Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
11,
No.
1,
February
2020,
pp.
182
200
ISSN:
2088-8708,
DOI:
10.11591/ijece.v11i1.pp182-200
r
182
P
o
wer
system
operation
considering
detailed
modelling
of
ener
gy
storage
systems
Ser
gio
Cantillo,
Ricardo
Mor
eno
Ener
gy
and
Mechanical
Department,
Uni
v
ersidad
Aut
´
onoma
de
Occidente,
Colombia
Article
Inf
o
Article
history:
Recei
v
ed
Apr
13,
2020
Re
vised
Apr
14,
2020
Accepted
May
28,
2020
K
eyw
ords:
Ener
gy
storage
systems
Generation
dispatch
Optimal
po
wer
flo
w
Rene
w
ables
sources
ABSTRA
CT
The
po
wer
system
operation
considering
ener
gy
storage
syst
ems
(ESS)
and
rene
w-
able
po
wer
represents
a
challenge.
In
a
24-hour
economic
dispatch,
the
generation
resources
are
dispatched
to
meet
demand
requirements
consi
dering
netw
ork
restric-
tions.
The
uncertainty
and
unpredictability
associated
with
rene
w
able
resources
and
storage
systems
represents
challenges
for
po
wer
system
operation
due
to
operational
and
e
conomical
restrictions.
This
paper
de
v
eloped
a
detailed
formulation
to
model
ener
gy
storage
systems
(ESS)
and
rene
w
able
sources
for
po
wer
system
operation
in
a
DCOPF
approach
considering
a
24-hour
period.
The
model
is
formulated
and
e
v
alu-
ated
with
tw
o
dif
ferent
po
wer
systems
(i.e.
5-b
us
and
IEEE
modified
24-b
us
systems).
W
ind
a
v
ai
lability
patterns
and
scenarios
are
used
to
assess
the
ESS
performance
un-
der
dif
ferent
operational
circumstances.
W
ith
r
e
g
ar
d
to
the
systems
proposed,
there
are
scenarios
in
or
der
to
e
v
aluate
ESS
performance.
In
one
of
them,
the
increase
in
capacity
did
not
represent
significant
sa
vings
or
performance
for
the
system,
while
in
the
other
it
w
as
quite
the
opposite
especially
during
peak
load
periods.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Ricardo
Moreno,
Ener
gy
and
Mechanical
Department,
Uni
v
ersidad
Aut
´
onoma
de
Occidente,
Calle
25
#
115-85,
Cali,
Colombia.
Email:
rmoreno@uao.edu.co
1.
INTR
ODUCTION
No
w
adays,
the
generation
portfolio
of
electricity
in
po
wer
systems
is
more
di
v
ersified
than
some
years
ago
by
the
inte
gration
of
rene
w
able
resources
[1].
En
vironmental
concerns
are
pushing
the
inte
gration
of
technologies
to
produce
electricity
with
rene
w
able
resources
[2].
As
a
result,
there
is
an
increasing
to
spur
in
v
estments
in
order
to
diminish
the
con
v
entional
fos
sil
fuel-based
po
wer
generation
[3–5].
Consequently
,
the
international
ener
gy
agenc
y
(IEA)
reports
that
rene
w
able
ener
gy
sources
ha
v
e
increased
at
an
a
v
erage
annual
rate
of
2.0
%
from
1990
[6].
Gro
wth
is
lar
gely
due
to
solar
PV
(37.4
%)
and
wind
po
wer
(23.4
%)
[6].
The
i
nherent
features
of
this
type
of
resources
as
uncertainty
and
v
ariability
impact
po
wer
system
operation
[7–10].
In
this
conte
xt,
po
wer
systems
require
strate
gies
to
inte
grate
such
intermittent
resources
with
fle
xibility
to
meet
the
demand
requirements
[11].
The
ener
gy
storage
systems
(ESS)
represent
a
technology
to
store
rene
w
able
ener
gy
according
to
their
a
v
ailability
during
the
day
(i.e.,
there
are
hi
gh
quantities
of
electricity
from
PV
systems
at
noon).
The
ESS
can
absorb
ener
gy
when
generation
e
xceeds
the
load
especially
when
this
surplus
come
from
rene
w
able
sources
and
supply
this
ener
gy
to
the
grid
during
load
peak
hours
[12,
13].
Thus,
the
ESS
pro
vides
fle
xibility
under
the
inte
gration
of
rene
w
able
resources
gi
v
en
that
the
po
wer
dispatch
can
be
settled
to
a
desirable
supply
profile
[14,
15].
