Electrical Power and Energy Systems 61 (2014) 305–317
Contents lists available at ScienceDirect
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 / i j e p e s
a ,
a
a
b
a
Department of Electrical, Electronic and Systems Engineering, Universiti Kebangsaan Malaysia, Malaysia b
Department of Engineering, Kerman Branch, Islamic Azad University, Kerman, Iran a r t i c l e i n f o
Article history:
Received 4 May 2013
Received in revised form 25 March 2014
Accepted 27 March 2014
Keywords:
Active power conditioner
Optimal placement
Dynamic firefly algorithm
Power quality
Electric vehicle
Dynamic optimization a b s t r a c t
This paper presents a novel solution for the optimal placement and sizing of active power conditioners in future smart distribution systems by using the dynamic discrete firefly algorithm. The proposed method aims to mitigate the power quality effects of hybrid renewable energy-based generators and electric vehicle stations in smart grids. A multi-objective optimization problem is formulated to improve the voltage profile, minimize the voltage total harmonic distortion, and reduce the total investment cost. The performance analysis of the proposed algorithm is conducted on a modified IEEE 16-bus test system by using
Matlab software. The results are then compared with the conventional stationary firefly algorithm, hybrid improved genetic algorithm, and dynamic particle swarm optimization. The comparison proves that the proposed optimization algorithm is the most effective method among the other methods and that the proposed method can precisely determine the optimum location and size of active power conditioners in distribution systems.
Ó 2014 Elsevier Ltd. All rights reserved.
Introduction
Environmental issues that are related to the CO
2 emissions of conventional power plants have gained considerable attention in the past decades. Thus, pollution-free renewable energy-based generators (REGs) such as photovoltaic (PV) systems and wind turbine (WT) or hybrid systems have been proposed as alternative sources of electricity, particularly in future smart distribution systems
[1] . Upgrading or planning conventional distribution systems
by using single or hybrid REGs have certain economic and operational advantages, such as improved power balance during peak demand and reduction in investment and operational costs because of the flexible REG capacities
[2] . However, the use of dis-
persed and time-varying hybrid REGs results in bidirectional power flow, which either improves or worsens power quality
(PQ)-related problems in smart distribution systems
[3]
. In addition to REGs, electric vehicle (EV) technology and electric vehicle stations (EVSs) are rapidly being developed to reduce oil dependence and minimize greenhouse gas emissions. However, the negative influence of EVs and EVSs on system performance and power quality such as voltage drop and harmonic distortion should be
⇑
Corresponding author. Tel.: +60 1112800403; fax: +60 3 89216146.
E-mail address: farhoodnea_masoud@yahoo.com
(M. Farhoodnea).
http://dx.doi.org/10.1016/j.ijepes.2014.03.062
0142-0615/ Ó 2014 Elsevier Ltd. All rights reserved.
considered in system planning
[4] . To mitigate the negative power
quality effects of hybrid REGs and EVSs and to improve general power quality to meet the system baseline and standard requirements, suitable types of custom power devices (CPDs) such as active power conditioners (APCs) should be used in strategic locations based on economic feasibility.
To date, many heuristic optimization-based techniques have been proposed to solve the optimal placement and sizing problems of CPDs under a steady-state condition. Different objective functions and constraints have been introduced in heuristic optimization-based techniques to minimize device cost and mitigate certain power quality disturbances such as voltage sag and harmonic distortion. A fuzzy system has been applied to locate APCs optimally by minimizing harmonic distortion in active power systems
[5] . The basic genetic algorithm (GA) and niching GA (NGA)
have been applied to install several CPDs optimally such as the dynamic voltage restorer and thyristor voltage regulator to minimize the imposed costs caused by voltage sags and improve the overall network sag performance of power systems
[6–8] . The
applied NGA has the ability to explore a wider search space and decrease the probability of convergence in local optima. A binary gravitational search algorithm has also been proposed to solve the optimal placement problem of D-STATCOM and improve the reliability index of distribution systems
[9] . Furthermore, given

306 M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317 the discrete nature of the optimal placement and sizing problems of CPDs, several discrete optimization techniques such as discrete non-linear programming
[10]
and discrete particle swarm optimization (DPSO)
[11,12]
have been proposed to minimize the harmonic distortion and improve system reliability.
Considering the dynamic nature of real power systems and the operation dependency of REGs and EVSs to varying weather and loading conditions, the use of the steady-state conditions of system components and their operations is no longer applicable to system analysis. Therefore, certain system components cannot be accurately modeled in the steady state. For example, the quasi steady-state model of batteries, which is widely used in power system analysis, cannot represent the rapid variations of the performance characteristics of a battery bank at a fully discharged state.
The same problem may arise for most REG systems when their characteristics vary with changing weather conditions. Therefore, given that time-to-time variations in system characteristics are necessary to apply the optimization process in hybrid power systems, the problem should be formulated as a dynamic optimization problem.
