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Two-Stage Stochastic Optimization of
Sodium-Sulfur Energy Storage
Technology in Hybrid Renewable Power
Systems
YOUSEF AL-HUMAID1, (Student Member, IEEE), KHALID ABDULLAH KHAN1, MOHAMMED
A. ABDULGALIL1and MUHAMMAD KHALID1,2,3, (Senior Member, IEEE)
1Electrical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2Center for Renewable Energy and Power Systems, Research Institute, KFUPM, Dhahran 31261, Saudi Arabia
3K.A.CARE Energy Research Innovation Center, Dhahran 31261, Saudi Arabia
Corresponding author: Muhammad Khalid (mkhalid@kfupm.edu.sa)
This work was supported in part by the Deanship of Research, King Fahd University of Petroleum and Minerals, under Project DF201011,
and in part by the K. A. CARE Energy Research and Innovation Center.
ABSTRACT Energy storage systems (ESS) are considered among the key elements for mitigating the
impact of renewable intermittency and improving the economics for establishing a sustainable power grid.
The high cost combined with the need for optimal capacity and allocation of ESS proves to be pertinent to
maintain the power quality as well as the economic and operational viability of a renewable integrated power
grid. In case of ESS sizing in terms of optimized power (kW) and energy (kWh) capacity, an oversized ESS
results in high capital investment and in some cases increases the system losses. Conversely, an undersized
ESS significantly impacts the reliability and availability of the power network. In this paper, a two-stage
stochastic optimization strategy is presented for sodium-sulfur (NaS) battery considering the output power
uncertainties of wind and solar energy sources. The objective aims at minimizing the total cost of NaS-
ESS incorporation while maintaining acceptable system operation using AC optimal power flow. Many
scenarios from the historical data are considered for the development of the system stochasticity on a 24-
bus reliability test system (RTS) that is incorporated with a hybrid renewable energy system (HRES), namely
solar and wind. Moreover, to demonstrate the efficacy of the proposed stochastic optimization framework a
comparative analysis is performed with a deterministic optimization technique based on several reliability
indices.
INDEX TERMS Energy storage, hybrid renewable energy, renewable uncertainty, sodium sulfur battery,
two-stage stochastic optimization
I. INTRODUCTION
Renewable energy resources (RES) are nowadays widely
preferred for electric power generation to satisfy the ever
increasing load demand. Wind and solar resources are among
the most preferred RES technologies. Nevertheless, most
RESs impose various challenges to settle their characteris-
tics with diesel generator’s characteristics [1], [2]. Usually
generators have different kind of variability levels [3], which
are regulated to sustain the grid operation. However, RES im-
poses a greater degree of challenge and difficultly in terms of
availability, predictability, and controllability that are perti-
nent to ensure grid stability. Many researchers and developers
have extensively invested to produce various techniques to
increase the overall controllability over RESs for numerous
different applications [4]–[6]. Among the novel solutions, the
mitigation of RES fluctuations and its associated challenges
can be multifariously solved by using the concept of renew-
able integrated microgrid (MG) systems [7]–[9].
A MG mainly consists of distributed generation (DG)
units, loads, and energy storage systems (ESS). MG has
the potential to link various technologies of DG units along
with distributed ESS into the power network [10]. MG based
renewable integration in a power network comparatively
enhances the system reliability and security with overall
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improved efficiency [11]–[13]. However, controlling the MG
with various types of DGs, different loads, and ESSs is very
complicated especially when it comes to higher level of RES
integration. This can be controlled by using maximum peak
power tracking algorithms [14]. In recent years, ESS systems
have been used frequently in MGs to manage and optimize
the variability of renewable resources and to control the peak
load [15]. Furthermore, in [16], an economic model of the
distributed system is presented using on a novel dissipativity
based prediction control theory. This enables the users of the
MG to optimize their economic gain and concurrently main-
tain the system stability and ensure appropriate performance
of the MG for residential scale application.
ESS is an important dispatchable energy source in the MG.
