Journal of Energy Storage 27 (2020) 101117
Contents lists available at ScienceDirect
Journal of Energy Storage
journal homepage: www.elsevier.com/locate/est
Grasshopper optimization algorithm based two stage fuzzy multiobjective
approach for optimum sizing and placement of distributed generations,
shunt capacitors and electric vehicle charging stations
Srinivasa Rao Gampaa, Kiran Jasthia, Preetham Golib, D. Dasc, R.C. Bansald,
T
⁎
a
Department of Electrical and Electronics Engineering, Gudlavalleru Engineering College, Gudlavalleru, Krishna District, Andhra Pradesh 521356, India
School of Computing and Engineering, University of Missouri Kansas City, Kansas City, MO 64110, USA
c
Department of Electrical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
d
Department of Electrical Engineering, University of Sharjah, Sharjah, P.O. Box 27272 United Arab Emirates
b
ARTICLE INFO
ABSTRACT
Keywords:
Electric Vehicles
Grasshopper optimization
Battery modeling
Charging stations
Distributed Generations
Shunt capacitors
In this paper a two stage Grasshopper Optimization Algorithm (GOA) based Fuzzy multiobjective approach is
proposed for optimum sizing and placement of Distributed Generations (DGs), Shunt Capacitors (SCs) and
Electric Vehicle (EV) charging stations for distribution systems. In the first stage Fuzzy GOA approach is used for
optimum sizing and allocation of DGs and SCs for improving the substation power factor, real power loss reduction and voltage profile improvement of the distribution system. In the second stage distribution system
integrated with DGs and SCs is considered and fuzzy GOA approach is used for identifying optimum locations for
EV charging stations and number of vehicles at the charging stations. EV battery charging load models are
developed from the Lithium ion battery charging characteristic curves for load flow analysis. Simulation results
are shown to show the advantages of fast converging properties of GOA over GA and PSO techniques. Simulation
results are demonstrated on 51 bus and 69 bus distribution networks to show the advantages of proposed
methodology compared to conventional objective based simultaneous optimization approach. The effect of EV
load growth and the effect of uncertainties in DGs and distribution system load are shown on the distribution
system performance.
1. Introduction
Electric Vehicles (EVs) are rapidly replacing gasoline fueled cars to
overcome the environmental problems associated with greenhouse
gases and to survive the depletion of fossil fuels. The rapidly increasing
numbers of EVs potentially raise the peak load demand and significantly increase the feeder currents and degrade the voltage profiles
of the distribution system. Placement of DGs at inappropriate locations
results in greater power losses and cause magnitude reduction in voltage profile. It is a common practice for the utility engineers to install
shunt capacitors (SCs) to improve the voltage profile of the distribution
system. In order to mitigate the vulnerabilities due to the presence of
EVs and DGs it is necessary to develop methodologies for optimal sizing
and placement of EVs, DGs and SCs in distribution systems.
Several studies on sitting and sizing of DG units and SCs have been
reported in the literature. Analytical and heuristic based approaches
[1,2] have been proposed for real power loss minimization for combined DGs and SCs allocation in distribution systems. Evolutionary
⁎
computing techniques, genetic algorithm (GA) [3,4], particle swarm
optimization (PSO) [5,6], imperialist competitive algorithm [7], MultiObjective Particle Swarm Optimization (MOPSO) [8], Intersect Mutation Differential Evolution (IMDE) [9], Biogeography-Based Optimization (BBO) [10], Improved PSO [11], shuffled bat algorithm [12], Ant
Lion optimization [13] and Improved Harmony search algorithm [14]
have been proposed for optimum allocation and sizing of DGs and shunt
capacitors for improving technical performance and economical profits
of the distribution system. Rastgou et al. [14] proposed improved
harmony search algorithm and Kumar et al. [15] have proposed a
multi-objective chaotic differential evolution for minimizing the economic losses and improving the voltage profile. Barik and Das [16]
proposed a sequential optimization method for minimizing the annual
energy loss and improving the voltage profile. Kansal et al.[17] proposed PSO based optimization technique for optimum sizing of DGs and
SCs considering real power loss minimization and improvement in
economic factors. The authors used GA based approach in [18] for
optimum sizing of DGs and shunt capacitors and in [19] the authors
Corresponding author.
E-mail address: rcbansal@ieee.org (R.C. Bansal).
https://doi.org/10.1016/j.est.2019.101117
Received 23 September 2019; Received in revised form 23 November 2019; Accepted 25 November 2019
2352-152X/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
considered environmental factors in addition to techno economical
factors. Ismael et al. [20] have proposed GOA for optimal network reconductoring of distribution systems for minimizing the investment cost
and real power losses.
Large-scale penetration of EVs can have a detrimental and destabilizing effect on the electric power grid and many authors have focused their research on the study of impacts on distribution network.
Gomez and Morcos [21] have developed a simple tool to find the impact of battery chargers on distribution system transformers, cables,
circuit breakers and switches. Hadley [22] studied the requirement of
fossil fuel resources due to the potential use of PHEVs in distribution
systems. Sharma and Bhattacharya [23] proposed smart distribution
frame work to analyze the short comings due to uncontrolled charging
of PEVs. Mu et al. [24]. developed a Spatial Temporal model using
Origin-Destination analysis using intelligent transportation research for
finding the impact of EVs on urban distribution networks. Teng et al.
[25] analyzed the benefits and impact of electric vehicles in overcoming the challenges in primary frequency control due to renewable
energy sources. Elnozahy and Salama [26] proposed probabilistic frame
work for estimating the impacts of uncontrolled charging of PHEVs on
residential distribution systems. Dubey and Santoso [27] studied the
impact of EV charging on residential distribution systems and showed
that the impact on secondary circuits’ voltage profile is more than the
primary wires. Papadopoulos et al. [28] analyzed the impact of charging electric vehicles considering uncertainties associated with residential loads on British distribution systems. Richardson et al. [29]
have proposed linear programming based technique for determining
optimal charging rate for each vehicle to maximize the power delivered
to EVs.
Recently, attempts have been made to mitigate the impacts of
charging EVs on distribution system by optimally sizing and sitting the
charging stations. Mixed-integer non-linear programming techniques
have been developed by the authors [30–32] for optimum charging
stations placement for minimizing the costs of power loss, voltage deviation, and improving network reliability. El-zonkoly and Coelho [33]
proposed a multi-objective approach for EV parking lot sizing and sitting problem. Simons [34] developed a bi-level optimization problem to
determine the optimal location and size of the charging stations with
respect to the minimal walking distance for the vehicle owners. Wang
et al. [35] proposed an analytical approach and Xu et al. [36] employed
a Tabu search and binary particle swarm optimization based hybrid
solution technique for optimal placement of EV charging stations. Wang
et al. [37] have developed an efficient power plant model of EVs based
on the travel characteristics of EVs to provide V2G service for active
power control of power systems with large wind power generation
systems. Dong et al. [38] have developed a charging price methodology
considering the travel characteristics of EV users for minimizing the
voltage deviations in distribution systems. Wang et al. [39] developed
combination of heuristic and GA based approach for finding the optimum vehicle flows in a network for efficiently managing the charging
infrastructure.
