Decentralized cooperative control strategy of microsources for stabilizing autonomous vsc based...

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 4, NOVEMBER 2012 1949

Decentralized Cooperative Control Strategyof Microsources for Stabilizing Autonomous

VSC-Based MicrogridsPoria Hasanpor Divshali, Arash Alimardani, Student Member, IEEE, Seyed Hossein Hosseinian, and

Mehrdad Abedi

Abstract—In designing procedure of a power sharing controllerfor a voltage source converter (VSC)-basedmicrogridwith no com-munication link, three issues should be considered. Firstly, in VSC-based microgrids, which use droop controller method, the desiredfrequency of VSCs is altering regarding the output active power.Consequently, the conventional load frequency control techniquesare inappropriate since their operation is based on a fixed pre-specified desired frequency. Secondly, to prevent circulating cur-rent and thermally overstressing, all DGs should participate in ac-tive power supply. In addition, since there is no communicationlink, the steady state value of each micro-source active power isunknown. Therefore, the conventional fixed active power controlmethod for DGs is not appropriate. Thirdly, when the microgridloads are increased, the output power of VSCs is increased rapidly;however, the output power of each VSC’s primary source couldnot change in the same rate to respond. It causes the DC voltage ofVSCs to decrease, which could affect the appropriate performanceof VSCs. In this paper, a novel control strategy for VSCs and an en-ergy storage system in a VSC-based microgrid without communi-cation link accompanied with a novel hybrid model of VSC-basedDGs, which considers primary source effect, is proposed.

Index Terms—Autonomous microgrids, distributed generation,frequency stability, frequency/voltage droop, small signal stability,storage system.

I. INTRODUCTION

C ONCERNS about environmental emissions from cen-tralized power plants, accompanied by the economical

and technical reasons, have increased interest in installation ofDGs. However, the penetration of DGs in a power system islimited due to the technical reasons such as stability constraints[1]. Therefore, indiscriminate application of individual DGscan cause as many problems as it may solve [2]. A better wayto realize the potential of a DG is to take a system approach,which views generation and associated loads as a subsystem ora microgrid [3]. Microgrids are required to operate in both gridconnected and islanding (autonomous) modes to increase reli-ability and power quality [4]. In an autonomous microgrid, allthe DGs are responsible for maintaining the system voltage and

Manuscript received July 12, 2011; revised October 28, 2011 and January 10,2012; accepted February 06, 2012. Date of publication April 10, 2012; date ofcurrent version October 17, 2012. Paper no. TPWRS-00653-2011.The authors are with the Department of Electrical Engineering, Amirkabir

University of Technology, Tehran, Iran (e-mail: [email protected]; [email protected]; [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.2012.2188914

frequency while sharing the active and reactive power. Sincemost DGs are of relatively low power capacity, maintainingthe balance of power in autonomous mode has required theparticipation of all DGs, and this has attracted the attention ofseveral researchers [5]–[8].The DGs in a microgrid, which is operated in islanding mode,

should share power between each other in an appropriate ratio toprevent circulating current and thermally overstressing or dam-aging of components [7]. In the conventional electrical networkwith synchronous generator, any alteration in active power bal-ance causes change in synchronous frequency. Consequently,the active power balancing is achieved by regulating the activepower produced by synchronous generators via the difference ofeach generator frequency from the reference frequency. How-ever, most DG technologies such as microturbines, fuel cells,and gas internal combustion engines with permanent magnetgenerator have a convertor to connect to the electrical distri-bution system [2]. These DG technologies have lower emis-sion, and higher efficiency rather than conventional DGs such asdiesel generator. In these DGs, the output frequency is indepen-dent from output power in nature. Therefore, when the micro-grid does not have any synchronous generator, the conventionaldroop method, which measures the error of rotating frequency,is not successful.In this situation, there are two methods to control voltage

source converter (VSC)-based microgrids. The first con-trol technique is based on communication links such as themaster-slave approach [8]. Such techniques can be adaptedin systems where DGs are connected to a common bus orlocated in close proximity. This is because it is impracticaland costly to distribute the dynamic sharing signals, whichare characterized by their high bandwidth in long connectiondistance [9]. Furthermore, reliability issues of the centralizedcontrol approach might counteract the positive reliability boostsgained by implementing microgrids [9]. The second controltechnique is based on frequency droop method [6]. In this droopmethod, unlike the conventional droop method, VSCs measurethe output active power and drop the frequency of voltagebased on the measured value. In other words, this methodemploys the frequency of the network instead of applying acommunication link. Although droop control does not ensureconstant frequency and amplitude of microgrid voltage, theadvantage in avoiding communication-based control makes ita competitive solution for controlling microgrids [10]. As aresult, this method is employed for power sharing controller ofmicrogrids in papers such as [5] and [6].