This paper presents a new optimization technique by using the dynamic discrete firefly algorithm (DDFA) to determine the optimal size and location of APCs in a distribution system with hybrid
REGs and EVSs. A multi-objective problem is formulated to minimize the average voltage total harmonic distortion ( THD
V
), the voltage deviation at each sampling instant, and the total investment cost, which includes installation and incremental costs. The voltage limits, APC capacity limits, power flow limits, and THD
V for each individual bus are considered constraints in the optimization problem. To evaluate the performance of the proposed DDFA, a modified IEEE 16-bus test system consisting of an EVS and three
REGs, including WT, PV, and fuel cell (FC) power generation systems, is used and simulated in Matlab. The results are compared with the results obtained by the stationary firefly algorithm
(SFA), hybrid improved genetic algorithm (HIGA)
[13]
, and DPSO
[14]
to evaluate the effectiveness and accuracy of the proposed
DDFA.
System modeling
This section briefly discusses the applied dynamic model and required control methodology of REGs, EVSs, and APCs.
WT system model
Among the various types of WT, the doubly fed induction generator (DFIG)-WT is relevant to this study because of its advantages in improving power system stability and reliability during peak load or disturbance conditions. The DFIG also provides more flexibility in controlling active and reactive powers independently. The
DFIG-WT is a three-phase machine with two stator windings, including power and control windings, and a special rotor cage that can operate in induction and synchronous modes. To model a
DFIG-WT in synchronous mode with p p pole pair, the voltages at stator and rotor windings can be expressed as follows
[15]
: v p
¼ R p i p
þ j x p k p
þ d k p dt v c
¼ R c i c
þ j x p
ð p p
þ p c
Þ x r k p
þ d k c dt
ð 1 Þ
ð 2 Þ v r
¼ R r i r
þ j ð x p p p x r
Þ k r
þ d k r dt
¼ 0 ð 3 Þ where v , R , i , x , k , and p are the voltage, resistance, current, angular speed, mechanical angular displacement, and pole number, respectively; subscripts p , c , and r represent the power, control, and rotor windings, respectively.
In the same manner, the flux linkage vector for all types of winding can be defined as follows: k k c p
¼ L p i p k r
¼ L pr i p
þ M pr
¼ L c i c
þ M cr i r i r
þ M cr i c
þ L r i r
PV system model
ð 4 Þ
ð 5 Þ
ð 6 Þ where L and M are the self and mutual inductance of the windings, respectively.
Therefore, the electromagnetic torque can be expressed as the following:
T e
¼
3
2 p p h i
Im k p i p
3
2 p c
Im k c i c
ð 7 Þ
If the d -axis of the rotating flux is aligned with the power winding flux linkage, the power winding reactive power and rotor speed can be controlled by the d - and q -axes of the control winding current.
Figs. 1 and 2
present the detailed rotor side and grid-side converter control diagrams of the DFIG-WT based on the d - and q -axes current control. The rotor-side converter must inject variable rotor currents into the rotor circuit to attain decoupled active and reactive power control, where the grid-side converter must balance the power injected into the direct current (DC)-link capacitor and maintain a constant voltage
[16] .
I
The electric characteristics of a PV unit are commonly expressed in terms of the current–voltage or power–voltage relationships of the cell. The equivalent electrical circuit of a typical crystalline silicon PV module is shown in
Fig. 3 a, where
I , I
L
, and I d are the output terminal current, light-generated current, and diode current, respectively; R s and R sh are the internal resistance and shunt resistance of the module, respectively. The value of R s strongly depends on the quality of the used semi-conductor, and any variations in R s value can dramatically change the PV output
[17] . Based on
Fig. 3 a,
the output current of the module is expressed as follows:
I ¼ I
L
I d
V o
R sh
ð 8 Þ where V o is the voltage on the shunt resistance.
By using the classical diode current expression
[18]
and ignoring the last term, the output current I can be rewritten as follows:
¼ I
L
I o e q ð V þ IR s
Þ = nKT r 1 ð 9 Þ
I where I o is the saturation current, q is the electron charge, curve-fitting constant, K is the Boltzmann constant, T r n is the is the temperature, and n is the ideality factor, which has a value between one and two.
Furthermore, the saturation current I o at different operating temperatures can be expressed as the following: o
¼ I o Tr
T
3 n
T r e nK qVg
ð 1 = T 1 = Tr Þ
ð 10 Þ where
I o T r
¼
I sc T e qVoc
Tr nKTr r ð 11 Þ
1
V g is the band gap voltage, V oc Tr is the open circuit voltage, and is the short circuit current at the rated operating conditions.
I sc Tr
The photocurrent I
L in Eq.
radiation level G (W/m 2
(9)
is directly proportional to the solar
) and can be expressed as follows:

M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317
P ref
+
P meas
_
PI I q-ref
Q ref
+
_
Q meas
PI I d-ref dq/abc
Transform
I abc-ref
+
_ error
I abc-meas
Hysteresis
Comparator
Fig. 1.
Block diagram of a rotor-side converter control.
Gating
Signals
V dc-ref
+
_
V dc-meas
Q ref
+
_
Q meas
PI 1
I d-ref
+
_
PI 2
I q-ref
+
I d-meas
I q-meas
_
PI 3
PI 4
Xc
_
V meas
+
V d-ref
+ dq/abc
Transform
V abc-ref
Xc
_ +
V q-ref
307
+
_ error Hysteresis
Comparator
Gating
Signals
V abc-meas
Fig. 2.
Block diagram of a grid-side converter control.
V
DC
I
L
(A)
D
I d
R sh
+
-
V o
R s
I
+
-
V
I
L
¼ I
L T r
ð 1 þ
PV
Panel
I meas
V ref
+
V meas
_ error
PI/MPPT
(B)
PWM
Generator
DC-DC
Converter
DC-AC
Converter
Grid
Interface
Fig. 3.
