Hierarchical control of intelligent microgrids

Black start operation, frequency and voltage stability, active and reactive power flow con-trol, active power filter capabilities, and storage energy management are the functionalities e

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

Integration of Distributed Energy Resources into the Smart Grid

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

and voltage stability, active and reactive power flow con-trol, 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

© COMSTOCK

& DIGITAL VISION

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

resour-ces 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

consump-tion areas The impact of these

distri-bution lines could result in low

efficiency due to the high conduction

losses, voltage collapse caused by

reactive power instabilities, low

reli-ability due to single point failures and

contingencies, among other problems

The main idea is to connect these

microgrids to the main grid or

inter-connect them through tie lines

form-ing microgrid clusters A microgrid

can be defined as a part of the grid

consisting of prime energy movers,

power electronics converters,

dis-tributed energy storage systems, and

local loads Microgrids should be able

to operate autonomously but also interact with the main grid The seam-less transfer from grid-connected mode

to islanded mode is also a desirable fea-ture These tie lines will act as inter-change energy channels to balance the energy required by each microgrid, thus the power flow of these lines will

be further reduced Moreover, micro-grids represent a new paradigm of low-voltage 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 elec-tronics 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 addi-tional performances such us low-voltage

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 distrib-uted 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 Never-theless, 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 with-out 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

PV Panel System

PCC

UPS

Common

ac Bus Microgrid Distributed Loads

Static Transfer Switch (IBS)

Utility

Grid

WT

Inverters

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

is the slow response at the control

sig-nals 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

bat-teries, 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

hier-archical order (black start

opera-tion) Similarly in this operation mode,

all the DG units must supply a

speci-fied 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

con-trolled 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

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

volt-age dips or general faults, among

others, islanded operation must

be started

n Nonplanned islanded operation: If

there is a blackout due to a

discon-nection of the main grid, the

microgrid should be able to

detect this fact by using

proper algorithms

In islanded mode, the

sys-tem dynamic is depicted by its

own DG units, which normally

regulates frequency and

ampli-tude voltage of the microgrid

Also, a small deviation from the

nominal frequency and

ampli-tude could be noticed As a

result, DS units will support all active power unbalances by injecting or absorbing active power proportion-ally 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 con-trol techniques are based on communi-cation links as a master–slave scheme, which can be adopted in systems where neighboring DG units are con-nected through a common bus How-ever, 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 regu-lated as reference within accepta-ble limits

n Supply and demand balancing:

In grid-connected mode, the fre-quency 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 lev-els The first is reactive power

compensation and harmonic cur-rent sharing inside the microgrid, and the second level is the reac-tive power and harmonic compen-sation at the PCC; thus, the microgrid can support the power quality of the main grid

Also, when the microgrid is oper-ating 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 con-tinuously supervising both the utility grid and the microgrid status (see Figure 2) When a power supply shut-down 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 re-duced as much as possible to ensure a high reliability level In such a case, this switch can readjust the power refer-ence 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 volt-age amplitude and frequency can be measured inside the microgrid, and operation points (Pand Q) 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, ampli-tude, phase, and frequency must be realized for connecting operation The restoration procedure aimed at the plant restart, system frequency syn-chronization, 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 voltages, balancing power gen-eration, starting sequence, and coordination of DG units Hierarchical Control

of Microgrids Functionally, the microgrid, in

a similar way as the main grid, can operate by using the

Bypass Off

Bypass On

Grid Connected

P = P∗; Q = Q∗

Import/Export P/Q

E = V∗

ω = ω∗

E = V g

ω = ω g

Islanding Operation

FIGURE 2 – Operation modes and transfers of the flexible microgrid and IBS grid status supervisory.

following three main

hier-archical control levels (see

Figure 3):

n Primary control is the droop

control used to share load

between converters

n Secondary control is

re-sponsible for removing any

steady-state error introduced

by the droop control

n Tertiary control concerning more

global responsibilities decides the

import or export of energy for the

microgrid

These three levels are described

in detail below

Primary Control:

