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Aalborg Universitet
Equalization Algorithm for Distributed Energy Storage Systems in Islanded AC
Microgrids
Aldana, Nelson Leonardo Diaz; Hernández, Adriana Carolina Luna; Quintero, Juan Carlos
Vasquez; Guerrero, Josep M.
Published in:
Proceedings of the 41th Annual Conference of IEEE Industrial Electronics Society, IECON 2015
DOI (link to publication from Publisher):
10.1109/IECON.2015.7392827
Publication date:
2015
Document Version
Accepted manuscript, peer reviewed version
Link to publication from Aalborg University
Citation for published version (APA):
Aldana, N. L. D., Hernández, A. C. L., Quintero, J. C. V., & Guerrero, J. M. (2015). Equalization Algorithm for
Distributed Energy Storage Systems in Islanded AC Microgrids. In Proceedings of the 41th Annual Conference
of IEEE Industrial Electronics Society, IECON 2015. (pp. 004661 - 004666). IEEE Press. DOI:
10.1109/IECON.2015.7392827
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Equalization Algorithm for Distributed Energy
Storage Systems in Islanded AC Microgrids
∗† , Adriana C. Luna∗
∗
∗
Nelson L.
L. Dı́az
Dı́az∗†
Nelson
, Adriana C. Luna∗ ,, Juan
Juan C.
C. Vásquez
Vásquez∗,, and
and Josep
Josep M.
M. Guerrero
Guerrero∗
∗∗Department
Department of
of Energy
Energy Technology,
Technology, Aalborg
Aalborg University,
University, Aalborg,
Aalborg, Denmark
Denmark
†† Faculty of Engineering, Universidad Distrital F. J. C., Bogotá, Colombia
Faculty of Engineering, Universidad Distrital F. J. C., Bogotá, Colombia
[email protected], [email protected],
[email protected], [email protected],
[email protected],
[email protected], [email protected]
[email protected]
www.microgrids.et.aau.dk
www.microgrids.et.aau.dk
Abstract—This paper
paper presents
presents aa centralized
centralized strategy
strategyfor
forequalequaAbstract—This
lizingthe
thestate
stateofofcharge
chargeof of
distributed
energy
storage
systems
izing
distributed
energy
storage
systems
in
in an
islanded
microgrid.The
Thestrategy
strategy isis based
based on
on aa simple
simple
an
islanded
ACacmicrogrid.
algorithm denoted
denoted as
as equalization
equalization algorithm,
algorithm, which
which modifies
modifies the
algorithm
the
charge or
or discharge
discharge ratio
ratio on
on the
the time,
time, for
for distributed
distributed energy
energy
charge
storage systems
systems, within
within aa determined
order
to
storage
determined period
periodofoftime
timein in
order
equalize
the the
statestate
of charge.
The The
proposed
approach
has been
to
equalize
of charge.
proposed
approach
has
testedtested
in a MATLAB/Simulink
modelofof the
the microgrid
microgrid where
where the
been
in a MATLAB/Simulink
the
performance of
of the
the proposed
proposed strategy
strategy was
was verified.
verified.
performance
Keywords—Distributed energy
energy storage
storage systems,
systems, Droop
Droop control,
control,
Keywords—Distributed
Equalization
algorithm,
State
of
Charge.
Equalization algorithm, State of Charge.
I. IINTRODUCTION
NTRODUCTION
I.
A microgrid
microgrid is
is an
an integration
integration of
of distributed
distributed energy
energy reA
resources,
loads
and
energy
storage
units
into
a
controllable
sources loads and energy storage units into a controllable
system, which
which is
is able
able to
to operate
operate either
either in
in grid
grid connected
connected or
system,
or
islanded
mode
[1].
Particularly,
islanded
microgrids
play an
islanded mode [1]. Particularly, islanded microgrids play
an
important role
role when
when economic
economic and
and environmental
environmental issues
issues do
do not
important
not
allow
interconnection
with
the
main
power
grid
[2].
Nowadays,
allow interconnection with the main power grid [2]. Nowadays,
renewable energy
energy sources
sources (RES)
(RES) such
such as
as photovoltaic
photovoltaic and
and wind
renewable
wind
turbine
generators
have
been
widely
used
in
order
to
replace
turbine generators have been widely used in order to replace
traditional coal,
coal, oil
oil and
and other
other non-renewable
non-renewable energy
energy resources.
resources.
traditional
Consequently, energy storage systems (ESS) have become an
Consequently, energy storage systems (ESS) have become an
indispensable element into a microgrid based on RES units for
indispensable element into a microgrid based on RES units for
smoothing the intermittent nature of RES’s [3].
smoothing the intermittent nature of RES’s [3].
As a matter of fact, the current trend is oriented to
As a matter of fact, the current trend is oriented to
distributed ESS’s instead of aggregated ESS’s. To be more
distributed ESS’s instead of aggregated ESS’s. To be more
precise, an ESS is associated to each RES integrated into
precise, an ESS is associated to each RES integrated into
a microgrid. As a result, more redundancy, energy support,
a microgrid. As a result, more redundancy, energy support,
and constant power production can be ensured when RES
and constant power production can be ensured when RES
are used [4]–[7]. Valve regulated lead-acid (VRLA) batteries
are used [4]–[7]. Valve regulated lead-acid (VRLA) batteries
are commonly used in islanded microgrids, since they offer
are commonly used in islanded microgrids, since they offer
a good commitment between deep-cycle life, transportability,
aavailability
good commitment
between
deep-cycle
transportability,
and cost [7],
[8]. Fig.
1 showslife,
the basic
scheme of
availability
and
cost
[7],
[8].
Fig.
1
shows
the
basic
scheme
an islanded microgrid composed by two RES, two
ESS’s
and
of
an
islanded
microgrid
composed
by
two
RES,
two
ESS
and
the load.
the load.
