IJSGSET TRANSACTIONS ON SMART GRID AND SUSTAINABLE ENERGY, VOL. 1, NO.

1, MAY 2017 1

Stability Cogitated Electric Vehicle Charging

Infrastructure Planning
C.H. Dharmakeerthi, Student Member, IEEE, and N. Mithulananthan, Senior Member, IEEE

Abstract—Electrification of the transportation is taking place Therefore it is wise to consider the issues during charging
at an accelerated rate. Even though, electric vehicles (EV) station planning so that potentially expensive remedies can be
evidently bring numerous environmental and economic benefits, completely avoided or delayed.
their impact on power systems should not be overlooked. It has A number of planning strategies have been introduced with
been identified that EV load characteristics can significantly affect different objectives in recent literatures for a successful
power system voltage stability and small signal stability. Hence, it transformation to an electrified transportation system. The
is important to consider mitigating of stability impacts right from
objectives of the planning study given in [11] are to minimize
the planning stage of bulk EV charging stations. However,
unavailability of suitable stability evaluating indexes that could fit charging station construction and operation costs and the
into planning algorithms is a hindrance. This study proposes two accessing cost to the charging facility. The planning study in
computationally efficient indexes to compare stability status in [12] identifies the location of the charging station based on the
different planning options. The developed indexes have been locations of residential communities, refuelling stations,
tested, verified and utilized in a multi objective planning algorithm parking lots and power transmission stations. The strategy
to identify a comprehensive solution, which satisfies the grid given in [13] aims providing services to most customers from
operator, EV customer and the charging facility investor the given investment, while [14] intends to serve the customers
optimally. reliably. Further, the studies in [15-18] consider minimization
of investment and operational cost of EV charging, while grid
Index Terms-- Eigenvalue analysis, electric vehicle, EV
limitations have been considered within the planning
charging stations, loading margin, oscillatory stability, power
system planning, steady state voltage stability. constraints. The planning study in [19] has concentrated on
maximum utilization of the charging station with lower power
I. INTRODUCTION losses and lower voltage deviations. It is evident that most of
the planning objectives are traditionally aiming to satisfy the
EPLETING fossil fuel resources, environmental and requirements of EV consumers or investors [11] [12], [15], [20-
D health problems associated with vehicular emissions and
the energy security concerns have highlighted the
24]. Only scant attention has been given to the power grid
aspects in planning studies so far. However, a comprehensive
requirement of electrified transportation. Hence, the countries planning strategy should consider not only geographical and
around the globe provide EV consumers with abundant economical aspects, but also the technical aspects of the power
financial and non-financial incentives to make EV popular [1, grid.
2]. These efforts have resulted in a rapid electrification of the Stability cogitated system planning become important as
transportation as reflected in recent increment in global EV system instabilities become more frequent, with the maximum
sales. According to [1] the global EV sales have increased by utilization of the system assets in modern power systems.
twofold during 2011 and 2012. One unavoidable concern However, system stability has not been considered in most of
associated with this transformation is the grid impacts of EV the present planning studies. Unavailability of suitable stability
charging. evaluating indexes to incorporate within planning algorithms
Researchers have identified several grid impacts associated suggests the importance of deriving computationally efficient
with EV grid integration. Overloading of primary system indexes which are having good physical interpretations. Hence,
components, voltage regulatory limit violations, increased this study introduces two indexes to identify oscillatory stability
system losses and harmonic issues are among them [3]. Further, and voltage stability preserves planning solution. The indexes
EV charging impacting power system oscillatory stability and are validated analytically and numerically. Finally, the derived
voltage stability have also been reported in [4-10]. indexes are utilized in an EV charging infrastructure planning
task to build charging facilities which not only satisfies the
requirements of EV customer and the charging facility investor,
which should also preserve a secured and economical grid
operation.
Manuscript received March 7, 2017; revised March 29, and April 9, 2017; The rest of the paper is organized as follow. Section II
accepted April 19, 2017.
C. H. Dharmakeerthi is with the School of Information Technology and describes EV load model and its influence on power system
Electrical Engineering, University of Queensland, Australia and Ceylon stability. The theoretical background relating oscillatory and
Electricity Board, Sri Lanka (e-mail: champa80@yahoo.com). static voltage stabilities is introduced in Section III. Section IV
N. Mithulananthan is with the School of Information Technology and develops and validates two indexes to examine stability impact
Electrical Engineering, University of Queensland, Australia (e-mail:
mithulan@itee.uq.edu.au) of EV loads, while section V reports a planning case study and
2 IJSGSET TRANSACTIONS ON SMART GRID AND SUSTAINABLE ENERGY, VOL. 1, NO. 1, MAY 2017

