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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 3, AUGUST 2013 3243

Some Aspects of Stability in MicrogridsRitwik Majumder, Member, IEEE

AbstractThis paper investigates some aspects of stability inmi-crogrids. There are different types of microgrid applications. Thesystem structure and the control topology vary depending on theapplication and so does the aspect of stability in a microgrid. Thispaper briefly encompasses the stability aspects of remote, utilityconnected and facility microgrids depending on the modes of op-eration, control topology, types of micro sources and network pa-rameters. The small signal, transient and the voltage stability as-pects in each type of the microgrid are discussed along with scopeof improvements. With a brief review of the existing microgridcontrol methods in the literature and different industry solutions,this paper sets up an initial platform for different types of micro-grids stability assessment. Various generalized stability improve-ment methods are demonstrated for different types of microgrids.The conventional stability study of microgrids presented in thispaper facilitates an organized way to plan the micro source oper-ation, microgrid controller design, islanding procedure, frequencycontrol and the load shedding criteria. The stability investigationsare presented with different control methods, eigen value analysisand time domain simulations to justify different claims.

Index TermsMicrogrid, stability, voltage source converter.

I. INTRODUCTION

T HE system stability issues in a microgrid are well knownand have been investigated by many researchers in the re-cent past, focusing on a particular aspect. Depending on the typeof microgrid, the control topology, network parameters, microsources etc. vary and so does the stability aspect. With more andmore voltage source converter (VSC) interfaced source integra-tion, the stability in a microgrid largely depends on the controltopology of the VSCs. However, other micro sources, storage,protection, compensation etc. also play a significant role in thesystem stability.The small signal stability of a microgrid is investigated in

[1][13]. While [1], [3] and [4] address the dynamic stabilitywith the power electronic distributed generators (DGs), [2]demonstrates the stability enhancement with double fed induc-tion motors. Load sharing with different current and voltagecontrol loops with associated stability is discussed in [5][8].The modeling and the stability analysis with VSC sources areaddressed in [9] and [10]. Eigen value analysis and time domainresults are presented to show the impact of feedback controllerin the system stability. In [11][13], the general stability issueswith the VSC sources are further emphasized, while a supple-mentary control loop is proposed in [13] to improve the systemstability.

Manuscript received July 23, 2012; revised August 11, 2012, October 31,2012, November 25, 2012, and December 04, 2012; accepted December 09,2012. Date of publication January 15, 2013; date of current version July 18,2013. Paper no. TPWRS-00864-2012.The author is with ABB Corporate Research, Vsters, Sweden (e-mail:

[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.2012.2234146

The microgrid stability in islanding is investigated in[14][17]. Impact of different loading conditions and constantpower loads in the microgrid stability during islanding areaddressed in [14] and [15]. In [16], an active damping controlwith a virtual resistance is proposed, while in [17] efficacyof frequency control with an internal oscillator and voltagefeedback signal to regulate the island voltage in the VSCs aredemonstrated after islanding.The transient stability analysis of a microgrid can ensure

system operability after large disturbances. With micro sourceswith current limit, very little spinning reserve and limitedreactive support, it is essential to carry out detailed transientanalysis with possible contingencies. The transient stability isinvestigated in [18][20]. A direct method with energy functionformulation for the transient stability analysis in a microgrid isproposed in [19], while [20] demonstrates the transient stabilitywith both synchronous machine and VSC interfaced sources.The microgrid stability with both inertial and converter in-

terfaced sources is investigated in [21][27]. The diesel gensetoperation in CERTS system is discussed in [21]. DifferentPV-diesel microgrid operations are investigated in [22], [24]and [25]. The system stability in decentralized operation withinertial and VSC sources in general is examined in [26].Different control topologies to improve the system stability

during the island transient are proposed in [27][31]. Thechange of converter control mode with voltage feedback isproposed in [28] and a master slave configuration for theisland transient is investigated in [29]. Smooth islanding withstate feedback control and islanding stability characteristicare discussed [30], [31].Various microgrid aspects, includingcontrol and system stability, are analyzed in the Europeanresearch program on microgrid [32], [33]. High penetration ofdistributed generations and advanced architecture of microgridsare investigated in these projects.This paper identifies various reasons for the stability issues in

different microgrids and describes the generalized approach toimprove the system stability. The possibility of different controlloops and stabilizers are presented for different microgrid types.