The techniques discussed above primarily focused on the placement
and sizing of EV charging stations without the presence of DG units.
Interaction between EVs, battery storage and renewable DGs in a microgrid environment has generated lot of curiosity with the change in
the landscape of the distribution system [40–43]. Kumar et al. [40]
developed a bi-level optimization framework using GA to allocate wind
generation units and battery energy storage systems with ancillary
provisions in a distribution network. Chen and Duan [41] proposed a
new method based on GA for optimal integration of EVs in microgrids
considering the uncertainties in solar power generation, electricity
market price and load demand. Longo [42] developed MILP based
technique for optimum design of fast charging station considering
economical aspects. Ahmad et al. [43] proposed an optimal energy
management system for minimizing the cost of energy to charge the EV.
Andebili et al. [44] have shown that optimal planning of EV charging
lots will improve the economical profits of utilities. Rezaei et al. [45]
proposed a multi-objective optimization based GA –PSO hybrid algorithm for optimal sizing and allocation of renewable energy sources and
EV charging stations simultaneously. Sabillion et al. [46] proposed a
dynamic scheduling method based on MILP model to optimize the joint
operation of photovoltaic units and EVs in a residential distribution
networks using energy storage systems.
Some studies considering the sizing and sitting of both DG units and
EV charging stations can be found in [47–52]. Jannesar et al. [47]
solved the problem of optimal placement and sizing of battery energy
storage PV units using GA. Awasthi et al. [48] proposed GA and PSO
based approach in order to determine the optimum location and optimum penetration levels of EVs. Pazouki et al. [49] proposed GA based
technique for optimum sizing of EV charging stations. The authors
[50–52] proposed multi-objective optimization problems to obtain the
optimal location and size of renewable DG units and charging stations.
Bukar et al. [53] proposed GOA for optimum sizing of autonomous
micro grid system. Kabir et al. [54] proposed community based grid
reinforcement process for coordinating roof top PVs and battery energy
storage systems. Islam et al. [55] proposed novel probabilistic EV
charging load models correlating with PV power supply for improving
the power quality. Tan and Wang [56] proposed hierarchical game
approach for effectively navigating the EVs to EV charging stations
during off peak hours in optimum time and improving economical
profits of the charging stations. Luo et al. [57] have developed second
order cone programming based technique for optimal allocation of DGs
and EV charging stations considering the objective of real time charging
navigation. Zhang et al. [58] proposed hysteresis control strategy of
power management based novel configuration for plug-in hybrid electric vehicles with three fuel cell stacks for enhancing the durability of
the fuel cells.
Kongjeen et al. [59] used exponential load models and Qian et al.
[60] used battery charging characteristic curves for modeling EV battery charging load for peak load conditions. Garcia-Valle and Vlachogiannis [61] developed P, Q load models using exponential functions
for modeling the transients and steady state conditions of EV battery
charging load. Bertoluzzo et al. [62] discussed the necessity for improving power factor of conventional battery chargers and Masoum
et al. [63] have studied the impact of different electric vehicle battery
charging rates on the performance of distribution system.
So far many researchers have proposed different charging rates for
EV batteries for avoiding the overloading of the network components. The sequence of the use of different charging rates with the
variations in load profiles will change every day and the use of
different charging rates for distribution load management may deteriorate the life span of batteries [63]. The incorporation of DGs
and SCs will improve the distribution system performance and can
effectively handle EV charging load. Hence in the present work the
optimum sizing and placement of DGs and SCs is considered for
handling the EV charging load at constant charging rates irrespective of the load variations simultaneously maintaining the desired
distribution system performance.
Recently some authors [45,51] have proposed conventional multiobjective based simultaneous placement of DGs and EV charging
stations using evolutionary computing techniques. The desired
performance is not guaranteed with incommensurable conventional
multiobjective techniques. Hence in the present work fuzzy multiobjective approach is used for effective planning of the distribution
system with desired specifications.
Since the optimum placement of DGs and SCs reduces and EV
charging load increases the real power loss of the distribution
system meeting the desired specifications is difficult with simultaneously planning methodology. For that it is required to have
knowledge of the distribution system performance before planning
optimal placement of EV charging stations. In the present work the
2
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
optimum sizing and allocation of Distributed Generations (DGs),
Shunt Capacitors (SCs) and EV Charging stations using Grasshopper
Optimization Algorithm is considered in two stages. In the first stage
a Grasshopper optimization algorithm based fuzzy multi-objective
optimization technique is developed for optimal placement of DG
units and shunt capacitors for achieving the desired distribution
system performance. In the second stage optimal placement of EV
charging stations is considered using fuzzy GOA approach based on
the performance improvement of distribution system gained with
the incorporation DGs and SCs obtained in the first stage.
The requirements of DG capacity and substation power supply capacity at various distribution system loads for operating charging
stations with full capacity are needed to be determined and the
performance of the distribution system analysis is required for reliable power supply to customers.
For finding the impact of EV charging load on distribution systems
and for analyzing the transient and steady state changes it is necessary to develop EV battery charging load models for the load flow
studies. In the present work battery charging load models are developed for analyzing the impact of EV charging load on distribution
system performance using load flow analysis.
fuzzy multiobjective function is formed considering the objectives of
desired real power loss reduction and voltage profile improvement. The
flow chart describing the Fuzzy GOA implementation process using
fuzzy multiobjective function for optimum placement of EV charging
stations is given in Section 5.2.
The role of DGs and SCs in improving distribution system performance and the impact of EV charging load on the substation power
supply and the result analysis are presented in Section 6. The conclusions are discussed in Section 7.
3. Modeling of electric vehicle battery charging load
For finding the impact of EV charging load on distribution systems
and for analyzing the transient and steady state changes it is necessary
to develop EV battery charging load models for the load flow studies.
The load of EV charging depends on the number of vehicles and the
initial state of charge (SOC) of the EV batteries. In the present case it is
assumed that all vehicles will recharge from fully discharged state.
