Hybrid Neuro Swarm

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Neural Computing and Applications

ISSN 0941-0643

Neural Comput & Applic

DOI 10.1007/s00521-012-0976-4

Hybrid neuro-swarm optimizationapproach for design of distributed

eneration power systems

T. Ganesan, P. Vasant & I. Elamvazuthi



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O R I G I N A L A R TI C LE

Hybrid neuro-swarm optimization approach for designof distributed generation power systems

T. Ganesan • P. Vasant • I. Elamvazuthi

Received: 27 August 2011 / Accepted: 21 May 2012 Springer-Verlag London Limited 2012

Abstract The global energy sector faces major chal-

lenges in providing sufficient energy to the worlds ever-increasing energy demand. Options to produce greener,

cost effective, and reliable source of alternative energy

need to be explored and exploited. One of the major

advances in the development of this sort of power source

was done by integrating (or hybridizing) multiple different

alternative energy sources (e.g., wind turbine generators,

photovoltaic cell panels, and fuel-fired generators, equip-

ped with storage batteries) to form a distributed generation

(DG) power system. However, even with DG power sys-

tems, cost effectiveness, reliability, and pollutant emissions

are still major issues that need to be resolved. The model

development and optimization of the DG power systemwere carried out successfully in the previous work using

particle swarm optimization (PSO). The goal was to min-

imize cost, maximize reliability, and minimize emissions

(multi-objective function) subject to the requirements of

the power balance and design constraints. In this work, the

optimization was performed further using Hopfield neural

networks (HNN), PSO, and HNN-PSO techniques. Com-

parative studies and analysis were then carried out on the

optimized results.

Keywords Particle swarm optimization (PSO)

Hopfield neural networks (HNN) Multi-objective Optimization strategy Hybrid algorithms Alternative

energy Distributed generation (DG)

List of symbols

COST ($/year) Total costw, s, b Wind, solar, and battery

storage indices

I i, S pi, OMpi ($/year) Initial cost, present worth

of salvage value, present

worth of operations, and

maintenance cost

N p (year) Lifespan of the project

C g Annual cost of

purchasing power from

the utility grid

aw, as, ab ($/m2) Initial cost of WTG, PV

panels, and storagebattery

Aw, As (m2) Swept area of WTG and

PV panels

S w, S s ($/m2) Salvage value of WTG

and solar per square

meter

b, T , m Inflation rate, interest

rate, and escalation rate

aOMw, aOMs, aOMb ($/m2 /year) Yearly operation and

maintenance cost for

wind, solar, and storage

batteries

N p, N w, N s, N b (year) Lifespan of project,

WTG, PV, and storage

batteries

gs, gw, gb Efficiency of PV,

WTG, and storage

batteries

Pg, t (kW) Purchased power from

the utility at hour t

psi ($/kW h) Grid power price

T. Ganesan P. Vasant (&) I. ElamvazuthiUniversity Technology Petronas, Tronoh, Malaysiae-mail: [email protected]

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DOI 10.1007/s00521-012-0976-4



EIR Energy index of

reliability

EENS (kW h/year) Expected energy not

served

E (kW h/year) Total power demand per

annum

k Ratio of purchased power

with respect to the hourly

insufficient power

PE (ton/year) Pollutant emission

X, u, U Coefficients

approximating the

generator emission

characteristic coefficients

Pbcap (kW) Capacity of storage

batteries

Pbsoc (kW) State of charge of storage

batteries

Pbmax (kW) Maximum conversion

capacity

Pbmin (kW) Minimum permissible

storage level

Pbcapmax (kW) Allowed storage capacity

Pbr (kW) Rated battery capacity

Pb(t ) (kW) Discharge power from

the storage batteries

Pgmax (kW) Maximum annual power

allowed to be purchased

from the utility grid

Pgmin (kW) Minimum annual power

allowed to be bought

from the utility grid

T (h) Period under observation,

8,760 h (per year)

Pbsup (t ) (kW) Surplus power at hour t

Pd (t ) (kW) Load demand during

hour t

Ptotal (t ) (kW) Total power from WTG,

PV, and FFG

Pg (kW) Power from the FFG

Pw (kW) Power from the WTG

Ps (kW) Power from the PV

R Ratio of maximum

permissible unmet power

Pdump (kW) Dumped power

PWTG (kW) Output power from th

WTG

V , V ci, V r, V co (m/s) Wind speed, cut-in wind

speed, rated wind speed,

and cutoff wind speed

Pr (kW) Rated WTG power

Awmax, Awmin (m2) Maximum and minimum

swept area of WTGs

Asmin, Asmax (m2) Minimum and maximum

swept area of PVs

1 Introduction

In recent times, the global energy sector faces two major

challenges in providing sufficient energy to the worlds

ever-increasing energy demand. First, there is a growing

need to produce greener and cleaner energy with respect to

stricter environmental regulations. Secondly, with the

diminishing fossil fuel reserves, a reliable and stable source

of alternative energy needs to be explored and exploited. In

seeking out these alternative power sources, it has been

identified that the capital investment as well as the main-

tenance costs are considerably high. Besides that, various

reliability issues have been addressed over the years. One

of the major advances, in developing a reliable and greener

[1] power source is by integrating or hybridizing multiple

different energy sources (e.g., wind turbine generators,

photovoltaic cell panels, and storage batteries) to form a

DG power system. These hybrid power generation systems

have been built and are now in stable operations [2–4].

