Hierarchical control of intelligent microgrids

JUAN C. VASQUEZ, JOSEP M. GUERRERO,
JAUME MIRET, MIGUEL CASTILLA,
and LUIS GARCI´A DE VICUN˜A

© COMSTOCK
& DIGITAL VISION

Integration of Distributed Energy
Resources into the Smart Grid

W

orldwide, electrical grids are
expected to become smarter in
the near future. In this sense, there
is an increasing interest in intelligent
and flexible microgrids, i.e., able to
operate in island or in grid-connected
modes. Black start operation, frequency

1932-4529/10/$26.00&2010IEEE

and voltage stability, active and reactive power flow control, active power filter capabilities, and storage energy
management are the functionalities expected for these
small grids. This way, the energy can be generated and
stored near the consumption points, thus increasing the
Digital Object Identifier 10.1109/MIE.2010.938720

DECEMBER 2010 n IEEE INDUSTRIAL ELECTRONICS MAGAZINE 23

reliability and reducing the losses
produced by the large power lines.
In this article, the main concepts related
to the configuration, control, and energy
management of intelligent microgrids
are reviewed.

Microgrids as a Key Point
to Integrate Distributed
Generation into the Grid
Intelligent microgrids are required
to integrate distributed generation
(DG), distributed storage (DS), and
dispersed loads into the future smart
grid. This will be a key point to cope
with new functionalities, as well as to
integrate renewable energy resources into the grid. Those small grids
should be able to generate and store
energy near to the consumption
points. This avoids large distribution
lines coming from big power plants
located far away from the consumption areas. The impact of these distribution lines could result in low
efficiency due to the high conduction
losses, voltage collapse caused by
reactive power instabilities, low reliability due to single point failures and
contingencies, among other problems.
The main idea is to connect these
microgrids to the main grid or interconnect them through tie lines forming microgrid clusters. A microgrid
can be defined as a part of the grid
consisting of prime energy movers,

power electronics converters, distributed energy storage systems, and
local loads. Microgrids should be able

to operate autonomously but also
interact with the main grid. The seamless transfer from grid-connected mode
to islanded mode is also a desirable feature. These tie lines will act as interchange energy channels to balance the
energy required by each microgrid,
thus the power flow of these lines will
be further reduced. Moreover, microgrids represent a new paradigm of lowvoltage distribution systems, since the
generation is not only based on small
generation machines but also on small
prime movers, such as photovoltaic
(PV) arrays, small wind turbines
(WTs), or fuel cells, that requires for
power electronics interfaces such as
ac–ac or dc–ac inverters. Those power
electronics equipments act very fast,
which has full control of the transient
response. However, in contrast with
the generation machines, power electronics do not have inherent inertia
that ensures the stability of the system
and the steady-state synchronization
of each unit.
With the objective to achieve this
performance, virtual inertias are often
implemented through control loops
known as the droop method. This
method consists on reducing the
frequency and the amplitude of the
inverter output voltage proportionally

to the active and reactive powers.
Thus, microgrids will be able to keep
active and reactive power balance, as
well as to avoid voltage collapses.
Further, microgrids should have additional performances such us low-voltage

WT
PV
Panel System

UPS

Inverters
PCC
Utility
Grid
Static
Transfer Switch
(IBS)

...
Distributed Loads

Common
ac Bus
Microgrid

FIGURE 1 – Typical structure of a flexible microgrid based on renewable energy resources.

24 IEEE INDUSTRIAL ELECTRONICS MAGAZINE n DECEMBER 2010

ride-through, active power filtering and
uninterruptible power supply (UPS)
capabilities, black start and islanding
operation, synchronization with the
main grid, fully and independent active
and reactive power flow control, and
energy management.
Figure 1 shows a microgrid based
on small wind generators, PV sources,
energy storage systems, and distributed loads. The microgrid is connected
to the point of common coupling
(PCC) of the main grid through the
intelligent bypass switch (IBS). The
overall system consists of a number
of DG and DS systems that requires
for power electronics inverters. It is
worth saying that the microgrid can
have several elements working like
current-source inverters (CSIs) and
other working like voltage-source
inverters (VSIs).
1) CSI units are normally used for
PV or WT systems that require
maximum power point tracker
(MPPT) algorithms. However, these
systems can also work as VSI,
operating outside the maximum
power point if necessary.
2) VSI units are used for storage

energy systems to support the
voltage and frequency of the
microgrid in island mode. Nevertheless, it is necessary to add
proper control loops when several
units are connected in parallel.