On top of that, when distributed ESS’s are used, it is
On topcoordinated
of that, when
distributed
ESS them
are used,
it is required
required
operation
between
in order
to avoid
coordinated
operation
them instorage
order to
deep-discharge
in onebetween
of the energy
unitavoid
and deepoverdischarge
of theDifferences
energy storage
unitSoC
andcould
over-charge
in
charge in intheone
others.
at the
limit the
the
others.
Differences
at
the
SoC
could
limit
the
life-time
life-time of the ESS with the smallest SoC, since this ESS
of
with tothebigger
smallest
since this[9].
ESS
will be
willthebeESS
exposed
deepSoC,
of discharge
Therefore,
exposed
biggerare
deep
of discharge
[9]. Therefore,
when the
the
when theto ESS’s
charged,
it is desirable
to prioritize
ESS
are
charged,
it
is
desirable
to
prioritize
the
charge
of
the
charge of the unit with the smallest state of charge (SoC). On
unit
with the when
smallest
charge
(SoC). the
On unit
the contrary,
the contrary,
the state
ESS’sofare
discharged,
with the
when the ESS are discharge, the unit with the highest SoC
WT
AC Bus
AC/AC Converter
DC/AC Bidirectional
Battery Array
Converter
AC Bus
IL
IL
Zrot
IWT V
WT
Vbat
ESS Primary Control
RES Primary Control
Battery Array
DC/AC Bidirectional
Converter
AC Bus
AC Bus
IL
IL
I bat Vbat
ESS Primary Control
I bat
DC/AC Converter
Load
VPV
PV Array
I PV
RES Primary Control
Fig. 1:
1: Islanded
Islanded AC
AC microgrid
microgrid configuration.
configuration.
Fig.
should provide
moreprovide
powermore
to the
microgrid
the others
highest
SoC should
power
to the than
microgrid
than
in order
energy
balance
[11].[10], [11].
the
otherstoinensure
order stored
to ensure
stored
energy[10],
balance
Commonly, droop
droop control
control strategies
strategies are
are used
used in
in order
order to
to
achieve power sharing
sharing between
between units
units [12].
[12]. Therefore,
Therefore, conconventional
loops for
for power
power sharing
sharing at
at each
each ESS
ESS are
is
ventional control
control loops
complemented
with
adaptive
strategies
which
adjust
the
droop
complemented with adaptive strategies which adjust the droop
coefficients
coefficients in
in accordance
accordance to
to the
the SoC.
SoC. In
In this
this way,
way, itit isis
possible
possible to
to reach
reach asymptotic
asymptotic approach
approach of
of the
the SoC.
SoC. At
At this
this
sense,
several
different
approaches
have
been
proposed
sense, several different approaches have been proposed for
for
equalizing
such as
as in
equalizing the
the SoC
SoC atat distributed
distributed ESS’s
ESS such
in [6],
[6], [7],
[7],
[13]–[19].
of them
them have
have been
been applied
applied to
to DC
dc
[13]–[19]. However,
However, all
all of
microgrids.
microgrids. In
In addition,
addition, equal
equal capacity
capacity isis assumed
assumed for
for all
all the
the
distributed
distributed ESS.
ESS. Besides,
Besides, the
the equalization
equalization time
time isis very
verysensitive
sensitive
to
the
parameters
of
the
equalization
functions.
to the parameters of the equalization functions. Because
Because of
of
this,
this, the
the stability
stability of
of the
the system
system can
can be
be compromised
compromised when
when
shorter
shorter equalization
equalization times
times are
are sought.
sought. Another
Another approach
approach which
which
considers
differences
at
the
capacity
of
the
energy
considers differences at the capacity of the energy storage
storage unit
unit
is
is presented
presented in
in [6].
[6].In
Inthis
thiscase,
case,the
theESS’s
ESS are
are based
based on
on electricelectricdouble-layer
double-layer capacitors
capacitors rather
rather than
than on
on batteries.
batteries. Although,
Although, the
the
stored
stored energy
energy is
is balanced,
balanced, long
long time
time and
and additional
additional control
control
loops
loops are
are required.
required.
This paper proposes a new function for the energy manThis paper
a new
functionacfor
the energy
manageagement
systemproposes
(EMS) of
an islanded
microgrid
based
on a
ment
system
(EMS)
of
an
islanded
AC
microgrid
based
on a
centralized equalization algorithm which achieves asymptotic
centralized
equalization
algorithm
which
achieves
asymptotic
approach of the SoC at distributed ESS based on batteries. The
approach equalization
of the SoC atalgorithm
distributed
ESS based
on batteries.
The
proposed
weights
the droop
coefficients
proposed
equalization
algorithm
weights
the droop
coefficients
of
the droop
control loops,
within
a defined
window
of time,
of the
droop
control asymptotic
loops, within
a definedofwindow
of time,
in
order
to obtain
approach
the SoC.
The
in
order
to
obtain
asymptotic
approach
of
the
SoC.
The
adaptive value of the droop coefficients is bounded what
adaptive
value
of
the
droop
coefficients
is
bounded
what
ensures the stability of the microgrid. Simulation results in
the stability of
the of
microgrid.
Simulation
results
in
aensures
MATLAB/Simulink
model
the microgrid
show the
effecativeness
MATLAB/Simulink
model
of
the
microgrid
show
the
effecof the proposed model even under differences at the
tiveness of
model even under differences at the
capacity
of the
eachproposed
ESS.
capacity of each ESS.
mportant to say that this paper will only consider the
of the microgrid when the ESS’s are being charged
rged. Anyhow, the operation of the microgrid should
emented by appropriate charge strategies that avoid
overcharge in
batteries,
such
as
[7],will
and
[19],
ItItisthe
to
that
paper
only
consider
isimportant
important
to say
say
that this
thisin
paper
will
only
consider the
the
operation
of
the
microgrid
when
the
ESS’s
are
being
charged
operation
of
the
microgrid
when
the
ESS’s
are
being
operationor
of actions
the microgrid
the ESS’s
s load-shedding,
for when
limiting
the deep of charged
or
discharged.
