Optimal Reactive Power Control in a Microgrid Considering Distributed Generations and Uncertainty of Wind Farms

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1 Optal Reactve Power Control n a Mcrogrd Consderng Dstrbuted Generatons and Uncertanty of Wnd Fars Benyan Khorradel, Hossen Khorradel, Soroush Kar, Jashd Aghae Abstract-- Due to the rapd growth of utlzaton of Dstrbuted Generatons (DGs) n crogrds, ther dfferent ssues are the subject of any recent researches. On the other hand, wnd power generaton s growng rapdly around the world and depends on the capacty of the wnd fars, t ay partcpate n crogrds. In such a case, the uncertanty of wnd affects the operaton of crogrds n any dfferent aspects. Consderng the stochastc effect of wnd fars on crogrd operaton and exstence of soe Electroncally Interfaced DGs (EIDGs) n a crogrd, ths paper proposes an Optal Power Flow (OPF) forulaton n order to deterne the optal control varables of each EIDG, such as PQ, PV and new odel of DGs whch s naed Q-sharng DGs n a crogrd to acheve the nu power loss. Nuercal studes on 34-bus IEEE dstrbuton test syste ncludng sx EIDGs wth wnd far show satsfactory results. Index Ters-- Dstrbuted Generatons; Mcrogrd; Mcrogrd Control Center; Optal Power Flow; Q-sharng DGs; Reactve Power Control; Voltage Droop Characterstc. I. INTRODUCTION Mcrogrd s an actve dstrbuton network whch ncludes both loads and Dstrbuted Generatons (DGs) and can operate n grd-connected or stand-alone ode []. Due to the novelty of crogrd concept, any ssues exst or are beng appeared n ther plannng and operaton. For nstance, accurate analyss of crogrd requres a powerful load flow study ethod whch consders the exstence of DGs. References []-[7] propose dfferent algorths for power flow analyss n dstrbuton systes and crogrds consderng the effect of DGs. Because the crogrd s a sall scale electrcal network and uses restrcted sources of eneres, ts optal plannng and operaton s very portant. Many researches are conducted and reported n the subject of optal placeent of DGs n dstrbuton networks [8]-[]. Optal allocaton of DGs for loss nzaton [], energy export optzaton and relablty proveent [3] are soe aspects of optal Afflaton footnotes: B. Khorradel s wth the Departent of power and control Eng., School of electrcal and coputer enneerng, Shraz Unversty, Shraz, Iran (eal: benyan.khorradel@gal.co). H. khorradel s wth the Departent of Electrcal Eng., Dezful Branch, Islac Azad Unversty, Dezful, Iran (e-al:hossen.khorradel@gal.co) plannng n crogrds. Also [4], [5] suggest dfferent ethods for optal operaton of crogrds n both autonoous and grd-connected odes. References [6]-[8] used frequency/voltage droop control for proper actve and reactve power sharng n the crogrd. In autonoous operaton, frequency and voltage control and keepng the n acceptable range s ore portant than optal operaton, but when the crogrd operates n grdconnected ode, optal operaton s the an object of the Mcrogrd Control Center (MGCC). Optal reactve power plannng proble s the optal placeent and szng of reactve power sources n a network to prove the syste voltage profle or reduce losses or enhance voltage stablty ndex. In Reference [9] ths proble s descrbed wth the object of nzng the operaton and nvestent costs. Many DGs such as Fuel cells, Fully Rated Converter (FRC) wnd turbnes, PV panels, croturbnes and ost of energy storage devces are Electroncally Interfaced DGs (EIDGs), and are connected to the crogrd by eans of a Voltage- Source Converter (VSC) []. Due to the controllablty of the VSC, EIDGs are flexble n operaton and can operate wth dfferent power anageent stratees. Three dfferent Reactve Power Control (RPC) stratees are defned for DGs n crogrds []. In addton to the well-known PV and PQ stratees, n the thrd strategy reactve power of the DG can be controlled