An Optimal Control Load Demand Sharing Strategy for Multi-Feeders in Islanded Microgrid

Transcription

1 (IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, An Optmal Control Load Demand Sharng Strategy for Mult-Feeders n Islanded Mcrogrd Muhammad Zahd Khan, Muhammad Mansoor Khan 2, Xu Xangmng 3, Umar Khald 4, Muhammad Ahmed Usman Rasool 5,2,4,5 School of Electronc, Informaton and Electrcal, Engneerng, Shangha Jao Tong Unversty (SJTU), Shangha, Chna 3 State Grd Zhenjang Power Supply Company, Jangsu, Chna Abstract For the operaton of autonomous mcrogrd (MG), an essental task s to meet the load demand sharng usng multple dstrbuted generaton (DG) unts. The conventonal droop control methods and ts numerous varatons have been developed n the lterature n order to realze proportonal power sharng amongst such multple DG unts. However, the conventonal droop control strateges are subjected to power sharng error because of non-trval feeder mpedances of medum-voltage MGs. Further, complex MGs confguratons (mesh or looped networks) usually make to reactve power sharng and system voltage regulaton more challengng. Ths paper presents an optmal control strategy n order to perform the proportonal power sharng and voltage regulaton for multple feeders n slanded AC MGs. The case study smulaton for optmzng the power sharng and voltage regulatons n proposed control strategy has been verfed through usng MATLAB/Smulnk systems. Keywords Optmal control; power sharng; voltage regulaton; MG I. INTRODUCTION The applcaton of dstrbuted power generaton such as wnd turbne, photovoltacs and fuel cell has been experenced a fast development n the past decades [] [2]. DG unts as compare to conventonal centralzed power generaton, provdes more clean and renewable power close to consumer s end [3][4]. Therefore, t can ease the stress of numerous tradtonal transmsson and dstrbuton framework[5]. Power electroncs converters are nterfaced between DG unts and the grd, are the vtal elements of the MGs [6], and perform the flexblty of slanded or grd connected operaton. On the other sde, hgh nfltraton of power electroncs based DG unts presents couple of ssues, such as voltage devatons, frequency and power flow varatons [7]. In order to sort out these aforementoned problems, the dea of MG has been emerged, whch s based on the control of multple DG unts. As compare to a soltary DG, MG can accomplsh predomnant power management wthn ts dstrbuton network [3]. The MG can operate ether n grd-connected mode or slandng mode. In grd connected mode, the MG s connected wth the man grd at the pont of common couplng (PCC) and accordng to dspatched references every DG unt provdes proper actve and reactve power. The most used control strateges are reported n [8] for grd connected nverters. In the operaton of slanded MG mode, the load demand should be approprately shared by DG unts accordng to ther respectve ratngs and avalablty of power from ether ther respectve prme movers or energy sources [3]. Communcaton based power sharng control strateges nclude master/slave control, concentrated control, and dstrbuted control[8], whle control strateges wthout communcaton are usually based on the droop concept, whch can be classfed nto four man categores: ) conventonal and varants of the droop control[9]; 2) construct and compensate based strateges[0]; 3) the hybrd droop/sgnal njecton strategy; 4) In [] vrtual framework structure-based method s developed. Tradtonal frequency and voltage magntude droop control approaches are adopted for nterfacng nverters n a decentralzed mode to attan power sharng and voltage regulaton [2]. However, a lttle whle back s observed that conventonal droop control strategy n low voltage MG has led to have few power control stablty ssues, as the DG feeders have largely resstve (hgh R/X raton) behavor [7]. It can also be observed that actve power at the steady state s usually proportonally shared among DG unts, whle the reactve power sharng deterorates due to msmatched of DG unts output and feeder mpedances [7]. The mpedances of transmsson lne be asymmetrcal due to dstnctve separatons amongst DG unts whle the desgn of LCL flters are depends on varyng system condtons and desgn consderatons whch leads to dssmlar DG unt s output flters mpedances [3] [7]. In addton, the presence of local loads and the complex network MG confguraton usually further ncrease load sharng performance. To resolve the power control problems, few enhanced droop control strateges [] and [4] have been reported n prevous lterature. In [5], an accurate power sharng control approach has been reported to restore the load pont voltage wth the decreased voltage devaton. Author proposed an enhanced reactve sharng strategy n[5]. Aforementoned, these two strateges are, however, attaned at cost of nverter termnal voltage devaton. Furthermore, the droop strateges based on vrtual mpedances methods are seen as a promsng strategy to handle power sharng ssue. The vrtual frequencyvoltage frame and vrtual power dea were reported n [4] [4]and [], that enhance the stable operaton of the MG system. However, these strateges cannot subdue the reactve power sharng errors n the meantme. In addton, approprate power sharng among nverter and electrc machne s subject 8 P age

2 (IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, to challengng n these strateges, when small synchronous generators are ncluded nto the MG. Although the author addressed the power sharng ssue n[6], but the respectve steady state voltage dstorton deterorates the overall power qualty of MG. Author proposed an Q-V dot droop strategy n [3], but t s notced that reactve power sharng enhancement s not evdent when the local loads are ncorporated. Author n [7] used addtonal PCC voltage measurement n order to mtgate the error of reactve power sharng. In [8], an enhanced vrtual mpedances control method has been reported for a DG unt, that s able to compensate for the unequal feeder mpedances. Although, the power sharng can be enhanced by vrtual mpedance based droop control strateges but voltage droop and vrtual mpedance deterorates the nverter termnal voltage qualty [9]. In order to reduce the tradeoff among reactve power sharng and bus voltage devatons n mult feeders a recent control strategy s developed n [20] where a Kalman flterbased state estmator used whch requred hgh bandwdth date rate. In addton, feeders can be located at consderable dstance from each other, therefore t ncreases complexty and reduce the relablty and flexblty of MG operaton. Therefore, ths paper proposed an optmal control load demand sharng strategy for mult-feeders whch s drectly based on load estmaton and optmal regulator as shown n Fg. 3. The salent contrbuton of ths work can summarzed as follows:) The load s estmated at respectve feeders whch reduces the bandwdth data requrements; 2) The proposed optmal control strategy acheved task of proportonal power sharng and system voltage regulaton for multple buses smultaneously. The rest of ths paper s organzed as follows. In Secton II, the operaton of MG s dscussed. The operatng prncpal of a proposed control approach s gven n secton III. The smulatons results are presented n secton IV and fnally secton V concludes the paper. V DG th I S=P+jQ Vk Fg.. An th Inverter Connected wth k th AC Bus. k MGs are consstng on consderable number of DG unts and connected load as shown n Fg. 2. Every DG unt s connected to the MG wth an nterfaced nverter where DG nverters connected to the PCC va ther correspondng feeders. The statues of man grd and MG are controller by the MG central controller. Dependng on operatons requrements, the