Operation Modes
of a Microgrid
Grid-Connected
Mode of Operation
The microgrid energy management
must be performed by considering
the energy storage systems and the
control of the energy flows in both
operation modes, i.e., with and without connection to the public grid. In
this sense, the microgrid must be
capable of exporting/importing energy
from/to the main grid to control the
active and reactive power flows and to
supervise the energy storage [1], [2].
In the grid-connected mode, system
dynamics is fixed to a large extent by
the utility grid because of the small
size of the DG units. Another problem


is the slow response at the control signals when a change of the output power
occurs. The absence of synchronous
machines connected to the low-voltage
power grid requires for virtual inertias

implemented within the control loops
of the power electronic interfaces.
Further, the power balancing during
the transient must be provided by
power storage devices, such as batteries, supercapacitors, or flywheels.
After a blackout, the microgrid should
start correctly imposing itself the
frequency and amplitude conditions
as well as connecting progressively
loads and DG units following a hierarchical order (black start operation). Similarly in this operation mode,
all the DG units must supply a specified power, e.g., to minimize the power
importing from the grid (peak shaving),
whose requirements depend on the
global energy management system. In
addition, each DG unit can be controlled through voltage regulation for
active and reactive power generation
using a communication bus. Typically,
depending on the custom desire, when
the microgrid is in grid-connected
mode, the main grids, together with
the local DG units, send all the power
to the loads.

result, DS units will support all active
power unbalances by injecting or
absorbing active power proportionally to the frequency deviation. To
operate isolated from the main grid,
the IBS will be open, disconnecting
the microgrid from the main grid [3].
Therefore, when the microgrid is in

islanded operation mode, the DG units
that feed the system are responsible
for nominal voltage and frequency
stability when power is shared by the
generation units. It is also important
to avoid overloading the inverters
and to ensure that load changes are
controlled in a proper form. Some control techniques are based on communication links as a master–slave scheme,
which can be adopted in systems
where neighboring DG units are connected through a common bus. However, a communication link through a
low-bandwidth system can be more
economic, more reliable, and finally,
attractive. Equally, in autonomous
mode, the microgrid must satisfy the
following issues:
n Voltage and frequency management:
The system acts like a voltage
source, controlling power flow
through voltage and frequency
control loops adjusted and regulated as reference within acceptable limits.
n Supply and demand balancing:
In grid-connected mode, the frequency of the DG units is fixed
by the grid. Changing the setting
frequency, new active power set
points that will change the power
angle between the main grid and
the microgrid can be obtained.
n Power quality: The power quality
can be established in two levels. The first is reactive power

compensation and harmonic current sharing inside the microgrid,
and the second level is the reactive power and harmonic compensation at the PCC; thus, the
microgrid can support the power
quality of the main grid.
Also, when the microgrid is operating in islanded mode, all the DG
units are constant power sources,
injecting the desired power toward
the utility grid.

