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: chung@caps.fsu.edu;dave@caps.fsu.edu; ecollins@eng.fsu.edu).

W. Liu is with the Klipsch School of Electrical and Computer Engineering,New Mexico State University, Las Cruces, NM 88003-8001 USA (e-mail:wliu@nmsu.edu).

S.-I. Moon is with the School of Electrical Engineering and Com-puter Science, Seoul National University, Seoul 151-744, Korea (e-mail:moonsi@plaza.snu.ac.kr).

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 MICROGRID SYSTEM 1079

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, MAY/JUNE 2010

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

CHUNG et al.: CONTROL METHODS OF INVERTER-INTERFACED DGs IN MICROGRID SYSTEM 1081

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

1082 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 3, MAY/JUNE 2010

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 MICROGRID SYSTEM 1083

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

1084 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 3, MAY/JUNE 2010

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 MICROGRID SYSTEM 1085

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.

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

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

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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