the results. Finally, Section VI provides conclusions of the The xi, yi and ui are system state variables, algebraic
paper. variables and input variables, respectively, while fi and gi are
II. EV LOAD MODEL non-linear functions. If the system equilibrium state is disturbed
by a small perturbation, the first order Taylor series expansion
The EV load is found to be having characteristics which can be applied to obtain a linear approximation to above
combines negative exponential and constant power load expressions by neglecting the higher order terms, as shown
behavior, as shown in (1) [7] . below.
−α
P V  ∆x& = A∆x + B∆y + E∆u (4)
= a   +b (1) 0 = C∆x + D∆y (5)
Po  Vo 
The negative exponential component has been resulted from The A is known as the system state or the plant matrix.
the resistances present in the ac to dc converter, ac filter and the Eliminating Δy from (4), will result
lead conductor. Studies show that the higher the resistances the
∆x& = Asys ∆x + E∆u (6)
bigger the negative exponential load component [7]. A load
model which is based on 1mΩ filter inductor parasitic where,
resistance, 2mΩ switch turn on state resistance and 0.02 Ω lead Asys = A − BCD −1
conductor resistance [7] is incorporated in this study. The load
model parameters are a=0.07, b=0.93 and α=3.1, as per (1). Eigenvalue analysis of Asys is carried out to determine the
The constant power load increase its current consumption at stability of the system. Eigenvalues (λi) can either be real or
lower system voltages while the negative exponential load complex. Real Eigenvalues represent non-oscillatory modes.
component increase its power consumptions at lower system Positive real Eigenvalues represents aperiodic instability.
voltages. Hence, the both load components contribute to Negative real ones represent decaying modes. The larger the
degrade system voltage stability significantly during a voltage magnitude is the faster the decay.
instability incident. Complex Eigenvalues represent oscillatory modes. They are
The EV load is found to be affecting the system voltage appearing as conjugate pairs. The associated damping ratios ζi
stability negatively as reported in [4, 6, 7]. On the other hand, of them can be described by,
studies in [4, 5, 10] have identified that EV charging affects
λi = σ i + jµi (7)
system oscillatory stability. Therefore, from power utility point
−σ i
of view, it is important to consider these issues during charging ζi = (8)
station planning. (σ i2 + µi2 )
III. THEORETICAL BACKGROUND The negative ࣌i values represent damped oscillations, while
Basic theory behind the oscillatory and static voltage the positive values corresponding to oscillations growing in
stability is explained in this section before introducing the new amplitude. The smaller the damping ratios (ζi) the lower the
indices developed for stability cogitated planning. system stability. Modes of oscillation can be identified by
analyzing participation factors.
A. Oscillatory Stability
The power system oscillatory stability describes the ability B. Voltage Stability
of the system to remain synchronism when undergoes small Voltage stability of a power system is preserved if
disturbances [25]. Understanding of the problem requires acceptable voltages are maintained in all network busses during
studying of the electromechanical oscillations in the system. normal operating conditions and after being subjected to a
Generation and load changes, fast exciters, negative interaction disturbance [25]. During a voltage instability event the system
among controllers are contributing to system oscillations [26]. voltages decline progressively and uncontrollably. This
The factors that determine the system response to such system happens majorly when system generation and transmission are
variations include the initial operating point, type of excitation unable to meet the system reactive power demand. Heavily
control and the strength of the transmission system [25]. loaded lines, system contingencies, increased reactive power
The oscillations should be damped, as sustained oscillations consumption of the loads, limitations in reactive power
cause excessive wear and fatigue in power system components. generations and actions of voltage control devices are some of
Furthermore, these oscillations could grow in amplitude and if the main factors which affect voltage instabilities. Performance
not controlled they could lead to instability and blackouts. The indexes are important to determine proximity to voltage
Eigenvalue analysis methodology for identifying system collapse. A widely accepted voltage stability assessment index,
oscillatory stability status is described below. the static loading margin is described below.
The power system dynamics can be described by a set of A quasi-steady state description of a power system which is
first order differential equations and a set of algebraic equations applicable to voltage stability analysis can be described by a set
as shown below. of differential and algebraic equations as given in (9),
x&i = f i ( x, y, u) (2) x& = f ( x, y, λ ) (9)
0 = gi ( x, y ) (3) 0 = g ( x, y, λ )
DHARMAKEERTHI AND MITHULANANTHAN: STABILITY COGITATED ELECTRIC VEHICLE CHARGING 3

