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1078 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 3,
MAY/JUNE 2010
Control Methods of Inverter-Interfaced DistributedGenerators in
a Microgrid System
Il-Yop Chung, Member, IEEE, Wenxin Liu, Member, IEEE, David A.
Cartes, Senior Member, IEEE,Emmanuel G. Collins, Jr., Senior
Member, IEEE, and Seung-Il Moon, Member, IEEE
AbstractMicrogrids are a new concept for future energy
dis-tribution systems that enable renewable energy integration
andimproved energy management capability. Microgrids consist
ofmultiple distributed generators (DGs) that are usually
integratedvia power electronic inverters. In order to enhance power
qualityand power distribution reliability, microgrids need to
operate inboth grid-connected and island modes. Consequently,
microgridscan suffer performance degradation as the operating
conditionsvary due to abrupt mode changes and variations in bus
volt-ages and system frequency. This paper presents controller
designand optimization methods to stably coordinate multiple
inverter-interfaced DGs and to robustly control individual
interface in-verters against voltage and frequency disturbances.
Droop-controlconcepts are used as system-level multiple DG
coordination con-trollers, and L1 control theory is applied to
device-level invertercontrollers. Optimal control parameters are
obtained by particle-swarm-optimization algorithms, and the control
performance isverified via simulation studies.
Index TermsControl-parameter tuning, distributed generator(DG),
droop controller, L1 theory, microgrid, optimal control,particle
swarm optimization (PSO).
I. INTRODUCTION
R ECENTLY, due to the development of power electronicsand
information technology, the performance and effi-ciency of
distributed generators (DGs) has been significantlyimproved.
Inverter-interfaced DGs can be flexibly deployed inpower systems in
order to mitigate peak loads and improvepower quality and
reliability. Microgrids constitute an advancedconcept for the
application of DGs and enable integration of
Paper 2009-PSEC-278.R1, presented at the 2008 IEEE
InternationalConference on Sustainable Energy Technologies (ICSET),
Singapore,November 2427, and approved for publication in the IEEE
TRANSACTIONSON INDUSTRY APPLICATIONS by the Power System
Engineering Committeeof the IEEE Industry Applications Society.
Manuscript submitted for reviewAugust 25, 2009 and released for
publication November 5, 2009. First pub-lished March 22, 2010;
current version published May 19, 2010. This workwas supported in
part by the Florida Energy Systems Consortium and in part bythe
Institute for Energy Systems, Economics and Sustainability at The
FloridaState University, Tallahassee, FL.
I. Chung, D. A. Cartes, and E. G. Collins, Jr. are with The
FloridaState University, Tallahassee, FL 32306 USA (e-mail:
[email protected];[email protected]; [email protected]).
W. Liu is with the Klipsch School of Electrical and Computer
Engineering,New Mexico State University, Las Cruces, NM 88003-8001
USA (e-mail:[email protected]).
S.-I. Moon is with the School of Electrical Engineering and
Com-puter Science, Seoul National University, Seoul 151-744, Korea
(e-mail:[email protected]).
Color versions of one or more of the figures in this paper are
available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIA.2010.2044970
multiple DGs and autonomous islanding operation accordingto
power system conditions [1][6]. Microgrids are designedas
autonomous cells in power systems, which might includesensitive
loads and multiple DGs [1]. These features can bringsubstantial
flexibility to power distribution control but also posecomplex
control problems.
Normally, microgrids operate in parallel to the grids becausethe
grids can support the system frequency and bus voltagesby covering
the power mismatch immediately. When a faultoccurs someplace in the
grids, microgrids need to operateindependently from the grid to
supply uninterrupted power tothe loads. The control method
presented in this paper is to im-prove the controlled performance
of microgrids by coordinatingthe output powers of multiple DGs in
microgrids for the twoconsiderations of operation (i.e.,
integration of multiple DGsand autonomous island operation) and by
optimizing the controlparameters. To this end, this paper applies
droop controllers thatcan automatically assign the amount of power
sharing for loadchanges without communication [7][10].