man grd can be connected or dsconnected from the MG by swtchng the state of statc transfer swtch STS at the common bus couplng pont. In the grd-connected operaton mode, the actve and reactve reference usually are allocated by central controller and n order to track the power the conventonal droop control strategy can be used. PI regulaton for the voltage magntude control used to mtgate the steady stated reactve power trackng errors. So, durng grd connected mode the power sharng s not concern. When mcro grd s operatng n slanded mode, the load demand of MG should be properly shared by DG unts. In ths mode of operaton, the DG unts can operate usng conventonal power frequency droop control strateges as ω = ω * D. P P V = V * D. Q Q Where, V *, ω, D and D are the nomnal voltage P Q magntude, nomnal frequency, real and reactve power slops, respectably for th DG unt. PCC Load th Dstrbuton Generator Dstrbuton feeder Feeder th X R STS Load Communcaton MGCC Xk Rk Substaton Mcrogrd Feeder k th Feeder n DG n Dstrbuton Generator 2 Fg. 2. Illustraton of the Mcrogrd Confguraton.Operaton of MG. () (2) Fg. 3. Block Dagram of Proposed Optmal Control Strategy. 9 P age

3 (IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, II. PROPOSED OPTIMAL CONTROL STRATEGY A radal type feeder s used n proposed optmal control strategy as llustrated n Fg. 2. All three buses V bus, V bus2, and V bus3 are fed through two DG unts DG and DG2 nterfaced usng three phase, three wre power electroncs nverters connectng through feeder mpedances wth three lnear loads R load, R load2 and R load3.ths proposed strategy s composed on load estmaton and optmal steady state estmator regulator. Load estmaton strategy used n order to estmate specfc feeder s mpedances whch have advantages that t reduces the data bandwdth requrements. Based on these load estmaton values Z load,, the optmal regulators are responsble to compute the optmal control command whch s a cost functon and send two optmal control commands u c and u c2 to power controllers n order to realze proportonal power sharng and voltage restoraton. Ld2/Rd2 and Ld3/Rd3 are dsturbance load whch are exerted to examne the effectveness of ths proposed strategy for both nductve and resstve MGs. Dfferent cases of dsturbance load addton are further dscussed n detal n secton 4. A. Mathematcal Model In order to explan operaton of a MG, a smplfed crcut n Fg., s llustrated where two th and k th DG unts are parallel connected. The complex power drawn towards the k th ac bus can be expressed as. Sk = Pk + jqk Where, actve power P and reactve power Q are ntroduced at every exstng node by DG converters. If power nverters are supposed to be an deal controllable voltage source whch s connected to lne mpedances va mans, then the movement of real and reactve powers n transmsson lne mpedances can be expressed as. V P =.[ RV RV cos + XV sn ] 2 2 k k k k R + x V Q =.[ RV sn + XV XV cos ] 2 2 k k k k R + x Where, =,2 represents the two branches n crcut. V s magntude of nverter output and V k represents the PCC bus voltage, whle P and Q are the actve and reactve powers flowng from th nverter termnal to k th common bus voltage, llustrates the dfference amongst the power angle phase of the output mpedance. In hgher voltage HV and medum MV network the nductve elements are typcally hgher then resstve as shown n table [], however, HV and MV networks have nductve behavor, therefore we can neglect the resstve part. As power angle s small n such type of lnes so we can assume that and the possble power flow n network can be wrtten as VV k P [ sn ] (6), Rx = 0 k x (3) (4) (5) Q R, x = 0 V V Where, P k V V Q k VV cos x 2 k k k Accordng to expresson (8) and (9), t s obvous that the real power P drawn towards k th node predomnately depends on power angle whle reactve power Q njected