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5106 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 31, NO. 6, NOVEMBER 2016

A Transient Stability Assessment Framework inPower Electronic-Interfaced Distribution Systems

Yun Zhang, Student Member, IEEE, and Le Xie, Member, IEEE

Abstract—This paper introduces a framework of transientstability assessment for future distribution systems that arecomprised of multiple microgrids. Enabled by the advances inpower electronics and synchrophasor technologies, an angledroop method is introduced for autonomous real power sharingamong coupling-operated microgrids. In our previous work, thesmall-signal stability criterion are derived. It is well-known thatonly regional transient stability can be established for conventionalmulti-machine systems interfaced with synchronous generators.In contrast, we show in this paper that asymptotical stabilityin the large can be achieved if angle droop method is adoptedfor real power sharing among coupled microgrids. Transientstability criterion is derived by formulating the linear matrix in-equality (LMI) version of the Kalman-Yakubovich-Popov (KYP)conditions corresponding to the multi-variable Popov criterion.Numerical studies show the effectiveness of the proposed transientstability assessment framework for future power electronic-inter-faced distribution systems.Index Terms—Transient stability, interconnected systems,

microgrids, Lyapunov methods, linear matrix inequalities, syn-chrophasor measurement.

I. INTRODUCTION

T HIS paper studies a qualitatively different architecture offuture distribution systems that support deep penetration

of distributed energy resources (DERs). One of the major chal-lenges in future electric energy systems is how to integrate largeamount of variable energy resources such as wind and solar.Revolutionary changes may not be seen in high voltage trans-mission networks [1]; however, distribution systems providegreat space for innovation since in current practice they aremostly passive, less reliable with little intelligence [2], [3].In order to successfully integrate large amount of DERs,

many technical challenges must be overcome to guaranteesystem dynamic performances and in the meantime ensuringthat the potential benefits of DERs are fully harnessed [5], [6].A promising solution is to configure the distribution systemas coupling operated microgrids interfaced through powerelectronic-based interfaces, shown in Fig. 1. As a well-designed

Manuscript received September 22, 2015; revised December 29, 2015; ac-cepted February 10, 2016. Date of publication February 25, 2016; date of cur-rent version October 18, 2016. This work was supported in part by NSF ECCS-1546682, 1150944, and in part by the Power Systems Engineering ResearchCenter. Paper no. TPWRS-01340-2015.The authors are with the Department of Electrical and Computer Engi-

neering, Texas A&M University, College Station, TX 77843 USA (e-mail:[email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRS.2016.2531745

Fig. 1. The schematic diagram of a microgrid-based distribution system [4].

cluster, each microgrid packages local DER units, energystorage systems and loads such that the uncontrollable orsemi-controllable units (renewable and loads) can be partneredwith controllable units (fuel-based sources) and storage [4],[7]. Then at the upper level, the distribution system operator(DSO) only needs to coordinate each microgrid interface anddistributes the task of controlling individual DER units toeach microgrid central controller (MGCC). Such hierarchicalsystem architecture is similar to the large transmission levelmulti-machine systems [8], whereas different system interfacesare adopted. In our previous work [4] small-signal stabilityproblems are addressed, while here we continue to investigatethe transient stability problems for such system configuration.In large multi-machine systems, synchronous generators (SGs)are generally considered as interfaces; however, for microgridintegration, voltage source inverters (VSI) are widely used asinterfaces due to their advantages in power conversion effi-ciency, flexible control implementation, compactness and lowinstallation cost [9]. With VSI-based interfaces, the physicalinertia on the resource side will be decoupled from the gridside. Thus the interaction among coupling operated microgridswill be primarily determined by the VSI interface control law[10].In current practice, microgrid interface control strategies fall

in to three categories, i.e., master/slave, current sharing, anddroop method. Both the master/slave and the current sharingcontrol require some form of online global communication,which introduce a common failure point for the system. On