P=QDroop Control

Each inverter will have an external

power loop based on droop control

[4]–[6], also called autonomous or

decentralized control, whose purpose

is to share active and reactive power

among DG units and to improve the

system performance and stability,

adjusting at the same time both the

frequency and the magnitude of the

out-put voltage The droop control scheme

can be expressed as (see Figure 4)

x¼ x mðP  PÞ ð1Þ

E¼ E nðQ  QÞ; ð2Þ

where x and Eare the frequency

and the amplitude of the output voltage,

respectively, and m and n coefficients define the corresponding slopes P and Q are the active and reactive power references, which are commonly set to zero when we connect UPS units

in parallel autonomously, forming the energetic island (see the control dia-gram in Figure 5) However, if we want

to share power with constant power sources, the utility grid is necessary to fix both active and reactive power sour-ces to be drawn from the unit This droop method increases the system performance because it is allowing the autonomous operation among the mod-ules This way, the amplitude and frequency output voltage can be influ-enced by the P=Q sharing through a self-regulation mechanism that uses both the active and reactive local power from each unit [7]

To obtain good power sharing, the frequency and amplitude output voltage must be fine-tuned in the control loop, with the aim of com-pensating the active and reactive power imbalance [8], [9] This concept

is derived from the classic high-power system theory, in which generator frequency decreases when the grid utility power is increased [10], [11]

In transmission systems, the grid impedance is mainly in-ductive; this is the reason why

it is used to adopt P x and

Q E slopes Hence, the inverter can inject desired active and reactive power to the main grid, regulating the output volt-age and responding to linear load changes However, when using power electronics converters and low-voltage microgrids, the imped-ance 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 cur-rent [14], [15] of the output filter to reach a fast dynamic response This control diagram provides a high viabil-ity 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 closed-loop inverter affects the power shar-ing 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 propor-tionally to the output current can be

E

P

E ∗

P ∗

Q

Q ∗

ω

ω ∗

ω = ω – m(P – P ∗)

E = E ∗ – n (Q – Q ∗)

(a)

(b)

FIGURE 4 – P  x and Q  E grid scheme

using P and Q as set points.

Secondary Control Primary Control

Tertiary Control B

W

FIGURE 3 – Hierarchical operation modes of the flexible microgrid.

− +

− +

− +

n

m P

Q

V o

V o∗

V o ∗ = E sin(ω ⋅ t – φ)

I o

Transformations and Power Calculation

E ∗

P ∗

Q ∗

FIGURE 5 – Droop control using P=Q.

dropped This fast control loop is

able to fix the output impedance of

the inverter by subtracting a

proc-essed 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

connec-tion 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

gener-ators by including virtual inertias by

means of the droop method It

specif-ically adjusts the frequency or

ampli-tude 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

oscilla-tions To avoid this fact, high

circulat-ing currents among the sources must

be eliminated through the voltage

con-trol 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

intercon-nection, transiting from islanded to

grid-connected mode The power

dis-tribution through the control stage is

based on a static relationship between

x P and E  Q, and it is

imple-mented as a droop scheme Likewise,

frequency and voltage restoration to their nominal values must be adjusted when a load change is realized Origi-nally, frequency deviation from the nominal measured frequency grid brings to an integrator implementation

For some parallel sources, this dis-placement cannot be produced equally because of measured errors In addi-tion, if the power sources are con-nected in islanded mode through the main grid at different times, the load behavior cannot be completely en-sured because all the initial conditions (historical) from the integrators are dif-ferent Hence, it is necessary that an external secondary control be able to measure the frequency and amplitude deviations and send the necessary

references to push up the droop charac-teristics of each DG unit (see Figure 8) Tertiary Control:

P=QImport and Export

In the third hierarchical control loop, the adjustment of the inverter’s refer-ences connected to the microgrid, and even of the generator’s MPPTs, is per-formed, so that the energy flows are optimized The set points of the micro-grid inverters can be adjusted to con-trol 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 con-troller 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 nega-tive value to absorb or inject P to the grid and fix Q-reference to zero to achieve unity power factor The con-troller will send the frequency and amplitude references to the secondary

Voltage Loop

PWM + UPS Inverter Current

Loop

Voltage Reference

E sin ( ωt ) ω

E

P and Q

Calculation

P

Q

Z o (s)

v i

+

−

Virtual Impedance Loop

Droop Control

P

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

E

ΔE

Q

Capacitive Load

Inductive Load

E ∗

E = E ∗ – nQ

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

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

control, saturating them with the

maxi-mum and minimaxi-mum allowed values

inside the microgrid By using this

con-trol level, extra functionalities can be

obtained, such as islanding detection

or voltage harmonic reduction of the

grid by harmonic injection

Conse-quently, the microgrid can be fully

controlled by using the multilevel

hier-archical approach, which conjugates

distributed and decentralized control

The implementation will be related to

the communication infrastructure and

the future smart-grid codes

Conclusions 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-con-trolled microgrids can operate in both grid-connected and islanded mode as

a flexible, grid-interactive microgrid

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

n improvement of not only the tran-sient 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 connec-tion of different ac sources acting like synchronous machines

n Secondary control avoids the am-plitude and frequency deviation produced by the primary control Only low-bandwidth communica-tions are needed to perform this control level A synchronization loop can be added in this level to transfer from islanding to grid-connected 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 volt-age harmonics in the PCC

