 0.1310 0.2690 50 10

D-25 0.0567 0.1932 50 30

2526 0.1048 0.2152 100 60

2627 0.2489 0.5111 100 70

2728 0.0486 0.1656 1800 1300

2829 0.1310 0.2690 200 120

E30 0.1965 0.3960 0 0

3031 0.1310 0.2690 1800 1600

3132 0.1310 0.2690 200 150

3233 0.0262 0.0538 200 100

3334 0.1703 0.3497 800 600

3435 0.0524 0.1076 100 60

3536 0.4978 1.0222 100 60

3637 0.0393 0.0807 20 10

3738 0.0393 0.0807 20 10

3839 0.0786 0.1614 20 10

3940 0.2096 0.4304 20 103841 0.1965 0.4035 200 160

4142 0.2096 0.4304 50 30

F-43 0.0486 0.1656 0 0

4344 0.0393 0.0807 30 20

4445 0.1310 0.2690 800 700

4546 0.2358 0.4842 200 150

G-47 0.2430 0.8280 0 0

4748 0.0655 0.1345 0 0

4849 0.0655 0.1345 0 0

4950 0.0393 0.0807 200 160

5051 0.0786 0.1614 800 600

5152 0.0393 0.0807 500 300

5253 0.0786 0.1614 500 350

5354 0.0524 0.1076 500 300

5455 0.1310 0.2690 200 80

H-56 0.2268 0.7728 0 0

5657 0.5371 1.1029 30 205758 0.0524 0.1076 600 420

5859 0.0405 0.1380 0 0

5960 0.0393 0.0807 20 10

6061 0.0262 0.0538 20 10

6162 0.1048 0.2152 200 130

6263 0.2358 0.4842 300 240

6364 0.0243 0.0828 300 200

I-65 0.0486 0.1656 0 0

6566 0.1703 0.3497 50 30

6667 0.1215 0.4140 0 0

6768 0.2187 0.7452 400 360

6869 0.0486 0.1656 0 0

6970 0.0729 0.2484 0 0

7071 0.0567 0.1932 2000 1500

7172 0.0262 0.0528 200 150

J-73 0.3240 1.1040 0 0

7374 0.0324 0.1104 0 0

Table 4 (continued)

Bus to bus Section

resistance (U)

Section

reactance (U)

End bus

real load (kW)

End bus reactive

load (kVAr)

7475 0.0567 0.1932 1200 950

7576 0.0486 0.1656 300 180

K-77 0.2511 0.8556 0 0

7778 0.1296 0.4416 400 360

7879 0.0486 0.1656 2000 1300

7980 0.1310 0.2640 200 1408081 0.1310 0.2640 500 360

8182 0.0917 0.1883 100 30

8283 0.3144 0.6456 400 360

555 0.1310 0.2690

760 0.1310 0.2690

1143 0.1310 0.2690

1272 0.3406 0.6994

1376 0.4585 0.9415

1418 0.5371 1.0824

1626 0.0917 0.1883

2083 0.0786 0.1614

2832 0.0524 0.1076

2939 0.0786 0.1614

3446 0.0262 0.0538

4042 0.1965 0.4035

5364 0.0393 0.0807

Table 5

Comparison of average and standard deviation for 20 trails (first objective

functionPLoss).

Method Average

(kWh)

Standard deviation

(kWh)

Worst solution

(kWh)

Best solution

(kWh)

FAPSO 8445.46 0 8445.46 8445.46

PSO 9077.63 356.08 9705.40 8445.46

ACO 8943.67 451.68 9234.92 8445.46

TS 9001.92 567.902 9713.72 8445.46

DE 8763.82 301.15 9103.28 8445.46

GA 9153.98 759.37 9835.34 8445.46

Table 6

Comparison of average and standard deviation for 20 trails (second objective

function Cost).

Method Average

($)

Standard deviation

($)

Worst solution

($)

Best solution

($)

FAPSO 35 683.44 0 35 683.44 35 683.44

PSO 37 365.25 1016.50 39 568.13 35 683.44

ACO 36 566.33 1508.31 38 573.57 35 683.44

TS 37 863.88 1923.83 39 982.38 35 683.44

DE 36 452.28 1206.97 38 527.92 35 683.44

GA 38 600.83 2563.12 40 128.17 35 683.44

Table 7

Comparison of average and standard deviation for 20 trails (third objective functionEmission).

