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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, Different studies model the VSC-based DGs with varioushave another drawback. When the demand power of the precisions. Some studies on DG modeling consider the primarymicrogrid is increased, the output power of VSC increases source without modeling the convertor. Reference [17] modelsimmediately. On the other hand, primary sources such as the primary source and its controllers completely withoutmicroturbine or fuelcell are limited by insufﬁcient dynamic modeling the convertor, and uses this model to design the DGperformance for load tracking [11]. Consequently, the DC bus controllers. References [13] and [14] used a ﬁrst-order lagvoltage of VSC could be changed in a manner, which can affect transfer function to model the dynamic response of differentthe VSC output voltage. Reference [6] has developed a load DGs output power regardless of the VSC dynamic. The timesharing method in order to stabilize the operation of microgrid constant of this ﬁrst-order transfer function is chosen equalwithout communication link. However, it assumes that the DC to the biggest time constant of the complete primary sourcevoltage is constant. Reference [12] indicates that a fast-re- model. Some other studies propose the complete model ofsponse energy storage module must be included in each DG to VSC and primary source together [18]; however, because ofprovide a constant DC voltage with different primary sources. the complexity of these models, they are not useful for stabilityInstallation of energy storage system (ESS) in each DG is very analysis. The others have modeled the VSC and its controllercostly. Hence, some papers focus on installing one ESS for the completely and neglect the dynamic of primary source, orwhole microgrid. References [13] and [14] study the microgrid assume that the DC voltage is ﬁxed, and employ this modelwith synchronous generators and a central ESS. These micro- for stability analysis [6], [12]. Reference [6] demonstratesgrids have synchronous generators and use the conventional that when the DC voltage is ﬁxed, the switching process canfrequency control method, which is used in large-scale power be assumed ideal, and it has no effect on stability analysis.systems. In these studies, the output power of convertor-based Reference [12] shows that each VSC-based DG should have anDGs is considered constant, and the frequency is applied as the energy storage module in order to keep the DC voltage ﬁxedinput to the control units of synchronous generators and storage and describes the speciﬁcations of this storage.system. However, in a microgrid with no communication link, In this paper, a hybrid model of a VSC-based DG, which con-the suitable steady state value of micro-sources active power is siders the primary source effect on VSC working, is proposed.unknown, since no micro-source has adequate information of In this model, the primary source is modeled with ﬁrst-orderthe state of the network. Moreover, no DG is large enough to transfer function as described in [13], the VSC is modeled com-compensate all the load variations, and all the DGs should par- pletely as described in [6] without the assumption of the ﬁxedticipate in active power supply. Hence, considering a constant DC voltage, and the DC voltage is calculated from the differ-active power for DGs is not appropriate. Reference [15] uses ence between the output power of the VSC and the primarya single ESS in a microgrid and shows the better frequency source. Consequently, the limitation of VSC’s performance duecontrol can be achieved by cooperative control strategy of ESS to the DC voltage can be considered. The following subsectionand DGs. However, this cooperative control strategy needs describes the hybrid model of a VSC-based DG.communication link. Thus, in this paper, a new cooperative control strategy for A. Proposed Hybrid ModelVSC-based microgrids with no communication link, which con- Fig. 1 shows the block diagram of the complete model ofsist of a single ESS and DGs, is proposed. The proposed method a VSC-based DG and its controller. This model consists ofdoes not need communication link and guarantees the stability power sharing controller, voltage controller, current controller,of the VSC-based microgrid with a single ESS. In addition, in switching process, output ﬁlter and coupling inductance, DCorder to consider the dynamic performance of primary source bus, and primary source. The dynamic and algebraic equationsand its effect on the VSC work, a new hybrid model for VSC- (DAE) of each component of this model are as follow:based DGs is proposed. 