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1950 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 4, NOVEMBER 2012

VSC-based DGs, which use this frequency droop method,have another drawback. When the demand power of themicrogrid is increased, the output power of VSC increasesimmediately. On the other hand, primary sources such asmicroturbine or fuelcell are limited by insufficient dynamicperformance for load tracking [11]. Consequently, the DC busvoltage of VSC could be changed in a manner, which can affectthe VSC output voltage. Reference [6] has developed a loadsharing method in order to stabilize the operation of microgridwithout communication link. However, it assumes that the DCvoltage is constant. Reference [12] indicates that a fast-re-sponse energy storage module must be included in each DG toprovide a constant DC voltage with different primary sources.Installation of energy storage system (ESS) in each DG is verycostly. Hence, some papers focus on installing one ESS for thewhole microgrid. References [13] and [14] study the microgridwith synchronous generators and a central ESS. These micro-grids have synchronous generators and use the conventionalfrequency control method, which is used in large-scale powersystems. In these studies, the output power of convertor-basedDGs is considered constant, and the frequency is applied as theinput to the control units of synchronous generators and storagesystem. However, in a microgrid with no communication link,the suitable steady state value of micro-sources active power isunknown, since no micro-source has adequate information ofthe state of the network. Moreover, no DG is large enough tocompensate all the load variations, and all the DGs should par-ticipate in active power supply. Hence, considering a constantactive power for DGs is not appropriate. Reference [15] usesa single ESS in a microgrid and shows the better frequencycontrol can be achieved by cooperative control strategy of ESSand DGs. However, this cooperative control strategy needscommunication link.Thus, in this paper, a new cooperative control strategy for

VSC-based microgrids with no communication link, which con-sist of a single ESS and DGs, is proposed. The proposed methoddoes not need communication link and guarantees the stabilityof the VSC-based microgrid with a single ESS. In addition, inorder to consider the dynamic performance of primary sourceand its effect on the VSC work, a new hybrid model for VSC-based DGs is proposed.The rest of this paper is organized as follows: microgrid mod-

eling including new proposed method for considering the ef-fect of primary source on VSC performance is described inSection II. Section III describes a review on the frequency droopmethod in VSC-based microgrid and explains the proposed de-centralize cooperative control strategy for autonomous VSC-basedmicrogrid. The configuration of test system is described inSection IV. The simulation results and discussions are reportedin Section V. Conclusions are stated in Section VI.

II. MICROGRID MODELING

Each VSC-based microgrid consists of three major parts in-cluding the network, loads, and VSC-based DGs. In stabilityanalysis of VSC-based microgrids, because of the fast dynamicof VSC and larger R/X ratio of distribution lines than transmis-sion lines, network and loads should be modeled dynamically.The dynamic models of network and RL loads are described inseveral papers such as [6] and [16].

Different studies model the VSC-based DGs with variousprecisions. Some studies on DG modeling consider the primarysource without modeling the convertor. Reference [17] modelsthe primary source and its controllers completely withoutmodeling the convertor, and uses this model to design the DGcontrollers. References [13] and [14] used a first-order lagtransfer function to model the dynamic response of differentDGs output power regardless of the VSC dynamic. The timeconstant of this first-order transfer function is chosen equalto the biggest time constant of the complete primary sourcemodel. Some other studies propose the complete model ofVSC and primary source together [18]; however, because ofthe complexity of these models, they are not useful for stabilityanalysis. The others have modeled the VSC and its controllercompletely and neglect the dynamic of primary source, orassume that the DC voltage is fixed, and employ this modelfor stability analysis [6], [12]. Reference [6] demonstratesthat when the DC voltage is fixed, the switching process canbe assumed ideal, and it has no effect on stability analysis.Reference [12] shows that each VSC-based DG should have anenergy storage module in order to keep the DC voltage fixedand describes the specifications of this storage.In this paper, a hybrid model of a VSC-based DG, which con-

siders the primary source effect on VSC working, is proposed.In this model, the primary source is modeled with first-ordertransfer function as described in [13], the VSC is modeled com-pletely as described in [6] without the assumption of the fixedDC voltage, and the DC voltage is calculated from the differ-ence between the output power of the VSC and the primarysource. Consequently, the limitation of VSC’s performance dueto the DC voltage can be considered. The following subsectiondescribes the hybrid model of a VSC-based DG.