In the island mode, the bus voltages and the system fre-quency
may vary with a certain amount of uncertainties becausethe droop
controllers adjust them to cover up instant powermismatch. This
paper also focuses on controller design forindividual power
inverters that accommodates variations in thebus voltages and the
system frequency. Many design theorieshave been developed for
optimal disturbance rejection, mostnotably, H2 and H control
[11][16]. H2 control considerswhite noise disturbances and H
control considers energy-bounded L2 disturbances [11]. In contrast,
L1 theory considerspersistent bounded uncertain disturbances (L
disturbances)[13][16]. Since the disturbances in the voltage and
systemfrequency are persistent due to continual power mismatch
inmicrogrids, particularly during island mode, L1 theory is themost
relevant in capturing the features of the disturbances andis used
in this research.
This paper proposes novel controller optimization algorithmsfor
the droop controllers and inverter-output controllers
forinverter-interfaced DGs using particle swarm optimization(PSO).
Since the PSO is a derivative-free and population-based stochastic
search algorithm, it has outstandingability to escape local minima
and less sensitivity to thecomplexity of the system [17]. PSO
algorithms are used inthe inverter-output controllers associated
with L1 theory andthe droop controllers with a time-weighted
error-integratingcost function. Control performance, power quality,
androbustness are considered during controller
optimizationprocesses.
0093-9994/$26.00 2010 IEEE
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CHUNG et al.: CONTROL METHODS OF INVERTER-INTERFACED DGs IN
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Fig. 1. Concept of multiple DG coordination control using droop
controllers in a microgrid.
II. MICROGRID CONTROL
A. Problem Statement
This paper focuses on how to design microgrid controllersand to
determine the control parameters for the droop (system-level) and
inverter-output (device-level) controllers. The mostcritical
problem for control-parameter optimization is the com-plexity of
overall systems due to the high state dimensions andnonlinearity of
microgrids. Common approaches are based onsmall-signal
linearization but small-signal models intrinsicallydepend on
specific operating points.
In our previous research [17], the PSO algorithm was
applieddirectly to a power-electronic-switch-level microgrid
simula-tion model instead of small-signal models. Optimization
wasperformed at various operating conditions to accommodate
thesystem nonlinearity and yielded good performance. However,since
the control parameters were optimized altogether regard-less of
levels or types of controllers, it is hard to analyze theeffects of
individual control parameters on overall performance.In this paper,
we propose to modularize controller designprocesses and optimize
parameters step by step to evaluate theoptimization
performance.
Reference [4] showed that there are three control modes
inmicrogrid control: high-, medium-, and low-frequency
modes.According to sensitivity analysis [10], the sensitivity of
acertain parameter to a specific mode, defined in the Appendix,is
particularly large, whereas the sensitivities to other modesare
negligible. For example, the high-frequency modes arecorrelated to
the DG output circuits such as inverter-output fil-ters.
Medium-frequency modes are associated with the inverter-output
voltage and current controllers. The droop controllers arelinked to
low-frequency modes so that they have a significanteffect on system
stability [18]. This fact supports our objectiveto independently
tune the parameters of each controller. There-fore, this paper
proposes two controller optimization methodsfor microgrid DG
controllers. The first optimization objectiveis to make the
individual inverter-output controller robust withrespect to changes
in the operating conditions. Second, thedroop-control-parameter
optimization is to enhance system-wide stable operation.
B. Microgrid System Model and Control Concept
Fig. 1 shows a schematic of a microgrid that includes mul-tiple
inverter-interfaced DGs. The microgrid is connected tothe grid
through an intertie breaker. During normal operation,the microgrid
becomes a part of a distribution system. Then, thegrid can maintain
the voltage of the point of common couplingand the system
frequency. When a fault occurs in the grid,the microgrid operates
in the island mode by disconnectingthe intertie breaker, thereby
increasing the reliability of themicrogrid [19]. In the island
mode, DGs are required to sharethe power mismatch instantly in
order to follow load demandsand also to maintain power quality.
As shown in Fig. 1, the DG controllers are composed of
twocontrollers: DG coordination controllers and
inverter-outputcontrollers. The coordination controllers need to
calculatethe output power references, whereas the inverter
controllersshould control the inverter-output voltages.