The characteristics of EV power charging demand and related stateof-charge profiles of different types of batteries are shown in [60]. The
lead-acid based battery has 27.19 kWh, lithium-ion based Nissan Altra
has 29.07 kWh and NiMH based Toyota has 32 kWh charging capacities
when they are fully charged from a fully discharged state. In this work
the P, Q model for battery charging load is developed by the characteristics of lithium-ion battery [60] which is used in the Nissan Altra
electric car produced by Nissan Motors.
The EV battery charging characteristic curve [60] for Lithium ion
battery is shown in Fig. 1. In Fig. 1 the battery power charging curve
from fully discharged state to fully charged state and the state of
charging (SOC) is shown.
From the Fig. 1 the battery charging load model equations can be
developed for load flow analysis. The batteries in EV systems are chemical storage systems and the charging and discharging characteristics
of chemical process are exponential functions over time. Hence the
power charging characteristics of batteries can be modeled by the following exponential equations. Eq. (1) represents the battery power
charging for steady state and transient conditions.
2. Problem formulation
In this work GOA is selected as a tool for obtaining optimum sizing
and allocation of DGs, SCs and EV charging stations because it is efficient in obtaining global optimum at fast convergence rate compared to
other evolutionary techniques [64]. The EV battery charging load
models required for load flow analysis are developed from battery
charging characteristics in Section 3. The basic GOA algorithm and
necessary mathematical equations are discussed in Section 4.
In the present work the optimum sizing and allocation of Distributed
Generations (DGs), Shunt Capacitors (SCs) and EV charging stations
using GOA is considered in two stages for efficient distribution system
planning and discussed in detail in Section 5.
In the first stage GOA is used for obtaining the optimum locations
and sizing of DGs and SCs using fuzzy multiobjective function. The
fuzzy multiobjective function formation for obtaining optimum DGs
and SCs is discussed in Section 5.1. The development and design of
fuzzy multiobjective function is discussed from Section 5.1.1 to
Section 5.1.4. The fuzzy multiobjective function is formulated considering the objectives of improving substation power factor, desired
DG penetration and distribution system performance in terms of loss
reduction and voltage profile improvement. The fuzzy multiobjective
function is optimized using GOA for obtaining optimum locations and
optimum sizing of DGs and SCs. In general Solar and wind power
system DG are most popularly available DG resources and Biomass DG
can be used for solving the uncertainties associated with Solar and
Wind DGs. Hence in this case three optimal locations for DG placement
and equal number of optimal locations for SCs placement are considered. The necessary modifications required for implementation of
GOA algorithm for optimum sizing of DGs and SCs are discussed in
Section 5.1.5. In Section 5.1.6 the necessary modification required for
optimum sizing of DGs and SCs using GOA are discussed. The flowchart
describing the gradual optimization process for implementing GOA algorithm using fuzzy multiobjective function described by for obtaining
optimum sizing and allocation of DGs and SCs is given at the end of
Section 5.1.
In the second stage the network integrated with optimum DGs and
SCs obtained in first stage is considered for optimal placement of EV
charging stations for effectively handling EV charging demand and
distribution peak loads simultaneously. In this case five locations nearly
10% of total distribution system nodes for optimum placement of
charging stations are considered. At each location the optimum numbers of EVs that can be charged without degrading the distribution
system performance are identified using Fuzzy GOA. In this case the
max
PEV
(1
PEV (t ) =
max
PEV
(
e(
t / tm2) ) for 0
tmax
t
tmax
tm2
t
) for t < t t
m2
tm2
max
0fort > t max
(1)
max
Where PEV(t) is the instantaneous EV battery charging load and PEV
is
the maximum battery charging load on the substation.
max
max
PEV
() = PEV (1 e
tm1/tm2)
Fig. 1. Charging characteristic of Lithium-ion Battery [60].
3
(2)
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
=
tm2
ln(1
tm1
)
attraction. In this work the value of ‘f’ is 0.5 and lg is 1.5 taken for
running optimization. Since the gravitational force effect is negligible
on the swarm behavior of grasshoppers, it is not considered and the
wind effect is modeled as the global best solution. Finally the grasshopper position can be updated by the following expression.
(3)
In the above Eqs. (1) and (2) tm1, tm2 are 0.25 h, 4.5 h and tmax is 5 h
respectively taken from the Fig. 1. Where α and β are the EV battery
characteristic constants. βis the fraction of maximum charging load and
max
the value taken as 0.95 which accounts 95% of PEV
at time tm1.The
value of α can be calculated from Eq. (3) which can be derived from Eq.
(2).
0
When the batteries are charging from an initial state of chargePEV
,
the power charging equation can be expressed by Eq. (4).
max
PEV (t ) = PEV
(1
e(
t / t fc ) ) + P 0 e (
EV
t / t fc ) for 0 < t < t
fc
x ik = C
(4)
max
QLEV (Ni ) = NVi (PEV
)tan( )
(7)
xi )
s (u) = fe u /lg
e u
(12)
th
th
Dijk is the
(13)
Where SkW and SkVA are real power supply and reactive power supply
drawn from the substation.
BN
NDG
PLi + Apl DGSC
SkW =
i=1
PDGj
(14)
j =1
th
Where PDGi is i DG capacity and NDG is the total number of DG installations. PLi is real power load at ith node and BN is the total number
of buses. AplDGSC is the active power loss of the distribution system with
DGs and SCs installation.
BN
NSC
QLi + Qpl DGSC
SkVAr =
i=1
NDG
QCj
j =1
(PDGk ×tan( DG ))
k=1
(15)
th
QLj is reactive power load at j node and NSC is the total number of
shunt capacitors. QplDGSC is the reactive power loss of the distribution
system with DGs and SCs installation. φDG is the power factor angle of
the DG units.
xi )
Dij
(11)
Cmax
Cmin
itermax
SkW
SkVA
PF = Cos
(8)
(x j
k
+ xgbest
5.1.1. Fuzzification of S/S power factor (μPF)
The DGs mainly operate at 0.95 lagging power factor (PF) and hence
in this it is aimed at improving substation (S/S) power factor also to
0.95 lagging as in the case of DGs. The substation power factor can be
calculated from the following equation.
Where Xi is the position of the i grasshopper in the search space, Si is
the advantage of social interaction gained by the ith grasshopper. Si,Gi
and Wi are the social interaction, gravitational and wind advection effects on the grasshopper.
s ( xj
x ik )
Dijk
The optimization problem focuses on improving the substation
power factor, reducing the real power losses, and improving the voltage
profile of the distribution system. For the objectives to achieve the
desired values, i.e. for substation (S/S) power factor and DG penetration
limit triangular membership functions are used. For other objectives
required to satisfy operational constraints, i.e. for active power loss
reduction and voltage limits trapezoidal membership functions are
used. The fuzzified objectives are shown in Fig. 2.
th
j=1
j i
(x jk
5.1. Optimum sizing and placement of DGs and SCs using fuzzy GOA
(GOA) [64] is an evolutionary computation technique developed by
mimicking the swarming behavior of grasshoppers while searching for
food. GOA is used an optimization tool for obtaining optimum sizing
and allocation of DG units and SCs for achieving the desired objectives.