II. STABILITY ISSUES IN MICROGRIDS

A microgrid can be represented with different micro sourcesand loads as shown in Fig. 1. However, the remotemicrogrids donot have the utility connections as shown in Fig. 1. The utilitymicrogrids span geographically a larger area compared to thefacility microgrids. The micro sources, loads, network parame-ters, control topologies vary in different microgrids [34].In general the microgrid is defined as an integrated energy

system consisting of distributed energy resources (DERs) andmultiple electrical loads operating as a single, autonomous grideither in parallel to or islanded from the existing utility powergrid [34].From the stability aspect the major differences can be de-

scribed as

0885-8950/$31.00 2013 IEEE

3244 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 3, AUGUST 2013

Fig. 1. General representation of a microgrid with DGs and loads.

Fig. 2. Different stability issues in microgrid and the usual reasons.

A utility microgrid, connected to the utility at one point(there could be also multiple connection points for gridconnected reliability) of common coupling (PCC), can op-erate in island, spans over a large area (compared to afacility microgrid) and contains different types of microsources and loads [34].

A remote microgrid is never connected to the utility andoperates mostly with decentralized control methods. Themaximum power use is limited for the customers and thepower quality requirements are much relaxed compared toa facility microgrid [34].

A facility microgrid is normally connected with the hostutility and commonly a single business-entity microgrid. Afacility microgrid can continue to operate in an intentionalor an unintentional island. Facility microgrids can be foran industrial or an institutional microgrid [34].

In this paper an institutional or campus microgrid (with fewmicro sources and diesel backup) capable to operate in islandfor a long time is considered as an example facility microgrid.Similar to a large power system, the stability issues in a mi-

crogrid can be divided as small signal, transient and voltage sta-bility. The recurring reasons of each stability problem are shown

Fig. 3. Different methods of stability improvement.

Fig. 4. Stability issues in different types of microgrids.

in Fig. 2. Small signal stability in a microgrid is related to feed-back controller, continuous load switching, power limit of themicro sources etc. A fault with subsequent island poses most ofthe transient stability problem in a microgrid.Reactive power limits, load dynamics and tap changers

create most of the voltage stability problems in a microgrid.Fig. 3 shows different stability improvement methods. Whilesupplementary control loops, stabilizers, coordinated controlof the micro sources can improve the small signal stability,the transient stability improvement is achieved through use ofstorage, load shedding and adaptive protection devices. On theother hand, voltage regulation with DGs, reactive compensa-tion, advanced load controller and modified current limiters ofthe micro sources can ensure the voltage stability in a micro-grid. Depending on the microgrid type, different stability issuescan be related to most frequent problems as shown in Fig. 4. Itcan be seen that the DG feedback controller with decentralizedcontrol methods creates most of the small signal stability issuesin a remote microgrid, while in a utility microgrid the mostcommon reason is the current limiters. In a facility microgrid,the frequent load switching within a small area often createsthe small signal stability problems.

MAJUMDER: SOME ASPECTS OF STABILITY IN MICROGRIDS 3245

Fig. 5. Small signal stability: Speed of the control loops.

Faults produce the obvious transient stability issues in alltypes of microgrids. While a fault and subsequent islanding ina utility or facility microgrid demonstrates the typical transientstability aspect, in a remote microgrid, a fault within the mi-crogrid and isolating the faulty part of the network creates thetransient stability problems.The voltage stability in a remote microgrid is related to the

reactive compensation of the network but in a utility micro-grid the main source of the voltage stability problems is the tapchangers. With few sources and confined loads, limiters in themicro sources and under voltage load shedding create most ofthe voltage stability problems in a facility microgrid.

III. SMALL SIGNAL STABILITY

The small signal stability in a microgrid is analyzed with alinearized model of micro sources and loads. The speed of thecontrol loops in a VSC is shown in Fig. 5. Most of the stabilityissues in the converter control loops (in a microgrid) arises fromthe outer most power controllers and their associated controlgains.