According to previous studies [3][9], droop controllers
haveturned out to be the most effective method to coordinate
powergeneration between multiple DGs because they can immedi-ately
adjust power outputs to stabilize the system and also donot need
instant communication between units. The speed andvoltage droop
controllers are applied for real and reactive powersharing, as
shown in Fig. 1(a) and (b). The droop controllers canbe expressed
as
P i =Poi + (fo + floadref f)/Ri (1)Qi =Qoi + (Voi + Vloadref
Vi)/Mi (2)
where i is the DG index; Ri and Mi are droop parameters; Piand
Qi, Vi, and f are the locally measured real and reactivepowers, the
bus root-mean-square voltage, and the systemfrequency,
respectively; and the subscript o represents the presetvalues of
normal operating points. In most cases, fo and Vo arethe nominal
values. Different settings of the droop constantscan assign
different amounts of power sharing between DGs.
Since the droop controller changes system frequency or
busvoltages to damp the power mismatches, the bus-voltage
andfrequency variation can occur particularly in the island
mode.
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1080 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 3,
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Fig. 2. Control block diagram for inverter-interfaced DGs (all
variables are represented in per unit).
To maintain the voltages and frequency close to the
nominalvalues, the load reference signals are periodically sent by
themicrogrid management system with a certain time delay.
Thevariables floadref and Vloadref represent the load
referencesignals of frequency and voltage, respectively.
The droop controller of inverters imitates the control
ofsynchronous generators. Therefore, the mechanism of load
fre-quency control of the microgrid is the same as the
conventionalpower grid. The phase-locked-loop circuits of power
inverterscan eliminate fast frequency deviation in the DG output
powerby employing relevant low-pass filters. The system
frequencycan be maintained in case the power mismatch can be
recoveredimmediately. Hence, enough power reserve or energy storage
isrequired to maintain system stability. In this paper, it is
assumedthat the DGs are designed to have enough power ratings to
coverload variation in the microgrid.
Fig. 2 shows the control block diagram of inverter-interfacedDGs
in the dq rotating reference frame. Since the dq trans-formation
decouples real and reactive powers, the d- andq-axis
inverter-output current references can be obtained fromreal and
reactive power references, respectively. Details of thedq
transformation and its sign convention are explained in
theAppendix.
The droop controllers generate the real and reactive
powerreferences according to the droop characteristics of (1)
and(2), respectively. The inverter-output controllers generate
theinverter voltage references with proportionalintegral
(PI)controllers. In this paper, three-level pulse-width
modulation(PWM) inverters, which contain less harmonic components,
areused. The equations of the inverter-output controller are
d
dtd = id
inv idinv (3)
d
dtq = iq
inv iqinv (4)
vd
inv = Kp1 (id
inv idinv
)+ Ki1 d Xinv iqinv + vdbus
(5)
vq
inv = Kp2 (iq
inv iqinv
)+ Ki2 q + Xinv idinv. (6)
C. Mathematical Model for Inverter Controller Tuning
The inverter-output controller is a device-level controllerwhose
performance is affected by the inverter-output circuitsand the bus
voltages and system frequency. The bus-voltage
Fig. 3. Microgrid equivalent circuit model. (a) Microgrid
simplified circuitmodel. (b) Microgrid equivalent model.
characteristics depend on the interaction between the
corre-sponding DG and the rest of the system. The
optimizationobjective is to make the inverter-output controller
robust withrespect to disturbances such as variations in bus
voltages andfrequency.
The microgrid system shown in Fig. 1 can be simplified fromthe
perspective of DG1, as shown in Fig. 3. The mathematicalequation of
the microgrid power circuit can be obtained fromFig. 3(b) as
d
dtidinv =
RinvLinv
idinv + wS iqinv +1
Linv
(vdinv vdbus
)(7)
d
dtiqinv =
RinvLinv
iqinv wS idinv +1
Linv(vqinv vqbus) (8)
d
dtidsys =
RsysLsys
idsys + wS iqsys +1
Lsys
(vdsys vdbus
)(9)
d
dtiqsys =
RsysLsys
iqsys wS idsys+1
Lsys
(vqsys vqbus
)(10)
d
dtidL =
1Lload
vdbus + wS iqL (11)
d
dtiqL =
1Lload
vqbus wS idL (12)
vdbus =Rload idinv + Rload idsys Rload idL (13)vqbus =Rload
iqinv + Rload iqsys Rload iqL. (14)
Since the PWM circuits and output filters have much
fasterdynamics than the inverter-output controller, it is
reasonable toassume that the actual inverter output voltage can
follow the
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CHUNG et al.: CONTROL METHODS OF INVERTER-INTERFACED DGs IN
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Fig. 4. Closed-loop control block diagram.