The state variables are represented by x, while y represents has been evaluated in this research. The system oscillatory
the algebraic variables. The λ represent a parameter or set of behavior is affected by the equilibrium point, which can be
parameters which are slowly changing with time. As the λ studied with steady state analysis. Hence, the significance of
changes system moves from one equilibrium point to another operating point in determining system oscillatory stability is
until it reaches the collapse point. The set of equations in (9) taken into consideration in deriving the index.
can also be represented by (10), alternatively. System oscillatory stability is determined by many factors
and initial operating point is dominant among them. It is evident
x& that when power systems are stressed or operating closer to
0 = F( x, y,λ) (10) their limits they are vulnerable to become unstable even due to
  a smaller system disturbance. Hence, it is advantageous to
An equilibrium point (x0, y0, λ0) can be characterized by, identify a quantity that can relate the influence of steady state
operating point to the system oscillatory stability status. Any
F ( x0 , y0 , λ0 ) = 0 (11) system planning strategy which relies only on steady state
system analysis can utilize that quantity to identify oscillatory
Based on the non-singularity assumption of algebraic
stability status of different planning solution. This research has
equations, an equilibrium point where the Jacobian of (9) is
introduced an index by considering the relationship between the
singular, is known as a singular bifurcation point (x*, y*, λ*)
network bus angles and the damping ratio of the critical modes.
[27]. If the system load is taken as the parameter which varies
The index is based on the sum of the individual bus voltage
slowly, loading margin or the static voltage stability margin
angle deviations of the system buses with respect to the system
(SVM) can be achieved by (12). The loading parameter at the
reference bus angle.
current operating point is denoted by λ0.
There are few studies which link bus voltage angle deviation
SVM = λ* − λ0 (12) to system stability. The study in [28] incorporates bus voltage
angle information to develop a methodology to build a two bus
The loading margin is the additional load increment equivalent of the whole network using synchrophasor data, to
(increased in a specific pattern) required to drive the system determine distance to the steady state stability limits. The study
towards instability from the current operating point. The pattern in [29] follows the same concept to describe how the angle
how the system loads are increased and how the system information from PMU data can be utilized to monitor system
generators are arranged to respond to that load increment is voltage stability status. An index called integral square
defined by the load and the generation directions, respectively. generator angle index has been introduced in [30] for
Loading margin identifies how close the current operating point contingency ranking and screening. Adapting the same method
to the voltage collapse point. It is an accurate index that [31] proposes integral square bus angle index for predicting
considers the system nonlinearities and limits like the generator instability and for designing remedies to loss of synchronism.
reactive power limits, the line MVA flow limits etc, which are The index takes the time integral of the summation of the
encountered during system load increments. weighted and squared angle deviations in selected network
The continuation of power flow (CPF) method is widely buses.
incorporated to determine the static loading margin. It The new index introduced in this study is named as
incorporates an iterative method consists of a predictor and oscillatory stable placement index (OSPI), which can be utilize
corrector to generate the PV curve. The nose of the curve to evaluate relative voltage stability status in different planning
represents the voltage collapse point. A static voltage stability solution. The voltage angle of a system bus (θbus,i) is a relative
study is carried out in this research using PSAT (Power System quantity. The total of individual bus angle deviations of the
Analysis Toolbox). Loading margin has been utilized to system busses with respect to the slack or the infinite bus angle
compare the performance of the proposed index (QRPI). (θinf), described in (13), is a fixed value for a steady system
operation point.
IV. DEVELOPMENT OF STABILITY INDEXES l