It ensures power quality as well as continuity of supply to the
power network in both islanded and grid-connected modes
while maintaining the economical significance of the MG
components. The study in [17], demonstrates the incorpo-
ration of ESS that aims to smooth the unstable generation
of hybrid renewable energy sources (HRES) comprising of
solar and wind energy sources. The ESS maintains a smooth
output power profile that inherently improves the reliability
and security of the power network [18]. Albeit, an optimal
size is pertinent considering the high cost of the available
ESS technologies. Optimal sizing of energy storage system
not only ensures system stability and optimal power flow
(OPF) but is identified to maintain a viable total cost of
operation and investment [19].
Similarly, identification and selection of suitable ESS
technology in accordance with the grid power quality re-
quirements considering renewable integration proves to be
a multi-faced challenge. While different ESS technologies
can be considered to provide energy buffering operation and
overcome the technical challenges associated with renewable
integration, intensive attention is also needed to maintain the
economical and operational viability of ESSs. Before large-
scale ESS installation, several technological, economic, and
operational constraints needs to be considered [20]–[22]. For
instance, the relatively low power density and slow dynamic
response of the popularly preferred lithium-ion battery leads
to over-sizing and pre-mature replacements that leads to high
capital cost in long-term large scale utility applications [23].
Ideally, ESS should possess high energy and power density
for optimal operation that can be facilitated by sodium-sulfur
(NaS) batteries that are among the most prominent storage
technologies with relatively high energy density, high power
density, moderate cost, safety, temperature stability, and low
self-discharge rate [24]. Considering the countries with high
renewable potential along with extreme climatic conditions
such as Saudi Arabia, the selection of ESS considering its
technical characteristics is pertinent to not only regulate
demand-generation mismatch but also to enable a feasi-
ble long-term energy solution [25]. Therefore, apart from
pumped hydro and compressed air energy storage system
that are limited by topographically dependency, NaS based
ESS technology proves to be suitable due to its technological
maturity, mobility, environmental applicability, and long-
term storage solutions [26]–[28].
Accordingly, numerous uncertainty analyses have been
presented based on distinct optimal power flow (OPF) strate-
gies to outline the impact of RESs [29]. The study in [30],
presented a combination of stochastic problem studies of an
OPF problem that is formulated based on a convex model
considering the DC model of the power network. This study
confers the unpredictably of the renewables and their impact
on the system power quality. Therefore, large data analysis
and accurate prediction of RES are necessary to address
different possible scenarios for enabling the grid operators
to overcome these challenges considering the worst case
scenarios [31]. In this front, a model is proposed in [32],
which presents a spectral analysis technique for hybrid RES
by gathering daily load figures. This model is utilized on an
off-grid system where the ESS is estimated for various level
of mean load. The ESS is developed for one day horizon
on an hourly basis (24-h) taking into account the worst
case scenario and the unserved energy that determines the
ESS size. In [33], an optimal ESS capacity optimization is
presented to maintain the power balance for various RES
fluctuations. This study utilizes discrete fourier transform
to resolve the required balancing power over different time
according to a variable periodic component that is utilized
to determine the ESS capacity for various types of storage
technologies.
The uncertainty in a renewable integrated power grid is
mainly due to integration of variable RESs as typically load
forecasting has a lower degree of errors (<2 %). With
the integration of bulk or systematic increment of RESs at
distinct locations, the power grid is subsequently exposed
to larger uncertainties in the form of aggregated forecast
errors [34] that contribute to demand-generation mismatch.
Therefore, the inclusion of non-dispatchable RESs into the
existing power grid will have consequences on system op-
eration and future expansions due to distinctive time and
scale of variability of RESs combined with the probability
of forecasting errors [35]. Hence, a probabilistic approach is
pertinent to comprehend these variabilities in order to obviate
additional operational cost, penalty costs, and load shedding
[36].