and shared by DGs accordng to a Voltage Droop Characterstc(VDC) [], []. Ths s called Q-sharng or voltage droop strategy. The concept of Q-sharng strategy s very slar to the concept of actve power sharng between large generatng unts n load frequency control of power systes. In autonoous operaton of crogrds, the strategy s extended to frequency/voltage droop technque. References [], [] use dfferent control stratees for an EIDG unt for stablty and voltage control n crogrd n grd-connected and autonoous odes. In contrast to EIDGs, soe DGs such as Fxed Speed Wnd Generators (FSWGs) whch use Squrrel Cage Inducton Generator (SCIG) work as a voltage dependent PQ generator. Reference [3] proposed a new operatng paradg that uses real-te nforaton whch obtaned fro the Sart Grd (SG), to apply the uncertantes of supply and deand. Soe researches consder probablstc subjects n crogrd operaton. Soe algorths were presented to evaluate the

2 Voltage (pu) perforance of crogrd whch addresses the deternstc and the stochastc natures of dstrbuted generaton systes, uncertantes n loads, DG output power and voltage control devces operaton [4], [5]. In crogrds, load pattern, generaton of DGs and all of essental nforaton are avalable for MGCC through a councaton syste; especally n the case of SGs the councaton syste s wde spread and very relable. Soe studes consder that the aount of load at all buses s known for the MGCC and t can run dfferent fors of OPF. Fg. shows a typcal crogrd equpped wth decentralzed controllers for loads (LCs) and cro sources (MCs). The an role of MGCC s coordnaton of these local controllers to have a secure, stable, relable and optal operatng pont [6], [7]. II. DIFFERENT STRATEGIES FOR DG REACTIVE POWER CONTROL Three dfferent voltage control stratees are applcable on EIDGs n a crogrd: PQ, PV and Q-sharng stratees []. Lke n power systes, n PQ and PV odes the DG controller controls the reactve power of DG to regulate the power factor and ternal voltage, respectvely. In Q-sharng ode, whch s specfc to EIDGs, the requred reactve power s shared between DGs accordng to ther voltage droop characterstc. Ths s slar to the frequency control n power syste whch s done by eans of frequency droop characterstc. Because of the sall scale of crogrds, the voltage of dfferent nodes ay not be controlled ndependently and ts control s soe knd slar to frequency control n large power systes. In addton, n any cases, due to the presence of prvate DGs and also n the lack of a central dspatchng centre, t s not possble to coordnate dfferent DGs of a crogrd and get the optal reactve power plan. Reference [8] presents two schees for Q-sharng EIDGs ncludng Conventonal Voltage Droop Strategy (CVDS) and Adaptve Voltage Droop Strategy (AVDS). Fg. shows a typcal voltage droop characterstc for CVDS, whch are expressed by ()..6.4 V. Fg.. Typcal Mcrogrd. Ths paper deals wth optal reactve power control n crogrd by use of Q-sharng DGs besde PV and PQ unts and wnd generaton s consdered as an uncertan factor. A full AC constraned OPF proble s presented to fnd the best schedule of reactve power produced by all EIDG unts and paraeters are appled n the syste wth a powerful load flow. There are any cases to put DG unts nto grd for optal reactve power control, but only soe cases are the best locaton and can be consdered for ths purpose due to network structure, ltaton of nstallaton and senstve load centers. Sutable odel for ncorporaton of all DGs n power flow progras are developed and analyzed. Secton ΙΙ ntroduces dfferent stratees for DG reactve power control. In Secton ΙII, the used AC OPF n ths work s forulated. The object of ths OPF s to optze the control varables of each EIDG to nze loss. Secton IV ntroduces probablstc odel for FSWGs and presents deternstc and expected paraeters for EIDGs. Fnally