The indexes for oscillatory stability and voltage stability

OSPI = ∑ (θbus,i − θinf ) (13)
i =1
cogitated planning are described in this section. The
performances of the indexes have been verified through A higher positive OSPI indicates a better oscillatory stable
established stability evaluating techniques. case, on the other hand higher negative indicates a worse case.
A. Index for oscillatory stability The validity of OSPI to determine relative oscillatory stability
status has been proved analytically and numerically by
It is important to evaluate impact of EV load on oscillatory verifying relationship between the OSPI and the damping ratio
stability during charging station planning, as it is a bulk system of the critical modes in the following section.
load. The Eigen value analysis and the time domain simulations
are the most widely used oscillatory stability analysis 1) Analytical Verification:
methodologies. These methodologies require detailed dynamic
representation of system components. However, most system Analytical verification of the relationship between OSPI and
planning studies are based on steady state system analysis. the damping ratio is carried out here considering two cases: A
Therefore, an index which can be incorporated in static single machine infinite bus (SMIB) system with second order
planning studies to identify a better oscillatory stable placement synchronous machine model and a three bus test system with
4 IJSGSET TRANSACTIONS ON SMART GRID AND SUSTAINABLE ENERGY, VOL. 1, NO. 1, MAY 2017

third order synchronous machine model, as described below. 40

The relationship between the OSPI and damping ratio of the

critical mode can be easily identified on a SMIB system with 35

the generator represented by the second order model. The

30
infinite bus is considered as the reference bus. Therefore, the
OSPI simply becomes machine angle δ. The damping ratio of

Damping Ratio%
25
the oscillatory mode associated with complex Eigenvalues can
be approximated by (14) [25]. 20

1 kD 15
ξ≈ (14)
4H  ωE cos δ  10
 
 2 XH 
5
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5
Total of bus voltage angle deviation w.r.t. reference (rad)
It is evident that the higher the δ the higher the damping ratio.
It proves that a higher OSPI indicates a better oscillatory stable Fig. 2. The relationship between the total bus angle deviation (OSPI) and the
system. This relationship can further verify analytically with a damping ratio of the critical mode.
SIMB and a load bust test system shown in Fig. 1, with the
generator represented by the third order model, which It is clear that the higher the total bus voltage angle deviations
incorporates field circuit dynamics. with respect to the reference bus voltage angle (OSPI) the
higher the damping ratio. It proves OSPI is a good indicator of
Vinf∟0 system damping status. Further, numerical investigations are
E∟δ Xinf carried out in IEEE 14 bus test system.
Iinf˂ φ
2) Numerical Verification:
PG R The Eigenvalue analysis and power flow analysis of the
1:a IL˂ ϒ VL∟θ IEEE 14 bus test system are carried out using power system
X analysis tool (PSAT). The network data is given in [32]. The
original network loads were reduced by 20%. A 0.2 p.u. load,
having 0.95 lagging power factor is connected at different
PL+jQL network busses, during each simulation. The generators are
modeled with sixth order dynamic models and with type two
Fig. 1. Single machine infinite and load bus test system. (IEEE model 1) exciters. The simulation results are shown in
Table I. The load connected busses are ranked according to
The linearized system state equations are derived following the impact on oscillatory stability. The obtained damping ratio
methodology given in [5]. The linearized system state equations associated with the critical modes and the total of individual bus
can be described in the following form, with the parameter angle deviations with respect to infinite bus (OSPI) are plotted
defined in Appendix. in Fig. 3.
 KD K Tδ K TΨ   1  TABLE I. THE SIMULATION RESULTS
∆ω& r  − 2H −
2H
−
2H  ∆ωr   2H 0 
 &       ∆Tm  Bus Number
Damping ratio
OSPI
Bus ranking
∆δ  =  ω0 0 0  ∆δ  + 0 0 
∆E fd 
(%) (Best to worse)
 &   0 K ΨΨ  ∆Ψfd  0 K Efd  
∆Ψ fd  
K Ψδ 6 4.505 -2.649 1
  
