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Title: Dynamic Placement Analysis of Wind Power Generation Units in Distribution Power Systems
Author: Mohammad Reza Baghayipour, Amin Hajizadeh, Amir Shahirinia and Zhe Chen

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energies
Article

Dynamic Placement Analysis of Wind Power
Generation Units in Distribution Power Systems
Mohammad Reza Baghayipour 1
1
2
3
4

*

ID

, Amin Hajizadeh 2, *

ID

, Amir Shahirinia 3 and Zhe Chen 4

Department of Electrical Engineering, Kosar University of Bojnord, Bojnord 1545894156, Iran;
mbpower@gmail.com
Department of Energy Technology, Aalborg University, 6700 Esbjerg, Denmark
Department of Electrical Engineering, University of the District of Columbia, Washington DC, DC 57206,
USA; amir.shahirinia@udc.edu
Department of Energy Technology, Aalborg University, 9220 Aalborg, Denmark; zch@et.aau.dk
Correspondence: aha@et.aau.dk

Received: 16 August 2018; Accepted: 3 September 2018; Published: 5 September 2018




Abstract: The placement problem of distributed generators (DGs) in distribution networks becomes
much more complicated in the case of using the DGs with renewable energy resources. Due to
several reasons such as, their intermittent output powers, the interactions between DGs and the rest
of the distribution network, and considering other involved uncertainties are very vital. This paper
develops a new approach for optimal placement of wind energy based DGs (WDGs) in which
all of such influences are carefully handled. The proposed method considers the time variations
of dynamic nodal demands, nodal voltage magnitudes, and wind speed in the WDG placement
process simultaneously. Thereby, an accurate dynamic model of the active and reactive powers
injected by the WDG to the system is employed in which the interactions between the WDG and the
distribution network are well regarded. Finally, simulation results are given to show the capability
of the proposed approach. As it is demonstrated in the numerical analysis of the radial 33-bus
distribution test network, the proposed placement algorithm can efficiently determine the optimal
bus for connecting the WDG and is suitable for real applications.
Keywords: dynamic placement; wind power; voltage stability; distribution grids

1. Introduction
Nowadays, there is an increasing effort for employing various types of distributed generations
(DGs) in distribution networks to supply some part of the electricity demand [1]. Proper placement of
DGs, such as wind turbines and photovoltaic units, in the distribution system is still a very challenging
issue for obtaining their maximum potential benefits [2]. The most significant concern posed regarding
such energy resources is their intermittent and uncertain natures [3]. The amount of electrical power
deliverable from a wind-based DG (WDG) is variable and may differ from its rated output power
and is dependent on the wind speed, and the other ambient characteristics such as the occasion and
geographical site in which the WDG is operated. This matter indeed affects the placement analysis of
WDGs in distribution networks, and is a significant problem which should be discussed in more detail.
Regarding the published literature, there are two different aspects of WDG installation in distribution
power systems. The first aspect is to locate the optimum topographical site for installing the renewable
energy-based DG and its optimum capacity, from the viewpoint of economic and technical concerns,
and is usually known as “DG feasibility, siting, and sizing study”, as investigated previously [4,5].
The second aspect is often known as the “DG placement problem” and aims to determine the optimum
electrical node to which the DG should be connected, with the objective of reforming some of the
Energies 2018, 11, 2326; doi:10.3390/en11092326

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electrical characteristics (e.g., loss, voltage profile, etc.) in the distribution system. For example,
the effects of sitting and optimal placement of DG units have been studied by many researchers [6];
different methods of optimal DG placement such as the use of a Kalman filter algorithm have been
studied [7] to find the suitable optimal size and location of DG units.
The authors of a previous study [8] present a decision-making algorithm that has been developed
for the optimum size and placement of distributed generation (DG) units in distribution networks.
The algorithm can estimate the optimum DG size to be installed, based on the improvement of voltage
profiles and the reduction of the network’s real and reactive power losses. The proposed algorithm has
been tested on the IEEE 33-bus radial distribution system.
Using the geographic information system environment for planning and analyzing the steady state
and dynamic behavior of distributed generation was introduced in a past paper [9]. The functionality
of this platform enables the utility internal business process with a single graphical analysis structure.
Equally the authors of a previous paper [10] did a comparative analysis to find the optimal
position of the synchronous condenser in an electrical grid, improve voltage stability, and mitigate
power losses. In the same vein, research indicating the best possible position of a wind farm in
a distribution power system was presented previously [11].
In this regard, most of the previous papers have exploited analytical or heuristic approaches in
order to solve the optimization problem of DG optimal placement subjected to the system operational
constraints (i.e., load flow equations and the system security limits). Most of them [10–12] have treated
the renewable energy-based DG as a constant power source in the placement problem. It is obvious
that due to the intermittent output powers of the renewable energy based DGs this treatment does
not yield accurate results. Here, a few papers have proposed the approaches of treating the variations
and uncertainties of the renewable energy resources. For example, two previous papers [13,14]
have treated the Wind and Solar type DGs as time-varying power sources with constant power
factors. In a past paper [14], a radial feeder with a time-varying loads and DG was simulated under
uniformly distributed, centrally distributed, and increasingly distributed loads. This study is helpful
in understanding the effect of variable power WDG sources on distribution systems with time-varying
loads. But, the detailed dynamic model of WDG, taking account of variation in wind speed and
variable nodal demand, has been investigated.
In addition, the authors of a past paper proposed [15] a bounded and symmetric uncertainty
optimization approach for generation and transmission planning under demand and wind generation
uncertainty. In fact, the combination of two uncertainty methods, i.e., robust and stochastic
optimization approaches are utilized and formulated in this paper. Besides, to handle with this
uncertainty, a Weibull distribution (WD) is considered as wind distribution, while load distribution is
counted by a normal distribution (ND).
Thereby, they have regarded the DGs in the placement process by solving several successive load
flow analyses for different time steps with different levels of DG generations and load demands. Those
two papers each have utilized some specific approaches in order to determine the amounts of electrical
power produced by the DGs in different times from those renewable resources (i.e., wind speed and
solar radiated energy for wind and solar type DGs, respectively). For this purpose, the authors of
a previous paper [14] employed some sample wind speed data in a simulation process to consider the
operation of 1 MW WDG. Alternatively, the authors of another past paper [13] extracted the output
power variations of DGs by considering some straight algebraic input-output functions for the DGs,
and ignoring their detailed dynamic behaviors. For example, the authors of a previous paper [14]
treated the WDG as a power source with a constant power factor, while, the reactive power exchanged
between a WDG (based on the induction generators); the distribution network was directly affected
by the voltage magnitude of the bus to which the DG was connected. On the other hand, the bus
voltage magnitude was in turn influenced by the amounts of demanded loads as well as the active
and reactive powers injected by DGs to the distribution system at different times. Therefore, using
VAR compensators to mitigate the power quality problems and reactive power control are vital [16].