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ZHANG AND XIE: A TRANSIENT STABILITY ASSESSMENT FRAMEWORK IN POWER ELECTRONIC-INTERFACED DISTRIBUTION SYSTEMS 5107

the other hand, droop methods do not require explicit com-munication among the VSI interfaces, which are inherentlysuitable for a distributed implementation [11]. The widely usedfrequency droop method origins from the idea of real-reac-tive power decoupling approximation in high voltage widearea power systems. Conventional droop controller emulatesbehavior of a classical synchronous generator and utilizes thefrequency deviation signal as the power balance indicator. Theconventional droop methods are implemented distributed sincebus frequency of each interface can easily be measured lo-cally; however, several factors limit their application for futuredistribution systems: 1) in order to achieve zero steady-statefrequency deviation, the synchronization frequency needto be accessed by each interface VSI, which is unfortunatelynot locally available. Thus the conventional droop methods donot allow for plug-and-play realization despite their distributedimplementation [11]; 2) the conflict between frequency reg-ulation requirement and the sensitivity of indicating powerimbalance [12]. The frequency regulation constraint limits theallowable range of the droop gains.In recent studies angle droop methods are emerging, which

utilize the VSI output voltage angle instead of frequencyto indicate power imbalance [12]–[14]. For the angle droopcontrol methods, signals from the global positioning system(GPS) are required for angle referencing, which is enabled byintelligent electronic devices (IEDs) with phasor measurementunits (PMUs) embedded [5], [15], [16]. It has been realizedthat better system transient performance could be expectedwith angle droop methods [17]; however, the transient stabilityfeature is not fully understood for multi-microgrid systemswith angle droop controlled interfaces. Transient stability isconsidered as a fundamental and important problem in powersystem design and operation [18], and a systematic transientstability assessment is indispensable to guarantee system dy-namic security. It had been shown that conventional powersystem interfaced through SGs are generally not asymptoticallystable in the large [19]. There are often multiple equilibriumsolutions due to two essential factors: 1) the second order SGswing equation; 2) the sinusoidal power angle relationship. Fora PMU and PE-enabled future distributed system with angledroop controlled VSI interfaces, it will be shown that asymp-totically stable in the large may be achieved with conservativedroop gain design. On the other hand if voltage phase angle ofall interfaces can be contained in a limited range, conservative-ness in droop gain design can be significantly reduced.In this paper, sufficient condition for system transient sta-

bility is derived for multi-microgrid systems with angle droopcontrolled interfaces. For the conventional SG-interfaced powersystems Lyapunov direct methods are widely used to provesystem transient stability, in which the Lyapunov function isformulated based on system transient energy. Here for the pro-posed multi-microgrid systems, the Lyapunov function provingtransient stability is obtained by solving the LMIs formulatedbased on the multi-variable Popov criterion [20]. Dependingon the nonlinear characteristic of microgrid interactions, globaltransient stability may be established with obtained assessmentcriterion, or the system transient stability region can be de-rived based on the nonlinearity sector conditions. As a general

numerical method, the proposed transient stability assessmentprocedure is well suited for automatic computation.This paper is organized as follows. Section II describes

the angle and voltage droop-based interface control strategy.Section III presents the system modeling for transient stabilitystudies. The corresponding LMI-based criterion is derivedin Section IV. A droop management procedure guaranteeingsystem transient stability is introduced in Section V. InSection VI, numerical studies are performed for a study systemdesigned based on the IEEE 123-node test feeder. Conclusionare drown in Section VII.

II. INTERFACE CONTROL STRATEGY ANDMODULE REPRESENTATION

Concerning interfacing to the distribution system, it is impor-tant that proper power sharing achieved among coupling oper-ated microgrids. Droop-based methods are highly desirable dueto their minimal communication requirement as the distributionsystems can be complex and span over large areas [17]. Moti-vated by the SG operation principle, frequency droop methodis mostly adopted using local frequency signals (real powerbalance indicator) as feedback to control respective interfaceoutput. The frequency droop control is developed heuristicallyfrom the physical intuition that in high voltage wide area elec-tric power systems (WAEPS) real power flow is mainly con-trolled by the power angle [11]. Depending on the stiffness of thepower-frequency curve, the steady state frequency will changewith the time varying power production and consumption mis-match [21]–[23].The conventional droop method attempts to emulate the