J
ournal
homepage:
http://ijece
.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
183
The
inte
gration
of
ener
gy
storage
systems
(ESS)
represent
a
challenge
for
the
operation
of
po
wer
systems
from
dif
ferent
perspecti
v
es
.
The
quality
and
reliability
can
be
compromised
due
to
mis
use,
misplacing
or
bad
sizing
of
ESS
[16].
Nonetheless,
other
challenges
for
po
wer
system
operation
are
recognized,
such
as
performance
and
safety
(vie
wed
from
its
constituent
materials,
interconnections
[17,
18],
and
service
life),
the
distrib
uted
generation
impacts
in
the
po
wer
system
coherenc
y
[19],
the
re
gulatory
en
vironment,
the
in
v
estment
costs,
and
the
industry
acceptance
[20].
These
issues
can
occur
because
system
operation
in
v
olv
es
decisions
in
dif
ferent
time
frames
(since
minutes
to
days)
including
weather
-dependent
rene
w
able
units
scheduling
and
their
reserv
es
[21]
(e.g.
wind
[22])
as
well
as
considering
other
relat
ed
v
ariables.
Ho
we
v
er
,
the
ESS
mathematical
modeling
and
its
inte
gration
to
po
wer
systems
is
a
challenge
with
great
impact
and
importance.
The
optimal
po
wer
flo
w
(OPF)
is
used
widely
by
po
wer
systems
operators
to
dispatch
economi
cally
the
generation
resources
according
to
operational
and
economical
restrictions
[23].
From
this
perspecti
v
e,
the
po
wer
system
operation
requires
a
detailed
modeling
of
storage
systems
in
order
to
be
included
in
the
OPF
mathematical
formulati
on.
There
are
se
v
eral
reasons
for
including
these
ener
gy
storage
models
in
the
economic
dispatch.
One
of
them
is
the
more
ef
ficient
inte
gration
of
rene
w
able
ener
gy
sources,
since
these
de
vices
contrib
ute
to
diminish
the
ef
fects
of
the
stochastic
nature
of
these
sources
[24].
Also,
the
ESS
contrib
ute
to
maintain
the
stability
in
the
po
wer
system
operation,
due
to
t
he
y
restrict
the
fluctuation
of
instantaneous
po
wer
coming
mostly
from
rene
w
able
sources
[25,
26].
Lik
e
wise,
the
y
allo
w
a
more
ef
ficient
economic
dispatch
since
these
de
vices
pro
vide
fle
xibility
that
reduces
the
amount
of
po
wer
coming
from
more
e
xpensi
v
e
sources
(i.e.,
the
y
deli
v
er
when
there
is
a
lack
of
ener
gy
,
and
store
when
there
is
a
surplus),
being
cheaper
and
with
less
w
aste
[27].
Ho
we
v
er
,
the
inte
gration
of
ESS’
s
into
an
OPF
model
introduces
inter
alia,
time
interdependence.
That
is
to
say
the
ESS
can
char
ge
in
periods
of
high
wind
or
lo
w
demand
(i.e.
is
absorbing
po
wer
from
the
grid),
and
dischar
ge
in
periods
of
lo
w
wind
a
v
ailability
or
load
peak
(i.e
is
injecting
po
wer
to
the
grid).
This
choice
depends
on
the
char
ge
status
(i.e.
SoC)
at
the
pre
vious
time
interv
al
and
their
respecti
v
e
ef
ficienc
y
.
Also,
technical
and
economical
conditions
are
required
to
a
v
oid
une
xpected
situations
as
char
ging
and
dischar
ging
simultaneously
.
In
other
w
ords,
this
situation
implies
that
ESS
w
ould
be
paid
for
char
ging
and
dischar
ging
at
once
[11].
Among
others,
the
dual
feature
of
absorbing
and
generating
po
wer
requires
a
precise
modelling
for
po
wer
system
operation.
This
paper
proposes
a
detailed
formulation
to
include
ESS
in
the
optimal
po
wer
flo
w
with
mult
i-
ple
generation
sources
to
pro
vide
a
24-hour
dispatching
to
meet
demand
requirements.
Since
ener
gy
storage
systems
could
be
defined
as
a
generator
and
load
due
to
the
dual
feature
and
also
are
time-correlated
as
men-
tioned
abo
v
e.
The
proposed
formulation
determines
the
optimal
outputs
for
all
g
e
neration
portfolio
as
well
as
ESS
char
ging/dischar
ging
schedules
seen
through
its
SoC,
all
of
them
under
dif
ferent
operation
conditions
and
scenarios.