A. Proposed Hybrid Model

Fig. 1 shows the block diagram of the complete model ofa VSC-based DG and its controller. This model consists ofpower sharing controller, voltage controller, current controller,switching process, output filter and coupling inductance, DCbus, and primary source. The dynamic and algebraic equations(DAE) of each component of this model are as follow:1) Power Sharing Controller: The power sharing controller

of VSC-based microgrids is based on microgrid frequency andvoltage droop method. This droop method is based on two as-sumptions. The resistance of line compared to its inductancecould be neglected and the power angle is very small. Conse-quently, the active power is related to the phase angles differ-ences, while the reactive power depends on the voltage magni-tudes. As controlling the frequency can dynamically control thephase angle, the active and reactive power can be controlled byadjusting the DG output frequency and magnitude of voltage,respectively. Therefore, the frequency and voltage droop char-acteristics can be expressed as follows:

(1)

(2)

(3)

where and are the reference frequency and magnitudeof the DG output voltage, respectively. and are frequency

DIVSHALI et al.: DECENTRALIZED COOPERATIVE CONTROL STRATEGY OF MICROSOURCES 1951

Fig. 1. Block diagram of VSC-based DG and its controller.

and magnitude of the DG voltage in and ; andare the average output active and reactive power of the DG,

which is generated by a low pass filter with cutoff frequencyequal to ; and are the gains of the and Q-E droops.In other words, this method employs the variable frequency

and magnitude of voltage instead of utilizing a communicationlink, and therefore, enables the DG to share the load demandwithout physical communications between them [5], [6]. Thedifferential equations of power sharing controller are as follows[6]:

(4)

(5)

(6)

where , , , and are the direct and quadratic com-ponent of output voltage and output current, respectively.and are the frequency of VSC and common microgridrotational frame, respectively. is the angle between commonmicrogrid rotational frame and VSC rotational frame. More de-tails about rotational frame and power sharing controller are de-scribed in [6].2) Voltage Controller: The DAEs of voltage controller are

as follows [6]:

(7)

(8)

(9)

(10)

where and are the state variable corresponding to voltagePI controller, and other parameters are shown in Fig. 1.3) Current Controller: The DAEs of current controller are

as follows:

(11)

(12)

(13)

(14)

where and are the state variable corresponding to currentPI controller, and other parameters are shown in Fig. 1.4) Switching Process: Reference [6] demonstrates that when

the DC voltage is fixed, the switching process can be neglectedand the inverter produces the reference voltage . Inthis condition, the dynamic of primary source has no effect onVSC output voltage. However, as shown in [12], the fixed DCvoltage needs the fast-response energy storage in each VSC,which is very costly.This paper focuses on the effect of DC voltage alterations

on the performance of VSC working in order to eliminate thefast-response energy storage in eachVSC-based DG. The outputvoltage of each inverter is related to DC voltage by modulationindex (MI) as (15). At any moment, the inverter controllers cal-culate theMI and then the fire angles of each switch are obtainedbased on this value and switching strategy. The MI has a max-imum allowable value based on inverter structure and switchingstrategy, which determines the conditions under which the in-verter can work properly. The maximum allowable value of anMI in a three-phase inverter with programmed PWM switchingsignal is 1.102, which is calculated in subsection B:

(15)

where and are the reference voltage and is the DCvoltage, which is obtained from (24). Consequently, if

, the inverter can produce the reference voltage. However, if DC voltage reduces drastically so that the

becomes greater than , the inverter cannot supply thereference voltage. As a result, should be calculated from (16)and (17):


(16)

(17)

5) Output Filter and Coupling Inductance: The DAE ofoutput filter and coupling inductance are as follows [6]:

(18)

(19)

(20)

(21)

(22)

(23)

where and are the direct and quadratic components offilter current and other parameters are shown in Fig. 1.6) DC Bus Voltage Model: Each VSC-based DG includes

a DC bus, which connects the primary source to the VSC. Thisbus is composed of a capacitor as shown in Fig. 1. The capacitorvoltage changes as follows:

(24)

where is the capacitor of DC bus, is the time interval ofsimulation, is the output power of primary source suchas fuelcell, which is obtained from (25), and is the inputpower of VSC, which is equal to the output power in losslessVSCs. Since the MI has a maximum value, the DC voltage ofVSC has a minimum acceptable margin in order to work prop-erly.The voltage of DC bus depends on output power of VSC,

output power of primary source, and the capacitor value. As aresult, the primary source model affects the DC voltage, and ashas been shown in the previous subsection, if the DC voltageis reduced from the specified value , the invertercannot produce the reference voltage. The primary sourcemodelis explained in the next subsection.7) Primary Source Model: Since each primary source has a

complicated model from which the output current and voltage

Fig. 2. Primary source model and simple DC voltage controller.

