Multi-objective optimal placement of distributed generations for dynamic loads

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 9, No. 4, August 2019, pp. 2303~2313
ISSN: 2088-8708, DOI: 10.11591/ijece.v9i4.pp2303-2313  2303
Journal homepage: http://iaescore.com/journals/index.php/IJECE
Multi-objective optimal placement of distributed generations
for dynamic loads
Shah Mohazzem Hossain1
, Abdul Hasib Chowdhury2
1
Department of EECE, Military Institute of Science and Technology (MIST), Bangladesh
2
Department of EEE, Bangladesh University of Engineering and Technology (BUET), Bangladesh
Article Info ABSTRACT
Article history:
Received Nov 25, 2018
Revised Dec 20, 2018
Accepted Mar 10, 2019
Large amount of active power losses and low voltage profile are the two major
issues concerning the integration of distributed generations with existing
power system networks. High R/X ratio and long distance of radial network
further aggravates the issues. Optimal placement of distributed generators can
address these issues significantly by alleviating active power losses and
ameliorating voltage profile in a cost effective manner. In this research, multi-
objective optimal placement problem is decomposed into minimization of total
active power losses, maximization of bus voltage profile enhancement and
minimization of total generation cost of a power system network for static and
dynamic load characteristics. Optimum utilization factor for installed
generators and available loads is scaled by the analysis of yearly load-demand
curve of a network. The developed algorithm of N-bus system is implemented
in IEEE-14 bus standard test system to demonstrate the efficacy of the
proposed method in different loading conditions.
Keywords:
Distributed generation
Dynamic loads
Optimal placement
Copyright © 2019 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Shah Mohazzem Hossain
Departement of Electrical, Electronic and Communication Engineering (EECE)
Military Institute of Science and Technology (MIST)
Dhaka-1216, Bangladesh.
Email: soneteee@gmail.com; mohazzem_hossain@eece.mist.ac.bd
1. INTRODUCTION
Neoteric power system network is incessantly being faced with an ever thriving load demand with
accretive load results aggravated burden and palliation of system voltage magnitude. A real power network has
emblematic behaviour that node voltages are waned at long distance bus location from substation buses.
Inappropriate placement of new distributed generations (DG) is the main cause of voltage droop. Even a certain
industrial area with critical loading, it may lead to voltage collapse of the whole network.
Thus, optimal placement of DG is an exigent issue to ameliorate the voltage magnitude for avoiding a sudden
voltage collapse. A distribution network causes a significant amount of power losses and a drop in voltage
magnitude along the radial lines due to its high R/X ratio than transmission networks [1]. However, financial
issues as well as overall efficiency of the distribution utilities is being influenced by these non-negligible losses.
Overall efficiency of power delivery towards consumers is being boosted by forcing the electrical utilities to
abate the system losses at distribution ends. A good number of arrangements has already been worked out to
curtail these losses like optimal distributed generator placement, network reconfiguration, shunt capacitor
placement for reactive power compensation etc. [2].
Integration of DG at optimal location can indulgence in reducing energy losses, peak demand losses
and enhancement of voltage profile, network stability and power factor of the whole network [3]. Thus, new
DGs are needed to be connected in such a manner that it abstains degradation of power quality and reliability.
Infelicitous allocation of DG in terms of its bus location may lead to rise in fault currents, causes voltage
variations, intervene in voltage-control processes, increase losses, system capital and operating costs etc.