In [37], the authors proposed a chance-constrained pro-
gramming methodology for optimal ESS sizing considering
the uncertainties of renewables. The methodology is based
on genetic algorithm technique joint with Monte-Carlo sim-
ulation. To solve the optimization problem that is targeted
to gain the optimum energy cost while guaranteeing balance
between the output power difference with the wind energy
source, ESS, and a predefined load profile. Similarly, optimal
energy storage operation during specified period based on
the cost optimization and forecasting the stochastic nature
of system is studied in [38]. The study in [39], aims to
maximize the utilization of wind power while the opera-
tion and investment costs are minimized. In this study, the
stochastic behaviour of wind power are modelled by the
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FIGURE 1. A schematic diagram of hybrid renewable energy system.
Monte–Carlo simulation to optimally determine the capacity
and location of BESS. A novel battery operation cost model
is presented in [36], which utilizes a battery as an equivalent
fuel-run generator to make it feasible in accordance with
the unit commitment problem. The constraint is used as a
probabilistic approach to combine it with the uncertainties
data of RESs as well as the load demand to formulate an
economic dispatch and unit commitment problem.
In this paper, a stochastic cost optimization methodology
is presented to formulate a strategic planning framework for
designing a hybrid renewable energy system. The objective
is to derive the optimal capacity and allocation of NaS
ESS under AC-OPF problem with the uncertainty of RES
(Fig. 1). The novelty and contribution of this paper includes
the development of the solar and wind stochasticity using
historical data sets while optimizing the ESS capacity and
allocation problem. The major advantage of this planning
framework is its robustness towards high nonlinearity of the
system model that obviates the need of developing meticu-
lous solar and wind energy models with faster convergence
and few simulations. Therefore, ten random scenarios of
solar, wind, thermal, and load demand profiles are considered
based on historical seasonal uncertainty data over a 24-
hour time interval that are used to develop the stochastic
model. The planning framework is tested on a day-ahead
data deriving the optimal allocation as well as capacity size
in term of power (kW) and energy (kWh) of the NaS ESS.
Accordingly, the proposed methodology is further compared
with the deterministic method to in terms of ESS cost and
reliability indices to highlight the relative efficacy.
The remainder of this paper is organized as follows: Sec-
tion II presents the problem statement and the description
of the equation used for identifying the optimal size and
location of ESS. Modelling and system constraints that are
used to design the power network are presented in Section
III. Section IV illustrates case study and presents the results
and discussion followed by the conclusion in Section V.
II. PROBLEM DESCRIPTION
A. TWO STAGE STOCHASTIC OPTIMIZATION
TECHNIQUE
The uncertainties of the solar and wind energy sources are
modeled and introduced in the optimization problem with
the probabilities being distributed to all the scenarios. Each
scenarios are multiplied with these probabilities and the
uncertainty is modeled using the probability density function
(PDF). Therefore, in the stochastic optimization problem,
some or all the parameters are probabilistic and it is divided
into two-stages of optimization. The first stage decisions have
to be made before the specific values of the random variables
are known, while the second stage decisions are made after
the specific values are known. The associated formulation of
two stage stochastic strategy are expressed as [40], [41]:
min
xcTx+EwQ(x, w)
Ax =b
x≤0
(1)
Q(x, w) = min
ydT
wy
Twx+Wwy=hw
y≥0
(2)
where, Ewis the expected scenario, wis the possible
outcome with respect to the defined probability (Ω,p). The
first stage variables are denoted with variable x, which is
determined before the result of the stochastic variable ω
is spotted. The variables yare the second-stage variables
that are identified and computed after ωvalue is concluded.
Further, considering only discrete distributions p, the formu-
lation is derived as:
EwQ(x, ω) = X
w∈Ω
p(w)Q(x, ω)(3)
Therefore, a huge linear programming (LP) can be formu-
lated that forms the deterministic equivalent problem as:
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FIGURE 2. Flowchar t for the proposed stochastic programming based
optimization technique.
min cTx+X
w
p(w)dT
wyw
Ax =b
Twx+Wwyw=hw∀ω
x≥0, yw≥0
(4)
The sequence of conditions in this model are stated as the
followings: Firstly, first stage decision xis made by the deci-
sion maker. Secondly, the outcome (w∈Ω) is determined by
subjecting the random process (Ω,p) to the system. Finally,
the second stage decision yis implemented by the decision
maker.