However, even with DG power systems, cost effectiveness,

reliability [5, 6], and pollutant emissions are still major

issues that need to be tackled. Therefore, to address the

previously mentioned issues, PSO methods have been

applied to the problem by Wang et al. [7]. Other works on

the design and sizing of hybrid power systems with solar

and wind power sources include Chedid et al. [8] and

Chedid et al. [9].

In this work, optimization methods such as HNN and

PSO (stand-alone and hybridized form) were incorporated

into this problem. Comparison studies as well as result

analysis were then performed to identify the best optimi-

zation strategy that achieves all the objectives and obeys all

the power balance and design constraints.

The HNN was developed in 1982 by Hopfield [10, 11].

These neural nets observed to have applications in opti-

mization problems (for instance, see Lee, Sode-Yome et al.[12] and Tank et al. [13]). One of the key features of the

HNN is that there is a decrease in the energy by a finite

amount whenever there is a change in the network’s state.

This essential property confirms convergence of the output

whenever the network state is changed. The HNN uses

reinforced learning (Hebbian learning) to update the

weights in each recursion. In this work, the HNN was used

as an optimization algorithm.


1 3



PSO is an optimization method developed based on the

movement and intelligence of swarms. PSO integrates the

concept of social interaction to problem solving and decision

making. PSO was developed by James Kennedy and Russell

Eberhart [14] in 1995. Particle swarm is the system model or

social structure of a basic creature which makes a group to

have some objectives such as food searching and predator–

prey interactions. Hence, the governing principle is that it isan important to take part with the most of the population in a

group that has the same activity. Recently, PSO has been

applied to various fields of power system including eco-

nomic dispatch problems as well as in optimization problems

in electric power systems (see [15]).

This paper is organized as follows: Sect. 2 introduces

the HNN, PSO and the HNN-PSO approaches; Sect. 3

presents the problem description for the optimization of the

DG system; and the analysis and computational results are

included in Sect. 4. The paper ends with concluding

remarks and recommendations for future research work.

2 Methodology

2.1 Hopfield neural network

The HNN consists of different components which are the

inputs, outputs, and weights (see Fig. 1). The other two

crucial subcomponents of the HNN are the Hebbian

learning mechanism and the energy function. The inte-

gration of all these features in the HNN makes it a good

optimization tool.

The outputs of the HNN are computed by the compo-sition of the inputs and the associated weights such as the

following:

hi ¼X

j

wil x j ð1Þ

where x j is the input column vector, hi is the output column

vector, and wij are the weights. Since this is a recurrent

network, hence the outputs are fed back as the inputs:

xT j

mþ1

¼ wij yT i

mð2Þ

where m is the number of iterations.

Due to its recursive nature, the inputs and outputs

change with respect to the number of iterations. Thus, the

modified Hebbian learning (a form of reinforced learning)

is used to alter the weights based on the network outputs

and the inputs:

wij ¼ xT j yi

hð3Þ

where h is the learning rate coefficient.

The energy function is computed as a sum for weights

and neurons for all i and j for each of the iterations:

E ¼X

ij

k wij x j yT i

ð4Þ

where k is a scalar constant.

Since the energy of the network reduces finitely as the

network states change, hence as the number of iterationsincreases to its maxima, the differential of the energy

between the states approximates to 0:

As m ! max; DE ! 0

DE ¼ E mþ1 E m ð5Þ

where m is the number of iterations.

At this point a convergence criterion is set, whereby if

the differential energy DE is lesser than some value then

the program is halted and solution (outputs of the network,

hi) is printed out. Otherwise, the iterations continue until

this criterion is satisfied. The differential energy continu-

ously minimizes as the neurons’ states change. Some

threshold value is required to avoid the energy differential

to minimize ad infinitum. Hence, in this work, a minimal

differential energy criterion is set (dE \ 1). Since at these

states the difference between the energy states are minimal,

the network ceases from performing further optimization.