Fig. 5. Closed-loop eigenvalue analysis. (a) Pole loci when Ki
varies (Kp = 15). (b) Dominant pole loci (Kp = 15). (c) Pole loci
when Kp varies (Ki = 100).(d) Dominant pole loci (Ki = 100).
inverter voltage reference fast enough. Then, the
small-signalclosed-loop model can be obtained as shown in Fig. 4,
wherex, xc, u, w, m, and y represent the vectors of the plant
states,controller states, control inputs, disturbance inputs,
measuredoutputs, and performance variables, respectively. The
small-signal state-space equations of microgrid circuits can be
ob-tained from (7)(14) as
x(t) = Ax(t) + [Bu Bw ][
u(t)w(t)
](15)
[m(t)y(t)
]=
[CmCy
]x(t) +
[0 Dmw
Dyu Dyw
] [u(t)w(t)
]. (16)
The small-signal state-space model of the controller also can
beobtained from (3)(6) as
xc(t) = Acxc(t) + [Bcw Bcm ][
w(t)m(t)
](17)
u(t) = Ccxc(t) + [Dcw Dcm ][
w(t)m(t)
]. (18)
Then, the closed-loop small-signal state-space model can
bederived from (15)(18) as
x(t) = Aclx(t) + Bclw(t), x(0) = 0 (19)y(t) = Cclx(t) + Dclw(t)
(20)
where x(t) = [x(t) xc(t)]T denotes the closed-loop state and
Acl =[
A + BuDcmCm BuCcBcmCm Ac
]
Bcl =[
Bw + BuDcwBcw
]
Ccl = [Cy + DyuDcmCm DyuCc ]Dcl =DyuDcw + Dyw.
The individual elements of Acl, Bcl, Ccl, and Dcl are given
atthe bottom of the next page.
Fig. 5 shows the closed-loop pole loci when the inverter-output
control parameters change. According to the participa-tion factors,
it is found that Modes 3 and 4 are sensitive to
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1082 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 3,
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the inverter control-parameter changes, whereas Modes 1 and2 are
tightly related to the power system parameters such assystem
resistance and inductance. Therefore, to achieve highcontrol
performance, the location of the eigenvalues of Modes3 and 4 should
be carefully located. A detailed controller designprocedure will be
presented in the next section.
III. OPTIMIZATION ALGORITHM
A. Particle Swarm Optimization (PSO)
PSO is a population-based intelligent searching algorithm.It has
excellent performance in searching for the global op-timum because
it can diversify the swarm with a stochasticvelocity term. PSO
resembles the social behavior of birdsor bees when they find food
together in a field [21][23].The performance of this evolutionary
algorithm is basedon the intelligent movement of each particle and
collaborationof the swarm. In the standard version of PSO, each
particlestarts from a random location and searches the space with
itsown best knowledge and the swarms best experience. Thesearch
rule can be expressed by simple equations with respect tothe
position vector Xi = [xi1, . . . , xin] and the velocity vectorVi =
[vi1, . . . , vin] in the n-dimensional search space as
V k+1i = wVki + c1 rd1
(Xpbki Xki
)+ c2 rd2
(Xgbk Xki
)(21)
Xk+1i = Xki + V
k+1i (22)
w = wmax k (wmax wmin)N
(23)
where i, k, and N are the particle, the iteration index, andthe
number of total iterations, respectively; V ki and X
ki are
the velocity and position vectors of particle i at iteration
k,respectively; w is the inertia weight; c1 and c2 are two
positiveconstants normally set to 2.0; rd1 and rd2 are random
numbersin [0, 1]; and Xpbki and Xgb
k are the best positions that particlei has achieved so far
based on its own experience and theswarms best experience,
respectively.
The boundaries of search space represent certain
physicallimitations and restrictions on the parameters. According
toprevious research, it is difficult to find optimal solutions
locatednear the boundaries. To solve this problem, the damped
reflect-ing boundary method [22], which is more robust and
consistentin finding a solution near the boundaries, is used in
this paper.The idea is that when the jth element of the ith
particle (xk+1ij )crosses the boundary (xlimj ), the position and
velocity vectorsare changed to
Xk+1i =[. . . , xki(j1), x
limj , x
ki(j+1), . . .
]
V k+1i =[. . . , vki(j1),rd vkij , vki(j+1), . . .