The
paper
is
or
g
anized
as
follo
ws.
The
problem
description
and
formulation
are
presented
in
Section
2.
In
Section
3,
the
5-b
us
and
IEEE
24-b
us
modified
systems
and
their
parameters
are
described.
Then,
the
proposed
procedure
is
tested
using
the
systems
described
abo
v
e.
At
the
end
of
this
section,
the
results
are
analyzed
and
discussed.
Section
4
pro
vides
some
concluding
remarks
about
this
topic.
-
Literature
re
vie
w
The
optimal
po
wer
flo
w
for
dispatching
generation
resources
including
rene
w
able
sources
has
been
widely
discussed.
The
DC
multi-period
optimal
po
wer
flo
w
(DCOPF)
formulation
ha
v
e
been
e
xtended
to
include
the
v
ariable
nature
of
rene
w
able
po
wer
generation,
elements
such
as
uncertainty
in
electricity
demand
and
wi
nd
a
v
ailability
[28–31].
Also,
in
some
w
orks
other
features
such
as
branches
and
generation
constraints
are
e
xplicitly
included
in
the
formulation
such
as
presented
in
[32–34].
Other
authors
ha
v
e
made
comparisons
and
anal
ysis
between
this
approach
and
con
v
entional
methods
without
these
v
ariables
[35].
On
the
other
hand,
some
w
orks
emplo
ys
heuristic
approaches
including
det
erministic
and
stochastic
methods
(e.g
Montecarlo
simulation)
to
solv
e
the
optimal
dispatching
[36–41].
Se
v
eral
studies
[42–45]
ha
v
e
researched
the
inte
gration
of
intermittent
wind
po
wer
using
a
probabil
is-
tic
approach.
In
order
to
pro
vide
better
tools
for
the
construction
of
gene
ration
scenarios
and
stochastic
dispatch
models
[46–48].
Consequently
,
optimal
po
wer
flo
w
has
also
been
used
with
ESS
in
order
to
assess
the
po
wer
system
operation
fle
xibility
[49],
due
to
these
units
can
absorb
ener
gy
in
case
of
e
xcessi
v
e
generation
or
lo
w
electricity
prices,
mitig
ating
the
uncertainty
in
the
rene
w
able
sources.
Also
in
this
research
topic,
studies
such
[50,
51]
ha
v
e
found
other
issues
such
as
inclusion
of
ESS
in
distrib
uted
generation
(DG)
and
RES
with
their
respecti
v
e
modelling
and
sizing.
P
ower
system
oper
ation
considering
detailed
modelling
of
...
(Ser
gio
Cantillo)
Evaluation Warning : The document was created with Spire.PDF for Python.
184
r
ISSN:
2088-8708
Other
studies
[11,
52–54]
propose
approaches
in
the
economic
dispatch
using
multi-period
OPF
due
to
specific
challenges
to
the
traditional
OPF
such
as
the
modeling
of
char
ge/dischar
ge
of
ESS,
or
a
specific
ESS
technology
featuring
[55].
Other
studies
ha
v
e
included
more
v
ariables
in
order
to
bring
the
problem
closer
to
a
more
precise
conte
xt
such
as
[56,
57]
using
po
wer
losses
constraints
on
the
transmission
branches
to
e
v
aluate
dif
ferent
generation
scenarios.
On
the
other
hand,
in
[58]
adds
an
en
vironmental
approach,
modeling
the
social
cost
using
v
ariables
such
as
emission
generation
in
order
to
optimize
the
total
production
costs,
using
as
little
as
possible
the
thermal
generati
on,
without
ne
glecting
the
reliability
in
the
system,
all
of
this
cases
w
orking
under
a
DC
approach.
2.
DC-B
ASED
OPTIMAL
PO
WER
FLO
W
WITH
ESS
This
secti
on
includes
t
h
e
notation
and
the
mathemati
cal
formulation
for
the
mul
tiperiod
DCOPF
dis-
patching
model
including
the
ESS
modeling.
This
model
also
includes
thermal
and
wind
po
wer
generation.
2.1.
Notation
g
Thermal
generation
unit.
i;
j
Netw
ork
b
uses
connected
by
transmission
branches.
t
T
ime
period
(hours).
c
,
d
Char
ging/Dischar
ging
ef
ficienc
y
of
the
ESS
units.
G
Number
of
thermal
generation
units.
L
Number
of
netw
ork
branches.
T
T
ime
period
in
the
operating
horizon,
in
this
case
24
hour
.