Method Average

(lb)

Standard deviation

(lb)

Worst solution

(lb)

Best solution

(lb)

FAPSO 6658.36 0 6658.36 6658.36

PSO 7057.48 143.60 7329.34 6742.17

ACO 6889.37 140.38 7103.72 6658.36

TS 7109.82 300.38 7421.91 6658.36

DE 6823.73 145.39 7001.98 6658.36

GA 7130.26 325.67 7495.59 6658.36



9/19

Both positive and negative corrections are required for the

inertia weight. Therefore, a range of1.0 to 1.0 has been preferred

for the inertia weight correction.

uk1 uk Du (12)

The BF measures the performance of the best candidate solution

found so far. Different optimization problems have different ranges

of BF value. To design a FAPSO applicable to a wide range of prob-

lems, the ranges of BF and NU are normalized into [0,1]. One

example of converting BF to be a normalized BF format (NBF) is

shown in (13):

NBF BF BFmin=BFmax BFmin (13)

Where BFmin and BFmax are the estimated or real minimum fitness

value and the fitness value greater or equal to maximum fitness

value which is not an acceptable solution for optimization problem

respectively. NUmay be converted into [0,1] in similar way. Other

converting methods are possible, of course. The values for u, c1and

c2are bounded in0:4 u 1, 1 c1 2 and 1 c2 2

The fuzzy system consists of four principal components: fuzzi-

fication, fuzzy rules, fuzzy reasoning and defuzzification, which are

described as following.

6.1. Fuzzification

Among a set of membership functions, triangular membership

functions are used forevery input andoutput as illustrated in Figs. 4

and 5.For the first membership function PS (positive small), PM

(positive medium), PB (positive big) and PR (positive bigger) are the

linguist variables for the inputs (NBF, NU) and outputs (c1; c2). Also

for the second membership function S (Small), M (Medium), L

10 20 30 40 50 60 70 80 90 1006600

6800

7000

7200

7400

7600

7800

X: 14

Y: 6658

Iteration

10 20 30 40 50 60 70 80 90 100

Iteration

Emissionobjectivefunction(lb)

FAPSO

6600

6800

7000

7200

7400

7600

7800

X: 39

Y: 6742

Emissionobjectivefunction(lb)

PSO

Fig. 9. Convergence characteristics of the FAPSO and PSO algorithms for best solution ( Emission).

10 20 30 40 50 60 70 80 90 100

3.6

3.7

3.8

3.9

4

X: 12

Y: 3.568e+004

Iteration

10 20 30 40 50 60 70 80 90 100

Iteration

Co

stobjectivefunction($)

FAPSO

3.6

3.8

4

4.2

x 104

x 104

X: 24

Y: 3.568e+004

Costobjectivefunction($)

PSO

Fig. 10. Convergence characteristics of the FAPSO and PSO algorithms for best solution ( Cost).



10/19

(Large) are three linguist values for inputs (NBF,u) and NE (Nega-

tive), ZE (Zero), PE (Positive) are the linguist values for output of

inertia weight correction (Du).

6.2. Fuzzy rules

The Mamdani-type fuzzy rule is used to formulate the

conditional statements. For example for the first membership

function:IF (NBF is PB) and (NU is PM), THEN (c1 is PM) and (c2 is

PM)

and for the second membership functionIF (NBF is S) and (u is

M), THEN (Du is NE)

The fuzzy rules in Tables 13 are used to adjust learning

factors (c1andc2) and inertia weight correction (Du), respectively.Each rule represents a mapping from the input space to output

space.

6.3. Fuzzy reasoning

The fuzzy control strategy is used to map from the given inputs

to the outputs. Mamdanis fuzzy inference method is used in this

paper. The AND operator is typically used to combine the

membership values for each fired rule to generate the membership

values for the fuzzy sets of output values in the consequent part of

the rule. Since there may be several rules fired in the rule sets, for

some fuzzy sets of the output variables there may be different

membership values get from different fired rules. These output

fuzzy sets are then aggregated into a single output fuzzy set by OR

operator. That is to take the maximum value as the membership

value of that fuzzy set.

To obtain a deterministic control action, a defuzzificationstrategy is required. It will be illustrated at a later point.