    9 4.487 -2.658 2
10 4.445 -2.678 3
13 4.398 -2.687 4
The generator data is given in Appendix- Table A-I. The system 14 4.308 -2.709 5
data incorporated in the analysis for Xinf, Vinf, PG, Xt, X, RL, a
and E are 0.4 p.u., 1 p.u., 1p.u., 0.15p.u., 0.1p.u., 0.15p.u., 1 and It is evident that there is a direct relationship between damping
1.08 p.u., respectively. The load is having a fixed power factor ratio of the critical mode and the total bus voltage angle
of 0.95 lagging. Its magnitude is varied from 0.2-0.3 p.u. to deviations with respect to the slack bus voltage angle (OSPI).
obtain different system operating points. The bus ranking based on the OSPI is the same as bus ranking
The damping ratio of the critical modes and the total of based on damping ratio.
system bus angle deviations with respect to the reference bus Both the analytical and the numerical studies indicate that
angle (OSPI) are calculated for different operating points. The there is a direct relationship between damping ratio of the
results are shown in Fig. 2. critical mode and OSPI.
DHARMAKEERTHI AND MITHULANANTHAN: STABILITY COGITATED ELECTRIC VEHICLE CHARGING 5

The QR,i,base is the RPR of the generator i at the base case,

while QR,i is the RPR of the generator i in a particular planning
case. Normalization is incorporated within the index to give
more emphasis to the generators which are having smaller RPR
(or which are about to reach the maximum reactive power limit)
at the base case. A weight (Wi) has been assigned to each
reactive power resource to indicate its relative importance in
maintaining system voltage stability. A higher weight is given
to more critical resources so that those will utilize least during
a planning exercise. Thus, placement of the EV load at locations
where the QRPI is lower will lower the impact on system
voltage stability.

1) Numerical Verification of QRPI:

Fig. 3. The relationship between the total bus angle deviation and the damping
ratio of the critical mode. A validation of the proposed QRPI model has been carried
out in the IEEE 14 bus test system. The network data is given
Further, it is evident that more positive total angle deviation is in [32]. The existing network loads are reduced by 20%. The
better. This indicates a lesser stress to the main grid as the load loading margin, reactive power reserve, the weighted reactive
is partially met by the distributed resources, with reduced line power reserve and the QRPI are evaluated when 2 MW load
flows and power losses. On the other hand, more negative total having 0.95 lagging power factor is connected at different
angle deviations with respect to the slack bus means higher network busses.
stress on the main grid and its generators. That will cause higher Each reactive power resource is weighed based on the
impact on oscillatory stability. Therefore, OSPI can be sequence they reach their reactive power limit during CPF
maximized during planning study to identify better oscillatory carried out for the base case. Higher weights are assigned to the
stable planning solution. OSPI is calculated based on load flow sources which reach the reactive power limit first, as shown in
results, hence involves less computational efforts. Although, Table II. The simulation results are shown in Table III. The
the index cannot quantify the system stability status,
relationship between the loading margin and the QRPI is
identification of a better solution will minimize the risk of
illustrated in Fig. 4.
system become unstable due to a vulnerable operating point.
TABLE II. THE WEIGHTS ASSIGNED TO EACH REACTIVE POWER SOURCE
B. Index for voltage stability Bus Name Assigned weights
Studies have identified that EV charging load can 1 0.1
deteriorate power system voltage stability [4, 6, 7]. Therefore, 2 0.15
incorporating system voltage stability within the EV charging 3 0.2
infrastructure planning process is of great importance. 6 0.25
Drawbacks of currently available techniques in utilizing 8 0.3
planning studies have been thoroughly discussed in [33]. The
importance of identifying simple and computationally efficient TABLE III. THE SIMULATION RESULTS
index yet having good physical interpretations has been Loading Reactive
Weighted
Bus
identified. This paper numerically validates the suitability of reactive
Bus margin power QRPI ranking
power
previously derived index QRPI in [33], for identifying a Name (loading reserve
reserve
% (Best to
relatively better voltage stable planning solution. parameter) (Mvar) worse)
(Mvar)
The evaluated index is based on the available reactive power 6 2.12 10.55632 1.112974 0.3005 1
reserve of the system. Reactive power resource management 9 2.1134 10.55529 1.112829 0.3135 2
plays a big role in system planning and operation to maintain 10 2.1105 10.55511 1.112769 0.3189 3
voltage stability of a power system. The reactive power reserve 14 2.0942 10.55422 1.112532 0.3401 4
(RPR) preserves the ability of a power system to act upon
contingencies. The reactive power reserve has been calculated It is clear from the simulation results that there is a direct
with respect to the maximum reactive power limit of the relationship between QRPI and loading margin. The bus
reactive power sources. The derived QRPI index in [33] is ranking based on the QRPI is the same as bus ranking based on
described in (15). loading margin. Hence, QRPI based on load flow analysis can
be incorporated to determine relative voltage stability between
N Qr
 (Q − QR ,i ) l different planning solutions efficiently with less computational
QRPI = ∑ Wi R ,i ,base  ∀Wi ∈ (0,1), ∑W = 1 i
(15) efforts.
i =1  QR ,i ,base  i =1
6 IJSGSET TRANSACTIONS ON SMART GRID AND SUSTAINABLE ENERGY, VOL. 1, NO. 1, MAY 2017