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For instance, in a previous paper [17] a relative control strategy based on the local reactive power
regulation was proposed to achieve the reactive power compensation without an upper communication
system. Improving the voltage profile and minimizing power losses to improve the power quality is
discussed previously [18] by proper regulation of the reactive power of the WDG. The authors of a past
paper [19] introduced a control approach and supplementary controllers for the operation of a hybrid
stand-alone system composed of a wind generation unit and a conventional generation unit based on
the synchronous generator (CGU). The proposed controllers allow the islanded or isolated operation
of small power systems with a predominance of wind generation. The voltage stability problem in the
presence of WDG was also discussed previously [20,21].
Hence, not only is it not possible to assume a constant value for the power factor of a WDG, but also
its accurate time variations cannot easily be calculated. This obviously demonstrates the complexity of
the placement problem for DGs with renewable energy resources that necessitate regarding all the
interactions between the different components of the system (i.e., the loads, DGs, and the distribution
network itself), which none of the previous papers have done. For this purpose, the dynamic behavior
of WDGs is taken into account while they are connected to the grid. In other former studies the DGs
have not been considered dynamic and have been simulated as static sources, ignoring the interactions
between the distribution system and DGs. Moreover, to implement the dynamic placement analysis,
the time variations of dynamic nodal demands, nodal voltage magnitudes, and wind speed in the WDG
placement procedure are taken into account simultaneously. By this means, an accurate dynamic model
of active and reactive powers injected by WDG to the system is employed in which the interactions
between the WDG and the distribution network are well-observed.
This paper aims to deal with the above problem by introducing a new placement algorithm for
WDGs in which all the mentioned interactions are well regarded. The rest of this paper is organized
as follows. First, in Section 2 the concept and structure of the intended WDG placement problem are
presented. Moreover, in this section, the ways of creating the different time-dependent data for the
purposed WDG placement problem are clarified, including the monthly average diurnal patterns of
demand, wind speed, and voltage magnitude of the candidate bus to which the WDG is going to be
connected. In Section 3, the model adopted for distribution load flow is also explained. Section 4
presents the kernel of the proposed WDG placement algorithm. The algorithm is then verified by the
numerical analysis in Section 5, and finally, Section 6 concludes the paper.
2. Problem Definition and Formulation
The general definition and structure of the WDG placement problem under study is illustrated in
Figure 1. According to this figure, the WDG placement problem is a kind of optimization problem with
some objective function and constraints. However, due to the intermittent and time-variant nature of
wind speed and demand, this optimization problem cannot be directly formulated. Thus, the block
diagram in Figure 1 is utilized here for the problem definition, including three principal blocks as
follows:





The first block models the objective function.
The second block is treated as the main equality constraint of the optimization problem.
It models the power balance constraint considering the interactions between WDG and the
distribution network.
The third block comprises the inequality constraints of the optimization problem.

The aim of this paper is to extract the detailed models of the above three blocks, as well as to
propose an efficient solution for solving the whole optimization problem. Hence, first, the detailed
models of the above blocks are presented in the rest of this section.

Energies 2018, 11, 2326
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4 of 16

Figure1.1.Schematic
Schematicdiagram
diagram
wind
energy
based
(WDG)
placement
problem
definition
Figure
of of
thethe
wind
energy
based
DGDG
(WDG)
placement
problem
definition
and
and
structure.
structure.

2.1.
2.1.Objective
ObjectiveFunction
FunctionModel
Model
The
find
the
optimal
bus
forfor
connecting
thethe
WDG
in
Theobjective
objectiveofofthe
theoptimization
optimizationproblem
problemisistoto
find
the
optimal
bus
connecting
WDG
aindistribution
network,
to minimize
the aggregate
electricelectric
energy energy
loss, as well
achieve
a distribution
network,
to minimize
the aggregate
loss,as
astowell
as toa smooth
achieve
nodal
voltage
profile
withprofile
less total
deviation
from
1 p.u during
planning
This objective
a smooth
nodal
voltage
with
less total
deviation
from the
1 p.u
duringperiod.
the planning
period.
function
is formulated
(1), where
symbols
and VDWithDG
denote and
the aggregate
This objective
functioninisEquation
formulated
in Equation
(1),ELossWithDG
where symbols
ELossWithDG
VDWithDG
electric
loss andelectric
voltageenergy
deviation
in the deviation
system with
the WDG,
denote energy
the aggregate
loss criteria
and voltage
criteria
in the respectively.
system withThe
the
EWDG,
LossNoDGrespectively.
and VDNoDG are
variables
the are
system
without
the WDG.
Vbus I,WithDG,t
and P
LossWithDG,t
Thesimilar
ELossNoDG
and VDin
similar
variables
in the system
without
the
WDG.
NoDG
are
voltageand
magnitude
of bus
andvoltage
the entire
active power
in the
with the
WDG,
and
Vbusthe
PLossWithDG,t
arei,the
magnitude
of busloss
i, and
thesystem
entire active
power
loss
in
I,WithDG,t
in
sampling
t, respectively.
Similarly, interval
Vbus i,NoDG,tt,and
PLossNoDG,t represent
variables
thethe
system
withinterval
the WDG,
and in the sampling
respectively.
Similarly,similar
Vbus i,NoDG,t
and
for
the caserepresent
withoutsimilar
the WDG.
Finally,
F case
is the
resultant
objective
function.
The
entire objective
voltage
PLossNoDG,t
variables
for the
without
the WDG.
Finally,
F is the
resultant
deviation
index
is defined
to Equation
(2), according
with symbol
Vbus i,t representing
the voltage
function. The
entire
voltageaccording
deviation index
is defined
to Equation
(2), with symbol
Vbus i,t
magnitude
ofthe
busvoltage
i in themagnitude
sampling of
interval
t, the
andsampling
in either interval
of the two
cases
(with of
orthe
without
the
representing
bus i in
t, and
in either
two cases
WDG).
(with or without the WDG).


Vi ,bus

PLossWithDG,t


∑ Vbus
PLossWithDG ,t
i,WithDG,t
WithDG
,t  1 − 1
ELossWithDG
VD
E
VD
All
times
t
All
times
t
All
Buses
WithDG
All
times
t
All
Buses

(1)(1)
F=
+
=  All times t
+
F  LossWithDG
 WithDG

ELossNoDGE
VD NoDG
PLossNoDG,t


∑ V Vbus i,NoDG,t
VD
P
1 − 1
LossNoDG


All times
t

NoDG

 

LossNoDG ,t

All times t

 

bus i , NoDG ,t
All times t All Buses
All times t All Buses

1
∑ V Vbus i,t −
VD All
 ∑
1


bus
i
,
t
times t All Buses


VD =

All times t All Buses



(2)
(2)

It is observable that in Equation (1) the values for the system, with the WDG, are divided by the
It is observable
that
Equation
the values
for the
system,
the WDG,
are dividedthe
by two
the
corresponding
values
forinthe
system (1)
without
the WDG.
The
reasonwith
for this
is to homogenize
corresponding
values
for
the
system
without
the
WDG.
The
reason
for
this
is
to
homogenize
the
two
terms of the objective function so that they both have similar dimensions. Moreover, since the problem
terms
the just
objective
function
so thatplacement
they bothofhave
similar
dimensions.
Moreover,
since
underof
study
considers
the optimal
WDG
(assuming
a fixed power
capacity
forthe
it),
problem
under cost
study
just considers
the optimal
placement of
WDG (assuming a fixed power
the investment
of WDG
is unimportant
and is disregarded
here.
capacity for it), the investment cost of WDG is unimportant and is disregarded here.
2.2. Model of the Power Balance Constraint (Interactions between WDG and Network)
2.2. Model of the Power Balance Constraint (Interactions between WDG and Network)
As is seen in Figure 1, the most significant block of the WDG placement problem under study,
is seen
the most
significant
blockasofthe
themain
WDG
placement
problem
under
study, is
is theAs
model
of in
theFigure
power1,balance
constraint,
treated
equality
constraint
of the
optimization
the
modelIn of
power
balance constraint,
main equality
constraint
of the
problem.
thisthe
block,
the time-dependent
input treated
data for as
thethe
optimization
problem
are produced
by
optimization problem. In this block, the time-dependent input data for the optimization problem are
produced by using the models of time-variant nodal demands and wind speed. These models extract