SG behavior in a lossless network by imposing an inverserelationship at each interface between frequency and the realpower injection, and between bus voltage and the reactivepower injection [8]. Such conventional droop method does notallow for plug-and-play realization. And also, the droopingcapability for real power sharing is limited by the frequencyregulation requirements. As mentioned in Section I, droopingthe VSI voltage angle instead of frequency can be a betteroption for real power sharing considering its advantages intransient performance and control flexibility [4], [17], [24].If all the microgrids are interfaced through VSIs as shown inFig. 1, angle droop method can be utilized if synchrophasormeasurement is available at each interface [4] because dampingwith respect to a synchronized angle reference can be addedinto the interface control function.In the proposed system configuration, each microgrid is con-

nected to the system at the point of common coupling (PCC)through a VSI interface with synchrophasor measurementcapability. Angle and voltage droop methods are utilized forautonomous real and reactive power sharing among intercon-nected microgrids. At the PCC of interface , wespecify the angle and voltage droop control law

(1)

where are the PCC voltage angle and magnitude.are the nominal real and reactive power injections.


Fig. 2. Feedback loop for the proposed droop controller.

are the actual real and reactive power injections. arethe angle and voltage tracking time constants. are theangle and voltage droop gains which represent the sensitivity ofindicating real and reactive power imbalance, respectively.Then in the -microgrid interconnected system, dynamical

behavior of each interface is determined by the control lawgiven in (1), and constrained by the network physics in aninstantaneously coupling manner, as shown in Fig. 2. For theth microgrid in the system, it is well known that its real andreactive power injection are related with the interfacestates through the power flow equations governed byKirchoff's law. and are not locally determined butthe result of system interaction, which can be considered asthe feedback from the network. The key idea of the proposedmicrogrid interface control strategy is to define the real andreactive power sharing characteristics according to the angleand voltage droop control function. The interface statesand are determined by the network feedback measurement

, together with the reference settingdispatched by the DSO.The nominal real and reactive power injections are

dispatched by the DSO solving an AC power flow problem andremain constant during a dispatch interval, e.g., 15 minutes. Theactual real and reactive power injections are determined by thefollowing power angle relationship.

(2)

where is the self-conductance of the th microgrid, andare, respectively, the modulus and phase angle of the transfer

admittance between the th and the th microgrids.For a -microgrid distribution system, the equilibrium states

are the solutions of the set of equations , and. The nominal power injec-

tions satisfy the AC power flow equationsgiven in (3).

(3)

III. SYSTEM MODELING FOR TRANSIENTSTABILITY ASSESSMENT

The local stability properties of the equilibrium solution, can be derived from linearizing

(1) and (2) around the equilibrium solution of (3). The corre-sponding small-signal (SS) model of the -microgrid systemcan be formulated as in (4).

(4)

where

in which , and

in which

is the extended power flow Jacobian matrix formatted as

.... . .

... (5)

Since the small-signal (SS) model (4) is linear and time in-variant, it suffices to consider the eigenvalues of the matrix

. Small signal stability of the system equi-librium can be concluded if all the eigenvalues of have neg-ative real parts.Small signal stability assessed through eigenvalue analysis

only suggests that the system solutions tend to the equilibriumof interest for initial conditions sufficiently close to it. However,it is important not only to establish such local stability proper-ties of the equilibrium solution, but also to study the transientstability properties when the system experiences large distur-bances. Similar with conventional transient analysis, we willfocus on the synchronization stability of interconnected sys-tems, which falls into the category of short-term angle stabilityproblems.In conventional power system transient stability analysis,

the interface voltage is commonly assumed constant duringthe transient period. This assumption is valid in most prac-tical situations, since the voltage dynamical behaviors ofsynchronous generators are generally much slower than thetransient phenomena of interest [19]. The synchronous machineis commonly represented by a constant voltage behind itstransient reactance [25]. Here for the proposed multi-microgridsystem, the PCC voltage can also be assumed constant duringthe transient period, i.e., , if by design is muchlarger than for each microgrid interface. And then thetransient stability problem can be significantly simplified basedon the idea of time-scale decomposition [26].In order to evaluate the transient stability from the initial con-

dition to the system equilibrium of interest , the transi-


Fig. 3. States transition from the initial condition to the equilibrium of in-terest .

tion can be divided into two subprocesses if the time scales areclearly separated between the voltage angle and magnitude dy-namics. Fig. 3 shows the transient process of a system with timescale separation between angle and voltage dynamics. Startingfrom initial condition the system states will ap-proach quickly to the intermediate point , andthen gradually converge to the equilibrium . Thesecond subprocess can be evaluated with the linearized small-signal model if is close to , an assumption satisfied forpractical situations that the voltage profiles for each operationpoint are tightly regulated. The stability of the first subprocess,from to , can be studied with the subsystem modelof each microgrid interface, together with the power angle re-lationship given by the nonlinear power flow equations, whichwill be discussed in the following.Note , and let be the number

of branches connected to the microgrid . The branch, connects microgrid and its neighbor microgrid .