by each DG nverter mostly controlled by voltage dfference V -V k of th and kth ac bus. B. Load Estmaton and Optmal Regulator Prncpal Proposed optmal control strategy used to estmate the load at specfed feeder follows varable frequency local voltage based park transformaton as expressed n (0) and elaborated n Fg. 4(a). Ths strategy, frstly sensed the voltage V bus, and current I bus, at local node of th feeder, later both voltage and current sgnals are converted nto abc dq0, where rotatng frame s algned 90 degrees behnd A axs. dq0 values converted from real-magnary nputs to a complex valued output sgnal, where load mpedances Z r c, I s acheved by rato of V and whch s also a complex valued sgnal as expressed n (). Snce, optmzed cost functon mpedances whch s expressed n (3), nput sgnals should be real-magnary valued sgnal, so a complex to real-magnary block s used as shown n Fg. 4(a), and elaborated n (2), whch converts the complex load mpedances sgnals to realmagnary valued mpedances sgnals. Aforementoned, these mpedances are estmated at respectve feeders whch reduce the bandwdth data requrements. Later these mpedances sgnals are sent to the proposed optmal controller acheved task of proportonal power sharng and voltage restoraton for multple buses smultaneously. Fg. 4. (a) Load Estmaton of th Feeder (b) Frequency Regulaton. (7) (8) (9) 20 P age

4 (IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, π j ωt 2 U = ( u + ju. ) = ( u + ju. ). e s d q α β u sn( ωt) cos( ωt) 0 u d a u cos( ωt) sn( ωt) 0 u q = b u 0 0 u 0 c (0) 2 2 V = ( V ) ( V ) ; = tan V / V mag Real Im ag Real Im ag 2 2 = ( ) ( ) ; = tan / mag Real Im ag Real Im ag () V = V cos ; V = V sn Real Im ag = cos ; = sn Real Im ag (2) Once the load mpedances founded, the optmal regulator s a followng crtcal step. The proposed optmal regulators are an optmzed cost functon whch s presented n order to compute control commands accordng to the estmated network mpedances. Dfferent type of optmzaton technques s beng used such as lnear, quadratc and hgher order optmzaton strateges n order to mnmze or maxmze cost functon of the system. Lnear optmzaton has wde area of applcaton and t s easy regardng solvablty but the lmtaton of lnear optmzaton s that t works only wth the varables that are lnear as well as problem formulaton s freaky. Hgher order cost functons are convenent but soluton s nconvenent. In ths paper, quadratc optmzaton based cost functon s used whch s easy regardng solvablty, problem formulaton and soluton s also convenent. Some cost functons have constraned reactve powers whch can be supposed to equal.e Q =Q 2 n order to vary the tradeoff among real power and nverter termnal voltages, but usually the reactve power requrement s not so strngent, so n ths case, ths paper used constrans real powers whch are supposed to be equal P =P 2 and the tradeoff among bus voltage and reactve powers s found through mnmzaton. Moreover, the desred control commands are acqured by computng the optmzaton cost functon that mnmze the reactve power sharng error Q and voltage error V at specfc bus, whch can be expressed as n b mn J= ( ω ( V V )) + ( ω ( Q Q )) + j= constransts P P = bj busj jref Q + (3) In the cost functon ω bj and ω Q are the weghts for network voltages at specfc bus and reactve power error, respectvely. V jref (j=,2,3) are set at nomnal voltage 300V, whle n b =3 s the number of buses that has been chosen. Nevertheless, the lmtaton wth s proposed strategy s that, t requres the accurate grd mpedances of every load node whch aggravates the computatonally complexty wth ncrease n feeder numbers. By consderng that lmtatons, n future the whole grd network mpedance can approxmated nto one load node whch wll reduce the computatonally burden over system. However, movng forward, after computng every optmal