The working algorithm of the HNN is as the following:

Step 1: Set xi as the inputs

Step 2: Initialize neural network weights, wij

Step 3: Compute neural network output, y j

Step 4: Compute an energy state of the neural network, E ij

Step 5: If the energy difference dE ij is greater than 1, goto step 2 and

Update neural network output, y j ¼ y0 j

Update the weights by Hebbian learning, wij ¼ w0ij

Step 6: If energy difference is less than 1, proceed to step 7

Step 7: Initialize DG system coefficients and compute

design parameters

Step 8: If any constraints are not satisfied, go to step 2,

otherwise proceed to step 9.Fig. 1 Hopfield recurrent neural network


1 3



Step 9: Compute fitness values of the design parameters.

If fitness criterion is satisfied then halt program and print

solutions, otherwise, go to step 2.

The stopping criterion used in this work is identical to

the fitness criterion. If the fitness criterion is not met, then

the program proceeds iteratively, otherwise it halts and

prints the solutions. The fitness criterion of the HNN is metif the network output converges to some constant value

(which means that no further optimization occurs in the

objective function), no constraints are broken, and all the

decision variables are nonnegative. If these conditions are

met, then it is considered that the solutions are at its fittest,

and thus, the program comes to a halt.

2.2 Particle swarm optimization

The PSO algorithm was initially developed in 1995 by

Kennedy and Eberhart [14]. This technique originates from

two different ideas. The first idea was based on the obser-vation of swarming or flocking habits of certain types of

animals (for instance: birds, bees, and ants). The second

concept was mainly related to the study of evolutionary

computation. The PSO algorithm works by searching the

search space for candidate solutions and evaluating them to

some fitness function with respect to the associated criterion.

The candidate solutions are analogous to particles in

motion (swarming) through the fitness landscape in search

for the optimal solution. Initially, the PSOalgorithmchooses

some candidate solutions (candidate solutions can be ran-

domly chosen or be set with some a priori knowledge). Then,

each particle’s position and velocity (candidate solutions)are evaluated against the fitness function. If the fitness

function is not satisfied, then update the individual and social

component with some update rule. Next, the velocity and the

position of the particles are updated. This procedure is

repeated iteratively until all candidate solutions satisfy the

fitness function and thus converge into a fix position. The

flowchart for the PSO algorithm is given in Fig. 2.

It is important to note that the velocity and position

updating rule is crucial in terms of the optimization capa-

bilities of the PSO algorithm. The velocity of each particlein

motion (swarming) is updated using the following equation:

viðn þ 1Þ ¼ wviðnÞ þ c1r 1½^ xiðnÞ xiðnÞ

þ c2r 2½gðnÞ xiðnÞ ð6Þ

where each particle is identified by the index i, vi(n) is the

particle velocity, and xi(n) is the particle position with

respect to iteration (n). The parameters w, c1, c2, r 1, and r 2are usually defined by the user. These parameters are

typically constrained by the following closed intervals:

w 2 ½0;1:2; c1 2 ½0;2; c2 2 ½0;2; r 1 2 ½0;1; r 2 2 ½0;1 ð7Þ

The term wvi(n) in Eq. 6 is the inertial term which keeps

the particles moving in the same direction as its original

direction. The inertial coefficient w serves as a dampener or

an accelerator during the particles motion. The termc1r 1½^ xiðnÞ xiðnÞ also known as the cognitive component

functions as memory. Hence, the particle tends to return to

the location in the search space where the particle had a

very high fitness value. The term c2r 2½gðnÞ xiðnÞ known

as the social component serves to move the particle to the

locations where the swarm has moved in the previous

iterations.

In the first loop in Fig. 2, the constant n0 is introduced.

The idea behind this loop is to prime the particles in motion

Stop

YES

NO

Is fitness criterion

satisfied?

Evaluate fitness of the

desi n arameters.

YES

Initialize power systemcoefficients and design

parameters

Is n > no+T ?

T = T +1

n = n +1

NO

Compute individual and

social influence

Compute position x i(n+1)

and velocity vi(n+1) at next

iteration

START

Initialize no of

articles, i

Initialize algorithm parameters w,

c1 ,c2 , r 1 , r 2 ,no

Set initial position

x i(n) and velocity vi(n)

Fig. 2 Flowchart for PSO algorithm


1 3



prior to applying them into the DG system. The larger the

value of n0, the longer the particles would be in motion

prior their application and evaluation. Thus, as the sec-

ondary loop (T = T ? 1) increases, the primary loop

(n = n ? 1) also increases. Since, the primary loop keeps

the particles in motion incrementally as the program is

executed, thus the particles gradually converge to some

constant position. This primary loop strengthens the algo-rithm in terms of its convergent properties.