N
Number
of
netw
ork
b
uses.
V
W
L
W
ind
po
wer
w
aste
v
alue
($/MWh).
C
ch
;
C
dch
ESS
Char
ging/Dischar
ging
mar
ginal
cost
($/MWh).
X
ij
Branch
reactance
connecting
the
i
-b
us
to
j
.
(p.u)
b
g
Fuel
cost
coef
ficient
of
thermal
units
($).
P
max
g
,
P
min
g
Maximum/Minimum
po
wer
generation
thresholds
of
the
thermal
unit
g
(MW).
P
L
max
ij
Maximum
po
wer
flo
w
boundaries
of
branch
connecting
the
i
-b
us
to
j
(MW).
P
ch
max
,
P
ch
min
Maximum/Minimum
char
ge
po
wer
limits
for
the
ESS
unit
connected
on
the
i
-b
us
(MW).
P
dch
max
,
P
dch
min
Maximum/Minimum
dischar
ge
po
wer
limits
for
the
ESS
connected
on
the
i
-b
us
(MW).
C
S
max
,
C
S
min
Maximum/Minimum
ener
gy
stored
(MWh).
D
i;t
Electric
po
wer
load
in
the
i
-b
us
at
time
t
.
Av
w
ind
t
W
ind
turbine
a
v
ailability
on
the
i
-b
us
at
time
t
(MW).
C
w
ind
t
W
ind
turbine
capacity
connected
on
the
i
-b
us
(MW).
R
up
g
,
R
dow
n
g
Ramp-up/do
wn
thresholds
of
thermal
generation
unit
g
(MW/h).
P
L
ij
;t
Acti
v
e
po
wer
flo
w
from
the
i
-b
us
to
j
-b
us
at
time
t
(MW).
P
Gen
i;t
Acti
v
e
po
wer
generated
by
thermal
unit
g
at
time
t
(MW).
P
w
ind
i;t
Acti
v
e
po
wer
of
wind
turbine
connected
to
i
-b
us
at
time
t
(MW).
P
w
l
i;t
Curtailed
po
wer
of
wind
turbine
connected
to
the
i
-b
us
at
time
t
(MW).
i;t
Dual
v
ariable
that
denote
Locational
Mar
ginal
Price
in
the
i
-b
us
at
time
t
($/MWh).
F
obj
24-hour
T
otal
operating
costs
($).
i;t
V
oltage
angle
of
the
i
-b
us
at
time
t
(rad).
C
S
i;t
Ener
gy
stored
in
the
i
-b
us
at
time
t
(MWh).
P
ch
i;t
,
P
dch
i;t
Po
wer
Char
ged/dischar
ged
to/from
ESS
connected
to
the
i
-b
us
at
time
t
(MW).
2.2.
F
ormulation
The
formulation
is
e
xpressed
as
optimization
problem
to
address
a
mi
nimum
total
operating
cost
associated
with
producing
electricity
to
meet
the
demand
for
a
24-hour
period
described
by
(1).
In
(2)
indicates
the
total
cost
of
ener
gy
production
with
g
thermal
units
during
an
interv
al
of
time
T
.
In
(3)
refers
to
the
production
costs
associated
with
not
taking
full
adv
antage
of
the
source
of
wind
generation
a
v
ailable
during
this
same
interv
al
of
time.
In
(4)
represents
a
condition
that
requires
that
the
ESS
are
not
char
ged
and
dischar
ged
simultaneously
,
this
pre
v
ents
the
payment
of
an
ESS
for
char
ging
and
dischar
ging
simultaneously
[11,
29,
59],
situation
that
cannot
occur
.
Int
J
Elec
&
Comp
Eng,
V
ol.
11,
No.
1,
February
2020
:
182
–
200
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
185
F
obj
=
C
G
+
W
L
+
C
E
S
S
(1)
C
G
=
T
X
t
=1
G
X
g
=1
b
g
P
Gen
g
(2)
W
L
=
T
X
t
=1
N
X
i
=1
V
W
L
P
w
l
i;t
(3)
C
E
S
S
=
T
X
t
=1
N
X
i
=1
(
C
dch
P
dch
i;t
C
ch
P
ch
i;t
)
(4)
The
restrictions
for
the
dispatching
model
are
gi
v
en
by
the
po
wer
flo
w
equations.
This
paper
uses
the
DC
approach
to
include
po
wer
flo
w
calculations.
The
po
wer
flo
w
balance
is
gi
v
en
by
(5).
The
po
wer
flo
wing
on
each
line
is
gi
v
en
by
(6).