The small signal modeling of the converter with the associ-ated controllers is also shown in Fig. 5. The converter model isrepresented with the converter capacitor voltage , con-verter current and the output current states . Each ofthe converter controllers is modeled with its states as shown inFig. 5. Together with the output voltage angle , real and reac-tive power output in power controller , voltagecontroller and the current controller states, the con-verter LCL filter states are combined to derive the state spacemodel of the converter with the controllers. For each of the con-verters this is done individually at their own reference frame(dq). The load and the network are also modeled with theirstate space equations. Depending on location of the DGs andthe loads in the network, the state space equations are com-bined to formulate the total microgrid state space equation ina common reference frame (DQ). The design of the controllersshould be done using this combined state space model throughsmall signal stability analysis [35].Different supplementary control loops can be added to im-

prove the system stability. Fig. 6 shows different possibility ofstability improvement with the supplementary control loops in


Fig. 6. Improving small signal stability in droop controlling mode.

Fig. 7. Improving small signal stability in power controlling mode.

Fig. 8. Modeling for transient stability study.

a droop controlled converter. Fig. 7 shows the supplementarycontrol loops possibilities for power controlling converters.

IV. TRANSIENT STABILITY

The transient stability of a microgrid can be assessed witha nonlinear model (combining the converter droop controllermodels through the network equations [19]). One method ofanalysis is based on the construction of the Lyapunov function.A microgrid model for the transient stability analysis with theconverter interfaced sources is shown in Fig. 8. The real andreactive power outputs of the converters relate the individualconverter state equations through the network equation to derivethe system model.To apply direct method of transient stability analysis, it is nec-

essary to construct a Lyapunov function. The Lyapunov func-tion for a microgrid can be selected from the droop controllervariables [19], which are converter operating frequency andfilter capacitor voltage . The function can be written as

(1)

Fig. 9. Transient stability modeling with mixed sources.

Fig. 10. Aspect of voltage stability: Stable (s) and unstable (u) points.

The function can be derived with a separate constant for eachstate variable or combination of them satisfying the Lyapunovcriteria. If a synchronous machine is present in the system, onecan model them in a simplified way employing a classical modelwhere the generators are represented with the swing equation(Fig. 9). The constant impedance loads are not generally in-cluded in the functions. However with a dynamic load, thesetechniques can be extended with the transient voltage depen-dency of the load. The source and the load behavior can be de-composed into slow and fast subsystems for transient analysis[36].

V. VOLTAGE STABILITY

The voltage stability problem in a microgrid may appear dueto various reasons as mentioned in Section II. The voltage sta-bility problem in a microgrid can be demonstrated using theP-V and Q-V curves. The P-V curve indicates themaximumloadability while Q-V curve shows the necessary amount of re-active power at the load end for desired voltage. In a microgrid,if a VSC is injecting (Fig. 10) power to a load , the loadpowers can be related with the terminal voltage and theload voltage .


The reactive power generation can be expressed interms of the terminal voltage , load voltage andthe load power . It must be noted that the reactive powercontrol is much faster with a VSC compared to a synchronousmachine. The reactive power sharing with a sudden changein the reactive power demand or supply must be controlledproperly to avoid converter reactive limit or system oscillation.With different types of loads, the reactive power demand may

vary with the load characteristics. Three voltage stability cri-teria related to the reactive power are shown in Fig. 10. For allthe cases, the system stability curves are shown with stableand unstable points. Condition-1 shows the stability curvefor the reactive power generation and the reactive powerconsumption . The system is stable when is pos-itive as indicated in Fig. 10. The rate of change in the reactivepower consumption with the load voltage is compared to the rateof change in the reactive power generation with the voltage incondition-2. Condition 3 is derived from condition-1 and con-dition 2. It shows the stability criteria for rate of change in theconverter terminal voltage with the load voltage.The key issues in this analysis would be 1. Reactive power

control strategy. 2. Load characteristics. 3. Slow increase of thepower demand. 4. Outage of one part of the network.