Transition Between
Grid-Connected and Islanded Mode
As previously commented, IBS is continuously supervising both the utility
grid and the microgrid status (see
Figure 2). When a power supply shutdown occurs, or a fault in the main grid
has been detected by the IBS, the
microgrid must be disconnected and
the restoration process must be reduced as much as possible to ensure a
high reliability level. In such a case, this
switch can readjust the power reference at nominal values, although it is
not strictly necessary. In addition to
this, if maximum permissible deviation
is not exceeded (typically, 2% for
frequency and 5% amplitude), the voltage amplitude and frequency can be
measured inside the microgrid, and
operation points (P Ã and QÃ ) avoid the
frequency deviation and amplitude of
the droop method. When the microgrid
is in islanded mode operation, and IBS
detects main grid fault-free stability,
synchronization among voltage, amplitude, phase, and frequency must be

realized for connecting operation. The
restoration procedure aimed at the
plant restart, system frequency synchronization, and power generation
of the main grid. During this stage, some
details must be considered, such
as the reactive power balance,
commutation of the transient
∗
E=V
∗
voltages, balancing power genω=ω
eration, starting sequence, and
Islanding
coordination of DG units.

Islanded Mode of Operation
The microgrid can be disconnected
from the grid in the following two
scenarios:
n Preplanned islanded operation: If
any events in the main grid are
presented, such as long-time voltage dips or general faults, among
others, islanded operation must
be started.
n Nonplanned islanded operation: If
there is a blackout due to a disconnection of the main grid, the
microgrid should be able to
detect this fact by using
Bypass Off
proper algorithms.

P = P ∗; Q = Q ∗
Import/Export
In islanded mode, the sysP/Q
Grid
tem dynamic is depicted by its
Connected
Operation
own DG units, which normally
regulates frequency and ampliE = Vg
tude voltage of the microgrid.
ω = ωg
Bypass On
Also, a small deviation from the
nominal frequency and ampli- FIGURE 2 – Operation modes and transfers of the flexible
tude could be noticed. As a microgrid and IBS grid status supervisory.

Hierarchical Control
of Microgrids
Functionally, the microgrid, in
a similar way as the main grid,
can operate by using the

DECEMBER 2010 n IEEE INDUSTRIAL ELECTRONICS MAGAZINE 25


following three main hierarchical control levels (see
Figure 3):
Tertiary
Control
B

n Primary control is the droop
W
Secondary Control
control used to share load
Primary Control
between converters.
n Secondary control is responsible for removing any FIGURE 3 – Hierarchical operation modes of the flexible
steady-state error introduced microgrid.
by the droop control.
respectively, and m and n coefficients
n Tertiary control concerning more
define the corresponding slopes. P Ã
global responsibilities decides the
import or export of energy for the
and QÃ are the active and reactive
microgrid.
power references, which are commonly
These three levels are described
set to zero when we connect UPS units
in detail below.
in parallel autonomously, forming the
energetic island (see the control diagram in Figure 5). However, if we want
Primary Control:
to share power with constant power
P=Q Droop Control
sources, the utility grid is necessary to
Each inverter will have an external
fix both active and reactive power sourpower loop based on droop control
ces to be drawn from the unit. This
[4]–[6], also called autonomous or

droop method increases the system
decentralized control, whose purpose
performance because it is allowing the
is to share active and reactive power
autonomous operation among the modamong DG units and to improve the
ules. This way, the amplitude and
system performance and stability,
frequency output voltage can be influadjusting at the same time both the
enced by the P=Q sharing through a
frequency and the magnitude of the outself-regulation mechanism that uses
put voltage. The droop control scheme
both the active and reactive local
can be expressed as (see Figure 4)
power from each unit [7].
x ¼ xà À mðP À P à Þ
ð1Þ
To obtain good power sharing,
Ã
Ã
the
frequency and amplitude output
E ¼ E À nðQ À Q Þ;
ð2Þ
voltage must be fine-tuned in the
control loop, with the aim of comwhere xà and E à are the frequency
pensating the active and reactive
and the amplitude of the output voltage,
power imbalance [8], [9]. This concept
is derived from the classic high-power
system theory, in which generator

ω = ω – m(P – P ∗)
frequency decreases when the grid
ω
utility power is increased [10], [11].