PV system, (A) equivalent circuit of the PV module, (B) block diagram of the grid-connected PV system.
a
I sc
ð T T r
ÞÞ where
I
L T r
¼
G I sc T r
G r and a
Isc is the short circuit temperature coefficient.
ð 12 Þ
ð 13 Þ
The open circuit voltage V oc
, which is sensitive to temperature, can also be obtained as follows:
V oc
¼ V oc T r
ð 1 b
V oc
ð T T r
ÞÞ ð 14 Þ where b
Voc is the open circuit temperature coefficient.
Any PV module can be modeled for dynamic analysis by using the manufacturer-provided coefficient and Eqs.
(8)–(14) . The pro-
duced DC voltage of a PV module can be raised to a specific level

308 M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317 by using a DC–DC boost converter, where the proportional–integral controller and maximum power point tracking technique can be used to control efficiently the boost converter and produced power of PV arrays as shown in
Fig. 3
b. The produced DC power is then converted into alternating current (AC) power by using a threephase three-level voltage source converter. The power is then injected into the system by using a coupling transformer at the desired voltage level.
by using a voltage source inverter (VSI) controller unit, which is connected to the grid through a coupling transformer.
Fig. 4
presents the dynamic model of a grid-connected SOFC stack.
EVS system model
FC system model
I
The (FC) is an electrochemical device that can directly convert the chemical energy of gaseous fuel into electricity. The general structure of an FC consists of porous anode and cathode electrodes with an electrolyte layer in the middle. The electrolyte can be solid, such as solid oxide FCs (SOFCs) or liquid, such as molten carbonate
FCs. The SOFC has high overall efficiency, high multi-fuel capability, and is the most suitable FC for stationary applications.
Considering Nernst’s equation and ohmic losses, the total output voltage of the stack can be expressed as follows
[19] :
V ¼ N
0
E
0
þ
RT
2 F
" ln p
H
2 p p 0 : 5
O
2
H
2
O
# !
rI ¼ V
0 rI where E
0 is the voltage associated with the reaction free energy, R is the gas constant, r is the resistance associated with the ohmic losses of the stack, I is the stock current, F is the Faraday constant, and T is the absolute temperature.
p
H
2
, p
O
2
, and p
H
2
O are the H, O, and H pressures, respectively, which are expressed as the following:
2
O p
H
2
¼
1 þ
K
1
H2 s
H
2
S
!
q
H
2
2 K r
I ð 16 Þ p
O
2
¼
1 þ
1
K
O2 s
O
2
S
!
q
O
2 q
H2 q
O2
+
_
2 K r
2 K r
I
+
_
K r r
ð 15 p
H
2
O
¼
1
1 þ
K
H2O s
H
2
O
S
!
ð 2 K r
I Þ ð 18 Þ where K r is a constant value; s
H
2
, s
O
2
, and s
H
2
O are the values of the system pole associated with the H, O, and H
2
O flows, respectively; q
H
2 and q
O
2 are the molar flows of H and O; K
H
2
, K
H
2
, and K
H2O are the valve molar constants of H, O, and H
2
O, respectively. The produced DC voltage of an SOFC can be converted to an AC voltage
Þ
ð 17 Þ
Given that the EVS performance depends on the charging scenarios and requirements of future EVSs to operate stations that are similar to petrol filling stations, charging should be conducted under a fast-charging mode to decrease charging time. However, this approach requires high power levels. Therefore, the EVS is modeled as a dynamic DC load connected to the grid through an
AC/DC power converter, which includes a phase-shifting power transformer, rectifier, and DC–DC full-bridge converter, to provide
the predetermined DC voltage level ( Fig. 5
)
[20]
. The main purpose of the phase-shifting power transformer is to mitigate current harmonic distortion and increase system power factor. The rectifier and DC–DC converter are fed through the secondary winding of the transformer to provide the required power of the EVS loads.
APC
An APC is a three-phase and parallel multi-function power electronic-based device that can compensate for voltage sag and harmonic distortion, conduct power factor correction, and improve the voltage profile. The insulated-gate bipolar transistor based
VSI is the main part of the APC, which converts the DC-link voltage into three-phase AC voltages with controllable amplitudes, frequencies, and phases. The required interface between the APC and the grid is usually arranged through an AC filter and a coupling transformer.
To control the APC in the presence of a harmonic polluting industrial load at the point of common coupling (PCC), the instantaneous load current i
Load
( t ) and PCC voltage v pcc
( t ) can be defined as follows
[21] :
i
Load
ð t Þ ¼ I
1 sin ð x t þ u
1
Þ þ
X
I h sin ð h x t þ u h
Þ h ¼ 2
ð 19 Þ v pcc
ð t Þ ¼ V m sin ð x t Þ ð 20 Þ where x , h , and u are the radial frequency, harmonic order, and phase angles of the load current and PCC voltage, respectively.
By using Eqs.