1) Power Sharing Controller: The power sharing controller The rest of this paper is organized as follows: microgrid mod- of VSC-based microgrids is based on microgrid frequency andeling including new proposed method for considering the ef- voltage droop method. This droop method is based on two as-fect of primary source on VSC performance is described in sumptions. The resistance of line compared to its inductanceSection II. Section III describes a review on the frequency droop could be neglected and the power angle is very small. Conse-method in VSC-based microgrid and explains the proposed de- quently, the active power is related to the phase angles differ-centralize cooperative control strategy for autonomous VSC- ences, while the reactive power depends on the voltage magni-based microgrid. The conﬁguration of test system is described in tudes. As controlling the frequency can dynamically control theSection IV. The simulation results and discussions are reported phase angle, the active and reactive power can be controlled byin Section V. Conclusions are stated in Section VI. adjusting the DG output frequency and magnitude of voltage, respectively. Therefore, the frequency and voltage droop char- II. MICROGRID MODELING acteristics can be expressed as follows: Each VSC-based microgrid consists of three major parts in-cluding the network, loads, and VSC-based DGs. In stability (1)analysis of VSC-based microgrids, because of the fast dynamic (2)of VSC and larger R/X ratio of distribution lines than transmis- (3)sion lines, network and loads should be modeled dynamically.The dynamic models of network and RL loads are described in where and are the reference frequency and magnitudeseveral papers such as [6] and [16]. of the DG output voltage, respectively. and are frequency
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DIVSHALI et al.: DECENTRALIZED COOPERATIVE CONTROL STRATEGY OF MICROSOURCES 1951Fig. 1. Block diagram of VSC-based DG and its controller.and magnitude of the DG voltage in and ; and (12) are the average output active and reactive power of the DG, (13)which is generated by a low pass ﬁlter with cutoff frequency (14)equal to ; and are the gains of the and Q-E droops. In other words, this method employs the variable frequency where and are the state variable corresponding to currentand magnitude of voltage instead of utilizing a communication PI controller, and other parameters are shown in Fig. 1.link, and therefore, enables the DG to share the load demand 4) Switching Process: Reference [6] demonstrates that whenwithout physical communications between them [5], [6]. The the DC voltage is ﬁxed, the switching process can be neglecteddifferential equations of power sharing controller are as follows and the inverter produces the reference voltage . In[6]: this condition, the dynamic of primary source has no effect on VSC output voltage. However, as shown in [12], the ﬁxed DC (4) voltage needs the fast-response energy storage in each VSC, (5) which is very costly. (6) This paper focuses on the effect of DC voltage alterations on the performance of VSC working in order to eliminate thewhere , , , and are the direct and quadratic com- fast-response energy storage in each VSC-based DG. The outputponent of output voltage and output current, respectively. voltage of each inverter is related to DC voltage by modulationand are the frequency of VSC and common microgrid index (MI) as (15). At any moment, the inverter controllers cal-rotational frame, respectively. is the angle between common culate the MI and then the ﬁre angles of each switch are obtainedmicrogrid rotational frame and VSC rotational frame. More de- based on this value and switching strategy. The MI has a max-tails about rotational frame and power sharing controller are de- imum allowable value based on inverter structure and switchingscribed in [6]. strategy, which determines the conditions under which the in- 2) Voltage Controller: The DAEs of voltage controller are verter can work properly. The maximum allowable value of anas follows [6]: MI in a three-phase inverter with programmed PWM switching signal is 1.102, which is calculated in subsection B: (7) (8) (9) (15) (10) where and are the reference voltage and is the DCwhere and are the state variable corresponding to voltage voltage, which is obtained from (24). Consequently, ifPI controller, and other parameters are shown in Fig. 1. , the inverter can produce the reference voltage 3) Current Controller: The DAEs of current controller are . However, if DC voltage reduces drastically so that theas follows: becomes greater than , the inverter cannot supply the reference voltage. As a result, should be calculated from (16) (11) and (17):