controller sends desred control commands to ther respectve power controllers and operates wth the control commands untl upcomng samplng update. Frequencally, the optmal regulator obtans new estmated mpedances due to measurements feedback and accordngly revses ts orgnal control plan. Then, the voltage control commands are send to compensate for voltage and reactve power sharng devatons. C. Power Flow Control Proposed control strategy s llustrated n Fg. 5. The output frequency and voltages of Inverter Brdge connected wth dc power source are adjusted by power, voltage and current controllers. Every ndvdual DG unt s formulated n ts d-q frame where they depend on ther both ndvdual angular frequency and angle. Every nverter nterfaced wth DG unts are transferred to the d-q frame by usng followng transformaton equatons as f D cos( ) sn( ) f d = f Q sn( ) cos( ) fq (4) The power controller block for proposed strategy s llustrated n Fg. 5, adopts P-ω droop as llustrated n (5) and provdes the angle of th DG unts whch can be express as ω = ω * m P P (5) = ( ω δω ) dt (6) Where ω* and m P are the reference frequency and the P-ω droop coeffcent, respectvely. Notceably, the voltage references u c as shown n Fg. 5, s used nstead of Q-V droop, whch can be calculated by optmzaton based cost functon as dscussed aforementoned n secton B. However, the average real power s acqured by nstantaneous power passng low-pass flters as expressed below P ω p c = s + ωc (7) Where, ω c s cutoff frequents of low pass flters Instantaneous actve power p can be represented n d-q frame as p = V. + V. od od oq oq (8) Here, v odq and odq are nverter termnal voltage and current, respectvely on d-q frame. Fg. 5. Proposed Optmal Control Strategy. 2 P age

5 (IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, D. Frequncy Regulaton The secondary controllers for MGs are based upon frequency restoraton. Snce, the real power hghly nfluences the frequency of generator-domnated grds. Ths feature s an edge, snce frequency s controllable varable that gves the nformaton regardng to generaton or consumpton balance of the grd. The frequency regulaton strategy whch s mplemented n order to restore the frequency of system s llustrated n Fg. 4(b) whch regulates the frequency devatons of th DGs unts to ts nomnal value. Frequency restoraton strategy can be expressed by ω* and ω avg are the nomnal reference frequency and measure system frequency that s beng sensed by each node of DGs unt s nterface nverters n the neghborhood of the node beng consdered. Frequency correcton s send to frequency reference of the th nverters node, whle K pf and K are the proportonal and ntegral gans, respectvely, for controllers. N ωk k= ω = avg N ω = ( ω* ω ) avg δω = k ω + k ω dt pf f (9) E. Mechansm of Reactve Power Sharng The output of the optmzer s set of voltage phasors and ts mplementatons requre the nformaton of voltage phasers of all nverters partcpatng the MG. A drect reconstructon of such nformaton needs very fast and relable communcaton and computaton nfrastructure. However, n presented approach the phases have been modfed through frequency/real power droop control and only voltage magntudes are updated n accordance wth the optmzer output. Ths combnaton wll render accelerates actve power sharng whch s also consdered as constrant n cost functon. Consequently, the correct phase angle wll automatcally be adjusted by system. III. RESULT AND DISCUSSION In order to verfy the effectveness of proposed control approach, the smulatons have been carred out on MATLAB/Smulnk for a three phase 50-Hz slanded MG. As llustrated n Fg. 6 the smulated MG s composed on two DG and DG2 untes connected n parallel wth three lnear loads va feeder mpedances. The crcut and control parameters are shown n Fg. 6 and Table, respectvely. Smulaton verfcatons