](24)
where rd is a random number in [0, 1].
B. Inverter-Output-Controller Optimization
This paper applies L1 theory to design robust inverter-output
controllers. L1 theory is more appropriate in situationsinvolving
persistent unknown but bounded exogenous distur-bances compared
with other robust control theories such asH2 and H theories. Using
L1 theory, the inverter-output con-troller can be designed to have
effective disturbance rejectionin the presence of voltage and
frequency variations in themicrogrids.
Acl =
Rinv+Kp1Linv WS XinvLinv 0 0 0 0 Ki1Linv 0WS + XinvLinv
Rinv+Rload+Kp2Linv
0 RloadLinv 0 RloadLinv 0 Ki2LinvRloadLsys 0
Rsys+RloadLsys
WSRloadLsys
0 0 0
0 RloadLsys WS Rsys+Rload
Lsys0 RloadLsys 0 0
RloadLload
0 RloadLload 0 RloadLload WS 0 00 RloadLload 0
RloadLload
WS RloadLload 0 01 0 0 0 0 0 0 00 1 0 0 0 0 0 0
Bcl =
Kp1Linv
0 0 0 Iqinv0 Kp2Linv 0 0 Idinv0 0 1Lsys 0 I
qsys
0 0 0 1Lsys Idsys0 0 0 0 IqL0 0 0 0 IdL1 0 0 0 00 1 0 0 0
Ccl =[1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0]
Dcl =[
1 0 0 0 00 1 0 0 0
]
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CHUNG et al.: CONTROL METHODS OF INVERTER-INTERFACED DGs IN
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The inverter-output-controller design criteria are as follows.1)
The undisturbed closed-loop system (19) and (20) should
be asymptotically stable (stability criterion).2) The inverter
control bandwidth should be large enough to
follow fast changes in output power references
(controllercriterion).
3) The L norm of the performance variable y(t) in (20)should be
minimized against persistent bounded distur-bances w(t)
(performance criterion).
The first criterion means that the closed-loop system matrixAcl
must be Hurwitz, which means that all the closed-looppoles are
located in the left-half plane. The second criterionis related to
the location of the eigenvalues of the closed-loopsystem in the s
plane. The third criterion can be achieved byminimizing the L1 norm
of the convolution operator as
G1 = supw()L
y,w,2 (25)
where the definitions of two -norms are explained in
theAppendix. The L1 norm of (25) can capture the worst case
peakamplitude response of y(t), which represents control errors,
asshown in Fig. 4, due to persistent disturbances w(t) in the
busvoltages and the system frequency.
If the first criterion is satisfied, G1 is bounded, whichmeans
that the closed-loop system (19) and (20) is bounded-input
bounded-output stable. Therefore, the meaning of theminimization of
(25) can be equivalent to minimizing theeffects of the voltage and
frequency disturbances to the currentcontrol performance of the
inverter.
The L1 optimal control problem was formulated byVidyasagar but
the optimal L1 controllers are irrational and,hence, impractical
[13], [14]. Hence, this paper applies a newmethod to minimize an
upper bound on the L1 norm, which isproposed by Chellaboina et al.
[15].
Assume that there exists a positive-definite matrix Q
satisfy-ing an algebraic Lyapunov equation such as
0 = AclQ + QATcl + Q +1
BclBTcl (26)
where > 0. Then, Acl is Hurwitz, and the L1 norm of
theconvolution operator G satisfies the bound
G21 max(CclQC
Tcl
)+ max
(DclD
Tcl
). (27)
The proof of (27) can be found in [15] and is summarized in
theAppendix. Since the algebraic Lyapunov equation of (26) has
apositive definite solution of Q if and only if Acl + (/2)In
isHurwitz where In is an identity matrix, the positive number
should satisfy
0 < < 2R(Acl) (28)where R (Acl) denotes the spectral
abscissa of Acl. Then,the tightest upper bound for the L1 norm of
the convolutionoperator G can be obtained as
G21 inf0
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1084 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 3,
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Fig. 6. Parameter tuning process using double-layer PSO.
paper, a power-electronic-switch-level simulation model
usingPSCAD/EMTDC, which is a professional electromagnetic
tran-sient power system simulation tool, is used for
optimizationinstead of a small-signal model.