After the computation of the particle velocity, the par-

ticle position is then calculated as follows:

xiðn þ 1Þ ¼ xiðnÞ þ viðn þ 1Þ ð8Þ

The iterations are then continued until all candidate

solutions are at their fittest positions in the fitness

landscape and some stopping criterion which is set by the

user is met. For more comprehensive texts on PSO

methods, refer to [16, 17] and [18]. The working

algorithm of the PSO in this work is as follows:

Step 1: Initialize no of particles, i and the algorithm

parameters w, c1, c2, r 1, r 2, noStep 2: Set initial position xi(n) and velocity v i(n)

Step 3: Compute individual and social influence

Step 4: Compute position xi(n ? 1) and velocity

vi(n ? 1) at next iteration

Step 5: If the swarm evolution time is n[ no ? T ,

update position x i and velocity v i and go to Step 3, else

proceed to step 6, where no is some constant, n is the

swarm iteration, and T is the overall program iteration

Step 6: Initialize DG system coefficients and design

parametersStep 7: Evaluate fitness of the design parameters

Step 8: If fitness criterion is satisfied, halt and print

solutions, else go to step 3.

As for the PSO algorithm, the fitness criterion used is

as follows:

If during the iteration process, the position of all the

particles converges to some constant value, no further

optimization occurs in the objective function, no

constraints are broken, and all the decision variables

are nonnegative then, it can be considered that the

fitness criterion is met. Then, the solutions are at itsfittest, and thus, the program comes to a halt.

2.3 Hybrid neuro: particle swarm optimization

In this work, the NN and the PSO algorithm was hybridized

and used as an alternative optimization tool in line with the

stand-alone NN and the PSO algorithms. The working

algorithm and the flow chart (see Fig. 3) of the hybrid

HNN-PSO technique are as follows:

Step 1: Set x i as the inputs and initialize neural network

weights, wij

Step 2: Compute network output, y j and energy differ-

ence, dE

Step 3: Check differential energy threshold: if (dE [ 1),

continue network recursion (Step 2)

else, proceed to step 4.

Step 4: Initialize no of particles, i and the algorithm

parameters w, c1, c2, r 1, r 2, noStep 5: Set initial position x i(n) and velocity v i(n)

Step 6: Compute individual and social influence

Step 7: Compute position xi(n ? 1) and velocity

vi(n ? 1) at next iteration

NO

T =T+1

Is n > no+T ?

Compute position x i(n+1) and

velocity vi(n+1)

YES

Set initial conditions for the

PSO segment

Is dE >1?

NO

n =n+1

Initialize power systemcoefficients and design

parameters

YES

Evaluate fitness of the design

parameters.

YES

Stop

Is fitness criterion

satisfied?

START

Set x i as the inputs and initialize

neural network weights, wij

Compute network output, y j &

energy difference, dE

NO

Update y j = x iwij= w’ij

m = m +1

Fig. 3 Flowchart for hybrid HNN-PSO algorithm


1 3



Step 8: If the swarm evolution time n[ no ? T , update

position xi and velocity vi and go to Step 2, else, proceed

to step 6, where no is some constant, n is the swarm

iteration, m is the network recursion, and T is the overall

program iterations

Step 9: Initialize DG system coefficients and design

parameters

Step 10: Evaluate fitness of the design parametersStep 11: If fitness criterion is satisfied, halt and print

solutions, else go to step 3

As for the HNN-PSO algorithm, since the PSO segment

comes after the HNN segment, thus the fitness criterion is

identical to the pure PSO algorithm. That is if during the

execution of the program, the position of all the particles

converges to some constant value, no further optimization

occurs in the objective function, no constraints are broken,

and all the decision variables are nonnegative then, it can

be considered that the fitness criterion is met. Then, the

solutions are at its fittest, and thus, the program comes to ahalt.

3 Description of problem statement

The goal of this work is to optimize the design parameters

of a hybrid DG power system with alternative energy

power sources (solar and wind power) with respect to

power balance as well as design constraints as done pre-

viously in [7]. The problem in this work is multi-objective,

thus the design parameters would have to be optimized

such that it minimizes the cost, maximizes the reliability,and minimizes pollutant emissions of the power system.

The configuration the grid-connected hybrid DG system is

as in Fig. 4.

The hybrid DG system consists of wind turbine gener-

ators (WTGs), photovoltaic cell panels (PVs), storage

batteries (SBs), and the fuel-fired generators (FFGs). The

usage of each of these power sources influences the reli-

ability, cost, and the environment criterions differently.

One of the cheaper fuel types that can be used for an

FFG would be coal. Coal is reliable, abundantly available,

and a relatively cheap fossil fuel source. The only major

drawback with fuel sources like coal is that they have a

high rate of pollutant emission (PE). Similar issues are

currently faced by other fossil fuel alternatives, for

instance: diesel, petrol, and natural gas (NG). Also take

note that other fossil fuels are not as cheap as coal, andthus, cost effectiveness is an issue. The oxidation of these

fuel types produces alarming levels of pollutant gases such

as NOx, SOx, carbon monoxide, and carbon dioxide. Thus,

with the increasingly stricter enactment of environmental

regulation, sole dependency on FFGs for power is clearly

an unfeasible option. This is the main factor that motivates

the development of hybrid DG systems which reduces the

global dependency on fossil fuel.