are composed on two cases. The case and case 2 nvestgates the effectveness of proposed control strategy on dfferent dsturbance locatons n nductve and resstve MG, respectvely. TABLE I. TYPICAL LINE IMPEDANCES Type of Lnes R(Ω /km) X(Ω/km) R/X Low voltage lne Medum voltage lne Hgh voltage lne Fg. 6. Proposed Crcut Confguraton. A. Case : Optmal Control Strategy for Inductve MG In ths secton, results obtaned from proposed strategy and wthout proposed strategy for nductve are dscussed. The key parameters and confguraton for nductve MG are gven n table 2 and Fg. 6, respectvely TABLE II. SYSTEM PARAMETERS FOR INDUCTIVE MICROGRID Parameters Symbol Value Frequency fs 50Hz Inverter Ratng VA 0kVA Flter mpedances R c+jx c 0.25+j0.785 Flter 2 mpedances R c2+jx c j0.785 Lne mpedances R lne+jx lne 0.2+j0.628 Lne 2 mpedances R lne2+jx lne2 0.2+j0.628 Load mpedances R load+jx load 20+j3.40 Load 2 mpedances R load2+jx load j3.5 Load 3 mpedances R load3+jx load3 20+j3.40 Dsturbance load at Bus 2 L d2/r d2 0mH/9 Dsturbance load at Bus 2, 3 L d2/r d2, L d3/r d3 7+j0.34, 0+j0.628 ) Power Sharng wth load varaton at bus 2: In ths case, the all buses voltage error weght ωa-c and reactve power error weght ωq are not changed and set at whch does not have any effect on cost functon. In order to realze proportonal power sharng and verfy the optmal control strategy a heavy dsturbance load Ld2/Rd2 wth value of 9+j3.40 exerted at bus 2 on 0.2 seconds. Fg. 7 and 8 depcts the performance of voltage regulatons and power sharng, respectvely, wth and wthout proposed control strategy. In conventonal control strategy the bus voltages drop (dotted curves) can be seen n Fg. 7(a-b). snce droop controllers decrease voltages n order to track the aggravated reactve power. More than 3 volts devaton at bus 2 and bus 3 has been compensated n proposed strategy as llustrated n Fg. 7(a-b) and stabled at V and V, respectvely. In addton, actve power sharng error 4.3KW and reactve power sharng error 70VARcan be notced n Fg. 7(c) and Fg. 8(b). Once the proposed optmal control strategy s actvated at 0.2 seconds, t can be observed n Fg. 8(a and c) that actve and reactve power sharng error are compensated n to almost zero wth a smaller startup dvergent behavor P age

6 (IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, V V V V Bus 2 Voltage (V) V wth proposed strategy wthout proposed strategy Bus 3 Voltage V wth proposed strategy wthout proposed strategy Fg. 7. Smulatons Results under Heavly Load Condtons (A)Voltage Response at Bus 2 (B) Voltage Response at Bus 3 (C) Actve Power Sharng wthout Proposed Strategy. (b) Actve Power (W) Actve Power (W) (b) Reactve Power (VAR) Fg. 8. (a)actve Power Sharng n Proposed Strategy, Reactve Power Sharng n wth and wthout Proposed Strategy s Illustrated n Fgure (B) and (C), Respectvely. Q-Q2=70 var P-DG P2-DG2 Reactve Power (VAR) V Bus 2 Voltages V wth proposed strategy wthout proposed strategy ( ) Bus 3 Voltages wth proposed strategy wthout proposed strategy Fg. 9. Smulatons Results under Heavly Load Condtons wth (Green Cure) and wthout (Yellow Dotted Lne) Proposed Control Strategy (a)voltage Response at Bus 2 (b) Voltage Response at Bus 3 (c)actve Power Sharng wthout Proposed Strategy (b) Reactve Power (VAR) Actve Power (W) (b) Reactve Power (VAR) Fg. 0. Smulaton Results wth Proposed Strategy for actve Power s Shown n Fgure (a), Whle Results Obtaned wth and wthout Proposed Strategy for Real and Reactve Power are Illustrated n (b) and (c), Respectvely. (c) Reactve Power (VAR) P age