Droop Control and Sine Generator

Voltage Restoration Level

Frequency Restoration Level

Gvr(s)

Gwr(s)

Current Control Loop Voltage Control Loop

Driver and PWM Generator

Virtual Impedance Loop

i o

ν

ωref

ω o

Vref

V o

Secondary Control

Low-Bandwidth

Communications

δV δω

Primary Control

P/Q

Calculation

Outer Loops

Inner Loops

ω = ω∗ – m(P ∗ – P) + δω

E = E∗ – n (Q ∗ – Q) + δV

P Q

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

IBS

Synchronization Loop Tertiary Control

+

+ +

–

+

–

–

P, Q

Main ac Grid

PLL RMS

Microgrid

Secondary Control

se

Gsw Gp

P

P ∗

Q ∗

Q

P

P/Q

Calculation δφ

δφ

φref

vref

Emax

Eminωmax

ωref

ωmin

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

Additional features are also

re-quired 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

flexi-bility 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

sys-tem in global terms

Biographies

Juan C Vasquez received his B.S

degree in electronics engineering from

the Universidad Autonoma de

Mani-zales, Colombia, and his Ph.D degree

in automatics, robotics, and vision

from the Technical University of

Cat-alonia, 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

guerrero@upc.edu) received his B.S

degree in telecommunications

engi-neering, his M.S degree in

electron-ics engineering, and his Ph.D degree

in power electronics from the

Techni-cal University of Catalonia, Barcelona,

Spain, in 1997, 2000, and 2003,

respec-tively He is an associate professor

with the Department of Automatic

Control Systems and Computer

Engi-neering, Technical University of

Cata-lonia, Barcelona, where he currently

teaches courses on digital signal

pro-cessing, control theory,

microproces-sors, 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

re-search 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 elec-tronics from the Technical Univer-sity 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 Uni-versity of Catalonia, Vilanova i la Gel-tru´, 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 telecommu-nication engineering from the Techni-cal University of Catalonia, Barcelona, Spain, in 1988, 1995, and 1998, respec-tively Since 2002, he has been an associate professor with the De-partment 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 Techni-cal University of Catalonia, Barcelona, Spain, in 1980 and 1990, respectively, and his Dr.Sci degree from the Universite Paul Sabatier, Toulouse, France, in 1992 He is currently an associate professor with the Depart-ment of Electronic Engineering, Techni-cal 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.

Green, ‘‘Modeling, analysis and testing of autonomous operation of an inverter-based microgrid,’’ IEEE Trans Power Elec-tron., vol 22, no 2, pp 613–625, Mar 2007.

[3] P Kundur, Power System Stability and Con-trol New York: McGraw-Hill, 1994 [4] J C Vasquez, R A Mastromauro, J M Guerrero, and M Liserre, ‘‘Voltage sup-port provided by a droop-controlled mul-tifunctional 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 sup-ply 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 consid-eration 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 instantane-ous PWM control,’’ in Proc IEEE 13th Int Telecommunications Energy Conf (INTE-LEC), 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 genera-tor sets,’’ in Proc IEE 2nd Int Conf Advan-ces 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 Engle-wood Cliffs, NJ: Prentice-Hall, 1986 [12] T F Wu, Y K Chen, and Y H Huang,

‘‘3C strategy for inverters in parallel oper-ation achieving an equal current distribu-tion,’’ 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 feed-back for UPS inverters,’’ in Proc IEEE Applied Power Electronics Conf and Exposi-tion, 1999, pp 951–957.

[14] J M Guerrero, L Garcia de Vicuna, J Matas, M Castilla, and J Miret, ‘‘A wire-less controller to enhance dynamic performance of parallel inverters in dis-tributed 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 multi-nverter systems achieving a weighted out-put current distribution,’’ in Proc IEEE Applied Power Electronics Conf and Exposi-tion, 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 Euro-pean Conf Power Electronics and Applica-tions (EPE’07), 2007, pp 1–9.