One of the cleanest and cheapest power sources

(despite the initial cost) known is wind power since it has

no pollutant emissions, and wind power is available with

no purchase cost. However, the magnitude of wind poweris heavily dependent on weather conditions. Thus, the

location where the wind turbine is placed (on-shore or off-

shore locations) is a critical factor. Due to varying

weather conditions, the reliability of wind power is

intermittent, and this makes sole dependency on wind

power unfeasible. Unfortunately, solar power also suffers

similar issues with wind power. Sunlight (insolation) is

the main source of energy for PV cells. Like wind, this

power source is very dependent on weather conditions

although relatively cheap (besides the initial cost) and

clean (with zero emissions). This makes solar power an

unreliable energy source due to fluctuations in weatherconditions.

Since wind and solar power are highly unreliable energy

source, thus including storage batteries into the DG system

is highly desirable. The energy storage mechanism can thus

filter-out the fluctuations and give a consistent amount of

power supply with respect to time [19]. The storage bat-

teries then can be considered to behave like a regulator that

balances the supply and demand variability.

Each power source caters differently for reliability, cost

effectiveness, and pollutant emissions. Therefore, the

development of the hybrid DG system seems to be an

attractive option in catering for all three criterions

simultaneously.

This is a nonlinear problem that involves 9 constraints

and 67 decision variables. The problem statement is for-

mulated as follows:

Min ? COST ($/year)

Min ? Pollutant emissions (PE ) (ton/year)

Max ? Energy index of reliability (EIR)

subject to power balance and design constraints.

WTG

PV

Other

Renewable

Energy

Sources

AC/DC

DC/DC

AC(DC)

/DC

Storage

Batteries

DC/AC

Dump

Load

Utility

Grid

Fig. 4 Schematic of the grid-connected hybrid DG system


1 3



For the definitions of the variables, please refer to the

nomenclature above. The objective functions (refer to [3, 4,

8, 9]), for the overall cost, COST ($/year) is as the

following:

COST ¼

Pi¼w;s;b ð I i S þ OMPi

Þ

N pþ C g ð9Þ

For the WTG:

I w ¼ aw Aw ð10Þ

S Pw ¼ S w Aw

1 þ b

1 þ c

N p

ð11Þ

OMPw ¼ aOMw

Aw X N p

i¼1

1 þ m

1 þ c

i

ð12Þ

For the PV:

I s ¼

as A

s ð13

Þ

S Ps ¼ S s As

1 þ b

1 þ c

N p

ð14Þ

OMPs ¼ aOMs

As X N p

i¼1

1 þ m

1 þ c

i

ð15Þ

For the storage battery:

I b ¼ ab Pbcap X X b

i¼1

1 þ m

1 þ b

ði1Þ= N b

ð16Þ

OMPb ¼ aOMb

Pbcap X N p

i¼1

1 þ m1 þ c

i

ð17Þ

The annual cost for purchasing power from the grid is

calculated as follows:

C g ¼XT

t ¼1

Pg;t u ð18Þ

The objective functions for the reliability (refer to [3, 4,

8, 9]) are as follows:

EIR ¼ 1 EENS

E ð19Þ

EENS ¼XT

t ¼1

ðPbmin Pbsocðt Þ Psupðt ÞÞ U ðt Þ ð20Þ

Ptotalðt Þ ¼ Pwðt Þ þ Psðt Þ þ Pgðt Þ ð21Þ

Pgðt Þ ¼ j ðPdðt Þ Pwðt Þ Psðt Þ Pbðt ÞÞ ð22Þ

The objective function for the pollutant emissions which

was quadratically approximated (see [20, 21]) is as follows:

PE ¼ X þ U XT

t ¼1

Pg;t ðt Þ

þ C XT

t ¼1

Pg;t ðt Þ " #2

ð23Þ

(A) Power balance constraints:

Pbðt Þ þ Pwðt Þ þ Psðt Þ þ Pgðt Þ ð1 RÞPdðt Þ ð24Þ

Pbðt Þ þ Pwðt Þ þ Psðt Þ þ Pgðt Þ Pdumpðt Þ Pdðt Þ ð25Þ

The WTG output power is calculated as follows:

PWTG ¼

0 iff V \V ci

a V 3 b P iff V ci V \V

Pr iff V r V V co

0 iff V [V co

8>><>>: ð26Þ

where

a ¼ Pr=ðV 3r V 3ciÞ ð27Þ

a ¼ V 3ci=ðV 3r V 3ciÞ ð28Þ

Pw ¼ PWTG Aw gw ð29ÞThe PV output power is calculated as follows:

Ps ¼ H As gs ð30Þ

(B) Design constraints:

Awmin Aw Awmax ð31Þ

Asmin As Asmax ð32Þ

Pbmin Pbsoc Pbcap ð33Þ

0 Pbcap Pbcapmax ð34Þ

Pb Pbmax ð35Þ

Pgmin XT

t ¼1

Pg;t Pgmax ð36Þ

0 j 1 ð37Þ

The input parameters considered in this work is as in

Table 1.