Anyhow,
the
operation
of
the microgrid
microgrid should
should
or
Anyhow,
ordischarged.
discharged.
Anyhow, the
the operation
operation of
of the
of the batteries
as proposed
in
[20].
be complemented by appropriate charge strategies that avoid
Z*
=Z*-m P
0 Bat1
Z
Z*
Z*
Z*
Z
(rad/sec)
Z (rad/sec)
(rad/sec)
Z
Z
=Z
Z
*-m P
P
=Z*-m P
Z=
Z*-m
Z
00 Bat2
Bat2=Z*-m 00P Bat1
Bat1
0 Bat2
Z
Z
Z
Z
Z
P
0 Bat1
Bat1 =
P
(a)
Z (rad/sec)
(W)
PP (W)
Bat1
(a)
(a)
Z=Z*-m D P
P (W)
Bat2
P
P
P
=P
Bat2
Bat1
Bat2
Bat1=
Bat2
ted in orderThe
to obtain
equalization
of Section
SoC. After
Z*
The paper
paper isis organized
organized as
as Follows.
Follows. Section
Section II
II explains
explains the
the
follows.
on III presents
the
centralized
equalization
algorithm,
operation
operationof
ofthe
themicrogrid
microgrid and
and how
how conventional
conventional droop
droop control
control
Z
Z (rad/sec)
(rad/sec)
y sectionsloops
IVadjusted
andadjusted
Vininpresent
resultsof
are
order
to
obtain
SoC.
After
Z
are
adjusted
order
toSimulation
obtain
equalization
ofofand
SoC.
Z*
are
in order
to
obtainequalization
equalization
SoC. After
Z*
that,
section
III
presents
the
centralized
equalization
algorithm,Z=Z*-m0D1PBat1
that,section
sectionIII
IIIpresents
presentsthe
thecentralized
centralized equalization
equalization algorithm,
that,
ns respectively.
I.
Z=Z*-m P
0 Bat2
be
becomplemented
complemented by
by appropriate
appropriate charge
charge strategies
strategies that
that avoid
avoid
excessive
overcharge
in
the
batteries,
such
as
in
[7],
and
[19],
excessive
overcharge
in
the
batteries,
such
as
in
[7],
and
[19],
aper is organized
as
Follows.
Section
II
explains
the
as
well
as
load-shedding,
or
actions
for
limiting
the
deep
as
well
as
load-shedding,
or
actions
for
limiting
the
deep
of
as well as load-shedding, or actions for
of
of the microgrid
how
conventional
droop
control
Z (rad/sec)
discharge
of
the
batteries
as
proposed
in
[20].
discharge
of
batteries
as
in
dischargeand
ofthe
the
batteries
as proposed
proposed
in [20].
and
finally
andfinally
finally sections
sections IV
IV and
and V
V present
present Simulation
Simulation results
results and
and
simulation
conclusions
respectively.
conclusionsrespectively.
respectively.
conclusions
Z (rad/sec)
Z=Z*-m D P
0 2 Bat2
Z
Z==Z
Z*-m
*-m0DD2P
PBat2
*-m DD PP
ZZ==ZZ*-m
Bat2
000 22 Bat2
0 1 Bat1
Bat2
00 22 Bat2
Z=Z*-m D P
Z
*-m0D
D1P
PBat1
Z==Z
Z*-m
0 1 Bat1
ZZ
Z==Z
Z*-m
*-m DD P
P
Z
00 11 Bat1
Bat1
Z*
Z*
0 1 Bat1
D ROOP C ONTROL L OOP A DJUSTMENT
P
II.
DDROOP
ROOP
CCONTROL
ONTROL
LLOOP
OOP
A
DJUSTMENT
ROOP
ONTROL
II. D
ROOPC
ONTROL L
OOP A
ADJUSTMENT
DJUSTMENT
II.
0 2 Bat2
(rad/sec)
ZZ(rad/sec)
P
Bat1
P
PBat1
Bat1
(b)
P (W)
Bat2
P
PBat2
Bat2
P
P (W)
Bat1
(c)
PPBat2
Bat2
Bat2
PPBat1
Bat1
P (W)
(W)
P
P (W)
(W)
P
Bat1
P
Bat2
(c)
(c)
(b)
ally, in an islanded microgrid all the primary conFig.
2:
Active
power
sharing:
(a)
for
equal
droop
coeffiNormally,
in
an
islanded
microgrid
all
the
primary
conNormally,
in
an
islanded
microgrid
all
the
primary
conNormally,
in an islanded
microgrid
all themode
primary conequal droop
droop coefficoeffisharing: (a)
(a) for
for equal
Fig. 2: Active power sharing:
coeffire typicallytrollers
set
up
operate
are
typically
set
up
to
operate
in
voltage
control
mode
trollers
areto
typically
setin
upvoltage
to operate
operatecontrol
in voltage
voltage control
control mode
mode
cients,cients,
(b) (b)
weighted
droop
coefficients
for
ESS
discharging,
trollers
are
typically
set
up
to
in
ESS discharging,
discharging,
coefficients for
weighted droop coefficients
coefficients
for ESS
y following
conventional
control
strategy.
In
(VCM)
by
following
conventional
droop
control
strategy.
In weighted
(VCM)
by following
followingdroop
conventional
droop
control strategy.
strategy.
(VCM)
by
conventional
droop
control
In
charging.
coefficients for
for
ESS
coefficients
ESS
charging.
(c) weighted
droopcoefficients
coefficients
(c)
droop
for
ESS
charging.
this
way,
isispossible
possible
to
regulate
the
bus
voltage
and
frequency
thisto
way,
possible
toregulate
regulate
thebus
busvoltage
voltage
and frequency
frequency
it is possible
regulate
the bus
voltage
and
frequency
this
way,
itititis
to
the
and
and
achieve
good
power
sharing
between
units
[12].
Even
and
achieve
good
power
sharing
between
units
[12].