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1952 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 4, NOVEMBER 2012 (16) Fig. 2. Primary source model and simple DC voltage controller. (17) of the DG can be obtained, previous works in stability analysis 5) Output Filter and Coupling Inductance: The DAE of assume that the DC voltage is ﬁxed and neglect the effect ofoutput ﬁlter and coupling inductance are as follows [6]: the primary source model [6], [12]. However, as discussed in the previous subsections, the effect of the primary source model (18) could be vital and should be considered. Therefore, in the pro- posed hybrid model, which is used for stability analysis, the pri- (19) mary source is modeled by a ﬁrst-order lag transfer function as described in [13] and [14]. This lag transfer function models the (20) delay of primary source to change its output power, which use for DC voltage calculation. (21) Fig. 2 depicts the primary source model with its proposed controller, which is responsible for regulating the DC voltage. (22) The input of this model is the active power reference of the pri- mary source, which is generated by the proposed proportional (23) differential (PD) controller to ﬁx the DC voltage. The output power of the primary source is limited by the maximum output power of it. Equation (25), shown at the bottom of the page, de-where and are the direct and quadratic components of scribes the primary source model regarding its controller, whereﬁlter current and other parameters are shown in Fig. 1. is the time constant of the primary source model and and 6) DC Bus Voltage Model: Each VSC-based DG includes are the proportional and differential gain of the DC voltagea DC bus, which connects the primary source to the VSC. This controller, respectively.bus is composed of a capacitor as shown in Fig. 1. The capacitor Generally, the proposed hybrid model considers the primaryvoltage changes as follows: source with the ﬁrst-order lag transfer function, and the VSC, on the other hand, is modeled completely. This proposed model (24) calculates the DC bus voltage and MI by solving the VSC and primary source equations, simultaneously. This proposed hy-where is the capacitor of DC bus, is the time interval of brid model adds two differential equations to the VSC model,simulation, is the output power of primary source such which is presented in [6] to determine MI variations. When MIas fuelcell, which is obtained from (25), and is the input crosses the maximum value, the inverter cannot produce thepower of VSC, which is equal to the output power in lossless reference voltage and reduces its output voltage. This problemVSCs. Since the MI has a maximum value, the DC voltage of could lead to a voltage collapse (instability) in microgrid.VSC has a minimum acceptable margin in order to work prop- The proposed hybrid model considers the effect of primaryerly. source without adding complicated primary source model; as The voltage of DC bus depends on output power of VSC, a result, it has the capability for stability analysis usage andoutput power of primary source, and the capacitor value. As a ensures that the VSC operates in a feasible operation point asresult, the primary source model affects the DC voltage, and as two advantages.has been shown in the previous subsection, if the DC voltageis reduced from the speciﬁed value , the inverter B. MI Allowable Rangecannot produce the reference voltage. The primary source modelis explained in the next subsection. A three-phase inverter and its typical output voltage with pro- 7) Primary Source Model: Since each primary source has a grammed PWM switching signal are shown in Figs. 3 and 4. Thecomplicated model from which the output current and voltage amplitude of the th harmonic of the output voltage is given by (25)
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DIVSHALI et al.: DECENTRALIZED COOPERATIVE CONTROL STRATEGY OF MICROSOURCES 1953 equal to zero to result in the maximum . It is noteworthy that assigning zero to imposes no further constraints on the other 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 which maximizes Z. To do so, the switching angles of each should be equal. Each thus would become zero and the maximum MI is reached. By employing such set of switching angles, is equal to 1 and the maximum MI is 1.102. The same analysis stands for minimum M ( 1.102), which is a negative value meaning a shift in the voltage phase.Fig. 3. Three-phase voltage source inverter conﬁguration. This argument shows that in order to maintain the output voltage in a desired value , the DC bus voltage should not decrease more than . In this paper, the programmed PWM switching pattern is chosen because it is one of the most effective mediums in harmonic elimination, control of fundamental harmonic mag- nitude, and loss minimization among available PWM schemes [19]–[26]. Whether the implemented method is programmed PWM or space vector modulation or any other standard switching method, the generality of this point is valid that the DC voltage of the converter should satisfy a limit such as what was mentioned above.Fig. 4. Typical output waveform of a PWM inverter. III. DECENTRALIZED COOPERATIVE CONTROL STRATEGY OF MICROSOURCES The droop method can share the active and reactive power between all DGs without communication link. However, this method has two drawbacks. Eliminating the physical commu- nication link causes the frequency and amplitude of microgrid voltage to be constant in different load levels. This makes it im- (26) possible to use the conventional load/frequency control method, which is based on constant frequency. The other major draw-where