Energies 2018, 11, 2326

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using the models of time-variant nodal demands and wind speed. These models extract the “typical
nodal demands and wind speed patterns” as some functions of time from those historical data in
a way that will be described in next section. The resulted data are applied to the models of distribution
load flow, and WDG is connected to the candidate bus of the distribution network. The distribution
network behavior, as is seen from the WDG bus, is also modeled by using the equivalent time-variant
Thevenin model at the WDG bus. This model is influenced by the time variations of the nodal voltage
profile and the electrical location of the WDG bus itself. On the other hand, it provides the supply
voltage for the WDG model, and thereby, the interactions of WDG and the distribution network are
well-regarded. The WDG model calculates the time-variant active and reactive power injections from
the WDG to the network (i.e., PWDG (t) and QWDG (t) in Figure 1). These variables participate in the
distribution load flow model as the kernel of the power balance constraint. By solving the distribution
load flow problem, for all the sampling intervals during the planning period, the nodal voltage profiles
and the values of the active power loss in each interval can be elucidated. These results not only are
utilized in the objective function formulation, but also affect the equivalent time-variant Thevenin
model at the WDG bus, and, consequently, the outputs of the WDG model (especially the reactive
power exchange between the WDG and network). This feedback loop evidently demonstrates the high
complexity of the defined power balance constraint block, as the principal equality constraint of the
optimization problem under study. In other words, such an equality constraint is indeed a complicated
time-variant model that necessitates using the new proposed algorithm or the solution.
2.3. Models of Time-Variant Wind Speed and Nodal Demands
Here, the time-profiles of input data (i.e., wind speed and nodal demands) are modeled regarding
the fact that the WDG placement problem is indeed a type of planning problem, in which the long-term
behaviors of the input data should be taken into account. In addition, time variations of such variables
mostly follow approximate diurnal (24 h) patterns; of course with some random variability. This is
mainly because of the sun radiation diurnal pattern influencing the time variations of the others.
Additionally, wind speed also has a different typical diurnal pattern, dependent on the seasonal and
geographical conditions. Nevertheless, it is impossible to consider all individual hours of a year in the
simulation process, since it takes a long solution time. Here, a good alternative is to define and obtain
the ‘typical’ or ‘average’ diurnal patterns for the input data and apply them to the simulation with
24 h (86,400 s) duration. Meanwhile, in order to regard the seasonal variations of the input signals,
such average diurnal profiles are extracted for each month in a year, and all are then applied to the
simulation, successively. Thus, the simulation is repeatedly run 12 times, each with 24 h (86,400 s)
duration and its own applied 24 h input data. The average diurnal patterns are all formulated as
some appropriate mathematical expressions by using the curve fitting technique, so as to simplify the
simulation model and reduce its runtime, as described in the following sections.
2.4. Monthly Average Diurnal Wind Speed Patterns
According to the above considerations, each of the monthly average diurnal wind speed patterns
is defined as the 24 h profile of the hourly mean values, obtained through averaging all the wind
speeds of that hour across the 30 days interval of the associated month, as formulated in Equation (3).
In this formula, vm (h,d) stands for the wind speed in hour (h) of the day (d), and month (m), while vm (h)
represents the resulted average wind speed corresponding, to the hour (h) of the typical day in month
m. Accordingly, v Load,1 (h) to v Load,12 (h) symbolize all the monthly load profiles resulted for each of the
12 months of the year.
vm ( h) =

1 30
vm (h, d) , h = 1, 2, . . . , 24 , m = 1, 2, . . . , 12
30 d∑
=1

(3)

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As2018,
described
for the purpose of simplification, the monthly average diurnal wind speed
Energies
11, x FORbefore,
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patterns are approximated by some mathematical formulations using the curve fitting technique.
According
According to the
the inherent
inherent nature
nature of
of wind
wind speed
speed profiles,
profiles, the
the monthly
monthly average
average diurnal
diurnal wind
wind speed
speed
patterns
patterns typically
typically have
have just
just one peak, and therefore,
therefore, they
they can
can be best approximated
approximated via
via using
using a single
biased sinusoidal
sinusoidal function,
function, as
as formulated
formulated in
in Equation
Equation (4)
(4) [22].
[22].




2π

2 
vmv(hm)(=
1,2,...,
2, . . .24
, 24
(4)
(hh−ϕ)   hh =
h ) VmV m 1+
1 δcos
cos 
 1,
(4)

2424 






where,
vm , δ, 𝑣̅and
ϕ denote
the overall
wind speed
in month
m, month
the magnitude
of sinusoidal
, δ,
and  denote
the average
overall average
wind
speed in
m, the magnitude
of
Where,
function
(called
‘diurnal
pattern
strength’),
and
its
phase
shift
hour
(called
‘mean
hour
of
peak
wind
sinusoidal function (called ‘diurnal pattern strength’), and its phase shift hour (called ‘mean
hour
of
speed’),
respectively,
and vm (h) yields
mean
wind
speed
hour speed
h of theintypical
in month
as
peak wind
speed’), respectively,
and 𝑣̅the(ℎ)
yields
the
meaninwind
hour hday
of the
typicalmday
ainsinusoidal
function
of
hour
(h).
The
resulted
monthly
wind
speed
profiles
exploited
in
this
paper
are
month m as a sinusoidal function of hour (h). The resulted monthly wind speed profiles exploited
all
depicted
Figure
2 besideintheir
associated
in this
paperinare
all depicted
Figure
2 besidefitted
theircurves.
associated fitted curves.
7.5
Main Data
Fitted Curve

7
6.5

Wind Speed (m/s)

6
5.5
5
4.5
4
3.5
3
2.5

24

48

72

96

120

144
Time (hour)

168

192

216

240

264

288

Figure 2.
2. Monthly
Monthly average
average diurnal
diurnal wind
wind speed
speed patterns
patterns utilized.
utilized.
Figure