VI. STABILITY IMPROVEMENT IN MICROGRIDIn this section various methods to improve the stability in a

microgrid are discussed.

A. StabilizerStabilizers can be used in the VSC interfaced micro sources

to improve the small signal stability. Fig. 11 shows the stabi-lizer for a DG and it can be seen that the voltage magnitude,frequency and the power output of the connected DG are fed tothe stabilizer. It is to be noted that the stabilizer can be includedin any of the control loop shown in Figs. 6 and 7. Separate stabi-lizing equipment (for existing VSCs) or a supplementary controlloop can improve the stability of a VSC interfaced DG.1) Modulating and provide a fast response stabiliza-tion but may lead to system oscillation in a continuous loadswitching scenario.

2) Modulating and can also provide an effectivestabilization loop. This option is suitable for both grid con-nected and grid forming sources.

3) Modulating and provide a much slower stabiliza-tion but effective in remote microgrid scenarios, where theregulations are not time critical.

B. Reactive Compensation With DSTATCOMThe reactive compensation in a microgrid is necessary to

maintain the voltage within acceptable limits. The voltage reg-ulation problems are more in utility and remote microgrids.1) In grid connected mode, the voltage regulation problemappears mostly on the load end of the feeder.

2) In islanded mode, the voltages may fall below acceptablelimit anywhere and identifying the compensation locationis harder.

Fig. 12 shows a DSTATCOM connected close to the crit-ical load to ensure required power quality. When the voltagesfall below the lower limit, the DSTATCOM can inject reactivepower.The DSTATCOM can be controlled

Fig. 11. Stabilizer for DGs.

Fig. 12. Reactive compensation with DSTATCOM.

based on local measurements of the point it is connected; based on communicated measurements and coordinatedcontrol with the DGs [37].

The communicated measurements can be used to modulatethe converter output voltage reference as shown inFig. 13.

C. Energy Storage System: FlywheelEnergy storage system provides the stability improvement in

a microgrid by injecting active (sometimes also reactive power)power during power shortage, DG trip, islanding, load dynamicsand ride through till the backup diesel gensets come live. Thereare many energy storage devices available in the market. Theflywheel is one of the high performance energy storage solu-tions. With a flywheel system it is possible to inject power inthe MW range even within one fourth of a cycle [38]. The basicstructure of a flywheel system connected to amicrogrid is shownin Fig. 14. The flywheel system is connected to the microgrid


Fig. 13. Converter control for DSTATCOM with communication.

Fig. 14. Flywheel storage for microgrid stability.

Fig. 15. Converter control for flywheel storage.

with back to back converters. The first converter works as fly-wheel drive and maintains the DC side voltage. The grid sideconverter injects real and reactive power based on the measuredfrequency and voltage. The power injection is usually based ondroop control outside an acceptable frequency or voltage range.A possible control solution is shown in Fig. 15.

D. Load Shedding for Stability Improvement

The most crucial role of load shedding in the microgrid sta-bility takes place during islanding. A sudden loss of the gridcreates power imbalance and the load shedding for the powerbalance is time critical in a microgrid. The load shedding canbe achieved with different methods,

Fig. 16. Different methods of load shedding for microgrid stability.

Breaker interlock: A fixed switch is interlocked with the is-landing switch to shed some fixed loads. This method is fast andeffective but fixed (Fig. 16, option 1). Under Frequency Relay: The most common way to shedload in a microgrid is to detect under frequency and trip therelays. However, this method is slow and could be muchslower with presence of a large storage.

PLC Based Load Shed: PLC based load shedding schemesare activated based on number of generators operatingunder frequency condition and amount of load connectedto the system. However it requires high amount of moni-toring and during transients the time to shed load is oftentoo long.

Advanced Methods: Advanced load shedding method(Fig. 16, option 2) can use monitored data and networkmodel for an optimization process.