of the DG can be obtained, previous works in stability analysisassume that the DC voltage is fixed and neglect the effect ofthe primary source model [6], [12]. However, as discussed inthe previous subsections, the effect of the primary source modelcould be vital and should be considered. Therefore, in the pro-posed hybrid model, which is used for stability analysis, the pri-mary source is modeled by a first-order lag transfer function asdescribed in [13] and [14]. This lag transfer function models thedelay of primary source to change its output power, which usefor DC voltage calculation.Fig. 2 depicts the primary source model with its proposed

controller, which is responsible for regulating the DC voltage.The input of this model is the active power reference of the pri-mary source, which is generated by the proposed proportionaldifferential (PD) controller to fix the DC voltage. The outputpower of the primary source is limited by the maximum outputpower of it. Equation (25), shown at the bottom of the page, de-scribes the primary source model regarding its controller, whereis the time constant of the primary source model and andare the proportional and differential gain of the DC voltage

controller, respectively.Generally, the proposed hybrid model considers the primary

source with the first-order lag transfer function, and the VSC,on the other hand, is modeled completely. This proposed modelcalculates the DC bus voltage and MI by solving the VSC andprimary source equations, simultaneously. This proposed hy-brid model adds two differential equations to the VSC model,which is presented in [6] to determine MI variations. When MIcrosses the maximum value, the inverter cannot produce thereference voltage and reduces its output voltage. This problemcould lead to a voltage collapse (instability) in microgrid.The proposed hybrid model considers the effect of primary

source without adding complicated primary source model; asa result, it has the capability for stability analysis usage andensures that the VSC operates in a feasible operation point astwo advantages.

B. MI Allowable Range

A three-phase inverter and its typical output voltage with pro-grammed PWM switching signal are shown in Figs. 3 and 4. Theamplitude of the th harmonic of the output voltage is given by

(25)


Fig. 3. Three-phase voltage source inverter configuration.

Fig. 4. Typical output waveform of a PWM inverter.

(26)

where is the th switching angle and is the number ofswitching angles in a quarter of period as shown in Fig. 4.Hence, the MI, which is calculated from the first harmony ofline to line voltage , is as

(27)

Mathematical analysis of the following equation indicatesthat the maximum possible value for MI is 1.102:

(28)

Considering the constraint in (26), it is obvious that all havenegative value. To maximize Z, first switching angle must be

equal to zero to result in the maximum . It is noteworthythat assigning zero to imposes no further constraints on theother angles since: .As all the have negative value, if one could reduce the sum

of them to zero, the best possible set of angles is resulted whichmaximizes Z. To do so, the switching angles of each shouldbe equal. Each thus would become zero and the maximumMI is reached. By employing such set of switching angles, isequal to 1 and the maximum MIis 1.102. The same analysis stands for minimum M ( 1.102),which is a negative value meaning a shift in the voltage phase.This argument shows that in order to maintain the output

voltage in a desired value , the DC bus voltage should notdecrease more than .In this paper, the programmed PWM switching pattern is

chosen because it is one of the most effective mediums inharmonic elimination, control of fundamental harmonic mag-nitude, and loss minimization among available PWM schemes[19]–[26]. Whether the implemented method is programmedPWM or space vector modulation or any other standardswitching method, the generality of this point is valid that theDC voltage of the converter should satisfy a limit such as whatwas mentioned above.

III. DECENTRALIZED COOPERATIVE CONTROLSTRATEGY OF MICROSOURCES

The droop method can share the active and reactive powerbetween all DGs without communication link. However, thismethod has two drawbacks. Eliminating the physical commu-nication link causes the frequency and amplitude of microgridvoltage to be constant in different load levels. This makes it im-possible to use the conventional load/frequency control method,which is based on constant frequency. The other major draw-back of droop method is as follows.When the active power demand of microgrid is increased, the

output powers of VSCs are increased rapidly and the demandchange is shared between all VSCs based on network parame-ters. The output power increasing rate of VSCs which are closerto the location of demand change are more than the others. Afterthat altering, the droop controllers change the frequency of allVSCs and after a few seconds, the output powers of VSCs areshared based on the droop gains. During this time, output powerof the primary source varies slowly based on its dy-namic performance. Hence, if VSC-based DG does not have anESS, the DC voltage is reduced and the MI might reach its limit.Therefore, the VSC would not work properly.In this paper, a new cooperative control method, which uses a

single ESS in the whole microgrid and maintains the DC voltageof all DGs, is proposed. This ESS consists of a battery storagesystem or super capacitor system (or a combination), which con-nects to the microgrid with a VSC. This method includes twomodifications in the present droop technique. The first is relatedto the droop controller of a single ESS and the other is related tothe droop controller of DGs. These modifications are describedin the two following subsections. It should be noticed that theproposed method does not require any communication link be-tween generation units.