Even
achieve
good power
sharing
between
[12]. Even
eve good and
power
sharing
between
units
[12].units
Even
PP
though,this
thisapproach
approachis
notthe
themost
most advisable
advisable for
for intermittent
intermittent
though,
this
approach
isisnot
not
the
most
advisable
for
intermittent
though,
P
his approach
is not
theasasmost
advisable
for
intermittent
Bat1
sources
such
RES
units,
which
are
more
likely
to
operate
sources
such
RES
units,
which
are
more
likely
to
operate
sources such as RES units, which are more likely to operate
m
under
algorithms
of
maximum
power
tracking
(MPPT)
in
order
uch as RES
units,
which
are
more
likely
to
operate
under
algorithms
of
maximum
power
tracking
(MPPT)
in
order
under algorithms of maximum power tracking (MPPT) in order
PP
toobtain
obtainfrom
frompower
themthe
the
maximum(MPPT)
amount of
ofin
available
energy.
tomaximum
obtain
from
them
the
maximum
amount
of
available
energy.
orithms ofto
tracking
order energy.
them
maximum
amount
available
P
Because of
of this,
this, RES
RES units
units assume
assume the
the role
role of
of grid-following
grid-following
Bat2
from themBecause
the
maximum
amount
of available
energy.
units,
behaving
as
current
sources
and
their primary
primary
control
are
units,
behaving
current
their
are
Because
of as
this,
RESsources
units and
assume
the rolecontrol
of gridm
of this, RES
units
assume
role
of grid-following
set up
up toto operate
operate
on the
current
control
mode (CCM)
(CCM)
[20],
[21].
set
on
current
control
mode
[20],
[21].
following
units,
behaving
as
current
sources
and their
primary
Consequently,
the
ESS
units
assume
the
role of
ofcontrol
grid-forming
Consequently,
ESS
units
assume
role
grid-forming
controllers
are the
setand
up their
to operate
onthe
current
aving as current
sources
primary
control
are mode
units
operating
inConsequently,
VCM
being(CCM)
the ESS
responsible
of regulating
regulating
units
operating
in
VCM
being
the
responsible
of
(CCM)
[20], control
[21].
units assume
the role
operate on
current
mode
[20],
[21].
thegrid-forming
AC bus.
bus. Meanwhile,
Meanwhile,
they will
will
be charged
charged
orresponsible
discharged
the
AC
they
be
or
discharged
of
units operating
in
VCM
being the
of the
the equalization
Fig. 3: Expected behavior of
equalization algorithm.
algorithm.
ently, the ESS
units
thethe
role
of grid-forming
order
compensate
power
unbalance
between
the
inin regulating
order
toto assume
compensate
power
unbalance
the
of
the ac bus. the
Meanwhile,
they willbetween
be charged
rating in or
VCM
being
the
responsible
regulating
generated
and consumed
consumed
power
[19].of the
generated
and
[19].
discharged
in
order
topower
compensate
power unbalance
Timeis
(1)
is(s)now
now rewritten
back to the point, equation (1)
rewritten as
as follows
follows
between
the
generated
and
consumed
power
[19].
bus. Meanwhile,
they
will
be
charged
or
discharged
When the
the ESS
ESS units
units are
are in
in the
the process
process of
of charge
charge or Fig. 3: Expected behavior
When
∗
of
the
equalization
algorithm.
ω = ω ∗ − m ·· α
(2)
αthe
Pequalization
ii ·· P
Bati
Bati
to compensate
unbalance
discharge,
thepower
powerunits
balance
is managed
managed
by P
P
−charge
droop
Fig. 3: Expected behavior00of
algorithm.(2)
discharge,
the
power
balance
by
−
ωω droop
Whenthe
the
ESS
are is
in
thebetween
process
ofthe
or
control power
loops
[12].
Therefore,
themanaged
frequency
atPthe
the
common
and consumed
[19].
control
loops
Therefore,
the
frequency
common
discharge,
the [12].
power
balance is
byat
−ω
droop
E QUALIZATION
LGORITHM
III. equation
QUALIZATION
LGORITHM
to the point,
(1) is AAnow
rewritten as follows
AC
bus
is
established
by
the
following
equation,
AC
bus
is
established
by
the
following
equation,
control loops [12]. Therefore, the frequency at the common back
ac
account when the weighting factors αi are determined. To get
The
algorithm
is
based
on
the
fact
that
of
the ESSbusunits
are inbythe
process equation,
of charge or
is established
the∗∗∗following
fact rewritten
that the
the rate
rate
of change
change
back to the point, equation
as follows
= ωω −
−m
m000 ··PPBati
(1)
ωdirectly
= ω ∗proportional
− m(1)0 the
·isαnow
·P
(2)
Bati
ωω =
(1)
ito
Bati
Bati
of
the
SoC
is
directly
the
battery
power
of
the
SoC
is
proportional
to
the
battery
power
, the power balance is managed
by P − ω droop
∗
∗
ω = ω − m0 · αi · PBati
(2)
ω = ω − m0 · PBati
(1)
the
droop
coefficient,at
is the
thecommon
angular frequency
frequency
where
m000 isis the
P
∝ m SoCi
(3)
oops [12]. where
Therefore,
the
frequency
the
droop
coefficient,
ωω is
angular
m
PBati
(3)
Bati ∝ mSoCi
∗∗∗ is the reference of the angular
III.
E
QUALIZATION
A
LGORITHM
at
the
common
bus,
ω
at
the
common
bus,
ω
is
the
reference
of
the
angular
s established
bymthe
following
equation,
where
droop coefficient,
ω is the angular frequency
0 is the
where
m
is
the
rate
of
change
for
the
SoC
at
each
ESS.
SoCiIII.