VII. EIGEN VALUE AND TIME DOMAIN RESULTSIn this section simulation results investigating different sta-

bility issues and stability improvement methods are presented(Figs. 2 and 3). Only a few key results, with the most commonstability improvement methods (Fig. 3, top row) for small signalstability, transient stability and voltage stability are presented todemonstrate the concepts. The simulation cases are shown inTable I. The cases are linked with the identified stability issuesin Sections IIIV and the improvement methods in Section V.The simulation cases are shown in Fig. 17. It is to be noted thatthese are simplified representations of the schemes. The microsource and the system parameters are presented in Tables IIVI.

A. Small Signal StabilityThe most common reason of small signal stability issues in

a microgrid is the feedback controller (Fig. 2). In this case, theimpact of the feedback gains on the system stability is tested bygradually increasing the power controller gain. The eigenvaluetrajectory with change in the power controller gain is shown inFig. 18 [for the example microgrid Fig. 17(a)]. It can be seen that the system becomes unstable for ahigher value of the feedback gain . However in manyscenarios a higher gain is required to ensure proper loadsharing.


Fig. 17. System structure in different stability study cases. (a) Small signalstability. (b) Islanding transients. (c) Load shedding. (d) Reactive compensation.

TABLE ISIMULATION CASES

TABLE IIGRID DATA

TABLE IIILOAD IN THE MICROGRID

A supplementary control loop (Figs. 3 and 11) can ensuresystem stability while using high feedback gain. For sim-ilar change in the power controller gain as in Fig. 18, theeigenvalue trajectory with the supplementary control loopis shown in Fig. 19.

TABLE IVCONVERTER AND CONTROLLER

TABLE VDG CONTROLLER GAINS

TABLE VIMICROGRID LINE IMPEDANCE

Fig. 18. Eigenvalue trajectory as function of power controller gain.

The time domain results with the high power controller gains(with and without the supplementary controller) are shown inFig. 20. The values of the power controller gains are changedfrom to at 0.2 s. The system becomes unstable with thehigh feedback gains as shown in Fig. 20(a). The supplementarycontroller can make the system stable as shown in Fig. 20(b).The active power output of the DG is shown as .The system damping with different converter control loops

(Fig. 9) are compared with 10% change in the power reference.The rise time and the settling time are shown in Fig. 21. It canbe seen that injecting damping signal in the current control loop alwaysprovides the fastest response (rise time);

the settling time is much higher in the remote microgrid ascompared to the facility microgrid;


Fig. 19. Eigen trajectory as function of power controller gain with supplemen-tary control loop.

Fig. 20. System stability with and without supplementary control loop.(a) System instability with high power controller gains. (b) Supplementarycontroller with high gain power controller.

Fig. 21. Damping in converter control loop.

the control loops for damping (Figs. 7 and 8) have differentimpacts on the facility and the remote microgrid in term ofthe response timings. The rise time varies in both the casesproportionally from current control loop to power controlloop. However the variations of control loops have littleimpact on settling time in case of the facility microgrid.

B. Islanding Transients

In this section, the transient stability issues following an is-land (Fig. 2) are demonstrated. There are various factors in afault and subsequent islanding. It is required to shed some load to achieve the powerbalance.

Fig. 22. System instability during islanding due to power imbalance.

Fig. 23. System stability during islanding with storage. (a) Power injection bystorage. (b) RMS voltage at load bus.

However, the load shedding procedure takes some time. In a fault, the system may lose stability very rapidly beforethe loads are cut off Fig. 22.

A fault ride through can be provided by a DSTATCOMFig. 12. (The normal operation of the DSTATCOM de-scribed in Fig. 13 can provide the reactive support.)

The support from the DSTATCOM provides time to shedload [39].

The value of the dc capacitor supplying the DSTATCOMshould be chosen such that there will be no appreciabledrop in the dc bus voltage during the transients.

Thus the DC capacitor value is derived from the energyrequirement during the transition.

It must be noted that this support from the DSTATCOM islimited with the device rating Fig. 13.

In a microgrid, storage plays an important role during islanding.The power injection from the storage (until the loads are cut off)can ensure 1) system stability, 2) power quality, and 3) normaloperation of the DGs.The storage can provide the stabilizer action (Figs. 14 and

15) throughout the system operation for both grid connectedand islanded mode. With battery storage it is possible to supplypower for longer time and this is useful following a major powerimbalance e.g., islanding.Fig. 23 shows the system response during an islanding with

power support from the storage. It can be seen that the extra loadrequirement is picked up by the battery at 0.15 s (islanding) andat 0.65 s the storage power output is reduced to zero as the loadsare shedded accordingly.