In transmission systems, the
grid impedance is mainly inductive; this is the reason why
it is used to adopt P À x and
Q À E slopes. Hence, the inverter
can inject desired active and
reactive power to the main
grid, regulating the output voltage and responding to linear
load changes. However, when
using power electronics converters
and low-voltage microgrids, the impedance is too far away to be inductive.
The multiloop droop control
scheme shown in Figure 6 is composed
of an external loop whose function is
to regulate the output voltage, whereas
the inner loop supervises the inductor
current [12], [13] or the capacitor current [14], [15] of the output filter to
reach a fast dynamic response. This
control diagram provides a high viability in parameters design and a low total
harmonic distortion, but it requires
both complex analysis and a parameter
synchronization algorithm. Similarly,
another relevant aspect to provide
proper output impedance is the virtual
output impedance loop.
Virtual Impedance Loop

The output impedance of the closedloop inverter affects the power sharing accuracy and determines the
droop control strategy. Furthermore,
the proper design of this output
impedance can reduce the impact of
the line impedance unbalance. To
program a stable output impedance,
the output voltage reference proportionally to the output current can be

ω∗

P∗
(a)

Q −

P
Io

−
n

+

E = E ∗ – n(Q – Q ∗)

+
E∗

Q∗
Transformations

and Power
Calculation

E
E∗

Q∗
(b)

Q

FIGURE 4 – P À x and Q À E grid scheme
using PÃ and QÃ as set points.

Vo

E

Vo∗

P
−

m

+
P∗
FIGURE 5 – Droop control using P=Q.

26 IEEE INDUSTRIAL ELECTRONICS MAGAZINE n DECEMBER 2010

φ

Vo∗ = E sin(ω ⋅ t – φ)


dropped. This fast control loop is
able to fix the output impedance of
the inverter by subtracting a processed portion of the output current
to the voltage reference of the
inverter, which is obtained from the
voltage reference of the inner control
loops as shown in Figure 6. Moreover,
hot-swap operation, i.e., the connection of more UPS’s modules without
causing large current disturbances,
can be achieved by using a soft-start
virtual impedance by programming a
high output impedance when the UPS
is connected to the microgrid and then
reduce it slowly to a proper value.
As a control inner loop, inverters
must be programmed to act as generators by including virtual inertias by
means of the droop method. It specifically adjusts the frequency or amplitude output voltage as a function of
the desired active and reactive power.
Thus, active and reactive power can
be shared equally among the inverters.
For reliability and to ensure local
stability, voltage regulation is needed.
Without this supervision control, most
of the DG units can present reactive

power and operation voltage oscillations. To avoid this fact, high circulating currents among the sources must
be eliminated through the voltage control in such a way that reactive power
generation of the DG unit be more
capacitive, reducing the voltage set
point value. In other words, while Q is
a high inductive value, the voltage
reference value will be increased as
shown in Figure 7.
Secondary Control: Frequency
and Voltage Restoration and
Synchronization
To restore the microgrid voltage to
nominal values, supervisor system
must send the corresponding signals
using low-bandwidth communication.
Also, this control can be used for
microgrid synchronization to the main
grid before performing the interconnection, transiting from islanded to
grid-connected mode. The power distribution through the control stage is
based on a static relationship between
x À P and E À Q, and it is implemented as a droop scheme. Likewise,

CSI units are normally used for PV or WT
systems that require maximum power point
tracker algorithms.

v
+

Voltage

Loop

−

PWM + UPS
Inverter

Current
Loop

i

Zo (s)
Virtual Impedance Loop
Q
Q∗

Voltage E
Vo∗Reference
E sin (ωt ) ω

P

Droop Control

P and Q
Calculation

P

FIGURE 6 – Multiloop control droop strategy with the virtual output impedance approach.

frequency and voltage restoration to
their nominal values must be adjusted
when a load change is realized. Originally, frequency deviation from the
nominal measured frequency grid
brings to an integrator implementation.
For some parallel sources, this displacement cannot be produced equally
because of measured errors. In addition, if the power sources are connected in islanded mode through the
main grid at different times, the load
behavior cannot be completely ensured because all the initial conditions
(historical) from the integrators are different. Hence, it is necessary that an
external secondary control be able to
measure the frequency and amplitude
deviations and send the necessary