The controller optimization can be done by minimizing
anerror-integrating cost function, which can yield a stable
systemwith small steady-state errors. There are four types of
error-minimizing cost functions such as integrated absolute error,
in-tegrated squared error, integrated time-weighted absolute
error(ITAE), and integrated time-weighted squared error.
Accordingto a previous study [24], the ITAE yields the best
performancefor the objectives.
To satisfy the first criterion under various operation
condi-tions, three conditions are considered: 1) the
grid-connectedmode (J1); 2) the transition period between the
grid-connectedand the island mode (J2); and 3) the island mode
(J3). Then,the cost function can be designed as
J =3
i=1
Ji =3
i=1
Kif
k=Koi
(k Kio) W Ei(k)
(34)
where i and k are the control performance index and the sam-pled
simulation time, respectively; Kio and K
fo are the starting
and ending times for calculating each control performanceindex;
W is a weighting matrix; and Ei(k) is the absolute errormatrix
defined as
Ei(k) =[P i(k),Qi(k),V i(k),freqi(k)
]T. (35)
Fig. 7. Droop controller optimization using PSCAD/EMTDC Multirun
simu-lation sequences.
The first and second elements, namely, P i(k) and
Qi(k),represent the error between the real and reactive power
ref-erences and measurements. The third and fourth elements,i.e., V
i(k) and freqi(k), mean the voltage and frequencydeviations from
the nominal values (1.0 p.u.). The weightingmatrix is set to [1.0,
1.0, 0.5, 0.5]. The particles are composed ofthe droop coefficients
such as [Ro,Mo]. Then, the actual droopcontrol parameters can be
obtained as
Ri = Ro ri Mi = Mo mi, i = 1, 2 (36)
where ri and mi are constants that determine the power
sharingratio between DGs. In this paper, r1 and r2 are arbitrarily
setto 0.05 and 0.07, respectively; both m1 and m2 are set to
0.05.Then, the power sharing ratio between DGs becomes 1/5 : 1/7for
real power and 1 : 1 for reactive power.
Fig. 7 shows the droop controller optimization processthrough
the PSCAD/EMTDC Multirun function. Each simu-lation contains three
control performance evaluations as ex-plained in (34). For
facilitating simulation speed, the dataduring the initialization
period (between 0.0 and 0.2 s) arestored to a snapshot file. Then,
all the simulations can startfrom the recorded settings and data.
Control parameters areupdated every 0.2 s. After each simulation,
the obtained costis compared with the previous best values. The
authors usedthe Multirun function from the PSCAD library to rerun
thesimulation multiple times. The PSO algorithm is implementedin
the ANSI C-code functions and integrated with PSCADsimulations.
IV. CASE STUDIES
The microgrid system model shown in Fig. 1 has beenimplemented
using PSCAD/EMTDC. The model contains twoinverter-interfaced DGs
with three-level PWM voltage sourceinverters. The DGs are
coordinated via droop controllers anda supervisory centralized
controller. Hence, the adjustments involtages and system frequency
are restored close to nominalvalues by the load reference signals
sent by the supervisorycontroller.
As explained in Section III, the microgrid DG controllersare
optimized in two steps. First, the inverter-output controlleris
optimized. The small-signal model of the inverter and therest of
the circuits described as (19) and (20) can be obtained
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CHUNG et al.: CONTROL METHODS OF INVERTER-INTERFACED DGs IN
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TABLE IMICROGRID PARAMETERS IN PER UNIT
Fig. 8. PSO optimization process. (Upper figure) Global-best
fitness searchprocess. (Bottom figure) Search process of Kp1 of a
particle.
from the operating-condition data listed in Table I, which
showsthe microgrid system parameters of three different
operatingconditions such as a grid-connected case and two
differentloading cases of island modes. Then, the cost function
of(30) is minimized, considering individual inverter stability
androbustness.
Fig. 8 shows the optimization procedure of the inverter-output
controller. Identical PI controllers are used as the d- andq-axis
current controllers. The particles for PSO1 and PSO2are defined as
[Kp,Ki] and []. The population sizes and thetotal iteration number
are set to 10 and 200 for PSO1 and 5and 100 for PSO2, respectively.
As a result, the optimal controlparameters are [Kp,Ki] = [15.11,
100.00].