The monthly sinusoidal functions fitted to the monthly average diurnal wind speed patterns are
The monthly sinusoidal functions fitted to the monthly average diurnal wind speed patterns are
all utilized consecutively in the simulation process to form the wind speed input signal of the wind
all utilized consecutively in the simulation process to form the wind speed input signal of the wind
turbine. Thus, not only are both the average diurnal and seasonal behaviors of wind speed perfectly
turbine. Thus, not only are both the average diurnal and seasonal behaviors of wind speed perfectly
modeled without a long solution time, but also, the sudden and sharp variations of wind speed are
modeled without a long solution time, but also, the sudden and sharp variations of wind speed are
not modeled. Thereby, the output power of the WDG is obtained according to the average long-term
not modeled. Thereby, the output power of the WDG is obtained according to the average long-term
behavior of wind speed. This is in agreement with the inherent definition of the DG placement
behavior of wind speed. This is in agreement with the inherent definition of the DG placement process,
process, having a planning and long-term nature, as explained earlier.
having a planning and long-term nature, as explained earlier.
2.5. Monthly
Monthly Average
Average Diurnal
Diurnal Demand
Demand Patterns
Patterns
2.5.
Similar to
to the
the previously
previously defined
defined wind
wind speed
speed patterns,
patterns, each
each of
of the
the monthly
monthly average
average diurnal
diurnal
Similar
demand
patterns
is
defined
as
the
24
h
profile
of
the
hourly
mean
values.
Each
value
is
obtained
by
demand patterns is defined as the 24 h profile of the hourly mean values. Each value is obtained
averaging
all
the
demand
values
of
that
hour
across
the
30-day
interval
of
the
associated
month.
This
by averaging all the demand values of that hour across the 30-day interval of the associated month.
definition
is formulated
in Equation
(5), (5),
where
PLoad,m
(h,d)(h,d)
denotes
the the
power
demand
in hour
h of
This
definition
is formulated
in Equation
where
PLoad,m
denotes
power
demand
in hour
h
day
d
and
month
m,
and
𝑃
(ℎ)
represents
the
resulted
average
power
demand
corresponding
,
of day d and month m, and P Load,m
(h) represents the resulted average power demand corresponding
to hour
hour hh of
of aa typical
𝑃
, (ℎ)
, (ℎ) encompass all of the monthly
to
typical day
day in
in month
month m.
m. Thus,
Thus, 𝑃P Load,1
to P
(h) to
Load,12 ( h ) encompass all of the monthly
profiles resulting
resulting from
from each
eachof
ofthe
the12
12months
monthsin
inaayear.
year.
profiles
1 30
PLoad ,m (h1) 30  PLoad ,m (h, d ), h  1, 2,...,24 , m  1,2,...,12
(5)
30Pd 1
P Load,m (h) =
(5)

Load,m ( h, d ) , h = 1, 2, . . . , 24 , m = 1, 2, . . . , 12
30 d=1
Like the diurnal wind speed patterns, for sake of simplification, the average diurnal demand
patterns should be approximated by some mathematical formulations via using the curve fitting
technique. Due to the inherent nature of non-industrial demands, such profiles mostly have two
(minor and major) peaks. On the other hand, such profiles all have daily periodic natures, i.e., the

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Like the diurnal wind speed patterns, for sake of simplification, the average diurnal demand
patterns should be approximated by some mathematical formulations via using the curve fitting
technique.
the
inherent
nature of non-industrial demands, such profiles mostly have two (minor
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11, x to
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REVIEW
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and major) peaks. On the other hand, such profiles all have daily periodic natures, i.e., the power
demand
at the beginning
of the day
equals t at equals
the endt of
0) =(𝑃
P Load,m
(24)=).
power demand
at the beginning
ofhabitually
the day habitually
at day
the (P
end
of (day
Load,m
, (0)
Therefore,
such
profiles can
best approximated
using a two-term
Fourier
series, Fourier
as formulated
𝑃
Therefore,
suchbeprofiles
can be best approximated
using
a two-term
series, in
as
, (24)).
Equation
(6),
which symbols
t andsymbols
P Load,m (tt)and
denote
time
(in
hours
or
any
other
appropriate
formulated
inin
Equation
(6), in which
𝑃 the
(𝑡)
denote
the
time
(in
hours
or
any
other
,
units),
and the
average
(in kW)
belonging
to belonging
time t and to
month
respectively.
appropriate
units),
anddemand
the average
demand
(in kW)
time m,
t and
month m, Additionally,
respectively.
parameters
a0 to
a2 and b1 toa0bto
the Fourier
and ω
is the fundamental
frequency
Additionally,
parameters
a2 and
b1 to b2coefficients,
are the Fourier
coefficients,
and ω isangular
the fundamental
2 are
of
the
signal
that
is
determined
according
to
the
signal
period
(i.e.,
one
day
or
24
hours),
as
seen
in
angular frequency of the signal that is determined according to the signal period (i.e., one day
or 24
Equation
The
are utilized
in that
this are
paper
are allindepicted
in
hours), as(6).
seen
in resulted
Equationmonthly
(6). The demand
resulted profiles
monthlythat
demand
profiles
utilized
this paper
Figure
3 beside their
associated
fitted
curves.
are all depicted
in Figure
3 beside
their
associated fitted curves.
 aa0 cos
a1 cos(
) bb1 sin
sin((ωt
t) 
a2 cos(
t () ωt
 b)2 sin(
) (ωt)
P Load,m (PtLoad
) =,m (at0) +
(ωt)t+
)+
a2 cos
+ b2 tsin
1
1
2 )
ω = 2π
(rad
 /hoursrad
24 
hours
24



(6)
(6)



7
Main Data
Fitted Curve
6

Power demand (kw)

5

4

3

2

1

24

48

72

96

120

144
Time (hour)

168

192

216

240

264

288

Figure 3. Monthly average diurnal demand patterns exploited.
Figure 3. Monthly average diurnal demand patterns exploited.

As this paper considers a distribution network for the WDG placement analysis, it is necessary
As thissome
papernodal
considers
distribution
for the
WDGforms
placement
analysis,
it is necessary
to provide
load aprofiles;
each network
having some
similar
to those
illustrated
in Figure to
3.
provide
some
nodal
load
profiles;
each
having
some
similar
forms
to
those
illustrated
in
Figure
3.
Then,
Then, in the numerical analysis section, the default nodal loads are all modified according to
in
the numerical
analysis
the default
nodal
loads arethe
allaverage
modified
according
Equation
(7),
Equation
(7), where
𝑃 section,
represent
diurnal
loadto
profile
applied
, (𝑡) and 𝑃
,
where
P Load
PLoad
diurnal
load profile
applied to
bus
in
i, m ( t ) and
de f ult represent
to bus (i)
in month
m, and
thei,previous
defaultthe
loadaverage
at bus (i),
respectively.
This equation
can
be (i)
used
month
m,
and
the
previous
default
load
at
bus
(i),
respectively.
This
equation
can
be
used
for
both
for both active and reactive nodal loads.
active and reactive nodal loads.
a  a cos(t )  b1 sin(t )  a2 cos(t )  b2 sin(t )
PLoad i ,ma(t )+a 0cos(1 ωt) + b sin
(7)
Load
(ωta) + a2 cos(ωt) + b2 sin(Pωt
) i ,default
0
1
1
0
P Load i,m (t) =
PLoad i,de f ault
(7)
a0
As is illustrated in Figure 1, the above nodal loads are not directly modeled in the simulation of
As is illustrated in Figure 1, the above nodal loads are not directly modeled in the simulation
the grid-connected WDG, but instead, they are regarded in the distribution load flow calculation
of the grid-connected WDG, but instead, they are regarded in the distribution load flow calculation
according to the way described in Section 3. The distribution load flow subsequently yields some,
according to the way described in Section 3. The distribution load flow subsequently yields some,
monthly average diurnal nodal voltage patterns, corresponding to each of the monthly average
monthly average diurnal nodal voltage patterns, corresponding to each of the monthly average diurnal
diurnal demand patterns, and such resulted voltage patterns for the candidate bus of WDG are
demand patterns, and such resulted voltage patterns for the candidate bus of WDG are modeled in the
modeled in the simulation of the grid-connected WDG, as described in the section below.
simulation of the grid-connected WDG, as described in the section below.
2.6. Equivalent Time-Variant Thevenin Model of Distribution Network Drawn from the WDG Bus (Monthly
Average Diurnal Grid Voltage Patterns)
The power grid is modeled here, as a time-variant equivalent Thevenin circuit for the base
power system (without DG), drawn from the bus at which the WDG is going to be connected. As
illustrated in Figure 1, it is composed of a time-variant Thevenin voltage source together with fixed