The mathematical equations are developed for GOA by utilizing the
characteristic food source seeking tendencies of grasshopper's swarms.
The grasshoppers swarming behavior is influenced by social interaction
among themselves, gravitational force and wind advection.
The position of the grasshopper in the search space can be mathematically modeled by the following equation.
Si =
x ik )
In this section the necessary fuzzy multiobjective [65–67] functions
are developed for optimum placement of DGs and SCs in the first stage
for enhancing distribution system performance and for optimum placement of EV charging stations in the second stage using GOA.
4. Grasshopper optimization algorithm (GOA)
NGH
s ( x jk
5. Optimum placement of DGs, SCs and EV charging stations using
fuzzy GOA
Where NVi is the number of vehicles at the ith optimum node Ni .
max
PEV
andφare maximum EV charging load and power factor angle.
PLEV(Ni)and QLEV(Ni)are the real and reactive power loads of EV batteries at the ith optimal node. The peak charging load is considered to
determine the impact on distribution system performance during peak
hours. For observing the transient response Eq. (1) can be used.
Xi = Si + Gi + Wi
2
j =1
j i
iter
k
x min
)
Where
k variable i position in the population,
k
distance between ith and jth position of the kth variable and x gbest
is the
global best of kth variable. The variables C, Cmax and Cmin are the GOA
parameters and in this work Cmax is 1 and Cmin is 0.00001.
The batteries should be disconnected from the power supply after
achieving 100% SOC for avoiding the demerits due to overcharging of
the battery. The conventional battery chargers will operate at lower
power factor and hence they require more time for reaching 100%
charging state of the batteries [59].
Hence modern battery chargers use power factor correction techniques for improving the battery charging speed. In this work it is
considered that the battery chargers operate at 0.95 power factor lagging [59, 62]. The battery charging load at the identified optimum
locations can be expressed by Eqs. (6) and (7) during peak charging
condition.
(6)
k
(x max
x ik is the
(5)
max
PLEV (Ni ) = NVi (PEV
)
C
C = Cmax
The tfc is the time taken for fully charging the battery from initial
charging position. The state of the power charging battery can be expressed by the following equation
SOC (t + 1) = SOC (t ) + PEV (t ) (t )
NGH
(9)
(10)
SkVA =
The social forces between the grasshoppers is calculated by the ‘s’
function described by Eq. (10) where ‘u’ is the distance between
grasshoppers,‘f’ is the intensity of attraction and ‘lg’ is the length of
(SkW )2 + (SkVAr )2
(16)
The fuzzy membership function shown in Fig. 2(a) for S/S power
factor (PF) can be calculated by the following equation.
4
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
Fig. 2. Fuzzy Membership functions for optimum sizing of DGs and SCs.
PFmin
(PF PFmin )
forPFmin
(PFD PFmin)
(PFmax PF )
forPFD
(PFmax PFD )
Where P(i + +1) and Q(i + +1) are the real and reactive power load
injections at the (i + +1)th node. Ri is the resistance of the ith branch
and V(i + +1) is the voltage of the (i + +1)th node of the distribution
system. The active power loss index (APLI) is determined as the ratio of
power loss with DGs and SCs to the base case as given in Eq. (22).
0forPF
µPF =
PF
PFD
PF
PFmax
(17)
Where PFD is the desired power factor level. In the above equation
PFmin =0.85, PFD=0.95 and PFmax = 1.0 are taken.
APLI =
DGSC
NDG
PDGi
i=1
BN
PLi
j =1
(18)
1forAPLI
µAPLI =
The fuzzification of DG penetration limit (PDGI) is shown in
Fig. 2(b). From Fig. 2(b), the fuzzy DG penetration index can be described mathematically using the following Eq. (19).
0forPGDI
µPGDI =
PGDI
PGDISP
(PGDImax PGDI )
forPGDISP
(PGDImax PGDISP )
PGDI
PGDImax
0forPGDI > PDGImax
(19)
0forVi
VL1
(Vi VL1)
forVL1 < Vi < Vmin
(Vmin VL1)
µVi = 1.0forVmin
Vi Vmax
(Vmax Vi)
forVmax < Vi < VL2
(Vmax VL2)
BN 1
LP (i )
0forVi > VL2
(20)
R (i) × (P 2 (i + 1) + Q2 (i + 1))
V (i + 1) 2
(24)
In this work, VL1= 0.94, Vmin= 0.95, Vmax=1.05 and VL2=1.06 are
considered.
In the present work the minimum of fuzzy membership values of all
the individual node voltages is considered as the fuzzy voltage profile
performance index (μV) of the distribution system.
Where LP(i) is the ith branch real power loss of the distribution system which can be
69
calculated from the load flow algorithm by the following equation[ ].
LP (i ) =
(23)
5.1.4. Fuzzified min and max voltage limits at distribution system nodes
The fuzzy membership functions (µVi ) of all the individual node
voltages are determined using the fuzzy set shown in the Fig. 2(d). From
Fig. 2(d), we can write,
5.1.3. Fuzzified active power loss index (μAPLI)
The active power loss of the distribution system (Apl) can be expressed by the following equation.
i=1
APLImax
In the present work it is aimed to reduce active power loss below a
certain previously considered level. Hence in this work APLImin is selected based on utility requirement and APLImax is unity. The APLImin
value is taken in such a way that to achieve the desired real power loss
reduction.
Where PGDISP is the desired DG penetration level. In the present case it
is aimed at placing DGs equal to 50% of total real load. PDGImin, PGDISP
and PDGImax are taken as 0.4, 0.5 and 0.6 respectively.
Apl =
APLI min
(APLImax APLI )
forAPLImin < APLI
(APLImax APLImin)
0forAPLI > APLImax
PGDImin
(PGDI PGDImin )
forPGDImin
(PGDISP PGDImin)
(22)
Base
Where APl
and APl are active power loss with DGs and SCs, and
with base case respectively. The conventional loss index (APLI) is fuzzified and the trapezoidal fuzzy set considered for active power loss
(μAPLI) is shown in Fig. 2(c). The fuzzy active power loss index can be
described mathematically using the following Eq. (23).
5.1.2. Fuzzification of DG penetration (μPDGI)
The DG penetration index (PDGI) is defined as the ratio of total DG
installed to the total real power load.