The
po
wer
flo
w
restrictions
are
gi
v
en
by
the
boundaries
in
the
(7).
G
X
g
=1
P
Gen
g
;t
+
P
w
ind
i;t
D
i;t
P
ch
i;t
+
P
dch
i;t
=
L
X
j
=1
P
L
ij
;t
(5)
P
L
ij
;t
=
1
X
ij
(
i;t
j
;t
)
(6)
P
L
max
ij
;t
P
L
ij
;t
P
L
max
ij
;t
(7)
The
dual
v
ariable
associated
to
(5)
correspond
to
the
locational
mar
ginal
price
(LMP)
of
each
b
us
hourly
.
On
the
other
hand,
the
restrictions
for
thermal
generation
units
are
defined
in
(8),
(9),
and
(10),
where
(8)
corresponds
to
the
operational
range
of
thermal
generators.
On
the
other
hand,
(9)
and
(10)
indicates
the
maximum
up
and
do
wn
ramps
limits
that
each
of
the
thermal
gener
ators
can
perform
from
one
hour
to
the
ne
xt.
P
min
g
;t
P
Gen
g
;t
P
max
g
;t
(8)
P
Gen
g
;t
P
Gen
g
;t
1
R
up
g
(9)
P
Gen
g
;t
1
P
Gen
g
;t
R
dow
n
g
(10)
The
ener
gy
le
v
el
(i.e.
State
of
char
ge)
of
ESS
were
defined
per
unit
in
the
i
-b
us
at
time
interv
al
t
,
depends
on
the
dif
ference
between
the
ESS
char
ged
and
dischar
ged
po
wer
with
their
respecti
v
e
operating
ef
ficiencies,
as
defined
in
(11).
The
maximum
and
minimum
limits
of
ESS
char
ge/dischar
ge,
and
ESS
Capacity
were
defined
in
(12),
(13)
and
(14)
respecti
v
ely
.
C
S
i;t
C
S
i;t
1
=
c
P
ch
i;t
P
dch
i;t
d
(11)
P
ch
i;min
P
ch
i;t
P
ch
i;max
(12)
P
dch
i;min
P
dch
i;t
P
dch
i;max
(13)
C
S
i;min
C
S
i;t
C
S
i;max
(14)
The
restrictions
for
wind
generation
(i.e.
wind
po
wer
loss)
are
defined
in
(15).
The
e
xpression
cor
-
responds
to
the
reduction
of
use
of
potentially
a
v
ailable
wind
ener
gy
.
In
(16)
describes
the
minimum
and
maximum
po
wer
range
that
a
wind
generator
can
produce,
considering
placing
and
wind
a
v
ailability
.
P
ower
system
oper
ation
considering
detailed
modelling
of
...
(Ser
gio
Cantillo)
Evaluation Warning : The document was created with Spire.PDF for Python.
186
r
ISSN:
2088-8708
P
w
l
i;t
=
Av
w
ind
t
C
w
ind
i
P
w
ind
i;t
(15)
0
P
w
ind
i;t
Av
w
ind
t
C
w
ind
i
(16)
3.
RESUL
T
AND
DISCUSSION
In
order
to
test
this
approach
to
study
a
wide
range
of
applications,
initially
,
a
small
case
and
then
a
modified
IEEE
standard
case
are
used
to
illustrat
e
the
ESS
modelling
in
a
multi-period
dispatching
and
sho
w
their
performance
according
to
dif
ferent
operational
situations.
This
section
pro
vides
a
comprehensi
v
e
e
xplanation
of
each
case
and
the
corresponding
analysis
to
observ
e
ESS
performance
during
a
24-hour
period.
All
simulations
were
completed
by
a
computer
(PC)
running
W
indo
ws
R
with
an
Intel
R
Core
I5+
8300H
processor
@2.3
GHz
with
12.00
GB
RAM,
using
Gurobi
R
Solv
er
(8.1.1)
[60]
under
the
JuMP
0.20.1
Julia
platform
[61].
3.1.
Load
cur
v
e
description
The
daily
load
curv
es
used
for
the
5-b
us
(orange)
and
24-b
us
(blue)
po
wer
systems
are
plotted
in
Figure
1.
The
load
curv
es
present
four
(4)
decreasing
trend
bands
with
its
lo
west
point
at
hour
4
(i.e.
787.1
MW
and
1950.6
MW
respect
i
v
ely),
and
three
(3)
increasing
trend
bands
with
a
load
peak
at
hour
20
(i.e.