B. OPTIMAL SIZING AND ALLOCATION OF STORAGE
SYSTEM
The optimal operational schedule of the power network is
dispatched using the AC-OPF. The optimization framework
is depicted in Fig. 2. In accordance with the load requirement
the generation and the storage units are utilized considering
their physical bounds and constraints under and optimized
cost function of the generation units. Stochastic technique
is applied in this study based on two stage stochastic op-
timization technique, which has been utilized to optimally
allocate and size the ESS corresponding to the uncertainties
of the integrated renewable sources and employing AC-OPF
to sustain the system’s power quality. The objective function
(ObjF) is postulated as follows:
ObjF=min X
i,t
bgPg
i,t +ICESS (5)
where, Pg
i,t denotes the generated active power from the
thermal unit glocated on bus ifor the time interval t. The
line susceptance between branch iand jis represented using
bgin p.u. The fixed cost of the thermal generation unit as well
as its variable costs along with the ESS investment costs are
incorporated in the objective function. ICESS is the cost of
capital investment for ESS that is further defined as:
ICESS =P CESSPR
ESS +ECESS ER
ESS (6)
The rated power and of ESS are denoted by PR
ESS and
ER
ES S , respectively. Accordingly, the power and energy cost
of the ESS are represented using P CESS and E CE SS . The
active power flow (Pij,t ) in the power network is calculated
as:
X
j∈Ωi
`
Pij,t =Pg
i,t +PP V
i,t +Pw
i,t −PL
i,t +PS
i,t (7)
where, Pw
i,t and PP V
i,t are the active power generated by wind
turbine and the solar PV connected respectively, connected
at bus i(in M W ), and PL
i,t is the active power component of
the load demand. The charging (Pc
i,t) and discharging (Pd
i,t)
characteristics for the active power component of the ESS
(PS
i,t) is further computed using:
PS
i,t =Pd
i,t −Pc
i,t (8)
Similarly, the reactive power flow (Qij,t) in the network in
the network is calculated using the following equation:
X
j∈Ωi
`
Qij,t =Qg
i,t +QP V
i,t +Qw
i,t −QL
i,t +QS
i,t (9)
where, QP V
i,t and Qw
i,t are the generated reactive power from
the solar PV and wind turbine, respectively. QL
i,t is the
reactive power component of the load demand. The charging
(Qc
i,t) and discharging (Qd
i,t) characteristics for the reactive
component of ESS (QS
i,t) is calculated as:
QS
i,t =Qd
i,t −Qc
i,t (10)
Finally, the total apparent power flow (Sij,t) in the power
network is based on the complex conjugate of the current
between the corresponding branch and the voltage profile that
is formulated as:
Sij,t = (Vi,t∠δi,t )I∗
i,t (11)
Iij,t =Vi,t∠δi,t −Vj,t ∠δj,t
Zij ∠θij
+bVi,t
2∠(δi,t +π
2)(12)
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FIGURE 3. 24 bus IEEE reliability test system with renewable energy
integration.
TABLE 1. Capacities and Placement of wind and solar RESs in the 24-bus
RTS.
Type of
RES Bus Location Capacity Rating
(MW)
Wind 21 100
Wind 19 150
Solar 14 60
Solar 10 60
Wind 8 200
Solar 3 60
where, Iij,t,b(p.u.), and Zij are the current flow, line suscep-
tance, and line impedance respectively, between branch iand
j. The voltage magnitude (p.u.) of bus iis represented by Vi,t,
δi,t is voltage angle (rad), and θij is the difference between
the phases of the voltage and the current in buses ij. The
active (Pij,t) and reactive power flow (Qij,t ) is represented
as:
Pij,t =V2
i.t
Zij
cos(θij )−Vi,tVj,t
Zij
cos(δi,t −δi,t +θij )(13)
Qij,t =V2
i.t
Zij
sin(θij )−Vi,tVj,t
Zij
sin(δi,t −δi,t +θij )−bVi,t
2
(14)
where, θij indicates the angle between real power and reac-
tive power at buses ij at time t, and sin(θij )is the angle
between reactive power and apparent power of buses ij at
time t.