The data used (obtained from [7]) for the hourly input of

the insolation, wind speed patterns, and the hourly load

demand in this simulation program are as in Figs. 5, 6, and

7, respectively.

4 Experimental results

The algorithms used in this work were programmed using

the C?? programming language on a personal computer

with an Intel dual core processor running at 2 GHz. The

objective functions, cost ($ year), EIR, and the emissions

(ton/year) were optimized using the HNN, PSO, and the

hybrid HNN-PSO approaches. The results were then

compared against each other as well with the results


1 3



obtained in [7]. In the analysis of the results, design 1 and

design 2 were the computational results obtained from [7]

while HNN, PSO, and the HNN-PSO are the results of the

algorithms used in this work.

The comparisons of the values of the objective functions

are as in Table 2. The comparisons of the design parame-

ters for each of the methods are provided in Table 3.

Figures 8, 9, and 10 provide the performance of the

methods employed with respect to their effect to the

objective functions [cost ($/year), EIR, and emissions (ton/

year)].

In Fig. 8, it can be observed that design 2 produces the

highest cost while the most minimum cost was achieved by

the HNN method. The second highest cost was obtained by

the design proposed by the PSO method, followed by the

HNN-PSO, and design 1 method. The design by the HNNmethod in this case is the most effective cost minimizer.

In Fig. 9, it is observed that the design produced by the

HNN method achieves the highest EIR while the lowest

EIR was produced by design 1. The second highest EIR

was produced by the design proposed by the PSO method,

followed by the HNN-PSO, and the design 2 methods,

respectively. Therefore, it can be observed that the design

obtained using the HNN method produces maximum

reliability.

The lowest pollutant emission rate (PE) was achieved

using the design produced by the PSO method while the

highest is given by design 2 which can be seen in Fig. 10.The second lowest PE was produced by the design pro-

posed by the HNN-PSO method followed by the HNN and

the design 1 method, respectively. Therefore, it can be

observed that the PSO method was the greenest design

option since it minimizes the PE effectively. In the scatter

plot in Fig. 11, the simultaneous optimization of all three

objectives with respect to the methods utilized in this work

could be observed.

It was also inferred that although the design option

achieved by the HNN method was cost effective and highly

reliable; it produces more emissions (PE) with respect to

the designs produced by the PSO and the HNN-PSO

method. As for the design proposed by the PSO method, it

can be seen that although it provides the lowest emissions

among all the other designs, it was not as cost effective as

the design proposed by design 1, HNN, and the HNN-PSO

method. Besides, the PSO method was not as reliable

compared with the design proposed by the HNN method

but more reliable than the design proposed by all the other

methods. The HNN-PSO method seems to be the middle

point in terms of performance between the HNN and the

Table 1 Input parameters for the hybrid DG system

System parameters Values

gs, gw, gb 50 %, 16 %, 82 %

b, T , m 9 %, 12 %, 12 %

N p, N w, N s, N b (year) 20, 20, 22, 10

aw, as, ab ($/m2) 100, 450, 100

S w, S s ($/m2) 10, 45

aOMw, aOMs, aOMb ($/m2 /year) 2.5, 4.3, 10

V ci, V r, V co (m/s) 2.5, 12.5, 20

Pr (kW) 4

Awmax, Awmin (m2) 10,000, 400

Asmin, Asmax (m2) 30, 8,000

Pbmax (kW) 3

Pbmin (kW) 3

Pbr (kW) 8

Pbcapmax (kW) 40

psi ($/kW h) 0.12

Fig. 5 Hourly insolation profile

Fig. 6 Hourly wind speed profile

Fig. 7 Hourly power demand profile


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PSO method. The design proposed by the HNN-PSO

method was more cost effective as compared to the design

by the PSO and design 2 method; however, it was morecostly than the design by the HNN and the design 1

methods. In terms of emissions, the design proposed by the

HNN-PSO method has lower PE as compared to all the

methods except the PSO method. Thus, it can be said that

the HNN-PSO method was the second greener alternative

design after the design by the PSO method. The design by

the HNN-PSO method was more reliable than the design 1

and design 2 but less reliable than the design proposed by

the HNN and the PSO method.