Sectons V and VI are nuercal study and concluson, respectvely Qn VQ Reactve power (pu) Fg.. Typcal voltage droop characterstc for Q-sharng unts. Q n Q V V K Q Q DGs wth CVDS () V V K K P K Q Q Q Q Q n P Q DGs wth AVDS V Q s the voltage correspondng to the u possble reactve power njecton of the DG and K n, K p and K Q are the odel paraeters. V Q and all paraeters are optzed by the OPF proble defned n secton III. III. OPF FORMULATION FOR REACTIVE POWER CONTROL In eerng SGs based on a relable councaton between loads and the MGCC, the load patterns of all load ponts are avalable for the OPF. In ths secton, the proposed forulaton for the OPF s expressed and all the necessary constrants for the OPF are presented. The an object of the OPF whch s defned by (3) s the nu total loss n the crogrd. ()

3 voltage (pu) 3 l loss loss n F P Q s.t. N P P V V Y cos( ) d j j j j j N Q Q V V Y sn( ) d j j j j j Q Kn V V Q Q DGs wth CVDS 3 K Q Q K K P Q Q V V Q n P Q DGs wth AVDS P P P n Q Q Q n V V V n K K K n n n n K K K n P P P K K K n Q Q Q V V V n Q Q Q where F : objectve functon (total loss of crogrd) N : total nuber of buses j:, ndex for buses (3) (4) (5) (6) (7) (8) (9) () () () (3) (4) P, Q : Actve and reactve power generaton at bus (p.u) P, Q : Actve and reactve power deand at bus (p.u) d : d V Voltage agntude at bus (p.u) Y : j Eleent of network adttance atrx (p.u) : Voltage angle at bus (radans) : j Phase angle of Y j (radans) K, K, K, V : Plannng Paraeters of Q-sharng DGs V n P Q Q : Q Ternal voltage of Q-sharng unts at ther u reactve power (p.u) n P, P : Maxu and nu generated actve power at bus (p.u) n Q, Q : Maxu and nu generated reactve power at bus (p.u) MAX MIN V, V : Lts on bus voltage levels (p.u) l : The nuber of branches The equalty constrants of the OPF, (4)-(7), reflect the power flow equatons whch requre that the total njecton of actve and reactve power at each bus su to zero. EIDGs have u and nu output actve and reactve powers whch add nequalty constrants, n addton, Q-sharng unts add other plannng paraeters to OPF proble whch should be consdered. For each bus n crogrd should be wrtten equatons (4) and (5), but for buses whch Q-sharng unts have been nstalled, should be wrtten (6) or (7) n addton to (5). The nequalty constrants of the OPF, (8)-(4), reflect the lts on physcal devces n the grd as well as the created lts to ensure syste securty and relablty. Consderng constrants of crogrd, there are soe dfferent types of voltage droop characterstc for Q-sharng unts. Fg.3 shows soe conventonal voltage droop characterstcs whch express behavor of Q-sharng unts and ther senstvty to voltage and reactve power ltatons; therefore, OPF proble adjusts Q-sharng unts n the best way and choces the best characterstc for voltage control strategy dependng crogrd condtons. In accordng to Fg.3, the ponts A and B show that characterstcs () and () cannot absorb ther nu possble reactve power when ternal voltage ncreases to ts upper lt. The ponts C and D show that characterstcs (4) and () cannot nject ther u possble reactve power when voltage decreases to ts lower lt; n these stuatons, Q-sharng unts wll not use fro entre of ther reactve power capacty and consequently, wll not gan optal operaton. Also the pont E shows that characterstcs (3) and (4) arrve to lower lt of ther reactve power when a lttle growth occurs n voltage, on the other hand, pont F shows that characterstcs () and (3) arrve to upper lt of ther reactve power when a declne occurs n voltage. Therefore characterstc () has sall senstvty to voltage varaton and causes sall effect n crogrd operaton and characterstc (3) has hgh senstvty to voltage varaton, consequently n soe cases causes nstablty n crogrd E () () B (3) (4) A reactve power (pu) Fg.3. soe dfferent types of conventonal voltage droop characterstcs for Q-sharng DG unts. C D F