10 20 30 40 50 60 70 80 90 100

8500

9000

9500

10000

10500

11000

X: 10

Y: 8445

Iteration

10 20 30 40 50 60 70 80 90 100

Iteration

P

Loss

objectivefunction(kWh)

FAPSO

8500

9000

9500

10000

10500

11000

X: 40

Y: 8445

PLoss


PSO

Fig. 11. Convergence characteristics of the FAPSO and PSO algorithms for best solution ( PLoss).

2 4 6 8 10 12 14 16 18 20 22 24

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

Vbus

#7

Voltages # Emission

2 4 6 8 10 12 14 16 18 20 22 24

0.96

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

Vbus

#29

Voltages # Emission

2 4 6 8 10 12 14 16 18 20 22 240.9

0.92

0.94

0.96

0.98

1

Vbus

#72

Time (h) Time (h)

2 4 6 8 10 12 14 16 18 20 22 240.9

0.92

0.94

0.96

0.98

1

Vbus

#82

with FC

without FC

Fig. 12. Variation of voltages in some buses with Emission objective function.



11/19

6.4. Defuzzification

For defuzzification, the method of centroid (center-of-sums) is

used as shown in Eq. (14). Defuzzified value is directly acceptable

values of PSO parameters, for example: Output1 y1

learning factorc1 ;y1 1:8 represents the valueof learning factor:

y

Zy

Xni1

y$mBiydy=

Zy

Xni1

mBiydy (14)

Concisely, the fuzzy system is an effective tool to represent andutilize human knowledge that is too complex for mathematical

approaches. The contribution of the proposed algorithm lies in the

fact that the determination of the heuristic parameters is assigned

to the fuzzy system, in contrast with the previous common practice

of running numerous experiments.

7. Implementation of FAPSO to OOM problem

This section presents the application of proposed algorithm to

solve the OOM problem. It should be noted that state variables are

active power of FCPPs. To apply the FAPSO algorithm to solve the

OOM problem, the following steps should be taken and repeated.

2 4 6 8 10 12 14 16 18 20 22 240.86

0.88

0.9

0.92

0.94

0.96

0.98

1

Vbus

#7

Voltages # Cost

2 4 6 8 10 12 14 16 18 20 22 240.96

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

Vbus

#29

Voltages # Cost

2 4 6 8 10 12 14 16 18 20 22 240.9

0.92

0.94

0.96

0.98

1

Vbus

#72

Time (h)

2 4 6 8 10 12 14 16 18 20 22 240.9

0.92

0.94

0.96

0.98

1

Vbus

#82

Time (h)

with FC

without FC

Fig. 13. Variation of voltages in some buses with Costobjective function.

2 4 6 8 10 12 14 16 18 20 22 240.86

0.88

0.9

0.92

0.94

0.96

0.98

1

Vbus

#7

Voltages # PLoss

2 4 6 8 10 12 14 16 18 20 22 240.96

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

Vbus

#29

Voltages # PLoss

2 4 6 8 10 12 14 16 18 20 22 240.9

0.92

0.94

0.96

0.98

1

Vbus

#72

Time (h)2 4 6 8 10 12 14 16 18 20 22 24

0.9

0.92

0.94

0.96

0.98

1

Vbus

#82

Time (h)

with FC

without FC

Fig. 14. Variation of voltages in some buses with PLoss objective function.



12/19


13/19

2 4 6 8 10 12 14 16 18 20 22 24

0

500

1000

1500

2000

Time (h)

Losses(kW)#PLoss without FC

2 4 6 8 10 12 14 16 18 20 22 24

0

200

400

600

800

1000

Losses(kW)#PLoss with FC

Time (h)

Fig. 17. Daily variation of active power losses (PLoss objective function).

Fig. 18. Distribution system of Taiwan Power Company after reconfiguration.

Table 9

Comparison of average and standard deviation for 20 trails (first objective function

PLoss).

Method Average

(kWh)

Standard deviation

(kWh)

Worst solution

(kWh)

Best solution

(kWh)

FAPSO 7438.02 0 7438.02 7438.02

PSO 8188.16 295.94 8611.04 7438.02

ACO 7893.64 400.38 8210.32 7438.02

TS 7996.17 550.38 8729.68 7438.02

DE 7802.33 350.67 8123.97 7438.02

GA 8001.61 563.91 8739.82 7438.02

Table 10

Comparison of average and standard deviation for 20 trails (second objective

function Cost).