PDGI =
APl DGSC
APl Base
(21)
5
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
Where NVT is the total number of variables, NDG and NSC are the
number of DG installations and SC installations. NDGL and NSCL are
the number of DG locations and SC locations. While updating the population values the distance calculation is limited to similar variables
only because the DGs sizing and SCs variables are real and the optimum
locations variables for DGs and SCs are integer values. In the population
total twelve variable are chosen for DGs and SCs optimum placement
and sizing. The first three variables, i.e. the variables from 1 to 3 are for
DG sizing and next three variables, i.e. the variables from 4 to 6 are for
shunt capacitor sizing which are considered. The distance calculation
(Dij) for DG variables and SC variables can be expressed by the following equations.
Dijk =
NDG
(x jk
x ik )2 + 1 for k = 1, 2, 3
k=1
Dijk =
NDG + NSC
(x jk
x ik ) 2 + 1 for k = 4, 5, 6
k = NDG + 1
(30)
(31)
In the above equations Eq. (30) can be used for finding the distance
between different population members of DG variables and Eq. (31) can
be used for finding the distance between different population members
of SCs variables. The variables from 7 to 9 are chosen for optimum DG
locations and the variables from 10 to 12 are chosen for optimum shunt
capacitor locations. Since these are integer variables the distance calculation is limited to similar variables.
Dijk =
NDG + NSC + NDGL
(x jk
x ik ) 2 + 1 fork = 7, 8, 9
k = NDG + NSC + 1
Dijk =
NVT
k = NDG + NSC + NDGL + 1
Now we define fuzzy voltage limit of the distribution system as
(25)
5.1.5. Fuzzy multiobjective function for optimum sizing of DGs and SCs
The fuzzy multiobjective function can be expressed by the following
equation.
JF = w1µ PGDI + w2 µ PF + w3µ APLI + w4 µ V
The weighting factors W1, W2, W3, W4, and W5 are taken as unity.
The fuzzy multiobjective function described by Eq. (26) is maximized
using GOA subject to various operational constraints. In the present
work the DG penetration at the optimum nodes is limited to 25% of the
total real power load and the reactive power injection is limited to 25%
of the total reactive power load of the distribution system.
PDGi
PDGmax fori = 1, 2, 3
(27)
0
QCj
QC max forj = 1, 2, 3
(28)
In the second stage the optimum sizing and placement of EV charging stations is considered using Fuzzy GOA approach for distribution
systems integrated with DGs and SCs while satisfying the restrictions on
real power loss and voltage profile. The maximum branch current
carrying capacity should not be exceeded. In this case the distribution
system is first integrated with DGs and SCs already obtained using
Fuzzy GOA approach in Section 5.1. The PQ models of EV battery
charging load models developed in Section 3 are used for load flow
analysis.
Where PDGi and QCj are the DG and shunt capacitor injections at the
optimum locations.
5.2.1. Fuzzy objective function formation for optimum placement of EVs
using GOA
Fuzzy multiobjective function framed with objectives of fuzzy real
power loss and fuzzy voltage profile is used for obtaining optimum
number of vehicles and locations considering distribution system peak
load simultaneously.
The power loss index with EVs can be written by Eq. (34). The fuzzy
active power loss index can be written by Eq. (35) from the Fig. 4.
The active power loss index with EVs (LPEVI) can be defined as
5.1.6. Modifications of GOA for optimum sizing of DGs and SCs
In this work it is required to find the optimal sizing of DGs and SCs
and optimal locations for DGs and SCs placement. Since the variables
are having different boundaries the distance calculation is modified and
is considered for each variable separately.
NVT = NDG + NSC + NDGL + NSCL
(33)
5.2. Optimum sizing and placement of EV charging stations using Fuzzy
GOA
(26)
0
x ik )2 + 1 fork = 10, 11, 12
In the above equations, Eq. (32) can be used for finding the distance
between different population members of optimum locations for DG
variables and Eq. (33) can be used for finding the distance between
different population members of optimum locations for SCs variables.
In all the distance equations unity value is added under square root to
avoid any zero value in the denominator in Eq. (4). A flow chart is
shown in Fig. 3 for the optimal placement of 0.95 lag pf DGs and shunt
capacitors using proposed fuzzy multiobjective method using GOA.
Fig. 3. Flow chart for optimum sizing of DGs and SCs using GOA.
µ V = min(µVi )
(x jk
(32)
(29)
6
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
Fig. 4. Membership function for real power loss with EVs.
LPEVI =
LPEV EVDGSC
LPEV DGSC
(34)
EVDGSC
In the Eq. (34) LPEV
is the real power loss with EVs, DGs and
SCs and LPEV DGSC is the real power loss with DGs and SCs.
0forLPEVI
µLPEVI =
LPEVImin
(LPEVI LPEVImin )
forLPEVImin
(LPEVISP LPEVImin )
LPEVI
LPEVISP
(LPEVImax LPEVI )
forLPEVISP
(LPEVImax LPEVISP )
LPEVI
LPEVImax
0forLPEVI > LPEVImax
(35)
The power loss will increase with EV load and hence the LPEVI will
always be greater than one. In this case 50% increase in power loss
during peak hours is allowed compared to the case with DGs and SCs
and the values of LPEVImin, LPEVISP and LPEVImax are taken as 1.0, 1.5
and 2.0 respectively. The Fuzzy voltage membership function μV described by Eq. (25) is also considered the same for optimum EV charging stations. The fuzzy objective function for optimum sizing and allocation of EV charging stations can be expressed by Eq. (36). In the
Eq. (36) the WL and WV are taken as unity.
JFEV = WL µLPEVI + WV µ V
Fig. 5. Flow chart for optimum sizing of EV charging stations using GOA.
(36)
Table 1
Optimum Sizing of DGs and SCs using Fuzzy GOA.
5.2.2. Fuzzy GOA based algorithm for optimum placement of EV charging
stations
The optimum numbers of vehicles at the optimum locations are
identified by maximizing the objective function described by Eq. (30)
using GOA. The algorithm aimed at allocating the maximum number of
vehicles at the optimum locations identified under distribution peak
load conditions. In this case both number of charging locations and
number of vehicles at the charging stations are integer variables. Hence
the equations for population updating for these integer variables in
GOA can be modified as in the case of number of optimal locations for
DGs and SCs used in Section 2. Maximizing the fuzzy objective function
limits the distribution losses to the predefined value while maintaining
constraints on voltage by taking care the branch current constraints.
The flow chart for optimum sizing and allocation of EVs using GOA is
shown in Fig. 5.
51 bus system
Node No.
37
51
26
DG
sizing
(kW)
423.71
372.31
435.53
69 bus system
Node No.
2
39
19
SC
sizing
(kVAr)
300
240
230
Node No.