(19) and (20)
, the instantaneous load power P
Load
( t ) can be expressed as follows:
P
Load
ð t Þ ¼ v pcc
ð t Þ i
Load
ð t Þ
¼ V m
I
1 sin
2
ð x t Þ cos ð u
1
Þ þ V m
I
1 sin ð x t Þ cos ð x t Þ sin ð u
1
Þ
þ V m sin ð x t Þ
X
I h sin ð h x t þ u h
Þ ¼ p f
ð t Þ þ p r
ð t Þ þ p h
ð t Þ h ¼ 2
ð 21 Þ where p f
( t ), p r
( t ), and p h
( t ) are the fundamental components of power, reactive power, and harmonic power, respectively.
p
H2 p
H2O p
O2
V
0
Fig. 4.
Grid-connected SOFC stack dynamic model.
+
_
V
R
S
T
Secondary
Winding
Primary
Winding
Rectifier
Set
DC-DC
Converter
Secondary
Winding
Phase-shifting Transformer
Fig. 5.
Block diagram of the EVS.
+ DC
Output

M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317
Measured the APC terminal voltage
V dc
V dc-ref error
LPF
PID
Controller
I s-ref
PLL
I
* s-ref
Hysteresis
Comparator
Gating Signal for the APF
Measured line current, I s
Fig. 6.
Block diagram of the APC controller.
309
After the full compensation, the desired source current i
0 pcc
ð t Þ , which is supplied by the PCC, should have a sinusoidal wave form: i
0 pcc
ð t Þ ¼ p f
ð t Þ = v pcc
ð t Þ ¼ I
1 cos ð u
1
Þ sin ð x t Þ ð 22 Þ
If the APC compensates for the total reactive and harmonic power, the PCC current i
0 pcc
ð t Þ will be in phase with the PCC voltage and will be purely sinusoidal. Thus, the injected compensation current i comp
( t ) can be expressed as follows: i comp
ð t Þ ¼ i
Load
ð t Þ i
0 pcc
ð t Þ ð 23 Þ
To use Eqs.
(19)–(23)
in the APC controller and estimate the required compensation current, a low-pass filter (LPF), proportional–integral–derivative (PID) controller, phase-locked loop
(PLL) unit, and hysteresis comparator are used (
Fig. 6
)
[22,23]
.
Therefore, the DC-link voltage of the APC is first measured and compared with the reference voltage to generate the DC voltage error. The LPF, which has a cut-off frequency of 50 Hz, smoothens the generated error signal and proceeds to the PID block. The PID block estimates the magnitude of the source current i
0 pcc
ð t Þ , which is considered the magnitude of the reference current I s ref
. The
PCC voltage phase u is extracted by using the PLL unit to compute the reference current I s ref ated I s ref
. Thereafter, the error between the generand line current is passed through a hysteresis comparator to generate the gating signals independently for each APC phase.
Proposed optimization algorithm
Discrete firefly algorithm
The firefly algorithm (FA) is an optimization technique that is inspired by the social behavior of fireflies in finding their mates.
This technique solves continuous multi-objective optimization problems with a proven superior success rate and efficiency compared with other optimization methods such as the particle swarm optimization and GA
[24]
. The conventional FA is formulated based on two key issues: the variation in light intensity I and firefly attractiveness b . Light intensity I and firefly attractiveness b , which varies with distance r under a fixed light absorption coefficient c , can be defined as follows:
I ð r Þ ¼ I
0 exp ð c r 2
Þ ð 24 Þ b ð r Þ ¼ b
0 exp ð c r 2 Þ ð 25 Þ where I
0 and b
0 are the light intensity and attractiveness at r = 0, respectively.
The distance between any two fireflies i and j , which are placed at locations x i and x j
, respectively, can be expressed in terms of the
Euclidean distance: r ij
¼ k x i x j k ¼ q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d 2 D
ð x i ; d x j ; d
Þ
2
ð 26 Þ where x i , d is the d -th component of the spatial coordinate th firefly, and D is the dimension of the problem.
x i of the i -
The movement of a firefly i to a more attractive firefly j can be expressed as the following: x i k þ 1 ¼ x k i
þ b
0 e c r k ij
2
ð x k j x k i
Þ þ a n i
ð 27 Þ where a is the randomization parameter, and n i is a vector of random numbers with Gaussian or uniform distributions.
To discretize the FA and improve its performance, a tangent hyperbolic sigmoid function is applied as a constraint to re-compute the distance r and update the movement x :
S 0
ð r k ij
Þ ¼ j tanh ð k r k ij
Þj x i k þ 1 ¼
8
< x i k
: x i k
þ b
0 e c r k
2 ij
ð x j k x i k Þ þ a n i if rand < S 0 ð r k ij
Þ else
ð 28 Þ where k is a constant coefficient that is close to one, and rand is a random number in the interval [0, 1].
Eq.
(28)
shows that by making the positions of the fireflies more attractive and by decreasing the distance, the probability of S 0 in
Eq.
(28)
tends to be zero. Therefore, when fireflies are far from each other, the probability of moving x i k in Eq.
(29)
to a new location x i k þ 1 is high, whereas the probability of moving x i k is decreased by decreasing the distance at further iterations. When the distance is zero, the position x i k remains unchanged as a new location x i k þ 1 .
Dynamic discrete firefly algorithm
Given the dynamic and non-deterministic nature of most optimization problems in the real world, static solutions are no longer applicable to new environments. Therefore, problems should be considered dynamic state optimization problems. In real dynamic environments, several local optima exist, and each local optimum can change to a global optimum after environmental changes. As opposed to static optimization problems, the main goal in dynamic environments is not only to find a global optimum but also to track the optimum in the problem space during environmental changes.