is the th switching angle and is the number of back of droop method is as follows.switching angles in a quarter of period as shown in Fig. 4. When the active power demand of microgrid is increased, theHence, the MI, which is calculated from the ﬁrst harmony of output powers of VSCs are increased rapidly and the demandline to line voltage , is as change is shared between all VSCs based on network parame- ters. The output power increasing rate of VSCs which are closer to the location of demand change are more than the others. After (27) that altering, the droop controllers change the frequency of all VSCs and after a few seconds, the output powers of VSCs are shared based on the droop gains. During this time, output power Mathematical analysis of the following equation indicates of the primary source varies slowly based on its dy-that the maximum possible value for MI is 1.102: namic performance. Hence, if VSC-based DG does not have an ESS, 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 voltage of all DGs, is proposed. This ESS consists of a battery storage system or super capacitor system (or a combination), which con- nects to the microgrid with a VSC. This method includes two modiﬁcations in the present droop technique. The ﬁrst is related to the droop controller of a single ESS and the other is related to (28) the droop controller of DGs. These modiﬁcations are described in the two following subsections. It should be noticed that the Considering the constraint in (26), it is obvious that all have proposed method does not require any communication link be-negative value. To maximize Z, ﬁrst switching angle must be tween generation units.
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1954 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 4, NOVEMBER 2012 (32) where means the absolute value; and are the reliability coefﬁcients. Equation (31) detects variations in the output power. This equation calculates the difference between the output power and the average output power, and compares the result with the minimum of them. If this difference is biggerFig. 5. Frequency droop slope of energy storage system. than a factor multiplied by the minimum of output power and the average output power, it means the output power isA. Control of a Single ESS considerably changed. The factor should be selected so that all major demand changes are detected in ESS. This value is The output power of an ESS should be equal to zero in steady dependent to and , the smaller or the larger leadsstate condition and it should be changed rapidly when the de- to smaller . To determine this value, the microgrid should bemand of the microgrid is altered in order to stabilize the micro- simulated in designing process and the and shouldgrid. In order words, the ESS should work similar to slack bus be monitored after the critical load increment. In general, whenin the conventional power system but with zero output power a load increases, initially the output power-increasing rate ofin steady state. For this purpose, the droop controller of the the closest VSC is more than others. In other words, the farthestESS should have a high active gain in steady state. When VSC to where the load senses the least change. Therefore, thethe demand is changed, the gain should be decreased rapidly critical load increment is the amount of load increment in theand then should be increased slowly back to the initial value farthest bus to the ESS, which leads the MI of one VSC toas demonstrated in Fig. 5. High gain of the ESS active droop reach the maximum value, if the ESS does not detect it.causes the ESS to produce approximate zero active power in Equation (32) compares the value of this difference with thesteady state condition, and low gain of active droop leads difference value in the previous step of simulation and checksthe ESS to produce or consume almost all the demand variation whether the change is new. If the output power is changed andin dynamic behavior of the microgrid. Consequently, the active this change is a new change, the value of is updated to . Thedroop gain of a single ESS in the proposed method could be ex- process of selecting is similar to selecting process.pressed by (29) B. Control of DGs The active output power of primary sources changes slowlywhere and are the high and low droop gains; is a co- in DGs. Therefore, if the output power of a VSC changes slowly,efﬁcient, which determines the velocity of increasing the droop too, the DC voltage tolerance is reduced. Therefore, a mecha-gain from to . The higher , the faster changing of the nism should be implemented to slow the response speed of thedroop, the less ESS energy supplying, and the more decrement VSC. For this purpose, the frequency droop gain of DGs shouldin DC voltage of DGs. is the last time that the microgrid’s de- be increased when their output active power changes.mand is changed and should be determined in the ESS locally References [9] and [28], for better dynamic response offor decentralized control. VSCs, drop