E
ΔE
E = E ∗ – nQ
Capacitive
Load
−Qnom

E∗

Inductive
Load

Q
Qnom

FIGURE 7 – Droop characteristic when
supplying capacitive or inductive loads.

references to push up the droop characteristics of each DG unit (see Figure 8).
Tertiary Control:
P=Q Import and Export
In the third hierarchical control loop,
the adjustment of the inverter’s references connected to the microgrid, and
even of the generator’s MPPTs, is performed, so that the energy flows are
optimized. The set points of the microgrid inverters can be adjusted to control the power flow in global (the
microgrid imports/exports energy) or
local terms (hierarchy of spending
energy). Normally, power flow depends
on economic issues. Economic data
must be processed and used to make
decisions in the microgrid. Each controller must respond autonomously to
the system changes without requiring
load data, the IBS, or other sources.
Thus, the secondary control uses P and
Q injected from the grid to control it
(see Figure 9). For instance, we can
adjust P-reference as a positive or negative value to absorb or inject P to the
grid and fix Q-reference to zero to
achieve unity power factor. The controller will send the frequency and
amplitude references to the secondary

DECEMBER 2010 n IEEE INDUSTRIAL ELECTRONICS MAGAZINE 27

ω = ω∗ – m (P ∗ – P) + δω
E = E∗ – n (Q ∗ – Q) + δV

Frequency Restoration Level
ω ref

δω

Gwr(s)

Droop Control
and Sine Generator

ωo
Vref

Current
Control
Loop

δV

Gvr(s)

P

Inner
Loops

Voltage

Control
Loop

Q

io

Driver and
PWM
Generator
ν

Vo
Virtual
Impedance Loop

Voltage Restoration Level

Secondary Control
Low-Bandwidth
Communications

P/Q
Calculation

Outer
Loops

Primary Control

FIGURE 8 – Primary and secondary control based on hierarchical management strategy.

Conclusions

control, saturating them with the maximum and minimum allowed values
inside the microgrid. By using this control level, extra functionalities can be
obtained, such as islanding detection
or voltage harmonic reduction of the
grid by harmonic injection. Consequently, the microgrid can be fully
controlled by using the multilevel hierarchical approach, which conjugates
distributed and decentralized control.
The implementation will be related to
the communication infrastructure and
the future smart-grid codes.

Main ac Grid

This article gives an overview about
the hierarchical control of intelligent
microgrids. Also, it was shown that a
number of interconnected DG and DS
units can perform a flexible microgrid,
showing the different operating modes
of a microgrid applying the concept of
multilevel control loops conceived as
a control hierarchical strategy. This
article has shown that droop-controlled microgrids can operate in both
grid-connected and islanded mode as
a flexible, grid-interactive microgrid.

IBS

Microgrid

P, Q
P/Q
Calculation
P
Q
–
∗
+
Q

P∗ +

δφ
Emax
Gq

P Emin ωmax
–
ωmin

RMS

PLL

Gp

Tertiary Control

+ –
+
δφ
φref +

Gse

vref

Gsw

ωref

Secondary
Control

+

Synchronization Loop

FIGURE 9 – Block diagram of the tertiary control and the synchronization control loop.

28 IEEE INDUSTRIAL ELECTRONICS MAGAZINE n DECEMBER 2010

The following improvements to
the conventional droop method
are required to integrate microgrids to the main grid [4], [5], [14],
[16], [17]:

n improvement of not only the transient response of the DG and DS
units but also of the microgrid
n virtual impedance: harmonic power
sharing and hot-swapping of DG
and DS units
n adaptive droop control laws to
increase the interactivity of the
system.
The following are the hierarchical
controls required for an ac microgrid:
n Primary control based on the
droop method allows the connection of different ac sources acting
like synchronous machines.
n Secondary control avoids the amplitude and frequency deviation
produced by the primary control.
Only low-bandwidth communications are needed to perform this
control level. A synchronization
loop can be added in this level to
transfer from islanding to gridconnected modes.
n Tertiary control allows import/
export active and reactive power
to the grid, estimates the grid
impedance, nonplanned islanding
detection, and harmonic current
injection to compensate for voltage harmonics in the PCC.