In Fig. 11, the optimum value labeled as ‘OPTIMA’ at

(0, 1, 0) which is the point with the most minimum cost,

maximum reliability (EIR), and minimum emissions (PE).

The method that provides the closest design option to the

optimum point is the HNN method while the furthest from

the optimum point is the PSO and the HNN-PSO method.

Thus, in this work, it can be said the HNN method pro-

duces the best design option in terms of the overall triple-

objective optimization. The HNN method would then rank

first in terms of providing the most optimal solution, fol-

lowed by the HNN-PSO, and the PSO algorithm,

respectively.

Table 2 Comparison of value of objective functions

Design 1 Design 2 HNN PSO HNN-PSO

Cost ($/year) 5,323 6,802 4,928.88 5,340.95 5,326.2

EIR 0.9394 0.9505 0.999988 0.998138 0.975175

Emissions (ton/year) 12.4609 65.3812 8.09501 4.91565 6.15164

Computational time (ms) – – 122 67 127

Table 3 Comparison of the optimized design parameters for each method

Design 1 Design 2 HNN PSO HNN-PSO

Aw (m2) 420 640 412.928 432.406 434.777

As (m2) 50 40 25.2482 43.2406 43.4777

Pbcap (kW h) 16 16 19.9243 16.2571 15.3477

j 0.2 0.58 0.16466 0.12225 0.136145

Fig. 8 Cost ($/year) against the methods

Fig. 9 EIR against the methods

Fig. 10 Emissions (ton/year) against the methods

Fig. 11 Cost versus EIR versus PE


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other classes of evolutionary algorithms. Hybridizing these

methods with algorithms like different evolution (DE)

search may provide it with a more efficient system for

handling constraints and thus pave the way for a solution

closer to the global optimum.

The HNN method can be considered robust and appli-

cable for a wide range of optimization problems. With

modifications to the energy function of the HNN and some of

the numerical parameters (see Table 4), the HNN method

could be customized for solving a broader class of nonlinear

Table 6 Advantages and the disadvantages of the PSO algorithm

Advantages Disadvantages

1. The PSO method takes lesser computational time to produce thesolution as compared to the HNN and the HNN-PSO approach

1. The PSO method unfortunately is a much poorer cost minimizer ascompared to the other techniques except the design 2 methodmentioned in [7]

2. The pure PSO method is more easily implemented as compared tothe HNN and the HNN-PSO approach since it is has low algorithmic

complexity

2. Due its poor qualities as a cost minimizer, the PSO method does notperform as well as the HNN-PSO or the HNN methods in terms of

overall optimization

3. The PSO method nevertheless outperforms all of the othertechniques in terms of reliability (EIR) maximization, emissions (PE)minimization as well as efficiency in terms of computational time.This may be attributed to the capabilities of the PSO approach inhandling nonlinearities since the emission approximate used in thisproblem is nonlinear in nature

Table 7 Advantages and the disadvantages of the HNN algorithm


1. The HNN method outperforms all of the other techniquesmentioned in this work in terms of overall optimization (seeFig. 9)

1. The HNN method takes longer computational time to produce thesolution as compared to the pure PSO approach. The HNN technique hasa high algorithmic complexity compared to the PSO method and thus thecomputation takes more time

2. The HNN method outperforms all of the other techniques interms of cost minimization and reliability (EIR) maximization

2. The HNN method is less easily implemented as compared to the PSOapproach since it is higher in terms of algorithmic complexity

3. In terms of emissions (PE) minimization, the HNN performsbetter than design 1 and design 2 [7]

3. The HNN was also observed to be very poor in terms minimization of emissions as compared to the PSO and the HNN-PSO method. Asmentioned previously, the emission approximate is a nonlinear function,thus this may be a factor that compromises its performance unlike thePSO and the HNN-PSO method

Table 8 Advantages and the disadvantages of the HNN-PSO algorithm


1. The HNN-PSO method outperforms the PSO and design 2[7] methods in terms of cost minimization

1. The HNN-PSO method takes longer computational time than all threemethods to produce the solution. This can be attributed to algorithmiccomplexity. Since the HNN-PSO technique is a hybrid of two methods, henceit has the highest algorithmic complexity compared to the PSO and the HNNmethod. This makes the computational time high

2. In terms of reliability (EIR) maximization, the HNN-PSOmethod performs better than design 1 and design 2

2. The HNN-PSO method is less easily implemented as compared to the HNNand PSO approach since it is higher with respect to algorithmic complexity

3. As for emissions (PE), the HNN-PSO technique is secondonly to the PSO method in terms of minimization

3. The HNN-PSO was also observed to have mediocre performance in termsminimization of cost, since it outperforms the PSO and design 2 [7] butunderperforms the HNN and design 1 methods

4. The HNN-PSO was also observed to have mediocre performance for themaximization of reliability (EIR), since it outperforms the PSO and design 2[7] but underperforms the HNN and design 1 methods


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problems. This robustness can mainly be attributed to the

convergence capabilities and the recursive nature of the

HNN network to handle multivariate and nonlinearities in a

particular problem. The PSO method on the other hand can

be said to be very suitable for handling nonlinearities.