Method Average

($)

Standard deviation

($)

Worst solution

($)

Best solution

($)

FAPSO 35 568.94 0 35 568.94 35 568.94

PSO 36 961.25 923.44 38 167.62 35 568.94

ACO 36 720.39 1000.58 37 293.83 35 568.94

TS 37 529.08 1892.39 38 923.72 35 568.94

DE 36 683.01 750.96 37 100.83 35 568.94

GA 37 680.98 1800.39 38 992.97 35 568.94



14/19

function incorporating penalty factors for any value violating the

constraints:

FXfXk1

PNeqj1

hjX

!2k2

PNueqj1

max

0;gjX

!2

hjX0;j1;2;3;.;Neq

gjX


15/19

population of swarms and then goes back to step 4. The last Gbestis

the solution of the problem.

The flowchart of the proposed algorithm is shown in Fig. 6.

8. Simulation results

In this part, the OOM problem in distribution networks

considering FCPPs is tested on two distribution systems. In both of

the two cases, it is assumed that daily energy price variations and

daily load variations are changed as shown in Fig. 7.

8.1. Practical distribution network of TPC before reconfiguration

The first example is a practical distribution network that is

shown in Fig. 8 and the relating data is shown in Table 4. It is

a three-phase, 11.4 kV system. It is also considered that a distribu-

tion company (Disco) operates this network and supplies the

demand power in its feeding substation via 11 feeders

A,B,C,D,E,F,G,H,I,J,K [30].

It is assumed that 34 FCPPs arelocated in this network. There are

three FCPPs at buses 6, 12, 19, 28, 31, 51, 71, 79 and two FCPPs at

buses 58, 75 and a FCPP at buses 8, 14, 24, 42, 45, 83 that each of

these sources can generate 250 kW active power.

Tables 5, 6, 7 present a comparison among the results of FAPSO,

PSO, ACO, TS, DE and GA algorithms for 20 random tails for three

objective functions. Figs. 9, 10, 11 depict the convergence charac-

teristic of the FAPSO and PSO algorithms for the best solution for

three objective functions. The voltage changes of some buses are

shown in Figs. 1214.

In Tables 5, 6, 7 the smallest and the largest values of the

minimized objective function are referred to as the Best Solution

and the Worst Solution, respectively. Comparison of the best and

worst solutions of the proposed optimization algorithm with the

corresponding those of the other methods confirms the effective-

ness of the proposed method. In addition to the best and worst

10 20 30 40 50 60 70 80 90 1003.5

3.6

3.7

3.8

3.9

4

4.1x 10

4

X: 13

Y: 3.557e+004

Iteration

10 20 30 40 50 60 70 80 90 100

Iteration


FAPSO

3.5

3.6

3.7

3.8

3.9

4

4.1

4.2x 10

4

X: 27

Y: 3.557e+004


PSO

Fig. 20. Convergence characteristics of the FAPSO and PSO algorithms for best solution ( Cost).

10 20 30 40 50 60 70 80 90 100

7500

8000

8500

9000

9500

10000

X: 13

Y: 7438

Iteration

10 20 30 40 50 60 70 80 90 100

Iteration

PLoss


FAPSO

7500

8000

8500

9000

9500

X: 28

Y: 7438

PLoss


PS O

Fig. 21. Convergence characteristics of the FAPSO and PSO algorithms for best solution ( PLoss).



16/19

solutions, these tables provides the standard deviation and average

value of the objective function (minimized) value, based on the

proposed method and the other ones. It can be noticed from these

tables that the foregoing variables assume considerably smaller

values under the proposed algorithm than the other methods.

It can be seen from Figs. 9, 10, 11 that the value of Emission

objective function settles at the minimum after about 14 iterations

with FAPSO method and does not vary thereafter while the PSO

algorithm converges to global optimum in about 39 iterations. Also

the value of Cost objective function settles at the minimum after

about 12 iterations with FAPSO method, while the PSO algorithmconverges to global optimum in about 24 iterations. The value of

PLossobjective function settles at the minimum after about 10 iter-

ations with FAPSO method, while the PSO algorithm converges to

global optimum in about 40 iterations.