Energies 2018, 11, 2326

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2.6. Equivalent Time-Variant Thevenin Model of Distribution Network Drawn from the WDG Bus (Monthly
Average Diurnal Grid Voltage Patterns)
The power grid is modeled here, as a time-variant equivalent Thevenin circuit for the base power
system (without DG), drawn from the bus at which the WDG is going to be connected. As illustrated
in Figure 1, it is composed of a time-variant Thevenin voltage source together with fixed Thevenin
impedance, respectively derived from the calculations of distribution load flow and the impedance
matrix in the base power system, without WDG. The time-variant Thevenin voltage source models
the time variations of the candidate bus voltage, before connecting to the WDG. Thus, by applying
the monthly average diurnal demand profiles, the nodal voltage profiles (resulted from distribution
load flow calculations) also follow from some similar monthly average diurnal patterns. Hence,
the time-variant voltage profile resulted for the candidate bus per hour of the typical day is applied to
the Thevenin voltage source in the simulation process (Figure 1).
2.7. Grid-Connected WDG Model
The grid-connected WDG system is simulated here via a simulation scheme including a simple
Squirrel-cage Induction Generator driven by a wind turbine [23] and directly connected to the candidate
bus of the distribution network (with the equivalent time-variant Thevenin model). The wind
turbine can be considered either with the pitch angle controlling system or without it. The wind
turbine-induction generator (WT-IG) model can completely be extracted from [24].
3. Distribution Load Flow Model and Solution Algorithm
In the proposed WDG placement algorithm, the static operation state of the distribution network is
modeled by a load flow problem, which is solved using a distribution load flow algorithm, as depicted
in the flowchart of Figure 4. This algorithm is extracted from a past paper [14] and is utilized here
by applying some extra simplifications, to reduce its solution time without impairing its accuracy.
According to the flowchart of Figure 4, the utilized procedure initially forms the admittance matrix
(Ybus) from the network structural data and extracts the impedance matrix (Zbus) from Ybus. This is
done by removing the row and column corresponding to the slack bus in Ybus, inverting the remainder
matrix, and inserting a row and column of all zeroes into the resultant inversed matrix at the place
of slack. Then, at the beginning of the iterative procedure, constant nodal voltages (V), all equal to
1 p.u ∠0◦ are assumed, and the nodal injective apparent powers are calculated. In each step, the solution
procedure repeatedly computes the nodal injective currents (I) from the nodal injective apparent
powers and the resulting nodal voltages, and updates the nodal voltages by multiplying by Zbus.
This iterative process is continued until the maximum change in nodal voltages between two successive
steps reaches under a predetermined tolerance (ε). Finally, the branch currents and the total active
power loss in the entire distribution network are obtained using Equations (8) and (9), respectively.
Where, Ibranches and Zbranches denote the vectors of branch currents and impedances, respectively and
Vsending buses and Vreceiving buses are the voltage vectors of sending and receiving nodes corresponding to
each branch, respectively. Additionally, Ibranch and Rbranch are the current and resistance of each branch
in the above vectors, while Ploss denotes the resulted active power loss.
Ibranches =
Ploss =

Vsending buses − Vreceiving buses
Zbranches



All branches

Rbranch | Ibranch |2

(8)
(9)

Energies 2018, 11, 2326
Energies 2018, 11, x FOR PEER REVIEW

9 of 16
9 of 16

Figure
Figure 4.
4. Flowchart
Flowchart of
of the
the utilized
utilized distribution
distribution load
load flow
flow algorithm.
algorithm.

3.1. Model of the Inequality Constraints
Model of the Inequality Constraints
As described before, the WDG placement problem under study is an optimization problem
As described before, the WDG placement problem under study is an optimization problem
with just one decision variable: the WDG bus number. On the other hand, the proposed objective
with just one decision variable: the WDG bus number. On the other hand, the proposed objective
function perfectly regards the time-variant nodal voltage profiles and tries to smooth them with as
function perfectly regards the time-variant nodal voltage profiles and tries to smooth them with as few
few deviations from 1 p.u as possible. The inequality constraints associated with the allowable
deviations from 1 p.u as possible. The inequality constraints associated with the allowable ranges of
ranges of the active and reactive power exchanges between the WDG and distribution network are
the active and reactive power exchanges between the WDG and distribution network are completely
completely considered in the simulation process of the grid-connected WDG. Therefore, there is no
considered in the simulation process of the grid-connected WDG. Therefore, there is no need to regard
need to regard the nodal voltage profiles and the active and reactive power exchanges of the WDG
the nodal voltage profiles and the active and reactive power exchanges of the WDG separately in the
separately in the inequality constraints block. Hence, the only significant inequality constraint that
inequality constraints block. Hence, the only significant inequality constraint that remained is related
remained is related to the allowable range of the WDG bus number, that is, between one, and the
to the allowable range of the WDG bus number, that is, between one, and the number of buses in the
number of buses in the whole distribution network.
whole distribution network.
4.
4. Proposed
Proposed Solution
Solution Algorithm
Algorithm for
for the
the WDG
WDG Placement
Placement Problem
Problem under
under Study
Study
In
WDG
placement
problem
is
In this
this section,
section, the
theproposed
proposedsolution
solutionalgorithm
algorithmfor
forthe
theintended
intended
WDG
placement
problem
presented.
The
fundamental
concept
of
this
algorithm
is
based
on
the
superposition
theorem.
is presented. The fundamental concept of this algorithm is based on the superposition theorem.
According
to this
this theorem,
theorem,the
theeffects
effectsofofboth
boththe
thetime-varying
time-varyingpower
power
demands
and
wind
speed
According to
demands
and
wind
speed
cancan
be
be
handled
in
this
way:
At
first
with
the
base
distribution
network
with
time-varying
loads,
but
handled in this way: At first with the base distribution network with time-varying loads, but without
without
WDG,
with the distribution
flow calculation
andvoltages
the nodal
voltages
From the
WDG, with
the distribution
load flow load
calculation
and the nodal
result.
From result.
the viewpoint
of
viewpoint
of
the
candidate
bus
for
the
WDG
placement,
the
voltage
obtained
above
is
treated
as
the
the candidate bus for the WDG placement, the voltage obtained above is treated as the open-circuit,
open-circuit,
or no-load
voltage,
makes
thevoltage
Thevenin
source
profile.theThen,
or no-load voltage,
which makes
thewhich
Thevenin
source
profile.
Then,voltage
by connecting
WDGby
to
connecting
the
WDG
to
the
candidate
bus,
the
distribution
network
is
abandoned,
and
its
behavior
is
the candidate bus, the distribution network is abandoned, and its behavior is completely modeled
completely
modeled
by the
Thevenin
voltagethe
source.
Therefore,
the actual voltage
variations
of the
by the Thevenin
voltage
source.
Therefore,
actual
voltage variations
of the WDG
bus during
WDG bus during its operation is calculated in the simulation process, and the time-varying profiles
of the active and reactive powers, injected by the WDG to the distribution network, are obtained as