III. MODELLING OF THE TEST SYSTEM
The system under consideration consists of a renewable
integrated (RI) IEEE 24 bus reliability test system (RTS)
[42]. The system is examined using the proposed optimal
strategy under the uncertainties of the wind and solar energy
sources. Therefore, the IEEE 24 bus RI-RTS consists of eight
distributed renewable based generators as shown in Fig. 3.
The bus allocation, capacity, and the type of the deployed
renewable energy source are tabulated in Table 1.
TABLE 2. Weibull parameters of Riyadh based on monthly wind speed
distribution.
Month k c
JAN 1.90 3.55
FEB 1.85 3.89
MAR 2.00 4.31
APR 1.95 3.93
MAY 2.00 3.86
JUN 2.00 4.42
JUL 2.05 4.56
AUG 1.85 3.87
SEP 1.90 3.12
OCT 1.75 2.56
NOV 1.72 2.85
DEC 1.83 3.24
The modelling of the solar and wind energy sources
are modelled using Wiebull distribution technique. Weibull
distribution density function can be used to determine the
frequency of wind speed for certain values (15). This allows
formulation of accurate data set patterns for synthetic time se-
ries based on historical data [43]. The wind speed frequency
curve is utilized to define the Weibull distribution of the wind
speed (v) in m/sec. The three parameters of wind speed
probability function can be defined as:
f(v) = k
cv
ck−1
exp−v
ck(15)
where, kis the shape factor which identifies the peaked
value of the wind distribution, cis the scale parameter,
and vdenotes the mean wind speed. The energy conversion
representation of the solar irradiance (G) to electrical energy
is expressed using:
PSt,s =
PsrG2
GstdRc,0< G < Rc
PsrG2
Gstd , G ≥Rc
(16)
where, Gstd it is denotes the solar irradiance in the normal
standard set as 800 w/m2.Rcis a determined irradiance
point set as 120 W/m2.Psr is the rated output power of the
solar PV unit.
To analyze the availability of the wind and solar, this study
utilizes the Weibull distribution technique for the selected
city (Riyadh) in Saudi Arabia. Besides, this technique allows
the generation of wind speed scenarios by scale and shape
factor. Hence, these parameters are approximated from the
historical data (Table 2), using the scale parameter (c) and
shape factor (k) [44]. Nevertheless, due to uncertainty of
the considered renewable resources, the time series profile
for different wind and solar profile cannot be accurately
predicted. Consequently, various scenarios are needed to
overcome the shortcoming of forecasting errors, handling of
the stochastic optimization’s randomness, and avoid potential
system failures.
A. SYSTEM CONSTRAINTS
The operation of the system is maintained using the equality
constraints. This constraint postulates that the total genera-
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tion by all the power sources (namely, the HREs, ESSs, and
the thermal generation units) should be equal to the total
demand load as well as the system losses, at all times. The
power balance equality constraint is formulated as:
Ns
X
s=1
{
NI
X
i=1
Pi,t,s +PS
i,t,s + (PWt,s +PP Vt,s ) + Pij,t,s}=PL,t
(17)
here, NI is the number of units, N s is number of scenarios
under consideration, PSt,s represents the power discharged or
stored at hour tunder scenario s,PWt,s is the power wind at
time tunder scenario s,PP Vt,s power of solar energy at time
tin scenario s,PL,t load demand at time t, in power storage
system PSthe system which is either to produce or to store
energy, the sign in this matter is alternating depending on the
operation. Furthermore, the transmission line capacity limits
the power exchange between the grid and ESS. The power
imported by the grid is denoted by a positive sign while a
negative sign is denoted when ESS power is discharged. The
transmission line constraint is expressed as:
−Smax
ij ≤Sij,t,s ≤Smax
ij (18)
where, Smax
ij represents the maximum transmission line ca-
pacity that allows the export/import of power to/from the
main grid. The generation capacity constraint limits their
active and reactive power generation that is based on the
following equations:
Pg,min
i≤Pg
i,t,s ≤Pg,max
i(19)
Qg,min ≤Qg
i,t,s ≤Qg,max
i(20)
where, Pg,min
i, and Pg,max
iare the minimum and maximum
real power, and Qg,min
i, and Qg,max
idenote the minimum
and maximum reactive powers of the generation unit i.