i i
F = Min ∑ ( µi ∗σ i ) ∀σ i ∈ (0,1), ∑σ i = 1 (17)
i =1 i =1
  (18)
F = Minσ1PLoss + σ 2QLoss + σ 3Dpl + σ 4 OSPI+ σ 5Cinvest + σ 6Chtot + σ 7 QRPI
 

Further, the following constraints are incorporated.

The problem constraints;

- The load bus voltages should be maintained within ± 6%.
- The power lines are kept within 90% of the thermal rating.
- QR,i, is not allowed fall below the 90% of the base case RPR
Fig. 4. The relationship between QRPI and loading margin. (QR,i,base).
- The number of allocated charging slots at each site should be
V. PLANNING EV CHARGING INFRASTRUCTURE kept within the site’s minimum required and the site’s
maximum possible.
A. Problem formulation Two planning scenarios are introduced for comparison
A number of planning strategies have been introduced in purpose. The Scenario 1 described the best placement in the
recent literatures for a successful transformation to an grid point of view, while the Scenario 2 is the most
electrified transportation. It is evident that most of the planning comprehensive one, which consider requirements of customer,
objectives are traditionally aiming to satisfy the requirements investor and grid operator, as described below.
of EV consumers or investors [11, 12, 15, 20-24]. The study in Scenario 1-The main concern is the power grid and it is
[34] describes how voltage stability can be incorporated within required to place the maximum number of chargers to avoid
a planning study. This study focuses on planning charging future unplanned charger integrations while causing the lowest
infrastructure which not only place less impact on both system impact to the power system in terms of system stability and real
oscillatory stability and voltage stability, but also satisfies the and reactive power losses.
investor and the customer requirements. Scenario 2- this is a comprehensive planning strategy which
The particle swarm optimization tool is utilized for problem considers to meet the requirements of EV consumer, the
solving. As EV load being a voltage dependent load the Newton charging facility investor and the grid operator, optimally.
Rapson power flow algorithm should be slightly modified to
accommodate load voltage dependency. The power flow B. Case Study
equations and the diagonal elements of the power flow A test case is created to identify optimal charger allocations
Jacobean matrix are modified as described in [33]. for four potential EV demand sites. The locations are marked as
A multi-objective planning framework is proposed to S1-S4 in the IEEE 30 bus test system as shown in Fig. 5. The
identify a customer, investor and power grid concerned IEEE 30 bus test system load flow data and line MVA flow
charging infrastructure. The optimization problem is limits were obtained from [35] and [36], respectively. The
formulated to maximize OSPI and to minimize QRPI, real and individual chargers are rated at 100 kW and 0.95 lagging power
reactive power losses (PLoss and QLoss) and charging station factor.
investment cost (Cinvest). Further, the total number of charger
integrations (Chtot) need to be maximized, while the charger
allocations are effectively following the demand distribution in
the area under consideration ( measured by Dpl). The index Dpl
measure the deviation of charger placement (Chk) from the
desired placement (τkChtot) considering the importance of the
site (τk), as shown in (16). Hence, Dpl needed to be minimized
during planning.
Ns Ns
1
D pl =
Ns
∑τ
k =1
k Chtot − Chk ∀τ k ∈ (0,1), ∑τ
i =1
k =1 (16)