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 9, No. 4, August 2019 : 2303 - 2313
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Evaluation of the technical impacts of DG is very tenacious and arduous work. Moreover, installation and
placement of DG units is not straight-forward and need to be precisely alluded especially for load varying
conditions with different variables like power loss, voltage profile, generation cost, load factor and
reliability [4].
A lot of complexity arises during optimization of these non-commensurable variables with different
types of equality and inequality constraints. A good number of optimization techniques and algorithm have
already proposed including analytical approach, computational approach and different types of artificial
intelligence approach to solve these tenacious optimization problem. A simple analytical method is applied for
real power loss abatement and voltage profile enhancement based on voltage sensitivity index and power flow
analysis by using forward-backward sweep method [5]. In mathematical approach based on power loss index
and load flow analysis, total active power loss of distribution lines with DG is enumerated in newton-raphson
extended method [6]. An alternate solution is vindicated to assuage the impact of DG reactive power demand
in transmission voltages and go beyond the distribution voltage rise barrier such that more DG is connected.
The fixed power factors of the installed generators and tap setting transformer is evaluated by linear
programming formulation technique [7].
In this modern era, analytical and computational optimization techniques are being phased out by the
most promising artificial intelligence techniques including especially genetic algorithm [8], particle swarm
optimization [9-11], artificial neural network [12-13], harmony search differential operator [14], immune
algorithm [15] and clonal selection etc. [16]. Genetic algorithm (GA) with real codes and backward forward
power flow method based on 20 bus distribution network is used to optimally locate DG for minimum system
losses and maximum voltage in radial distribution networks. The optimization problem with minimization of
real power loss subjected to different constraints is solved on the basis of active power loss sensitivity of real
power injection through DG [17].
Particle swarm optimization (PSO) based hybrid objective approach for optimal placement of DG is
used with power loss reduction and reliability improvement index for only active power losses [18].
Evolutionary PSO has provided superior results with less number of iteration, computation time and also avoid
the problem of being trapped in a local minimum by selecting the survival particles to remain in the next
iteration [19].
Advanced pareto-front non-dominated sorting with fuzzy decision technique has recently applied to
essence the trade-off solution set from different objective functions like power loss, voltage stability and
deviation optimization in IEEE-33 bus test system [10]. A smart grid system with DG is developed in immune
algorithm based on the cost of different sections i.e. environmental compensation, traditional DG capacity, DG
operation and maintenance, purchased power and network loss for IEEE-30 bus test system. The optimal
solution in dynamic programming method is effectively resolved the DG planning problem of smart grid
system. In a hybrid technique consisting GA and artificial neural network is applied for placing DGs at worthy
locations and evaluating generated power based on load variations to ensure optimal power quality and
reliability [20].
Optimal location is determined considering the power losses at each DG connected bus by using the
newton-raphson extended method in neplan simulation technique [8]. In combination of GA and PSO is
implemented to minimize real power losses and increase voltage stability of a 52 bus system with load
uncertainty during optimal placement [21].
A new methodology using simple data from distribution network operators control center of the region
connecting feeders is also used to determine the optimal location of medium size DGs with uncertain topologies
in Monte Carlo simulation analysis [22]. Algorithm has also been developed to optimize both power losses and
voltage profile by bus injection to branch current and branch-current to bus voltage matrices. In most of the
proposed techniques, generation cost is ignored and only static loads are considered during optimal placement
of distributed generators.
2. PROBLEM STATEMENT FORMULATION
Multi-objective non-commensurable functions with a number of equality and inequality constraints
are being optimized for the DG placement in the power system network.
Optimize F(x) = [min FLoss (x) × max Vbus (x)] × min Fcost (x)
Where, FLoss (x) = System active power loss
Vbus (x) = Improved bus voltage profile &
Fcost (x) = Total generation cost of the network

Int J Elec & Comp Eng ISSN: 2088-8708 
Multi-objective optimal placement of distributed generations for dynamic loads (Shah Mohazzem Hossain)
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2.1. Minimization of system power loss
As the current entering a bus is considered positive and leaving the bus is negative that causes
correspondingly the real power and reactive power entering that bus is positive and negative. The complex
power at bus-i of Figure 1 is then given by,
Pi – jQi = Vi
*
Ii = Vi
* ∑ 𝑌𝑖𝑘 𝑉𝑘
𝑛
𝑘=1
From per-unit system, Sik = Pik + j Qik = Vi Iik
*
Where, Iik = [
𝑃 𝑖𝑘+ 𝑗𝑄 𝑖𝑘
𝑉 𝑖
]
∗
Taking only the magnitude, |𝐼𝑖𝑘| =
√ 𝑃 𝑖𝑘
2+ 𝑄 𝑖𝑘
2
|𝑉 𝑖|
|𝐼𝑖𝑘|2
=
𝑃 𝑖𝑘
2+ 𝑄 𝑖𝑘
2
|𝑉 𝑖|2
|𝐼𝑖𝑘|2
× 𝑅𝑖𝑘 =
𝑃 𝑖𝑘
2+ 𝑄 𝑖𝑘
2
|𝑉 𝑖|2 × 𝑅𝑖𝑘
𝑃𝑖𝑘 𝐿𝑜𝑠𝑠
=
𝑃 𝑖𝑘
2+ 𝑄 𝑖𝑘
2
|𝑉 𝑖|2 × 𝑅𝑖𝑘
The total active power loss for N number of bus sections is expressed as
min FLoss = 𝑃𝑇 𝐿𝑜𝑠𝑠
= ∑ 𝑃𝑖𝑘 𝐿𝑜𝑠𝑠𝑖, 𝑘;𝑖≠𝑘
Figure 1. Single bus system network
2.2. Voltage profile maximization
Bus voltage profile is analysed by gauss-seidal load flow study where, updated bus voltage profile
value is determined in following way from the complex power equation.
Vi =
1
𝑌 𝑖𝑖
[
𝑃 𝑖−𝑗𝑄 𝑖
𝑉 𝑖
∗ - Yi1V1 - Yi2V2 - Yi3V3 - ∙∙∙∙∙∙∙∙∙ - YinVn]
Updated final total bus voltage of all buses is represented by
max VBus = ∑ 𝑉𝑖
𝑁 𝑏𝑢𝑠
𝑖=1
2.3. Generation cost optimization
The total costs include the fixed costs during initial investment and variable costs including the
maintenance cost and utilization factor of DG units which is expressed through following equation.
min Fcost = a + bP + cP2
+ dP3
Where a, b, c, d is the corresponding coefficient value for fixed and variable cost of the network.
3. SYSTEM CONSTRAINTS
The objective functions for the DG placement problem is needed to meet certain security constraints
and network constraints. 𝑃𝑠𝑦𝑠 and 𝑄𝑠𝑦𝑠 are injected active and reactive powers to the distribution network