Furthermore, each generation unit consists of ramp up/down
rates in accordance with their capacity and technology that
are formulated as:
RUi≥Pg
i,t −Pg
i,t−1,s (21)
RDi≥Pg
i,t−1,s −Pg
i,t,s (22)
where, RDgis the ramp down rating, and RUgis the ramp
up rating. In accordance with this constraint, the unit remains
at their respective state for a certain time interval before their
incremental or decremental transition to the second state.
The electrical power generated by the wind turbine is
determined by the power curve, where the established con-
nection between the power delivered and wind speed is
expressed by the following [45]:
PWt,s =
0, vt,s < vCI , vt,s ≥vC O
Pmax
W
vt,s−vC I
VR−vCI , vC I ≤vt,s < vR
Pmax
W, vR≤vt,s < vCO
(23)
FIGURE 4. Wind power curve.
where, PWt,s is electrical wind power at time (t) in scenario
(s); vCI is cut in wind speed; vRis rated wind speed; vC O is
cut out wind speed; Pmax
Wis rated wind power. Fig. 4 [46],
shows the relationship between wind speed and wind power
[47]. In this study, vCI ,vR, and vCO are respectively taken
as 2 m/s, 5 m/s, and 10 m/s. Wind power is identified
as the development of air in the atmosphere to control and
balance the mismatch in the heat that is brought by unequal
heating of air by the master energy source, which is the
Sun. This irregular heating provides kinetic energy which
is changed to mechanical energy by wind energy conversion
system (WECS). Therefore, wind power is the average of the
alteration of the kinetic energy and can be computed with
(15) and the formation of the output power is expressed as:
PW=1
2ρAv3=1
2ρπR2v3(24)
where, Ris radius of rotor blades (m) and ρis the density of
the air (kg/m3). It can be observed that a minor difference
in wind speed could shape major effect on output of wind
turbine as wind power is basically subjected to the cube of
wind speed. Hence, a precise knowledge of the wind speed
values is very important for an effective utilization of the
wind energy source from a specific location [48].
The charging/discharging capability of ESS is subjected to
the limit imposed by the power rating of the ESS (PR
ESS),
which is lower than or equal to the rated power of the
ESS (25). In this respect, ESS operates as a load and as a
generation unit during its charging and discharging process,
respectively. In this study, discharging power has positive
sign, whereas charging power has negative sign. Accordingly,
in accordance with the rated energy (ER
ESS), the energy
stored will always be greater than zero but less than or equal
to the rated energy (26) and the rated power (27).
−PR
ESS ≤PESSt,s ≤PR
ESS ∀t∈T(25)
0≤EESSt,s ≤ER
ESS ∀t∈T(26)
EESSt,s ≤EES St,s ≤PES St,s ∀t∈T(27)
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0 5 10 15 20
Time (hr)
0
2
4
6
8
10
12
Wind Speed (m/s)
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
FIGURE 5. Hourly wind speed for ten scenarios considered in summer and
winter season.
0 5 10 15 20
Time (hr)
0
0.2
0.4
0.6
0.8
1
1.2
Power (p.u.)
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
FIGURE 6. Hourly solar PV power for ten scenarios considered in summer
and winter season.
where, the energy stored in ESS for scenario sat time interval
tis denoted by EESSt,s . This represents the state-of-charge
(SoC) of the ESS that is calculated hourly for each scenario.