LGORITHM
where mSoCi
is theE QUALIZATION
rate of change A
for
the SoC at each ESS.
frequency,
the
active
power
at each
eachofi-th
i-th
ESS
unit
Bati bus,
frequency,
PPBati
isis the
power
at
unit
Bati
at
the common
ω ∗active
is the
reference
theESS
angular
Foralgorithm
that reason,
reason, is
by based
adjusting
m
itit is
achieve
SoCi
The
on
the
fact
that
theto
of change
For
that
by
adjusting
m
is possible
possible
torate
achieve
(i
=
[1,
·
·
·
,
n])
and
n
is
the
number
of
distributed
active
SoCi
(i = [1,
· Bati
, n]) and
is the power
numberat ofeach
distributed
∗ · ·P
is then active
i-th(1)
ESSactive
unit
The algorithm
isthebased
on
the fact thatESS
the as
rate
of
change
an
equalization
of
SoC
at
distributed
is
shown
in
ωfrequency,
=
ω
−
m
·
P
an
equalization
of
the
SoC
at
distributed
ESS
as
is
shown
in
0
Bati
generators
(RES+ESS)).
When
the
same
droop
coefficient
of
the
SoC
is
directly
proportional
to
the
battery
power
generators
(RES+ESS)).
When
the
same
droop
coefficient
(i = [1, · · · , n]) and n is the number of distributed active
of
Fig.the3.SoC is directly proportional to the battery power
Bat1
Bat2
88
88
88
86
86
86
Bat1
Bat1
Bat1
(Decreases)
(Decreases)
(Decreases)
m
m
mSoC1
SoC1
SoC1
84
84
82
82
82
80
80
(Decreases)
SoC1
SoC
SoC (%)
(%)
84
Bat2
Bat2
Bat2
(Increases)
(Increases)
(Increases)
SoC (%)
78
78
80
m
mSoC2
m
SoC2
SoC2
76
76
78
76
74
72
(Increases)
74
74
SoC2
72
72
70
70
70
68
68
68
000
11
1
2
22
333
444
555
666
777
Time
Time (s)
(s)
Time
(s)
70
68
0
(m000))isis applied
applied
to each
each ESS
ESS
unit,the
thesame
powerdroop
is shared
shared
equally
(m
to
unit,
the
power
is
equally
generators
(RES+ESS)).
When
coefficient
Fig. 3.
1
2
3
4
5
6
7
between
ESS units
units as
as
we
can see
see
in Fig.
Fig.frequency
2a.
coefficient,
ω we
is can
the
angular
∝mm
(3)
PBati
(3)
First of
of all,
all, the
the P
SoC
at
each
ESS
is
between
ESS
in
2a.
0 is the droop
Bati
SoCi
SoCi
First
SoC
at ∝
each
ESS
is estimated
estimated by
by ampereampere(m
0 ) is applied to each ESS unit, the power is shared equally
∗
hour (Ah)
(Ah) counting
counting method
ommon bus,
ω
is
the
reference
of
the
angular
hour
method
between
ESS
units
as
we
can
see
in
Fig.
2a.
Under the
the discharge
discharge process,
process, for
for balancing
balancing the
the SoC,
SoC, the
the
mSoCi
rate of
of change
forfor
the the
SoC SoC
at eachatESS.
Under
Δt
wherewhere
mSoCi
is isthetherate
change
each ESS.
y, PBati isESS
the
active
power
at
each
i-th
ESS
unit
ESS
with
the highest
highest
SoC
should
supply
more power
power to
to the
the
Δtit is possible
I
(τ
)to
Bati
For
that
reason,
by
adjusting
m
achieve
with
the
SoC
should
supply
more
I
(τ
)
SoCi
Under the discharge process, for balancing the SoC, the
Bati
SoC(Δt)
=
SoC(0)
−
η
dτ
(4)
For that
reason,
byof SoC(0)
adjusting
mSoCiηBati
itESS
isC possible
achieve
Bati
microgrid
than
the
others. On
On
the
other hand,active
when the
the ESS
−
dτ to
(4)
Bati =
Bati
Bati
· · · , n]) and
nwithis the
thehighest
number
of the
distributed
microgrid
than
the
others.
other
anSoC(Δt)
equalization
the SoCBati
at distributed
as is shown
in
Bati
ESS
SoC should
supplyhand,
morewhen
power toESS
the
00
C
Bati
units
are
being
charged,
the
ESS
with
the
smallest
SoC
should
an
equalization
of
the
SoC
at
distributed
ESS
as
is
shown
in
units are When
being
theOn
ESSthe
with
thecoefficient
smallest
SoCthe
should
Fig. 3.
microgrid
than charged,
thethe
others.
other
hand,
when
ESS
s (RES+ESS)).
same
droop
where SoC(0)
SoC(0)Bati
the
initial
SoC,
C
is
the
capacity
Bati is
Bati
get more
more energy
energy from
from the
the microgrid
microgrid than
than the
the others.
others. This
This
where
is
the
initial
SoC,
C
is
the
capacity
Bati
get
Fig.
3.
units are
being
charged,
the ESS is
with
the smallest
SoC should
pplied to each
ESS
the power
shared
in (A/h),
(A/h),
is SoC
the
charging/discharging
efficiency,
and
First ofηηall,
each ESS is estimated
by ampereBatithe
behavior
canunit,
be achieved
achieved
by weighting
weighting
the equally
droop coefficient
coefficient
in
is
the at
charging/discharging
efficiency,
and
Bati
behavior
can
be
by
the
droop
get
more
energy
from
the
microgrid
than
the
others.
This
IBati(τ
(τ )) is
iscounting
the instantaneous
instantaneous
current
at
each
battery
array
[8].
hour
(Ah)
method
(m
)
by
a
factor
α
as
is
shown
in
Fig.
2b
and
Fig.
2c
for
ESS units behavior
as
we
can
see
in
Fig.
2a.
0
i
I
the
current
at
each
battery
array
[8].ampereBatiof all, the SoC at each ESS is estimated by
(m00) by can
a factor
αii as is by
shown
in Fig.the2bdroop
and Fig.
2c for First
be
achieved
weighting
coefficient
By considering
considering aa constant
constant current
the
power
at
each
discharge and
and charge
charge of
of ESS
ESS units
units respectively.
respectively. In
In the
the case
case of
of
Z charge,
By
current
charge,
the
power
at
each
discharge
∆t
(m
by and
a factor
α
as isassumed
shown inthat
Fig.