Fig. 5. Frequency droop slope of energy storage system.

A. Control of a Single ESS

The output power of an ESS should be equal to zero in steadystate condition and it should be changed rapidly when the de-mand of the microgrid is altered in order to stabilize the micro-grid. In order words, the ESS should work similar to slack busin the conventional power system but with zero output powerin steady state. For this purpose, the droop controller of theESS should have a high active gain in steady state. Whenthe demand is changed, the gain should be decreased rapidlyand then should be increased slowly back to the initial valueas demonstrated in Fig. 5. High gain of the ESS active droopcauses the ESS to produce approximate zero active power insteady state condition, and low gain of active droop leadsthe ESS to produce or consume almost all the demand variationin dynamic behavior of the microgrid. Consequently, the activedroop gain of a single ESS in the proposed method could be ex-pressed by

(29)

where and are the high and low droop gains; is a co-efficient, which determines the velocity of increasing the droopgain from to . The higher , the faster changing of thedroop, the less ESS energy supplying, and the more decrementin DC voltage of DGs. is the last time that the microgrid’s de-mand is changed and should be determined in the ESS locallyfor decentralized control.When the microgrid’s demand is changed, the output power

of all DGs and the ESS are changed based on network parame-ters. To detect the demand changes of microgrids in ESS locally,a method, which operates based on monitoring output power ofthe ESS, is proposed in this paper. For this purpose, first, theoutput power of the ESS is compared with its averagein last few seconds. When the output power changed suddenly,the output power goes away from its average value and based onthis compression, the moment of demand variation is detected.The average of the output power in last few seconds

is obtained by crossing the output power from first-order lagsystem with time constant equal to . Therefore, based ontrapezoidal rule [27], is calculated from

(30)

Based on the proposed method, the last time that the micro-grid demand is changed can be detected locally when (31) and(32) are satisfied:

(31)

(32)

where means the absolute value; and are the reliabilitycoefficients. Equation (31) detects variations in the outputpower. This equation calculates the difference between theoutput power and the average output power, and compares theresult with the minimum of them. If this difference is biggerthan a factor multiplied by the minimum of output powerand the average output power, it means the output power isconsiderably changed. The factor should be selected so thatall major demand changes are detected in ESS. This value isdependent to and , the smaller or the larger leadsto smaller . To determine this value, the microgrid should besimulated in designing process and the and shouldbe monitored after the critical load increment. In general, whena load increases, initially the output power-increasing rate ofthe closest VSC is more than others. In other words, the farthestVSC to where the load senses the least change. Therefore, thecritical load increment is the amount of load increment in thefarthest bus to the ESS, which leads the MI of one VSC toreach the maximum value, if the ESS does not detect it.Equation (32) compares the value of this difference with the

difference value in the previous step of simulation and checkswhether the change is new. If the output power is changed andthis change is a new change, the value of is updated to . Theprocess of selecting is similar to selecting process.

B. Control of DGs

The active output power of primary sources changes slowlyin DGs. Therefore, if the output power of a VSC changes slowly,too, the DC voltage tolerance is reduced. Therefore, a mecha-nism should be implemented to slow the response speed of theVSC. For this purpose, the frequency droop gain of DGs shouldbe increased when their output active power changes.References [9] and [28], for better dynamic response of

VSCs, drop the frequency of VSCs based on the derivation ofthe output power with respect to time. In this paper, this methodis used to increase the frequency droop gain when the outputpower changes. Hence, the DGs droop gain is defined as

(33)

where is the th DG frequency gain in steady state condi-tion and is the coefficient of increasing frequency droopgain of corresponding DG in relation to absolute of output ac-tive power derivation . Equation (33) results in in-creasing the droop gain in dynamic condition. Hence, activeoutput power of VSC will change less and DC voltage will bemaintained in its constraint. In other words, the proposed droopmethod for DGs helps the single ESS to supply the whole de-mand variations initially. Afterwards, ESS reduces its output ac-tive power to zero gradually, on the other hand, DGs increase therate of their participation in supplying the microgrid demandslowly. After some seconds, the output of ESS becomes zero,the storage is ready for next change in demand, and the demandis shared perfectly between all DGs.