1150
MW
and
2850
MW
respecti
v
ely).
Figure
1.
Load
curv
e
pattern
for
po
wer
systems
testing
3.2.
W
ind
a
v
ailability
pr
ofiles
Three
(3)
wind
profiles
are
construc
ted
to
e
v
aluate
the
ESS
performance
during
the
operation
of
both
po
wer
systems
considering
wind
po
wer
a
v
ailability
(i.e.
lo
w
,
moderate,
and
high)
as
sho
wn
in
Figure
2.
The
simulation
results
of
both
po
wer
systems,
such
as
the
the
thermal
generators
scheduling
and
the
ESS
performance
as
well
as
their
respecti
v
e
analysis
can
be
found
in
the
follo
wing
subsections.
Figure
2.
W
ind
a
v
ailability
profiles
used
for
po
wer
systems
testing
Int
J
Elec
&
Comp
Eng,
V
ol.
11,
No.
1,
February
2020
:
182
–
200
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
187
3.3.
ESS
perf
ormance
in
a
5-Bus
system
3.3.1.
Case
description
The
one-line
diagram
for
a
5-Bus
system
is
sho
wn
in
Figure
3.
This
system
includes
thermal
genera-
tion,
wind
generation
and
st
o
r
age.
The
thermal
unit
parameters
are
listed
in
T
able
1,
modifying
the
information
from
[49].
The
load
is
distrib
uted
in
4
b
uses.
Figure
3.
One-line
diagram
of
modified
5-b
us
po
wer
system
T
able
1.
Thermal
generation
info
for
the
5-b
us
po
wer
system
Gen
Bus
P
min
g
(MW)
P
max
g
(MW)
Mar
ginal
Cost
(MW)
R
up
g
(MW/h)
R
dow
n
g
(MW/h)
1
1
0
140
17
20
20
2
1
0
170
18
25
25
3
3
0
360
20
30
30
4
5
0
490
21
35
35
T
able
2
lists
the
netw
ork
grid
information
such
as
reactance
and
rating
in
MV
A
(i.e
po
wer
line
con-
straints),
all
of
them
modified
from
[49].
T
able
2.
Branch
info
for
the
5-b
us
test
system
Fr
om
T
o
X
ij
(p.u)
Rating
(MV
A)
1
2
0.0281
400
1
5
0.0064
400
2
3
0.0108
400
4
5
0.0297
240
The
5-b
us
test
system
includes
a
wind
po
wer
plant
connected
to
the
b
us
4.
The
wind
po
wer
generation
site
and
capacity
is
listed
in
T
able
3.
Also,
this
system
includes
an
ESS
connected
in
the
b
us
2.
In
other
w
ords,
the
ESS
is
not
on
the
same
b
us
as
the
wind
po
wer
plant.
The
ESS
parameters
considered
are
ESS
capacity
,
char
ging
and
dischar
ging
ef
ficienc
y
,
and
operating
v
alues.
Such
features
are
listed
in
T
able
4.
T
able
3.
W
ind
po
wer
generation
info
for
the
5-b
us
system
Gen
Bus
C
w
ind
i;t
(MW)
1
4
240
T
able
4.
ESS
info
for
5-b
us
system.
ESS
Bus
Capacity
(MW)
c
(%)
d
(%)
C
S
i;min
(%)
C
S
i;max
(%)
1
2
50
90
90
10
90
P
ower
system
oper
ation
considering
detailed
modelling
of
...
(Ser
gio
Cantillo)
Evaluation Warning : The document was created with Spire.PDF for Python.
188
r
ISSN:
2088-8708
3.3.2.
Results
The
simulations
use
the
5-b
us
po
wer
system
with
the
parameters
gi
v
en
before
(i.e.
load
curv
e
and
wind
profiles)
to
e
xplore
and
e
v
aluate
dif
ferent
operational
situations.
Initially
,
the
performance
of
the
po
wer
system
w
as
e
v
aluated
according
to
gradual
increases
of
the
ESS
capacity
,
starting
from
its
base
capacity
(i.e.
25
MW
steps,
starting
at
50
MW
up
to
200
MW).
The
analysis
highlights
changes
in
the
thermal
generation
scheduling
and
ESS
performance
during
the
24-hour
period.
The
ESS
performance
(i.e
State
of
Char
ge
(SoC))
during
a
24-hour
period
is
sho
wn
in
Figure
4.
Lik
e
wise,
the
ESS
char
ging
interv
als
occurs
at
hours
3
t
o
7,
16
to
18,
and
23
to
24.