the frequency of VSCs based on the derivation of When the microgrid’s demand is changed, the output power the output power with respect to time. In this paper, this methodof all DGs and the ESS are changed based on network parame- is used to increase the frequency droop gain when the outputters. To detect the demand changes of microgrids in ESS locally, power changes. Hence, the DGs droop gain is deﬁned asa method, which operates based on monitoring output power ofthe ESS, is proposed in this paper. For this purpose, ﬁrst, the (33)output 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 on where is the th DG frequency gain in steady state condi-this compression, the moment of demand variation is detected. tion and is the coefﬁcient of increasing frequency droop The average of the output power in last few seconds gain of corresponding DG in relation to absolute of output ac-is obtained by crossing the output power from ﬁrst-order lag tive power derivation . Equation (33) results in in-system with time constant equal to . Therefore, based on creasing the droop gain in dynamic condition. Hence, activetrapezoidal rule [27], is calculated from output power of VSC will change less and DC voltage will be maintained in its constraint. In other words, the proposed droop (30) method for DGs helps the single ESS to supply the whole de- mand variations initially. Afterwards, ESS reduces its output ac- Based on the proposed method, the last time that the micro- tive power to zero gradually, on the other hand, DGs increase thegrid demand is changed can be detected locally when (31) and rate of their participation in supplying the microgrid demand(32) are satisﬁed: slowly. After some seconds, the output of ESS becomes zero, the storage is ready for next change in demand, and the demand (31) is shared perfectly between all DGs.
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DIVSHALI et al.: DECENTRALIZED COOPERATIVE CONTROL STRATEGY OF MICROSOURCES 1955Fig. 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 in Fig. 7. Output active power of VSC-based DGs in case A.this 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 static state condition. The dynamic response of the microgrid is ob-transfer switch (STS), and four loads. The ESS is placed near tained by applying trapezoidal rule [27] in these state equations.the point of common coupling (PCC) of low voltage microgrid The details of the obtaining the operation point and dynamic re-and medium voltage distribution network to be utilized when sponse are described in [30].the system transits to islanding operation mode. The STS can In this section, three cases are considered. Case A considersdisconnect the microgrid from the distribution network when it the microgrid with an ESS in each DG. In case B, there is nois necessary. The detailed aspects of the test system are as fol- ESS in the microgrid. Case C simulates the proposed methodlows, and the VSCs parameters are listed in the Appendix. and considers a single ESS at bus 1 (Fig. 6) with no ESS in each 1) Single energy storage system DG. In this case, the single ESS without any communication a) ESS: 10-kW battery energy storage. link detects the network alteration and produces or absorbs ad- 2) Load (constant impedance): equate active power. In all cases, the simulation is run for 75 a) Load 1:10 kW j6.5 kVAr. s; initially, the microgrid is connected to the distribution net- b) Load 1:5 kW. work and receives 10 kW j 10 kVAr from it. On , STS c) Load 1:50 kW j20 kVAr. is opened and the microgrid becomes islanded, and ﬁnally, on d) Load 1:8 kW 8 kVAr. , all loads are increased 10%. 3) DGs: a) DG1: 10-kVA fuelcell. A. Case A b) DG2: 70-kVA microturbine. In this case, the central ESS (in Fig. 6) is not connected; how- c) DG3: 70-kVA fuelcell ever, all DGs have an ESS in the DC link. Since the battery d) DG4: 20-kVA microturbine. storage system has rapid dynamic ( [14]), all DC 4) Line: voltages are almost ﬁxed and the MI remains in allowable range a) Line 1: . during simulation. The output active power of each DG in this b) Line 2: . case is shown in Fig. 7. c) Line 3: . As shown in this ﬁgure, in , disconnecting from the d) Line 4: . utility, DGs output active power are changed rapidly. Among 5) Network: Injects 10 kW j6.5 kVAr. them, 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 droop V. SIMULATION STUDY gain, and the system reaches the steady state condition. In To evaluate the dynamic behavior of the microgrid with and , the loads are increased 10%, and this demand incrementwithout the proposed cooperative control strategy, the microgrid is shared between all DGs perfectly. The DC voltage and MI ofstate space equations are modeled in MATLAB. The state space DGs in case A are shown in Figs. 8 and 9, respectively. Theseequations are obtained from VSCs, loads, and network DAE. ﬁgures show that the DC voltage of DG1 is changed more thanThese equations are solved by Newton method [29] for steady other DGs because its output power is changed more rapidly.