Fig. 24. Oscillations in system frequency and load shedding in islanding.

Fig. 25. Settling time of system frequency with load shedding in differentmicrogrids.

C. Load Shedding

The impact of the load shedding on the system stability isshown in this section. With the example microgrid [Fig. 17(c)],an islanding with 20% extra load is simulated. The islanding isfollowed by a load shedding to achieve the power balance. Thesystem responses with different load sheddingmethods (Fig. 16)are shown in Fig. 24. It can be seen that the performance of the conventionalfrequency relay deteriorates with presence of a motor load.

For critical network it is recommended to use the advancedload shedding method with superior performance Fig. 16.

The settling times in different microgrids are comparedin Fig. 25. It can be seen that with the motor load, thefrequency based load shedding has a longer settling timeand that is quite high in case of the remote microgrid.

D. Reactive Compensation

The reactive compensation method with the DSTATCOM(Figs. 12 and 13) is used in different types of microgrids. Asmentioned the compensation is achieved by the coordinatedcontrol of the DSTATCOM and the other DGs.This improves the RMS voltage in the feeders as shown

Fig. 26(b). It can be seen that without compensation the volt-ages fall much below the acceptable level [Fig. 26(a)]. TheRMS voltage drops (%) for different microgrids with reactivecompensation are shown in Fig. 27. It is to be noted that for the facility and the utility microgrids the voltage dropremains well within acceptable limit;

Fig. 26. Reactive compensation with DSTATCOM. (a) RMS voltage withoutreactive compensation. (b) RMS voltage with reactive compensation.

Fig. 27. Reactive compensation with different microgrid: voltage drop.

for the remote microgrid however, the voltage drops arearound 6%8% (generally the acceptable value is 10% insuch microgrid);

critical load (in remote microgrid) should be close to theDSTATCOM or other power quality equipment to havetighter voltage regulation.

VIII. CONCLUSIONS

Overall this paper focuses on various types of microgrids toinvestigate different stability issues and their main reasons; different improvement methods and comparative perfor-mances.

While stability problems are instigated by different factors invarious types of microgrids, efficacy of the stability improve-ment methods may vary largely depending on the applicationand the system scenarios. Generalized and methodical stabilitystudies of various types of microgrids are described with dif-ferent control methods, eigenvalue analysis and time domainsimulations.

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[30] R. Majumder, A. Ghosh, G. Ledwich, and F. Zare, Control of parallelconverters for load sharing with seamless transfer between grid con-nected and islanded modes, in Proc. IEEE Power and Energy Soc.General Meeting, Pittsburgh, PA, Jul. 2024, 2008.

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[35] R. Majumder, Modeling, stability analysis and control of microgrid,Ph.D. dissertation, Queensland Univ. Technol., Brisbane, Australia,2010.

[36] I. A. Hiskens and R. J. Davy, Lyapunov function analysis of powersystems with dynamic loads, Proc. 35th IEEE Decision and Control,vol. 4, pp. 38703875, Dec. 1996.

[37] R.Majumder, Reactive power compensation in single phase operationof microgrid, IEEE Trans. Ind. Electron., to be published.

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[39] R. Majumder, A. Ghosh, G. Ledwich, and F. Zare, Power sharing andstability enhancement of an autonomous microgrid with inertial andnon-inertial DGs with DSTATCOM, in Proc. Int. Conf. Power Sys-tems, 2009 (ICPS 09), Dec. 2729, 2009, pp. 16.

RitwikMajumder (M10) received the Ph.D. degree from Queensland Univer-sity of Technology, Brisbane, Australia.He is working at ABB Corporate Research, Vsters, Sweden. From 2004

to 2007, he worked with Siemens and ABB Corporate Research Centre, India.His interests are in power systems dynamics, distributed generation and powerelectronics applications.

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