Therefore, the dynamic optimization problem can be defined as a sequence of static problems linked by several dynamic mechanisms to find the best solutions or solutions that are closest to the global optimum
[25]
. The applied mechanisms on the DFA to enable it to operate in a dynamic environment are presented as follows.
Finder–tracker mechanism
The main task of finder fireflies is to find the peaks in the current search space, wherein the tracker fireflies should cover the discovered peaks and track them after environmental changes.
Therefore, at the beginning of algorithm execution, only the finder

310 M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317
Initialize Finder Fireflies population x i-finder
each Finder Fireflies i-finder
Determine the light intensity I and
Move Finder Fireflies to a better location by using Eqs, (28) and (29)
Evaluate new solutions and update light intensity
Finder Fireflies converged
Rank the Finder Fireflies in ascending order
Replace Finder Fireflies with Tracker Fireflies (activate Tracker Fireflies)
Reinitialize Finder Fireflies
Fig. 7.
Implementation procedure for the finder–tracker mechanism.
Insert objective function f ( x ), x = ( x
1
, x
2
, …, x d
)
T
Set monitoring Fireflies x i-monitor
, i-monitor = 1, 2, …, k
Initialize Finder Firefly population x i-finder
, i-finder = 1, 2, …, n
Determine light intensity I i-finer
at x i-finer
using f ( x i-finer
)
Set light absorption coefficient , randomize coefficient
Evaluate and record the objective function by using x i-monitor while ( t < simulation time ) for i-finer = 1: n all n fireflies for j-finer = 1: n if ( I i-finer
< I j-finer
), Move Firefly i-finer towards j-finer ; end if
Vary attractiveness with distance r via exp[− r
2
]
Discrete the distance between Fireflies and movement by using Eqs. (28) and (29)
Evaluate new solutions by using Tracker Fireflies and update light intensity end for j end for i if Finder Fireflies converged
Rank Finder Fireflies in ascending order
Replace Finder Fireflies with Tracker Fireflies end if
Reinitialize Finder Fireflies
Evaluate the objective function by using x i-monitor
and compare with recorded ones if environments change
Apply diversity maintenance mechanism on Tracker Fireflies by using Eq. (30) end if
Revaluate new solutions by using Tracker Fireflies and update light intensity
Rank Tracker Fireflies and find the current global best end while
PrintResults
Fig. 8.
Implementation procedure of DDFA.

M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317 mechanism is activated by random initialization in the search space, and the tracker fireflies should be activated by replacing the finder fireflies on the finder position at the peak.
Fig. 7
describes the finder–tracker mechanism in terms of a pseudocode.
311 underloading, unacceptable voltage fluctuations, voltage drops, or voltage flickers.
Environment change detection
Given the significance of detecting environmental changes, several monitoring fireflies are set in the search space to re-evaluate the fitness landscape in each iteration. A change in the resulting fitness indicates that an environmental change has occurred
[26]
.
After environment change detection by monitoring fireflies, the diversity maintenance mechanism should be applied to adopt the movement of the fireflies in a new environment.
Harmonic distortion
Harmonic distortion may occur because of the embedded power inverters in REG, EVS, and harmonic polluting loads. Harmonic distortion can increase the risk of parallel and series resonances, overheating in capacitor banks and transformers, neutral overcurrent, and false operations of protective devices.
Multi-objective problem formulation
To solve the optimal APC placement and sizing problems, mitigate the negative power quality effects of REGs and EVS, and improve the general power quality of the system while minimizing the total investment costs of the located APCs, a multi-objective optimization problem is formulated that consists of three subfunctions and three constraints to represent the control variables.
Diversity maintenance mechanism
Given the convergence probability of finder fireflies and the activation of tracker fireflies before environmental changes, the distance between fireflies may be considerably small. Thus, the movement of tracker fireflies toward the new position in Eq.
(29)
is almost unchanged. The diversity maintenance mechanism should be essentially applied on the firefly population to change the movements of tracker fireflies based on their position before an environmental change: x k þ 1 i tracker
¼ x k i tracker
þ ð rand
D p Þ ð 30 Þ where rand is a uniform random vector with a value between 1 and 1, D is the problem dimension, and p is the shift length. Diversity maintenance for finder fireflies is not required after an environmental change because they are automatically reinitialized after convergence.
By employing the aforementioned mechanisms, the described
DDFA solves multi-objective optimization problems in dynamic environments.
Fig. 8
describes the procedure in implementing the DDFA in terms of a pseudocode.
Problem formulation
Power quality effects of REGs and EVSs
Sub-objective functions
Normalized average voltage deviation.
To minimize the voltage deviation of the entire system caused by PV and WT because of the variations in weather conditions, the voltage deviation index is expressed as the deviation of the voltage magnitudes of all buses from the reference voltage in an M -bus system:
V de v
¼ s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
M
V i ref
V i
2 i ¼ 1 V i ref
ð 31 Þ where V i ref and V i are the i -th bus reference voltage and measured voltage at bus I , respectively. Therefore, the normalized average voltage deviation index of the given system can be derived from
Eq.
(31)
:
V de v a v r
¼
V p ffiffiffiffiffi
M
ð 32 Þ
Eq.