4 probablty () Output power (MW) 4 IV. OPTIMAL SETTING OF CONTROLLABLE DGS BY STOCHASTIC METHOD Q-sharng DGs are consdered as an portant subject about stablty, relablty and optal operaton of crogrd and should be exactly adjusted n any prograng and plannng probles. Relable and Desrable operaton of a crogrd n grd connected and slandng odes at presence of Q-sharng DGs requres effcent power control and voltage regulaton technques and depend on optal settng of ths knd of DG. Therefore, for accurate analyss of crogrd operaton consderng uncertanty of wnd generatons, ths paper consders two levels of wnd power penetraton n crogrd and two dfferent Raylegh Probablty Densty Functons (RPDFs) for odelng of wnd, and proposes a stochastc ethod to adjust plannng paraeters of Q-sharng DGs (V Q,K n ), optal aount of reference voltage for PV unts and optal generaton of PQ unts consderng expected and probable wnd speed. Plannng paraeters whch obtan by stochastc ethod are naed Expected Paraeters (EPs) and those whch are calculated by Probable Wnd Speed (PWS) are naed PWSPs, therefore by ths stochastc ethod whch consders uncertanty of wnd generaton, the best plannng paraeters are selected to have nu loss. The expected paraeters can be calculated by (5): N PWS E( X ) P( PWS). X (5) where, N PWS s the nuber of quantzed level of RPDFs. A. Probablstc odel for fxed-speed wnd turbnes n power flow studes Nowadays the penetraton of wnd energy has been ncreased n crogrds across the globe. Therefore the ssue of plannng n electrcal grds should be carefully changed. Therefore, to nvestgate of wnd turbnes behavor n steady state, we need correct odel of the, also the effect of wnd nature should be consdered for crogrd plannng. Interttency of wnd and randoness of ts speed cause uch uncertanty n crogrd and ts prograng. Ths uncertanty affects on soe plannng paraeters and power flow structure. Usng power curve of wnd turbnes whch s defned by anufacturer can be calculated output actve power for each wnd speed. Fg.4 shows power curve of a.5(mw) ptch regulated FSWG. As entoned prevously, FSWGs are coposed of nducton achne, therefore consue reactve power depend on produced actve power and bus voltage and are odeled as voltage dependent PQ generator n load flow studes. Reference [9] presents sutable odel for load flow studes whch can be used to calculate consued reactve power by a FSWG. Knowng actve power output of generator (Pe), ternal voltage (V) and all other paraeters of the nducton achne, the consued reactve power of FSWG can be coputed as follow: [ X X ( ) ( ) ( )] S X X l l X ls X X l R X X V (6) l Q [ R R S( X ( X X )( X X ))] [ R( X X l) S R( X X l)] l l b S n b a 4ac (7) (8) a PeR ( X l X ) Pe( X X l X l( X l X )) V R( X l X ) Pe R R X V R X b (9) c PeR ( X l X ) Pe( RR ) V RR () Therefore based on forecasted wnd speeds, can be coputed the probablty of wnd speeds and wnd turbnes generaton usng Raylegh dstrbuton. In ths paper has been used RPDF to specfy optal adjustent of plannng paraeters Cut n wnd speed Rated wnd speed Cut out wnd speed Wnd speed (/s) Fg.4. Power curve of fxed speed wnd turbne. B. Expected and probable wnd speed paraeters As prevously dscussed power flow results show operaton of crogrd. As wnd speed specfy actve and reactve power output of a wnd turbne n a crogrd whch contans the wnd far, paraeters of Q-sharng DGs, voltage reference of PV unts and generaton of PQ unts are changed wth wnd speed fluctuaton, therefore wll change power flow results. Thus consderng two dfferent knds of wnd probablty odels, ths paper proposes new EPs and PWSPs for optal settng of all controllable DGs. In these odels, the ost probable of wnd speeds are 6/s and 3/s and ther Raylegh curves are shown n Fg.5, and naed and RPDF, respectvely. To calculate plannng paraeters, RPDFs are quantzed to 5 and 9 levels of soe PWSs, respectvely. Consderng these curves, actve and reactve power outputs of wnd far are deterned and power flow s studed for each wnd speed. The probabltes of wnd speeds n both RPDFs are shown n TABLE I Wnd speed (/s) (a)