 ISSN: 2088-8708
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by sub-transmission network. 𝑃𝐷𝐺 and 𝑄 𝐷𝐺 are associated active and reactive powers of DGs. Pd and Qd are
total power demand of network loads. 𝑃𝐿𝑜𝑠𝑠 and 𝑄 𝐿𝑜𝑠𝑠 are both active and reactive power losses of the network.
Network power balance equation for the network is expressed as
𝑃𝑠𝑦𝑠 + 𝑃𝐷𝐺 = 𝑃𝑑 + 𝑃𝐿𝑜𝑠𝑠
𝑄𝑠𝑦𝑠 + 𝑄 𝐷𝐺 = 𝑄 𝑑 + 𝑄 𝐿𝑜𝑠𝑠
Electrical network contains some imperative constraints like bus voltage (Vi), thermal current (Iij) limits of each
line and power limits of connected DG.
Vi
min
≤ Vi ≤ Vi
max
Iij ≤ Iij
max
PDG
min
≤ PDG ≤ PDG
max
QDG
min
≤ QDG ≤ QDG
max
4. MODEL SYSTEM OPTIMIZATION
In this work, multi-objective optimal placement problem is decomposed into different types of real
time variable functions. An algorithm is developed in MATLAB to optimize these variables in N-bus system
network. The developed technique is applied in IEEE-14 bus test systems of Figure 2 where, bus-1 is selected
as slack bus of the network. Bus-13 and bus-14 are generator (PV) bus, except all rest are load (PQ) buses.
The line impedances with the line charging admittances, bus voltage magnitudes, installed generator rating,
operating cycle, cost coefficient of the network is shown in Table 1 to Table 4. The operation of power systems
has been complicated by the rapid diversification of loads in recent days especially in industrialize areas.
Load characteristics analysis has become one of the most significant part in modern energy management system
to find the optimal bus location of DG and network reliability. Unstable loading conditions causes difficulties
in determining the available load in a certain time period. Mostly, load values are forecasted from the available
load curves of the particular section of a network.
Figure 2. IEEE-14 bus system network
Table 1. Line impedances and line charging admittances
Line
(Bus to Bus)
Impedance (pu) Line Charging
(Y/2)R ohm X ohm
1 2 0.01938 0.05917 0.0264
1 5 0.05403 0.22304 0.0219
2 14 0.04699 0.19797 0.0187
2 4 0.05811 0.17632 0.0246
2 5 0.05695 0.17388 0.017
14 4 0.06701 0.17103 0.0173
4 5 0.01335 0.04211 0.0064
4 7 0.0121 0.20912 0.0014
4 13 0.0211 0.55618 0.00241
5 6 0.03217 0.25202 0.0014
Line
(Bus to Bus)
Impedance (pu) Line Charging
(Y/2)R ohm X ohm
6 11 0.09498 0.1989 0.00611
6 12 0.12291 0.25581 0.00121
6 8 0.06615 0.13027 0.0014
7 9 0.04131 0.17615 0.0111
7 13 0.02133 0.11001 0.00131
13 10 0.03181 0.0845 0.0164
13 3 0.12711 0.27038 0.0025
10 11 0.08205 0.19207 0.0114
12 8 0.22092 0.19988 0.0164
8 3 0.17093 0.34802 0.00347