A
one
ESS
dischar
ging
interv
al
occurs
in
the
load
peak
v
alue
(hours
19
to
21).
The
ESS
is
char
ged
in
v
alle
y
hours
(lo
w
demand)
and
dischar
ged
at
load
peak
hours
(i.e.
time
shifting
ef
fect
and
transmission
curtai
lment
reduction)
as
e
xpected.
On
the
other
hand,
the
ESS
performance
sho
ws
a
g
ap
when
its
capacity
reaches
150
MWh
and
the
wind
a
v
ailability
impro
v
es
(i.e.
moderate
and
high
a
v
ailability).
This
finding
is
presented
in
hours
where
there
is
no
char
ging
or
dischar
ging
beha
vior
(i.e.
hours
5
to
16).
Figure
4.
(a)
Comparison
of
ESS
performance
between
the
lo
w-wind
a
v
ailability
,
(b)
the
moderate
wind
a
v
ailability
,
(c)
and
high-wind
a
v
ailability
The
description
of
the
ESS
performance
leads
to
the
analysis
that
the
of
ESS
installed
capacity
could
be
o
v
ersized
due
to
wind
a
v
ailability
.
This
could
happen
in
lo
w-wind
a
v
ailability
due
to
wind
turbines
and
Int
J
Elec
&
Comp
Eng,
V
ol.
11,
No.
1,
February
2020
:
182
–
200
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Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
189
thermal
units
w
ouldn’
t
ha
v
e
enough
po
wer
to
contrib
ute
meeting
demand
and
char
ge
the
ESS
at
the
same
time,
unless
the
wind
a
v
ailability
increases.
Therefore,
tw
o
or
more
ESS
with
dif
ferent
capacities
could
ha
v
e
similar
SoC
v
alues
where
the
higher
capacities
are
underutilized.
Since
it
w
ould
not
ha
v
e
complete
char
ging
c
ycles
(e.g
200
MW
and
175
MW
ESS
capacities
in
all
wind
patterns)
thus
decreasing
its
life
c
ycle,
and
represents
a
smaller
reducti
on
in
operating
costs.
This
analysis
sho
ws
that
e
v
en
in
s
mall
po
wer
systems,
features
such
as
the
ESS
capacity
must
be
analyzed
technically
and
economically
in
a
strict
w
ay
.
On
the
other
hand,
the
dif
ferent
thermal
generation
schedules
according
to
the
ESS
capacity
increas
es
during
a
24-hour
period
are
sho
wn
in
Figure
5.
Similar
performances
to
the
proposed
demand
curv
e
are
presented
especially
in
the
lo
w-a
v
ailability
wind
pattern.
Nonetheless,
such
performances
mo
v
ed
a
w
ay
as
wind
a
v
ailability
increases
(i.e.
moderate
and
high
a
v
ailability
patterns)
as
in
the
case
of
ESS
performance.
Furthermore,
it
ca
n
be
appreciated
dif
ferences
in
thermal
scheduling
between
ESS
capacities
on
v
alle
y
hours
(i.e
hours
2
to
6,
and
hours
17
and
18)
of
the
load
curv
e
for
all
wind
patterns.
Also,
another
dif
fer
ence
between
scheduling
is
presented
at
the
peak
of
the
load
curv
e
(i.e
hours
20
and
21).
Figure
5.
(a)
Comparison
of
thermal
scheduling
between
the
lo
w-wind
a
v
ailability
,
(b),
the
moderate
wind
a
v
ailability
,
(c),
and
high-wind
a
v
ailability
Additionally
,
the
thermal
units
dispatching
under
dif
ferent
wind
a
v
ailability
patterns
sho
ws
that
wind
a
v
ailability
determines
the
dispatching
of
therm
al
units.
The
proposed
system
has
a
limited
generation
portfolio
P
ower
system
oper
ation
considering
detailed
modelling
of
...
(Ser
gio
Cantillo)
Evaluation Warning : The document was created with Spire.PDF for Python.
190
r
ISSN:
2088-8708
with
a
strong
dependence
on
thermal
units
and
lo
w
wind
po
wer
par
ticipation.
this
f
actor
e
xplains
the
closeness
between
thermal
scheduling
and
the
load
curv
e
specially
under
lo
w
wind
a
v
ailability
patterns
and
ho
w
similar
beha
viour
is
maintai
ned
re
g
ardless
of
wind
a
v
ailability
.
In
the
same
w
ay
,
the
thermal
unit
scheduling
between
the
highest
proposed
ESS
capacities
(e.g.