Then from (1), (2) and (3) we have,

(6)

where , and.

Formulate the incidence matrix and the connectivity matrixsuch that the -microgrid system with states

and output can be represented as follows.

(7)

where .. . The system

nonlinearities .It should be noted that here equals to twice the

total number of system branches.

IV. LMI-BASED TRANSIENT STABILITY CRITERIONThe -microgrid system represented by (7) is a multi-vari-

able Lur'e system with time invariant sector-bounded memo-ryless nonlinearities. From (6) we see that the functions

satisfy the sector conditions

(8)

for all .

In order to prove stability of the system (7) with nonlinearitysector conditions given in (8), a loop transformation procedurecan be performed [20]. Define

(9)

where the sector lower bound and the sector upperbound for all .Obviously for all . Let

and , so that. Substitute into (7), we have

(10)

where and .Now the nonlinearities are contained within sectors

(11)

or, equivalently,

(12)

for all .To prove stability of the -microgrid system represented by

(10), consider the Lyapunov function of the form

(13)

where denotes the th row of .According to Lyapunov theorem, seek and ,

such that

(14)

for all nonzero satisfying (10) and (11).The -procedure [20] can be utilized to derive sufficient con-

dition for (14):The LMIs in

, and

(15)

holds.The above stability condition is actually the LMI version of

the Kalman-Yakubovich-Popov conditions corresponding to themulti-variable Popov criterion [27]. The system will be asymp-totically stable in the large if the LMIs given in (15) are feasible.However, this global stability criterion will require the angledroop gains to be sufficiently small, which, ifutilized, may result in over-conservative design of angle droopgains limiting its drooping capability for real power sharingamong microgrids. Such conservativeness can be significantlyreduced by limiting the argument range of the system nonlin-earities. Fig. 4 shows a nonlinearity given in (6) with

. The red dash dots and green dashes show the uni-versal lower bound and upper bound 1 for any nonlinear-ities in the form given in (6). The blue solid curve shows the


Fig. 4. System nonlinearity with and its argument range withsector [0, 1].

actual nonlinearity considered. It can be shown that iscontained in sector for any argument .Here if we consider a limited range of the argument range

of this nonlinearity, e.g., , a smaller sector [0, 1]can be used instead of for system transient stability as-sessment. Then with the specified nonlinearity sector conditionsand their corresponding argument range, regional stability canbe established if the LMIs formulated in (15) are feasible.Accordingly the system transient stability can be evaluated

with the following procedure, and formulated into the assess-ment framework shown in Fig. 5.

Step 1: consider the sectors ;Step 2: transform the sectors to [0, 1] according to (10);Step 3: solve the LMIs formulated in (15);Step 4: if (15) is feasible the system (7) is asymptoticallystable in the large, otherwise go to Step 5;Step 5: take the upper half of the sectors and perform Step2;Step 6: perform Step 3;Step 7: if (15) is feasible regional stability can be con-cluded and goto Step 6, otherwise goto Step 5;Step 6: calculate guaranteed stability region according tothe sector condition specified in Step 5;Step 7: if for the initial condition falls intothe stability region, the system (7) will be transient stablefrom to , otherwise droop management will berequested for smaller angle droop gains.