5. Numerical Analysis
The proposed WDG placement algorithm is applied to the radial 33-bus distribution test
network, presented previously [14,21], via programming in MATLAB. On the other hand, the WDG
Energies 2018, 11, 2326
10 of 16
under study is of 1.5 MW capacity with base wind speed equal to 6 m/s. It was modeled using
Simulink and is then linked to the main written program. Thus, the simulation was run via calling
its
operation
is calculated
the simulation
process,
andas
thedescribed
time-varying
profiles
of the
active and
during
the main
program in
procedure,
wherever
needed,
in Section
3. The
performance
reactive
powers, injected
by the
WDG to here
the distribution
network,
are obtained
The proposed
of the proposed
algorithm
is verified
by comparing
the results
with as
thewell.
conventional
DG
solution
procedure
is graphically
in the flowchart
of Figure were
5. Accordingly,
the optimization
placement
algorithm.
The DGs scheduled
with renewable
energy resources
simply modeled
as fixed
active and
reactive
sources
fixedmethod.
negativeConsequently,
active and reactive
In this
problem
was
solvedgeneration
by using the
direct(or
search
all thedemands).
system buses
are way,
tried
the mentionedfor
33-bus
distribution
systemsearch
is considered,
with used.
near-actual
and wind
consecutively
DG placement;
no test
stochastic
methods were
In this demand
way, the inequality
speed data,ofadopted
from two
template
files ofbus
HOMER
software.
constraint
the allowable
range
of the WDG
number
is automatically satisfied too.

Figure
5. Flowchart
WDG placement
placement algorithm.
algorithm.
Figure 5.
Flowchart of
of the
the proposed
proposed WDG

5. Numerical Analysis
The proposed WDG placement algorithm is applied to the radial 33-bus distribution test network,
presented previously [14,21], via programming in MATLAB. On the other hand, the WDG under study
is of 1.5 MW capacity with base wind speed equal to 6 m/s. It was modeled using Simulink and is then
linked to the main written program. Thus, the simulation was run via calling during the main program
procedure, wherever needed, as described in Section 3. The performance of the proposed algorithm
is verified here by comparing the results with the conventional DG placement algorithm. The DGs
with renewable energy resources were simply modeled as fixed active and reactive generation sources
(or fixed negative active and reactive demands). In this way, the mentioned 33-bus distribution test

Energies 2018, 11, 2326

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system is considered, with near-actual demand and wind speed data, adopted from two template files
of HOMER
software.
Energies 2018,
11, x FOR PEER REVIEW
11 of 16
They contain 8760 sample data per hour of a year, respectively, corresponding to power demand
They
contain
8760during
sample
data per
hour these
of a year,
to demand,
power
and wind
speed
values
a year.
By using
data,respectively,
the monthlycorresponding
average diurnal
and wind
speed
during
a year. By
using
these data,
the monthly
average
diurnal
anddemand
wind speed
patterns
arevalues
calculated
according
to the
methods
described
in Section
2, as illustrated
demand,
and
wind
speed
patterns
are
calculated
according
to
the
methods
described
in
Section
as33
in the graphs of Figures 2 and 3, respectively. The nodal active and reactive demands for all 2,
the
illustrated in the graphs of Figures 2 and 3, respectively. The nodal active and reactive demands for
buses in the 33-bus distribution network were extracted from the above-mentioned sample demand
all the 33 buses in the 33-bus distribution network were extracted from the above-mentioned sample
data according to Equation (8). The resulted monthly average diurnal patterns for all the nodal active
demand data according to Equation (8). The resulted monthly average diurnal patterns for all the
and reactive demands are given to the proposed algorithm. Accordingly, by performing the successive
nodal active and reactive demands are given to the proposed algorithm. Accordingly, by performing
power flow analyses in the base distribution system without WDG, all the monthly average diurnal
the successive power flow analyses in the base distribution system without WDG, all the monthly
Thevenin source voltage profiles, for all the 33 buses, were obtained and simultaneously plotted in
average diurnal Thevenin source voltage profiles, for all the 33 buses, were obtained and
thesimultaneously
graphs of Figure
6a. After
proposed
placement
algorithm,
the monthly
average
plotted
in the running
graphs ofthe
Figure
6a. After
running the
proposedallplacement
algorithm,
diurnal
patterns
of
the
active
and
reactive
powers
injected
by
the
WDG,
when
connecting
to each
all the monthly average diurnal patterns of the active and reactive powers injected by the WDG,
of the
33 connecting
buses in the
network,
arethe
available
as plotted
in Figure
6b (beside
the graphs
when
todistribution
each of the 33
buses in
distribution
network,
are available
as plotted
in
of the
monthly
average
diurnal
wind
speed
patterns,
in
order
to
achieve
more
clearness).
With the
Figure 6b (beside the graphs of the monthly average diurnal wind speed patterns, in order to achieve
attention
to these three
it is observable
variations
of the active
power
injectedofby
more clearness).
Withplots,
the attention
to these that
threethe
plots,
it is observable
that the
variations
thethe
WDG
are power
mostlyinjected
in directby
proportion
themostly
wind speed
variations.
Although
active
power
injection
active
the WDGtoare
in direct
proportion
to the the
wind
speed
variations.
of Although
WDG mostly
has positive
display
negative
values
(i.e., ait motor
operation)
when
the active
power values,
injectionitofmay
WDG
mostly
has positive
values,
may display
negative
a motor
operation) when
theOn
wind
facesthe
significant
drops. injection
On the contrary,
the
thevalues
wind (i.e.,
speed
faces significant
drops.
thespeed
contrary,
active power
of the WDG,
active powerhas
injection
the WDG,
approximately,
has similar
behaviors
thebuses
WDGinisthe
approximately,
similarof
behaviors
when
the WDG is connected
to each
of the when
different
connected
each of
thethe
different
buses
system.
This
implies
that theare
variations
of the
WDGby
system.
This to
implies
that
variations
ofin
thethe
WDG
active
power
injection
not greatly
affected
active
power
injection
are
not
greatly
affected
by
the
different
voltage
magnitudes
in
the
different
the different voltage magnitudes in the different buses. On the other hand, the reactive power injection
On thebehavior.
other hand,
the reactive
power6b,
injection
has a different
behavior.power
According
to Figure
hasbuses.
a different
According
to Figure
it is obvious
that the reactive
injection
always
6b,
it
is
obvious
that
the
reactive
power
injection
always
has
negative
values
(because
of
the
inherent
has negative values (because of the inherent characteristic of induction generator). In other words,
of inductionalways
generator).
In other
Induction
machine-WDG
always
thecharacteristic
Induction machine-WDG
consumes
some words,
reactive the
power.
The reactive
power consumption
consumes some reactive power. The reactive power consumption level is in direct proportion to the
level is in direct proportion to the wind speed, and reverse proportion to the bus voltage magnitude,
wind speed, and reverse proportion to the bus voltage magnitude, as seen in Figure 6b. It increases
as seen in Figure 6b. It increases wherever the wind speed increases and has lower values for the nodes
wherever the wind speed increases and has lower values for the nodes with higher voltage
with higher voltage magnitudes (e.g., the first nodes near to the Slack bus).
magnitudes (e.g., the first nodes near to the Slack bus).