To show that the constraints are satisfied under the proposed

optimization method the voltages of buses #7, #29, #72 and #82,

for instance, are illustrated in Figs. 12, 13, 14 for two cases (with FC

and without FC). It can be observed from the figures that the bus

voltages are maintained within the permitted range of tolerance,

i.e. 5% of the nominal value in two cases. The simulation results

show that the FCPPs improve the performance of system.

To minimize the Emission objective function, the active power of

all FCPPs must be set to its maximum value (250 kW) during all the

day. In order to minimize the Costobjective function, active power

ofall FCPPs mustbe set to0 kW. Alsoto minimizethe PLossobjectivefunction, active power of all FCPPs must be set to250 kW, except for

some FCPPs during the day that must generate less than 250 kW.

The powers that FCPPs generate with PLossobjective function are

shown in Table 8.

2 4 6 8 10 12 14 16 18 20 22 240.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Voltages # Emission

2 4 6 8 10 12 14 16 18 20 22 240.95

0.96

0.97

0.98

0.99

1

Vbus

#40

Vbus

#81

Vbus

#71

Vbus

#6

Voltages # Emission

2 4 6 8 10 12 14 16 18 20 22 24

0.92

0.94

0.96

0.98

1

Time (h)2 4 6 8 10 12 14 16 18 20 22 24

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Time (h)

with FC

without FC

Fig. 22. Variation of voltages in some buses with Emission objective function.

2 4 6 8 10 12 14 16 18 20 22 240.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

Vbus

#6

Voltages # Cost Voltages # Cost

2 4 6 8 10 12 14 16 18 20 22 240.95

0.96

0.97

0.98

0.99

1

Vbus#

40

2 4 6 8 10 12 14 16 18 20 22 240.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

Vbus

#71

2 4 6 8 10 12 14 16 18 20 22 240.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

Vbus#

81

Time (h)Time (h)

with FCwithout FC

Fig. 23. Variation of voltages in some buses with Costobjective function.



17/19

The simulation results obtained in Figs. 15, 16, 17 show that the

summation of losses while there are FCs is 8446.27 kWh with

Emission objective function and 8445.46 kWh withPLossobjective

function and is 18 255.17 kWh with Cost objective function and

while there are not FCs is 18 255.17 kWh with all objective

functions.

The average computing time for this method isw5 min running

on a P4 1.8 GHz/512 MB RAM.

2 4 6 8 10 12 14 16 18 20 22 240.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Vbus#

71

Vbus#

6

Vbus#

40

Vbus#

81

Voltages # PLoss

2 4 6 8 10 12 14 16 18 20 22 240.95

0.96

0.97

0.98

0.99

1

Voltages # PLoss

2 4 6 8 10 12 14 16 18 20 22 24

0.92

0.94

0.96

0.98

1

Time (h)

2 4 6 8 10 12 14 16 18 20 22 240.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Time (h)

with FCwithout FC

Fig. 24. Variation of voltages in some buses with PLossobjective function.

Table 12

Power generated by FCPPs during the day with PLossobjective function (second example).

NO.

FCPP

Hour(h)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1 250 250 250 101 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 2502 250 100 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

3 250 250 250 250 200 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

4 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

5 250 250 250 131 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

6 250 131 250 250 250 235 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

7 250 250 250 246 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

8 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

9 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

10 250 250 21 25 112 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

11 250 23 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

12 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

13 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

14 250 250 226 222 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

15 250 250 160 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

16 250 160 250 157 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

17 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

18 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

19 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

20 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

21 250 250 250 234 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

22 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

23 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

24 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

25 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

26 250 195 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

27 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

28 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

29 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

30 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

31 250 191 250 199 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

32 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

33 250 197 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

34 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

35 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250



18/19

8.2. Practical distribution network of TPC after reconfiguration

The second example is the same distribution network of TPC

after reconfiguration that is shown in Fig. 18.

It is supposed that there are 35 FCPPs which are located three

FCPPS at buses 6,12,19,28, 31, 71, 75, 79 and two FCPPs at buses 45,

51, 58 and a FCPP at buses 22, 24, 54, 62, 83 that each of these

sources can generate 250 kW active power.