7 (IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, 2) Power Sharng for dfferent dsturbance locatons: Ths secton further nvestgates the effectveness of system voltage regulatons and power sharng behavor to unknown multple dsturbances. In ths case, a serous dsturbance load (Ld2/Rd2) and (Ld3/Rd3) are exerted on same tme on 0.2 seconds at bus 2 and 3, respectvely, as shown n Fg. 5 whch led up to20.4v and 23.4Volts devatons at bus 2 and bus 3, respectvely. Proposed strategy s actvated at 0.2 seconds, whch reduces devatons of 3.4 V at bus 2 and stabled voltage curve at 293 V as llustrated n Fg. 9 (a), whle 4.9V devaton has been compensated at bus 3 as shown n Fg. 9(b), and voltage curve s stabled wthn acceptable V range. Further, multple dsturbance load at dfferent locatons effects power sharng, as actve power error 8.0Kw and reactve power error.08kvar s notced n Fg. 0(c) and 0(b). When the proposed control strategy s actvated at 0.2 seconds power sharng error s compensated to almost zero as shown n Fg. 9 and 0. Optmal Control Strategy for Resstve MG. TABLE III. SYSTEM PARAMETERS FOR RESISTIVE MICROGRID Parameters Symbol Value Flter mpedances Rc+jXc.5+j0.34 Flter 2 mpedances Rc2+jXc2.5+j0.34 Lne mpedances Rlne+jXlne 0.75+j0.57 Lne 2 mpedances Rlne2+jXlne j0.57 Load mpedances Rload+jXload 30+j3.40 Load 2 mpedances Rload2+jXload j3.5 Load 3 mpedances Rload3+jXload3 35+j3.40 Dsturbance load at Bus 2 Ld4/Rd4 mh/20 To further nvestgates the effectveness of proposed optmal control strategy, the results are obtaned for resstve MG as shown n Fg., 2 and 3. System confguraton and parameters for resstve MG are llustrated n Fg. 6 and table 3 respectvely. In ths case II, the objectve of optmal control strategy s to realze proportonal power sharng and hold bus 2 voltages at ts nomnal voltage V ref valued 300 V, n the presence of load dsturbance Ld4/Rd4. Fg.. Reactve Power Sharng wthout Proposed Control Strategy. Fg. 2. Reactve Power Sharng wth Proposed Control Strategy. (d) (e) (f) Fg. 3. Bus 2 and 3 Voltages wth and wthout Proposed Strategy Illustrated n Fgure (a) and (b), Respectvely, Keepng Weght Ω b=, Whle at Ω b=300 s Illustrated n Fgure (c) and (d). Fgure (e) and (f) Illustrates actve Power Sharng wthout and wth Proposed Control Strategy P age

8 (IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, 3) Power Sharng and Bus 2 Voltage Control: To valdate the optmal control strategy, a dsturbance load Ld4/Rd4 wth valued mh/20ohm s exerted at bus 2 on 0.2 seconds. Voltage devaton of valued 3 V and 2 V s observed n conventonal control strategy at bus 2 and 3. Ths voltage devaton has been compensated wth help proposed control strategy, whch stabled bus 2 voltage at 296 V and bus 3 voltage at 298 V, whle keepng weght values wb= and wc= as llustrated n Fg. 3(a- b). Stll 4V volts devaton occurred at Bus 2 n proposed control strategy as shown n Fg. 3(a). To hold bus 2 voltage at ts nomnal value Vref n presence of dsturbance load, the voltage error weght Wb s set 300 whle all other buses and reactve power weghts are set at. The results obtaned for Bus 2 after changng of ts weght, are shown n Fg. 3(c-d) where t stabled to ts nomnal value 300 V voltage. Further, actve power error 2260W and reactve power error 75 VAr has been observed n conventonal control strategy as llustrated n Fg. and 3(e), respectvely. Ths power sharng error has been compensated to zero n proposed control strategy as depcted n Fg. 2 and Fg. 3(f), respectvely. The strategy adopted for frequency regulaton s llustrated n Fg. 4(b). Frequency devaton s elmnated at 0.2 seconds as shown n below Fg. 4, whch s wthn acceptable range ±0.5 Hz. Fg. 4. Frequency Regulaton. IV. CONCLUSION In ths paper an optmal control strategy was proposed whch performs the twofold objectves n order to realze proportonal power sharng and system voltage regulaton for multple feeders n slanded AC MGs. The strategy frstly, estmates the load mpedances of specfed buses by usng slow communcaton channel. Secondly, an optmal controller based optmzed cost functon wth mmunty to parameters perturbatons has been developed