Voltage Magnitude (p.u)

1

0.95

0.9

0.85

24

48

72

96

120

144
Time (hour)

168

(a)
Figure 6. Cont.

192

216

240

264

288

bus1
bus2
bus3
bus4
bus5
bus6
bus7
bus8
bus9
bus10
bus11
bus12
bus13
bus14
bus15
bus16
bus17
bus18
bus19
bus20
bus21
bus22
bus23
bus24
bus25
bus26
bus27
bus28
bus29
bus30
bus31
bus32
bus33

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Active Power (MW)

Wind Speed (m/s)

Energies 2018, 11, x FOR PEER REVIEW
8
Main Data
Fitted Curve

6
4
2
2

24

48

72

96

120

144
Time (hour)

168

192

216

240

264

288

24

48

72

96

120

144
Time (hour)

168

192

216

240

264

288

24

48

72

96

120

144

168

192

216

240

264

288

1

0

-0.5

Reactive Power (MVar)

12 of 16

-0.2
-0.4
-0.6
-0.8

Time (hour)

bus1
bus2
bus3
bus4
bus5
bus6
bus7
bus8
bus9
bus10
bus11
bus12
bus13
bus14
bus15
bus16
bus17
bus18
bus19
bus20
bus21
bus22
bus23
bus24
bus25
bus26
bus27
bus28
bus29
bus30
bus31
bus32
bus33

(b)
Figure 6. (a) Plots of all the monthly average diurnal Thevenin source voltage patterns for all the 33
Figure 6. (a) Plots of all the monthly average diurnal Thevenin source voltage patterns for all the
buses in the 33-bus distribution network. (b) monthly average diurnal wind speed patterns, besides
33 buses in the 33-bus distribution network. (b) monthly average diurnal wind speed patterns, besides
the patterns of active and reactive powers, injected by WDG when connected to each of the 33 buses
thein
patterns
of active and reactive powers, injected by WDG when connected to each of the 33 buses in
the network.
the network.

The main outcome, of any DG placement procedure, is to find the best bus to which the DG
The main
outcome,After
of any
DG placement
procedure,
is to find
the best bus
bus 12
to was
which
the DG
should
be connected.
running
the proposed
WDG placement
algorithm,
obtained
as thebebest
candidate
bus, running
while using
conventional
algorithm [14]
(in which
the
is treatedas
should
connected.
After
the the
proposed
WDG placement
algorithm,
bus
12WDG
was obtained
a fixed
load demand),
bus
18 was
to algorithm
be the best.[14]
As(in
presented
in aWDG
previous
paperas
theas
best
candidate
bus, while
using
the determined
conventional
which the
is treated
[14], load
the modeling
WDG
is based
on the time-varying
DGAs
source
and itinisasimulated
a fixed
demand),ofbus
18 was
determined
to be the best.
presented
previous based
paper on
[14],
statistical
wind
data.
Therefore,
the
effect
of
the
dynamic
model
has
not
been
considered
in
the
the modeling of WDG is based on the time-varying DG source and it is simulated based on statistical
placement
process. Moreover,
onlymodel
the annual
dailybeen
average
output power
of
wind
data. Therefore,
the effectinofthis
thepaper,
dynamic
has not
considered
in the profile
placement
WDG
with
the
daily
average
demand
of
a
typical
house
has
been
regarded.
process. Moreover, in this paper, only the annual daily average output power profile of WDG with the
The main
outcomes
the two
approaches,
well as those of the base system without WDG,
daily average
demand
of a of
typical
house
has beenas
regarded.
are illustrated in Table 1. It clearly demonstrates the effectiveness of the proposed WDG placement
The main outcomes of the two approaches, as well as those of the base system without WDG,
mechanism, as it yields lower values for the global objective function in Equation (1) and the average
are illustrated in Table 1. It clearly demonstrates the effectiveness of the proposed WDG placement
active power loss. However, a comparison of the resulted voltage profile and active power loss
mechanism, as it yields lower values for the global objective function in Equation (1) and the average
between the two cases of using either of the two algorithms can further prove the merit of the newly
active power loss. However, a comparison of the resulted voltage profile and active power loss
proposed algorithm.
between the two cases of using either of the two algorithms can further prove the merit of the newly
proposed
algorithm.
Table
1. Comparison of the main outcomes of the conventional [14] and proposed WDG placement
algorithms, along with the corresponding results of the base system without WDG.
Table 1. Comparison of the main outcomes of the conventional [14] and proposed WDG placement
Case of Analysis Resulted Variable
Base System without WDG New Algorithm Conventional Algorithm [14]
algorithms,
along with the corresponding
results of the base system without WDG.

Optimal Bus for Connecting the WDG
Overall Average Active Power Loss in kW
235.5
CaseAverage
of Analysis
Resulted
Variable
without WDG
Overall
Voltage
Deviation
Index in p.u Base System 0.0521
Resulted
Global
Objective
Optimal
Bus for
Connecting
theValue
WDG
- 2
Overall Average Active Power Loss in kW
235.5
Overall Average Voltage Deviation Index in p.u
0.0521
Accordingly,
FigureValue
7a displays the resultant
monthly
Resulted
Global Objective
2

12
223.0
New 0.0485
Algorithm

18
238.5
Conventional
Algorithm [14]
0.0485

1.8778
12
223.0
0.0485
average
diurnal
1.8778

1.9419
18
238.5
0.0485
profiles
1.9419

voltage
of bus
12 when connected to the WDG. In contrast, Figure 7b illustrates a similar profile for bus 18 when
the bus is instead connected to the WDG. Figure 7c illustrates the monthly average diurnal active
Accordingly, Figure 7a displays the resultant monthly average diurnal voltage profiles of bus 12
power loss patterns resulted from each of the three cases: the base distribution system without
when connected to the WDG. In contrast, Figure 7b illustrates a similar profile for bus 18 when the bus
WDG, the system with the WDG connected to bus 12, and the system with the WDG connected to
is instead connected to the WDG. Figure 7c illustrates the monthly average diurnal active power loss
bus 18. According to Figure 7, WDG placement based on the new algorithm proposed in this paper
patterns resulted from each of the three cases: the base distribution system without WDG, the system
yields better results, from the viewpoints of voltage profile smoothness and of active power loss
with
the WDGMoreover,
connectedintoFigure
bus 12,
andthe
thevoltage
systemprofiles
with the
WDG connected
to bus 18. According
reduction.
7a,b
resulted
from the simulation
models are to
Figure
7,
WDG
placement
based
on
the
new
algorithm
proposed
in
this
paper
yields
better
results,
plotted together with those obtained from the load flow calculations, separately for the cases
of
from the viewpoints of voltage profile smoothness and of active power loss reduction. Moreover, in