5 Probablty (RPDF) In ths study, Q-sharng DGs use CVDC; therefore two paraeters V Q and K n should be optzed n OPF proble. () P P A V AV A d d Q Q R V RV R d d where A A A R R R () Wnd speed (/s) (b) Fg.5. (a) Quantzed (b) RPDF. WS (/s) P(ws) n TABLE I WIND SPEED PROBABILITIES P(ws) n RPDF WS(/s) P(ws) n P(ws) n RPDF V. NUMERICAL STUDIES In order to deonstrate the accuracy and effectveness of the proposed algorth, t has been appled to odfed IEEE- 34 bus test syste whch s shown n Fg.6, and the results are dscussed. The base values are 5MVA and 4.9 KV. The frst bus s slack bus, and reanng buses are consdered as canddate buses to nstallaton of EIDGs. The ratng of EIDGs output reactve power s consdered n range of -.8 Mvar. In ths study, t s supposed that these unts n crogrd operate n u aount of output actve power (.8 Mw), and loads have been consdered ZIP voltage dependent load whch ts odel s shown by (), (). The syste conssts of sx DGs (PQ, PV and Q-sharng), whch TABLE II shows locaton and type of the. TABLE II DGS CHARACTERISTICS Bus DG Type 8 PQ 85 PV 8 Q-sharng 83 PQ 858 PV 848 Q-sharng Fg.6. IEEE 34 bus test syste. Two dfferent cases are studed on crogrd and show accuracy of proposed stochastc reactve power control algorth under dfferent other stuatons. A. Hgh load condton (Case) The load s hgh and near the peak load. Because total generaton of EIDGs s close to deand, output power fro substaton s low, consequently the total loss n ths stuaton s low. Therefore, ncreent n wnd generaton helps to decrease of loss. B. Lght load condton (Case) Because, n the lght load condton, the total generaton of EIDGs s ore than total actve load and output power fro substaton s hgh, causes hgh loss n grd, consequently growth n wnd speed causes hgher loss n grd. In each case two dfferent other cases are studed. Frst, a.5mw ptch regulated FSWG whch ts paraeters has been shown n [9], s located n bus 838 and optal reactve power proble s perfored. Because the wnd turbne s fxed speed and s nstalled n place that s far fro substaton, consues ore reactve power and causes worst case wth respect to reactve power flow and loss n grd, especally n lght loadng condton. Second for ncreasng of wnd power penetraton, uncertanty and fluctuaton n whole of grd n order to optal choce between EPs and PWSPs, n addton to bus 838 another FSWG s located n dfferent place at bus 88 and ts effect on stochastc ethod s studed. Uncertanty of wnd, affects on output reactve power of FSWG and then reactve power flow n grd. Reacton of other DGs n response to wnd power fluctuatons should be carefully consdered n order to nzng of loss. For exact evaluaton n these cases, effect of two dfferent wnd probablty odels whch were descrbed n secton IV s studed. To show the advantage of proposed stochastc

6 6 algorth for reactve power control to nze total loss of grd n each stuaton, has been used two stratees for optal settng of controllable DGs. In the frst strategy, EPs are selected to have optal operaton and n the second strategy, reactve power control s perfored based on PWSPs. These paraeters are DGs regulatory paraeters whch load flow study s perfored wth the, separately. The best choce depends on loadng condtons, level of wnd power penetraton n crogrd and wnd probablty odel. In ths study, the effects of these factors have been consdered altogether for better reactve power control. EPs and PWSPs for low and hgh level of wnd power penetraton for optal settng of DGs have been presented n TABLE III, IV, respectvely. These paraeters are used for load flow