22
63
64
DG
sizing
(kW)
761.38
451.47
688.26
Node No.
69
2
59
SC
sizing
(kVAr)
105
675
675
obtaining the optimum sizing of DGs and SCs using GA, PSO and GOA
methods. The Fuzzy GOA method is compared with conventional objective function based method [4], Fuzzy GA and Fuzzy PSO methods to
show the advantages of performance and convergence properties of
GOA. The distribution system performance is shown in Tables 2 and 3
for the considered two distribution networks.
From the Tables 2 and 3 it can be found that with the proposed
Fuzzy GOA methodology the performance of the distribution system is
better in terms loss reduction, voltage profile improvement while
achieving the desired substation power factor and DG penetration limits
compared to Fuzzy based GA, PSO and conventional techniques.
The voltage profile comparison with proposed Fuzzy GOA with
other techniques is shown in Fig. 6 and it is observed that the voltage
profile is improved compared to base case value with the incorporation
of DGs and Shunt capacitors. The voltage profile is improved to desired
limits, i.e., voltage at all the nodes improved to above the desired level
0.95 p.u. with Fuzzy GA, PSO and GOA techniques for both 51 and 69
distribution systems. It can be observed that with proposed method the
voltage at all the nodes is close to unity and its performance is better as
the size of the distribution system increases.
6. Results and discussions
For the present analysis 11 kV, 51 node [18] and 12.66 kV, 69 node
[68] radial distribution networks are considered. Initially the optimum
sizing and allocation of DGs and SCs is considered and three nodes for
DG units placement and an equal number of shunt capacitor units are
considered.
The optimum sizing values of DGs and SCs and the optimum locations obtained using Fuzzy GOA are shown in Table 1 for 51 and 69 bus
systems.
6.1. Performance improvement of distribution systems with DGs and SCs
The fuzzy multiobjective function described by Eq. (26) is used for
7
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
Table 2
Performance comparison for 51 node system.
51 bus system
Base Case
Conventional Method [4]
Fuzzy GA
Fuzzy PSO
Fuzzy GOA
S/S Active Power (kW)
S/S Reactive Power (kVAr)
S/S power factor
Total DG penetration (kW)
Real power loss (kW)
Voltage Min (V(p.u.))
2592.56
1680.68
0.8391 lag
…
129.56
0. 9081
1348.54
628.81
0.9063 lag
1147.79
33.33
0.9730
1263.90
419.70
0.9490 lag
1231.50
32.39
0.9726
1263.80
415.00
0.9500 lag
1232.25
33.12
0.9743
1263.73
416.04
0.9500 lag
1231.55
32.28
0.9752
From the convergence comparison of fuzzy multiobjective function
with number of iterations shown in Fig. 7, it can be observed that the
GOA has much better convergence properties compared to GA and PSO.
From the above discussion it can be concluded that the GOA technique
is superior to GA and PSO methods in terms of convergence properties
and performance improvement of distribution systems. The number of
evolutionary characteristic parameters and constants to be fixed or initiated is very much less for GOA technique compared to other evolutionary approaches.
power loss with the simultaneous optimization approach is 67.38 and
105. 82 kW and with the proposed two stage methodology is 64.56 kW
and 41.01 kW for 51 node and 69 node distribution systems respectively at full load condition. The minimum voltage is 0.9463 p.u.
0.9375 p.u. with the simultaneous optimization technique and it is
0.9608 p.u. and 0.9659 with the proposed two stage fuzzy multiobjective based approach for 51 bus and 69 bus respectively at full load.
From this it can be said that the performance of the distribution system
can be improved with the proposed approach compared to simultaneous optimization technique for the same EV charging load. As the
load increases the distribution system voltage profile and loss reduction
are comparatively better in the case of proposed technique.
The effect of increase in distribution system load while maintaining
initial EV charging load for both 51 bus and 69 bus systems is shown in
Figs. 8 and 9. From Figs. 8 and 9 it can be observed that the real power
losses can be minimized with the optimum placement of DGs and SCs to
great extent compared to the base case. The feeder load capacity of the
distribution improved with DGs and SCs can be utilized for handling the
EV charging load efficiently. From Figs. 8 and 9 it can be observed that
the loss reduction is much better as the size of the distribution system
increases with the proposed two stage methodology compared to conventional objective based simultaneous optimization technique.
6.2. Fuzzy GOA based optimum sizing of EV charging stations
In the second stage, since the GOA technique has better convergence
properties Fuzzy GOA has been chosen as a tool for optimum sizing and
placement of EV charging stations for the network integrated with DGs
and SCs. The EV load and distribution system peak load are considered
simultaneously.
In the present work it is aimed at finding five optimum locations for
charging stations in the distribution network and the number of EVs
that can be charged at the peak load conditions. The maximum limit for
number of EVs at each charging station is taken as 50 and all the vehicles are assumed to be incorporated with Nissan Altra Lithium ion
battery. The five number of stations are considered, which is nearly
equal to 10% of the total number of buses of the both the distribution
systems. From the charging characteristic curve shown in Fig. 1 it can
be observed that the maximum charging load of Lithium ion battery
during steady charging condition is 6.5 kW. The optimum locations and
optimum number of vehicles identified using proposed Fuzzy GOA algorithm are shown in Table 4 for 51 bus and 69 bus respectively.
In Table 5 the real and reactive power load demands due to EV
charging load are shown for 51 bus and 69 bus systems respectively.
6.4. EV load growth factor analysis
In this section effect of EV charging load on distribution system
performance is analyzed at various load factors with the integration of
DGs and SCs. Since performance improvement is much better with the
proposed Fuzzy GOA methodology compared to simultaneous approach
the analysis is considered with DGs and SCs obtained with the proposed
technique.
The effect of increase in EV load on minimum node voltage is shown
in Tables 8 and 9 at different load conditions. The DGs and SCs magnitudes at different load conditions are taken proportional to their
distribution load factor. It can be observed from the Tables 8 and 9 that
with the support of DGs and SCs up to 50% increase in EV load the
voltage profile can be maintained within the standard limits.
The effect of increase in EV load on real power losses at different
distribution load conditions is shown in Tables 10 and 11 for 51 and 69
bus systems. From the Tables 10 and 11 it can be observed that the real
power loss at different load conditions increases with increase in EV
load and with the incorporation of DGs and SCs it can be maintained
well below the base case condition even with increase in EV load.
The real power requirement from the substation is shown in
6.3. Distribution system load growth factor analysis
The proposed fuzzy GOA based two stage multiobjective approach is
compared with conventional multiobjective based simultaneous optimization approach [51]. In the case of simultaneous conventional
multiobjective based approach it is not possible to consider the parameters for achieving the desired distribution system performance which
can be achieved with fuzzy membership functions. For effective comparison of performance between the two methods the limits on total DG
penetration, total EV charging load and total shunt capacitor sizing is
considered same.