Energies 2018, 11, 2326

13 of 16

Energies7a,b
2018,the
11, xvoltage
FOR PEER
REVIEWresulted from the simulation models are plotted together with13those
of 16
Figure
profiles
obtained from the load flow calculations, separately for the cases of connecting the WDG to buses
the WDG toFor
buses
12clarity,
and 18,
respectively.
For18
more
clarity, theingraphs
18 are
12connecting
and 18, respectively.
more
the
graphs of bus
are replotted
Figure of
7dbus
beside
the
replotted
in
Figure
7d
beside
the
Thevenin
source
voltage
profile
at
bus
18
(i.e.,
the
voltage
profile
of
Thevenin source voltage profile at bus 18 (i.e., the voltage profile of bus 18 when not connected to the
bus 18According
when not connected
to the WDG).
According
figures,
theresulted
voltagefrom
profile
the WDG
WDG).
to these figures,
the voltage
profiletoofthese
the WDG
bus
theofsimulation
bus
resulted
from
the
simulation
model
exactly
coincides
with
that
resulted
from
the
distribution
model exactly coincides with that resulted from the distribution load flow calculation, while the bus
load flow
calculation,
bus voltage
profile
case of different.
not connecting
to the validates
WDG is
voltage
profile
in the casewhile
of notthe
connecting
to the
WDGinisthe
obviously
This strongly
obviously
different.
This
strongly
validates
the
concept
of
the
proposed
WDG
placement
the concept of the proposed WDG placement mechanism, described in Section 3. Furthermore, in
mechanism, described in Section 3. Furthermore, in figure 7c, it is observable that the active power
Figure
7c, it is observable that the active power loss profile corresponding to the case of connecting
loss profile corresponding to the case of connecting the WDG to bus 12 (the result of the new
the WDG to bus 12 (the result of the new proposed method) includes lower values than the other two
proposed method) includes lower values than the other two profiles. Therefore, not only is the
profiles. Therefore, not only is the proposed WDG placement algorithm completely valid, but it also
proposed WDG placement algorithm completely valid, but it also has good performance and
has good performance and effectiveness, as it regards all the effects of power demands as well as wind
effectiveness, as it regards all the effects of power demands as well as wind speed variations in the
speed variations in the WDG placement algorithm.
WDG placement algorithm.
1
Load Flow Voltage
Simulink Voltage

0.99
0.98

Voltage Magnitude(p.u)

0.97
0.96
0.95
0.94
0.93
0.92
0.91
0.9
0.89
0.88
0.87

24

48

72

96

120

144
Time (hour)

168

192

216

240

264

288

(a)

1

Load Flow Voltage
Simulink Voltage

0.99
0.98
0.97
Voltage Magnitude(p.u)

0.96
0.95
0.94
0.93
0.92
0.91
0.9
0.89
0.88
0.87
0.86
0.85
0.84

24

48

72

96

120

144
Time (hour)

(b)
Figure 7. Cont.

168

192

216

240

264

288

Energies 2018, 11, 2326

14 of 16

Energies 2018, 11, x FOR PEER REVIEW

14 of 16

600

Without Wind DG
Wind DG at bus 12
Wind DG at bus 18

Active Power Loss(kW)

500

400

300

200

100

0

24

48

72

96

120

144
Time (hour)

168

192

216

240

264

288

(c)

1

Load Flow Voltage
Simulink Voltage
Thevenan Voltage (without Wind DG)

0.99
0.98
0.97

Voltage Magnitude(p.u)

0.96
0.95
0.94
0.93
0.92
0.91
0.9
0.89
0.88
0.87
0.86
0.85
0.84

24

48

72

96

120

144
Time (hour)

168

192

216

240

264

288

(d)
Figure 7. (a) Monthly average diurnal voltage patterns of bus 12, when connecting to the WDG; (b)
Figure 7. (a) Monthly average diurnal voltage patterns of bus 12, when connecting to the WDG; (b)
Monthly average diurnal voltage patterns of bus 18, when connecting to the WDG; (c) Monthly
Monthly average diurnal voltage patterns of bus 18, when connecting to the WDG; (c) Monthly average
average diurnal active power loss patterns, compared among three cases: Without WDG; when
diurnal active power loss patterns, compared among three cases: Without WDG; when connecting
connecting the WDG to bus 12; and when connecting the WDG to bus 18; (d) Monthly average
the WDG to bus 12; and when connecting the WDG to bus 18; (d) Monthly average diurnal voltage
diurnal voltage patterns of bus 18, in different cases of either connecting or not connecting to the
patterns of bus 18, in different cases of either connecting or not connecting to the WDG.
WDG.

6.6.Conclusions
Conclusions
InInthis
paper,
a new
algorithm
for the
placement
of one WDG
on (base
induction
generator)
this
paper,
a new
algorithm
foroptimal
the optimal
placement
of one(base
WDG
on induction
ingenerator)
the distribution
networks has
been presented
minimizetothe
aggregate
lossenergy
as wellloss
as the
in the distribution
networks
has beento
presented
minimize
the energy
aggregate
as
nodal
voltage
deviations
(from
1
p.u).
The
proposed
scheme
considers
the
time
variations
of
dynamic
well as the nodal voltage deviations (from 1 p.u). The proposed scheme considers the time variations
nodal
demands,
nodal
voltage magnitudes,
and
wind speedand
in the
WDG
placement
altogether.
of dynamic
nodal
demands,
nodal voltage
magnitudes,
wind
speed
in the process
WDG placement
By
this
means,
an
accurate
dynamic
model
of
the
active
and
reactive
powers
injected
by
to
process altogether. By this means, an accurate dynamic model of the active and reactive WDG
powers
the
system
is
employed
in
which
the
interactions
between
the
WDG
and
the
distribution
network
injected by WDG to the system is employed in which the interactions between the WDG and the
are
well-viewed.
distribution
network are well-viewed.
Accordingly,
days, each
each representing
representingaadifferent
different
Accordingly,the
thesimulation
simulation is
is executed
executed for
for 12 typical (24 h) days,
month
of
the
year.
Thereby,
the
accurate
time-varying
model
of
the
active
and
reactive
powers
injected
month of the year. Thereby, the accurate time-varying model of the active and reactive powers
by
WDG by
to the
distribution
network is
considered
in the solution
the placement
problem.
injected
WDG
to the distribution
network
is considered
in the process
solutionof
process
of the placement
The
results The
obtained
from
the numerical
analysis
confirm
the validity,
accuracy,
and effectiveness
the
problem.
results
obtained
from the
numerical
analysis
confirm
the validity,
accuracy, ofand
effectiveness of the proposed WDG placement algorithm. According to these results, unlike the

Energies 2018, 11, 2326

15 of 16

proposed WDG placement algorithm. According to these results, unlike the conventional placement
algorithms for DGs with intermittent energy resources, the new algorithm of this paper further regards
the actual situations of both the distribution network and the DG system, and consequently yields
much more accurate results.
Author Contributions: M.B. designed the MATLAB-based simulation of the proposed work and prepared the
initial draft of paper. A.H. designed the formulation of the overall work and contributed significantly in writing
the paper. A.S. edited the initial draft of paper. Z.C proposed some technical comments and edited the final draft
of paper.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflicts of interest. The funding sponsors had no role in the design
of the study; the collection, analyses, or interpretation of data; the writing of the manuscript; and in the decision
to publish the results.

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