study n crogrd. TABLE III LOW LEVEL OF WIND POWER PENETRATION Data n Case RPDF EPs PWSPs EPs PWSPs Q-8(Mvar) Q-83(Mvar) Vref- 85(pu) Vref -858(pu) Kn V Q-8(pu) Kn V Q-848(pu) Ploss(Kw) Qloss(Kvar) (a) Data n Case RPDF EPs PWSPs EPs PWSPs Q-8(Mvar) Q-83(Mvar) Vref- 85(pu) Vref -858(pu) Kn V Q-8(pu) Kn V Q-848(pu) Ploss(Kw) Qloss(Kvar) The results of load flow study wth EPs and PWSPs are shown n TABLE V. Results are satsfactory and proposed algorth s accurate and can be used for ths purpose. As TABLE V shows the load flow result, when grd s n hgh load condton (Case) and wnd probablty odel s whch the ost probable wnd speed s n low speeds and wnd power s low, EPs have sgnfcant effect on decreasng of loss than PWSPs, whle at the oent, RPDF whch expresses the ost probable wnd speed s n hgh speeds and FSWG generates ts u actve power, there s no sgnfcant dfference between EPs and PWSPS. (b) TABLE IV HIGH LEVEL OF WIND POWER PENETRATION Data n Case RPDF EPs PWSPs EPs PWSPs Q-8(Mvar) Q-83(Mvar) Vref- 85(pu) Vref -858(pu) Kn V Q-8(pu) Kn V Q-848(pu) Ploss(Kw) Qloss(Kvar) (a) (b) TABLE V LOAD FLOW RESULT Input for Load Flow Study n Expected Low Level of Wnd Penetraton Ploss (Kw) Case Case RPDF RPDF Input for Load Flow Study n Hgh Level of Wnd Penetraton Case Case Data n Case RPDF EPs PWSPs EPs PWSPs Q-8(Mvar) Q-83(Mvar) Vref- 85(pu) Vref -858(pu) Kn V Q-8(pu) Kn V Q-848(pu) Ploss(Kw) Qloss(Kvar) RPDF RPDF Expected Qloss (Kvar) EPs PWSPs EPs PWSPs EPs PWSPs EPs PWSPs (a) Expected Ploss (Kw) Expected Qloss (Kvar) EPs 38 4 PWSPs EPs PWSPs 33 EPs PWSPs EPs PWSPs The percentages of loss reducton by EPs and PWSPs n case are shown n TABLE VI. In lght load condton (Case) total loss of grd s ore than hgh load condton but contrary of hgh load condtons, although there s no sgnfcant reducton n loss, PWSPs have a lttle better perforance than EPs n dfferent levels of wnd penetraton and wnd probablty odels, whch can be gnored. (b)

7 7 Therefore, dfferences between EPs and PWSPs can be copared depends on ther effects on actve and reactve power loss n TABLE VI. TABLE VI REDUCTION IN LOSS Actve Case Low level of wnd power penetraton- EPs- Hgh level of wnd power penetraton- EPs- Hgh level of wnd power penetraton -PWSPs-RPDF VI. CONCLUSION Reactve.8%.6%.48%.9% 4.75% 4.75% In ths paper a new algorth proposed for reactve power control n crogrd by use of new odel of DGs that s called Q-sharng DGs. Because of the nfluence of reactve power plannng on both econoc and techncal aspects of the crogrd operaton, at frst an exact odel proposed for Q- sharng DG unts then ths odel besde PQ and PV unts, appled to odfed copensaton based forward/backward sweep power flow and then usng a new optzaton algorth the best paraeters selected for DGs to satsfy objectve functon. On the other hand for accurate evaluaton of wnd power uncertanty, dfferent wnd probablty odels were used n two cases of load condtons and n each case the best optal paraeters were selected. Applyng these optal paraeters to IEEE 34-bus test syste to schedule reactve power for DGs shows that total loss of crogrd n soe cases by use of EPs and n soe other cases by use of PWSPs, decreased. Also ths paper shows that schedule of reactve power n crogrd by Q-sharng DGs requres new optal power flow forulaton. VII. REFERENCES [] S.Chowdhury, S.P.Chowdhury, and P.Crossley,Mcrogrds and Actve Dstrbuton Networks, Insttuton of Enneerng and Technology, London, Unted Kngdo,9. [] G. W. Chang, S. Y. Chu, and H. L. Wang, "An Iproved Backward/Forward Sweep Load Flow Algorth for Radal Dstrbuton Systes," IEEE Trans. Power Syste, Vol., pp , May. 7. [3] Shqong Tong, and Karen Nan Mu, "A Network-Based Dstrbuted Slack Bus Model for DGs n Unbalanced Power Flow Studes," IEEE Trans. Power Syste, Vol.,pp , May 5. 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