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Table 2. Bus voltage magnitudes and generator rating
Bus Type Bus No.
Bus Voltage Power Generated
Magnitude (pu) Angle (deg) P (MW) Q (MVAR)
Slack 1 1.06 0 40 -
PV bus
13 1.01 - 35 -
14 1.045 - 25 -
DG - 1.00 - 3 -
Table 3. Installed generator operating cycle
Generator
Max
(MW)
Mi
(MW)
Up Time
(Hr)
Down Time
(Hr)
Priority
Order
Gen-1 40 20 6 3 1
Gen-2 35 10 5 2 2
Gen-3 25 8 4 2 3
DG 3 0.5 2 1 4
Table 4. Installed generator cost coefficient values
Generator a b c d
Gen-1 25.5 12.3 0.2 206
Gen-2 27.62 15.4 2.2 281
Gen-3 20.41 11.7 1.7 250
DG 22.21 18.31 15.23 505
A load curve reflects the change of electrical power consumption by consumers over a particular time
cycle like a day, week, month or year. Cognisant values of consumer’s load make the load calculation very
much straightforward in any section. Consumers factor and time factor mainly influence the dynamic load
modelling and forecasting. The customer factor is related with the total number, type and power consumption
rate of the installed electrical appliances in consumer’s end. The electrical load usually varies with time
depending on human and pecuniary activity. There is more load in the day time and less load at night.
Large amount of load variation occurs in week days compared with weekend. This cyclic time dependency
forced to peruse the loads in hourly, daily, weekly or yearly basis. Climate change has also an impact on load
characteristics especially change of humidity results variation in use of electrical appliances. Real power
system network causes a significant voltage drops and higher power loss due to this natural load factors.
Interconnection of DG to the grid may have different implications on the distribution network due to the load
characteristics. In this work, worst possible load-demand curve of a zone is analysed to ensure optimal
placement of DG [23]. Dynamic load connected 13 buses are analysed on basis of their data of respective
zone’s yearly load-demand curves of the network which are depicted in Figure 3 and Figure 4.
Figure 3. Load connected buses real power variations

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Figure 4. Load connected buses reactive power variations
5. PROCESS DESCRIPTION
A load-flow study has done to determine the voltages, currents and real and reactive power flows in
a network under a given load conditions for various hypothetical situations. Non-linear basic power flow
equations are solved by using gauss-seidal iteration method. Self-admittance of each bus and the mutual
admittance between the buses forms admittance matrix using the value of line impedances and line charging
admittances of Table 1. 1+ j0 per unit voltage value is initialized for all buses to find-out the unknown bus
voltage magnitudes and angles of the PQ buses and angles of the PV buses. After convergence progress of
iteration solutions final bus voltage is determined beyond the tolerance level. Voltage difference between two
buses causes the current flow to the network. Due to the presence of resistive property a certain amount of
power is lost in the network. Large distance of the network line corresponds the large amount of power loss.
While total generation cost of the system depends on its capability to meet the maximum demand with
minimum power loss in the network. Generator active operating hour is a concerning issue for estimating the
overall cost of the system by using the cost-coefficient values of Table 4. Usually DG units are being used to
meet up the peak load or certain demand of the load in the network. Calculated active operating hour using
respective generator characteristics of Table 3 in different time span of a year for the selective section of the
model network in is shown Figure 5. The flow chart to determine the summation of all bus voltage, line to line
loss and generation cost is depicted in Figure 6 to Figure 8.
In the first stage of multi-objective optimization process candidate DG is placed in all available buses
independently except slack bus to calculate the change of bus voltage profiles using gauss-seidal iteration
method. The loss factor is determined to find the amount of power loss in a particular line with respect to the
change in bus voltage profiles. Then calculated cost factor is used to estimate the total generation cost with
respect to the change in line losses. A heuristics approach is used in the second stage through lagrangian
multiplier function to find the optimal bus location for integration of DG units in a power system network.
Flow chart for optimization process is depicted in Figure 9.
Figure 5. Installed generators active operating hour

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Figure 6. Flow chart for bus
voltage calculation
Figure 7. Flow chart for line to
line loss calculation
Figure 8. Flow chart for
generation cost calculation
Figure 9. Flow chart for optimization of bus voltage and line to line loss of the network
6. RESULTS AND DISCUSSIONS
In the process of optimization selected new DG is connected to all possible bus location to find the
change in bus voltage, line loss and generation cost with respected to normalized system values. Change of bus
voltage magnitudes after DG insertion in each bus of the network except the swing bus is depicted in Figure
10 to Figure 13. Optimal bus location is selected when maximum voltage profile improvement, minimum
power loss and generation cost is ensured in the network. Total change in bus voltage, power loss and
generation cost for DG placement in each bus location is depicted in Figure 14 to Figure 16. Optimal bus
location for the given network of dynamic loads is selected bus number 12 from the Table 5.