V. STABILITY RESERVE AND DROOP MANAGEMENT

For each microgrid interface, the angle and voltage droopgains determine the sensitivity of real and reactive power mis-match indication, respectively. If the droop gains are designedtoo small, the capability of indicating local power imbalancewill be overly constrained, which limits the power sharing ef-fect through interconnection. On the other hand, the system willbe unstable due to over interaction of the microgrids if the inter-face droop gains are too large. In order to guarantee system-widestability, the constraint on interface droop gains will be depen-dent on system operation conditions. With fixed interface droopgains, over-conservative design cannot be avoided since systemstability need to be guaranteed for all possible operation condi-tions. Thus, the interface droop gains should be managed in areal time manner according to the transient stability assessmentresult as discussed in Section IV, which can be realized by con-figuring stability reserve for each microgrid.In current practice, operating reserve is used in large power

systems to correct the energy imbalance resulted from system

Fig. 5. Transient Stability Assessment Framework.

variability and uncertainty. The operating reserves can beclassified into two categories, non-event and event reserves.Deployed during normal operation conditions, the non-eventcategory can be subdivided into the regulating and followingreserves based on different response speed and type of controlimplemented. The event reserves are called upon rare severeevents and can be subdivided into primary, secondary, andtertiary reserves based on the required response speed [28]. Infuture distribution systems with high penetration of variableenergy resources (VERs), such as wind and solar power, thesystem disturbances will be much larger together with highramping rates compared with traditional power systems. Theexisting reserve management rules should be accompanied byinnovative methods to account for the increased variability anduncertainty introduced [28].In traditional power systems, regulating reserves participate

in the finest scale of balancing during normal conditions. Reg-ulating reserves are responsible for correcting the imbalancefrom the total load or generation that differs from the forecastcondition. Provided by the governor response, regulating re-serves modify the droop gain of each synchronous generatorparticipating in primary level control. Since normal imbalancesusually do not trigger frequency response, the governor con-trol parameters are designed based on system regulation re-quirement and stability constraint through contingency anal-ysis [28]. Reserves are commonly not used for system stabi-lization due to the response speed limit of conventional units.However in future distribution systems with high penetrationof VSI interfaced units (or clusters), stability reserves might beapplicable taking advantage of the fast responsive power elec-tronic interfaces. Other than the regulating and following re-serves commonly configured in conventional large power sys-tems, here we propose to deploy stability reserves to ensure realtime system-wide stability. Energy battery storage systems canbe good candidates for stability reserves since 1) they can bedeployed at the DC link of each microgrid PCC and controlledby the fast responding interface VSI; 2) they can provide bothupward and downward reserves for automatic stabilization.In order to fully harness the potential of VERs and at the

meantime guarantee system stability, droop gains of microgrid


interfaces should be tuned online by managing the back uppower in a timely manner according to the real time system op-eration condition since large disturbances can be expected evenin normal operation. The back up power can be provided bythe battery energy storage systems (BESS) configured in eachmicrogrid, here defined as stability reserve. It is different fromthe conventional operating reserve in the sense that stabilityreserve is used for stabilization purpose instead of supportingoperating imbalance. In the following we will show that modelreference control (MRC) scheme can be adopted for each in-terface VSI to track a designed reference model by controllingits stability reserve. If the transient stability criterion derived inSection IV is satisfied with the designed reference model droopgains, system-wide stability can be guaranteed.The proposed stability reserve is different in nature from the

conventional spinning and unspinning operating reserve. First,the conventional operating reserve is the generation capacityavailable to the system operator within a short interval of time tomeet demand in case a generator fail to supply. It is designed tosupport system operation. However, the proposed stability re-serve is for system stabilization purpose provided by the en-ergy storage units in the microgrid to modify its interface droopcharacteristic. Such stabilizing resources are proposed to guar-antee system stability without over-conservative droop gain de-sign for the application scenario that high penetration level ofintermittent renewable energy is integrated.Consider the following interface control function for the th

microgrid

(16)

where are the controllable real and reactive power,respectively. Without stability reserves configured they will beequal to the dispatched reference setting , and (16) willbe the same as (1). Note the stability reserve for real and reactivepower as and , we have

(17)

The objective is to choose an appropriate control law such thatall signals in the closed-loop plant are bounded and the states

track the following reference model with parameterstuned in a real time manner.