Each individual objective (μi) is normalized before fixing

into the final objective function, following the methodology
given in [34]. The weighed aggregated method described in
(17) is incorporated to build the objective function shown in
(18).
Fig. 5. The locations of the EV sites on IEEE 30 bus network diagram[35].
The objective function;
DHARMAKEERTHI AND MITHULANANTHAN: STABILITY COGITATED ELECTRIC VEHICLE CHARGING 7

Each individual site is assigned with a weight (τk) to indicate satisfied solution as it has not followed the EV demand
its relative importance, as shown in Table IV. Further the distribution which is indicated by a higher Dpl. The scenario 2
assumed investment costs and the charger requirements in each provides a better solution with an overall objective satisfaction.
individual site are also shown in TABLE IV. TABLE VIII. THE PLANNING RESULTS
TABLE IV. PLANNING DATA FOR THE EV SITES Objective values Scenario 1 Scenario 2
PLoss/(MW) 18.0166 18.0747
Site S1 S2 S3 S4
QLoss/(MVar) 24.2334 24.2958
Weight assigned to indicate Dpl 10.4 0.25
0.3 0.35 0.2 0.15
importance of the site(τk) OSPI -7.6018 -7.6067
Fixed investment cost 1.265 0.195 0.557 1.094 QRPI 0.3094 0.3032
Variable investment cost/ Cinvest/(Units) 50.7640 50.2870
1.812 1.629 1.527 1.354
charging space Chtot 31 29
Min required charging spaces 1 1 1 1 Charger distribution S1-S4 1,2,27,1 9,10,6,4
Max allowable charging
30 30 30 30
spaces
It satisfies the investor and the grid operator moderately. It
A random weight is assigned to each reactive power resource has followed the demand distribution satisfactorily as described
to indicate its relative importance for the purpose of calculating by a lower Dpl. Hence, it will provide a customer satisfied
QRPI. The values are given in Table V. solution.
TABLE V. WEIGHTS ASSIGNED TO EACH REACTIVE POWER SOURCE VI. CONCLUSIONS
Q resource G2 C5 C8 C11 C13 Evaluation of system stability status in planning studies is
Weight
assigned
0.3 0.15 0.1 0.25 0.2 an important task. Two indexes have been evaluated which can
be utilized to determine relative voltage and oscillatory stability
Initially, the PSO program is executed to get the maximum status. The OSPI index, which based on the total of individual
and minimum of each individual objective, subjected to the bus voltage angle deviations with respect to the reference bus
problem constraints, the results are shown in Table VI. These angle is in good agreement with the damping ratio of the critical
maximum and minimum values will be utilized to normalize the mode, while QRPI based on system reactive power reserve
individual objectives before fixing to the final minimization follows the system loading margin. Hence, the indexes OSPI
function.
and QRPI, which are based on load flow results, can efficiently
TABLE VI. THE MAXIMUMS AND THE MINIMUMS OF THE OBJECTIVES incorporate in steady state system planning programs to
Objective PLoss QLoss Dpl OSPI QRPI Cinvest Chtot determine the relative voltage and oscillatory stability status in
/(MW) /(MVar) /(Units) different planning options.
Minimum 17.6807 22.5963 0 -7.614 0.0521 11.062 5
Maximum 18.1517 24.4436 10.325 -7.491 0.3099 55.446 31
A multi-objective planning framework has been developed
here to achieve satisfied planning solution for customer,
The grid preferred scenario (scenarios 1), consider a investor and grid operator. The OSPI and QRPI indexes could
placement which results lowest grid impacts. It also considers easily integrate into planning algorithms to identify better
placing maximum chargers in their favored locations to avoid planning solutions. Hence, these indexes can be incorporated in
future abrupt charger placements. The grid stability is foremost panning studies which are based on steady state system
important compared to grid real and reactive power loss, analysis, to identify stability cogitated planning solutions.
therefore relatively high weights are allocated to QRPI and
OSPI compared to PLoss and QLoss. The comprehensive planning
scenario (scenarios 2) gives priority to accommodate maximum VII. APPENDIX
number of chargers according to demand distribution, followed
by a more grid stable and a lesser expensive solution. The other 1 E sin δ ( Li + L ′) 
objectives are weighted less as those are lesser significant in the K qδ =  E cos δ + 
n Ra 
final overall objective. The weights assigned to each objective,
L′
in two planning Scenarios are shown in Table VII. The planning K qψ = −
outcomes are shown in Table VIII. nL fd
TABLE VII. THE WEIGHTS GIVEN TO INDIVIDUAL OBJECTIVES 1  E cos δ ( Li + Laq ) 
K dδ =  − E sin δ 
Scenario PLoss QLoss Dpl OSPI QRPI Cinvest Chtot n Ra 
Scenario 1 0.10 0.08 0 0.18 0.18 0 0.46
Scenario 2 0.08 0.04 0.12 0.10 0.10 0.10 0.46
( Ll + Laq ) L′
K dψ = −
It is evident from the results that scenario 1 has identified a nRa L fd
grid preferred solution as indicated by lower real and reactive Kψqd = − Laq K qδ
power losses and higher OSPI, even for a higher number of EV
Kψqδ = − Laq K qδ
integrations. However, it is not an EV customer and the investor
8 IJSGSET TRANSACTIONS ON SMART GRID AND SUSTAINABLE ENERGY, VOL. 1, NO. 1, MAY 2017