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1956 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 4, NOVEMBER 2012Fig. 8. DC voltage of VSC-based DGs in case A. Fig. 12. Important eigenvalues of the microgrid of case B.Fig. 9. MI of VSC-based DGs in case A. Fig. 13. Primary source active power of VSC-based DGs in case B.Fig. 10. Important eigenvalues of the microgrid of case A. Fig. 14. DC voltage of VSC-based DGs in case B.Fig. 11. Frequency of microgrid in case A. Fig. 15. Modulation index of VSC-based DGs in case B.However, the MI of all DGs is in the acceptable range and there- ESS, are shown in Fig. 12. This ﬁgure shows that this case hasfore, the microgrid works properly. The important eigenvalues zero eigenvalues and therefore, this microgrid is unstable whenof microgrid in case A demonstrate the small signal stability the demand is changed.(SSS) of this case as shown in Fig. 10. In order to demonstrate the reason of this instability, it is as- When the microgrid is in the connected mode, the frequency sumed that the VSC can work perfectly the same as case A. Inof the microgrid is equal to the network frequency. However, this condition, since this case has no ESS and the primary sourcein the islanding mode, the frequency changes based on demand dynamic is slow, the DC bus voltage is reduced rapidly and theand droop gains. The frequency alteration of the microgrid in MI reaches its maximum limit. By this assumption, the primarythis case is shown in Fig. 11. source power, which is obtained from (25), the DC bus voltage, which is calculated from (24), and the MI, which is obtainedB. Case B from (15), are shown in Figs. 13–15, respectively. In this case, it is assumed that none of the DGs has ESS, and As stated in (16) and (17), the VSC can produce desiredthe single ESS of Fig. 6 is not connected either. Based on the voltage, when the MI is smaller than , which is equalproposed hybrid VSC-based DG model, which is developed in to 1.102 in this case. When the MI is greater than , thethis paper, the important eigenvalues of this case, which has no output voltage is less than the desired voltage as obtained in
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DIVSHALI et al.: DECENTRALIZED COOPERATIVE CONTROL STRATEGY OF MICROSOURCES 1957(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 ESScannot 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 controller Fig. 16. Output and average of active power of ESS in case C.and 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 Fig. 17. Frequency droop slope of VSC-based DGs and ESS in 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 is modeled by ﬁrst 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- Fig. 18. Output active power of VSC-based DGs in case C.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 observed Fig. 19. Primary source active power of VSC-based DGs in case C.that 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 zero power in steady state, the steady state output active powerare used for demand change detection . As shown in of DGs in this case is similar to case A (Fig. 7).this ﬁgure, the output power of ESS is increased suddenly and When the VSC output power of the ESS changes slowly, thedecreased slowly in order to provide the opportunity of increase output power of primary source has the opportunity to followof the DGs primary source output power and follow the demand it. Hence, the DC voltage will have less variation. The activevariations. power of primary source and the DC voltage of DGs are shown The frequency droop gain of ESS and DGs, which change in Figs. 19 and 20, respectively.in time based on the proposed cooperative control strategy are By comparing Fig. 20 with Fig. 14, which shows the DCshown in Fig. 17. voltage of case B, it is demonstrated that the proposed coop- The proposed cooperative control strategy causes to increase erative strategy can reduce the DC voltage tolerance of all DGs.the DGs droop gain when DGs output power changes and de- The MI of all DGs in case C are depicted in Fig. 21.crease the ESS droop gain when the demand changes as shown Fig. 21 shows that the MI remains in its limits in case C. Itin Fig. 17. This method leads to slow change in the output ac- means that the microgrid with the proposed control strategy cantive power of VSCs as shown in Fig. 18. Since the ESS produces work by a single storage system without communication link