Fig. 6. Configuration of the sample microgrid.

In order to keep DC voltage of all VSC-based DGs fixed, theESS should provide almost the whole demand power variationsin the few initial seconds. Consequently, the ESS power rateshould be equal to the largest demand changes in the microgrid.Otherwise, it is possible that the DC bus of DGs reduces moreand the voltage collapse occurs.

IV. CONFIGURATION OF THE TEST SYSTEM

Fig. 6 presents the configuration of the studied microgrid inthis paper. This microgrid is the test study of [15] with somemodifications. This system includes two fuelcells and two mi-croturbines as DGs, a battery storage system as an ESS, a statictransfer switch (STS), and four loads. The ESS is placed nearthe point of common coupling (PCC) of low voltage microgridand medium voltage distribution network to be utilized whenthe system transits to islanding operation mode. The STS candisconnect the microgrid from the distribution network when itis necessary. The detailed aspects of the test system are as fol-lows, and the VSCs parameters are listed in the Appendix.1) Single energy storage system

a) ESS: 10-kW battery energy storage.2) Load (constant impedance):

a) Load 1:10 kW j6.5 kVAr.b) Load 1:5 kW.c) Load 1:50 kW j20 kVAr.d) Load 1:8 kW 8 kVAr.

3) DGs:a) DG1: 10-kVA fuelcell.b) DG2: 70-kVA microturbine.c) DG3: 70-kVA fuelcelld) DG4: 20-kVA microturbine.

4) Line:a) Line 1: .b) Line 2: .c) Line 3: .d) Line 4: .

5) Network: Injects 10 kW j6.5 kVAr.

V. SIMULATION STUDY

To evaluate the dynamic behavior of the microgrid with andwithout the proposed cooperative control strategy, the microgridstate space equations are modeled in MATLAB. The state spaceequations are obtained from VSCs, loads, and network DAE.These equations are solved by Newton method [29] for steady

Fig. 7. Output active power of VSC-based DGs in case A.

state condition. The dynamic response of the microgrid is ob-tained by applying trapezoidal rule [27] in these state equations.The details of the obtaining the operation point and dynamic re-sponse are described in [30].In this section, three cases are considered. Case A considers

the microgrid with an ESS in each DG. In case B, there is noESS in the microgrid. Case C simulates the proposed methodand considers a single ESS at bus 1 (Fig. 6) with no ESS in eachDG. In this case, the single ESS without any communicationlink detects the network alteration and produces or absorbs ad-equate active power. In all cases, the simulation is run for 75s; initially, the microgrid is connected to the distribution net-work and receives 10 kW j 10 kVAr from it. On , STSis opened and the microgrid becomes islanded, and finally, on

, all loads are increased 10%.

A. Case A

In this case, the central ESS (in Fig. 6) is not connected; how-ever, all DGs have an ESS in the DC link. Since the batterystorage system has rapid dynamic ( [14]), all DCvoltages are almost fixed and the MI remains in allowable rangeduring simulation. The output active power of each DG in thiscase is shown in Fig. 7.As shown in this figure, in , disconnecting from the

utility, DGs output active power are changed rapidly. Amongthem, DG1 is closer to PCC, and therefore, its output power-in-creasing rate is more than the other DGs. After a few seconds,the active power is shared between all DGs based on their droopgain, and the system reaches the steady state condition. In

, the loads are increased 10%, and this demand incrementis shared between all DGs perfectly. The DC voltage and MI ofDGs in case A are shown in Figs. 8 and 9, respectively. Thesefigures show that the DC voltage of DG1 is changed more thanother DGs because its output power is changed more rapidly.


Fig. 8. DC voltage of VSC-based DGs in case A.

Fig. 9. MI of VSC-based DGs in case A.

Fig. 10. Important eigenvalues of the microgrid of case A.

Fig. 11. Frequency of microgrid in case A.

However, the MI of all DGs is in the acceptable range and there-fore, the microgrid works properly. The important eigenvaluesof microgrid in case A demonstrate the small signal stability(SSS) of this case as shown in Fig. 10.When the microgrid is in the connected mode, the frequency

of the microgrid is equal to the network frequency. However,in the islanding mode, the frequency changes based on demandand droop gains. The frequency alteration of the microgrid inthis case is shown in Fig. 11.

B. Case B

In this case, it is assumed that none of the DGs has ESS, andthe single ESS of Fig. 6 is not connected either. Based on theproposed hybrid VSC-based DG model, which is developed inthis paper, the important eigenvalues of this case, which has no

Fig. 12. Important eigenvalues of the microgrid of case B.