2b and >Fig.
2c for
hour (Ah)
method
0 ) 2b
i it
IBati (τ )
batterycounting
array can
can be
approximated
as
Fig.
Fig. 2c
2c
SoC
SoC
Bat2 >
Bat1..
battery
array
approximated
r the discharge
for
balancing
the
SoC,
the
SoC(∆t)
SoC(0)
dτ (4)
Fig.
2b process,
and
Fig.
itofisis
assumed
that
SoC
SoC
Bat2
Bati = be
Bati − as ηBati
Bat2
Bat1
discharge
and
charge
ESS
units
respectively.
In
the
case
of
CBati
In
the
figures,
it
is
possible
to
see
that
for
the
charging
process
Δt
0
In
the
figures,
it
is
possible
to
see
that
for
the
charging
process
≈
V
∗
I
P
h the highest
SoC
should
supply
more
power
to
the
Bati
Bati
Fig.
2b |and
2c On
it istheassumed
SoCdischarging
IBati (τ (5)
)(5)
Bat2 > SoC
Bat1 .
PBati
Bati ≈ V Bati ∗ I Bati
|PBat1
>|P
|PFig.
contrary,that
for the
the
process
Bat2|.|.On
|P
|
>
the
contrary,
for
discharging
process
SoC(Δt)
=
SoC(0)
−
η
dτ (4)
Bat1
Bat2
Bat1
Bat2
Bati
Bati
Bati
In
the
figures,
it
is
possible
to
see
that
for
the
charging
process
where
SoC(0)
is
the
initial
SoC,
C
is
the capacity
Bati
Bati
d than the others.
On
the
other
hand,
when
the
ESS
where
(V
|P
|
>
|P
|,
this
characteristic
has
to
be
taken
into
)
is
the
nominal
voltage
of
the
battery
array.
Bat2 > |P Bat1|, this characteristic has to be taken into
Bati ) is the nominal voltage of the battery
CBati
where
(VBati
|PBat1
array.
0
Bat2|| >
Bat1
Bat2
Bat1
|P
|P
|.
On
the
contrary,
for
the
discharging
process
in
(A/h),
η
is
the
charging/discharging
efficiency,
and
Bat2
Bati
account
when
thewith
weighting
factors ααi are
Despite this
this approximation is
accurate,
itit provide
us
are determined.
get
being charged,
the
ESS
the smallest
SoC
should To get
account
when
the
weighting
factors
is not
not at
accurate,
provide
us
ii hasdetermined.
|P
to be takenTointo
IDespite
(τ ) is theapproximation
instantaneous
current
eachCbattery
array
[8].
Bat2 | > |PBat1 |, this characteristic
Bati
where
SoC(0)
is
the
initial
SoC,
is
the
capacity
Bati
Bati
energy from the microgrid than the others. This
in (A/h), ηBati is the charging/discharging efficiency, and
can be achieved by weighting the droop coefficient
I
Bati (τ ) is the instantaneous current at each battery array [8].
a factor αi as is shown in Fig. 2b and Fig. 2c for
By
considering a constant current charge, the power at each
and charge of ESS units respectively. In the case of
By considering a constant current charge, the power at each
battery array can be approximated as
Obtain
External
Data
(5)
PBati ≈ VBati ∗ IBati
where (VBati ) is the nominal voltage of the battery array.
Despite this approximation is not accurate, it provides us
enough information about the battery capacity at every ESS.
Then, from (4) and (5), it is possible to obtain
∆SoCBati VBati CBati
PBati ≈ −
≈ −mSoCi KBati (6)
∆t
ηBati
(Power and SoC)
Solve
X  A1  B
No
Charge
If
where, mSoCi is the rate of the SoC, and KBati is a proportionality constant that depends on the main parameters of the
ESS.
In a general case, where n distributed active generators
(RES+ESS) are integrated into the microgrid, it is easy to
derive the power balance equation as:
n
X
i=1
PBati +
n
X
i=1
i=1
(7)
PRESi − Pload = 0
−mSoCi KBati +
n
X
i=1
PRESi − Pload = 0
(8)
SoC(0)Bati + mSoCi ∆t = SoC(0)Bat(i+1) + mSoC(i+1) ∆t
Reorganizing the equation system formed by expressions
(8) and (9), we can derive the following symbolic matrix
representation as
(10)
[A][X] = [B]
and
If e = 1 & v = i;
If e = i + 1 & v = i;
If e = i + 1 & v = i + 1;
Otherwise .
(11)
is the entry in the e-th row and v-th column of A.
T
(12)
[X] = [mSoC1 , mSoC2 , · · · , mSoCn ]


[B] = 

Discharge
If
SoC (0) Bat1  SoC (0) Bat 2
Yes No
1   K min K max 
 2  1  K Bat1mSoC1 K Bat 2 mSoC 2 
Wait until
Time  t
No
Yes
Pn
−( i=1 PRESi − Pload )
(SoC(0)Bat2 − SoC(0)Bat1 )
..
.
(SoC(0)Batn − SoC(0)Batn−1 )




(13)
Consequently, the adequate values for each mSoCi that
ensure the equalization of the SoC within a defined period
of time (∆t) can be obtained as
[X] = [A]−1 × [B]
1   2  K Bat 2 mSoC 2 K Bat1mSoC1 
END
When an equalization of the SoC is required within a
defined period (∆t), SoC(∆t)Bat(i−1) = SoC(∆t)Bati =
SoC(∆t)Bat(i+1) . Because of this, the straight-line equation
of a particular i-th ESS unit can be equalized with the straightline equation of other i-th ESS unit as
where, [A] = (ae,v )nxn

−KBati ,



∆t,
ae,v =

−∆t,


0,
SoC (0) Bat1  SoC (0) Bat 2
Yes
 2   K min K max 
where Pload is the load consumption, and PRESi is the power
supplied for each RES. Combining (6) and (7), we have:
n
X
If Pbat>0
(14)
Fig. 4: Equalization algorithm diagram.