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1958 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 4, NOVEMBER 2012 TABLE I VSC PARAMETERSFig. 20. DC voltage of VSC-based DGs in case C. 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 the power sharing, the output power of VSCs should be changed rapidly. However, the dynamic response of pri- mary source is slow. Hence, the DC bus voltage and the output voltage of VSC may have ﬂuctuations. To analyze this situation, the hybrid VSC-based DG model, whichFig. 21. Modulation index of VSC-based DGs in case C. considers the primary source effect, is proposed in this paper. In this model, the modulation index is calculated and the VSC can work properly, if this index remains in its limitation. • VSC-based microgrids without synchronous generator and communication link do not have ﬁxed frequency. Hence, the conventional load/frequency control method cannot be employed in these networks. Previous works use the droop method with an EES in each VSC for load/frequency con- trol. In this paper, the cooperative control method for ESS and DGs is proposed which needs only one single ESS inFig. 22. Frequency of microgrid in case C. the whole microgrid and no communication link. • Because of problem of communication link in wide mi- crogrid, the demand change should be detected in the ESS locally. The proposed ESS control method detects the de- mand change in ESS locally and does not need physical communication link. The simulation results show the proposed method can guar- antee the active power balancing in autonomous microgrid and maintain DC voltage of VSC-based DGs in acceptable range without an ESS in each of VSC or communication link. In ad- dition, proposed method satisﬁes the small signal stability ofFig. 23. Important eigenvalues of the microgrid of case C. microgrid. APPENDIXand maintain its stability. The frequency deviation of the micro- VSC PARAMETERSgrid in this case is shown in Fig. 22. The important eigenvalues The VSC model and controller parameters are as follows:of microgrid with the proposed cooperative control strategy are , , , , ,shown in Fig. 23. It is noteworthy that since case C has more , , , ,VSCs (adding a VSC for a single ESS), this case has a little , , , , , ,smaller damping ratio than case A [31]. These ﬁgures show the , and . Other parameters are listed inperformance of this method to keep frequency regulation and Table I.SSS in dynamic behavior. Thus, any need to costly ESS in eachDG or the communication link are eliminated. REFERENCES [1] M. Reza, “Stability analysis of transmission systems with high pen- VI. CONCLUSION etration of distributed generation,” Ph.D. dissertation, Delft Univ. Technol., Delft, The Netherlands, 2006. This paper is focused on the problem of the active power bal- [2] R. H. Lasseter, “Microgrids and distributed generation,” J. Energyance between supply and demand in autonomous VSC-based Eng., vol. 133, no. 144, 2007.
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Hoft, “GTO inverter optimal PWM wave- forms,” in Proc. IEEE IAS Annual Meeting, 1987, pp. 303–311. [23] M. T. Haque and A. Taheri, “Using neural network for execution of Mehrdad Abedi received the B.Sc. degree in programmed pulse width modulation (PPWM) method,” World Acad. electrical engineering from the University of Tehran, Sci. Eng. Technol., vol. 6, pp. 58–61, 2005. Tehran, Iran, in 1970, the M.Sc. degree from the [24] P. N. Enjeti, P. D. Ziogas, J. F. Lindsay, and M. H. Rashid, “A new Electrical Engineering Department, Imperial Col- PWM speed control system for high-performance AC motor drives,” lege, University of London, London, U.K., in 1973, IEEE Trans. Ind. Electron., vol. 37, pp. 143–151, 1990. and the Ph.D. degree in electrical engineering from [25] M. T. Hagh, H. Taghizadeh, and K. Razi et al., “Harmonic mini- Newcastle University, Newcastle, U.K., in 1977. mization in multilevel inverters using modiﬁed species-based particle He is currently Professor of the Electrical Engi- swarm optimization,” IEEE Trans. Power Electron., vol. 24, pp. neering Department in Amirkabir University of Tech- 2259–2267, 2009. nology, Tehran.
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