From the Tables 6 and 7 it can be observed that the full load real
Table 3
Performance comparison for 69 node system.
69 bus system
Base Case
Conventional Method [4]
Fuzzy GA
Fuzzy PSO
Fuzzy GOA
S/S Active Power (kW)
S/S Reactive Power (kVAr)
S/S power factor
Total DG penetration (kW)
Real power loss (kW)
Voltage Min (V(p.u.))
4027.19
2796.77
0.8214 lag
—
225.00
0. 9092
2075.69
1281.10
0.8510 lag
1766.91
40.42
0. 9690
1938.93
640.22
0.9500 lag
1901.10
37.83
0. 9734
1930.11
641.08
0.9500 lag
1905.57
33.49
0. 9752
1928.42
631.08
0.9500 lag
1901.11
27.34
0. 9761
8
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
Fig. 6. Voltage profile comparison.
the substation can be limited to base case full load to supply EV real
power load. Even with increase in EV load up to 50% also the substation
can supply real power under almost all loading conditions for 69 bus
system and for 51 distribution system.
The reactive power requirement from the substation is shown in
Tables 14 and 15 with increase in EV charging load at different distribution system load conditions. From the Tables 14 and 15 it can be
observed that the reactive power requirement from the substation is
well beyond the base case at all the considered load conditions.
6.5. Transient response analysis
The effect of EV charging load on the node voltages at the charging
stations when batteries are charging from completely discharged state
to fully charged state is shown in Fig. 10 for 51 bus and 69 bus systems
respectively for peak load conditions.
From the Fig. 10 it can be observed that the voltage transients depend on the distribution system general loading conditions at the node
and the number of EVs at the charging station. It can also be observed
that with the availability of total DG capacity and shunt capacitor installations the effect voltage quality can be maintained at well-deserved
standards even with EV charging load.
Fig. 7. Convergence comparison of GA and PSO with GOA.
Table 4
Optimum sizing of EV stations.
51 bus system
Total No of
EVs
Optimum Node
for EV location
20
49
19
31
5
6.6. Effect of DG power supply fluctuations
69 bus system
Optimum No.
of EVs
13
37
20
33
34
137
Optimum Node
for EV location
48
36
65
46
26
The distribution system load varies consistently and the DGs based
on renewable energy sources are associated with uncertainties, therefore it is important to observe the effect of these uncertainties on distribution system performance during EV charging load.
For observing these uncertainties the load variations are taken into
account and considering more than 50% of total DG capacity available
and randomness is incorporated into the DG penetration using Matlab.
The distribution system load variations and the randomness incorporated into DGs and their effect is shown in Fig. 11 for 69 bus
distribution system. From Fig. 11 it can be observed that the effect of
distribution system load variation is more on voltage profile and real
power loss. The DG uncertainties causes fluctuations proportional to the
randomness associated with power supplied by DGs and has less effect
Optimum No.
of EVs
50
25
32
50
33
190
Tables 12 and 13 with increase in EV charging load at different distribution system load conditions. It can be observed from the Tables 12
and 13 that with the support of DGs and SCs the real power supply from
Table 5
Load drawn by the EV batteries.
EV Load
51 Bus system
Initial EV load
With 25% Increase in EV Load
With 50% Increase in EV load
Real power load (kW)
890.50
1131.00
1345.50
69 Bus system
Reactive power load (kVAr)
292.71
371.76
442.27
9
Real power load (kW)
1235.00
1560.00
1859.00
Reactive power load (kVAr)
405.94
512.77
611.05
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
Table 6
Distribution system load growth effect on 51 bus system.
Load factor 51
bus
Real power loss (kW)
Simultaneous optimization
methodology [51]
Proposed two stage Fuzzy GOA
based approach
Minimum voltage (p.u.)
Simultaneous optimization
methodology [51]
Proposed two stage Fuzzy GOA
basedapproach
1.0
1.1
1.2
1.3
1.4
1.5
67.38
84.89
105.35
128.88
155.65
185.73
64.56
79.74
97.73
118.64
142.61
169.77
0.9463
0.9389
0.9316
0.9241
0.9165
0.9087
0.9608
0.9564
0.9505
0.9412
0.9317
0.9221
Table 7
Distribution system load growth effect on 69 bus system.
Load factor 69
bus
Real power loss (kW)
Simultaneous optimization
methodology [51]
Proposed two stage Fuzzy GOA
based approach
Minimum voltage (p.u.)
Simultaneous optimization
methodology [51]
Proposed two stage Fuzzy GOA
basedapproach
1.0
1.1
1.2
1.3
1.4
1.5
105.82
134.48
168.72
208.90
255.39
308.62
41.01
59.22
82.22
110.27
143.65
182.66
0.9375
0.9279
0.9182
0.9083
0.8984
0.8877
0.9659
0.9569
0.9478
0.9385
0.9290
0.9194
Table 8
EV Load effect on minimum voltage (p.u.) for 51 bus system.
Fig. 8. Effect of distribution system load growth on 51 distribution system
performance.
51 Bus
load
factor
Base case
With DGs
and SCs
only
With
initial EV
Load
With 25%
increase in EV
load
With 50%
increase in EV
load
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.9650
0.9559
0.9466
0.9373
0.9277
0.9180
0.9081
0.9902
0.9878
0.9853
0.9828
0.9803
0.9777
0.9752
0.9711
0.9702
0.9693
0.9682
0.9657
0.9633
0.9608
0.9640
0.9631
0.9622
0.9612
0.9603
0.9589
0.9564
0.9576
0.9566
0.9557
0.9548
0.9538
0.9529
0.9519
Table 9
EV Load effect on minimum voltage (p.u.) for 69 bus system.
Fig. 9. Effect of distribution system load growth on 69 distribution system
performance.
69 Bus
Load
factor
Base Case
With DGs
and SCs
only
With
Initial EV
Load
With 25%
Increase in EV
load
With 50%
Increase in EV
load
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.9656
0.9567
0.9476
0.9383
0.9288
0.9191
0.9092
0.9906
0.9883
0.9859
0.9835
0.9810
0.9786
0.9761
0.9789
0.9768
0.9746
0.9725
0.9703
0.9681
0.9659
0.9756
0.9735
0.9713
0.9691
0.9669
0.9647
0.9625
0.9724
0.9702
0.9680
0.9658
0.9636
0.9614
0.9592
Table 10
EV Load effect on Real power loss (kW) for 51 bus system.
on minimum voltage, i.e. ON voltage profile of the distribution system
compared to real power loss variations.