The second process is to optimize the droop controller
con-sidering the power-sharing performance and stable operation
ofthe overall microgrid system by minimizing the cost functionof
(34). During this optimization process, the parameters of
theindividual inverter-output controllers are set to the
optimizationresult of inverter-output controllers. Both
grid-connected andisland modes as well as transients during mode
transitionperiods and abrupt load changes are considered in
time-domain
Fig. 9. RMS Bus1 voltage and system frequency.
simulations. The obtained optimal droop control parameters
are[Ro,Mo] = [0.683, 15.582].
To gain good performance for different operating conditions,two
solutions can be adopted. One solution is to change thecontrol
gains (i.e., the control parameters) adaptively and theother is to
find optimal gains so that the controller is robust
foroperating-condition changes. Limited by control structure,
thePI-based controls adaptability is limited. This paper adopts
thesecond method, which is to find a good set of control
parametersrobustly tuned for different operating conditions.
Figs. 912 show the simulation verification of the
microgridoperation with the optimal control parameters. The
simulationsequence is as follows.
1) 0.00.3 s (simulation initialization period). Load1 andLoad2
are set to 2.0 MW and 1.0 MVar each (4.0 MWand 2.0 MVar in total).
The outputs of the DGs are setto zero.
2) 0.3 s. The power inverters of DG1 and DG2 start gener-ating
real and reactive powers as much as 1.5 MW and1.0 MVar each
(grid-connected mode).
3) 0.6 s. The intertie breaker disconnects the microgrid fromthe
grid so that the microgrid switches to the island mode(island
mode).
4) 0.9 s. The load reference signals are sent to the droop
con-trollers of DGs to restore nominal voltage and
frequencyvalues.
5) 1.2 s. The local loads suddenly decrease (load variationin
island mode).
Fig. 9 shows the bus rms voltage and system frequencyvariation
during the simulation. In the grid-connected mode, thebus voltage
and system frequency are well maintained aroundthe nominal values
(1.0 p.u. and 60 Hz). However, in the islandmode, they vary
according to the instant power mismatch andthe droop control
characteristics. At 0.9 s, the voltage andfrequency are restored
close to the nominal values by the loadreference signals.
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1086 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 3,
MAY/JUNE 2010
Fig. 10. Active and reactive power measurement: power consumed
by loads,power generated by DGs, and power supplied from the grid
side.
Fig. 11. Bus1 voltage waveform and inverter-output current
waveform.
Fig. 10 shows the simulation results of real and reactive
pow-ers. Note that both real and reactive power control
performancesare stable due to optimization using an
error-integrating-typecost function. Fig. 11 shows the voltage and
current waveforms.
Fig. 12 shows the control performance of the inverter
currentcontroller. The q-axis current signals are negative due to
thesignal convention of the dq transformation used in this paper,as
explained in the Appendix. The dq current reference signalsare from
the droop controllers. Since the bus voltage is around1.0 p.u., the
per-unit values of the d- and q-axis currents aresimilar to real
and reactive powers, respectively.
V. CONCLUSION
In this paper, microgrid DG controllers have been designedand
optimized. Coordination between multiple DGs in a mi-
Fig. 12. Reference current inputs (idinv and iqinv) and
measurements (i
dinv and
iqinv) of inverter current controller.
crogrid system can be realized by using droop controllers,which
can automatically find the amount of power sharingso that the
microgrid can be stabilized quickly. The droopconstants are
optimized by PSO with power-electronic-switch-level
simulations.
For the inverter-output controllers, a robust controller
designscheme has been proposed. To deal with persistent voltage
andfrequency disturbances in a microgrid, an L1 robust
controltheory with the double-layer PSO algorithm has been
proposed.The double-layer PSO algorithm finds the tightest bound
ofthe L1 system operator norm so that the closed-loop systemis
robust to exogenous disturbances such as bus-voltage andfrequency
variations. The system nonlinearity is accommodatedby considering
various power system operating conditions.
APPENDIX
1) dq Transformation: The transformation from an abcreference
frame to a dq rotating reference frame can beobtained as
Xdq = C1 Xabc (A1)
where
C1 =23[
cos() cos( (2/3)) cos( + (2/3)) sin() sin( (2/3)) sin( +
(2/3)
].