whch sends control command to nner loop n order to realze proportonal power sharng and voltage control for the specfed bus. Fnlay, the effectveness of proposed optmal control strategy was nvestgated under load parameters uncertantes n both nductve and resstve MGs. The obtaned smulaton results show that the proposed optmal control strategy s not senstve to MG s confguratons and able to realze proportonal power sharng and controls the specfed multple feeder s voltages n ac slanded MG whch, thus enhances the relablty and flexblty of slanded MG. REFERENCES [] S. Member, J. A. Mueller, S. Member, J. W. Kmball, and S. Member, An Accurate Small-Sgnal Model of Inverter- Domnated Islanded Mcrogrds Usng dq Reference Frame, vol. 2, no. 4, pp , 204. [2] R. H. Lasseter and P. Pag, Mcrogrd : A Conceptual Soluton, no. June, pp , [3] K. Hashm et al., A Vrtual Mcro-Islandng-Based Control Paradgm for Renewable Mcrogrds, pp. 23, 208. [4] M. Shahd, Muhammad Umar Mansoor Khan, K. Hashm, S. Habb, J. Huawe, and H. Tang, A Control Methodology for Load Sharng System Restoraton n Islanded DC Mcro Grd wth Faulty Communcaton Lnks, Electroncs, vol. 7, no. 90, pp. 5, 208. [5] J. He and Y. W. L, An Enhanced Mcrogrd Load Demand Sharng Strategy, vol. 27, no. 9, pp , 202. [6] F. Blaabjerg, R. Teodorescu, M. Lserre, and A. V. Tmbus, Overvew of control and grd synchronzaton for dstrbuted power generaton systems, IEEE Trans. Ind. Electron., vol. 53, no. 5, pp , [7] M. Umar and S. Id, An Improved Control Strategy for Three-Phase Power Inverters n Islanded AC Mcrogrds, 208. [8] Han et al., Aalborg Unverstet Revew of Power Sharng Control Strateges for Islandng Operaton of AC Mcrogrds, I E E E Trans. Smart Grd, vol. 7, no., pp , 206. [9] W. Yao, M. Chen, J. Matas, J. M. Guerrero, and Z. M. Qan, Desgn and analyss of the droop control method for parallel nverters consderng the mpact of the complex mpedance on the power sharng, IEEE Trans. Ind. Electron., vol. 58, no. 2, pp , 20. [0] C. K. Sao and P. W. Lehn, Autonomous Load Sharng of Voltage Source Converters, IEEE Trans. Power Delv., vol. 20, no. 2, pp , [] K. De Brabandere et al., A voltage and frequency droop control method for parallel nverters, Power Electron. Spec. Conf PESC IEEE 35th Annu., vol. 4, no. 4, p Vol.4, [2] J. M. Guerrero, J. C. Vasquez, J. Matas, L. G. De Vcuña, and M. Castlla, Herarchcal control of droop-controlled AC and DC mcrogrds - A general approach toward standardzaton, IEEE Trans. Ind. Electron., vol. 58, no., pp , 20. [3] C. T. Lee, C. C. Chu, and P. T. Cheng, A new droop control method for the autonomous operaton of dstrbuted energy resource nterface converters, IEEE Trans. Power Electron., vol. 28, no. 4, pp , 203. [4] G. Modes, A. Mehrz-san, G. S. Member, and R. Iravan, Potental- Functon Based Control of a Mcrogrd n, vol. 25, no. 4, pp , 200. [5] J. He and Y. W. L, An accurate reactve power sharng control strategy for DG unts n a mcrogrd, 8th Int. Conf. Power Electron. - ECCE Asa "Green World wth Power Electron. ICPE 20-ECCE Asa, pp , 20. [6] M. N. Marwal, J. Jung, S. Member, and A. Keyhan, Control of Dstrbuted Generaton Systems Part II : Load Sharng Control, vol. 9, no. 6, pp , [7] P. Cheng, C. Chen, T. Lee, and S. Kuo, A Cooperatve Imbalance Compensaton Method for Dstrbuted-Generaton Interface Converters, vol. 45, no. 2, pp , [8] J. M. Guerrero, L. G. De Vcuña, J. Matas, J. Mret, and M. Castlla, Output mpedance desgn of parallel-connected UPS nverters, IEEE Int. Symp. Ind. Electron., vol. 2, no. 4, pp , [9] D. N. Zmood and D. G. Holmes, Statonary frame current regulaton of PWM nverters wth zero steady-state error, IEEE Trans. Power Electron., vol. 8, no. 3, pp , [20] Y. Wang, S. Member, X. Wang, Z. Chen, and S. Member, Dstrbuted Optmal Control of Reactve Power and Voltage n Islanded Mcrogrds, vol. 53, no., pp , P age