The objective of DG integration with distribution system is to supply
EV charging load demand continuously along with conventional load.
The hybrid system consisting wind and solar DGs depends on weather
conditions and it is important to handle these uncertainties for handling
EV charging load efficiently. When the power generation by wind and
solar DGs is insufficient to meet the changing demands due to severe
weather conditions the charging system should be supported with
10
51 Bus
Load
factor
Base Case
With DGs
and SCs
only
With
Initial EV
Load
With 25%
Increase in EV
load
With 50%
Increase in EV
load
0.4
0.5
0.6
0.7
0.8
0.9
1.0
19.10
30.23
44.11
60.85
80.58
103.43
129.56
5.03
7.89
11.42
15.61
20.47
26.03
32.28
24.93
29.76
35.29
41.52
48.47
56.15
64.56
34.93
40.32
46.41
53.23
60.77
69.06
78.10
45.60
51.49
58.10
65.44
73.53
82.36
91.96
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
Table 11
EV Load effect on Real power loss (kW) for 69 bus system.
69 Bus
Load
factor
Base Case
With DGs
and SCs
only
With
Initial EV
Load
With 25%
Increase in EV
load
With 50%
Increase in EV
load
0.4
0.5
0.6
0.7
0.8
0.9
1.0
32.51
51.61
75.53
104.54
138.90
178.95
225.00
4.28
6.71
9.70
13.25
17.37
22.06
27.34
13.59
16.69
20.37
24.63
29.49
34.95
41.01
18.33
21.59
25.44
29.88
34.92
40.57
46.83
23.75
27.18
31.21
35.84
41.08
46.93
53.39
Table 15
EV load effect on reactive power (kVAr) requirement from substation for 69 bus
system.
69 Bus
Load
factor
Base Case
Considering
DGs and SCs
With
Initial EV
load
With 25%
Increase in
EV Load
With 50%
Increase in
EV Load
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1092.69
1370.85
1651.20
1933.83
2218.88
2506.48
2796.77
248.45
311.38
374.65
438.24
502.18
566.46
631.08
660.10
723.52
787.29
851.41
915.87
980.68
1045.85
769.69
833.24
897.14
961.39
1025.98
1090.94
1156.25
871.07
934.75
998.78
1063.16
1127.89
1192.98
1258.43
Table 12
EV load effect on Real power (kW) requirement from substation for 51 bus
system.
51 Bus
Load
factor
Base Case
With DGs
and SCs
only
With
Initial EV
load
With 25%
Increase in
EV Load
With 50%
Increase in
EV Load
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1004.30
1261.73
1521.91
1784.95
2050.98
2320.13
2592.56
497.61
623.62
750.29
877.62
1005.63
1134.33
1263.73
1408.02
1535.99
1664.66
1794.03
1924.13
2054.95
2186.51
1658.51
1787.04
1916.28
2046.24
2176.93
2308.36
2440.54
1883.68
2012.72
2142.47
2272.96
2404.19
2536.17
2668.91
Table 13
EV load effect on Real power (kW) requirement from substation for 69 bus
system.
69 Bus
Load
factor
Base Case
With DGs
and SCs
only
With
Initial EV
load
With 25%
Increase in
EV Load
With 50%
Increase in
EV Load
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1553.39
1952.70
2356.84
2766.07
3180.66
3600.92
4027.19
764.71
957.25
1150.35
1344.01
1538.23
1733.04
1928.42
2009.02
2202.23
2396.02
2590.39
2785.35
2980.92
3177.09
2338.76
2532.13
2726.09
2920.64
3115.79
3311.54
3507.91
2643.18
2836.72
3030.86
3225.60
3420.94
3616.90
3813.47
Fig. 10. Voltage transients at EV charging stations.
Table 14
EV load effect on reactive power (kVAr) requirement from substation for 51 bus
system.
51 Bus
Load
factor
Base Case
With DGs
and SCs
only
With
Initial EV
load
With 25%
Increase in EV
Load
With 50%
Increase in EV
Load
0.4
0.5
0.6
0.7
0.8
0.9
1.0
644.11
810.62
979.49
1150.83
1324.73
1501.30
1680.68
161.06
202.42
244.21
286.47
329.19
372.37
416.04
471.95
515.47
559.47
603.96
648.95
694.44
740.44
559.54
603.68
648.31
693.43
739.06
785.21
831.88
639.05
683.75
728.95
774.65
820.86
867.60
914.88
storage systems and diesel generators [70].
7. Conclusions
In this work Fuzzy GOA based approaches are developed for optimum sitting and sizing of DGs, SCs and EV charging stations to supply
EV charging load simultaneously along with distribution system peak
load. In the first stage fuzzy multiobjective based GOA is developed for
optimum sizing and allocation of DGs and SCs for improving the substation power factor, voltage profile improvement and real power loss
Fig. 11. Effect of DG uncertainties on 69 bus system.
11
Journal of Energy Storage 27 (2020) 101117
S.R. Gampa, et al.
reduction of distribution system. From the simulation results it can be
observed that with the proposed fuzzy GOA technique that the required
DG penetration level is achieved simultaneously improving the distribution system performance to the desired level. It can be said that
from the performance improvement point of view fuzzy GOA based
approach is slightly better and the convergence of the GOA algorithm is
much faster compared to GA and PSO techniques. The active distribution system integrated with DGs and SCs is considered for the placement of EV charging stations. The P, Q load models are developed for
EV battery charging load using Lithium ion battery charging characteristic curves for load flow analysis. The optimum sizing and placement of EV charging stations is obtained using fuzzy based GOA algorithm by satisfying voltage and current constraints of the distribution
system and restricting the real power losses to a certain maximum
value. From the simulation results it can be observed that with the
proposed two stage methodology the desired performance of the distribution system can be obtained which is not obtained with conventional multiobective function based simultaneous approach. The advantage gained with DGs and SCs incorporation can be efficiently used
for handling distribution system load growth simultaneously supplying
the EV charging stations with full capacity. The effect of EV load growth
is analyzed at different loading conditions and it can be said from the
results that substation can allow EV load up to its maximum real power
supply. The voltage levels can be maintained to satisfactory level with
the support of DGs and SCs even with increase in EV load. The effect of
transient battery charging load has the impact on node voltages at the
charging stations and during steady state charging the node voltages
can be maintained to satisfactory levels with the support of DGs and
SCs. The uncertainties in distribution load has more impact on voltage
and loss variations and the effect of uncertainties in DGs on voltage and
real power loss depends on the uncertainties associated with DG power
supply.
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Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence the work reported in this paper.
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