Then, the d-axis phasor in the dq reference frame is alignedto
the rotating phase-a phasor of the abc reference frameand the
q-axis phasor leads /2 from the d-axis phasor. If thed-axis is
aligned to the phase-a voltage phasor, then the d-axiscurrent
accounts for the real power and the q-axis current is thereactive
current as
P 32vdid, Q 32vdiq (A2)
ConteinerHighlight
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CHUNG et al.: CONTROL METHODS OF INVERTER-INTERFACED DGs IN
MICROGRID SYSTEM 1087
where the sign convention of reactive power is positive
forinductive reactive power.
2) Sensitivity of Control Modes to Control Parameters:
Thesensitivity of the control mode whose eigenvalue is i to
thecontrol parameter ck can be defined as
pki =ick
. (A3)
3) Vector Norms: Two -norms of continuous-time vectory(t), w(t)
Rn are defined as
y, = sup
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1088 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 3,
MAY/JUNE 2010
Wenxin Liu (S01M05) received the B.S.and M.S. degrees from
Northeastern University,Shenyang, China, in 1996 and 2000,
respectively,and the Ph.D. degree in electrical engineering
fromMissouri University of Science and Technology(formerly
University of MissouriRolla), Rolla,in 2005.
From 2005 to 2009, he was an Assistant ScholarScientist with the
Center for Advanced Power Sys-tems, The Florida State University,
Tallahassee. Heis currently an Assistant Professor in the
Klipsch
School of Electrical and Computer Engineering, New Mexico State
University,Las Cruces. His current research interests include
neural network control,swarm intelligence, control and optimization
of microgrids, and renewableenergy.
David A. Cartes (S97A99M03SM07) re-ceived the Ph.D. degree in
engineering science fromDartmouth College, Hanover, NH.
Since January 2001, he has been an AssociateProfessor in the
Department of the Mechanical En-gineering, The Florida State
University, Tallahassee,where he heads the Power Controls
Laboratory, Cen-ter for Advanced Power Systems, and where he isalso
the Director of the Institute for Energy Systems,Economics and
Sustainability. His research inter-ests include distributed control
and reconfigurable
systems, real-time system identification, and adaptive control.
In 1994, hecompleted a 20-year U.S. Navy career with experience in
operation, conversion,overhaul, and repair of complex marine
propulsion systems.
Dr. Cartes is a member of the American Society of Naval
Engineers.
Emmanuel G. Collins, Jr. (S83M86SM99) re-ceived the B.S. degree
from Morehouse College,Atlanta, GA, in 1981, the B.M.E. degree from
theGeorgia Institute of Technology, Atlanta, in 1981,and the M.S.
degree in mechanical engineering andthe Ph.D. degree in aeronautics
and astronautics fromPurdue University, West Lafayette, IN, in 1982
and1987, respectively.
He was with the Controls Technology Group,Harris Corporation,
Melbourne, FL, for seven yearsbefore joining the Department of
Mechanical Engi-
neering, Florida Agricultural and Mechanical UniversityFlorida
State Univer-sity, Tallahassee, where he currently serves as the
John H. Seely Professorand the Director of the Center for
Intelligent Systems, Control and Robotics.His current research
interests include navigation and control of autonomousvehicles
(ground, water, and air) in extreme environments and
situations,multirobot and humanrobot cooperation, control of
aeropropulsion systems,and applications of robust control. He is
the author of over 200 technicalpublications in control and
robotics.
Dr. Collins served as an Associate Editor of the IEEE
TRANSACTIONSON CONTROL SYSTEMS TECHNOLOGY from 1992 to 2001. In
1991, hewas the recipient of the Honorary Superior Accomplishment
Award from theNational Aeronautics and Space Administration Langley
Research Center forcontributions in demonstrating active control of
flexible spacecraft.
Seung-Il Moon (M93) received the B.S. degreein electrical
engineering from Seoul National Uni-versity, Seoul, Korea, in 1985,
and the M.S. andPh.D. degrees in electrical engineering from
TheOhio State University, Columbus, in 1989 and
1993,respectively.
Currently, he is a Professor in the School ofElectrical
Engineering and Computer Science, SeoulNational University. He is
the Editor-in-Chief of theJournal of Electrical Engineering and
Technology.His special fields of interest include power
quality,
flexible ac transmission systems, renewable energy, and
distributed generation.Dr. Moon has been the Vice Chairman of the
Editorial Board of the Korean
Institute of Electrical Engineers since 2008.
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