175
and
200
MW)
are
similar
.
This
finding
pro
v
ed
the
misuse
of
ESS
from
a
certain
capacity
and
wind
a
v
ailability
as
mentioned
abo
v
e.
Lik
e
wise,
this
issue
represents
a
non-impro
v
ement
of
the
po
wer
system
performance
as
wel
l
as
a
ne
gligible
reduction
of
thermal
generation
compared
with
increases
in
the
ESS
capacity
.
Moreo
v
er
,
The
ESS
performance
seen
from
its
SoC
during
a
24-hour
period
is
sho
wn
in
Fi
gure
6.
Unlik
e
the
pre
vious
scenario,
It
sho
ws
no
dif
ferences
for
some
of
the
proposed
a
v
ailability
patterns.
Since
in
lo
w
a
v
ailability
pattern,
the
ESS
presents
the
same
beha
vior
re
g
ardless
of
the
increase
in
mar
ginal
cost
(i.e
from
1.0
to
2.0
times).
In
all
cases,
char
ging
and
dischar
ging
patterns
are
presented
depending
on
the
respecti
v
e
wind
pattern
beha
vior
.
Ho
we
v
er
,
there
is
a
consistent
unloading
pattern
during
peak
hours
(i.e.
from
hours
19
to
21).
This
represents
the
correct
ESS
modeling
and
operation
since
it
deli
v
ered
po
wer
during
the
load
peak
as
e
xpected.
Figure
6.
(a)
Comparison
of
ESS
performance
with
re
g
ard
to
the
mar
ginal
cost
increasing,
between
the
lo
w-wind
a
v
ailability
,
(b)
the
moderate
wind
a
v
ailability
,
(c)
and
high-wind
a
v
ailability
Also,
the
ESS
performance
sho
ws
a
direct
influence
by
wind
a
v
ailabili
ty
due
to
the
f
act
that
the
ESS
Int
J
Elec
&
Comp
Eng,
V
ol.
11,
No.
1,
February
2020
:
182
–
200
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Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
191
finds
some
operation
fle
xibility
by
increasing
wind
a
v
ailability
.
Thus,
in
lo
w
wind
a
v
ailability
the
storage
system
in
most
of
the
time
tends
to
char
ge
until
load
peak
hours
re
g
ardless
of
the
mar
ginal
cost
of
the
thermal
units,
while
in
moderate
or
high
wind
a
v
ailability
depending
on
the
mar
ginal
cost
dif
ferent
beha
viors
can
be
presented
(that
is
to
say
po
wer
amounts
and
char
ge
or
dischar
ge
decisions)
of
the
ESS.
Nonetheless,
although
dif
ferent
performances
according
to
the
mar
ginal
fuel
cost
are
presented,
in
general
terms
the
ESS
performed
in
a
similar
w
ay
.
In
other
matters,
the
thermal
units
dispatch
according
to
wind
a
v
ailability
and
compared
to
the
load
curv
e
is
sho
wn
in
Figure
7.
It
sho
ws
similar
beha
viors
between
the
thermal
scheduling
and
the
load
curv
e
for
all
wind
a
v
ailability
profiles,
in
some
cases
(i.e.
hours
1
to
7
in
lo
w-wind
a
v
ailability)
the
load
curv
e
and
the
thermal
units
dispatch
ha
v
e
matched.
Thus,
the
thermal
unit
dispatch
also
sho
ws
fe
w
changes
by
increasing
the
mar
ginal
cost
to
the
proposed
v
alue.
These
changes
were
presented
when
load
f
alls
(i.e.
hours
3
to
7
and
hours
19
to
24)
and
e
xist
high
wind
a
v
ailability
,
as
sho
wn
in
c).
F
or
all
other
wind
a
v
ailability
patterns,
the
same
thermal
units
po
wer
dispatch
w
as
presented.
Figure
7.
(a)
Comparison
of
thermal
unit
scheduling
with
re
g
ard
to
the
mar
ginal
cost
increasing,
between
the
lo
w-wind
a
v
ailability
,
(b)
the
moderate
wind
a
v
ailability
,
(c)
and
high-wind
a
v
ailability
Furthermore,
the
the
wind
a
v
ailability
ef
fect
on
the
po
wer
system
is
e
vident
since
the
dif
ference
be-
tween
load
and
thermal
units
po
wer
is
greater
(i.e.
dif
ferences
between
lo
w
,
moderate
and
high
wind
a
v
ailability
P
ower
system
oper
ation
considering
detailed
modelling
of
...
(Ser
gio
Cantillo)
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