Tables 9, 10, 11 present a comparison among the results of

FAPSO, PSO, ACO, TS, DE and GA algorithms for 20 random tails for

three objective functions. Figs. 19, 20, 21 depict the convergence

characteristic of the FAPSO and PSO algorithms for the best solutionfor three objective functions. The voltage changes of some buses are

shown in Figs. 2224. It can be seen from Figs.19, 20, 21 that FAPSO

method converges faster than the others.

It can be observed from these tables that the foregoing variables

assume considerably smaller values under the proposed algorithm

than the other methods.

It can be observed from the figures that the bus voltages are

maintained within the permitted ranges.

In order to minimize the Emission objective function, the active

power of all FCPPs must be set to its maximum value (250 kW)

during all the day. To minimize the Cost objective function, active

power of all FCPPs must be set to 0 kW. Also to minimize the

PLossobjective function, active power of all FCPPs must be set to

250 kW, except for some FCPPs during the day that must generateless than 250 kW. The powers that FCPPs generate with

PLossobjective function are shown in Table 12.

Variation of power losses obtained in Figs. 25, 26, 27 shows

that the summation of losses while there are FCs is 7439.99 kWh

with Emission objective function and 7438.02 kWh withPLossobjective function and 15 997.78 kWh with Costobjective function

and while there are not FCs is 15 997.78 kWh with all objective

functions.

The power factor of FCPPs has been considered about 0.9 in

these simulations.

The average computing time for this method isw5 min running

on a P4 1.8 GHz/512 MB RAM.

The FAPSO method is very precise and converges faster than the

other methods. In other words, this method not only reachesa better optimal solution than other methods, but also its standard

deviation for different trails is zero.

The FCPPs are more beneficial for the distribution system when

the optimization goal is to minimize the electrical energy losses

compared to the case where the optimization goal is to minimize

the total cost of electrical energy or emission of these sources.

However, the FCPPs are mostly run by private owners and the

ultimate goal of their connection to the system is the electric power

generation. Therefore reducing the electrical energy losses cannot

be used as an incentive to persuade them to generate electric

power. Since FCPPs have high cost to generate electrical energy,

distribution operator must use some indexes to encourage the

owners to generate electric power.

The minimum voltage with the emission objective is more thanother objectives, therefore when the load increases, the system has

more security with the emission objective function. So from

2 4 6 8 10 12 14 16 18 20 22 24

0

500

1000

1500

Time (h)

Losses(kW)#Emission

without FC

2 4 6 8 10 12 14 16 18 20 22 24

0

200

400

600

800

Losses(kW)#Emission with FC

Time (h)

Fig. 25. Daily variation of active power losses (Emission objective function).

2 4 6 8 10 12 14 16 18 20 22 240

500

1000

1500

Time (h)

Losses(kW)#Cost without FC

Time (h)

2 4 6 8 10 12 14 16 18 20 22 240

500

1000

1500

Losses(kW)#Cost

with FC

Fig. 26. Daily variation of active power losses (Costobjective function).

Time (h)

2 4 6 8 10 12 14 16 18 20 22 240

200

400

600

800

Losses(kW)#PLoss with FC

2 4 6 8 10 12 14 16 18 20 22 240

500

1000

1500

Time (h)

Losses(kW)#PLoss without FC

Fig. 27. Daily variation of active power losses (PLossobjective function).



19/19

operator point of view the system has a better performance,

compared to the two other cases, when the optimization goal is to

minimize total emission of FCPPs.

9. Conclusion

This paper presented a new approach for daily Optimal Opera-

tion Management (OOM) problem in distribution system with

regard to Fuel Cell Power Plants (FCPPs). Due to the small X/R ratio

and radial configuration of distribution systems, FCPPs have much

impact on this problem. Reduction of losses and emission in spite of

relatively high cost was proposed as a proper signal to encourage

owners of FCPPs in active power generation. The simulation results

show that the defined factor has caused more reduction in the total

electrical energy losses in the system. The voltages magnitude is in

the desired limits. Besides the above objective functions, a new

evolutionary optimization method based on Fuzzy Adaptive

Particle Swarm Optimization has been proposed to solve the opti-

mization problem. The simulation results indicate that this opti-

mization method is very precise and converges very rapidly so that

it can be used in the practical systems.

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