The main task of the equalization algorithm is to solve the
equation (14), in order to obtain the values of mSoCi . Once the
value for each mSoCi is calculated, the weighting factor αi in
(2) is obtained for each ESS droop control loop in accordance
to:
α1 · PBat1 = α2 · PBat2 = αi · PBati
(15)
Then, the next step in the algorithm is to identify if
the ESS’s are being charged or discharged. Afterwards, it
(9) is necessary to identify which ESS has the biggest value of
SoC. The idea is to weight the nominal droop factor m0
in accordance to the SoC and battery array capacity. To be
more precise, during the operation of the algorithm, when the
ESS units are being charged, the largest weight is assigned to
the ESS unit with the biggest value of SoC. This maximum
weight is defined by (Kmin /Kmax ), where Kmin and Kmax
are the minimum and maximum values of the proportionality
constant defined in (6). In this way, it is ensured that the droop
coefficient (α·m0 ) will never be bigger than its nominal value,
what avoids under-damped behaviors in the response of the
microgrid [22]. On the contrary, for the process of discharging
the ESS’s, the largest value of the weighting factor will be
assigned to the ESS unit with the lowest SoC. To illustrate, the
algorithm for two active generators based microgrid (n = 2) is
summarized in Fig. 4, where the initial step of the centralized
algorithm is to obtain the external data from the distributed
units.
Since the proposed algorithm is based on simple matrix
operation, the computational time is very small (around 0.15s).
This time can be negligible compared with the time scale
required for charging batteries (normally hours).
Apart from that, since the equalization is only defined
during a specified period, it is required to define how the
weighting factor will be established during periods of no equalization. In this case, a similar charge/discharge rate is expected
for each i-th ESS, this is (mSoCi−1 = mSoCi = mSoCi+1 ).
AC Bus
EMS
AC Bus
AC/AC Converter
y EMS
MPPT
IWT V
WT
Vbat
RES Primary Control
Battery Array
I PV
VPV
IL
IL
rot
IL
DC/AC Bidirectional
Battery Array
Converter
AC Bus
DC/AC Bidirectional
Converter
xRES 1
xESS 1
ESS Primary Control
AC Bus
AC Bus
IL
xLOAD
IL
DC/AC Converter
Load
I bat Vbat
ESS Primary Control
xESS 2
 PLL
I bat
VPV
PLL
PV Array
abc
dq
 PLL
 PLL
abc
dq
Current
Control Loop
abc
dq
abc
dq
I*
+
PI
-
P*
Q*
VCdq
xESSi
PRESi
Power
Calculation
I PV
CCM
Current
Reference
Generator
 PLL
I Ldq
VCdq
 PLL
PWM
Encoder
RES Primary Control
xRES 2
Communication channel
WT
PV Array
DC/AC Converter
Communication Channel
RES Primary Control
Fig. 5: Diagram of the AC islanded microgrid with centralized
EMS.
Fig. 6: Control diagram for RES.
DC/AC Bidirectional
Converter
Battery Array
AC Bus
IL
Kmin
αi =
KBati
(16)
I bat
Communication channel
This is also the behavior expected once the SoC’s have been
equalized. Regarding differences at the ESS’s capacities, the
largest value of the weighting factor (αi = 1) will be assigned
to the ESS with the smallest capacity. Meanwhile, the others
ESS units will get a weighting factor in accordance to:
xESSi
SoC
Encoder
i
Decoder
SoC
Estimator
K Bati

-
*
+
+
E
-
E*
Voltage
Reference
Generator
Vdq* +
-
 ref
Kq
m0
Droop Coefficients
IV.
O PERATION OF THE M ICROGRID
The data sent from each RES unit (XRESi ), each ESS unit
(XESSi ), and the load (XLOAD ) are set as
(17)
T
XESSi = [KBati , SoCBati ]
XLOAD = [Pload ]
I Ldq
 ref
Q
 ref
abc
dq
VCdq
Power
Calculation
P
ESS Primary Control
Meanwhile, the ESS operate in voltage control mode
(VCM) being responsible of regulating the bus voltage. At
this mode, the batteries will be charged or discharged in order
to compensate the unbalance between the energy generated by
RES and load consumption [19], [13]. The power unbalance is
shared between ESS by means of conventional droop control
loop adjusted by the weighting factor αi in order to achieve
SoC equalization. In this case, a typical double-loop VCM
controller is implemented for a bidirectional inverter, as can
be seen in Fig. 7. The reactive power flow Q is equally shared
between distributed ESS in accordance to conventional Q − E
droop control loops as
(18)
(19)
The data sent from the EMS to each RES unit YEM S , is
just the weighting factor (αi )
YEM S = [αi ]
VCM
 ref
abc
dq
Fig. 7: Control diagram for ESS.
The general scheme of the microgrid considered for this
study is composed by two RES generators (a photovoltaic
(PV) generator and a wind turbine (WT) generator), two ESS
units based on batteries, a critical load, a centralized EMS
for performing the equalization algorithm and a dedicated
full-duplex communication channel as can be seen in Fig. 5.
User Datagram Protocol (UDP) is used for interchanging data
between each distributed energy unit and the EMS.
XRESi = [PRESi ]
Current
PWM
Control Loop
abc
PI
dq
-
I* +
PI
(20)
As aforementioned, in islanded operation for charging/discharging process of the ESS units, the RES units assume
the role of grid-following units operating under (CCM) inner
loop that follows maximum power point tracking (MPPT)
algorithm. MPPT strategies are out of the scope of this paper,
interested readers may also refer to [23] and [24]. To get back
to the point, the inductor current of the converter is controlled
by typical inner current loops. Fig. 6 shows the scheme of
the inner current control for a RES based on PV generator.
In general, the control scheme for a RES based on WT is the
same as shown in Fig. 6 taking into account differences at the
power converter and MPPT method [24].