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Figure 10. Change in each bus voltage magnitudes
after DG insertion at Bus-2 to Bus-4
Figure 14. Change in total bus voltage magnitudes
after DG insertion in each bus
Figure 15. Change in total line to line loss after DG
insertion in each bus
Figure 16. Change in total generation cost after DG insertion in each bus

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Table 5. Optimal decision for DG placement
DG
Placement
Total Change in %
DecisionLoss
(MW)
Voltage
(pu)
Cost
(USD)
Without DG 0.825 14.342 1420.5
Bus-2 (+)1.05 (+)0.19 (+)0.53
Bus-3 (-)10.7 (+)0.18 (+)0.44
Bus-4 (-)0.52 (+)0.19 (+)0.54
Bus-5 (-)0.52 (-)0.17 (+)0.53
Bus-6 (-)2.60 (-)0.13 (+)0.51
Bus-7 (+)4.30 (+)0.16 (+)0.58
Bus-8 (-)8.22 (+)0.15 (+)0.45
Bus-9 (-)3.50 (+)0.18 (+)0.50
Bus-10 (-)0.41 (-)0.18 (+)0.53
Bus-11 (-)4.66 (+)0.19 (+)0.49
Bus-12 (-)11.0 (+)0.18 (+)0.42 Selected
Bus-13 (-)0.81 0.00 (+)0.53
Bus-14 (+)2.36 (-)0.17 (+)0.56
7. COMPARISON WITH STATIC LOADS
In the literature study most of the researcher has solved the multi objective optimization for static
loads which are usually considered as the maximum demand during a particular time of span for a network
[24]. If the given system is analyzed for corresponding maximum loads of Figure 17 and Figure 18 for the
same section of the network with yearly same time of span. Corresponding change in total bus voltage, line to
line loss and generation cost for static loads of the network are depicted in Figure 19 to Figure 21. Optimal
decision for DG placement is found bus number 8 for static loads from Table 6. It is clear that, optimized value
varies due to the load variation in any time span.
Figure 17. Maximum loads of the network in each
bus (Real power)
Figure 18. Maximum loads of the network in each
bus (Reactive power)
Figure 19. Change in total bus voltage magnitudes
after DG insertion in each bus (Static Load)
Figure 20. Change in total line to line loss after DG
insertion in each bus (Static Load)

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Figure 21. Change in total line to line loss after DG insertion in each bus (Static Load)
Table 6. Optimal decision for DG placement
DG
Placement
Total Change in %
DecisionLoss
(MW)
Voltage
(pu)
Cost
(USD)
Without DG 1.84 14.246 2212.9
Bus-2 (-)3.99 (+)0.12 (+)0.53
Bus-3 (-)7.80 (+)0.15 (+)0.45
Bus-4 (-)1.64 (+)0.13 (+)0.58
Bus-5 (-)2.35 (-)0.13 (+)0.57
Bus-6 (-)3.53 (+)0.14 (+)0.54
Bus-7 (+)3.33 (+)0.14 (+)0.68
Bus-8 (-)11.3 (+)0.15 (+)0.38 Selected
Bus-9 (+)0.08 (+)0.15 (+)0.62
Bus-10 (-)3.51 (+)0.14 (+)0.54
Bus-11 (+)2.70 (+)0.15 (+)0.56
Bus-12 (-)10.6 (-)0.11 (+)0.40
Bus-13 (-)4.21 (+)0.00 (+)0.53
Bus-14 (-)1.49 (-)0.10 (+)0.58
In modern days, load variation is one of the common problem for electrical network systems specially
for distribution sectors. These loading effect issue cannot be ignored during analysing optimization problem.
For the given system considering loading effect system optimal decision ensures 2.78% less line to line loss,
0.03% more bus voltage improvement and 0.03% less generation cost in a year. Different types of load curves
need to be analysed for effective solution of optimization problem for uncertain load conditions of the network.
8. CONCLUSION
The integration of DG units in power system networks has become more protruding to revamp overall
system efficiency by augmenting system voltage magnitudes, assuaging power losses and dwindling total
generation cost. In this work, an algorithm is proposed to locate DG in the optimal bus location with multiple
number of objective function and constraints of N-bus network. The developed adaptive algorithm provides
the most appeasement and admissible result among all the approach discussed in the literature study especially
for different load characteristics. The convergence criterion of the algorithm is well acceptable for not only
time invariant but also time variant loads. The probabilistic dynamic load and generation model ensconce the
optimal place of DG without violating the thermal limit and other constraints of the network. Due to the load
and generation uncertainty, the system has different bus location at static and dynamic loading conditions.
From this work, it is clear that final decision for optimal placement of DG need to take on considering dynamic
loading conditions due to the large variations in load characteristics of power system networks.
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