(23)
can be used as a measure to evaluate the deviation of bus voltages caused by unregulated voltage and voltage drops because of high EVS load demand or motor starting in the system.
Despite the proven benefits of REGs and their significance to future distribution systems, REGs may cause serious operational issues to distribution systems. The severity of these problems directly depends on the applied technology, penetration level, and geography of the installation. Therefore, the negative effects of EVS as a critical part of future transportation systems must also be considered. The following are the major technical problems related to the power quality of the system caused by hybrid REGs and EVSs.
Undervoltage or overvoltage
Undervoltage or overvoltage typically occurs in distribution because of the active power injections of REGs and rate changes of reactive power flow in the system. Thus, nearby buses may experience undervoltage or overvoltage problems because of the lack of reactive power. An unmanaged EVS load demand can cause severe problems that are related to the system voltage profile, such as overheating of cables and transformers.
REG power fluctuation
Power fluctuations are commonly observed in grid-connected
WT and PV systems because of the minute-to-minute variations in wind speed or solar irradiance. The severity of such a problem strongly depends on weather conditions and installation geography. Power fluctuations can increase the likelihood of overloading,
Average voltage total harmonic distortion.
To control the THD
V level of the entire system caused by embedded inverters in REGs, EVS, and harmonic polluting loads, the average of the normalized THD
V of the system buses is expressed as the following:
THD
V a v r
¼
P
M i ¼ 1
THD norm
V i
M
ð 33 Þ where THD norm
V i is the normalized THD
V at bus i .
Total device investment costs.
The total cost of an APC, including installation and incremental costs
[27] , can be defined as a normal-
ized polynomial function:
C
APC
¼
P k i ¼ 1
ð a S 2
APC i b S
APC i
Cost max
þ C
0 i
Þ
ð 34 Þ where C
APC
, C
0
, and S
APC are the normalized total cost, fixed installation cost, and operating range of the APC, respectively; a and b are fixed coefficients, which are assumed in this study as 0.0002466
and 0.2243, respectively.
All sub-objective functions in Eqs.
(32)–(34)
have been converted per unit by normalizing each component to maintain the average values between 0 and 1.
Controlling constraints
Bus voltage limits.
To maintain the system stability margin and power quality considerations, the recovered voltage level of all sys-

312 tem buses should not violate the specified voltage limits and should satisfy the following inequality:
V i min
6
V i
6
V i max
ð 35 Þ where V i
, V i min
, and V i max are the bus voltage and the minimum and maximum permissible voltages at bus i , respectively.
Device capacity limits.
Given the limited energy storage capacity of the APC, the size of the installed APC should be constrained within a permissible band and should satisfy the following inequality:
S
APC min
6 S
APC
6 S
APC max
ð 36 Þ where S
APC
, S
APC min
, and S
APC max are the APC size and the minimum and maximum permissible values of the capacity of each APC, respectively.
S l
6
S l max
M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317
Power flow limits.
The apparent power S l transmitted through branch l must not exceed the maximum thermal limit S l max the steady-state operation or at any sampling time: in
ð 37 Þ
Voltage THD limits.
The THD
V value at each bus i should be less than its maximum value to meet the limits defined in IEEE Standard 519
[28]
:
THD
V i
6
THD
V max
Overall objective function
ð 38 Þ active and reactive powers of the APC at fundamental and harmonic frequencies, as well as the possible installation locations
(system buses), are considered the optimization variables. After initializing the locations and active and reactive powers of APCs as the tracker firefly population x i finder
( Fig. 8 ), the bus voltages
of the system in fundamental and harmonic frequencies are calculated at each sampling time to calculate the voltage variation THD
V
, total device cost of the system, and objective function in Eq.
(39)
.
Thus, by activating and ranking the tracker fireflies to find the current local or global solution, the algorithm can proceed to the next iteration. If convergence is not achieved at each sampling time, the algorithm continues with the next generation until the sampling period is finished.
Fig. 9
presents the flowchart of the implementation procedure for the proposed DDFA.
Given the consecutive environment changes caused by weather and EVS load variations, the DDFA necessarily finds different solutions (APC location and size) based on the current environment at each sampling time. These solutions may vary for the next environmental changes. Therefore, the number of required APCs to be installed should be selected to allow some APCs to be switched on simultaneously for the current environment. The remaining
APCs are maintained in standby mode for the next environment.
The on and off states of the installed APCs can be managed and controlled through a coordination center equipped with a fast communication system such as optical fibers, global positioning system, and simple time network protocols. Such a coordination center, which is beyond the scope of this paper, can provide time synchronization with nanosecond precision and can be used to cover the premium power park concept
[29] .
Simulation and test results To solve the aforementioned constrained multi-objective optimization problem, which consists of the defined sub-objective functions in Eqs.
(32)–(34) , a single-objective optimization prob-
lem is formed by using the weighted sum method. The penalty function approach is also applied to insert the constraint violations in Eqs.