E = E ∗ − Kq · Q
(21)
where, E is the voltage amplitude of the inverter, Q is
the reactive power at the respective unit, E ∗ is the voltage
reference and Kq is the droop coefficient [25].
The microgrid has been designed to supply a nominal
resistive load in a balanced three phase system. An aggregated
model based on a detailed model of a VRLA battery array,
proposed in [7] has been used for simulating the batteries.
Table I summarizes the main parameters of the microgrid.
V.
R ESULTS AND D ISCUSSION
A MATLAB/Simulink model of the ac microgrid has been
used in order to test the operation of the equalization algorithm.
The microgrid is composed by a PV, a WT, the communication
channel and their corresponding ESS as is shown in Fig. 5.
Three main cases have been considered for the evaluation
of the equalization algorithm. Those are, CBat1 = CBat2 ,
CBat2 > CBat1 , and CBat2 < CBat1 . All the cases were
TABLE I: Main Parameters of the Microgrid
Value
2 ∗ π ∗ 50
√(rad/sec)
230 ∗ 2 (V)
1600 (W )
2200 (W)
672 (V)
93%
0.02 (Ah)
5 (sec)
1.25 ∗ 10−5 (rad)/(sec)/(W)
5 ∗ 10−4 V/(VAr))
0 (VAr)
implemented by considering a total generation from RES of
PRES1 + PRES2 = 3000W and PRES1 + PRES2 = 0W
for charging and discharging respectively. Particularly, small
values of capacity (Cmax = 0.02Ah) have been selected in
order to speed up the simulation time. For simulation purpose,
the equalization will be activated at 5 and 15 s for a period
∆t = 5s. Therefore, we can also see the behavior of the
system during periods of no equalization. In general the time
for running the equalization can be adjusted in accordance to
the requirements of the EMS.
(%)
(%)
Parameter
Nominal Bus Frequency (ω ∗ )
Nominal Bus Voltage (E ∗ )
Nominal Load
Maximum (RES) Power Rating
Nominal Battery Voltage (VBat )
Charging/discharging efficiency (ηBati )
Nominal Battery Capacity (CBat )
Period of the Equalization Algorithm (∆t)
Nominal Droop Coefficient (m0 )
(Q − E) Droop Coefficient (Kq )
Reactive power Reference (Q∗ )
(a)
(b)
Fig. 8: Case CBat1 = CBat2 : (a) Charge (b) Discharge.
Dif f (SoC) = SoCBat2 − SoCBat1
(22)
where, it is possible to see that the difference is practically
zero after two iterations. Similarly, Fig. 8b shows the response
of the microgrid when the ESS’s are being discharged. In this
case, an initial SoC of 85% and 95% have been established for
ESS1 and ESS2 respectively. Comparing Fig. 8a and Fig. 8b
during the equalization, we can see that for the discharging
process |PBat2 | > |PBat1 |. Meanwhile, for the charging
process |PBat1 | > |PBat2 |. We can also see in Figs. 8a and
8b that the power is equally shared during periods of no
equalization (10s to 15s) and (20s to 25s), since both ESS
have the same capacity.
B. Case CBat2 > CBat1
Fig. 9a and 9b show the response of the microgrid when
CBat1 = 0.01(A/h). Similar initial conditions to the previous
case have been established. We can see that when the equalization is not applied (10s to 15s, and 20s to 25s), we have
|PBat2 | > |PBat1 |. The reason of this is that ESS2 requires
much more power in order to achieve mSoC1 = mSoC2 .
However, when the algorithm is applied, the current is adjusted
in order to equalize the SoC’s.
(%)
Fig. 8a shows the performance of the equalization algorithm when the ESS’s are being charged. An initial SoC of 55%
and 65% have been established for ESS1 and ESS2 respectively. Fig. 8a shows the equalization process for SoCBat1 and
SoCBat2 , the active power at each ESS unit where we can see
how the power is shared and adjusted during the equalization
in order to achieve the objective. At the end, Fig. 8a shows
the difference between SoC
(%)
A. Case CBat1 = CBat2
(a)
(b)
Fig. 9: Case CBat1 < CBat2 : (a) Charge (b) Discharge.
C. Case CBat2 < CBat1
Fig. 10a and 10b show the response of the microgrid
when CBat2 = 0.01(A/h). Compared to the previous case,
|PBat2 | < |PBat1 |, when the equalization is not applied.
We can see how the difference is reduced when the algorithm is applied. Nevertheless, they are required two iterations
of the equalization algorithm in order to reach Dif f = 0, this
is because the transitory and dynamic response have not been
considered by the algorithm. Apart from that, the approximation in (5) can lead to small errors in the equalization process.
Nevertheless, the proposed approach has proved to be faster
and more accurate for the equalization of the SoC compared
to other approaches such in [4], [17]–[19]. Additionally, for
the proposed approach, we have considered differences at the
capacities of the distributed ESS’s, and the equalization is
ensured despite the differences. Moreover, one of the main
advantages of the proposed method is that it is based on simple
algebraic operations what makes its processing time very small
(less than 160 ms).
VI.
C ONCLUSION
The proposed strategy has demonstrated to be effective
for SoC equalization in distributed ESS’s. Despite, they were
[9]
[10]
[11]
(%)
(%)
[12]
[13]
(b)
(a)
[14]
Fig. 10: Case CBat1 > CBat2 : (a) Charge (b) Discharge.
established several approximations for defining the model and
transitory response is not considered by the algorithm (linear
behavior is assumed), the algorithm is able to equalize the SoC
within few iterations. This algorithm can be complemented by
an optimization process in order to minimize the period of
time ∆t, and more accurate models can be evaluated. Additionally, power constraints should be taken into account for
the optimization by considering the maximum power ratings
of the ESS’s. On the other hand, for a complete operation of
the islanded microgrid, it is necessary to consider a adequate
architecture for the operation of the microgrid which considers
changes at the operation mode of batteries or curtailment of
RES’s generation when batteries are fully charged. As well as
consider load shedding strategies for avoid deep discharge of
batteries.
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