IV. RESULT AND DISCUSSION
Based on the modelling framework formulated in Section III,
five scenarios of wind and solar are randomly selected from
the historical data [49], for the winter and summer seasons
over a horizon of 24 hours. Fig. 5 and Fig. 6 depicts the
hourly data sets of the wind speed and solar irradiance sce-
narios encountered during the winter and summer seasons,
respectively. The probabilities (ρs) are uniformly distributed
between all the scenarios by 0.2, so the total sum of the
scenarios is equal to 1. The values of kand cin accordance
with the annual numerical values of Riyadh in are taken as
1.95 and 3.70, respectively. The efficiency of the NaS-ESS
0 5 10 15 20
Time (hr)
-5
0
5
10
15
20
25
30
Power (MW)
Thermal
Demand
Hybrid
ESS
FIGURE 7. Economic dispatch with ESS during summer case.
0 5 10 15 20
Time (hr)
0
5
10
15
20
25
30
Power (MW)
Thermal
Demand
Hybrid
FIGURE 8. Economic dispatch without ESS during summer case.
is taken at 95% and the power and energy cost is taken as
350 $/kW and 300 $/kW h, respectively [50], [51]. The
optimization is performed on GAMS platform [52].
The optimization is achieved based on the two-stage
stochastic programming technique. The total cost includes
the operation of the thermal generation units, power ex-
changed from the grid with minimized investment cost of the
NaS-ESS. The optimal size and location of the NaS-ESS is
calculated at the rated power of 5.61 MW and rated energy
of 21.61 MWh. The seasonal based economic dispatch and
operation of the HRES system are depicted in Figs. 7–10,
with and without the support of the NaS-ESS. From these
results, the formulation has been performed for the output
power of all the HRES and thermal units for all buses in
the network considering an hourly time step. The NaS-ESS
acts as an energy buffer to reduce the difference between the
varying RES supply, i.e., it servers as a alternative generation
VOLUME 4, 2016 7
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10.1109/ACCESS.2021.3133261, IEEE Access
Author et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALS
0 5 10 15 20
Time (hr)
-5
0
5
10
15
20
25
30
Power (MW)
Thermal
Demand
Hybrid
ESS
FIGURE 9. Economic dispatch with ESS during winter case.
0 5 10 15 20
Time (hr)
0
5
10
15
20
25
30
Power (MW)
Thermal
Demand
Hybrid
FIGURE 10. Economic dispatch without ESS during winter case.
source or an additional load which is highlighted by its pos-
itive and negative values during its charging and discharging
intervals. Accordingly, the SoC is taken as positive during
the discharging and negative during the charging hour t.
The design and operation of the ESS, depicts an observable
difference in the total cost of the energy system.
Furthermore, Table 3 highlights the efficacy of the pro-
posed stochastic methodology over the deterministic method.
The results obtained for all the scenarios including the ten
cases for the deterministic approach as well as the stochas-
tic method are presented. The advantage of the proposed
stochastic optimization technique is the formulation of the
second-optimal solution (SP). The results obtained for the
deterministic method (S1-S10) facilitates distinctive results
and an over-optimistic selection of ESS capacity is required
for suitable and economic system operation. This means that
the operators will have to dispatch different sets of storage
0 5 10 15 20
Time (hr)
0
5
10
15
20
25
30
Power (MW)
Thermal
Demand
Hybrid
FIGURE 11. Economic dispatch and operation without ESS for the SP
solution.
0 5 10 15 20
Time (hr)
-5
0
5
10
15
20
25
30
Power (MW)
Thermal
Demand
Hybrid
ESS
FIGURE 12. Economic dispatch and operation with ESS for the SP solution.
TABLE 3. Comparative results obtained through deterministic approach
(S1-S10) and proposed two-stage stochastic approach (SP).