(18)

In order to track the reference model (18), we propose the fol-lowing control law

(19)

where are the control parameters to be calcu-lated. Substitute (17) and (19) into (16), we have the closed-loopmodel combining the controller and the plant

(20)

Match (20) with the reference model (18), the control parame-ters can be calculated as

(21)

We can see from (19) that the proposed stability reserve isactually different from the conventional spinning and non-spin-ning operating reserve. Conventional operating reserve refersto stand-by capacity available to the system operator within ashort interval of time to meet demand in case a generator fail tosupply. It is designed to support steady state system operation.In contrast, the proposed stability reserve is for stabilization pur-pose. Such stabilizing power is provided by the energy storageunits in each microgrid to modify its interface droop charac-teristic when the network becomes over-stressful. The idea is toperform instantaneous managing of and according to theMRC control law given in (19) so that the equivalent droop char-acteristic for each microgrid is strictly following the referencedroop provided by the DSO. Such stabilizing proce-dure is proposed to guarantee system stability without over-con-servative droop gain design, especially for application scenarioswith high penetration level of intermittent renewable energyintegrated.The above reference model matching technique guarantees

that the closed-loop states converge to the reference model ex-ponentially fast for any bounded signal [29], [30]

(22)

Adaptive laws can be implemented with VSI model parametersestimated online if they are unknown to the MGCCs respon-sible for reserve control. And the corresponding model refer-ence adaptive control (MRAC) schemes can be adopted for theaforementioned control objective [30], [31].The key idea of the proposed MRC-based reserve control

scheme is to reshape the interface droop gains according toa designed reference model satisfying the stability criteriondiscussed in Section IV. With (21) both the interface droopgains and the time constants can be reshaped.In order guarantee system transient stability, only the droopgains need to managed. With the fixed interface time constants

, the control parameters become

(23)

And the control law (19) simplifies to

(24)


Fig. 6. Study system based on IEEE 123-node test feeder.

Fig. 7. Diagram of the 5-microgrid study system.

TABLE IPARAMETERS OF THE TIE-BRANCHES

VI. NUMERICAL EXAMPLES

A 5-microgrid study system is designed based on IEEE 123-node test feeder to demonstrate the proposed transient stabilityassessment procedure. Fig. 6 shows the system partition andFig. 7 shows the one line diagram at the interconnection levelwhen the system is configured as coupling operated microgrids.The tie-branch parameters are given in Table I.

A. Transient Stability AssessmentIn this section, the transient stability of the study system will

be evaluated for the study case formulated as follows.For the designed 5-microgrid system, we consider the sce-

nario that a three-phase ground fault on tie-branch triggerssystem protection. If this fault is timely isolated by the pro-tection scheme, the system configuration will become radial asshown in Fig. 8. Transient stability should be evaluated beforere-closing the circuit breakers. Assuming that the system is op-erated at after the fault is cleared, we will investigate in thefollowing if the system will be transient stable from the initialcondition to the post-fault equilibrium given in Table II.In order to study the impact of microgrid droop gain settings

on system stability, three study cases are formulated. The inter-face control time constants and droop gains for each microgridare given in Table III.The local stability of can be evaluatedwith the small-signal

model (4) formulated in Section II. The system eigenvalues

Fig. 8. Radial configuration after fault isolation.

TABLE IIINITIAL CONDITION AND POST-FAULT EQUILIBRIUM OF INTEREST

TABLE IIIINTERFACE CONTROL TIME CONSTANTS AND DROOP GAINS

Fig. 9. Eigenvalues for small-signal system model.

for each study case are plotted in Fig. 9. For Case A and B,the system equilibrium is small-signal stable since all theeigenvalues have negative real parts. For Case C, the systemequilibrium is small-signal unstable with a positive eigen-value 0.0014. Obviously, with smaller interface droop gains thesystem tends to have better stability feature.Now that the system equilibrium is small-signal stable

for Case A and B, transient stability from the initial conditionto the intermediate point need to be evaluated

according to the assessment framework in Fig. 5.With the assessment procedure given in Section IV, the tran-

sient stability feature can be evaluated for Case A and B, givenin Table IV. For Case A, the LMIs formulated in (15) are fea-sible with the sector condition ,


TABLE IVSTABILITY ASSESSMENT RESULTS

TABLE VTRANSIENT STABILITY REGION

Fig. 10. Time domain simulation results—plant model parameter: Case C; ref-erence model parameter: Case A.

thus global stability can be concluded. For Case B, feasible solu-tion of (15) cannot be obtained with sector condition

, whereas regional stability can be estab-lished with sector condition . Thecorresponding stability region is given in Table V, in which

. From Table II, we have

. Clearly, the initial condition falls into the sta-bility region of , thus transient stability can be concluded forCase B.