Fig. 13. Primary source active power of VSC-based DGs in case B.

Fig. 14. DC voltage of VSC-based DGs in case B.

Fig. 15. Modulation index of VSC-based DGs in case B.

ESS, are shown in Fig. 12. This figure shows that this case haszero eigenvalues and therefore, this microgrid is unstable whenthe demand is changed.In order to demonstrate the reason of this instability, it is as-

sumed that the VSC can work perfectly the same as case A. Inthis condition, since this case has no ESS and the primary sourcedynamic is slow, the DC bus voltage is reduced rapidly and theMI reaches its maximum limit. By this assumption, the primarysource power, which is obtained from (25), the DC bus voltage,which is calculated from (24), and the MI, which is obtainedfrom (15), are shown in Figs. 13–15, respectively.As stated in (16) and (17), the VSC can produce desired

voltage, when the MI is smaller than , which is equalto 1.102 in this case. When the MI is greater than , theoutput voltage is less than the desired voltage as obtained in


(16) and (17). Fig. 15 demonstrates that the MI is so larger than1.102, when this microgrid is disconnected from the utility in

, and Fig. 14 shows that the is equal to zero in thistime. Therefore, the output voltage of first VSC is reduced tozero at this time. Thus, the voltage collapse is occurred and themicrogrid becomes unstable.Consequently, case B shows that the microgrid with no ESS

cannot work properly. Based on the same reason, previousworks use ESSs in a microgrid. As mentioned above, someof them use single ESS in microgrid with central controllerand use the communication link to determine when and howmuch the ESS should generates or absorbs the active power.Others assume all DGs have an ESS and the DC voltage isfixed. Utilizing a communication link or several ESSs willimpose large cost to microgrid. Therefore, in this paper, anew method is proposed, which works with a single ESS andwithout employing communication link. Case C presents thesimulation results of this proposed method.

C. Case C

In this case, the ESS is connected to bus 1 with the proposedcontroller and no DG has separate ESS. The ESS is a batterystorage system, which ismodeled byfirst order lag transfer func-tion with time constant equal to 0.1 s as described in Section II.The proposed hybrid model is considered in all DGs and ESS,and the MI is traced. If the MI reaches its allowable limit, theVSC output voltage is reduced and the system may become un-stable. Initially, the system is connected to the distribution net-work. In , the microgrid is disconnected from the dis-tribution network. In this time, the output power of all VSCsis changed. The proposed method based on the conditions de-scribed in (31) and (32) determines the demand changing (dis-connecting from network) in (detected with a delay,which is equal to the sampling time interval), and drop the fre-quency droop gain suddenly. Also, in , the detec-tion algorithm of ESS identifies the demand changing and de-creases the droop gain of ESS. In this case, is set equal to0.1 and is equal to 0.5. In order to set these values, the crit-ical load increment is considered (load changes in bus 5, whereis the farthest bus to the ESS). It worth mentioning that severaldemand changes are simulated in this case, in order to analyzethe claim of the farthest bus is the critical one and it is observedthat the and , which are selected based on critical bus(bus 5) lead to detect all load changes.Fig. 16 shows the ESS output power and its average, which

are used for demand change detection . As shown inthis figure, the output power of ESS is increased suddenly anddecreased slowly in order to provide the opportunity of increaseof the DGs primary source output power and follow the demandvariations.The frequency droop gain of ESS and DGs, which change

in time based on the proposed cooperative control strategy areshown in Fig. 17.The proposed cooperative control strategy causes to increase

the DGs droop gain when DGs output power changes and de-crease the ESS droop gain when the demand changes as shownin Fig. 17. This method leads to slow change in the output ac-tive power of VSCs as shown in Fig. 18. Since the ESS produces

Fig. 16. Output and average of active power of ESS in case C.

Fig. 17. Frequency droop slope of VSC-based DGs and ESS in case C.

Fig. 18. Output active power of VSC-based DGs in case C.

Fig. 19. Primary source active power of VSC-based DGs in case C.

zero power in steady state, the steady state output active powerof DGs in this case is similar to case A (Fig. 7).When the VSC output power of the ESS changes slowly, the

output power of primary source has the opportunity to followit. Hence, the DC voltage will have less variation. The activepower of primary source and the DC voltage of DGs are shownin Figs. 19 and 20, respectively.By comparing Fig. 20 with Fig. 14, which shows the DC

voltage of case B, it is demonstrated that the proposed coop-erative strategy can reduce the DC voltage tolerance of all DGs.The MI of all DGs in case C are depicted in Fig. 21.Fig. 21 shows that the MI remains in its limits in case C. It

means that the microgrid with the proposed control strategy canwork by a single storage system without communication link


Fig. 20. DC voltage of VSC-based DGs in case C.