Sizing Allocation
Scenario Total cost
($)
PS
R
(MW)
ES
R
(MWh) Bus No. NaS Rating
(MW)
S1 482995.90 6.08 24.85 3 0.558
S2 477248.95 5.63 22.08 4 0.122
S3 491459.99 5.26 22.38 5 0.605
S4 440403.02 5.43 21.62 6 0.38
S5 470737.52 4.95 17.11 7 1.056
S6 480382.18 5.41 21.08 8 0.46
S7 482691.76 5.38 21.18 9 0.445
S8 473275.98 4.32 15.99 10 0.308
S9 422227.20 5.43 21.62 13 0.219
S10 451735.91 2.54 10.16 14 0.482
SP 432429.00 5.12 21.61 15 0.249
19 0.232
8VOLUME 4, 2016
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Author et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALS
TABLE 4. Reliability comparison between the stochastic and deterministic
technique.
Index Deterministic Stochastic
Optimized Cost 480382 432429
ASAI 98.4% 99.76%
ASUI 0.0155% 0.0024%
SAIFI (failure/customer) 5.4571 4.8951
SAIDI (hr./customer) 36.4098 28.2045
CAIDI (hr/customer interruption) 6.672 5.761
size in accordance with the variation in the generation which
introduces further complexities in optimal ESS dispatch and
capacity. On the other hand, the stochastic approach facil-
itates second optimal solution that reduces over-optimistic
selection ensuring optimal energy dispatch considering gen-
eration, load, and energy storage. The operational aspect of
the power components in the HRES for the SP, without and
with the incorporation of NaS in shown in Figures 11 and 12,
respectively.
Accordingly, the aim of optimal sizing and allocation of
ESS is to improve the reliability of the power network [53].
To demonstrate the reliability enhancement achieved with
proposed methodology, a reliability analysis considering the
average service availability index (ASAI), average service
unavailability index (ASUI), system average interruption fre-
quency index (SAIFI), system average interruption duration
index (SAIDI), and customer average interruption duration
index (CAIDI) is performed with the deterministic case to
analyze the equipment availability between the two method-
ologies.
Table 4 shows that reliability indices of the proposed
stochastic technique is more enhanced with higher contribu-
tion towards the reliability of the HRES system. Observably,
deterministic approach facilitates optimization in accordance
with the associated generation and load profiles. However,
it proves to be sub-optimal due to the increment in the
degree of variation introduced with the incorporation of
RES. Therefore, the proposed two-stage stochastic program-
ming technique provides a global optimal solution that is
reasonably cost efficient in comparison to the deterministic
technique. The stochastic technique is implemented in cases
that requires a single optimal solutions for multiple scenarios.
This provides an advantage to the stochastic programming
technique over the deterministic technique that heavily relies
on the accuracy and availability of a bulk historical data of
the RES and the system.
V. CONCLUSION
In this paper, a two-stage stochastic optimization method-
ology is formulated for capacity optimization and optimal
allocation of NaS-ESS units to optimize the overall system
costs. The optimization framework is tested and validated
on a hybrid renewable based 24-bus RTS network. A 24-
hour data set of ten scenarios are considered to formulate
the planning framework of the test system. Based on the
uncertainty probabilistic data and operation an optimal size
and placement of the ESS is determined to facilitate a cost-
efficient solution. The results obtained illustrated the positive
impact of ESS towards the cost reduction by facilitating a
cheaper solution to the uncertainty of the power flow through
controllable charging and discharging process. Furthermore,
a comparative analysis based on reliability indices of power
system was presented to demonstrate the efficacy of the
proposed two-stage stochastic programming over the deter-
ministic method. Based on the results obtained, an observable
reliability enhancement combined with minimized cost is
achieved by the proposed stochastic optimization technique.
Besides, the proposed programming technique has a promis-
ing applicability towards power system planning wherein the
uncertainty variables are very high, especially in large power
system networks.
VI. ACKNOWLEDGMENTS
The authors acknowledge the funding support provided from
the Deanship of Research (DSR), King Fahd University of
Petroleum & Minerals by Project No. DF201011. Also, this
research work was financially supported by the King Abdul-
lah City for Atomic and Renewable Energy (K.A.CARE).
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