(35)–(38)
into the designed single-objective optimization problem:
F ¼ w
1
V de v a v r
þ w
2
THD
V a v r
þ w
3
C
APC
þ c
V
X
½ max ð V i
V i max
; 0 Þ þ max ð V i min
V i
; 0 Þ þ i 2 M c l
X max ðj S l j
j S l max j ; 0 Þ þ
þ max ð S
APC min c
APC
X
½ max ð S
APC i 2 P
S
APC
; 0 Þ þ c
THD
X l 2 L
S
APC max
; 0 Þ max ð THD
V i i 2 M
THD
V max
; 0 Þ ð 39 Þ where w i ual sub-objective function in which ables
P w i
= 1 and 0 < w i
< 1. Varic , L , P , and M are the penalty multipliers for the violated constraints, namely, large fixed scalar number, total line number, total APC number, and total bus number, respectively. The assigned weight factors depend on the significance of each objective function, which may vary based on system preferences. In this study, the assumed weighting factors in Eq.
(39)
are w
1
= w
2
= 0.4 and w
3
= 0.2, in which the voltage deviation and harmonic distortion are considered to be more important than the total investment cost.
Application of the proposed DDFA
To determine the optimal location and size of the APC in radial distribution systems, mitigate the negative power quality effects of
REGs and EVS, and improve general power quality, DDFA is applied to minimize the objective function in Eq.
(39)
. The number of required APCs and system data are considered DDFA inputs. The
To verify the effectiveness and applicability of the proposed
DDFA on radial distribution systems with hybrid REGs–EVS pene-
tration, the IEEE 16-bus test system ( Fig. 10 ) is modified and mod-
eled by using Matlab
[17]
. The IEEE 16-bus test system is intended to feed a heavy induction motor load at bus 15 and distributed linear and non-linear loads with a total power of 9.34 MVA, which vary between 70% and 100% of the nominal power during simulation. The non-linear loads that distort system voltages and current waveforms are modeled as harmonic current sources with the harmonic components described in
[30] . A 1 MW FC, 1.3 MW grid-
connected PV system, and 1.6 MW wind farm are placed on buses
4, 14, and 16, respectively, to supply the required power for local loads and exchange the remaining power with a system with a high-penetration level of approximately 37%. A 1.3 MW EVS is also placed on bus 6.
The data required to model the PV arrays, WT, and FC are gathered from commercially manufactured devices such as SunPower
SPR-305
[31] , Sanyo HIP-225 [32]
, General Electric 2.5–100 WT
[33] , and FuelCell Energy DFC3000 [34]
. Meteorological data related to solar irradiance and wind speed under different weather conditions within a year are collected from the Malaysian Meteorological Service
[35]
and are used to generate different patterns for slow and fast weather variations (
Fig. 11
). The pattern of EVS load demand is also normalized and included in
Fig. 11 [36]
. A total of 700 samples are created, which represent every 2 min sampling over 24 h. The samples are normalized and created in the form of a step signal to provide sufficient time for the proposed and applied optimization algorithms to find the optimum or near optimum solutions (
Fig. 11
). The produced power of the FC is assumed constant because of slow H and O molar flows. Therefore, the FC unit contributes to harmonic distortion.
To validate the proposed DDFA optimization method, five APCs with power rating limits of [01] p.u. and with base powers of
100 kVA are placed in the system. However, only three APCs are

M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317
Set the monitoring Fireflies
Discrete the Fireflies movements
Rank the Finder Fireflies and a
Reinitialize the Finder Fireflies
No
Environments change Yes
Apply diversity maintenance mechanism using (30)
No
Revaluate new solutions using Tracker Fireflies and update light intensity for new environments
313
End of sampling Time
Yes
Fig. 9.
DDFA implementation procedure to solve the APC placement and sizing problems.
simultaneously switched on, and the remaining APCs are in standby mode. The number of APCs can be chosen as any integer number. Nonetheless, by increasing the number of APCs, the power assigned to each APC decreases. The total APC cost may also increase because of the fixed installation cost.
The minimum and maximum voltage limits of the system are considered 0.95 and 1.05 p.u., respectively. The objective of the proposed method are to mitigate the negative power quality effects of REGs and EVS, including harmonic distortion mitigation and voltage profile degradation, by using the optimal placement of APCs. To find the best values for the DDFA parameters, the sensitivity analysis is applied for the 10 run times and the best parameter setting, which result in the smallest average objective function value, are bolded as shown in
Table 1 . The optimization
results of DDFA are then compared with the results of SFA, HIGA, and DPSO
[14]
.
Table 2
reports the simulation and comparison results for the 16-bus test system.
The DDFA achieves better performance in minimizing F and determining the optimal location and size of the APCs than the
DPSO and SFA, which return a larger F value because of the inability to track global or near global solutions (
Table 2 ). The estimated
total cost of all five APCs based on DDFA is significantly smaller than those of other methods, thus indicating lighter installation and operational burdens on utilities for system planning or further

314
B1
Utility
Grid
M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317
L 9
B15
Non linear load
Linear load
B2
B16
L 1
Tie 1
L10 WT
B3 B8
T 7
B4 B5 B9 B11
L 2 FC
B6
L 3 EVS
Tie 2
B10 B12
B7
L 5
L 6
L 4
Fig. 10.
Single line diagram of the IEEE 16-bus test system.
Tie 3
B13
B14
L 7
L 8
PV
Table 1
Sensitivity analysis of DDFA parameters.
a
0.5
0.6
0.7
0.8
0.9
1
0.1
0.2
0.3
0.4
b
0
0.6
0.5
0.4
0.3
0.2
0.1
1
0.9
0.8
0.7
c
5
6
7
8
9
10
3
4
1
2
Fig. 11.