Fig. 21. Modulation index of VSC-based DGs in case C.

Fig. 22. Frequency of microgrid in case C.

Fig. 23. Important eigenvalues of the microgrid of case C.

and maintain its stability. The frequency deviation of the micro-grid in this case is shown in Fig. 22. The important eigenvaluesof microgrid with the proposed cooperative control strategy areshown in Fig. 23. It is noteworthy that since case C has moreVSCs (adding a VSC for a single ESS), this case has a littlesmaller damping ratio than case A [31]. These figures show theperformance of this method to keep frequency regulation andSSS in dynamic behavior. Thus, any need to costly ESS in eachDG or the communication link are eliminated.

VI. CONCLUSION

This paper is focused on the problem of the active power bal-ance between supply and demand in autonomous VSC-based

TABLE IVSC PARAMETERS

Time constant of primary source.

microgrids with no communication link. In such microgrids,three important issues should be considered:• During islanding, to maintain power balancing and thepower sharing, the output power of VSCs should bechanged rapidly. However, the dynamic response of pri-mary source is slow. Hence, the DC bus voltage and theoutput voltage of VSC may have fluctuations. To analyzethis situation, the hybrid VSC-based DG model, whichconsiders the primary source effect, is proposed in thispaper. In this model, the modulation index is calculatedand the VSC can work properly, if this index remains inits limitation.

• VSC-based microgrids without synchronous generator andcommunication link do not have fixed frequency. Hence,the conventional load/frequency control method cannot beemployed in these networks. Previous works use the droopmethod with an EES in each VSC for load/frequency con-trol. In this paper, the cooperative control method for ESSand DGs is proposed which needs only one single ESS inthe whole microgrid and no communication link.

• Because of problem of communication link in wide mi-crogrid, the demand change should be detected in the ESSlocally. The proposed ESS control method detects the de-mand change in ESS locally and does not need physicalcommunication link.

The simulation results show the proposed method can guar-antee the active power balancing in autonomous microgrid andmaintain DC voltage of VSC-based DGs in acceptable rangewithout an ESS in each of VSC or communication link. In ad-dition, proposed method satisfies the small signal stability ofmicrogrid.

APPENDIXVSC PARAMETERS

The VSC model and controller parameters are as follows:, , , , ,

, , , ,, , , , , ,

, and . Other parameters are listed inTable I.

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Poria Hasanpor Divshali was born in Tehran, Iran,in 1984. He received the B.Sc. and M.Sc. degreesfrom the Electrical Engineering Department ofAmirkabir University of Technology (AUT), Tehran,in 2006 and 2008, respectively. He is currentlypursuing the Ph.D. degree in electrical engineeringin AUT.His research interests include power system

stability, distribution system planning, electricitymarket, and microgrid.

Arash Alimardani (S’09) was born in Gorgan, Iran,in 1985. He received the B.Sc. degree in electricalengineering from Isfahan University of Technology,Isfahan, Iran, and the M.Sc. degree from AmirkabirUniversity of Technology (Tehran Polytechnic),Tehran, Iran. He is currently pursuing the Ph.D.degree in the University of British Columbia, Van-couver, BC, Canada.His research interests include state estimation in

smart grids, optimum control of renewable energiesutilities, power electronics particularly in energy

storage systems, and electricity market.

Seyed Hossein Hosseinian was born in Iran in 1961.He received both the B.Sc. and M.Sc. degrees fromthe Electrical Engineering Department of AmirkabirUniversity of Technology (AUT), Tehran, Iran, in1985 and 1988, respectively, and the Ph.D. degree inthe Electrical Engineering Department, Universityof Newcastle, Newcastle, U.K., in 1995.At the present, he is a Professor of the Electrical

Engineering Department at the AUT. His specialfields of interest include transient in power systems,power quality, restructuring, and deregulation in

power systems.

Mehrdad Abedi received the B.Sc. degree inelectrical engineering from the University of Tehran,Tehran, Iran, in 1970, the M.Sc. degree from theElectrical Engineering Department, Imperial Col-lege, University of London, London, U.K., in 1973,and the Ph.D. degree in electrical engineering fromNewcastle University, Newcastle, U.K., in 1977.He is currently Professor of the Electrical Engi-

neering Department in Amirkabir University of Tech-nology, Tehran.

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