Additional features are also required to the flexible microgrids:
n voltage ride-through and power
quality in the PCC

n black start operation
n grid impedance estimation and
islanding detection
n storage energy management and
control.
These new features will allow
microgrids more intelligence and flexibility to integrate DG and DS resources
into the future smart grid. This concept
will be an impulse for the integration
of clean energy resources, allowing a
more sustainable electrical grid system in global terms.

Biographies
Juan C. Vasquez received his B.S.
degree in electronics engineering from
the Universidad Autonoma de Manizales, Colombia, and his Ph.D. degree
in automatics, robotics, and vision
from the Technical University of Catalonia, Barcelona, Spain, in 2004 and
2009, respectively. He has been an
assistant professor teaching courses
on digital circuits, servo systems, and
flexible manufacturing systems. His
research interests include modeling,
simulation, and management applied
to the DG in microgrids.
Josep M. Guerrero (josep.m.
) received his B.S.
degree in telecommunications engineering, his M.S. degree in electronics engineering, and his Ph.D. degree
in power electronics from the Technical University of Catalonia, Barcelona,
Spain, in 1997, 2000, and 2003, respectively. He is an associate professor

with the Department of Automatic
Control Systems and Computer Engineering, Technical University of Catalonia, Barcelona, where he currently
teaches courses on digital signal processing, control theory, microprocessors, and renewable energy. Since
2004, he has been responsible for the
Renewable Energy Laboratory, Escola
Industrial de Barcelona. He is the
editor-in-chief of International Journal
of Integrated Energy Systems. His research interests include PVs, wind

energy conversion, UPSs, storage
energy systems, and microgrids. He
is a Senior Member of the IEEE.
Jaume Miret received his B.S.
degree in telecommunications and
his M.S. and Ph.D. degrees in electronics from the Technical University of Catalonia, Barcelona, Spain,
in 1992, 1999, and 2005, respectively.
Since 1993, he has been an assistant
professor with the Department of
Electronic Engineering, Technical University of Catalonia, Vilanova i la Geltru´, Spain, where he teaches courses
on digital design and circuit theory.
His research interests include dc–ac
converters, active power filters, and
digital control. He is a Member of
the IEEE.
Miguel Castilla received his B.S.,
M.S., and Ph.D. degrees in telecommunication engineering from the Technical University of Catalonia, Barcelona,
Spain, in 1988, 1995, and 1998, respectively. Since 2002, he has been an
associate professor with the Department of Electronic Engineering,
Technical University of Catalonia,
Vilanova i la Geltru´, Spain, where he

teaches courses on analog circuits
and power electronics. His research
interests include power electronics,
nonlinear control, and renewable
energy systems.
Luis Garcı´a de Vicun
˜ a received
his Ingeniero de Telecomunicacio´n
and Dr.Ing. degrees from the Technical University of Catalonia, Barcelona,
Spain, in 1980 and 1990, respectively,
and his Dr.Sci. degree from the
 Paul Sabatier, Toulouse,
Universite
France, in 1992. He is currently an
associate professor with the Department of Electronic Engineering, Technical University of Catalonia, Vilanova
i la Geltru´, Spain, where he teaches
courses on power electronics. His
research interests include power
electronics modeling, simulation and
control, active power filtering, and
high-power-factor ac/dc conversion.

References
[1] P. Piagi and R. H. Lasseter, ‘‘Autonomous
control of microgrids,’’ in Proc. IEEE Power
Engineering Society General Meeting (PES),
June 2006, p. 8.