Therefore, in this work, since the level of nonlinearity is

considerably low, the PSO and the HNN-PSO method are

less robust as compared to the HNN method.The level of nonlinearity is considerably low where the

only nonlinear scenario in the problem is the quadratic

approximation of the emissions (PE) based on the load. The

recursive nature of the HNN gives it the capacity to handle

this issue where the degrees of nonlinearities are tolerable.

However, it is important to take note in the sense of min-

imization of emissions, the PSO method seems supreme to

all other methods including the HNN method due to its

capabilities in handling nonlinearities.

The HNN, HNN-PSO, and the PSO methods make about

300, 9490, and 85 function evaluations to reach the optimal

solution. Thus, the PSO method is the most efficient inprogram execution as compared to the HNN and the HNN-

PSO methods. The reason for this can be attributed to the

difference in terms of algorithmic complexity where the

HNN-PSO method has the highest degree of complexity

followed by the HNN and PSO methods. Due to the network

energy component in the HNN segment in methods (HNN

and HNN-PSO), the stability and the convergence of the

computations are assured in both these methods. As for the

PSO method, the oscillations dampen out with the number of

iterations due to the balancing of the social and the personal

interaction mechanisms for each particle. Thus, the stability

of the computations and the convergence of the solutions arealso assured in the PSO method (see Figs. 12 and 13).

A global solution with a better computational time may

be obtained by implementing the HNN, PSO, and the

HNN-PSO methods on a high-performance computer. It

was also inferred that the HNN, PSO, and the HNN-PSO

methods were easily implemented using the language of

C??. However, The HNN-PSO method is slightly more

complicated to implement compared with the PSO and the

HNN approach since it has high algorithmic complexity.

All three methods perform very well in terms of feasibility.

This can be concluded since all three methods do not break

any of the given constraints in this problem. In terms of

computational efficiency, it can be concluded that the

PSO method outperforms all three methods. The PSO

method is easily executable and taking very low compu-

tational time.

The HNN method takes about 122 ms, HNN-PSO

method takes 127 ms, and the PSO method takes 67 ms of

computational time to reach the optimal solution. The

computational time is closely related to the algorithmic

complexity. Hence, the variation of this factor in the

methods proposed in this work heavily influences the

computational time.

Artificial neural networks have been used extensively in

solving issues in power systems operations and as control

strategies [22–24]. Artificial neural networks [25, 26] and

HNN [27, 28] have been specifically used for solving the

economic dispatch problem. DG with multiple renewableenergy sources is also a power system related problem and

thus has many similarities with the economic dispatch

problem in terms of its multivariate nature and degree on

nonlinearities. Thus, the similarity between the DG prob-

lem and the economic dispatch problem may be the reason

why the HNN algorithm performs very well in this work.

6 Conclusions and recommendation

The overall optimization of the objective function wascarried very well by the HNN method, followed by the

HNN-PSO, and the PSO methods. The HNN-PSO method

also performs fairly well and hence ranks second to the

HNN method. The PSO method seems to singularly min-

imize the emissions (PE) very well although not as well in

the optimization of the other objectives. In this work, a new

local optimum was reached for the objective functions

using the HNN, PSO, and the HNN-PSO method. The

HNN method can be considered to be the most robust

followed by the HNN-PSO and the PSO methods. The

HNN method can be applicable for a wide range of non-

linear-class optimization problems provided that thedegrees of nonlinearities are not too high. In the event such

a scenario comes, then the PSO or its hybrids would do

well in the optimization. The HNN method is the most

efficient optimizer in this problem as compared to the PSO

and the HNN-PSO approaches although in compromises in

terms of computational time with the PSO method. In

terms of constraint satisfaction, all the methods perform

almost on an equal level. The PSO method is more easily

implemented compared with the HNN and the HNN-PSO

methods in terms of ease of implementation. To improve

the constraint satisfaction while optimizing the objective

functions further approaching the global optimal, other

optimization techniques such as genetic programming and

simulator annealing should be implemented and tested in

their pure form or as hybrids.

Acknowledgments This work was supported by STIRF grant(STIRF CODE NO: 90/10.11) of University Technology Petronas(UTP), Malaysia. The authors sincerely thank the anonymous refereesfor their valuable and constructive comments and suggestions for theimprovement of the overall quality on this paper.


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