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DHARMAKEERTHI AND MITHULANANTHAN: STABILITY COGITATED ELECTRIC VEHICLE CHARGING 9

Dr. Mithulan received his B.Sc. (Eng.) and M. Eng. degrees from the He was invited to join the editorial board of American Institute of Mathematical
University of Peradeniya, Sri Lanka, and the Asian Institute of Technology Sciences Electronic Engineering Journal-an international open access journal.
(AIT), Bangkok, Thailand, in May 1993 and August 1997, respetively. His He is a senior member of IEEE
Ph.D. degree from University of Waterloo, Ontario, Canada. Prior to joining
the University of Queensland from 2009, Mithulan was attached to Energy
Field of Study at AIT as an Associate Professor. His previous professional C.H Dharmakeerthi received her B.Eng.Sc degree with first class honor and
positions include: Planning Engineer at Generation Planning division for 2 M.Sc. degree from the University of Peradeniya, Sri Lanka in 2005 and 2008,
years at Ceylon Electricity Board (CEB), Sri Lanka and Project Leader, at the resepectively. Her Ph.D degree in Electrical Engineering earned from the
Centre of Excellence in Electric Power Technology (CEEPT) for one year at University of Queensland, Brisbane, Australia, in 2014. Currently, Dr. Champa
is Chief Electrical Engineer the Ceylon Electric Board Trainning Center,
Chulalongkorn University, Thailand. His main areas of research interests are
Castlereagh, Sri Lanka. She is also a member of the Institution of Engineering
analytical studies on electric power grids, power system interconnections,
application of FACTS devices in power system, integration of renewable and Technology (UK) (MIET) , Associate Member of the Institution of
Engineers, Sri Lanka (AMIESL), and also Chartered Engineer, Engineering
energy and Electric Vehicle. Based on his research, he published over 200
articles, including one book, book chapters, technical reports, refereed journal Council, UK (CEng). Dr. Champa research interest are Electrical Vehicle Grid
Integration and Renewable Energy.
and conference papers