B. Stability Reserve and Droop ManagementAs discussed in Section V, stability reserve can be configured

to manage the droop gains of each microgrid interface. For aspecific system operation condition, model reference trackingcan be performed the MGCC by controlling its stability reserve.From Section VI-A, we know that the operation point is

small-signal unstable if the plant model of each microgrid in-terface has the droop gains specified as in Table III—Case C;whereas transient stability can be established with the Case Aand B droop gains. Design the reference model of each micro-grid with Case A droop gains, and consider the scenario thatstarting from the initial condition , each MGCC spent 10 s fortheir reserved to be committed. The system can be stabilizedthrough controlling the stability reserve of each microgrid ac-cording to the control law given in (24). As can be seen fromthe time domain simulation result plotted in Fig. 10, startingwith the initial condition thesystem is unstable as the interface states

do not converge to zero as time goes on. The systembehavior can be explained with the stability assessment resultgiven in Table IV since with the Case C interface control pa-rameters, the system will be unstable. At s droop gain

Fig. 11. The stability reserve responses—plant model parameter: Case C; ref-erence model parameter: Case A.

Fig. 12. The stability reserve responses—plant model parameter: Case C; ref-erence model parameter: Case A with voltage droop gains changed to 1%.

tuning is performed to tract the reference model with Case A pa-rameters, we can see from Fig. 10 that the interface states

and the corresponding interaction variables arestabilized and approaching zero at the steady state.Fig. 11 shows the response of the stability reserve of each mi-

crogrid, from which we can observe that of each microgridconverge to zero at the steady state. Such phenomena are con-sistent with our theoretical analysis since from (24)

(25)

At the steady state , thenaccording to (4) and (5) we have,

(26)

In the study case above only real power reserve is config-ured. Actually according to the discussion in Section V, reactivepower reserve can be used for voltage droop management withthe control law given in (19). Now consider the scenario thatthe microgrid interface plants have Case C parameters and thecorresponding reference models have the same , andas in Case A, but with % for each microgrid interface.The response of system states and the stability reserves

are plotted in Fig. 12, from which we see that all thesevariables approach zero at the steady state.

VII. CONCLUSIONIn this paper, a novel control strategy is proposed for micro-

grid interface to achieve much better transient performance intheir coupling operation. Angle and voltage droop methods areemployed respectively for autonomous real and reactive powersharing among coupling operated microgrids. Built upon thisframework, a LMI-based transient stability criterion is derived,which is integrated into the online assessment framework.The proposed transient stability criterion is numerically

tested in a study system designed based on IEEE 123-node test


feeder. According to the transient stability assessment result,the proposed model reference control (MRC)-based droopmanagement scheme is evaluated with the study system.Our future work will focus on testing the proposed transient

stability criterion and the stability reserve control scheme inreal-world settings. Applications such as bottom up black startfor post fault system restoration will also be investigated.

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Yun Zhang (S'13) received the B.E. and M.S. de-grees in electrical engineering from Harbin Instituteof Technology, Harbin, China, in 2005 and 2007respectively. From 2007 to 2010 he worked as asenior power design engineer at ZTE Corporation,Shenzhen, China.He is currently pursuing Ph.D. degree in the De-

partment of Electrical and Computer Engineeringat Texas A&M University, College Station. Hisresearch interests include large-scale system DSA,data-driven load modeling, operation and control

of microgrids.

Le Xie (S'05–M'10) received the B.E. degree in elec-trical engineering from Tsinghua University, Beijing,China, in 2004, the M.Sc. degree in engineering sci-ences from Harvard University, Cambridge, MA, in2005, and the Ph.D. degree in electrical and computerengineering from Carnegie Mellon University, Pitts-burgh, PA, in 2009.He is currently an Associate Professor with the

Department of Electrical and Computer Engineering,Texas A&M University, College Station. His in-dustry experience includes an internship (June to

August 2006) with ISO-New England and an internship with Edison MissionEnergy Marketing and Trading (June to August 2007). His research interestincludes modeling and control of large-scale complex systems, smart gridapplication with renewable energy resources, and electricity markets.

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