Solar irradiance, wind speed, and EVS load patterns.
Average objective function, F
0.406371
0.399237
0.392657
0.376319
0.364825
0.358962
0.359209
0.366177
0.381919
0.397103
system development. To evaluate better the performance of the proposed method, the convergence characteristics of the DDFA for the 16-bus system are shown and compared in
Fig. 12 . The
DDFA converges smoothly and quickly in tracking the environment
changes ( Fig. 12 ). The DPSO and HIGA are not as accurate as the
DDFA, and the SFA has the worst performance among other methods because of its lack of tracking and diversity maintenance mechanisms.
To measure the efficiency of the algorithms, the offline performance index (OPI) is used. The OPI is defined as the average of the best solutions found over a given number of periods
[37]
. In minimization problems, the OPI value is a positive number, a smaller OPI value corresponds to better algorithm performance.

M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317
Table 2
Optimization results of the 16-bus test system.
Solver
SFA
HIGA
DPSO
DDFA
Location (Bus)
3, 4, 9,11, 15
2, 8, 10,13, 14
2, 5, 9, 11, 14
2, 4, 7, 10, 15
Maximum required APC power rating (p.u.)
0.863, 0.879, 0.837,0.475, 0.623
0.835, 0.771, 0.761, 0.418, 0.659
0.721, 0.834, 0.805, 0.359, 0.512
0.673, 0.794, 0.736, 0.317, 0.472
APC total cost (US $)
6,104,000
5,851,000
5,623,000
5,492,000
Max. objective function,
0.4842
0.4713
0.4498
0.4172
F
315
Min. objective function, F
0.3667
0.3645
0.3440
0.3378
Fig. 12.
Convergence characteristics in the IEEE 16-bus test system.
Fig. 13
shows the OPI curve of the first 300 samples for the 25 run times of the SFA, DDFA, HIGA, and DPSO.
Fig. 13
also demonstrates that the DDFA has a smaller OPI in the 300 samples than the other methods, thus indicating the high accuracy of the DDFA in the optimal placement of APCs in distribution systems. Note that the average execution time of the OPI test for DDFA, DPSO, HIGA and SFA are 1296, 1847, 2563 and 3291 s, respectively.
The switching states of the applied APCs, which are placed at buses 2, 4, 7, 10, and 15, and the voltage profile of the system for typical bus 5, 9, and 15 before and after optimal APC placement are measured and shown in
Figs. 14 and 15
, respectively. At each sampling time, three APCs out of five are operated, and the remaining APCs are switched off by the coordination center (
Figs. 14 and
15 ). The APCs in the sample buses can accurately regulate voltage
fluctuations and compensate for the undervoltage caused by the induction motor and EVS peak demand. The spikes at the beginning of the regulated voltage profiles are created because of the effort of the DDFA to find the global or near global optimum, as well as the tracker firefly activation. Therefore, smooth voltage profiles are observable in other samples, thus indicating that the proposed DDFA can find suitable solutions during environmental changes.
Fig. 13.
OPI characteristics of DDFA, DPSO, HIGA, and SFA.

316 M. Farhoodnea et al. / Electrical Power and Energy Systems 61 (2014) 305–317
Fig. 14.
On and off states of the APCs in the 16-bus test system.
Fig. 15.
Measured voltages of bus 5, 9, and 15 over the sampling period.
Table 3
Calculated average THD
V and average voltage deviation.
Bus no.
9
10
11
12
13
14
15
16
5
6
7
8
3
4
1
2
THD
V
(%)
No APC
7.675
9.088
12.086
12.457
12.108
12.113
12.117
18.376
25.148
25.148
18.491
18.492
18.505
18.416
18.906
18.922
With APCs
1.563
1.561
4.779
4.658
4.826
4.953
4.214
4.213
1.247
2.310
2.228
3.796
4.259
4.218
3.230
4.851
Voltage dev. (%)
No APC With APCs
10.329
10.329
10.167
10.167
10.235
9.802
11.140
11.215
0.000
2.727
5.426
5.741
5.596
5.633
5.666
9.606
0.025
0.025
0.015
0.015
0.014
0.020
0.031
0.032
0.000
0.021
0.012
0.027
0.011
0.022
0.032
0.018
The average THD
V and average voltage deviation observed at each bus in the 16-bus test system before and after APC installation are computed. The results are reported in
Table 3
. After the optimal
APC placement, the voltage fluctuations in the PV and WT, which also result in a voltage drop because of the presence of EVS, are
obviously improved ( Table 3 ). The average voltage harmonic dis-
tortions caused by the power electronic-based inverters of REGs,
EVS, and harmonic polluting loads are reduced below 5% at each bus and meet IEEE Standard 519 requirements.
Conclusion
We have proposed a method to place APCs optimally to mitigate the negative power quality effects of REGs and EVS in distribution systems under dynamic environments. The proposed method is based on a multi-objective function optimization problem, which is solved by using the proposed DDFA to enhance the system voltage profile and by minimizing the THD
V and total investment cost over the sampling time. The performance of the proposed method

is then evaluated on the radial IEEE 16-bus test system. The results are compared with the results of the SFA and DPSO to verify the superiority of the proposed DDFA. The simulation and comparison results prove the ability and accuracy of the DDFA compared with other optimization techniques in minimizing the objective function F and in improving the general power quality of the system.
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