[2] N. Pogaku, M. Prodanovic, and T. C.
Green, ‘‘Modeling, analysis and testing of

autonomous operation of an inverterbased microgrid,’’ IEEE Trans. Power Electron., vol. 22, no. 2, pp. 613–625, Mar.
2007.
[3] P. Kundur, Power System Stability and Control. New York: McGraw-Hill, 1994.
[4] J. C. Vasquez, R. A. Mastromauro, J. M.
Guerrero, and M. Liserre, ‘‘Voltage support provided by a droop-controlled multifunctional inverter,’’ IEEE Trans. Ind.
Electron., vol. 56, no. 11, pp. 4510–4519,
Nov. 2009.
[5] J. C. Vasquez, J. M. Guerrero, A. Luna, P.
Rodriguez, and R. Teodorescu, ‘‘Adaptive
droop control applied to voltage-source
inverters operating in grid-connected and
islanded modes,’’ IEEE Trans. Ind. Electron.,
vol. 56, no. 10, pp. 4088–4096, Oct. 2009.
[6] E. A. Coelho, P. C. Cortizo, and P. F.
Garcia, ‘‘Small signal stability for parallel
connected inverters in stand alone ac supply systems,’’ IEEE Trans. Ind. Applicat.,
vol. 38, no. 2, pp. 533–541, 2002.
[7] A. Tuladhar, H. Jin, T. Unger, and K.
Mauch, ‘‘Control of parallel inverters in
distributed ac power systems with consideration of line impedance effect,’’ IEEE
Trans. Ind. Electron., vol. 36, no. 1, pp. 131–
138, Jan. 2000.
[8] H. Oshima, Y. Miyazawa, and A. Hirata,
‘‘Parallel redundant UPS with instantaneous PWM control,’’ in Proc. IEEE 13th Int.
Telecommunications Energy Conf. (INTELEC), 1991, pp. 436–442.
[9] W. Liu, R. Ding, and Z. Wang, ‘‘Investigated
optimal control of speed, excitation of load
sharing of parallel operation diesel generator sets,’’ in Proc. IEE 2nd Int. Conf. Advances in Power System Control, Operation and
Management, Dec. 1993, pp. 142–146.
[10] O. I. Elgerd, Electric Energy Systems Theory,

An Introduction, 2nd ed. New York:
McGraw-Hill, 1982.
[11] A. R. Bergen, Power System Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1986.
[12] T. F. Wu, Y. K. Chen, and Y. H. Huang,
‘‘3C strategy for inverters in parallel operation achieving an equal current distribution,’’ IEEE Trans. Ind. Electron., vol. 47,
no. 2, pp. 273–281, 2000.
[13] H. Wu, D. Lin, Z. Zhang, K. Yao, and J.
Zhang, ‘‘A current-mode control technique
with instantaneous inductor-current feedback for UPS inverters,’’ in Proc. IEEE
Applied Power Electronics Conf. and Exposition, 1999, pp. 951–957.
[14] J. M. Guerrero, L. Garcia de Vicuna, J.
Matas, M. Castilla, and J. Miret, ‘‘A wireless controller to enhance dynamic
performance of parallel inverters in distributed generation systems,’’ IEEE Trans.
Power Electron., vol. 19, no. 5, pp. 1551–
1561, 2004.
[15] Y. K. Chen, Y. E. Wu, T. F. Wu, and C. P.
Ku, ‘‘Cwdc strategy for paralleled multinverter systems achieving a weighted output current distribution,’’ in Proc. IEEE
Applied Power Electronics Conf. and Exposition, 2002, pp. 1018–1023.
[16] J. M. Guerrero, L. Garcia de Vicuna, J.
Matas, M. Castilla, and J. Miret, ‘‘Output
impedance design of parallel-connected
UPS inverters with wireless load-sharing
control,’’ IEEE Trans. Ind. Electron., vol. 52,
no. 4, pp. 1126–1135, 2005.
[17] J. M. Guerrero, J. C. Vasquez, J. Matas, J.
L. Sosa, and L. G. de Vicuna, ‘‘Parallel
operation of uninterruptible power supply
systems in microgrids,’’ in Proc. 12th European Conf. Power Electronics and Applications (EPE’07), 2007, pp. 1–9.

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